8. Calculate the average of the numbers 20, 19.2 and 21.5.

The intersection points of the lines in discuss form coinciding lines and hence, the two equations form a system with infinitely many solutions.

The solution (infinitely many solutions) in this case means the runners are at the same place at any point in time.

A system of linear equations in which case the solution is such that the system has infinitely many solutions indicates that the graph of the linear equations coincide.

Ultimately, in the context of the runners in discuss, it follows that the runners are at the same distance from the starting line at every instance of time.

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Kanoi and Ale'a can weed the same garden together in 22.22 minutes

Rate of work refers to amount to of work completed at a given time

Information from the question include

Kanoi can weed a garden in 40 minutes

Kanoi's rate = 1/40 per minute

Ale'a can weed the same garden in 50 minutes

Ale'a rate = 1/50 per minute

When both are working together the rate will be

1/40 per minute + 1/50 per minute

= 9/200 per minute

The time is solved

1 / 9/200

= 200/9

= 22.2222 minutes

= 22.22 minutes to the nearest hundredth

The time it will take both of them to weed is 22.22 minute

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Answer:

36%

Step-by-step explanation:

Step-by-step explanation:

Loss percentage= loss/cost× 100%

250-180=70

70/180=0.3888

0.3888×100%=39%

To find the value of N, we need the future value of the retirement fund. If you provide the desired future value, I can calculate the exact value of N.

To find the value of N, we need to calculate the number of monthly deposits Sam made for his retirement fund over 20 years.

Sam deposited $1000 every month for 20 years, which is a total of 20 x 12 = 240 deposits. Each deposit has a compounded interest rate of 5% per year, compounded monthly.

The formula to calculate the future value of a series of monthly deposits is given by:

FV = P * [(1 + r)^n - 1] / r

Where:

FV is the future value of the investment,

P is the monthly deposit amount,

r is the monthly interest rate, and

n is the number of deposits.

In this case, P = $1000, r = 5% / 12 = 0.05 / 12 = 0.00417 (monthly interest rate), and FV is the value of the retirement fund after 20 years.

By rearranging the formula, we can solve for n:

n = log((FV * r) / (P * r + FV)) / log(1 + r)

Plugging in the values, we get:

n = log((FV * 0.00417) / (1000 * 0.00417 + FV)) / log(1 + 0.00417)

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Step-by-step explanation:

To determine the constant of proportionality (k) in a proportional relationship, we need to compare corresponding values of x and y and calculate the ratio between them.

Let's examine the given values:

2. UX: x 6 15 9 y 42 200

To find the constant of proportionality (k), we can take any pair of corresponding values and calculate their ratio. Let's choose the first pair: (6, 42).

k = y / x

k = 42 / 6

k = 7

So, the constant of proportionality (k) is 7.

Now, let's find the missing values for the second set of values:

d. X: 14 y: 21 6 15 3 7 8

Since we know the constant of proportionality is 7, we can calculate the missing values of y by multiplying each corresponding x value by 7.

Missing values for y:

- For x = 21, y = 21 * 7 = 147

- For x = 6, y = 6 * 7 = 42

- For x = 15, y = 15 * 7 = 105

- For x = 3, y = 3 * 7 = 21

- For x = 7, y = 7 * 7 = 49

- For x = 8, y = 8 * 7 = 56

Therefore, the missing values of y are: 147, 42, 105, 21, 49, and 56.

Step-by-step explanation:

To work out the height of the cuboid, we need to use the formula:

Volume = Length x Width x Height

We have been given the volume and the length, so we can substitute those values into the formula:

540 = 6 x Width x Height

Now we need to convert the width from millimeters to centimeters, so we divide it by 10:

150mm ÷ 10 = 15cm

Substituting this value into the formula:

540 = 6 x 15 x Height

Simplifying:

540 = 90 x Height

Dividing both sides by 90:

6 = Height

Therefore, the height of the cuboid is 6cm.

Answer:

(4,0)

Step-by-step explanation:

You basically are plotting a point on the positive number 4 on the x line. Since they're only asking for an X and not a Y, you'd leave it as (4,0). Hope this helps!

Answer:

C

D

Step-by-step explanation:

C. It is in quadrant I and III

D. It is a hyperbola

Answer:

8

Step-by-step explanation:

By using the trigonometric identities we get  ∅ = 0.5542.

The six trigonometric ratios serve as the foundation for all trigonometric equations. Sine, cosine, tangent, cosecant, secant, and cotangent are some of their names. The sides of the right triangle, such as the adjacent side, opposite side, and hypotenuse side, are used to describe each of these trigonometric ratios.

The given figure is a right-angled triangle.

We can use trigonometric identities,

Sin∅ =\(\frac{adjacent }{hypotenuse}\)

Here we get the value adjacent = 10 and the hypotenuse = 19

Therefore we get the value,

sin∅ = \(\frac{10}{19}\) = 0.5263

∅ = \(sin^{-1} (0.5263)\)

∅ = 0.5542

Therefore the angle ∅ = 0.5542

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The firm's federal income tax is $57,168.

