The list represents the number of students who left school early in a 12-day period.

85, 30, 42, 49, 60, 77, 68, 64, 36, 45, 72, 50

Find the mean and interpret its meaning as it relates to the number of students who left school early.

The mean is about 56.5, and it represents the most common number of students who left school early.
The mean is about 62, and it represents the most common number of students who left school early.
The mean is about 56.5, and it represents the average number of students who left school early.
The mean is about 62, and it represents the average number of students who left school early.

1)The expression 4x^2-16x+12/x^2-9 is undefined when the denominator, x^2-9, equals zero because division by zero is undefined.

x^2-9 equals zero when x equals 3 or x equals -3. Therefore, the expression is undefined at x = 3 and x = -3. In all other cases, the expression is defined.

2) The given expression is:

(5-2x)/(x+2) + x^2/(x^2-4) - 5

To simplify this expression, we need to first find the LCD (least common denominator) of the two fractions. The denominator of the first fraction is x+2, and the denominator of the second fraction is x^2-4, which can be factored as (x+2)(x-2). So the LCD is (x+2)(x-2). Now we can rewrite the expression with this common denominator:

[(5-2x)(x-2) + x^2(x+2) - 5(x+2)(x-2)] / [(x+2)(x-2)]

Expanding the brackets and simplifying, we get:

(-x^3 - 3x^2 - 3x + 5) / [(x+2)(x-2)]

This expression is undefined when the denominator, (x+2)(x-2), equals zero because division by zero is undefined.

(x+2)(x-2) equals zero when x equals -2 or x equals 2. Therefore, the expression is undefined at x = -2 and x = 2. In all other cases, the expression is defined.

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The investment amount that is receiving simple interest is $35 divided by the interest rate.

To find the investment amount that is receiving simple interest, we can use the formula:

Total Interest = Principal * Interest Rate * Time

Given that the interest earned in the first year is $35, and the total interest for the next 10 years is $350, we can set up two equations:

35 = Principal * Interest Rate * 1
350 = Principal * Interest Rate * 10

Since the interest rate remains the same, we can divide the second equation by 10 to get:

35 = Principal * Interest Rate * 1
35 = Principal * Interest Rate

Now, we can divide both sides of the equation by the interest rate to isolate the principal:

35 / Interest Rate = Principal

Therefore, the investment amount that is receiving simple interest is $35 divided by the interest rate.

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Answer: 81

Step-by-step explanation: If you add all of the numbers, then you end up getting 81.35 and 81.35 estimated to the nearest whole number is 81 because that's the closest whole number to 81.35.

Answer:

The correct answers is -8.3232

Step-by-step explanation:

Answer:

61.5 in 41 mins 90 in one hour,

Step-by-step explanation:

i multiplied 1 1/2 by 41 and by 60

hope this helps i am very sorry if it is incorrect..

\(\cfrac{6^{\frac{1}{4}}}{36^{-\frac{x}{2}}}=1\implies 6^{\frac{1}{4}}=36^{-\frac{x}{2}}\implies 6^{\frac{1}{4}}=(6^2)^{-\frac{x}{2}}\implies 6^{\frac{1}{4}}=6^{-2\cdot \frac{x}{2}} \\\\\\ \stackrel{\textit{same base, exponents must be the same}}{6^{\frac{1}{4}}=6^{-x}\implies \cfrac{1}{4}=-x}\implies -\cfrac{1}{4}=x\)

Answer:

its E

Step-by-step explanation:

The probability that a randomly chosen customer's drink will be cold is 0.08 or 8%.

To calculate the probability that a randomly chosen customer's drink will be cold, we need to determine the number of customers who ordered a cold drink and divide it by the total number of customers.

From the given data, we can see that there were 8 customers who ordered a cold drink. The total number of customers is 100.

Therefore, the probability that a randomly chosen customer's drink will be cold is:

P(cold) = Number of customers who ordered a cold drink / Total number of customers

P(cold) = 8 / 100

Simplifying the fraction:

P(cold) = 0.08

So, the probability that a randomly chosen customer's drink will be cold is 0.08 or 8%.

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The probability that a randomly chosen customer's drink will be cold is 25/100.

To calculate the probability that a randomly chosen customer's drink will be cold, we need to determine the number of cold drinks out of the total number of customers.

