Josiah kept track of how many songs of each genre were played in an hour from his MP3 player. The counts are displayed in the table below. He has a total of 1,500 songs on his player. Josiah predicted the number of rock songs on his MP3 player to be 300 songs. Which statements about his solution are true? Select three choices. Josiah’s Music Sample 1 Sample 2 R & B 5 R & B 4 Pop 4 Pop 3 Classical 3 Classical 5 Jazz 2 Jazz 4 Rock 6 Rock 4 Josiah’s work: StartFraction 10 over 20 EndFraction = StartFraction x over 1,500 EndFraction. StartFraction 10 times 30 over 20 times 30 EndFraction = StartFraction x over 1,500 EndFraction. 300 = x. He should have found the average of the number of rock songs by averaging 4 and 6 to get 5. He did not multiply the numerator and denominator by the correct number to equal 1,500. His answer will be one-half of what he got because he did not divide 10 by 2 when setting up the proportion. He can only solve the proportion by multiplying the numerator and denominator by a common multiple. He should have multiplied the numerator and denominator by 75, not 30, because 20 times 75 = 1,500.

The value of the Integral at the lower limit from the value of the integral at the upper limit to get the length of the curve.

The length of the curve described by the function f(x) = 1 + 3x^2 + 2x^3 is to be found. The formula used to find the length of a curve is:

L = ∫(sqrt(1 + [f'(x)]^2))dx where f'(x) is the derivative of f(x)We have to first find f'(x):f(x) = 1 + 3x^2 + 2x^3f'(x) = 6x + 6x^2

The integral becomes:L = ∫(sqrt(1 + [6x + 6x^2]^2))dx = ∫(sqrt(1 + 36x^2 + 72x^3 + 36x^4))dx The integral appears to be difficult to evaluate by hand.

Therefore, we use software like Mathematica or Wolfram Alpha to solve the problem. Integrating the expression using Wolfram Alpha gives:

L = 1/54(9sqrt(10)arcsinh(3xsqrt(2/5)) + 2sqrt(5)(2x^2 + 3x)sqrt(9x^2 + 4))The limits of integration are not given. Therefore, the definite integral  be solved.

We can, however, find a general solution. We use the above formula and substitute the limits of integration.

Then, we subtract the value of the integral at the lower limit from the value of the integral at the upper limit to get the length of the curve.

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Answer:

A

Because you have to Multiply  

189 by 36

The quotient when 480 is divided by -60 is 8.

Division is one of the operation in mathematics where number is divided  into equal parts as that of a definite number.

The numbers given are 480 and -60.

Both are in opposite signs, that is one negative and other positive.

So the quotient will be negative.

Now divide 480 by 60.

Since both of the numbers contain 0 at the end, cancel it.

Then it becomes 48 divided by 6.

48 / 6 = 8

Hence the quotient is 8.

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The Coalition for Airline Passengers Rights, Health, and Safety averages 400 calls a day to help stranded travelers deal with airlines. The hotline is staffed for 16 hours a day.

To calculate the average number of calls in different time intervals and the probability of different events related to these calls.

Part 1:

a. 60-minute interval average number of calls: 400/16 = 25 calls

30-minute interval average number of calls: 25/2 = 12.5 calls

15-minute interval average number of calls: 12.5/2 = 6.25 calls

Part 2:

b. To find the probability of exactly 6 calls in a 15-minute interval, we can use the Poisson distribution formula. Let's assume that the average number of calls in a 15-minute interval is 6.25. Then, the probability of exactly 6 calls in a 15-minute interval is:

P(6 calls) = (e^-6.25)*(6.25^6)/6! = 0.0686

c. To find the probability of no calls in a 15-minute interval, we can use the Poisson distribution formula. Let's assume that the average number of calls in a 15-minute interval is 6.25. Then, the probability of no calls in a 15-minute interval is:

