A manufacturer knows that their items have a normally distributed lifespan, with a mean of 5.8 years, and
standard deviation of 1.7 years.
The 10% of items with the shortest lifespan will last less than how many years?
Round your answer to one decimal place.

Answers

Answer 1

Answer:

Less than 3.6 years.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Mean of 5.8 years, and  standard deviation of 1.7 years.

This means that [tex]\mu = 5.8, \sigma = 1.7[/tex]

The 10% of items with the shortest lifespan will last less than how many years?

Less than the 10th percentile, which is X when Z has a p-value of 0.1, so X when Z = -1.28.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]-1.28 = \frac{X - 5.8}{1.7}[/tex]

[tex]X - 5.8 = -1.28*1.7[/tex]

[tex]X = 3.6[/tex]

Less than 3.6 years.


Related Questions

A toddler is allowed to dress himself on Mondays, Wednesdays, and Fridays. For each of his shirt, pants, and shoes, he is equally likely to put it on correctly as incorrectly. Getting these articles of clothing on correctly are independent of each other. On the other days, the mother dresses the toddler with 100% accuracy. Given that the toddler is correctly dressed, what is the probability that today is Monday

Answers

Answer:

0.0286 = 2.86% probability that today is Monday.

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

P(B|A) is the probability of event B happening, given that A happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Dressed correctly

Event B: Monday

Probability of being dressed correctly:

100% = 1 out of 4/7(mom dresses).

(0.5)^3 = 0.125 out of 3/7(toddler dresses himself). So

[tex]P(A) = 0.125\frac{3}{7} + \frac{4}{7} = \frac{0.125*3 + 4}{7} = \frac{4.375}{7} = 0.625[/tex]

Probability of being dressed correctly and being Monday:

The toddler dresses himself on Monday, so (0.5)^3 = 0.125 probability of him being dressed correctly, 1/7 probability of being Monday, so:

[tex]P(A \cap B) = 0.125\frac{1}{7} = 0.0179[/tex]

What is the probability that today is Monday?

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.0179}{0.625} = 0.0286[/tex]

0.0286 = 2.86% probability that today is Monday.

If the lengths of the legs of a right triangle are 5 and 12, what is the length of the hypotenuse?

Answers

Answer:

13

Step-by-step explanation:

If we have a right triangle, we can use the Pythagorean theorem to find the hypotenuse

a^2+b^2 = c^2 where a and b are the legs and c is the hypotenuse

5^2 + 12^2 = c^2

25+144= c^2

169 = c^2

Take the square root of each side

sqrt(169) = sqrt(c^2)

13= c

Answer:

The length of the hypotenuse is 13.

Step-by-step explanation:

[tex]a^{2}[/tex] = [tex]b^2 + c^2[/tex]

[tex]a^2 = 12^2 + 5^2[/tex]

[tex]a^2 = 144 + 25[/tex]

[tex]a^2 = 169[/tex]

a=[tex]\sqrt{169}[/tex]

a= 13

Here we use the idea of the Pythagoras' theorem. Which suggests that [tex]a^{2}[/tex] = [tex]b^2 + c^2[/tex] in which  [tex]a^{2}[/tex] is the hypotenuse of the triangle and [tex]b^2[/tex] and [tex]c^{2}[/tex] are the two other lengths of the triangle.

HOPE THIS HELPED

A ball is thrown from an initial height of
1 meter with an initial upward velocity of
1 m/s. The ball's height h
(in meters) after t
seconds is given by the following. h=1+30t-5t^2
Find all values of t
for which the ball's height is 11
meters.

Round your answer(s) to the nearest hundredth.

Answers

Answer:

Step-by-step explanation:

If we are looking for the times that the ball was 11 meters off the ground, we sub in 11 for the height on the left and solve for t:

[tex]11=-5t^2+30t+1[/tex] and

[tex]0=-5t^2+30t-10[/tex] and factor this however it is you are factoring in class to solve for t to get

t = .35 seconds and t = 5.6 seconds

Because the ball reaches this point in its way up and then passes it again on its way down, the ball will have 2 times at this height.

there is a 400 meter track. tom rides a bike at the speeed of 450 meters/minute. mike runs at the speed of 250 meters/minute. if both of them set out at the same time and same place, how soon will they meet for the first time?

Answers

Answer: Distance: 2250

Step-by-step explanation:

Find GCF of 450 and 250

Instructions: State what additional information is required in order
to know that the triangles in the image below are congruent for the
reason given
Reasory. AAS Postulate

Answers

Answer:

YWX = DFE

Step-by-step explanation:

AAS means angle angle side. so, we need 2 angles and 1 side.

we have 1 side and one angle confirmed.

so, we need one of the other two angles (W or Y vs. F or D) confirmed.

they probably want W and F as answer, as Y and D would make it a special case of AAS : ASA.

một công ty kinh doanh 1 loại sản phẩm có
- Đơn giá bán là 20.000 đồng
- Định phs là 150.000 đồng khi mức tiêu thụ nhỏ hơn 30.000 sản phẩm
- Biến phí đơn vị là 10.000 đồng
y/ cầu:
a. Hãy xác định tỷ lệ biến phí và tỷ lệ đảm phí?
b. Hãy xác định điểm hòa vốn?
c. Công ty sẽ lời hoặc lỗ tại mức tiêu thụ là 12.000 sản phẩm? 17.000 sản phẩm?
d. Độ lớn đòn bẩy kinh doanh của cty là bao nhiêu tại mwucs tiêu thục là 12.000 snar phẩm? 17.000 sản phẩm ? Nêu ý nghĩa của các con số đó
e. Nếu giá bán tăng lên 25.000 đ/sp và biến phí tăng lên 17.000 đ/sp thid điểm hòa vốn của cty sẽ như thế nào

Answers

Answer:

ask in English then I can help u

Solve triangles: angle bisector theorem
DAC = BAD.
What is the length of CD?
Round to one decimal place.

Answers

Answer:

Step-by-step explanation:

CD/6.5 = 2.6/4.9    This is the result of the angle bisector theorem.

The theorem basically says that the side opposite the angle being bisected is divided  the ratio of the sides enclosing the angle.

Multiply both sides of the proportion by 6.5

CD = 2.6 * 6.5 / 4.9

CD = 3.4489

CD = 3.4 rounded.

The average mileage per gallon for cars built since 1940 approximates to the following curve 0.0075*t^2-.2672*t+14.8 where t is year -1940.

Answer the following questions:

What is the expected MPG in 2025?
How about 2050?
Is this a valid function?
Is there a top end to MPG?

Answers

9514 1404 393

Answer:

46.3 in 202576.2 in 2050

Step-by-step explanation:

The attached shows the predicted mileage for cars built in 2025 to be 46.3 mpg, 76.2 mpg for cars built in 2050.

__

No doubt, the function is valid over the time period used to derive it. It may or may not be valid for predicting MPG beyond that period.

Virtually any function that predicts future increases without bound will turn out to be unreliable at some point. In this universe, there are always limits to growth.

Carmen Abdul and David sent a total of 78 text messages over their cell phones during the weekend . Abdul sent 10 fewer messages then Carmen . David sent two times as many messages as Abdul how many messages did they each send?

Answers

Answer:

Carmen:27

Abdul:17

David=34

Step-by-step explanation:

Carmen+Abdul+David = 78

Carmen-Abdul=10

David=2Abdul

Carmen=Abdul+10

Carmen+Abdul+David = Abdul+10+Abdul+2Abdul=78

4Abdul=68

Abdul = 68/4=17

Carmen = 17+10=27

David = 2 * 17 = 34

27+17+34=78

One number is 6 less than a second number.
Twice the second number is 9 less than 5 times
the first. Find the two numbers.

Answers

Answer:

-7

Step-by-step explanation:

x = y - 6

2x = 5y - 9

Use the internet for full steps

x = -7

y = -1

Question 3 of 10
What is the value of p?
V140
140°
90-
A. 50°
ООО
B. 90°
C. 60°
D. 40°

Answers

Answer:

A. 50º

Step-by-step explanation:

we are given the exterior angles 140º and 90º

exterior angles + corresponding interior angles = 180º

that means the two other angles of the triangle are:

180 - 140 = 40º

and

180 - 90 = 90º

the sum of interior angles in a triangle = 180

p = 180 - (40 + 90)

p = 180 - 130

p = 50º

What is the value of x when y equals 66?

y=0.985897x+0.194185

Answers

Answer:

x = 66.74715005725

Step-by-step explanation:

First you bring over the added variable. 0.194185, and subtract it from 66. Then you divide your difference by 0.985897. This gives you 66.74715005725

3.06 as. a fraction PLEASE HELP​

Answers

Answer:

153/50

Step-by-step explanation:

3.06

Rewriting as

There are two numbers after the decimal so we put the number over 100

306/100

Divide top and bottom by 2

153/50

To write 3.06 as a fraction you have to write 3.06 as numerator and put 1 as the denominator. Now you multiply numerator and denominator by 10 as long as you get in numerator the whole number.

3.06 = 3.06/1 = 30.6/10 = 306/100

And finally we have:

3.06 as a fraction equals 306/100

Drag each factor to the correct location on the image.
If p(1) = 3, p(-4) = 8, p(5) = 0, p(7) = 9, p(-10) = 1, and p(-12) = 0,
P(x).

