Adding fractions

1/5 + 2/22

Answer:

8

Step-by-step explanation:

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Answer:

24 sides

Step-by-step explanation:

An exterior angle of a regular polygon is 360 divided by the number of sides. The exterior angle is equal to the interior angle subtracted from 180. We can say an exterior angle of this polygon is 180 - 165 or 15. From the first property, we can write an equation:

360/n = 15

360 = 15n

n = 24

24 sides

Another way to do this, is the formula for an interior angle of a regular polygon is:

180(n - 2)/n

This is equal to the interior angle:

180(n-2)/n = 165

180n - 360 = 165n

15n - 360 = 0

15n = 360

n = 24

Answer:

B

Step-by-step explanation:

4 represents the number of bounces

and 1/2 represents the decreases in the height of  bounce

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Answer:

Step-by-step explanation:

Equation:

-3k = 108

We need to separate -3 from k. So we must do the inverse operation.

Divide both sides by -3

k = -36

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Answer:

sqrt(2) sqrt(5) sqrt(2) sqrt(5)

Step-by-step explanation:

sqrt(2) sqrt(5) sqrt(2) sqrt(5)

We know sqrt(a) sqrt(b) = sqrt(ab)

sqrt(2*2) sqrt(5*5)

sqrt(4) sqrt(25)

2 * 5

10

This is a rational number

Answer:

\(\sqrt{2}\) · \(\sqrt{5}\) · \(\sqrt{2}\) · \(\sqrt{5}\)

Step-by-step explanation:

In mathematics, a rational number is a number that can be written as a fraction. Clear and sensible numbers are all real numbers and can be positive or negative. A number that is not clear and sensible is called weird (because of wrong thinking). Most of the numbers that people use in everyday life are clear and sensible. These include fractions and integers.

\(\sqrt{2}\) · \(\sqrt{5}\) · \(\sqrt{2}\) · \(\sqrt{5}\) is a rational number!

Answer:

0.37

Step-by-step explanation:

3.7 ➗ by 10 = 0.37^1 = 0.37

By comparing the speeds of all the people, Bob picked apple the fastest.

Speed is generally the change in distance per unit time. In this case instead of distance we can use the number of apples.

For this question, speed of picking apples = no of apples / time (in minutes). For Bob, speed = 15/8 = 1.88 apples/minute

For Mary, speed = 16/16 = 1 apples/minute

For Suie, speed = 10/19 = 0.526 apples/minute

This shows that Bob picked apples the fastest.

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Answer:

the answer would be C

Step-by-step explanation:

Answer:

No it wouldn’t be

Step-by-step explanation:

Well lets say the cost of 6.99 is rounded up to 7 since its a penny short.

There are 6 people and 6*7=42

So the answer would be about 42 dollars which is 12 dollars off.

Even if we round down the 6.99 to 6 it would still be 6 dollars off and thats still a low estimate

Answer:18

Step-by-step explanation:3^3 times 2

Maria spends $22 on lottery tickets every week and $133 every month on food yearly

This means that in a year

there are 52 weeks and she spends 22 x 52 = $1,144 on Lottery tickets

and there are 12 months in a year, so she spends 133 x 12 = $1,596 on food

The money spent to buy lottery tickets in relation to the money spent on food yearly in percentage is

Answer: D. height when first thrown

Step-by-step explanation:

         The constant term, 5, in this equation represents the height of the ball when it was first thrown. This means that our answer is option D.

         This constant term (5) is also the y-intercept. When we graph this equation, the line starts at (0, 5) if you ignore the negative values since we cannot have a negative time for this scenario. This is a visual representation of the ball being thrown.

To solve a question like this, you will need to factorise the first term of the expression out.

So, our expression becomes

Now, you will need to find the factors of 28 whose sum will give you -3

Always remember to express it in terms of x.

The answer to that is -7x and +4x. Thus we can rewrite the expression as;

In summary 3x^2-9x-84​ can be factorized as

Answer:

Sorry if I’m wrong but is it ... 90???

