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3 years ago

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A square on the coordinate plane has vertices at (−2, 2), (2, 2), (2, −2), and (−2, −2). A dilation of the square has vertices a

t (−4, 4), (4, 4), (4, −4), and (−4, −4). Find the scale factor and the perimeter of each square.

2 answers:

shepuryov [24]3 years ago

8 0

It a sqaure dude come on

Alla [95]3 years ago

7 0

The smaller square has length of 4. So its perimeter is 4*4 = 16
The larger square has length of 8 and its perimeter is 8*4 = 32

The scale factor is 2. Since the larger square is twice the size of the smaller square (Or you can say that the scale factor is 1/2 if you are looking at the perspective of the larger square to the smaller square).

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A cylinder’s radius is reduced to 2004-06-01-04-00_files/i0480001.jpg its original size and the height is quadrupled. How has th

asambeis [7]

I can't answer this question if we don't know by what scale the cylinder's radius was reduced. Luckily, I found the same problem that says the radius was reduced to 2/5. So, we find the ratio of both volumes.

V₁ = πr₁²h₁
V₂ = πr₂²h₂

where r₂ = 2/5*r₁ and h₂ = 4h₁

V₂/V₁ = π(2/5*r₁ )²(4h₁)/πr₁²h₁= 8/5 or 1.6

<em>Thus, the volume has increased more by 60%.</em>

6 0

3 years ago

If a metal sheet is 1.2mm thick how must be put together to have thickness of 1.44 cm

dedylja [7]

First convert 1.2mm to cm

10mm = 1cm

so 1.2mm = 0.12cm

Then divide 1.44cm by 0.12cm
that equals to 12.

so you need 12 sheets to make it 1.44cm

6 0

3 years ago

The Damon family owns a large grape vineyard in western New York along Lake Erie. The grapevines must be sprayed at the beginnin

vazorg [7]

Answer:

$z=\frac{0.0955-0.0611}{\sqrt{0.08(1-0.08)(\frac{1}{440}+\frac{1}{360})}}=1.784$

$p_v =2*P(Z>1.784) =0.074$

Comparing the p value with the significance level given $\alpha=0.1$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can say that the two proportions differes at 10% of significance.

Step-by-step explanation:

Data given and notation

$X_{1}=42$ represent the number of infested vines for Pernod5

$X_{2}=22$ represent the number of infested vines for Action

$n_{1}=440$ sample of Pernod5

$n_{2}=360$ sample of Action

$\hat p_{1}=\frac{42}{440}=0.0955$ represent the proportion of residents of infested vines for Pernod5

$\hat p_{2}=\frac{22}{360}=0.0611$ represent the proportion of infested vines for Action

z would represent the statistic (variable of interest)

$p_v$ represent the value for the test (variable of interest)

$\alpha=0.1$ significance level given

Concepts and formulas to use

We need to conduct a hypothesis in order to check if is there is a difference between thw two population proportions, the system of hypothesis would be:

Null hypothesis: $p_{1} - p_{2}=0$

Alternative hypothesis: $p_{1} - p_{2} \neq 0$

We need to apply a z test to compare proportions, and the statistic is given by:

$z=\frac{\hat p_{1}-\hat p_{2}}{\sqrt{\hat p (1-\hat p)(\frac{1}{n_{1}}+\frac{1}{n_{1}})}}$ (1)

Where $\hat p=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{42+22}{440+360}=0.08$

z-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.

Calculate the statistic

Replacing in formula (1) the values obtained we got this:

$z=\frac{0.0955-0.0611}{\sqrt{0.08(1-0.08)(\frac{1}{440}+\frac{1}{360})}}=1.784$

Statistical decision

Since is a two sided test the p value would be:

$p_v =2*P(Z>1.784) =0.074$

Comparing the p value with the significance level given $\alpha=0.1$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can say that the two proportions differes at 10% of significance.

4 0

3 years ago

Can someone plz help me on this I really need help

Usimov [2.4K]

When dividing fractions these are the steps you will take:

1. The first number in the expression stays the same. If it is a whole number then you may just place a one in the denominator and keep the numerator as the whole number like so:

$\frac{3}{1}$ ÷ $\frac{3}{4}$

2. Change the division sign into a multiplication sign

$\frac{3}{1}$ × $\frac{3}{4}$

3. Take the reciprocal (switch the places of numerator and denominator) of the second number in the expression

$\frac{3}{1}$ × $\frac{4}{3}$

4. Multiply across

$\frac{3*4}{1*3}$

$\frac{12}{3}$

^^^This can be further simplified:

4

Hope this helped!

~Just a girl in love with Shawn Mendes

5 0

4 years ago

Sam invests a sum of money in a retirement account with a fixed annual interest rate of 7%

Zolol [24]

Answer:

The initial amount of investment was $7,822

Step-by-step explanation:

The formula for compound interest, including principal sum is:

$A=P(1+\frac{r}{n})^{nt}$ , where

<em>A</em> is the future value of the investment/loan, including interest

<em>P</em> is the principal investment amount

<em>r</em> is the annual interest rate (decimal)

<em>n</em> is the number of times that interest is compounded per unit t

<em>t</em> is the time the money is invested or borrowed for

Let us use this rule to solve the question

∵ Sam invests a sum of money in a retirement account with a fixed

annual interest rate of 7% compounded quarterly

∴ <em>r </em>= 7% = $\frac{7}{100}$ = 0.07

∴ <em>n</em> = 4 ⇒ compounded quarterly

∵ After 13 years, the balance reaches $19,280.02

∴ <em>A</em> = 19,280.02

∴ <em>t </em>= 13

Substitute these values in the rule above to find <em>P</em>

∵ $19,280.02=P(1+\frac{0.07}{4})^{4(13)}$

∴ $19,280.02=P(1.0175)^{52}$

→ Divide both sides by $(1.0175)^{52}$

∴ 7,821.99888 = <em>P</em>

→ Round it to the nearest dollar

∴ 7,822 = <em>P</em>

∴ <em>P</em> = $7,822

∴ The initial amount of investment was $7,822.

8 0

4 years ago