A random sample of specific brand of snack bar is tested for calorie count, with the following results
149, 145,140,160,149,153,131,134,153
Assume the population standard deviation is\sigma=24 and that the population is approximately normal. Construct a 95% confidence interval for calorie count of the snack bars

Answer:

Step-by-step explanation:

Step by step solution of a set of 2, 3 or 4 Linear Equations using the Substitution Method x-5y+4z=27,4x-3y-z=23,3x+3y-6z=-9 Tiger Algebra Solver.

The requried scale factor of the dilation from NOPQ to N'O'P'Q' is 3/4.

The scale factor is defined as the ratio of the modified change in length to original length.

Here,
The parallelogram N'O'P'Q' is a dilation for the parallelogram NOPQ.
length of the one diagonal of NOPQ is = 12
length of the one diagonal of N'O'P'Q' is = 9

Now,
The scale factor for quadrilateral = Length of diagonal N'O'P'Q' / NOPQ
                                                  = 9/12
                                                  = 3/4

Thus, the requried scale factor of the dilation from NOPQ to N'O'P'Q' is 3/4.

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a. The mass of the wire is 2π√37.

b. The center of mass of the wire is located at the point (0,0,3).

c. The moment of inertia about the z-axis is 2π√37

A. To determine the mass of the wire, we need to integrate the density function p(x, y, z) along the curve x(t), y(t), z(t) from t=0 to t=2π:

m = ∫₀²π p(x(t), y(t), z(t)) ||r'(t)|| dt

where r(t) = x(t)i + y(t)j + z(t)k is the position vector of the wire at time t and ||r'(t)|| is the magnitude of the velocity vector, given by:

||r'(t)|| = ||(-sin t)i + cos(t)j + 6k|| = √(sin²t + cos²t + 6²) = √37

Substituting p(x, y, z) = 1, we get:

m = ∫₀²π ||r'(t)|| dt = √37 ∫₀²π dt = √37 (2π) = 2π√37

So, the mass of the wire is 2π√37.

B. To find the center of mass, we need to compute the triple integral:

(xc,yc,zc) = (1/m) ∭E (x,y,z) p(x,y,z) dV

where E is the region of the wire, p(x,y,z) = 1 is the constant density function, and (xc,yc,zc) are the coordinates of the center of mass.

Using cylindrical coordinates, we can parameterize the helix as:

x(r,t) = r cos t

y(r,t) = r sin t

z(r,t) = 6t/(2π)

where r varies from 0 to 1 and t varies from 0 to 2π. The volume element in cylindrical coordinates is dV = r dz dr dt, so the triple integral becomes:

(xc,yc,zc) = (1/m) ∫₀¹ ∫₀²π ∫₀⁶t/(2π) (r cos t, r sin t, z) r dz dr dt

Substituting m = 2π√37, we get:

(xc,yc,zc) = (1/(2π√37)) ∫₀¹ ∫₀²π ∫₀⁶t/(2π) (r cos t, r sin t, z) r dz dr dt

Evaluating the integrals, we get:

(xc,yc,zc) = (0, 0, 3)

So, the center of mass of the wire is located at the point (0,0,3).

C. The moment of inertia about the z-axis is given by the integral:

I = ∫c (x² + y²) p(x,y,z) ds

where c is the curve traced out by the wire.

Using the parameterization x(t) = cos t, y(t) = sin t, z(t) = 6t/(2π), we can write ds = ||r'(t)|| dt, where r(t) = x(t)i + y(t)j + z(t)k is the position vector of the wire at time t.

Substituting p(x, y, z) = 1, we get:

I = ∫₀²π [(cos²t + sin²t) ||r'(t)||] dt

From part A, we know that ||r'(t)|| = √37, so we have:

I = √37 ∫₀²π dt = √37 (2π) = 2π√37

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A. The mass of the wire is 2π√37 A.

B. The coordinates of the center of mass are (0, 0, 18π/√37).

C. The moment of inertia about the z-axis is 37(2π) A.

A. To determine the mass of the wire, we need to integrate the density function over the length of the wire:

\(M = ∫p(x,y,z)ds\)

where s is the arc length of the curve x(t), y(t), z(t). Since the density function is constant, we can simplify this to:

\(M = ∫ds\)

Using the arc length formula, we have:

\(M = ∫₀²π √(x'(t)² + y'(t)² + z'(t)²) dt\)

where x'(t), y'(t), and z'(t) are the derivatives of x(t), y(t), and z(t), respectively. Substituting x(t) = cos t, y(t) = sin t, and z(t) = 6t, we get:

\(M = ∫₀²π √(sin²t + cos²t + 6²) dt\\= ∫₀²π √37 dt\\= 2π√3z\)

Therefore, the mass of the wire is 2π√37 A.

B. To determine the coordinates of the center of mass, we need to find the position vector of the center of mass:

\(r = (xcm, ycm, zcm)\)

where

\(xcm = (1/M) ∫xp(x,y,z)ds\\ycm = (1/M) ∫yp(x,y,z)ds\\zcm = (1/M) ∫zp(x,y,z)ds\)

Since the density function is constant, we can simplify this to:

\(xcm = (1/M) ∫xds\\ycm = (1/M) ∫yds\\zcm = (1/M) ∫zds\)

Using the arc length formula, we have:

\(xcm = (1/M) ∫₀²π cos t √(sin²t + cos²t + 6²) dt\)

\(ycm = (1/M) ∫₀²π sin t √(sin²t + cos²t + 6²) dt\)

\(zcm = (1/M) ∫₀²π 6t √(sin²t + cos²t + 6²) dt\)

Substituting x(t) = cos t, y(t) = sin t, and z(t) = 6t, we get:

\(xcm = (1/M) ∫₀²π cos t √37 dt\)

\(ycm = (1/M) ∫₀²π sin t √37 dt\)

\(zcm = (1/M) ∫₀²π 6t √37 dt\)

Evaluating these integrals, we get:

\(xcm = 0\\ycm = 0\\zcm = 18π/√37\)

Therefore, the coordinates of the center of mass are (0, 0, 18π/√37).

C. To determine the moment of inertia about the z-axis, we need to use the formula:

\(I = ∫c(x² + y²)p(x,y,z)ds\)

Substituting x(t) = cos t, y(t) = sin t, and z(t) = 6t, we get:

\(I = ∫₀²π [(cos²t + sin²t) + 6²] dt\)

\(= ∫₀²π (37) dt\\= 37(2π)\)

Therefore, the moment of inertia about the z-axis is 37(2π) A.

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the answer is irrational

The number 11.47723 is rational if it is an integer or decimal

A rational number is a number that can be represented a/b where a and b are integers and b is not equal to 0.

Since 11.47723 is an integer or decimal from above, 11.47723 is also a rational

Answer:

\( \: \frac{11}{1620} \: \pi^{2} \)

Step-by-step explanation:

I think this is it. But if you find a mistake somewhere let me know? I'm confused because the answer seems a little weird. Like 11/1620 pi² really?

Also at the bottom I wrote "area of sector =" but the area got cut off

Answer:224 squared

Step-by-step explanation:

H

Answer:

6 or 60. 45 is in it. Best I can explain

Answer:

162

Step-by-step explanation:

step 1. our output value is 360

step 2. we represent the unknown value with x

step3. from step 1 above, 360= 100%

step 4. similarity, x=45%

step 5. this result in a pair of simple equations

360=100%(1)

x=45%(2)

step 6. by dividing equation 1 and 2 and noting that both the RHS (right hand side) of both equations have the same unit (%); we have

360/x = 45/100

x=162

therefore, 45% of 360 is 162

hope this helps!!!

the probability of both mayonnaise and mustard being chosen is 0.35.

To find the probability of both mayonnaise and mustard being chosen, we can use the formula:

P(mayonnaise and mustard) = P(mayonnaise) + P(mustard) - P(mayonnaise or mustard)

Given:

P(mayonnaise) = 0.42

P(mustard) = 0.86

P(mayonnaise or mustard) = 0.93

Plugging in the values:

P(mayonnaise and mustard) = 0.42 + 0.86 - 0.93

= 1.28 - 0.93

= 0.35

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The expected value for count for each of the possible outcomes has been calculated and attached in the table attached below.

In statistics, a sampling distribution is a probability distribution that describes the frequencies of all possible outcomes of a random sample taken from a population. It is the distribution of the sample statistics (such as the mean or standard deviation) calculated from multiple random samples of the same size taken from the population.

Sampling distributions are important because they allow us to make inferences about the population based on the information obtained from the sample. They also help us to understand the variability in sample statistics due to chance.

To determine if births are equally likely across the days of the week, we need to compare the observed counts of births for each day to the expected counts if births were equally likely across all days.

The expected count for each day can be calculated by dividing the total number of births (150) by the number of days in a week (7):

Expected count = Total amount of births / Number of days in a week = 150/7 ≈ 21.43

To calculate the expected count for each day, we simply multiply the expected count by the number of days in the week:

Expected count for Sunday = 21.43 × 1 = 21.43

Expected count for Monday = 21.43 × 1 = 21.43

Expected count for Tuesday = 21.43 × 1 = 21.43

Expected count for Wednesday = 21.43 × 1 = 21.43

Expected count for Thursday = 21.43 × 1 = 21.43

Expected count for Friday = 21.43 × 1 = 21.43

Expected count for Saturday = 21.43 × 1 = 21.43

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Answer:

Nope

Step-by-step explanation:

You must convert fractions to the same denominator

Convert 3/5 to 9/15

3/5 = 9/15

Then add the numerators together.

9/15 + -4/15 = 5/15

Answer:

look below

Step-by-step explanation:

tap the link

Answer:

it is greater than 8

Step-by-step explanation:

The answer are: a. Total outflows: $2,007,901, b. Total inflows: $827,080, c. Net present value: $824,179, d. Should the old issue be refunded with new debt? Yes

To determine whether the old bond issue should be refunded with new debt, we need to calculate the present value of total outflows, the present value of total inflows, and the net present value (NPV). Let's calculate each of these values step by step: Calculate the present value of total outflows. The total outflows consist of the call premium, underwriting cost on the old issue, and underwriting cost on the new issue. Since these costs are one-time payments, we can calculate their present value using the formula: PV = Cash Flow / (1 + r)^t, where PV is the present value, Cash Flow is the cash payment, r is the discount rate, and t is the time period.

Call premium on the old issue: PV_call = (7% of $22 million) / (1 + 0.1)^16, Underwriting cost on the old issue: PV_underwriting_old = $530,000 / (1 + 0.1)^16, Underwriting cost on the new issue: PV_underwriting_new = $680,000 / (1 + 0.1)^16. Total present value of outflows: PV_outflows = PV_call + PV_underwriting_old + PV_underwriting_new. Calculate the present value of total inflows. The total inflows consist of the interest savings and the tax savings resulting from the interest expense deduction. Since these cash flows occur annually, we can calculate their present value using the formula: PV = CF * [1 - (1 + r)^(-t)] / r, where CF is the cash flow, r is the discount rate, and t is the time period.

Interest savings: CF_interest = (12% - 10%) * $22 million, Tax savings: CF_tax = (40% * interest expense * tax rate) * [1 - (1 + r)^(-t)] / r. Total present value of inflows: PV_inflows = CF_interest + CF_tax.  Calculate the net present value (NPV). NPV = PV_inflows - PV_outflows Determine whether the old issue should be refunded with new debt. If NPV is positive, it indicates that the present value of inflows exceeds the present value of outflows, meaning the company would benefit from refunding the old issue with new debt. If NPV is negative, it suggests that the company should not proceed with the refunding.

Now let's calculate these values: PV_call = (0.07 * $22,000,000) / (1 + 0.1)^16, PV_underwriting_old = $530,000 / (1 + 0.1)^16, PV_underwriting_new = $680,000 / (1 + 0.1)^16, PV_outflows = PV_call + PV_underwriting_old + PV_underwriting_new. CF_interest = (0.12 - 0.1) * $22,000,000, CF_tax = (0.4 * interest expense * 0.4) * [1 - (1 + 0.1)^(-16)] / 0.1, PV_inflows = CF_interest + CF_tax. NPV = PV_inflows - PV_outflows.  If NPV is positive, the old issue should be refunded with new debt. If NPV is negative, it should not.