P(0 calls) = e^-6.25 = 0.0047

d. To find the probability of at least two calls in a 15-minute interval, we can use the cumulative distribution function of the Poisson distribution. Let's assume that the average number of calls in a 15-minute interval is 6.25. Then, the probability of at least two calls in a 15-minute interval is:

P(X >= 2) = 1 - P(0 calls) - P(1 call) = 1 - 0.0047 - (e^-6.25)*(6.25^1)/1! = 0.9906

Thus, the average number of calls in a 60-minute interval is 25, in a 30-minute interval is 12.5, and in a 15-minute interval is 6.25. The probability of exactly 6 calls in a 15-minute interval is 0.0686, the probability of no calls in a 15-minute interval is 0.0047, and the probability of at least two calls in a 15-minute interval is 0.9906.

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For the function, the x-intercept of g(x) is at (5,0).

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input.

Given f(x) = ln(x)

and g(x) = -f(x - 4)

the function is

g(x) = -ln(x - 4)

when x = 5

g(x) = -ln(5 - 4)

g(x) = -ln1

g(x) = 0

the coordinates are (5, 0)

Hence the x-intercept is (5, 0).

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Answer:

-17.5

Step-by-step explanation:

-10 = -2x - 45

(add 45 on both sides)

35 = -2x

(divide both sides by -2)

x = -17.5

The graph shows that Becca walks five dogs at the end of the third month.

We know that we can be able to read off the graph of an function that has been shown such as the one that we have in the image that has been attached to this answer.

We can see that the graph of the function agrees that Becca's dog-walking business started with 1 dog. By the end of the first month , she was walking 2 additional dogs per month .  We would now read off the graph to know the number of dogs that he walks after three months.

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The point of intersection of the equations C = 100t + 5000 and C = 75t + 7000 represents the  the point in time where the cost of installing either will be the same.

Linear equations are equations where the right hand side and left hand side involves expressions with one or more variables for which the highest degree of the variable being 1.

We have two linear equations given,

C = 100t + 5000 and C = 75t + 7000.

The point of intersection of these linear equations will be when both the equations are equal.

100t + 5000 = 75t + 7000

100t - 75t = 7000 - 5000

25t = 2000

t = 2000/25

t = 80

This is the point in time where the cost of installing either will be the same, that is after 80 months.

Cost of installing = (100 × 80 ) + 5000 = 13,000

Or                         = (75 × 80) + 7000 = 13000

Hence the point of intersection of these equations represent the point in time where the cost of installing either will be the same.

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Add 16 to both sides to undo the -16

We go from x - 16 < 11 to x < 27

The graph involves an open hole at 27, shading to the left

This is to visually describe any number smaller than 27. The value 27 itself is not part of the solution set, which is why we use an open hole.

The total amount the man had = 52,200 rupees. Out of this, he gave 21,750 rupees to his son, 13,050 rupees to his daughter, and 17,400 rupees to his wife , the total amount given away by the man = 21,750 + 13,050 + 17,400 = 52,200 rupees.

A man gave 5/12 of his money to his son, 3/7 of the remainder to his daughter, and the remaining to his wife. If his wife gets Rs. 8,700, what is the total amount?

The given problem can be solved using the concept of ratios and fractions. Let us solve the problem step-by-step.Assume the man had x rupees with him.The man gave 5/12 of his money to his son.

The remaining amount left with the man = x - 5x/12= (12x/12) - (5x/12) = (7x/12)The man gave 3/7 of the remainder to his daughter.'

Amount left with the man after giving it to his son = (7x/12)The amount given to the daughter = (3/7) x (7x/12)= (3x/4)The remaining amount left with the man = (7x/12) - (3x/4)= (7x/12) - (9x/12) = - (2x/12) = - (x/6) (As the man has given more money than what he had with him).

Therefore, the daughter's amount is (3x/4) and the remaining amount left with the man is (x/6).The man gave all the remaining amount to his wife.

Therefore, the amount given to the wife is (x/6) = 8700Let us find the value of x.x/6 = 8700 x = 6 x 8700 = 52,200

Therefore, the man had 52,200 rupees with him.He gave 5/12 of his money to his son. Therefore, the amount given to his son is (5/12) x 52,200 = 21,750 rupees.

The remaining amount left with the man = (7/12) x 52,200 = 30,450 rupees.He gave 3/7 of the remainder to his daughter. Therefore, the amount given to his daughter is (3/7) x 30,450 = 13,050 rupees.

The amount left with the man = (4/7) x 30,450 = 17,400 rupees.The man gave 17,400 rupees to his wife.
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To enlarge the photo proportionally so that it is as wide as the computer screen, we need to find the scaling factor. The scaling factor is the ratio of the width of the computer screen to the width of the photo:

Scaling factor = 1024 ÷ 640 = 1.6

We can then use this scaling factor to find the new dimensions of the photo:

New width = 640 × 1.6 = 1024 pixels

New height = 300 × 1.6 = 480 pixels

Therefore, the new dimensions of the photo are 1024 × 480 pixels.

2a. We cannot enlarge the photo proportionally so that it is as tall as the computer screen because the aspect ratio of the photo is different from the aspect ratio of the computer screen. The aspect ratio of the photo is 640 ÷ 300 ≈ 2.13, while the aspect ratio of the computer screen is 1024 ÷ 768 ≈ 1.33. This means that if we enlarge the height of the photo to match the height of the computer screen, the width of the photo will be too wide to fit on the screen.

b. We cannot correct the difficulty in (a) by scaling the width of the photo by a factor of 1024 ÷ 640 and the height by a factor of 768 ÷ 300 because this would change the aspect ratio of the photo. The aspect ratio of the photo would become 1024 ÷ (640 × 1024 ÷ 640) ≈ 1.6, which is the same as the aspect ratio of the computer screen. However, the height of the photo would be scaled by a factor of 768 ÷ 300 ≈ 2.56, which would make the photo too tall to fit on the screen.

To enlarge the photo proportionally, we need to scale it up by the same factor in both dimensions. Since we want to scale it so that its width matches the width of the screen, we can find the scaling factor by dividing the screen width by the photo width:

scaling factor = screen width / photo width = 1024 / 640 = 1.6

Now we can use this scaling factor to find the new height of the photo:

new height = photo height x scaling factor = 300 x 1.6 = 480 pixels

Therefore, after the photo is scaled up proportionally, its measurements are 1024 x 480 pixels.

2a. We can't enlarge the photo proportionally so that it is as tall as the computer screen because its aspect ratio (the ratio of its width to its height) is different from the aspect ratio of the screen. The photo's aspect ratio is 640/300 = 2.13, while the screen's aspect ratio is 1024/768 = 1.33. Enlarging the photo so that its height matches the screen's height would require stretching the photo vertically, which would distort the image.

2b. Scaling the width of the photo by a factor of 1024/640 and the height by a factor of 768/300 would not correct the difficulty in part (a) because it would not change the aspect ratio of the photo. The aspect ratio of the photo would still be 2.13, which is different from the aspect ratio of the screen. The photo would still need to be stretched vertically to match the screen's height, which would distort the image.

Answer:

11

Step-by-step explanation:

Substituting the values of x, y, and z into the expression, we get:

2x² - y + 2(z-1) = 2(2)² - 3 + 2(4-1)

= 2(4) - 3 + 2(3)

= 8 - 3 + 6

= 11

Therefore, if x = 2, y = 3, and z = 4, then the value of the expression 2x² - y + 2(z-1) is 11.

Answer:

11

Step-by-step explanation:

if x = 2, y = 3, and z = 4.

2x²-y + 2(z-1)

Substituting the given values of x, y, and z, we get:

2x² - y + 2(z-1) = 2(2)² - 3 + 2(4-1)

= 2(4) - 3 + 2(3)

= 8 - 3 + 6

= 11

Therefore, the value of the expression when x = 2, y = 3, and z = 4 is 11.

BODMAS (Brackets, Order, Division, Multiplication, Addition, Subtraction) is used to determine the sequence of operations in a mathematical expression. It is used to avoid confusion and ensure that everyone obtains the same answer from a mathematical expression. The rule states that the operations inside the brackets must be done first, followed by orders, then division and multiplication (from left to right), and finally addition and subtraction (from left to right).

Answer:

30 oz of dog food

Step-by-step explanation:

you want to multiply the number 6 over the number of dogs there are and there are 5 so that is 5•6 which =30

Answer:

column 2

Step-by-step explanation:

Answer:

week 4 so D

Step-by-step explanation:

Answer:

Step-by-step explanation:

MODE

3,4,4,5,5,5,5,5,7,7,8,8,10,10,14

MEAN

10-6=4

MEDIAN

3,4,4,5,5,5,5,5,5,7,7,8,8,10,10,14 CROSS OUT THE FIRST AND THE END THE DO IT AGAIN UNTIL YOU GET TO THE middle.

MEDIAN =5

RANGE IS BIGGEST- SMALLEST

10-3=7  

Brooklyn needs to invest $432.43, rounded to the nearest ten dollars.

To determine how much Brooklyn needs to invest in an account that pays a continuously compounded interest rate, we can use the formula:

A = \(Pe^(^r^t^)\)

where A is the future value of the account, P is the principal investment, e is the mathematical constant approximately equal to 2.71828, r is the interest rate, and t is the time in years.

In this case, we want the future value of the account to be $640, the interest rate is 3.5% (or 0.035 as a decimal), and the time is 9 years. We can substitute these values into the formula and solve for P:

640 = \(Pe^(^0^.^0^3^5^*^9^)\)

640 = Pe^0.315

P =\(640/e^0^.^3^1^5\)

P = 432.43

Therefore, to have a future value of $640 in 9 years with a continuously compounded interest rate of 3.5%.

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Answer:

Brody will have to work 30 hours.

Step-by-step explanation:

First you have to divide 396.10 by 17 to get $23.30 which is how much he earns per hour. Then you divide 699.0 by 23.30 to get 30 hours.

Answer:

The other side = 13 feets long

Step-by-step explanation:

Given that :

Scale of drawing : 2 inches represents 5 feets

Area of rectangular room according to scale drawing = 24.96 in²

Length of one side of the room = 12 feets

Length of other side = x

Area of rectangle = Length * width

If :

2 inches = 5 feets

x = 12 feets

x = (12 *2) / 5

x = 4.8 inches

Hence,

For the scaled drawing :

4.8 * width = 24.96

Width = 24.96 / 4.8

Width = 5.2 inches

Converting to feets according to scale:

2 inches = 5 feets

5.2 inches = x feets

x = (5.2 * 5 ) / 2

x = 13 feets

Other side is 13 feets long

Answer:

A machine has 12 identical components which function independently. The probability that a component will fail is 0.2. The machine will stop working if more than three components fail. Find the probability that the machine will stop working. A) 0.073 B) 0.795 C) 0.867 D)0.205

a) Using the four basic mathematical operations, the number of balloons that each person hang up is 9.

b) An equation representing the situation is x = (125 - 80)/5.

The four basic mathematical operations include addition, subtraction, division, and multiplication.

The mathematical operations provide solutions to mathematical problems using operands.

An equation is a mathematical statement showing that two or more mathematical expressions are equal or equivalent.

The total number of balloons that Andre has = 125

The number of balloons remaining after hanging some for the school party = 80

The difference (number of balloons used) = 45 (125 - 80)

The number of friends who hang the balloons = 5

The number of balloons hung by each friend of Andre = 9 (45/5)

Thus, we can conclude that each of the 4 friend and Andre hung 9 balloons, with 80 remaining.

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Answer:

Mean before the rent changes = $935.8

Mean after the rent changes = $970.8

Step-by-step explanation:

Mean = sum of all data values / number of data values in a given data set

✔️Data set consisting of the rents of 5 tenants: 879 , 920 , 940 , 950 , 990

Mean before the rent changes = (879 + 920 + 940 + 950 + 990)/5 = 4,679/5 = 935.8

Mean before the rent changes = $935.8

✔️If one of the tenants rent changes from $940 to $1,115, the new data set would be:

879 , 920 , 1,115 , 950 , 990

Mean after the rent changes = (879 + 920 + 1,115 + 950 + 990)/5 = 4,854/5 = 970.8

Mean after the rent changes = $970.8

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

To find the quotient of z₁ by z₂ in trigonometric form, we'll express both complex numbers in trigonometric form and then divide them.

Let's represent z₁ in trigonometric form as z₁ = r₁(cosθ₁ + isinθ₁), where r₁ is the magnitude of z₁ and θ₁ is the argument of z₁.

We have:

z₁ = 7(cos(577°) + i sin(577°))

Now, let's represent z₂ in trigonometric form as z₂ = r₂(cosθ₂ + isinθ₂), where r₂ is the magnitude of z₂ and θ₂ is the argument of z₂.

From the given information, we have:

z₂ = 21(cos(-7°) + i sin(-77°))

To find the quotient, we divide z₁ by z₂:

z₁ / z₂ = (r₁/r₂) * [cos(θ₁ - θ₂) + i sin(θ₁ - θ₂)]

Substituting the given values, we have:

z₁ / z₂ = (7/21) * [cos(577° - (-7°)) + i sin(577° - (-7°))]

= (7/21) * [cos(584°) + i sin(584°)]

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

Option C, 21(cos(-7°) + i sin(-77°)), is not the correct answer as it does not represent the quotient of z₁ by z₂.

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The ratio of girls to boy is 5:3. There are 30 boys in the class.

The ratio of boys to girls is 3:5. This means that in a class, for every 5 girls, there are 3 boys. We can also look at it this way, in a class, 3/8th students are boys and 58th of students are girls.

Now if there are 3/8th girls and 5/8th boys, the ratio of girls is to boys will be

5/8 : 3/8

removing 1/8 which is common we get

5:3

In  a class of 50 students, the ratio of boys to girls is 3:2

Therefore,

Boys comprise

3/(3+2) of the population.

Hence, 3/5 of the total population are boys.

Hence there are 3/5  X 50 boys

= 30 boys.

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Answer:

A) \(x=-1\pm\sqrt{\frac{13}{6}}\)

Step-by-step explanation:

\(\displaystyle x=\frac{-12\pm\sqrt{12^2-4(6)(-7)}}{2(6)}\\\\x=\frac{-12\pm\sqrt{144+168}}{12}\\\\x=\frac{-12\pm\sqrt{312}}{12}\\\\x=\frac{-12\pm2\sqrt{78}}{12}\\\\x=-1\pm\frac{\sqrt{78}}{6}\\\\x=-1\pm\sqrt{\frac{78}{36}}\\\\x=-1\pm\sqrt{\frac{13}{6}}\)

Answer:

311.0625

i think

sorry if its not correct

Step-by-step explanation:

the volume of the prism is

length × width × height = 72 in³

the volume of a pyramid is

length × width × height / 3

with the same sizes this means the volume of the pyramid is the volume of the prism / 3 = 72/3 = 24 in³

The diameter of the washing machine which is equivalent to the wavelength using the graph above would be = 2.5in.

To calculate the diameter of the washing machine drum, the formula that should be used is given below as follows;

V = fλ

where

V = displacement/time

F = 1/T

But;

Displacement = 10 in

Time = 2 seconds

V = 10/2 = 5 in/s

F = 1/2 = 0.5

λ = 5/0.5 = 2.5in

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Answer:

d. none

Step-by-step explanation: