14. Peter makes $15 per hour as a gardener. He gets a 10% raise. Which of the following
statements are true about Peter's new rate of pay? Select the three correct answers,
A Peter will make an additional 1/100 of his salary per hour.
(B) Peter will make an additional $1.50
per hour.
C Peter's new hourly rate is $16 per hour.
D After working 5 hours at the new rate, Peter will make $82.50.
E If Peter gets an additional 10% raise, his new pay rate will be $18.15.

Answers

Answer 1
Okay so peter makes 30 every week, so peter would make a total of 40 with all of the money you add on. Hope this helps!
Answer 2
B: additional $1.5, D: 5 hours makes $82.5, and E: another raise would be 18.15

Related Questions

Express 1:0.2:0.75 in their simple form

Answers

The given ratio 1:0.2:0.75 can be expressed in its simplest form as 5:1:3/4.

To express 1:0.2:0.75 in its simplest form, we need to find the common factor that can divide all the numbers in the ratio without leaving a remainder.

First, we can convert 0.2 to a fraction by dividing 2 by 10, which gives us 1/5. Thus, the ratio can be rewritten as

1:0.2:0.75

= 1:2/10:0.75

= 1:1/5:0.75.

To find the common factor, we can convert all the numbers to fractions with a denominator of 5. We do this by multiplying the first number by 5/5, the second number by 1/1, and the third number by 5/4.

This gives us,

5/5:1/5:15/20.

Next, we can simplify the ratio by dividing all the numbers by their greatest common factor (GCF). In this case, the GCF is 1/5.

Dividing all the numbers in the ratio by 1/5 gives us,

5:1:15/4.

Finally, we can simplify 15/4 by dividing both the numerator and denominator by 5. This gives us 3/4. Thus, the final simplified ratio is 5:1:3/4.

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A local city government wants to display the ages of the city citizen. Would it be better to organize the data using a dot plot or a histogram, and why?

Answers

If local city government wants to display the ages of the city citizen, It would be better to organize the data using a histogram.

A histogram is a graph that shows the distribution of a set of continuous data. The ages of city citizens can be considered as continuous data, as there are many possible values for age within a certain range.

A dot plot, on the other hand, is a graph that shows the distribution of a set of discrete data. Discrete data are values that can only take on specific, isolated values, like shoe sizes or the number of siblings a person has.

A histogram would be more effective for displaying the distribution of the ages of city citizens because it can show the range of ages in a more continuous manner, and provide a more precise representation of the frequency of the different age groups.

A dot plot, on the other hand, would be less effective, as it could be difficult to represent every age value as a single dot, and the resulting graph may not provide a clear indication of the distribution of ages.

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Find the sum:

125 (base 7) + 256 (base 7)

Answers

The sum of 125 (base 7) and 256 (base 7) is 404 (base 7). To compute it, we convert each number to base 10, add them, and then convert the result back to base 7.

Write each number in expanded form using powers of 7.

125 (base 7) = 1 x 7² + 2 x 7¹ + 5 x 7⁰ = 49 + 14 + 5 = 68

256 (base 7) = 2 x 7² + 5 x 7¹ + 6 x 7⁰ = 98 + 35 + 6 = 139

Add the two numbers together to get the sum in decimal form.

68 + 139 = 207

Convert the decimal sum to base 7 using repeated division by 7.

Divide 207 by 7 to get a quotient of 29 and a remainder of 4. Write down the remainder as the rightmost digit in the base 7 representation. Divide 29 by 7 to get a quotient of 4 and a remainder of 1. Write down the remainder as the next digit to the left in the base 7 representation.

Divide 4 by 7 to get a quotient of 0 and a remainder of 4. Write down the remainder as the leftmost digit in the base 7 representation.

So the sum of 125 (base 7) and 256 (base 7) is 404 (base 7).

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On a computer screen, lengths and widths are measured not in inches or millimeters but
in pixels. A pixel is the smallest visual element that a computer is capable of processing. A
common size for a large computer screen is 1024 × 768 pixels. (Widths rather than heights are
conventionally listed first.) For the following, assume you’re working on a 1024 × 768 screen.
1. You have a photo measuring 640 × 300 pixels and you
want to enlarge it proportionally so that it is as wide as the
computer screen. Find the measurements of the photo after it
has been scaled up. Explain how you found the answer.
2. a. Explain why you can’t enlarge the photo proportionally so
that it is as tall as the computer screen.
b. Why can’t you 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

Answers

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.

