A statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed between 50.0 and 52.0 minutes. Find the probability that a given class period runs between 50.5 and 51.0 minutes.

The function [tex]f(x) = 648 × { (\frac{1}{3} )}^{x} [/tex] represents the same relationship.

Here given a function f(x)

When x= 0,1,2,3,4 the value of f(x) will be 648,216,72,24,8 respectively.

The function that represents the same relationship as the table is [tex]f(x) = 648 × { (\frac{1}{3} )}^{x} [/tex]

We can see that each successive value of f(x) is one-third of the previous value. So, we know that the function is of the form [tex]f(x) = a { (\frac{1}{3} )}^{x} [/tex] for some constant a.

To find the value of a, we can use the fact that f(0) = 648.

Substituting x = 0 into the equation gives f(0) = a(1/3)⁰ = a = 648

So, the function is [tex]f(x) = 648 × { (\frac{1}{3} )}^{x} [/tex]

Therefore, the correct answer is [tex]f(x) = 648 × { (\frac{1}{3} )}^{x} [/tex]

So, option D is the correct option.

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2:1

Step-by-step explanation:

So first you want to lay down all the information by writing down the number of gorillas and orangutans at Westside Zoo (6,4)

Next you want to write down the number of gorillas and orangutans at Central Zoo (4,3)

Now we want to put them in a subtraction like-form of equation

6-4 4-3

Now we take the remaining values and that's our answer for the ratio to gorillas and orangutans (2:1)

-Hope this helps!

Answer:

70

Step-by-step explanation:

Ill give it to you if you really need it its gonna take a while to explain

:)

Answer:

p = 125

Step-by-step explanation:

Given p is inversely proportional to q³ then the equation relating them is

p = [tex]\frac{k}{q^3}[/tex] ← k is the constant of proportion

To find k use the condition p = 9 when q is 5, then

9 = [tex]\frac{k}{5^3}[/tex] = [tex]\frac{k}{125}[/tex] ( multiply both sides by 125 )

k = 1125

p = [tex]\frac{1125}{q^3}[/tex] ← equation of proportion

When q = 3, then

p = [tex]\frac{1125}{3^3}[/tex] = [tex]\frac{1125}{9}[/tex] = 125

I measured it with a protractor and it is around 135 degrees.

I honestly don't know if this is correct but I hope this helps. Feel free to remove my answer if you think this is wrong.

The inequality shown by the graph is 4y+3x≤8x+2y+16 (option C).

In mathematics, an inequality is a statement that compares two values, expressing that one value is greater than, less than, or equal to the other. It is represented by symbols such as <, >, ≤, ≥, and ≠. For example, 5 > 3 is an inequality that means "5 is greater than 3", while 2x + 3 ≤ 7x - 2 is an inequality that means "the sum of 2 times x and 3 is less than or equal to 7 times x minus 2". Inequalities are commonly used in algebra, geometry, and real analysis to express relationships between quantities and to find solutions to equations and systems of equations.

To determine the inequality shown by the graph with coordinates (0,8) and (0, 3.25), we need to find the slope-intercept form of the equation for the line passing through these points.

The slope of the line is:

(y2 - y1) / (x2 - x1) = (3.25 - 8) / (0 - 0) = -4.75 / 0 (which is undefined)

Since the line is vertical, its equation is x = 0.

Substituting this into the inequality options, we can see that only option C results in a true statement:

A) 4y+3x≤8x+6y+16 -> 4(8) + 3(0) ≤ 8(0) + 6(8) + 16 -> 32 ≤ 64 (not true)

C) 4y+3x≤8x+2y+16 -> 4(8) + 3(0) ≤ 8(0) + 2(8) + 16 -> 32 ≤ 32 (true)

B) 4y-3x≤5x+2y+16 -> 4(8) - 3(0) ≤ 5(0) + 2(8) + 16 -> 32 ≤ 32 (true)

D) 4y-3x≤8x+2y+16 -> 4(8) - 3(0) ≤ 8(0) + 2(8) + 16 -> 32 ≤ 32 (true)

Therefore, the inequality shown by the graph is 4y+3x≤8x+2y+16 (option C).

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Answer:

The formula is: x = -y + z

We are given that y = 3 and z = 1. Substituting these values in the formula, we get:

x = -y + z

x = -(3) + 1

x = -3 + 1

x = -2

Therefore, when y = 3 and z = 1, the value of x is -2.

