Which of the points below correctly plots the point (4,π/3)?

The volume of this rectangular prism is equal to: B. 8 in³.

In Mathematics and Geometry, the volume of a rectangular prism can be calculated by using the following formula:

Volume of a rectangular prism = L × W × H

Where:

Since this rectangular prism is filled with 16 cubes and each cube is a 1/2 inch cube, the dimensions of the rectangular prism is given by;

Dimensions = 16 × (1/2)³ = 2inches.

By substituting the given dimensions (parameters) into the formula for the volume of a rectangular prism, we have the following;

Volume of rectangular prism = 2 × 2 ×  2

Volume of rectangular prism = 8 cubic inches.

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Complete Question:

A rectangular prism is filled with 16 cubes. Each cube is a 1/2 inch cube. What is the volume of the rectangular prism?

A. 2 in³

B. 8 in³

C. 16 in³

D. 32 in³

Answer:

Jasper should use the median to make an inference about the house values in his neighborhood because there is an outlier that affects the mean. The outlier in this case is the house with a value of $2,500,000, which is significantly higher than the other house values in the sample. The mean is sensitive to outliers, which means that the outlier can significantly affect the value of the mean. In contrast, the median is not affected by outliers, which makes it a better measure of central tendency for this data set. Therefore, Jasper should use the median because it is in the center of the data and is not affected by the outlier. Answer: He should use the median because there is an outlier that affects the mean.

Answer:

The answer to your problem is, C. He should use the median because there is an outlier that affects the mean. &;  A & E $150,000 ‘n’ $200,000

Step-by-step explanation:

The outlier is represented as ‘ E ‘ the highest price value and lowest between, $150,000 to $200,000.

But since ‘ E ‘ is represented highest it is an outlier making ‘ E ;

$150,000 ‘n’ $200,000

So ‘ E ‘ is represented as, $150,000 ‘n’ $200,000

The second option for ‘ 10 points ‘ is He should use the median because there is an outlier that affects the mean, being the ‘ Option C ‘

Thus the answer to your problem is, C. He should use the median because there is an outlier that affects the mean. &;  A & E $150,000 ‘n’ $200,000

The true statements about the samples:

Both groups have the same median (4).

Group A has a lower mean than Group B (4 vs 4.25).

Both groups have multiple modes.

The range of values in Group B is greater than in Group A.

For Group A, the average number is 4 with a range of numbers from 2 to 6. The middle value, also known as the median, is 4.

Using this information, we find that values 3, 4, and 5 occur twice each within the dataset.

For Group B, the mean, or average, number is found to be 4.25 among eight total entries ranging from a low of 1 to a high of 7.

Calculating for the middle value, which is defined as the median, it can be seen that the resulting output is again equivalent to 4. Of all data inputs, the two top-occurring amounts are 4 and 5, both appearing twice in the listing.

Here are the true statements about the samples:

Both groups have the same median (4).

Group A has a lower mean than Group B (4 vs 4.25).

Both groups have multiple modes.

The range of values in Group B is greater than in Group A.

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A company sampled two groups of students and asked them "How many books did you read this month?" The table shows the data they collected:

Group A: [3, 4, 5, 2, 5, 6, 3, 4]

Group B: [1, 6, 4, 5, 2, 5, 4, 7]

Figure O is reflected followed by a translation of 4 units in the left direction.

Given that:

Figure O and Figure P are shown on the graph.

The translation does not change the shape and size of the geometry. But changes the location.

Figure O is translated leftward by 4 units.

The reflection does not change the shape and size of the geometry. But flipped the image. A reflection is a transformation that maps every point P over a line such that the line segment PP' will intersect the line of reflection at a right angle.

The translated figure O is reflected across the x-axis.

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Based on the information, the Stafford loan will have a lower balance by $527.14 at the time of repayment

Using the formula for compound interest, the total cost of the loan can be calculated as follows:

Total cost of Stafford loan = $11,650 x (1 + 0.0595/12)^(12*0.5) = $12,652.14

Total cost of PLUS loan = $12,436.41 x (1 + 0.0655/12)^12 = $13,179.28

Therefore, the Stafford loan will have a lower balance at the time of repayment by $527.14 ($13,179.28 - $12,652.14).

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a. 3 students read comics and novel only.

b. 1 student read textbook and novel only.

c. 31 students read none of the three categories.

