To prepare for the town's race, Andrew runs around a rectangular field. The dimensions of the field are 450 feet
by 225 feet. How many times must Andrew run around the field in order to run 12 miles? One mile is 5,280
fect.
Round the answer to one decimal place if necessary?

Answer:

125

Step-by-step explanation:

To find the common ratio, take the second term and divide by the first term

1000/2000 = 1/2

We multiply each term by 1/2

2000, 1000, 500

To find the next term 500*1/2 = 500/2 = 250

To find the 5th term

250*1/2 = 125

Answer:

A. This test is very resistant to departures from normal distributions.

Step-by-step explanation:

The Ftest or Fratio usually used to obtain the test statistic during hypothesis testing using the analysis of variance, is used to compare the equality or differences in population vatfuance or standard devuation. The critical values of the Ftest or Fratio is obtained using the F distribution table. When testing hypothesis using the F test, it requires that both populations follow a normal distribution.

Hence, the option, that F test is resistant to departures for normal distribution is not true of the Ftest.

In triangle it is given that,

→ Height (h) = 38 cm

→ Base (b) = 44 cm

The formula we use,

→ Area of triangle = ½ × b × h

Now we have to,

find the area of the triangle,

→ ½ × b × h

→ ½ × 44 × 38

→ (44 × 38)/2

→ 1672/2 = 836 cm²

So, 836 cm² is area of triangle.

Answer:

167.6 cm³

Step-by-step explanation:

the volume of a cone :

ground area × height / 3 = pi×r² × height / 3

r = 4 cm

height = 10 cm

pi×4² × 10 / 3 = pi×16×10/3 = pi×160/3 = 167.6 cm³

Answer:

scientists

Step-by-step explanation:

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Answer:

  (2x -4) +1/(x -2) -2/(x +4)

Step-by-step explanation:

The attached shows the quotient is (2x -4) and the remainder expressed as a fraction is ...

  r = (8 -x)/(x^2 +2x -8)

So, the problem is to write the partial fraction expansion of this remainder. It will be of the form ...

  r = A/(x -2) +B/(x +4)

where (x-2)(x+4) is the factorization of the divisor quadratic.

The value of A can be found by evaluating (x -2)r at x=2.

 (x -2)r for x=2 is (8 -2)/(2 +4) = 6/6 = 1

The value of B can be found by evaluating (x +4)r at x=-4.

  (8 -(-4))/(-4-2) = 12/-6 = -2

Then the quotient and remainder, written as partial fractions is ...

  = (2x -4) +1/(x -2) -2/(x +4)

_____

Additional comment

In the form ...

  [tex]r=\dfrac{8-x}{x^2+2x-8}[/tex]

we can see that (x -2)r will be ...

  [tex](x -2)r = \dfrac{(x-2)(8-x)}{(x-2)(x+4)}=\dfrac{8-x}{x+4}[/tex]

This can be evaluated at x=2, as we have done above. Similar factor cancellation works to give (x+4)r = (8-x)/(x-2).

This method of arriving at the "A" and "B" values may not pass technical scrutiny regarding where r is defined or undefined--but it works. One could consider the work to be finding a limit, rather than evaluating a rational function at points where it is undefined.

Answer:

A. 2x-4- 2/x+4 +1/x-2

Step-by-step explanation:

Edge

Answer:

x^(d+18)

Step-by-step explanation:

using the law of indices

you must add the powers

Answer:

[tex] {x}^{d + 18} [/tex]

Step-by-step explanation:

Answer:

For some reason I cannot open the photo you have provided.

Step-by-step explanation:

Please try to re-upload?

Answer:

upper left...

there are zeros at (x)(x+3) (x-2)

Step-by-step explanation:

Answer:

2520

Step-by-step explanation:

210×12=2520

2520three

the answer would be -1,224 because the parentheses is your multiplication and the it is a negative

Answer:

5886$ is the ans

Step-by-step explanation:

Paid amount= 6000-600

Total Amount or Interest applicable amount = 5400$

Then

Interest Rate= 9%

by using formula

=. Total amount + Interest rate × Total

=. 5400+0.09×5400

=. 5886$

First, let's expand the inside expression.

