The real interest rate is 6 percent a year and the income tax rate is 50 percent.
With no​ inflation, what is the real​ after-tax interest​ rate?
If the inflation rate rises to 4 percent a​ year, what is the real​ after-tax interest​ rate?

The distribution that is needed for the problem that we have here is the t distribution.

With its bell-shaped structure and heavier tails, the t-distribution, commonly referred to as the Student's t-distribution, is a kind of probability distribution that resembles the normal distribution.

When there are insufficient samples or unknown variances, it is used to estimate population parameters. T-distributions have broader tails than normal distributions because they are more likely to contain extreme values.

We have tn-1

where n = 70

so that we would have

t70 - 1

= t69

Therefore we would have to use the t distribution here.

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The integers that would make the inequality true is the set of integers less than 20.

From the question we are to determine the integer that would make the given inequality true

The given inequality is

x - 4 < 16

To determine the integer that would make the inequality true, we will solve the inequality for the variable x

Solving the inequality

x - 4 < 16

Add 4 to both sides of the inequality

x - 4 + 4 < 16 + 4

x < 20

Hence, the solution to the given inequality is x < 20. All integers less than 20 will make the inequality true.

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The answer to the questions from 4 through 12 are below:

4. z³ + 5z + 3z² + 1 - 4 - 2z²

= z³ + 5z² + 5z + - 3

5. Perimeter of the square = Addition of all the sides

= (2d - 3) + (3c) + (2d - 3) + (3c)

= 2d - 3 + 3c + 2d - 3 + 3c

= 4d + 6c - 6

6. Perimeter of the triangle = Addition of all the sides

= (4a - 2b) + (9a - 4) + (7a + 3)

= 4a - 2b + 9a - 4 + 7a + 3

= 20a - 2b - 1

7. Perimeter of a square = 4 × side length

= 4 × 10x

= 40x

8. Perimeter of a rectangle = 2(length + width)

= 2{(2x + 7) + (3x + 8y)}

= 2(2x + 7 + 3x + 8y)

= 2(5x + 8y + 7)

= 10x + 16y + 14

Simplify the following

9. 3a + a² + 5(a - 2)

= 3a + a² + 5a - 10

= a² + 8a - 10

10. 8(v + w) + 7(v + 2w)

= 8v + 8w + 7v + 14w

= 15v + 22w

11. 4c² + 6(c + c²) - 2c

= 4c² + 6c + 6c² - 2c

= 10c² + 4c

12. z³ + 5(z + 3) + 4(2 - 2z²)

= z³ + 5z + 15 + 8 - 8z²

= z³ - 8z² + 5z + 23

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Answer:

-----------------------------------

Answer:

Perimeter = -3h + 24

Step-by-step explanation:

Forming the expression,

→ 7 + (14 - 6h) + (3h + 3)

Let's simplify the expression,

→ 7 + (14 - 6h) + (3h + 3)

→ 7 + 14 - 6h + 3h + 3

→ (-6h + 3h) + (7 + 14 + 3)

→ -3h + 24

Hence, answer is -3h + 24.

The length of BC is 50 miles (approx).

What is Trigonometry?

Trigonometry is a field of mathematics that explores the connections between triangle side lengths and angles.

Solution:

In the triangle ABC,

The perpendicular = BC

The Base = AB = 6 miles

by using the trigonometric ratio "tan"

tan (58) = BC / AB

8.33 = BC / 6

49.98 miles = BC

BC = 50 miles (approx)

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If a man is 6 feet 2 inches tall, his z-score is equal to 1.82.

If a woman is 5 feet 10 inches tall, her z-score is equal to 2.92.

The 5 feet 10 inches American woman is relatively taller.

In a normal distribution, the z-score of a given sample score can be calculated by using this formula:

Z-score = (x - μ)/σ

Where:

Next, we would convert the height in feet to inches as follows:

American man = 6 × 12 + 2 = 74 inches.

American woman = 5 × 12 + 10 = 70 inches.

For the American man's z-score, we have:

Z-score = (74 - 69.2)/2.64

Z-score = 4.8/2.64

Z-score = 1.82

For the American woman's z-score, we have:

Z-score = (70 - 64.2)/2.53

Z-score = 5.8/2.53

Z-score = 2.92

Therefore, the 5 feet 10 inches American woman is relatively taller because she has a higher z-score (2.92 > 1.82).

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Complete Question:

The heights of adult men in America are normally distributed, with a mean of 69.2 inches and a standard deviation of 2.64 inches. The heights of adult women in America are also normally distributed, but with a mean of 64.2 inches and a standard deviation of 2.53 inches.

a) If a man is 6 feet 2 inches tall, what is his z-score (to two decimal places)?

b) If a woman is 5 feet 10 inches tall, what is her z-score (to two decimal places)?

c) Who is relatively taller?

The 6 feet 2 inches American man

The 5 feet 10 inches American woman

Josephine have £3882.9 amount after 2 years and £3994.9 amount after 3 years.

Using the formula of compound interest we can find the amount after t years compounded annually at the r per cent rate.

The formula of compound interest is as follows,

[tex]A=p(1+\frac{r}{100} )^t[/tex]

Where P is the principal value, A is the amount, r is the rate and t is the time.

Here we have a principal value of £3,500 and a rate is 4.5%.

Now, finding the amount after 2 years by putting the values in the formula of compound interest,

[tex]A=p(1+\frac{r}{100} )^t\\\\A=3500(1+\frac{4.5}{100} )^2\\\\A=3500(1+0.045 )^2\\A=3500(1.045)^2\\A=3500\times1.092025\\A=3882.0875[/tex]

So, After 2 years Josephine will have £3882.9.

Now, finding the amount after 3 years,

[tex]A=p(1+\frac{r}{100} )^t\\\\A=3500(1+\frac{4.5}{100} )^3\\\\A=3500(1+0.045 )^3\\A=3500(1.045)^3\\A=3500\times1.141166125\\A=3994.0814375[/tex]

So, After 3 years Josephine will have £3994.9.

Therefore, After 2 years Josephine will have £3882.9 and after 3 years Josephine will have £3994.9 when 4.5% interest is compounded annually.

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The dimensions of the rectangle is 83 feet x 46 feet

What is the Perimeter of a Rectangle?

The perimeter P of a rectangle is given by the formula, P=2 ( L + W) , where L is the length and W is the width of the rectangle.

Perimeter P = 2 ( Length + Width )

Given data ,

The perimeter P of the rectangle = 258 feet

Let the length of the rectangle be = L

Let the width of the rectangle be = W

And , The width is 37 feet less than the length. ,

So , W = L - 37

Perimeter P = 2 ( Length + Width )

Substituting the values of L and W in the equation , we get

Perimeter P = 2 ( L + L - 37 )

2 ( L + L - 37 ) = 258

( L + L - 37 ) = 129

2L - 37 = 129

Adding 37 on both sides , we get

2L = 166

Divide by 2 on both sides , we get

Length L of the rectangle = 83 feet

Substituting the value of L in equation ,we get

W = L - 37

Width W of the rectangle = 46 feet

Therefore , Length = 83 feet and Width = 46 feet

Hence , the dimensions of the rectangle is 83 feet x 46 feet

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By the sequence of term to term rule the value of : a)  [tex]U_{1}[/tex]= [tex](U_{0})^{2}[/tex] + 3 =[tex]1^{2}[/tex] + 3 = 4    b). [tex]U_{2}[/tex] = [tex](U_{1})^{2}[/tex] + 3 = [tex]4^{2}[/tex] + 3 =19     c). [tex]U_{3}[/tex] = [tex](U_{2})^{2}[/tex] + 3 = [tex]19^{2}[/tex] + 3 = 364 .