Answers

Answer:

(x-7) and (x+12) are the factors and the rest are non factors...

What is the value of x?

Answers

Answer:

x=30°

hopefully this answer can help you to answer the next question

Add :-

a+2b-3c, -3a+b+2cand 2a -3b+c​

Answers

Answer:

[tex]a + 2b -3 c + - 3a + b + 2c + 2a - 3b + c \\ = a - 3a + 2a + 2b + b - 3b - 3c + 2c + c \\ 0a + 0b + 0c \\ thank \: you[/tex]

a+2b-3c+(-3a+b+2c) +(2a-3b+c)

=a+2b-3c-3a+b+2c+2a-3b+c

=a-3a+2b+2b+b-3b-3c++2b+c

=0a+0b+0c

=0

Therefore, the addition of the expressions, a+2b-3c+(-3a+b+2c) +(2a-3b+c) is zero or 0.

To know more about algebraic expressions

https://brainly.com/question/28307605

5 less than three times a number is 37 what is the number​

Answers

Answer:

x = 14

General Formulas and Concepts:

Pre-Algebra

Equality Properties

Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of Equality

Step-by-step explanation:

Step 1: Define

Identify

3x - 5 = 37

Step 2: Solve for x

[Addition Property of Equality] Add 5 on both sides:                                    3x = 42[Division Property of Equality] Divide 3 on both sides:                                 x = 14

Samantha bought m candies at the store. There are n candies in a pound, and each pound costs c dollars. Write an expression for how much Samantha paid.

Answers

Answer:

total = m/n * c

m/n gives u the number of pounds u have bought, multplied by the cost of the candies per pound gives u the total amount of money she paid

father of economics

Answers

I’m going to assume you meant who is the father of economics

Answer: Adam Smith

apter 3 If a driver uses of a tank of gas every day, what fraction of a tank will he use in a) 3 days? b) 1 week? 21​

Answers

You need to re copy and paste it, I can’t see the full possible answers/question.

The length of the shadow of a flagpole was found to be 72 feet. The shadow of a 3 foot picket fence in line with the flagpole was 4 feet. What is the height of the flagpole.

Answers

Answer:

54ft

Step-by-step explanation:

if 3foot is 4ft tall

then a shadow of 72 ft will be how tall?= x

4x =3ft by 72ft

4x= 216ft

x= 216/4

×=54

Naomi invested $3,425 in an account that
pays 3% simple interest. what was the total
balance of the account after 15 years?

Answers

Answer:

$4,966.25

Step-by-step explanation:

3 x 15 = 45

After 15 years, Naomi would have earned a total of 45% interest rate.

3,425 x 1.45 = 4,966.25

Don't use .45 as the multiplier

3,425 x .45 = 1,541.25 <- incorrect

Answer: 4,966.25

Explanation: start by diving 3425 by .03 to get the amount of interest it is yearly giving you 102.75 and then multiply that by 15 since that’s the amount of years and get 1541.25 then add 3425 and 1541.25 together to get the final product of 4,966.25

Can you please help me

Answers

9514 1404 393

Answer:

  1/63

Step-by-step explanation:

There are various ways the question "how much larger" can be answered. Here, we choose to answer it by telling the difference between the two fractions:

  4/9 -3/7 = (4·7 -9·3)/(9·7) = 1/63

The larger fraction is 1/63 unit larger than the smaller fraction.

I will give brainliest if you answer properly.

Answers

Answer:

See below

Step-by-step explanation:

a)

[tex]2\sin(x) +\sqrt{3} =0 \implies 2\sin(x)=-\sqrt{3} \implies \boxed{\sin(x)=-\dfrac{\sqrt{3}}{2} }[/tex]

[tex]\therefore x=\dfrac{4\pi }{3}[/tex]

But note, as sine does represent the [tex]y[/tex] value, [tex]\dfrac{5\pi }{3}[/tex] is also solution

Therefore,

[tex]x=\dfrac{4\pi }{3} \text{ and } x=\dfrac{5\pi }{3}[/tex]

This is the solution for [tex]x\in[0, 2\pi ][/tex], recall the unit circle.

Note: [tex]\sin(x)=-\dfrac{\sqrt{3}}{2} \implies \sin(x)=\sin \left(\pi +\dfrac{\pi }{3} \right)[/tex]

b)

[tex]\sqrt{3} \tan(x) + 1 =0 \implies \tan(x) = -\dfrac{1}{\sqrt{3} } \implies \boxed{ \tan(x) = -\dfrac{\sqrt{3} }{3} }[/tex]

Once

[tex]\tan(x) = -\dfrac{\sqrt{3} }{3} \implies \sin(x) = -\dfrac{1}{2} \text{ and } \cos(x) = \dfrac{\sqrt{3} }{2}[/tex]

As [tex]\tan(x) = \dfrac{\sin(x)}{\cos(x)}[/tex]

[tex]\therefore x=-\dfrac{\pi }{6}[/tex]

c)

[tex]4\sin^2(x) - 1 = 0 \implies \sin^2(x) = \dfrac{1}{4} \implies \boxed{\sin(x) = \pm \dfrac{\sqrt{1} }{\sqrt{4} } = \pm \dfrac{1}{2}}[/tex]

Therefore,

[tex]\sin(x)=\dfrac{1}{2} \implies x=\dfrac{\pi }{6} \text{ and } x=\dfrac{5\pi }{6}[/tex]

[tex]\sin(x)=-\dfrac{1}{2} \implies x=\dfrac{7\pi }{6} \text{ and } x=\dfrac{11\pi }{6}[/tex]

The solutions are

[tex]x=\dfrac{\pi }{6} \text{ and } x=\dfrac{5\pi }{6} \text{ and }x=\dfrac{7\pi }{6} \text{ and } x=\dfrac{11\pi }{6}[/tex]

How is the series 6+13+20+...+111 represented in summation notation?

Answers

Notice that

6 + 7 = 13

13 + 7 = 20

so if the pattern continues, the underlying sequence in this series is arithmetic with first term a = 6 and difference d = 7. This means the k-th term in the sequence is

a + (k - 1) d = 6 + 7 (k - 1) = 7k - 1

The last term in the series is 111, which means the series consists of 16 terms, since

7k - 1 = 111   ==>   7k = 112   ==>   k = 16

Then in summation notation, we have

[tex]\displaystyle 6+13+20+\cdots+111 = \boxed{\sum_{k=1}^{16}(7k-1)}[/tex]

Use the tables to answer the question.
How can you determine which store offers a better price on guitar lessons?
A. You cannot determine this from the information given.
B. Compare the most expensive price from each store’s table.
C. Compare the least expensive price from each store’s table.
D. Find the cost of 1 week of guitar lessons for each store and compare.

Answers

Answer:

D. Find the cost of 1 week of guitar lessons for each store and compare.

Step-by-step explanation:

Find the cost for 1 week of guitar lessons by finding the slope of the data.

[tex]\frac{y_2-y_1}{x_2-x_1}\\\\ A.)\frac{132-66}{6-3}=\frac{66}{3}=22\\\\ B.)\frac{168-84}{8-4}=\frac{84}{4}=21[/tex]

Therefore, Store B would be the best choice.

1->dương vô cùng 1/x*(9+lnx^2)dx

Answers

It looks like you are trying to compute the improper integral,

[tex]I = \displaystyle\int_1^\infty \dfrac{\mathrm dx}{x(9+\ln^2(x))}[/tex]

or some flavor of this. If this interpretation is correct, substitute u = ln(x) and du = dx/x. Then

[tex]I = \displaystyle\int_0^\infty \dfrac{\mathrm du}{9+u^2} \\\\ = \frac13\arctan\left(\frac u3\right)\bigg|_{u=0}^{u\to\infty} \\\\ = \frac13\lim_{u\to\infty}\arctan\left(\frac u3\right) \\\\ = \frac13\times\frac\pi2 = \boxed{\frac\pi6}[/tex]

Part E
1e. Subtract the binomial 12y2 – 4y3 from the trinomial 7y - 2y3 + 5y2

Answers

Answer:

2y^3-7y^2+7y

Step-by-step explanation:

7y - 2y^3 + 5y^2 - (  12y^2 – 4y^3)

Distribute the minus sign

7y - 2y^3 + 5y^2 - 12y^2 + 4y^3

Combine like terms

2y^3-7y^2+7y

PLS HELP QUICK IM BEGGINGGGG!!!!! PLEASE HELP ME!!

The following box plot represents the heights of the students in Mr. Taylor's fourth grade math class.

In a complete sentence, answer the following question:
One of the values in this data set is 138. In this box plot, what does this value mean?

Answers

Answer:

The value 138 means that this height (138cm) is less than the average height of a 4th grader.

Answer: No credit wanted

Step-by-step explanation:

The other guy is completely right.

I need help Plz help

Answers

2 Eyes =2*(1*1/2)/2 = 0.5ft^2
Nose = ((1+1/2)*1)/2 = 0.75^2
Mouth = 3*(1ft/2)/2= 0.75ft^2
Board = 2/2/3*3 =8ft^2
Area = 8-0.5-0.75-0.75 = 6ft^2
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