A pool measuring 8 meters by 26 meters is surrounded by a path of uniform width, as shown in the figure. If the area of the pool and the path combined is 1008 square meters, what is the width of the path?

Answers

Answer 1

Answer: Let the width path be x.
Length of the outer rectangle = 26 + 2x.
Width of the outer rectangle = 8 +2x.

Combined Area = (2x + 26)*(2x + 8) = 1008

2x*(2x + 8) + 26*(2x + 8 ) = 1008

4x² + 16x + 52x + 208 = 1008

4x² + 68x + 208 - 1008 = 0
4x² + 68x - 800 = 0. Divide through by 4.
x² + 17x - 200 = 0 . This is a quadratic equation.

Multiply first and last coefficients: 1*-200 = -200

We look for two numbers that multiply to give -200, and add to give +17

Those two numbers are 25 and -8.

Check: 25*-8 = -200 25 + -8 = 17

We replace the middle term of +17x in the quadratic expression with 25x -8x

x² +17x - 200 = 0

x² + 25x - 8x - 200 = 0

x(x + 25) - 8(x + 25) = 0

(x+25)(x -8) = 0

x + 25 = 0 or x - 8 = 0

x = 0 -25 x = 0 + 8

x = -25 x = 8

The width of the path can not be negative.

The only valid solution is x = 8.

The width of the path is 8 meters.

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the distribution of daily sleep duration among college students is normal with a mean of 8.13 and standard deviation of 1.87. suppose you plan to take an simple random sample (srs) of size 64, what is the mean of the sampling distribution of mean sleep duration time for college students? the distribution of daily sleep duration among college students is normal with a mean of 8.13 and standard deviation of 1.87. suppose you plan to take an simple random sample (srs) of size 64, what is the mean of the sampling distribution of mean sleep duration time for college students? 0 1.355 1.87 8.13

Answers

The mean of the sampling distribution of mean sleep duration time for college students is 8.13.

The sampling distribution of the mean is a probability distribution that shows all possible sample means that can be obtained from a population. When we take a sample of size n from a population, calculate the mean of that sample, and repeat this process many times, we obtain a sampling distribution of the mean. The mean of this distribution is called the expected value of the sample mean, and it represents the average value of all possible sample means.

In this question, the population mean and standard deviation of sleep duration among college students are given as 8.13 and 1.87, respectively. We are asked to find the mean of the sampling distribution of the mean for a simple random sample of size 64.

The mean of the sampling distribution of the mean is equal to the population mean, which is 8.13 in this case. This means that if we take many simple random samples of size 64 from this population, calculate the mean of each sample, and plot these means on a histogram, the distribution of these means will be centered around 8.13.

The mean of the sampling distribution of the mean sleep duration time for college students can be calculated using the formula:

Sampling distribution mean = Population mean = 8.13

Therefore, the mean of the sampling distribution of mean sleep duration time for college students is 8.13.

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70. Suppose that you currently have one credit card with a balance of $10,000 at an annual rate of 24.00% interest. You have stopped adding any additional charges to this card and are determined to pay off the balance. You have worked out the formula bbn = b0r n − R(1 + r+r2 +....+ r n−1), where b0 is the initial balance, bn is the balance after you have maden payments, r= 1 + i, wherei is the monthly interest rate, and R is the amount you are planning to pay each month.b. Explain why we can rewrite the given formula as bn= b0rn − R(1-rn/1-r).????????

Answers

Answer:

$1+r+r^(2)+r^(3)+.....+r^(n-1) = (1-r^(n))/(1-r)$

Step-by-step explanation:

Taking the succession:

$1+r+r^(2)+r^(3)+.....+r^(n-1)$

You can multiply and divide by 1-r without chaging the result:

$(1-r)/(1-r) (1+r+r^(2)+r^(3)+.....+r^(n-1))$

Distributing the upper part of the fraction you have:

$(1)/(1-r) (1-r+r-r^(2)+r^(2)-r^(3)+r^(3)-r^(4)+.....+r^(n-1)-r^(n))$

As can be seen all the intermediate members will be canceled by a same member with opposite sign, only $(1-r^(n))$ will be left so:

$1+r+r^(2)+r^(3)+.....+r^(n-1) = (1-r^(n))/(1-r)$

The Guptas figured out the earth was round by observing lunar eclipses.
a. True
b. False

Answers

it is true. Guptas did figure out the earth was round by observing lunar eclipses.

the answer is A. true

3 radical 7 - radical 7
= 3
why is this incorrect?

Answers

$3√(7) - √(7)$

Let x represent $√(7)$ , then you can rewrite the expression as 3x - x.

3x - x = 2x. Now replace "x" with $√(7)$ and you get 2 $√(7)$ .

The reason 3 is incorrect is because you are supposed to perform the operation (+, -, x, ÷) with the coefficients, not with the variable or radical.

Algebraically, you have to factor the square root of 7 to see why you're wrong:

$3√(7)-√(7) = √(7)(3-1) = 2√(7)$

Conceptually, think that any object - say an apple - represents the square root of seven.

So, you have three apples, and you take away one apple. You have two apples remaining, i.e. $2√(7)$

Can someone help me with this graph

Answers

just plot the points on the graph so if x+y=-6 just make a list of all of the points that will work (remember that the left-to-right line is x and the up-to-down line is y, and right and up is positive and left and down is negative)

so make a list (in graphs we write [x,y] or (x,3)) so here are some points that will work
(-3,-3)
(-4,-2)
(-2,-4)
(-1,-5)
(-5,-1)
(0,-6)
(-6,0)
(-7,1)
(1,-7)
and so on, just plot those points and more that will work for x+y=-6 and you should be good,

there is another way that this is supposed to be done but this way is easier

Help Me Please!!!!!!!