Answer: 35.553
Step-by-step explanation:
PLEASE HELP ME PLEASE SHOW EXPLANATION WHEN SOLVING IT OR I WILL REPORT YOUUU
Answer:
[tex]x {}^{2} - 5[/tex]
Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options. The radius of the circle is 3 units. The center of the circle lies on the x-axis. The center of the circle lies on the y-axis. The standard form of the equation is (x – 1)² + y² = 3. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
Answer:
Correct options are A, B, E--------------------------
Standard form for the equation of a circle is:
(x − h)² + (y − k)² = r², where (h, k) is the center and r is the radiusConvert the given equation into standard form:
x² + y² - 2x - 8 = 0x² - 2x + 1 + y² - 9 = 0(x - 1)² + y² = 9(x - 1)² + y² = 3²Its center is ( 1, 0) and radius is r = 3.
Let's verify the statements:
A) The radius of the circle is 3 units - TRUE, r = 3;B) The center of the circle lies on the x-axis - TRUE, point (1, 0) is on the x-axis;C) The center of the circle lies on the y-axis - FALSE, the x- coordinate of the center is not zero; D) The standard form of the equation is (x – 1)² + y² = 3 - FALSE, r²= 9 but not 3;E) The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9, TRUE, its radius is r² = 9 ⇒ r = 3.Answer:
See below
Step-by-step explanation:
To find:-
Which statements are true .Answer:-
The given equation of the circle is ,
[tex]\longrightarrow x^2+y^2-2x-8 = 0 \\[/tex]
For finding the correct statements , we need to convert this equation into standard form for a circle.
The standard equation of circle is given by,
[tex]\boxed{\begin{tabular}{c}\textbf{\underline{ \red{Standard\ equation\ of \ circle }}} \\ \\ \text{ The standard equation of a circle is given by:-} \\\\ \longrightarrow \underline{\underline{ (x-h)^2+(y-k)^2 = r {}^{2}}} \\\\ \text{where} , \\\\ \bullet\text{ (h,k) is the centre of the circle.}\\\\\bullet\text{ "r" is the radius of the circle. }\\\end{tabular}}[/tex]
Now for that we need to complete the square for "x" . This can be done by ,
Rearrange the terms,
[tex]\longrightarrow x^2-2x + y^2-8 = 0 \\[/tex]
Add and subtract 1² .
[tex]\longrightarrow ( x^2 -2x +1^2 ) - 1^2 + y^2-8=0 \\[/tex]
Simplify,
[tex]\longrightarrow (x^2-2(1)x+1^2) - 1-8 + y^2=0 \\[/tex]
Notice that the terms inside the small brackets are in the form of a² - 2ab + b² , which is the whole square of (a-b) . So we can write it as,
[tex]\longrightarrow (x-1)^2 +y^2 - 9 = 0 \\[/tex]
Add 9 on both the sides ,
[tex]\longrightarrow (x-1)^2 + y^2 = 9\\[/tex]
This can be written as,
[tex]\longrightarrow \underline{\underline{ \boldsymbol{(x-1)^2+(y-0)^2 = 3^2}}} \\[/tex]
On comparing it to the standard form, we have;
[tex]\longrightarrow\boxed{ \text{Center = (1,0) }} \\[/tex]
[tex]\longrightarrow\boxed{ \text{ Radius = 3 \ units}} \\[/tex]
Let's check the given statements ,
Statement 1: The radius of the circle is 3 units.
This statement is true as we just calculated the radius to be 3 units.Statement 2: The centre of the circle lies on the x-axis.
This statement is also true as you can see that the y coordinate to the centre is 0 , and the x coordinate is 1 , so it will be on x-axis .Statement 3: The statement of the circle lies on the y-axis.
This statement is false since in the previous statement we proved that the centre lies on the x-axis .Statement 4: The standard equation of the circle is (x-1)²+y² = 3
This statement is false as we calculated the value of r² to be 9 .Statement 5: The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
The given equation of circle is x² + y² = 9 , if we convert this into standard form, we will get ; x² + y² = 3² . Now on comparing it to the standard equation, we see that the radius is 3 units . Hence the given statement is also true .The graph for the same has been attached.
