Checkpoint: Angle Relationships in Triangles
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Question
In triangle ABC, m∠A=(6x+9)∘, m∠B=(x−8)∘, and the exterior angle at C is 141∘What is the measure of angle B?

Based on the given information, the company estimates its sales to be 200,000 units in the first quarter. Assuming a 20,000 unit increase each quarter over the year, the second quarter's sales would be 220,000 units, the third quarter's sales would be 240,000 units, and the fourth quarter's sales would be 260,000 units.

To calculate the desired ending inventory of finished goods, we take 25% of the expected sales for the next quarter. For example, to determine the desired ending inventory for the first quarter, we take 25% of 220,000 units (the expected sales for the second quarter), which equals 55,000 units.

Each unit sells for $35, so the total sales revenue for the first quarter would be 200,000 units x $35 = $7,000,000.

Of the sales, 70% are for cash, so the company would receive $4,900,000 in cash for the first quarter's sales. The remaining 30% of sales are credit sales, and assuming that 70% of credit customers pay within the quarter, the company would receive an additional 21,000 units x $35 = $735,000 in the first quarter. The remainder of the credit sales, which is 30% x 30,000 units = 9,000 units, would be received in the following quarter.

Overall, the company expects to have increasing sales throughout the year and desires to maintain a 25% ending inventory of finished goods. The company also expects a mix of cash and credit sales, with 70% of credit customers paying within the quarter and the remainder paying in the following quarter.

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The semiconductor manufacturer can demonstrate process capability for the customer, as the fraction of defective devices is less than 0.05 at the α = 0.05 significance level.

To answer your question, we will test the hypothesis with the given data. The hypothesis to be tested is:

H0: p = 0.05 (null hypothesis)
H1: p < 0.05 (alternative hypothesis)

Here, α = 0.05 (significance level), and the sample consists of 200 devices.

Step 1: Calculate the sample proportion of defective devices.
Sample proportion (p-hat) = (Number of defective devices) / (Sample size) = 4 / 200 = 0.02

Step 2: Calculate the test statistic (z-score).
z = (p-hat - p) / sqrt((p * (1 - p)) / n)
z = (0.02 - 0.05) / sqrt((0.05 * (1 - 0.05)) / 200) = -2.18

Step 3: Determine the critical z-score (z-critical) for the given α.
For α = 0.05 and a one-tailed test, the z-critical is -1.645.

Step 4: Compare the test statistic (z) with the critical z-score (z-critical).
Since z = -2.18 < z-critical = -1.645, we reject the null hypothesis (H0).

Conclusion: Based on the sample, the semiconductor manufacturer can demonstrate process capability for the customer, as the fraction of defective devices is less than 0.05 at the α = 0.05 significance level.

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The theoretical probability of flipping heads and rolling a 1 or 2 is 1/6.

Now, We have;

The sample space for flipping a coin and rolling a number cube are:

Flipping a coin: {H, T}

There are 2 possible outcomes, since the coin is fair.

Rolling a number cube: {1, 2, 3, 4, 5, 6}

Since, There are 6 possible outcomes, since the number cube is standard

So, the total number of outcomes for the combined experiment is,

2 x 6 = 12.

The events of flipping heads and rolling a 1 or a 2 are independent,

Hence, The probability of flipping heads is,

⇒ 1/2,

And, The probability of rolling a 1 or 2 is,

⇒ 2/6,

So, the probability of flipping heads and rolling a 1 or 2 is;

= (1/2) x (2/6)

= 1/6

Therefore, the theoretical probability of flipping heads and rolling a 1 or 2 is 1/6.

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The possible observed values of a discrete random variable can be listed in a countable collection. A random variable is a measurement to be taken in a probability experiment.

An observed value of a random variable is the measurement that has been taken. A discrete random variable is a random variable in which there is a countable collection of possible observed values. That is, the discrete random variable can only take on specific values within a given range, and the probability associated with each value can be calculated. This countable collection of possible observed values is finite or countably infinite, and the probabilities sum up to 1.

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Answer:

4 units left

Step-by-step explanation:

Since you are changing the x value by negative 4, you move left towards the negatives 4 units.

In the equation for the two-sample t-test for independent samples, the difference between sample means is divided by b. standard error of the difference between means.

The correct answer is b. The difference between sample means is divided by the standard error of the difference between means in the equation for the two-sample t-test for independent samples. This is because the standard error of the difference between means takes into account both sample sizes and sample variances, providing a more accurate estimate of the standard deviation of the difference between the two population means.
In the equation for the two-sample t-test for independent samples, the difference between sample means is divided by b. standard error of the difference between means.

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a. The new revenue can be estimated as R(20,11) = 150 - 24 = $126.

b. The food truck would need to sell 20 + 8 = 28 tacos to compensate for the decrease in burrito sales and keep the revenue at $150.

a. To estimate the food truck's revenue when 4 fewer burritos are sold, we can use the given information. We know that Rb(20,15) = 6, which means that the revenue changes by $6 for every additional burrito sold. If 4 fewer burritos are sold, the change in revenue would be 4 * (-6) = -$24.
b. To maintain a revenue of $150 despite selling 4 fewer burritos, we need to find out how many more tacos must be sold. We know that Rt(20,15) = 3, meaning the revenue changes by $3 for every additional taco sold. Since the loss in revenue due to selling 4 fewer burritos is $24, we need to sell enough tacos to make up for this loss. So, 24/3 = 8 more tacos need to be sold.

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There is 20 students in her class.

Here, we have,

3/10= size of slice;

we can get 3 slices from one pizza.

There are 6 pizzas..... 3x6=18;

there will be a remained of 1/10 from each pizza

because 3/10 is not an even number.

Now u would have (6) 1/10's.... So 1/10+1/10+1/10= 3/10 and 1/10+1/10+1/10=3/10.....

That makes two more slices for two more students......

18+2=20 slices for 20 kids in the class.

Hence, There is 20 students in her class.

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There are 36 cards in the box.  In this scenario, we are given that the probability of choosing a red card from a box is one-third. We also know that there are 24 blue cards in the box. Our goal is to find the total number of cards in the box.

Let's use the concept of probability to solve this problem. The probability of an event is defined as the ratio of the number of favorable outcomes to the total number of possible outcomes. In this case, the probability of choosing a red card is given as 1/3, and the favorable outcome is selecting a red card. Let R be the number of red cards, and T be the total number of cards in the box. The probability formula can be represented as:

Probability of choosing a red card = R / T

We are given that the probability of choosing a red card is 1/3:

1/3 = R / T

Since there are 24 blue cards in the box, we can represent the total number of cards as the sum of red and blue cards:

T = R + 24

Now, we can solve the system of equations to find the values of R and T:

1. 1/3 = R / T
2. T = R + 24

From equation 1, we can express R as:

R = (1/3) * T

Substitute this expression for R in equation 2:

T = (1/3) * T + 24

Multiplying both sides by 3 to eliminate the fraction, we get:

3T = T + 72

Subtracting T from both sides:

2T = 72

Now, divide by 2 to find the total number of cards, T:

T = 36

So, there are 36 cards in the box.

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There are 200.96 square inches that make up half of the cookie cake.

We have to given that;

The diameter of a circular cookie cake is 16 inches.

Now, We know that;

Area of circle = πr²

Here, Diameter = 16 inches

Hence, Radius = 16 / 2

                       = 8 in

Thus, Area of circular cookie cake is,

⇒ A = πr²

⇒ A = 3.14 × 8²

⇒ A = 200.96 inches²

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The answer resulted in x = 5 after the operation as the picture suggests, hope this helps

The probability of observing a test statistic as extreme or more extreme than -0.56, assuming the null hypothesis is true, is 0.575. The correct answer is 2) Test Statistic: -0.56, P-Value: 0.575.

The test statistic is calculated by taking the difference between the observed proportion (9/26 = 0.346) and the hypothesized proportion (0.4), and dividing by the standard error of the proportion. This gives a test statistic of -0.56.

The p-value is the probability of observing a test statistic as extreme or more extreme than the one calculated, assuming the null hypothesis is true. In this case, we are conducting a two-tailed test, since the alternative hypothesis is not specified as being greater than or less than 0.4. Using a standard normal distribution table or calculator, we can find the area under the curve that corresponds to a test statistic of -0.56, which is 0.575. This means that the probability of observing a test statistic as extreme or more extreme than -0.56, assuming the null hypothesis is true, is 0.575.

Therefore, the correct answer is 2) Test Statistic: -0.56, P-Value: 0.575.

In this scenario, the student is testing the null hypothesis (p = 0.4) against the alternative hypothesis (p ≠ 0.4) to determine if the proportion of students using iPhones is different from 0.4. The sample size is 26, with 9 students using iPhones. The test statistic is -0.56 and the p-value is 0.575. Therefore, the correct answer is option 2) Test Statistic: -0.56, P-Value: 0.575.

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Therefore, the vector form of the equation y = x² - 8x + 15 is y = (x - 4)² + 14. The vertex of the parabola is at the point (4, 14).

To convert the quadratic equation y = x² - 8x + 15 from standard form to vertex form, we need to complete the square by adding and subtracting a constant term. Here's the step-by-step explanation:

Factor the coefficient of x²: The coefficient of x² is 1, so we don't need to factor it.

Group the x terms: Rewrite the quadratic equation as y = (x² - 8x) + 15.

