According to Fidelity Investment Vision Magazine, the average weekly allowance of children varies directly as their grade level. In a recent year, the average allowance of a 9th-grade student was 9.66 dollars per week. What was the average weekly allowance of a 5 th-grade student?​

Considering the given function, we have that:

a) 28.31 years.

b) 0.3382 years a decade.

c) 2.6184.

The median age of the U.S. population in t decades after 1960 is:

f(t) = -0.2176t³ + 1.962t² - 2.833t + 29.4.

1970 is one decade after 1960, hence the median was:

f(1) = -0.2176 x 1³ + 1.962 x 1² - 2.833 x 1 + 29.4 = 28.31 years.

The rate of change was is the derivative when t = 1, hence:

f'(t) = -0.6528t² + 3.924t - 2.933

f'(1) = -0.6528 x 1² + 3.924 x 1 - 2.933 = 0.3382 years a decade.

The second derivative is:

f''(t) = -1.3056t + 3.924

Hence:

f''(1) = -1.3056 x 1 + 3.924 = 2.6184.

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The first three terms of the Arithmetic Progression are 12, 17 and 22.

For an ARITHMETIC PROGRESSION, AP ;

First term = a

Second term = a + d

Third term = a + 2d

Where, d = common difference ;

If third term exceeds smallest by 10 ;

Third term - first term

a + 2d - a = 10

2d = 10

d = 10/2

d = 5

Sum of the three terms :

a + (a + d) + a + 2d = 51

3a + 3d = 51

d = 5

3a + 3(5) = 51

3a + 15 = 51

3a = 51 - 15

3a = 36

a = 12

The AP would be:

First term, a = 12

Second term, a + d = 12 + 5 = 17

Third term = a + 2(d) = 12 + 10 = 22

Therefore , the first three terms of the AP are :

12, 17 and 22

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Answer:

Step-by-step explanation:

Answer:

3/6=?/10

Step-by-step explanation:

multiply by together. ?=5

Answer:

Male & action movie among a group of total 479

Step-by-step explanation:

We only choose male from action movie category so:

p = 105/ 479 = 0.22

The probability that a randomly chosen person from this group is male and attended an action movie will be 0.22. Then the correct option is C.

Its basic premise is that something will almost certainly happen. The percentage of favorable events to the total number of occurrences.

This table shows how many male and female students attended two different movies.

                   Action      Drama          Total

Mala             105            124              229

Female         99             151               250

Total            204           275              479

Then the probability that a randomly chosen person from this group is male and attended an action movie will be

Favorable event = 105

Total event = 479

Then the probability will be

P = 105 / 479

P = 0.219

P ≈ 0.22

Then the correct option is C.

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The equation has 2 valid solutions; no extraneous solutions

The given equation is:

[tex]\sqrt{x - 1} - 5= x - 8[/tex]

First, we determine the solutions

[tex]\sqrt{x - 1} - 5= x - 8[/tex]

Add 5 to both sides

[tex]\sqrt{x - 1} = x - 8 + 5[/tex]

[tex]\sqrt{x - 1} = x - 3[/tex]

Square both sides

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

Expand

[tex]x - 1 = x^2- 3x - 3x + 9[/tex]

[tex]x - 1 = x^2- 6x + 9[/tex]

Collect like terms

[tex]x^2 - 6x - x + 9 + 1 = 0[/tex]

[tex]x^2 - 7x + 10 = 0[/tex]

Expand again

[tex]x^2 - 2x-5x + 10 = 0[/tex]

Factorize

[tex]x(x - 2) -5(x -2)= 0[/tex]

Factor out x - 2

[tex](x - 5)(x -2)= 0[/tex]

Split

[tex]x - 5=0[/tex] or [tex]x - 2 = 0[/tex]

[tex]x= 5[/tex] or [tex]x = 2[/tex]

The above values are valid values of x.

Hence, the equation has 2 valid solutions; no extraneous solutions

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Answer:

That person is wrong, First blank is : one valid solution , Second blank is : one extraneous solution, and I'm not sure what the 3rd blank is but I think It's 4.

