PLEASE HELP ME APSPPPPP!!!!!!!!!

Answer:

The circumference of a circle is given by the formula:

C = πd

where C is the circumference, d is the diameter, and π is a mathematical constant approximately equal to 3.14.

In this case, the diameter of the circle is given as 12.5 cm.

Substituting this value into the formula, we get:

C = π(12.5)

C = 39.25 cm

Therefore, the circumference of the circle is 39.25 cm.

Hence, the answer is 39.25 cm.

a) The zero rates for the five maturities are: 1 year is 2.01%, 2 years is 2.48%, 3 years is 2.77%, 4 years is 1.73%, and 5 years is 4.32%.

b) The price of the security is $128.31.

a) To find the zero rates for all 5 maturities, we can use the formula for the present value of a bond:

PV = C / [tex](1+r)^n[/tex]

where PV is the present value,

C is the coupon payment,

r is the zero rate, and

n is the number of years to maturity.

We can solve for r by rearranging the formula:

r = [tex](C/PV)^{(1/n) }[/tex]- 1

Using the bond data given in the question, we can calculate the zero rates for each maturity as follows:

For the 1-year bond, PV = 98 and C = 0, so r = 2.01%.

For the 2-year bond, PV = 101, C = 2.48, and n = 2, so r = 2.48%.

For the 3-year bond, PV = 103, C = 2.91, and n = 3, so r = 2.77%.

For the 4-year bond, PV = 101, C = 2, and n = 4, so r = 1.73%.

For the 5-year bond, PV = 103, C = 5, and n = 5, so r = 4.32%.

Alternatively, we can use linear algebra to find the zero rates. We can write the present value equation in matrix form:

PV = A × x

where A is a matrix of coefficients, x is a vector of unknowns (the zero rates), and PV is a vector of present values.

To solve for x, we can use the equation:

x = ([tex]A^{-1}[/tex]) x PV

where ([tex]A^{-1}[/tex]) is the inverse of matrix A.

Using this method, we can solve for the zero rates as follows:

[2.01% ]

[2.48% ]

[2.77% ] = x

[1.73% ]

[4.32% ]

PV = [tex]A^{-1}[/tex] x  [98]

                   [101]

                   [103]

                   [101]

                   [103]

PV =   [-0.0201]

          [ 0.0248]

          [ 0.0277]

          [-0.0173]

          [ 0.0432]

b) To find the price of the security which pays cash flows of $10 in one year, $25 in two years, and $100 in four years, we can use the formula for the present value of a series of cash flows:

PV = [tex]C1/(1+r)^1 + C2/(1+r)^2 + C3/(1+r)^4[/tex]

where PV is the present value, C1, C2, and C3 are the cash flows, r is the zero rate, and the exponents correspond to the number of years until each cash flow is received.

Using the zero rates calculated in part (a), we can calculate the present value of each cash flow:

PV1 = $10 /(1+2.01 % [tex])^1[/tex] = $9.80

PV2 = $25/(1+2.48%[tex])^2[/tex] = $22.15

PV3 = $100/(1+1.73%[tex])^4[/tex] = $81.36

Then, the price of the security is the sum of the present values:

PV = $9.80 + $22.15 + $81.36 = $128.31

Therefore, the price of the security is $128.31.

For similar question on price of the security

https://brainly.com/question/29245385

#SPJ11

1.  The radius of V is approximately 14.04 meters.2.The circumference of V is approximately 88.24 meters. 3.mST arc is  26.85 degrees. 4.the length of ST arc is approximately 6.61 meters. 5.34.69 meters. 6.88.24m.

In geometry, a sector is a part of a circle enclosed by two radii and an arc. Essentially, a sector is a slice of a circle. The two radii that form the sector are equal in length and share a common endpoint, which is the center of the circle. The arc of the sector is a portion of the circumference of the circle and its length is proportional to the measure of the central angle that it subtends.

