You sell instruments at a Caribbean music festival. You earn $326 by selling 12 sets of maracas, 6 sets of ​claves, and x djembe drums. Find the number of djembe drums you sold.

Answer:

Bellow

Step-by-step explanation:

1a) The point estimate of the population price difference between red and white wines is given by:

$$\bar{x}_1 - \bar{x}_2 = 20.87 - 19.33 = 1.54$$

Therefore, the point estimate of the population price difference between red and white wines is $1.54.

1b) The margin of error for alpha=0.01 can be calculated using the following formula:

$$ME = z_{\alpha/2}\cdot\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}$$

where $z_{\alpha/2}$ is the critical value of the standard normal distribution for the given level of significance, $s_1$ and $s_2$ are the sample standard deviations, and $n_1$ and $n_2$ are the sample sizes for the two populations.

For alpha=0.01, the critical value of the standard normal distribution is $z_{\alpha/2}=2.58$. Substituting the given values, we get:

$$ME = 2.58\cdot\sqrt{\frac{2.88^2}{40} + \frac{3.05^2}{40}} \approx 1.01$$

Therefore, the margin of error for alpha=0.01 is approximately $1.01.

1c) The confidence interval for the difference between the two population means can be calculated using the following formula:

$$(\bar{x}_1 - \bar{x}_2) \pm z_{\alpha/2}\cdot\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}$$

For alpha=0.05, the critical value of the standard normal distribution is $z_{\alpha/2}=1.96$. Substituting the given values, we get:

$$(20.87 - 19.33) \pm 1.96\cdot\sqrt{\frac{2.88^2}{40} + \frac{3.05^2}{40}}$$

Simplifying this expression, we get:

$$(1.54) \pm 1.11$$

Therefore, the 95% confidence interval for the difference between the two population means is approximately $(0.43, 2.65)$.

1. The determination of the predetermined overhead rate using the estimated direct labor costs is $5.30.

2. The actual overhead costs incurred are $2,426,200 while the amount of overhead cost applied to movies using the predetermined overhead rate is $2,438,000.

2b. Overhead is overapplied by $11,800.

3. The journal entry to close the overapplied overhead to the Cost of Goods Sold is as follows:

Debit Manufacturing Overhead $11,800

Credit Cost of Goods Sold $11,800

(To close the overapplied overhead to the cost of goods sold.)

Overhead is overapplied when the applied overhead is more than the actual overhead incurred.

The applied overhead is based on a predetermined overhead rate, which relies on estimates.

Overhead costs = $2,438,000

Direct labor costs = $460,000

Predetermined overhead rate = $5.30 ($2,438,000 ÷ $460,000)

Overhead costs incurred = $2,426,200

Direct labor costs = $460,000

Overhead Applied = $2,438,000 ($5.30 x $460,000)

Overhead overapplied = $11,800 ($2,438,000 - $2,426,200)

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To determine the relationship between drag force and speed, you can conduct an experiment using 5 coffee filters and a motion detector. First, set up the motion detector to track the speed of the coffee filters as they fall through the air. Then, drop each coffee filter one at a time and record the drag force measured by the motion detector.

Plot the drag force on the y-axis and the speed on the x-axis, and you should be able to observe a relationship between the two variables. As the speed of the coffee filter increases, the drag force will also increase. This relationship is due to air resistance, which causes the coffee filter to experience a drag force as it falls through the air.

By analyzing the data and creating a graph, you can determine the specific relationship between drag force and speed for these coffee filters. This information can be useful in understanding how air resistance affects the motion of objects and in designing experiments or models that take air resistance into account.

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The missing part of the table is completed as shown below

x      y

-1   1 / 6

0    1

3     216

Exponential function is a function of the form f(x) = a(b)^x

Considering the given problem,

the starting = a

the base = b

the exponents = x

Using the formula, y = 6^x the table is completed by substitution

for x = -1

y = 6^(-1) = 1/ 6

for x = 0

y = 6^(0) = 1

for x = 3

y = 6^(3) = 216

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The rays of the angle from the measure 1/2 turn is 180 degrees

From the question, we have the following parameters that can be used in our computation:

Angle measure = 1/2 turn

By definition, rays have two endpoints where they extend indefinitely on  one of the endpoints

As a general rule, we have

Substitute the known values in the above equation, so, we have the following representation

Angle measure = 1/2 * 360

Evaluate

Angle measure = 180

Hence, the angle measure is 180 degrees

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James had a longer commute to work than Samuel did.

We need to figure out how far each person went from their starting point to their destination in order to evaluate whose journey was longer. The formula for calculating the distance between two locations is as follows:

[tex]d = \sqrt{((x_2 - x_1)^2 + (y_2 - y_1)^2)[/tex]

For James:

Distance from his house to the gas station:

[tex]d_1 = \sqrt{((4 - 3)^2 + (1 - 4)^2)}\\ = \sqrt{(10)[/tex]

Distance from the gas station to his job:

[tex]d_2 = \sqrt{((9 - 4)^2 + (8 - 1)^2)}\\ = \sqrt{(90)}[/tex]

Total distance traveled:

[tex]d_1 + d_2 = \sqrt{(10)} + \sqrt{(90) }\\= 12.016[/tex]

For Samuel:

Distance from his house to his mother's house:

[tex]d_1 = \sqrt{((5 - 10)^2 + (8 - 2)^2)} \\= \sqrt{(74)[/tex]

Distance from his mother's house to his job:

[tex]d_2 = \sqrt{((4 - 5)^2 + (5 - 8)^2})\\ = \sqrt{(10)[/tex]

Total distance traveled:

[tex]d_1 + d_2 = \sqrt{(74)} + \sqrt{(10)} \\ =10.872[/tex]

Therefore, Samuel's journey to his job was shorter than James'

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Without the degrees of freedom, we cannot provide a specific p-value. If the chi-square statistic is 2.71 or more, the p-value will be equal to or less than the value corresponding to 2.71 in the chi-square distribution table for the given degrees of freedom.

1. The chi-square statistic is a measure of the difference between observed and expected frequencies in a contingency table. When the observed frequencies are similar to the expected frequencies, the chi-square statistic is low. When they are different, the chi-square statistic is high.

2. The p-value is a probability that indicates how likely it is to observe a chi-square statistic as extreme as the one obtained, assuming the null hypothesis (i.e., no association between the variables) is true. A lower p-value means there is stronger evidence against the null hypothesis, suggesting an association between the variables.

3. To determine the p-value corresponding to a chi-square statistic of 2.71, you would look up the value in a chi-square distribution table or use statistical software. The p-value depends on the degrees of freedom, which is determined by the size of the contingency table.

Without the degrees of freedom, we cannot provide a specific p-value. However, if the chi-square statistic is 2.71 or more, the p-value will be equal to or less than the value corresponding to 2.71 in the chi-square distribution table for the given degrees of freedom.

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Answer:

100

Step-by-step explanation:

To solve for y in the equation Y/1/5=20, we can multiply both sides of the equation by 1/5 to isolate y on one side of the equation. This gives us:

Y/1/5 * 1/5 = 20 * 1/5

Simplifying this expression gives us:

Y = 100

Therefore, the value of y is one hundred.

Answer:

Y = 4

Step-by-step explanation:

Now we have to,

→ Find the required value of Y.

The equation is,

→ Y/(1/5) = 20

Then the value of Y will be,

→ Y/(1/5) = 20

Simplifying the left hand side:

→ Y × (5/1) = 20

→ 5Y/1 = 20

→ 5Y = 20

Dividing 20 by the number 5:

→ Y = 20/5

→ [ Y = 4 ]

Hence, the value of Y is 4.

The best estimate for the dolphin population in the region is 600 dolphins.

Estimated Population Size = (Number of dolphins captured) × (Number of dolphins recaptured) / (Number of marked dolphins recaptured)

In this case, the equation would be:

Estimated Population Size = (60) × (330) / (33)

This equation simplifies to:

Estimated Population Size = 600

Therefore, the best estimate for the dolphin population in the region is 600 dolphins.

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The correct answer based on chi-square test is (c) No, because 0.12 > 0.05.

In a chi-square test, the p-value represents the probability of obtaining a test statistic as extreme or more extreme than the observed value, assuming that the null hypothesis is true. In this case, the null hypothesis is that there is no association between the two variables in the 2 x 2 table.

If the p-value is less than or equal to the significance level (0.05 in this case), then we reject the null hypothesis and conclude that there is a statistically significant association between the variables. However, if the p-value is greater than the significance level, we fail to reject the null hypothesis and conclude that there is not enough evidence to support a significant association.

In this scenario, the p-value is 0.12, which is greater than the significance level of 0.05. Therefore, we fail to reject the null hypothesis and conclude that the chi-square test based on the 2 x 2 table is not statistically significant.

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The alternative Hypothesis is that at least one of the mean total cholesterol levels is different from the others in the four groups of subjects.

A researcher can use an analysis of variance (ANOVA) parametric statistical method to determine if the mean total cholesterol level of the population is the same for four groups of subjects (Group 1 = Diet Restriction; Group 2 = Exercise; Group 3 = Both Diet and Exercise; Group 4 = None).

a. Statistical Test is ANOVA.
b. Null Hypothesis is that the mean total cholesterol level of the population is the same for all four groups.
c. Alternative Hypothesis is that the mean total cholesterol level of the population is different for at least one group.

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Answer:

Step-by-step explanation:

Answer:72

Answer:

72 feet square

Step-by-step explanation:

18 x 8 ÷ 2 = 72

The probability that a student living in a dormitory at ASU does not receive a coupon for a free sandwich is 0.6436.

The probability that a student lives in West Hall is 0.58 and the probability that a student lives in South Tower is 0.42. The probability that a student in West Hall receives a coupon is 0.26, and the probability that a student in South Tower receives a coupon is 0.19.

To find the probability that a student does not receive a coupon, we can use the complement rule: the probability of the event happening plus the probability of the event not happening is equal to 1. So, the probability of a student not receiving a coupon is 1 minus the probability of a student receiving a coupon.

Using a tree diagram, we can find the probability of a student receiving a coupon or not. Starting with the first branch of the tree, we have:

West Hall (0.58)
- Coupon (0.26)
- No Coupon (0.74)

South Tower (0.42)
- Coupon (0.19)
- No Coupon (0.81)

To find the probability of a student not receiving a coupon, we add the probability of no coupon from each branch of the tree and multiply by the probability of being in that branch. So, the probability of a student not receiving a coupon is:

(0.58 x 0.74) + (0.42 x 0.81) = 0.6436

Therefore, the probability that a student living in a dormitory at ASU does not receive a coupon for a free sandwich is 0.6436.
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The sample proportion of rainbow lollipops in the festival promoter's sample is 0.33 (27/82), rounded to two decimal places. The population proportion of rainbow lollipops among all products offered at the stop of the tour is 0.32 (17/53), rounded to two decimal places.

The sample proportion and population proportion of rainbow lollipops in the given situation.

For the entire population (all products offered) at the stop, there were 17 rainbow lollipops out of every 53 products offered. To find the population proportion (P), we can use the formula:

P = Number of Rainbow Lollipops / Total Number of Products
P = 17 / 53

Now let's calculate the population proportion:
P ≈ 0.32 (rounded to two decimal places)

For the festival promoter's sample, he found that 27 of the 82 products offered were rainbow lollipops. To find the sample proportion (p'), we can use the formula:

p' = Number of Rainbow Lollipops in Sample / Total Number of Products in Sample
p' = 27 / 82

Now let's calculate the sample proportion:
p' ≈ 0.33 (rounded to two decimal places)

So, in proper notation, the population proportion (P) is approximately 0.32, and the sample proportion (p') is approximately 0.33.

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The Net Pay for the year for gross annual pay is $19 163. Employment insurance premiums are deducted at a rate of 2 with income taxes at a rate of 17% on all amounts over $8131 is $16,137.03.

To find the net pay for the year, we need to subtract the deductions from the gross pay and then subtract the income tax from the remaining amount.

First, we need to find the total amount deducted for EI and CPP premiums:

EI premium = 2.25% of $19,163 = $431.67

CPP premium = 3.75% of $19,163 = $720.86

Total deductions = $431.67 + $720.86 = $1,152.53

Next, we need to find the taxable income by subtracting the basic personal amount from the gross pay:

Taxable income = $19,163 - $8,131 = $11,032

Then, we need to calculate the income tax on the taxable income:

Income tax = 17% of ($11,032) = $1,873.44

Finally, we can calculate the net pay by subtracting the total deductions and income tax from the gross pay:

Net pay = $19,163 - $1,152.53 - $1,873.44 = $16,137.03

Therefore, the net pay for the year is $16,137.03.

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Using the given ratio we can see that there are 19 used cars.

We know that the dealership reported that they have 5 new cars for every 1 used car on the lot, so we need to use that ratio.

5/6 of the cars are new.

1/6 of the cars are used.

The total number is 114, then the number of used cars is:

(1/6)*114 = 19

There are 19 used cars.

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The cost of 4 burgers and 6 hot dogs is $25.

We are given that;

Expression= 3.25+2ℎ

Number of burgers=444

Number of hot dogs= 666

Now,

To find the cost of 4 burgers and 6 hot dogs, we need to substitute b = 4 and h = 6 in the expression 3.25b+2h. We get:

3.25(4)+2(6)

Using the order of operations, we first multiply 3.25 by 4 and 2 by 6. We get:

13+12

Then we add 13 and 12. We get:

25

Therefore, by the given expression the answer will be $25.

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The answer to the mathematical expression of Cos (90°-0) / sin (180°- 0) - sin^2 (-0) is:

= -1

To calculate the expression, we can begin by determining the values and subtracting or dividing as is the case. First, we begin by determining the values as follows:

Cos 90° = 0

Cos 0 = 1

Sin 180° = 0

Sin -0 = 0

Now we express the values as follows:

Cos (90°-0) / sin (180°- 0) - sin^2 (-0)

0 - 1/0 - 0

= -1

So, the answer obtained from resolving this expression is -1.

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The probability of drawing two green cards is 25/169

From the question, we have the following parameters that can be used in our computation:

Cards = 13

Green = 5

Selecting the first card we have

P(Green) = 5/13

The card is returned

So, we have the probablility of the second to be

P(Green) = 5/13

The probability of drawing two green cards is

P = 5/13 * 5/13

Evaluate

P = 25/169

Hence, the probability is 25/169

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Based on the information given, we can conclude that there is a significant difference between the two populations.

The calculated z-score of 1.51 is greater than the critical value of 1.96 (at the 5% level of significance), which indicates that the sample mean differences are unlikely to have occurred by chance. Therefore, we reject the null hypothesis and conclude that household debt is different in the two cities.
At this level of significance, we cannot conclude that there is a significant difference between the two populations.

Explanation:
To determine if there is a significant difference between the mean household debt of Regina and Saskatoon households at the 5% level of significance, we need to compare the calculated z-score of 1.51 to the critical z-score for a two-tailed test. For a 5% level of significance, the critical z-scores are -1.96 and 1.96. Since 1.51 is between -1.96 and 1.96, we cannot reject the null hypothesis, which means we cannot conclude that there is a significant difference between the two populations at the 5% level of significance.

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Answer:

a

Step-by-step explanation:

a

The angles of the cyclic quadrilateral are

In a cyclic quadrilateral the opposite angles are supplementary hence we have that

x - 4 + x + 8 = 180 degrees

gathering like terms

2x = 180 - 8 + 4

2x = 176

isolating x

x = 88 degrees

angles on each side

x- 4 = 88 - 4 = 84

x + 8 = 88 + 8 = 96

2x - 78 = 2(88) - 78 = 98

sum of the angles of a cyclic quadrilateral is 360

the fourth angle = 360 - 84 - 96 - 98

the fourth angle = 80 degrees

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The solutions in radical form is

This is of the form

(3 ± √7)²

Then we have to write this in two cases such that

Case 1: (3 + √7)²

Case 2: (3 - √7)²

Solve the first case

(3 + √7)²

(3 + √7)(3 + √7)

= 3² + 2(3)(√7) + (√7)² =

9 + 6√7 + 7

= 16 + 6√7

Next we have to solve for case 2

(3 - √7)²

(3 - √7)(3 - √7)

= 3² - 2(3)(√7) + (√7)²

= 9 - 6√7 + 7

= 16 - 6√7

The values and solutions would be:

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Answer: The diver's elevation below sea level after both dives is 22 feet.

The diver starts 16 feet below sea level, and then dives another 6 feet. This means the diver is now 16 + 6 = 22 feet below sea level.

Step-by-step explanation:

The value of x based on the stated expression using mathematical operations is -1.

The calculation of x will be performed using mathematical operations in following format. Here are the steps -

Solve the parenthesis

18x + 72 = 54

Switch the position of number 72 from Left Hand Side to Right Hand Side

18x = 54 - 72

Performing subtraction on Right Hand Side of the equation

18x = -18

Rewrite the equation according to x

x = -18/18

Performing division on Right Hand Side of the equation

x = -1

Hence, the value of x is -1.

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The average of the three points A, B and C is M(x, y) = (- 7 / 9, 17 / 9).

In this problem we need to find the average of three points (A, B, C), each point has different weights. The average can be found by means of following expression:

[tex]M(x, y) = \frac{\sum\limits_{i = 1}^{n} w_{i}\cdot P_{i}(x, y)}{\sum \limits_{i = 1}^{n}w_{i}}[/tex]

Where:

Then, the average of points A, B and C are described below:

M(x, y) = [1 · (8, - 6) + 4 · (9, - 5) + 4 · (- 6, 7)] / (1 + 4 + 4)

M(x, y) = [(8, - 6) + (9, - 5) + (- 24, 28)] / 9

M(x, y) = (- 7, 17) / 9

M(x, y) = (- 7 / 9, 17 / 9)

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The points that would form a square are (2, 2), (2, -2), (-2, 2), (-2, -2)

From the question, we have the following parameters that can be used in our computation:

Forming a square

As a general rule

A square has equal sides and the angles at the vertices are 90 degrees

Since it must make a point with origin at its center, then the center must be (0, 0)

So, we have the following points (2, 2), (2, -2), (-2, 2), (-2, -2)

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If these conditions/assumptions are met, then the two-sample test for means with independent samples can be used to determine if there is a statistically significant difference between the means of two independent groups.

In order for the two-sample test for means with independent samples to be appropriate, the following conditions/assumptions must be met:

Independent samples: The samples for each group should be selected independently of each other.

Normality: The population distributions should be approximately normal, or the sample sizes should be large enough (n > 30) for the central limit theorem to apply.

Equal variances: The variances of the two populations should be approximately equal. This assumption is important for calculating the pooled variance estimate, which is used in the t-test formula.

Random sampling: The samples should be randomly selected from the populations of interest.

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