The lengths of bolts in a batch are distributed normally with a mean of 3 cm and a standard
deviation of 0.04 cm.
What is the probability that a bolt has a length greater than 2.96 cm?

Answers

Answer 1

Answer:

0.8413 = 84.13% probability that a bolt has a length greater than 2.96 cm.

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 3 cm and a standard deviation of 0.04 cm.

This means that [tex]\mu = 3, \sigma = 0.04[/tex]

What is the probability that a bolt has a length greater than 2.96 cm?

This is 1 subtracted by the p-value of Z when X = 2.96. So

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

[tex]Z = \frac{2.96 - 3}{0.04}[/tex]

[tex]Z = -1[/tex]

[tex]Z = -1[/tex] has a p-value of 0.1587.

1 - 0.1587 = 0.8413

0.8413 = 84.13% probability that a bolt has a length greater than 2.96 cm.


Related Questions

why can you use cross products to solve the proportion 18/5 = x/100 for x ?

Answers

Answer:

Yes, you can use cross products to solve for x in this proportion. Also, x is 360.

Step-by-step explanation:

Yes, you can use cross products to solve for x in that proportion.

Here's how you do it :

[tex]\frac{18}{5} = \frac{x}{100}[/tex]

We cross product, getting :

18 * 100 = 5 * x

1800 = 5x

Divide by 5 on both sides to get x by itself.

360 = x

Yes, you can use cross products to solve for x in this proportion. Also, x is 360.

Hope this helps, please mark brainliest if possible. Have a great day.

Find the value of x such that l ⊥ m.

Answers

Answer:

The answer is 16

Step-by-step explanation:

Hi there!

The angles shown are supplementary

Supplementary angles have a measure of 90 degrees

This means that 3x + 5 + 37 = 90

3x + 5 + 37 = 90

Combine like terms

3x + 42 = 90

Take away 42 from each side

3x = 48

Divide by 3

x = 16

Hope this helps! :)

Answer:

O B) 16

Step-by-step explanation:

90° (total) - 37° = 53°

(3x+5) = 53°

(3x-5)  = -5°         Subtract 5 from both sides!

3x = 48               Solve

x = 16

translate the following word phrases into algebraic experessions.
1.seven more than k
2.five added to q
3.three subtracted from m
4.c increased ny 12
5.twice n​

Answers

Your answers listed below run from first question answered to last.

7+K
5+Q
3-M
12+C
2n

Can someone answer these questions for me? (Questions are in the picture)

Answers

1. (2/3)

2. (7/12)

3. (4/21)

To divide fractions all you have to do is take a dividend, the first number, and multiply it by the inverse of the divisor, which is the second number.
1 is A
2 is c
3 is B

Find area of ABC. Plz help !!!

Answers

I believe the answer is A

6 tons equals how many lbs?

Answers

Answer:

12000

Step-by-step explanation:

Done

Answer:

12000 lbs

Step-by-step explanation:

configuration for tons to pounds is by multiplying the tons by 2000 lbs

1 ton = 2000 lbs

6 ton= ?

6 ton x 2000 lbs = 12000 lbs

PLS HELP IM BEING TIMEDWhich of these statements is true? A) 349 > 456 B) 456 < 792 792 < 456 D) 792 > 863​

Answers

Answer:

B

Step-by-step explanation:

792 is a bigger number than 456

Answer: B

Step-by-step explanation: 792 is larger than 456

Someone please help with this question, thank you

Answers

Answer:

2.4

Step-by-step explanation:

i saw the answeres

option 2: (2,4) is the correct answer

Consider two countries, A and B, whose respective industries produce goods A and B. Total world output of the good is given by Q = 9A + 9B. There is a world demand given by P = 100 – Q. Suppose that the cost function for country A is given by cA (CA) = 89 A while the cost function in country B is given by CB(9B) = 398. The production of the good generates greenhouse gas emissions which cause global climate change. Total world emissions are 0.5 per unit of good, such that total world emissions are 0.5Q. If the two countries' industries compete in a Cournot fashion, what will the total world emissions be? Now suppose country A imposes a tax on A's production of A to curb emissions. Country B, however, is not taxed. A's cost function is now CA(CA) = 492A, while B's cost function is CB(9B) = 493. World demand is P = 99 – Q. The amount of greenhouse gas emissions per unit is still 0.5, such that total world emissions are given by 0.5Q.
What are total world emissions after country A enacts a carbon tax?

