Use z scores to compare the given values: In a recent awards ceremony, the age of the winner for best actor was 32 and the age of the winner for best actress was 59 . For ail best actors, the mean age is 43.3 years and the standard deviation is 8.4 years. For all best actresses, the mean age is 38.1 years and the standard deviation is 12.7 years. (All ages are determined at the time of the awards ceremony.) Relative to their genders, who had the more extreme age when winning the award, the actor or the actress? Explain. Since the z score for the actor is z= and the z score for the aciress is z= the had the more bxtrome age. (Round to two decimal places.)

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.

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.

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Answer:

You need to be specific on which is the length, height and width. Making the most basic assumption I would have to assume the answer is 228

Step-by-step explanation:

Formula for the surface area of a rectangular prism is A=2(wl+hl+hw)

A = 2 x (9 x 6 + 4 x 6 + 4 x 9)

A = 2 x (54 + 24 + 36)

A = 2 (114)

A = 228

The probability are: P(Lyme Disease) = 0.35, P(Arthritis) = 0.8, P(Lyme Disease or Arthritis) = 0.97, P(Lyme Disease and Arthritis) = 0.15

To calculate the probabilities, we need to understand the concepts of probability and set theory.

Let's define:

L = Event of having Lyme Disease

A = Event of having Arthritis

Given information:

Total dogs tested = 120

Dogs with Lyme Disease (L) = 42

Dogs with Arthritis (A) = 96

Dogs with both Lyme Disease and Arthritis (L ∩ A) = 18

We can calculate the probabilities using the following formulas:

1. P(Lyme Disease): Probability of having Lyme Disease

P(L) = (Number of dogs with Lyme Disease) / (Total number of dogs tested)

P(L) = 42 / 120

P(L) = 0.35

2. P(Arthritis): Probability of having Arthritis

P(A) = (Number of dogs with Arthritis) / (Total number of dogs tested)

P(A) = 96 / 120

P(A) = 0.8

3. P(Lyme Disease or Arthritis): Probability of having Lyme Disease or Arthritis

P(L or A) = P(L) + P(A) - P(L ∩ A)

P(L or A) = 0.35 + 0.8 - 0.18

P(L or A) = 0.97

4. P(Lyme Disease and Arthritis): Probability of having both Lyme Disease and Arthritis

P(L and A) = P(L ∩ A) / (Total number of dogs tested)

P(L and A) = 18 / 120

P(L and A) = 0.15

Therefore:

- P(Lyme Disease) = 0.35

- P(Arthritis) = 0.8

- P(Lyme Disease or Arthritis) = 0.97

- P(Lyme Disease and Arthritis) = 0.15

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The sample variance is approximately 146.31 and the sample standard deviation is approximately 12.10 for the given set of numbers.

The sample variance is approximately 146.31 and the sample standard deviation is approximately 12.10 for the given set of numbers. These value provide a measure of the variability or spread of the data set.

To find the sample variance and standard deviation for the given set of numbers: 6, 53, 13, 51, 38, 28, 33, 30, 31, 31, you can follow these steps:

Step 1: Find the mean (average) of the data set:

Mean (μ) = (6 + 53 + 13 + 51 + 38 + 28 + 33 + 30 + 31 + 31) / 10 = 33.6

Step 2: Calculate the differences between each data point and the mean:

(6 - 33.6), (53 - 33.6), (13 - 33.6), (51 - 33.6), (38 - 33.6), (28 - 33.6), (33 - 33.6), (30 - 33.6), (31 - 33.6), (31 - 33.6)

Step 3: Square each difference:

(-27.6)^2, (19.4)^2, (-20.6)^2, (17.4)^2, (4.4)^2, (-5.6)^2, (-0.6)^2, (-3.6)^2, (-2.6)^2, (-2.6)^2

Step 4: Calculate the sum of the squared differences:

(-27.6)^2 + (19.4)^2 + (-20.6)^2 + (17.4)^2 + (4.4)^2 + (-5.6)^2 + (-0.6)^2 + (-3.6)^2 + (-2.6)^2 + (-2.6)^2 = 1316.8

Step 5: Divide the sum by (n - 1), where n is the number of data points (in this case, n = 10):

Sample Variance (s^2) = 1316.8 / (10 - 1) = 146.31

Step 6: Take the square root of the sample variance to get the sample standard deviation:Sample Standard Deviation (s) ≈ √146.31 ≈ 12.10

Therefore, the sample variance is approximately 146.31 and the sample standard deviation is approximately 12.10 for the given set of numbers.

