The volume of the given figure is __ ft3

Answer: 6 feet describes the center, and 9 feet describes the spread

Step-by-step explanation:

The center of a data set is mostly considered as the median or the mean

Here mean is 6 (given). And median is also 6. As 6 is exactly at the middle of the data set. (When arranged in ascending order)

Now, one of the way of calculating the spread is calculating the range, here it's given that the range is 9.

Therefore, 6 feet describes the center, and 9 feet describes the spread is correct.

Answer:

The equation of the tangent line is given by the following equation:

[tex]\displaystyle y - \frac{1}{e} = \frac{-1}{e} \bigg( x - 1 \bigg)[/tex]

General Formulas and Concepts:

Algebra I

Point-Slope Form: y - y₁ = m(x - x₁)

Calculus

Differentiation

Derivative Property [Multiplied Constant]:
[tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]

Derivative Rule [Basic Power Rule]:

Derivative Rule [Chain Rule]:
[tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]

Step-by-step explanation:

*Note:

Recall that the definition of the derivative is the slope of the tangent line.

Step 1: Define

Identify given.

[tex]\displaystylef(x) = e^{-x} \\x = -1[/tex]

Step 2: Differentiate

Step 3: Find Tangent Slope

∴ the slope of the tangent line is equal to  [tex]\displaystyle \frac{-1}{e}[/tex].

Step 4: Find Equation

∴ our point is equal to  [tex]\displaystyle \bigg( 1, \frac{1}{e} \bigg)[/tex].

Substituting in our variables we found into the point-slope form general equation, we get our final answer of:

[tex]\displaystyle \boxed{ y - \frac{1}{e} = \frac{-1}{e} \bigg( x - 1 \bigg) }[/tex]

∴ we have our final answer.

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Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

Answer:

12

Step-by-step explanation:

n(AUB) = n((A) + n(B) – n(AnB)

Step 1:

Identify the values for each function of the formula. n(A) = 10, n(B) = 5, n(AnB) = 3

Step 2:

Replace each function with its values

n(AUB) = n(A) + n(B) – n(AnB)

n(AUB) = 10 + 5 – 3

Step 3:

Carry on the simple arithmetic

n(AUB) = 10 + 5 – 3 (follow the BODMAS method)

= 15–3

= 12

Therefore, the n(AUB) is 12

Answer:

51

Step-by-step explanation:

5x^2 - x + 9

5(3^2) - 3 + 9

5(9) + 6

45 + 6

= 51

Answer: 1500

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Answer:

6.3

Step-by-step explanation:

151.2/24 in order to find out how many miles he drove per day

the answer is 6.3 miles per day

Answer:

6.3 Miles

Step-by-step explanation:

just divide 151.2 by 24.

To determine if you have enough money to buy this product, calculate the sales tax and the final price of the product.

Sales tax is usually expressed as a percentage. Moreover,  this percentage can slighly change depending on the state where you live.

Here is an example:

Final price = 138.12

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The rate of gallons per square foot is 0.624 gallons per square foot.

A rate demonstrates how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B). This indicates that you're dividing information A by B.

In this scenario, watering a lawn requires 623 gallons of water for every 1000 sq. ft.

The rate of gallons per square foot will be:

= Number of gallons / Square foot

= 623 / 1000

= 0.623

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Answer:

[tex]y = 2x -4[/tex]

Step-by-step explanation:

[tex]y = -\frac{1}{2}x - 2\ \ \ \ \ \ (0, -4)[/tex]

To find the perpendicular equation of a line,

You need the product of their gradients to be -1

[tex]-\frac{1}{2} \times ? = -1[/tex]

Divide both sides by [tex]-\frac{1}{2}[/tex]

? = 2

The gradient of the perpendicular line is 2

Straight line formula is in the form [tex]y = mx + c[/tex]

[tex]y = 2x + c[/tex]

We're nearly there, we just need to find out c.

Luckily, we're given a point [tex](0, -4)[/tex]

[tex](x, y) = (0, -4)[/tex]

[tex]y = 2x + c[/tex]

[tex]-4 = 2(0) + c\\-4 = 0 + c\\c = -4[/tex]

We then end up with...

[tex]y = 2x -4[/tex]

The total amounts of money which Mrs. Reynolds now has according to the descriptions in the task content is; $68.

It follows from the task content that;

On this note;

Hence, it follows that the amount of money, s she has now is;

Read more on addition and subtraction;

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Answer:

35 pages per minute is the unit rate

Step-by-step explanation:

Divide 175 by 5 to find the unit rate

Answer:

11 years

Step-by-step explanation:

x = years to equal

45 + 10x  =  23 + 12x

22 = 2x

x = 11 years

It will take 11 years for Dean to read as many books as Lillie.

An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.

Given that,

Number of books read by Lillie every year = 10 books

Total number of books already read = 45 books

The number of books, n, read by Lillie in t years,

n = 45 + 10t

Number of books read by Dean every year = 12 books

Total number of books already read = 23 books

The number of books, n, read by Lillie in t years,

n = 23 + 12t

Dean read as many books as Lillie, when,

23 + 12t = 45 + 10t

12t - 10t = 45 - 23

2t = 22

t = 11

Hence the number of books read by both will be same in 11 years.

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The center and shape of the distribution are 2.5 and symmetric. Then the correct option is B.

Binomial distributions consist of n independent Bernoulli trials.

Bernoulli trials are those trials that end up randomly either on success (with probability p) or on failures( with probability 1- p = q (say))

Suppose we have random variable X pertaining to a binomial distribution with parameters n and p, then it is written as

[tex]X \sim B(n,p)[/tex]

The probability that out of n trials, there'd be x successes is given by

[tex]\rm P(X =x) = \: ^nC_xp^x(1-p)^{n-x}[/tex]

Then the center and shape of the distribution will be 2.5.

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Answer:

Center : 2.5 Shape: Symmetric

Step-by-step explanation:

Trust Fam

Answer: 5/2

To convert 2.5 into a fraction, firstly we will write the number in x/y form, where x and y are positive integers. So, 2.5 can be written as 2.5/1. For the removal of the decimal, we multiply and divide by 10. And we get, 2.5/1 x 10/10 = 25/10 = 5/2.

Surface area is the sum of the area of faces of a figure. The ratio of their surface area is 2268 : 112

A prism is a solid shape with 6 faces

The formula for calculating the total surface area is expressed as:

TSA = 2(lw+wh+lh)

For the Red prism

Ar = 2(162 +324 + 648)
Ar = 2268 square units

For the blue prism

Ab = 2(8 + 16 + 32)
Ab = 112 square units

Take the ratio of the surface area

Ratio = 2268 : 112

Hence the ratio of their surface area is 2268 : 112

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Surface area is the sum of the area of faces of a figure. The ratio of their surface area is 4:81.

How to calculate the surface area of a prism?

A prism is a solid shape with 6 faces

The formula for calculating the total surface area is expressed as:

TSA = 2(LW+WH+LH)

For the Red prism

For the blue prism

Take the ratio of the surface area

Ratio = 4:81

Hence the ratio of their surface area is 4:81

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Answer:

it will depend on what state you are in

Step-by-step explanation:

depending on what state you are in will depend on the voting polls. and it would most likely be democratic

Answer:

[tex]\sqrt{28}[/tex]

Step-by-step explanation:

the point lies between 5 and 6 , that is between

[tex]\sqrt{25}[/tex] and [tex]\sqrt{36}[/tex]

therefore the poi nt approximates to the [tex]\sqrt{28}[/tex]

Answer:

45 degrees      

right angle =90 degrees

remaining :90

angles are equal

so 45 each

Answer: 2,-2

Step-by-step explanation: 9-7 is 2 and -9 minus -7 is minus 2.

Answer:

x=24

Step-by-step explanation:

you need 300.

10x + 60?

10 x 3 = 300

300 - 60 = 240

300 = (10 x 24) + 60

Answer:

See below.

Step-by-step explanation:

1) We know that the circumference of a circle can be found using the formula [tex]c=\pi d[/tex], so for this circle the circumference will be [tex]c=3.14 \times 40=125.6 \text{ yards}[/tex]. The formula for the area of a circle is [tex]A=\frac{1}{4}\pi d^2[/tex], so the area of this circle will be [tex]A=\frac{1}{4} \times 3.14 \times 40^2=1256 \text{ yards}[/tex].

2) First we'll work out the length of the curved side of the shape. That's [tex]\frac{1}{2}\times\pi d =\frac{1}{2} \times 3.14 \times 12=18.84 \text{ mm}[/tex]. Then, we'll add the length of the other two straight sides to get [tex]10.82 \times 2 + 18.84=40.48 \text{ mm}[/tex]. Next: the area of the semi-circle is [tex]\frac{1}{2} \times \frac{1}{4} \pi d^2 = \frac{1}{8} \times 3.14 \times 144 = 56.52 \text{ mm}[/tex]. Adding this to the areas of the two triangles: [tex]56.52+2 \times \frac{1}{2}bh=56.52+(\sqrt{10.82^2-9^2)}\times9 \approx 110.57 \text{ to 2 d.p.}[/tex]

Answer:

25

Step-by-step explanation:

ABC is a right angle so ABD and DBC are complementary angles and their sum is equal to 90:

x + 55 = 90 subtract 55 from both sides

x = 25

Answer:

6825 in^3

Step-by-step explanation:

First break the shape into two shapes a square prism and triangular prism

the volume of a square prism is equal to s^2 * h

and the volume of a triangular prism is 1/2 b * l *h

square prism:

v = s^2 * h

v = 13^2 * 30

v = 5070 in^3

triangular prism:

v = 1/2 b * l * h

v = 1/2 * 9 * 30 * 13

v = 1755 in^3

then you add the two volumes to get the total volume

5070 + 1755 = 6825 in^3

Answer:

4:9

Step-by-step explanation:

Find the area in inch first:

20 inch × 10 inch = 200 inch

Area in feet:

(20×15) + (10×15) = 450 inch

Area of the drawing : Area of the actual playground

200:450

Simplify it by dividing by 5

Last answer =4:9

Answer:

The answer is e. (x - 10 * y^2 * z) (x + 10 *y^2 *z)

Step-by-step explanation:

To explain it test all the options by distributing them.

Using an online website that I plugged into the calculator to factory gets answer e.

Answer:

  C.  16π

Step-by-step explanation:

You want to know the area of a circle whose radius is twice the edge of a cube that has a surface area of 24 square units.

The relevant area formulas are ...

  As = 6s² . . . . . . area of cube with edge s

  Ac = πr² . . . . . . area of circle with radius r

Here, we have r = 2s, so the area of the circle is ...

  Ac = π(2s)² = 4πs²

And we have the area of the square as 24, so the value of s² is ...

  As = 24 = 6s²

  24/6 = 4 = s²

Using this in the circle area expression, we have the area of the circle as ...

  Ac = 4π(4) = 16π . . . . . square units

The area of the circle is 16π square units.

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