use a standard normal distribution table to find the percentage of area above the standard normal curve that is specified above Z= 1.37

Since , A club has 42 members and 17 pledges. The club selects a 5-member executive committee composed of a chair and vice-chair, who must be members, and an advisory committee of 3 pledges. The executive committee can be formed in 850668 ways.

a. The number is ⁴²P₅ = 42!/37!

                                    =42×41×40×39× 38 ×37!/37!

                                    =102080160 ways.

b. The number is ⁴²C₅ = 42!/ 5! × 37!

                               =42× 41× 40× 39 ×38×37!/ 5×4×3×2×1 ×37!

                               = 850668 ways.

If you have trouble applying concepts, consider pure mathematics. Select 4 objects out of 24 to replace the first problem. Since there is a replacement, it is a permutation. So the answer is ⁴²P₅= 102080160 possibilities. Obviously there can't be a substitute for the next, so it's a combo. So the answer is ⁴²C₅= 850668 ways.

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The box in the middle of the plot spans from the first quartile (Q1) to the third quartile (Q3), with a line inside representing the median.

A whisker plot, also known as a box and whisker plot, is a graphical representation of a set of numerical data through their quartiles. The plot consists of a box with whiskers extending from the top and bottom, showing the spread and distribution of the data. The five-number summary, which includes the minimum value, first quartile (Q1), median, third quartile (Q3), and maximum value, is used to create the whisker plot.

Here,

To create a box and whisker plot, we need to find the five-number summary of the data set, which includes:

Minimum value: the smallest value in the data set.

First quartile (Q1): the median of the lower half of the data set.

Median: the middle value in the data set.

Third quartile (Q3): the median of the upper half of the data set.

Maximum value: the largest value in the data set.

First, we need to put the data in order:

10, 12, 14, 15, 16, 18, 22, 24, 25, 28

The minimum value is 10 and the maximum value is 28.

The median is the middle value, which is 18.

To find the first quartile, we need to find the median of the lower half of the data set, which is:

10, 12, 14, 15, 16

The median of this lower half is 14.

To find the third quartile, we need to find the median of the upper half of the data set, which is:

22, 24, 25, 28

The median of this upper half is 24.

So, the five-number summary for this data set is:

Minimum value = 10

First quartile (Q1) = 14

Median = 18

Third quartile (Q3) = 24

Maximum value = 28

Now we can use this information to create the box and whisker plot:

      |          |      

 ----+----+----+----+----

    10   14   18   24   28

The box in the middle of the plot spans from the first quartile (Q1) to the third quartile (Q3), with a line inside representing the median. The whiskers extend from the box to the minimum and maximum values in the data set.

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Answer:

The problem is telling you to find g ( f ( x ) )

Since we know that f(x) is square root of x, we can put the function this way.

g(√x)

Then, we use  √x as our x in our g(x) function.

You plug in  √x for x and you solve.

(√x ) ^2 is just x.

Finally the answer is

x-3

hope this helps :)

Step-by-step explanation:

Answer:

5 paperback books

Step-by-step explanation:

From the question:

A used bookstore sells hardback books and paperback books. A hardback book costs $11, including tax. A paperback book costs $5, including tax. Jamal spent $47.

Let the number of paper backs = p

Let the number rod hardbacks = h

Hence:

$11 × h + $5 × p = $47

11h + 5p = 47

Jamal bought 3 more paperback books than hardback books.

h + 3 = p

h = p - 3

How many paperback books did Jamal buy?

Hence:

11h + 5p = 47

11(p - 3) + 5p = 47

11p - 33 + 5p = 47

16p = 47 + 33

16p = 80

p = 80/16

p = 5

Hence, he bought 5 paper back books

Answer:

6,6.5

Step-by-step explanation:

Answer:

\((\frac{5}{\sqrt{34}} ,\frac{-3}{\sqrt{34}} )\)

Step-by-step explanation:

The vector v:

(2,4)-(-3,7)

=(5,-3)

norm:

||(5,-3)||=\((5^2+3^2)^{ 1/2}=\sqrt{34}\)

unit vector:

\((\frac{5}{\sqrt{34}} ,\frac{-3}{\sqrt{34}} )\)

Answer:

x = 25°

y = 65°

Step-by-step explanation:

One angle is marked with the small square showing it is a right angle. Two pieces are x and 65°. These will add together to make 90°.

Use this idea to write an equation:

x + 65° = 90°

subtract 65 from both sides.

x = 90 - 65

x = 25°

x + y also add up to 90°.

x + y = 90°

25° + y = 90

subtract 25°

y = 65°

Answer:

(48, 3), (80, 5), (160, 10)

Comparing the √17 and 29/7 using <, > or = , we have √17 < 29/7.