4th root [ x^4 * x^4 * x^2 ]

Then, we need to determine how many x^4s we can take the 4th root of. In this case, that is 2. So, the 4th root of x^4 is x.

x * x is x^2

ANSWER: x^2( 4th root [ x^2 ] )

(Option 1)

Hope this helps!

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Answer:

Step-by-step explanation:

Let x represent the quantity of 15% alcohol required. Then (5-x) is the amount of 10% alcohol needed. The amount of alcohol in the mix is ...

  0.15x +0.10(5-x) = 0.13(5)

  0.05x +0.5 = 0.65 . . . . . . . simplify

  0.05x = 0.15 . . . . . . . . . subtract 0.5

  x = 3 . . . . . . . . . . . . . divide by 0.05

3 gallons of 15% alcohol and 2 gallons of 10% alcohol should be mixed.

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Answer:

  $794.30

Step-by-step explanation:

The account balance for principal P invested at rate r compounded daily for t years is ...

  A = P(1 +r/365)^(365t)

We have P=$9538, r=0.08, t=1, and we want the value of P-A, the interest earned.

  P-A = P(1 +0.08/365)^365 -1) = $9538(1.08327757 -1) ≈ $794.30

The interest earned in one year is $794.30.

Answer:

b 34 the higest is 40 an the lowest 6 the diferens is 34

Step-by-step explanation:

Mark me brainlest pliz

Answer:

i would but this not my question this is theres he right A.

Step-by-step explanation:

Answer:

Step-by-step explanation:

x=120°

Answer:

Decreased by 20%

Step-by-step explanation:

0.5 x ? = 0.4

? = 0.4/0.5

? = 0.8

1 - 0.8 = 0.2

0.2 = 20%

To check, 20% of 0.5 is 0.1. 0.5 - 0.1 is 0.4. So the answer is correct.

Answer:

Red ball=3/10

White ball=1/5

Step-by-step explanation:

Red balls=6. And all the balls are equal to 20. So probability of red ball=6/20=3/10.

White balls=4. So probability of white ball=4/20=1/5.

NB: Since the first ball was replaced, there's no need to deduct a ball from the original 20 balls.

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Answer:

  c. y = (x +2)² -5

Step-by-step explanation:

If you replace the squared term with zero, you are choosing the minimum of the remaining values. (A squared term cannot have a negative value.)

  a) 3

  b) 4

  c) -5 . . . . the graph with the least possible y-value

  d) 0

Answer:

73,188

Step-by-step explanation:

fees plus costs minus expenses

Answer:

11.2

Step-by-step explanation:

Given the linear equation :

2.6(5.5p-12.4)=127.92 ; solve for p

Open the bracket :

14.3p - 32.24 = 127.92

Add 32.24 to both sides

14.3p - 32.24 + 32.24 = 127.92 + 32.24

14.3p = 160.16

Divide both sides by 14.3

14.3p/14.3 = 160.16/ 14.3

p = 11.2

The value of p = 11.2

Answer:

(x, y, z) = (-8,4,-2)

Step-by-step explanation:

.......................................

Answer:

a) 0.1927 = 19.27% probability that none of the selected adults say that they were too young to get tattoos.

b) 0.3651 = 36.51% probability that exactly one of the selected adults says that he or she was too young to get tattoos.

c) 0.5578 = 55.78% probability that the number of selected adults saying they were too young is 0 or 1.

Step-by-step explanation:

For each person, there are only two possible outcomes. Either they say they were too young to get tattoos, or they do not say this. The probability of a person saying this is independent of any other person, which means that the binomial probability distribution is used 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.

24​% say that they were too young when they got their tattoos.

This means that [tex]p = 0.24[/tex]

Six adults

This means that [tex]n = 6[/tex]

a. Find the probability that none of the selected adults say that they were too young to get tattoos.

This is P(X = 0). So

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

[tex]P(X = 0) = C_{6,0}.(0.24)^{0}.(0.76)^{6} = 0.1927[/tex]

0.1927 = 19.27% probability that none of the selected adults say that they were too young to get tattoos.

b. Find the probability that exactly one of the selected adults says that he or she was too young to get tattoos.

This is P(X = 1). So

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

[tex]P(X = 1) = C_{6,1}.(0.24)^{1}.(0.76)^{5} = 0.3651[/tex]

0.3651 = 36.51% probability that exactly one of the selected adults says that he or she was too young to get tattoos.

c. Find the probability that the number of selected adults saying they were too young is 0 or 1.