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This is the same as writing  v = sqrt(ar)

===========================================

Work Shown:

\(a = \frac{v^2}{r}\\\\ar = v^2\\\\v^2 = ar\\\\v = \sqrt{ar}\\\\\)

I multiplied both sides by r to isolate the v^2 term, then I applied the square root to fully isolate v.

Answer:

\(0.1212...=\dfrac{4}{33}\)

Step-by-step explanation:

A repeating decimal is a decimal number with a digit (or group of digits) that repeats forever.

There are three ways to show a repeating decimal:

0.1212... is a repeating decimal as there are two duplicates of the repeating block of digits "12" followed by an ellipsis.

To express a repeating decimal as a rational number, begin by assigning the decimal to a variable:

\(x=0.1212...=0.\overline{12}\)

Multiply both sides by 100:

\(\implies x \cdot 100=0.\overline{12}\cdot 100\)

\(\implies 100x=12.\overline{12}\)

Subtract the first equation from the second to eliminate the part after the decimal:

\(\begin{array}{crcr}& 100x & = & 12.\overline{12}\\- & x & = & 0.\overline{12}\\\cline{2-4} & 99x & = & 12\phantom{.12}\\\end{array}\)

Divide both sides of the equation by 99:

\(\implies \dfrac{99x}{99}=\dfrac{12}{99}\)

\(\implies x=\dfrac{12}{99}\)

Reduce the fraction to is simplest form by dividing the numerator and denominator by 3:

\(\implies x=\dfrac{12 \div 3}{99 \div 3}=\dfrac{4}{33}\)

\(\textsf{Therefore, $0.1212...$ expressed in the form of a rational number is\;$\dfrac{4}{33}$}.\)

The number of periods is approximately 26.98.

To calculate the number of periods it takes to double your money at 5.25 percent interest, you can use the formula for compound interest:

Future value = Present value * (1 + interest rate) ^ number of periods

In this case, the future value is twice the present value, so the equation becomes:

2 = 1 * (1 + 0.0525) ^ number of periods

To solve for the number of periods, you can take the logarithm of both sides:

log(2) = log((1 + 0.0525) ^ number of periods)

Using the logarithmic properties, you can bring the exponent down:

log(2) = number of periods * log(1 + 0.0525)

Finally, you can solve for the number of periods:

number of periods = log(2) / log(1 + 0.0525)

Using a calculator, the number of periods is approximately 13.27.

To calculate the number of periods it takes to quadruple your money at 5.25 percent interest, you can follow the same steps as above, but change the future value to four times the present value:

4 = 1 * (1 + 0.0525) ^ number of periods

Solving for the number of periods using logarithms:

number of periods = log(4) / log(1 + 0.0525)

Using a calculator, the number of periods is approximately 26.98.

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The approximate sample variance for the given frequency distribution is 13.5.

To approximate the sample variance, we can use the following formula:

Var(x) = (∑f * x²) / N - (∑f * x)² / N²

Where:
- ∑f * \(x^2\) is the sum of the product of each class frequency and the midpoint squared
- ∑f * x is the sum of the product of each class frequency and the midpoint
- N is the total number of observations

First, we need to calculate the midpoint of each class. The midpoints are:

4.5, 14.5, 24.5, 34.5, and 44.5

Next, we calculate the sum of the product of each class frequency and the midpoint squared. This gives us:

(8 * 4.5²) + (18 * 14.5²) + (10 * 24.5²) + (19 * 34.5²) + (15 * 44.5²) = 63448

Then, we calculate the sum of the product of each class frequency and the midpoint. This gives us:

(8 * 4.5) + (18 * 14.5) + (10 * 24.5) + (19 * 34.5) + (15 * 44.5) = 1730

Finally, we calculate the sample variance using the formula:

Var(x) = (63448 / 70) - (1730² / 70²)

= 13.482857142857143

Approximating the sample variance, we get 13.5. Therefore, the correct answer is b) 13.5.
In conclusion, the approximate sample variance for the given frequency distribution is 13.5.

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Answer:

37*

Step-by-step explanation:

Find 37* on the scale.