Mathematical number comparison is the process or method of comparing two numbers to determine whether one is less, bigger, or equal to the other. The comparison symbols for numbers are "=", which stands for "equal to," "=", which stands for "greater than," and " ", which stands for "less than." Comparing amounts is a technique for figuring out how much to compare units in relation to a different standard or reference unit. A common reference point is necessary for two comparing units to be compared; otherwise, they cannot be compared.

Given,

Comparing the following using <, > or = ,

Numbers:

√17 and 29/7

For √17

Simplifying,

√17 = 4.123

For 29/7

29/7 = 4.14

√17 < 29/7

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Answer:

V = 460.68

Step-by-step explanation:

V=(lwh)/3

Answer:

Slope formula is given as (y2-y1) ÷ (x2-x1) or (y1-y2) ÷ (x1-x2), where x and y are the coordinates of the points.

Slope = (-7-(-6)) ÷ (0-(-8))

= (-7+6) ÷ (0+8)

= -1/8

The measures of the non-right angles of each triangle are 40 degrees and 50 degrees.

The sum of the interior angles of a regular 18-gon can be found using the formula:

S = (n - 2) × 180 degrees

n is the number of sides of the polygon.

Substituting n = 18 we get:

S = (18 - 2) × 180 degrees

= 2880 degrees

The 18-gon into 36 right triangles need to draw 18 lines from the center of the polygon to its vertices dividing the polygon into 36 congruent sectors each with a central angle of 360 degrees / 18 = 20 degrees.

Each sector is an isosceles triangle with two sides of equal length radiating from the center of the polygon.

The vertex angle of each isosceles triangle is equal to twice the central angle or 40 degrees.

Since the vertex angle of a right triangle is 90 degrees the two non-right angles of each right triangle are 40 degrees and 50 degrees.

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Answer:

$43.75

Step-by-step explanation:

(35/8)x10=43.75

Answer:

√121 = 11

Explanation:

11 × 11 = 121

Answer:

11

Step-by-step explanation:

The square root of 121 is 11.

= 11*11 = √(121)

= 121 = 11

done

Answer:

169

Step-by-step explanation:

Larger Number = 196

Smaller Number = 169

Step-by-step explanation:

larger sum = 196/

smaller sum = 169/

hope it helps. :)

Answer:

1. like

2.unlike

3.unlike

4.like

5. ......

6. ......

Step-by-step explanation:

Answer:

The number 5 and 6 is both unlike

I hope i it help's you

Julio will be 30 years old when his father is twice his age.

To determine the age at which Julio will be twice his father's age, we need to find the age difference between them and then add that difference to Julio's current age.

Currently, Julio is 12 years old, and his father is 42 years old. The age difference between them is 42 - 12 = 30 years.

For Julio to be twice his father's age, the age difference needs to remain the same as it is currently. Therefore, when Julio is x years old, his father will be x + 30 years old.

Setting up an equation to solve for x:

x + 30 = 2x

Simplifying the equation, we subtract x from both sides:

30 = x

Thus, when Julio is 30 years old, his father will be 30 + 30 = 60 years old. At this point, Julio will indeed be twice his father's age.

Therefore, Julio will be 30 years old when his father is twice his age.

Note : the translated question is Julio is 12 years old and his father is 42 years old. How old will Julio be when his father is twice his age?

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Answer:

B. 2⁵ + 7²

Step-by-step explanation:

2 to the fifth power is: 2⁵

7 squared (7 to the second power) is: 7²

Answer: x = -3

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

The correlation coefficient between X and Y is Corr(X, Y) = 0.

To calculate the marginal distribution of X and Y, we need to integrate the joint probability density function (PDF) over the appropriate ranges.

a. Marginal distribution of X:

To find the marginal distribution of X, we integrate the joint PDF over the range of Y:

∫[0, 1] J(x, y) dy

Since the joint PDF is defined as J(x, y) = 1 for 0 ≤ y ≤ x ≤ 1 and J(x, y) = 0 otherwise, the integral becomes:

∫[0, x] 1 dy = x, for 0 ≤ x ≤ 1

So, the marginal distribution of X is simply X(x) = x for 0 ≤ x ≤ 1.

b. Expectation of X:

The expectation (mean) of X can be calculated as the integral of x times the marginal PDF of X:

\(E(X) = ∫[0, 1] x * X(x) dx = ∫[0, 1] x^2 dx = [x^3/3] from 0 to 1 = 1/3\)

Therefore, the expectation of X is E(X) = 1/3.

c. Variance of X:

The variance of X can be calculated using the formula:

\(Var(X) = E(X^2) - (E(X))^2E(X^2) = ∫[0, 1] x^2 * X(x) dx = ∫[0, 1] x^3 dx = [x^4/4] from 0 to 1 = 1/4Var(X) = 1/4 - (1/3)^2 = 1/4 - 1/9 = 5/36\)

