PLEASE HELP ASAP 50 PTS, Please explain answer (:

Assuming the region is of uniform density, compute the mass of the region and its moments.

If n > m, then in the interval [0, 1] we have f(x) ≤ g(x). This means the mass is

\(M=\displaystyle\int_0^1(g(x)-f(x))\,\mathrm dx=\left(\frac{x^{m+1}}{m+1}-\frac{x^{n+1}}{n+1}\right)\bigg|_0^1=\frac1{m+1}-\frac1{n+1}\)

The moments are

\(M_x=\displaystyle\int_0^1\frac{g(x)^2-f(x)^2}2\,\mathrm dx=\frac12\left(\frac{x^{2m+1}}{2m+1}-\frac{x^{2n+1}}{2n+1}\right)\bigg|_0^1=\frac12\left(\frac1{2m+1}-\frac1{2n+1}\right)\)

\(M_y=\displaystyle\int_0^1x(g(x)-f(x))\,\mathrm dx=\int_0^1(x^{m+1}-x^{n+1})\,\mathrm dx=\left(\frac{x^{m+2}}{m+2}-\frac{x^{n+2}}{n+2}\right)\bigg|_0^1=\frac1{m+2}-\frac1{n+2}\)

Then the centroid is

\((\overline x,\overline y)=\left(\dfrac{M_y}M,\dfrac{M_x}M\right)=\boxed{\left(\dfrac{(m+1)(n+1)}{(m+2)(n+2)},\dfrac{(m+1)(n+1)}{(2m+1)(2n+1)}\right)}\)

Answer:

1) μ = 8000

2)  H0:  μ ≥8000

3)   Ha: μ  < 8000

4)  α= 0.10

5)  If the sample size is at least 15 a student's t test can be used.And we assume that the variances of the two independent groups are almost equal.

6) t= x`- μ/ s.d/ √n  = -0.816

7) The P- value = 0.214083.

8) The critical region is [-∞, -1.345]

9) Fail to Reject the Null Hypothesis

Step-by-step explanation:

1) The population characteristic is the population mean =μ = 8000

2) The claim is that the  addition of nitrates results in a decrease in the mean rate of uptake i.e μ < 8000

The null hypothesis is that  μ ≥ 8000

2) Null hypothesis: H0:  μ ≥8000

3) Alternative hypothesis:  Ha: μ  < 8000

4) The significance level alpha = α= 0.10

5)  If the sample size is at least 15 a student's t test can be used.And we assume that the variances of the two independent groups are almost equal.

Calculating mean and standard deviation using a calculator

Sample Size, n: 15

Mean= ∑ x/n = x`=: 7788.8

∑ x/n= 116832/15

St Dev, s.d(n-1) : 1002.4307

6) Test Statistic: student's t Test with d.f = n-1 = 14

t= x`- μ/ s.d/ √n  

t= 7788.8-8000/1002.4307/√15

t= -0.816

7) The P- value for the observed t value  is 0.214083.

The result is not significant at p < 0.10. H0 is accepted.

8) The Critical value for one sided t test at α =0.1 with 14 d.f is  less than t=  -1.3406

Hence the critical region is [-∞, -1.345]

Since the calculated t -0.816  value does not fall in the critical region  [-∞, -1.345] there is not sufficient evidence to reject H0

9) Fail to Reject the Null Hypothesis

Sample does not provide enough evidence to support the null hypothesis and conclude that  the data suggest that the addition of nitrates do not  result in a decrease in the mean rate of uptake. The claim is rejected.

Answer:

Step-by-step explanation:

The probability of drawing a number that is divisible by 3 is 1/3, since there are 3 numbers (3, 6, and 9) out of the 9 possible numbers (1, 2, 3, 4, 5, 6, 7, 8, and 9) that are divisible by 3.

The probability of drawing a 1 after drawing a number that is divisible by 3 is 1/10, since there is only one 1 among the 10 possible digits (0-9) that could be drawn after the first number.

To find the probability of both events happening together (drawing a number divisible by 3 and then drawing a 1), we need to multiply the probability of the first event by the probability of the second event. Therefore, the probability of drawing a number divisible by 3 and then drawing a 1 is:

(1/3) x (1/10) = 1/30

So the probability of drawing a number divisible by 3 and then drawing a 1 is 1/30, or approximately 0.0333, or about 3.33%

Answer:

If I understand this correctly you can draw a 9 and then draw the one if I'm wrong just delete this

Step-by-step explanation:

PR = 32

Equation:

Perimeter = PR + RQ + QP

67 units = (4x) + (x + 2) + (3x + 1)

67 = 8x + 3

64 = 8x

x = 8 units

Substitute x:

PR = (4x) = 4 * 8 = 32 units

RQ = (x + 2) = 8 + 2 = 10 units

QP = (3x + 1) = 3 * 8 + 1 = 25 units

PR = 32

Equation:

Perimeter = PR + RQ + QP

67 units = (4x) + (x + 2) + (3x + 1)

67 = 8x + 3

64 = 8x

x = 8 units

Substitute x:

PR = (4x) = 4 * 8 = 32 units

RQ = (x + 2) = 8 + 2 = 10 units

QP = (3x + 1) = 3 * 8 + 1 = 25 units

Answer:

The price of the shirt is $24.63.

Step-by-step explanation:

Let's assume the price of the shirt is x. Then the price of the wallet will be x - 15. We know that the total cost before tax is 34.26, so we can set up the equation:

x + (x - 15) = 34.26

Simplifying, we get:

2x - 15 = 34.26

Adding 15 on both sides:

2x = 49.26

Dividing by 2:

x = 24.63

Therefore, the price of the shirt is $24.63.

Answer:

b

Step-by-step explanation:

Answer:  $130 money did Brenda and Hazel have all together before buying decorations and snacks.

Here, we have,

You want to know Brenda and Hazel's combined money when the ratio of their remaining balances is 1 : 4 after Brenda spent $58 and Hazel spent $37. They had the same amount to start with.

Setup

Let x represent the total amount the two women started with. Then x/2 is the amount each began with, and their fnal balance ratio is ...

 (x/2 -58) : (x/2 -37) = 1 : 4

Solution

Cross-multiplying gives ...

 4(x/2 -58) = (x/2 -37)

 2x -232 = x/2 -37 . . . . . . eliminate parentheses

 3/2x = 195 . . . . . . . . . . . . add 232-x/2

 x = (2/3)(195) = 130 . . . . . multiply by 2/3

Brenda and Hazel had $130 altogether before their purchases.

Alternate solution

The difference in their spending is $58 -37 = $21.

This is the same as the difference in their final balances.

That difference is 4-1 = 3 "ratio units", so each of those ratio units is $21/3 = $7.

Their ending total is 1+4 = 5 ratio units, or $35.

The total they started with is $58 +37 +35 = $130.

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complete question:

Brenda and Hazel decide to throw a surprise party for their friend, Aerica. Brenda and Hazel each go to the store with the same amount of money. Brenda spends $58 on decorations, and Hazel spends $37 on snacks. When they leave the store, the ratio of Brenda’s money to Hazel’s money is 1 : 4. How much money did Brenda and Hazel have all together before buying decorations and snacks?

Answer:

  D.  f(0) = 11, f(n) = f(n-1) +13

Step-by-step explanation:

You want the recursive definition for the sequence ...

  11, 24, 37, 50, 63, ...

The first term is 11. This means the initial value for the recursive definition will be 11:

  f(0) = 11 . . . . .   eliminates choices A and B

Each term of a recursive sequence is defined in terms of previous terms. That is, f(n) will be defined in terms of f(n-1). Here, the previous term has 13 added to it. (11 +13 = 24, for example).

The remaining part of the recursive definition is ...

  f(n) = f(n -1) +13 . . . . .  eliminates choice C

The recursive definition is ...

<95141404393>

The time Jack left Santa Clara is 1 : 55 pm

A word problem in math is a math question written as one sentence or more. These statements are interpreted into mathematical equation or expression.

The time for Jack to walk to lose Altos is 25 min and he uses another 25mins to work to Palo alto.

Therefore, the total time he spent is

25mins + 25 mins = 50 mins

He arrived Palo at 2 :45 pm, therefore the time he left Santa Clare will be ;

2:45 pm = 14 :45

= 14:45 - 50mins

= 13:55

= 1 : 55pm

Therefore he left at 1:55 pm

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Answer:

The quen is as following:

ABC is a right triangle at C,

Acute angles are in the ratio 5:1, i.e. ∠BAC : ∠ABC = 5:1

If CH is an altitude to AB and CL is an angle bisector of ∠ACB, find m∠HCL.

The solution is:  m∠HCL = 30°

Step-by-step explanation:

See the attached figure.

