HELP
Identify the domain of the function shown in the graph.

I've attached a sketch of one such cross section (light blue) of the solid (shown at x = 0). The planes x = ±1 are shown in gray, and the two parabolas are respectively represented by the blue and orange curves in the (x, y)-plane.

For every x in the interval [-1, 1], the corresponding cross section has a diagonal of length (2 - x ²) - x ² = 2 (1 - x ²). The diagonal of any square occurs in a ratio to its side length of √2 : 1, so the cross section has a side length of 2/√2 (1 - x ²) = √2 (1 - x ²), and hence an area of (√2 (1 - x ²))² = 2 (1 - x ²)².

The total volume of the solid is then given by the integral,

[tex]\displaystyle\int_{-1}^1 2(1-x^2)^2\,\mathrm dx = \int_{-1}^1 (2-4x^2+4x^4)\,\mathrm dx = \boxed{\frac{32}{15}}[/tex]

Answer:

D. 4x² + 3x/2 - 7

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

f(x) = x/2 - 3

g(x) = 4x² + x - 4

(f + g)(x) is f(x) + g(x)

Step 2: Find

Answer:

The answer is C.

Step-by-step explanation:

(f+g)(x)= f(x)+g(x).

So that would be x/2-3 + 4x^2+x-4.

If you combine like terms that would be:

4x^2+x/2+x-4-3=

4x^2+3/2x-7

Answer:

1. centimeter

2. kilogram

3. gram

4. milligram

5. centimeter

6. meter

7. kilometer

8. liter

9. kiloliter

10. millimeter

Step-by-step explanation:

you really cannot answer that yourself ?

you don't understand yet the difference between length or distance, area, volume, weight, ... ?

I how this helps then

1. is length, and it is rather short. so, we use a rather small unit to express it.

2. is weight. and a big one. so, we use a bigger unit.

3. is weight. but a small one.

4. is weight. and a really tiny one.

5. is length. similar dimension of size as the finger.

6. is length. and a bigger one.

7. is length. and a truly big one.

8. is volume. liquid volume at that. but rather small.

9. is volume. and again liquid volume. also very big. but still, kiloliter is practically never used by anybody ...

10. is length. and a very tiny one.

Hi there!

[tex]\large\boxed{f(9) = 12}[/tex]

Evaluating f(x) at x = 9 means we must use the piecewise function where x = 9 is included.

f(x) = 12 includes 9 because a "≤" is inclusive of the interval. Thus:

f(9) = 12

Answer:

A: f(t) = t2(4t) - 14

B: It is a maximum because it continues redistributing forever.

C: Assuming you plotted this on a 0/0 grid, your axis of symetry would be at 18/28

Hope this helps, please mark brainliest

Step-by-step explanation:

A: it is simple really, your just redistributing each T to itself, which is what makes a square / vertex.

Answer:

what r u answers picks

Step-by-step explanation:

cant answer with out of t

9514 1404 393

Answer:

Step-by-step explanation:

The formula for figuring the amount that can be borrowed (P) is shown on the first line of the attachment. (The second line rounds it to the nearest cent.) In this formula, ...

  a = monthly payment, r = annual interest rate, t = number of years

The amounts requested by the problem statement are shown in the attachment, and above. b is the amount that can be borrowed, p is the total of payments, and i is the interest paid. There are 360 monthly payments in 30 years, so the total paid is 360 times the monthly payment amount.

Answer:

different question

Step-by-step explanation:

question is wrong

Answer:

It is A and B

Step-by-step explanation:

Answer:

Heat flux boundary condition.

Step-by-step explanation:

Heat flux is boundary condition in positive x-direction. The specified temperature is constant and steady heat conduction. Temperature of exposed surface can be measured directly with the thermal condition expression.

Answer:

The margin of error for her confdence interval is of 0.3757.

Step-by-step explanation:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 18 - 1 = 17

99% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 17 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.99}{2} = 0.995[/tex]. So we have T = 2.8982

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}}[/tex]

In which s is the standard deviation of the sample and n is the size of the sample.

Standard deviation of 0.55 meters.

This means that [tex]s = 0.55[/tex]

What is the margin of error for her 99% confidence interval?

