determine the area of the composite figure shown below

A rectangular prism measuring 10m and 7m along the base and 12m tall.

The volume of the rectangular prism is 840 cubic meters.

Suppose that the right rectangular prism in consideration be having its dimensions as 'a' units, 'b' units, and 'c' units, then its volume is given as:

[tex]V = a\times b \times c \: \: unit^3[/tex]

A rectangular prism measuring 10m and 7m along the base and 12m tall.

a = 10

b = 7

c = 12

The volume of the rectangular prism

= 10 x 7 x 12

= 840

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Statement 1 is true: the majority of seniors read between 0 and 5 books. Statement 2 is false: the average number of books read is around 6-7, not between 10 and 11. Statement 3 is true: more seniors read 11-15 books than 16-20 books.

To determine which statement is true, let's first analyze the data provided in the table. Since the table isn't available, I'll make some assumptions to guide us through the explanation. Let's say the table looks like this:

Number of Books Read                Number of Seniors

0-5                                                  20

6-10                                                 15

11-15                                                 10

16-20                                               5

Now, we'll examine each statement to see if it aligns with the data:

"The majority of seniors read between 0 and 5 books in the past year."

This statement is true if the number of seniors who read 0-5 books is greater than the total number of seniors who read in other ranges. In this case, 20 seniors read 0-5 books, which is the highest count among all ranges. So, this statement is true.

"The average number of books read by seniors is between 10 and 11."

To find the average, we multiply the midpoint of each range by the number of seniors in that range, sum them up, and then divide by the total number of seniors. Doing the calculation, the average comes out to around 6-7 books, not 10-11. So, this statement is false.

"More seniors read 11-15 books than 16-20 books."

To verify this, we check the counts for each range. If the count for 11-15 books is greater than the count for 16-20 books, the statement is true. In this case, if 10 seniors read 11-15 books and 5 seniors read 16-20 books, the statement is true.

Based on this analysis, statements 1 and 3 are true, while statement 2 is false.

complete question=

Which statement is true regarding the survey conducted by a researcher who randomly surveyed seniors at a high school and asked about the number of books they read in the past year, as depicted in the provided table?

Answer:

[tex]y=28.5x[/tex]

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a direct variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]

In this problem

Let

x------> the number of gallons

y------> the number of miles

the relationship between the number of miles and the gallons of gas represent a linear direct variation

The constant of proportionality k is equal to the slope m

[tex]m=\frac{465.3}{16.5}= 28.2\frac{miles}{gallon}[/tex]

therefore

the equation of the linear equation

[tex]y=28.5x[/tex]

Answer:

The answer is 99.5 for future people!

Step-by-step explanation:

Answer:

1 x 10^-1m or A on edge

Step-by-step explanation:

just took the test

The inequality for a maximum ceiling height of 8 feet in new buildings is expressed as h <= 8, where h is the height in feet.

To represent the maximum ceiling height of 8 feet as an inequality, we use the following expression: h <= 8, where h represents the height of a building's ceiling in feet. This inequality states that the ceiling height must be less than or equal to 8 feet to comply with the regulations for new buildings.

Final answer:

The price of organic sugar at the Belleville store increased from $4 to $5 per pound, which is a 25% increase in price.

Explanation:

The percent of increase in the price of organic sugar from $4 to $5 per pound can be calculated through a few steps. To determine the percentage increase, you subtract the old value from the new value, then divide the result by the old value. Finally, you multiply by 100 to convert it into a percentage.

Here is the step-by-step calculation:

Determine the increase in price: $5 - $4 = $1.

Divide the increase by the original price: $1 ÷ $4 = 0.25.

Multiply by 100 to get the percentage: 0.25 × 100 = 25%.

Therefore, the price of organic sugar increased by 25%.

The price of organic sugar at a healthy foods store in Belleville was recently increased from $4 per pound to $5 per pound. The percent of increase in the price of this item is 25%.

To find the percent of increase in the price of the organic sugar, we can use the formula:

Percent increase = ((new price - old price) / old price) * 100

First, let's calculate the percent increase:

Percent increase = (($5 - $4) / $4) * 100 = (1 / 4) * 100 = 25%

Therefore, the percent of increase in the price of organic sugar is 25%.

Answer:

Step-by-step explanation:

Now, assuming those angles are supplementary, then

[tex]m\angle 7+ m \angle 2=180\°[/tex]

Beacuse, sumplementary angles sum 180\°, due to their position on a straight angle.

We know by given that [tex]m \angle 7 =115\°[/tex], replacing this value, we have

[tex]115\°+ m\angle 2= 180\°\\m \angle 2=180\° - 115\°\\m \angle 2= 65\°[/tex]

Therefore, the measure of [tex]\angle 2[/tex] is 115°.