Give the first number in the sequence and then describe the pattern of the numbers to get the term-to-term rule. Three is the first number. The rule for terms to terms is "add 4." All of the terms in the series can be located once the initial term and term to

[tex]$$\mathrm{u}_0=1$$[/tex]

The difference is given by[tex]$u_{n+1}=\left(u_n\right)^2[/tex]+ 3

We have to simply put the value in their places to get the proper answer -

a). Put the [tex]$u_{n+1}=u_1$[/tex]

n+1 = 1  ⇒ n = 0

put n = 0in the formula[tex]$\mathrm{u}_{n+1}=\left(\mathrm{u}_n\right)^2[/tex] +3

we wil get

[tex]$$u_1=\left(u_0\right)^2[/tex] + 3 = [tex]1^{2}[/tex] =3 = 4

b). Put the [tex]$u_{n+1}=u_2$[/tex]

n + 1 = 2 => n = 1

put  n=1 in the formula [tex]$u_{n+1}=\left(u_n\right)^2[/tex]+3

we wil get:

[tex]$$u_2=\left(u_1\right)^2[/tex]+3= [tex]4^2[/tex]+3=19

c). Put the  [tex]$u_{n+1}=u_3$[/tex]

n + 1 = 3 => n = 2

Put n=2 in the formula+3

we wil get :

[tex]$$u_3=\left(u_2\right)^2[/tex] +3= [tex](19)^2[/tex] +3 =364

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The angle x will be 34°.

From the properties of circles we get to know that the angle at the center and the angle between two tangents are always supplementary.

Supplementary angles are those which always sum to to 180°.

For example ∠HJK is supplementary to ∠HIK the their sum will come out to be 180°.

similarly ∠ROP + ∠RQP = 180°

∠RQP = 180° - ∠ROP

∠ROP is given to us 146°

After putting it in the equation above we get ∠RQP = 34°

Therefore x comes out to be 34°.

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-1.5 is the difference in the sequence

An arithmetic sequence is a sequence of numbers where the differences between every two consecutive terms are the same.

The difference is usually called the common difference. For example, the sequence 3, 6, 9, 12 have a common difference of 3 i.e. 6-3 = 3 or 9-6 = 3

Given: the sequence 4.5,3,1.5,0

The difference = 3 - 4.5 = -1.5 or 1.5-3 = -1.5

Note: You can pick any two consecutive terms to get the difference

Therefore, the difference in the sequence is -1.5

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The time taken to reaches its maximum height is 3s.

In the question,

It is given that,

Height, h(t) = [tex]96t - 16t^{2}[/tex]

The maximum value of the function is obtained if the first derivative of the function h (t) = 0.

[tex]\frac{dh(t)}{dt} = 96 - 32t = 0[/tex]

⇒ [tex]t = 3[/tex]

So, time taken to reach its max height is 3 seconds.

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The number of tongue depressors = 56

The number of Band-Aids = 128

What is an equation?

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.

Let x be the number of tongue depressors.

Let y be the number of Band-Aids

Convert cents to dollars

1 cent = $0.01

So, 4 cents = 0.01*4 = $0.04

     8 cents = 0.01* = $0.08

The materials are worth $12.48 .

This means, 0.04x+0.08y=12.48......(1)

There are 184 individual packages in total.

This means,  x+y=184.......(2) => x=184-y.....(3)

Substitute (3) in (1),

0.04(184-y)+0.08y=12.48

7.36-0.04y+0.08y=12.48

=> y= 128

(3) => x=184-128=56

So, the number of tongue depressors = 56

     The number of Band-Aids = 128

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Answer: [tex]\frac{3}{5}[/tex]of the class like blue

Step-by-step explanation:

There are : 40 - 12 - 4 = 24 ( students like blue )

[tex]\frac{24}{40}[/tex]= [tex]\frac{3}{5}[/tex]

The critical points of the given inequality are; x=-6 and x=2

1) When the denominator is equal to zero, at that point, we will have a critical point.

We are given the inequality;

(2x + 5)/(x - 2) ≥ (x - 1)/(x - 2)

Thus, x - 2 = 0

x = 2.

Thus, x = 2 is a critical point

2) Simplify the numerator to get the expression such that p(x) ≥ 0 or p(x) ≤ 0.

Thus, at p(x) = zero, we have other critical point(s)

Multiply both sides by (x - 2) to get;

2x + 5 = x - 1

2x - x = - 1 - 5

x = - 6

Then, the two critical points are x = 2 and x = - 6.

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Answer:

45

Step-by-step explanation:

the pattern adds 3 if you look at it care fully

Answer:

20 units

Step-by-step explanation:

we find the side lengths by looking at the coordinates and just counting up

Sides are 6,4,6,4

So we just add

6+4+6+4

10+10

20

Hopes this helps please mark brainliest

Answer: Your answer is 20 units, because the height is 6 units, and the length is 4 units, so we then multiply by 2 for both numbers, then add them together, having a sum of 20 units.

