A jar of peanut butter is in the shape of a cylinder. The jar has a radius of 4 centimeters. It is filled with peanut butter to an inside height of 12 centimeters.

The length of the new ballroom (in reality, the ballroom is designed according to scale drawing) is given by: Option D: 77 m

For a particular scale drawing, it is already specified that all the measurements' some constant scaled version will be taken. For example, let the scale be K feet to s inches.

Then it means

[tex]\rm 1\: ft : \dfrac{s}{k}\: in.[/tex]

All feet measurements will then be multiplied by s/k to get the drawing's corresponding lengths.

We're given that:

Since in the drawing, 11 inches was representing 44 m length of the ballroom when 1 inch: 4 metre scale was being used (as 11×4=44), so when the scale is 1 inch: 7 meters, then the new length of the ballroom in reality would be: 7 metre 11 times (since there is 11 inches as length of ballroom in the scale drawing)

This evaluates to [tex]7 \times 11 = 77 \: \rm metre[/tex]

Thus, the length of the new ballroom (in reality, the ballroom is designed according to scale drawing) is given by: Option D: 77 m

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The length or the longer side of the new ballroom is 77m.

Dimensions of the model = 11 inches*4 inches

1 inch = 4m

A scale factor is a factor by which the dimension of an object is enlarged.

So, the dimensions of the ballroom will be:

Length = 11*4 = 44m

Width = 4*4 =16m

But, Mika decides to change the scale to 1 inch: 7metres

So, the length of the new ballroom = 11*7 =77m

So, the length of the new ballroom =77m

Hence, the length of the new ballroom is 77m.

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Answer:

x = 11 cos 22 = 11 * .927 = 10.2

Answer:

Step-by-step explanation:

                   48 + 9 + 29 + x + 5 + 32 + 22 + 5 = 63

                   by adding all numbers except x, we get

                                  150 + x = 63

                                       x = 63 - 150

                                       x = - 87

There are 24 students in the class in which 75% of the students are boys (18 boys)

An equation is an expression used to show the relationship between two or more numbers and variables.

Let x represent the total amount of students in the class.

75% of the students are boys.There are 18 boys in the class, hence:

0.75x = 18

x = 24

There are 24 students in the class in which 75% of the students are boys (18 boys)

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Answer:

6√2=z

Step-by-step explanation:

As we are given a right angle we simply can apply the formula a²+b²=c².
A = 3
B = z

C =  8+1 which we add to get 9
Now, we plug this into the equation

9²=z²+3²

81=z²+9

72=z²

√72=z

√2x2x2x3x3 (expanding 72)

6√2=z

Answer:

5

Step-by-step explanation:

The probability that the first student chosen is a senior and the second student chosen is a sophomore is 11/320.

Probability of an event is the ratio of number of favorable outcome to the total number of outcome of that event.

Twice during the assembly, a student is chosen at random to assist with the presentation.

After the first student has finished assisting, the student returns to the group and can be chosen a second time.

There are total 80 number of students in which 22 are senior students. Thus, probability of choosing first student a senior

[tex]P(A)=\dfrac{22}{80}\\P(A)=\dfrac{11}{40}[/tex]

There are total 22 sophomores. Thus, probability of choosing second student a sophomore is,

[tex]P(B)=\dfrac{10}{80}\\P(B)=\dfrac{1}{8}[/tex]

By the chain rule, the probability that the first student chosen is a senior and the second student chosen is a sophomore is

[tex]\dfrac{11}{8}\times \dfrac{1}{8}=\dfrac{11}{320}[/tex]

Thus, the probability that the first student chosen is a senior and the second student chosen is a sophomore is 11/320.