∵The triangle is right at C   ∴∠C = 90°

∴∠A + ∠B = 90° ⇒(1)

∵ Acute angles are in the ratio 5:1, i.e. ∠BAC : ∠ABC = 5:1

∴∠A = 5 times ∠B

Substitute at (1)

∴ 5 ∠B + ∠B = 90° ⇒⇒⇒ ∴∠B = 15°  and ∠A = 75°

∵CL is an angle bisector of ∠ACB

∴ ∠ACL = 90°/2 = 45°

∵ CH is an altitude to AB ⇒ ∠CHA = 90°

At the triangle AHC:

∠ACH = 180° - (∠CHA + ∠CAH) = 180° - (90° + 75°) = 15°

∴ ∠HCL = ∠ACL - ∠ACH = 45° - 15° = 30°

Answer: A

Step-by-step explanation:
Your answer is A.

Value of 3.78 x 10=37.8

Value of 5.99 x 102=699.98

value of 7.35 x 10-12=61.5

Value of 9.46 x 10-10=84.6.

Least value to greatest value

3.78 x 10=37.8 Least value

7.35 x 10 - 12=61.5 Sencond least value

9.46 x 10 - 10=84.6  Sencond greatest value

5.99 x 102=699.98  Greatest value

Hope it helps have a great day:)

Answer:

The answer is

Step-by-step explanation:

\(f(x) = - 3 {x}^{2} - 8 \\ \)

To find f(-4) , substitute the value of x that's - 4 into f(x). That is for every x in f(x) , replace it with - 4

We have

\(f( - 4) = - 3 ({ - 4})^{2} - 8 \\ = - 3(16) - 8 \\ = - 48 - 8 \: \: \: \: \: \)

We have the final answer as

\(f( - 4) = - 56\)

Hope this helps you

The two expressions are not equivalent.

To simplify the expression (p^2n^1/2)^0 √ p^5n^4, we first need to understand the properties of exponents and radicals.

Recall that any number raised to the power of zero is equal to 1, so (p^2n^1/2)^0 = 1.

Next, we can simplify the radical term by multiplying the exponents inside and outside the radical:

√ p^5n^4 =

(p^5n^4)^(1/2)

= p^(5/2)n^(4/2)

= p^(5/2)n^2

Combining this result with the previous step, we have:

(p^2n^1/2)^0 √ p^5n^4

= 1 * p^(5/2)n^2

= p^(5/2)n^2

This is not equivalent to p^18n^6 √p. In fact, p^(5/2)n^2 cannot be simplified any further without additional information about the expression.  ,

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Answer:

Step-by-step explanation:

If {0, 3, 6, 9} are are your x's or domain  or input and there are no repeats, then yes TRUE it is a function.

The number that does not belong with the other three is D. 10 x 9.2 ⁻¹³

With the first three numbers, the base of the exponential that is being multiplied by the first number is 10. These numbers are:

With the last number however, we see that the base of the exponential is 9. 2 and not 10 like the others. This is why 10 x 9 . 2 ⁻¹³ does not belong with the rest.

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Answer:

24√2

Step-by-step explanation:

Let the side of the square be x

If the diagonal is 12m (hypotenuse), then;

x^2 + x^2 = 12^2

2x^2 = 144

x^2 = 144/2

x^2 = 72

x = √72

x = √36*2

x = 6√2

Perimeter of the square garden = 4x

Perimeter of the square garden = 4(6√2)

Perimeter of the square garden = 24√2

The solution to the equation is x = 7.

What is the linear equation in one variable?

A linear equation in one variable is an equation of the form ax + b = 0, where a and b are constants and x is the variable. The general form of a linear equation in one variable is ax + b = 0, where a and b are constants and x is the variable. The graph of a linear equation in one variable is a straight line.

The first step in solving the equation 2x - 4 = 10 using algebra tiles would be to add 4 to both sides of the equation to get 2x = 14. The next step would be to divide both sides of the equation by 2 to get x = 7.

Hence, the solution to the equation is x = 7.

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Answer:

circumference (c) = 43.96cm

Area (A) = 615.44cm²

Step-by-step explanation:

Here,

Radious (r) = 7 cm

circumference (c) = \(2\pi r\)

                            = 2×3.14×7

                            =43.96cm

Area (A) = \(4\pi r^{2}\)

              = 4×3.14×7²

               =12.56×49

               = 615.44cm²

Answer:

area:153.86m²

circumfrence:43.96m

Step-by-step explanation:

Answer:

5x+3x=8x, 6w+2w=8w is the answer

Answer:

Yes

Step-by-step explanation:

To know if a table is a function or not, we have to see if 1 input only has 1 output.

Looking at the table each input only has 1 output, so it is a function.

Answer:

negative 400 over 9−  

400

9

=negative 44 and 4 over 9− 44

4

9

≈negative 44.444−44.444

Step-by-step explanation:

I'M NOT SURE

Step-by-step explanatioI'M NOTN SURE

Answer:

when you see 30 60 90 trangle always remembee this important information

30 degree meet x

90 degree meet 2x

60 degree meet xsqrt3

for example if we Saw the 90 degree meet 4 and unknown degree meet 2 we have to know that unknown degree is 30 hopefully you can understand what iam saying because my engilish begin come bad when i explain any thing

Mrs. Wu initially had $1062.40.

Let's break down the given information step by step:

1. Mrs. Wu spent 1/6 of her money on a dress and 2 blouses.

  Let's assume Mrs. Wu's total money is represented by the variable M. She spent 1/6 of M on the dress, which means she spent (1/6)M on the dress and the same amount on two blouses.

2. The dress cost 3 times as much as each blouse.

  Let's assume the cost of each blouse is represented by the variable B. Therefore, the cost of the dress would be 3B.

3. Mrs. Wu spent 3/4 of her remaining money on a watch.

  After spending on the dress and blouses, Mrs. Wu has (M - (1/6)M) = (5/6)M remaining. She spent 3/4 of this remaining money on a watch, which is (3/4) * (5/6)M = (15/24)M.

4. She spent $220.50 more on the watch than on the dress.

  The amount spent on the watch is (15/24)M, and the amount spent on the dress is (1/6)M. The difference between these amounts is $220.50.

To find the value of M, we can set up an equation:

(15/24)M - (1/6)M = $220.50

Simplifying the equation:

(15/24 - 1/6)M = $220.50

(5/24)M = $220.50

Multiplying both sides by (24/5):

M = $220.50 * (24/5)

M = $1062.40

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Option D is the correct answer.

From the graph, we can conclude that,

1. The two lines are continuous lines and not broken lines. So, the inequality sign should be either ≤ or ≥.

2. The points on the lines of the shaded region are also included in the solution.

The only option that matches with the above conditions is option D. So, option D is the correct answer.

Let us verify it.

Now, let us consider a point that is inside the shaded region and also on any one line.

Let us take (0, 2).

Plug in 0 for x and 2 for y in each of the options and check which inequality holds true.

Considering the inequalities,

y ≥ 3x - 2

x + 2y ≤ 4

Solving we get,

2 ≥ 3(0) - 2

2 ≥ -2

x + 2y ≤ 4

0 + 2(2) ≤ 4

4 ≤ 4

Here, both inequalities are correct.

So, option D is the correct answer.

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The complete question is =

Which system of linear inequalities is graphed?

A. y < 3x-2

x + 2y ≥ 4

B. y < 3x - 2

x + 2y > 4

C. y > 3x - 2

x + 2y < 4

D. y ≥ 3x - 2

x + 2y ≤ 4

Answer:

2.38 pounds of almonds

Step-by-step explanation:

35% - 00.35

6.8

×

00.35

--------

2.38

a) P(psychology student)  = 1/3. b) P(psychology or anthropology student)  = 5/6. c) P(not sociology student)= 5/6

(a) The probability of choosing a psychology student is the number of psychology students divided by the total number of students:

P(psychology student) = 4/(6+2+4) = 4/12 = 1/3

(b) The probability of choosing a psychology student or an anthropology student is the sum of the number of psychology and anthropology students divided by the total number of students:

P(psychology or anthropology student) = (4+6)/(6+2+4) = 10/12 = 5/6

(c) The probability of not choosing a sociology student is the number of non-sociology students divided by the total number of students:

P(not sociology student) = (6+4)/(6+2+4) = 10/12 = 5/6

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The least common denominator needed to solve the equation is given as follows:

D. x(x - 3).

The equation in this problem is given as follows:

1/x + 2/(x - 3) = 5.

The denominators of each expression are given as follows:

x and x - 3 are not factors of each other, hence we multiply them and the least common denominator needed to solve the equation is given as follows:

D. x(x - 3).

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