Find the value of two numbers if their sum is 12 and their difference is 4.

A survey of 35 people was conducted to compare their self-reported height to their actual height. The difference between reporte

Over [174]

Answer:

The test statistic is t = 3.36.

Step-by-step explanation:

You're testing the claim that the mean difference is greater than 0.7.

At the null hypothesis, we test if the mean difference is of 0.7 or less, that is:

$H_0: \mu \leq 0.7$

At the alternate hypothesis, we test if the mean difference is greater than 0.7, that is:

$H_1: \mu > 0.7$

The test statistic is:

$t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}$

In which X is the sample mean, $\mu$ is the value tested at the null hypothesis, s is the standard deviation of the sample and n is the size of the sample.

0.7 is tested at the null hypothesis:

This means that $\mu = 0.7$

A survey of 35 people was conducted to compare their self-reported height to their actual height.

This means that $n = 35$

From the sample, the mean difference was 0.95, with a standard deviation of 0.44.

This means that $X = 0.95, s = 0.44$

Calculate the test statistic

$t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}$

$t = \frac{0.95 - 0.7}{\frac{0.44}{\sqrt{35}}}$

$t = 3.36$

The test statistic is t = 3.36.

3 0

3 years ago

Sierra left $4.50 as a tip for a waiter. THis was 18% of the bull before the tip, How much was her total bill before the tip?

andreyandreev [35.5K]

let's say the bill without the tip is "x" amount, so that'd be the 100% of the bill, but we also know that 4.50 is the 18% of "x".

so if 4.50 is the 18% of "x", how much is "x"?

$\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} 4.50&18\\ x&100 \end{array}\implies \cfrac{4.5}{x}=\cfrac{18}{100}\implies 450=18x \\\\\\ \cfrac{450}{18}=x\implies 25=x$

4 0

3 years ago

Polygon ABCDEF is translated 12 units to the left to create polygon A′B′C′D′E′F′. If DE = 7 units, what is D′E′ ?

gizmo_the_mogwai [7]

A translation is a rigid transformation, which means angle measures and distances from two points do not change.
Polygon ABCDEF is congruent to polygon A'B'C'D'E'F'

DE = D'E' = 7

8 0

3 years ago

Read 2 more answers

Tommy is using a bucket to collect nuts from a nut tree. He then dumps the bucket into a barrel for shipping of the nuts. He not

NISA [10]

Answer:

3/8 bucket

Step-by-step explanation:

Given that 1/4 bucket of nuts fills 2/3 of the barrel

PART A

<u>To find the amount of nuts that fills entire basket we can put this as:</u>

1/4 bucket → 2/3 barrel
x bucket → 1 barrel

<u>Use cross-multiplication to find the value of x:</u>

x×2/3 = 1×1/4
x = 1/4 ÷ 2/3
x = 1/4×3/2
x = 3/8 bucket

PART B

Using the bucket to barrel ratio to solve the problem. Having the number of required buckets as x and considering full barrel as 1 helps to find the value of x.

6 0

3 years ago

Triangle ABC is a scaled copy of triangle DEF. Side AB measures 12 cm and is the longest side of ABC. Side DE measures 8 cm and

evablogger [386]

Answer:

a) 3/2 or 1.5

b) 2/3 or ≈.66

Step-by-step explanation:

AB corresponds to DE because they are both the longest sides of their respective triangles.

a) The scale factor would be what you would multiply 8 by to get 12. 12/8 is 3/2 or 1.5

b) The scale factor would be what you multiply 12 by to get 8. 8/12 is 2/3 or ≈.66

4 0

3 years ago