If A=1+r+7r^2 and B=1-r^2, find an expression that equals A+3B in standard form.
Answer:
To find A+3B, we need to first find A and B. A = 1 + r + 7r^2 B = 1 - r^2 Now we can substitute these expressions into A+3B: A+3B = (1 + r + 7r^2) + 3(1 - r^2) Simplifying this expression, we get: A+3B = 1 + r + 7r^2 + 3 - 3r^2 A+3B = 4 + r + 4r^2 So the expression that equals A+3B in standard form is 4 + r + 4r^2.
a river starts by flowing south about 1.1x10 to the seventh power then it flows southeast for about 3.2x10 to the sixth power ft before it empties into the ocean. what is the length of the river? write your answer using scientific notation show your work
1.143 x 10⁷ ft, or approximately 11.43 million feet is the length of the river.
To find the length of the river, we need to use the Pythagorean theorem, which states that the square of the length of the hypotenuse (the diagonal line connecting the two endpoints of a right triangle) is equal to the sum of the squares of the lengths of the other two sides.
Let's call the length of the southward flowing part of the river "a" and the length of the southeastward flowing part of the river "b". Then we have:
a = 1.1 x 10⁷ ft
b = 3.2 x 10⁶ ft
The length of the river is given by the hypotenuse of a right triangle with sides a and b. Therefore, we can calculate the length of the river, c, as follows:
c² = a² + b²
c² = (1.1 x 10⁷ ft)² + (3.2 x 10⁶ ft)²
c² = 1.21 x 10¹⁴ ft² + 1.024 x 10¹³ ft²
c² = 1.3104 x 10¹⁴ ft²
c = √(1.3104 x 10¹⁴ ft²)
c = 1.143 x 10⁷ ft
Therefore, the length of the river is 1.143 x 10⁷ ft, or approximately 11.43 million feet
To learn more about Pythagorean theorem click here
brainly.com/question/14930619
#SPJ1
A rectangular prism has a base area of 54 m (to the 2nd power) and a volume of 702 m (to the 3rd power). What is its height?
Answer:
13 meters.
Step-by-step explanation:
We can use the formula for the volume of a rectangular prism, which is:
Volume = length x width x height
We are given that the base area (length x width) of the prism is 54 m², so we can write:
length x width = 54 m²
We are also given that the volume of the prism is 702 m³, so we can write:
Volume = length x width x height = 702 m³
We want to find the height of the prism, so we can rearrange the formula for the volume to solve for height:
height = Volume / (length x width)
Substituting the given values, we get:
height = 702 m³ / 54 m²
Simplifying this expression, we can divide both the numerator and the denominator by the greatest common factor of 54 and 702, which is 18:
height = (702/18) m / (54/18) m = 39 m / 3 m
height = 13 meters
Therefore, the height of the rectangular prism is 13 meters.
A scientist is studying bacterial growth over time. Her research is conducted by placing 10 strep bacteria in a petri dish containing enough food for the bacteria to live and thrive for the course of the research. She records the number of bacteria present every two hours for 6 hours. The collected data is shown in the table below and on the given graph.
a. What function, linear or exponential, do you think would be the best choice to model this data? Explain why you think your choice is the best-fit.
b. Explain how to determine which function is the best choice mathematically, without using a graph.
Demonstrate your method.
c. Think of an example of at least 4 data points that would be best modeled by the function you did NOT choose in part a. Explain how you set up the data so that it worked with this type of function.
This is reflected in the data as the number of bacteria doubles every two hours, which is a characteristic of exponential growth.
What do you mean by exponential data ?Data that changes or grows at an exponential rate over time is referred to as exponential data. This indicates that the data changes quickly, either increasing or decreasing, and that the pace of change quickens over time. Exponential data frequently consists of numbers that rise steadily over time, with the rate of rise accelerating over time.
a.) exponential function would be the ideal option to model this data. An exponential curve is produced as the quantity of bacteria multiplies at an ever-increasingly rapid rate.
b. One way to determine which function is the best choice is to examine the rate of change of the data. In this case, we may calculate the average rate of change for each time period and see if it is constant. If the rate of change is constant, the data can be represented by a linear function. However, if the rate of change increases or decreases, an exponential or quadratic function might be a better fit.
From 0 to 2 hours: (25-10)/(2-0) = 7.5
From 2 to 4 hours: (50-25)/(4-2) = 12.5
From 4 to 6 hours: (100-50)/(6-4) = 25
c. The distance travelled by an automobile at a constant pace is an illustration of data that would be best characterised by a linear function. Imagine a car driving for four hours at a speed of 60 mph. Below is a list of the distance covered each hour:
After 1 hour: 60 miles
After 2 hours: 120 miles
After 3 hours: 180 miles
After 4 hours: 240 miles
In this case, the distance traveled is directly proportional to the time, so a linear function would be the best fit.
Learn more about acceleration here
https://brainly.com/question/14371355
#SPJ1
Please help I need these differential equations done by today and cannot do it.
the particular solution to the differential equation. we use the positive sign: [tex]y = -1 + e^(1/2 x^2 + x - 5.605)[/tex]
What is the differential equation?To find the particular solution to the differential equation {dy}/{dx} = (x+1) (y+1) with the initial condition y(4) = 3, we can use separation of variables and integration.
First, we can rewrite the equation as:
[tex]{1}/{(y+1)} dy = (x+1) dx[/tex]
Next, we can integrate both sides:
[tex]∫ {1}/{(y+1)} dy = ∫ (x+1) dx[/tex]
[tex]ln|y+1| = 1/2 x^2 + x + C[/tex]
where C is the constant of integration.
To determine the value of C, we can use the initial condition y(4) = 3:
[tex]ln|3+1| = 1/2 (4)^2 + 4 + C[/tex]
[tex]ln|4| = 10 + C[/tex]
[tex]C = ln|4| - 10 = -5.605[/tex]
Therefore, the particular solution to the differential equation with the initial condition y(4) = 3 is:
[tex]ln|y+1| = 1/2 x^2 + x - 5.605[/tex]
Solving for y:
[tex]|y+1| = e^(1/2 x^2 + x - 5.605)[/tex]
[tex]y+1 = \pm e^(1/2 x^2 + x - 5.605)[/tex]
[tex]y = -1 \pm e^(1/2 x^2 + x - 5.605)[/tex]
Since [tex]y(4) = 3[/tex], we can determine which sign to use:
[tex]3 = -1 + e^(1/2 (4)^2 + 4 - 5.605)[/tex]
[tex]3 = -1 + e^(7.395)[/tex]
[tex]4 = e^(7.395)[/tex]
Therefore, we use the positive sign: [tex]y = -1 + e^(1/2 x^2 + x - 5.605)[/tex]
Learn more about equation here:
https://brainly.com/question/10413253
#SPJ1
DUE TODAY PLEASE HELP!!!!
For which angles is the cosine positive? Select all that apply.
a
0 radians
b
5π/12 radians
c
5π/6 radians
d
3π/4 radians
e
5π/3 radians
Step-by-step explanation:
if it is between 0 and pi/2 (90°), or between 3pi/2 (270°) and 2pi (360°).
for angle = 0, cos = 1. therefore, positive.
0 <= 5pi/12 <= pi/2. therefore, positive.
pi/2 <= 5pi/6 <= pi. therefore, negative.
pi/2 <= 3pi/4 <= pi. therefore, negative.
3pi/2 <= 5pi/3 <= 2pi. therefore, positive.
you do know how to compare fractions, right ?
you need to bring then to the same denominator by multiplying numerator and denominator by the same factor.
e.g. comparing 5pi/12 with pi/2.
to bring them both to .../12, we have to multiply pi/2 by 6/6.
so, we are comparing 5pi/12 and 6pi/12.
and we see, 5pi/12 is smaller.
the others work the same way.
3pi/6 <= 5pi/6 <= 6pi/6
2pi/4 <= 3pi/4 <= 4pi/4
9pi/6 <= 10pi/6 <= 12pi/6
now you see it clearly.
Please help and include scratch thank you.
Hence, the value of y is 23 when x = 7.
Describe equation?
