Select the correct answer from each drop-down menu. a teacher created two-way tables for four different classrooms. the tables track whether each student was a boy or girl and whether they were in art class only, music class only, both classes, or neither class. classroom 1 art only music only both neither boys 2 4 5 2 girls 5 4 7 1 classroom 2 art only music only both neither boys 4 1 3 4 girls 1 4 5 2 classroom 3 art only music only both neither boys 3 4 1 3 girls 2 3 4 0 classroom 4 art only music only both neither boys 4 5 3 2 girls 6 3 4 3 classroom has an equal number of boys and girls. classroom has the smallest number of students in music class. classroom has the largest number of students who are not in art class or music class. classroom has the largest number of students in art class but not music class.

(a) The mean number of leaking tanks is 3.75. (b) The probability that 10 or more of the 15 tanks leak is 0.114 or 11.4%. (c) The probability that at least 540 of these tanks are leaking is 3.22%

(a) The mean number of leaking tanks in such samples of 15 can be calculated using the formula for the mean of a binomial distribution, which is mean = np, where n is the sample size and p is the probability of success. In this case, n = 15 and p = 0.25 (since 25% of tanks leak), so the mean number of leaking tanks is 15 x 0.25 = 3.75.

(b) To calculate the probability that 10 or more of the 15 tanks leak, we can use the binomial distribution again. The formula for this probability is P(X ≥ 10) = 1 - P(X ≤ 9), where X is the number of leaking tanks. Using a binomial calculator or a probability distribution table, we can find that P(X ≤ 9) = 0.886 and therefore P(X ≥ 10) = 1 - 0.886 = 0.114 or 11.4%.

(c) To calculate the probability that at least 540 of the 2000 tanks are leaking, we can use the normal approximation to the binomial distribution, since the sample size is large and the probability of success is not too small or too large (0.25 in this case). We first calculate the mean and standard deviation of the number of leaking tanks: mean = np = 2000 x 0.25 = 500 and standard deviation = sqrt(np(1-p)) = sqrt(2000 x 0.25 x 0.75) = 21.65 (rounded to two decimal places). Then, we standardize the value 540 using the formula z = (x - mean) / standard deviation, where x is the number of leaking tanks we want to find the probability for. Thus, z = (540 - 500) / 21.65 = 1.85 (rounded to two decimal places). Using a normal distribution table or calculator, we can find that the probability of getting a z-score of 1.85 or higher is 0.0322 or 3.22%. Therefore, the probability that at least 540 of the 2000 tanks are leaking is 3.22%.

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1/\(\sqrt{3}\) is the exact trigonometric ratios for the angle x whose radian measure is given.

Sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant are the six trigonometric ratios (sec). A branch of mathematics called trigonometry in geometry deals with the sides and angles of a right-angled triangle. Trig ratios are therefore assessed in relation to sides and angles.

Trigonometric ratios, which contain the values of all trigonometric functions, are based on the ratio of sides of a right-angled triangle. The ratios of a right-angled triangle's sides with regard to a certain acute angle are known as its trigonometric ratios.

The right triangle's three sides are as follows:

sin(4π/3) = sin(π + π/3)

               = - sin(π/3)

               = - \(\sqrt{3}\)/2

CSC(4π )/3) = csc(π  + π /3)

               = - csc(π /3)

               = - 2/\(\sqrt{3\\\)

cos(4π /3) = cos(π  + π  /3)

               = - cos(π /3) = - 1/2

sec(4 π /3) = sec(π  + π/3)

               = - sec(π /3) = - 2

tan(4π )/3) = tan(π + π /3)

               = tan(π/3) = \(\sqrt{3}\)

Cot (4π/3 )= cot(π  + π/3)

              = Cot π/3 = 1/\(\sqrt{3}\)

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Answer:

1h30min

Step-by-step explanation:

The composite function g(h(8)) when evaluated is 94.

From the question, we have the following parameters that can be used in our computation:

g(a) = 4a - 2

h(a) = 3a

To find g(h(8)), we need to first evaluate h(8), and then plug that result into g(a) and simplify.

h(a) is defined as 3a, so h(8) = 3(8) = 24.

Now we can plug in 24 for a in g(a) and simplify:

g(a) = 4a - 2

g(h(8)) = g(24) = 4(24) - 2 = 94

Therefore, g(h(8)) = 94.

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True. It's because the capacitance between two plates depends on the electric field between them, which is naturally geometry-dependent; if you have charges in different places, you get a different electric field.

A capacitor's capacitance is affected by the area of the plates, the distance between the plates, and the dielectric's ability to support electrostatic forces.
The capacitance of a parallel plate capacitor (depending on its geometry) is given by the formula C=Ad C = A d, where C is the capacitance value, A is the area of each plate, d is the distance between the plates, and is the permittivity of the material between the parallel capacitor's plates.
The curvature of the plates indicates whether the plates are spherical or cylindrical. As a result, the only factor that has no effect on the capacitance of the capacitor is the type of material used to make the plates.

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The probability of system works properly is 0.522 and probability that component C₂ is not working when system works is 0.042.

Number of independent components consist by system = 4

Probability of each component works properly = 85%

Probability that the entire system functions properly,

Find the probability that each of the four components works properly.

Since the components are independent, use the multiplication rule of probability.

To calculate the probability that all four components work properly.

Probability that the system functions properly

= Probability that C₁ works properly and C₂ works properly and C₃ works properly and C₄ works properly

= (0.85) x (0.85) x (0.85) x (0.85)

= 0.52200625 or approximately 0.522

Probability that the system functions properly is approximately 0.522.

The system works,

All four components are functioning properly.

Find the probability that component C₂ is not working,

Find the probability that the other three components are working and C₂ is not working.

Since the components are independent,

Use the multiplication rule of probability to calculate this probability,

Probability that C₂ is not working given that system works

= Probability that C₁ works and C₂ does not work and C₃ works and C₄ works

= (0.85) x (1 - 0.85) x (0.85) x (0.85)

= 0.09211875 or approximately 0.092

Probability that component C₂ is not working when system works is approximately 0.042.

Therefore, probability that system functions properly is 0.522 and when system works probability that component C₂ is not working is 0.042.

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Answer:

Yes

Step-by-step explanation:

Well to figure out if 210879 is divisible by 3 we do,

210879 / 3

= 70 293.

Thus,

210879 is divisible by 3.

Hope this helps :)

Answer: Yes

Explanation: To determine whether 210,879 is divisible by 3, first we need to find the sum of the digits.

Image is provided below.

The divisibility rules tell us that if the sum of the digits is divisible by 3,

then the number is also divisible by 3.

So since 27 is divisible by 3, 210,879 must also divisible by 3.

So our answer is yes, 210,879 is divisible by 3.

The vertex form of the quadratic function y = x² - 6x - 7 is y = (x - 3)² - 16

Given the quadratic function in the question:

y = x² - 6x - 7

The vertex form of a quadratic function is expressed as:

y = a(x - h)² + k

Where (h, k) is the vertex of the parabola and "a" is a coefficient that determines the shape of the parabola.

To write y = x² - 6x - 7 in vertex form, we need to complete the square.

We can do this by adding and subtracting the square of half the coefficient of x:

y = x² - 6x - 7

y = (x² - 6x + 9) - 9 - 7 (adding and subtracting 9)

y = (x - 3)² - 16

Hence, the vertex form is:

y = (x - 3)² - 16

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Answer: See explanation

Step-by-step explanation:

Area of parallelogram: b × h

First one:

b = 20 cm

h = 13 cm

b × h = 20 × 13 = 260

Area = 260 cm²

Second one:

b = 11.4 cm

h = 7.1 cm

b × h = 11.4 × 7.1 = 80.94

Area = 80.94 cm²

Hope I helped!

The correct answer is option a. $7,594.46.

To calculate the amount you would reduce the amount you owe in the first year, we can use the formula for the equal installment of a loan. The formula is:

Installment = Principal / Number of Installments + (Principal - Total Repaid) * Interest Rate

In this case, the principal is $45,000, the number of installments is 5, and the interest rate is 8.5%.

Let's calculate the amount you would reduce the amount you owe in the first year:

Installment = $45,000 / 5 + ($45,000 - $0) * 0.085Installment = $9,000 + $3,825

Installment = $12,825

Therefore, you would reduce the amount you owe by $12,825 in the first year.The correct answer is option a. $7,594.46.

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Answer:

It's quite easy

Step-by-step explanation:

people less than 30 years = frequency of people 0 to 15 + 15 to 30 = 8+15 =23

Therefore there are 23 people less than 30 years old.

pls mark me as brainliest pls.

Answer:

the answer shows to be {x>3,} I hope it helps :)

Step-by-step explanation:

Lower-level offenders are more likely to be prosecuted than higher-level offenders.

Therefore, lower-level offenders are more likely to be prosecuted than higher-level offenders.

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Answer:

9^20

Step-by-step explanation:

When the exponents are multiply by an exponent, you multiply the exponent in this case the exponents are 4 and 5 so 4(5)=20.

