The vending machine in the school cafeteria usually dispenses about 6 ounces of soft drink. Lately, it is not working properly, and the variability of how much soft drink it dispenses has been gettin greater. The amounts are normally distributed with a standard deviation of 0.2 ounces.

1. What percent of the time will you get between 5.6 and 6.4 ounces?
(a) 13.5%
(b) 34%
(c) 50%
(d) 95%

2. What percent of the time will you get between 6 ounces and 6.2 ounces?
(a) 13.5%
(b) 34%
(c) 50%
(d) 95%

1,000,000,000 social Security numbers can be formed using the numerals 0-9.

A combination is grouping or sub-setting of items from a set where the order in which the selection is being made does not matter.

[tex]^{n}C_r = \frac{n!}{(n-r)!r!}[/tex]

where, n = Total number of items to be selected from.

r = Number of items to be selected.

According to the given problem,

Social security number contains nine digits.

A digit can be any number between 0-9.

For the first digit there are 10 choices which is 0-9 and the amount of numbers to be chosen is 1.

Thus there are [tex]^{10}C_{1}[/tex] ways for filling up first spot.

Similarly for the second digit , numbers available are 10 and numbers to be chosen is 9.

Thus there are [tex]^{10}C_{1}[/tex] ways for achieving this.

Same for third, fourth .. . . ninth digit.

Using the formula of combination, total number of ways would be,

= [tex]9 ~times~~ ^{10}C_{1}[/tex]

= [tex](\frac{10!}{1!\times (10-1)!})^9[/tex]

= 1000,000,000 ways

Hence we can conclude that there are 1000,000,000 ways of choosing 10 numbers from 0 to 9 for nine spots.

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Answer:

The answer is $704.73

Step-by-step explanation:

Answer:

The answer is A. $704.73

Step-by-step explanation:

Answer:

Based on calculations the correct answer is A

Step-by-step explanation:

One degree is equal 0.01745329252 radians:

1° = π/180° = 0.005555556π = 0.01745329252 rad

The angle α in radians is equal to the angle α in degrees times pi constant divided by 180 degrees:

α(radians) = α(degrees) × π / 180°

or

radians = degrees × π / 180°

Convert 30 degrees angle to radians:

α(radians) = α(degrees) × π / 180° = 30° × 3.1459 / 180° = 0.5236 rad

The angle α in radians is equal to the angle α in degrees times pi constant divided by 180 degrees:

α(radians) = (α(degrees) / 180°) × π

Convert 30 degrees angle to radians in terms of pi:

α(radians) = (α(degrees) / 180°) × π = (30° / 180°) × π

 = (1/6) × π = π/6 rad = 0.166667π rad

Final answer:

To convert degrees to radians, multiply the number of degrees by π and then divide by 180, or simply multiply by π/180. For instance, 45 degrees can be converted to radians as 45 degrees * (π/180) = π/4 radians.

Explanation:

To convert degrees to radians, you can use the basic formula that π radians equal 180 degrees. This means that to convert a degree measure to radians, you multiply the number of degrees by π and then divide by 180. This can be simplified to multiplying the number of degrees by π/180.

For example, if you wanted to convert 45 degrees to radians, you would perform the following calculation:

That means 45 degrees is equivalent to π/4 radians. Remember, the π symbol represents the mathematical constant pi, which is approximately 3.14159.

The median size of the four water parks, given as 66, 70, 60, 60 acres, is 63 acres.

To find the median of the sizes of the four water parks, we first need to list the sizes in ascending order. Given the sizes are 66, 70, 60, 60, the arranged list becomes 60, 60, 66, 70.

As there are four numbers, the median is the average of the middle two numbers. So by adding 60 and 66 and then dividing by 2, we find that the median size of the water parks is 63 acres.

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Answer:

7.

Step-by-step explanation:

The value of y is 50

Using the expression given:

substitute the value of q into the expression

Now we have :

y = 10 × 5

y = 50

Hence, the value of y is 50

The coordinates of the point that divides the line segment AB in the ratio of 1:4 are (8, 6).

To find the coordinates of the point that divides the line segment AB in the ratio of 1:4, we can use the formula:

x = (x1 + 1/n * (4 * x2)) / (1 + 1/n)

y = (y1 + 1/n * (4 * y2)) / (1 + 1/n)

Substituting the given coordinates into the formula, we have:

x = (10 + 1/4 * (4 * 2)) / (1 + 1/4) = 8

y = (4 + 1/4 * (4 * 8)) / (1 + 1/4) = 6

Therefore, the coordinates of the point that divides the line segment AB in the ratio of 1:4 are (8, 6).

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The simple interest paid on a $1,400 loan with an annual interest rate of 4% for 1 year is $56.

The subject of your question is simple interest calculation. The formula for calculating simple interest is: principal amount x interest rate x time. You are asked to calculate the simple interest paid on a $1,400 loan with an annual interest rate of 4% for 1 year. Let's proceed step-by-step:

So, the simple interest paid on the loan for 1 year is $56.

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Final answer:

Jason needs 4,257 square centimeters of fabric to cover the sides and top of his rectangular prism shaped ottoman, calculated by finding the area of each side and adding them together.

Explanation:

To calculate the amount of fabric needed to cover the sides and top of a rectangular prism shaped ottoman with dimensions 37 cm in length, 21 cm in width, and 30 cm in height, we start by determining the surface area of the ottoman that needs covering. We ignore the bottom surface, assuming the ottoman sits directly on the floor.

First, calculate the area of each side:

Top/bottom surface (only top applies here) = length × width = 37 cm × 21 cm = 777 cm²

Front/back surface = length × height = 37 cm × 30 cm = 1,110 cm² (two sides, so × 2)

Left/right side = width × height = 21 cm × 30 cm = 630 cm² (two sides, so × 2)

Next, add all the calculated areas together:

777 cm² (top) + 2,220 cm² (front/back) + 1,260 cm² (left/right) = 4,257 cm²

Therefore, Jason needs 4,257 square centimeters of fabric to cover the sides and top of the ottoman.

The number is given by the equation n = 8

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Let the number be represented as n

And , a number is the same as the square root of the product of 8 and the number

Substituting the values in the equation , we get

n = √ ( 8 x n )   be equation (1)

On simplifying the equation , we get

n = √8n

Taking squares on both sides of the equation , we get

n² = 8n

Divide by n on both sides of the equation , we get

n = 8

Therefore , the number is 8

Hence , the equation is n = 8

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Answer:

Option: B is the correct answer.

Enjoying movies and concerts are not independent since,

[tex]P(movies|concerts)\neq P(movies)[/tex]

and  [tex]P(concerts|movies)\neq P(concerts)[/tex]

Step-by-step explanation:

We know that if two events A and B are independent then:

[tex]P(A\bigcap B)=P(A)\times P(B)[/tex]

where P denote the probability of an event.

Now, we know that:

[tex]P(movies|concerts)=\dfrac{P(movies\bigcap Concerts)}{P(concerts)}[/tex]

Similarly:

[tex]P(concerts|movies)=\dfrac{P(movies\bigcap Concerts)}{P(movies)}[/tex]

If movies and concerts are independent then:

[tex]P(movies|concerts)=P(movies)[/tex]

Similarly:

[tex]P(concerts|movies)=P(concerts)[/tex]

We have:

[tex]P(movies)=0.6[/tex]

[tex]P(concerts)=0.55[/tex]

[tex]P(concerts|movies)=\dfrac{0.25}{0.6}[/tex]

[tex]P(movies|concerts)=\dfrac{0.25}{0.55}[/tex]

Hence,

Enjoying movies and concerts are not independent

Since,

[tex]P(movies|concerts)\neq P(movies)[/tex]

and  [tex]P(concerts|movies)\neq P(concerts)[/tex]

#1) 163.81 m

#2) About 9.8 laps.

#3) 1314 square meters

Explanation

#1) We first add all of the horizontal and vertical sections:

30+8+6+6+12+30+20 = 112 m

Now we find the distance around each curve.  The distance around a circle is the circumference; the formula for circumference is 

C=πd. 

We will use 3.14 for π for each curve:

Curve 5:  The radius is 3, so the diameter is 2*3 = 6.  This is 1/4 of a curve, so we multiply the circumference by 1/4:

1/4(3.14)(6) = 4.71

Curve 4:  This is another 1/4 curve with a radius of 3, so the distance around is 4.71.

Curve 3:  This is 1/2 of a curve, so we will multiply the circumference by 1/2.  The radius is 2.25, so the diameter is 2*2.25 = 4.5:

1/2(3.14)(4.5) = 7.065

Curve 2:  This is another 1/4 curve with a radius of 3, so the distance around is 4.71.

Curve 1:  This is another 1/4 curve with a radius of 3, so the distance around is 4.71.

Curve 9:  This is another 1/4 curve with a radius of 3, so the distance around is 4.71.

Curve 8:  This is another 1/4 curve with a radius of 3, so the distance around is 4.71.

Curve 7:  This is another 1/2 curve with a radius of 2.25, so the distance around is 7.065, just as curve 3.

Curve 6:  This is 1/2 of a curve with a radius of 3, so the distance around is 1/2(3.14)(2*3) = 9.42

The total distance around the curved parts is:

4.71+4.71+7.065+4.71+4.71+4.71+4.71+7.065+9.42 = 51.81

Together this gives us 112+51.81 = 163.81.

#2) To find the number of laps it takes to go 1609 meters, divide:

1609/163.81 = 9.8

#3) To find the rectangular area, we first need the total distance across and the total distance vertically.

Horizontally, we have a radius of 3, a horizontal distance of 30, and another radius of 3:

3+30+3 = 36

(looking at the right hand side)

Vertically, we have a radius of 3, vertical distance of 8, radius of 3, radius of 2.25, radius of 2.25, radius of 3, vertical distance of 12, and radius of 3:

3+8+3+2.25+2.25+3+12+3 = 36.5

The area is then 36(36.5) = 1314 m²

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Jessica added exactly ¼ cup of vanilla powder, weighing 32 grams, to her recipe. This is the perfect amount as stated by the cake recipe.

Jessica is tasked with following a cake recipe that requires 32 grams of vanilla powder. She knows that 1 cup of vanilla powder weighs 128 grams. Since she added only ¼ cup of vanilla powder, we need to calculate if this amount is equivalent to the required 32 grams.

First, let's determine how many grams are in ¼ cup of vanilla powder:

Therefore, Jessica has added the perfect amount of vanilla powder to her recipe.