What is the mean of the data set?

10, 15, 14, 8, 18, 11, 12, 12, 10, 10, 17, 16


12.00

12.25

12.75

15.50

The consecutive even integers whose squares sum to 164 are [tex]\(8\) and \(10\) or \(-10\) and \(-8\).[/tex]

Let the two consecutive even integers be  [tex]\( x \) and \( x + 2 \).[/tex]

The sum of their squares is given by:

[tex]\[ x^2 + (x + 2)^2 = 164 \][/tex]

Expanding and simplifying this equation:

[tex]\[ x^2 + (x^2 + 4x + 4) = 164 \]\[ 2x^2 + 4x + 4 = 164 \]\[ 2x^2 + 4x + 4 - 164 = 0 \]\[ 2x^2 + 4x - 160 = 0 \]\[ x^2 + 2x - 80 = 0 \][/tex]

Now, solve the quadratic equation [tex]\( x^2 + 2x - 80 = 0 \).[/tex]  We use the quadratic formula  [tex]\( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \),[/tex]  where [tex]\( a = 1 \), \( b = 2 \), and \( c = -80 \).[/tex]

[tex]\[ x = \frac{-2 \pm \sqrt{2^2 - 4 \cdot 1 \cdot (-80)}}{2 \cdot 1} \]\[ x = \frac{-2 \pm \sqrt{4 + 320}}{2} \]\[ x = \frac{-2 \pm \sqrt{324}}{2} \]\[ x = \frac{-2 \pm 18}{2} \][/tex]

This gives us two solutions:

[tex]\[ x = \frac{-2 + 18}{2} = \frac{16}{2} = 8 \]\[ x = \frac{-2 - 18}{2} = \frac{-20}{2} = -10 \][/tex]

So, the two pairs of consecutive even integers are  [tex]\( 8 \) and \( 10 \), or \( -10 \) and \( -8 \).[/tex]

Therefore, the integers are [tex]\( 8 \) and \( 10 \), or \( -10 \) and \( -8 \).[/tex]

Answer:  The correct option is

(C) The point was reflected over the y-axis and translated up.

Step-by-step explanation:  Given that a point undergoes two transformations as follows :

"The x-coordinate's sign changes and the y-coordinate increases."

We are to select the correct transformations.

We know that

when x co-ordinate's sign changes, the point (x, y) becomes (-x, y). This is reflection across y-axis.

And, if y co-ordinate increases by k units, then (x, y) becomes (x, y+k). That is, the point (x, y) is translated k units upwards.

Thus, the required transformations are

The point was reflected over the y-axis and translated up.

Option (C) is CORRECT.

To find the exact length of the curve, we can use the concept of arc length. The formula for the arc length of a curve y = f(x) on the interval [a, b] is given by: L = ∫√(1 + (f'(x))^2) dx, where f'(x) is the derivative of f(x). In this case, y2 = 4(x + 1)3 can be rewritten as y = 2√(x + 1)^3. Taking the derivative of y with respect to x, we get y' = 3(x + 1)^(3/2). Plugging this into the formula for arc length: L = ∫√(1 + (3(x + 1)^(3/2))^2) dx = ∫√(1 + 9(x + 1)^3) dx. We can then evaluate this integral over the interval [0, 1] to find the exact length of the curve.

To find the exact length of the curve y2 = 4(x + 1)3, 0 ≤ x ≤ 1, y > 0, we can use the concept of arc length. The formula for the arc length of a curve y = f(x) on the interval [a, b] is given by:

L = ∫√(1 + (f'(x))^2) dx, where f'(x) is the derivative of f(x).

In this case, y2 = 4(x + 1)3 can be rewritten as y = 2√(x + 1)^3. Taking the derivative of y with respect to x, we get y' = 3(x + 1)^(3/2). Plugging this into the formula for arc length:

L = ∫√(1 + (3(x + 1)^(3/2))^2) dx = ∫√(1 + 9(x + 1)^3) dx

We can then evaluate this integral over the interval [0, 1] to find the exact length of the curve.

Answer:

b.

21

Step-by-step explanation:

Answer: 10% -APEX

2 year late answer lol.

Answer:

Central High School plays Eastern High School in a basketball game. Eastern had double the score of Central before Central scored a three-pointer as the game ended.

The variable, c, represents Central's score before the three-pointer. Express the total points scored in the game as a variable expression. Check all that apply.

Step-by-step explanation:

The total points scored in the game as a variable expression is 2c + c + 3.

Those expressions who might look different but their simplified forms are same expressions are called equivalent expressions.

It is given that Central High School plays Eastern High School in a basketball game. Eastern had double the score of Central before Central scored a three-pointer as the game ended:

Let consider Central High School score be c

We knowt that the variable, c, represents Central's score before the three-pointer.

So, when Eastern doubled the score of Central, it is 2c

A Central scored a three-pointer as the game ended, it is + 3

To get the total points scored in the game, add all the actual variables

= (Eastern double points + Central single point + Central three-pointer)

= 2c + c + 3

So, the total points scored in the game as a variable expression is 2c + c + 3.

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By setting up an equation equating the cost of shipping with both Mailboxes Plus and United Packages, we determine that Mr. Molinari's package weighs 30 ounces.

Mailboxes Plus charges a flat rate of $5 plus $0.25 per ounce, while United Packages charges $2 plus $0.35 per ounce. Since the cost is the same for either service, we can equate the two expressions and solve for the weight of the package in ounces.

Let x represent the weight of the package in ounces. The cost for Mailboxes Plus is then $5 + $0.25x, and for United Packages, it is $2 + $0.35x. Setting these two expressions equal to each other, we get:

$5 + $0.25x = $2 + $0.35x

Now, we will solve for x:

Therefore, Mr. Molinari's package weighs 30 ounces.

Answer:

Step-by-step explanation:33

Answer:

B) Y- Intercept

Step-by-step explanation:

I Took The USATP Quiz ^_^

The solution is, the independent variable is number of stars, in the situation.

Division is the process of splitting a number or an amount into equal parts. Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.

here, we have,

from the given information, we get,

Points are a function of stars, so stars is the independent variable.

The variable that depends on that, the dependent variable, is points.

now, we have,

2400/6= 400

4000/10= 400

5200/13= 400

we get,

y=400x

Every star is 400 points and the independent variable is number of stars Brian picks up because the amount of points he gets is dependent on the number of stars he has.

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Based on the 80% figure, we'd expect 320 out of 400 adult smokers to have started before they turned 18. Observing 360 in this situation could be unusual but would require a statistical test to confirm.

This question pertains to concepts of probability and statistics. If 80% of adult smokers began smoking before they turned 18, then in a group of 400 randomly selected adult smokers, we would expect 80% (or 0.8) of that 400 to have started smoking before the age of 18. This means 320 out of the 400 individuals started smoking before turning 18.

As for the second part of the question, if we observed 360 smokers out of 400 who started smoking before turning 18, this number is higher than our expectation of 320. This could be seen as unusual, but it also might occur by chance. To determine how unusual it is, we would typically conduct a statistical test, which would require additional information not provided in the question.

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Final answer:

To determine the amount of almonds needed for a third of the recipe, if one full batch requires 3 cups, you would divide 3 cups by 3, resulting in 1 cup of almonds for a third of the recipe.

Explanation:

To calculate the amount of almonds needed for a third of the recipe, we first need to determine the total number of cups used for the full recipe. If the original recipe calls for 3 cups of almonds to make one batch, and the person is making 5 batches, they would initially need 15 cups of almonds (since 3 cups per batch multiplied by 5 batches equals 15 cups).

If they only want to make a third of one batch, we would take the amount needed for one batch, which is 3 cups, and divide it by 3 to find the required amount. So, 1 cup of almonds is needed for a third of the recipe, because 3 cups divided by 3 equals 1 cup.

The probability that a student earned an A on the last test is 7/12. This is found by dividing the number of students who earned an A by the total number of students and simplifying the fraction.

To find the probability that a randomly chosen student earned an A on the last test, we need to consider the total number of students and the number of students who earned an A.

The total number of students is 24, and 14 of them earned an A. The probability is calculated by dividing the number of students who earned an A by the total number of students:

Probability = Number of Students Who Earned an A / Total Number of Students = 14/24.

Next, we simplify the fraction 14/24 by finding the greatest common divisor (GCD) of 14 and 24, which is 2. Dividing both the numerator and the denominator by 2, we get:

Simplified Probability = (14 ÷ 2) / (24 ÷ 2) = 7/12.

Therefore, the probability that a student earned an A on the last test is 7/12.

The radius of the circle is 1 meter.

We have,

The formula for the circumference of a circle is:

C = 2πr

where C is the circumference, r is the radius, and π is a constant equal to approximately 3.14.

We are given the circumference of the circle as 6.28 meters, so we can substitute this value into the formula:

6.28 = 2πr

Dividing both sides by 2π gives:

r = 6.28 / (2π)

r = 6.28 / (2 x 3.14)

r = 1

Therefore,

The radius of the circle is 1 meter.

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Final answer:

To find the circle's radius with a circumference of 6.28 meters using π=3.14, use the formula C=2πr. By rearranging and solving for r, the radius is found to be 1 meter.

Explanation:

The question is about finding the radius of a circle when the circumference is given as 6.28 meters and using 3.14 for π (pi). To find the radius, we use the formula for the circumference of a circle, C = 2πr, where C is the circumference, r is the radius, and π is Pi. Given C=6.28 m and π=3.14, we rearrange the formula to solve for r: r = C / (2π).

Plugging in the given values, r = 6.28 / (2×3.14) = 6.28 / 6.28 = 1. Therefore, the radius of the circle is 1 meter.

Mr. Dell taught six members of the chess club who then taught 18 classmates, and those classmates taught 36 friends, resulting in 60 people being taught how to play chess in total.

To find the total number of people taught, we compute as follows:

First level (by Mr. Dell): 6 members

Second level (6 members x 3 classmates each): 18 classmates

Third level (18 classmates x 2 friends each): 36 friend

To determine the total number of people taught to play chess, we sum the three levels: 6 members + 18 classmates + 36 friends = 60 people. Therefore, a total of 60 people were taught to play chess