MATHEMATICS MIDDLE SCHOOL

X=y+6
X+6y=20


Solving systems of equations using substitution

Answers

Answer 1
Answer: To get the answer we can subsittute first equation into second.
x+6y=20
y+6+6y=20
6+7y=20        /-6
7y=14        /:2
y=2
Now we can back substitute
x=y+6
x=2+6
x=8
Finally we get
x=8
y=2

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What is the percent of 9 out of 106

Answers

1. i assume, that the number 106 is 100% - because it's the output value of the task.
2. We assume, that x is the value we are looking for.
3. If 100% equals 106, so we can write it down as 100%=106.
4. We know, that x% equals 9 of the output value, so i can write it down as x%=9.
5. Now we have two simple equations:
1) 100%=106
2) x%=9
where left sides of both of them have the same units, and both right sides have the same units, so we can do something like that:
100%/x%=106/9
6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

7. Solution for 9 is what percent of 106

100%/x%=106/9
(100/x)*x=(106/9)*x       - i multiply both sides of the equation by x
100=11.7777777778*x       - i divide both sides of the equation by (11.7777777778) to get x
100/11.7777777778=x
8.49056603774=x
x=8.49056603774

now the answer is
9 is 8.49056603774% of 106
=9/106×100
=900÷106
=8.49 R 8.5

If 1/4 of X is 16 what is 3/4 of x

Answers

in this question x= 64

so 3/4 of x would be 48
16*3=48, so 48
3/4 is 3 times 1/4

A survey was conducted to determine the average age at which college seniors hope to retire in a simple random sample of 101 seniors, 55 was theaverage desired retirement age, with a standard deviation of 3.4 years. A 96% confidence interval for desired retirement age of all college students is:
54.30 to 55.70
54.55 to 55.45
54.58 to 55.42
54 60 to 55.40

Answers

Answer:

96% confidence interval for desired retirement age of all college students is [54.30 , 55.70].

Step-by-step explanation:

We are given that a survey was conducted to determine the average age at which college seniors hope to retire in a simple random sample of 101 seniors, 55 was the  average desired retirement age, with a standard deviation of 3.4 years.

Firstly, the Pivotal quantity for 96% confidence interval for the population mean is given by;

                         P.Q. =  (\bar X-\mu)/((s)/(√(n) ) )  ~ t_n_-_1

where, \bar X = sample average desired retirement age = 55 years

            \sigma = sample standard deviation = 3.4 years

            n = sample of seniors = 101

            \mu = true mean retirement age of all college students

Here for constructing 96% confidence interval we have used One-sample t test statistics as we don't know about population standard deviation.

So, 96% confidence interval for the population mean, \mu is ;

P(-2.114 < t_1_0_0 < 2.114) = 0.96  {As the critical value of t at 100 degree

                                               of freedom are -2.114 & 2.114 with P = 2%}  

P(-2.114 < (\bar X-\mu)/((s)/(√(n) ) ) < 2.114) = 0.96

P( -2.114 * {(s)/(√(n) ) } < {\bar X-\mu} < 2.114 * {(s)/(√(n) ) } ) = 0.96

P( \bar X-2.114 * {(s)/(√(n) ) } < \mu < \bar X+2.114 * {(s)/(√(n) ) } ) = 0.96

96% confidence interval for\mu = [ \bar X-2.114 * {(s)/(√(n) ) } , \bar X+2.114 * {(s)/(√(n) ) } ]

                                           = [ 55-2.114 * {(3.4)/(√(101) ) } , 55+2.114 * {(3.4)/(√(101) ) } ]

                                           = [54.30 , 55.70]

Therefore, 96% confidence interval for desired retirement age of all college students is [54.30 , 55.70].

1) 2x + 8y = 20 what's the solution so confused
y = 2

Answers

if y is equal to 2 then you can find x by putting 2 for y so you will have:
2x + 8(2) = 20 
2x + 16 = 20 
2x = 20 - 16
2x = 4 
x = 4/2 
x=2 :)))
i hope this is helpful
have a nice day
2x + 8y = 20 
y = 2

Substitute y with its value.

2x + 8y = 20
2x + 8(2) = 20
2x + 16 = 20
2x = 20 - 16
2x = 4
x = 4/2
x = 2

x = 2; y = 2

2x + 8y = 20
2(2) + 8(2) = 20
4 + 16 = 20
20 = 20

6(4)+4(5)-4^2 I need help with this, please :)

Answers

Answer:58

Step-by-step explanation:
The answer is 28
6(4)+4(5)-4^2
24+20-16
=28

Arusha draws a rectangular prism that is made up of 2 connected cubes, each with side length e. The surface area of a certain rectangular prism with edge length e is represented by the formula SA = 10e (squared), and the volume of the prism is represented by the formula V = 2e (cubed). A: What is the surface area of the prism if its edge length is 5 cm?
B: Arusha plans to build the prism and partially fill it with 150 cubic cm of sand. What fraction of the prism's volume will be filed by the sand?

Answers

the surface area of the prism if the edge lenght is 5 centimeters would be 2500 because we already know that 10 is the lenght of the prism so if the width is 5 then what you would have to do is 10*5 which is 50 and then you would do 50 to the 2nd power which equals 2500 and that is your answer :)
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