Hope that helps.

Answer:

  4/3

Step-by-step explanation:

You want the limit as t→1 of (t³+t²-5t+3)/(t³-3t+2).

The fact that each polynomial evaluates to 0 at t=1 tells you that (t-1) is a factor of each. Factoring that out gives ...

  [tex]\dfrac{t^3+t^2-5t+3}{t^3-3t+2}=\dfrac{(t-1)(t^2+2t-3)}{(t-1)(t^2+t-2)}=\dfrac{(t-1)(t-1)(t+3)}{(t-1)(t-1)(t+2)}\\\\=\dfrac{t+3}{t+2}[/tex]

The limit at t = 1 is found by direct substitution:

  lim = (1 +3)/(1 +2) = 4/3

Answer:

G LCM (least common multiple) of 3, 9, and 12. After doing that, find the number that is between 61 and 107.

Step-by-step explanation:

Least common multiple (lcm) is where g finds out the number that can be divided by all the numbers (3, 9, and 12 in this case) and still come out with a whole number.

Answer:

The answer is 55, you can figure this out as each number is increasing by 10

a_n=-5+10n

hope it helps

Answer: dont be rude

Step-by-step explanation:

The values of x and y are -1 and 6 respectively, this forms an ordered pair of (-3,6) and (-1,2).

Given the equation and ordered pair in the question;

Find the y-value by substituting the x-value into the equation and solving for y.

y = 4x + 6

Plug in x = -3

y = 4( -3 ) + 6

y = -12 + 6

y = 6

Find the x-value by substituting the y-value into the equation and solving for x.

y = 4x + 6

Plug in y = 2

2 = 4x + 6

2 - 6 = 4x

-4 = 4x

x = -4/4

x = -1

Therefore, the ordered pair are (-3,6) and (-1,2).

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(I suggest using desmos graphing calculator for the future.)

(0,5) and (4,0) or the one in the left upper corner. Hope this helps.

The correct option regarding the area of the figure is given as follows:

14+16.25π units².

The figure, given with no scale at the end of the answer, is composed by:

The sides of the right-triangle are given as follows:

The area of a right triangle is given by half the multiplication of the sides, hence:

At = 0.5 x 7 x 4 = 14 units.

The radius of the semicircle is half the hypotenuse of the right triangle, hence, applying the Pythagorean Theorem:

h² = 7² + 4²

h = sqrt(7² + 4²)

r = 0.5sqrt(7² + 4²)

r = 4.03 inches.

The area of a semicircle of radius r is:

As = πr².

Hence:

As = π(4.03)² = 16.25 π.

The total area is obtained as the sum of the areas of each separate part, hence:

A = At + As = 14+16.25π units².

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Answer:

Step-by-step explanation:

14+8.125

C

Answer:

D.) 11

Step-by-step explanation:

-9=-k^2-7k+k Plugging in k for x

-9=k^2-6k Combine like terms

0=k^2-6k+9 Add 9 to both sides

0=(k-3)(k-3) Factor

k=3

The equation is now

f(x)=x^2-7x+3

so

f(-1)=(-1)^2-7(-1)+3

f(-1)=1+7+3

f(-1)=11

The budget of KT's Restaurant for newspaper advertising for the coming year is $58,533,500

Given,

The length of advertisement of KT's Restaurant in Vidalia Times in week days = 5,000

The length of advertisement of KT's Restaurant in Vidalia Times in Saturdays = 10,000

The cost of daily column = $27.55 per column inch

The cost of Saturdays = $29.35 per column inch

We have to find the budget of KT's Restaurant for newspaper advertising for the coming year;

Here,

There are approximately 53 Saturdays in a year.

So,

365 - 53 = 312

Then,

The budget of advertisement on daily column = 312 × 5000 × 27.55 = $42,978,000

The budget of advertisement on Saturday column = 53 × 10,000 × 29.35 = $1,555,500

Therefore,

The total budget for advertisement = 42,978,000 + 1,555,500 = $58,533,500

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