after 1 year on the job, Grady got a raise from $10.50 per hour to $11.34 per hour. what was the percent increase in his hourly wage

Final answer:

Tripling the side lengths of a pentagon multiplies its perimeter by three, resulting in a new perimeter that is three times the original perimeter.

Explanation:

When we triple the side lengths of a pentagon, we essentially multiply the length of each side by three. Since a pentagon has five sides, if each side is tripled, the new perimeter will be three times the original perimeter. This is because the perimeter of any polygon is the sum of the lengths of its sides. In a more mathematical expression, if the original length of a side of the pentagon is s, the perimeter (P) of the original pentagon is 5s. When we triple the side length, each side becomes 3s, making the new perimeter P' to be 5(3s) = 3(5s) or simply three times the original perimeter, which is 15s.

Answer:  The required product is [tex]\dfrac{5}{4k^2}.[/tex]

Step-by-step explanation:  We are to calculate the following product:

[tex]P=5\dfrac{k}{6}\times \dfrac{3}{2k^3}.[/tex]

We will be using the following property of exponents:

[tex]\dfrac{a^x}{a^y}=a^{x-y}.[/tex]

We have

[tex]P\\\\\\=5\dfrac{k}{6}\times\dfrac{3}{2k^3}\\\\\\=\dfrac{5}{6}\times\dfrac{3}{2}k^{1-3}\\\\\\=\dfrac{5}{4}k^{-2}=\dfrac{5}{4k^2}.[/tex]

Thus, the required product is [tex]\dfrac{5}{4k^2}.[/tex]

Answer:

Step-by-step explanation:

Without the specific results from the survey, we cannot determine which juice is most popular. Based on the description, it seems the juice bar used a systematic sampling method to survey customers.

Without more specific information presented from the juice bar's survey, such as the breakdown of customer preferences for each juice drink, we cannot determine which juice drink is most popular. The provided options - Power Pear, Tangy Apple, Lemon Lift, or Wild Berry - don't have accompanying survey data. So, any inference about the most popular juice would be a guess and not based on survey results.

However, what we can infer from the provided information is about the sampling method used by the juice bar. The juice bar appeared to use a systematic sampling technique, selecting every 10th customer over a week and surveyed a total of 75 customers.

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The given polynomial is classified as a trinomial because it has three terms. The highest exponent is 5, making the degree of the polynomial 5. Therefore, the correct answer is D) trinomial; 5.

The given polynomial is 3y2 - y4 + y5. This polynomial consists of three terms, so it is a trinomial.

To find the degree of the polynomial, we look for the term with the highest exponent in the polynomial.

In this case, it is y5, so the degree of the polynomial is 5. Therefore, the correct classification and degree for the given polynomial is D) trinomial; 5.

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Answer:

6/31

Step-by-step explanation:

4 1/3 divided by 5 1/6

Change the mixed numbers to improper fractions

4 1/3 = (3*4+1)/3 =13/3

5 1/6 = (6*5+1)/6 =31/6

13/3 ÷ 31/6

Copy dot flip

13/3 * 6/31

13*2/31

26/31

The question is asking what fraction should we end up multiplying by(the flip fraction)

That is 6/31

Answer:

The Answer is A) 6/31

Step-by-step explanation:

To find the probability that a person actually has the disease given a positive test result, we can use Bayes' theorem. Given the probabilities of a positive test result given the person has the disease and does not have the disease, as well as the probability of having the disease, we can calculate the conditional probability.

To find the probability that a person actually has the disease given a positive test result, we can use Bayes' theorem. Let's define the events: A = person has the disease, B = person tests positive. We are given that P(B|A) = 0.9 (probability of a positive test given the person has the disease), P(B|A') = 0.06 (probability of a positive test given the person does not have the disease), and P(A) = 0.16 (probability that a person has the disease).

Bayes' theorem states: P(A|B) = (P(B|A) * P(A)) / P(B).

Substituting the given values, we have: P(A|B) = (0.9 * 0.16) / P(B).

We don't have the value of P(B), but we can calculate it as follows: P(B) = (P(B|A) * P(A)) + (P(B|A') * P(A')). Plugging in the values, we have: P(B) = (0.9 * 0.16) + (0.06 * 0.84).

Now we can substitute the value of P(B) into the formula for P(A|B) to calculate the probability.

Therefore, the probability that the person actually has the disease given a positive test result is approximately 0.231.

The length of the sides of a square with a perimeter between 14 and 72 feet inclusive ranges from 3.5 to 18 feet. By dividing the perimeter limits by 4, we find the possible side lengths, leading to the answer: 3.5 ≤ x ≤ 18 (option a)).

The student is asking about the possible lengths of the sides of a square given that the perimeter must be between 14 and 72 feet inclusive. To solve this, we recall that the perimeter (P) of a square with side length (a) is given by P = 4a. Therefore, if P is between 14 and 72 feet, we divide these values by 4 to find the possible values for a.

The lower limit for the side length is 14 ÷ 4 = 3.5 feet, and the upper limit is 72 ÷ 4 = 18 feet. So the possible values for the side length of the square can be represented as 3.5 ≤ x ≤ 18. Hence, the correct answer to the student's question is option a).

Answer: D) 4.5 Standard Deviations Above the Mean

Step-by-step explanation:

Answer:

The number of large size candles sells are 12 and the number of small size candles are 5 .

Step-by-step explanation:

As given

Sia sells large candles for $3 each and small candles for $2 each.

She sold 17 candles for $46.00.

Let us assume that the large size candle sells are x .

Let us assume that the small size candle sells are y.

Equation becomes

x + y = 17

3x + 2y = 46

Multiply x + y = 17 by 3 and subtracted from 3x + 2y = 46 .

3x - 3x + 2y - 3y = 46 - 51

-y = - 5

y = 5

Put in the equation x + y = 17 .

x + 5 = 17

x = 17 - 5

x = 12

Therefore the number of large size candles sells are 12 and the number of small size candles are 5 .

Sia sells 12 large candles and 5 small candles in order to earn $46 and this can be determined by forming the linear equation in two variables.

Given :

Let the total number of large candles be 'x' and the total number of small candles be 'y'. So the linear equation that represents the total number of candles is:

x + y = 17

x = 17 - y       ---- (1)

Now, the linear equation that represents the total earning of Sia is:

3x + 2y = 46     ---- (2)

Substitute the value of 'x' in equation (2).

3(17 - y) + 2y = 46

Simplify the above equation in order to determine the value of 'y'.

51 - 3y + 2y = 46

51 - 46 = y

y = 5

Now, substitute the value of 'y' in equation (1).

x = 17 - 5

x = 12

So, Sia sells 12 large candles and 5 small candles in order to earn $46.

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Answer:

33.2

Step-by-step explanation:

Given that Coach King is holding a free-throw shooting contest for some students in his PE class. The students participating in the contest shoot 10 free throws each.

For finding mean we sum up all the entries and divide by total number here 10

Total

=[tex]26+34+42+40+38+35+20+34+45+18\\=332[/tex]

Mean =[tex]\frac{332}{10} \\=33.2[/tex]

Out of the four options given, we find that Option C is right

Answer:

272

Step-by-step explanation:

Mutilpy the base then divide by 1/2

[tex]4\\[/tex] more workers are needed to do this job in 12 hours.

Given,

Three workers can do a job in 28 hours.

Let [tex]x[/tex] no. of worker needed.

workers          3       [tex]x[/tex]

time (hours)   28      12

The fewer workers there are the more the hours that are required,  

and the more workers there are the fewer hours that are required.  

Therefore workers and hours are inversely proportional.

So,  

[tex]3 \times28=x \times12[/tex]

[tex]x=\frac{3 \times28}{12} \\\\x=7[/tex]

So, 7 workers can do that job in 12 hours.

Hence ([tex]7-3=4[/tex]) [tex]4[/tex] more workers needed to do this job in 12 hours.

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Final answer:

To complete a job in 12 hours rather than 28, 4 additional workers are needed, considering the work rate is directly proportional to the number of workers.

Explanation:

The question relates to the optimization of workers to complete a job in a certain amount of time, a common problem in work-rate mathematics.

To solve it, we first determine the rate at which three workers complete the job: since they can complete one job in 28 hours, their combined rate is 1 job per 28 hours, or 1/28 job per hour. Now, we need to find out how many workers are required to complete the job in 12 hours. This means we want the workers to work at a rate that completes 1 job in 12 hours, or 1/12 job per hour.

To find the number of workers needed, we set up the proportion: (3 workers)/(1/28 job per hour) = (x workers)/(1/12 job per hour). Solving for x gives us x = (3 workers) × (1/12 job per hour) / (1/28 job per hour), which simplifies to x = 7 workers. Since we already have 3 workers, we need an additional 4 workers to complete the job in 12 hours.

Answer:

Both P & Q

Step-by-step explanation

Just a bit late..