Answer: 60
Step-by-step explanation:
To form a 3-digit positive integer using the digits 1, 3, 5, 7, and 9 without repeating any digit, we can use the counting principle.
There are 5 choices for the first digit (hundreds place) since any of the 5 digits (1, 3, 5, 7, or 9) can be placed there.
5 (choices for the first digit) × 4 (choices for the second digit) × 3 (choices for the third digit) = 60
There are 60 ways to write a 3-digit positive integer using the digits 1, 3, 5, 7, and 9 without using any digit more than once.
Order the set of numbers from least to greatest: (4 points)
2.71 repeating 71, 2 and 3 over 4, square root 5, 5 over 2
Group of answer choices
2.71 repeating 71, 2 and 3 over 4, square root 5, 5 over 2.
square root 5, 5 over 2, 2.71 repeating 71, 2 3 over 4
5 over 2, square root 5, 2.71 repeating 71, 2 3 over 4
2 3 over 4, 2.71 repeating 71, 5 over 2, square root 5
The correct order of the set of numbers from least to greatest is 2 3 over 4, 2.71 repeating 71, 5 over 2, square root 5, the correct option is D..
To order the given set of numbers from least to greatest, we need to compare their values. We start by noticing that 2 and 3 over 4 are equivalent to 2.75. Next, we compare the values of the remaining numbers. Since the square root of 5 is approximately 2.236 and 5 over 2 is equivalent to 2.5, we have:
2 3 over 4 < 2.71 repeating 71 < 2.5 < square root 5
Therefore, the set of numbers in order from least to greatest is 2, 3 over 4, 2.71 repeating 71, 5 over 2, square root 5.
Ordering the set of numbers from least to greatest, we get:
2 3 over 4, 2.71 repeating 71, square root 5, 5 over 2.
To learn more about numbers follow the link:
brainly.com/question/17429689
#SPJ1
An exam has two papers, Paper 1 and Paper 2
Paper 1 has 65 marks.
Paper 2 has 75 marks.
The pass mark is of the total number of marks.
Stephanie gets 80% of the marks for Paper 1
How many of the marks for Paper 2 must Stephanie get in order to get the pass mark?
ANSWER:
Therefore, Stephanie cannot pass the exam even if she gets full marks in Paper 2.
Step-by-step explanation:
Pass mark = 65 + 75 = 140
Stephanie got 80% of the marks for Paper 1, which is:
0.8 x 65 = 52
To pass the exam, Stephanie must get a total of 140 marks, and she already has 52 from Paper 1. Therefore, she needs to get the remaining marks from Paper 2:
140 - 52 = 88
So, Stephanie must get at least 88 marks out of 75 in Paper 2 to pass the exam. However, this is not possible as the maximum marks for Paper 2 are 75.
Valley Bank has four tellers. It takes a teller 8 minutes to serve one customer. What is the capacity of the bank in customers per hour? A. 15 B. 10 C. 8 D. 30
Since there are four tellers, the capacity of the bank in customers per hour = 4 x 7.5 = 30.
What is the capacity of the bank in customers per hour?Valley Bank has four tellers. It takes a teller 8 minutes to serve one customer.
The correct option is D. 30.
We are given that
Valley Bank has four tellers. It takes a teller 8 minutes to serve one customer.
To calculate the capacity of the bank in customers per hour, we need to find how many customers each teller can serve in an hour. To do this, we first need to convert the time taken to serve one customer from minutes to hours.
1 minute = 1/60 hoursSo, time taken to serve one customer
= 8 minutes
= 8/60 hours
= 2/15 hours
One teller can serve one customer in 2/15 hours.In one hour, the number of customers one teller can serve = 1/(2/15) = 15/2 = 7.5 (customers/hour)
Therefore, the capacity of one teller in customers per hour is 7.5.
Now, we need to find the capacity of the bank in customers per hour. Since there are four tellers, the capacity of the bank in customers per hour = 4 x 7.5 = 30.
So, the correct option is D. 30.
Learn more about Valley Bank.
brainly.com/question/31230033
#SPJ11
46. around 1910, the indian mathematician srinivasa ramanujan discovered the formula william gosper used this series in 1985 to compute the first million digits of . verify that the series is convergent. how many correct decimal places of do you get if you use just the first term of the series? what if you use two terms?
a) The series 1/pi = 2sqrt(2)/9801 × summation n=0 to infinity of (4n)!(1103+26390n)/((n!)^4*396^4n) is convergent by the ratio test.
b) If we use just the first term of the series, we get an approximation of pi to one correct decimal place: pi ≈ 6533.008.
If we use two terms of the series, we get an approximation of pi to 14 correct decimal places: pi ≈ 3.14159265358979324.
a) To verify the convergence of the given series, we can use the ratio test.