Answer:

37°Celsius I think

Answer:

A

Step-by-step explanation:

The difference of squares formula is a² - b² = (a + b)(a - b). We want this polynomial to be in the form a² - b². We notice that x² and 49 are perfect squares already which means that we don't need the x term. To get rid of it, its coefficient must be 0 because 0 times anything is 0, thus the x term will be removed and we'll be left with x² - 49 which is a difference of squares.

The equation of parabola that open upwards with focus 6 units is x²=24y.

A parabola is a plane curve which is mirror symmetrical and is approximately U-shaped. A parabola is a curve where any point at an equal distance from a fixed point  (the focus) and a fixed straight line (the directrix).

A curve formed by the intersection of a cone with a plane parallel to a straight line in its surface is also Parabola.

The general equation of Parabola is given by

y = a(x-h)²+ k

where (h,k) is the vertex of parabola.

And the equation of parabola open upward is,

(x-h)² = 4a(y-k)

where (h,k) is vertex and a is focus unit.

⇒ (x-0)² = 4(6)(y-0)

⇒ x² = 24y

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Answer:

282

Step-by-step explanation:

100⋅x=300⋅94

Cross multiply

100

100x

​

Divide both sides by 100

282

Answer:

The measure of a using the law of sines is 36 approximately.

Answer:

36 ounces or if over 150 lbs drink more water than 36 ounces

Step-by-step explanation:

For every pound of sweat you lose you need to drink 16 ounces of water!

The number of balls, given the ratio of white balls to yellow balls that could not be in the bag is C. 42 balls.

The number of balls that could not be in the bag, given the ratio of white balls to yellow balls, is the number that would not give a whole number when multiplied by the ratio of white balls to yellow balls.

26 balls :

= 3 / ( 10 + 3 white balls ) x 26

= 3 / 13 x 26

= 6 balls

39 balls :

= 3 / 13 x 39

= 9 balls

42 balls :

= 3 / 13 x 42

= 9.69 balls

There therefore cannot be 42 balls.

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Options for this question include:

The values in the question obtained by reading the attached graph are as follows;

Question 7

Question 8

Question 9

Question 10

A graph is a pictorial representation of the relationship between two or more variables on a coordinate plane by locating each point according to the magnitude of the variable and the axis that bears the variable's parameters.

Question 7;

The cost rate of each cab, which can be found from the cab equations are as follows;

The points on the graph of The Red Cabs are; (0, 2), and (3, 8)

The slope of the graph of The Red Cabs is; (8 - 2)/(3 - 0) = 2

The equation of the graph of The Red Cabs is therefore;

y - 2 = 2 × x

The equation for the cost of The Red Cabs is; y = 2·x + 2

Points on the graph of The Green Cabs are; (0, 5), and (3, 8)

The slope = (8 - 5)/(3 - 0) = 1

The equation is therefore;

y - 5 = x

The equation for the cost of The Green Cabs is; y = x + 5

The cost of traveling 2 miles on the The Red Cabs is; x = 2

y = 2 × 2 + 2 = 6

The cost of traveling 2 miles on The Green Cabs is; x = 2

y = 2 + 5 = 7

The Red Cabs is more affordable when traveling 2 miles

Question 8

From the graph, the cost of The Red Cabs when traveling 6 miles is $14

The cost of The Green Cabs when traveling 6 miles is $11

The Green Cabs cost less when traveling for 6 miles and should be called

Question 9

The point when the cost are the same for both taxis is specified by the point of intersection of the two graphs, which is the point (3, 8)

The point (3, 8) corresponds to a distance of 3 miles at a cost of $8

Therefore;

Question 10

The cost of traveling with The Red Cabs for 8 ,miles from the graph is $18

The cost of traveling with The Green Cabs for 8 miles is $13

The difference in the cost between the two companies is therefore;

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The MATLAB program uses the fixed-point iteration method to find a real root of the equation 4x + cos(x) - e* = 0. It starts with an initial approximation of xo = 1 and iteratively applies the function g(x) = e* - cos(x) until convergence. The program also calculates the absolute and relative percentage error for the obtained root.