Answers

Answer: hello your question is poorly written attached below is the complete question

answer :

a) 31.5

b) 24.5

Step-by-step explanation:

Total world output of good given ( Q ) = qA + qB

world demand ( P ) = 100 - Q

cost function for country A = cA (qA) = 8qA

cost function of country B = cB(qB) = 3qB

total world emission = 0.5Q

emission per unit good = 0.5

a) Determine total world emissions when both countries compete in a Cournot fashion

Q = 63

therefore Total world emission = 0.5 ( Q )

                                                    = 0.5 ( 63 ) = 31.5

attached below is the detailed solution

b) Determine the total world emissions after Country A enacts a carbon tax

Q = 49

Therefore Total world emission after tax = 0.5 ( Q )

                                                                    = 0.5 ( 49 ) = 24.5

attached below is the detailed solution

I NEED HELP PLZ, PLZ, I NEED HELP, I AM BEGGING YOU

Answers

Answer:

tn = 8n -7

Step-by-step explanation:

given : t2=9, t4=25

the formula is:

tn = t1 + (n-1) d

gonna find d first:

d = (25-9) /(4-2) = 16/2 = 8

and find tn1:

t1 = 9-8 = 1

so, tn = 1 + (n-1) (8) = 1 +8n -8

tn = 8n -7

Answer:

Solution given

n th term[tn]=?

1st term =a

difference =d

we have

t2=9

a+(n-1)d=9

a+(2-1)d=9

a+d=9

a=9-d..................[1]

again

t4=25

a+(n-1)d=25

a+(4-1)d=25

now

substituting value of a

9-d+3d=25

2d=25-9

d=16/2

d=8

substituting value of d in equation 1.

,a=9-8

a=1

we have

tn term =a+(n-1)d=1+(n-1)8=1+8n-8=8n-7

n th term =8n-7

What is the volume of a rectangular prism
8 inches long, 3 inches wide, and 5 inches high?
A
120 cubic inches
B
220 cubic inches
16 cubic inches
158 cubic inches

Answers

Answer:

A; 120 cubic inches

Step-by-step explanation:

Let us start with the formula of the volume of a rectangular prism,[tex]V=l*w*h[/tex], where l represents the length of the prism, w represents the width of the prism, and h represents the height of the prism. It is given to us that h =5 inches, w =3 inches, and l =8 inches. Let's plug the values in:

[tex]V= 8*3*5\\V=120[/tex]

A. The volume of the rectangular prism is 120 cubic inches.

I hope this helps! Let me know if you have any questions :)

In this diagram, a triangular prism is cut by a plane as shown. What is the shape of the cross section?

Answers

Answer: it’s a triangle

Step-by-step explanation:

Answer:

triangle

Step-by-step explanation:

I need help, Thank you

Answers

Answer:

It should be 33 degrees!

Step-by-step explanation:

This can be found out when we realize that all complimentary degrees add up to 90!

Answer:

33 degrees

Step-by-step explanation:

Solve. Use the basic percent equation. 212.5 is 85% of what?

Answers

Answer:

250

Step-by-step explanation:

85% · n = 212.5

[convert 85% to .85]

.85n = 212.5

n = 212.5/.85

n = 250

PLEASE HELP !!!! WHOEVER GETS IT RIGHT GETS BRAINLIEST

Answers

x=22/y=6
Step by step below

Answer:

x = 22

y = 6

Step-by-step explanation:

GIVEN :-

AB ⊥ CF∠ABE = (4y + 2)°∠FBE = (3x - 2)°∠FBD = (5x + 6)°

TO FIND :-

The value of x & y

GENERAL CONCEPT TO BE USED IN THIS QUESTION :-

Complementary angles :- Two angles are said to be complementary if sum of measure of both angles is equal to 90°. Linear Pair :- Two angles are said to be a linear pair if both the angles lie on a straight line & sum of both angles is equal to 180°.