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Answer:

A

Step-by-step explanation:

Answer:

We can determine that Option A, y = 0.4x - 2 is the correct answer

Step-by-step explanation:

Step 1:  Plug in 30 into the x-value to see if the y-value matches

Equation 1 --> y = 0.4(30) - 2 = 10

Equation 2 --> y = 0.3(30) + 2 = 11  <--  WRONG Y-VALUE

Equation 3 --> y = 0.3(30) + 1 = 10

Step 2:  Plug in 50 into the x-value to see if the y-value matches

Equation 1 --> y = 0.4(50) - 2 = 18

Equation 3 --> y = 0.3(50) - 2 = 13  <--  WRONG Y-VALUE

Answer: We can determine that Option A, y = 0.4x - 2 is the correct answer

Answer:

The input-ouput is B.

Step-by-step explanation:

By plugging in 3, -4, and 5 into the x-values of the equation [tex]f(x)=2x-7[/tex] you provided you get

[tex]f(3) = 1 , f(-4) = -15 , f(5) = 3[/tex]

Step-by-step explanation:

here ! I used the formula area = length × width

and just some algrbric expressions solving

Answer:

45 pencils

Step-by-step explanation:

15%/100% ×300

15% ×3

=45 pencils that needed to be sharpened and it is at easy as that

15% of 300 =

10%= 30

5%= 15

30+15 = 45

45 pencils need to be sharpened

Answer:

q = 204

Step-by-step explanation:

25 + 954 = 979

979 - 775 = 154

Answer:

[tex]\boxed{\tt q=985}[/tex]

Step-by-step explanation:

[tex]\tt 25(q-954)=775[/tex]

Let's apply the Distributive property:-

[tex]\tt 25q-23850=775[/tex]

Add 23850 to both sides:-

[tex]\tt 25q-23850+23850=775+23850[/tex]

[tex]\tt 25q=24625[/tex]

Divide both sides by 25:-

[tex]\tt \cfrac{25q}{25}=\cfrac{24625}{25}[/tex]

[tex]\boxed{\tt q=985}[/tex]

Or we can solve it by .....

Dividing both sides by 25

[tex]\tt q-950=\cfrac{775}{25}[/tex]

[tex]\tt q-954=31[/tex]

Add 954 to both sides:-

[tex]\tt q=31+954[/tex]

[tex]\boxed{\tt q=985}[/tex]

__

Answer:

The length does not change

Step-by-step explanation:

Only dilations will change the size of something, the line is just changing locations. because it is across the x axis, apply the rule

x,-y

-4, -8

4, 1

Answer:

2 and 4 is repeated mode of the data

Answer:

2 and 4

Step-by-step explanation:

The volume of the cylinder (282.74 in.³) is less than the volume of the square prism (360 in.³). Then the correct option is C.

A rectangular prism is a closed solid that has two parallel rectangular bases connected by a rectangle surface.

A cylinder is a closed solid that has two parallel circular bases connected by a curved surface.

A square prism has a height of 12 inches and a base with an area of 30 square inches.

A cylinder is inscribed inside the prism.

The volume of the square prism will be

[tex]V_{square} =Base[/tex] [tex]area*Height[/tex]

[tex]V_{square}=30*12[/tex]

[tex]V_{square} =360[/tex] [tex]in^3[/tex]

The volume of the cylinder will be

[tex]V_{cylinder}=\pi r^2h[/tex]

The radius of the base circle of the cylinder will be

[tex]r=\frac{\sqrt[]{30}}{2}[/tex]

[tex]r=2.7386[/tex]

Then volume will be

[tex]V_{cylinder}=\pi *(2.7368)^2*12[/tex]

[tex]V_{cylinder}=282.74[/tex] [tex]in^3[/tex]

The volume of the cylinder (282.74 in.³) is less than the volume of the square prism (360 in.³). Then the correct option is C.

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Answer:

(2,-1)

Step-by-step explanation:

[tex]midpoint = ( \frac{ - 2 + 6}{2} , \frac{ - 4 + 2}{2} ) \\ [/tex]

[tex]midpoint = ( \frac{4}{2} , \frac{ - 2}{2} ) \\ [/tex]

[tex]midpoint = (2, - 1)[/tex]

Answer:

  (d)  y' = 3/2x

Step-by-step explanation:

The transformation for rotating a figure 180° about the origin is ...

  (x, y) ⇒ (-x, -y)

__

Given the line ...

  y = 3/2x

The translation of it is ...

  -y' = 3/2(-x)

Simplifying gives ...

  y' = 3/2x

_____

Additional comment

Rotation 180° about the origin is equivalent to reflection across the origin. For a line that passes through the origin, that reflection is simply the original line, as we can see in the equations above.

Answer:

-126.66

Step-by-step explanation:

£££££££££££££₩₩₩¥₩₩

Answer:

5

Step-by-step explanation:

Tina started with $20, but had to spend $3.25 on the bat.

$20-$3.25 = $16.75, which is all she has left for rounds.

Each round costs $3.00

$16.75 divided by $3.00 comes out to 5.58 rounds, but since she can't play 1/2 a round, that means she could only play 5 rounds

5 rounds X $3.00 per round comes to $15.00

The true inferences from the double dot plot for this case from the available options is given by: Option D) The Interquartile range for Ander’s data is 0. 5 greater than the interquartile range for Marcus’s data

When we get data which can be compared relatively with each other, for finding quartiles, we arrange them in ascending or descending order.

Quartiles are then selected as 3 points such that they create four groups in the data, each groups approximately possessing 25% of the data.

Lower quartile, also called first quartile has approx 25% in its left partition, and on its right lies approx 75% of the data.

Similarly, second quartile (also called median) is approximately in mid of the data.

Third quartile (also called upper quartile)  has approx 75% in its left partition, and on its right lies approx 25% of the data.

Left to right is said in assumption that data was arranged increasingly from left to right

IQR(inter quartile range)  is the difference between third and first quartile.

Suppose we're measuring something whose values are numeric. For each value of that thing we observe, we plot a dot above that value in the number line. Thus, the total number of dots in the dot plot tells us the total number of observations of the values of that thing we did.

Thus, suppose if we observed the value 'x', then we will make a dot above 'x'. If there is already a dot over 'x', then we will make a new dot over that dot.

If instead of only observations, the table of unique observation and frequency is given, then we plot dots that many times as the count written in the frequency table. Thus, if its written that the value 2 has 3 has its frequency, then we plot 3 dots one over the other above the value 2 in the horizontal axis.

For this case, getting the quartiles of each dataset one by one.

The number of dots show frequencies, therefore, from the image attached below, the data we get for Anders is:

1,2,2,3,3,5,5,5,5,5,5,6,6,6,6,7,7,7,7,7

These are total 20 observations.

Mean is the ratio of sum of all observations to the number of observations.

Sum of these values is 100, and therefore, we get:

Mean = 100/20 = 5

50% of 20 is 10 (its half). And 25% is 5, and 75% is 15.

Now, any number between the 10th and 11th value will be median because before and after that will lie ten-ten observations.

We usually take mean of these two values in such case.

The 10th value is 5, and so as the 11th value.

Thus, median of this data set is 5

Similarly, the first quartile can be taken as the average of 5th and 6th value as in mid of both lie values before which lies 25% of the data and after which lies 75% of the data.

The 5th and 6th values are 3 and 5. Their average is (3+5)/2=4

Thus, the first quartile of this data set is 4

Similarly, third quartile can be taken as average of 15th and 16th value = (6+7)/2 = 6.5

Now, the interquartile range of this dataset = third - first quartile = 6.5 - 4 = 2.5

2,3,5,6,6,6,7,7,7,7,7,7,8,8,8,8,8,9,10,10

These are total 20 observations.

Mean is the ratio of sum of all observations to the number of observations.