A mathematical equation is a formula that uses the equals symbol (=) to denote the equality of two expressions.
A formula would be 3x - 5 = 16,
for instance. We may determine the value of the variable x by solving this equation: x = 73.
The slope-intercept representation of the equation can be used to determine the equation of a line running through the points (x1, y1) and (x2, y2):
y - y1 = m(x - x1) (x - x1)
where m is the line's slope. The following formula can be used to determine the line's slope:
m = (y2 - y1) / (x2 - x1) (x2 - x1)
Now put the x and y value in this:
slope of the line using the points (1, 5) and (3, 11):
m = (11 - 5) / (3 - 1) = 6 / 2 = 3
We can use the slope of the line to determine the equation of the line now that we know it:
y - y1 = m(x - x1) (x - x1)
y - 5 = 3(x - 1) (x - 1)
y - 5 = 3x - 3 = 3x + 2
In light of this, the equation for the line connecting points (1, 5) and (3, 11) is y=3x+2
To determine the value of y for x = 7, we can utilize the equation of the line we discovered earlier:
y = 3x + 2
y = 3(7) + 2
y = 21 + 2
y = **23**
Graph calculation given below:
To know more about equation visit:
brainly.com/question/2965798
#SPJ1
PLEASE HELPP
Linus wants to have 500 copies of his resume printed. His local print shop charges $18.50 for the first 200 copies and $9 for every 100 additional copies. How much will the 500 copies cost?
A)$46.25
B)$45.50
C)$45.00
D)$46.00
stratified random sampling is a method of selecting a sample in which . a. the population is first divided into groups, and then random samples are drawn from each group b. the elements are selected on the basis of convenience c. various strata are selected from the sample
The stratified random sampling is a method of various strata are selected from the sample. So, the right choice for answer is option(c).
The four probability sampling methods mainly applied in research methods include simple random sampling, cluster sampling, stratified sampling, and systematic sampling. In certain situations, we need to remove the sampling bias, and for that, we opt for stratified random sampling. Here we talking about stratified random sampling. A method of probability sampling (where all members of the population have an equal chance of being included) Population is divided into 'strata' (sub populations) and random samples are drawn from each. Therefore, the required choice is option (c), that is various strata are selected from the sample.
For more information about stratified random sampling, visit :
https://brainly.com/question/29852583
#SPJ4
An investor has an account with stock from two different companies. Last year, her stock in Company A was worth $5800 and her stock in Company B was worth $7470. The stock in Company A has decreased 1% since last year and the stock in Company B has decreased 20%. What was the total percentage decrease in the investor's stock account? Round your answer to the nearest tenth (if necessary).
To find the total percentage decrease, we first need to find the new values of the stocks in Company A and Company B after the decrease.
The new value of the stock in Company A is: $5800 - (1% \times $5800) = $5742
The new value of the stock in Company B is: $7470 - (20% \times $7470) = $5976
To find the total value after the decrease, we add these two values: $5742 + $5976 = $11718
To find the percentage decrease from the original total value ($5800 + $7470 = $13270) to the new total value ($11718), we use the formula:
percentage decrease = [(original value - new value) / original value] x 100%
percentage decrease = [($13270 - $11718) / $13270] x 100%
percentage decrease = 11.7%
Therefore, the total percentage decrease in the investor's stock account is 11.7%.
Jason goes to the sandwich shop for lunch. The prices for sandwiches are listed below.
What number completes the number sentence 3m = ?
2g
3g
4g
5g
The number completes the number sentence 3m= 5g.
What number completes the number sentence 3m = ?The m refers the meatball which prices $2.50
so for 3m = 3*2.50
3m = $7.5
g refers to grilled cheese which prices $1.50
so we have to find for how many grilled cheese which equals $7.5
On dividing we get, 7.5/1.50 = 5
Hence 3 meatballs equal 5 grilled cheese, 3m = 5g
To know more about Division visit:
brainly.com/question/15381501
#SPJ1
Work out and simplify 3/8 - 1/16
Answer:
3/8 - 1/16 simplifies to 5/16.
Step-by-step explanation:
To subtract two fractions, we need to find a common denominator. In this case, the least common multiple of 8 and 16 is 16.