Here's a Venn diagram that shows the information given:

  _________

     /         \

    /           \

   /             \

  /               \

 /        A       \

/                   \

/__________\

|          |          |

|          |          |

|     C  |     B    |

|          |           |

|__________|__________|

  \         |         /

    \       |       /

      \     |     /

        \   |   /

          \ |  /

           \ | /

            \|/

             |

             |

             |

            D

The three circles represent the three categories: novel, comics, and textbook.

The overlap between the circles represents the number of students who read more than one category.

The letters A, B, C, and D represent the following regions:

A: Only comics and novel (not textbook)

B: Only textbook and novel (not comics)

C: Only textbook and comics (not novel)

D: All three categories

To answer the questions:

a. To find the number of students who read comics and novel only (region A), we need to add up the number of students who read both comics and novel (5) and subtract from it the number of students who also read textbook (2).

So, the number of students who read comics and novel only is 5 - 2 = 3.

b. To find the number of students who read textbook and novel only (region B), we follow the same process.

We add up the number of students who read both textbook and novel (3) and subtract from it the number of students who also read comics (2).

So, the number of students who read textbook and novel only is 3 - 2 = 1.

c. To find the number of students who read none of the three categories, we start with the total number of students (50) and subtract from it the number of students who read at least one category.

To find the latter number, we add up the number of students who read only novel (3), only comics (9), only textbook (2), and all three (5), which gives us 19. So, the number of students who read none of the three categories is 50 - 19 = 31.

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Answer:

23

Step-by-step explanation:

Assume the digits are

1, 4 or 2,3

The number can be 14, 41, 23, 32

Test each one:

14 + 9 = 23 does not work

41 + 9 = 50 does not work

23 + 9 = 32 works

32 + 9 = 41 does not work

The volume of the sphere as shown in the diagram is 904.3 cm³.

A sphere is a three-dimensional round-shaped object.

To calculate the volume of the sphere, we use the formula below

Formula:

Where:

From  the question,

Given:

Substitute these values into equation 1

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Answer:

[tex]100000( {.70}^{3} ) = 34300[/tex]

Kathy worked 9.14 hours for Job A and 18.86 hours for job B to make 186.10

Assuming hours of work for job A is x while that of job B is y

According to the given information, Kathy works a total of 28 hours per week

x + y = 28

Job A pays $6.10 per hour, and Job B pays $6.80 per hour, to make $184.10, we have the equation below

6.10x + 6.80y = 184

x + y = 28

6.10x + 6.80y = 184

solving simultaneously using calculator

x = job A = 9.143 = 9.14 (to 2 decimal places)

y = job B = 18.857 = 18.86 to 2 decimal places))

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An equation giving the relationship between the air temperature T and the number of chirps per min N of the crickets is N = 4T - 160.

The rate at which the crickets chirp when the temperature is 104°F is 256 chirps/min.

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical expression;

y = mx + c

Where:

Based on the information provided above, the linear relationship can be modeled by using this system of linear equations:

y = mx + c

120 = 70x + c

200 = 90x + c

By solving the system of equations simultaneously, we have:

200 = 90x + 120 - 70x

20x = 80

x = 4.

c = 120 - 70(4)

c = -160

Therefore, the linear relationship is given by;

y = 4x - 160 ≡ N = 4T - 160.

When T = 104°F, N is given by;

N = 4(104) - 160

N = 256 chirps/min.

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Answer:

$1,000.

Step-by-step explanation:

200 kids divided by 25% or 4 = 50 then 50 x 20 = 1,000.

The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

It is used to find the length of one of the sides of a right-angled triangle when the lengths of the other two sides are known. It is also used to determine if a triangle is a right-angled triangle or not, by checking if the lengths of the sides satisfy the theorem.

The Pythagorean Theorem has many practical applications, such as in construction, engineering, and physics. For example, it can be used to calculate the distance between two points in a two-dimensional plane, the height of a building or tower, or the force required to move an object up a ramp at a given angle.

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The requried inverse function is [tex]f^{-1}(y) = (y + 3)/2[/tex].

To find the inverse of y = 2x - 3, we need to solve for x in terms of y.

