The amount of time a certain brand of light bulb lasts is normally distributed with a mean of 1400 hours and a standard deviation of 75 hours. What is the probability that a randomly chosen light bulb will last less than 1380 hours, to the nearest thousandth?

Answer:no, (5,1) is not a solution for the equation. (1/7,1) will be a solution for the equation.

Step-by-step explanation:

one way to do it is to plug 1 as the y-value into the first equation which does work but when you plug 5 as the x-value and 1 as the y-value in the second equation, it will get you to 41 which does not match so it will not be an equation. the other way to check is to solve by substitution which for the first equation, you divide both side by -5 and get y=1 then substitute y with 1 in the second equation and subtract both side by 6 and get 7x=1 and divide both side by 7 to get 1/7. the y-value match but the x-value don't so (5,1) is not a solution.

Answer:

[tex]144 $ Square feet[/tex]

Step-by-step explanation:

The given triangular prism comprises of two equal right triangles and three rectangles.

The Surface Area of the Prism

=Area of Two Triangles + Area of Three Rectangles

[tex]=2(0.5X6X8)+(6X4)+(10X4)+(8X4)\\=48+24+40+32\\=144 $ Square feet[/tex]

Answer: 144

Step-by-step explanation:32+24+4-+48=144

Answer:

The calculated value Z = 1.8368 < 1.96 at 0.05 level of significance

The null hypothesis is accepted

The samples have been drawn from the same Population

Step-by-step explanation:

Step(i):-

Given first sample size 'n₁' = 49

Mean of the first sample 'x₁⁻ = 609.86

Standard deviation of the sample S₁ = 55.96 calories

Given first sample size 'n₂' = 78

Mean of the first sample 'x₂⁻ = 641.02

Standard deviation of the sample S₂ = 109.14 calories

Step(ii):-

Null hypothesis : H₀: x₁⁻ = x₂⁻

Alternative Hypothesis : H₁: x₁⁻ ≠ x₂⁻

Level of significance ∝ = 0.05

Test statistic

[tex]Z = \frac{x^{-} _{1}-x^{-} _{2} }{\sqrt{S.D^2(\frac{1}{n_{1} } }+\frac{1}{n_{2} } }[/tex]

where

 [tex]S.D^{2} = \frac{n_{1} S^2_{1}+ n_{2} S^2_{2} }{n_{1} + n_{2} -2}[/tex]

 [tex]= \frac{49 X (55.96)^2+ 78X(109.14)^2 }{49 + 78 }[/tex]

 σ² =  8660.357

Step(iii):-

Test statistic

[tex]Z = \frac{x^{-} _{1}-x^{-} _{2} }{\sqrt{S.D^2(\frac{1}{n_{1} } }+\frac{1}{n_{2} } }[/tex]

[tex]= \frac{ 609.86-641.02 }{\sqrt{8660.357(\frac{1}{49 } }+\frac{1}{78 } ) }[/tex]

[tex]Z = \frac{-31.16}{16.9638} = -1.8368[/tex]

|Z| = |-1.8368| = 1.8368

The tabulated value Z₀.₉₅ = 1.96

The calculated value = 1.8368 < 1.96 at 0.05 level of significance

The null hypothesis is accepted

Final answer:-

The samples have been drawn from the same Population

Answer:

2.3 units

Step-by-step explanation:

Answer:

[tex]0.60 - 1.96\sqrt{\frac{0.60(1-0.60)}{1019}}=0.570[/tex]

[tex]0.60 + 1.96\sqrt{\frac{0.60(1-0.60)}{1019}}=0.630[/tex]

The 95% confidence interval for the true proportion would be given by (0.570;0.630) .