Step-by-step explanation:

========================================================

Work Shown:

The given list is {95, 89, 99, 85, 82, 81, 99}

Sort this list from smallest to largest.

We then have this: {81, 82, 85, 89, 95, 99, 99}

Next we will erase the first and last items in that sorted list above

Doing so leads to this smaller list: {82, 85, 89, 95, 99}

Repeat the step from before. Erase the first and last items

We now have {85, 89, 95}

One more time lets erase the first and last items getting {89}

This shows that 89 is the very center item

Going back to {81, 82, 85, 89, 95, 99, 99} we see that 89 is at the center with three items below it (81,82,85) and three items above it (95,99,99)

Therefore, the median is 89.

----------------------------------

Another route to take is to count the number of items in {81, 82, 85, 89, 95, 99, 99}. You should count 7 items.

Add 1 and divide by 2 to get (7+1)/2 = 8/2 = 4

The median is in slot 4, which is exactly where 89 is located in the list {81, 82, 85, 89, 95, 99, 99}

Note: this trick only works if you have an odd number of items in a set.

The value of the given sine function is √3/2, so the correct option is 2nd.

Given that an function Sin (-5π/3) we need to evaluate the expression,

To evaluate the trigonometric function sine of the angle (-5π/3), we can use the periodicity of the sine function.

Since the sine function has a period of 2, the sine of any given angle is equal to the sine of that angle plus or minus any multiple of 2.

To find an equal angle inside the main range (between -π and π), we can add 2 to the angle (-5/3).

Once adding 2:

(-5π/3) + 2π = (-5π/3) + (6π/3) = π/3

Now we can evaluate the sine of π/3, which is a commonly known angle. The sine of π/3 is √3/2.

Therefore, sin(-5π/3) = sin(π/3) = √3/2.

Hence the correct option is √3/2

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Answer:

The number is 6

Step-by-step explanation:

let the number=x

4(x-1)=3x+2

4x-4=3x+2

4x-3x=2+4

x=6

The number of  boys and girls in a class of 150 students is 90 and 60 respectively.

RATIO:

Comparing two quantities of the same units and determining the ratio tells us how much of one quantity is in the other.

i.e., it shows how many times a number contains another.

Total number of students = 150

ratio of boys to girls = 3 : 2

B:G = 3 : 2

now

3x + 2x = 150

5x = 150

x = 30

the number of boys = 3x = 3 X 30 = 90 boys.

the number of girls = 2x = 2 X 30 = 60 girls.

The number of  boys and girls in a class of 150 students is 90 and 60 respectively.

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PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right, Addition and Subtraction. The solution to the Expression (3^0 * 8^2)^-2 is 1/4096.

The expression (3^0 * 8^2)^-2, the order of operations, which is typically referred to as PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right, Addition and Subtraction from left to right).

Step 1: Simplify the exponent expressions within the parentheses:

(3^0 * 8^2) = (1 * 64) = 64

Step 2: Rewrite the expression with the simplified value:

(64)^-2

Step 3: Apply the exponent rule for a negative exponent:

(64)^-2 = 1 / (64)^2

Step 4: Evaluate the expression within the parentheses:

(64)^2 = 64 * 64 = 4096

Step 5: Rewrite the expression with the simplified value:

1 / 4096

Therefore, the solution to the expression (3^0 * 8^2)^-2 is 1/4096.

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Using the properties of mean and standard deviation, the mean of the total volume of the beverage in the case is 480.24 ounce and the standard deviation of the total volume of the beverage in the case is 0.48 ounce.

Mean is the average of all numbers given. Whereas, standard deviation is the measure of spread of the numbers.

The properties of mean and standard deviation used :

\(\mu_{aX+b} = a\mu+b\\\\\sigma_{aX+b} = a\sigma+b\\\)

Given,

mean of fill volume of bottles = 20.01 ounce

standard deviation of fill volume of bottles = 0.02 ounce

number of bottles in case = 24

Using the properties above:

mean of case = number of bottles in case * mean of fill volume of bottles = 24 * 20.01 = 480.24 ounce

standard deviation of case = number of bottles in case * standard deviation of fill volume of bottles = 0.02 * 24 = 0.48 ounce

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complete question is given below:

A machine that fills bottles with a beverage has a fill volume whose mean is 20.01 ounces, with a standard deviation of 0.02 ounces. A case consists of 24 bottles randomly sampled from the output of the machine. a. Find the mean of the total volume of the beverage in the case. b. Find the standard deviation of the total volume of the beverage in the case.

The length of the rectangular  playground is 241.86 foot.

Given that area of rectangle is 19,500 sq.ft and length of rectangle is three times its width.The area for rectangle is given by formula: A=LW.

Now according to the given condition, L= 3W. Further we'll solve by putting L= 3W in the formula for rectangle.

A=LW

As given A= 19,500 sq.ft and considering L=3W,

19,500 = 3W*W

19,500 = 3W^2

∴ W^2 = 6500

∴ W = \(\sqrt{6500}\)

∴ W = 80.6225 ft. ≈ 80.62 ft.

Now putting the value W = 80.62 in equation L =3W,

L = 3* 80.62

L = 241.86 ft.

The length of the rectangular playground is 241.86 foot.

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Answer:

The slope is -2

Step-by-step explanation:

In any equation that is in the form of this question, the slope is always the number next to x. An example could be y = 6x - 1, the slope would be 6. If we had y = -100x - 5, the slope would be -100.

The length of arc BC is 8/3 feet.

To find the length of arc BC, we first need to find the measure of angle BOC, where O is the center of the circle. Since angle BAC is 1/3 of one radian, and the central angle BOC intercepts the same arc BC, we know that angle BOC is three times angle BAC, or one radian.

Since the radius of the circle is 8 feet, the circumference is 2πr, or 16π feet. Since angle BOC is one radian, it subtends an arc on the circumference that is 1/2 of the total circumference, or 8π feet.

Therefore, the length of arc BC is 1/3 of arc BOC, or 8π/3 feet.

To find the length of arc BC, we will follow these steps:

1. Identify the given information: The radius of the circle is 8 feet, and the angle BAC is 1/3 of a radian.

2. Determine the central angle in radians: Since angle BAC is 1/3 of a radian, the central angle (θ) of the circle that corresponds to arc BC is also 1/3 of a radian.

3. Calculate the length of arc BC using the formula: Arc length (L) = radius (r) × central angle (θ).

In this case, r = 8 feet and θ = 1/3 radian.

L = 8 × (1/3)
L = 8/3

4. Simplify the expression: L = 8/3 feet.

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To verify that all sales that have been shipped to customers have been recorded, a test of transactions should be completed on a representative sample drawn from the sales records or shipping records.

The sample should be chosen randomly and be large enough to provide a reasonable level of confidence in the accuracy of the recorded transactions. This test will help ensure that all sales have been properly recorded in the accounting system and that there are no unrecorded sales. It is important to perform this test on a regular basis to maintain the integrity of the financial records.

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Answer:

There are 68,640 different ways the runners can finish first, second, and third in the race.

Concept of Permutations

The number of different ways the runners can finish first, second, and third in a race can be calculated using the concept of permutations.

Brief Overview

Since there are 42 runners competing for the top three positions, we have 42 choices for the first-place finisher. Once the first-place finisher is determined, there are 41 remaining runners to choose from for the second-place finisher. Similarly, once the first two positions are determined, there are 40 runners left to choose from for the third-place finisher.

Calculations

To calculate the total number of different ways, we multiply the number of choices for each position:

42 choices for the first-place finisher × 41 choices for the second-place finisher × 40 choices for the third-place finisher = 68,640 different ways.

Concluding Sentence

Therefore, there are 68,640 different ways the runners can finish first, second, and third in the race.

Answer:

1/2,187

1/367

3^-7

Step-by-step explanation:

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Answer:

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