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IRINA_888 [86]
2 years ago
12

Bruce retiled his kitchen. Originally, he bought three boxes of tile with the same number of tiles in each. He ran out of tile a

nd had to go back to get three extra boxes of tile. However, he only used two tiles from the last box to finish the job.
Felicia also retiled her kitchen. She bought five boxes of tile, and each box contained the same number of tiles as each of Bruce’s boxes. She also ran out of tile. She had to go back to the store and get five more tiles to finish the job.

determine whether Bruce and Felicia used the same number of tiles and whose tiles cover the most area per tile.
Write an expression for the number of tiles Bruce used and an expression for the number of tiles Felicia used. Use x to represent the number of tiles in a box.
Mathematics
1 answer:
agasfer [191]2 years ago
6 0

Answer:

Expression for the number of tiles Bruce used: 5x+2

Expression for the number of tiles Felicia used: 5x+5

Step-by-step explanation:

irst want you'll want to do is translate the question into something easily understood. So for Bruce, we know that he bought three boxes with the same number of tiles in each, so 3, then he had to buy three more, another 3, but didn't finish the last box only using two, 2. So, we know he completely used the first 3 he bought then 2 of the 3 more boxes he bought.

For boxes completely used we can show it like this: 3+2=5 or 5x to represent the not known number of tiles in each box. Now we have to include the last box he bought, but he only used two tiles out of the whole box so it wouldn't be added to the same number as the other five (so not 6x).

To represent those last two tiles we can simply add +2.

Now putting it all together we get 5x+2

5x is the number of boxes multiplied by unknown number of tiles. so 5x=tiles in 5 boxes. and the 2 is those two tiles that were taken out of the last box.

For Felicia we go through the same process. We know she bought five boxes with the same number of tiles that Bruce had, 5, then bought five more individual tiles (not in a box), 5.

Not too much to do, so we know she got 5 boxes, so now we add our variable to represent the tiles in the boxes. so that 5 becomes 5x. Now with like we did with the two tiles Bruce only used, we do not add the 5 additional tiles into that number (so not 10x).

Because those were individual tiles they are simply 5.

Putting the whole thing together we get 5x+5

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Solve each equation you must use
n200080 [17]

1) The solution for m² - 5m - 14 = 0 are x=7 and x=-2.

2)The solution for b² - 4b + 4 = 0 is x=2.

<u>Step-by-step explanation</u>:

The general form of quadratic equation is ax²+bx+c = 0

where

  • a is the coefficient of x².
  • b is the coefficient of x.
  • c is the constant term.

<u>To find the roots :</u>

  • Sum of the roots = b
  • Product of the roots = c

1) The given quadratic equation is m² - 5m - 14 = 0.

From the above equation, it can be determined that b = -5 and c = -14

The roots are -7 and 2.

  • Sum of the roots = -7+2 = -5
  • Product of the roots = -7\times2 = -14

The solution is given by (x-7) (x+2) = 0.

Therefore, the solutions are x=7 and x= -2.

2) The given quadratic equation is b² - 4b + 4 = 0.

From the above equation, it can be determined that b = -4 and c = 4

The roots are -2 and -2.

  • Sum of the roots = -2-2 = -4
  • Product of the roots = -2\times-2 = 4

The solution is given by (x-2) (x-2) = 0.

Therefore, the solution is x=2.

5 0
3 years ago
A sample of 1200 computer chips revealed that 45% of the chips fail in the first 1000 hours of their use. The company's promotio
yaroslaw [1]

Answer:

z=\frac{0.45 -0.48}{\sqrt{\frac{0.48(1-0.48)}{1200}}}=-2.08

p_v = P(Z

So the p value obtained was a low value and using the significance level given \alpha=0.05 we see that p_v so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the proportion of chips that fail in the first 1000 hours of their use is not significantly less than 0.48.   

Step-by-step explanation:

Data given and notation

n=1200 represent the random sample taken

\hat p=0.45 estimated proportion of chips that fail in the first 1000 hours of their use

\mu_0 =0.48 is the value that we want to test

\alpha=0.05 represent the significance level

Confidence=95% or 0.95

z would represent the statistic (variable of interest)

p_v represent the p value (variable of interest)  

Concepts and formulas to use  

We need to conduct a hypothesis in order to test the claim that the true proportion si less then 0.48:  

Null hypothesis:p\geq 0.48  

Alternative hypothesis:p < 0.48  

When we conduct a proportion test we need to use the z statistic, and the is given by:  

z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}} (1)  

The One-Sample Proportion Test is used to assess whether a population proportion  is significantly different from a hypothesized value .

Calculate the statistic  

Since we have all the info requires we can replace in formula (1) like this:  

z=\frac{0.45 -0.48}{\sqrt{\frac{0.48(1-0.48)}{1200}}}=-2.08

Statistical decision  

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.  

The significance level provided \alpha=0.05. The next step would be calculate the p value for this test.  

Since is a left tailed test the p value would be:  

p_v = P(Z

So the p value obtained was a low value and using the significance level given \alpha=0.05 we see that p_v so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the proportion of chips that fail in the first 1000 hours of their use is not significantly less than 0.48.  

6 0
3 years ago
8/20 greater than or less than 2/10
kumpel [21]
8/20 is greater than 2/10. If you were to make the denominators the same, by mulipling 2x2 and 10x2, you would get 4/20, which is less than 8/20.
6 0
3 years ago
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Five less than nine times a number is the same as nineteen more than the number
Xelga [282]

Answer:


Step-by-step explanation:

The first thing you need to do is develop the equation. Less in this case means subtract.

On the left side you have

9 times a number which is 9*x

5 less than 9 times a number means 9x - 5

Now you shift to the right

x = 3

x + 19  What you get is

9x - 5 = x + 19        Subtract x from both sides of the equation

9x - x - 5 = 19        Combine both x terms on the left

8x - 5 = 19             Add 5 to both sides.

8x - 5 + 5 = 19 + 5 Combine terms

8x = 24                  Divide by 8

x = 24/8

x = 3

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2 years ago
I need help with number 17. I have no idea what I’m doing!
kakasveta [241]

is there anther way you can put the pic i cant see

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