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andrezito [222]
3 years ago
12

Keith ran in a marathon. It took him 3 hours and 2 minutes to run 26 miles. If he ran at the same rate for the whole race, how m

any minutes did it take him to run each mile? (1 hour = 60 minutes)
A.) 6 minutes


B.) 7 minutes


C.) 8 minutes


D.) 9 minutes
Mathematics
1 answer:
Lynna [10]3 years ago
5 0
Distance Keith ran = 26 miles

Time it took
= 3 hours 2 minutes = [(3 * 60) + 2] minutes = (180 + 2) minutes = 182 minutes

Hence, 

Speed (Rate) = \frac{Distance}{Time} =  \frac{26}{182} =  \frac{13}{91} =  \frac{1}{7} miles per minute

Hence,

Time taken to complete 1 mile
= \frac{Distance}{Speed} =  \frac{1}{ \frac{1}{7} } = 1 *  \frac{7}{1}
= 7 minutes 

Hence, the answer is B.
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$6000 are invested in a bank account at an interest rate of 10 percent per year.
Licemer1 [7]

The amount for the investment of $6000 will be a.$6369  b. $6090  and c.$6030.

<h3>What is compound interest?</h3>

Compound interest is the interest levied on the interest. The formula for the calculation of compound interest is given as:-

A=P[1+\dfrac{r}{n}]^{nt}

a) The amount in the bank after 6 years if interest is compounded annually.

A=P[1+\dfrac{r}{1}]^{t}\\\\\\A=6000[1+\dfrac{0.01}{1}]^{  6}

A= $6369

b) The amount in the bank after 6 years if interest is compounded quarterly.

A=P[1+\dfrac{r}{4}]^{4t}\\\\\\A=6000[1+\dfrac{0.01}{4}]^{4\times 6}

A= $6090

c ) The amount in the bank after 6 years if interest is compounded monthly.

A=P[1+\dfrac{r}{12}]^{4t}\\\\\\A=6000[1+\dfrac{0.01}{12}]^{12\times 6}

A=$6030

Hence the amount for the investment of $6000 will be a.$6369  b. $6090  and c.$6030.

To know more about Compound interest follow

brainly.com/question/24924853

#SPJ1

7 0
2 years ago
Of those women who are diagnosed to have early-stage breast cancer, one-third eventually die of the disease. Suppose a screening
Finger [1]

Answer:

A) Alternative hypothesis; Ha: p_o > ⅔

B) Null hypothesis;

H0: p_o = ⅔

C) There is sufficient evidence to support the claim that the community screening programme was effective

D) p-value = 0

Its less than the significance value and so we will reject the null hypothesis and conclude that the community screening programme was effective

Step-by-step explanation:

A) We are told that ⅓ of those diagnosed eventually die of the disease. Thus, ⅔ is the fraction that will survive the disease.

Thus, the null hypothesis is;

H0: p_o = ⅔

We are told that a screening programme was started to increase the survival rate. Thus,the alternative hypothesis is;

Ha: p_o > ⅔

B) null hypothesis is;

H0: p_o = ⅔

C) 164 out of the 200 women selected survived the disease.

Thus sample proportion is;

p^ = 164/200

p^ = 0.82

For the z-score value, we will use the formula;

z = (p^ - p_o)/√((p_o(1 - p_o)/n)

Now, p_o = ⅔ = 0.67

Thus;

z = (0.82 - 0.67)/√((0.67(1 - 0.67)/200)

z = 4.51

From online p-value from z-score calculator, we have p-value ≈ 0

This is less than the significant level of 0.05 and therefore we will reject the null hypothesis and conclude that the community screening program was effective.

D) p-value ≈ 0

Reject the null hypothesis

4 0
2 years ago
The absolute value function, f(x) = –|x| – 3, is shown.
Elanso [62]

Answer: D. all real numbers less than or equal to –3

5 0
3 years ago
Question 3 of 10 What is the solution to this equation? 4(x-8) + 10 = -10 O A. x= 3 OB. x = 5 O c. x=2 O D. x= 4​
krek1111 [17]

Answer:

O A. x = 3

Step-by-step explanation:

4(x - 8) + 10 = -10

4x - 32 + 10 = -10

4x = 12

x = 3

5 0
2 years ago
Marco has drawn a line to represent the perpendicular cross-section of the triangular prism. Is he correct? Explain. triangular
evablogger [386]

Answer:

The correct option is;

Yes, the line should be perpendicular to one of the rectangular faces

Step-by-step explanation:

The given information are;

A triangular prism lying on a rectangular base and a line drawn along the slant height

A perpendicular bisector should therefore be perpendicular with reference to the base of the triangular prism such that the cross section will be congruent to the triangular faces

Therefore Marco is correct and the correct option is yes, the line should be perpendicular to one of the rectangular faces (the face the prism is lying on).

8 0
2 years ago
Read 2 more answers
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