YOU HAVE TO BE SURE ABOUT YOUR ANSWER BEFORE YOU POST! A slice is made parallel to the base of a right rectangular pyramid, as shown.

What is the area of the resulting two-dimensional cross-section?

Enter your answer in the box.

Answer:

the answer is 189

Answer:

n=21

Step-by-step explanation:

Ik im late but hopefully it can help other people :)

The equation is :

4(9+n)=120

n+9=120/4

n+9=30

n+9-9=30-9

n=21

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The answer is 6,500 pounds.

To convert tons to pounds, you can use the conversion factor that 1 ton is equal to 2,000 pounds. So, to convert 3.25 tons to pounds:

Therefore, 3.25 tons is equal to 6,500 pounds.

Final answer:

The derivation of the quadratic formula involves several steps, including identifying the unknown, identifying the knowns, choosing an equation, finding additional equations if necessary, solving simultaneous equations, eliminating terms, substituting known quantities, and checking the answer for reasonableness.

Explanation:

Derivation of the Quadratic Formula

The seventh step is to take the square root of both sides. The eighth step is to isolate x by subtracting [tex]\(\frac{B}{2a}\)[/tex]. The ninth step simplifies the expression.

The seventh step is:

7. Take the square root of both sides to isolate x:

[tex]\[ x + \frac{B}{2a} = \pm \sqrt{\frac{b^2 - 4ac}{4a^2}} \][/tex]

The eighth step is:

8. Solve for x by subtracting [tex]\(\frac{B}{2a}\)[/tex] from both sides:

[tex]\[ x = -\frac{B}{2a} \pm \sqrt{\frac{b^2 - 4ac}{4a^2}} \][/tex]

The ninth step is:

9. Simplify and solve for x:

[tex]\[ x = \frac{-B \pm \sqrt{b^2 - 4ac}}{2a} \][/tex]

This is the quadratic formula, which gives the solutions for the equation [tex]\( ax^2 + bx + c = 0 \)[/tex].

The exact surface area of the cylinder with a radius of 30 ft and height of 19 ft is calculated using the formula 2πr(h + r), resulting in an area of 2940π ft², which matches option D.

To find the exact surface area of a cylinder, we use the formula that states the surface area (SA) is SA = 2πr(h + r), where r is the radius and h is the height of the cylinder. Given that the radius (r) is 30 ft and the height (h) is 19 ft, we plug these values into the formula:

SA = 2π(30)(19 + 30)

SA = 2π30(49)

SA = 60π(49)

SA = 2940π ft²

Therefore, the exact surface area of the cylinder is 2940π square feet, which corresponds to option D.

Answer:

Option E - Box plot E

Step-by-step explanation:

Given : Data,

67, 66, 64, 62, 60, 56, 54, 50, 46, 42, 41, 40, 40, 38, 35, 21, 19

To find : Which choice below is a boxplot for the following distribution?

Solution :

Step 1- Arranging the data from lowest to highest,

{19,21,35,38,40,40,41,42,46,50,54,56,60,62,64,66,67}  

Step 2 - Find the median of the data  

As the data is odd numbers so the median is [tex]\frac{n+1}{2}[/tex] th term.

[tex]\frac{n+1}{2}=\frac{17+1}{2}=9th[/tex] term.

9th term is 46

∴ [tex]Q_2=46[/tex]  

Step 3 - To find Upper quartile and lower quartile  

Lower quartile data set is the median of the upper terms from median

{19,21,35,38,40,40,41,42}

Median of the set is [tex]M=\frac{38+40}{2}=39[/tex]

∴ [tex]Q_1=39[/tex]  

Upper quartile data set is the median of the lower terms from median

{ 50,54,56,60,62,64,66,67}

Median of the set is [tex]M=\frac{60+62}{2}=61[/tex]

∴ [tex]Q_3=61[/tex]  

We have plot the box plot attached below.

Our box plot is matched with Box plot E.

Therefore, Option E is correct.

Answer: Box plot E

Step-by-step explanation:

A P E X

Answer:

65 meters off the ground.