Step-by-step explanation:

for plato users

Answer:

it's too much for me im a child u know

Answer:

356 streams

Step-by-step explanation:

From the graph, you will see that the line cross the x-axis at x = 8.8

Substitute into the expression y = 40x + 4

y = 40(8.8)+4

y = 352 + 4

y = 356

Hence the distributor charges will be paid for after 356 streams

Answer:

1. cube

2. square pyramid

4. cone

5. cube

Answer:

x=0

Step-by-step explanation

I think that's what you're looking for :l/

Answer:

11, 14, 17, 20, ...

Step-by-step explanation:

An arithmetic sequence is one where each term increases by the same number every time. This is called the common difference and is always added to the previous term to get the current term. The only sequence that follows this is the third once. Every term increases by 3; therefore, it is an arithmetic sequence.

Answer:

yes it is. a polygon is any closed shape with at least 3 connected lines (eg. triangle, square, pentagon, hexagon, heptagon, octagon, etc)

Step-by-step explanation:

Answer:

[tex]125 \: \: degrees[/tex]

Step-by-step explanation:

As the 2 lines are parallel

<A = <B ( Alternative Angles)

[tex]6x + 5 = 4x + 45 \\ 6x - 4x = 45 - 5 \\ 2x = 40 \\ x = 20[/tex]

[tex]<A = 6x + 5 \\ = 6 \times 20 + 5 \\ = 120 + 5 \\ = 125[/tex]

<A=6x+5

=6×20+5

=120+5

=125

<B=4x+45

=4×20+45

=80+45

=125

it is alternate angle they are equal each other

<A = < B

[tex]6x + 5 = 4x + 45 \\ 6x - 4x = 45 - 5 \\ 2x = 40 \\ x = \frac{40}{2} \\ x = 20 \\ \\ [/tex]

the answer is 2B divided by A minus 3

Step-by-step explanation:

At first you need to take its lateral surface area by using the perimeter of base of the triangle and the height of prism.

Then after calculating it you need to find out its total surface area which is asked in the question and that is calculated by adding the area of both triangles of the prism in the lateral surface area.

Then that's your answer.

9514 1404 393

Answer:

  544 square units

Step-by-step explanation:

The surface area is the sum of the area of the two triangular bases and the three rectangular faces. The relevant area formulas are ...

  A = 1/2bh . . . . area of a triangle with base b and height h

  A = LW . . . . . are of a rectangle of length L and width W

__

  SA = 2(1/2)(12)(8) + (10 +10 +12)(14)

  SA = 96 +448 = 544 . . . square units

Solution :

a). The probability that the student will [tex]\text{correctly answer}[/tex] the 1st question after the 4th attempt.

P (correct in the 4th attempt)

= [tex]$(1-0.75)^3 \times 0.75$[/tex]

= 0.01171875

b). The probability that the student will [tex]\text{correctly answer}[/tex] 3 questions after 10 total attempts.

P( X = 3) for X = B in (n = 10, p = 0.75)

= [tex]$C(10,30) \times 0.75^3 \times 0.25^7$[/tex]

= 0.0031

c). The mean and the standard deviation for the number of attempts up to when the students gets all the questions correct is :

There are = 6 success, p = 0.75.

Therefore, this is a case of a negative binomial distribution.

[tex]$E(X)=\frac{k}{p}$[/tex]

         [tex]$=\frac{6}{0.75}$[/tex]

         = 8

So, [tex]$\sigma = \frac{\sqrt{k(1-p)}}{p}$[/tex]

     [tex]$\sigma = \frac{\sqrt{6(1-0.75)}}{0.75}$[/tex]

        = 1.6330

Step-by-step explanation:

The prime 43 appears in the sixth twin-prime pair 41, 43. As a sum of four or fewer squares: 43 = 32 + 32 + 52 = 12 + 12 + 42 + 52 = 32 + 32 + 32 + 42. ... As a difference of two squares: 43 = 222 − 212.

