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3 years ago

6

A gym charges a $20 sign-up fee plus $25 per month. You have a $120 gift card for the gym. When does the total spent on your gy

m membership exceed the amount of your gift card?

2 answers:

vichka [17]3 years ago

7 0

Found this online. Hope it helps

ANEK [815]3 years ago

3 0

4 months........................

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The length of time that an auditor spends reviewing an invoice is approximately normally distributed with a mean of 600 seconds

Bumek [7]

Answer: 11.5%

Explanation:

Since 1 minute = 60 seconds, we multiply 12 minutes by 60 so that 12 minutes = 720 seconds. Thus, we're looking for a probability that the auditor will spend more than 720 seconds.

Now, we get the z-score for 720 seconds by the following formula:

$\text{z-score} = \frac{x - \mu}{\sigma}$

where

$t = \text{time for the auditor to finish his work } = 720 \text{ seconds}
\\ \mu = \text{average time for the auditor to finish his work } = 600 \text{ seconds}
\\ \sigma = \text{standard deviation } = 100 \text{ seconds}$

So, the z-score of 720 seconds is given by:

$\text{z-score} = \frac{x - \mu}{\sigma}
\\
\\ \text{z-score} = \frac{720 - 600}{100}
\\
\\ \boxed{\text{z-score} = 1.2}$

Let

t = time for the auditor to finish his work
z = z-score of time t

Since the time is normally distributed, the probability for t > 720 is the same as the probability for z > 1.2. In terms of equation:

$P(t \ \textgreater \ 720) 
\\ = P(z \ \textgreater \ 1.2)
\\ = 1 - P(z \leq 1.2)
\\ = 1 - 0.885
\\ \boxed{P(t \ \textgreater \ 720) = 0.115}$

Hence, there is 11.5% chance that the auditor will spend more than 12 minutes in an invoice.

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3 years ago

40 and 400 <br>The value of 4 in ___ is______ times the value of 4 in _____

Nat2105 [25]

The value of 4 in the 400 is ten times the value of 4 in the 40's place

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3 years ago

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Find the points of intersection of the lines y= 4x + 1 and y= -2 x + 4

Novosadov [1.4K]

Answer:

use desmos. It really helps!

Step-by-step explanation:

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3 years ago

If t follows a t7 distribution, find t0 such that (a) p(|t | < t0) = .9 and (b) p(t > t0) = .05.

Thepotemich [5.8K]

Answer:

a) $P(-t_o < t_7$

Using the symmetrical property we can write this like this:

$1-2P(t_7$

We can solve for the probability like this:

$2P(t_7$

$P(t_7$

And we can find the value using the following excel code: "=T.INV(0.05,7)"

So on this case the answer would be $t_o =\pm 1.895$

b) For this case we can use the complement rule and we got:

$1-P(t_7$

We can solve for the probability and we got:

$P(t_7$

And we can use the following excel code to find the value"=T.INV(0.95;7)"

And the answer would be $t_o = 1.895$

Step-by-step explanation:

Previous concepts

The t distribution (Student’s t-distribution) is a "probability distribution that is used to estimate population parameters when the sample size is small (n<30) or when the population variance is unknown".

The shape of the t distribution is determined by its degrees of freedom and when the degrees of freedom increase the t distirbution becomes a normal distribution approximately.

The degrees of freedom represent "the number of independent observations in a set of data. For example if we estimate a mean score from a single sample, the number of independent observations would be equal to the sample size minus one."

Solution to the problem

For this case we know that $t \sim t(df=7)$

And we want to find:

Part a

$P(|t|$

We can rewrite the expression using properties for the absolute value like this:

$P(-t_o < t_7$

Using the symmetrical property we can write this like this:

$1-2P(t_7$

We can solve for the probability like this:

$2P(t_7$

$P(t_7$

And we can find the value using the following excel code: "=T.INV(0.05,7)"

So on this case the answer would be $t_o =\pm 1.895$

Part b

$P(t>t_o) =0.05$

For this case we can use the complement rule and we got:

$1-P(t_7$

We can solve for the probability and we got:

$P(t_7$

And we can use the following excel code to find the value"=T.INV(0.95;7)"

And the answer would be $t_o = 1.895$

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3 years ago

What is the approximate volume of a sphere with a radius of 6 cm? Use 3.14 to approximate pi and express your answer in hundredt

ikadub [295]

I think the answer is 1286.22

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3 years ago

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