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3 years ago

What is the correct classification of the system of equations below? 14x + 2y = 10 y + 7x = -5 parallel coincident intersecting

Mathematics

1 answer:

marissa [1.9K]3 years ago

5 0

In standard form the two equations are
7x +y = 5
7x +y = -5

The equations describe lines that are parallel.

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a boat traveled 160 miles downstream and back. the trip downstream took 8 hours. the trip back took 40 hours. find the speed of

Nana76 [90]

Let speed of the boat in still water = x miles per hour

Let speed of the current = y miles per hour

When water and current both flow in same direction then effective speed will be sum of both speeds that is (x+y)

now plug the given values in formula speed=distance/time

we get equation:

(x+y)=160/8

or x+y=20...(i)

When water and current both flow in opposite direction then effective speed will be difference of both speeds that is (x-y)

now plug the given values in formula speed=distance/time

we get equation:

(x-y)=160/40

or x-y=4

or x=4+y...(ii)

plug value of x into (i)

4+y+y=20

4+2y=20

2y=16

y=8

plug value of y into (ii)

x=4+8=12

Hence final answer is given by:

Speed of the boat in still water = 12 miles per hour

Speed of the current = 8 miles per hour

4 0

3 years ago

A box contains 19 large marbles and 10 small marbles. Each marble is either green or white. 8 of the large marbles are green, an

notsponge [240]

Answer:

25/29

Step-by-step explanation:

see the attached picture.

7 0

3 years ago

An SRS of 350 high school seniors gained an average of x¯=21 points in their second attempt at the SAT Mathematics exam. Assume

Lynna [10]

Answer:

a) $21-2.58\frac{52}{\sqrt{350}}=13.83$

$21+2.58\frac{52}{\sqrt{350}}=28.17$

So on this case the 99% confidence interval would be given by (13.83;28.17)

b) $ME=2.58\frac{52}{\sqrt{350}}=7.17$

c) $ME=2.58\frac{52}{\sqrt{100}}=13.42$

d) D. Decreasing the sample size increases the margin of error, provided the confidence level and population standard deviation remain the same.

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

Part a

$\bar X=21$ represent the sample mean

$\mu$ population mean (variable of interest)

$\sigma=52$ represent the population standard deviation

n=350 represent the sample size

99% confidence interval

The confidence interval for the mean is given by the following formula:

$\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

Since the Confidence is 0.99 or 99%, the value of $\alpha=0.01$ and $\alpha/2 =0.005$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.005,0,1)".And we see that $z_{\alpha/2}=2.58$

Now we have everything in order to replace into formula (1):

$21-2.58\frac{52}{\sqrt{350}}=13.83$

$21+2.58\frac{52}{\sqrt{350}}=28.17$

So on this case the 99% confidence interval would be given by (13.83;28.17)

Part b

The margin of error is given by:

$ME=2.58\frac{52}{\sqrt{350}}=7.17$

Part c

The margin of error is given by:

$ME=2.58\frac{52}{\sqrt{100}}=13.42$

Part d

As we can see when we reduce the sample size we increase the margin of error so the best option for this case is:

D. Decreasing the sample size increases the margin of error, provided the confidence level and population standard deviation remain the same.

6 0

2 years ago

What is the solution to the linear equation?<br><br> 4b + 6 = 2 – b + 4

Reil [10]

Answer:

$\large\boxed{b=0}$

Step-by-step explanation:

$4b+6=2-b+4\qquad\text{combine like terms}\\\\4b+6=(2+4)-b\qquad\text{add}\ b\ \text{to both sides}\\\\5b+6=6\qquad\text{subtract 6 from both sides}\\\\5b=0\qquad\text{divide both sides by 5}\\\\b=0$

8 0

3 years ago

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A farmer will divide a 1/4 acre plot of land into three equal-sized sections what will be the size of each section?

Natalija [7]

1/4:3= 1/4•1/3=1/12acre - size of each section

1/2•1/5=1/10yard

8 0

3 years ago

Read 2 more answers