The mean height of women in a country (ages 20-29) is 63.6 inches. A random sample of 70 women in this age group are selected. What is the probability that the mean height for the sample is greater than 64 inches?Assuming sigma= 2.53 inches

Given that two cars are 188 miles apart, travelling at different speeds, meet after two hours.

To Determine: The speed of both cars if the faster car is 8 miles per hour faster than the slower car

Solution:

Let the slower car has a speed of S₁ and the faster car has a speed of S₂. If the faster speed is 8 miles per hour faster than the slower car, then,

It should be noted that the distance traveled is the product of speed and time. Then, the total distance traveled by each of the cars before they met after 2 hours would be

It was given that the distance between the faster and the slower cars is 188 miles. Then, the total distance traveled by the two cars when they meet is 188 miles.

Therefore:

Combining equation 1 and equation 2

Substitute equation 1 into equation 2

Divide through by 4

Substitute S₁ in equation 1

Hence,

The slower car travels at 43 miles per hour(mph), and

The faster car travels as 51 miles per hour(mph)

The distance between 2 points (x1, y1) and (x2, y2) is calculated as:

So, if we replace (x1, y1) by (4, -9) and (x2, y2) by (-8,0), we get:

Answer: the distance is 15

The value of dy/dx is 5x^4 / (x + 1)^6.

What is the derivative?

A function's sensitivity to change with respect to a change in its argument is measured by the derivative of a function of a real variable.

The given function is y = (x / (x + 1))^5

Taking derivative on both sides,

dy/dx = d/dx (x / (x + 1))^5)

Using chain rule,

dy/dx = 5(x /  x + 1)^4 x d/dx (x / x + 1)

Using the quotient rule of derivative,

d/dx (x / x + 1) = 1 / (x + 1)^2

So,

dy/dx = 5(x / x+1)^4 x (1 / (x + 1)^2)

dy/dx = 5x^4 / (x + 1)^6

Therefore, the derivative of the given function is, dy/dx = 5x^4 / (x + 1)^6.

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ANSWER:

The value of AB is 23

STEP-BY-STEP EXPLANATION:

We know that AB is part of AC, and that DB cuts into two equal parts (half) since it is a median, therefore the value of AB would be

To get the value of x,

We use triangle sum theorem:

Triangle Sum Theorem:

The sum of all angles in a triangle is equal to 180 degrees.

In the triangle

We have 90 degree, 22 degree and one x

So,

x + 90 + 22 =180

x + 112 = 180

x = 180-112

x = 68 degree

Answer: x = 68

Part A.

Given:

P = (5, 4), Q = (7, 3), R = (8, 6), S = (4, 1)

Let's find the component of the vector PQ + 5RS.

To find the component of the vector, we have:

For vector RS, we have:

Hence, to find the vector PQ+5RS, we have:

Solving further:

Therefoee, the component of the vector PQ+5RS is:

<-18, -26>

• Part B.

Let's find the magnitude of the vector PQ+5RS.

To find the magnitude, apply the formula:

Thus, we have:

Therefore, the magnitude of the vector is:

ANSWER:

Part A. <-18, -26>

Part B. 10√10

Answer:

31/55

Step-by-step explanation:

Remember that the formual for the area of a circle is:

And the formula for the circumference is:

Using this formulas and the data given,

The cookie has an area of 78.54 square inches and a circumference of 31.42 inches

We have to find the parameter a of a quadratic equation knowing the following

• The vertex is (3,-6).

• A random point is (-7,14).

Based on the given information, we have the following

The vertex form of a quadratic equation is

Replacing all the givens, we have

Now, we solve for a

We have the following:

I)

It´s true

II)

It´s true

III)

It´s false

IV)

It´s true

V)

It´s false

Given:

There are given the equation:

Explanation:

To find the factor of the given equation, first, we need to take a common variable from the given equation:

Then,

Final answer:

Hence, the factor of the given equation is shown below:

Answer:

C. 930 square centimeters

Explanation:

First, recall the standard conversion between cm and ft.

