How much would you pay for 14.2 gallons of gas that cost $2.08 per gallon?

396 cm²

Volume of rectangular prism - -

Formula's :

Here base area:

Length * Width

4 * 9

36 cm²

Volume:

Base area * Height

36 * 11

396 cm²

Answer:

(a) 8.35

(b) 5.98

(c) 3.86

Step-by-step explanation:

The complete question is:

In a recent study on world​ happiness, participants were asked to evaluate their current lives on a scale from 0 to​ 10, where 0 represents the worst possible life and 10 represents the best possible life. The mean response was 5.4 with a standard deviation of 2.3. ​(a) What response represents the 90th ​percentile? ​(b) What response represents the ​60th percentile? ​(c) What response represents the ​first quartile? ​

Solution:

Assume that the world​ happiness ratings follows a Normal distribution with parameters μ = 5.4 and σ = 2.3.

(a)

Compute the response representing the 90th ​percentile as follows:

P (X < x) = 0.90

⇒ P (Z < z) = 0.90

The value of z for the above probability is, z = 1.282.

Compute the value of x as follows:

[tex]x=\mu+z\sigma[/tex]

   [tex]=5.4+(1.282\times 2.3)\\\\=5.4+2.9486\\\\=8.3486\\\\\approx 8.35[/tex]

Thus, the response representing the 90th ​percentile is 8.35.

(b)

Compute the response representing the 60th ​percentile as follows:

P (X < x) = 0.60

⇒ P (Z < z) = 0.60

The value of z for the above probability is, z = 0.25.

Compute the value of x as follows:

[tex]x=\mu+z\sigma[/tex]

   [tex]=5.4+(0.25\times 2.3)\\\\=5.4+0.575\\\\=5.975\\\\\approx 5.98[/tex]

Thus, the response representing the 60th ​percentile is 5.98.

(c)

Compute the response representing the first quartile of the 25th percentile as follows:

P (X < x) = 0.25

⇒ P (Z < z) = 0.25

The value of z for the above probability is, z = -0.67.

Compute the value of x as follows:

[tex]x=\mu+z\sigma[/tex]

   [tex]=5.4+(-0.67\times 2.3)\\\\=5.4-1.541\\\\=3.859\\\\\approx 3.86[/tex]

Thus, the response representing the first quartile is 3.86.

Answer:

[tex]y(x)=-2x-\frac{11}{6}e^{-x}+\frac{3}{2}e^x+\frac{1}{3}e^{-4x}[/tex]

Step-by-step explanation:

[tex]y''-y=5e^{-4x}+2x,\: y(0)=y'(0)=0\\\\\mathcal{L}\{y''\}-\mathcal{L}\{y\}=\mathcal{L}\{5e^{-4x}\}+\mathcal{L}\{2x\}\\\\s^2Y(s)-sy(0)-y'(0)-Y(s)=\frac{5}{s+4}+\frac{2}{s^2}\\ \\s^2Y(s)-Y(s)=\frac{5}{s+4}+\frac{2}{s^2}\\ \\(s^2-1)Y(s)=\frac{5}{s+4}+\frac{2}{s^2}\\ \\Y(s)=\frac{5}{(s+4)(s^2-1)}+\frac{2}{s^2(s^2-1)}\\ \\Y(s)=\frac{5s^2+2(s+4)}{s^2(s+4)(s^2-1)}\\ \\Y(s)=\frac{5s^2+2s+8}{s^2(s-1)(s+1)(s+4)}[/tex]

Perform the partial fraction decomposition

[tex]\frac{5 s^{2} + 2 s + 8}{s^{2} \left(s - 1\right) \left(s + 1\right) \left(s + 4\right)}=\frac{A}{s}+\frac{B}{s^{2}}+\frac{C}{s + 1}+\frac{D}{s - 1}+\frac{E}{s + 4}\\\\5 s^{2} + 2 s + 8=s^{2} \left(s - 1\right) \left(s + 1\right) E + s^{2} \left(s - 1\right) \left(s + 4\right) C + s^{2} \left(s + 1\right) \left(s + 4\right) D + s \left(s - 1\right) \left(s + 1\right) \left(s + 4\right) A + \left(s - 1\right) \left(s + 1\right) \left(s + 4\right) B[/tex]