This is:

[tex]p = P(X = 0) + P(X = 1) = 0.1927 + 0.3651 = 0.5578[/tex]

0.5578 = 55.78% probability that the number of selected adults saying they were too young is 0 or 1.

Answer:

The constant is StartFraction 5 over 6 EndFraction

Step-by-step explanation:

StartFraction 5 over 6 EndFraction + one-fourth x minus y

5/6 + 1/4x - y

A. The constant is StartFraction 5 over 6 EndFraction.

True

B. The only coefficient is One-fourth.

False

There are two coefficients: the coefficient of x which is 1/4 and the coefficient of y which is 1

C. The only variable is y

False

There are 2 variables: variable x and variable y

D. The terms StartFraction 5 over 6 EndFraction and One-fourth x are like terms.

False

5/6 and 1/4x are not like terms

The only true statement is: The constant is StartFraction 5 over 6 EndFraction

Answer:

It's A if you don't want to read. A). The constant is 5/6

Step-by-step explanation:

Answer:

The point estimate that should be used in constructing the confidence interval is 3.5.

The 95% confidence interval for the true mean difference between the mean height of the American students and the mean height of the non-American students, in inches, is (2.25, 4.75).

Step-by-step explanation:

Before building the confidence interval, we need to understand the central limit theorem and subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

American students:

Sample of 12, mean height of 68.4 inches with a standard deviation of 1.64 inches. This means that:

[tex]\mu_A = 68.4[/tex]

[tex]s_A = \frac{1.64}{\sqrt{12}} = 0.4743[/tex]

Non-American students:

Sample of 17, mean height of 64.9 inches with a standard deviation of 1.75 inches. This means that:

[tex]\mu_N = 64.9[/tex]

[tex]s_N = \frac{1.75}{\sqrt{17}} = 0.4244[/tex]

Distribution of the difference:

[tex]\mu = \mu_A - \mu_N = 68.4 - 64.9 = 3.5[/tex]

[tex]s = \sqrt{s_A^2+s_N^2} = \sqrt{0.4743^2 + 0.4244^2} = 0.6365[/tex]

The point estimate that should be used in constructing the confidence interval is 3.5.

Confidence interval:

[tex]\mu \pm zs[/tex]

In which

z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].  

The lower bound of the interval is:

[tex]\mu - zs = 3.5 - 1.96*0.6365 = 2.25[/tex]

The upper bound of the interval is:

[tex]\mu + zs = 3.5 + 1.96*0.6365 = 4.75[/tex]

The 95% confidence interval for the true mean difference between the mean height of the American students and the mean height of the non-American students, in inches, is (2.25, 4.75).

Let missing side be x

Using basic proportionality theorem

[tex]\\ \sf\longmapsto \dfrac{45}{35}=\dfrac{x}{56}[/tex]

[tex]\\ \sf\longmapsto \dfrac{9}{7}=\dfrac{x}{56}[/tex]

[tex]\\ \sf\longmapsto 7x=9(56)[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{9(56)}{7}[/tex]

[tex]\\ \sf\longmapsto x=72[/tex]

Answer:

a.5

b.3a+3

Step-by-step explanation:

in a,u need to replace 2 with x,so it will be 4-2+3

in b,replace 3a with x and so it will be6a-3a+3

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Answer:

  1/3

Step-by-step explanation:

The scale factor is the ratio of image lengths to original lengths.

  B'C' = 1 unit

  BC = 3 units

The scale factor is B'C'/BC = 1/3.

_____

Additional comment

The center of dilation in this figure is 3 units below D' on the same vertical line. (It is 1 unit off the bottom of the grid shown.)

Answer:

The score of a person who did better than 85% of all the test-takers was of 624.44.

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.

One year, the average score on the Math SAT was 500 and the standard deviation was 120.

This means that [tex]\mu = 500, \sigma = 120[/tex]

What was the score of a person who did better than 85% of all the test-takers?

The 85th percentile, which is X when Z has a p-value of 0.85, so X when Z = 1.037.

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

[tex]1.037 = \frac{X - 500}{120}[/tex]

[tex]X - 500 = 1.037*120[/tex]

[tex]X = 624.44[/tex]

The score of a person who did better than 85% of all the test-takers was of 624.44.