Let's take the limit of the ratio of the (n+1)th term to the nth term as n approaches infinity:
limit as n approaches infinity of [(4(n+1))!(1103+26390(n+1))/((n+1)!^4396^4(n+1))] / [(4n)!(1103+26390n)/(n!)^4396^4n]
= [(4n+4)(4n+3)(4n+2)(4n+1)(1103+26390n+26390)/(n+1)^4*396^4]
= [(4n+1)^4(1103+26390n+26390)/(n+1)^4*396^4]
= (4n+1)^4(1103+26390n+26390)/(n+1)^4(396^4)
= (4n+1)^4(1103/n+26390+26390/n)/(396^4)
As n approaches infinity, the terms inside the parentheses approach constant values, and we can ignore the n-dependent terms in the numerator and denominator. Thus, the limit simplifies to
= (4^4 × 1103) / (396^4) = 1/(\pi)
Since the limit is less than 1, the series converges by the ratio test.
b) If we use just the first term of the series, we get
1/pi ≈ (2sqrt(2)/9801)×(4!/396^4) = 1.2337 x 10^-4
Taking the reciprocal of both sides, we get
pi ≈ 807104 / 1.2337 ≈ 6533.008
This approximation gives us only one correct decimal place of pi.
If we use two terms of the series, we get
1/pi ≈ (2sqrt(2)/9801)[(4!(1103)+(8!26390))/(396^4(1!^4))]
= 3.1415927300133055 x 10^-1
Taking the reciprocal of both sides, we get
pi ≈ 3.14159265358979324
This approximation gives us 14 correct decimal places of pi.
Learn more about convergence here
brainly.com/question/15415793
#SPJ4
The given question is incomplete, the complete question is:
Around 1910, the Indian mathematician Srinivasa Ramanujan discovered the formula:
1/pi = 2sqrt(2)/9801 * summation n=0 to infinity of (4n)!(1103+26390n)/((n!)^4*396^4n)
William Gosper used this series in 1985 to compute the first 17 million digits of pi.
a) Verify that the series in convergent.
b) How many correct decimal places of pi do you get if you use just the first term of the series? What if you use two terms?
There are 28 students whose last names begin with the letters G, H, J, or K. Information about the probability of randomly selecting one of these students is listed below • probability of selecting a student whose last name begins with G: 7 • probability of selecting a student whose last name begins with G or H: 5 14 O How many of these students have a last name that begins with H?
A4
B5
C6
D7
5
We know that there are 28 students in total, so:
G + H + J + K = 28
We also know the following probabilities:
P(G) = 7/28
P(G or H) = 5/14
The probability of selecting a student whose last name begins with G or H can be expressed as:
P(G or H) = P(G) + P(H) - P(G and H)
Since the events "selecting a student whose last name begins with G" and "selecting a student whose last name begins with H" are mutually exclusive (a student cannot have a last name that begins with both G and H), P(G and H) = 0. Therefore, we have:
5/14 = 7/28 + P(H)
Simplifying the equation, we get:
P(H) = 5/14 - 7/28 = 5/28
So the probability of selecting a student whose last name begins with H is 5/28. To find the number of students whose last name begins with H, we can multiply this probability by the total number of students:
H = P(H) x 28 = 5/28 x 28 = 5
Therefore, there are 5 students whose last name begins with H.
*IG: whis.sama_ent*
answerrrrr pleaseeeeeeeeeeeeeeeeeeeeeeee <3..
the scale factor for the dilation is 1.0625. According to the given question
how to find scale factor?
To find the scale factor for the dilation that transforms quadrilateral QRST to Q'R'ST, we need to compare the corresponding side lengths of the two figures. Since the figures are similar, the corresponding sides are proportional to each other.
Let the scale factor be represented by k. Then, we have:
|QR| / |Q'R'| = |RS| / |R'S'| = |ST| / |S'T'| = k
We can use the given information about the coordinates of the vertices to calculate the lengths of the sides.
|QR| = √((4-(-2))² + (1-(-4))²) = √(85)
|RS| = √((2-4)²+ (7-1)²) = √(40)
|ST| = √(((-4)-2)² + (1-7)²) = √(72)
|Q'R'| = √(((-4)-(-8))²+ ((-1)-(-7))²) = √(80)
|R'S'| = √(((-8)-(-2))² + ((-7)-1)²) = √(170)
|S'T'| = √(((-2)-(-4))² + (1-7)²) = √(20)
Therefore, we have:
√(85) /√(80) = √(40) / √(170) =√(72) / √(20) = k
Simplifying, we get:
k = √(85/80) = √(17/16) = 1.0625
Thus, the scale factor for the dilation is 1.0625.
Note: It's important to keep track of the order of the vertices when calculating the lengths of the sides. In this case, we assumed that the vertices were listed in clockwise order around the quadrilateral.
To know more about factors visit :-
https://brainly.com/question/25829061
#SPJ1
Solve for x someone please
The length of the third side is x= 8 (nearest rounded to the tenth).
What is the midpoint theorem?The line segment in a triangle connecting the midway of two sides of the triangle is said to be parallel to its third side and is also half the length of the third side, according to the midpoint theorem.
By using the midpoint theorem, we get
The line is parallel to its third side x and is also half the length of the third side, therefore we can write
X= [tex]\frac{1}{2} * 15[/tex]
X = 7.5
Rounded the value nearest tenth
X = 8
Learn more about the mid-point theorem here:
https://brainly.com/question/13677972
#SPJ1
Two of the angles in a triangle measure 73° and 24°. What is the measure of the third angle?
A triangle has two angles that are 73° and 24° in size. The third angle is 83 degrees in length.
The sum of all the angles in a triangle is always 180 degrees. So, we can utilize this fact to get the third angle's measurement:
Let's call the third angle "x". Then we have:
73° + 24° + x = 180°
Simplifying this equation, we get:
97° + x = 180°
Subtracting 97 degrees from both sides, we get:
x = 83°
Therefore, the measure of the third angle is 83 degrees.
To learn more about triangle, refer:-
https://brainly.com/question/2773823
#SPJ1
At the school carnival, Nicole is in charge of a spinner game where students can win prizes. The spinner is divided into 4 unequal sections labeled book, sticker, eraser, and keychain. Nicole keeps track of what prizes the spinner lands on for the first 8 students who play. Here are her results: sticker, book, eraser, keychain, sticker, eraser, sticker, keychain Based on the data, what is the probability of the spinner landing on keychain?
The probability of the spinner landing on keychain is 1/4 or 0.25, which means that for every 4 spins, the spinner is expected to land on keychain once on average.
What is probability?The measure of the likelihood that an event will occur is known to be Probability.
This is a number between 0 and 1, where 0 represents an impossible event (has no chance of occurring) and 1 represents a definite event (100% chance of occurring).
An event with a probability of 0.5 is equally likely to occur and not to occur.
To find the probability of the spinner landing on keychain, we need to first determine the total number of spins and the number of times the spinner landed on keychain.
From the given data, we can see that the spinner was spun 8 times, and it landed on keychain twice. Therefore, the probability of the spinner landing on keychain is:
Probability of keychain = Number of times the spinner landed on keychain / Total number of spins
Probability of keychain = 2/8 = 1/4
To know more about number visit:
https://brainly.com/question/11197798
#SPJ1
Triangle ABC is rotated 90° counterclockwise about the origin to produce triangle A'B'C'. Then, triangle A'B'C' is dilated by a scale factor of 1/2 with respect to the origin to produce A''B''C''.
Write coordinates of each vertex in the final image.
A"
B"
C"
Answer:
Step-by-step explanation:
your university is upgrading the computers on campus. a national student survey revealed that 62% of college students preferred pcs to macs. a recent poll of 200 social science majors at your university revealed that 82% of students preferred macs to pcs. how do social science majors at your university compare to national mac computer preference norms for college students? what is the correct statistical decision?
The social science majors at your university compare to national mac computer preference norms for college students statistical decision is 5.83.
The gathering, characterization, analysis, and drawing of inferences from quantitative data are all tasks that fall under the purview of statistics, a subfield of applied mathematics. Probability theory, linear algebra, and differential and integral calculus play major roles in the mathematical theories underlying statistics.
Finding valid inferences about big groups and general occurrences from the behaviour and other observable features of small samples is a major challenge for statisticians, or persons who study statistics. These tiny samples are representative of a small subset of a larger group or a small number of isolated occurrences of a widespread phenomena.
Proportion of students who preferred PC's to Mac (P) = 0.62
Sample size (n) = 200
Sample proportion of students who prefer Mac's to PCs = 0.82
To compare the proportion of students with Mac preference for college students a Z-test for single proportion will e conducted. The hypothesis is formulated as follows:
H o: There is no significant difference in the national proportion and college preference
H1 : There is a significant difference in the national proportion and college preference
The test statistic is computed below:
[tex]z=\frac{p-p_0}{\sqrt{\frac{p_0(1-p_0)}{n} } }[/tex]
[tex]z=\frac{0.82-0.62}{\sqrt{\frac{0.62(1-0.62)}{200} } }[/tex]
= 5.8272
Thus, the value of the test statistic is 5.83.
Learn more about Statistical decision:
https://brainly.com/question/20116913
#SPJ4
How many hours after the culture was started and the maximum population is approximately what?
Check the picture below, so that's the picture of a parabolic path with a certain initial velocity.
so anyhow, not to bore you to death, the maximum or peak point occurs at the vertex, as you see in the picture, and the x-coordinate is how long it took to get there.