Complete the square: To complete the square, we need to add and subtract a constant term that will make the expression inside the parentheses a perfect square trinomial. The constant we need to add is half of the coefficient of x, squared: (8/2)² = 16.

y = (x² - 8x + 16 - 16) + 15 // add and subtract 16

y = (x - 4)² - 1 + 15 // factor and simplify

Simplify: Now we can simplify the expression by combining the constants -1 and 15 to get 14.

y = (x - 4)² + 14

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The probability that the student chosen will walk to school is 0.5156. 

Out of the 64 understudies (students) overviewed, let x be the number of understudies overviewed in Year 9.

At that point, we know that x = 1.3*20 = 26.

Out of the 20 understudies (students) studied in Year 7, 75% strolled to school, so 15 understudies in Year 7 strolled to school.

In Year 9, 8 more understudies strolled to a school than did not walk. Let w be the number of understudies in Year 9 who strolled to school.

At that point, the number of understudies in Year 9 who did not walk to school is x - w. So we have:

w + (x - w) = 26 (since x is the entire number of understudies overviewed in Year 9)

w - (x - w) = 8 (since 8 more understudies strolled to a school than did not walk)

Understanding this framework of conditions, we get w = 17 and x - w = 9

Out of the remaining understudies studied, which are in Year 11, we know that more strolled to a school than in Year 9.

In this manner, the likelihood that an understudy chosen at irregular strolls to school is:

P(walk to school) = (15 + 17 + x/4)/64

where x/4 is the number of understudies overviewed in Year 11 who strolled to school. We do not know the esteem of x/4, but we do know that it is more prominent than 9, since more understudies strolled to school in Year 11 than in Year 9.

In this manner, ready to say that:

P(walk to school) > (15 + 17 + 9)/64 = 0.5156

So the likelihood that a student chooses irregular walks to school is more noteworthy than 0.5156. 

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In order to place 8 distinguishable rooks on an 8x8 chessboard without any of them being able to capture each other, you will need to ensure that each rook occupies a unique row and column.

Step 1: Place the first rook. There are 8 different locations to choose from (one in each row).
Step 2: Place the second rook. There are 7 remaining locations to choose from, as you cannot place it in the same row or column as the first rook.
Step 3: Place the third rook. There are 6 remaining locations to choose from, avoiding the rows and columns of the first two rooks.
Step 4: Continue this process until all 8 rooks have been placed.

To find the total number of ways to place the 8 distinguishable rooks, multiply the number of choices for each step:

8 (choices for rook 1) * 7 (choices for rook 2) * 6 (choices for rook 3) * 5 (choices for rook 4) * 4 (choices for rook 5) * 3 (choices for rook 6) * 2 (choices for rook 7) * 1 (choice for rook 8) = 40,320 ways.

To solve this problem, we can use the principle of multiplication. We start by placing the first rook in any of the 64 squares on the chessboard. There are 64 choices for the first rook.

Next, we need to place the second rook in a location that is not attacked by the first rook. Since rooks can attack any square in the same row or column as them, we need to choose a square that is not in the same row or column as the first rook. There are 7 rows and 7 columns remaining, so there are 14 squares in which the second rook can be placed.

For the third rook, we need to choose a location that is not attacked by either the first or second rook. This means we need to choose a square that is not in the same row or column as the first two rooks. There are 6 rows and 6 columns remaining, so there are 12 squares in which the third rook can be placed.

Continuing in this way, we see that the number of choices for the nth rook is equal to the number of rows and columns remaining after the (n-1)th rook has been placed. So, the total number of ways to place all 8 rooks on the chessboard is:

64 × 14 × 12 × 10 × 8 × 6 × 4 × 2 = 16,777,216

Therefore, there are 16,777,216 ways to place 8 distinguishable rooks on an 8 × 8 chessboard so that none can capture any other.

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The solution of the formula for the variable, m as required to be determined is; m = Fr² / GM.

It follows from the task content that the complete question indicates a formula;

F = GMm / r²

Hence, to solve for the variable m; multiply both sides by r² so that we have;

Fr² = GMm

Finally divide both sides by GM so that we have;

m = Fr² / GM

Ultimately, the formula with m as the subject is; m = Fr² / GM.

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The cafeteria should buy 40 bags of onions.

To find how many bags the cafeteria should buy, we need to divide the total number of onions needed by the number of onions in each bag:

Number of bags = Total number of onions / Number of onions in each bag

Substituting the given values, we get:

Number of bags = 800 onions / 20 onions per bag

Simplifying the expression on the right-hand side, we get:

Number of bags = 40 bags

The solution is a simple arithmetic calculation based on the formula for determining the number of bags needed to purchase, given the total number of onions necessary and the amount of onions in each bag. This approach includes dividing the total number of onions by the amount of onions in each bag to determine the number of bags needed.

