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3/4 yard long and 1/2 yard tall what is the area of the poster frame

zmey [24]

The area is 3/8 yd².

Area = length x width

Given:
length = 3/4 yard
width = 1/2 yard

Area = 3/4 yd * 1/2 yd
Area = 3*1/4*2
Area = 3/8 yd²

In multiplying fractions, multiply the numerators, then, multiply the denominators. lastly, simplify the fraction. 3/8 yd² is already in its simplest form.

3 0

4 years ago

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Quadrilateral ABCD is dilated by a scale factor of 1 over 3 centered around (1, 2).

Ostrovityanka [42]

9514 1404 393

Answer:

B'D' ║ BD and will be shorter than segment BD.

Step-by-step explanation:

A scale factor of 1/3 means all image segments are 1/3 the length of the preimage segments (that is, <em>shorter</em>).

Image segments not on a line through point A(1, 2) will be parallel to the preimage segments.

For this dilation, ...

segment B prime D prime will be parallel to segment BD and will be shorter than segment BD.

8 0

3 years ago

An auto company claims that the fuel efficiency of its sedan has been substantially improved. A consumer advocate organization w

zzz [600]

Answer:

$t=\frac{\bar d -0}{\frac{s_d}{\sqrt{n}}}=\frac{0.983 -0}{\frac{1.685}{\sqrt{12}}}=2.021$

$df=n-1=12-1=11$

$p_v =P(t_{(11)}>2.021) =0.0342$

If we compare the the p value with the significance level provided $\alpha=0.1$ , we see that $p_v < \alpha$ , so then we can reject the null hypothesis. and there is a significant increase in the miles per gallon from 2017 to 2019 at 10% of significance.

Step-by-step explanation:

Previous concepts

A paired t-test is used to compare two population means where you have two samples in which observations in one sample can be paired with observations in the other sample. For example if we have Before-and-after observations (This problem) we can use it.

Let put some notation :

x=test value 2017 , y = test value 2019

x: 28.7 32.1 29.6 30.5 31.9 30.9 32.3 33.1 29.6 30.8 31.1 31.6

y: 31.1 32.4 31.3 33.5 31.7 32.0 31.8 29.9 31.0 32.8 32.7 33.8

Solution to the problem

The system of hypothesis for this case are:

Null hypothesis: $\mu_y- \mu_x \leq 0$

Alternative hypothesis: $\mu_y -\mu_x >0$

Because if we have an improvement we expect that the values for 2019 would be higher compared with the values for 2017

The first step is calculate the difference $d_i=y_i-x_i$ and we obtain this:

d: 2.4, 0.3, 1.7,3,-0.2, 1.1, -0.5, -3.2, 1.4, 2, 1.6, 2.2

The second step is calculate the mean difference

$\bar d= \frac{\sum_{i=1}^n d_i}{n}= \frac{11.8}{12}=0.983$

The third step would be calculate the standard deviation for the differences, and we got:

$s_d =\frac{\sum_{i=1}^n (d_i -\bar d)^2}{n-1} =1.685$

We assume that the true difference follows a normal distribution. The 4th step is calculate the statistic given by :

$t=\frac{\bar d -0}{\frac{s_d}{\sqrt{n}}}=\frac{0.983 -0}{\frac{1.685}{\sqrt{12}}}=2.021$

The next step is calculate the degrees of freedom given by:

$df=n-1=12-1=11$

Now we can calculate the p value, since we have a right tailed test the p value is given by:

$p_v =P(t_{(11)}>2.021) =0.0342$

If we compare the the p value with the significance level provided $\alpha=0.1$ , we see that $p_v < \alpha$ , so then we can reject the null hypothesis. and there is a significant increase in the miles per gallon from 2017 to 2019 at 10% of significance.

4 0

3 years ago

What is the difference quotient of the function f(x)=12^x+1 ?

seraphim [82]

Answer:

The Answer is D or 12^x+1 (12^h - 1) / h

Step-by-step explanation:

3 0

3 years ago

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Sophie earns a salary of $600per month for working 5hours a day. In May, Sophie worked additional hours at $8per hour and earned

Setler [38]

Answer: equation = $600 + tx$8 = $640 ; t = 5 additional hours in May

Step-by-step explanation:

Equation = $600 + tx$8/hour = $640

t = ($640 - $600)/$8/hour

t = $40/$8/hour = 5 hours

Answer: Equation = $600 + tx$8 = $640 ; t = 5 additional hours in May

<h2><em>Spymore</em></h2>

6 0

3 years ago