Mrs. Balcon owes the dentist $342. She wants to have her payments taken from her checking account over the next 7 1/2 months. By what amount will her account change each month for the first 7 months?

Answer:

The probability that the sample mean of men heights is more than 5 inches greater than the sample mean of women heights is 0.0885.

Step-by-step explanation:

We are given that the population of men at UMBC has a mean height of 69 inches with a standard deviation of 4 inches. The women at UMBC have a mean height of 65 inches with a standard deviation of 3 inches.

A sample of 50 men and 40 women is selected.

The z-score probability distribution for the two-sample normal distribution is given by;

                          Z  =  \(\frac{(\bar X_M-\bar X_W)-(\mu_M-\mu_W)}{\sqrt{\frac{\sigma_M^{2} }{n_M}+\frac{\sigma_W^{2} }{n_W} } }\)  ~ N(0,1)

where, \(\mu_M\) = population mean height of men at UMBC = 69 inches

           \(\mu_W\) = population mean height of women at UMBC = 65 inches

           \(\sigma_M\) = standard deviation of men at UMBC = 4 inches

           \(\sigma_M\) = standard deviation of women at UMBC = 3 inches

           \(n_M\) = sample of men = 50

           \(n_W\) = sample of women = 40

Now, the probability that the sample mean of men heights is more than 5 inches greater than the sample mean of women heights is given by = P(\(\bar X_M-\bar X_W\) > 5 inches)

 P(\(\bar X_M-\bar X_W\) > 5 inches) = P( \(\frac{(\bar X_M-\bar X_W)-(\mu_M-\mu_W)}{\sqrt{\frac{\sigma_M^{2} }{n_M}+\frac{\sigma_W^{2} }{n_W} } }\) > \(\frac{(5)-(69-65)}{\sqrt{\frac{4^{2} }{50}+\frac{3^{2} }{40} } }\) ) = P(Z > 1.35)

                                         = 1 - P(Z \(\leq\) 1.35) = 1 - 0.9115 = 0.0885

The above probability is calculated by looking at the value of x = 1.35 in the z table which has an area of 0.9115.      

Answer:

56x+21

Step-by-step explanation:

7times 8x is 56x

7 times 3 is 21

add them together and you get 56x+21

Answer:

B

Step-by-step explanation:

millimeter means one-thousandth of a meter meaning the number of millimeters will be larger by a factor of 1000.

Answer:

B

Step-by-step explanation:

Millimetres is A LOT smaller than meters, meaning the individual number of millimetres is larger than the individual number of meters.

The solution is

a) The number is 6

b) The equation of the parabola is y = x² + 4x + 96 with vertex ( -2 , 92 ) and the y intercept is ( 0 , 96 ) and the axis of symmetry is x = -2

What is a Parabola?

A Parabola, open curve, a conic section produced by the intersection of a right circular cone and a plane parallel to an element of the cone. A parabola is a plane curve generated by a point moving so that its distance from a fixed point is equal to its distance from a fixed line

The equation of the parabola is given by

( x - h )² = 4p ( y - k )

where ( h , k ) is the vertex and ( h , k + p ) is the focus

y is the directrix and y = k – p

The equation of the parabola is also given by the equation

y = ax² + bx + c

where a , b , and c are the three coefficients and the parabola is uniquely identified

Given data ,

a)

Let the equation be represented as A

Now , the value of A is

Let the number be = n

A = Two-fifth of the sum of a number and 24 is equal to 5 times the number decreased by 18

Substituting the values in the equation , we get

2/5 ( n + 24 ) = 5n - 18

On simplifying the equation , we get

Multiply by 5 on both sides of the equation , we get

2 ( n + 24 ) = 25n - 90

2n + 48 = 25n - 90

Subtracting 2n on both sides of the equation , we get

23n - 90 = 48

Adding 90 on both sides of the equation , we get

23n = 138

Divide by 23 on both sides of the equation , we get

n = 6

Therefore , the number is 6

b)

The equation of parabola is given as

y = x² + 4x + 96

Now , the equation can be simplified as

y = (x + 2)² + 92

The equation of the parabola is given by

( x - h )² = 4p ( y - k )

where ( h , k ) is the vertex and ( h , k + p ) is the focus

Substituting the values in the equation , we get

The vertex of the parabola is P ( -2 , 92 )

The y intercept of the parabola is ( 0 , 96 )

The axis of symmetry of parabola is x = -2

Hence , the equation of parabola is y = (x + 2)² + 92

To learn more about parabola click :

https://brainly.com/question/24042022

#SPJ1

Answer:

25

Step-by-step explanation:

4(4) + 3^2 ---> plug in 4 for v and 3 for r into the expression

16 + 9 = 25

hope this helps!

