In the figure, side AB is given by the expression (5x + 5)/(x + 3), and side BC is (3x + 9)/(2x - 4).The simplified expression for the area of rectangle ABCD is ___, and the restriction on x is .

Answers

Answer 1

Answer:

Answer:

The simplified expression for the area of rectangle ABCD is $( 15(x + 1))/(2(x - 2))$ , and the restriction on x is x≠2 .

Step-by-step explanation:

Side AB = Width of rectangle = (5x + 5)/(x + 3)

Side BC = Length of rectangle = (3x + 9)/(2x - 4)

Area of Rectangle = Length * Width

Putting values:

$Area\,\,of\,\,rectangle =( (3x + 9))/((2x - 4)) * ((5x + 5))/((x + 3))$

Solving,

$Area\,\,of\,\,rectangle =( 3(x + 3))/((2x - 4)) * (5x + 5)/((x + 3)) \nArea\,\,of\,\,rectangle =( 3)/(2(x - 2)) * 5x + 5\nArea\,\,of\,\,rectangle =( 3(5x + 5))/(2x - 4)\nArea\,\,of\,\,rectangle =( 15x + 15)/(2x - 4)\nArea\,\,of\,\,rectangle =( 15(x + 1))/(2(x - 2))$

The restriction on x is that x ≠ 2, because if x =2 then denominator will be zero.

So, the answer is:

The simplified expression for the area of rectangle ABCD is $( 15(x + 1))/(2(x - 2))$ , and the restriction on x is x≠2 .

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Determine which consecutive integers do not have a real zero of f(x) = x^3 + 9x^2 + 8x – 5 between them.A.) (–8, –7)B.) (4, 5)C.) (0, 1)D.) (–2, –1)
The tread life on tires produced at one factory has a standard deviation of sigma equals 4 comma 000 miles. What is the standard deviation of the sampling distribution of the sample means given the sample size is 4

A Pew Internet poll asked cell phone owners about how they used their cell phones. One question asked whether or not during the past 30 days they had used their phone while in a store to call a friend or family member for advice about a purchase they were considering. The poll surveyed 1003 adults living in the United States by telephone. Of these, 462 responded that they had used their cell phone while in a store within the last 30 days to call a friend or family member for advice about a purchase they were considering.A) Identify the sample size and the count.
B) Calculate the sample proportion.
C) Explain the relationship between the population proportion and the sample proportion.

Answers

Answer:

Given:

n = 1003

$p' = (462)/(1003) = 0.4606$

q = 1 - 0.4606 = 0.5394

a) The sample size and count.

Here the sample size is the number that took part in the poll. It is denoted as n = 1003.

The count is the number that answered yes. Count = 462

b) The sample proportion.

The formula for sample proportion is: $p' = (x)/(n)$

Therefore, sample proportion =

$p' = (462)/(1003) = 0.4606$

c) The relationship between population proportion and sample proportion.

Since the sample size is greater than 30 (n>30), the sample size is large. Hence, for a large sample, the population proportion is approximately equal to the sample proportion.

This means the population proportion, p = 0.4606

Answer:

A) Sample size n=1003

Count x=462

B) Sample proportion p=0.46

C) The population proportion can be estimated with a confidence interval, with the information given by the sample proportion.

The 95% confidence interval for the population proportion is (0.429, 0.491).

Step-by-step explanation:

A) The sample size include all the adult that answer the poll. The sample size is then n=1003.

The count is the number of adults that answer Yes in this case. The count is x=462.

B) The sample proportion can be calculated dividing the count by the sample size:

$p=(x)/(n)=(462)/(1003)=0.46$

C) The population proportion is not known. It can only be estimated with the information given by samples of that population. The statistical inference is the tool by which the sample information can be used to estimate the population characteristics.

With the sample proportion p we can estimate a confidence interval for the population proportion.

We can calculate a 95% confidence interval.

The standard error of the proportion is:

$\sigma_p=\sqrt{(p(1-p))/(n)}=\sqrt{(0.46*0.54)/(1003)}\n\n\n \sigma_p=√(0.00025)=0.0157$

The critical z-value for a 95% confidence interval is z=1.96.

The margin of error (MOE) can be calculated as:

$MOE=z\cdot \sigma_p=1.96 \cdot 0.0157=0.031$

Then, the lower and upper bounds of the confidence interval are:

$LL=p-z \cdot \sigma_p = 0.46-0.031=0.429\n\nUL=p+z \cdot \sigma_p = 0.46+0.031=0.491$

The 95% confidence interval for the population proportion is (0.429, 0.491).

We have 95% that the population proportion is within this interval

Suppose Jesse won five bags of eight goldfish use math you know to represent the problem and find the number of goldfish Jesse won

Answers

Answer:

Step-by-step explanation:

5(8) = x

use 5 as bags and use 8 as number of goldfish

then times the 2 number

A company can use two workers to manufacture product 1 and product 2 during a business slowdown. Worker 1 will be available for 20 hours and worker 2 for 24 hours. Product 1 will require 5 hours of labor from worker 1 and 3 hours of specialized skill from worker 2. Product 2 will require 4 hours from worker 1 and 6 hours from worker 2. The finished products will contribute a net profit of $60 for product 1 and $50 for product 2. At least two units of product 2 must be manufactured to satisfy a contract requirement. Formulate a linear program to determine the profit maximizing course of action. (Hint: the simplest formulation assigns one decision variable to account for the number of units of product 1 to produce and the other decision variable to account for the number of units of product 2 to produce.)

Answers

Answer:

The linear problem is to maximize $Z = C_ {1} X_ {1} + C_ {2}X_ {2} = 60X_ {1} + 50X_ {2}$ , s.a.

subject to

$\frac {1} {5} X_ {1} + \frac {1} {4} X_ {2} \leq 20\n\n\frac {1} {3} X_ {1} + \frac {1} {6} X_ {2} \leq 24\n\nX_ {2} \geq 2\n\nX_ {1}, X_ {2} \geq 0$

Step-by-step explanation:

Let the decision variables be:

$X_ {1}$ : number of units of product 1 to produce.

$X_ {2}$ : number of units of product 2 to produce.

Let the contributions be:

$C_ {1} = 60\n\nC_ {2} = 50$

The objective function is:

$Z = C_(1) X_(1)+ C_(2)X_(2) = 60X_ {1} + 50X_ {2}$

The restrictions are:

$\frac {1} {5} X_ {1} + \frac {1} {4} X_ {2} \leq 20\n\n\frac {1} {3} X_ {1} + \frac {1} {6} X_ {2} \leq 24\n\nX_ {2} \geq 2\n\nX_ {1}, X{2} \geq 2\n\n$

The linear problem is to maximize $Z = C_ {1} X_ {1} + C_ {2}X_ {2} = 60X_ {1} + 50X_ {2}$ , s.a.

subject to

$\frac {1} {5} X_ {1} + \frac {1} {4} X_ {2} \leq 20\n\n\frac {1} {3} X_ {1} + \frac {1} {6} X_ {2} \leq 24\n\nX_ {2} \geq 2\n\nX_ {1}, X_ {2} \geq 0$

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6. Nadia is comparing costs for two brands of garden compost. For
Brand A, the cost y for x bags is shown in the table For Brand B,
the cost y can be represented by the equation y = 1,99%, where
x represents the number of bags, Which brand costs less for
6 bags of compost? How much less?

Answers

Brand B costs less for 6 packs of compost. It costs $5.99 less.

Which brand costs less for 6 bags of compost?

To discover which brand costs less for 6 sacks of compost, let's calculate the fetched of 6 packs of each brand:

Brand A:

6 sacks * $2.99/bag = $17.94

Brand B:

y = 1.99x

For 6 packs of compost, x = 6:

y = 1.99 * 6 = $11.94

In this manner, Brand B costs less for 6 sacks of compost, and it costs $5.99 less.

Brand B costs less for 6 packs of compost. It costs $5.99 less.

Learn more about compost here:

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When we multiply a number by 3, wesometimes/always/never v

get the same value as if we added 6

to that number.

Stuck? Watch a video or use a hint.

Report a problem

7 of 7 ..

nyone, anywhere

Imnact

Math by grace

O

Answers

Answer:

? what's the question??????????????????

Final answer:

Multiplying a number by 3 usually does not yield the same result as adding 6 to it, except in the case of the number 3. For all other numbers, the results are different.

Explanation:

In mathematics, when we multiply a number by 3 it does not usually yield the same value as when we add 6 to the number. However, there is one instance in which this statement is incorrect. Let's consider the number 3. If we multiply 3 by 3 we get 9, and if we add 6 to 3 we also get 9. In all other instances, multiplying a number by 3 will not yield the same result as adding 6 to that number. For example, if we take the number 4, multiplying it by 3 gives us 12, but adding 6 to it gives us 10, which are different.

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Given below are the analysis of variance results from a Minitab display. Assume that you want to use a 0.05 significance level in testing the null hypothesis that the different samples come from populations with the same mean. Identify the P-value.

Answers

Answer:

hello your question has some missing parts below is the missing part

Identify the p-value.

Source DF SS MS F p

Factor 3 13.500 4.500 5.17 0.011

Error 16 13.925 0.870

Total 19 27.425

A) 0.011 B) 4.500 C) 5.17 D) 0.870

answer : p-value = 0.011 ( A )

Step-by-step explanation:

using this information

Source DF SS MS F P

Factor 3 13.500 4.500 5.17 0.011

Error 16 13.925 0.870

Total 19 27.425

significance level = 0.05

given that the significance level = 0.05

and

F statistics are given as : F = 5.17 , F critical = 3.25

hence the p-value = 0.011

from the analysis the p-value is less than the significance level is lower than the significance level

Final answer:

The p-value in a Minitab analysis of variance (ANOVA) test helps determine whether to reject or accept the null hypothesis that the samples all come from populations with the same mean. You would reject the null hypothesis if your p-value is less than the significance level (α = 0.05). Please refer back to your Minitab results to find this p-value.

Explanation:

In the context of your Minitab analysis of variance (ANOVA) results, the p-value that you should be looking at to determine the null hypothesis is not explicitly mentioned in your question. However, based on your description, you want to test the hypothesis that the different samples come from populations with the same mean (null hypothesis).

The p-value represents the probability that you would obtain your observed data (or data more extreme) if the null hypothesis were true. Therefore, if the p-value is less than the significance level (α = 0.05), you would reject the null hypothesis, suggesting that the samples do not all come from populations with the same mean. Conversely, if the p-value is larger than 0.05, you would fail to reject the null hypothesis, suggesting that the samples could come from populations with the same mean.

Please refer back to your Minitab results to find this p-value. Usually, it's labeled in the ANOVA table output as 'P' or 'Prob > F'.