An arts academy requires there to be 4 teachers for every 88 students and 5 tutors for every 45 students. How many students does the academy have per​ teacher? Per​ tutor? How many tutors does the academy need if it has 108 students​?

Answer:

Step-by-step explanation:

Base area =[tex]x^2[/tex]

side area=[tex]h*x[/tex]

Volume=[tex]x^2*h[/tex]=14

Surface area =[tex]4hx+2x^2[/tex]

upon substituting [tex]h=14/x^2[/tex]

surface area = [tex]4*\frac{14}{x^2}*x+2x^2[/tex]

upon differentiating and solving we get  f"([tex]\sqrt[3]{14\\}[/tex]) >0 proves that this point is of minima

hence, dimensions are

[tex]x=\sqrt[3]{14}[/tex] ,h=[tex]\sqrt[3]{14}[/tex]

Answer: A null hypothesis is a statistical hypothesis that is tested for possible rejection under the assumption that it is true.

Step-by-step explanation:

The null hypothesis[tex](H_0)[/tex] and alternative hypothesis[tex](H_a)[/tex] both are statements as per the researcher's claim that involves population parameter .

Null hypothesis has  ≤,≥ ,= signs

Alternative hypotheses has < , > , ≠ signs.

A null hypothesis is a statistical hypothesis that is tested for possible rejection under the assumption that it is true.

Answer:

The probability that the lacrosse goalie will make at least 10 saves is 0.558.

Step-by-step explanation:

Let X denote the number of saves the lacrosse goalie will successfully make.

It is provided that the probability of the lacrosse goalie making a successfully save is, p = 0.80.

It is assumed that all save attempts are independent.

Suppose that the lacrosse goalie attempts to make n = 12 saves.

The random variable X follows a binomial distribution with parameters n = 12 and p = 0.80.

Compute the probability that the lacrosse goalie will make at least 10 saves as follows:

[tex]P(X\geq10 )=P(X=10)+P(X=11)+P(X=12)[/tex]

                 [tex]={12\choose 10}(0.80)^{10}(0.20)^{2}+{12\choose 11}(0.80)^{11}(0.20)^{1}+{12\choose 12}(0.80)^{12}(0.20)^{0}\\\\=0.2835+0.2062+0.0687\\\\=0.5584\\\\\approx 0.558[/tex]

Thus, the probability that the lacrosse goalie will make at least 10 saves is 0.558.

Answer:

I confirm that the person above me is right.

Step-by-step explanation:

Enjoy your brainliest ;)

Answer:

432 cm[tex]^{3}[/tex]

Step-by-step explanation:

The volume of the box can be determine by using derivative function:

V = (18 - 2x) (18 - 2x) x

dV/dx = 4x^3 + 324 + 144x

equating to zero;

(x - 9) (x - 3) = 0

x = 9 , 3

putting the values in the equation;

V = (18 - 2 [3]) (18 - 2[3]) 3

volume = 432.

Answer:

The correct interpretation of the 95% confidence interval is that there is 95% confidence that the true proportion of people who own a tablet computer is within the upper limit (0.78) and  the lower limit (0.62) of the confidence interval

Step-by-step explanation:

From the question we are told that

  The  95% confidence interval  is  (0.62,0.78)

Generally the correct interpretation of the 95% confidence interval is that there is 95% confidence that the true proportion of people who own a tablet computer is within the upper limit (0.78) and  the lower limit (0.62) of the confidence interval

Answer:

C, 34 inches

Step-by-step explanation:

1. We can see that 30 is the length of one of the sides on the larger parallelogram. The same side has a length of 12 inches on the smaller one. So, we need the difference of these 2 to figure out PQ.

30 - 12 = 18 inches (the difference)

2. Add 18 to 16 (the bottom side on the small parallelogram) to figure out what the bottom side of the large parallelogram would be.

16 + 18 = 34 inches (answer C)

Answer:

21/10

Step-by-step explanation:

Answer:

It is 1/2

Step-by-step explanation:

Please mark me brainiest and like and rate 5 stars ;)

Answer:

0.33

Step-by-step explanation:

Because you have 2 apples that weigh 0.33 pounds you gain 2 from your parents then give 2 to your friends so you have 2 left or....0.33 pound left.

Hope this helps☺️

Answer:

13r/4

Step-by-step explanation:

aha i looked it up xD

The explanation is you have to put the whole number over its self.Then they have to have common denominator.Then add

Answer:

-103n = 0

Step-by-step explanation:

Watch my following steps:

8 - 81n - 18 = -10 + 22n

8 - 81n - 22n = -10 + 18

-81n - 22n = 8 - 8

-103n = 0

Pls consider marking my answer as Brainliest! It would mean a lot!

Answer:

Shape of sampling distribution of sample mean being approx normal or not depends upon sample size.

Step-by-step explanation:

'The shape of the sampling distribution of the sample mean is approximately normal' might be true or false, depending on sample size.

