Find the solution of the system of equations 8x-4y=-32 -3+4y=42

Hemant and Ajay start a two-length swimming race at the same moment but from opposite ends of the pool. They swim in the lane an

Alenkinab [10]

Answer:

Let length of the pool be L.

Deep

A —————————————><———————————----———————————— H

.................(18.5m)

H ——————————————————————————-———><————————- A

..............................................................................................................(10.5)

In same time, Andy covers 18.5 and Hardy covers L - 18.5.

In same time, Andy covers L - 18.5 + 10.5 while Hardy covers 18.5 + L - 10.5

The ratio of these distances covered would be the same since the speeds of both people are constant.

18.5/(L - 18.5) = (L - 8)/(L + 8)

Plug in the options to find that L = 45 works.

5 0

3 years ago

In one day, The Tool Shed rented out 25 self-propelled and riding mowers for a total fee of $900. The dolly rental cost was $20

masha68 [24]

They rented out 5 self-propelled mowers and 20 riding mowers.

Data;

Total number of tool rented out = 25
Cost of tools rented = $900

<h3>System of Equations</h3>

To solve this problem, we have to write a system of equations to represent the problem.

since we have

x = self - propelled mower
y = riding mowers

Let's write equations with these variables.

$x+y = 25...equation (i)\\20x+40y = 900...equation(ii)$

From equation (i)

$x+y= 25\\x = 25 - y...equation(iii)$

Put equation (iii) into equation (ii)

$20x+40y=900\\x = 25-y\\20(25-y)+40y=900\\\\500-20y+40y=900\\500+20y=900\\20y=900-500\\20y=400\\\frac{20y}{20}=\frac{400}{20}\\ y=20$

Let's substitute the value of y into equation(i)

$x+y =25\\x+20 = 25\\x = 25 - 20\\x = 5$

From the calculations above, they rented 5 self-propelled mowers and 20 riding mowers.

Learn more on system of equations here;

brainly.com/question/13729904

4 0

2 years ago

What are the values for the coefficients and constant term of 0 = 2 + 3x2 – 5x?

luda_lava [24]

Answer:

Coefficients:

3, -5

Constant:

2

Step-by-step explanation:

I'm going to rewrite it:

$3x^2-5x+2=0$

Coefficients:

3, -5

Constant:

2

4 0

3 years ago

Read 2 more answers

a rectangular park has an area of 2/3 square miles the length of the park is 2 and 2/3 the width of the park what is the Widht o

r-ruslan [8.4K]

1.33333333333 thats the answer

5 0

3 years ago

Suppose that the population of the scores of all high school seniors who took the SAT Math (SAT-M) test this year follows a Norm

Vlad1618 [11]

Answer:

Confidence = $1-\alpha=1-0.01=0.99$

And then the confidence level would be given by 99%

Step-by-step explanation:

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".

Assuming the X follows a normal distribution

$X \sim N(\mu, \sigma)$

The distribution for the sample mean is given by:

$\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

$\bar x =512$ represent the sample mean

$\sigma=100$ represent the population standard deviation

n= 100 sample size selected.

The confidence interval is given by this formula:

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

The marginof error for this case is given by Me=25.76. And we know that the formula for the margin of error is given by:

$Me=z_{\alpha/2} \frac{\sigma}{\sqrt{n}}$

$25.76=z_{\alpha/2} \frac{100}{\sqrt{100}}$

And we can find the critical value $z_{\alpha/2}$ like this:

$z_{\alpha/2}=\frac{25.76(\sqrt{100})}{100}=2.576$

And we know that on the right tail of the z score =2.576 we have $\alpha/2$ of the total area. We can find the area on the right of the z score using this excel code:

"=1-NORM.DIST(2.576,0,1,TRUE)" or using a table of the normal standard distribution, and we got 0.004998= $\alpha/2$ , so then $\alpha=0.00498*2=0.009995 \approx 0.01$ , and then we can find the confidence like this:

Confidence = $1-\alpha=1-0.01=0.99$

And then the confidence level would be given by 99%

8 0

3 years ago