Find the area AND perimeter of the shaded regions below. Give your answer as a completely simplified exact value in terms of π (no approximations).

Answer:

Step-by-step explanation:

area of top face = π15² = 225π in²

volume = 225π × 40 = 9000π ≅28,260 in³

Answer:

c. The researchers are 95% confident that the true mean difference in ALT values between the population of drinkers and population of non-drinkers is between 24.32 and 39.68.

Step-by-step explanation:

Given :

Groups:

x1 = 69 ; s1 = 19 ; n1 = 38

x2 = 32 ; s2 = 14 ; n2 = 37

1 - α = 1 - 0.95 = 0.05

Using a confidence interval calculator to save computation time, kindly plug the values into the calculator :

The confidence interval obtained is :

(24.32 ; 39.68) ; This means that we are 95% confident that the true mean difference in ALT values between the two population lies between

(24.32 ; 39.68) .

Answer:

Each group has 1 fiction book and 2 nonfiction book(s).

Answer:

Step-by-step explanation:

                  4km

[tex]\frac{3 }{27} \frac{miles}{minutes}[/tex] * [tex]\frac{60}{1} \frac{min}{hour}[/tex] * [tex]\frac{1}{.6213} \frac{km}{mile}[/tex]

4km ÷ 10.73 km/hr = .37 hr = 22.3 minutes

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Answer:

  1/2 year

Step-by-step explanation:

Put the numbers into the interest formula and solve for t.

  I = Prt

  8100 = 180000(0.09)t

  t = 8100/16200 = 1/2

It will take 1/2 year to earn N8100 in interest at 9%.

The given expression 1/4 (2.6x+0.25)-5/8 (2.5-0.88x) when simplified is 1.2x - 1.5.

To simplify the expression 1/4 (2.6x + 0.25) - 5/8 (2.5 - 0.88x), we'll apply the distributive property and combine like terms.

First, let's simplify the expression within the first set of parentheses:

2.6x + 0.25

Next, we multiply this expression by 1/4:

(1/4) * (2.6x + 0.25) = (2.6/4)x + (0.25/4) = 0.65x + 0.0625

Now, let's simplify the expression within the second set of parentheses:

2.5 - 0.88x

We'll multiply this expression by -5/8:

(-5/8) * (2.5 - 0.88x) = (-5/8)(2.5) - (-5/8)(0.88x) = -1.5625 + 0.55x

Finally, we can combine the simplified expressions:

0.65x + 0.0625 - 1.5625 + 0.55x = (0.65x + 0.55x) + (0.0625 - 1.5625) = 1.2x - 1.5

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Complete question is:

Simplify the expression 1/4 (2.6x+0.25)-5/8 (2.5-0.88x)

Answer:

-200

Step-by-step explanation:

ATQ, a+11d=-13 and a+a+d+a+2d+a+3d=24, 4a+6d=24. Solving this, we get a=9 and d=-2. Sum of the first 20 terms is 10*(18+(19)*(-2))=-200

Answer:

Step-by-step explanation:

The next term is going to be simply 38*19 = 722

The series is geometric which means that you multiply from one term to get to the next.

The ratio of 19, and the current term is 38. So to get to the next term, multiply 38 * 19

=======================================================

Explanation:

Let's solve the given equation for the variable 'a'

a(2+1) = 36

a*(3) = 36

3a = 36

a = 36/3

a = 12

There are 12 students in the class. This must mean there are 12 lemonades, because each person gets 1 lemonade.

Since there are 24 cookies, each student gets 24/12 = 2 cookies

Since each student gets 2 cookies and 1 lemonade, this is where the "2+1" comes from in the original equation. Each student gets 3 items total, which explains the notation 3a.

The value of 'a' from the given expression would be 13.

Given that;

At snack time, Ms. Rivera passes out 24 cookies to her class. She also passes out 1 glass of lemonade to each student.

Here, the equation is,

a(2+1)=36

Solve for a;

a × 3 = 36

3a = 36

Divide both sides by 3;

a = 36/3

a = 13

Thus, the value of a is 13.

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9514 1404 393

Answer:

  √5 +√6

Step-by-step explanation:

We know that the square of a binomial is ...

  (a +b)^2 = a^2 +2ab +b^2

Then the square root of it is ...

  a + b = √(a^2 +b^2 +2ab)

Using a=√x and b=√y, this is ...

  √x +√y = √(x + y + 2√(xy))

__

For the given expression, we need to find x and y such that ...

  xy = 30 and x+y = 11

Using x=5, y=6, we meet those requirements.

  [tex]\displaystyle \sqrt{11+2\sqrt{30}}=\sqrt{5+6+2\sqrt{5\cdot6}}=\boxed{\sqrt{5}+\sqrt{6}}[/tex]

Answer:

√5+√6 ≈ 4.68555772

Step-by-step explanation:

I hope it's correct

Answer:

M=$75

Step-by-step explanation:

I used M for money that Heather earned.

$20+M=$95

Answer:

Time and rate is 4 years and 4% respectively.