From the given data, we see that there were 25 cold drinks out of 100 total customers.

Therefore, the probability is calculated as the number of cold drinks (8) divided by the total number of customers (100), which results in a probability of 25/100.

Hence, the probability that a randomly chosen customer's drink will be cold is 25/100.

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The 99% confidence interval for the proportion of executives who want to strengthen innovation is: CI = (0.199, 0.261)

What is confidence interval?

A confidence interval is a statistical measure that provides a range of values within which the true population parameter, such as the mean or proportion, is estimated to lie with a specified level of confidence.

To find the confidence interval for a proportion, we need to use the formula:

CI = p ± z\(\sqrt{(pq/n)\)

where:

CI: confidence interval

p: sample proportion

q: 1 - p

z: z-score from the standard normal distribution for the desired confidence level (99% in this case)

n: sample size

From the problem statement, we know that p = 0.23, n = 1,379, and we want a 99% confidence interval. To find the z-score, we can use a standard normal distribution table or calculator, which gives us a value of 2.576.

Substituting the values into the formula, we get:

CI = 0.23 ± 2.576\(\sqrt{(0.230.77/1379)\)

CI = 0.23 ± 0.031

Therefore, the 99% confidence interval for the proportion of executives who want to strengthen innovation is:

CI = (0.199, 0.261)

This means we can be 99% confident that the true proportion of executives who want to strengthen innovation falls within this range.

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By the triangle congruence we can use the SSA method to prove the base angles are congruent.

If two or more triangles are congruent, it depends on how big their sides and angles are. The three sides and three angles of a triangle determine its size and shape, accordingly. Two triangles are said to be congruent if the pairings of respective sides and corresponding angles are equal.

These are exactly the same size and shape. There are several different congruence conditions that triangles might meet.

In the figure given,

It is necessary to demonstrate the congruence of the triangles PYX and QXY.

Both triangles have the same XY base.

PX must equal QY because the lines PX and QY are perpendicular on congruent sides.

Angles PYX and QXY are equal since the axiom "Angles opposed to equal sides are equal" states that they are.

As a result, it can be shown that the two triangles PYX and QXY have two sides and an equal angle.

As a result, using SSA criteria, the two triangles will be congruent.

Hence, option C is the best one.

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The force F = r^2k(r^) is not conservative because its curl is nonzero. The force is central because it depends only on r and acts along the radial direction. Since it is not conservative, there is no potential energy function V(r) associated with this force

To determine whether the force F = r^2k(r^) is conservative and central, let's analyze its properties.

A force is conservative if it satisfies the condition ∇ × F = 0, where ∇ is the gradient operator. In Cartesian coordinates, the force can be written as F = Fx i + Fy j + Fz k, where Fx, Fy, and Fz are the components of the force in the x, y, and z directions, respectively. The curl of F is given by:

∇ × F = (∂Fz/∂y - ∂Fy/∂z)i + (∂Fx/∂z - ∂Fz/∂x)j + (∂Fy/∂x - ∂Fx/∂y)k.

Calculating the components of F = r^2k(r^):

Fx = 0, since there is no force component in the x-direction.

Fy = 0, since there is no force component in the y-direction.

Fz = r^2kr^.

Taking the partial derivatives, we have:

∂Fz/∂x = ∂/∂x (r^2kr^) = 2rkr^2(∂r/∂x) = 2rkr^2(x/r) = 2xkr^3.

∂Fz/∂y = ∂/∂y (r^2kr^) = 2rkr^2(∂r/∂y) = 2rkr^2(y/r) = 2ykr^3.

Substituting these values into the curl equation, we get:

∇ × F = (2ykr^3 - 2xkr^3)k = 2k(r^3y - r^3x).

Since the curl of F is not zero, ∇ × F ≠ 0, we conclude that the force F = r^2k(r^) is not conservative.

Now let's determine if the force is central. A force is central if it depends only on the distance from the origin (r) and acts along the radial direction (r^).

For F = r^2k(r^), the force is indeed central because it depends solely on r (the magnitude of the position vector) and acts along the radial direction r^. Hence, it can be written as F = Fr(r^), where Fr is a function of r.

Since the force is not conservative, it does not possess a potential energy function. In conservative forces, the potential energy function V(r) can be defined, and the force can be expressed as the negative gradient of the potential energy, i.e., F = -∇V. However, since F is not conservative, there is no potential energy function associated with it.

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There are a total of 3 x 10 x 10 = 300 possible combinations of suits, ties, and shirts that a person can select from. However, when selecting a traveling wardrobe, there are only 10 possible suit combinations, 10x10 = 100 possible tie combinations, and 10x10x10 = 1000 possible shirt combinations. This makes a total of 10 x 100 x 1000 = 100,000 possible selections of two suits, four ties and six shirts.

The sheer number of possible combinations indicates how important it is to choose wisely. The two suits should be complementary and appropriate to the occasion; the four ties can be chosen to match the suits, and the six shirts should be selected to mix and match with the ties and suits. Care should be taken to avoid repeating clothing items, and the person should also consider the climate and purpose of the trip in order to select the most suitable wardrobe.

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If Ariana removes the $4,800 rent from the set, the mean and median of the remaining rents will decrease because $4,800 is a very high value compared to the other rents.

Before removing the $4,800 rent, the mean can be calculated by adding up all the rents and dividing by the total number of rents (5):

Mean = (1,000 + 1,200 + 1,300 + 1,400 + 4,800) / 5 = 2,540

The median is the middle value in the set, which is 1,300.

After removing the $4,800 rent, the new mean can be calculated by adding up the remaining rents and dividing by the new total number of rents (4):

New Mean = (1,000 + 1,200 + 1,300 + 1,400) / 4 = 1,225

The new median is still 1,300 because it is the middle value in the remaining set.

Therefore, removing the $4,800 rent will decrease both the mean and median of the remaining rents.

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The probability that both pencils picked at random with replacement from a basket containing 5 purple and 9 brown pencils are purple is 9/98.

To calculate the probability of picking two purple pencils with replacement, we need to use the multiplication rule of probability. The probability of picking the first purple pencil is 5/14, and the probability of picking a second purple pencil from the basket is also 5/14 since we are replacing the first pencil. Therefore, the probability of picking two purple pencils with replacement is (5/14) × (5/14) = 25/196. However, we also need to account for the possibility of picking a brown pencil first and a purple pencil second.

The probability of picking a brown pencil first is 9/14, and the probability of picking a purple pencil second is 5/14. So, the probability of picking a brown pencil followed by a purple pencil is (9/14) × (5/14) = 45/196. Adding the probability of picking two purple pencils and the probability of picking a brown pencil followed by a purple pencil gives us the total probability of (25/196) + (45/196) = 9/98.

Therefore, the probability that both pencils picked at random with replacement from a basket containing 5 purple and 9 brown pencils are purple is 9/98.

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The person's total salary over the first 6 years is $231,750.

To determine the person's total salary over the first 6 years, we need to calculate the sum of the salary for each year.

Given information:

- Initial salary: $34,000

- Annual raise: $1,850

- Number of years: 6

To calculate the total salary, we can use the arithmetic progression formula:

[ S = frac{n}{2} left(2a + (n - 1)dright) ]

Where:

- ( S ) is the sum of the salaries

- ( n ) is the number of terms (years)

- ( a ) is the first term (initial salary)

- ( d ) is the common difference (annual raise)

Substituting the given values, we have:

[ S = frac{6}{2} left(2(34000) + (6 - 1)(1850)right) ]

Simplifying the expression:

[ S = 3 left( 68000 + 5 times 1850 right) ]

[ S = 3 left( 68000 + 9250 right) ]

[ S = 3 times 77250 ]

[ S = 231750 ]

Therefore, the person's total salary over the first 6 years is $231,750.

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The expression for the total length of ribbons left is: r - 16 . But we can also write this expression as: 4 x (r - 4) because 4 x (r - 4) = 4r - 16, which is equivalent to r - 16.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

The expression that represents the total length of ribbons left is:

4 x (r - 4)

This is because Ava uses 4 inches from each roll of ribbon, and there are 4 rolls of ribbon in total. So the total length of ribbon used is 4 x 4 = 16 inches.

To find the total length of ribbon left, we need to subtract the length of ribbon used from the original length of ribbon, which is r inches.

Therefore, the expression for the total length of ribbons left is: r - 16

But we can also write this expression as: 4 x (r - 4) because 4 x (r - 4) = 4r - 16, which is equivalent to r - 16.

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Answer:

yes

P(x) = (x + 2)(2x² + x + 3)

Step-by-step explanation:

see attachment for step by step

Answer:

Y = 1/4x+2

Step-by-step explanation:

So to find the slope of the line you can use rise/run to do this you can pick two points and count how may squares is going up and how many is going to the left.

For this problem the two points can be (0,2) and (4,1) and if we count how many squares it goes up by we can see its 1 and if we count from (0,2) to (4,1) horizontally the space is 4

To find y-int it is just where the line crosses the y axis

Answer:

Step-by-step explanation:

According to the solving by  using substitution method the  x and y are x = 6/5 and y = -8/5 respectively.

The algebraic approach to solving simultaneous linear equations is known as substitution method. The value of one variable through one equation is substituted in the second equation in this procedure, as the name implies.

given equations are 2x+4y = 4 and -2x+ y = -4

Now, simplifying -2x+y = -4

-2x+y = -4

∴ y = -4 + 2x

i.e. y = 2x - 4

By substitution method,

y = 2x - 4 in other given equation 2x+4y = 4,

 2x+4y = 4

 2x+4(2x - 4) = 4

∴ 2x + 8x - 8 = 4

∴ 10x = 4 + 8

∴10x = 12

∴ x = 12/10

∴ x = 6/5

Now ,

substituting x = 6/5 in y = 2x - 4,

 y = 2(6/5) - 4

∴ y = - 8/5

∴ x = 6/5  &  y = - 8/5.

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Answer:

V  =  38.47 in^3

Step-by-step explanation:

The container base radius is half the diameter, that is, 1.75 in, and the height is 12 in.  The formula for the volume of a cylinder of radius r and height h is V = (1/3)(pi)(r)^2h, which in this particular case comes out to:

V = (1/3)(3.14)(1.75 in)^2*(12 in), or

V  =  38.47 in^3

Answer:

115.40 in3

that is the correct answer to this question.

Answer:

12

Step-by-step explanation:

Factoring out a 1/4 from 1/4a - 3, you get 1/4 (a - 12) as 12 * 1/4 = 3. Thus, ? = 12.

The factor form of the polynomials are listed below:

Case 1: (x + i 3) · (x - i 3) · (x + 3) · (x - 3)

Case 2: 2 · (x - 2) · (x + 2) · (x - i 2) · (x + i 2)

Case 3: 16 · (x + 1 / 2) · (x - 1 / 2) · (x + i 1 / 2) · (x - i 1 / 2)

Case 4: (x + √5) · (x - √5) · (x + 1) · (x - 1)

Case 5: (x + 3) · (x - i 2) · (x + i 2)

Case 6: 2 · (x + √2) · (x - √2) · [x + i √(5 / 2)] · [x - i √(5 / 2)]

Case 7: (2 · x + 1) · (x + i √6) · (x - i √6)

Case 8: x · y · (x + 1) · (x - 0.5 - i 0.5√3) · (x - 0.5 + i 0.5√3)

Case 9: (x + i √2) · (x - i √2)

Case 10: x²ⁿ - y²ⁿ = (xⁿ - yⁿ) · (xⁿ + yⁿ)

Case 11: x² · (x - 2) · (x² + 2 · x + 4)

Case 12: (x + i 1) · (x - i 1) · (x + 1) · (x - 1)

Case 13: x² · (x + i 1) · (x - i 1) · (x + 1) · (x - 1)

Case 14: (x + i 2√5) · (x - i 2√5) · (x + 2√5) · (x - 2√5)

In this problem we find 14 polynomials whose factor form must be found by algebra properties. Now we proceed to find the roots of the polynomials:

Case 1:

x⁴ - 81

(x² + 9) · (x² - 9)

(x + i 3) · (x - i 3) · (x + 3) · (x - 3)

Case 2:

2 · x⁴ - 32

2 · (x⁴ - 16)

2 · (x² - 4) · (x² + 4)

2 · (x - 2) · (x + 2) · (x - i 2) · (x + i 2)

Case 3:

16 · x⁴ - 1

16 · (x⁴ - 1 / 16)

16 · (x² - 1 / 4) · (x² + 1 / 4)

