The sum of two consecutive Integers is 123. What is the smallest of the two integers?

A survey of Massachusetts high school students showed that the mean number of hours these students reported watching crime TV sh

masha68 [24]

Answer:

a) $Z = -0.5$

b) $Z = 1.5$

c) 93.32% of students watch less than 3.6 hours of shows a week

d) 62.57% of the sample watches between 2 hours and 3.6 hours of crime shows a week

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 problem, we have that:

$\mu = 2.4, \sigma = 0.8$

a. Find the z-score for a student who reported watching 2 hours of crime shows a week.

This is Z when X = 2. So

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

$Z = \frac{2 - 2.4}{0.8}$

$Z = -0.5$

b. Find the z-score for a student who reported watching 3.6 hours of crime shows a week

X = 3.6. So

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

$Z = \frac{3.6 - 2.4}{0.8}$

$Z = 1.5$

c. What percentage of students watch less than 3.6 hours of shows a week?

pvalue of Z when X = 3.6.

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

$Z = \frac{3.6 - 2.4}{0.8}$

$Z = 1.5$

$Z = 1.5$ has a pvalue of 0.9332

93.32% of students watch less than 3.6 hours of shows a week

d. What percentage of the sample watches between 2 hours and 3.6 hours of crime shows a week?

pvalue of Z when X = 3.6 subtracted by the pvalue of Z when X = 2.

X = 3.6

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

$Z = \frac{3.6 - 2.4}{0.8}$

$Z = 1.5$

$Z = 1.5$ has a pvalue of 0.9332

X = 2

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

$Z = \frac{2 - 2.4}{0.8}$

$Z = -0.5$

$Z = -0.5$ has a pvalue of 0.3075

0.9332 - 0.3075 = 0.6257

62.57% of the sample watches between 2 hours and 3.6 hours of crime shows a week

7 0

3 years ago

Define a variable and write an equation to model each situation. Then solve. Show your work. Tickets to the county fair for four

Citrus2011 [14]

If x is the childrens ticket
$4(x + 1.5) + 5x = 33.30 \\ 4x + 6 + 5x = 33.3 \\ 9x = 33.3 - 6 \\ 9x = 27.3 \\ x = \frac{27.3}{6} \\ x = 4.55$
so that means that the adults ticket is
$x + 1.50 = 4.55 + 1.50 = 6.05$

4 0

4 years ago

Alan wants to buy a bike that has a regular price of $169. This week the bike is on sale at a 35% discount.

sammy [17]

Answer:

Alan can buy the bike for $109.85

Step-by-step explanation:

Start with 100% and subtract the 35% discount. This results in 65%. The bike sells for 65% of $169, which is calculated as follows:

0.65($169) = $109.85

Alan can buy the bike for $109.85 under the terms of this sale.

6 0

3 years ago

Find the area of the surface. The surface with parametric equations x = u2, y = uv, z = 1 2 v2, 0 ≤ u ≤ 2, 0 ≤ v ≤ 1.

ehidna [41]

Answer:

Area = 32/3

Step-by-step explanation:

x = u ²

y = uv

z = 12v ²

0 ≤ u ≤ 2

0 ≤ v ≤ 1

Since ru = <2u, v, 0> and rv = <0, u, 24v>, we have

Where ru is the differentiation of x, y, z with respect to u and rv is the differentiation of x, y, z wit respect to v.

we find the cross product of ru and rv

ru × rv = 24v²i - 48uv²j + 2u²k

absolute value of ru × rv = 2u² + 24v²

We can now find the area

∫₀² du ∫₀¹ dv (2u² + 24v²) = ∫₀² du [2u²v + 8v³]₀¹ = 32/3

Detailed description can be found in the attachment

5 0

3 years ago

Read 2 more answers

Elizabeth has $10, $5, and $1 bills worth $101. she has five more five dollar bills than ten dollar bills and 4 times more 1 dol

vesna_86 [32]

Let x be number of $10 dollar bills

Let y be number of $5 dollar bills

Let z be number of $1 dollar bills

From the question, we can come up with three equations (so we can find the values of x, y & z) :

10x + 5y + z = 101
y - x = 5
z = 4x

The first equation comes from finding the total money Elizabeth has, which is $101.

The second equation comes from value of y (number of $5 bills) is more than value of x (number of $10 bills) by 5 dollars.

The third equation comes from the value of z (number of $1 bills) being 4 times more than the value of x (number of $10 bills).

Now, we will begin to find the value of x, y & z.

From the first equation,

10x + 5y + z = 101

Substitute the third equation (z = 4x) into z:

10x + 5y + 4x = 101

Simplify this and you get,

14x + 5y = 101

Now, we use the second equation. The second equation is y - x = 5. If we try to make y as the subject, it becomes y = 5 + x.

Now, substitute this into the value of y of the last working we did:

14x + 5(5+x) = 101

Simplify that and it becomes:

x = 4

Then, substitute this value of x into the second and third equations to find y and z.

y - x = 5

y - 4 = 5

y = 9

z = 4x

z = 4(4)

z = 16

Finally, let's check these answers by substituting them into the first equation to try and see if the total value is <em>really</em> $101.

10x + 5y + z = 10(4) + 5(9) + 16

10x + 5y + z = 40 + 45 + 16

10x + 5y + z = 101

Thus, our answers are correct. Elizabeth has FOUR $10 bills, NINE $5 bills and SIXTEEN $1 bills.

6 0

3 years ago

Read 2 more answers