And if we convert this into % we got (57.0%, 63.0%)

Step-by-step explanation:

The information given we have the following info given:

[tex] n = 1019[/tex] represent the sampel size

[tex] \hat p=0.6[/tex] represent the sample proportion of interest

The confidence level is 95%, our significance level would be given by [tex]\alpha=1-0.95=0.05[/tex] and [tex]\alpha/2 =0.025[/tex]. And the critical value would be given by:

[tex]z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96[/tex]

The confidence interval for the mean is given by the following formula:  

[tex]\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex]

Replacing the info given we got:

[tex]0.60 - 1.96\sqrt{\frac{0.60(1-0.60)}{1019}}=0.570[/tex]

[tex]0.60 + 1.96\sqrt{\frac{0.60(1-0.60)}{1019}}=0.630[/tex]

The 95% confidence interval for the true proportion would be given by (0.570;0.630) .

And if we convert this into % we got (57.0%, 63.0%)

Answer:

4/5

Step-by-step explanation:

just divide by 10 since that's the largest number that both numbers can equally be divisible by

Answer:

4/5 because 40/50 simplified is 4/5 bc you knock off the zeros for question like that

Step-by-step explanation:

Step-by-step explanation:

(11.99+23.98+9.95)= 45.92

she has to pay = 45.92 - 20/100 (45.92)

= 45.92 - 9.18 = 36.74

so option

about 37 is right

Answer:

y=210x+78

Step-by-step explanation:

y=-16x*2+242x+78

y=-32x+242x+78

y=210x+78

Answer:

It seems like it is 110 degrees.

Step-by-step explanation:

Answer:

the answer is d

Step-by-step explanation:

Answer:

The answer is D

Step-by-step explanation:

Answer:

  1024 pi

Step-by-step explanation:

The area formula is ...

  A = πr^2

So, the radius is ...

  r = √(A/π)

For the given area, the radius of the cylinder is ...

  r = √(64π/π) = 8 . . . . cm

The height is said to be twice this value, so is 16 cm.

__

The volume of the cylinder is found from ...

  V = Bh

where B is the base area and h is the height. Our cylinder has a volume of ...

  V = (64π cm^2)(16 cm) = 1024π cm^3

Answer:

Step-by-step explanation:

Pi is the ratio of a circle's circumference to its diameter.

_____

We suspect you have answer choices for filling in these blanks. Besides the words shown above, there are other ways they can be filled:

  Pi is the ratio of a circle's area to its radius squared.

  Pi is the measure of a circle's central angle to its diameter endpoints.

Answer:

D

If you put the equation into a calculator, it will show a graph of it.

Answer:3hk - 12.4h

Step-by-step explanation:

h(3k-12.4)

h x 3k - h x 12.4

3hk - 12.4h

Answer: Equilateral, isosceles and scalene.

Step-by-step explanation:

Answer:3.3

Step-by-step explanation:

Circumference=8

Φ=288

π=3.14

Radius=r

Circumference=2 x π x r

8=2 x 3.14 x r

8=6.28 x r

Divide both sides by 6.28

8/6.28=(6.28 x r) /6.28

1.3=r

r=1.3

Length of arc =Φ/360 x 2 x π x r

Length of arc =288/360 x 3.14 x 1.3

Length of arc =0.8 x 3.14 x 1.3

Length of arc =3.3

Answer:32/5

Step-by-step explanation: did it in khan

Answer:

151 * 17 * 3^4 * 2

Step-by-step explanation:

2567 | 17

151 | 151

1

162 | 2

81 | 3

27 | 3

9 | 3

3 | 3

1

Answer:

415854.

Step-by-step explanation:

A multiplication.

Using a calculator it is:

415854,

Step-by-step explanation:

This problem on depreciation of price.

Given data

initial price = $18,250

rate of depreciation = 11%

to solve for the new price we must find 11 percent of the initial price (depreciated value) and subtract from the initial price, we have

depreciation=

[tex]\frac{11}{100} *18250\\0.11*18250= 2007.5[/tex]

Hence the depreciation= $2007.50

the new amount is [tex]= initial amount - depreciation[/tex]

[tex]=18250-2007.50\\= 16242.50[/tex]

the new amount is $16242.50

Answer:

not a solution

Step-by-step explanation:

p > -5

Let p = -11

-11 > -5

This is a false statement

It is not a solution

Answer:

(0,1)

Step-by-step explanation:

i got it right

Answer:

Measure of first angle: 42 degrees,

Measure of second angle: 138 degrees

Step-by-step explanation:

Let us say x ⇒ measure of the smaller angle, y ⇒ measure of the larger angle

1. Now given that the measure of the larger angle is 12° more than 3 times the smaller angle: y = 12 + 3x

2. If these angles are supplementary, we could formulate another equation were the two angles add to 180°: x + y = 180

3. In this situation it is convenient to apply substitution as to solve for x, y:

1. x + ( 12 + 3x ) = 180

2. x + 12 + 3x = 180

3. 4x + 12 + 180

4. 4x = 168

5. x = 42 degrees

4. Now substitute this value of x into the first equation y = 12 + 3x, and to solve for y as well:

1. y = 12 + 3 ( 42 )

2. y = 12 + 126

3. y = 138 degrees

Here we need to find two angles given that the angles are supplementary and one is 12° larger than the other.

the two angles are 84° and 96°.

We should start by defining what supplementary angles are.

Two angles a and b are supplementary if:

a + b = 180°.

Now, we also know that one of the angles is 12° larger than the other, so we can write:

a = b + 12°

Now that we have that equation, we can replace it in the first one, so we get:

a + b = 180°

(b + 12°) + b = 180°

Now we can solve this for b.

2*b + 12° = 180°

2*b = 180° - 12°  = 168°

b = 168°/2 = 84°

To find the value of a, we can use the equation:

a = b + 12°

a = 84° + 12° = 96°.

Then the two angles are:

84° and 96°.

If you want to learn more, you can read:

https://brainly.com/question/18164299

Answer:

  y = 12

Step-by-step explanation:

Ordinarily, in math, when we say "the difference between ..." we mean the second listed item is subtracted from the first. (In English, we often mean "the positive difference between ..." so the order doesn't matter.)

We'll assume we are only interested in the case where the difference is in the order listed.

  [tex]\dfrac{y+12}{y-4}-\dfrac{y}{y+4}=\dfrac{y+12}{y-4}\cdot\dfrac{y}{y+4}\\\\\dfrac{(y+12)(y+4)-(y-4)(y)}{y^2-16}=\dfrac{(y+12)(y)}{y^2-16}\\\\0=\dfrac{y^2-8y-48}{y^2-16}=\dfrac{(y-12)(y+4)}{(y-4)(y+4)}=\dfrac{y-12}{y-4}\qquad\text{$y\ne -4$}\\\\\boxed{y=12}[/tex]

There is one solution.

_____

Comment on the solution

If you were to "clear fractions" by multiplying the equation by (y^2-16), you would also obtain the extraneous solution y=-4. That is why we did not solve it that way.

Answer:

D. 221.7 cm

Step-by-step explanation:

Surface area of a sphere is: [tex]SA=4\pi r^2[/tex]

'r' - radius

We are given the radius of 4.2 centimetres.

[tex]SA=4\pi 4.2^2\\4 * \pi * 4.2^2\\\rightarrow 4.2^2 =17.64\\\text {Using 3.14 for pi: }\\4 * 3.14 *17.64\\12.56*17.64\\\boxed {221.5584}[/tex]

221.5584 ≈ 221.6

The closest answer is Option D, therefore it should be the correct answer.

Answer:

10000000000000

Step-by-step explanation:

I do not know how to explain

Answer:

The area 2730 possible arrangements of first, second, and third place.

Step-by-step explanation:

The order in which the students finish is important. For example A, B and C is a different finishing order(outcome) than B, A and C. So we use the permutations formula to solve this question.

Permutations formula:

The number of possible permutations of x elements from a set of n elements is given by the following formula:

[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]

In this question:

3 from a set of 15. So

[tex]P_{(15,3)} = \frac{15!}{(15-3)!} = 2730[/tex]

The area 2730 possible arrangements of first, second, and third place.