Answer:
0.394 = 39.4% probability that a randomly chosen light bulb will last less than 1380 hours
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question, we have that:
[tex]\mu = 1400, \sigma = 75[/tex]
What is the probability that a randomly chosen light bulb will last less than 1380 hours, to the nearest thousandth?
This is the pvalue of Z when X = 1380. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{1380 - 1400}{75}[/tex]
[tex]Z = -0.27[/tex]
[tex]Z = -0.27[/tex] has a pvalue of 0.394
0.394 = 39.4% probability that a randomly chosen light bulb will last less than 1380 hours
please answer this correctly I have to finish this today as soon as possible
Estimate the measure of this angle within 10°.
Answer:
It seems like it is 110 degrees.
Step-by-step explanation:
Write the expanded form of h(3k-12.4)
Answer:3hk - 12.4h
Step-by-step explanation:
h(3k-12.4)
h x 3k - h x 12.4
3hk - 12.4h
Express this number in scientific notation 0.0008235
A dietician believes that people who eat a high-fiber cereal as part of their breakfast will consume, on average, fewer calories at lunch than people who do not eat a high-fiber cereal as part of their breakfast. To test this claim, he measured the lunchtime calorie intake of 49 adults who did eat a high-fiber cereal for breakfast on a given day (group 1). For those individuals, the average number of calories consumed at lunch was 609.86, with a standard deviation of 55.96 calories. He also measured the lunchtime calorie intake of 78 adults who did not eat a high-fiber cereal for breakfast on a given day (group 2). For those individuals, the average number of calories consumed at lunch was 641.02, with a standard deviation of 109.14 calories. The dietician wishes to test this claim at the 5% significance level.
If Welch's two-sample test for equality of means is used, then what is the value of the test statistic tobs, rounded to two decimal places?
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
Is p = –11 a solution to the inequality below?
p
> –5
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
The value of a car with an initial purchase price of $18,250 depreciates by
11% per year.
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
what sock price should the company set to earn a maximum profit
Answer:
10000000000000
Step-by-step explanation:
I do not know how to explain
Select the closest answer. *
20 points
1. Find the surface area of a sphere with a radius of 4.2 centimeters.
A. 235.6 cm?
C. 121.4 cm
B. 310.3 cm
D. 221.7 cm
A
B
С
OD
Select the closest answer.
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.
tell me the answer to the question plz
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
What is volume of a cylinder with base area 64pi cm² and a height equal to twice the radius? Give your answer in terms of pi.
512 pi
256 pi
1024 pi
4096 pi
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
Which types of triangles can be formed by taking the cross-section of a rectangular prism like the one shown above?
Answer: Equilateral, isosceles and scalene.
Step-by-step explanation:
Will mark brainlist and give extra points bth grade math
Answer:
the answer is d
Step-by-step explanation:
Answer:
The answer is D
Step-by-step explanation:
Find the values of the variable y, for which:
the difference between the fractions y+12/y-4 and y/y+4 is equal to their product
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.
There were 15 students running in a race. How many different arrangements of first, second, and third place are possible?
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.
y = -16x2 + 242x + 78
Answer:
y=210x+78
Step-by-step explanation:
y=-16x*2+242x+78
y=-32x+242x+78
y=210x+78
Giving brainliest to CORRECT answer.
Answer:
D
If you put the equation into a calculator, it will show a graph of it.
When plotting points on the coordinate plane below, which point would lie on the y-axis?
(0, 1)
(7, 0)
(6, 8)
(8, 2)
Answer:
(0,1)
Step-by-step explanation:
i got it right
−5y=−5
7x+6y=7
Is (5,1) a solution of the system
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.
Simplify.
2567 · 162
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,
ivana has 5.50 luc has 1.4 times as much as ivana, how many indian rupees would ivana get if the value of rupees are 61.92 per dollar rate
PI is the _ of a circle's _ to its _
Answer:
ratiocircumferencediameterStep-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.
40/50 to a simpel fraction
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:
A circle with circumference 8 has an arc with a 288 central angle what is the length of the arc
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
What is the length of AC? Brainliest for right answer
Answer:
2.3 units
Step-by-step explanation:
Please help ASAP! Will give BRAINLIEST! Please read the question THEN answer correctly! No guessing.
What statement accurately describes the scatter point?
A. There are three distinct clusters.
B. There are no outliers.
C. There is one outlier.
D. There are two outliers.
Two angles are supplementary. The measure of the larger angle is 12 degrees more than three times the smaller angle. Find the measures of the angles
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
Solve for I.
3x -8 < 23 AND
- 4x + 26 > 6
A wedge of cheese in the shape of a triangular prism is shown below.
Find the surface area of the cheese.
_______Square feet
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
Harris Interactive® conducted a poll of American adults in August of 2011 to study the use of online medical information. Of the 1,019 randomly chosen adults, 60% had used the Internet within the past month to obtain medical information. Use the results of this survey to create an approximate 95% confidence interval estimate for the percentage of all American adults who have used the Internet to obtain medical information in the past month.
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%)
