What is the radius of a sector when 0+3pi/8 radians and the area is 75pi/16 square units

Step-by-step explanation:

To solve this problem, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = the amount of money Billy will have when the investment ends

P = the principal amount he invested, which is $18,000

r = the annual interest rate, which is 1.5%

n = the number of times the interest is compounded per year, which is monthly or 12 times per year

t = the time period in years, which is 10 years

Plugging these values into the formula, we get:

A = 18000(1 + 0.015/12)^(12*10)

A ≈ $24,134.44

Therefore, Billy will have approximately $24,134.44 when the investment ends.

Billy can calculate his investment with the compound interest formula, using his initial investment amount, the monthly interest rate, and the number of compounding periods in 10 years. Doing so gives an end balance of approximately $20,448.24.

Billy's investment in the CD can be calculated using the compound interest formula, which is A = P (1 + r/n)^(nt). In this formula, A represents the amount of money accumulated after n years, including interest. P is the principal amount (the initial amount of money), r is the annual interest rate (in decimal format), n is the number of times that interest is compounded per year, and t is the time in years that the money is invested for.

Plugging the given values into the formula, we have A = 18000 (1 + 0.015/12)^(12*10). Calculating this expression gives a result of approximately $20,448.24. Therefore, after 10 years, Billy will have approximately $20,448.24 in his CD.

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The numbers arranged in the ascending order is A = 2/5 , 2/3 , 5/7 , 3/4

Given data ,

Let the numbers be represented as A

Now , the value of A is

A = { 2/3 , 3/4 , 5/7 , 2/5 }

On simplifying , we get

The value of 2/3 = 0.67

The value of 3/4 = 0.75

The value of 5/7 = 0.71

The value of 2/5 = 0.4

And , 0.4 < 0.67 < 0.71 < 0.75

Hence , the ascending order is  2/5 , 2/3 , 5/7 , 3/4

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Answer:

23

Step-by-step explanation:

replace x with 2 8×2+7=23

Answer:23

Step-by-step explanation: its actually really simple, all you have to do is replace x for 2, giving you the equation: f(2) = 8x2 + 7 then all you have to do is solve, 8x2 is 16 and 16+7 is 23, and thats how you get the answer.

Answer:

For y = tan(x), there is no horizontal or vertical shift (h = 0, k = 0). The amplitude is not applicable in this case. The frequency is b = 1 and the period is P = π.

For y = cot(x), there is no horizontal or vertical shift (h = 0, k = 0). The amplitude is not applicable in this case. The frequency is b = 1 and the period is P = π.

The margin of error is given as 4.22 mph

Margin of Error = t * (sample standard deviation / √(sample size))

degrees of freedom (df), which is calculated as:

df = n - 1 = 13 - 1 = 12

95% confidence level with 12 degrees of freedom = 2.179.

Margin of Error = t * (s / √n)

Margin of Error = 2.179 * (7 / √13)

Margin of Error ≈ 2.179 * (7 / 3.606)

Margin of Error ≈ 2.179 * 1.939

Margin of Error ≈ 4.22 mph

The margin of error is given as 4.22 mph

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Answer:

1 2/7

Step-by-step explanation:

State that 1 = 7/7

2 2/7 - 7/7

Convert 2 2/7 into improper fraction

= 16/7

=16/7 - 7/7

16 - 7 = 9

= 9/7

Simplify back to mixed fraction

= 1 2/7

The range of h(x)=-4x^2-6x-4 is  (∞, -13).

Using the vertex notion, find the range of the function h(x)=-4x2-6x-4.

The function's vertex is at x = -b/2a,

where a and b are the coefficients of x2 and x, respectively.

Because a = -4 and b = -6 in this situation, the vertex is at x = -(-6)/(2*(-4)) = 3/4.

To find the vertex's y-coordinate, enter x = 3/4 into the function:

h(3/4) = -4(3/4)^2 - 6(3/4) - 4 = -13

As a result, the function's vertex is at (3/4, -13).

Hence, the function's range is (∞, -13).

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The exact values of x and y in the triangles are calculated and listed below

Figure 7

Here, we have

y = √(6² + 1²) --- pythagorean theorem

This gives

y = √37

And, we have

x = √(10² - 6²) --- pythagorean theorem

x = 8

Figure 8

Here, we have

x = 1/2 * 10 --- midsegment of equilateral triangle

This gives

x = 5

And, we have

y = √(10² - 5²) --- pythagorean theorem

y = 5√5

Figure 10

Here, we have

2x = √(6² + 8²) --- pythagorean theorem

2x = 10

x = 5

So, we have

x = y = 5

Figure 11

Here, we have

y = 5

And we have

x = √(13² - 5²) --- pythagorean theorem

x = 12

Figure 13

By similar triangles, we have

x/5 = (x + y)/10

This gives

x = y

So, we have

x = y = 3

Figure 14

By similar triangles, we have

x = 6/3 * 4

x = 8

And then, we have

y = √(6² + 8²) --- pythagorean theorem

y = 10

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Answer:

C

Step-by-step explanation:

The correct equation that represents the relationship between d (the number of dollars Rajindri earns) and t (the amount of time Rajindri works in hours) is: C

The surface area is about 157.08 square feet. use formula for the surface area of a right cylinder  to get answer .

what is surface area ?

Surface area is the measure of the total area that the surface of a three-dimensional object occupies. In other words, it is the sum of the areas of all the faces or surfaces of the object. Surface area is usually measured in square units

In the given question,

The formula for the surface area of a right cylinder is:

S = 2πr² + 2πrh

where r is the radius of the cylinder, h is its height, and π is a mathematical constant approximately equal to 3.14159.

Substituting the given values, we get:

S = 2π(2.5)² + 2π(2.5)(7.5)

S ≈ 2π(6.25) + 2π(18.75)

S ≈ 39.27 + 117.81

S ≈ 157.08

Rounding this to the nearest hundredth, we get:

The surface area is about 157.08 square feet.

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7) The probability of not being dealt a queen is: 12/13

8) The probability of not being dealt a 9 is: 12/13

9) The probability of not being dealt a heart is: 3/4

7) We know that in a standard deck of cards, that we have:

(4 Aces, 4 Kings, 4 Queens, 4 jacks)

Thus, probability of not selecting a queen is:

48/52 = 12/13

8) There are 4 nines in a standard deck of 52 cards. The probability of selecting the first nine is thus: 4/52.

Probability of not being dealt a 9 is: 48/52 = 12/13

9) In a standard deck of 52 cards, we know that there are 4 suits (Clubs, Hearts, Diamonds, and Spades) and there are 13 cards in each suit (Clubs/Spades are black, Hearts/Diamonds are red)

Thus, probability of not being dealt a heart = (52 - 13)/52

= 39/52

= 3/4

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Answer:

Step-by-step explanation:

11.7

Answer:

1 min = 60s

1 h = 60 mins

14277s/60s = 237 mins and 57s = 237.95 mins

237.95mins/60mins = 3 hours 57 mins 57s

= 3.97 h （cor.ti 3 sig fig.）

Answer: 237.95 minutes and 3.97 hours

Step-by-step explanation:

If you have 14,277 seconds and need to convert them into minutes, you can set up the equation 1(minute)/60(seconds) x 14,277(seconds), which equals 237. 95 minutes. To convert into hours, you just take the minutes and set up the equation 1(hour)/60(minutes) x 237.95, which equals approximately 3.966 hours. I assume your asking to convert to seconds was an accident because you started with seconds to begin with.

the probability that all 6 prizes are gift certificates to restaurants is: 0.083.

There are a total of 9 prizes, out of which 7 are gift certificates to restaurants. If 6 prizes are randomly raffled away in the first hour, there are a total of 9 choose 6 possible outcomes, or 84 possible sets of 6 prizes.

The number of outcomes in which all 6 prizes are gift certificates to restaurants is 7 choose 6, or 7 possible sets of 6 gift certificates.

Therefore, the probability that all 6 prizes are gift certificates to restaurants is:

7/84 = 0.0833 or approximately 8.33%

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Step-by-step explanation:

7 m   = - 4.9t^2 + 29.8t + 62       <====solve for 't'

 0 = - 4.9t^2 + 29.8t + 56     <=====  Use Quadrtatic Formula

                                                         with a = - 4.9      b = 29.8      c = 55

     to find t = 7.57 seconds

Answer:

(x+10)/(x+8).

Step-by-step explanation:

(x+5)/(x+8) = (x+5)/(x+8) + (x+5)/(x+1)

= (x+5) + (x+5)/(x+1)

= (x+10)

the limit of (x² - 1)/(x³ - 1) as x approaches 1 is equal to 2/3. got answer by  try substituting x = 1 directly into the expression

what is limit of equation ?

In calculus, the limit of a function is the value that the function approaches as the input (usually denoted by x) approaches a certain value (usually denoted by a). In other words, it describes the behavior of a function as the input value gets closer and closer to a certain point.

In the given question,

To evaluate the limit of (x² - 1)/(x³ - 1) as x approaches 1, we can try substituting x = 1 directly into the expression:

(1² - 1)/(1³ - 1) = 0/0

We cannot determine the limit using direct substitution because we get an indeterminate form of 0/0.

One way to evaluate this limit is to factor the numerator and denominator and cancel out any common factors. We can factor the numerator using the difference of squares formula:

x² - 1 = (x + 1)(x - 1)

We can factor the denominator using the difference of cubes formula:

x³ - 1 = (x - 1)(x² + x + 1)

Canceling out the common factor of (x - 1) in the numerator and denominator, we get:

(x + 1)/(x² + x + 1)

Now we can substitute x = 1 directly into this expression:

(1 + 1)/(1² + 1 + 1) = 2/3

Therefore, the limit of (x² - 1)/(x³ - 1) as x approaches 1 is equal to 2/3.

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The transformation rule used for the diagram is: Shift by 3 units upwards and a shift by 5 units to the left.

There are different methods of transformation such as:

Reflection

Dilation

Rotation

Translation

Now, from the given graph, we see that both objects remain the same size and the object on the right was first if all shifted by 3 units upwards.

Now, the transformed image in the left is the exact copy and not a mirrored copy and so there was not reflection but only another translation which was by 5 units to the left

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2 students to get a grade C and 0 students to get a grade A.

In mathematics , in addition to the mode and median, the mean is one of the measures of central tendency. the mean is the average of the values in the given set. It indicates that values in a particular data set are distributed equally.The total values provided in a datasheet must be added, and the sum must be divided by the total number of values in order to determine the mean.

The relation between a value and a set of values of  mean is described by the statistical measurement is known as the Z-score. Standard deviations from the mean are used to measure Z-score. A Z-score of zero means the data point of  score is the same as the mean score.

We require the distribution of scores in order to estimate the number of students who should earn a given grade. We may determine the z-score for each grade using the mean and standard deviation, presuming that the scores have a normal distribution.

(a) We must locate the z-score equivalent to a C grade in order to establish the number of pupils who should receive a C. Assuming that a C equals a score between 70 and 79, the following formula can be used to determine the z-scores for these values:

(70 - 60) / 5 = 2 is the z-score for 70.

79's z-score is (79 - 60) / 5 = 3.8

We can calculate the percentage of the distribution that falls between these two z-scores using a z-table or a calculator:

P(2 ≤ z ≤ 3.8)

This implies that roughly 4.55% of the students to get a C grade. We can multiply this percentage by the total number of students  Than we get

0.0455 x 35 ≈ 2

therefore,approximately 2 students to get a grade C.

b)  the z-score  to calculate the number of pupils who should receive an grade A. Considering that a grade A of 90 or above 90,Now we can calculate the z-score for 90

than we get .

the z-score for 90 = (90 - 60) / 5 = 6 .

We calculate the percentage of the distribution that lies to the right of this z-score using a z-table or a calculator:

P(z ≥ 6) ≈ 0

therefore,0 students to get a grade A.

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The probability that a card greater than 4 or less than 5 is 1 or 100%

A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.

The probability of picking a card greater than 4 i.e 5 or 6 = 2/3

The probability of picking a card less than 5 i.e

4 = 1/3

Therefore the probability of picking of a card greater than 4 or less than 5 = 2/3 + 1/3 = 3/3

= 1

the total probably is given by 1.

therefore in percentage , it will be 1/1 × 100 = 100%

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84cm³

V= 12 x 7 = 84

volume is always cubed btw

The exponential function that represents the net value of the antique desk is: f(x) = -37 × [tex]0.7027^{x}[/tex]

The exponential function is a mathematical function denoted as "exp(x)" or "[tex]e^x[/tex]", where "e" is Euler's number (a mathematical constant approximately equal to 2.71828) and "x" is the input variable. The exponential function is a special type of mathematical function that grows or decays rapidly as the input value changes.

"Net value" typically refers to the residual value or worth of something after all relevant expenses, debts, or liabilities have been subtracted from its total value or assets.

The table provides values of f(x) for x = 0, 1, 2, 3, 4, and 5. The corresponding values of f(x) are -37, -26, -13, 0, 15, and 32, respectively.

Using the given data, we can create the following exponential function in the form f(x) = a × [tex]b^{x}[/tex], where a and b are constants to be determined:

f(0) = a ×[tex]b^{0}[/tex] = -37

f(1) = a × b¹= -26

f(2) = a × b² = -13

f(3) = a × b³ = 0

f(4) = a × b⁴ = 15

f(5) = a × b⁵ = 32

To find the values of a and b, we can use a system of equations. We can divide the equations f(1) = a × b¹ = -26 by f(0) = a ×b⁰ = -37 to eliminate a:

(-26) / (-37) = b¹ / b⁰

0.7027 ≈ b

Substituting the value of b back into any of the equations, we can solve for a. Using f(0) = a ×b⁰ = -37:

-37 = a × 1

a = -37

So, the exponential function that represents the net value of the antique desk is:

f(x) = -37 × [tex]0.7027^{x}[/tex]

The values are rounded to the nearest whole dollar.

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Answer:

During the first three years Trevor owned the desk, the resale value was less than the cost. Then it exceeded the cost after year 3.

Step-by-step explanation:

See attachment

What is proration?

It's when you only pay for part of something you used.

Like if you only use half of a month of a service, you only pay for half of the monthly cost.y cost.

When is proration used?

When you sign up for a service that you don't use for a full month.

When you change your service in the middle of a billing cycle.

Why is proration used?

To make sure people only pay for what they use.

To be fair and not overcharge people for services they didn't fully use.

chatgpt

Answer:

Step-by-step explanation:

a) This is a minimization problem. The objective is to minimize the daily cost of feed for the horses while meeting their minimum nutritional requirements.

b) Let X1, X2, and X3 represent the number of pounds of oat product, enriched grain, and mineral product, respectively, that the stable owner should feed to the horses daily.

The objective function is:

Minimize 0.8X1 + 0.9X2 + 1.1X3

The constraints are:

Ingredient A: 0.15X1 + 0.20X2 + 0.25X3 >= 2.5

Ingredient B: 0.10X1 + 0.15X2 + 0.05X3 >= 2.0

Ingredient C: 0.05X1 + 0.05X2 + 0.10X3 >= 1.0

Ingredient D: 0.02X1 + 0.04X2 + 0.03X3 >= 0.3

Ingredient E: 0.08X1 + 0.07X2 + 0.06X3 >= 1.4

Non-negativity: X1 >= 0, X2 >= 0, X3 >= 0

c) To set up this problem in Excel, we can create a spreadsheet with the following columns: "Feed Mix," "Ingredient A," "Ingredient B," "Ingredient C," "Ingredient D," "Ingredient E," "Cost per Pound," and "Amount to Feed."

We can then enter the data from the table provided in the problem, and add formulas to calculate the total amount of each ingredient in each feed mix and the total cost of each feed mix based on the amount fed.

Next, we can use Solver to find the optimal mix of feed for the horses. We will set the objective to minimize the total cost of feed, subject to the constraints listed above. Solver should be able to find the optimal values of X1, X2, and X3 that meet the nutritional requirements and minimize the cost of feed.

The measure that is more typical of the data is the Median.

In comparison to the mean, utilizing the median is oftentimes a more suitable option when analyzing data sets with significant outliers or extreme values.

As these likely cause an aberrant affect on the mean, it can provide an unreliable measure of central tendency; without being subject to anomalies, the median serves as a more reliable gauge of the typical salary. Here, the Median proves significantly less than the Mean, reaffirming its superiority in cases involving considerable disparities.

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a) n = 4148

b) n = 2449

The sample size for proportion:

Given that,

E = 2% = 0.02

c = 99% = 0.99

Using the z table,

= 2.576 for 99% confidene level.

Using the z-table, search for 0.9950 probability and see where is 0.9950 cumulative probability nearly and then see the corresponding z value.

Step 2/2

a)

Here p is unknown.

In this case, take p = 0.5

n =  4147.36

= 4148

b Here, p = 18% = 0.18

Now,

n =  2448.601344

= 2449

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The measures of the central and circumscribed angles are :

m ∠EFG=83∘, m ∠GCE=97∘

The correct option is (b)

There are two tangents on the circle C at the point E and G.

m ∠EFG=(3x+11)∘, and m ∠GCE=(5x−23)∘

Now, We have to find the measures of the central and circumscribed angles.

The line joining the center of circle to the point on circle on which there is a tangent, make an angle of 90° with the tangent itself.

∠CGF = ∠CEF = 90° ( G and F are the points on circle's tangent drawn from point F.)

Now, we can see that CGFE is a quadrilateral.

And sum of all internal angles of a quadrilateral is equal to 360°

∠C + ∠G + ∠F + ∠E = 360°

(5x - 23) + 90 + 3x + 11 + 90 = 360

=> 8x - 12 + 180 = 360

8x - 12 = 360 - 180

8x = 180 + 12

=> x = 24°

m ∠EFG = (3x + 11)°

m ∠EFG = (3× 24 + 11)° = 83°

m ∠GCE=(5x−23)∘

m ∠GCE = (5 × 24 −23)∘

m ∠GCE = 97°

The correct option is (b)

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For complete question , to see the attachment.

a) The minimum sample size required is 45.

b) The population mean could be within 10% of the sample mean, but less likely that it could be within 11% of the sample mean.

(a) How to determine the minimum sample size?

To determine the minimum sample size required to construct a 90% confidence interval for the population mean with a margin of error of 1.5 years, we use the formula n = (z ×σ / E)²

where n is the sample size, z is the z-score for the desired confidence level (in this case, 1.645 for a 90% confidence level), σ is the population standard deviation (1.8 years), and E is the margin of error (1.5 years).

Substituting the given values,

n = (1.645 × 1.8 / 1.5)² = 6.67² = 44.5

Rounding up to the nearest whole number, the minimum sample size required is 45.

(b) Using the minimum sample size of 45 with a 90% confidence level, the margin of error is 1.5 years. Therefore, the 90% confidence interval for the population mean is:

20 - 1.5 ≤ μ ≤ 20 + 1.5

18.5 ≤ μ ≤ 21.5

To determine whether it is likely that the population mean could be within 10% or 11% of the sample mean, we need to calculate the ranges of values that correspond to these percentages of the sample mean,

10% of 20 = 2

11% of 20 = 2.2

The range of values that are 10% of the sample mean is 20 ± 2 = 18 to 22

The range of values that are 11% of the sample mean is

20 ± 2.2 = 17.8 to 22.2

Comparing these ranges to the 90% confidence interval for the population mean, we see that:

The range of values that are 10% of the sample mean (18 to 22) is completely within the 90% confidence interval (18.5 to 21.5), so it is likely that the population mean could be within 10% of the sample mean.

The range of values that are 11% of the sample mean (17.8 to 22.2) extends slightly beyond the 90% confidence interval, so it is less likely that the population mean could be within 11% of the sample mean.

Therefore, we can conclude that it is likely that the population mean could be within 10% of the sample mean, but less likely that it could be within 11% of the sample mean.

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