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Grant is making muffins for a reunion. The recipe to makes 12 muffins. The recipe for bran muffins makes 18 muffins. He wants to make the same number of each kind of muffin using only recipes of each. A. What is the least number of each type of muffin Grant can make B. How many batches of each recipe will Grant make if he makes t number of each type of muffin possible? Blueberry: batches Bran: batches

Answers

Answer 1

Answer:

Answer:

a 36

b 3 blueberry, 2 bran

Answer 2

Answer:

Final answer:

The least number of each type of muffin that Grant can make is 36. This would entail creating three batches of the blueberry recipe and two batches of the bran recipe. If Grant makes a 't' type of each muffin, where 't' equals 36, he would need three batches of blueberry muffins and two bran muffins.

Explanation:

In this question, Grant is trying to find the least common multiple (LCM) of the two muffin recipes. The LCM of a set of numbers is the smallest positive integer, a multiple of each number in the set. In this case, the blueberry muffin recipe makes 12 muffins, and the bran muffin recipe makes 18. The LCM of 12 and 18 is 36.

Therefore, the smallest number of each type of muffin Grant can make is 36. To achieve this, Grant will need to make three batches of the blueberry muffin recipe (because 3 * 12 = 36) and two batches of the bran muffin recipe (because 2 * 18 = 36).

So, if he makes 't' number of each type of muffin possible, that means 't' = 36, he would make 't/12' = three batches of blueberry muffins and 't/18' = 2 batches of bran muffins.

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What is the volume of the prism shown below?A. 16 cubic inchesB. 21 cubic inchesC. 90 cubic inchesD. 126 cubic inchesHELP ASAP
A paint manufacturer made a modification to a paint to speed up its drying time. Independent simple random samples of 11 cans of type A (the original paint) and 9 cans of type B (the modified paint) were selected and applied to similar surfaces. The drying times, in hours, were recorded. The following 98% confidence interval was obtained for μ1 - μ2, the difference between the mean drying time for paint cans of type A and the mean drying time for paint cans of type B: 4.90 hrs < μ1 - μ2 < 17.50 hrs What does the confidence interval suggest about the population means?A. The confidence interval includes 0 which suggests that the two population means might be equal. There doesn't appear to be a significant difference between the mean drying time for paint type A and the mean drying time for paint type B. The modification does not seem to be effective in reducing drying times. B. The confidence interval includes only positive values which suggests that the mean drying time for paint type A is greater than the mean drying time for paint type B. The modification seems to be effective in reducing drying times. C. The confidence interval includes only positive values which suggests that the two population means might be equal. There doesn't appear to be a significant difference between the mean drying time for paint type A and the mean drying time for paint type B. The modification does not seem to be effective in reducing drying times. D. The confidence interval includes only positive values which suggests that the mean drying time for paint type A is smaller than the mean drying time for paint type B. The modification does not seem to be effective in reducing drying times.
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Describe how to simplify the expression 3^-6/3^-4a. Divide the bases and then add the exponents.
b. Keep the base the same and then add the exponents.
c. Multiply the bases and then subtract the exponents.
d. Keep the base the same and then subtract the exponents.

Answers

Answer:

The correct option is d. To simplify the given expression we should keep the base the same and then subtract the exponents.

Step-by-step explanation:

The given expression is

$(3^(-6))/(3^(-4))$

In the above expression we have common base 3 but the exponents are different.

According to the rule of exponent, if the numerator and denominator have same base and different exponent, then the base remains the same and the exponent of denominator subtracted from exponent of numerator.

$(a^m)/(a^n) =a^(m-n)$

Use this rule in the given expression.

$(3^(-6))/(3^(-4))=3^(-6-(-4))$

$(3^(-6))/(3^(-4))=3^(-2)$

Therefore the correct option is d.

Answer:

d or Keep the base the same and then subtract the exponents.

Step-by-step explanation:

At the U.S. Open Tennis Championship a statistician keeps track of every serve that a player hits during the tournament. The statistician reported that the mean serve speed was 100 miles per hour (mph) and the standard deviation of the serve speeds was 15 mph. Assume that the statistician also gave us the information that the distribution of serve speeds was mound- shaped and symmetric. What percentage of the player's serves were between 115 mph and 145 mph

Answers

Answer:

15.74% of the player's serves were between 115 mph and 145 mph

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = (X - \mu)/(\sigma)$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

$\mu = 100, \sigma = 15$

What percentage of the player's serves were between 115 mph and 145 mph

This is the pvalue of Z when X = 145 subtracted by the pvalue of Z when X = 115.

X = 145

$Z = (X - \mu)/(\sigma)$

$Z = (145 - 100)/(15)$

$Z = 3$

$Z = 3$ has a pvalue of 0.9987

X = 115

$Z = (X - \mu)/(\sigma)$

$Z = (115 - 100)/(15)$

$Z = 1$

$Z = 1$ has a pvalue of 0.8413

0.9987 - 0.8413 = 0.1574

15.74% of the player's serves were between 115 mph and 145 mph

Final answer:

A total of 27% of the player's serves at the U.S. Open Tennis Championship were between 115mph and 145mph. This was found using the Empirical Rule which applies to a normal distribution of serve speeds.

Explanation:

This problem is a classic example of the use of the Empirical Rule in statistics. The Empirical Rule, also known as the 68-95-99.7 rule, applies to a normal distribution, which is a bell-shaped curve (mound-shaped and symmetric) as mentioned in the problem. This rule states that approximately 68% of the data falls within one standard deviation from the mean, 95% within two standard deviations, and 99.7% within three standard deviations.

Given that the mean serve speed is 100 mph and the standard deviation is 15 mph, serves of 115 mph are one standard deviation above the mean and serves of 145 mph are three standard deviations above the mean. Therefore, we are looking for the percentage of serves between these two values. According to the Empirical Rule, this would be 95% (coverage for up to 2 standard deviations) minus 68% (coverage for up to 1 standard deviation), which equals 27%. So, 27% of the player's serves were between 115 mph and 145 mph.

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What is the product of 4.201 and 5.3? Round to the nearest hundredth

Answers

Answer:

22.2653 or 22.27

Step-by-step explanation:

hope this helps

Answer: 22.265

Step-by-step explanation: 4.201x5.3 = 22.265

A small theater had 9 rows of 25 chairs each. An extra 6 chairs have just been brought in. How many chairs are in the theater now?

Answers

231 chairs because 9 times 25 is 225, plus 6 is 231

4*25=100 4*25=100 add 6 =206+25= 231

A local charity sponsors a 5K race to raise money. It receives $55 per race entry and $10,000 in donations, but it must spend $15 per race entry to cover the cost of the race. Write and solve an inequality to determine the number of race entries the charity needs to raise at least $55,000.

Answers

Final answer:

The charity needs to earn 55,000 dollars. Subtracting the donation of 10,000 they need to make 45,000 dollars from the race entries. They make 40 dollars per entry, so dividing 45,000 by 40 gives the number of race entries needed: 1125.

Explanation:

The charity makes $40 per race entry ($55 entry fee minus the $15 cost). It also receives an additional $10,000 in donations. To raise at least $55,000, the charity would need to make at least $45,000 from race entries because $55,000 - $10,000 = $45,000. This is the target earnings from the race entries.

The race entry is $40 so we divide the target by the amount earned per race to find out the number of race entries needed: $45,000 / $40 = 1125. Therefore, the charity would need to have at least 1125 race entries to raise at least $55,000.

So the inequality would be: 40x + 10,000 ≥ 55,000, where x is the number of race entries. Solving the inequality would give x ≥ 1125.