Step-by-step explanation:

The height of the monument is 9.80 m

To find the height of the monument, we can use the Pythagorean theorem. The rectangle on the pedestal forms a right triangle with the longest side of the monument being the hypotenuse. Let's call the height of the monument 'h'. Using the Pythagorean theorem, we have:

[tex]h^2 = (11^2) - (5^2)[/tex]

[tex]h^2 = 121 - 25[/tex]

[tex]h^2 = 96[/tex]

[tex]h = \sqrt{96[/tex]

h ≈ 9.80 meters

In algebra, the variable 'm' in the expression 'm + 8' can indeed take on any value; therefore, the statement is true because variables are meant to be placeholders for a wide range of numbers.

In the expression m + 8, it is true that the variable m can have any value, which means that this expression does not impose any restrictions on the possible values of m. This type of statement involving a variable is common in mathematics, particularly in algebra where variables represent unknown quantities that can take on various values.

When evaluating statements for truth or false, the statement 'in m + 8, the variable m can have any value' is true. Variables, by their nature, are symbols that can represent any number, so unless specific limitations are given, we assume variables to have the full set of numbers (real numbers, integers, etc.) as potential values.

Given is a sculpture that is built up of metal and wood, and the weight of this sculpture is 14.9 kilograms.

It says that three-fourth of the total weight is metal and says to find the weight of wooden part.

We can find the weight of metal part and then subtract it from the total weight to calculate the answer.

Total weight = 14.9 kilograms.

Metal part = three-fourth of total weight = [tex] \frac{3}{4} *14.9=\frac{44.7}{4} =11.175 \;kilograms [/tex]

Wooden part = 14.9 - 11.175 = 3.725 kilograms.

Hence, the wooden part is 3.725 kilograms.

3.725 kilograms or ¹/₄ part

Given:

An artist builds a sculpture out of metal and wood that weighs 14.9 kilograms.

Question:

How much does the wood part of the sculpture weighs?

The Process:

From the information above, we make a diagram that matches the composition of the sculpture material.

[tex]\boxed{metal}\boxed{metal}\boxed{metal}\boxed{wood} = 14.9 \ kilograms[/tex]

And now, let us calculate the wood part of the sculpture weighs.

[tex]\boxed{ \ = \frac{1}{4} \times 14.9 \ kilograms \ }[/tex]

Both 4 and 14.9 are multiplied by 10.

[tex]\boxed{ \ = \frac{1}{40} \times 149 \ kilograms \ }[/tex]

[tex]\boxed{ \ = \frac{149}{40}  \ kilograms \ }[/tex]

Both the numerator and denominator are divided by 4.

[tex]\boxed{ \ = \frac{37.25}{10}  \ kilograms \ }[/tex]

[tex]\boxed{ \ = \frac{3,725}{1,000}  \ kilograms \ }[/tex]

[tex]\boxed{\boxed{ \ 3.725 \ kilograms \ }}[/tex]

Thus, the wood part of the sculpture weighs is 3.725 kilograms or ¹/₄ part.

Keywords: an artist, builds a sculpture, out of metal and wood, that weighs 14.9 kilograms, 3/4, metal, the rest is wood, how much, the wood part, of the sculpture weighs

Answer:

1.29 x 10^7 people

Step-by-step explanation:

1.29 x 10^7 people

The value of Terrence's car after x years is

A = 20,000 ( [tex]1-0.15)^x[/tex]

Subtract the asset's salvage value (what you expect it to be worth at the end of its useful life) from its cost to calculate depreciation using the straight-line technique. The depreciable basis, or the amount that can be depreciated, is the result. Divide this figure by the number of years the asset will be useful.

Depreciation is the rate at which an object's value declines over time.

it is given by the formula,

A = P [tex](1-r)^t[/tex]

where A is the value of object after x period of time, P is the principal amount, r is the rate of depreciation, and t is the for the time period.

Given:

Terrence buys a new car for $20,000,

rate of depreciation = 15%,

We know the formula of the rate of depreciation,

A = P [tex](1-r)^t[/tex]

Here A= $20, 000

r = 15% = 0.15

So, the value of Terrence's car is A = 20,000 ( [tex]1-0.15)^x[/tex].

Learn more about Depreciation here:

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1,289,845 rounded to the nearest ten thousand is 1,290,000.

To round 1,289,845 to the nearest ten thousand, we need to look at the digit in the ten thousandth place, which is the 8 in this case. If the digit is 5 or greater, we round up, and if it is less than 5, we round down. Since the 8 is greater than 5, we round up. To do this, we keep the digit in the ten thousandth place as it is and change all the digits to the right of it to zeros. Therefore, 1,289,845 rounded to the nearest ten thousand is 1,290,000.

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