whats pi the math number

Answer:

Step-by-step explanation:

area of shaded region=area of whole region-area of white space

=9×13-5×[13-(3+2)]

=117-5×8

=117-40

=77 m²

According to Pythagorean theorem:

To find the missing length of the leg we'll convert the equation:

Simplify:

\(\large\bf{\underline{\underline{\mathfrak{Question}:}}}\)

The hypotenuse of a right triangle has a length of 14 units and side that is 9 units long. which equation can be used to find the length of the remaining side?

\(\large\bf{\underline{\underline{\mathfrak{Solution}:}}}\)

To solve the problems of a right angle triangle we commonly used Pythagoras theorem. It is the most widely used theorem which helps in finding the missing length of a right angle triangle.

According to Pythagoras theorem, the sum of square of base and the square of perpendicular give us square of hypotenuse.

\(:{\Longrightarrow{\large{\rm{H^2=P^2+B^2}}}}\)

In a right angle triangle there are two legs and a hypotenuse.

Given that,

\({:\Longrightarrow{\small{\rm{Hypotenuse\:of\:a\:right\:triangle=14\:units.}}}}\)

\(:{\Longrightarrow{\small{\rm{A\:side\:of\:a\:right\:triangle=9\:units.}}}}\)

By putting these values in the Pythagoras theorem we get;

\(:{\Longrightarrow{\small{\rm{14^2=9^2+B^2}}}}\)

Let B = x

\(:{\Longrightarrow{\small{\rm{196=81+x^2}}}}\)

\(:{\Longrightarrow{\small{\rm{196-81=x^2}}}}\)

\(:{\Longrightarrow{\small{\rm{115=x^2}}}}\)

\(:{\Longrightarrow{\small{\rm{\sqrt{115}=x}}}}\)

a) The range is 14.

b) The sample variance is 20.78.

c) The sample standard deviation is 4.56.

a) Range

The range of a given set of data values is the difference between the maximum and minimum values in the set. In this case, the maximum value is 15 and the minimum value is 1. So, the range is:

Range = maximum value - minimum value

Range = 15 - 1

Range = 14

b) Sample variance

To calculate the sample variance, follow these steps:

1. Calculate the sample mean (X). To do this, add up all of the data values and divide by the total number of values:

n = 9

∑x = 7 + 4 + 6 + 12 + 8 + 15 + 1 + 9 + 13 = 75

X = ∑x/n = 75/9 = 8.33

2. Subtract the sample mean from each data value, square the result, and add up all of the squares:

(7 - 8.33)² + (4 - 8.33)² + (6 - 8.33)² + (12 - 8.33)² + (8 - 8.33)² + (15 - 8.33)² + (1 - 8.33)² + (9 - 8.33)² + (13 - 8.33)² = 166.23

3. Divide the sum of squares by one less than the total number of values to get the sample variance:

s² = ∑(x - X)²/(n - 1) = 166.23/8 = 20.78

Therefore, the sample variance is 20.78 (rounded to two decimal places).

c) Sample standard deviation

To calculate the sample standard deviation, take the square root of the sample variance:

s = √s² = √20.78 = 4.56

Therefore, the sample standard deviation is 4.56 (rounded to two decimal places).

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The probability that the wedding planner will have too many pollotarian meals is 0.998.

To calculate this, we can use the binomial probability formula. The binomial probability formula is used to calculate the probability of obtaining a certain number of successes in a certain number of trials. In this case, the number of trials is the total number of guests, and the number of successes is the number of guests who are pollotarian.

The formula is: P(x) =\(nCx * p^x * (1-p)^(n-x)\), where n is the number of trials, x is the number of successes, and p is the probability of success.In this case, n = 300, p = 0.03, and x = 9. Plugging these numbers into the formula, we get: P(x) = \(300C9 * 0.03^9 * (1-0.03)^(300-9)\) = 0.998.

Therefore, the probability that the wedding planner will have too many pollotarian meals is 0.998, or 99.8%.