Starting with y = 2x - 3:

Add 3 to both sides: y + 3 = 2x

Divide both sides by 2: (y + 3)/2 = x

Therefore, the inverse of y = 2x - 3 is:

x = (y + 3)/2

We can also express this as:

[tex]f^{-1}(y) = (y + 3)/2[/tex]

Thus, the inverse function is [tex]f^{-1}(y) = (y + 3)/2[/tex]

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Answer:

The correct number line that shows the solutions to x+8 > 15 is option B.

Step-by-step explanation:

The correct number line that shows the solutions to x+8 > 15 is option B.

On this number line, you can see that the values of x that make the inequality true are greater than 7. Therefore, the solution set for this inequality is x > 7.

Answer:

Yes.

Step-by-step explanation:

8:120 = 4:60 = 2:30 = 1:15

You divide by two each time to simplify.

The graph that best shows `y=x^2` translated `2` units down is graph d

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

y = x^2

When the function y=x^2` is translated `2` units down, we do the following

We subtract 2 from the function equation

So, we have

y = x^2 - 2

This means that the translated function is 2 units below the function y = x^2

From the list of options, this is represented with graph (d)

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Answer:6

Step-by-step explanation:

7w-6 + 8w+6 = 90

15w=90

w=90/15

w=6

The triangle which can be drawn as per the condition described is only option 2. an isosceles triangle with measure  20° and 80°.

Triangle which can be drawn as per the measurements are,

An acute triangle with sides measuring 7, 4, 2.

In an acute triangle, the square of the longest side is less than the sum of the squares of the other two sides.

According to the Pythagorean theorem.

7²< 4² + 2²

49 < 16 + 4

49 < 20

This is a contradiction, since 49 cannot be less than 20.

It is not possible to draw triangle.

An isosceles triangle with measures of angle 20° and 80°.

Sum of interior angles  of a triangle is 180°

Here, third angle = 180° - ( 20° + 80° )

⇒Third angle = 80°

Two angles are congruent ⇒ opposite sides to congruent angles are also congruent.

It forms a isosceles triangle.

An obtuse triangle with sides measuring 5, 10 and 15.

Side lengths 5, 10, and 15 do not form a triangle at all.

Since the sum of the two shorter sides is less than the longest side.

5 + 10 = 15

It is not possible to have an obtuse triangle with sides measuring 5, 10, and 15.

An scalene triangle with angle measuring 110° and 35°.

Sum of the interior angles is always 180°.

Measure of the third angle ,

180° - 110° - 35° = 35°

Three angles of the triangle measure 110°, 35°, and 35°.

It represents isosceles triangle.

Therefore, the possible triangle as per the given condition is only option 2. isosceles triangle with measure 20° and 80°.

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The perimeter of rectangle W'X'Y'Z is 16 units

he rectangle has four sides. There are two lengths and two widths in a rectangle. Therefore, the perimeter of the rectangle is twice the sum of two adjacent sides that are length and width. The formula is given by:

Perimeter of rectangle = 2(l + b)

We have :

Rectangle WXYZ will be the dilated by a scale factor of 1/2 creating rectangle W'X'Y'Z'

So, By the image:

The analysis will be the:

Rectangle of WXYZ = 2 × 4

and, The rectangle of W'X'Y'Z' = 2 × WXYZ

                                                   = 16

W'X' = 4

W'Z' = 4

Hence, The perimeter of rectangle is = 4 + 4 + 4 + 4 = 16

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The given question is incomplete, So i take the similar question :

Rectangle WXYZ will be the dilated by a scale factor of 1/2 creating rectangle W'X'Y'Z'. What is the perimeter of rectangle W'X'Y'Z?

And also to see the attachment.

Answer:

x ≈ 6.5

Step-by-step explanation:

using the tangent ratio in the right triangle

tan25° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{x}{14}[/tex] ( multiply both sides by 14 )

14 × tan25° = x , then

x ≈ 6.5 ( to the nearest tenth )

If professor Snozz earns 8% of "total-sales", then the amount that the professor make on selling of 300 copies is $708.

In order to find out how much Professor Snozz makes, we first calculate the "total-sales" revenue of the 300 copies of the book;

⇒ Total sales revenue = (number of copies sold) × (price per copy),

⇒ Total sales revenue = 300 × $29.50,

⇒ Total sales revenue = $8850;

Next, we calculate amount of royalty that Professor Snozz earns, which is 8% of the total sales revenue;

So, Royalty = 8% of "Total sales revenue";

⇒ Royalty = 0.08 × $8850,

⇒ Royalty = $708;

Therefore, Professor Snozz earns $708 as a royalty for selling 300 copies of his book.