Therefore, the variance of X is Var(X) = 5/36.

d. Covariance of X and Y:

The covariance of X and Y can be calculated as:

Cov(X, Y) = E(XY) - E(X)E(Y)

Since the joint PDF J(x, y) = 1 for 0 ≤ y ≤ x ≤ 1, the integral becomes:

\(E(XY) = ∫[0, 1] ∫[0, x] xy dy dx = ∫[0, 1] [(x^2)/2] dx = [(x^3)/6] from 0 to 1 = 1/6\)

\(E(X) = 1/3 (from part b)E(Y) = ∫[0, 1] ∫[0, x] y J(x, y) dy dx = ∫[0, 1] [(x^2)/2] dx = [(x^3)/6] from 0 to 1 = 1/6\)

Cov(X, Y) = 1/6 - (1/3)(1/6) = 0

Therefore, the covariance of X and Y is Cov(X, Y) = 0.

e. Correlation coefficient between X and Y:

The correlation coefficient can be calculated using the formula:

Corr(X, Y) = Cov(X, Y) / √(Var(X) * Var(Y))

Since the covariance of X and Y is 0, the correlation coefficient will also be 0.

Therefore, the correlation coefficient between X and Y is Corr(X, Y) = 0.

f. Conclusion based on the correlation coefficient:

The correlation coefficient of 0 indicates that there is no linear relationship between X and Y. In this case, the fraction of male runners (X) and the

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The graph of the function f(x) = 5(2)^x is an upward-sloping exponential curve that starts at (0, 5) and increases rapidly as x moves to the right, never crossing the x-axis.

The function f(x) = 5(2)^x represents exponential growth. Let's analyze its graph.

As x increases, the value of 2^x grows exponentially. Multiplying it by 5 further amplifies the growth. Here are a few key points to consider:

When x = 0, 2^0 = 1, so f(0) = 5(1) = 5. This is the y-intercept of the graph, meaning the function passes through the point (0, 5).

As x increases, 2^x grows rapidly. For positive values of x, the function will increase quickly. As x approaches positive infinity, 2^x grows without bound, resulting in the function also growing without bound.

For negative values of x, 2^x approaches zero. However, the function is multiplied by 5, so it will not reach zero. Instead, it will approach y = 0, but the graph will never touch or cross the x-axis.

The function is always positive since 2^x is positive for any value of x, and multiplying by 5 does not change the sign.

Based on these observations, we can conclude that the graph of f(x) = 5(2)^x will be an exponential growth curve that starts at (0, 5) and increases rapidly as x moves to the right, never crossing or touching the x-axis.

The graph will have a smooth curve that rises steeply as x increases. The rate of growth will be determined by the base, in this case, 2. The larger the base, the steeper the curve. The function will approach but never reach the x-axis as x approaches negative infinity.

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Answer:

18

Step-by-step explanation:

1 ft=12in

3ft=36in

divide 36 by 2 and you get 18

Answer:

What are they making you do

Step-by-step explanation:

Answer:

Skateboarder B will have traveled 1,680 feet farther.

Step-by-step

Possible reasoning: There are 240 seconds in 4 minutes

Answer:

12

Step-by-step explanation:

mean is calculated as

mean = \(\frac{sum}{count}\)

Here mean = 316 and sum = 3792 , count n is required to be found, so

\(\frac{3792}{n}\) = 316 ( multiply both sides by n )

3792 = 316n ( divide both sides by 316 )

12 = n

There are 12 observations in the data

Answer:

y=3x+1

Step-by-step explanation:

4--2=6

1--1=2

6/2=3

slope is 3

4=3(1)+b

4=3+b

4-3=3-3+b

1=b

1 is the y intercept

Answer:

    y = 3x + 1

Step-by-step explanation:

(x₁, y₁) = (-1, -2)   & (x₂ , y₂) = (1, 4)

\(slope = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\)

        \(= \frac{4-[-2]}{1-[-1]}\\\\= \frac{4+2}{1+1}\\\\= \frac{6}{2}\\\\= 3\)

m = 3

y -y₁ = m(x - x₁)

y - [-2] = 3(x - [-1])

y + 2 = 3(x +1)

y + 2 = 3x + 3

      y = 3x + 3 -2

      y = 3x + 1

Answer:

The perimeter is 26cm

Step-by-step explanation:

Given

See attachment for shape

Required

The perimeter

This implies that, we add up the length of all sides (see attachment 2 for complete lengths)

So, we have:

\(Perimeter = 6cm + 4cm + 2cm + 3cm + 4cm + 7cm\)

\(Perimeter = 26cm\\\)

Answer:

The probability that one marble drawn at random is not blue is 70%