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The assessment that the student gave about resolution is correct hence the statement is true.

A resolution is a decision that a person makes and it has to do with the will of the individual. As such the resolution has a lot to do with the ability of a person to be able to stand by the decision  that he or she has been able to make as a result of careful thought.

In this case, the resolution neatly wraps up any unresolved issues, demonstrates the character's growth and lessons learned, and introduces a general theme.

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Answer

the third side can measure 2 in, 3 in, or 4 in

Explanation

inequality theorem

a + b > c

a + c > b

b + c > a

2 = a

b = 3

c = x

a + b > c

2 + 3 > x

5 > x

x= 4, 3, 2, or 1 in

a + c > b

2 + x > 3

x = 4, 3, or 2

b + c > a

3 + x > 2

x = 4, 3, or 2

Answer: D

Step-by-step explanation:

If something is to the power of it means multiply the fractions.

since all inside the parenthesis is being multiplied you can distribute that exponent

[tex](64h^{16} x^{4} )^{\frac{1}{2} }[/tex]            

[tex]64^{\frac{1}{2} } h^{16(\frac{1}{2}) } x^{4(\frac{1}{2} )} }[/tex]          reduce fraction in exponents

[tex]64^{\frac{1}{2} } h^{8 } x^{2} }[/tex]                now for the 64^1/2   than means take the square root

[tex]8 h^{8 } x^{2} }[/tex]                   fractions are actually roots

Hypothesis testing is a procedure based on sample evidence and probability theory to determine whether the hypothesis is a reasonable statement. The statement is true.

Yes, that is correct. Hypothesis testing involves collecting sample evidence and using probability theory to analyze the likelihood of the hypothesis being true. The process involves setting up a null hypothesis, which is the statement being tested, and an alternative hypothesis. The sample evidence is then gathered and analyzed using statistical tests to determine the probability of observing the results if the null hypothesis were true. If the probability is sufficiently low, the null hypothesis is rejected in favour of the alternative hypothesis. The use of probability theory in hypothesis testing allows for a more objective and rigorous approach to drawing conclusions from data.

The complete question is:-

Hypothesis testing is a procedure based on sample evidence and probability theory to determine whether the hypothesis is a reasonable statement. True/False

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The number that is two more than the quotient of a number and is equal to 4 is 16. Let's break down the sentence into a numerical condition:

"Two more than the remainder of a number and 8" can be spoken to as (x/8) + 2, where x is the number we are attempting to discover.

The sentence moreover states that this expression is "equal to 4", so we are able to type in

(x/8) + 2 = 4

To fathom for x, we will confine the variable on one side of the condition. We will start by subtracting 2 from both sides:

(x/8) = 4 - 2

Streamlining the right-hand side gives:

(x/8) = 2

At long last, we are able to illuminate for x by increasing both sides by 8:

x = 2 x 8

x = 16

thus, the number we are seeking out is 16.

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complete question: What is the number which is two more than the quotient of a number and 8 is equal to 4?

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A gumball machine contains 8 blue gumballs and 8 red gumballs. two gumballs are purchased, one after the other, without replacement. The probability that the second gumball is red is 2/15.

Unravel the issue, we are able to utilize the conditional likelihood equation, which says that the likelihood of an occasion A given that occasion B has happened is rise to the likelihood of both A and B happening isolated by the likelihood of B happening:

P(A|B) = P(A and B) / P(B)

P(A|B) = P(A and B) / P(B)

where:  P(A and B) = (8/16) * (8/15) = 32/240

P(B) is the likelihood that the primary gumball isn't ruddy, which is break even with to the likelihood of selecting a blue gumball on the to begin-with draw, i.e., P(B) = 8/16

Substituting these values into the equation, we get:

P(A|B) = P(A and B) / P(B) = (32/240) / (8/16) = 2/15

thus, the likelihood that the moment gumball is ruddy, given that the primary gumball isn't ruddy, is 2/15.

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Answer:

74.0 lb

Step-by-step explanation:

Since 15% melts in 1 hour, after 1 hour, 85% of 520 lb is left.

After each subsequent hour, 85% of the previous weight is left.

Original weight: 520 lb

After 1 hour: 520 lb × 0.85

After 2 hours: 520 lb × 0.85 × 0.85 = 520 × 0.85²

After 3 hours: 520 lb × 0.85² × 0.85 = 520 lb × 0.85³

...

After n hours: 520 lb × 0.85^n

Here, we need the weight after 12 hours, so n = 12.

weight after 12 hours = 520 lb × 0.85^12

weight after 12 hours = 73.96569... lb

Answer: 74.0 lb

Answer:

Step-by-step explanation:

Answer:

16 tiles

Step-by-step explanation: