The Vilas County News earns a profit of $20 per year for each of its 3,000 subscribers. Management projects that the profit per subscriber would increase by 1¢ for each additional subscriber over the current 3,000. How many subscribers are needed to bring a total profit of $123,525?

The statistical questions for this problem are given as follows:

A question is classified as statistical if it can receive answers of data that vary, that is, questions that do not have an exact answer.

When the answer is exact, it must be composed by a set of data, such as the number of students that like football in each school, the number will vary for each school.

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The number of units that need to be sold for the company to make a profit of $ 100, 000 would be 140, 000 units.

The number of units to sell to make break even is 120, 000 units.

The breakeven point is:

Breakeven Point (in units) = Total Fixed Costs / Contribution Margin per Unit

This means that the breakeven point can be found to be :

= 600, 000 / ( 20 - 15 )

= 600, 000 / 5

= 120, 000 units

The units to sell to make a profit of $ 100, 000 would be:

= ( 600, 000 + 100, 000 ) / 5

= 140, 000 units

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\(~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$10000\\ P=\textit{original amount deposited}\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &4 \end{cases}\)

\(10000=P\left(1+\frac{0.05}{4}\right)^{4\cdot 4} \implies 10000=P(1.0125)^{16} \\\\\\ \cfrac{10000}{(1.0125)^{16}}=P\implies 8197.46\approx P\)

The rate at which the distance between the car and the truck is changing when the car is 9 m from the intersection and the truck is 40 m from the intersection is about 19.187 m/s

The rate of change of a function is an indication of how fast the function's output changes per unit change in the input of the function.

Let y represent the distance of the car from the intersection, and let x represent the distance of the truck from the intersection, we get;

The distance between the car and the truck, d, can be obtained from Pythagorean Theorem as follows;

d² = y² + x²

2·d·d/dt = 2·y·dy/dt + 2·x·dx/dt

dy/dt = The speed of the car = 48 km/h = 40/3 m/s

dx/dt = The speed of the truck = 60 km/h = 50/3 m/s

y = The distance of the car from the intersection = 9 m

x = The distance of the truck from the intersection = 40 m

d² = 9² + 40² = 1681

d = √(1681) = 41

d = 41 m

Therefore;

2×41×d/dt = 2×9 × 40/3 + 2 × 40 × 50/3 = 4720/3

d/dt = 4720/3/(2 × 41) = 2360/123 ≈ 19.187

d/dt ≈ 19.187 m/s

The rate of change distance between the car and the truck d/dt is about 19.187 m/s

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Answer:

Before a variable there is no coefficient.

There is an invisible 1 infront bc there is no real number. so the 1 appears.

The number of standard deviations from the mean that include all

data values is two.

From the gathering of information, we will see that the minimum worth is $19.95 and also the most worth is $29.95. So , we would like to seek out the amount of normal deviations, let's decision it "a" , such that\(\overline x $\color \ - a\cdot\sigma \le 19.95}\) and   \(\overline x $\color \ +a\cdot\sigma \geq 29.95}\)

Use the given values of mean  \(\overline x\) and normal deviation (σ) to notice the worth of "a".

         \(\overline x $\color \ - a\cdot\sigma \le 19.95}\\25.07\ - 2.62a \leq 19.95\\5.12\leq 2.62a\\1.9541\leq a\)

On rounding off we get a = 2

Checking another inequality

         \(\overline x $\color \ + a\cdot\sigma \geq 29.95}\\25.07 \ + 2(2.62) \geq 29.95\\25.07 + 5.24 \geq 29.95\\30.31\geq 29.95\)

Thus , 2 standard deviation include the all values from the given set of data .

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The term that can be added to the list so that the greatest common factor of the three terms  12h3 36h3, 12h6, is 48h5

A group of numbers' greatest common factor (GCF) is the biggest factor that all the numbers have in common. For instance, 12, 20, and 24 all share two characteristics.

The term that  can fit in to the list so the GCF is 12h3 would be 48h5, this is so because 48 is first divisible by 12  without any  fraction, and we can remove upon dividing 3 h's from this term as it contains a total of 5 h's.

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Answer:

3.45

Step-by-step explanation:

you have to do tihis then that

Answer:

348 calories

Step-by-step explanation:

1 oz=116÷8=14.5

24oz=14.5×24=348

The area of the rectangle with a length of 12 units and a width of 8 units is 96 sqaure units.

A rectangle is a 2-dimensional shape with parallel opposite sides equal to each other and four angles are right angles.

The area of a rectangle is expressed as;

Area = length × breadth

From the image:

Length of the rectangle = 12 units

Breadth of the rectangle = 8 units

Area of the rectangle = ?

Plug the given values into the above formula and solve for the area:

Area = length × breadth

Area = 12 units × 8 units

Area = 96 sqaure units

Therefore, the measure of the area is 96 sqaure units.