Step-by-step explanation:

P = Rs 66000

so

T = R

I = 10560

so

I = PTR/100

Rs 10560 = (66000*T^2)/100

or, Rs 1056000 = 66000*T^2

or. 1056000/66000 = T^2

or, 16 = T^2

OR, T =√16

so T = 4

Then

T = R

so, R = 4

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Answer:

  A. the mean

Step-by-step explanation:

The Greek letter μ is customarily used to represent the mean of a distribution or data set. Its location in this figure at the highest point and the line of symmetry is consistent with μ identifying the mean of this normal distribution.

Answer:

3.5 inches

Step-by-step explanation:

Sample mean basically means that we need to find the average of the samples.

So the formula for finding average is

Number of observations/ Number of Occurrences

So when we add the values together we get

42.

So there are 12 numbers

So, 42/12 =

3.5 inches

The sample mean of the heights of the plants in Susan's garden is

3.5 inches.

Here,

Susan randomly selected a sample of plants to determine the average height of the total 35 plants in her garden.

She measured the heights (in inches) of 12 randomly selected plants and recorded the data:

1.0, 1.4, 1.8, 2.0, 2.5, 3.5, 4.2, 4.5, 4.8, 5.0, 5.3, 6.0

We have to find the sample mean of the heights of the plants in Susan's garden.

What is Average?

Average value in a set of given numbers is the middle value, calculate as dividing the total of all values by the number of values.

Now,

The recorded data is;

1.0, 1.4, 1.8, 2.0, 2.5, 3.5, 4.2, 4.5, 4.8, 5.0, 5.3, 6.0

To find the sample mean of the heights of the plants in Susan's garden we have to find the average of the recorded data.

Formula for average = [tex]\frac{sum of number of observation}{ number of occurrence}[/tex]

Hence, Average = [tex]\frac{1.0+ 1.4+1.8+2.0+ 2.5+3.5+4.2+4.5+ 4.8+ 5.0+ 5.3+ 6.0}{12} = \frac{42}{12} = 3.5[/tex]

Therefore, The sample mean of the heights of the plants in Susan's garden is 3.5 inches.

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Answer:

side AC is 5

Step-by-step explanation:

by using th pythagorean theorm you would square both sides add them together and the square root the sum to get you answer.

AB =3 BC=4

9+16=25

25 square root is 5

makeing AC=5

Answer:

Your wrong, it's 65%.

Step-by-step explanation:

The reason why: You can calculate the percentage by dividing the number of accepted students by the total of business students, 65/100 which equals 65%.

yw :)

The probability that a student was accepted is 5.0% since option  b be the correct answer.

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1,

We have to find out the probability of the selection of a student applied for the business program.

We know that, Probability= Total number of events occurred÷ Total number of possible outcomes/events

So, Probability that a student applying to the business program got selected= No of accepted students for business program÷Total number of students applied for business program=65÷100=0.65For converting a number into percentage we multiply the number by 100 that is 0.65*100=65%So, probability that a student applying for business program gets selected is 65%.

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Answer:

To find critical points, take the first derivative and set it equal to zero:

f(x) = -2x^2 + 4x + 5

f'(x) = -4x + 4

-4x+4 = 0

-4x = -4

x = 1

Critical point at x = 1

Alternatively, if you mean zeros, or where the x intersects, you can use the quadratic equation.

Answer:

Center: (1,3)

Radius: 6

Step-by-step explanation:

Hi there!

[tex]x^2-2x + y^2 - 6y = 26[/tex]

Typically, the equation of a circle would be in the form [tex](x-h)^2+(y-k)^2=r^2[/tex] where [tex](h,k)[/tex] is the center and [tex]r[/tex] is the radius.

To get the given equation [tex]x^2-2x + y^2 - 6y = 26[/tex] into this form, we must complete the square for both x and y.

1) Complete the square for x

Let's take a look at this part of the equation:

[tex]x^2-2x[/tex]

To complete the square, we must add to the expression the square of half of 2. That would be 1² = 1:

[tex]x^2-2x+1[/tex]

Great! Now, let's add this to our original equation:

[tex]x^2-2x+1+y^2-6y = 26[/tex]

We cannot randomly add a 1 to just one side, so we must do the same to the right side of the equation:

[tex]x^2-2x+1+y^2-6y = 26+1\\x^2-2x+1+y^2-6y = 27[/tex]

Complete the square:

[tex](x-1)^2+y^2-6y = 27[/tex]

2) Complete the square for y

Let's take a look at this part of the equation [tex](x-1)^2+y^2-6y = 27[/tex]:

[tex]y^2-6y[/tex]

To complete the square, we must add to the expression the square of half of 6. That would be 3² = 9:

[tex]y^2-6y+9[/tex]

Great! Now, back to our original equation:

[tex](x-1)^2+y^2-6y+9= 27[/tex]

Remember to add 9 on the other side as well:

[tex](x-1)^2+y^2-6y+9= 27+9\\(x-1)^2+y^2-6y+9= 36[/tex]

Complete the square:

[tex](x-1)^2+(y-3)^2= 36[/tex]

3) Determine the center and the radius

[tex](x-1)^2+(y-3)^2= 36[/tex]

[tex](x-h)^2+(y-k)^2=r^2[/tex]

Now, we can see that (1,3) is in the place of (h,k). 36 is also in the place of r², making 6 the radius.

I hope this helps!

Answer:

[tex]\sqrt{g^2+f^2-c}[/tex]

[tex]g=-1,f=-3,c=-26[/tex]

so, the Center of the equation is [tex](1,3)[/tex]

[tex]\sqrt{(-1)^2+(-3)^2-(-26})[/tex]

[tex]=\sqrt{1+9+26}[/tex]

[tex]=\sqrt{36}[/tex]

[tex]=6[/tex]

OAmalOHopeO

Answer:

30.2

Step-by-step explanation:

We know that quadrilateral KLMN is larger than quadrilateral GHIJ by a scale factor. In order to figure out that scale factor, we must divide a value of a side of KLMN by the value of the side that it corresponds to on GHIJ. One said side is NM, because we know it corresponds to JI on GHIJ. The value of NM is 56, and the value of JI is 13, so to figure out the scale factor, we must divide 56 by 13. We have the scale factor as 56/13, so to figure out the measure of side NM, we must find the side it corresponds to on GHIJ. The side it corresponds to is side JG, which has a value of 7. To get the value of NK, we must multiply the scale factor by 7, and the scale factor is 56/13. 56/13 times 7 is equal to 392/13. Rounding to the nearest tenth, we have the answer as 30.2

Answer:

0.08 ; 0.16

Step-by-step explanation:

Given :

x = 32 ; n = 267 ; phat = x / n = 32 / 267 = 0.11985

The Zcritical at 95% = 1.96

The confidence interval for proportion :

C. I = Phat ± Z*√(phat(1-phat))/n

C. I = 0.11985 ± 1.96√(0.11985(1-0.11985))/267

C. I = 0.11985 ± 1.96(0.0198765)

C. I = 0.11985 ± 0.0389581

C. I = 0.08 ; 0.158

C. I = 0.08 ; 0.16

Answer:

AB

Step-by-step explanation:

For the multiplication of two matrices to be defined then the number of columns of the first matrix must be equal to the number of rows of the second matrix. For example, 2*3 and 3*2 matrices can be multiplied since the number of columns of the first matrix must be equal to the number of rows of the second matrix.

Matrix A = 2*2

Matrix B = 2*3

Matrix C = 3*3

Matrix D = 1 * 3

From the matrices given, we can see that the matrices that can be multiplied together are AB and BC since the number of columns of the first matrix must be equal to the number of rows of the second matrix. Hence the correct option is AB

Answer:

[tex]\displaystyle \frac{dy}{dx} = \frac{1}{(x - 2)^2\sqrt{\frac{x}{2 - x}}}[/tex]

General Formulas and Concepts:

Pre-Algebra

Algebra I

Algebra II

Calculus

Differentiation

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

Derivative Property [Addition/Subtraction]:                                                         [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]

Basic Power Rule:

Derivative Rule [Quotient Rule]:                                                                           [tex]\displaystyle \frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}[/tex]

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

Step-by-step explanation:

*Note:

You can simply just use the Quotient and Chain Rule to find the derivative instead of using ln.

Step 1: Define

Identify

[tex]\displaystyle y = \sqrt{\frac{x}{2 - x}}[/tex]

Step 2: Rewrite

Step 3: Differentiate

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

Unit: Differentiation

Book: College Calculus 10e

Answer:

The lines are:

and

Since after multiplying by -3 the equations sum to 0, the equations are same.

Same equations produce overlapping lines, hence you can see one line only.

Divide second equation by 3

LInes are same so you can see only one line

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Answer:

  Rate

Step-by-step explanation:

Since there are no currency units involved, it is not a price or unit price.

Since the denominator (days) is not 1, it is not a unit rate.

The usual wording for a ratio is "to" rather than "in", so we probably would not say this is a ratio. Though, the usual reason for expressing the numbers this way is to indicate we might be interested in their ratio.

There is time involved, so it is reasonable to call this a "rate," which is usually the ratio of some quantity to the time associated with that quantity.

Answer:

240 cm

Step-by-step explanation:

Let x = tail   y = body

x = 30 + 1/2y

y = 30 + x

Let's plug in the x equation at the bottom

y = 30 + 30 + 1/2y

y = 60 + 1/2y

Bring the like terms to one side

y = 60 + 1/2y

-1/2y    -1/2y

1/2y = 60

Multiply both sides by 2 to get the length of the body

1/2y x 2 = 60 x 2

y = 120

Now we can plug in the new y into another equation, let's use the top one

x = 30 + 1/2(120)

x = 30 + 60

x = 90 = length of the tail

Add em all up

120 + 90 + 30 = 240

Answer:

in three (3) ways a committee can formed