Here is an example MATLAB program that implements the fixed-point iteration method to find the real root of the given equation:

function root = fixedPointIteration()

   e_star = % Enter the desired value for e* here

   xo = 1; % Initial approximation

   % Set the tolerance for convergence

   tolerance = 1e-6;

   % Initialize variables

   x = xo;

   previous_x = xo;

   iteration = 0;

   % Perform the fixed-point iteration

   while true

       iteration = iteration + 1;

       x = e_star - cos(previous_x);

       % Calculate the absolute and relative percentage errors

       abs_error = abs(x - previous_x);

       rel_error = abs_error / abs(x);

       % Check for convergence

       if abs_error < tolerance

           break;

       end

       previous_x = x;

   end

   % Display the results

   disp('Root:')

   disp(x)

   disp('Absolute Error:')

   disp(abs_error)

   disp('Relative Error (%):')

   disp(rel_error * 100)  

   root = x;

end

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The equation of line after solving with last line says 12 = 12 has

''infinite solution''.

What is mean by infinity solution of equation?

An equation of line has infinity solution if we solve the equation and get a variable or a number equal to itself.

Given that;

After solving equation we get the last line says 12 = 12 that is same constant.

Now, After solving the equation has number equal to itself.

That is, 12 = 12

Hence, By the condition of infinity solution of equation,

We get an equal number to itself after solving the equation.

So, The equation of line has ''infinite solution''.

Thus, The equation of line after solving with last line says 12 = 12 has

''infinite solution''.

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The radius of the circle is approximately 10.17 units (rounded to two decimal places).

To find the radius of the circle, we need to use the formula that relates the central angle to the length of the arc and the radius of the circle. The formula is given as:

arc length = radius x central angle

In this case, the arc length is given as 24.4 and the central angle is given as 2.4 radians. Substituting these values in the formula, we get:

24.4 = r x 2.4

Solving for r, we get:

r = 24.4 / 2.4

r ≈ 10.17

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A. The formula for the arithmetic sequence is (n/2)(2a + (n-1)d), where n is the number of terms, a is the first term, and d is the common difference.

B. To understand the formula for the arithmetic sequence, let's break it down step by step:

1. The arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant.

For example, 2, 5, 8, 11 is an arithmetic sequence with a common difference of 3.

2. The sum of an arithmetic sequence can be calculated using the formula Sn = (n/2)(2a + (n-1)d), where Sn represents the sum of the first n terms, a is the first term, and d is a common difference.

3. The formula consists of three parts:

  - (n/2) represents the average number of terms in the sequence. It is multiplied by the sum of the first and last term to account for the sum of the terms in the sequence.

  - 2a represents the sum of the first and last term.

  - (n-1)d represents the sum of the differences between consecutive terms.

4. By multiplying these three parts together, we can find the sum of the arithmetic sequence.

In summary, the formula for the arithmetic sequence, when given the sum of the sequence, is (n/2)(2a + (n-1)d), where n is the number of terms, a is the first term, and d is the common difference.

This formula allows us to calculate the sum of an arithmetic sequence efficiently.

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Answer:u 2

Step-by-step explanation:

The type of hypothesis which posits a difference between groups, but the difference is not specified is (c) nondirectional hypothesis.

The Non-Directional hypothesis explains that there is a difference between two groups without specifying the direction of the difference.

The non-directional hypothesis is also known as a two-tailed hypothesis.

For example, a nondirectional hypothesis might be "there is a difference in intelligence between males and females" without specifying whether males or females have higher intelligence.

A nondirectional hypothesis is appropriate when there is no prior knowledge or expectation about the direction of the difference between two groups.

Therefore, the correct option is (c).

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The given question is incomplete, the complete question is

What type of hypothesis posits a difference between groups, but the difference is not specified?

(a) directional hypothesis

(b) research hypothesis

(c) nondirectional hypothesis

(d) null hypothesis.

The image of the figure using the 90 degrees counterclockwise rotation is the graph (a)

The given figure is represented by the image in the attachment 2

From the attachment, we can see that:

Figure = triangle

The coordinates of the triangle are given as

W (-2, -2), X (-5, -3) and V(-2, -4)

The transformation is given as

90 degrees counterclockwise rotation

The rule of the 90 degrees counterclockwise rotation is

(x,y) becomes (-y,x)

When this is applied to the coordinates, we have

W' (2, -2), X (3, -5) and V(4, -2)

The graph represented by this is the graph (a)

Hence, the image of the figure after the transformation is (a)

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Answer:

a. 44 cm b. 126 cm

Step-by-step explanation:

a. it is semi circle

perimeter is πd

22/7*14

44 cm

b. it is equilateral triangle

so perimeter is side* 3

42 *3 = 126cm

Answer:

Step-by-step explanation:

(a)

The figure perimeter it is half of a circle with a diameter d₁=14 cm and two halfs of circle with a diameter d₂=14 cm÷2=7 cm.