[tex]\textit{vertex of a vertical parabola, using coefficients} \\\\ P(t)=\stackrel{\stackrel{a}{\downarrow }}{-1698}t^2\stackrel{\stackrel{b}{\downarrow }}{+85000}t\stackrel{\stackrel{c}{\downarrow }}{+10000} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left(-\cfrac{ 85000}{2(-1698)}~~~~ ,~~~~ 10000-\cfrac{ (85000)^2}{4(-1698)}\right) \implies \left( - \cfrac{ 85000 }{ -3396 }~~,~~10000 - \cfrac{ 7225000000 }{ -6792 } \right)[/tex]
[tex]\left( \cfrac{ -21250 }{ -849 } ~~~~ ,~~~~ 10000 +\cfrac{ 903125000 }{ 849 } \right) \\\\\\ \left( \cfrac{ 21250 }{ 849 } ~~~~ ,~~~~ \cfrac{ 911615000 }{ 849 } \right) ~~ \approx ~~ (\stackrel{ hrs }{25}~~,~~\stackrel{ population }{1,074,000})[/tex]
I need help (don't mind the circle btw bc I don't know its right)
Answer:
3/7
Step-by-step explanation:
The total is 7 blocks. There are three stars. Probability is PART/WHOLE.
3/7
Can you Solve these Problems ASAP
Find the set of solutions for each of the following absolute value inequalities
The set of solutions for each of the inequalities are given by:
(b) - 4.8 < m < 6.4
(e) x [tex]\geq[/tex] 5
(g) - 11.6 < z < 14
(h) either k < -19/3 or k > 7
Solving the given absolute value inequalities we get,
(b) The given inequality,
|2 - 5m/2| < 14
- 14 < 2 - 5m/2 < 14
-14 - 2 < -5m/2 < 14 - 2
-16 < -5m/2 < 12
-12 < 5m/2 < 16
-12*2 < 5m < 16*2
-24/5 < m < 32/5
- 4.8 < m < 6.4
(e) The given inequality,
2> - |(x-8)/5 + 3/5|
|(x-8)/5 + 3/5| > -2
|(x-8)/5 + 3/5| [tex]\geq[/tex] 0 [Since absolute value is always positive or zero]
(x-8)/5 + 3/5 [tex]\geq[/tex] 0
(x-8+3)/5 [tex]\geq[/tex] 0
x - 5 [tex]\geq[/tex] 0
x [tex]\geq[/tex] 5
(g) The given inequality,
|(5z - 6)/8| < 8
-8 < (5z - 6)/8 < 8
-64 < 5z - 6 < 64
-64 + 6 < 5z < 64 + 6
-58 < 5z < 70
-58/5 < z < 70/5
-58/5 < z < 14
- 11.6 < z < 14
(h) The given inequality,
|(3k - 1)/4| > 5
either, (3k - 1)/4 < -5
3k - 1 < -20
3k < -19
k < -19/3
or, (3k - 1)/4 > 5
3k - 1 > 20
3k > 20 + 1 = 21
k > 21/3
k > 7
Hence the solution sets are:
(b) - 4.8 < m < 6.4
(e) x [tex]\geq[/tex] 5
(g) - 11.6 < z < 14
(h) either k < -19/3 or k > 7
To know more about inequality here
https://brainly.com/question/24372553
#SPJ1
Convert 5pi/2 radians into degrees
Answer:Tan 5pi/2 can also be expressed using the equivalent of the given angle (5pi/2) in degrees (450°).
Step-by-step explanation:
5π/2 radians is equivalent to 450 degrees.
We have,
To convert radians to degrees, we can multiply the value in radians by the conversion factor of 180 degrees/π radians.
To convert 5π/2 radians into degrees, we can use the conversion factor that states 180 degrees is equal to π radians.
Let's set up the conversion:
(5π/2 radians) × (180 degrees/π radians)
Here, the π radians in the numerator and denominator cancel out, leaving us with:
(5/2) × 180 degrees
Simplifying further, we have:
(5/2) × 180 = 900/2 = 450 degrees
Therefore,
5π/2 radians is equivalent to 450 degrees.
Learn more about unit conversion here:
https://brainly.com/question/13899873
#SPJ6
find the frequency for which the particular solution to the differential equation has the largest amplitude. you can assume a positive frequency . probably the easiest way to do this is to find the particular solution in the form and then minimize the modulus of the denominator of over all frequencies .
Answer:
Step-by-step explanation:
To find the frequency for which the particular solution to the differential equation has the largest amplitude, we first need to know the differential equation we are working with. However, since you didn't provide the specific differential equation, let's work with a general example: a forced harmonic oscillator. The equation for a forced harmonic oscillator can be written as:
m * d²x/dt² + c * dx/dt + k * x = F0 * cos(ωt)
where:
m is the mass of the oscillator
x is the displacement of the oscillator
c is the damping coefficient
k is the spring constant
F0 is the amplitude of the external force
ω is the angular frequency of the external force
For this type of equation, we can find the particular solution in the form:
x_p(t) = X * cos(ωt - δ)
where:
X is the amplitude of the particular solution
δ is the phase angle
We can rewrite the differential equation in the frequency domain by substituting x(t) = X * cos(ωt - δ) and its derivatives into the original equation, then applying the trigonometric identities. After simplifying, we can find the expression for X, the amplitude of the particular solution:
X = F0 / sqrt((k - mω²)² + (cω)²)
To find the frequency for which the particular solution has the largest amplitude, we need to maximize X with respect to ω. To do this, we can find the critical points by differentiating X with respect to ω and setting the result to zero:
dX/dω = 0
To simplify the problem, we can define the damping ratio ζ = c / (2 * sqrt(m * k)) and the undamped natural frequency ω_n = sqrt(k / m). The expression for X becomes:
X = F0 / sqrt((ω_n² - ω²)² + (2 * ζ * ω_n * ω)²)
Now, we differentiate X with respect to ω and set it to zero. Solving for ω, we get:
ω = ω_n * sqrt(1 - 2ζ²)
This is the frequency for which the particular solution to the differential equation has the largest amplitude, assuming a positive frequency and that the damping ratio ζ is less than 1 / sqrt(2). Otherwise, the system will be overdamped, and there will be no resonant frequency.