[tex]5 s^{2} + 2 s + 8=s^{4} A + s^{4} C + s^{4} D + s^{4} E + 4 s^{3} A + s^{3} B + 3 s^{3} C + 5 s^{3} D - s^{2} A + 4 s^{2} B - 4 s^{2} C + 4 s^{2} D - s^{2} E - 4 s A - s B - 4 B\\\\5 s^{2} + 2 s + 8=s^{4} \left(A + C + D + E\right) + s^{3} \left(4 A + B + 3 C + 5 D\right) + s^{2} \left(- A + 4 B - 4 C + 4 D - E\right) + s \left(- 4 A - B\right) - 4 B[/tex]

Solve for each constant

[tex]\begin{cases} A + C + D + E = 0\\4 A + B + 3 C + 5 D = 0\\- A + 4 B - 4 C + 4 D - E = 5\\- 4 A - B = 2\\- 4 B = 8 \end{cases}[/tex]

[tex]-4B=8\\B=-2[/tex]

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

[tex]A+C+D+E=0\\C+D+E=0\\E=-C-D[/tex]

[tex]-A+4B-4C+4D-E=5\\4(-2)-4C+4D-(-C-D)=5\\-8-4C+4D+C+D=5\\-3C+5D=13\\5D=13+3C[/tex]

[tex]4A+B+3C+5D=0\\4(0)+(-2)+3C+13+3C=0\\-2+6C+13=0\\11+6C=0\\6C=-11\\C=-\frac{11}{6}[/tex]

[tex]5D=13+3C\\5D=13+3(-\frac{11}{6})\\5D=13-\frac{33}{6}\\5D=\frac{15}{2}\\D=\frac{15}{10}\\D=\frac{3}{2}[/tex]

[tex]E=-C-D\\E=-(-\frac{11}{6})-(\frac{3}{2})\\E=\frac{11}{6}-\frac{3}{2}\\E=\frac{2}{6}\\E=\frac{1}{3}[/tex]

Take the inverse transform and solve for the IVP

[tex]Y(s)=\frac{0}{s}+\frac{-2}{s^2}+\frac{-\frac{11}{6}}{s+1}+\frac{\frac{3}{2}}{s-1}+\frac{\frac{1}{3}}{s+4}\\ \\y(x)=-2x-\frac{11}{6}e^{-x}+\frac{3}{2}e^x+\frac{1}{3}e^{-4x}[/tex]

Answer:

The answer is -46,8

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The area of the equilateral triangular pyramid is the amount of space on it

The total surface area is 107 square feet

The given parameters are:

Base (b) = 6 feet

Slant height (l) = 10 feet

The lateral surface area is calculated using:

L = 1.5bl

So, we have:

L = 1.5 * 6 * 10

Evaluate the product

L = 90

The total surface area is calculated using:

T = L + 0.25√3b^2

So, we have:

T = 90 + 0.25√3 * 6^2

Evaluate

T = 107

Hence, the total surface area is 107 square feet

Read more about areas at:

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Answer:

107 sq ft

Step-by-step explanation:

Got it right on Edmentum

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Answer:

  7 - (-3)

Step-by-step explanation:

You want the sum 7 + 3 expressed as a difference.

The difference of A and B is written A - B. The subtraction operation is involved.

Subtraction is the same as addition of the opposite. Or, addition is the same as subtracting the opposite:

  7 + 3 = 7 - (-3)

__

Additional comment

We can also write the difference as ...

  3 - (-7)

<95141404393>

This value is slightly over 1.2 million

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

How I got that answer:

We have 45*44*43*42*41 = 146,611,080 different permutations. I started with 45 and counted down by 1 until I had 5 values multiplied out.

If order mattered, then we would stop here. But order doesn't matter. All that matters is the group overall rather than any particular individual or how they rank in the group.

There are 5! = 5*4*3*2*1 = 120 different ways to arrange a five item set, so the very large result we got earlier is overcounting by a factor of 120.

To fix this, we divide by 120 to get

(146,611,080)/120 = 1,221,759

This represents the number of combinations in which we're selecting 5 members from a pool of 45 total.

You could use the nCr formula

[tex]_nC_r = \frac{n!}{r!*(n-r)!}[/tex]

with n = 45 and r = 5 to get the same answer in bold above.

Using the principle of Combination, the number of different random samples of size five which can be obtained form a population of 45 is 1221759

Using the principle of combination, which is defined as :

Hence,

45C5 = 45! ÷ (45 - 5)!5!

45C5 = 45! ÷ 40!5!

45C5 = (45 × 44 × 43 × 42 × 41) / (5 × 4 × 3 × 2 × 1)

45C5 = 1221759

Therefore, there are 1221759 ways of making a selection of 5 samples from a population of size 45.