The measure of m<7 is equal to the measure of m<2 by alternate exterior angle. The measure of <2 is 115 degrees.

Angles formed by the transverse line cut by the transversal-

Given information-

Two parallel lines are shown in the given image (attached below).

Here the measure of angle of 7 is 115 degrees.

The angle 5 is the supplementary angle of the angle 7. Thus,

[tex]\angle 5+\angle 7 =180\\\angle 5+115=180\\\angle 5=180-115\\\angle 5=65[/tex]

Thus the measure of angle 5 is 65 degrees.

Now again the angle 5 is the supplementary angle of the angle 3. Thus,

[tex]\angle 3+\angle 5 =180\\\angle 3+65=180\\\angle 3=180-65\\\angle 3=115[/tex]

Thus the measure of angle 3 is 115 degrees.

The angle 3 and the angle 2 cuts by the same line at the opposite side. Thus, angle 3 is equal to the angle 2.

Hence. the measure of angle 2 is 115 degrees.

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The solution according to the given question is provided below in the explanation segment.

According to the question,

The cost of drilling x feet is:

[tex]c(x) = f(x) \ dollars[/tex]

(a) [tex]f'(x) = \frac{df(x)}{dx} \ \frac{dollars}{feet}[/tex]

(b) Throughout the practical terms,

[tex]f'(x)[/tex] represents how many dollars its going to cost one feet.

(c) [tex]f'(x)[/tex] is positive,

The cost of drilling increases as "x" feet increases.

(d) The cost of drilling an additional foot at 300 feet will be [tex]f'(x) \Delta \ x[/tex]

here,

then,

= [tex]1000\times 1[/tex]

= [tex]1000 \ dollars[/tex]

If you want drill 1 more feet at 300 feet, its going to cost 100 dollars in one.

Thus the above answer is correct.              

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Answer:

(1,14)

Step-by-step explanation:

Answer:

Vertex of the parabola is ( 1 , 14 ).

Step-by-step explanation:

Given Equation of parabola is [tex]y=-2^2+4x+12[/tex]

We have to find the vertex of the parabola.

We first convert the given equation of parabola in standard equation of parabola using completing the square method.

Standard equation of parabola,

[tex](x-h)^2=4a(y-k)[/tex]  

here, ( h , k ) is coordinates of the vertex of the parabola.

consider,

y = -2x² + 4x + 12

y = -2( x² - 2x - 6 )

y = -2 ( x² - 2x  + 1² - 1² - 6 )

y = -2 ( x -1 )² - 7 × ( -2 )

y - 14 = -2 ( x - 1 )²

[tex](x-1)^2=\frac{1}{2}(y-14)[/tex]

By comparing,

vertex = ( 1 , 14 )

Therefore, Vertex of the parabola is ( 1 , 14 ).

Absolute values in mathematics and Kelvin temperatures both provide 'absolute' measurements, with absolute value indicating distance from zero and the Kelvin scale starting at absolute zero, the theoretical absence of kinetic energy.

Both absolute values in mathematics and temperatures on the Kelvin scale represent 'absolute' measurements in their respective fields. In mathematics, the absolute value indicates the distance of a number from zero on the number line, irrespective of direction. Similarly, the Kelvin scale is used in physics and deals with the absolute temperature, where 0 K (absolute zero) represents a theoretical state where particles possess minimal vibrational motion, implying no kinetic energy.

The Kelvin scale is important in scientific work because it starts at this absolute zero point. Therefore, it allows for the measurement of true thermal energy. The Kelvin scale is similar to the Celsius scale in that the size of its degree is the same, but the Kelvin scale does not start at the freezing point of water. Instead, it starts at absolute zero, making it a true absolute scale that measures the fundamental property of temperature.

Answer:

[tex]2x^2y + x^2 - 3x + 4~ (4)>3x + y + z ~(3)>x + 2xyz ~(2)>9x^2yz~ (1)[/tex]  

Step-by-step explanation:

We are given expressions in the question.

Term in an expression:

We need to find the number of terms in each expression:

1)

[tex]x + 2xyz\\\text{Number of terms}= 2[/tex]

2)

[tex] 3x + y + z\\\text{Number of terms}= 3[/tex]

3)

[tex]2x^2y + x^2 - 3x + 4\\\text{Number of terms} = 4[/tex]

4)

[tex]9x^2yz\\\text{Number of terms} = 1[/tex]

Arranged  from greatest to least by number of terms:

[tex]2x^2y + x^2 - 3x + 4~ (4)>3x + y + z ~(3)>x + 2xyz ~(2)>9x^2yz~ (1)[/tex]