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Katena32 [7]
2 years ago
8

1

Mathematics
1 answer:
KIM [24]2 years ago
3 0

Answer:

-3

Step-by-step explanation:

Perpendicular slopes are always the opposite reciprocal of the original slope.

opposite= flip it

EX: 2→1/2, 1/4→4

reciprocal=change the sign

EX: 2→-2, 1/4→-1/4

So...

1/3→-3

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At a large university, the mean amount spent by students for cell phone service is $58.90 per month with a standard deviation of
zhenek [66]

Answer:

2.28% probability that the mean amount of their monthly cell phone bills is more than $60

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are 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.

Central Limit Theorem

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

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

In this problem, we have that:

\mu = 58.90, \sigma = 3.64, n = 44, s = \frac{3.64}{\sqrt{44}} = 0.54875

What is the probability that the mean amount of their monthly cell phone bills is more than $60?

This is 1 subtracted by the pvalue of Z when X = 60. So

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

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{60 - 58.90}{0.54875}

Z = 2

Z = 2 has a pvalue of 0.9772

1 - 0.9772 = 0.0228

2.28% probability that the mean amount of their monthly cell phone bills is more than $60

4 0
3 years ago
Liam bought a comic book and had $5 left. If he had a total of $8 walking into the store, how much did he spend on the comic boo
laiz [17]

Answer: The comic book was $3.

Step-by-step explanation:

Instead of 5x=8, it should have been 5+x=8 because he only purchased a single comic book. Subtract 5 from 8 and your X value is 3.

7 0
3 years ago
Read 2 more answers
The value of the cumulative standardized normal distribution at z is 0.8770. what is the value of​ z?
Vinvika [58]
<span>The value of z is 0.8770. This answer was derived from information in the question, which states that the value of z is 0.8770. Granted, I don't understand what is meant by "cumulative standardized normal distribution." I only passed statistics because the professor felt sorry for me.</span>
4 0
3 years ago
Read 2 more answers
A bridge constructed over a bayou has a supporting arch in the shape of an inverted parabola. Find the equation of the parabolic
babymother [125]

Answer: f(x) = -0.016x² + 1.6x

Step-by-step explanation:

If the lenght of the road over the arch is 100m, we can consider a coordinate plane and say that the road starts at point (0,0) and finishes at (100,0). The vertice of the parabola is at point (50,40), because the maximum height is 40 and it is always in the middle point of the roots.

So, we have

(0,0) (50,40) (100,0)

A quadratic function is always on the form: f(x) = ax² + bx + c

0 = a0² + b0 + c

40 = a50² + b50 + c

0 = a100² + b100 + c

0 = a0² + b0 + c → c = 0 ∴

40 = a50² + b50

0 = a100² + b100

_________________________

2500a + 50b = 40 (*2)

10000a + 100b = 0

_________________________

5000a + 100b = 80

10000a + 100b = 0 (-)

__________________________

-5000a = 80

-a=80/5000

a=-0.016

∴

2500a + 50b = 40

2500.(-0.016) + 50b = 40

-40 + 50b = 40

50b = 80

b = 80/50

b = 1.6

This way f(x) = -0.016x² + 1.6x

6 0
3 years ago
Plz help !!!!!!!! A rectangular park is 400 m long and 200 m wide. If you walked around the park twice, how far would you walk?
aliina [53]

Answer:

160,000

Step-by-step explanation:

400 * 200 is 80,000 just walking around once, so then multiply it by two.

80,000 * 2 is 160,000

4 0
3 years ago
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