Learn more :https://brainly.com/question/10699405?referrer=searchResults

Answer:

0,180

Step-by-step explanation:

[tex]8 \tan(x) = 0[/tex]

[tex] \tan(x) = 0[/tex]

[tex]x = 0 + 180n[/tex]

This means 0, 180 are the solutions.

Step-by-step explanation:

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Using trigonometric identity sin²θ+cos²θ=1, the given identity is proved.

The given trigonometric identity is 1-2cos²x = 2sin²x-1.

Trigonometric Identities are the equalities that involve trigonometry functions and holds true for all the values of variables given in the equation. There are various distinct trigonometric identities involving the side length as well as the angle of a triangle.

Using trigonometric identity sin²θ+cos²θ=1

Here, 1-2cos²x = 2sin²x-1

⇒ 1+1=2sin²x+2cos²x

⇒ 2=2(sin²x+cos²x)

⇒ 2=2(1)

⇒ 2=2

LHS=RHS

Therefore, using trigonometric identity sin²θ+cos²θ=1, the given identity is proved.

Learn more about the trigonometric identity here:

https://brainly.com/question/24377281.

#SPJ2

Answer:

3/8 of the total distance.

Step-by-step explanation:

After Saturday = 8/8 - 3/8 = 5/8 of distance left.

Sunday = 5/8 x 3/5 = 3/8 distance.

Hope this helps!

Answer:

c=102°

b=(360-204)/2 = 78°

Answers:

b = 78

c = 102

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

Explanation:

Let's find angle b. This angle adds to the 102 to get 180 since the two angles form a straight angle.

102+b = 180

b = 180-102

b = 78

Then we can apply the same idea to find angle c

b+c = 180

78+c = 180

c = 180-78

c = 102

A shortcut to find angle c is to recall that vertical angles are congruent. The proof of the vertical angle theorem is effectively the steps shown above.

Answer:

I think it is -12

Multiply -0.75 (3 quarters) by 16.

The negative cancels out the positive number.

Since the exponent is not saying multiply the number by itself a number of times, we could make a hypothesis that this is just multiplication.

Normally, this ↑ is not the case, but here, I could make an exception.

I hope this helps you, let me know if you need something else.

Answer:

10,000 is the answer

Step-by-step explanation:

14 465

round up the 4 which is 0 then your answer would be 10000

Answer:

-90x^3y^3

Step-by-step explanation:

[tex]3x\sin y+2\cos y=\sin x[/tex]

[tex]\dfrac{\mathrm d(3x\sin y+2\cos y)}{\mathrm dx}=\dfrac{\mathrm d(\sin x)}{\mathrm dx}[/tex]

[tex]\dfrac{\mathrm d(3x)}{\mathrm dx}\sin y+3x\dfrac{\mathrm d(\sin y)}{\mathrm dx}+\dfrac{\mathrm d(2\cos y)}{\mathrm dx}=\cos x[/tex]

[tex]3\sin y+3x\cos y\dfrac{\mathrm dy}{\mathrm dx}-2\sin y\dfrac{\mathrm dy}{\mathrm dx}=\cos x[/tex]

Solve for dy/dx :

[tex]3\sin y+\left(3x\cos y-2\sin y\right)\dfrac{\mathrm dy}{\mathrm dx}=\cos x[/tex]

[tex]\left(3x\cos y-2\sin y\right)\dfrac{\mathrm dy}{\mathrm dx}=\cos x-3\sin y[/tex]

[tex]\dfrac{\mathrm dy}{\mathrm dx}=\boxed{\dfrac{\cos x-3\sin y}{3x\cos y-2\sin y}}[/tex]

Answer:

[tex]x=27[/tex]

[tex]y=-6[/tex]

Step-by-step explanation:

substitute in values

[tex]x=21-y[/tex]

[tex](21-y)+3y=9[/tex]

[tex]21+2y=9[/tex]

[tex]2y=-12[/tex]

[tex]y=-6[/tex]

[tex]x+(-6)=21[/tex]

[tex]x=27[/tex]

No, because the confidence interval do not overlap we do not have enough evidence to say that the parameters are different.

The confidence interval will help to determine if there is enough evidence in the statistical data draw conclusion that Vicente has the lead.

The confidence interval is 48% - 3% to 48% + 3%, which is equivalent to 45% to 51%.

Since 52% does not lie in the above interval, therefore we can say no, because the confidence interval do not overlap we do not have enough evidence to say that the parameters are different.

