Step-by-step explanation:
If a polynomial function has roots at x=-5 and x=√3, it means that it can be factored as follows:
h(x) = a(x+5)(x-√3)
where 'a' is a constant coefficient that represents the leading term of the polynomial function.
To find the value of 'a' and express the polynomial function in standard form, we can multiply the factors and simplify as follows:
h(x) = a(x+5)(x-√3)
h(x) = a(x^2 - √3x + 5x - 5√3)
h(x) = a(x^2 + 2x√3 - 5√3)
To find the value of 'a', we can substitute one of the given roots into the equation and solve for 'a'. Let's choose x = -5:
h(-5) = a((-5)^2 + 2(-5)√3 - 5√3)
h(-5) = a(25 - 10√3 - 5√3)
Since x=-5 is a root, h(-5) = 0. Therefore:
0 = a(25 - 15√3)
a = 0 or a = (15√3)/25 = (3√3)/5
Since the coefficient 'a' cannot be zero, the polynomial function h(x) of lowest degree in standard form is:
h(x) = (3√3/5)(x^2 + 2x√3 - 5√3)
h(x) = (3√3/5)x^2 + (6/5)√3x - 3√3
the depths (in inches) at which 10 artifacts are found in a remote area are the following: 20.7, 24.8, 30.5, 26.2, 36.0, 34.3, 30.3, 29.5, 27.0, 38.5 what is the range? do not round your answer.
The range of the depths of the 10 artifacts is 18.5 inches.
The range in statistics is a measure of variability, which represents the difference between the largest and smallest values in a data set. To calculate the range, we simply subtract the smallest value from the largest value. In this case, the largest value is 38.5 inches, and the smallest value is 20.7 inches.
Therefore, the range of the depths of the artifacts in the remote area is:
Range = 38.5 - 20.7
Range = 17.8
So the range of depths is 17.8 inches. This tells us that there is quite a bit of variability in the depths at which the artifacts were found. The smallest depth was 20.7 inches, while the largest depth was 38.5 inches.
This information could be useful for archaeologists or other researchers who are interested in understanding the distribution of artifacts in the area, as well as the possible reasons for why some artifacts were found at certain depths while others were found at different depths.
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The letters a and b represent nonzero constants. Solve ax+b=53 for x.
The solution to x=
Please hurry
Answer:
the solution for x is (53 - b)/a.
Which Number should be added to both sides of this quadratic equation to complete the square?
The number which could be added to both sides of the quadratic equation to complete the square is; -2.25.
What in mathematics is a quadratic equation?
ax² + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. a 0. The fundamental theorem of algebra ensures that it has at least one solution because it is a second-order polynomial problem. Real or complicated solutions are also possible.
The quadratic equations give in the task content is; 1=x²-3x. Hence, to express the equation by completing the square method; we have;
1 - 2.25 = (x -3/2)² - 2.25
Hence, the number which should be added to both sides of the equation is; -2.25.
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One year of classes at the University of Texas in Brownsville costs $15,000. Mariano has received a grant that will pay $800 and a scholarship for $1,700. He wants to get a job to pay 20% of the remainder of the costs and hopes to get a loan to cover the rest of the costs for one year.
How much does he need to earn on his job? (Hint: 20% of the remaining balance)
The amount Mariano must make from his job is
$2,500 ($12,500 * 0.2) = $2500.
A number can be divided by five or multiplied by 0.2 to determine 20% of that amount.
Mariano, for instance, would have to pay $12,500 ($15,000 - $800 - $1,700)
if he had to pay $15,000 for a year of classes at the University of Texas at Brownsville but had also been awarded a grant for $800 and a scholarship for $1,700.
We can divide $12,500 by 5 or multiply it by 0.2 to calculate how much he must make from his employment to cover 20% of the remaining expenses.
The amount Mariano must make from his job is
$2,500 ($12,500 * 0.2) = $2500.
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please help will give brainliest
The explicit rule is 2000 + 3500n
The salesperson has earned $33500 after 9 months since starting the job.
What is Linear Equation?
A linear equation is a mathematical equation that involves two variables and forms a straight line when graphed. It can be represented in the form of y = mx + b, where m is the slope and b is the y-intercept.
The explicit rule for the amount of money the salesperson has earned since starting the job can be given by:
Earnings = 2000 + 3500n
Where n represents the number of months since the salesperson started the job.
To find out how much money the salesperson has earned after 9 months, we can substitute n = 9 in the above formula:
Earnings = 2000 + 3500(9)
= 2000 + 31500
= $33500
Therefore, the salesperson has earned $33500 after 9 months since starting the job.
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Emily buys a shirt that originally costs $54. The price is marked down by 15% due to a sale, but Emily has a coupon for an additional 10%. How much did Emily pay for the shirt?
Emily has to pay $41.31 for the shirt after adding coupon and discount.
How to find the Cost Price (CP) of any discounted item?
Lets say CP = 54 and the discount is of 15% i.e. marked price
So, Marked Price= 85% of CP = 45.9
Lets apply the additional coupon of 10% on Marked Price.
Therefore, the payment amount = 90% of MP
payment amount = $41.31
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URGENT
Find the length of side x in simplest radical form with a rational denominator.
value of side x in the triangle is 6 ( simplest radical form with a rational denominator is 6/1).
Define right triangleA right triangle is a triangle that has one angle measuring 90 degrees, which is also called a right angle. The hypotenuse is the side that faces the right angle, while the legs are the other two sides.
Define trigonomteric functionTrigonometric functions are a set of mathematical functions used to relate the angles and sides of a right triangle. Sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent are the six fundamental trigonometric functions (cot).
In the given right angles triangle
Using trigonomteric function
Tan30°=√12/x
1/√3=√12/x
x=√12×√3
x=√36
x=6
Hence, value of side x in the triangle is 6.
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Need help with Algebra I
The area of triangle in given figure is = 60 cm²
What do you mean by Triangle ?A triangle is a three-sided polygon that is formed by connecting three non-collinear points in a plane.The sum of the interior angles of a triangle is always 180 degrees, and the length of each side can be determined by the application of the Pythagorean theorem or other trigonometric functions, depending on the given information. Triangles can also be classified based on the size of their angles and the lengths of their sides, which give rise to various types of triangle such as equilateral, isosceles, scalene, acute, right, and obtuse triangles.
According to quesrtion
Given height = 3cm
Base = 10cm
if the height is quadrupled then height = 4 × 3 = 12cm
Area = 1/2 × base × height
= 1/2 × 70 × 12
to solve this we get
Area = 60cm²
So, the area of this triangle is 60cm²
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Can someone please HELP ME with this problem!!!!! I need HELP ASAP!!! RIGHT NOW!!!
The population of bacteria after I days is P(I) = 3700 * e^(0.11 * I) and percentage rate of change per hour is 0.4285%
What is exponential growth?
Exponential growth is a pattern of data that shows greater increases with passing time, creating the curve of an exponential function.
Equation:The population of bacteria in the petri dish is growing exponentially at a rate of 11% per day. This means that the daily growth rate r is 0.11, or 11/100.
The formula for exponential growth is:
P(t) = P0 * e^(rt)
Where:
P(t) is the population after t days
P0 is the initial population
r is the growth rate per day
e is the mathematical constant approximately equal to 2.71828
Using the given information, we have:
P0 = 3700
r = 0.11
So, the formula for the population of bacteria after I days is:
P(I) = 3700 * e^(0.11 * I)
To find the percentage rate of change per hour, we need to convert the daily growth rate to an hourly growth rate. There are 24 hours in a day, so the hourly growth rate h is:
h = (1 + r)^(1/24) - 1
Substituting the value of r, we get:
h = (1 + 0.11)^(1/24) - 1
Simplifying this expression, we get:
h = 0.004285
So, the hourly growth rate is 0.4285%, or 0.004285 expressed as a decimal.
Therefore, the population of bacteria after I days is:
P(I) = 3700 * e^(0.11 * I)
And the percentage rate of change per hour is:
0.4285% (rounded to the nearest hundredth of a percent)
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The percentage rate of change per hour is approximately 0.46%.
How to calculate percentage?
The formula for exponential growth is:
N(t) = N0 * e raise to the power (r*t)
where:
N(t) is the population at time t
N0 is the initial population
r is the growth rate
e is the mathematical constant approximately equal to 2.71828
t is the time elapsed
In this case, we have:
N0 = 3700
r = 11% per day, or 0.11/24 = 0.0045833 per hour (since there are 24 hours in a day)
t is the time elapsed in days
To convert the time elapsed in days to hours, we can multiply t by 24. Therefore, the function for the population of bacteria after t days is:
f(t) = 3700 * e raise to the power (0.004583324t)
To round the coefficients in the function to four decimal places, we can use the round() function in Python:
f(t) = round(3700 * e**(0.004583324t), 4)
To determine the percentage rate of change per hour, we can calculate the percentage increase in the population per hour using the formula:
Percentage increase = (e raise to the power (r*h) - 1) * 100
where:
r is the growth rate per day
h is the time elapsed in hours
In this case, we have:
r = 11% per day, or 0.11/24 = 0.0045833 per hour
h = 1 hour
Plugging these values into the formula, we get:
Percentage increase = (e raise to the power (0.0045833*1) - 1) * 100 = 0.4646%
Therefore, the percentage rate of change per hour is approximately 0.46%.
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a statistics teacher wants to know if the student birth month is distributed equally across all months. he uses school records to determine the birth month of all the students at the school and calculates a chi-square statistic to test this hypothesis. why is this not an appropriate use of a chi-square goodness-of-fit test?
The chi-square goodness-of-fit test is not an appropriate statistical test to use in this situation.
A statistics teacher wants to know if the student birth month is distributed equally across all months. He uses school records to determine the birth month of all the students at the school and calculates a chi-square statistic to test this hypothesis.
This is not an appropriate use of a chi-square goodness-of-fit test because chi-square goodness-of-fit tests are used to compare the distribution of categorical data to a theoretical distribution.
The chi-square goodness-of-fit test compares observed frequencies of categorical data to expected frequencies based on a theoretical distribution. It is used to determine if a sample of data comes from a specific population or not.
In this case, the teacher is not comparing observed frequencies to expected frequencies, but instead is testing the hypothesis that the distribution of student birth months is equal across all months.
This is not a proper use of a chi-square goodness-of-fit test because the hypothesis being tested is not related to the expected frequencies of a categorical variable. Therefore, the chi-square goodness-of-fit test is not an appropriate statistical test to use in this situation.
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What is and equation of the line that passes through the points ( − 4 , − 6 ) and (8,−6)
Answer: y= -6
Step-by-step explanation: use the slope formula and slope intercept; y=mx+b
s varies directly as t, and = 8 when = 16. Find the constant of variation and write a direct variation equation relating s and t. Then find t when = 16. (Write answers in decimal form.)
constant of variation:
direct variation equation:
when s=16, t=
Direct variation equation relating s and t as: S = 0.5t and t=32 when s=16.
What is direct variation equation?
A direct variation equation is a mathematical equation that describes a relationship between two variables that varies proportionally. In other words, if one variable increases or decreases, the other variable also increases or decreases in proportion to it.
Given, S varies directly as t, and S = 8 when t = 16.
Let's find the constant of variation (k) using the given information:
k = S/t = 8/16 = 0.5
So, the constant of variation is 0.5.
Using the constant of variation, we can write a direct variation equation relating s and t as:
S = kt
Substituting k = 0.5 in the above equation, we get:
S = 0.5t
When S = 16, we can find t as follows:
16 = 0.5t
t = 16/0.5
t = 32
Therefore, when S = 16, t = 32.
Therefore, direct variation equation relating s and t as: S = 0.5t and t=32 when s=16.
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A boat is heading towards a lighthouse, where
Jeriel is watching from a vertical distance of 113
feet above the water. Jeriel measures an angle of
depression to the boat at point A to be 8°. At
some later time, Jeriel takes another
measurement and finds the angle of depression
to the boat (now at point B) to be 52°. Find the
distance from point A to point B. Round your
answer to the nearest tenth of a foot if necessary.
P(-11, -24) Q (21, 40)
Find the slope
Answer:
To find the slope between two points (x1, y1) and (x2, y2), we use the formula:
slope = (y2 - y1) / (x2 - x1)
Using the given points P(-11, -24) and Q(21, 40), we can substitute the values into the formula:
slope = (40 - (-24)) / (21 - (-11))
slope = 64 / 32
slope = 2Therefore, the slope between points P(-11, -24) and Q(21, 40) is 2.
Answer:
2
Step-by-step explanation:
To find the slope, we can use the slope formula
m = ( y2-y1)/(x2-x1)
= ( 40 - -24)/(21 - -11)
= ( 40+24)/(21+11)
= 64/32
= 2
what is the precent of change from 22 to 26
Answer: 15.4% (rounded to the nearest tenth)
Step-by-step explanation:
Pleaseee Help Meeeeeeeeeee
"if You don't Know the Answer DON'T ANSWER THE QUESTION."
(If you Answer the question and You don't Know it, It takes away From someone else being able to Answer it and Give me the Correct Answer.)
PS. IT'S MULTIPLE CHOICE, WHICH MEANS IT'S MORE THAN ONE ANSWER. PLEASE DO NOT RESPOND TO THE QUESTION- IF YOU DON'T HAVE MORE THAN ONE ANSWER.
PLEASE AND THANK YOU,
if the mean for 1 hour is 1 pound and the standard deviation is 0.2 pound, what is the probability that the amount dispensed per box will have to be increased?
The probability that the amount dispensed per box will have to be increased is 0.
To answer this question, we need to know the target amount that should be distributed per carton.
Assuming that the target amount is also 1 pound, we can use the concept of the normal distribution to estimate the likelihood that we will have to increase the amount distributed per case.
hence the probability of having to increase the amount is 0.
z = (target volume - mean) / standard deviation
z = (1 - 1) / 0.2
z = 0
A Z-score of 0 indicates that the target volume is equal to the mean. A standard normal distribution table or calculator can be used to find the probability that the amount should be increased.
However, the target amount is equal to the mean value,
In summary, without knowing the target amount to be dispensed in each case, it is not possible to determine the potential for volume increases.
If the target amount is to be £1 and the mean and standard deviation is also £1 and 0.2 respectively, then the probability of having to increase the amount is 0.
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Multiply
28845by 6502
Answer:
187,550,190
Step-by-step explanation:
$3,423.55+
$2,737.69+
$2,014.95+
$1,253.34+
$450.76+
$12,752.45+
$13,438.31+
$14,161.05+
$14,922.66+
$15,725.24
Answer:
the final answer is 80800 exactly
Answer: $80 880 US$
Step-by-step explanation:
Add all up
Mason's mother wants to make 8 curtains that each require 2 1/5 metres of material in a standard width, but she only has 16-metres of material. There are to be no seams in her curtains. She asks Mason to buy more material.
a. How much more material must Mason buy?
B. How much material is left over?
Answer:mason must need 33.6 m of materail to make 8 curtains.
so he need to 17.6m of material
Step-by-step explanation:
A school has 800 students. The staff plans to order a bag for each student. They ask 120 randomly selected students which color bag they prefer. Based on this sample, how many bags of each color should the staff order? Show your work.
Blue 48
Black 54
Gray 18
Answer:
Therefore, the staff should order 320 blue bags, 360 black bags, and 120 gray bags.
Step-by-step explanation:
To determine how many bags of each color to order, we need to estimate the proportion of students who prefer each color based on the sample of 120 students. We can then use these proportions to predict the number of bags of each color needed for all 800 students. Here's how we can do it:
Determine the number of students in the sample who prefer each color:
Let B be the number of students who prefer blue
Let K be the number of students who prefer black
Let G be the number of students who prefer gray
Based on the sample of 120 students, we know:
B + K + G = 120
Estimate the proportion of students who prefer each color:
The proportion of students who prefer each color in the sample is:
p(B) = B/120
p(K) = K/120
p(G) = G/120
Predict the number of bags of each color needed for all 800 students:
The predicted number of bags of each color needed for all 800 students is:
Bags of blue = p(B) * 800
Bags of black = p(K) * 800
Bags of gray = p(G) * 800
So, using the sample results, we get:
Bags of blue = (48/120) * 800 = 320
Bags of black = (54/120) * 800 = 360
Bags of gray = (18/120) * 800 = 120
Find the distance between the points and given below.
(That is, find the length of the segment connecting and .)
Round your answer to the nearest hundredth.
Answer:
AB = 6.71 to nearest hundredth.
Step-by-step explanation:
To get from A to B we move 3 units to the right then 6 units up.
This form a right angled triangle so we use Pythagoras theorem:
AB^2 = 3^2 + 6^2
= 9 + 36
= 45
So AB = √45
= 3√5 = 6.7082
What is the area of a triangle whose sides have length $\sqrt{70},$ $\sqrt{70},$ and $\sqrt{28}$?
The area of a triangle whose sides have lengths √70,√70,√and 28 is 10.45.
What is the area of the triangle?
A triangle is a polygon that has three sides and three vertices. It is one of the basic figures in geometry.
The area of the triangle is defined as the product of half the base and the height of the triangle.
The area of the triangle = (0.5)x b x h
Length of its base = b units
Its height = h units long,
Given;
The sides of the triangle √70,√70,√28
Now,
H²=70-28/4
H²=70-7
H=7.9
[tex]Area= b *\frac{ h}{2}[/tex]
[tex]=\sqrt{28}\frac{7.9}{2}[/tex]
=10.45
Therefore, the area of the triangle will be 10.45.
The complete question is-
What is the area of a triangle whose sides have length √{70},√{70}, and √{28} ?
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sean makes 225 a week with a standard deviation of 35, evan makes 240 with a standard deviation of 15, what is the probability that's sean will make more than evan on a randomly selected week?
The probability that Sean will make more than Evan on a randomly selected week is approximately 0.3446 or 34.46%.
To calculate the probability that Sean will make more than Evan in a randomly selected week, we need to compare their incomes in terms of standard deviations from the mean.
First, we need to calculate the difference between their means:
Mean difference = Sean's mean income - Evan's mean income = $225 - $240 = -$15
Next, we need to calculate the standard deviation of the difference between their incomes:
Standard deviation of difference = √[(Sean's standard deviation)^2 + (Evan's standard deviation)^2] = √[(35)^2 + (15)^2] = 37.42
Now, we can use a z-score table to find the probability that Sean's income will be higher than Evan's income:
Z-score = (Sean's income - Evan's income - Mean difference) / Standard deviation of difference = (225 - 240 - (-15)) / 37.42 = 0.40
From the z-score table, we find that the probability of a z-score of 0.40 or higher is 0.3446.
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Can someone help me ASAP it’s due tomorrow. I will give brainliest if it’s all done correctly.
The first, second, and third one.
A toy rocket is shot vertically into the air from a launching pad 4feet above the ground with an initial velocity 96of feet per second. The height h, in feet, of the rocket above the ground at t seconds after launch is given by the function h=-16t^2+96+4 . How long will it take the rocket to reach its maximum height? What is the maximum height?
Question content area bottom
Part 1
The rocket will reach its maximum height ? after launch
(Simplify your answer.)
Part 2
The maximum height reached by the object is ?
(Simplify your answer.)
Step-by-step explanation:
Height = - 16 t^2 + 96 t + 4
max will occur at t = - b/2a = - 96/(2*-16) = 3 seconds
The max height at t = 3
Height = -16 (3^2) + 96 (3) + 4 = 148 ft
PLEASE HELP I NEED THIS ASAP!!!
identify any outliners in the graph
Answer:
The outlier in this graph is (4, 55)
Step-by-step explanation:
Outliers can be seen graphically when we first draw a line of best fit. When we draw the line of best fit it connects through the middle of the string of points near the top of our graph. We can see that any given point on the graph is either on the line of best fit or very close to it. This can be said about all points but one... the point (4,55). This point lies far away from the line we've created and can be identified as an outlier for this reason.
solve this problem pleasee
The measure of following values for the given circle is:
Sector AE = (2/3)π square units
Sector AB = (10/9)π square units
Sector ECB = (1/3)π square units
Angle BOC = 160 degrees
What is circle?In geometry, a circle is a two-dimensional shape that is defined as the set of all points in a plane that are equidistant from a given point called the center. The distance from the center to any point on the circle is called the radius of the circle.
Here,
Sector AE:
The central angle of 60 degrees represents one-sixth (60/360) of the circle, so the sector AE has an area of one-sixth of the total area of the circle. The area of the circle is πr² = 4π square units, so the area of sector AE is:
(1/6) x 4π = (2/3)π square units
Sector AB:
The central angle of 50 degrees represents 5/18 (50/360) of the circle, so the sector AB has an area of 5/18 of the total area of the circle. The area of the circle is πr² = 4π square units, so the area of sector AB is:
(5/18) x 4π = (10/9)π square units
Sector ECB:
Since angles EOC and BOC are complementary (they add up to 90 degrees), the central angles they subtend are also complementary. Therefore, the central angle of sector ECB is 90 - 60 = 30 degrees. This represents one-twelfth (30/360) of the circle, so the sector ECB has an area of one-twelfth of the total area of the circle. The area of the circle is πr² = 4π square units, so the area of sector ECB is:
(1/12) x 4π = (1/3)π square units
Angle BOC:
Since angles AOB and COE are both right angles (as they subtend diameters of the circle), we know that angle AOC is 90 degrees. Therefore, angle BOC is:
360 - 90 - 60 - 50 = 160 degrees
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simplify. (write each expression without using the absolute value symbol)
|x+3| if x>2
To given expression |x + 3| simplifies solution is x + 3.
What is expression?
In mathematics, an expression is a combination of symbols, numbers, and operators that represent a quantity or a mathematical relationship. It can be a single number or a combination of numbers, variables, and operators that can be evaluated to give a numerical result.
If x > 2, then the expression |x + 3| can be simplified as follows:
|x + 3| = x + 3
since x + 3 is already non-negative when x > 2.
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(y+4)^2 * (y-4)^2
Pls help, will mark brainliest
(Use factoring)
Answer:
Step-by-step explanation: