The city's budget is 8,000,000. the city actually spends 12,000,000 what is the city's deficit

In buffalo new York the temperature was -14 Fahrenheit in the morning. if the temperature dropped 7F and then rose 9 what is the

lutik1710 [3]

14-7= -7 Fahrenheit + 9 = 2 fahrenheit

4 0

3 years ago

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You want to obtain a sample to estimate how much parents spend on their kids birthday parties. Based on previous study, you beli

zhuklara [117]

Answer:

We need to sample at least 1069 parents.

Step-by-step explanation:

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1-0.9}{2} = 0.05$

Now, we have to find z in the Ztable as such z has a pvalue of $1-\alpha$ .

So it is z with a pvalue of $1-0.05 = 0.95$ , so $z = 1.645$

Now, find the margin of error M as such

$M = z*\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

How many parents do you have to sample?

We need to sample at least n parents.

n is found when $M = 4, \sigma = 79.5$ . So

$M = z*\frac{\sigma}{\sqrt{n}}$

$4 = 1.645*\frac{79.5}{\sqrt{n}}$

$4\sqrt{n} = 1.645*79.5$

$\sqrt{n} = \frac{1.645*79.5}{4}$

$(\sqrt{n})^{2} = (\frac{1.645*79.5}{4})^{2}$

$n = 1068.92$

Rounding up

We need to sample at least 1069 parents.

6 0

3 years ago

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Determine the value of x which satisfies the following equation. <br> ln(4x+1)=6

Anika [276]

Answer:

Not Determinable

Step-by-step explanation:

Simplifying

Ln(4x + 1) = 6

Reorder the terms:

nL(1 + 4x) = 6

(1 * nL + 4x * nL) = 6

(1nL + 4nxL) = 6

Solving

1nL + 4nxL = 6

Solving for variable 'n'.

Move all terms containing n to the left, all other terms to the right.

Reorder the terms:

-6 + 1nL + 4nxL = 6 + -6

Combine like terms: 6 + -6 = 0

-6 + 1nL + 4nxL = 0

The solution to this equation could not be determined.

6 0

4 years ago

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What is the estimate for 23 3/8

Bumek [7]

23 x 8 = 184

184 + 3 = 187 = 187/8

187 / 8 = 23 3/8

Answer: 187/8

8 0

3 years ago

The amount of time that people spend at Grover Hot Springs Spa is normally distributed with a mean of 63 minutes and a standard

PtichkaEL [24]

Answer:

a) $X \sim N(63,18)$

Where $\mu=63$ and $\sigma=18$

b) $P(X>90)=P(\frac{X-\mu}{\sigma}>\frac{90-\mu}{\sigma})=P(Z>\frac{90-63}{18})=P(Z>1.5)$

And we can find this probability using the complement rule and with the normal standard table or excel:

$P(Z>1.5)=1-P(Z$

c) $P(X$

$P(Z$

d) $P(60$

$P(-0.167$

e) IQR = 75.13-50.87=24.26

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Part a

Let X the random variable that represent the amount of time that people spend at Grover Hot Springs of a population, and for this case we know the distribution for X is given by:

$X \sim N(63,18)$

Where $\mu=63$ and $\sigma=18$

Part b

We are interested on this probability

$P(X>90)$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

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

If we apply this formula to our probability we got this:

$P(X>90)=P(\frac{X-\mu}{\sigma}>\frac{90-\mu}{\sigma})=P(Z>\frac{90-63}{18})=P(Z>1.5)$

And we can find this probability using the complement rule and with the normal standard table or excel:

$P(Z>1.5)=1-P(Z$

Part c

We are interested on this probability

$P(X$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

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

If we apply this formula to our probability we got this:

$P(X$

And we can find this probability using the normal standard table or excel:

$P(Z$

Part d

If we apply this formula to our probability we got this:

$P(60$

And we can find this probability with this difference:

$P(-0.167$

And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.

$P(-0.167$

Part e

Q1

For this part we want to find a value a, such that we satisfy this condition:

$P(X>a)=0.75$ (a)

$P(X$ (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.

As we can see on the figure attached the z value that satisfy the condition with 0.25 of the area on the left and 0.75 of the area on the right it's z=-0.674. On this case P(Z<-0.674)=0.25 and P(z>-0.674)=0.75

If we use condition (b) from previous we have this:

$P(X$