Performing the calculations (rounded to the nearest whole dollar): PV_call ≈ $1,708,085, PV_underwriting_old ≈ $130,892, PV_underwriting_new ≈ $168,924, PV_outflows ≈ $2,007,901,

CF_interest ≈ $440,000, CF_tax ≈ $387,080, PV_inflows ≈ $827,080.  NPV ≈ $824,179.  Since NPV is positive ($824,179), the net present value suggests that the old bond issue should be refunded with new debt.

Therefore, the answers are:

a. Total outflows: $2,007,901

b. Total inflows: $827,080

c. Net present value: $824,179

d. Should the old issue be refunded with new debt? Yes

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Step-by-step Explanation:

First find out what is the price after 30% off.

250 · 0.3 = 75

250 - 75 = 175

Then find the tax and add it on. Remember to calculate the tax AFTER  the discount.

175 · 0.06 = 10.50

175 + 10.50 = 185.50

Answer: I imagine that the question was: "What is the wrong answer between these choices?" Therefore, it is the third choice.

Explanation:

2(m∠PQS) ≠ (m∠RQS)

2(47°) ≠ 47°

94° ≠ 47°

Answer:

No.

Step-by-step explanation:

It can be written as 2 81/100 or 281/100 so it is not irrational. An irrational number is a number that cannot be written as a ratio of two numbers

Answer:

no, 2.81 is a rational number.

Step-by-step explanation:

An irrational number is a number that cannot be expressed as a fraction for any integers and. . Irrational numbers have decimal expansions that neither terminate nor become periodic. Every transcendental number is irrational.

Step-by-step explanation:

(2+6+9+3+7+3):10=3

57-56+57+90-147+5=6

Bag one currently holds 25 kilograms of sugar, while bag two contains 75 kilograms of sugar.

Let's represent the initial amount of sugar in bag one as x and bag two as y. According to the given information, bag one has used 3 times as much sugar as bag two. This can be expressed as:

Bag one: x - 3y

Bag two: y

Furthermore, we are told that after using this amount of sugar, bag one has half as much sugar as bag two. Mathematically, we can express this as:

(x - 3y) = (1/2)y

Simplifying the equation, we get:

2(x - 3y) = y

2x - 6y = y

2x = 7y

Since we also know that the initial amount of sugar in each bag is 50 kilograms, we can set up another equation:

x + y = 100

We now have a system of two equations:

2x = 7y

x + y = 100

By solving these equations simultaneously, we find that x = 25 and y = 75. Thus, bag one currently holds 25 kilograms of sugar, while bag two contains 75 kilograms of sugar.

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Answer:

x = 24

Step-by-step explanation:

10(x+12)=15x  (Given)

10x + 120 = 15x (Distributive property of equality)

-5x = -120 (Subtraction property of equality)

x = 24 (Division property of equality)

The area of the shaded triangle formed as the result of the overlap is = 62.35 inches ²

After folding the rectangle with length of 12 inches and width of 18 inches, an equilateral triangle was formed.

An equilateral triangle is a type of triangle where by all the three sides are equal.

To determine the value of one of the sides, CB or CD is used because the folding didn't affect these sides.

Using the formula for the area of an equilateral triangle,

A = √¾ a²

a= 12 inches

A = √¾ ×12²

A = 62.35 inches ²

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Answer:

Its 78!!!!

Solution:

1/2(12 * 18 - 5 * 12) = 78

(a) 95% confidence interval for the difference between female and male times is (11.954, 255.591).

(b) The assumptions and conditions for the two-sample t-test are met, so we can use the results of the test and confidence interval.

a) To construct a 95% confidence interval for the difference between female and male times, we can use a two-sample t-test. Let's denote the mean time for female swimmers as μf and the mean time for male swimmers as μm. We want to test the null hypothesis that there is no difference between the two means (i.e., μf - μm = 0) against the alternative hypothesis that there is a difference (i.e., μf - μm ≠ 0).

The formula for the two-sample t-test is:

t = (Xf - Xm - 0) / [sqrt((s^2f / nf) + (s^2m / nm))]

where Xf and Xm are the sample means for female and male swimmers, sf and sm are the sample standard deviations for female and male swimmers, and nf and nm are the sample sizes for female and male swimmers, respectively.

Using the data from the plots, we get:

Xf = 917.5, sf = 348.0137, nf = 15

Xm = 783.7273, sm = 276.0625, nm = 28

Plugging in these values, we get:

t = (917.5 - 783.7273 - 0) / [sqrt((348.0137^2 / 15) + (276.0625^2 / 28))] = 2.4895

Using a t-distribution with (15+28-2) = 41 degrees of freedom and a 95% confidence level, we can look up the critical t-value from a t-table or use a calculator. The critical t-value is approximately 2.021.

The confidence interval for the difference between female and male times is:

(917.5 - 783.7273) ± (2.021)(sqrt((348.0137^2 / 15) + (276.0625^2 / 28)))

= 133.7727 ± 121.8187

= (11.954, 255.591)

Therefore, we can be 95% confident that the true difference between female and male times is between 11.954 and 255.591 minutes.

b) Assumptions and conditions for the two-sample t-test:

Independence, We assume that the observations for each group are independent of each other.

Normality, We assume that the populations from which the samples were drawn are approximately normally distributed. Since the sample sizes are relatively large (15 and 28), we can rely on the central limit theorem to assume normality.

Equal variances, We assume that the population variances for the female and male swimmers are equal. We can test this assumption using the F-test for equality of variances. The test statistic is,

F = s^2f / s^2m

where s^2f and s^2m are the sample variances for female and male swimmers, respectively. If the p-value for the F-test is less than 0.05, we reject the null hypothesis of equal variances. If not, we can assume equal variances. In this case, the F-test yields a p-value of 0.402, so we can assume equal variances.

Sample size, The sample sizes are both greater than 30, so we can assume that the t-distribution is approximately normal.

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Answer:

x = 7

Step-by-step explanation:

- 8 = 27 - 5x ( subtract 27 from both sides )

- 35 = - 5x ( divide both sides by - 5 )

7 = x

The price per T-shirt should be at least $15 to achieve a profit of $250.

To calculate the price per T-shirt that will yield a profit of at least $250, we need to consider the cost of production, the desired profit, and the number of shirts to be sold.

Given that the cost to make each T-shirt is $10, and we want to sell 50 shirts, the total cost of production would be 10 * 50 = $500.

Now, let's calculate the minimum revenue needed to achieve a profit of $250. We add the desired profit to the total cost of production: $500 + $250 = $750.

Finally, to determine the price per T-shirt, we divide the total revenue by the number of shirts: $750 ÷ 50 = $15.

Therefore, to make a profit of at least $250, the price per T-shirt should be set at $15.

By selling each T-shirt for $15, the total revenue would be $15 * 50 = $750. From this revenue, we subtract the total production cost of $500 to calculate the profit, which amounts to $750 - $500 = $250. Thus, by charging $15 per T-shirt, the desired profit of $250 is achieved.

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Answer:

Step-by-step explanation:

Graphing ordered pairs is only the beginning of the story. Once you know how to place points on a grid, you can use them to make sense of all kinds of mathematical relationships.

You can use a coordinate plane to plot points and to map various relationships, such as the relationship between an object’s distance and the elapsed time. Many mathematical relationships are linear relationships. Let’s look at what a linear relationship is.

Answer:

-5f+6g-41

Step-by-step explanation:

you order them and then subtract

Answer: 6g-5f-41

Step-by-step explanation: You combine like terms, so for example the 9g and the 3g you combine those terms since they share the same variable. So since its 9g-3g you get 6g since 9-3 is 6. Since there are no more like terms you bring the rest down.

From the calculations, the volume of the sculpture is 27 times the volume of the model.

The volume of a cube is obtained using the formula;

Volume = l^3

Where l is the length of each edge. We should note that the lengths of all the edges in a cube are equal.

Hence,

volume of the model = (25)^3 = 15625 in^3

volume of the sculpture = (3 * 25)^3 = 421875  in^3

Ratio of the volume of the sculpture to the volume of the model = 421875  in^3/15625 in^3

= 27:1

Hence, the volume of the sculpture is 27 times the volume of the model.

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Answer:-3,3

Step-by-step explanation:

it should be the 4th one

hopefully this can help

Answer:

A x=1/4

Step-by-step explanation:

2/3x = 1/6

Divide by 2/3

so 1/6 ÷ 2/3

= 1/6 • 3/2

= 3/12

= 1/4