the frequency for which the particular solution to the differential equation has the largest amplitude is:
ω = √(γ/2 - β^2)
To find the frequency for which the particular solution to the differential equation has the largest amplitude, we can assume that the particular solution is of the form:
y(t) = A*cos(ωt + φ)
where A is the amplitude, ω is the frequency, and φ is the phase angle.
Substituting this form of y(t) into the differential equation gives:
-ω^2Acos(ωt + φ) - 2βωAsin(ωt + φ) + γA*cos(ωt + φ) = f(t)
Simplifying this equation gives:
(A/|D|)[γcos(ωt + φ) - ω^2cos(ωt + φ) - 2βω*sin(ωt + φ)] = f(t)
where |D| is the modulus of the denominator of A*cos(ωt + φ) and is given by:
|D| = √[ (γ - ω^2)^2 + (2βω)^2 ]
To find the frequency for which the amplitude of the particular solution is largest, we need to minimize the modulus of the denominator |D| over all frequencies ω. We can do this by finding the critical points of |D| with respect to ω and then checking which of these critical points correspond to a minimum.
Differentiating |D| with respect to ω gives:
d|D|/dω = [2ω(γ - ω^2) - 4β^2ω]/|D|
Setting this equal to zero and solving for ω gives:
ω = ±√(γ/2 - β^2)
We can see that there are two critical points for |D|, one positive and one negative. To check which of these corresponds to a minimum, we can use the second derivative test:
d^2|D|/dω^2 = (2γ - 6ω^2)/|D|^3
Substituting ω = ±√(γ/2 - β^2) into this expression gives:
d^2|D|/dω^2 = ±4√2β^3/γ^(3/2)
Since β and γ are both positive, the second derivative is negative for both critical points, which means that they both correspond to maxima of |D|. The positive critical point corresponds to the frequency for which the amplitude of the particular solution is largest.
for more questions on frequency
https://brainly.com/question/17803539
#SPJ11
The
An online teacher sends updates to students via text.
probability distributions shows the number of texts (X) the
teacher may send in a day.
Texts Sent 0 1 2 3 4 5
P(X)
0.05 0.05 0.1 0.1 0.4 0.3
What is the probability that the teacher sends 3 or 4 texts in
a day?
The probability that teacher send 3 or 4 text every day is option B = 0.5
How to find Probability?Probability is the measure of the likelihood of an event occurring. It is typically represented as a number between 0 and 1, where 0 indicates that the event is impossible, and 1 indicates that the event is certain.
To find the probability of an event, you need to identify the number of ways the event can occur and the total number of possible outcomes.
The formula for probability is:
Probability = Number of favorable outcomes / Total number of outcome
The probabilities of P(X=3) and P(X=4) must be added in order to determine the likelihood that the teacher sends 3 or 4 texts per day:
P(X=3 or X=4)=P(X=3) + P(X=4)=0.1 + 0.4 = 0.5
The likelihood that the teacher will send three or four texts every day is therefore 0.5.
Learn more about Formula of Probability here
https://brainly.com/question/28564973
#SPJ1
the coefficient of determination: group of answer choices indicates whether the correlation coefficient is significant. is a measure of the amount of variability in one variable that is shared or accounted for by the other. is the square root of the variance. is the square root of the correlation coefficient.
The coefficient of determination is not the square root of the correlation coefficient.
The coefficient of determination refers to the proportion of the variance in the dependent variable that is accounted for by the independent variable.
It is the square of the correlation coefficient and ranges between 0 and 1, with 0 indicating no correlation, while 1
indicates a perfect correlation.
The coefficient of determination is a measure of how much variation exists between two variables, with a higher value
indicating a stronger relationship between the two variables.
Additionally, the group of answer choices can indicate whether the correlation coefficient is significant, and the
coefficient of determination is not the square root of the correlation coefficient.
for such more question on coefficient
https://brainly.com/question/4219149
#SPJ11
A $1 million grant is to be divided among
four charities, J, K, L, and M. If L and M will
be awarded $125,000 more than K and
$325,000 less than J, how much of the grant
will be awarded to M?