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Answer:

Step-by-step explanation:

NO

Answer:

Each of them would play 2 games to get the same cost amount

Step-by-step explanation:

for example

#1) $5 + $3 = $8 x 2 = $16

#2) $6 + $2 = $8 x 2 = $16

Answer:

[tex] \dfrac{3(a + 8)}{(a - 7)(a - 2)(a + 8)} [/tex]

[tex] \dfrac{8a(a - 2)}{(a - 7)(a - 2)(a + 8)} [/tex]

Step-by-step explanation:

[tex] \dfrac{3}{a^2 - 9a + 14} = [/tex]

[tex] = \dfrac{3}{(a - 7)(a - 2)} [/tex]

[tex] = \dfrac{3(a + 8)}{(a - 7)(a - 2)(a + 8)} [/tex]

[tex] \dfrac{8a}{a^2 + a - 56} = [/tex]

[tex] = \dfrac{8a}{(a + 8)(a - 7)} [/tex]

[tex] = \dfrac{8a(a - 2)}{(a - 7)(a - 2)(a + 8)} [/tex]

Answer:

B. Adjacent

Step-by-step explanation:

Supplementary angles add up to 180 degrees, so cross of A. Vertical angles are directly across from each other, so cross off C. Corresponding angles are related to lines and a transversal which you don't have, so you can cross of D, leaving the answer as B.

Hopefully this helps - let me know if you have any questions!

Considering the situation described in the exercise, it is found that the correct null and alternative hypothesis for this test are given by, respectively:

[tex]H_0: \mu = 350[/tex]

[tex]H_1: \mu \neq 350[/tex]

At the null hypothesis, it is tested if the mean is of 350 degrees, that is:

[tex]H_0: \mu = 350[/tex]

At the alternative hypothesis, it is tested if the mean is different of 350 degrees, hence:

[tex]H_1: \mu \neq 350[/tex]

More can be learned about the test of an hypothesis at https://brainly.com/question/26454209

Answer:

235.62 Cubic centimeters

Step-by-step explanation:

[tex]v = \frac{1}{3}\pi \: r {}^{2} h \: = \frac{1}{3} \times \pi \times 5 {}^{2} \times 9 \\ \\ = 75\pi = 235.62[/tex]

Answer:

235.62 Cubic centimeters

Step-by-step explanation:

have a nice day.

Answer:

1, 1/2, 3/2

Step-by-step explanation:

This is a prism (a 3d rectangle) and so your formula for finding the volume is V= L x W x H.

For the prism:

L= 1 (4 cubes x 1/4 = 4)

W = 1/2 (2 cubes x 1/4 = 1/2)

H = 3/2 (6 cubes x 1/4 = 6/4 = 3/2)

That's your answer, the tile 1, 1/2, 3/2

Answer:

$3.43

Step-by-step explanation:

Multiply 7 by 0.49

Answer:

4:3

Step-by-step explanation:

24:18

Divide each side by 6

24/6 : 18/6

4:3

Answer:

452.16 in. or 144π if the answer needs to be in terms of pi.

Step-by-step explanation:

In this case, all of the information is given to you. You can determine this is a cylinder because of its circular bases. Your height is given on the side as 9in. Your radius is given on the base as 4in. You can tell that this value is the radius and not the diameter because the line only covers half of the circular base. If the line went from one edge to the other, you would need to divide the given value by 2. From there, you can just plug the numbers into the proper equation.

V = πr²h​

V = π(4)²(9)

V = 452.16 or 144π

Answer:

The input is a contradiction: it has no solutions

Answer:

y = 1/2x

Step-by-step explanation:

Points are (8,4)

x = 8

x = 8y = 4

y= −2/1x

4= -2(8)

4= -16

That's wrong

y= −1/2x

4= -1/2(8)

4= -4

That's wrong

y=1/2x

4=1/2(8)

4=4

That's right

y=2/1x

4=2(8)

4=16

That's wrong

So the answer is choice C

Answer:

H+ = 0.001

Step-by-step explanation:

3 = -log[H+]

Identity to use: [tex]-log_{b}(a) = log_{b}(1/a)[/tex]

3 = log[ 1 / H+ ]

Identity to use: [tex]10^{log(x)} = x[/tex]

Therefore, I am going raise each side of the equation to the power of 10 to isolate [ 1 / H+ ]

10³ = [tex]10^{log(\frac{1}{H+} )}[/tex]

1000 = 1 / H+

H+ = 1 / 1000

Answer: H+ = 0.001