A geometric series is one in which there is a constant between two successive numbers in the series.

When there is a constant between the two successive numbers in the series then it is called a geometric series. In other words, every next term is multiplied by that constant term to form a geometric progression.

The sequence in which every next number is the addition of the constant quantity in the series is termed the arithmetic progression

Suppose the series is given as

2,4,8,16,32,64.........

The common difference is defined as the ratio of the next term to the previous term.

From the above series, the common ratio is calculated as,

Common ratio = 4 / 2

Common ratio = 2

To know more about geometric progression follow

https://brainly.com/question/12006112

#SPJ1

Answer:

I dont understand what you says

Step-by-step explanation:

I only speak eng not other language

m∠s + m∠y = 90

m∠s = 90 - m∠y            

m∠s= 2(m∠y) - 75

90 - m∠y = 2 m∠y -75

90 + 75 = 3 (m∠y)

165 = 3 (m∠y)

55= m∠y

The cost of the each stamp is a 4$ and the 9$.

According to the statement

We have to find that the cost of the each stamp.

So, For this purpose, we know that the

The cost function can be used to find the average cost, which is the average amount of money it costs to produce a unit.

From the given information:

Neil needs to mail a USB drive to a friend. He uses 43-cent stamps and 8-cent stamps to pay $2.01 in postage.

Then

48x + 7y = 255

let the value of the two unknowns.

Then

If x = 1, then y = 29.57, which is not a whole number.

If x = 2, then y = 122.71, which is not a whole number.

If x = 3, then y = 15.86, which is not a whole number.

If x = 4, then y = 9, which a a whole number.  This is a solution

And we know that the answer will be in a whole number.

So, The cost of the each stamp is a 4$ and the 9$.

Learn more about cost function here

https://brainly.com/question/2021001

#SPJ9

Answer

37

Step by Step explanation

replace x with -7

which gives

-(-7)^2-10(-7)+16

= 37

Answer:

Hey there!

30/40 are cheddar flavored, so 10/40 are cream cheese flavored.

10/40=25, so 25% of the chips are cream cheese flavored (assuming that the rest of the chips are all cream cheese flavored)

Let me know if this helps :)

Answer:

Option D is your correct answer

I think it will help.

9514 1404 393

Answer:

  x = 12.5

Step-by-step explanation:

The value of x is part of the value of an angle in a triangle where the other angles are known. This suggests that the relevant theorem is the "angle sum theorem," which tells you the sum of angles in a triangle is 180°.

This gives you the equation ...

  60° +60° +(4x+10°) = 180° . . . . total of all angles is 180°

  4x +130° = 180° . . . . . . . . . . collect terms

  4x = 50° . . . . . . . . . . . . subtract 130° from both sides

  x = 12.5° . . . . . . . . . divide both sides by 4

The exponential function that models the population of tiger gar in the lake is given as follows:

\(y = 322.63(1.25)^x\)

An exponential function has the definition presented as follows:

\(y = ab^x\)

In which the parameters are given as follows:

Considering x as the number of years since 2016, the points are given as follows:

(0, 322), (1, 399), (2, 507), (3, 618), (4, 785), (5, 957).

Inserting these points into an exponential regression calculator, the equation is given as follows:

\(y = 322.63(1.25)^x\)

More can be learned about exponential functions at brainly.com/question/2456547

#SPJ1

Answer:

x =  − 4  ±  √ 10,

Step-by-step explanation:

2(x + 4)² = 20

=> 2(x + 4)  (x + 4) = 20

=> 2x + 8 (x + 4) = 20

=> 2x² + 8x + 8x + 32 = 20

=> 2x² + 16x + 32 = 20

=> 2x² + 16x + 12 = 0

=> Now solve using the quadratic formula:

x =  − 4  ±  √ 10,

Radical form: − 4  ±  √ 10,

Decimal form: -0.84, -7.16

Hope this helps!

By the fundamental theorem of calculus,

\(\displaystyle y = \int_0^v \sqrt{3+4t^2} \, dt \implies \boxed{\frac{dy}{dv} = \sqrt{3+4v^2}}\)

In general,

\(\displaystyle \frac{d}{dx} \int_0^{g(x)} f(u) \, du = f(g(x)) \frac{dg}{dx}\)

The exponential function obtained from the table is represented by the formula y is 650(1.045)x.

A function with the exponential shape is:

y = abˣ

where an is y's initial value, b are multipliers, and y and x are variables.

The bacterial population at x hours should be represented by y.

With 650 bacteria cells at the beginning, the group.

a = 650

4.5% is the growth rate.

b = 100% + 4.5% = 104.5% = 1.045

The exponential function obtained from the table is represented by the formula y = 650(1.045)x.

