Alex was hired to unpack 576 items of glass wear, at five cents per piece unpacked. For every item broken in the process, however, Alex had to pay $1.98. At the end of the job, Alex received $22.71. How many items did Alex break.

The greatest common factor for the expression  27x+9y will be 9.

The highest number that is a factor of all the numbers is known as the greatest common factor of two or more numbers. The largest factor that splits both numbers is said to be the greatest common factor.

List the prime factors of each integer before calculating the greatest common factor.

It is given that the expression is,

27x+9y

We can take out 9 commons in the expression because it does not affect the expression,

The greatest common factor is,

9( 3x + y)

We obtain 9 as the value that we can take commonly from the complete expression. As a result, it is the greatest common factor.

Thus, the greatest common factor for the expression  27x+9y will be 9.

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Final answer:

The point estimate of the population proportion defective, given 30 defects in a 500 item sample, is 0.06 or 6%.

Explanation:

The point estimate of the population proportion defective can be calculated by dividing the number of defective items in the sample by the total number of items in the sample.

In this case, there are 30 defective items out of a sample of 500 items.

So the point estimate of the population proportion defective is:

Point estimate = Number of defective items / Total number of items

Point estimate = 30 / 500 = 0.06

The state in question produces 78% of the country's total annual tart cherry production.

The state in question produces 78 out of every 100 tart cherries annually, which is the same as 78 out of 100 or 78/100. When written as a fraction, this can be turned into a decimal by dividing the numerator (78) by the denominator (100). This will give 0.78. To convert this decimal into a percentage, we then multiply by 100 which leads to 78%. This means the state produces 78% of the total tart cherries grown in the country each year.

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Answer:

The area of the canvas, including the floor is 1548 sq. feet.          

Step-by-step explanation:

Given : A conical tent made of canvas has a base that is 34 feet across and a slant height of 12 feet.

To find : What is the area of the canvas, including the floor?

Solution :  

A conical tent made of canvas has a base that is 34 feet.

The diameter of the base is D=34 feet.

The radius of the base is [tex]r=\frac{34}{2}=17[/tex]

The slant height l=12

The area of the canvas, including the floor is

[tex]A=\pi r l+\pi r^2[/tex]

[tex]A=\pi r(l+r)[/tex]

[tex]A=3.14\times 17(17+12)[/tex]

[tex]A=3.14\times 17\times29[/tex]

[tex]A=1548.02[/tex]

In nearest whole unit, A=1548 sq. feet.

Therefore, The area of the canvas, including the floor is 1548 sq. feet.

To find when a publisher makes or loses money, compare the cost function C=96,000+20x to the revenue function R=26x. The break-even point is at x=16,000 books produced and sold weekly. Below this, the company incurs losses.

When determining when a publishing company makes or loses money, we investigate the relationship between cost and revenue functions. The cost function given is C=96,000+20x and the revenue function is R=26x, with x representing the number of books produced and sold per week. A company loses money when costs exceed revenues, that is when C > R.

To find the quantity of books where this happens, we equate the two equations:

Therefore, at the production and sale of 16,000 books, the company will break even. Producing fewer than 16,000 books would result in a loss because the cost would be higher than the revenue generated.

Answer:

Option A. is the answer.

Step-by-step explanation:

Charlie is making a scale model of his kitchen.

The kitchen measures 12 feet by 11 feet.

We can use the unitary method to get the scale measures.

Since his scale is 3 feet = 2 inches.

So 1 feet = [tex]\frac{2}{3}[/tex] inches

and 12 feet = [tex]\frac{(2)(12)}{3} = 8[/tex] inches

Similarly 11 feet = [tex]\frac{(11)(2)}{3}=7.3[/tex] inches

Therefore, scale measures of the kitchen will be = 8 in by 7.3 in

Option A. is the correct answer.

Answer:  The given equation will have infinite number of solutions.

Step-by-step explanation:  We are given to check the number of solutions to the following equation :

[tex]25-4x=15-3x+10-x~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

To find the number of solutions, we must solve the given equation.

The solution of equation (i) is

[tex]25-4x=15-3x+10-x\\\\\Rightarrow 25-4x=25-4x\\\\\Rightarrow 4x-4x=25-25\\\\\Rightarrow 0=0,[/tex] which is always true.

Thus, the given equation will have infinite number of solutions.

Answer:

Correct Answer: vertex form

Step-by-step explanation:

Using the properties of normal distribution and the Z-score related to the given percentile, it can be inferred that the minimum grade for a 'C' in this college statistics class is approximately 72.