We can use the given information to solve for the following:

1. Radius of V:

The area of a circle is given by the formula A = πr². We are given the area of V as 624.36 square meters, so we can solve for the radius r as:

A = πr²

624.36 = πr²

r² = 624.36/π

r ≈ 14.04 meters

Therefore, the radius of V is approximately 14.04 meters.

2. Circumference of V:

The circumference of a circle is given by the formula C = 2πr. Using the radius we just found, we can solve for the circumference of V as:

C = 2πr

C = 2π(14.04)

C ≈ 88.24 meters

Therefore, the circumference of V is approximately 88.24 meters.

3. mST arc:

The area of the sector SVT is given as 64.17 square meters. The area of a sector is given by the formula A = (θ/360)πr², where θ is the central angle of the sector in degrees. We are not given the value of θ, but we can solve for it as:

A = (θ/360)πr²

64.17 = (θ/360)π(14.04)²

θ ≈ 26.85 degrees

Therefore, the central angle of the sector SVT is approximately 26.85 degrees, and mST arc is also 26.85 degrees.

4. Length of ST arc:

The length of an arc of a circle is given by the formula L = (θ/360)C, where θ is the central angle of the arc in degrees, and C is the circumference of the circle. We can use the values we have already calculated to solve for the length of ST arc as:

L = (θ/360)C

L = (26.85/360)(88.24)

L ≈ 6.61 meters

Therefore, the length of ST arc is approximately 6.61 meters.

5. Perimeter of shaded region (sector):

The perimeter of a sector is the sum of the length of the arc and the lengths of the two radii that form the sector. Using the values we have already calculated, we can solve for the perimeter of the shaded sector as:

Perimeter = L + 2r

Perimeter = 6.61 + 2(14.04)

Perimeter ≈ 34.69 meters

Therefore, the perimeter of the shaded region (sector) is approximately 34.69 meters.

6. Perimeter of unshaded region (remaining circle part):

The perimeter of a circle is given by the formula C = 2πr. Using the radius we previously calculated, we can solve for the perimeter of the unshaded region as:

Perimeter = 2πr

Perimeter = 2π(14.04)

Perimeter ≈ 88.24 meters

Therefore, the perimeter of the unshaded region (remaining circle part) is approximately 88.24 meters.

To know more about length visit:

https://brainly.com/question/29141691

#SPJ1

a) The probability of a given woman in this age group having a cholesterol level less than 200mg/dl is 6.68%.

b) The probability of a given woman in this age group having a cholesterol level more than 200mg/dl is 93.32%.

c) The probability of a given woman in this age group having a cholesterol level between 190mg/dl and 210mg/dl is 15.87%.

d) If a woman in this age group has a cholesterol level higher than 230mg/dl, it is considered high and puts her at risk of heart disease

To calculate the probability of a given woman in this age group having a cholesterol level less than 200mg/dl, we need to find the z-score first. The z-score is the number of standard deviations that a given value is from the mean. The formula to calculate the z-score is:

z = (x - μ) / σ

where x is the given value, μ is the mean, and σ is the standard deviation.

For a cholesterol level of 200mg/dl, the z-score is:

z = (200 - 230) / 20 = -1.5

We can then use a z-table or calculator to find the probability of a z-score being less than -1.5, which is 0.0668 or approximately 6.68%.

Next, to find the probability of a given woman in this age group having a cholesterol level more than 200mg/dl, we can use the same process but subtract the probability of a z-score being less than -1.5 from 1 because the total probability is always 1.

So, the probability of a given woman in this age group having a cholesterol level more than 200mg/dl is:

1 - 0.0668 = 0.9332 or approximately 93.32%.

Finally, to find the probability of a given woman in this age group having a cholesterol level between 190mg/dl and 210mg/dl, we need to find the z-scores for both values.