If a $1 million grant is to be divided among four charities, J, K, L, and M. M will be awarded $200,000 of the grant.
How much of the grant will be awarded to M?Let the amount awarded to K be x. Then the amounts awarded to L and M will be x + 125,000 and y - 325,000, respectively.
Since the total grant is $1 million, we have:
x + (x + 125,000) + (y - 325,000) + y = 1,000,000
Simplifying this equation, we get:
2x + 2y - 200,000 = 1,000,000
2x + 2y = 1,200,000
x + y = 600,000
We also know that:
y - 125,000 = x + 325,000
y = x + 450,000
Substituting this into the equation x + y = 600,000, we get:
x + (x + 450,000) = 600,000
2x + 450,000 = 600,000
2x = 150,000
x = 75,000
Therefore, the amount awarded to M is:
y - 325,000 = x + 450,000 - 325,000 = $200,000
So, M will be awarded $200,000 of the grant.
Learn more about grant here:https://brainly.com/question/1559476
#SPJ1
What are the factors of 6x2 + 37x - 60? a. 3x - 4 and 2x + 15 b. 3x + 4 and 2x - 15 c. 2(x - 2) and 3(x + 5) d. 2(x + 2) and 3(x - 5)
The factors of 6[tex]x^{2}[/tex]+ 37x - 60 are 2(x - 2) and 3(x + 5), which is answer c.
To factor the polynomial 6[tex]x^{2}[/tex] + 37x - 60, we need to find two numbers whose product is -360 (the product of the leading coefficient and the constant term) and whose sum is 37 (the coefficient of the linear term).
One way to do this is to list all the possible factor pairs of -360 and look for a pair that adds up to 37. Some of the factor pairs are:
1, -360
2, -180
3, -120
4, -90
5, -72
6, -60
8, -45
9, -40
10, -36
12, -30
15, -24
18, -20
We can see that 15 and -24 add up to 37, so we can use them as the coefficients of the linear term. To get the correct sign, we need to use -24 and 15 instead of 15 and -24.
So we have:
6[tex]x^{2}[/tex] + 37x - 60 = 6[tex]x^{2}[/tex] + 15x - 24x - 60
= 3x(2x + 5) - 12(2x + 5)
= (3x - 12)(2x + 5)
= 6(x - 2)(x + 5)
Therefore, the factors of 6[tex]x^{2}[/tex] + 37x - 60 are 2(x - 2) and 3(x + 5), which is answer c.
To learn more about factors:
https://brainly.com/question/1863222
#SPJ4
A freezer is at -14°C and then it is unplugged. It gets warmer by 3°C an hour. It is checked once an hour and when it gets above 0 °C, it is plugged back in. After it is plugged in again, it gets colder by 4°C per hour.
Copy and complete the table to show the sequence of temperatures for the first 8 hours after it was unplugged.
What is the temperature of the freezer (in °C) 8 hours after it was unplugged?
After 8 hours, the freezer is at a temperature of 8°C.The temperature sequence for the first 8 hours after the freezer was unplugged is as follows:
Time (hours) Temperature (°C)
0 -14
1 -11
2 -8
3 -5
4 -2
5 1
6 0
7 4
8 8
Temperature is a physical quantity that expresses the degree of hotness or coldness of an object or a living being.
The direction in which heat energy will spontaneously flow from a hotter body (one at a higher temperature) to a colder body (one at a lower temperature) is indicated by temperature, and it is expressed in terms of any of several arbitrary scales
Find out more about Temperature
brainly.com/question/13454793
#SPJ4
Help me solve ignore the pyramid it’s for a different question
Are these triangles similar, congruent or neither? What theorem supports your answer?
options:
Similar: SAS
Similar: HL
Similar: AA
Congruent: SAS
Congruent: HL
Congruent: SSS
Neither
Answer:
The triangles are not similar because
12/24 is not equal to 3/5.
"Neither" is the correct answer.
Given a circle with a diameter whose endpoints are (3, -1) and (7, 5), write the
equation of the circle.
(x - 5)² + (y-2)² = 169
(x − 3)² + (y + 1)² = 52
(x-3)² + (y + 1)² = 169
(x - 5)² + (y-2)² = 13
(x - 5)² + (y - 2)² = 26
The circle equation is [tex](x-5)^{2} +(y-2)^{2}[/tex][tex]=52[/tex]. Hence the appropriate answer is [tex](x-3)^{2} +(y+1)^{2} =52[/tex]
What is the centre?A centre is a point in geometry that connects to a polyhedron or other structure. (or centre). The centre of the figure or object may have distinctive characteristics that are significant when studying it.
For example, the centre of a circle is thought to be the spot that is evenly spaced from all other points on the circle. This term, which is commonly represented by the character "O," is defined in terms of the radius, diameter, and circumference of a circle.
Additionally, other geometric constructions like tangent lines and inscribed polygons use the middle of a circle as well. Other geometric shapes may define the middle differently.
Given
The circle's centre is found at the midpoint of the circumference, which can be established by averaging the [tex]x[/tex]- and[tex]y[/tex]-coordinates of the ends:
[tex]centre = (3+7)/2,(-1+5)/2(,5,2)[/tex]
Distance =[tex]\frac{1}{2}[/tex] of diameter= circle radius
[tex]r=\sqrt{(7-3)}[/tex]
[tex]\sqrt{52/2}[/tex][tex]= \sqrt{2+(5-(-1)2)/2}[/tex][tex]13[/tex]
Therefore the circle equation[tex](x-5)^{2} +(y-2)(y-2)^{2}= \sqrt[2]{13^{2} }[/tex]
[tex](x-5)^{2} +(y-2)^{2} =52[/tex]
Hence the appropriate answer is [tex](x-3)^{2} +(y+1)^{2} =52[/tex]
Learn more about circle
https://brainly.com/question/29142813
#SPJ1
Mr. Rodriguez is packing bags of snacks for his children’s lunchboxes. He plans to use 20 blueberries and 30 grapes. Each snack bag will have the same number of blueberries and grapes. How many bags can he make if each bag needs to be the same?
5 bags
10 bags
50 bags
60 bags
As a result, Mr. Rodriguez can produce 10 sacks, each containing two blueberries and three grapes.
So, 10 bags must be the solution.
Which meaning of "common factor" is the best?The largest number that can split evenly into two other numbers is known as the greatest common factor in mathematics. For instance, the number 6 is the most frequent factor between 12 and 30. The greatest common denominator is another name for the greatest common component.
We must find the GCF, or greatest common factor, between 20 and 30 to calculate how many bags Mr. Rodriguez can produce. This is necessary because each bag must contain the same quantity of blueberries and grapes, requiring that they both have a similar factor of 20 or 30.
1, 2, 4, 5, 10, and 20 are the elements that make up 20.
1, 2, 3, 5, 6, 10, 15, and 30 make up the number 30.
1, 2, 5, and 10 are the common variables between 20 and 30.
Since the quantity of blueberries and grapes in each bag must be the same, we can split both 20 and 30 by the GCF of 10, which is 10.
The correct number of bags needed is 10 .
This results in:
2 blueberries are in each container of 20/10.
3 grapes per container (30/10)
To know more about GCF, visit
brainly.com/question/11444998
#SPJ1
sphere a has radius 2 cm. sphere b has radius 4 cm what is there volumes
The volume of sphere a is 32π/3 cubic cm, and the volume of sphere b is 256π/3 cubic cm.
What is volume of sphere?
The volume of a sphere is given by the formula:
V = (4/3)πr³
where r is the radius of the sphere, and π (pi) is a mathematical constant approximately equal to 3.14159.
The volume of a sphere can be calculated using the formula:
V = (4/3)π[tex]r^3[/tex]
where r is the radius of the sphere and π is the mathematical constant pi.
Using this formula, we can find the volumes of spheres a and b as follows:
Volume of sphere a:
V = (4/3)π([tex]2^3[/tex]) = (4/3)π(8) = 32π/3 cubic cm
Volume of sphere b:
V = (4/3)π([tex]4^3[/tex]) = (4/3)π(64) = 256π/3 cubic cm
Therefore, the volume of sphere a is 32π/3 cubic cm, and the volume of sphere b is 256π/3 cubic cm.
To learn more about volume of sphere visit:
https://brainly.com/question/22807400
#SPJ1
The rectangular room shown 20 feet long, 48 feet wide, and 10 feet tall. Use the Pythagorean Theorem to find the distance from B to C and the distance from A to B . Round to the nearest tenth, if necessary.
Answer:
Step-by-step explanation:
We can use the Pythagorean Theorem to find the distances from B to C and from A to B.
The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
Let's first find the distance from B to C. We can see that the length from B to C is the hypotenuse of a right triangle with legs of length 10 feet and 20 feet. So, using the Pythagorean Theorem, we can write:
distance from B to C = sqrt(10^2 + 20^2)
distance from B to C = sqrt(500)
distance from B to C ≈ 22.36 feet (rounded to the nearest tenth)
Therefore, the distance from B to C is approximately 22.36 feet.
Now, let's find the distance from A to B. We can see that the width of the room, from A to B, is the hypotenuse of a right triangle with legs of length 10 feet and 48 feet. So, using the Pythagorean Theorem, we can write:
distance from A to B = sqrt(10^2 + 48^2)
distance from A to B = sqrt(2354)
distance from A to B ≈ 48.5 feet (rounded to the nearest tenth)
Therefore, the distance from A to B is approximately 48.5 feet.
What exponential function can be used to determine the number of transistors in a car that doubles every TWO years? The year is 1974 and there are 4100 transistors. For this function to work, we should be able to find the amount of transistors in a car in the year 1989,1993,1997 etc. (or any odd number of years).
(also I asked this earlier just without the year part)
We can use the exponential function [tex]N(t) = N0 * 2^(t/2)[/tex] to determine the number of transistors in a car that doubles every two years.
An exponential function with the following form can be used to calculate the number of transistors in an automobile whose number doubles every two years:
[tex]N(t) = N0 * 2^(t/2)[/tex]
Where t is the amount of time in years after the initial measurement, N0 is the number of transistors at the start, and N(t) is the number of transistors at time t.
We can use this technique to determine the number of transistors in the car in any odd year since 1974, when there were 4100 in it.
For instance, we may insert in t = 15 to determine the quantity of transistors in 1989:
transistors N(15) = 4100 * 2(15/2) = 261,632
Similarly, we may enter t = 19 to calculate the number of transistors in 1993:
522,724 transistors are found in N(19) = 4100 * 2(19/2)
In 1997, we can enter t = 23:
1,045,449 transistors make up N(23) = 4100 * 2(23/2)
In summary, we may calculate the number of transistors in an automobile whose number doubles every two years using the exponential equation [tex]N(t) = N0 * 2(t/2)[/tex]. We can determine the number of transistors in a car in any odd year with an initial measurement of 4100 transistors in 1974.
Learn more about exponential function here:
https://brainly.com/question/14355665
#SPJ1
Two parallel lines are graphed on a coordinate plane as shown. The lines are rotated about the origin. The graph of the image of the lines after the rotation is also shown.
Which conclusion is supported by the image of the lines?
The conclusion supported by the image of the lines is that when two parallel lines are rotated about the origin, they remain parallel to each other.
1. Observe the initial graph with two parallel lines.
2. Rotate the lines about the origin by the given angle.
3. Observe the image of the lines after the rotation.
4. Notice that the lines still maintain the same distance apart and do not intersect, meaning they are still parallel to each other.
If two lines do not intersect, they are said to be parallel.
The lines' slopes are identical. If m1=m2, then f(x) =m1x + b1 and
g(x)= m2x + b2 are parallel.
If m 1 = m 2, then f (x) = m 1 x + b 1 and g (x) = m 2 x + b 2 are parallel equations.
The coordinate axes are rotated about the origin (0,0) in counter clockwise direction through an angle of 60∘ .
For similar question on parallel.
https://brainly.com/question/1439696
#SPJ11
For the situations below, define a random variable X for the situation and then decide if they follow a binomial distribution model by commenting on the four requirements.
1. You roll a DnD dice (20-sided), 20 times and record the number that shows on the dice.
2. A basketball player can make 60% of their free throws. The coach plans on having a free throw shooting competition and the player will be shooting 100 shots.
3. From a standard deck of cards, you pull out a card, record the suit, put it back and reshuffle. You continue until you get two spades in a row.
4. You are conducting a survey at your school to see how many students own smartphones. The probability that a student will own a smartphone is 0.85. You plan on having 200 students participate in your survey.
By answering the presented question, we may conclude that Because the likelihood of a student possessing a smartphone is the same for each participant, the trials are similar.
What is a Variable?A variable is something that may be changed in the context of a mathematical problem or experiment. A variable is often indicated by a single letter. Variables are commonly represented by the letters x, y, and z. A variable is a property that can be measured and has a large range of values. A few examples of criteria are size, age, affluence, location of birth, academic status, and kind of dwelling. Variables may be classified into two basic groups using both category and numerical methods.
X is a random variable that represents the amount of times a given number is rolled in 20 rolls of a 20-sided dice. This circumstance does not fit the binomial distribution model because the following four conditions are not met:
The trials are not independent since the outcome of each dice roll influences the odds of the succeeding rolls.
The success probability is not set since it is determined by the number chosen to count as a success.
Because the possibilities of each event are not equal, the trials are not similar.
The number of trials is predetermined.
X is a random variable that represents the number of successful free throws out of 100. Because the four prerequisites are satisfied, this scenario follows a binomial distribution model:
Because the outcome of one free throw does not impact the outcome of another, the trials are independent.
The success probability is set at 0.6.
Because the probability of making a free throw is the same for each shot, the trials are similar.
The trial count is set at 100.
X is a random variable that represents the number of cards drawn before receiving two spades in a row. This circumstance does not fit the binomial distribution model because the following four conditions are not met:
The trials are not independent since the outcome of each draw influences the likelihood of subsequent pulls.
The likelihood of success is not fixed because it is determined by the outcome of the prior pull (s).
Because the possibilities of each event are not equal, the trials are not similar.
The number of trials is not predetermined.
X is a random variable that represents the number of students out of 200 who own smartphones. Because the four prerequisites are satisfied, this scenario follows a binomial distribution model:
The trials are independent since one student's possession of a smartphone has no bearing on the outcome of another student.
The success probability is set at 0.85.
Because the likelihood of a student possessing a smartphone is the same for each participant, the trials are similar.
The trial count is set at 200.
To know more about variable visit:
https://brainly.com/question/2466865
#SPJ1