To calculate the firm's federal income tax, we need to determine its taxable income first. Taxable income is calculated by subtracting deductions from the firm's total income.

In this case, the firm's total income consists of income from operations, interest income, and dividend income.

Total income:

Income from operations = $231,000

Interest income = $23,100

Dividend income = $29,700

Total income = $231,000 + $23,100 + $29,700 = $283,800

Next, we deduct expenses from the total income. In this case, the only relevant expense is the interest paid to bondholders:

Total expenses = Interest paid to bondholders = $11,000

Taxable income = Total income - Total expenses = $283,800 - $11,000 = $272,800

Now, we can calculate the federal income tax by applying the federal tax rate of 21% to the taxable income:

Federal income tax = Taxable income * Federal tax rate

Federal income tax = $272,800 * 0.21 = $57,168

Therefore, the firm's federal income tax is $57,168.

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Answer:

y=7

x°=15°

Step-by-step explanation:

First we see that there is a equilateral triangle (all angles and also sides should be equal to each other) meaning that 4y=28, which simplifies to y=7

Additionally, we can see that one of the acute angles of the equilateral triange is complementary with the 2x° angle, so 2x°+(the acute angle)=90°

Since the triangle is equilateral each angle must be equivalent and since there is only 180° in a triangle each angle is 180°/3=60°

so 2x°+(60°)=90°

simplify for x°

2x°=30°

x°=15°

Answer:

See below

Step-by-step explanation:

Using the two pairs of (a, p) to determine the function:

The function would be:

Slope is:

p-intercept:

So the function is:

(a)

(b) Slope is negative, indicating the lower probability at greater age. P-intercept of 120.5 is of the non-real case as for zero age it gives more than 100% probability.

(c) The domain needs restriction in line with law, so minimum age and maximum to be determined in order not to have unrealistic outcome. It should be ok between 18 and 48.

(d) The values at given points:

Refer to the images attached. Now I am guessing when it says "use geometry" was to graph it? I wasn't completely sure. I attached how I would normally evaluate that problem and a graph of the piecewise function. It has been a while since I have dealt with integrating piecewise function, please let me know what process you were supposed to use if you figure it out. Hope this helps you a bit, have a good one!

Answer:

B) n = 6

Step-by-step explanation:

4n + 12 = 8n - 12

Combine like terms

24 = 4n

n = 6

Answer: 6

Step-by-step explanation:

set 4n+12 and 8n-12 equal to each other and you should get 6

(A) The required down payment is $48,000.

(B) The amount of the mortgage is $192,000.

(C) Monthly payment = $192,000 * (0.085/12) * (1 + (0.085/12))^(3012) / (((1 + (0.085/12))^(3012)) - 1)

(a) To find the required down payment, we need to calculate 20% of the house price.

Down payment = 20% of $240,000

Down payment = 0.2 * $240,000

Down payment = $48,000

The required down payment is $48,000.

(b) The amount of the mortgage is equal to the total cost of the house minus the down payment.

Mortgage amount = Total cost of the house - Down payment

Mortgage amount = $240,000 - $48,000

Mortgage amount = $192,000

The amount of the mortgage is $192,000.

(c) To find the monthly payment for the mortgage, we can use the formula for the monthly payment on a fixed-rate mortgage:

Monthly payment = P * r * (1 + r)^n / ((1 + r)^n - 1)

Where:

P = Principal amount (mortgage amount)

r = Monthly interest rate (8.5% annual interest divided by 12 months and converted to a decimal)

n = Total number of monthly payments (30 years multiplied by 12 months)

Monthly payment = $192,000 * (0.085/12) * (1 + (0.085/12))^(3012) / (((1 + (0.085/12))^(3012)) - 1)

Using this formula and performing the calculation will give you the monthly payment amount.

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Answer:

Kay bought 18 more cookies than Carmen

Step-by-step explanation:

bc 5 times 18 is 90 and 3 times 36 is 108

The simplification will give;

Here, we want to make a simplification

We proceed as follows;

As we can see, the power of 9 and 7 are not perfect squares since they are odd

Thus, we have the expression as;

According to laws of indices;

Answer:

x = 27 , ∠ EAF = 27°

Step-by-step explanation:

∠ GAF = 90° , then

∠ GAC + ∠ CAF = ∠ GAF , that is

x + 63 = 90 ( subtract 63 from both sides )

x = 27

∠ DAE = 90°

since CD is a straight angle of 180° , then

∠ CAE = 90° , so

∠ CAF + ∠ EAF = ∠ CAE , that is

63° + ∠ EAF = 90° ( subtract 63° from both sides )

∠ EAF = 27°

Probability when one card is drawn from a deck of cards

1. P ( not ace)=6/13

2. P(red)=1/2

3. P(red and ace)=1/26

These probabilities are for a standard deck of 52 playing cards, with 4 suits (hearts, diamonds, clubs, and spades) each containing 13 cards (Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King).

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First let's find the value of g(x):

The functions f(x) and g(x) are different, so they have different graphs.

The difference between the functions it that the function g(x) is the function f(x) translated by two units to the left.

The calculated measure of m∠PNM is 87 degrees

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

The circle

Where, we have

PM = 360 - 64 - 122

Evaluate

PM = 174

Next, we have

m∠PNM = 1/2 * 174

So, we have

m∠PNM = 87

Hence, the measure of m∠PNM is 87 degrees

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The solution of the system is x = -5, and y = 3.

One or many equations having the same number of unknowns that can be solved simultaneously are called simultaneous equations. And the simultaneous equation is the system of equations.

We have the system of equations,

y = -2x -7  {equation 1}

2y -x = 1   {equation 2}

Substituting the value of y from equation 1 to equation 2,

we get,

2(-2x -7) - x = 1

-4x -14 -x = 1

-5x = 15

x = -5, and y = 3.

Therefore, the solution is x = -5, and y = 3.

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Answer:

\(y=\frac{5}{4} x\)+17

Step-by-step explanation:

Okay for this you take the point (-8+7) and plug it into the equation getting you this 7=\(\frac{5}{4}\)(-8)+b

If you multiple \(\frac{5}{4\\}\) by -8 you get -10

You then add -10 to the other side to get 17

that means 17=b

meaning you get \(y=\frac{5}{4} x\)+17 by plugging in 17 to b

The confidence level in this report of survey of student atheletes concerning their gambling-related behaviors is equals to 87.88%.

The confidence interval when calculated with the two tails methods then it can be used to test the two tail hypothesis for the same parameter provided that the confidence level. We have, National Collegiate Athletic Association (NCAA) take a survey of randomly selected student athletes concerning their gambling-related behaviors.

repoted participation of students, x = 3547

Sample size,n = 5594

Margin of error, E = 1% = 0.01

The sample proportion is a number of successes divided by the sample size, p-cap = 3547/5594

= 0.6341

The margin of error is for a confidence interval for a proportion, which is determined by using the following formula is

\(CL = Zα/₂ \sqrt{ \frac{ \hat{p} \: (1- \hat{p})}{n} }\)

= Zα/₂√(1 - 0.6341)0.6341/5594

= 0.0064 Zα/₂

This margin of error also has to be equal to 1% or

0.0064 Zα/₂ = 0.01

=> Zα/₂ = 0.01/0.0064 ~ 1.55

The confidence level is the probability of obtaining this value or less extreme, determine the probability using z- table,

P(-1.55< Z < 1.55) = P(Z < 1.55) - P(Z < -1.55)

= 0.9394 - 0.0606 = 0.8788 = 87.8

Thus the confidence level is 87.88%.

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Answer:

The general solution to this differential equation is \(P(t) = \frac{Ke^{kt} + h}{k}\)

Step-by-step explanation:

We are given the following differential equation:

\(\frac{dP}{dt} = kP - h\)

Solving by separation of variables:

\(\frac{dP}{kP-h} = dt\)

Integrating both sides:

\(\int \frac{dP}{kP-h} = \int dt\)

On the left side, by substitution, u = kP - h, du = kDp, Dp = du/k. Then

\(\frac{1}{k} \ln{kP-h} = t + K\)

In which K is the constant of integration.

\(\ln{kP-h} = kt + K\)

\(e^{\ln{kP-h}} = e^{kt + K}\)

\(kP - h = Ke^{kt}\)

\(kP = Ke^{kt} + h\)

\(P(t) = \frac{Ke^{kt} + h}{k}\)

The general solution to this differential equation is \(P(t) = \frac{Ke^{kt} + h}{k}\)

Answer:

3.2 because 16 divided by 5 is 3.2

Sorry my handwriting is so bad!!

Answer:

3.2

Step-by-step explanation:

16/5

   3.2

5)16

 -15

    10

    -10

       0

Answer:

1 ale 2 no se 3 saca de tu mente 4

The result is 16, which matches the information given in the problem. Thus, our solution is correct. Thao originally had 30 coins.

Let's solve this problem step by step.

Let's assume the number of coins Thao originally had is x.

According to the problem, Thao gives two fifths of her coins to her sister. Two fifths of x can be represented as (2/5)x.

After giving away two fifths of her coins, Thao receives 4 coins for her birthday. So, the number of coins she has now is (2/5)x + 4.

The problem states that she now has 16 coins. Therefore, we can set up the following equation:

(2/5)x + 4 = 16

To solve for x, we need to isolate x on one side of the equation. We can start by subtracting 4 from both sides:

(2/5)x = 16 - 4

(2/5)x = 12

To get rid of the fraction, we can multiply both sides of the equation by 5:

5 * (2/5)x = 5 * 12

2x = 60

Next, divide both sides of the equation by 2 to solve for x:

(2x)/2 = 60/2

x = 30

Therefore, Thao originally had 30 coins.

To verify our answer, we can substitute x = 30 back into the equation (2/5)x + 4 and see if it equals 16:

(2/5) * 30 + 4 = 12 + 4 = 16

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Answer:

45-32 = 13 / 32 *100= 40.625 round to the nearest percent is 41%

Step-by-step explanation: Brainlest plzzz