In Exercises 26 and 27 write an equation of the line with the given slope and y-intercept.

26. slope: -7/3 and y-intercept: 0

27. slope: 0 and y intercept: -10

Bryleigh have to pay 1260 cents because this is the cost of three dozen brownies.

According to the question,

We have the following information:

Bryleigh needs three dozen brownies for a party. Each brownie costs 35¢.

Now, we know that one dozen of a product means that there are 12 products in total.

So, 3 dozens of brownies means that 12*3.

So, we have 36 products in total.

Now, we have cost of 1 brownie as 35 cents.

So, the cost of 36 brownies can be easily found by multiplying the cost of 1 brownie by 36.

1 brownie = 35 cents

Cost of 36 brownies = 36*35 cents

Cost of 36 brownies = 1260 cents

Hence, the cost of three dozen brownies for which Bryleigh have to pay is 1260 cents.

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Answer:

The measure of the complement =

= 80°

The measure of the supplement=

= 170°

Step-by-step explanation:

Let

90-x equal the degree measure of its complement

180-x equal the degree measure of its supplement.

We are told in the question that: the supplement of a given angle is 10 degrees more than twice its complement.

Hence, the Equation is;

(180 - x) = 10° + 2(90 - x)

180 - x = 10 + 180 - 2x

Collect like terms

-x + 2x = 10 + 180 - 180

x = 10°

Hence,

The measure of the complement =

90 - x

= 90 - 10

= 80°

The measure of the supplement=

180 - x

= 180 - 10

= 170°

Marisa has started a company to manufacture earrings. She will make $1.00 profit on each pair of earrings sold, but expects 1 pair in 30 to be returned for repair, which will cost $45.00. At this, Marisa will not make a profit and the expected loss is $15

information from the question

She will make $1.00 profit on each pair of earrings sold

but expects 1 pair in 30 to be returned for repair, which will cost $45.00

This makes that total revenue

= $1.00 * 30 earrings

= $30

for this 30, it is expected to have a repair that costs $45. the profit remaining is

= $30 - $45

= -$15

this signifies a loss of $15

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Answer:

9

Step-by-step explanation: 6+3=9

The rent is $9

Answer: Greater than 10.

The absolute value of the error in the instructor's estimate is 0.644.

To find the absolute value of the error in the instructor's estimate, we need to calculate the difference between the sample mean and the population mean.

Given:

Population mean (μ) = 3.15

Sample mean (\(\bar{X}\)) = (3.89 + 4.00 + 3.85 + 3.77 + 3.81 + 3.43 + 3.28 + 3.27 + 3.56 + 3.92) / 10

= 36.78/10

= 3.678

Absolute value of the error = |\(\bar{X}\) - μ|

|\(\bar{X}\) - μ| = |3.678 - 3.15| = 0.528

Therefore, the absolute value of the error in the instructor's estimate is 0.644.

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The simplified form of the expression -6w + (–8.3) + 1.5+ (–7w) is -13w - 6.8.

Given the expression in the question;

-6w + (–8.3) + 1.5+ (–7w)

To simplify, first remove the parenthesis

Note that;

-6w + × - 8.3 + 1.5 + × - 7w

-6w - 8.3 + 1.5 - 7w

Next collect and add like terms

-6w - 7w - 8.3 + 1.5

Add -6w and -7w

-13w - 8.3 + 1.5

Add -8.3 and 1.5

-13w - 6.8

Therefore, -13w - 6.8 is the simplified form.

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If you did 69 pushups in 5.17 minutes, then the total number of pushups you would have done in under 30 minutes would be more than 264. To explain how this is so, we can use proportions and ratios.

To find out how many pushups you can do in under 30 minutes, we can use ratios. If you divide 30 minutes by 5.17 minutes, you get approximately 5.8. This means that you can do the 69 pushups in 5.17 minutes almost 6 times in under 30 minutes. To get an estimate of the total pushups you can do in under 30 minutes, you can multiply 69 by 6, which gives you 414 pushups. However, this is just an estimate.