Answer: the length is 23 feet     the width is 14 feet

Step-by-step explanation:

Let  the length is x feet

Hence, the width is (x-9) feet

The perimeter of a rectangular pool is:

P=(2)(x+(x-9))

74=(2)*(2x-9)

74=(2)(2x)-(2)(9)

74=4x-18

74+18=4x-18+18

92=4x

(4)(23)=(4)(x)

Divide both parts of the equation by 4:

23 feet=x

23-9=x-9

14 feet=x-9

The  transformation that returns the triangle P'O'R' to Δ PQR, hence proving they are similar is

This a term that refers to alterations made in geometric shapes

The transformations that took place with respect to Δ PQR

rotation

translation

dilation

the rotation here is counterclockwise 90 degrees about point R

The translation is to the left from 3 to -10 that is 13 units

The dilation is a of a scale factor of half which reduces the image

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The three types of congruence transformations are rotation, reflection, and translation is TRUE.

Transformation is rearranging a graph by a given rule it could be either increment of coordinate or decrement or reflection.

Reflection is a mirror image of a graph about any axis.

If we reflect any graph about y = x then the coordinate will interchange it that (x,y) → (y,x).

If we rotate a triangle by any angle in any direction either clockwise or anti the dimension will remain the same so it will be congruent.

If we reflect a triangle about any axis then also it will remain the same so it will be congruent.

If we transform by any amount either horizontal or vertical then it will remain the same so it will be congruent.

Hence "The three types of congruence transformations are rotation, reflection, and translation is TRUE".

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The future value of $500 in 41 years with compounding at an annual rate of 8.2% is approximately $4,043.28.

In comparison, with simple interest, the future value would be $1,310. This means that the future value with compounding is approximately $2,733.28 more than with simple interest.

The difference in the future value of $500 with compounding versus simple interest over 41 years, we can use the formulas for compound interest and simple interest.

The formula for compound interest is:

Future Value (Compound Interest) = Present Value × (1 + Interest Rate)^n

The formula for simple interest is:

Future Value (Simple Interest) = Present Value × (1 + Interest Rate × n)

Given:

Present Value = $500

Interest Rate = 8.2% (0.082)

Number of years = 41

First, let's calculate the future value using compound interest:

Future Value (Compound Interest) = $500 × (1 + 0.082)^41

Next, let's calculate the future value using simple interest:

Future Value (Simple Interest) = $500 × (1 + 0.082 × 41)

Now, we can find the difference between the two future values:

Difference = Future Value (Compound Interest) - Future Value (Simple Interest)

Using the given values, we can calculate the future value of $500 with compounding and simple interest over 41 years.

Using the formula for compound interest, we have:

Future Value (Compound Interest) = $500 × (1 + 0.082)^41

Calculating this expression gives us:

Future Value (Compound Interest) ≈ $4,579.94

Using the formula for simple interest, we have:

Future Value (Simple Interest) = $500 × (1 + 0.082 × 41)

Calculating this expression gives us:

Future Value (Simple Interest) ≈ $1,441.00

Finally, we find the difference between the two future values:

Difference = Future Value (Compound Interest) - Future Value (Simple Interest)

Difference ≈ $4,579.94 - $1,441.00

Difference ≈ $3,138.94

Therefore, the future value of $500 after 41 years with compounding is approximately $3,138.94 more than with simple interest.

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Answer:

(2x-3) and (x-5)

Step-by-step explanation:

To factor the expression (2x-3)(x-5), we can use the distributive property of multiplication over addition or subtraction:

(2x-3)(x-5) = 2x(x-5) - 3(x-5)

Now we can use the distributive property again to factor out the common factor of (x-5):

2x(x-5) - 3(x-5) = (2x - 3)(x - 5)

So the factors of (2x-3)(x-5) are (2x-3) and (x-5).

Natalie bought pistachios at a lower price per pound compared to Nicholas.

To compare the prices of pistachios at store A and store B, we need to calculate the price per pound for each store based on the given information.

Natalie's purchase at store A:

Weight of pistachios = 3 4/5 pounds

Cost of pistachios = $17.75

To calculate the price per pound at store A, we divide the total cost by the weight:

Price per pound at store A = $17.75 / (3 4/5) pounds.

To simplify the calculation, we can convert the mixed fraction 3 4/5 to an improper fraction:

3 4/5 = (3 \(\times\) 5 + 4) / 5 = 19/5

Substituting the values, we have:

Price per pound at store A = $17.75 / (19/5) pounds

Price per pound at store A = $17.75 \(\times\) (5/19) per pound

Price per pound at store A = $3.947 per pound (rounded to three decimal places).

Nicholas's purchase at store B:

Weight of pistachios = 4 7/10 pounds

Cost of pistachios = $19.50

To calculate the price per pound at store B, we divide the total cost by the weight:

Price per pound at store B = $19.50 / (4 7/10) pounds

Converting the mixed fraction 4 7/10 to an improper fraction:

4 7/10 = (4 \(\times\) 10 + 7) / 10 = 47/10

Substituting the values, we have:

Price per pound at store B = $19.50 / (47/10) pounds

Price per pound at store B = $19.50 \(\times\) (10/47) per pound

Price per pound at store B = $4.149 per pound (rounded to three decimal places).

Comparing the prices per pound, we find that the price per pound at store A ($3.947) is lower than the price per pound at store B ($4.149).

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Answer:

8/3 or 5 1/3

Step-by-step explanation:

here's a visual tutorial I don't feel like writing, sorry

The box plot given by the number of students read 8 books is the centre quartile which is 5.

Three values called quartiles divide sorted data into four equal portions with the same amount of observations in each. One kind of quantile is a quantile.

Thus, for the stated question.

The box plot given by the number of students read 8 books is the centre quartile which is 5.

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Answer:

4 is a factor. Also, (3n - 5) is a factor.

The factored form of 12n - 20 is:

4(3n - 5)

Step-by-step explanation:

We're looking for the biggest number (sometimes its a variable with the biggest exponent, but not this time)

that goes into 12n and also goes into 20. 4 is the biggest number that goes into both 12n and 20. So we factor it out...this is like "un-distributive property" (if you have been studying distributive property, this is like reversing it)

12n - 20

= 4(3n - 5)

Answer:

B

Step-by-step explanation:

The lower the degree is the colder it is

Answer:

B

Step-by-step explanation:

Fahrenheit temperature depends on which is the highest to be the hottest. Since the negatives are lower than 0 the correct order would be

-12

-10

-8

-3

0

Answer:

I'm pretty sure the answer to the 1st question is 2.46 and the answer to the 2nd question is just 15. (I'm sorry if I'm wrong!)

The rate of change of y with respect to x is given by dy/dx = xy - (3/2)x²y.

To find the rate of change of y with respect to x, we need to differentiate the given equation. The rate of change can be determined by taking the derivative of both sides of the equation with respect to x.

First, let's differentiate each term separately using the rules of differentiation.

Differentiating x²y with respect to x gives us 2xy using the product rule.

To differentiate 5, we know that a constant has a derivative of 0.

Differentiating 2ln(y) with respect to x requires the chain rule. The derivative of ln(y) with respect to y is 1/y, and then we multiply by dy/dx. So, the derivative of 2ln(y) is 2/y * dy/dx.

Differentiating x³ gives us 3x² using the power rule.

Now, we can rewrite the equation with its derivatives:

2xy - 2/y * dy/dx = 3x²

To solve for dy/dx, we can isolate it on one side of the equation. Rearranging the equation, we get:

2xy = 2/y * dy/dx + 3x²

To isolate dy/dx, we move the term 2/y * dy/dx to the other side:

2xy - 2/y * dy/dx = 3x²

2xy = 2/y * dy/dx + 3x²

2/y * dy/dx = 2xy - 3x²

Now, we can solve for dy/dx by multiplying both sides by y/2:

dy/dx = (2xy - 3x²) * (y/2)

Simplifying further, we have:

dy/dx = xy - (3/2)x²y

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The sequences of transformations that could be applied to the parent function are (e) Reflect over the y-axis, vertically stretch by a factor of 2, and then shift up 6 units

The graph that completes the question is added as an attachment

From the attached graph, we have the following points

(3, 0) and (0, 6)

Calculate the equation of the line using

\(g(x) = \frac{y_2 - y_1}{x_2 -x_1} * (x - x_2) + y_2\)

This gives

\(g(x) = \frac{6 - 0}{0 -3} * (x - 0) + 6\)

Evaluate the quotient

g(x) = -2 * (x) + 6

Expand

g(x) = -2x + 6

This means that the equation of the line is:

g(x) = -2x + 6

So, we have:

f(x) = x as the parent function and g(x) = -2x + 6 as the transformed function.

The transformations from f(x) to g(x) are as follows:

Hence, the sequences of transformations that could be applied to the parent function are (e) Reflect over the y-axis, vertically stretch by a factor of 2, and then shift up 6 units

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Answer:

Large boxes are 18.25 kg

Small boxes are 15.25 kg

Step-by-step explanation:

This is a system of equations. You need to set up each equation first.

I am assigning x to be big boxes and y to be small boxes.

5x + 3y = 137

2x + 6y = 128

To solve, you will need to eliminate a variable. That means you will have to multiply one of the equations by a number to make it so a variable will be eliminated. I will be multiplying the top equation by -2.

-2 ( 5x + 3y = 137)

    2x + 6y = 128

Distribute the -2 to everything in the parentheses in the first equation.

-10x - 6y = -274

2x + 6y = 128

Notice the 6y will go away because -6y + 6y = 0. Now add the equations together. The remaining equation is:

-8x = -146

Solve for x by dividing by -8.

x = 18.25

Now plug that into one of the original equations.

2(18.25) + 6y = 128.

36.5 + 6y = 128                Subtract 36.5 from each side

-36.5            -36.5

6y = 91.5                          Divide by 6 to solve

y = 15.25