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9514 1404 393

Answer:

  4.3 in

Step-by-step explanation:

The Law of Cosines is applicable when you have two sides and the angle between them. The third side satisfies ...

  f² = d² + e² -2de·cos(F)

  f² = 6.4² + 7.8² -2·6.4·7.8·cos(33°) ≈ 18.0671

  f ≈ √18.0671 ≈ 4.2505

The length of f is about 4.3 inches.

Robert, Juan, Susan, and Linda scored above the mean, Joel scored on the mean, and Jan scored below the mean on the advanced first aid course's final exam based on their z-score. Their final exam scores were 172, 184, 190, 150, 166, and 182, respectively.

The students with positive z-scores scored above the mean. So, Robert, Juan, Susan, and Linda scored above the mean. The student with a z-score of 0.00 scored on the mean. So, Joel scored on the mean. The student with a negative z-score scored below the mean. So, Jan scored below the mean.

To find the final exam score for each student, we can use the formula:

z = (x - m) / s

where z is the z-score, x is the final exam score, m is the mean score, and s is the standard deviation.

Rearranging the formula, we get:

x = z * s + m

Using the given values of z, s, and m, we can find the final exam score for each student:

Robert: x = 1.10 * 20 + 150 = 172

Juan: x = 1.70 * 20 + 150 = 184

Susan: x = 2.00 * 20 + 150 = 190

Joel: x = 0.00 * 20 + 150 = 150

Jan: x = 0.80 * 20 + 150 = 166

Linda: x = 1.60 * 20 + 150 = 182

So, the final exam scores for Robert, Juan, Susan, Joel, Jan, and Linda are 172, 184, 190, 150, 166, and 182, respectively.

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The percent yield is calculated as the ratio of the actual yield to the theoretical yield, multiplied by 100.

Percent yield is a measure of how efficient a chemical reaction or process is in producing the desired product.

The formula for percent yield is:

Percent Yield = (Actual Yield / Theoretical Yield) * 100

The actual yield is the amount of product obtained from the reaction or process, typically measured in grams or moles. It represents the actual amount of product obtained in the laboratory.

The theoretical yield, on the other hand, is the maximum amount of product that can be obtained based on stoichiometry and other factors. It is calculated using balanced chemical equations and the starting amounts of reactants.

By dividing the actual yield by the theoretical yield and multiplying by 100, we get the percent yield, which is expressed as a percentage.

This value provides insight into the efficiency of the reaction or process, with a higher percent yield indicating a more efficient conversion of reactants into products.

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To calculate the volume of a rectangular box, you multiply the lengths of its sides.

In this case, the given box has sides measuring 7 inches, 9 inches, and 13 inches. Therefore, the volume can be calculated as:

Volume = Length × Width × Height

Volume = 7 inches × 9 inches × 13 inches

Volume = 819 cubic inches

So, the volume of the given box is 819 cubic inches. The formula for volume takes into account the three dimensions of the box (length, width, and height), and multiplying them together gives us the total amount of space contained within the box.

In this case, the box has a volume of 819 cubic inches, representing the amount of three-dimensional space it occupies.

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Answer:

7

Step-by-step explanation:

rate of change of function not necessary mean linear, it can be the slope of a tangent line.

a: y=8x+3    slope = 8

b: rate of change: 1

8-1=7

I wish this is true...

It could be slightly lower or higher, but we can be confident that it falls somewhere between 0.32 minutes and 1.47 minutes.

The most accurate interpretation of the given confidence interval is as follows:

We are 95% confident that the true difference in mean wait time between Facility A and Facility B falls within the range of 0.32 minutes to 1.47 minutes.

This means that if we were to repeat the study multiple times and calculate a new confidence interval each time, we would expect that approximately 95% of those intervals would contain the true difference in mean wait time between the two facilities.

Furthermore, based on the observed data and the calculated confidence interval, we can conclude that the difference in mean wait time between Facility A and Facility B is likely to be positive, with Facility B having a higher mean wait time than Facility A. However, we cannot say with certainty that the true difference is exactly within this specific range; it could be slightly lower or higher, but we can be confident that it falls somewhere between 0.32 minutes and 1.47 minutes.

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Answer:

Step-by-step explanation:

y-3 = 6(x-9)

A box with a square base and a top is to be constructed from 10 square meters of material. 40 square meters will maximize the volume that the box can hold.

LSD use among secondary school understudies is a specific concern. More Volume is a proportion of consumed three-layered space. It is frequently evaluated mathematically utilizing SI inferred units or by different supreme units. Volume is characterized as the space involved inside the limits of an article in three-layered space. It is otherwise called the limit of article. Volume is a proportion of consumed three-layered space. It is frequently measured mathematically utilizing the SI determined unit, the cubic meter. The volume of a compartment is by and large comprehended to be the limit of the compartment, how much liquid (gas or fluid) that the holder could hold, instead of how much space the actual holder dislodges. Three layered numerical shapes are additionally relegated volumes.

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a) The probability that a battery does not reach the milestone in its first 8 hours of usage is 0.014 or 1.4%. b)  The probability of this goal being met is 0.002 or 0.2%. c) The smallest value of n that satisfies P(X >= 10) > 0.01 is n = 13.

(a) To calculate the probability that a battery does not reach the milestone in its first 8 hours of usage, we need to calculate the area under the normal curve to the right of 8 hours. We can use the standard normal distribution to do this by first standardizing the value of 8 hours using the formula:

z = (x - mu) / sigma

where x is the value of 8 hours, mu is the mean of the distribution (7.36 hours), and sigma is the standard deviation (0.29 hours). Substituting these values, we get:

z = (8 - 7.36) / 0.29 = 2.21

Using a standard normal table or a calculator, we can find that the area to the right of z = 2.21 is approximately 0.014.

(b) We want to find the probability that at least 10 batteries out of a pack of 12 last until 7.5 hours of usage. This is a binomial distribution with n = 12 and p = the probability that a single battery lasts until 7.5 hours.

To find p, we can use the standard normal distribution again by standardizing the value of 7.5 hours:

z = (7.5 - 7.36) / 0.29 = 0.48

Using a standard normal table or a calculator, we can find that the area to the right of z = 0.48 is approximately 0.316. Therefore, the probability that a single battery lasts until 7.5 hours is 0.316.

Now we can use the binomial distribution formula to calculate the probability that at least 10 batteries out of 12 last until 7.5 hours:

P(X >= 10) = 1 - P(X < 10)

where X is the number of batteries that last until 7.5 hours, and P(X < 10) is the cumulative probability of 9 or fewer batteries lasting until 7.5 hours. Using a binomial calculator or a standard normal table, we can find that:

P(X < 10) = 0.998

Therefore, P(X >= 10) = 1 - 0.998 = 0.002 or 0.2%.

(c) We want to find the smallest value of n such that the probability of at least 10 batteries out of n lasting until 7.5 hours is greater than 1%. This is equivalent to finding the smallest n such that:

P(X >= 10) > 0.01

Using a binomial calculator or a standard normal table, we can find that:

P(X < 10) = 0.989 when n = 10

P(X < 10) = 0.970 when n = 11

P(X < 10) = 0.942 when n = 12

Therefore, the smallest value of n that satisfies P(X >= 10) > 0.01 is n = 13.

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Your question is incomplete, but probably the complete question is :

Suppose that a brand of AA batteries reaches a significant milestone to their death on average after 7.36 hours, with standard deviation of 0.29 hours. Assume that when this milestone occurs follows a normal distribution.

(a) Calculate the probability that a battery does not reach this milestone in its first 8 hours of usage.

(b) Suppose that the company wants to sell a pack of n batteries of which (at least) 10 will last until 7.5 hours of usage. If n 12, what is the probability of this goal being met?

(c) How many batteries n should be in the package in order for the probability to exceed 1%? Give the smallest number n which works.

Answer:

B=28

Step-by-step explanation:

Answer:

A = 10W - W²

Step-by-step explanation:

Perimeter of a rectangle = 2(L+W)

Area of a rectangle =LW

L is the length

W is the width

Given

Perimeter = 20m

20 = 2 (L+W)

10 = L+W

L = 10 - W ....2

Substitute equation 2 into the formula for calculating the area

Recall that A = LW

A = (10-W)W

A = 10W - W²

Hence the area of the rectangle as a function of the length of ones its side is expressed as A = 10W - W²

Based on the given information, the correct statement is: The area of the rectangle is twice the area of the shaded triangle.

The shaded triangle is a part of the rectangle, as indicated by the given dimensions of 10 in. and 4 in. The shaded triangle is formed by one of the shorter sides of the rectangle and a diagonal line connecting the opposite corner of the rectangle to the midpoint of that shorter side.

Since the area of the rectangle is given by the formula length × width, the area of the rectangle is 10 in. × 4 in. = 40 square inches.

On the other hand, the area of the shaded triangle is given by the formula 1/2 × base × height, where the base is the length of the shorter side of the rectangle (4 in.) and the height is the length of the longer side of the rectangle (10 in.) divided by 2, since the triangle only occupies half of the height of the rectangle.

So, the area of the shaded triangle is 1/2 × 4 in. × (10 in./2) = 1/2 × 4 in. × 5 in. = 10 square inches.

Comparing the area of the rectangle (40 square inches) to the area of the shaded triangle (10 square inches), we can see that the area of the rectangle is indeed twice the area of the shaded triangle. Therefore, the correct statement is "The area of the rectangle is twice the area of the shaded triangle."

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There are 11 questions worth 5 points and 3 questions worth 15 points.

To find the correct number of questions:

Let, 5-point questions are x and 15 marks questions are y.

The total points are 100 so the other equation will be:

Now, multiply equation (1) by 5 and then subtract it by equation (2) as follows:

Therefore, there are 11 questions worth 5 points and 3 questions worth 15 points.

Now,

So, questions worth 15 marks are 3 then, and questions worth 5 marks will be 14 - 3 that is 11.

Therefore, there are 11 questions worth 5 points and 3 questions worth 15 points.

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In simple linear regression, the predictor variable is the independent variable, which is used to predict the value of the dependent variable. It is also referred to as the explanatory variable, as it is used to explain the variability in the response variable.

For example, in a study that examines the relationship between the hours studied and exam scores, the predictor variable is the number of hours studied, and the dependent variable is the exam score.

The predictor variable is plotted on the x-axis, while the dependent variable is plotted on the y-axis in a scatter plot. The relationship between the predictor and the dependent variable is represented by a straight line, which is determined by the regression equation.

The slope of the line represents the change in the dependent variable for each unit change in the predictor variable.

In summary, the predictor variable is the variable that is used to predict or explain the changes in the dependent variable in simple linear regression.

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a. Pooled proportion = 0.6,

b. Test statistic = 2.67,

c. Critical value = 1.645,

d. P-value = 0.0038,

e. Reject null hypothesis.

a. To compare the pass rates, we need to calculate the pooled proportion. The formula for pooled proportion is,

⇒ pooled proportion = (number of successes in group 1 + number of successes in group 2) / (total number of individuals in group 1 + total number of individuals in group 2)

⇒ pooled proportion = (70 + 104) / (140 + 260)

                                   = 0.6

b. The test statistic for a two-proportion z-test is calculated as,

⇒ test statistic = (p1 - p2) / √(pooled proportion (1 - pooled proportion) (1/n1 + 1/n2))

where p1 and p2 are the sample proportions,

n1 and n2 are the sample sizes,

And pooled proportion is the proportion of successes in both samples combined.

Using the given values, we get,

⇒ test statistic = (0.5 - 0.4) / √(0.6 0.4 (1/140 + 1/260))

                        = 2.67

c. The critical value for a right-tailed test at  = .05

can be determined using a z-table or a calculator. For a significance level of .05, the critical value is 1.645.

d. The p-value is the probability of obtaining a test statistic as extreme or more extreme than the observed one, assuming the null hypothesis is true.

Since this is a right-tailed test, the p-value is the area to the right of the observed test statistic under the standard normal distribution.

Using a z-table, we find that the p-value is 0.0038.

e. With a significance level of .05, we compare the p-value to the level of significance. Since the p-value is less than .05, we reject the null hypothesis.

Therefore, we can conclude that the pass rate at Blue Yonder Institute is significantly higher than the pass rate at Fly-More Academy.

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Answer: 3:5

Step-by-step explanation: heres the answer

Answer:

2400 cm^2

Step-by-step explanation:

The surface area of one side of this 6-sided figure is (20 cm)^2, or

400 cm^2.  Multiplying this result by 6, we get the total surface area:

6(400 cm^2) = 2400 cm^2

Answer:

You need 14 panels of fencing to enclose the yards

Step-by-step explanation:

Division

There are two backyards with respective perimeters of 65 ft and 45 ft. It's needed to enclose them with fencing.

The total fencing needed to do the job is 65 ft + 45 ft = 110 ft

Since the fencing comes in panels of 8 ft, we need 110/8 = 13.75 panels of fencing.

But we cannot order a decimal number of panels, we need to round up to the next integer, thus

Answer:

See below

Step-by-step explanation:

Which is the closest to 6

\(\sqrt{34}\)

\(\sqrt{39\\\)

\(\sqrt{35\)

or \(\sqrt{38}\)

So, find the square root of each ( I suggest using a calculator)

\(\sqrt{34} = 5.83\\\sqrt{39} = 6.24\\\sqrt{35} = 5.91 \\\sqrt{38} = 6.16\)

Which is closest? Let's see.

6 - 5.83 = 0.17

6.24 - 6 = 0.24

6 - 5.91 = 0.09

6.16 - 6 = 0.16

Find the smallest #

0.09 is the smallest, so 5.91 is the closest. Square the #, we get \(\sqrt{35}\)

Hope this helps! =D

The volume of the cylinder B is 25 \(in^{3}\).

A dilation is a changing the size of an object or its shape by increasing or decreasing the dimension of an object.

The volume of cylinder A is 200 in³.

Cylinder B is the image of cylinder A after dilation by a scale factor of 1/2.

To find the volume of cylinder B.

Since we are talking about volume, get the cube of the scale factor 1/2.

\((\frac{1}{2}) ^{3} =\frac{1}{2}*\frac{1}{2} *\frac{1}{2}=\frac{1}{8}\)

Multiply the result by the volume of the cylinder A.

\(\frac{1}{8}*200=25\)

Hence, the volume of the cylinder B is 25 \(in^{3}\).

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The monthly payment for Jeanne's loan, with a loan amount of $14800, an interest rate of 8.57%, and a term of 42 months, is $491.90. This is calculated using the formula: loan amount x (interest rate / 12) / (1 - (1 + (interest rate / 12))^-term in months).

The monthly payment for Jeanne's loan can be calculated using the following formula: loan amount x (interest rate / 12) / (1 - (1 + (interest rate / 12))^-term in months). In this case, the loan amount is $14800, the interest rate is 8.57%, and the term is 42 months. First, divide the interest rate by 12 to get the monthly rate. Then, subtract 1 from 1 plus the monthly rate. Finally, raise this result to the negative power of the term in months. Multiply this result by the loan amount and the monthly rate, and you will get the monthly payment: $491.90. Therefore, Jeanne's monthly payment for this loan is $491.90.

14800 x (0.0857 / 12) / (1 - (1 + (0.0857 / 12))^-42) = $491.90

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x= -11

Hope this helps

:T

:B

:D

The required answer is the approximately 5.98 feet.

The area of a circular trampoline is given as 112.07 square feet.

To find the radius of the trampoline,

area of a circle:

A = πr^2

where A is the area and r is the radius of the circle.

To find the radius,

r = √(A/π)

Substituting the given area, we have:

r = √(112.07/π)

Now,  calculate the value of the radius using a calculator or estimation. the value of π to be approximately 3.14:

r = √(112.07/3.14)
r ≈ √(35.70675)
r ≈ 5.98

Therefore, the radius of the circular trampoline is approximately 5.98 feet.

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