[tex]M = T\frac{s}{\sqrt{n}}[/tex]

[tex]M = 2.8982\frac{0.55}{\sqrt{18}}[/tex]

[tex]M = 0.3757[/tex]

The margin of error for her confdence interval is of 0.3757.

Margin of error is the distance between the mean and the limit of confidence intervals. The margin of error for the given condition is 3.28 approximately.

Suppose that we have:

Sample size n  < 30

Then the margin of error(MOE) is obtained as

Margin of Error = [tex]MOE = T_{c}\dfrac{\sigma}{\sqrt{n}}[/tex]

[tex]MOE = T_{c}\dfrac{s}{\sqrt{n}}[/tex]

where [tex]T_{c}[/tex] is critical value of the test statistic at level of significance

For the given case, taking the random variable X to be tracking the height of trees in the sample taken of trees from the considered forest.

Then, by the given data, we get:

[tex]\overline{x} = 4.8[/tex], [tex]s = 4.8[/tex], n = 18

The degree of freedom is n-1 = 17

Level of significance = 100% - 99% = 1% = 0.01

The critical value of t at level of significance 0.01 with degree of freedom 17 is obtained as T = 2.90 (from the t critical values table)

Thus, margin of error for 99% confidence interval for considered case is:

[tex]MOE = T_{c}\dfrac{s}{\sqrt{n}}\\\\MOE = 2.9 \times \dfrac{4.8}{\sqrt{18}} \approx 3.28[/tex]

Thus, the margin of error for the given condition is 3.28 approximately.

Learn more about margin of error here:

https://brainly.com/question/13220147

Answer:

[tex]2(-36 - 3i) +(5 +2i)(12 - 2i) \\ \implies - 72 - 6i + 60 - 10i + 24i + 4\\ \implies \: - 8 + 8i[/tex]

Answer:

2×8-4^2

=16-16

=0

0 is the porduct

Answer: 130%

Step-by-step explanation:

[tex]40 + 40(x) = 9240\\40(1 + x) = 92\\1+x=\frac{92}{40} \\x=\frac{92}{40} -1=2.3-1=1.3[/tex]

x = 1.3 = 130%

Answer:

(-4, -1)

Step-by-step explanation:

Answer:

y2-y1 / x2-x1

-4/3

Step-by-step explanation:

Answer:

-4/3

Step-by-step explanation:

When given two points, the slope is found by

m = (y2-y1)/(x2-x1)

   = (-3- -7)/(3 -6)

    = (-3+7)/(3-6)

    = 4/-3

   = -4/3

Answer:

Yes, P(E1)=P(E2)

Step-by-step explanation:

We are given that

Number of dice=3

Total outcomes of 1 die=6

Therefore,

Total number of outcomes =[tex]6^3=216[/tex]

E1={{(1,4,6),(2,3,6),(1,5,5),(2,4,5),(3,3,5),(3,4,4)}

E2={(1,5,6),(2,4,6),(3,3,6),(2,5,5),(4,4,4),(3,4,5)}

We have to show that E1 and E2 have the same probability P(E1) = P(E2).

Probability, [tex]P(E)=\frac{Favorable\;outcomes}{Total\;outcomes}[/tex]

Using the formula

[tex]P(E_1)=\frac{6}{216}[/tex]

[tex]P(E_1)=0.0278[/tex]

[tex]P(E_2)=\frac{6}{216}[/tex]

[tex]P(E_2)=0.0278[/tex]

Hence, P(E1)=P(E2)

Answer:

E. by the SAS similarity theorem.

Step-by-step explanation:

Included angle x° in ∆ ABC ≅ included angle x° in ∆EDC (vertical angles are equal)

DC/BC = 240/150 = 1.6

EC/AC = 320/200 = 1.6

This implies that the ratio of two corresponding sides of both triangles are the same.

Two triangles are considered similar to each other by the SAS similarity theorem of they have a corresponding included angle that is equal and two corresponding sides that are congruent to each other. Therefore, both triangles are similar by the SAS similarity theorem.

Answer:

a) {3,5}{3,10}{5,10}

b) [tex]P(A)=\frac{1}{3}[/tex]

c) [tex]P(B)=\frac{2}{3}[/tex]

d) [tex]P(C)=\frac{1}{3}[/tex]

e) [tex]P(A and C)=0[/tex]

f) [tex]P(A or B)=1[/tex]

g) [tex]P(B and C)=\frac{1}{3}[/tex]

h) [tex]P(A or C)=\frac{2}{3}[/tex]

i) [tex]P(C given B)=\frac{1}{2}[/tex]

j) [tex]P(C given A)=0[/tex]

k) [tex]P(not B)=\frac{1}{3}[/tex]

l) [tex]P(not C)=\frac{2}{3}[/tex]

Yes, events A and B are mutually exclusive. Because the results can either be even or odd, not both. No, events B and C are not mutually exclusive because the result can be both, odd and prime.

Step-by-step explanation:

a)

In order to solve part a of the problem, we need to find the possible outcomes, in this case, the possible outcomes are:

{3,5}{3,10} and {5,10}

We could think of the oppsite order, for example {5,3}{10,3}{10,5} but these are basically the same as the previous outcomes, so we will just take three outcomes in our sample space. We can think of it as drawing the two chips at the same time.

b)

Now the probability of the sum of the chips to be even. There is only one outcome where the sum of the chips is even, {3,5} since 3+5=8 the other outcomes will give us an odd number, so:

[tex]P=\frac{#desired}{#possible}[/tex]

[tex]P(A)=\frac{1}{3}[/tex]

c) For the probability of the sum of the chips to be odd, there are two outcomes where the sum of the chips is odd, {3,10} since 3+10=13 and {5,10} since 5+10=15 the other outcomes will give us an even number, so:

[tex]P(B)=\frac{2}{3}[/tex]

d) The probability of the sum of the chips is prime. There is only one outcome where the sum of the chips is prime, {3,10} since 3+10=13 the other outcomes will give us non prime results, so:

[tex]P(C)=\frac{1}{3}[/tex]

e) The probability of the sum of the chips to be even and prime. There are no results where we can get an even and prime number, since the only even and prime number there is is number 2 and no outcome will give us that number, so:

P(A and C)=0

f) The probability of the sum of the chips is even or odd. We can either get even or odd results, so no matter what outcome we get, we will get an odd or even result so:

[tex]P(A or B)=1[/tex]

g) The probability of the sum of the chips is odd and prime. There is only one outcome where the sum of the chips is odd and prime, {3,10} since 3+10=13 the other outcomes will give us non prime results, so:

[tex]P(B and C)=\frac{1}{3}[/tex]

h) The probability of the sum of the chips is even or prime. There are two outcomes where the sum of the chips is even or prime, {3,10} since 3+10=13 and {3,5} since 3+5=8 so:

[tex]P(A or C)=\frac{2}{3}[/tex]

i) The probability of the sum of the chips is prime given that the sum of the chips is odd. There are two possible results where the sum of the chips is odd {3,10} and {5,10} and only one of those results is even, {3,10}, so

[tex]P(C given B)=\frac{1}{2}[/tex]

j) The probability of the sum of the chips is prime given that the sum of the chips is even. There is only one possible even result: {3,5} but that result isn't prime, so

[tex]P(C given A)=0[/tex]

k) The probability of the sum of the chips is not odd. There is only one outcome where the sum of the chips is not odd (even), {3,5} so:

[tex]P(not B)=\frac{1}{3}[/tex]

l) The probability of the sum of the chips is not prime. There are two outcomes where the sum of the chips is not prime, {3,5} and {5,10} so:

[tex]P(not C)=\frac{2}{3}[/tex]

Are events A and B mutually exclusive?

Yes, events A and B are mutually exclusive.

Why or why not?

Because the results can either be even or odd, not both.

Are events B and C mutually exclusive?

No, events B and C are not mutually exclusive.

Why or Why not?

Because the result can be both, odd and prime.

Answer:

The average rate of change is 5.

Step-by-step explanation:

First plug in the x values.

y=5x+1

=(0)5+1

=1

y=5x+1

=(4)5+1

=21

Average rate of change = the change in the output divided by the change in the input.

Output change: 21-1=20

Input change: 4-0=4

20/4=5

Answer:

On a coordinate plane, a rectangle is 3 units high and 6 units wide.

Answer:

option "B"

You Welcome

Step-by-step explanation:

Answer:

c) tan

Step-by-step explanation:

tan = Opposite side / close side

When close side = v         and     Opposite side = 2,8m

Answer:

-73, -71, -69

Step-by-step explanation:

Suppose the middle of the 3 integers is x.

(x-2)+(x)+(x+2)=-213

x-2+x+x+2=-213

3x=-213

x=-71

The integers are -69, -71, and -73

Answer:

-73,-71,-69

Step-by-step explanation:

Let x represent an odd interger

Odd intergers are serpated by the value of 2 so let the three consective intergers be represented by

[tex](x )+ (x + 2) +( x + 4)[/tex]

Set that equation equal to 213.

[tex]x + x + 2 + x + 4 = - 213[/tex]

[tex]3x + 6 = - 213[/tex]

[tex]3x = - 219[/tex]

[tex]x = - 73[/tex]

Plug -73 in the consective intergers expression.

[tex] - 73 + ( - 73 + 2) + ( - 73 + 4)[/tex]

So our three intergers are

[tex] - 73[/tex]

[tex] - 71[/tex]

[tex] - 69[/tex]

Answer:

36 (maybe...)

Step-by-step explanation:

Technically there is no way to answer this question, it says that 120 ADULTS were surveyed and then asks how many STUDENTS rank themselves as introverts.  But if we a supposed to assume that all adults are students:

The ratio of 3:7 means that for every 3 introverts, there are 7 extroverts.

In other words for every 10 people (total introvert+extrovert) there are 3 introverts.

So to find the number of introverts in the group of 120, just multiply by 3/10 or 0.3

The answer would be 36

Answer:

The critical value is [tex]Z_c = -2.327[/tex]

Step-by-step explanation:

A hypothesis will be used to test that a population mean equals 5 against the alternative that the population mean is less than 5

Test if the mean is less than a value, so a one-tailed hypothesis test is used.

Known variance σ.

This means that the z-distribution is used to solve this question.

What is the critical value for the test statistic for the significance level of 0.010?

Z with a p-value of 0.01, so, looking at the z-table, [tex]Z_c = -2.327[/tex]

*see attachment for missing diagram

Answer:

AC = 5 and BC = 5√3

Step-by-step explanation:

Given:

m<A = 60°

m<B = 30°

AB = 10

Required:

AC and BC

Solution:

Recall, SOH CAH TOA

✔️Find AC:

Reference angle (θ) = 30°

Hypotenuse = 10

Opposite = AC

Apply SOH:

Sin θ = Opp/Hyp

Substitute

Sin 30° = AC/10

10*Sin 30° = AC

10*½ = AC (sin 30° = ½)

5 = AC

AC = 5

✔️Find BC:

Reference angle (θ) = 60°

Hypotenuse = 10

Opposite = BC

Apply SOH:

Sin θ = Opp/Hyp

Substitute

Sin 60° = BC/10

10*Sin 60° = BC

10*√3/2 = BC (sin 60° = √3/2)

5*√3 = BC

BC = 5√3

Your answer is July.

From least to greastest:

January: $50

February: $80

September: $80

May: $95

April: $100

March: $110

June: $250

August: $300

July: $320

I hope this helps!

The month that had the largest deposit is the month of; July

How do you Interpret a Histogram?

From the given histogram with savings account on the x-axis and amount deposited on the y-axis, we can see the following amounts deposited for each month as follows;

The month with the largest deposit is clearly July

Read more about Histograms at; https://brainly.com/question/25983327

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Explanation:

There are a few ways to do this.  

One method involves drawing a horizontal line to form three rectangles as show below. Note the labels A,B,C.

Add up those three sub areas found: A+B+C = 42+40+28 = 110 square miles

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

There are other methods you could do. A second method is to draw two vertical lines to form 3 other rectangles, then add up the sub areas to get 110.

A third method is to draw a horizontal line across the top to form one large rectangle (20 mi by 9 mi) and subtract off the area of the 7 mi by 10 mi inner rectangle (the empty space), so you'd say 20*9 - 7*10 = 180-70 = 110