Answer:

1.9385 kg

Step-by-step explanation:

Given :

Total kilogram of chicken = 2 kilograms

Amount left after dinner = 61.5 gram

Recall :

1000 grams = 1 kilogram

Hence,

61.5 grams = x kg

x = (61. 5 / 1000) = 0.0615 kg

Hence,

Amount eaten = Total chicken - amount left

Amount eaten = (2 - 0.0615) kg

Amount eaten = 1.9385 kg

Answer:

number 7 the answer is 50,000

Answer:

[tex]\sqrt{-(x +72)^3} - 72 = -(3\sqrt x - 72 +72)^3[/tex]

Step-by-step explanation:

Given

[tex]g(x) = 3\sqrt x - 72[/tex]

[tex]h(x) = -(x +72)^3[/tex]

Required

Show that they are inverse functions

For g(x) and h(x) to be inverse, then:

[tex]g(h(x)) = h(g(x))[/tex]

We have:

[tex]g(x) = 3\sqrt x - 72[/tex]

Replace x with h(x)

[tex]g(h(x)) = 3\sqrt{h(x)} - 72[/tex]

Substitute value for h(x)

[tex]g(h(x)) = 3\sqrt{-(x +72)^3} - 72[/tex]

Similarly;

[tex]h(x) = -(x +72)^3[/tex]

Replace x with g(x)

[tex]h(g(x)) = -(g(x) +72)^3[/tex]

Substitute value for g(x)

[tex]h(g(x)) = -(3\sqrt x - 72 +72)^3[/tex]

Recall that:

[tex]g(h(x)) = h(g(x))[/tex]

So:

[tex]\sqrt{-(x +72)^3} - 72 = -(3\sqrt x - 72 +72)^3[/tex]

Its c

explanation:

on edge

both angles are 90 degrees

Answer:

A

Step-by-step explanation:

Try graphing the function on desmos

Answer:

see image...

the (x-h) shifts the curve left right (east west)

and the +k at the end shifts it up/down (north/south)

Step-by-step explanation:

Answer:

6.3 Kwhr

Step-by-step explanation:

Given :

Power = 8827 watts

Time in minutes = 43 minutes

To obtain the amount of CO2 that was created :, which is the energy :

Recall

Energy = power * time

Energy in kw/hr = (8827/100) * (43/60)

Energy = 8.827 * 0.7166666

Energy = 6.326 Kwhr

Answer:

Step-by-step explanation:

Tìm cc

Step 2

−2y = 15 − 2z

should be

−2y = -30 + 4a

Answer:

216 m²

Step-by-step explanation:

Surface area of a cube = 6a², when a = length of one side

so,

6a²

= 6×6²

= 6×36

= 216 m²

Answered by GAUTHMATH

Answer:

216 m²

Step-by-step explanation:

Answer:

a) The p-value of the test is 0.2076 > 0.05, which means that the sample indicates that the resistors are conforming.

b) The 95% confidence interval for the average resistance is (0.147, 0.153). 0.152 is part of the confidence interval, which means that as the test statistic in item a), it indicates that the resistors are conforming.

Step-by-step explanation:

Question a:

The resistors produced by a manufacturer are required to have an average resistance of 0.150 ohms.

At the null hypothesis, we test if this is the average resistance, that is:

[tex]H_0: \mu = 0.15[/tex]

We are interested in testing the hypothesis that the resistors conform to the specifications.

At the alternative hypothesis, we test if it is not conforming, that is, the mean is different of 0.15, so:

[tex]H_1: \mu \neq 0.15[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.

0.15 is tested at the null hypothesis:

This means that [tex]\mu = 0.15[/tex]

Sample mean of 0.152, sample of 10, population standard deviation of 0.005.

This means that [tex]X = 0.152, n = 10, \sigma = 0.005[/tex]

Value of the test statistic:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{0.152 - 0.15}{\frac{0.005}{\sqrt{10}}}[/tex]

[tex]z = 1.26[/tex]

P-value of the test and decision:

The p-value of the test is the probability of the sample mean differing from 0.15 by at least 0.152 - 0.15 = 0.002, which is P(|z| > 1.26), given by two multiplied by the p-value of z = -1.26.

Looking at the z-table, z = -1.26 has a p-value of 0.1038.

2*0.1038 = 0.2076

The p-value of the test is 0.2076 > 0.05, which means that the sample indicates that the resistors are conforming.

Question b:

We have to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]

Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].

That is z with a p-value of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.

Now, find the margin of error M as such

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

[tex]M = 1.96\frac{0.005}{\sqrt{10}} = 0.003[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is 0.15 - 0.003 = 0.147.

The upper end of the interval is the sample mean added to M. So it is 0.15 + 0.003 = 0.153.

The 95% confidence interval for the average resistance is (0.147, 0.153). 0.152 is part of the confidence interval, which means that as the test statistic in item a), it indicates that the resistors are conforming.