The length of a circle is  L₀ = πd, where d is the diameter.

Therefore:

\(\bold{L=\frac12d_1+2\cdot\frac12d_2 = \frac12\cdot14\pi+\frac12\cdot2\cdot7\pi=14\pi\,cm\approx44\,cm}\)

(b)

A full circle it is 360°, so the circle sector of 60° is  \(\frac{60^o}{360^o}=\frac16\)  of the circle. So the arc of 60° is ¹/₆ of the full circle length.

The figure is an equilateral triangle and two 60°-sectors of circles with radiuses of length of the triangle's side (r=42 cm).

Its perimetr it's two radiuses, two arcs of 60° and one side of the triangle.

The length of a circle is  L₀ = 2πr, where r is a radius.

Therefore:

\(\bold{L=2r+2\cdot\frac16\cdot 2\pi r+r=3r+\frac23\pi r}\\\\\bold{L=3\cdot42+\frac23\pi\cdot42=(126+28\pi)\,cm\approx214\,cm}\)

Answer:

x= 3.7 hope this helps

Step-by-step explanation:

Answer:

x = 3.74

Step-by-step explanation:

x² = 14

Square root both sides to make x the subject.

x = √14

x = 3.74

Answer:

$4.13

Step-by-step explanation:

let x = the regular price of tickets

23x-4=184

subtract 4 from each side

23x=180

divide 23 by each side to get x by itself

x= $.13 per ticket add 4 because she got $4 off

the original price is $4.13

The set of points (x , 1 , 8) describe a line that has constant value of y and z coordinates, i.e., is parallel to x-axis in the plane.

The equation of a plane in R has the generic form: ax + by + cz + d = 0, where a, b, and c are the elements of the normal vector n = (a, b, c) that is perpendicular to the plane or any vector parallel to the plane.

Given: Equations of the lines:

To find: description of the points (x, y, z) in the plane.

Finding:

According to the given conditions, the lines y = 1 and z = 8 describe two lines with constant values of y and z coordinates respectively in the plane.

The set of points (x , 1 , 8) describe a line that has constant value of y and z coordinates, i.e., is parallel to x-axis and can have infinitely many values of x in the plane.

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The probability that the sum of the rolls is divisible by 6 is 1/1296, which is approximately 0.00077 or 0.077%.

To find the probability that the sum of the rolls is divisible by 6, we need to determine the favorable outcomes and the total number of possible outcomes.

First, let's identify the favorable outcomes. In this case, the sum of the rolls can be divisible by 6 if the sum is either 6 or 12.

1. For the sum of 6:
  - One possible outcome is rolling a 6 on the first roll and rolling a 1 on the remaining four rolls.
  - Another possible outcome is rolling a 5 on the first roll and rolling a 2 on the remaining four rolls.
  - We can also have rolling a 4 on the first roll and rolling a 3 on the remaining four rolls.
  - Similarly, rolling a 3 on the first roll and rolling a 4 on the remaining four rolls.
  - Finally, rolling a 2 on the first roll and rolling a 5 on the remaining four rolls.
  - This gives us a total of 5 favorable outcomes.

2. For the sum of 12:
  - One possible outcome is rolling a 6 on all five rolls.
  - This gives us a total of 1 favorable outcome.

Now let's determine the total number of possible outcomes. Since we are rolling a fair 6-sided die 5 times, the total number of possible outcomes is 6^5 (since each roll has 6 possible outcomes).

Therefore, the probability that the sum of the rolls is divisible by 6 is:

(total number of favorable outcomes) / (total number of possible outcomes)
= (5 + 1) / (6^5)
= 6 / 7776
= 1 / 1296

So, the probability that the sum of the rolls is divisible by 6 is 1/1296, which is approximately 0.00077 or 0.077%.

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Answer:

5

Step-by-step explanation: