When it is operating properly, a chemical plant has a daily production rate that is normally distributed with a mean of 885 tons/day and a standard deviation of 42 tons/day. During an analysis of period, the output is measured with random sampling on 60 consecutive days, and the mean output is found to be x=875 tons/day. The manager claims that at least 95 % probability that the plant is operating properly. Is he right? Justify your answer!

Answer:

8+5=13

13+2=15

your answer is 15

You have to add : )

Step-by-step explanation:

Hope this helps : )

Answer:

t=411

Step-by-step explanation:

t+55=466

466-55

Subtract the numbers

t=411

Answer:

3.375 bags of soil are needed for Paj to fill the flower pot

Step-by-step explanation:

This question can be solved using a rule of three.

One bag contains 2 + (2/3) = (8/3) cubic inches of soil. How many bags are needed to fill 9 cubic inches of soil?

1 bag - (8/3) cubic inches

x bags - 9 cubic inches

[tex]\frac{8x}{3} = 9[/tex]

[tex]8x = 27[/tex]

[tex]x = \frac{27}{8}[/tex]

[tex]x = 3.375[/tex]

3.375 bags of soil are needed for Paj to fill the flower pot

Paj needs 3.375 bags of soil to fill the bag.

Each bag contains 2²/₃ inch³ of soil and they need to fill up a 9 inch³ pot of soil.

First convert the mixed fraction to an improper one:

2²/₃ = 8/3

The number of bags needed is:

= Volume of pot / Quantity of soil in each bag

= 9 ÷ 8/3

= 9 x 3/8

= 3.375 bags of soil

Paj therefore needs 3.375 bags of soil to fill the pot

Find out more at https://brainly.com/question/17205287.

Answer:

Step-by-step explanation:

The population average number of raisins per box is 30.

The type of statistical analysis to be run here is the inferential statistical analysis and its assumptions include normality, linearity and equality of variance.

Null hypothesis: Average number of raisins per box is 30: u = 30

Alternative hypothesis: Average number of raisins per box is not 30: u ≠ 30

To perform a two tailed single sample test, we have

z statistic = (the sample mean - hypothesized mean) / (SD/√n)

sample mean = 28.05, SD = 3.87 hypothesized mean = 30 n = 36

Thus, we have 28.05 - 30 / (3.87/√36)

= -1.95 / (3.87/6)

= -1.95 / 0.645

= -3.023

we say this is a left tailed test and use the negative z table

where -3.02 = 0.0013

To determine whether the average number of raisins per box differs from the expected 30.

Using p < 0.05, since the observed value 0.0013 is less than 0.05, we conclude the the average number of raisins per box differs from the expected 30.

The ratio of Reeta's age and Site's age is 3:5 and the sum of their ages is 80 years. The ratio of their ages after 10 years will be

By the chain rule,

[tex]\dfrac{\mathrm dw}{\mathrm dt}=\dfrac{\partial w}{\partial x}\dfrac{\mathrm dx}{\mathrm dt}+\dfrac{\partial w}{\partial y}\dfrac{\mathrm dy}{\mathrm dt}+\dfrac{\partial w}{\partial z}\dfrac{\mathrm dz}{\mathrm dt}[/tex]

We have

[tex]w=7ye^x-\ln z\implies\begin{cases}\dfrac{\partial w}{\partial x}=7ye^x\\\\\dfrac{\partial w}{\partial y}=7e^x\\\\\dfrac{\partial w}{\partial z}=-\dfrac1z\end{cases}[/tex]

and

[tex]\begin{cases}x=\ln(t^2+1)\\y=\tan^{-1}t\\z=e^t\end{cases}\implies\begin{cases}\dfrac{\mathrm dx}{\mathrm dt}=\dfrac{2t}{t^2+1}\\\\\dfrac{\mathrm dy}{\mathrm dt}=\dfrac1{t^2+1}\\\\\dfrac{\mathrm dz}{\mathrm dt}=e^t\end{cases}[/tex]

Putting everything together, we get

[tex]\dfrac{\mathrm dw}{\mathrm dt}=\dfrac{14ye^xt}{t^2+1}+\dfrac{7e^x}{t^2+1}-\dfrac{e^t}z[/tex]

[tex]x=\ln(t^2+1)[/tex], so [tex]e^x=e^{\ln(t^2+1)}=t^2+1[/tex], and [tex]z=e^t[/tex], so [tex]\frac{e^t}z=1[/tex].