Therefore:

The correct choice is C.

In order to determine what is the correct statement, calculate the amount of money Elsie can spend per month, based on her earnings per year.

Divide 45,000 by 12:

45,000/12 = 3,750

You can notice that the amount of money Elsie can spend per month is lower than the total expenses shown in the table.

Hence, the correct statement is:

C. No, because she will only make $3750 per month before taxes are taken out.

the expression is

(a+b)^2=a+b^2

substitute a=1 and b=1

(1+1)^2 = 1+1^2

4=2

that is not possible. so these are the values of a and b that is not counterpart example to the conjecture.

now substitute a=0, b=1

(0+1)^2 = 0+1^2

1=1

so this is true for the above expression.

now for a=-1, b=1

(-1+1)^2 = -1+1^2

0=0

this is true.

now for a=-1, b=2

(-1+2)^2 = -1+2^2

1=3

that is not possible

so a=1, b=1 and a=1,b=2 is the values that not counterpart example to the conjecture.

cost of the jacket = $125

money saved = $42

extra savings = $25/week

Ok

125 = 42 + 25w

w = number of weeks

Solve for w

125 - 42 = 25w

83 = 25w

w = 83/25

w = 3.3

She needs to save at least 3.3 weeks

Given:

• Slope, m = 1/5

• y-intercept = 13

Let's write the equation of the line.

To write the equation of the line, apply the slope-intercept equation of a line:

Where:

m is the slope

b is the y-intercept.

Thus, we have:

m = 1/5

b = 13

Plug in the values in the equation:

Therefore, the equation of the line is:

The required exponential function would be W = 106 × 1.04ⁿ for the weight after n weeks.

An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.

It is a relation of the form y = aˣ  in mathematics, where x is the independent variable

The given starting weight for the diet program is 106 pounds. Because the weight is expected to be multiplied by 1.04 pounds each week, the weight will develop exponentially with an initial value of 106 pounds and a growth factor of 1.04 pounds. Then, for the weight after weeks, the exponential function is given by,

W  = W(n) = Pb'

Here P = 106 and b = 1.04

Hence the required formula is,

⇒ W = 106 × 1.04ⁿ

Thus, the required exponential function would be W = 106 × 1.04ⁿ for the weight after n weeks.

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The question seems to be incomplete the correct question would be

A woman who has recovered from a serious illness begins a diet regimen designed to get her back to a healthy weight. She currently weighs 106 pounds. She hopes each week to multiply her weight by 1.04 each week. Then, find the exponential function for the weight after weeks.

Compound Shape

The shape of the figure attached consists on four triangles and one square.

The base of each triangle is B=12 cm and the height is H=10 cm, thus the area is:

Calculating:

The area of each triangle is 60 square cm.

Now for the square of a side length of L=12.

The area of a square of side length a, is:

Calculate the area of the square:

The total surface area is:

A = 60*4 + 144

A= 240 + 144

A = 384 square cm

4 : 15

The point that best represents 1/3 is point M .

The number line ranges from 0 to 0.5 with 10 divi

C. 6

To evaluate an algebraic expression means to find the value of the expression when the variable is replaced by a given number.so

Step 1

given

a)let

b) now, replace and calculate

therefore, the answer is

C. 6

I hope this helps you

Let P(x) be the polynomial such that the given set is its solution set.

Now notice that:

Therefore (x-4) and (3x+1) divide to P(x), then:

Simplifying the above result we get:

Setting k=1 we get that:

Answer: Second option.

Given a quadratic equation of the form:

The equation of the axis of symmetry is obtained using the formula:

From the given quadratic equation:

Therefore, the equation of the axis of symmetry of g(x) is:

The correct option is B.

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data

(4xy³y⁴)(5x²y)

Step 02:

This is the solution.

A bus travels 8.4 miles east and then 14.7 miles north.