SOLUTION :-

In the figure given in the question , ∠FBE & ∠FBD are linear pair.

⇒ (3x - 2)° + (5x + 6)° = 180°

⇒ 8x + 4 = 180

⇒ 8x = 176

x = 22°

Also , AB⊥CF.

⇒ ∠ABE & ∠FBE are complementary angles.

⇒ (4y + 2)° + (3x - 2)° = 90°

⇒ 4y + (3×22) = 90   [∵ Putting x = 23]

⇒ 4y + 66 = 90

⇒ 4y = 24

y = 6

someone please help! (listing BRAINLIST and giving points) ​:D​

Answers

Answer:

opp/adj

havent u pay attention in ur math class?

you will have to find the opp using a^2+b^2+c^2

Step-by-step explanation:

I hope this is help full to you

In circle Q, the mLKM is 255º. Find the measurement of

Answers

Hope this help!!!

Have a nice day!!!


T
55
R
45

Find Q.
A. 40°
B. 80°
C. 130°
D. 260°

Answers

Answer:

B. 80°

Step-by-step explanation:

55+45=100

180-100=80

Q=80°

Hannah leans a 16-foot ladder against a wall so that it forms an angle of 61° with the
ground. What's the horizontal distance between the base of the ladder and the wall?
Round your answer to the nearest tenth of a foot if necessary.

Answers

Answer:

7.8 feet

Step-by-step explanation:

We can determine the Horizontal distance using trigonometry ;

Using the relation :

Cosθ = adjacent / hypotenus

Cos 61 = x / 16

x = cos 61 * 16

x = 0.4848096 * 16

x = 7.756

x = 7. 8 feet

Georgia, a florist, charges $7.95 per flower bundle plus a $12 delivery charge per order. If Charlie orders 8 flower bundles and has them delivered, how much does Georgia charge Charlie?

Answers

Answer:

75.6

Step-by-step explanation

HOPE I HELPED ;)

159.60$ i think someone might need to double check

The table of values represents a polynomial function f(x).

How much greater is the average rate of change over the interval [5, 7] than the interval [2, 4] ?

x f(x)
2 230
3 638
4 1048
5 3452
6 4568
7 5002
8 6294
Enter your answer in the box.

Answers

Given:

The table of values of the function f(x).

To find:

How much greater is the average rate of change over the interval [5, 7] than the interval [2, 4]?

Solution:

The average rate of change of a function f(x) over the interval [a,b] is:

[tex]m=\dfrac{f(b)-f(a)}{b-a}[/tex]

The average rate of change over the interval [5, 7] is:

[tex]m_1=\dfrac{f(7)-f(5)}{7-5}[/tex]

[tex]m_1=\dfrac{5002-3452}{2}[/tex]

[tex]m_1=\dfrac{1550}{2}[/tex]

[tex]m_1=775[/tex]

The average rate of change over the interval [2,4] is:

[tex]m_2=\dfrac{f(4)-f(2)}{4-2}[/tex]

[tex]m_2=\dfrac{1048-230}{2}[/tex]

[tex]m_2=\dfrac{818}{2}[/tex]

[tex]m_2=409[/tex]

The difference between the average rate of change over the interval [5, 7] and the interval [2, 4] is:

[tex]Difference=m_1-m_2[/tex]

[tex]Difference=775-409[/tex]

[tex]Difference=366[/tex]

Therefore, the average rate of change over the interval [5, 7] is 366 more than the interval [2, 4].

Answer:

366

Step-by-step explanation:

I took the test lol

5 more than the quotient of 3 and t ​

Answers

Answer and Step-by-step explanation:

[tex]\frac{3}{t}[/tex] + 5

Above is the answer.

#teamtrees #PAW (Plant And Water)

please help me with this i’m begging!!!

Complete the proof.

Answers

Answer:

here u go

Step-by-step explanation:

is givenDef of midpointVertical angles theorem SAS

1.  Given -- that's pretty much always the first step

2. LN=NW, SN=NK.     That's the Definition of Midpoint.

3. angle LNS=WNK.   That's the Vertical Angles Theorem - vertical angles are congruent.

4. Triangle LNS=WNK.  That's SAS, side-angle-side congruence.

Divide x3 + 5x2 + 5x – 3 by x + 3

Answers

Answer:

[tex]x^{2} + 2x - 1[/tex]

Step-by-step explanation:

We are solving for :

[tex]\frac{x^{3}+ 5x^{2} + 5x - 3 }{x + 3}[/tex]

Factor [tex]x^{3} + 5x^{2} + 5x - 3 : (x + 3)(x^{2} + 2x - 1)[/tex]

[tex]\frac{(x + 3)(x^{2} + 2x - 1)}{x + 3}[/tex]

= [tex]x^{2} + 2x - 1[/tex]

The answer is in the picture shown below:

Linear function please help it’s due in 30 mins

Answers

Y=2x+1 Hope that helps

Get brainiest if right!!
10 points!!

Answers

Answer:

Next three terms 0.28, 0.41 and 0.54

The formula for the nth term of an AP is a+(n-1)d

How many 34 cup servings of granola can be measured from a box containing six cups of granola?

Answers

9514 1404 393

Answer:

  8

Step-by-step explanation:

The number of servings can be found by dividing the quantity available by the amount per serving.

  (6 cups)/(3/4 cup/serving) = (6)(4/3) servings = 8 servings

Derek is skiing on a circular ski trail that has a radius of 0.6 km. Derek starts at the 3-o'clock position and travels 2.4 km in the counter-clockwise direction.
a. How many radians does Brian sweep out?
b. When Brian stops skiing, how many km is Brian to the right of the center of the ski trail?
c. When Brian stops skiing, how many km is Brian above of the center of the ski trail?

Answers

Answer:

a) Brain sweep out 4 radians

b) Brian is -0.3922 km to the right of the center of the ski trail

c) Brian is -0.4541 km above of the center of the ski trail

Step-by-step explanation:

Given the data in the question;

circular ski trail radius = 0.6 km

Derek starts at the 3-o'clock position and travels 2.4 km in the counter-clockwise direction.

a) How many radians does Brian sweep out?

arc length = 2.4 km

from the diagram;

arc length = rθ

θ = arc length / r

θ = 2.4 / 0.6

θ = 4 radians

Therefore, Brain sweep out 4 radians

b) When Brian stops skiing, how many km is Brian to the right of the center of the ski trail?

from the diagram;

x = rcosθ

we substitute

x = 0.6 × cos(4)

x = 0.6 × -0.65364

x = -0.3922 km

Therefore Brian is -0.3922 km to the right of the center of the ski trail

c) When Brian stops skiing, how many km is Brian above of the center of the ski trail?

from the diagram;

m = rsinθ

m = 0.6 × -0.7568

m = -0.4541 km

Therefore, Brian is -0.4541 km above of the center of the ski trail

A survey of 423 people shows that 321 have never received a traffic violation. Find the sample proportion of those who have received a traffic violation. *
1 point
A. 13%
B. 24%
C. 32%
D. 76%

Answers

24% :)

(please mark me as brainliest) <3

find the missing angle measure in each triangle. Then classify the triangle as acute, right, or obtuse. PLEASE ANSWER QUICK ILL MARK BRAINLIEST

Answers

Answer:

40     Right Angle Triangle

Step-by-step explanation:

180-50-90=x

x=40

Right angle triangle

Answer:

40

Step-by-step explanation:

90 + 50 = 140

A triange = 180

A right angle(aka the square) = 90

180 - 140 = 40

x = 40

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