[tex]\dfrac{\mathrm dw}{\mathrm dt}=14yt+7-1[/tex]

[tex]\dfrac{\mathrm dw}{\mathrm dt}=14t\tan^{-1}t+6[/tex]

Then when [tex]t=1[/tex], the derivative has a value of [tex]\frac{7\pi}2+6[/tex].

Answer:

There would be

- 12 bags of 1/6-ounce rice.

- 6 bags of 1/3-ounce of rice.

- 4 bags of 1/2-ounce of rice.

-The line plot is presented in the attached image to this answer.

1) There are 22 bags that weigh at least 1/6 of an ounce.

2) There are 4 bags that weigh more than 1/3 of an ounce.

3) The combined total of the 1/2-ounce bags = 2 ounces.

4) The average weight of the bags = (3/11) of an ounce.

Step-by-step explanation:

Complete Question

Raine divides three 2-ounce bags of rice into smaller bags. The first bag is divided into bags weighing 1/6-ounce each, the second bag is divided into bags weighing 1/3-ounce each and the third bag is divided into bags weighing 1/2- ounce each. Find the number of 1/6, 1/3 and 1/2 bags and graph it in a line plot.

1) How many bags weigh at least 1/6 of an ounce?

2) How many bags are more than 1/3 of an ounce?

3) What is the combined total of the 1/2 ounce bags?

4) What is the average weight of each of the bags?

Solution

Let the number of 1/6-ounce, 1/3-ounce and 1/2-ounce bags be x, y and z respectively.

(1/6) × x = 2

x = 2 × 6 = 12 bags of 1/6-ounce rice.

(1/3) × y = 2

y = 2 × 3 = 6 bags of 1/3 ounce of rice.

(1/2) × z = 2

z = 2 × 2 = 4 bags of 1/2-ounce rice.

The line plot is presented in the attached image to this answer.

1) All of the bags weigh at least 1/6 of an ounce. Hence, the number of bags that weigh more than 1/6 of an ounce = 12 + 6 + 4 = 22 bags

2) The bags that weigh more than 1/3 of an ounce are the 1/2-ounce bags, and there are only 4 of them. Hence, 4 bags weigh more than 1/3 of an ounce.

3) Combined total of the 1/2 ounce bags

= 4 bags × (1/2-ounce per bag) = 2 ounces.

4) The average weight of the bags is given as the sum total of the weight of the bags divided by the number of bags.

Total weight of the bags = [12 × (1/6)] + [6 × (1/3)] + [4 × (1/2)] = 2 + 2 + 2 = 6 ounces.

Total Number of bags = 12 + 6 + 4 = 22 bags

Average weight of the bags = (6/22) = (3/11) ounce per bag.

Hope this Helps!!!

Answer:

None of the inequalities are correct if p = 3.4

Step-by-step explanation:

Mathematical inequality is an order relation proposition existing between two algebraic expressions connected through the signs: unequal than ≠, greater than>, less than <, less than or equal to ≤, as well as greater than or equal to ≥, resulting in both expressions of different values. That is, an inequality is a relationship that exists between two quantities or expressions and, which indicates that they have different values.

To check an inequality, you must replace the inequality variable with the value of the solution.  In this case, being p=3.4, you must do it with each of the inequalities, as shown below:

A. 3p<10.2 ⇒ 3*3.4<10.2 ⇒ 10.2 <10.2  

This inequality is not true, because 10.2 is not less than 10.2, but they are equal.

B. 13.6<3.9p ⇒ 13.6<3.9*3.4 ⇒ 13.6<13.26  

This inequality is not true, because 13.6 is greater than 13.26 and not less as the inequality shows.

C. 5p>17.1 ⇒ 5*3.4 >17.1 ⇒ 17 > 17.1  

This inequality is not true, because 17 is less than 17.1 and not greater as the inequality shows.

D. 8.5> 2.5p ⇒ 8.5 >2.5*3.4 ⇒ 8.5 > 8.5

This inequality is not true, because 8.5 is not less than 8.5. These values ​​are the same.

None of the inequalities are correct if p = 3.4

The correct answer is C. By substituting the greatest number in each set for p, you can quickly tell which sets make the inequality false.

Answer:

(1) 23.55mm³

(2) 340.17in³

Step-by-step explanation:

Volume of a cone is: [tex]V=\frac{1}{3} \pi r^2h[/tex]

'r' - radius

'h' - height

The height of Cone 1 is 10 mm. The Diameter of Cone 1 is 3mm.

Radius is half the Diameter.

[tex]3/2=1.5[/tex]

The radius is 1.5 mm.

[tex]\text {Using 3.14 as pi: }\\V=(1/3)3.14*1.5^2*10\\V=(1/3)3.14*2.25*10\\V=(1/3)70.65\\\boxed{V=23.55}[/tex]

The volume of Cone 1 should be about 23.55mm³.

The height of Cone 2 is 13 in. The Radius of Cone 2 is 5 in.

Using 3.14 as pi:

[tex]V=(1/3)3.14*5^2*13\\V=(1/3)3.14*25*13\\V=(1/3)1020.5\\\boxed {V=340.166666667}[/tex]

340.166666667 ≈ 340.17

The volume of Cone 2 should be about 340.17in³.

If the final weight is halved then the mass of the object will be 500,550 grams

1 kg of an object = 1000 grams

If an object weighs a quarter of a kilogram, then

New weight = 1/4(1000) = 250 grams

If  I add one-half of a kilogram to the object, then the new weight will be 750grams

If the final weight is halved then the mass of the object will be 500,550 grams

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Answer:

2 nickels

6 quarters

Step-by-step explanation:

Let quarters be 3x and nickels be $x

if Mark had 3 times as many quarters as nickels, and if he had $1.60 in all, than

( 0.25)3x + 0.05x=1.6

0.75x+ 0.05x=1.6

0.8x=1.6

x=1.6/0.8

x=2 nickels

and 3 (2)=6 quarters

Answer:

There are 4 quarters and 12 nickels.

Step-by-step explanation:

A quarter is equal to $0.25.

A nickel is equal to $0.05.

Let the number of nickels be y.

Let the number of quarters be x.

Mark had 3 times as many quarters as nickels. This means that:

y = 3x

3x represents the number of nickels.

We are told that he had $1.60 in all. This means that:

0.25x + 0.05y = 1.60

=> 0.25x + 0.05 * 3x = 1.60

0.25x + 0.15x = 1.60

0.40x = 1.60

=> x = 1.6 / 0.4 = 4

Therefore:

y = 3 * 4 = 12

There are 4 quarters and 12 nickels.

William can do 1/4 of the job every hour by himself.

Stephanie can do 1/6 of the job every hour by herself.

If they don't distract each other while working together, they can do (1/4 + 1/6) of the job every hour.

That's (3/12 + 2/12) = 5/12 job per hour working together.

The complete job will take them (12/5) hour .

That's 2-2/5 hours, or 2 hours 24 minutes.

They both can do the painting in 2hours 24 minutes by solving the fraction.

It is a combination of numerator and denominator. It is always in decimal

if solved properly.

William can do 1/4 of the job every hour himself. Stephanie can do 1/6 of the job every hour  herself,  they can do (1/4 + 1/6) of the job every hour.

That's (3/12 + 2/12) = 5/12 job per hour working together.

The complete job will take them (12/5) hour .

or 2 hours 24 minutes.

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Answer:

12 %

Step-by-step explanation:

The fraction of men that are left handed is 3/25

Percent means out of 100, so get the fraction with a denominator of 100

3/25 *4/4 = 12/100

12 %

Answer:

Step-by-step explanation:

52units

Answer:

A

Step-by-step explanation:

In the attached file

Answer:

9: 89°

Step-by-step explanation:

Inside of a triangle is 180, so 180-39-52=89

I'm sorry I can't answer 10 for you

Answer:

cube game

Step-by-step explanation:

one of them wins every time

A number cube is rolled. Player 1 gets a point for any number that is 3 or higher, and player 2 gets a point for any number less than 3

If a number cube is rolled and Player 1 gets a point for any number that is 3 or higher and Player 2 gets a point for any number less than 3 it wouldn't be fair to Player 2 because Player 1 has a higher chance of getting points because he/she has more opportunities.

I hope this is correct

Answer:

a) [tex] p = 0.5[/tex]

b) [tex] \hat p= \frac{X}{n}= \frac{154}{329}= 0.468[/tex]

c) [tex]0.468 - 1.64 \sqrt{\frac{0.468(1-0.468)}{329}}=0.423[/tex]

[tex]0.468 + 1.64 \sqrt{\frac{0.468(1-0.468)}{329}}=0.513[/tex]

And the 90% confidence interval for the true proportion is given by (0.527;0.593).

Step-by-step explanation:

Part a

For this case we don't have any prior info given so then the probability assumed for this case is:

[tex] p = 0.5[/tex]

Part b

For this case the proportion of success is given by:

[tex] \hat p= \frac{X}{n}= \frac{154}{329}= 0.468[/tex]

Part c

The confidence interval for the true proportion would be given by this formula

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

For the 90% confidence interval the value of and , and the critical value would be given by:

[tex]z_{\alpha/2}=1.64[/tex]

The confidence interval is given by:

[tex]0.468 - 1.64 \sqrt{\frac{0.468(1-0.468)}{329}}=0.423[/tex]

[tex]0.468 + 1.64 \sqrt{\frac{0.468(1-0.468)}{329}}=0.513[/tex]

And the 90% confidence interval for the true proportion is given by (0.527;0.593).

Answer:

Your rate of change is [tex]\frac{3}{2}[/tex].

Step-by-step explanation:

Well, all you have to do is subtract the points.

[tex]\frac{changeiny}{changeinx} \\\\\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\\frac{9-7.5}{6-5}\\\\\frac{1.5}{1}[/tex]

This is also know as the rate of change of [tex]\frac{3}{2}[/tex].

Answer:

erm

Step-by-step explanation:

25

Answer:

40 miles

Step-by-step explanation:

In the attached diagram, Point A is the starting point and C is the end point. We want to determine the distance from A to C.

The path driven forms a right triangle in which AC is the hypotenuse.

We therefore use the Pythagorean Theorem to solve for the AC.

Pythagorean Theorem: [tex]Hypotenuse^2=Opposite^2+Adjacent^2[/tex]

[tex]|AC|^2=32^2+24^2\\|AC|^2=1600\\|AC|=\sqrt{1600}\\ |AC|=40$ miles[/tex]

The  straight  line distance from the starting point is 40 miles.

Answer:

point B is located at 6 on the number line

Step-by-step explanation:

u subtract 5 from 11

Answer:

23.75

Step-by-step explanation:

95/4

23.75

Answer:

A≈9.75

Step-by-step explanation:

The side length can be found by getting the square root of 95.

Since all sides are the same on a square, this means that 9.75² gives us 95, which it does.

Hope this helps!

-MoCKEry

Answer:

0.55% probability that exactly 5 out of the first 13 customers buy a magazine

Step-by-step explanation:

For each customer, there are only two possible outcomes. Either they buy a magazine, or they do not. The probability of a customer buying a magazine is independent of other customers. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

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

And p is the probability of X happening.

10% of his customers buy a magazine

This means that [tex]P = 0.1[/tex]

What is the probability that exactly 5 out of the first 13 customers buy a magazine?

This is P(X = 5) when n = 13. So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 5) = C_{13,5}.(0.1)^{5}.(0.9)^{8} = 0.0055[/tex]

0.55% probability that exactly 5 out of the first 13 customers buy a magazine

Answer:

[tex] P(X=5) = (13C5) (0.1)^5 (1-0.1)^{13-5}= 0.00554[/tex]

So then  he probability that exactly 5 out of the first 13 customers buy a magazine is 0.0554

Step-by-step explanation:

Let X the random variable of interest "number of customers that buy a magazine", on this case we can model the variable of interest with this distribution:

[tex]X \sim Binom(n=13, p=0.1)[/tex]

The probability mass function for the Binomial distribution is given as:

[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]

Where (nCx) means combinatory and it's given by this formula:

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

We want to find this probability:

[tex] P(X=5)[/tex]

And using the probability mass function we got:

[tex] P(X=5) = (13C5) (0.1)^5 (1-0.1)^{13-5}= 0.00554[/tex]

So then  he probability that exactly 5 out of the first 13 customers buy a magazine is 0.0554

Answer:

Check the explanation

Step-by-step explanation:

Kindly check the attached image below to see the step by step explanation to the question above.

Answer:

John have to pay back $23,327.50 at the end of two years

Step-by-step explanation:

Simple Interest (I) = (PRT) ÷ 100

where P = Principal, R = Rate, T= Time

I = ($150500 × 7.75 × 2) ÷ 100

I = ($2332750) ÷ 100

I = $23,327.50

Answer:

g=56

Step-by-step explanation:

In similar shapes, corresponding sides are always in the same ratio.

For example,

if the sides in triangle 1 were a and b, and triangle 2 had side lengths c and d, c and a had the same ratios, and b and d had the same ratios

and triangle 1 was similar to triangle 2, the ratio between the sides of the triangles would be

a/c, which is also equal to b/d

What that means is that in this situation, 8/5=g/35.

8/5=g/35

Cross multiply.

(8)*(35)=g*(5)

280=5g

g=56

Answer:

Perimetrul triunghiului ABC este egam cu 36 cm, iar AB = 15 cm si AC = 13 cm. Lungimea segmentului BC = cu...

Step-by-step explanation:

Answer:

growth

Step-by-step explanation:

Answer:

Each Shirt ≈ $2.49

Each Pair of Slacks ≈ $5.99

Each Sports Coat ≈ $7.99

Step-by-step explanation:

Mike took clothes to the cleaners three times last month.​

Let S denotes shirts, P denotes pair of slacks and C denotes sports coat.

First, he brought 4 shirts and 1 pair of slacks and paid ​$15.95.

Mathematically,

4S + P = 15.95      eq. 1

Then he brought 7 ​shirts, 4 pairs of​ slacks, and 1 sports coat and paid ​$49.38.

Mathematically,

7S + 4P + C = 49.38      eq. 2

​Finally, he brought 3 shirts and 1 sports coat and paid ​$15.46.

Mathematically,

3S + C = 15.46      eq. 3

We are asked to find how much was he was charged for each​ shirt, each pair of​ slacks, and each sports​ coat.

4S + P + 0C = 15.95               eq. 1

7S + 4P + C = 49.38              eq. 2

3S + 0P + C = 15.46               eq. 3

We have 3 equations and 3 unknowns, they can be solved simultaneously using calculator or using online system of equations solver.

Using online system of equations solver yields,

S ≈ $2.49

P ≈ $5.99

C ≈ $7.99

So that means Mike was charge $2.49 for each shirt, $5.99 for each pair of slacks and $7.99 for each sports coat.

Answer:

A

Step-by-step explanation:

The form for a parabola with vertex form is y=(x-h)^2+k, where h is the x coordinate and k is the y. Therefore, since the x coordinate of the graph is -2, the answer is A. Hope this helps!

Answer:

its A

hop this helps