Option A) 96 sqaure units is the correct answer.

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Answer:

b=2a/h

Step-by-step explanation:

The correct answer is B. Readmitting states when 10 percent of the electorate took a loyalty oath.

Explanation:

The election of Abraham Lincoln as the President of the U.S. motivated states of the South to secede from the United States and began the Civil War, which was influenced by the slavery issue. In this context, one of the purposes of Lincoln was to end slavery and re-integrate states of the South.

This was possible only at the end of the Civil War. Moreover, the plan Lincoln implement was known as the Ten percent plan and involved the 10% of the people who could vote in a state (electorate) needed to take a loyalty oath or declare complete loyalty and support to the U.S. government for the state to be admitted in the U.S. again.

Answer:

The answer to your question is "B" and/or the second option "readmitting states when 10% of the electorate took a loyalty oath"...

Step-by-step explanation:

I already took the test and I got this question right! Hope this helps :)

Answer:

t = 21

Step-by-step explanation:

The ball strikes the groujd when h = 0.

\(-3.2t^2 + 54.4t+268.8=0 \\ \\ 32t^2 - 544t-2688=0 \\ \\ t^2 - 17t-84=0 \\ \\ (t-21)(t+4)=0 \\ \\ t=-4, 21\)

Since time must be positive, t = 21.

Answer:

yes

Step-by-step explanation:

you can simplify 5/15 by dividing the numerator and denominator by 5. when you do that, you get 1/3

Answer: yes 5/15 and 1/3 is equivalent

Step-by-step explanation: 5/15 =0.333333333333 and 1/3=0.333333333333

The two angles are related in that they are supplementary angles

Supplementary angles would add tuo to 180 degrees according to the angle Theorem.

Adding the two given angles :

These angles are supplementary

The angles aren't vertical in that , vertical angles should have the same vertex. Complementary angles on the other hand add to 90 degrees. While the angles doesn't share the same side, hence, they aren't adjacent.

Hence, the angles are related as they are supplementary angles .

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The solution of the equations 6x = 52 − 2y and 5x + 7y = 70 by elimination method will be (7, 5).

In other words, the collection of all feasible values for the parameters that satisfy the specified mathematical equation is the convenient storage of the bunch of equations.

The equations are given below.

6x = 52 - 2y

6x + 2y = 52

3x + y = 26                   ...1

5x + 7y = 70

(5/7)x + y = 10              ...2

Subtraction equation 2 from equation 1, then we have

3x - (5/7)x = 26 - 10

(16/7)x = 16

x = 7

Then the value of 'y' is given as,

3(7) + y = 26

21 + y = 26

y = 5

The solution of the equations 6x = 52 − 2y and 5x + 7y = 70 by elimination method will be (7, 5).

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Answer:

Increasing a number by 5% and then by 20% is the same as increasing the original number by 26%.

Step-by-step explanation:

Take a number, x.

Now increase it by 5%.

1.05x

Now increase it by 20%.

1.2 * 1.05x = 1.26x

1.26x = 126% of x = 100% of x + 26% of x

100% of x is the same as x, so it is the same as the original x.

The increase is 26% of the original number.

Increasing a number by 5% and then by 20% is the same as increasing the original number by 26%.

Answer:

x = 11

Step-by-step explanation:

3/x+1=2/x-3

Solve by using cross products

2 (x+1) = 3 (x-3)

Distribute

2x+2 = 3x-9

Subtract 2x

2x+2-2x = 3x-2x-9

2 = x-9

Add 9 to each side

2+9 =x-9+9

11 =c

Answer:

f(x) = x³ - 4x + 6

f'(x) = 3x² - 4

a) f'(2) = 3(2²) - 4 = 12 - 4 = 8

6 = 8(2) + b

6 = 16 + b

b = -10

y = 8x - 10

b) 3x² - 4 = 0

3x² = 4, so x = ±2/√3 = ±(2/3)√3

= ±1.1547

f(-(2/3)√3) = 9.0792

f((2/3)√3) = 2.9208

c) 3x² - 4 = 8

3x² = 12

x² = 4, so x = ±2

f(-2) = (-2)³ - 4(-2) + 6 = -8 + 8 + 6 = 6

6 = -2(8) + b

6 = -16 + b

b = 22

y = 8x + 22

f(2) = 6

y = 8x - 10

The equation perpendicular to the tangent is y = -1/8x + 25/4

-The smallest slope on the curve is 2.92

The curve has the smallest slope at the point (1.15, 2.92)

The equations at tangent points are y = 8x + 16 and  y = 8x - 16

From the question, we have the following parameters that can be used in our computation:

y = x³ - 4x + 6

Differentiate

So, we have

f'(x) = 3x² - 4

The point is (2, 6)

So, we have

f'(2) = 3(2)² - 4

f'(2) = 8

The slope of the perpendicular line is

Slope = -1/8

So, we have

y = -1/8(x - 2) + 6

y = -1/8x + 25/4

We have

f'(x) = 3x² - 4

Set to 0

3x² - 4 = 0

Solve for x

x = √[4/3]

x = 1.15

So, we have

Smallest slope = (√[4/3])³ - 4(√[4/3]) + 6

Smallest slope = 2.92

So, the smallest slope is 2.92 at (1.15, 2.92)

Here, we set f'(x) to 8

3x² - 4 = 8

Solve for x

x = ±2

Calculate y at x = ±2

y = (-2)³ - 4(-2) + 6 = 6: (-2, 0)

y = (2)³ - 4(2) + 6 = 6: (2, 0)

The equations at these points are

y = 8x + 16

y = 8x - 16

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Answer:

81

Step-by-step explanation:

Given data:

mean μ = 70.

standard deviation σ, 9.6.

P(Z < 1.123) = 0.13

z = 1.13

Use the z-score formula,

x = z×σ +μ

Substitute the values in the above equation.

x = 1.13 9.6 + 70 = 81

The minimum score required for an A grade is = 81

Statistical significance is achieved when the outcome is highly unlikely to happen by chance. The practical significance concerns whether conventional treatment makes a difference enough to justify its use. It is possible for a treatment to be statistically significant, but not practical. The correct answer is d.

Given testing new treatments and the difference between statistical and practical significance.

Statistical hypothesis testing is used to determine if the results of a data set are statistically significant. The difference in statistical significance  can be very small.

Statistical significance (reject the null hypothesis) is achieved when the outcome is not likely to occur.

But practical significance means determining whether the difference between samples is significant enough to be of actual significance/meaning simply by common sense.

While statistical significance is concerned with whether or not an effect exists, actual significance is concerned with the magnitude of the effect. However, there is no statistical test that can tell you whether the impact is large enough to matter in your field of study.  Possibly statistically significant but not practical.

Therefore, statistical significance is achieved when the outcome is highly unlikely to happen by chance. Although practical significance is achieved when there is a general perception that the treatments make a large enough difference, the results may be statistically significant but not in practice.

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The solution to the equations are b = 15, b = 22, c = 21 and n = 28

From the question, we have the following equations that can be used in our computation:

31 - b = 16

28 + b = 50

33 + c = 54

52 - n = 24

Next, we collect the like terms in each of the equation

This gives

b = 31 - 16

b = 50 - 28

c = 54 - 33

n = 52 - 24

Lastly, we evaluate the like terms

b = 15

b = 22

c = 21

n = 28

The above are the solutions to the equations

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Question

Solve the following equations:

31 - b = 16

28 + b = 50

33 + c = 54

52 - n = 24

Answer:

1.1667

Step-by-step explanation:

Slope = change in y / change in x

Slope  = (-6 - -6) / (-7 - 7)

Slope = 0/-14

Because the change in y is 0 the slope would be 0

Slope = 0

The measure of side n is √(m^2 - 64).

According to the given question.

We have a right angle triangle.

Here, we have to find the measure n.

Since, the given triangle is divided into two right angle triangles.

Now in the right angled triangle with the side measure m, n and 8.

By the Pythagoras theorem we can say that

m^2 = 8^2 + n^2

⇒ m^2 = 64 + n^2

⇒ m^2 -64 = n^2 ...(i)

⇒ n = √(m^2 - 64)

Hence, the measure of side n is √(m^2 - 64).

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Answer:

1. CYNARG

Step-by-step explanation:

This a example of Caesar's Cipher, in which each letter in the original word leads to a ciphered letter according to the following equation:

\(C = (P + o) \text{mod} 26\)

In which C is the index of the Ciphered letter in the alphabet, P is the index of the original letter and o is the offset.

Finding the offset:

O is coded B

O is the 15th letter in the alphabet, so \(P = 15\).

B is the 2nd letter in the alphabet, so \(C = 2\)

\(C = (P + o) \text{mod} 26\)

\(2 = (15 + o) \text{mod} 26\)

\(|o = |2-15| \text{mod} 26\)

\(o = 13\)

So

\(C = (P + 13) \text{mod} 26\)

PLANET:

P

P is the 16th letter in the alphabet.

\(C = (16 + 13) \text{mod} 26 = 3\)

So P is coded C.

L

L is the 12th letter in the alphabet:

\(C = (12 + 13) \text{mod} 26 = 25\)

L is coded Y(25th letter in the alphabet)

A

A is the 1st letter in the alphabet

\(C = (1 + 13) \text{mod} 26 = 14\)

A is coded N

N

N is the 14th letter in the alphabet

\(C = (14 + 13) \text{mod} 26 = 1\)

N is coded A

E

E is the 5th letter in the alphabet

\(C = (5 + 13) \text{mod} 26 = 18\)

E is coded R

So the correct answer is:

1. CYNARG