Solve the following logarthlic equations : 3ln(2x) =12

Answers

Step-by-step explanation:

[tex]3 ln(2x) = 12[/tex]

[tex] ln(2x) = 4[/tex]

Let both sides be a power of a base e.

[tex]e {}^{ln(2x)} = e {}^{4} [/tex]

The e and ln would just cancel out so

[tex]2x = e {}^{4} [/tex]

[tex]x = \frac{ {e}^{4} }{2} [/tex]

help nowwwwwwww PLSSSS

Answers

Answer: y = -|x + 1| + 1

Step-by-step explanation:

This is a "V" shaped graph, so we know it uses the absolute value function. This is the parent function:

    y = |x|

This represents the possible transformations:

➜ a is amplitude

➜ h is horizontal shift

➜ k is vertical shift

    f(x) = a | x - h | + k

Next, we see it is shifted one unit upwards.

    y = |x| + 1

Then, we see it is also shifted one unit left.

➜ Note that this shift is -h units, so we will use positive for moving left.

    y = |x + 1| + 1

Lastly, we see this graph is flipped and has a negative slope, or amplitude.

    y = -|x + 1| + 1

A company sells cereal in two different-sized boxes. The smaller box has the dimensions shown below. The height of the smaller box is 80% of the height of the larger box, while the other two dimensions are the same for both boxes. What is the volume of the two boxes?

Answers

Since the other two dimensions are the same for both boxes, we only need to compare the volumes based on their height.

Let's assume the height of the larger box is h, then the height of the smaller box is 0.8h.

The volume of the larger box is:

V1 = lwh = (8)(11)(h) = 88h

The volume of the smaller box is:

V2 = lwh = (8)(11)(0.8h) = 70.4h

Therefore, the volume of the larger box is 88h and the volume of the smaller box is 70.4h.

Since the two boxes have the same length and width, we only need to consider the difference in height to calculate their volumes.

Let H be the height of the larger box. Then the height of the smaller box is 0.8H.

The volume of the larger box is given by:

V_large = L × W × H

The volume of the smaller box is given by:

V_small = L × W × 0.8H

Since the length and width are the same for both boxes, we can factor them out:

V_large = L × W × H
= (L × W × 1) × H
= A × H

V_small = L × W × 0.8H
= (L × W × 0.8) × H
= 0.8A × H

where A = L × W is the area of the base of each box.

Therefore, the volume of the smaller box is 0.8 times the volume of the larger box.

We can also write this as:

V_small/V_large = 0.8

So, if we know the volume of one of the boxes, we can find the volume of the other box by multiplying by 0.8.

Without specific information about the dimensions of the boxes, we cannot calculate their volumes.

which graph represents the linear equation y = 1/4 x + 1 on the coordinate plane

the line is passing through -2 for y and 4 for x

the line is passing through 2 for y and -4 for x

the line is passing through 1 for y and -5 for x

the line is passing through 1 for y and -4 for x

Answers

Answer:

the line is passing through 1 for y and -4 for x

Step-by-step explanation:

The function y = 1/4 + 1 contains all the information you need. The + 1 indicates the y intercept, so it is given. Since the slope of the line is 1/4, the graph would pass through (-4, 0) and (0, 1) as starting from a point would go up one unit and right 4 units.

Suppose that the function g is defined, for all real numbers, as follows. Find g(-5) ,g (-2), and g(-1)

Answers

If the function g(x) is defined for all real-numbers, then the value of g(-5) is 7/2, g(-2) is -1 and g(-1) is 0.

A piecewise function is a function that is defined by different rules or formulas on different parts of its domain. The piecewise function "g(x)" is given as :

g(x) = {-(1/2)x + 1,    for x<-2

       = {-(x+1)²,        for -2≤x≤1

      =  {4                 for x>1

We have to find the value of g(-5) ,g (-2), and g(-1),

For x = -5, the number -5 is less than -2, so the first function "-(1/2)x + 1" will be used,

⇒ g(-5) = -(1/2)(-5) + 1 = 5/2 + 1 = 7/2,

For x = -2, the number -2 lies in the interval "-2≤x≤1", so second function

"-(x+1)²" will be used,

⇒ g(-2) = -(x+1)² = -(-2+1)² = -(-1)² = -1,

For x = -1, the number -1 lies inn the interval "-2≤x≤1", so second function "-(x+1)²" will be used,

⇒ g(-1) = -(x+1)² = -(-1+1)² = -(0)² = 0,

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answer pls my state test is cominggggg

Answers

Answer:

- 9/16

Step-by-step explanation:

When multiplying fractions, you can multiply them straight across.

We can focus simply on the fractions first and then add the negative back in later since you always get a negative number when you multiply a negative and positive number:

- (3 /4) * (3 / 4)

- (3 * 3) / (4 * 4)

- (9/16)

-9/16

Complete the following using compound future value. (Use the Table provided.)
Note: Do not round intermediate calculations. Round your final answers to the nearest cent.
Time
6 years
Principal
$ 15,300
Rate
8 %
Compounded
Quarterly
What is amount &
Interest?

Answers

Answer:

We can use the formula for compound interest to calculate the amount and interest:

A = P * (1 + r/n)^(n*t)

I = A - P

Where:

P = Principal = $15,300

r = Rate = 8% = 0.08

n = Compounding frequency per year = 4 (since it is compounded quarterly)

t = Time period = 6 years

Plugging in the values, we get:

A = 15,300 * (1 + 0.08/4)^(4*6) = $23,659.28

I = 23,659.28 - 15,300 = $8,359.28

Therefore, the amount after 6 years is $23,659.28 and the interest earned is $8,359.28.

I hope this helps.

Mrs Smith uses 5 lemons to make 2/3 gallon lemonade. How many gallons of lemonade can Mrs Smith make with 15 lemons?​

Answers

If Mrs. Smith uses 5 lemons to make 2/3 gallon of lemonade, we can set up a proportion to find out how many gallons she can make with 15 lemons:

5 lemons / (2/3 gallon) = 15 lemons / x gallons

To solve for x, we can cross-multiply:

5 lemons * x gallons = (2/3 gallon) * 15 lemons

5x = 10

x = 2

Therefore, Mrs. Smith can make 2 gallons of lemonade with 15 lemons.
Answer: 2 gallons.
Explanation: Since Mrs. Smith uses 5 lemons for 2/3 of a gallon, you can multiply 2/3 by 3. (You will end up with the product 2. This then translates into 2 gallons.) Hope that helped!

Which equation accurately represents this statement? Select three options. Negative 3 less than 4.9 times a number, x, is the same as 12.8. Negative 3 minus 4.9 x = 12.8 4.9 x minus (negative 3) = 12.8 3 + 4.9 x = 12.8 (4.9 minus 3) x = 12.8 12.8 = 4.9 x + 3

Answers

The  equation accurately represents this statement is "Negative 3 less than 4.9 times a number, x, is the same as 12.8"

how to determine the equation that accurately represents the statement

The statement is "Negative 3 less than 4.9 times a number, x, is the same as 12.8." We can break it down into two parts:

"4.9 times a number, x": This means we need to multiply a number, x, by 4.9. So the first part of the equation is 4.9x.

"Negative 3 less than 4.9 times a number, x, is the same as 12.8":

This means we need to subtract 3 from the result of multiplying x by 4.9. So the second part of the equation is -3.

Putting it all together, we get:

4.9x - 3 = 12.8

This equation accurately represents the given statement.

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Find the value of x.

Answers

The value of x in the chord is 3 units.

How to find line segment when chord intersect?

The chord intersection theorem states that the products of the lengths of the line segments on each chord are equal.

Therefore,

6(x + 5) = 4(2x + 6)

Open the brackets

6x + 30 = 8x + 24

subtract 8x from both sides of the equation

6x - 8x + 30 = 24

-2x + 30 = 24

subtract 30 from both sides of the equation'

-2x + 30 - 30 = 24 - 30

-2x = -6

divide both sides by -2

x = -6 / 2

x = 3

Therefore,

x = 3

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Help with this question please l need it

Answers

Answer:

(x+4)(x-9)!!!!!!!!!!!!!!!!!!

what is the nearest tenth to 3.5

Answers

The answer: 3.5
The number is already rounded to the nearest tenth

Answer: 3.5

Step-by-step explanation: i got it right on the quiz

The company performed another experiment in which they tested three website designs to see which one would lead to the highest probability of a purchase. The first (design A) used enhanced product information, the second (design B) used extensive iconography, and the third (design C) allowed the customer to submit their own product ratings. After 6 weeks of testing, the designs delivered probabilities of purchase of 4.5%, 5.2%, and 3.8% respectively. Equal numbers of customers were sent randomly to each website design. what is the probability that a customer who visited made a purchase?

Answers

The probability that a customer who visited any of the three website designs made a purchase is 4.5%.

To find the probability that a customer who visited any of the three website designs made a purchase, we need to find the average probability of purchase across all three designs.

We can do this by taking the mean of the three probabilities:

Mean probability = (4.5% + 5.2% + 3.8%) / 3

= 13.5% / 3

= 4.5%

This assumes that the customers were randomly assigned to each design and that there were no other factors that may have influenced their purchasing behavior. Additionally, the sample size and duration of the experiment may also affect the accuracy of the results.

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Can someone help me find if the function is increasing or decreasing and why the c intercept is (look at the photo)

Answers

I believe it’s decreasing because it is going like this ( \ ) when intersecting the x and y intercept

Brynen is driving to a new job five days this week. He drives 27 miles each way. His car gets 35 miles per gallon of gas. How many gallons of gas will he use driving to and from work this week? Round to the nearest tenth.

Answers

The number of gallons of gas Brynen will use in driving to and from work, during the week, obtained using arithmetic operations is 7 5/7 gallons

What are arithmetic operations?

Arithmetic operations are operations involving addition, subtraction, multiplication, and division.

The distance Brynen travels each way to his new job = 27 miles

The distance his car gets per gallon of gas = 35 miles

The number of gallons he will use in a week (five days of driving in the week), can therefore, be found by arithmetic operations follows;

The distance Brynen travels = 27 × 2 × 5 = 270 miles

The number of gallons = 270 miles/(35 miles/gallon) = 270/35 = 7 25/35

7 25/35 = 7 5/7

The volume of gas he will use to and from work this week is; 7 5/7 gallons

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A student wants to know which type of pizza the students at his high school prefer. Which
option would give a unbiased, representative sample:
Average

Answers

Answer:

Step-by-step explanation:

In November 1998, former professional wrestler Jesse “The Body” Ventura was elected governor of Minnesota. Up until right before the election, most polls showed he had little chance of winning. There were several contributing factors to the polls not reflecting the actual intent of the electorate:

Ventura was running on a third-party ticket and most polling methods are better suited to a two-candidate race.

Many respondents to polls may have been embarrassed to tell pollsters that they were planning to vote for a professional wrestler.

The mere fact that the polls showed Ventura had little chance of winning might have prompted some people to vote for him in protest to send a message to the major-party candidates.

But one of the major contributing factors was that Ventura recruited a substantial amount of support from young people, particularly college students, who had never voted before and who registered specifically to vote in the gubernatorial election. The polls did not deem these young people likely voters (since in most cases young people have a lower rate of voter registration and a turnout rate for elections) and so the polling samples were subject to sampling bias: they omitted a portion of the electorate that was weighted in favor of the winning candidate.

SAMPLING BIAS

A sampling method is biased if every member of the population doesn’t have equal likelihood of being in the sample.

So even identifying the population can be a difficult job, but once we have identified the population, how do we choose an appropriate sample? Remember, although we would prefer to survey all members of the population, this is usually impractical unless the population is very small, so we choose a sample. There are many ways to sample a population, but there is one goal we need to keep in mind: we would like the sample to be representative of the population.

Returning to our hypothetical job as a political pollster, we would not anticipate very accurate results if we drew all of our samples from among the customers at a Starbucks, nor would we expect that a sample drawn entirely from the membership list of the local Elks club would provide a useful picture of district-wide support for our candidate.

One way to ensure that the sample has a reasonable chance of mirroring the population is to employ randomness. The most basic random method is simple random sampling.

Given the following similar triangles, what is the area of triangle B?
A 1
B 1.8
C 3.2
D 5

Answers

The area of the similar triangle B is derived to be equal to 1.8 which makes option B correct.

What are similar triangles

Similar triangles are two triangles that have the same shape, but not necessarily the same size. This means that corresponding angles of the two triangles are equal, and corresponding sides are in proportion.

We shall represent the hight of triangle B with the letter h so that;

h/2 = 3/5

h = (2 × 3)/5 {cross multiplication}

h = 1.2

area of triangle B = 1/2 × 3 × 1.2

area of triangle B = 1.8

Therefore, the area of the similar triangle B is derived to be equal to 1.8

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Drag each tile to the correct location on the table. Each tile can be used more than once.
Match each equation to the value(s) of x that make the equation true.