Step-by-step explanation:

The given formula is: x = -y + z

We are given that y = 3 and z = 1.

Substitute the values of y and z into the formula.

x = -y + z

x = -(3) + 1

x = -3 + 1

Simplify the expression.

x = -2

Therefore, when y = 3 and z = 1, the value of x is -2.

Therefore, the manager should not mix any cashews with the peanuts to ensure no change in revenue.

Revenue is the total amount of money a business or organization earns from selling goods or services during a specific period. It is calculated by multiplying the price of each unit sold by the total number of units sold. Revenue represents the income generated by a company's normal business activities and is used to pay for expenses, invest in future growth, and distribute profits to shareholders or owners. It is an important metric for measuring the financial health and performance of a business.

by the question.

Let's assume that x pounds of cashews are mixed with the 30 pounds of peanuts.

The total weight of the mixture would then be 30 + x pounds.

To ensure no change in revenue, the amount earned by selling the peanuts and cashews separately should be equal to the amount earned by selling the mixture.

The revenue earned by selling 30 pounds of peanuts is 30 x $1.50 = $45.

If y pounds of cashews are sold separately, the revenue earned would be y x $4.00 = $4y.

The total revenue earned by selling the peanuts and cashews separately would be $45 + $4y.

When the 30 pounds of peanuts and x pounds of cashews are mixed together and sold for $3.50 per pound, the total revenue earned would be (30 + x) x $3.50 = $105 + $3.50x.

Since the revenues from selling the mixture and selling the peanuts and cashews separately are equal, we can set the equations equal to each other and solve for x:

$45 + $4y = $105 + $3.50x

$3.50x - $4y = -$60

x - 4/7y = -60/7

We still have one unknown variable y, so we need another equation to solve for both x and y.

We know that the total weight of the mixture is 30 + x pounds. If we add y pounds of cashews to the mixture, the total weight becomes:

30 + x + y

We can set this equal to the total weight of the peanuts and cashews sold separately:

30 + y

Solving for y:

30 + x + y = 30 + y

x = 0

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Answer:

X=4

Step-by-step explanation:

First you would simplify the numbers on the right which would give you 168=18x+24x. Since the two numbers have the same variable you can add them which would then give you 168=42x. Lastly you isolate the x by dividing 42 so that x=4.

Answer:

Step-by-step explanation:

The perimeter of a quarter circle can be calculated by adding the length of the arc and the two radii that make up the quarter circle.

The length of the arc of a quarter circle is given by (πr)/2, where r is the radius of the quarter circle and π is approximately 3.142 (as given in the question).

So, for a quarter circle with a radius of 7 cm, the length of the arc would be:

(πr)/2 = (3.142 x 7)/2 = 10.997 cm (rounded to 3 decimal places)

The two radii that make up the quarter circle are each equal to the radius of the quarter circle, so the total length of the two radii would be:

2r = 2 x 7 = 14 cm

Therefore, the perimeter of the quarter circle would be:

10.997 cm + 14 cm = 24.997 cm (rounded to 3 decimal places)

So the perimeter of the quarter circle is approximately 24.997 cm. The digits given by the calculator will depend on the specific calculator used.

Answer: If it is pythagorean theorem than it is 10

Step-by-step explanation:

8^2+6^2=100

Squareroot of 100 is 10

The rational zeros for the function, f(x) = 2·x³ + 3·x² - 10·x + 7, found using the rational roots theorem are;

-7, -7/2, -1, -1/2, 1/2, 1, 7/2, 7

The rational roots theorem is a theorem in algebra that can be used to find the roots of a polynomial equation. According to the theorem, the rational roots of a polynomial that has integer coefficients have the form p/q, where, p is a factor of the constant term and q is a factor of the leading coefficient.

The rational roots theorem can be used to find the possible rational zeros of a polynomial.

The rational roots theorem states that if a polynomial function has integer coefficients, then any rational zero of the function must have the form p/q, where p is a factor of the constant term and q is a factor of the leading coefficient

The specified function, f(x) = 2·x³ + 3·x² - 10·x + 7, the constant term is 7 and the leading coefficient is 2. Therefore, the possible rational zeros of the function are of the form p/q, where p is a factor of 7 and q is a factor of 2.

The factors of 7 are 1, and 7, and the factors of 2 are 1 and 2, Therefore, the possible rational zeros of the functions are;

±1/1, ±7/1, ±1/2, ±7/2

The possible rational zeros of the function f(x) = 2·x³ + 3·x² - 10·x + 7 are;

-7, -7/2, -1, -1/2, 1/2, 7/2, 7

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Therefore , the solution of the given problem of equation comes out to be Michelle has 12 nickels and 8 dime in her coin purse.

Complex algorithms frequently employ variable words to demonstrate coherence between two opposing assertions. Equations are academic expressions that are used to demonstrate the equality of different academic figures. Consider the information provided by y + 7, when combined with generate y + 7, raising instead produces b + 7 within this situation, as opposed to another technique that could divide 12 into two parts.

Here,

Permit x and y to represent the amount of dimes and nickels, respectively.

Since there are 20 pieces in total, the following is true:

=>  x + y = 20 ...(1)

=>  10x + 5y = 140 ...(2)

We can now solve for x in terms of y using equation (1):

=>  x = 20 - y

When we enter this formula in place of x in equation (2), we obtain:

=>  10(20 - y) + 5y = 140

By enlarging the parentheses and streamlining, we obtain:

=>  200 - 10y + 5y = 140

Further simplification results in:

=>  -5y = -60

When we multiply both parts by -5, we get:

=>  y = 12

To find x, we can solve equation (1) by substituting this number of y. The result is:

=> x + 12 = 20

=>  x = 8

Michelle has 12 nickels and 8 dime in her coin purse.

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Answer:

To find the smallest integer value that the frequency density axis needs to reach, we need to first calculate the frequency density for each class interval. The frequency density is calculated by dividing the frequency of each interval by its corresponding class width.

The class widths are:

14 - 0 = 14

18 - 14 = 4

20 - 18 = 2

25 - 20 = 5

40 - 25 = 15

The frequency densities are:

21 / 14 = 1.5

28 / 4 = 7

17 / 2 = 8.5

22 / 5 = 4.4

33 / 15 = 2.2

To plot all of the data, we need to find the maximum frequency density and round it up to the nearest integer. In this case, the maximum frequency density is 8.5, so we need to round it up to 9. Therefore, the smallest integer value that the frequency density axis needs to reach is 9.

No, a binomial experiment cannot be used to determine the probability that the rods are the correct length or an incorrect length.

A binomial experiment has the following characteristics:

1. It consists of a fixed number of trials.

2. Each trial has only two possible outcomes: success or failure.

3. The trials are independent.

4. The probability of success is constant for each trial.

In the case of metal rods, the length can vary continuously, so it is not a binary outcome. Therefore, a binomial experiment cannot be used to determine the probability of the rods being the correct length or an incorrect length. Instead, a probability distribution such as a normal distribution could be used to model the distribution of rod lengths and calculate the probability of a rod being the correct length.

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The value of x/y is 35/37. The correct answer is option B).

Let's start by the first right triangle and the inscribed square. We know that the square has side length x and is inscribed in the right triangle with sides 3, 4, and 5, where 5 is the hypotenuse. Since one vertex of the square coincides with the right-angle vertex of the triangle, we have that the side length x of the square is also the length of the altitude from the right angle to the hypotenuse of the triangle. Therefore, we can write:

x = [tex](3*4)/5 = 12/5[/tex]

Now the second right triangle and the inscribed square:

We know that the square has side length y and is inscribed in the right triangle with sides 3, 4, and 5, where 5 is the hypotenuse. Since one side of the square lies on the hypotenuse of the triangle, we have that the sum of the areas of the two smaller squares is equal to the area of the larger square. Therefore, we can write:

[tex]x^{2} + y^{2} = 5^{2} = 25[/tex]

Substituting[tex]$x = {12}/{5}[/tex] gives

[tex](12/5)^{2} + y^{2} = 25[/tex]

Simplifying this equation gives

[tex]y^{2} = 25 - (144/25) = (25^{2} - 144)/25 = 481/25[/tex]

Taking the square root of both sides gives

y = [tex]\sqrt{481}/5[/tex]

Finally, we compute x/y:

x/y = [tex]12*\sqrt{481}/ \sqrt{481}*5[/tex]

x/y = 35/37

The correct option is B)

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--The given question is incomplete, the complete question is

"A square with side length x is inscribed in a right triangle with sides of length 3, 4, and 5 so that one vertex of the square coincides with the right-angle vertex of the triangle. A square with side length y is inscribed in another right triangle with sides of length 3, 4, and 5 so that one side of the square lies on the hypotenuse of the triangle. What is x/y?

(A) 12/13

(B) 35/37

(C) 1

(D) 37/35

(E) 13/12"

After answering the provided question, we can conclude that As a result, equation 315 kids did not select soda.

An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x + 3" equals the value "9". The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. The variable x is raised to the second power in the equation "x2 + 2x - 3 = 0." Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.

According to the circle graph, 14% of pupils preferred soda. As a result, 100% - 14% = 86% of pupils did not select soda.

We know that 35% of students, or 110 kids, chose milk. Hence we may calculate the fraction of pupils that did not drink soda as follows:

35/100 = 110/x

When we solve for x, we get:

x = (110*100)/35 = 314.29

x = 315

As a result, 315 kids did not select soda.

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Considering the Pythagorean Theorem, we have that:

The length of the rectangular plot is of 264 ft.

The Pythagorean Theorem states that in a right-angled 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.

The theorem is expressed as follows:

c² = a² + b².

In which:

For this problem, we have that:

Hence the length is obtained as follows:

l² + 170² = 314²

l = sqrt(314² - 170²)

l = 264 ft.

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The required 95% confidence interval representing the true population mean falls within the given interval, based on the given sample mean is  equals to (233.00, 271.90).

Use the t-distribution,

To construct a confidence interval for the population mean,

The sample size is relatively small (n = 64)

And the population standard deviation is unknown.

The formula for the confidence interval is,

[tex]\bar{x}[/tex] ± tα/2 × (s/√n)

where [tex]\bar{x}[/tex] is the sample mean,

s is the sample standard deviation,

n is the sample size,

And tα/2 is the critical value of the t-distribution with (n-1) degrees of freedom, corresponding to the desired confidence level.

For a 95% confidence interval, the critical value of the t-distribution with 63 degrees of freedom is approximately 1.998.

Plugging in the given values, we get,

252.45 ± 1.998 × 74.50/√64)

Simplifying we get,

252.45 ± 19.45

This implies,

The 95% confidence interval for the mean amount spent per day by a family of four visiting Niagara Falls is (233.00, 271.90)

Therefore, 95% confidence interval that the true population mean falls within this interval, based on the given sample is  (233.00, 271.90).

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The above question is incomplete , the complete question is:

A survey conducted by the American automobile association showed that a family of four spends an average of $215.60 per day while on vacation. suppose a sample of 64 families of four vacationing at Niagara falls resulted in a sample mean of $252.45 per day and a sample standard deviation of $74.50.

a. Develop a 95% confidence interval estimate of the mean amount spent per day by a family of four visiting Niagara Falls (to 2 decimals).

answer 5y - 12 = 8.

In order to use the subtraction property of equality to solve equations, the subtraction of the same quantity should be done on both sides of the equation.

Here are the equations in which you can use the subtraction property of equality to solve:7x + 2 = 25-2y = 10-4r = 28-1/3p = 15+9z = -27

The only equation from the options given in the question is 5y - 12 = 8. So, we can use the subtraction property of equality to solve this equation as follows:5y - 12 = 8Add 12 to both sides5y - 12 + 12 = 8 + 125y = 20Divide both sides by 55y/5 = 20/5y = 4 Therefore, the equation in which we can use the subtraction property of equality to solve is 5y - 12 = 8.

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The area of the sector with a central angle of 180° and a diameter of 5.6 cm is approximately 11.8 [tex]cm^2[/tex].

To find the area of a sector, we need to know the central angle and the radius or diameter of the circle that the sector is a part of. In this case, we are given a central angle of 180° and a diameter of 5.6 cm.

