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3 years ago

15

A wholesale novelty shop sells some embroidered scarves for $12 each and others for $15 each. A customer pays $234 for 17 scarve

s. How many scarves at each price did she buy?
she bought ___ $12 and ___ $15 scarves

1 answer:

Ann [662]3 years ago

5 0

She bought 7 $12 and 10 $15 scarves

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If h(x) is the inverse of f(x), what is the value of h(f(x))?

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Hello,

f(x) has as inverse f^(-1)(x)
and (fof^(-1))(x)=(f^(-1)of)(x)= x (the neutral function)
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A fishing boat was out to sea for 6 months and traveled a total of 8,578 miles. In the first month, the boat traveled 659 miles.

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Solve 5x^2 − 3x + 17 = 9.

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Answer:

The roots of the equation are x = $\frac{3+\sqrt{151}i}{10}$ and x = $\frac{3-\sqrt{151}i}{10}$

and there are no real roots of the equation given above

Step-by-step explanation:

To solve:

5x² − 3x + 17 = 9

or

⇒ 5x² − 3x + 17 - 9 = 0

or

⇒ 5x² − 3x + 8 = 0

Now,

the roots of the equation in the form ax² + bx + c = 0 is given as:

x = $\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

in the above given equation

a = 5

b = -3

c = 8

therefore,

x = $\frac{-(-3)\pm\sqrt{(-3)^2-4\times5\times8}}{2\times5}$

or

x = $\frac{3\pm\sqrt{9-160}}{10}$

or

x = $\frac{3+\sqrt{-151}}{10}$ and x = $\frac{3-\sqrt{-151}}{10}$

or

x = $\frac{3+\sqrt{151}i}{10}$ and x = $\frac{3-\sqrt{151}i}{10}$

here i = √(-1)

Hence,

The roots of the equation are x = $\frac{3+\sqrt{151}i}{10}$ and x = $\frac{3-\sqrt{151}i}{10}$

and there are no real roots of the equation given above

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3 years ago

How do I simplify 6y-y

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4 years ago

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The mean finish time for a yearly amateur auto race was 186.32 minutes with a standard deviation of 0.305 minute. The winning c

uranmaximum [27]

Complete Question

The mean finish time for a yearly amateur auto race was 186.94 minutes with a standard deviation of 0.305 minute. The winning car, driven by Roger, finished in 185.85 minutes. The previous year's race had a mean finishing time of 110.7 with a standard deviation of 0.115 minute. The winning car that year, driven by Karen, finished in 110.48 minutes.

Find their respective z-scores.

Who had the more convincing victory?

A. Roger had a more convincing victory because of a higher z-score.

B. Karen a more convincing victory because of a higher z-score.

C. Roger had a more convincing victory, because of a lower z-score.

D. Karen a more convincing victory because of a lower z-score.

Answer:

The correct option is D

Step-by-step explanation:

From the question we are told that

The mean of the current year is $\mu_c = 186.32 \ minutes$

The standard deviation is $\sigma_c = 0.305 \ minutes$

The time taken by the winning car for the current year is $x = 185.85 \ minutes$

The mean of the previous year is $\mu_p = 110.7 \ minutes$

The standard deviation the previous year is $\sigma_p = 0.115 \ minutes$

The time taken by the winning car for the previous year is $y = 110.48 \ minutes$

Generally the z-score for current year is mathematically evaluated as

$z_c = \frac{x- \mu_c}{\sigma_c }$

=> $z_c = \frac{ 185.85- 186.32}{0.305 }$

=> $z_c = -1.536$

Generally the z-score for previous year is mathematically evaluated as

$z_p = \frac{y- \mu_p}{\sigma_p }$

=> $z_p = \frac{ 110.48-110.7}{0.115 }$

=> $z_p = -1.913$

From the value obtained we see that $z_p < z_c$ , Hence Karen had a more convincing victory because of the lower z -score.

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3 years ago