Answers

Sure, here are the solutions for each equation:

3(x-5) = 2(11) has a solution of x = 7.

4(3x+7) = 512x + 8 has no real solution.

3(x+1)- 2x = x + 3 has a solution of x = 9.

3 = 3 is true for all values of x, so it doesn't have a specific solution.

What is equation?

An equation is a mathematical statement that shows the equality of two expressions. An equation typically has one or more variables, which are unknown values that we want to solve for. In an equation, the expressions on both sides of the equal sign are equivalent, meaning they have the same value. Equations can involve different mathematical operations, such as addition, subtraction, multiplication, division, and exponentiation, and they can be solved using various techniques, such as algebraic manipulation, factoring, and substitution. Equations are used in various fields of mathematics, as well as in science, engineering, and other disciplines, to model and solve problems.

Here,

1. 3(x-5) = 2(11)

To solve for x, we can distribute the 3 on the left side to get 3x - 15 = 22, then add 15 to both sides to get 3x = 37, and finally divide both sides by 3 to get x = 37/3 or x = 12.33. However, we can see that this answer doesn't make sense because plugging it back into the original equation doesn't give us a true statement. Instead, we can see that if we solve for x using the steps above, we get x = 12.33, which is approximately equal to 7 when rounded to the nearest whole number. Therefore, the solution for this equation is x = 7.

2. 4(3x+7) = 512x + 8

To solve for x, we can first distribute the 4 on the left side to get 12x + 28 = 512x + 8. Then, we can simplify by subtracting 12x from both sides to get 28 = 500x + 8, and subtracting 8 from both sides to get 20 = 500x. However, this means that x = 20/500 or x = 0.04. Plugging this value back into the original equation doesn't give us a true statement, so there is no real solution to this equation.

3. 3(x+1)- 2x = x + 3

To solve for x, we can first distribute the 3 on the left side to get 3x + 3 - 2x = x + 3, then simplify by combining like terms to get x + 3 = x + 3, which is a true statement for any value of x. Therefore, this equation has a solution for all values of x.

4. 3 = 3

This equation is already true for any value of x, as both sides are equal to 3. Therefore, it doesn't have a specific solution for x.

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A sequence can be generated using an + 1 = –0.25 + an, where a1 = 5 and n is a whole number greater than 1.
What are the first 5 terms in the sequence?

Answers

The first 5 terms in the sequence are 5, 4.75, 4.5, 4.25 and 4

What are the first 5 terms in the sequence?

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

Sequence generated using an + 1 = –0.25 + ana1 = 5n is a whole number greater than 1.

Using the above as a guide, we have the following:

a2 = -0.25 + a1

So, we have

a2 = -0.25 + 5 = 4.75

For other terms. we have

a3 = -0.25 + 4.75 = 4.50

a4 = -0.25 + 4.50 = 4.25

a5 = -0.25 + 4.25 = 4.0

Hence, the first 5 terms in the sequence are 5, 4.75, 4.5, 4.25 and 4

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26) What is the area of Rectangle A?
is 1 unit square.
Rectangle A

Answers

The  required area of the rectangle is 8 sq. units

What is rectangle?

Any mathematical statement with numbers, variables, and an arithmetic operation between them is an expression or algebraic expression. For instance, the expression 4m + 5 is one in which the terms 4m and 5 and the variable m are separated by the arithmetic sign +.

According to question:

From the diagram

Length = 4 units, width = 2 units

Area of rectangle = length×width

Area of rectangle = 4×2

Area of rectangle = 8 sq. units

Thus, required area of the rectangle is 8 sq. units

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Select all the polygons that can be formed by the intersection of a plane and a cylinder either parallel or perpendicular to the base?

Answers

The polygons that can be formed by the intersection of a plane and a cylinder either parallel or perpendicular to the base include :

B. SquareC. RectangleE. Circle

How to find the polygons ?

If a plane intersects three distinct vertices of the cube while bypassing any other vertices, a triangle is produced. To visualize this, suppose a corner of the cube were removed with a knife; picture that cut surface as a triangle.

On the other hand, if a plane coincides with four points on the cube and outlines a square shape, it creates what's called a "square cross-section." This transpires when said plane parallels one side of the cube while intersecting only the midpoints of its opposite face's edges.

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Full question is:

Select all the polygons that can be formed by the intersection of a plane and a cylinder either parallel or perpendicular to the base

A triangle

B square

C. rectangle

D pentagon

E circle

The base of a chest shaped as a rectangular prism is 12 feet² and the height is 4 feet.
What is the volume?

Answers

Answer:

The answer is 576

Step-by-step explanation:

the formula for a right rectangular prism is L*W*H. We know that the height is 4, and the base is 12^2. Which means that the length and width are both 12. So if ew do 12*12*4 you get 576.

Use the given vectors to find v• w and v•v. v= - 8i – 3j, w= - 9i – 7j

Answers

Using the given vectors v and w, we found v•w =  66 and v•v = 73.

To find v • w, which is the dot product of vectors v and w, we need to multiply the corresponding components of the two vectors and then add the products. In other words,

v • w = (-8i)(-9i) + (-3j)(-7j)

= 72 + 21

= 93

So, v • w = 93.

To find v • v, we again need to multiply the corresponding components of vector v and then add the products. In other words,

v • v = (-8i)(-8i) + (-3j)(-3j)

= 64 + 9

= 73

So, v • v = 73.

Note that the dot product of a vector with itself (like v • v) is also known as the magnitude squared of the vector. In this case, ||v||² = v • v = 73.

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a camper lights an oil lantern at 12 noon and let’s it burn continuously

Answers

The amount of oil in the lantern at 12 noon is 64.33 ounces

Calculating the amount in the lantern at 12 noon?

The time can be represented with x and the amount with y

Note that

x = number of hours from 12 noon

So, we have the following ordered pairs

(x, y) = (0, y) (2, 63), (5, 61)

Using the slope formula, we have

(y - 63)/(0 - 2) = (61 - 63)/(5 - 2)

So, we have

(y - 63)/-2 = -2/3

This gives

y - 63 = 4/3

Add 63 to both sides

y = 63 + 4/3

Evaluate

y = 64.33

Hence, the amount in the lantern at 12 noon is 64.33 ounces

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Complete question

A camper lights an oil lantern at 12 noon and lets it burn continuously. Once the lantern is lit, the lantern burns oil at a constant rate each hour. At 2 p.m., the amount of oil left in the lantern is 63 ounces. At 5 p.m., the amount of oil left in the lantern is 61 ounces.

Based on the average rate of oil burning per hour, how much oil, in ounces, was in the lantern at 12 noon?

There are 200 end-of-the-year school dance tickets available. Students who have perfect attendance are able to purchase them in advance. If 18 tickets were purchased in advance, what percent of the tickets were purchased in advance?

Answers

Thus, 9 percent of the total dance tickets available is found to be purchased in advance.

Explain about the percentage:

Although the usage of percent and percentage differs slightly, they both signify the same thing. It is customary to use percent or the symbol (%) along with a numerical value. One tenth of something is one percent.

Hence, it can be expressed as a fraction as well as a decimal. In mathematics, a percentage is a number or ratio that may be expressed as a fraction of 100. The Latin word "per centum," which meaning "per 100," is where the word "percent" comes from. % is the symbol used to represent percentages.

Given data:

Total dance tickets = 200

Advanced purchased tickets = 18

Let x be the percentage of advance booked tickets.

Then,

x% of 200 = 18

x*200 / 100 = 18

2x = 18

x = 18/2

x = 9%

Thus, 9 percent of the total dance tickets available is found to be purchased in advance.

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The stemplot below represents the number of bite-size snacks grabbed by 32 students in an activity for a statistics class.

A stemplot titled Number of Snacks has values 15, 15, 16, 16, 16, 17, 17, 18, 18, 18, 18, 19, 19, 20, 20, 20, 21, 21, 21, 22, 22, 23, 23, 27, 29, 29, 29, 32, 32, 34, 38, 42.

Which of the following best describes the shape of this distribution?

skewed to the left
bimodal symmetric
skewed to the right
unimodal symmetric

Answers

Answer: The stemplot shows that the distribution is unimodal and skewed to the right.

The stem values (tens digits) are:

1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 4, 4

The leaf values (ones digits) are:

5, 5, 6, 6, 6, 7, 7, 8, 8, 8, 8, 9, 9, 0, 0, 0, 1, 1, 1, 2, 2, 3, 3, 7, 9, 9, 9, 2, 2, 4, 8, 2

The data is unimodal because there is one clear peak in the distribution. The data is skewed to the right because the long tail of the distribution extends to the right, with a few large values pulling the mean to the right.

Therefore, the best description of the shape of this distribution is skewed to the right.

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