Find the radius of the circle is the first step. We can do this by dividing the diameter by 2:

radius = diameter/2 = 5.6/2 = 2.8 cm

Next, we can use the formula for the area of a sector:

Area of sector = (central angle/360°) x π x [tex]radius^2[/tex]

Plugging in the given values, we get:

Area of sector = [tex](180/360) * \pi * (2.8)^2[/tex]

= [tex](1/2) * 3.14 * 2.8^2[/tex]

= [tex]11.77 cm^2[/tex]

Rounding to the nearest tenth, we get:

Area of sector ≈ 11.8 [tex]cm^2[/tex]

Therefore, the area of the sector is approximately 11.8 [tex]cm^2[/tex].

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The cube root function that tells the side lengths of the​ container, x, in inches for a given​ cost, C is x = (C^(1/3))^3.

We can use the formula for the volume of a cube, which is V = x^3, where x is the side length of the cube. If the cost of producing one cube-shaped container is C dollars, then the cost of producing one unit of volume is C/V = C/x^3 dollars per cubic inch. Solving for x, we get:

x = (C/V)^(1/3)

Substituting V = x^3, we get:

x = (C/x^3)^(1/3)

Simplifying, we get:

x = (C^(1/3)) / (x^(1/3))

Multiplying both sides by x^(1/3), we get:

x^(2/3) = C^(1/3)

Taking the cube of both sides, we finally get:

x = (C^(1/3))^3

Therefore, the cube root function for a given cost, C, is x = (C^(1/3))^3.

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Answer:

D(1,0)

Step-by-step explanation:

to find midpoint add x1 and x2 then divide by 2 same with y

Answer:

6.17 hours every week

Step-by-step explanation:

1. Asymptotic slope of the best line for the equation y = 5x⁴ + 3 plotted on a log-log plot is 4. To find this, first note that the dominant term in the equation is 5x⁴. On a log-log plot, the slope corresponds to the exponent of the dominant term. In this case, the exponent is 4.

2. The maximum number of inversions in a list of 100 distinct elements is 4,950. This occurs when the list is sorted in descending order.

To calculate the maximum number of inversions, use the formula n * (n - 1) / 2, where n is the number of elements. In this case, n = 100, so the maximum number of inversions is 100 * 99 / 2 = 4,950.

3. The minimum number of inversions in a list of 100 distinct elements is 0. This occurs when the list is already sorted in ascending order, meaning no inversions are present.

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Output z obtained as: multiply w with 5 and then subtract 3 from the result: w --> *5 ---> -3 ---> z.

There are only one or two variables in a linear equation.

The given expression is:

z = 5w-3

Here:

Input value : 5w-3

Output value : z

So,

Output z obtained as:

multiply w with 5 and then subtract 3 from the result:

w --> *5 ---> -3 ---> z

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From  following equations option B  will produce the hyperbola graph shown in the figure

what is hyperbola ?

A hyperbola is a type of conic section, which is a curve that is formed by the intersection of a plane and a double cone. A hyperbola can also be defined as the set of all points in a plane, the difference of whose distances from two fixed points (called the foci) is a constant.

In the given question,

Based on the shape of the hyperbola shown on the y-axis graph, we can tell that the hyperbola has a vertical transverse axis, which means that its equation must have the form:

(y - k)² / a² - (x - h)²/ b² = 1

where (h, k) is the center of the hyperbola, a is the distance from the center to the vertices, and b is the distance from the center to the co-vertices.

Option A is not correct because it produces a hyperbola with a horizontal transverse axis, whereas the given graph has a hyperbola with a vertical transverse axis.

We can eliminate option D since its equation has a transverse axis that is not vertical.

Next, we can eliminate option A since the coefficient of x² is positive, which means that the transverse axis is horizontal.

Option C has a transverse axis that is also horizontal, so we can eliminate it as well.

That leaves us with option B, which has a vertical transverse axis and its equation fits the form we determined earlier. Therefore, the equation Y²/9 - x²/4=1 will produce the hyperbola shown on the y-axis graph

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Only two options are necessarily true for the triangle,

m∠r > 90°

m∠s + m∠t < 90°

In any triangle, the sum of the three angles is 180 degrees. If m∠r > m∠s + m∠t, then angle r must be the largest angle in the triangle. Additionally, the sum of the other two angles (s and t) must be less than 90 degrees.

Option m∠s = m∠t is not necessarily true because the two angles could be different and still add up to be less than m∠r. Options m∠r > m∠t, m∠r > m∠s, and m∠s > m∠t are not necessarily true and depend on the specific values of the angles in triangle RST.

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