If the sample size satisfies the condition of being sufficiently large, the shape of sampling distribution of sample mean becomes more bell shaped normally distributed (even more normally distributed than actual population).

Central Limit theorem also states this - Larger the sample size, shape of sampling distribution of sample mean becomes more normally distributed around population mean.

Answer:

The minimum exam score to be awarded an A is about 8.52.

Step-by-step explanation:

Let X represent the scores on a common final exam.

It is provided that X follows a normal distribution with mean, μ = 71 and standard deviation, σ = 9.

It is provided that according to the department policy is that the top 10% of students receive an A.

That is, P (X > x) = 0.10.

⇒ P (X < x) = 0.90

⇒ P (Z < z) = 0.90

The corresponding z-score is:

z = 1.28

Compute the value of x as follows:

[tex]z=\frac{x-\mu}{\sigma}\\\\1.28=\frac{x-71}{9}\\\\x=71+(1.28\times 9)\\\\x=82.52[/tex]

Thus, the minimum exam score to be awarded an A is about 8.52.

Answer:

-3(x+4)

Step-by-step explanation:

you just factor out -3

Answer: -3(x+4)

Step-by-step explanation:

Hii, do you need to factor -3x-12? No problem!

Note that -3x and -12 have a -3 in common, so we can factor it out by dividing both -3x and -12 by -3.

x+4 (A negative number divided by a negative number gives us a positive result)

Next, we put parentheses around x+4

(x+4)

Now we put -3 outside these parentheses

-3(x+4)

Voila! There's our solution, cheers!

--

Hope that this helped! Best wishes.

--

Answer:

45

Step-by-step explanation:

Square root 2025 and you will get 45

45 times 45= 2025

Answer:

Step-by-step explanation:

If you are multiplying then 45 * 45 = 2025

If you are adding then 1012.5 + 1012.5 = 2025

Answer:

$410

Step-by-step explanation:

15*6=90

90-80=10

400+10=410

$410

Answer:

the third answer

Step-by-step explanation:

parallel lines will have the same slope (in this case -4) and you plug in the points

Answer:

34.5744 ≈ 35

Step-by-step explanation:

The formula for Margin of Error

= z × σ/√n

Where

z = z score of the confidence interval = z score of 95% = 1.96

σ = 15 pounds

n = number of samples = ??

Margin of Error = 5

Hence,

5 = 1.96 × 15/√n

Cross Multiply

5 × √n = 1.96 × 15

Divide both sides 5

√n = 1.96 × 15/5

√n = 1.96 × 3

√ n = 5.88

Square both sides

n = 5.88²

n= 34.5744

Approximately the size = 35

Answer:

6.8

Step-by-step explanation:

Answer:

that is correct

Step-by-step explanation:

your welcome

Answer:

-3/5x+6

Step-by-step explanation:

I'm assuming they want it in slope-intercept form, because that's more common. If it's not then I will be wrong. See screenshot for proof.

Answer:

[tex]10^{2}[/tex]

Step-by-step explanation:

[tex]10^{6} /10^{4}[/tex]

=> [tex]10^{2}[/tex]

Proof,

10 * 10 * 10 * 10 * 10 * 10 / 10 * 10 * 10 * 10

4 ten's cancel each other, leaving behind 2 ten's, and,

10 * 10 is the same thing as [tex]10^{2}[/tex]

If my answer helped, kindly mark me as the brainliest!!

Thank You!!

Step-by-step explanation:

the answer is y=1/4 ×-2

Step-by-step explanation:

we are looking for the inequality of X

i can tell from this question that the first 2 are wrong, which leaves the last 2

first step, we add 1/3

5/6x> 1 2/3

now we divide 1 2/3 by 5/6 which gives us 2

taking a look at the sign posted in the question, i can confirm that C is correct

Answer:

Confidence Interval Meaning, Implication, Formula

Step-by-step explanation:

95% confidence interval is the range around the stable estimate, which has 95% certainty (or probability) of containing true population parameter.

Formula : x' + z (s/ √n)

Where : x' = sample mean, confidence level value, s = standard deviation, sample size

By using sample size, sample mean, sample standard deviation of US people 'considering health care access most important' - & using above formula - range containing actual population proportion (with 95% sure probability) thinking the same.

Answer:

X-

(7/6,0)

y-

(0,-7/3)

Step-by-step explanation:

To find the x-intercept, substitute in 0 for y and solve for x. To find the y-intercept, substitute in 0 for x and solve for y.

x-intercept(s):

(7/6,0)

y-intercept(s):

(0,−7/3)

Answer:

F.   [tex] 5x^{4} [/tex]

Step-by-step explanation:

[tex] \dfrac{15x^6}{3x^2} = [/tex]

[tex] = \dfrac{3 \times 5}{3} \times \dfrac{x^6}{x^2} [/tex]

[tex] = 5 \times x^{6 - 2} [/tex]

[tex] = 5x^4 [/tex]

Answer: 399÷28= 14.25

Step-by-step explanation:

Divide 399 by 28 = 14.25 gal