For a cholesterol level of 190mg/dl, the z-score is:

z = (190 - 230) / 20 = -2

For a cholesterol level of 210mg/dl, the z-score is:

z = (210 - 230) / 20 = -1

We can then use the z-table or calculator to find the probability of a z-score being between -2 and -1, which is 0.1587 or approximately 15.87%.

Finally, a brief report on the guidance that you would give a woman having high cholesterol levels in this age group is:

It is essential to make lifestyle changes such as eating a healthy diet, exercising regularly, quitting smoking, and managing stress to lower cholesterol levels.

To know more about probability here

https://brainly.com/question/11234923

#SPJ4

Answer:

  $9.50

Step-by-step explanation:

You want Suzie's hourly rate on Saturday if she babysat for 3.5 hours on Friday, earning 8.50 per hour, and for 4.5 hours on Saturday, earning a total of 72.50 from both jobs.

For (hours, rates) of (h1, r1) and (h2, r2), Suzie's total earnings for the two jobs are ...

  earnings = h1·r1 +h2·r2

Filling in the known values, we can find r2:

  72.50 = 3.5·8.50 +4.5·r2

  72.50 = 29.75 +4.5·r2 . . . . . . . simplify

  42.75 = 4.5·r2 . . . . . . . . . . . subtract 29.75

  9.50 = r2 . . . . . . . . . . . . divide by 4.5

Suzie earned $9.50 per hour on Saturday.

__

Additional comment

The steps of the "multistep" problem are ...

Effectively, these are the steps to solving the equation we wrote.

Answer:

1. y = 4x + 2

2.  y = 3x – 7

3. y = 7x + 6

4. y= 2x + 8

Step-by-step explanation:

1. y = 4x + 2

2.  y = 3x – 7

3. y = 7x + 6

4. y= 2x + 8

These 4 equations have a positive slope because remember in the equation (y=mx+b) m = slope and since these equations have positive numbers in the m spot the slope of these equations are positive.

The given information describes the measures of two angles, A and B. Angle A is represented as ∠A and has a measure of 6x-2 degrees. Angle B is represented as ∠B and has a measure of 4x+48 degrees. These measures are respectively shown in the colors #11accd and #28ae7b.

The question gives us two equations, one for angle A and one for angle B, in terms of x. We will have to solve for x and then find the measure of angle A.

To solve for x, we can set the expressions for ∠A and ∠B equal to each other and solve for x

∠A = ∠B

6x - 2 = 4x + 48

Subtracting 4x from both sides we get

2x - 2 = 48

Adding 2 to both sides we get

2x = 50

Dividing by 2 we get

x = 25

Now that we have found the value of x, we can substitute it into the expression for ∠A

∠A = 6x - 2

∠A = 6(25) - 2

By multiplying 6 with 25 we get

∠A = 150 - 2

By Subtracting we get

∠A = 148

Hence, the measure of angle A is 148 degrees.

To know more about information here

https://brainly.com/question/29043744

#SPJ4

The function which has range (2, ∞) is,

D) y = 5ˣ + 2

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Now, For a function: y = 5ˣ

Range is,

⇒ ( 0 , + ∞ )

And, we have:

y = 5ˣ + 2 ,

which is translated 2 units up.

So, the range is ( 2, + ∞ ).

Hence, The function which has range (2, ∞) is,

D ) y = 5ˣ + 2

Learn more about the function visit:

https://brainly.com/question/11624077

#SPJ5

The value of "a" is approximately 1.83 given that the absolute value of the difference of the two roots of the quadratic equation "ax squared plus 5x minus 3 equals 0" is the square root of 61 divided by 3, and "a" is positive.

We are given that the absolute value of the difference between the two roots of the quadratic equation "ax squared plus 5x minus 3 equals 0" is the square root of 61 divided by 3, and "a" is positive. We need to find the value of "a".

Let the two roots of the equation be r1 and r2, where r1 is not equal to r2. Then, we have:

|r1 - r2| = √(61) / 3

The sum of the roots of the quadratic equation is given by r1 + r2 = -5 / a, and the product of the roots is given by r1 × r2 = -3 / a.

We can express the difference between the roots in terms of the sum and product of the roots as follows:

r1 - r2 = √((r1 + r2)² - 4r1r2)

Substituting the expressions we obtained earlier, we have:

r1 - r2 = √(((-5 / a)²) + (4 × (3 / a)))

Simplifying, we get:

r1 - r2 = √((25 / a²) + (12 / a))

Taking the absolute value of both sides, we get:

|r1 - r2| = √((25 / a²) + (12 / a))

Comparing this with the given expression |r1 - r2| = √(61) / 3, we get:

√((25 / a²) + (12 / a)) = √(61) / 3

Squaring both sides and simplifying, we get:

25 / a² + 12 / a - 61 / 9 = 0

Multiplying both sides by 9a², we get:

225 + 108a - 61a² = 0

Solving this quadratic equation for "a", we get:

a = (108 + √(108² + 4 × 61 × 225)) / (2 × 61)

Since "a" must be positive, we take the positive root:

a = (108 + √(108² + 4 × 61 × 225)) / (2 × 61) ≈ 1.83

Therefore, the value of "a" is approximately 1.83.

Learn more about absolute value at

https://brainly.com/question/1301718

#SPJ4

The question is -

Given that the absolute value of the difference of the two roots of the quadratic equation "ax squared plus 5x minus 3 equals 0" is the square root of 61 divided by 3, and "a" is positive, what is the value of "a"?

Answer:

[tex]y=5-2x[/tex]

Step-by-step explanation:

You have to give the equation in the form [tex]y=mx+c[/tex], where m is the gradient and c is the y-intercept (where the line crosses the y-axis).

From the graph, we can see the line crossed the y-axis at (0,5), so the y-intercept is (0,5), which means c is 5.

We can work out the gradient with the two points (2,1) and (1,3) by doing:

[tex]\frac{change in y}{change in x} =\frac{1-3}{2-1}=-2[/tex]
So the gradient of the line, m, is -2.

Thus the equation of the line is [tex]y=5-2x[/tex].

1. x = 4.7 for f(x) and x = 25 for g(x), f(x) reaches 50 first.

2. x = 9.7 for f(x) and x = 50 for g(x), f(x) reaches 100 first.

1. Which function reaches 50 first?

To answer this, we need to solve for x in each function when the output is 50:

For f(x): 50 = 10x + 3

47 = 10x

x = 4.7

For g(x): 50 = 2x

x = 25

Since x = 4.7 for f(x) and x = 25 for g(x), f(x) reaches 50 first.

2. Which function reaches 100 first?

Similarly, we'll solve for x in each function when the output is 100:

For f(x): 100 = 10x + 3

97 = 10x

x = 9.7

For g(x): 100 = 2x
x = 50

Since x = 9.7 for f(x) and x = 50 for g(x), f(x) reaches 100 first.

for such more question on word problem

https://brainly.com/question/21405634

#SPJ11

Answer:

[tex] \sqrt{7y} ( \sqrt{27y} + 5 \sqrt{12y} )[/tex]

[tex] \sqrt{7y} ( \sqrt{9} \sqrt{3y} + 5 \sqrt{4} \sqrt{3y} )[/tex]

[tex] \sqrt{7y} (3 \sqrt{3y} + 10 \sqrt{3y} )[/tex]

[tex]13 \sqrt{7y} \sqrt{3y} [/tex]

[tex]13y \sqrt{21} [/tex]

If you are given a sample percentage of 43%, you would need to know the sample size in order to convert this percentage to a proportion.

The conversion formula is proportion = percentage/100. However, the proportion alone does not give information about the sample size, which is necessary for inference and hypothesis testing. The other statements are not true.

The test statistic is not affected by the sample size, but its value can be used to determine the significance of a hypothesis test. A larger p-value indicates weaker evidence against the null hypothesis, not stronger evidence. Finally, we assume the null hypothesis is true until we have sufficient evidence to reject it.

Learn more about percentage:

https://brainly.com/question/24304697

#SPJ11

The probability that the mean clock life would be less than 13.6 years in a sample of 40 wall clocks is 0.1337

The probability that the mean clock life would be less than 13.6 years in a sample of 40 wall clocks can be calculated using the t-distribution since the population variance is unknown. The formula for t-distribution is:

t = (x-bar - μ) / (s / √n)

where x-bar is the sample mean, μ is the hypothesized population mean (14 years), s is the sample standard deviation (the square root of the sample variance), and n is the sample size (40).

Using the given variance, we can calculate the sample standard deviation as √16 = 4. Plugging in the values, we get:

t = (13.6 - 14) / (4 / √40) = -1.118

Using a t-distribution table with degrees of freedom (df) = n - 1 = 39, we find that the probability of getting a t-value less than -1.118 is 0.1337. Therefore, the probability that the mean clock life would be less than 13.6 years in a sample of 40 wall clocks is 0.1337 (rounded to four decimal places).

Learn more about probability

https://brainly.com/question/24756209

#SPJ4

Given statement "We conduct a test of hypothesis by assuming that ha is correct, since that is the hypothesis we are trying to show is true." is true. Because we start by assuming that the null hypothesis is correct, not the alternative hypothesis, when conducting a test of the hypothesis.

When conducting a test of hypothesis, we do not assume that Ha (the alternative hypothesis) is correct.

Instead, we begin by assuming that the null hypothesis (H0) is true.

The null hypothesis typically represents a statement of "no effect" or "no difference" between two groups or variables.

The alternative hypothesis (Ha) represents the statement we are trying to prove or gather evidence for but we must start with the assumption that the null hypothesis is correct.

State the null hypothesis (H0) and the alternative hypothesis (Ha).

The null hypothesis typically represents the status quo or a baseline assumption, while the alternative hypothesis represents the claim you want to prove or gather evidence for.

Determine the level of significance (α), which is the probability of rejecting the null hypothesis when it is actually true. Common significance levels are 0.05, 0.01, and 0.001.

Select an appropriate test statistic, which depends on the type of data and the hypothesis being tested. Examples include the t-test, chi-square test, and ANOVA.

Collect data and calculate the value of the test statistic based on the data.

Compare the calculated test statistic value to the critical value for the chosen level of significance.

If the test statistic is more extreme than the critical value, we reject the null hypothesis in favor of the alternative hypothesis.

Otherwise, we fail to reject the null hypothesis.

Hence, the statement is false.

For similar question on hypothesis.

https://brainly.com/question/27170372

#SPJ11

The cardholder will pay an additional $1,471.66 in interest by making monthly payments of $200 until the balance is paid off instead of paying off the current balance in full.

First, we need to calculate the total interest that will accrue on the current balance of $4,528.34. We can do this using the formula

Interest = Balance x (APR/12)

where APR is the annual percentage rate and is divided by 12 to get the monthly interest rate. Plugging in the values, we get:

credit card Interest = $4,528.34 x (22.99%/12) = $87.80

So the total interest that will accrue on the current balance is $87.80.

Next, we need to calculate how long it will take to pay off the balance by making monthly payments of $200. We can use a credit card repayment calculator to do this, but we'll use a simplified formula here

Months = -log(1 - (Balance x (APR/12))/Payment) / log(1 + (APR/12))

where Payment is the monthly payment amount. Plugging in the values, we get

Months = -log(1 - ($4,528.34 x (22.99%/12))/$200) / log(1 + (22.99%/12)) = 29.6 months

So it will take about 30 months (or 2.5 years) to pay off the balance by making monthly payments of $200.

Finally, we can calculate how much more the cardholder will pay in total by subtracting the current balance from the total amount paid over 30 months

Total amount paid = $200 x 30 = $6,000

Total interest paid = $6,000 - $4,528.34 = $1,471.66

Learn more about Credit card interest here

brainly.com/question/29641204

#SPJ4

Using probability, there is only one outcome that represents rolling an odd number and landing on blue.

What exactly is probability?

Probability is a measure of the possibility or chance that an event will occur. It is represented by a number between 0 and 1, with 0 representing an improbable occurrence and 1 representing a certain event. A given event's probability is estimated by dividing the number of favourable outcomes by the total number of potential possibilities. Probability theory is frequently used to analyse and forecast the likelihood of occurrences in domains such as statistics, physics, economics, and finance.

Now,

The probability of rolling an odd number is 3/6, which can be simplified to 1/2. The probability of landing on blue= 1/3. Since the events of rolling an odd number and landing on blue are independent, we can multiply the probabilities to find the probability of both events occurring:

(1/2) × (1/3) = 1/6

So, there is only one outcome that represents rolling an odd number and landing on blue. The answer is 1.

To know more about probability visit the link

brainly.com/question/30034780

#SPJ1

Step-by-step explanation:

Use Pythagorean theorem to find the base of the right triangle

221^2 = 195^2 + b^2

b = 104 km

triangle area = 1/2 base * height =  1/2 * 104 * 195 = 10140 km^2

Now multiply by the height to find volume

10140 km^2  * 15 km  = 152100 km^3

Sue works 5 out of 7 days a week, which implies that she has two days off. We need to discover how numerous conceivable plans there are for her to work on Tuesday or Friday or both.

There are two cases to consider:

1. Sue works on Tuesday as it were, Friday as it were, or both Tuesday and Friday.

2. Sue does not work on Tuesday or Friday.

For the primary case, there are three conceivable outcomes:

1. Sue works on Tuesday as it were and has Friday off.

2. Sue works on Friday as it were and has Tuesday off.

3. Sue works on both Tuesdays and Fridays.

For the moment case, there are two conceivable outcomes:

1. Sue works on one of the other 5 days of the week and has both Tuesday and Friday off.

2. Sue has Tuesday and Friday off.

In this manner, there are added up to 3 + 2 = 5 conceivable plans for Sue to work on Tuesday or Friday or both. 

To know more about possible schedules for the week refer to this :

https://brainly.com/question/23689163

#SPJ4

The graphical representation that is best and most appropriate for the data is Box plot, because the median can easily be determined from the large set of data. That is option A.

The box plot is a type of graphical representation of data that gIves more than one detail about the data set such as;

Box plots allow you to compare multiple data sets better than others dues to the above listed features that it has.

Learn more about histogram here:

https://brainly.com/question/28164315

#SPJ1

An airline passenger is planning a trip with three connecting flights from airports A, B, and C.

The least total amount of time the passenger must spend between flights, assuming all flights keep to their schedules, is 55 minutes.

This occurs when the passenger takes the first flight from airport A at 8:00 a.m., arriving at airport B at 10:30 a.m., catches the second flight from airport B at 10:40 a.m., arriving at airport C at 11:50 a.m., and then takes the third flight from airport C at 12:45 p.m.

Learn more about airline:

https://brainly.com/question/29579489

#SPJ11

Answer:sasa

Step-by-step explanation:

The number of batches of pancakes made by Hugo using 3 cups of milk is equal to 9 batches.

Number of cups of milk used by Hugo for each batch =  1/3 cup of milk ,

The total amount of milk used for b batches would be,

Total milk = (1/3) × b

The total milk used was 3 cups,

Substitute the value in the equation we have,

⇒ (1/3) × b = 3

Solve for b we get,

Multiply both sides of the equation by the reciprocal of 1/3,

Reciprocal of ( 1/3 ) = 3/1 or simply 3

⇒ (1/3) × b × 3 = 3 × 3

⇒ b = 9

Therefore, Hugo made 9 batches of pancakes.