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Answer:

153.94 square centimeters.

Step-by-step explanation:

To calculate the area of a circle when the circumference is given, you can use the formula:

Circumference = 2 * pi * r, where pi is approximately equal to 3.14 and r is the radius of the circle.

We can rearrange this formula to solve for the radius:

r = Circumference / (2 * pi)

Substituting the given value of circumference:

r = 44 cm / (2 * 3.14) = 7.006 cm (rounded to three decimal places)

Now that we have the radius, we can calculate the area of the circle using the formula:

Area = pi * r^2

Substituting the value of r:

Area = 3.14 * 7.006^2 = 153.94 cm^2 (rounded to two decimal places)

Therefore, the area of the circle is approximately 153.94 square centimeters.

Answer:

To find the coordinates for all three possible locations of the fourth vertex, we need to consider the three different ways that a parallelogram can be formed on a 9 by 9 grid.

Method 1: The fourth vertex is directly below the first vertex.

In this case, the coordinates of the fourth vertex are (5, 9), as shown below:

Y 9 8 7 6 5 4 3 2 1 0

X 1 2 3 4 5 6 7 8 9

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . X

Method 2: The fourth vertex is directly to the right of the first vertex.

In this case, the coordinates of the fourth vertex are (1, 5), as shown below:

Y 9 8 7 6 5 4 3 2 1 0

X 1 2 3 4 5 6 7 8 9

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

X . . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

Method 3: The fourth vertex is diagonal to the first vertex.

In this case, the coordinates of the fourth vertex are (5, 5), as shown below:

Y 9 8 7 6 5 4 3 2 1 0

X 1 2 3 4 5 6 7 8 9

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . X . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

Therefore, the coordinates for all three possible locations of the fourth vertex are (5, 9), (1, 5), and (5, 5).

a. The home's value is increasing at a rate of approximately 1.55% per year.

b. The exponential model is V(t) = [tex]95000e^{(0.0155t)}[/tex]

c. The predicted value of the home in 2022 is approximately $123,240.

d. The home's value reached $130,000 approximately 20 years after 2011, which is in the year 2031.

To find the growth rate k, we can use the formula [tex]V(t) = V0e^{(kt)}[/tex]. We have two data points: V(0) = 95000 and V(7) = 105000 (since 2018 is 7 years after 2011). Inputting these values into the formula yields:

V(0) =[tex]V0e^{(0k)}[/tex] = V0

V(7) = [tex]V0e^{(7k)}[/tex]= 105000

When the second equation is divided by the first, the result is:

V(7)/V(0) = [tex]e^{(7k)}[/tex] = 105000/95000 = 1.1053

Taking the natural logarithm of both sides and calculating k yields:

ln(1.1053) = 7k

k ≈ 0.0155

This means that the home's value is increasing at a rate of approximately 1.55% per year.

b. The exponential model is V(t) = [tex]95000e^{(0.0155t)}[/tex].

c. The predicted value of the home in 2022 is approximately $123,240.

To predict the home's value in 2022, we need to find the value of V(t) when t = 11 (since 2022 is 11 years after 2011). Substituting into the exponential model gives:

V(11) = [tex]95000e^{(0.0155*11)}[/tex] ≈ $123,239.62

So the predicted value of the home in 2022 is approximately $123,240.

d. The home's value reached $130,000 approximately 20 years after 2011, which is in the year 2031.

We need to solve for t in equation V(t) = 130,000.

130,000 = [tex]95,000e^{(0.0155t)}[/tex]

Dividing both sides by 95,000 and taking the natural logarithm of both sides, we get:

ln(130,000/95,000) = 0.0155t

Simplifying, we get:

t = (ln(130,000/95,000))/0.0155

t = (ln(1.368)/0.0155

t = 0.313 / 0.0155

t ≈ 20.23

Therefore, the home's value reached $130,000 approximately 20 years after 2011, which is in the year 2031.

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Complete question:

A young couple purchases their first new home in 2011 for $95,000. They sell it to move into a bigger home in 2018 for $105,000. First, we will develop an exponential model for the value of the home. The model will have the form V(t) = V0e^(kt) . Let t be years since 2011 and v (t) be the value of the home.

a. What is the growth rate k for the model? What does that number mean?

b. What is the exponential model?

c. Predict the value of the home in 2022.

d. During what year did the value of the home reach $130,000?

Answer:

B

Step-by-step explanation:

N(0) = 5

m = 2 individuals per unit time

t = 20 unit time

N(20) = 2*20+5 = 45 individuals

The linear growth equation, M(t) = M(0) + m*t, can be used to calculate population growth at a constant rate. By substituting in the given starting population of 5 and growth rate of 2, it is determined that the population at 20 units of time is 45.

In the context of this question, we're dealing with a simple linear growth equation, which can be expressed algebraically as M(t) = m*t + M(0), where M(t) is the population at time t, m is the rate of growth, and M(0) is the starting population.

In this case, the starting population, M(0), is 5 and the growth rate, m, is 2 individuals per unit of time. So if we want to calculate the population at 20 units of time, we would substitute these values into the equation.

According to the equation, M(20) = M(0) + m*20 = 5 + 2*20 = 5 + 40 = 45. Therefore, the population at 20 units of time would be 45 individuals.

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The fractional part of 70/28 is 35/14 i.e., 2.5

Percentage:

A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100

28 of 70 can be written as:

=> [tex]\frac{28}{70}[/tex]

To find percentage, we need to find an equivalent fraction with denominator 100. Multiply both numerator & denominator by 100

[tex]\frac{28}{70}[/tex] × [tex]\frac{100}{100}[/tex]

=> (28 × 100) /70 ×[tex]\frac{1}{100}[/tex]

=> 40/100

Therefore, the answer is 40%

The fractional part of 70/28 is 35/14 i.e., 2.5

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The possible first mistake Noah made in the evaluation of the sine and cosine of the acute angles of a right triangle is that the acute angles are complementary and are not always congruent. The correct option is the  option (A).

(A) Angles ∠B and ∠C are complementary, not congruent

Complementary angles are angles that when added together are equivalent to 90°

The possible two column table Noah used to attempt to prove that cos(θ) = sin(θ) obtained in a similar proof on the website can be presented as follows;

Statement [tex]{}[/tex]                   Reason

1 m∠B = θ [tex]{}[/tex]                   The acute angles in a right triangle are congruent

2 sin(θ) = AB/BC    [tex]{}[/tex]     Definition of sine

3 cos(m∠B) = AB/BC [tex]{}[/tex] Definition of cosine

4 cos(θ) = AB/BC [tex]{}[/tex]       Substitution

5 cos(θ) = sin(θ) [tex]{}[/tex]         Substitution

Part of the question is; What is the first mistake in Noah's statement used to prove that cos(θ) = sin(θ)

The first mistake is the statement and reason that angle m∠B = θ because all acute angles are congruent.

The acute angles in the right triangle are ∠B and ∠C

The sum of the acute angles in a right triangle is; ∠B + ∠C = 90°

Therefore the acute angles in a right triangle are always complementary, and not always congruent.

The correct option is therefore the option (A)

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Answer:

To simplify 9 1/8 - 2 1/4, we need to first convert the mixed numbers to improper fractions.

9 1/8 = (8 x 9 + 1)/8 = 73/8

2 1/4 = (4 x 2 + 1)/4 = 9/4

Now we can subtract the two fractions:

73/8 - 9/4

Since the two fractions have different denominators, we need to find a common denominator. The least common multiple of 8 and 4 is 8, so we can convert the second fraction to have a denominator of 8:

73/8 - (9/4)x(2/2) = 73/8 - 18/8 = 55/8

Therefore, 9 1/8 - 2 1/4 = 55/8, which is an improper fraction. If we want to convert it back to a mixed number, we can divide the numerator by the denominator:

55/8 = 6 7/8

So the simplified answer is 6 7/8. Answer: 6 7/8.

Answer:

6 7/8

Step-by-step explanation:

9 1/8 - 2 1/4 =

      9 1/8

  -   2 1/4

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

The common denominator for the fractions is 8.

      9 1/8

  -   2 2/8

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

Since the bottom fraction is greater than ther upper fraction, we borrow 1 from the nine. 1 is the same as 8/8, so we take 1 from 9 and add 8/8 to 1/8.

      8 9/8

  -   2 2/8

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

      6 7/8

Answer: 6 7/8