So, we need to rewrite 3/8 and 1/16 with a denominator of 16:
3/8 = 6/16
1/16 = 1/16
Now we can subtract:
6/16 - 1/16 = 5/16
AnswerAns
5/6
Step-by-step explanation
3/8 - 1/16 = (3×2 -1)÷16 = 5/16
A Christmas promotion included a $2.5 mail-in rebate for the purchase of a 10-liter bottle of milk and a store coupon for $1.39 off a 5-liter bottle of vegetable oil. Jesse Gatling bought one 10-liter bottle of milk for for $33.00 and a 5liter bottle of vegetables oil for $26.89. Calculate his total cost if an envelope costs $0.10 and a stamp costs $0.28
Answer:
can u break that down
Step-by-step explanation:
consider the following data for two independent random samples taken from two normal populations. sample 1 sample 2 10 7 13 7 9 8 8 4 6 9 8 7 a. compute the two sample means. b. compute the two sample standard deviations. c. what is the point estimate of the difference between the two population means? d. what is the 90% confidence interval estimate of the difference between the two population means?
a. The sample mean for sample 1 is 9.2, and the sample mean for sample 2 is 7.17.
b. The sample standard deviation for sample 1 is approximately 3.29, and the sample standard deviation for sample 2 is approximately 3.65.
c. The point estimate of the difference between the two population means is 2.03.
d. The 90% confidence interval estimate of the difference between the two population means is [-0.44, 4.50].
a. The sample mean for sample 1 is
(10 + 13 + 9 + 8 + 6) / 5 = 9.2
The sample mean for sample 2 is
(7 + 7 + 8 + 4 + 9 + 8) / 6 = 7.1667 ≈ 7.17
b. The sample standard deviation for sample 1 is:
√[((10-9.2)² + (13-9.2)² + (9-9.2)² + (8-9.2)² + (6-9.2)²) / (5-1)]
= √[10.8] ≈ 3.29
The sample standard deviation for sample 2 is
√[((7-7.17)² + (7-7.17)² + (8-7.17)² + (4-7.17)² + (9-7.17)² + (8-7.17)²) / (6-1)]
= √[13.33] ≈ 3.65
c. The point estimate of the difference between the two population means is:
9.2 - 7.17 = 2.03
d. To calculate the 90% confidence interval estimate of the difference between the two population means, we need to first calculate the standard error of the difference between the sample means:
s.e.(difference between sample means) = √[(s1²/n1) + (s2²/n2)]
= √[(3.29²/5) + (3.65²/6)]
= √[2.60]
≈ 1.61
Next, we can use the t-distribution with degrees of freedom equal to the smaller of n1-1 and n2-1 (in this case, 4) and a 90% confidence level to find the critical value, t*:
t* = 1.533 (from t-distribution table or calculator)
Finally, we can construct the confidence interval estimate:
9.2 - 7.17 ± (t* * s.e.(difference between sample means))
= 2.03 ± (1.533 * 1.61)
= 2.03 ± 2.47
= [ -0.44 , 4.50 ]
Learn more about standard deviation here
brainly.com/question/14747159
#SPJ4
Complete the proof that the alternate interior angles of transversals of
parallel lines are congruent.
Note: this proof is for the case where m/1 is less than 90°.
This proof uses the following theorem: Any point on one parallel line is the
same distance from the other line on a perpendicular transversal.
Statement or construction
1 ABCĎ
2 Construct BE perpendicular to such
that point E is on CD
3 Construct CF perpendicular to AB such
that point F is on AB
4 m/CFB=m/BEC = 90°
5 CF=
6
BC= BC
7 ABCF ACBE
8 LFBC ZECB
Reason
Given
All perpendicular angles measure 90° (2.
3).
Any point on one parallel line is the same
distance from the other line on a
perpendicular transversal (1, 2, 3).
They are measures of the same segment.
congruence (4, 6,5)
Corresponding parts of congruent figures
are congruent (7)
The two column proof is completed as follows
Statement Reason
1. AB || CD Given
2 Construct BE perpendicular to Construction of side BE
CD such that point E is on CD
3 Construct CF perpendicular to Construction of side CF
AB such that point F is on AB
4 ∠ CFB = ∠ BEC = 90° All perpendicular angles measure 90°
5 CF = BE Any point on one parallel line is the
same distance from the other line on
a perpendicular transversal (1, 2, 3)
6. BC = BC They are measures of the same
segment.
7. Δ BCF ≅ Δ CBE SAS congruence (4, 6,5)
What is SAS congruence theoremThe SAS congruence theorem, also known as the Side-Angle-Side congruence theorem, states that if two triangles have two sides and the included angle of one triangle congruent to the corresponding parts of another triangle, then the triangles are congruent.
The equality of the included angle is by the alternate interior angles theorem.
Learn more about SAS at
https://brainly.com/question/3999145
#SPJ1
If <1 and <2 are vertical angles and m<22 = 180°, find m<1
If ∠1 and ∠2 are vertical angles and m∠22 = 180°, then m∠1 = 90°
Vertical angles are pairs of angles that are opposite to each other when two lines intersect. Vertical angles are always equal in measure. Therefore, if ∠1 and ∠2 are vertical angles, then:
∠1 = ∠2
We are also given that m∠22 has a measure of 180°. Since ∠1 and ∠2 are vertical angles, they form a straight line, and their measures add up to 180°. Therefore:
∠1 + ∠2 = 180°
Since ∠1 = ∠2, we can substitute ∠1 for ∠2 in the above equation:
∠1 + ∠1 = 180°
Simplifying the equation, we get:
2∠1 = 180°
Dividing both sides by 2, we get:
∠1 = 90°
Therefore, ∠1 has a measure of 90°.
To learn more about Vertical angles click here
brainly.com/question/24460838
#SPJ1
in the last 10 softball games delisa has scored the following number of runs for her team: 2, 1, 3, 3, 1, 3, 2, 4, 3, 5. the mode number of runs for delisa would be:
In the last 10 softball games, the mode number of runs for Delisa is 3.
Mode is the value that appears most frequently in a given data set. It is one of the three measures of central tendency, along with mean and median.
To find the mode, we need to determine which number appears most frequently in the data set. In this case, the number of runs that Delisa scored in each game.
We have been given the data points,
2,1,3,3,1,3,2,4,3,5
The number 3 appears most frequently, occurring three times. Therefore, the mode number of runs for Delisa is 3.
Learn more about Mode on
https://brainly.com/question/30891252
#SPJ4
If a function is defined as f(x)=2x+3 , find the value of f(4
Answer: f(4) = 11
Step-by-step explanation: See image below.
Answer: 11
Step-by-step explanation:
you need to put 4 where the X is: f(4)=(2*4)+3 = 11
the variance of a sample of 144 observations equals 576. the standard deviation of the sample equals group of answer choices 12. 63,504. 21. 441.
The sample's standard deviation is equal to 12. Thus, choice B is the right choice.
The variance of a sample of 144 observations equals 576.
Variance S² = 144
The standard deviation is a measure of how spread out a set of data is. It is calculated by taking the square root of the variance, which is the average of the squared differences from the mean.
The standard deviation can be used to measure the amount of variation or dispersion of a set of data values from the mean.
Standard Deviation = √Variance
Standard Deviation = √144
Standard Deviation = 12
The standard deviation of the sample equals 12. So the option B is correct.
To learn more about standard deviation link is here
brainly.com/question/13905583
#SPJ4
The complete question is:
The variance of a sample of 144 observations equals 576. The standard deviation of the sample equals:
A. 441
B. 12
C. 63,504
D. 21
please help, i do not understand. thank you!
Answer: it's 1
Step-by-step explanation:
The x in the numerator determines that the x is in absolute value, meaning only positive integers.
That wouldn't matter anyway, because since any value of x would have to be greater than 0 (meaning only positive values), and both x's are the same x, the equation would have to equal one.
For example, you could plug in 2 to both x's. 2/2 is 1.
Or you could plug in 289 to both x's, in which 289/289 is 1.
No matter what number, as long as it's positive, will be 1.
evaluate the triple integral. f 1 dv where f = {(x, y, z) | 0 ≤ x ≤ 2, 0 ≤ y ≤ 4 − x2 , 0 ≤ z ≤ 4 − x2 }
The triple integral evaluates to 8/15.
Evaluate the triple integral?To evaluate the triple integral f 1 dv where f = {(x, y, z) | 0 ≤ x ≤ 2, 0 ≤ y ≤ 4 − x^2, 0 ≤ z ≤ 4 − x²},
Set up the triple integral
The triple integral is written as ∭(1) dV, with the limits of integration for x, y, and z as given in the problem.
Integrate with respect to z
∫(∫(∫(1) dz) dy) dx
The limits for z are 0 to 4-x², so integrate with respect to z:
∫(∫[(z)|from 0 to 4-x²] dy) dx
Substitute the limits for z
∫(∫[(4-x²)] dy) dx
Integrate with respect to y
∫[(4-x²)y|from 0 to 4-x²] dx
Substitute the limits for y
∫[(4-x²)²] dx
Integrate with respect to x
Integrate the function with respect to x:
∫(16 - 16x² + x⁴) dx from 0 to 2
Substitute the limits for x
[4x³/3 - 16x³/3 + x⁵/5]|
from 0 to 2
Calculate the final result
(4(2)³/3 - 16(2)³/3 + (2)⁵/5) - (0) = (32/3 - 128/3 + 32/5) = 8/15
So, the triple integral evaluates to 8/15.
Learn more about limits.
brainly.com/question/29795597
#SPJ11
which statement about a quadrilateral is true? responses a rhombus has exactly one pair of parallel sides. a rhombus has exactly one pair of parallel sides. a trapezoid has two pairs of parallel sides. a trapezoid has two pairs of parallel sides. all rectangles are squares. all rectangles are squares. some rhombuses have four right angles.
The statement that is true about rhombus is d. some rhombuses have four right angles.
A rhombus is a parallelogram with equal-length sides, though the angles at the opposing ends need not be equal, nor must the sides be parallel. If a rhombus is also a cube, it can have four right angles. It can be viewed as an equal-sided trapezoid as well.
A parallelogram has two sets of parallel sides, whereas a trapezoid only has one pair of parallel sides. Therefore, it is untrue that a trapezoid has two sets of parallel edges. Not all rectangles are squares, but they are all quadrilaterals with four right angles. A unique variety of parallelogram called a square has equal-length edges. Therefore, it is untrue to say that all circles are squares.
Complete Question:
which statement about a quadrilateral is true?
a. a rhombus has exactly one pair of parallel sides.
b. a trapezoid has two pairs of parallel sides.
c. all rectangles are squares.
d. some rhombuses have four right angles.
Read more about rhombus on:
https://brainly.com/question/29629002
#SPJ4
suppose 40% of the people at a large meeting are republican. a sample of 20 is randomly selected to take part in a certain activity. to determine the probability that less than 45% of the sample is republican, what would be the standard deviation used in the z-score calculation?
3 Seventy-two books were to be divided up among 18 children. Which of the following expressions are equivalent to this fraction? Select THREE that apply. A. 8 6 B. }+ 8 D. 2•7 E. F. 3.
72 books were divided up among 18 children means 18 kids and 72 books equal 4 books for each youngster.
What is a fraction?An element of a whole is a portion. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a straightforward fraction. A fraction appears in the numerator or denominator of a complicated fraction. The numerator of a perfect fraction is less than the denominator.0
1) 8/3 split by 6/9: To begin, we divide both the numerator and denominator by 3 to reduce 6/9 to 2/3.
8/3 ÷ 2/3 = (8/3) x (3/2) = 4
The fraction we began with is not equivalent to this expression.
2) 8/3 times 2/3: By multiplying the numerators and denominators, we can reduce this expression:
(8/3) x (2/3) = 16/9
The fraction we began with is not equivalent to this expression.
3) 2/9 split by 8/9: We multiply the first fraction by the reciprocal of the second fraction to divide fractions:
(2/9) ÷ (8/9) = (2/9) x (9/8) = 1/4
The fraction we began with is not equivalent to this expression.
