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3 years ago

There are 12 runners in a race. In how many ways can these runners place first , second, and third?

Mathematics

2 answers:

lisov135 [29]3 years ago

5 0

The correct answer should be B

bonufazy [111]3 years ago

3 0

Answer is C 220. because there are 12 runners

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Find the missing side lengths. leave your answers as radicals in simplest form.

Murrr4er [49]

Answer:

x = 4 , y = 2

Step-by-step explanation:

Using the sine / tangent ratios in the right triangle and the exact values

sin60° = $\frac{\sqrt{3} }{2}$ and tan60° = $\sqrt{3}$ , then

sin60° = $\frac{opposite}{hypotenuse}$ = $\frac{2\sqrt{3} }{x}$ = $\frac{\sqrt{3} }{2}$ ( cross- multiply )

x $\sqrt{3}$ = 4 $\sqrt{3}$ ( divide both sides by $\sqrt{3}$ )

x = 4

and

tan60° = $\frac{opposite}{adjacent}$ = $\frac{2\sqrt{3} }{y}$ = $\sqrt{3}$ ( multiply both sides by y )

y $\sqrt{3}$ = 2 $\sqrt{3}$ ( divide both sides by $\sqrt{3}$ )

y = 2

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2 years ago

Which of the following p-values will lead us to reject the null hypothesis if thelevel of significance equals 0.05?a.0.15b.0.10c

Ipatiy [6.2K]

Answer: 0.025

Step-by-step explanation: we reject null hypothesis if p<0.05

8 0

3 years ago

Solve y=f(x) for x. Then find the input when the output is -3.

DochEvi [55]

Answer:

Please check the explanation

Step-by-step explanation:

Given the function

$f\left(x\right)\:=\:\left(x-5\right)^3-1$

Given that the output = -3

i.e. y = -3

now substituting the value y=-3 and solve for x to determine the input 'x'

$\:\:y=\:\left(x-5\right)^3-1$

$-3\:=\:\left(x-5\right)^3-1\:\:\:$

switch sides

$\left(x-5\right)^3-1=-3$

Add 1 to both sides

$\left(x-5\right)^3-1+1=-3+1$

$\left(x-5\right)^3=-2$

$\mathrm{For\:}g^3\left(x\right)=f\left(a\right)\mathrm{\:the\:solutions\:are\:}g\left(x\right)=\sqrt[3]{f\left(a\right)},\:\sqrt[3]{f\left(a\right)}\frac{-1-\sqrt{3}i}{2},\:\sqrt[3]{f\left(a\right)}\frac{-1+\sqrt{3}i}{2}$

Thus, the input values are:

$x=-\sqrt[3]{2}+5,\:x=\frac{\sqrt[3]{2}\left(1+5\cdot \:2^{\frac{2}{3}}\right)}{2}-i\frac{\sqrt[3]{2}\sqrt{3}}{2},\:x=\frac{\sqrt[3]{2}\left(1+5\cdot \:2^{\frac{2}{3}}\right)}{2}+i\frac{\sqrt[3]{2}\sqrt{3}}{2}$

And the real input is:

$x=-\sqrt[3]{2}+5$

$x=3.74$

4 0

2 years ago

Which equation can be used to find the value of b if side a measures 8.7 cm? 8.7 + b = 54.6 17.4 + b = 54.6 26.1 + b = 54.6 34.8

Gnom [1K]

The correct equation is 8.7 + b = 54.6
because it is given that measure of side a is 8.7cm, in all other equations the values of a is different.
from the first equation we can find the value of b, that is
b = 54.6 - 8.7 = 45.9
so, value of b is 45.9cm

5 0

3 years ago

Suppose management could improve the process by reducing the mean time required for an oil change (but keeping the standard devi

Alja [10]

This question is incomplete, the complete question is;

The owners of Spiffy Lube want to offer their customers a 10-minute guarantee on their standard oil change service. If the oil change takes longer than 10 minutes to complete, the customers is given a coupon for a free oil change at the next visit. Based on past history, the owners believe that the timer required to complete an oil change has a normal distribution with a mean of 8.6 minutes and a standard deviation of 1.2 minutes.

Suppose management could improve the process by reducing the mean time required for an oil change (but keeping the standard deviation the same). How much change in the mean service time would be required to allow for a 10-minute guarantee that gives a coupon to no more than 1 out of every 25 customers on average

Answer:

Required change in the mean service time is 7.8988

Step-by-step explanation:

Given the data in the question;

How much change in the mean service time would be required to allow for a 10-minute guarantee that gives a coupon to no more than 1 out of every 25 customers on average

let mean = μ

p( x > 10 ) ≤ (1/25)

p( x > 10 ) ≤ 0.4

p( x-μ / 1.2 > 10-μ / 1.2 ) ≤ 0.4

(10-μ / 1.2 ) ≤ 0.4

(10-μ / 1.2 ) ≥ $q_{norm}$ ( 0.96 )

(10-μ / 1.2 ≥ 1.751

10-μ = ≥ 1.751 × 1.2

10-μ ≤ 2.1012

μ ≤ 10 - 2.1012

μ ≤ 7.8988

Therefore, required change in the mean service time is 7.8988

8 0

3 years ago