Learn more about batches here

brainly.com/question/856537

#SPJ4

The above question is incomplete, the complete question is:

Hugo made a bunch of batches of pancakes for his summer camp. For each batch, Hugo used 1/3 cup of milk. Hugo used a total of 3 cups of milk. Let b represent the number of batches Hugo made . Find the value of b?

The number of hamburgers sold on Sunday was 89

Let's assume that the number of hamburgers sold on Sunday was x.

According to the problem, the number of cheeseburgers sold was three times the number of hamburgers sold.

Therefore, the number of cheeseburgers sold can be expressed as 3x.

The total number of hamburgers and cheeseburgers sold was 356.

Therefore, we can write an equation to represent this information:

x + 3x = 356

Simplifying the left-hand side of the equation, we get:

4x = 356

Dividing both sides by 4, we get:

x = 89

Therefore, the number of hamburgers sold on Sunday was 89, and the number of cheeseburgers sold was 3 times that, or 267.

Read more about ratio at

https://brainly.com/question/21003411

#SPJ1

Answer: 2(n6)

And true states are

The two operations are mulitplication and substraction

The constants are 2 and 6

The expression is written as  2(n-6)

Step-by-step explanation:

Answer:

A,C,D,E should be correct.

A. Replace “a number” with the variable, n.

C. The two operations are multiplication and subtraction.

D. The constants are 2 and 6.

E. The expression is written as 2(n – 6).

hope this helped!

Answer: Of the two numbers you provided, +3 is greater than -7. So, +3 is the most upper of the two numbers.

Answer: +3

Step-by-step explanation: Positive 3 is greater than negative 7. Therefore, +3 is the greater value.

Since a side of the triangle below has been extended to form an exterior angle of 67°, the value of x is equal to 52°.

In Mathematics, the exterior angle theorem or postulate can be defined as a theorem which states that the measure of an exterior angle in a triangle is always equal in magnitude (size) to the sum of the measures of the two remote or opposite interior angles of that triangle.

By applying the exterior angle theorem, we can reasonably infer and logically deduce that the sum of the measure of the two interior remote or opposite angles in the given triangle is equal to the measure of angle x (∠x);

∠y + 67° = 180°

∠y = 180° - 67°

∠y = 113°

∠x = 180° - (15° + 113°)

∠x = 52°

Read more on exterior angle theorem here: brainly.com/question/28034179

#SPJ1

Answer:

Step-by-step explanation:

y = abx

a is the y-intercept

y = 16bx

Now substitute 2 for x and 1296 for y

1296 = 16(b)2

81 = b2

b = 9

y = 16(9)x

Answer: -37.5

Step-by-step explanation: You can simply do this in the calculator by doing 3 times -12.5. the parenthesis is a sign to multiply

Answer:

the answer is -75/2= - 37.5

Approximately 0.357 or 35.7% of customers require more than 12 minutes to check out.

Since the checkout times are exponentially distributed with a mean of 5.5 minutes, we can use the exponential distribution formula to find the probability that a customer will take more than 12 minutes to check out:

P(X > 12) = 1 - P(X ≤ 12)

where X is the checkout time.

To find P(X ≤ 12), we can use the cumulative distribution function (CDF) of the exponential distribution, which is:

F(x) = 1 - e^(-λx)

where λ is the rate parameter of the distribution. For an exponential distribution with mean μ, the rate parameter λ is equal to 1/μ.

So, in our case, λ = 1/5.5 = 0.1818, and we can calculate P(X ≤ 12) as:

P(X ≤ 12) = F(12) = 1 - e^(-0.1818 × 12) ≈ 0.643

Therefore, the probability that a customer will take more than 12 minutes to check out is:

P(X > 12) = 1 - P(X ≤ 12) ≈ 1 - 0.643 ≈ 0.357

To learn more about statistics click on,

https://brainly.com/question/15291758

#SPJ4