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3 years ago

On a coordinate plane, rectangle E F G H has points (2, 3), (5, 3), (5, 2), (2, 2).

Mathematics

2 answers:

ollegr [7]3 years ago

8 0

Answer: (3,-5)

Step-by-step explanation:

It is

shepuryov [24]3 years ago

4 0

Answer:

3, -5

Step-by-step explanation:

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This is my last question. Please help me!

sesenic [268]

Okay so first you want to simplify the given equation (7x+3y)(7x-3y)

in order to do this you multiply the first number of the first equation (7x) with the first number of the second equation (7x) this gives you 49x^2

Now you want to multiply the second number of the first equation (3y) by the second number of the second equation (-3y) this gives you -9y^2

Its as easy as pie!

3 0

3 years ago

Flow meters are installed in urban sewer systems to measure the flows through the pipes. In dry weatherconditions (no rain) the

ziro4ka [17]

Answer:

a) $\frac{(8)(30.23)^2}{20.09} \leq \sigma^2 \leq \frac{(8)(30.23)^2}{1.65}$

$363.90 \leq \sigma^2 \leq 4430.80$

Now we just take square root on both sides of the interval and we got:

$19.08 \leq \sigma \leq 66.56$

b) For this case we are 98% confidence that the true deviation for the population of interest is between 19.08 and 66.56

Step-by-step explanation:

423.6, 487.3, 453.2, 402.9, 483.0, 477.7, 442.3, 418.4, 459.0

Part a

The confidence interval for the population variance is given by the following formula:

$\frac{(n-1)s^2}{\chi^2_{\alpha/2}} \leq \sigma^2 \leq \frac{(n-1)s^2}{\chi^2_{1-\alpha/2}}$

On this case we need to find the sample standard deviation with the following formula:

$s=sqrt{\frac{\sum_{i=1}^8 (x_i -\bar x)^2}{n-1}}
And in order to find the sample mean we just need to use this formula:
[tex]\bar x =\frac{\sum_{i=1}^n x_i}{n}$

The sample deviation for this case is s=30.23

The next step would be calculate the critical values. First we need to calculate the degrees of freedom given by:

$df=n-1=9-1=8$

The Confidence interval is 0.98 or 98%, the value of $\alpha=0.02$ and $\alpha/2 =0.01$ , and the critical values are:

$\chi^2_{\alpha/2}=20.09$

$\chi^2_{1- \alpha/2}=1.65$

And replacing into the formula for the interval we got:

$\frac{(8)(30.23)^2}{20.09} \leq \sigma^2 \leq \frac{(8)(30.23)^2}{1.65}$

$363.90 \leq \sigma^2 \leq 4430.80$

Now we just take square root on both sides of the interval and we got:

$19.08 \leq \sigma \leq 66.56$

Part b

For this case we are 98% confidence that the true deviation for the population of interest is between 19.08 and 66.56

4 0

3 years ago

The surface area of this rectangular prism is 34 square centimeters. What is the volume is the width is 1 cm, the length is 2 cm

Bezzdna [24]

Answer: $10\ cm^3$

Step-by-step explanation:

Given

The surface area of a rectangular prism is $34\ cm^2$

Width of prism $w=1\ cm$

Length of prism $l=2\ cm$

height of prism $h=x\ cm$

Surface area is given by

$S.A.=2[lw+wh+hl]$

Put values

$34=2[2\times 1+1\times x+2x]\\17=2+3x\\15=3x\\x=5\ cm$

Now, the volume of Prism is given by

$V=l\times w\times h$

$\Rightarrow V=2\times1\times 5=10\ cm^3$

8 0

2 years ago

Marty made a $220 bank deposit using $10 bills and $5 bills. She gave the teller a total of 38 bills, how many $5 bills were in

Luda [366]

ANSWER: 32 five-dollar bills

======

EXPLANATION:

Let x be number of $5 bills

Let y be number of $10 bills

Since we have total of 38 bills, we must have the sum of x and y be 38

x + y = 38 (I)

Since the total amount deposited is $220, we must have the sum of 5x and 10y be 220 (x and y are just the "number of" their respective bills, so we multiply them by their value to get the total value):

5x + 10y = 220 (II)

System of equations:

$\left\{ \begin{aligned} x + y &= 38 && \text{(I)} \\ 5x + 10y &= 220 && \text{(II)} \end{aligned} \right.$

Divide both sides of equation (II) by 5 so our numbers become smaller

$\left\{ \begin{aligned} x + y &= 38 && \text{(I)} \\ x + 2y &= 44 && \text{(II)} \end{aligned} \right.$

Rearrange (I) to solve for y so that we can substitute into (II)

$\begin{aligned} x + y &= 38 && \text{(I)} \\ y &= 38 - x \end{aligned}$

Substituting this into equation (II) for the y:

$\begin{aligned} x + 2y &= 44 && \text{(II)} \\ x + 2(38 - x) &= 44\\ x + 76 - 2x &= 44 \\ -x &= -32 \\ x &= 32 \end{aligned}$

We have 32 five-dollar bills

======

If we want to finish off the question, use y = 38 - x to figure out number of $10 bills

$y = 38 - 32 = 6$

32 five-dollar bills and 6 ten-dollar bills

7 0

3 years ago

All freshmen, sophomores, juniors, and seniors attended a

Trava [24]

Answer:

The probability is .034375 or 11/320

Step-by-step explanation:

the probability of a senior being chose first is 22 (seniors) divided my total number of students (80) is .275 percent.

multiplied by the probability of a sophomore being chosen 10/80 which equals .125.

multiply those together and you get your probability. 0.034375 or 11/320

5 0

3 years ago

Read 2 more answers