16 · (x + 1 / 2) · (x - 1 / 2) · (x + i 1 / 2) · (x - i 1 / 2)

Case 4:

x⁴ - 6 · x² + 5

(x² - 5) · (x² -  1)

(x + √5) · (x - √5) · (x + 1) · (x - 1)

Case 5:

x³ + 3 · x² + 4 · x + 12

x³ + 4 · x + 3 · x² + 12

x · (x² + 4) + 3 · (x² + 4)

(x + 3) · (x² + 4)

(x + 3) · (x - i 2) · (x + i 2)

Case 6:

2 · x⁴ + x² - 10

2 · [x⁴ + (1 / 2) · x² - 5]

2 · (x² - 2) · (x² + 5 / 2)

2 · (x + √2) · (x - √2) · [x + i √(5 / 2)] · [x - i √(5 / 2)]

Case 7:

2 · x³ + x² + 12 · x + 6

2 · x³ + 12 · x + x² + 6

2 · x · (x² + 6) + (x² + 6)

(2 · x + 1) · (x² + 6)

(2 · x + 1) · (x + i √6) · (x - i √6)

Case 8:

x⁴ · y + x · y

x · y · (x³ + 1)

x · y · (x + 1) · (x² - x + 1)

x · y · (x + 1) · (x - 0.5 - i 0.5√3) · (x - 0.5 + i 0.5√3)

Case 9:

x² + 2

(x + i √2) · (x - i √2)

Case 10:

x²ⁿ - y²ⁿ = (xⁿ - yⁿ) · (xⁿ + yⁿ)

Case 11:

x⁵ - 8 · x²

x² · (x³ - 8)

x² · (x - 2) · (x² + 2 · x + 4)

Case 12:

x⁴ - 1

(x² + 1) · (x² - 1)

(x + i 1) · (x - i 1) · (x + 1) · (x - 1)

Case 13:

x⁶ - x²

x² · (x⁴ - 1)

x² · (x² + 1) · (x² - 1)

x² · (x + i 1) · (x - i 1) · (x + 1) · (x - 1)

Case 14:

x⁴ - 100

(x² + 10) · (x² - 10)

(x + i 2√5) · (x - i 2√5) · (x + 2√5) · (x - 2√5)

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Answer:

deductive

Step-by-step explanation:

When selecting the smallest number from a set of data, the appropriate function to use is the "Min" function.

The "Min" function is specifically designed to determine the smallest value among a set of data. It compares all the values within the data set and returns the minimum (smallest) value.

The "Count" function, on the other hand, is used to count the number of items in a data set or a specific condition. It does not provide information about the actual values within the set.

The "Max" function is used to find the maximum (largest) value in a set of data, which is the opposite of what is needed in this scenario.

The "If" function is a conditional function that allows for logical comparisons and returns different values based on specified conditions. While it can be used to identify the smallest number under certain conditions, it is not specifically designed for finding the overall minimum value in a set of data.

Therefore, the appropriate function to select the smallest number from a set of data is the "Min" function.

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The probability that a customer spends more than 53 minutes in the supermarket is 0.0548. The probability of this happening is 0.16, or 16%.

We are given that the amount of time customers spend in the supermarket is approximately normally distributed with a mean of 45 minutes and a standard deviation of 5 minutes.

This means that 68% of customers will spend between 40 and 50 minutes in the supermarket, 16% of customers will spend less than 40 minutes in the supermarket, and 16% of customers will spend more than 50 minutes in the supermarket.

A customer who spends more than 53 minutes in the supermarket is in the 16% of customers who spend more than 50 minutes in the supermarket. The probability of this happening is 0.16, or 16%.

We can also use a z-score to calculate the probability of a customer spending more than 53 minutes in the supermarket. The z-score is a measure of how many standard deviations a particular value is away from the mean. In this case, the z-score is 1.6, because 53 is 1.6 standard deviations above the mean of 45.

The probability of a customer spending more than 53 minutes in the supermarket is equal to the area under the standard normal  to the right of a z-score of 1.6.

This area can be found using a z-table. The z-table shows that the probability of a customer spending more than 53 minutes in the supermarket is 0.0548.

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Step-by-step explanation:

we cannot see any graphic or so.

no clue, what these sides (?) are, and how they are related to GI and to each other.

so, it is not possible to give you an answer.