In this scenario, the professor's grades reflect a normal distribution, therefore, we can utilize the properties of normal distribution to answer your question. The probability given, 67.36%, corresponds to a Z-score of -0.45 (you can find this in standard statistical tables).

We'll utilize the formula Z = (X - μ) / σ, Z is the Z-score, X is the data point, μ is the mean, and σ is the standard deviation. Therefore, if we rearrange the formula to find X (the data point,or in this case, the lowest grades for students receiving a C or above), it will be X = Z * σ + μ. Substituting the given values in the equation gives X = -0.45 * 9 + 76.5. This results in a minimum score approximately equal to 72.45, or 72 if we consider only whole marks. Hence, our conclusion that the minimum grade for a 'C' is 72.

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The minimum score required to receive at least a grade of C in this normally distributed class is approximately 72.54.

To determine the minimum score that students need to receive at least a grade of C in a class where grades are normally distributed, we analyze the problem with a mean [tex](\mu)[/tex] of 76.5 and a standard deviation [tex](\sigma)[/tex] of 9.

We know that 67.36% of the students received a grade of C or above.

This corresponds to the top 67.36% of the distribution.

The bottom 32.64% of the distribution received less than a C.

The z-score associated with the 32.64th percentile can be found using z-tables or a standard normal distribution calculator:

z = -0.44

Next, we convert this z-score to the actual score using the formula:

[tex]X = \mu + z\cdot \sigma[/tex]

Substituting the given values:

X = 76.5 + (-0.44 * 9) = 76.5 - 3.96 = 72.54

Thus, the minimum score required for a grade of at least C is approximately 72.54.

2.) Simplify a fraction:

3/7 divided by 6 is equal to 1/14.

To divide 3/7 by 6, you can multiply the numerator (3) by the reciprocal of the denominator (6).

The reciprocal of 6 is 1/6.

So, (3/7) divided by 6 can be calculated as:

(3/7) × (1/6)

= (3 × 1) / (7× 6)

= 3/42

Divide numerator and denominator by 3:

= 1/14

Therefore, 3/7 divided by 6 is equal to 1/14.

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The solutions of the quadratic equation x^2 = 9x + 6 are (9 + sqrt(105))/2 and (9 - sqrt(105))/2.

To find the solutions of the quadratic equation x^2 = 9x + 6, we can use the quadratic formula. The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the solutions are given by:

x = (-b +- sqrt(b^2 - 4ac)) / (2a)

In this case, a = 1, b = -9, and c = -6. Plugging in these values, we get:

x = (-(-9) +- sqrt((-9)^2 - 4(1)(-6))) / (2(1))

Simplifying further:

x = (9 +- sqrt(81 + 24)) / 2

x = (9 +- sqrt(105)) / 2

So the solutions of the quadratic equation x^2 = 9x + 6 are:

x = (9 + sqrt(105)) / 2

x = (9 - sqrt(105)) / 2

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The solutions to the quadratic equation x² = 9x + 6 are x = 3 and x = 6. This is done by rearranging the equation and then factoring into two binomials (x - 3) and (x - 6) equals 0, then set each binomial equal to zero.

The given quadratic equation is x² = 9x + 6. To find the solutions of the quadratic equation, we first move all the terms to one side. This gives us: x² - 9x - 6 = 0. This is now a standard quadratic equation, and can be solved by either factoring or using the Quadratic Formula.  

If we opt to solve via factoring, we're looking to factorize the original expression into two binomial expressions, essentially looking for two numbers which both add up to -9 and multiply to -6. These two numbers are -3 and 6. Therefore, the quadratic equation can be factored as follows: (x - 3)(x - 6) = 0. Setting each factor equal to 0 gives the possible solutions for x, in this case, x = 3 and x = 6.

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To calculate the probability of selecting no female voters in a sample of 5, given that 40% of the registered voters are female, we multiply the probability of selecting a male voter (60%) five times, which equals to (0.6)⁵ or 7.776% probability.

The question involves calculating the probability that none of the five randomly selected voters are female, given that 40% of registered voters are female. To find this probability, we need to use the complementary probability, which is the probability of the opposite event occurring (that is, selecting a male voter).

The probability of selecting one male voter randomly is 60% (or 0.6), as females account for 40% of the registered voters. When we select 5 voters independently, we multiply the individual probabilities together because the events are independent. Therefore, the probability of selecting no female voters in 5 trials is calculated as:

(0.6) × (0.6) × (0.6)  × (0.6) × (0.6) = (0.6)⁵ = 0.07776 or 7.776%.
This is the probability that a random sample of 5 voters will contain no females.