Sum of these values is 139, and therefore, we get:

Mean = 139/20 = 6.95 (approx 7)

Also, we get:

Median can be average of 10th and 11th value = (7+7)/2 = 7

First quartile can be average of 5th and 6th value = (6+6)/2 = 6

Third quartile can be average of 15th and 16th value = (8+8)/2 = 8

Thus, IQR = third - first quartile = 8-6 = 2

So we see that option A and B are wrong as IQR and median both are different for both the datasets.

Option C is wrong since for Ander's data, we see that both mean and median (which are central measures) evaluates to 5, so Ander's data centers around 5 instead of 6.

Option D is correct as IQR for Ander's data = 2.5 is 0.5 greater than 2 which is IQR for Marcus' data.

Thus, the true inferences from the double dot plot for this case from the available options is given by: Option D) The Interquartile range for Ander’s data is 0. 5 greater than the interquartile range for Marcus’s data.

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#SPJ1

Answer:

11286.33333

Step-by-step explanation:

1) The numerator (1) always multiplies the number (33,859.00). "Of" implies multiplication and division.

= [tex]1 * 33,859.00[/tex]

= [tex]33,859.00[/tex]

2) The denominator (3) always divides the number (33,859.00)

= 33,859.00 ÷ 3

= 11286.33333

An expression is defined as a set of numbers, variables, and mathematical operations. The expression that will result in the difference in the squares is (7x+4)(7x-4).

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The difference between the squares can be written as,

[tex]a^2-b^2=(a+b)(a-b)[/tex]

The expression that will result in the difference in the squares will be

[tex](7x+4)(7x-4)=(7x)^2-(4)^2[/tex]

Thus, the expression that will result in the difference in the squares is (7x+4)(7x-4).

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[tex]0.86\\\\=\dfrac{86}{100}\\\\=\dfrac{43}{50}[/tex]

Answer:

$127

Step-by-step explanation:

[tex]i = \sf \frac{prt}{100} [/tex]

=> 100 × 3 × 9/100

=> 3×9 = 27

Total amount= 27 + 100

=> 127

Answer :-- $127

Answer:

  x = 15

Step-by-step explanation:

Where a transversal crosses parallel lines, alternate exterior angles are congruent. This lets you write an equation relating the measures of the marked angles.

__

  (6x +8)° = (7x -7)° . . . . the angles have the same measure

  15 = x . . . . . . . . . . . . divide by °, add 7-6x

Answer:

The vertex of Function 2 is at (2,7)

The function that has the smaller minimum value is Function 1

The smaller minimum value is 3

Step-by-step explanation:

hope this helps :)

Answer:

54:1

Step-by-step explanation:

That is the right answer and is actually the only one written as a unit rate. All the other are not even written correctly.

Answer:

54:1

Step-by-step explanation:

Because the rate would be 162:3 but simplified, you would divide by 3 and get 54:1.

Answer:

13.747... meters

Step-by-step explanation:

Refer to image attached~

In this case, the longest side of the triangle formed is AC. Thus, our hypotenuse is AC (17 m).

To determine the height of the building, we need to use pythogoras theorem.

Pythogoras theorem: (Hypotenuse)² = (Side)² + (Side)²

Take square root both sides:

Answer:

13.75 ft (nearest hundredth)

Step-by-step explanation:

The ladder creates a right triangle with the wall and ground, where:

Pythagoras' Theorem: a² + b² = c²

(where a and b are the legs, and c is the hypotenuse, of a right triangle)

Given:

Substitute the given values into the formula and solve for b:

⇒ 10² + b² = 17²

⇒ b² = 17² - 10²

⇒ b² = 289 - 100

⇒ b² = 189

⇒ b = ±√(189)

As distance is positive, b = √(189) ft only

Therefore, the ladder reaches 13.75 ft (nearest hundredth) up the wall.

Answer:

26 cups

Step-by-step explanation:

24 cups is 6 quarts, 25 cups is 6.25 quarts, and 26 cups is 6.5 quarts.

Therefore, 26 cups = 6.5

6.5>6

26 cups is larger than 6 quarts.