The exponential function obtained from the table is represented by the formula y is 650(1.045)x.

Thirty hours later:

y = 650(1.045)³⁰ = 2434.

To learn more about the exponential function refer to    brainly.com/question/12940982

#SPJ1

Answer: 13

Explanation:

21-8=13

z = 13  is the solution of the equation z +8 = 21.

When a mathematical expression is converted into an equivalent, typically shorter statement, it becomes simpler. Procedure simplification is one method to encourage uniformity in work effort, expense, and duration. It reduces diversity and variation that is detrimental, pointless, or unnecessary.

Given, an expression  z + 8 = 21

Simplifying it,

z = 21 - 8

z = 13

Therefore, The answer to the equation z + 8 = 21 is z = 13.

Learn more about simplification here:

brainly.com/question/24242989

#SPJ2

Answer:

112 is the area of this figure...

Hope it helps!!!

Answer:

Huh?

Step-by-step explanation:

By using the concept of dilation factor, length of BC obtained is 3 units

What is dilation factor?

Dilation is a transformation which changes the size of a figure by a certain factor.

That factor is called the scale factor

In the figure, A'B'C'D' is the image of ABCD under dilation with a scale factor of 3

A'B'C'D' is the dilated figure

Length of B'C' = 9 units

Length of BC = \(9 \div 3\) = 3 units

To learn more about dilation factor, refer to the link-

https://brainly.com/question/3457976

#SPJ9

Complete Question

The figure has been attached here

Original Cost = $1549

Sales Price = $1149

1549 - 1149 = 400 -----> discount

400/1549 = 0.25 = 25%

Using the Chain Rule, we have: dy/dx = f'(g(x)) * g'(x) = 1 * 1 = 1.The derivative of y with respect to x is 1.

When we compose a function, it may be possible to write it in a variety of different ways. Differentiating such functions can result in different derivatives, but the Chain Rule indicates that the derivatives of the compositions should be the same regardless of how the function is written, if the function is continuous and differentiable.For instance, consider the function f(x) = sin(x²). It can be written as f(g(x)) where g(x) = x² and f(x) = sin(x). Furthermore, it can be written as f(h(x)) where h(x) = x² and f(x) = sin(x). These are both compositions of functions, but they are different compositions that lead to different derivatives.However, if the function is a composite of differentiable functions, the Chain Rule tells us that the derivative of a composite function is the derivative of the outer function multiplied by the derivative of the inner function.

To find dy/dx if y = x using the Chain Rule with y as a composite of the following functions, we must first rewrite y as a composite function: y = f(g(x)) where g(x) = x and f(x) = x. This composite function can be written in a variety of different ways, such as y = f(h(x)) where h(x) = x and f(x) = x, or y = f(k(x)) where k(x) = x and f(x) = x. However, regardless of how we write it, the Chain Rule tells us that the derivative of y is equal to the derivative of the outer function (f(x) = x) multiplied by the derivative of the inner function (g(x) = x).

For more such questions on derivative

https://brainly.com/question/26369159

#SPJ8

Log22/Log9 express log_9 22 in terms of common logarithms

Common logarithms, is commonly describd as base-10 logarithms.

It is a type of logarithm that involve taking the logarithm of a number with respect to the base of 10.

This means that common logarithms show how many powers of ten must be increased to get a particular number. The usual logarithm of 100, for example, is 2, because 10 raised to the power of 2 equals 100.

The answer provided is based on the full question below;

-------------express log_9 22 in terms of common logarithms

a. Log 22/9

b. Log 198

c. Log22/Log9

d. Log9/Log22

Find more exercises on common logarithms;

https://brainly.com/question/30085872

#SPJ1

Answer:

0.75 g ≤ 35

Step-by-step explanation:

if each games costs $0.75, then the answer of g will be given by 35/0.75.

he can go up to exactly $35 but not over

so, the inequality is given by 0.75 g ≤ 35

The maximum price you can offer for a home is approximately $82,352.94 for a 17% down payment.

To determine the maximum price you can offer for a home, you need to calculate 17% of the total price, which will be your down payment of $14,000.

Let's assume the maximum price you can offer for the home is P dollars.

According to the given information, the down payment requirement is 17% of the total price. So, we can set up the following equation:

\(0.17P = $14,000\)

To solve for P, divide both sides of the equation by 0.17:

P = $14,000 / 0.17

Calculating this expression, we find:

P ≈ $82,352.94

Therefore, the maximum price you can offer for a home in order to have enough money for the 17% down payment is approximately $82,352.94.

For more questions on down payment

https://brainly.com/question/1698287

#SPJ8

Answer:

27

Step-by-step explanation:

3x + 9 = 90

3x = 90 - 9

3x = 81

x =27