MATHEMATICS HIGH SCHOOL

In a trivia game, Levi answered 8 questions correctly out of 10 turns in the game. Then, he answered the next 3 questions correctly. He reasoned that because he added 3 the both the total questions and his correct responses, that the ratio of correct answer to total questions remained the same. Is he correct? Justify the answers

Answers

Answer 1

Answer:

Answer:

He is not correct as the ratios are;

First ratio is 4:5,

Second ratio 11:13

Which are different values

Step-by-step explanation:

The number of correct questions Levi answered = 8 questions

The number of questions in the game = 10

The ratio of correctly answered questions to total number of questions in the first 10 question is given as follows

Correctly answered questions : Total number of questions = 8:10

Which can be simplified as 8:10 = 8/2:10/2 = 4:5

The number of correct questions Levi answered in the next three turns = 3 questions

The total number of questions attempted by Levi becomes 10 + 3 = 13 questions

The total number of correct answers given by Levi = 8 + 3 = 11 correct answers

The new ratio of correctly answered questions to total number of questions is therefore;

New correctly answered questions : Total number of questions = 11:13.

Therefore, the ratios do not remain the same as 4:5 ≠ 11:13.

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Given a test statistic of t=2.315 of a left tailed test with n=8

Answers

Answer:

Null hypothesis: $\mu =110$

Alternative hypothesis: $\mu \neq 110$

The sample size on this case is n=8, then the degrees of freedom are given by:

$df = n-1= 8-1=7$

The statistic is given by:

$t= (\bar X -\mu)/((s)/(√(n)))$

For this case the value of the statistic is given $t = 2.315$

Since we are using a bilateral test the p value would be given by:

$p_v = 2*P(t_(7)>2.315) =0.054$

And we can use the following excel code to find it:

"=2*(1-T.DIST(2.315;7;TRUE))"

Since the p value is higher than the significance level given we FAIL to reject the null hypothesis. And the best conclusion would be:

0.05<P-value <0.10, fail to reject the null hypothesis

Step-by-step explanation:

Assuming this complete question :"Given a test statistic of t=2.315 of a left-tailed test with n=8, use a 0.05 significance level to test a claim that the mean of a given population is equal to 110.

Find the range of values for the P-value and state the initial conclusion 1 point) 0.05<P-value <0.10; reject the null hypothesis

0.05<P-value <0.10, fail to reject the null hypothesis

0.025 < P-value <0.05; reject the null hypothesis

0.025< P-value<0.05; fail to reject the null hypothesis"

For this case they want to test if the population mean is 110 or no, the systemof hypothesis are:

Null hypothesis: $\mu =110$

Alternative hypothesis: $\mu \neq 110$

The sample size on this case is n=8, then the degrees of freedom are given by:

$df = n-1= 8-1=7$

The statistic is given by:

$t= (\bar X -\mu)/((s)/(√(n)))$

For this case the value of the statistic is given $t = 2.315$

Since we are using a bilateral test the p value would be given by:

$p_v = 2*P(t_(7)>2.315) =0.054$

And we can use the following excel code to find it:

"=2*(1-T.DIST(2.315;7;TRUE))"

Since the p value is higher than the significance level given we FAIL to reject the null hypothesis. And the best conclusion would be:

0.05<P-value <0.10, fail to reject the null hypothesis

if the recycling club collected 48 aluminum cans 3/4 of the cans was from 6th grade was 1/6 was from 7 grade and the rest was from 8th grade how many cans were collected by 8th grade

Answers

Answer: 4 cans

Step-by-step explanation:

If you evaluate all the amounts of cans collected from each grade you get 44 so the remainder is 4 so the number of cans that came from eighth grade is 4

Choose the correct simplification of the expression (x2y)2. x4y3
x6y6
x4y2
xy4

Answers

Answer: The correct option is (C) $x^4y^2.$

Step-by-step explanation: We are given to select the correct expression that is equivalent to the expression below:

$E=(x^2y)^2.$

We will be using the following properties of exponents:

$(i)~(a^b)^c=a^(b* c),\n\n(ii)~(ab)^c=a^cb^c.$

We have

$E=(x^2y)^2=(x^2)^2y^2=x^(2* 2)y^2=x^4y^2.$

Therefore, the required equivalent expression is $x^4y^2.$

Thus, (C) is the correct option.

The correct simplification of the expression $(x^2y)^2$ is $x^4y^2$ .

Option C. is correct.

Here, we have,

To simplify the expression, we apply the power of a power rule,

which states that $(a^m)^n = a^{m*n$ .

In this case, $x^2y$ raised to the power of 2 can be simplified as follows:

$(x^2y)^2 = x^{2^(2) * y^(2)$

$=x^4y^2$

Therefore, the correct simplification of $(x^2y)^2$ is $x^4y^2$ .

Option C. is correct.

To learn more on Expression click:

brainly.com/question/14083225

#SPJ6

To break even in a manufacturing business, income or revenue R must equal the cost of production C. The revenue R from selling x number of computer boards is given by R=40x, and the cost C of producing them is given by C=30x+1000. Find how many boards must be sold to break even. Find how much money is needed to produce the break-even number of boards.

Answers

Answer:

To find the number of boards that must be sold to break even, we need to set the revenue equal to the cost and solve for x.

Given:

Revenue R = 40x

Cost C = 30x + 1000

Since the break-even point is when revenue equals cost, we have the equation:

40x = 30x + 1000

To solve for x, we subtract 30x from both sides of the equation:

40x - 30x = 30x + 1000 - 30x

Simplifying:

10x = 1000

Dividing both sides by 10:

x = 100

Therefore, to break even, 100 computer boards must be sold.

To find the amount of money needed to produce the break-even number of boards, we substitute the value of x into the cost equation:

C = 30x + 1000

C = 30 * 100 + 1000

C = 3000 + 1000

C = 4000

Therefore, $4000 is needed to produce the break-even number of boards.

Step-by-step explanation:

Express 59/100 as a decimal

Answers

59/100=.59 when you are dividing by hundred whatever you're dividing by will be the same answer in decimal form

The graph of f (x)=√x is transformed to create thegraph of g (x)= -2√x+6. Which of these describes a
transformation used to create the graph of g?

Answers

The transformation used to create the graph of g(x) from the graph of f(x) is a vertical and horizontal transformation.

The "-2" in the equation of g(x) reflects a vertical stretch by a factor of 2, which causes the graph to become narrower and steeper than f(x).

The "+6" in the equation of g(x) reflects a vertical shift upward by 6 units, which moves the entire graph of g(x) upward by 6 units.

Therefore, the transformation used to create the graph of g(x) from the graph of f(x) is a vertical and horizontal transformation.

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