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3 years ago

Describe a real world situation that can be modeled by the equation 8.35x=4.25x+36.90

1 answer:

3 0

Lets reduce the equation.

8.35x = 4.25x + 36.90
8.35x - 4.25x = 36.90
4.10x = 36.90

X = 9

1 bag a of assorted fruit cost $4.10 how much will it cost if I want to buy 9 bags of assorted fruit.

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3 years ago

Stephanie was doing a science experiment to see what brand of cereal with raisins

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3 years ago

Quick Start Company makes a 12-volt car batteries. After many years of product testing, the company knows the average life of a

Ghella [55]

Answer:

The company will expect to replace 13.03% of batteries.

The company should guarantee the batteries for 35 months.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

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 pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

$\mu = 45, \sigma = 8$

If Quick start guarantees a full refund on any battery that fails within the 36 month period after purchase, what percentage of its batteries will the company expect to replace?

This is the pvalue of Z when X = 36. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{36 - 45}{8}$

$Z = -1.125$

$Z = -1.125$ has a pvalue of 0.1303.

The company will expect to replace 13.03% of batteries.

If quick Start does not want to make refunds for more than 10% ofits batteries under the full refund guarantee policy, for how longshould the company guarantee the batteries

They should guarantee to the 10th percentile, which is X when Z has a pvalue of 0.1. So it is X when Z = -1.28.

$Z = \frac{X - \mu}{\sigma}$

$-1.28 = \frac{X - 45}{8}$

$X - 45 = -1.28*8$

$X = 34.76$

Rounding to the nearest month

The company should guarantee the batteries for 35 months.

4 0

3 years ago

Solve 8sin(pi/6 x) = 4 for the four smallest positive solutions

ryzh [129]

Simplify the given expression as shown below

$\begin{gathered} 8sin(\frac{\pi}{6}x)=4 \\ \Rightarrow sin(\frac{\pi}{6}x)=\frac{4}{8}=\frac{1}{2} \\ \Rightarrow sin(\frac{\pi}{6}x)=\frac{1}{2} \end{gathered}$

On the other hand,

$\begin{gathered} sin(y)=\frac{1}{2} \\ \end{gathered}$

Solving for y using the special triangle shown below

Thus,

$\begin{gathered} \Rightarrow y=30\degree\pm360\degree n=\frac{\pi}{6}\pm2\pi n \\ and \\ y=150\degree+360\degree n=\frac{5\pi}{6}+2\pi n \end{gathered}$

Then,

$\begin{gathered} \Rightarrow\frac{\pi}{6}x=y \\ \Rightarrow\frac{\pi}{6}x=\frac{\pi}{6}+2\pi n \\ \Rightarrow x=1+12n \\ and \\ \frac{\pi}{6}x=\frac{5\pi}{6}+2\pi n \\ \Rightarrow x=5+12n \end{gathered}$

The two sets of solutions are

$x=1+12n,5+12n$ <h2>Then, the four smallest positive solutions are</h2> $\Rightarrow x=1,5,13,17$ <h2>The answers are 1,5,13,17</h2>

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1 year ago

Question 13 and 14 and 15

erik [133]

If you know the rules, you don't actually have to graph these to check if they're perpendicular, parallel, or neither.

parallel slopes are the same
perpendicular slopes are the opposite reciprocals
"neither" slopes fall into neither category

you should still follow directions and graph them if your teacher expects it, but with that knowledge:
13. y = 4x+7 and y = (-1/4)x-3
the slopes here, 4 and -1/4, are opposite reciprocals, so these lines are perpendicular

14. y = 3x-4 and y = 3x+1
the slopes here, 3 and 3, are the same, so these lines are parallel

15. y = x+5 and y = -5x-1
the slopes here, 1 and -5, have no relation in this case, so these lines are neither

3 0

3 years ago