4) In order to simplify this equation, let's first reduce 8/2 to 4:
2 x 4 = 8
The fraction we began with is not equivalent to this expression.
The fraction that accurately describes the circumstance cannot be expressed using any of the given expressions.
Learn more about fractions here:
https://brainly.com/question/10354322
#SPJ1
a survey asks teachers and students whether they would like the new school mascot to be a viking or a patriot. this table shows the results. which statement is true
Answer:
Option D.
Step-by-step explanation:
According to this survey results:
Students: 80 like viking and 20 like patriot.
Teachers: 5 like viking and 15 like patriot.
In Option A it is given that patriot is more popular in students while viking is more popular in teachers which is not correct.
In option C patriot is equally popular in students and teachers, which is also not correct. because patriot is popular in 20% of students but 80% in teachers, which is not correct.
In option B there is no difference between students and teachers, this statement is also not correct because there is lots of differences in their choices.
In Option D it is said that viking is more popular in students but patriot is more popular in teachers. this is correct.
4. if an athlete eats a large meal before a competition, how many hours before the competition should she finish eating? a. 1 hour b. 1.5 hours c. 2 hours d. 2.5 hours e. 3 hours
Option D is the correct option i.e., 2.5 hours. Timing is everything when it comes to dining before a fight. Athletes must ingest enough calories to power their efforts without developing gastrointestinal pain or bloating while competing. Typically, a substantial dinner should be eaten two to three hours prior to the game.
The body needs time to process and assimilate nutrients, which is the cause of this. A big dinner requires the body to divert a lot of blood flow to the digestive system, which can have an impact on an athlete's performance. Athletes' performance can be hampered by sluggishness, gastrointestinal pain, or even vomiting brought on by eating too close to a competition.
In general, it is recommended that athletes experiment with different meal timings and types of food during their training to determine what works best for their individual needs.
They should also consider the length of the event and the intensity of their activity to determine the amount and timing of their meals. A registered dietitian or sports nutritionist can help athletes create a personalized nutrition plan to optimize their performance.
To know more about Athletes-
brainly.com/question/26036756
#SPJ4
a programmer plans to develop a new software system. in planning the operating system, he needs the estimate the % of computers that use a new operating system. how many computers must be surveyed in order to be 95% within 4% margin of erro
To be 95% confident within a 4% margin of error, the programmer must survey at least 601 computers.
To estimate the percentage of computers that use a new operating system with a 95% confidence level and a 4% margin of error, you must first determine the required sample size. Here's a step-by-step explanation:
Identify the confidence level and margin of error: In this case, the confidence level is 95% and the margin of error is 4%.
Determine the standard value (Z-score) for the desired confidence level: For a 95% confidence level, the Z-score is 1.96. This value can be found using a Z-score table or an online calculator.
Use the formula for sample size calculation:
n = (Z^2 * p * (1-p)) / E^2
Where n is the required sample size, Z is the Z-score, p is the estimated proportion of computers using the new operating system, and E is the margin of error.
Since we do not have an estimate for the proportion (p), we will assume the worst-case scenario (p=0.5) to ensure the largest possible sample size:
n = (1.96^2 * 0.5 * 0.5) / 0.04^2
Calculate the sample size:
n ≈ (3.8416 * 0.25) / 0.0016
n ≈ 0.9604 / 0.0016
n ≈ 600.25
Round up to the nearest whole number: Since we cannot survey a fraction of a computer, we will round up to the next whole number, which is 601.
for more questions on survey
https://brainly.com/question/30433207
#SPJ11
Find the area of the Trapezoid
24mi
8.2mi
9 mi
9.7mi
please explain I'll mark brainlisest
Answer:
A = 46.74 mi²
Step-by-step explanation:
the area (A) of a trapezoid is calculated as
A = [tex]\frac{1}{h}[/tex] (b₁ + b₂ )
where h is the perpendicular height between the bases b₁ and b₂
here h = 8.2 , b₁ = 9 , b₂ = 2.4
then
A = [tex]\frac{1}{2}[/tex] × 8.2 × (9 + 2.4) = 4.1 × 11.4 = 46.74 mi²