What is the angle of the bus resultant vector?

see the figure below to better understand the problem

The angle of the bus resultant vector R is equal to

tan(x)=14.7/8.4

mm

1) We can fill in the gaps, this way since we can write the following when we translate into mathematical language:

Note that we could do it in two steps. Subtracting and then multiplying and dividing

Step 1

Given the triangle, ABC translated to A'B'C'

Required to find the algebraic description that maps triangle ABC and A'B'C'

Step 2

The coordinates of points A, B,C are in the form ( x,y)

Hence

Step 3

Find the algebraic description that maps triangle ABS TO A'B'C'

The algebraic description is found using the following;

Hence,

Hence the answer is option B

The values of x and y obtained by inverse matrix method are 2 and 3 respectively

An inverse of a matrix, A, is a matrix [tex] A^{-1}[/tex], that multiplies matrix A to give an identity matrix.

The inverse matrix method involves defining and making use of a coefficient matrix, A, a variable matrix, X, and a constant matrix, B, which are obtained from the system of equations as follows;

A·X = B
The system of equations is presented as follows;

3·x + 4·y = 18

4·x - y = 5

From the above system of equations, we have:

[tex]The \ coefficient \ matrix, \ A = \begin{bmatrix} 3&4 \\ 4& -1 \end{bmatrix}[/tex]

[tex]The \ variable \ matrix, \ X = \begin{bmatrix} x \\ y \end{bmatrix}[/tex]

[tex]The \ constant \ matrix, \ B = \begin{bmatrix} 18 \\ 5 \end{bmatrix}[/tex]

From the equation, A·X = B, we have;

[tex]\therefore X = \dfrac{B}{A} = A^{-1} \times B[/tex]

Where: A⁻¹ is the inverse matrix of A, which is found as follows;

[tex]If\ A = \begin{bmatrix} a&b \\ c&d \end{bmatrix}[/tex]

[tex]Then, \ A^{-1} = \dfrac{1}{a\cdot d-b\cdot c} \cdot \begin{bmatrix} d& -b \\ -c& a \end{bmatrix}[/tex]

Which gives the value of A⁻¹ obtained from the coefficient matrix, A = [tex]\begin{bmatrix} 3&4 \\ 4& -1 \end{bmatrix}[/tex] as follows;

[tex]A^{-1} = \begin{bmatrix} 3 & 4 \\ 4 & - 1 \end{bmatrix}^{ - 1} = \dfrac{1}{(3 \times - 1) - (4 \times 4)} \times \begin{bmatrix} - 1 & - 4 \\ - 4 & 3 \end{bmatrix}[/tex]

[tex]A^{-1} = \dfrac{1}{(3 \times - 1) - (4 \times 4)} \times \begin{bmatrix} - 1 & - 4 \\ - 4 & 3 \end{bmatrix} = \begin{bmatrix} \dfrac{ - 1}{ - 19} & \dfrac{ - 4}{ - 19} \\\\ \dfrac{ - 4}{ - 19} & \dfrac{3}{ - 19} \end{bmatrix}[/tex]

The variable matrix, [tex]X = A^{-1} \times B[/tex], which gives the value of the variables in the solution is therefore;

[tex]X = \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} \dfrac{ - 1}{ - 19} &\dfrac{ - 4}{ - 19} \\ \\\dfrac{ - 4}{ - 19} &\dfrac{3}{ - 19} \end{bmatrix} \times \begin{bmatrix} 18 \\ 5 \end{bmatrix} = \begin{bmatrix} 2 \\ 3 \end{bmatrix}[/tex]

[tex]\begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 2 \\ 3 \end{bmatrix}[/tex]

Therefore;

x = 2 and y = 3

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Given that 11v - 8 = 3

add 8 to both sides

11v = 3 + 8

11v = 11

Divide both sides by 11

v = 1

to simplify 4v - 8

= 4 (1) - 8

= 4 - 8

= -4