To find a more accurate estimate, you can use proportions. If you did 69 pushups in 5.17 minutes, you can find out how many pushups you would have done in 1 minute by dividing 69 by 5.17, which gives you approximately 13.36 pushups per minute. To find out how many pushups you would have done in 30 minutes, you can multiply 13.36 by 30, which gives you 400.8 pushups. Therefore, it can be concluded that you would have done more than 264 pushups in under 30 minutes.

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The bank can borrow $6440 based on the $7000 deposit.

The following deposit amount: $7000

Because the reserve rate is 8%, the bank will reserve 8% of the 7000. The remaining funds can be lent by the bank.

7000 × (8/100) = amount set aside

= $560

Thus, the reserve deposit is $560.

Amount the bank is willing to lend = 7000 - 560 = $6440

Thus, the bank can lend $6440 based on a deposit of $7000.

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Answer:

525/50=10.5 it will take 10.5 weeks to get rid of every car we however only need to have below 75 so 525/50w<75

Step-by-step explanation:

First you need to divide 525 by 50 to show how many weeks it will take to sell all the cars. And then it should be one less week than the answer you just reacieved.

Answer:

5.4864

Step-by-step explanation:

to the nearest tenth probably 0.5

Calculated t-test statistic (-2.21) is less than the critical value (-1.711), we reject the null hypothesis

The critical value for this hypothesis test can be found using a t-distribution with degrees of freedom (df) equal to the sample size minus one (df = 25-1 = 24) and a significance level of 5%.

Using a t-distribution table or calculator, the critical value for a one-tailed test (since we are testing if the mean is less than 1,150 hours) with 24 degrees of freedom and a 5% significance level is approximately -1.711. Therefore, the answer is B) -1.711.

To conduct the hypothesis test, we would calculate the t-test statistic using the formula:

\(t = (sample mean - hypothesized population mean) / (sample standard deviation / \sqrt{sample size})\)
In this case, the sample mean is 1,097 hours, the hypothesized population mean is 1,150 hours, the sample standard deviation is 133 hours, and the sample size is 25. Plugging these values into the formula, we get:

\(t = (1,097 - 1,150) / (133 / \sqrt{25} )\)= -2.21

Since the calculated t-test statistic (-2.21) is less than the critical value (-1.711), we reject the null hypothesis and conclude that there is sufficient evidence to support the claim that the mean life of light bulbs produced by this company is less than 1,150 hours.

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1. The null hypothesis is H₁: μ = 40 and the alternative hypothesis is H₁: μ ≠ 40

2. The level of significance, alpha (a), is 0.05

3. The test statistic is the z-statistic.

4. The rejection region consists of the values that fall outside the critical test statistic.

5. Tthe z-statistic is 2.88

6. We can reject the null hypothesis.

We are solving based on the provided steps:

Step 1. State the null and research hypotheses:

Step II. State the level of significance, alpha (a):

The level of significance, alpha (a), is 0.05, which relates to a 95% confidence level.

Step III. Select a sampling distribution and state the test statistic:

Since the sample size (n = 81) is greater than 30, we shall use the z-test.

The test statistic is the z-statistic.

Step IV. State the rejection region (critical test statistic):

Since we have a two-tailed test and an alpha level of 0.05, we divide the alpha value equally between the two tails, resulting in an alpha/2 (0.05/2 = 0.025).

To find the critical test statistic, we look up the z-value corresponding to the 0.025 significance level in the standard normal distribution table.

The rejection region consists of the values that fall outside the critical test statistic.

Step V. Then, we calculate the research test statistic to see if it falls in the rejection region:

The formula to calculate the z-statistic is:

z = (x-bar - μ) / (σ / √n)

Where:

Given:

x-bar = 44.1

μ = 40

σ = 12.8

n = 81.

Substitute the values:

z = (44.1 - 40) / (12.8 / √(81))

z = 4.1 / (12.8 / 9)

z = 4.1 / 1.422

z ≈ 2.88

Step VI: State your conclusion in terms of the problem:

After comparing the research test statistic to the critical test statistic from step 5, we find that the z-value of 2.88 falls in the rejection region.

In conclusion, we can reject the null hypothesis.

Hence,

a) Using the sample data from the 2010 GSS, there is evidence to suggest that the population mean workweek for workers is different from 40 hours per week.

b) The research test statistic, with a value of 2.88, falls within the rejection region when compared to the critical test statistic. So, the null hypothesis is rejected.

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The answers are =

a) 0.8647.

b) 25.1302 minutes

c) 0.9990881.

d) 0.0027937.

e) as time approaches infinity, the expected number of cats in the building is 2.

(a) To compute the probability we can use the concept of inter-arrival times in a Poisson process.

The inter-arrival time between student arrivals follows an exponential distribution with a rate of λ = 4.8 students per minute.

Similarly, the inter-arrival time between cat arrivals follows an exponential distribution with a rate of λ' = 1 cat per 5 minutes.

Let T be the time until the 10th student arrives.

The probability that at least one cat has entered before the 10th student is equivalent to the probability that the time until the first cat arrival, denoted by S, is less than T.

The time until the first cat arrival, S, follows an exponential distribution with a rate of λ' = 1 cat per 5 minutes.

To find this probability:

P(S < T) = 1 - exp(-λ'T)

Here, λ'T = 1 × (10/5) = 2, as the time until the 10th student is 10 minutes and the rate for the cat arrival is one cat per 5 minutes.

P(S < T) = 1 - exp(-2) ≈ 0.8647

(b) To compute the mean, variance, and PDF of the time until the third arrival, we need to consider both student and cat arrivals.

Let X be the time until the third arrival.

The time until the third arrival is a random variable composed of the sum of two exponential random variables: the time until the third student, denoted by Xs, and the time until the first cat, denoted by Xc.

The time until the third student, Xs, follows an Erlang distribution with parameters (k = 3, λ = 4.8 students per minute) since we are interested in the third arrival.

The time until the first cat, Xc, follows an exponential distribution with a rate of λ' = 1 cat per 5 minutes.

The mean and variance of Xs can be calculated using the formulas for the Erlang distribution:

Mean of Xs = k/λ = 3/(4.8 students per minute) = 0.625 minutes

Variance of Xs = k/(λ^2) = 3/(4.8^2) = 0.1302 minutes^2

The mean of Xc is given by the inverse of the rate:

Mean of Xc = 1/λ' = 1/(1 cat per 5 minutes) = 5 minutes

Since Xs and Xc are independent, the mean and variance of their sum, X, can be calculated by summing their means and variances:

Mean of X = Mean of Xs + Mean of Xc = 0.625 minutes + 5 minutes = 5.625 minutes

Variance of X = Variance of Xs + Variance of Xc = 0.1302 minutes² + 5 minutes² = 25.1302 minutes²

(c) To find the probability that among the first 24 arrivals there is at least one cat, we can use the complement rule and the fact that the arrivals are independent.

Let A be the event that there is at least one cat among the first 24 arrivals.

The complement of this event, denoted by Ac, is the event that there are no cats among the first 24 arrivals.

The probability of no cats among the first 24 arrivals can be calculated using the Poisson distribution with a rate of λ' = 1 cat per 5 minutes.

We are interested in the probability of no cat arrivals, so we calculate the probability of 0 cat arrivals in 24 inter-arrival times:

P(Ac) = P(0 cats in 24 inter-arrival times) = (exp(-λ' × 5))²⁴ = (exp(-1))²⁴ ≈ 0.0009119

(d) To compute the probability that the 24th arrival is the second cat entering the building, we need to consider the cumulative probability up to the 24th arrival.

Let B be the event that the 24th arrival is the second cat.

The probability of the 24th arrival being the second cat can be calculated using the Poisson distribution with a rate of λ' = 1 cat per 5 minutes. We are interested in the probability of exactly 1 cat arrival in 24 inter-arrival times:

P(B) = P(1 cat in 24 inter-arrival times) = (24 × λ' × 5) × (exp(-λ' × 5))²⁴ = (24 × 1/5) × (exp(-1))²⁴ ≈ 0.0027937

(e) To compute the expected number of cats in the building at any time, t, as t approaches infinity, we can use the concept of shot noise. The shot noise model describes the random process that results from a superposition of random events occurring at different times.

In this case, the arrival of cats can be modeled as a Poisson process with a rate of λ' = 1 cat per 5 minutes.

Each cat stays in the building for exactly 10 minutes and then leaves through the other door.

This means that the arrival and departure processes can be considered as a superposition of Poisson processes.

The expected number of cats in the building at any time, t, as t approaches infinity, is given by the ratio of the arrival rate to the departure rate. In this case, the arrival rate is λ' = 1 cat per 5 minutes, and the departure rate is 1 cat per 10 minutes since each cat stays for 10 minutes.

Expected number of cats = λ' / (1/10) = 1 cat per 5 minutes × 10 minutes = 2 cats

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The correct answer is  you will get approximately £1.30 for one Australian dollar.

To find out how many British pounds you will get for one Australian dollar, we need to determine the exchange rate between the British pound and the Australian dollar.

Given that £1 = US$1.11316 and A$1 = US$0.8558, we can calculate the exchange rate between the British pound and the Australian dollar as follows:

£1 / (US$1.11316) = A$1 / (US$0.8558)

To find the value of £1 in Australian dollars, we can rearrange the equation:

£1 = (A$1 / (US$0.8558)) * (US$1.11316)

Calculating this expression, we get:

£1 ≈ (1 / 0.8558) * 1.11316 ≈ 1.2992

Therefore, you will get approximately £1.30 for one Australian dollar.

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The range of the possible values of r^2 is 0 to 1. It represents the proportion of the dependent variable’s variance that can be explained by the independent variable(s).


The coefficient of determination, often denoted as r^2, measures the proportion of the dependent variable’s variance that can be explained by the independent variable(s) in a statistical model. The value of r^2 ranges from 0 to 1.
A value of 0 for r^2 indicates that the independent variable(s) does not explain any of the variance in the dependent variable. On the other hand, a value of 1 implies that the independent variable(s) fully explain the observed variance in the dependent variable.
Therefore, the range of the possible values of r^2 is 0 to 1. Any positive numerical value within this range indicates a degree of explanatory power, while values outside this range are not meaningful in the context of r^2. It serves as a useful tool for assessing the strength of a statistical relationship and the predictive ability of a model.

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Answer: 7.785,7.476,7.293,8.37.7.9

Step-by-step explanation:

Answer:

-5=m

Step-by-step explanation:

-3/4m-1/2=2+1/4m

-2/4m-1/2=2

-2/4m=2 1/2

m=-5

The quotients of the long division expressions are 6x^2 + 2x - 6, 7x^3 - 4x^2 + 6x + 10 and 7x^3 + x^2 - 5x - 8

Polynomial set up 2

The long division expression is represented as

x + 5 | 6x^3 + 32x^2 + 4x - 21

So, we have the following division process

           6x^2 + 2x - 6

x + 5 | 6x^3 + 32x^2 + 4x - 21

           6x^3 + 30x^2

           --------------------------------

                      2x^2 + 4x - 21

                       2x^2 + 10x

           -------------------------------------

                       -6x - 21                      

                       -6x - 30

------------------------------------------

                                   9

Polynomial set up 3

The long division expression is represented as

2x - 3 | 14x^4 - 29x^3 + 24x^2 + 2x - 29

So, we have the following division process

            7x^3 - 4x^2 + 6x + 10

2x - 3 | 14x^4 - 29x^3 + 24x^2 + 2x - 29

            14x^4 - 21x^3

           --------------------------------

                       -8x^3 + 24x^2 + 2x - 29

                       -8x^3 + 12x^2                        

           -------------------------------------

                        12x^2 + 2x - 29

                        12x^2 - 18x

     ------------------------------------------

                                  20x - 29

                                  20x - 30

     ------------------------------------------

                                               1

Polynomial set up 5

The long division expression is represented as

2x - 1 | 14x^4 - 5x^3 - 11x^2 - 11x + 8

So, we have the following division process

            7x^3 + x^2 - 5x - 8

2x - 1 | 14x^4 - 5x^3 - 11x^2 - 11x + 8

            14x^4 - 7x^3

           --------------------------------

                       2x^3 - 11x^2 - 11x + 8

                       2x^3 - x^2                        

           -------------------------------------

                        -10x^2  - 11x + 8

                        -10x^2 + 5x

     ------------------------------------------

                                  -16x + 8

                                  -16x + 8

     ------------------------------------------

                                               0

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The median of complaints received per week is 2.

To find the median of complaints received per week, we need to arrange the probabilities in ascending order and then find the probability at the middle position.

Arranging the probabilities in ascending order, we get:

Number of complaints 0 1 2 3 4 5
Probability 0.05 0.07 0.09 0.18 0.26 0.35

The median position is (n+1)/2, where n is the total number of probabilities. In this case, n=6, so the median position is (6+1)/2=3.5.

The probability at position 3 is 0.09 and the probability at position 4 is 0.18. Therefore, the median probability is the average of these two probabilities, which is (0.09+0.18)/2=0.135.

To find the median number of complaints, we need to find the number of complaints that corresponds to the median probability. Starting from the first probability, we add up the probabilities until we reach a total of at least 0.135.

0.05 + 0.07 + 0.09 = 0.21

Therefore, the median number of complaints is 2.
So, the answer is 2 (rounded to the nearest integer).

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The median of complaints received per week is 2.

To find the median of complaints received per week, we need to arrange the probabilities in ascending order and then find the probability at the middle position.

Arranging the probabilities in ascending order, we get:

Number of complaints 0 1 2 3 4 5
Probability 0.05 0.07 0.09 0.18 0.26 0.35

The median position is (n+1)/2, where n is the total number of probabilities. In this case, n=6, so the median position is (6+1)/2=3.5.

The probability at position 3 is 0.09 and the probability at position 4 is 0.18. Therefore, the median probability is the average of these two probabilities, which is (0.09+0.18)/2=0.135.

To find the median number of complaints, we need to find the number of complaints that corresponds to the median probability. Starting from the first probability, we add up the probabilities until we reach a total of at least 0.135.

0.05 + 0.07 + 0.09 = 0.21

Therefore, the median number of complaints is 2.
So, the answer is 2 (rounded to the nearest integer).

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Answer:

:> so sorry Could you help me?

Step-by-step explanation:

a standard wooden pencil typically measures around 7 inches to 7.5 inches in length.

The average length of a pencil can vary depending on factors such as the type of pencil, region, and manufacturer. However, a standard wooden pencil typically measures around 7 inches to 7.5 inches in length. This range encompasses the most common lengths found in the market.

It's important to note that there may be slight variations in length between different pencil brands and styles. Additionally, specialty or novelty pencils may have different lengths based on their design or intended purpose.

To obtain a more accurate average length for a specific set of pencils or a particular region, you would need to measure a representative sample of pencils and calculate the average length based on the measurements obtained.

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Answer:

$0.22

Step-by-step explanation:

Ellen has a coupon of 1.55 off a loaf of bread

The regular price of the bread is 4.63, the loaf is cut into 14 slices

Therefore if she uses her coupon the price per slice can be calculated as follows

= 4.63-1.55

= 3.08

3.08/14

= 0.22

Hence the price is $0.22

The image is decomposed as follows: H1 and H2. Where original graph is Hx.

Hence, {H1 , H2} are valid decomposition of G.

A decomposition of a graph Hx is a set of edge-disjoints sub graphs of H, H1, H2, ......Hn, such that UHi = Hx

See the attached for the Image Hx - Pre decomposed and the image after the graph decomposition.

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Answer:

T.S.A = 233.29 cm²

volume of the cone = 235.84 cm³

Step-by-step explanation:

Given;

diameter of the cone, d = 9 cm

radius of the cone, r = 4.5 cm

slant height of the cone, l = 12 cm

The total surface of the cone is calculated as;

T.S.A = πr²  +  πrl

T.S.A = πr(r + l)

T.S.A = 3.142 x 4.5(4.5 + 12)

T.S.A = 233.29 cm²

The volume of the cone is calculated as;

\(V = \frac{1}{3} \pi r^2h\)

Where;

h is height of the cone

h² = 12² - 4.5²

h² = 123.75

h = √123.75

h = 11.12 cm

\(V = \frac{1}{3} \pi \times (4.5)^2 \times 11.12\\\\V = 235.84 \ cm^3\)

The expected value of the "Buy New" option is 724732.60.

Decision Tree:

To solve the given problem, the first step is to create a decision tree. The decision tree for the given problem is shown below:

Expected Value Calculation: The expected value of the "Buy New" option can be calculated using the following formula:

Expected Value = (Prob. of Prosperity * Payoff for Prosperity) + (Prob. of Recession * Payoff for Recession)

Substituting the given values in the above formula, we get:

Expected Value for "Buy New" = (0.7 * 1,035,332) + (0.3 * -150,000)Expected Value for "Buy New" = 724,732.60

Therefore, the expected value of the "Buy New" option is 724,732.60.

Conclusion:

To conclude, the decision tree is an effective tool used in decision making, especially when the consequences of different decisions are unclear. It helps individuals understand the costs and benefits of different choices and decide the best possible action based on their preferences and probabilities.

The expected value of the "Buy New" option is 724,732.60.

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Answer:

I think the answer is A=49

19.6x -2.1y + 13 is a simplified form of the 18.4x - 2.1y +9.6 - (-1.2x) + 3.4 equation.

Simplifying procedures is one way to achieve uniformity in job efforts, expenses, and time. It reduces diversity and variation that is pointless, harmful, or unneeded. Parenthesis, exponents, multiplication, division, addition, and subtraction are all referred to as PEMDAS. The order of the letters in PEMDAS informs you what to calculate first, second, third, and so on, until the computation is finished, given two or more operations in a single statement.

Given expression 18.4x - 2.1y +9.6 - (-1.2x) + 3.4

Simplifying using PEMDAS

=> 18.4x - 2.1y +9.6 - (-1.2x) + 3.4

First, we will open the bracket

=> 18.4x - 2.1y +9.6 + 1.2x + 3.4

Calculating the like terms

=> 19.6x -2.1y + 13

Therefore, a simplified form of the given equation is  19.6x -2.1y + 13.

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The system of linear equations which could be used to determine the number of free throws isaiah made and the number of two point shots he made is;

Let the number of free throws isaiah made be; x.

Let the number of two point shots he made be; y.

On this note, since the individual, isaiah scored a total of 12 points. The algebraic equations which represents the word phrase is;

x + 2y = 12.

Also, it follows from the task content that;

Isaiah made 4 times as many free throws as two point shots. The equation which represents the situation as described is;

x = 4y.

Consequently, the system of linear equations which correctly could be used to determine the number of free throws and two point shots isaiah made is;

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Answer:

zczczczczczcz

Step-by-step explanation:

According to the line of best fit, 79 consumers are predicted to use their card to pay during a day when 90 customers pay in cash. The correct answer is C.

The answer is 79. This is because the equation of the line of best fit is:

Which is a linear equation that represents the relationship between the number of customers who pay by cash (x) and the number of customers who pay by card (y).

To use this equation to predict the number of customers who pay by card on a day when 90 customers pay by cash, we can substitute x = 90 into the equation:

79.28 ≈ 79, hence the correct answer is C.

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