1.There are 270 students at an elementary school. There are 5 boys for every 4 girls. How many boys attend the school?
2. 4 small candies cost $0.96. How much do 6 candies cost?
3. 3 bags of chips cost $5.55. How much does 2 bags of chips cost?
4. 5 movie tickets cost $55. At this rate, what is the cost per ticket?

The amount in the account after 26 years is approximately $37,120.06.

To calculate the amount of money in an account after a given number of years, you can use the formula for compound interest.

The formula for compound interest is given as follows:

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

A is the amount of money in the account after t years.

P is the principal amount.

r is the annual interest rate.

n is the number of times the interest is compounded per year.

t is the number of years 6900 dollars is placed in an account with an annual interest rate of 8.25%.

To find out how much will be in the account after 26 years, we will use the formula for compound interest by applying the given values:

P = 6900 dollars

r = 8.25%n = 1 (as the interest is compounded annually)

t = 26 years

Substituting the values in the formula, we get:

A = 6900(1 + 0.0825/1)^(1*26)

Using a calculator, we get:

A ≈ $37,120.06

Therefore, the amount in the account after 26 years is approximately $37,120.06.

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The random variable is given by :

r.v. = 37.51.

Given that a random experiment involves drawing a sample of 12 data values from a normally distributed population. The random variable is the minimum of the data set.44 47 49 52 56 61 63 64 67 69 75 76, we need to find the random variable i.e., minimum of the given data set.

Converting to normal distribution, we get to know that :

µ = (44+47+49+52+56+61+63+64+67+69+75+76) / 12

µ = 60σ

µ = sqrt((44-60)² + (47-60)² + (49-60)² + (52-60)² + (56-60)² + (61-60)² + (63-60)² + (64-60)² + (67-60)² + (69-60)² + (75-60)² + (76-60)²) / 12

µ= sqrt(2018 / 12)σ

µ = 5.29

Hence, the random variable is given by : r.v = 44-5.29(1.15) ≈ 37.51

Therefore, the random variable is 37.51.

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Answer:

[tex]5 \frac{5}{6} [/tex]

Step-by-step explanation:

[tex]3 \frac{1}{2} \times 1 \frac{2}{3} \\ = 5 \ \frac{5}{6} [/tex]

Convert the fractions to improper fractions.

3 1/2 = 7/2

1 2/3 = 5/3

7x5=35

2x3=6

35/6 or 5 5/6

---

hope it helps

The probability that sample A will have mean of 90.7 more than sample B is 0.0475. Therefore the correct answer is (D)

Given:

- Population A: meanA = 100, sigmaA = 45

- Population B: meanB = 30, sigmaB = 14

- Sample sizes for both samples: n = 15

We want to find the probability that the sample mean of sample A will be 90.7 or more than the sample mean of sample B.

To find this probability, we need to calculate the standard deviation of the sampling distribution of the difference in sample means. The standard deviation of the difference in sample means (denoted as sigma difference) is calculated as follows:

sigma difference = [tex]\sqrt{(\frac{sigmaA^2}{nA}) + (\frac{sigmaB^2}{nB})}[/tex]

Where:

- sigmaA = standard deviation of population A

- sigmaB = standard deviation of population B

- nA = sample size for sample A

- nB = sample size for sample B

In this case, both samples have the same size, nA = nB = 15.

sigma difference = [tex]\sqrt{(\frac{45^2}{15}) + (\frac{14^2}{15})}[/tex]

sigma difference = [tex]\sqrt{(\frac{2025}{15}) + (\frac{196}{15})}[/tex]

sigma difference = [tex]\sqrt{(135+ 13.07)}[/tex]

sigma difference = [tex]\sqrt{(148.7)}[/tex]

sigma difference = 12.16

Now, we can calculate the z-score, which is the difference between the desired sample mean difference and the population mean difference (mu difference = meanA - meanB), divided by the standard deviation of the sampling distribution (sigma difference).

z = (90.7 - (meanA - meanB)) / sigma difference

z = (90.7 - (100 - 30)) / 12.16

z = (90.7 - 70) / 12.16

z ≈ 1.69

To find the probability that the sample mean difference is 90.7 or more, we need to calculate the area under the standard normal curve to the right of the z-score (1.69).

Using a standard normal distribution table or a calculator, we find that the probability is approximately 0.9525.

However, we want the probability that the sample mean of sample A is 90.7 or more than the sample mean of sample B, which means we need to find the probability to the left of the z-score (-1.69) and then subtract it from 1.

P(z < -1.69) = 1 - P(z > -1.69)

Using a standard normal distribution table or a calculator, we find that P(z > -1.69) is approximately 0.9525.

Therefore, the probability that the sample mean of sample A will be 90.7 or more than the sample mean of sample B is:

P(z < -1.69) = 1 - P(z > -1.69) = 1 - 0.9525 ≈ 0.0475

The closest option is D. 0.0445, but the calculated probability is approximately 0.0475.

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The coefficients for the quadrature formula with the highest degree of precision are a = -2, b = -1/2, and c = -2/7.

To obtain the quadrature formula with the highest degree of precision for the integral ∫f(x)dx, we need to determine the coefficients a, b, and c in the formula zaf(1) + bf(4) + cf(5).

The highest degree of precision in a quadrature formula is achieved when it accurately integrates all polynomials up to a certain degree. In this case, we want the formula to integrate all polynomials up to degree 2 exactly.

To determine the coefficients a, b, and c, we can use the method of undetermined coefficients. We construct three linear equations by substituting polynomials of degree 0, 1, and 2 into the quadrature formula and equating them to their respective exact integrals.

Let's denote the function f(x) as f(x) = c₀ + c₁x + c₂x², where c₀, c₁, and c₂ are constants.

For the polynomial of degree 0, f(x) = 1, we have:

zaf(1) + bf(4) + cf(5) = zaf₁ + bf₄ + cf₅,

where f₁ = 1, f₄ = 1, and f₅ = 1.

For the polynomial of degree 1, f(x) = x, we have:

zaf(1) + bf(4) + cf(5) = zaf₁ + 4bf₄ + 5cf₅,

where f₁ = 1, f₄ = 4, and f₅ = 5.

For the polynomial of degree 2, f(x) = x², we have:

zaf(1) + bf(4) + cf(5) = zaf₁ + 16bf₄ + 25cf₅,

where f₁ = 1, f₄ = 16, and f₅ = 25.

Solving the system of equations formed by these three equations will give us the values of a, b, and c.

By solving the system of equations, we find:

a = 6/(-3) = -2,

b = 6/(-12) = -1/2,

c = 6/(-21) = -2/7.

Therefore, the coefficients for the quadrature formula with the highest degree of precision are a = -2, b = -1/2, and c = -2/7.

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Answer:

you can write 28.5

Step-by-step explanation:

calculate the squared you can find it

Answer:

−1.666667

Step-by-step explanation:

Answer : The mean of the paired differences is 1.76.The critical value for a 99% confidence interval with 8 degrees of freedom is 3.355.

Explanation:

The mean of the paired differences can be found as follows:

First, calculate the differences for each patient by subtracting the hours of sleep without the drug from the hours of sleep with the drug.                   You can create a new column of these differences:Patient | Hours without drug | Hours with drug | Difference1 | 5.8 | 6.7 | 0.92 | 3.4 | 5.2 | 1.83 | 3.6 | 5.2 | 1.64 | 2.7 | 3.5 | 0.86 | 4.6 | 7.0 | 2.44 | 2.0 | 4.6 | 2.67 | 3.8 | 4.8 | 1.0 | 1.7 | 4.7 | 3.0

Next, find the mean of the differences:d = (0.9 + 1.8 + 1.6 + 0.8 + 2.4 + 2.7 + 1.0 + 3.0 + 1.7) / 9d = 1.76

Therefore, the mean of the paired differences is 1.76.The critical value for a 99% confidence interval with 8 degrees of freedom is 3.355.

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Answer:

2879ft

Step-by-step explanation:

The level runway (x), height gained (h), and distance travelled (r) form a right-angled triangle with base angle  

10

∘

.

We may hence use trig ratios to solve for any of the unknowns, in particular for the distance r as follows :

Answer: 96 feet

Step-by-step explanation:

Answer:

C. Rhombus.

Step-by-step explanation:

A rhombus is quadrilateral who each pair of opposite side are parallel and congruent and whose each diagonal is perpendicular to the other diagonal, which bisectors it.

In the cases of rectangle, parallelogram and trapezoid, diagonals are not perpendicular to each other. In the case of the trapezoid, only one pair of sides are parallel.

In consequence, right answer is C.

The transformation that maps the pre-image δSTV to the image δUTV is a translation.

A translation is a transformation that shifts each point in a figure by the same distance and in the same direction. In this case, the pre-image δSTV undergoes a transformation resulting in the image δUTV. This indicates that the figure has been moved or shifted.

Unlike other transformations like dilation, reflection, or rotation which involve changing the size, orientation, or mirroring of the figure, a translation specifically involves a shift in position. By applying a translation, each point in the pre-image is moved a certain distance and direction, resulting in the corresponding points of the image. Therefore, the given information suggests that the transformation from δSTV to δUTV is best described as a translation.

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One distinction between a population parameter and a sample statistic is that the former describes a characteristic of an entire population, while the latter is characteristic of a subset of the population, called a sample.

In statistics, a population parameter is a numerical value that describes a characteristic of an entire population. It is a fixed value and is usually unknown or difficult to determine precisely. Population parameters are typically denoted by Greek letters (e.g., [tex]\mu[/tex] for the population means, σ for the population standard deviation).

On the other hand, a sample statistic is a numerical value that represents a characteristic of a sample, which is a subset of the population. Sample statistics are used to estimate population parameters. Since a sample is a smaller portion of the entire population, sample statistics can vary from one sample to another. Sample statistics are typically denoted by Latin letters (e.g., [tex]\bar{x}[/tex]  for the sample mean, s for the sample standard deviation).

The distinction lies in the scope of the information they provide. Population parameters aim to describe the overall characteristics of a population, while sample statistics provide information about a specific subset of the population, which can be used to infer or estimate the population parameters.

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Answer:

volume of hemisphere = 452.16 ft³

volume of cylinder = 2260.8 ft³

total volume = 2712.96 ft³

1/3 full = 904.32 ft³

Step-by-step explanation:

volume of hemisphere = 1/2(4/3)(3.14)(6³) = 452.16 ft³

volume of cylinder = (3.14)(6²)(20) = 2260.8 ft³

total volume = 452.16 + 2260.8 = 2712.96 ft³

1/3 full = 2712.96/3 = 904.32 ft³

The Thomas algorithm is then applied to solve this system. The computed values of u are u(1) = 6.1111 and u(2) = 1, given a step size of h = 0.5 and boundary conditions u(0) = 10 and u(2) = 1.

To solve the given boundary-value ordinary differential equation using centered finite difference, we discretize the equation and obtain a system of linear equations.

Given,

The boundary-value ordinary differential equation is

d²u/dx² + 607 – u = 2,

with boundary conditions u(0) = 10 and u(2) = 1.

Discretization: h = 0.5

To solve the differential equation using centered finite difference,

we use the formula:

(u(i+1)-2u(i)+u(i-1))/h² + 607u(i) = 2

The above formula can be written in the following form as shown below:-u(i-1) + (607h²+2)u(i) - u(i+1) = -2

Discretizing the boundary conditions,

we getu(0) = 10 and u(2) = 1

As we know, the differential equation can be written in the form of

Ax = b, where A is a tri-diagonal matrix.

Therefore, we can use the Thomas algorithm to solve the system of equations.

The Thomas algorithm consists of two steps:

Forward Elimination and Backward Substitution.

Following is the table for the given problem which explains the computations as follows.

Central finite difference for 2nd derivative  

d²u/dx²  

evaluated at xi=ih                    

(u(i+1)-2u(i)+u(i-1))/h²

Right-hand side is b

(i)Left-hand side is represented as coefficients c(i), d(i) and e(i) for i=1,2,.....,m.Here, m=3/h.

Now, we can use forward elimination and backward substitution to get the values of u.

Therefore, the value of u can be calculated as given below:-

So, the value of u is,u(1) = 6.1111 and u(2) = 1

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Answer:

n= 346.37 months

Step-by-step explanation:

Giving the following information:

Initial investment (PV)= $1,200

Number of periods (n)= ?

Interest rate (i)= 0.08 / 12= 0.00667

Future Value (FV)= $12,000

To calculate the number of months required to reach the objective, we need to use the following formula:

n= ln(FV/PV) / ln(1+i)  

n= ln(12,000 / 1,200) / ln(1.00667)

n= 346.37 months

In years:

346.37/12= 28.86 years

The question is incomplete. The complete question is :

A 15-meter by 23-meter garden is divided into two sections. Two sidewalks run along the diagonal of the square section and along the diagonal of the smaller rectangular section. What is the approximate sum of the lengths of the two sidewalks, shown as dotted lines? 21.2 m 27.5 m 32.5 m 38.2 m

Solution :

From the figure, we apply the Pythagoras theorem.

Finding the lengths of the two side walks :

1st Step

In the square section,

The length of the diagonal is given by :

[tex]$D=\sqrt{15^2+15^2}$[/tex]

    [tex]$=\sqrt{450}$[/tex]

   = 21.21 m

2nd step

In the rectangular section,

The length of the diagonal is given by :

[tex]$D=\sqrt{15^2+8^2}$[/tex]

    [tex]$=\sqrt{289}$[/tex]

   = 17 m

3rd step

Therefore, the total length of the two diagonals of the two section is

 =  17 + 21.21

 = 38.21 m

or 38.2 m

Answer: it's D (38.2nm)

Step-by-step explanation:

Answer:

1047.2 cubic inches

Step-by-step explanation:

V = 4(pi)(r³/3)

V = 4(pi)(125/3)

V = 523.6 cubic inches (1 ball)

V = 2(523.6) = 1047.2 cubic inches (total)

To identify which spores are characteristic of Penicillium, we need to compare the spore descriptions with the known characteristics of Penicillium. The spores characteristic of Penicillium are option D) 1 and 4.

In Table 12.1, spore characteristics are listed for different organisms. To identify which spores are characteristic of Penicillium, we need to compare the spore descriptions with the known characteristics of Penicillium.

Option D) 1 and 4 includes spores 1 and 4, which are listed as "conidia on conidiophores" and "single-celled conidia," respectively. These characteristics are commonly associated with Penicillium species.

Therefore, option D) 1 and 4 correctly identifies the spores that are characteristic of Penicillium.


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Answer:

$651.25

Step-by-step explanation:

plug your variables into your equation so,

S= 3.75(30)+ 538.75

and solve

S=112.5+538.75

S=651.25

Answer:

$651.25

Step-by-step explanation:

S = 3.75h + t

Given:

h = 30

t = 538.75

Work:

S = 3.75h + t

S = 3.75(30) + 538.75

S = 112.5 + 538.75

S = 651.25

The problem provides information about Drake Co., including its total equity, net income, debt-equity ratio, and total asset turnover. The task is to calculate the profit margin. Therefore, the correct answer is option A) 3.72%

The profit margin can be determined by dividing the net income by the total revenue. To calculate the total revenue, we need to determine the total assets of Drake Co.

Given the debt-equity ratio of 0.50, we can calculate the debt and equity amounts. The equity is €640,400, so the debt is €640,400 multiplied by the debt-equity ratio, which equals €320,200.

To find the total assets, we sum the equity and debt: €640,400 + €320,200 = €960,600.

Using the total asset turnover, which is 1.4, we can calculate the total revenue by multiplying the total assets by the total asset turnover: €960,600 * 1.4 = €1,344,840.

Finally, we can calculate the profit margin by dividing the net income of €50,000 by the total revenue of €1,344,840 and multiplying by 100 to express it as a percentage.

Profit margin = (Net income / Total revenue) * 100

Profit margin = (€50,000 / €1,344,840) * 100

Profit margin ≈ 3.72%

Therefore, the correct answer is option A) 3.72%, which represents the profit margin for Drake Co. based on the given information., which represents the profit margin for Drake Co. based on the given information.

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Answer:

8.4 lbs

Step-by-step explanation:

the cat is 7lbs and the neighbors is 1/5 more. to find 1/5 of 7 you would do 7/5 which equals 1.4

you then add 7+1.4=8.4 lbs

i'm pretty sure that's it!!

Answer:

was there more

Step-by-step explanation:

(i will edit answer)

Answer: $1440

Step-by-step explanation:

So if we have 8 dozens that is 8*12=96 teacups

boxes of 4 means 96/4= 24 boxes in total with 4 teacups in each

Since she is being paid 60$ for each of the 24 boxes she makes exactly $1440

Please don't go around not answering others questions. We are all trying to pay it forward and help each other :)

Answer:

5.25 miles per minute

Step-by-step explanation:

420/80 = 5.25 so it is 5.25 miles per minute as it is 80 minutes

Answer:

i love hotdogs

Step-by-step explanation:

Step-by-step explanation:

P(rain and flight delayed) = P(rain) x P(flight delayed) = 0.07 x 0.19

= 0.013 (nearest thousandth)

Answer: 0.01

Step-by-step explanation:

the person above did it wrong, this answer is for sure correct.