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A polynomial whose GCF is 2x is 2x(x² + 2x + 3), a polynomial with a factor of (x + 1) is x = (-1 ± sqrt(-3))/2, a polynomial with a factor of (2y - 3x) is -3x(2y² + 1) + 5, a polynomial that is a difference of perfect squares is (4x + 3y)(4x - 3y), and a trinomial with a factor of (y + 4) and a GCF of 3y is (3y + 4x)(y + 4).

1. To create a polynomial whose GCF is 2x, we can start by choosing two terms that have 2x as a common factor. For example, 2x³ and 4x². To make it a polynomial, we can add another term, say 6x. The polynomial in standard form is:

2x³ + 4x² + 6x

To write it in factored form, we can factor out 2x from all terms:

2x(x² + 2x + 3)

2. To create a polynomial with a factor of (x + 1), we can start by choosing two terms that multiply to x², such as x and x. To make it a trinomial with (x + 1) as a factor, we can add another term, such as 1. The polynomial in standard form is:

x² + x + 1

To write it in factored form, we can use the quadratic formula to find the roots:

x = (-1 ± sqrt(1 - 4))/2

x = (-1 ± sqrt(-3))/2

Since the roots are complex, the polynomial cannot be factored further over the real numbers.

3. To create a polynomial with a factor of (2y - 3x), we can start by multiplying two terms that have 2y and 3x as coefficients, respectively. For example, 2y² and -3x. To make it a polynomial, we can add another term, say 5. The polynomial in standard form is:

-6xy² - 3x + 5

To write it in factored form, we can factor out -3x from the first two terms:

-3x(2y² + 1) + 5

4. To create a polynomial that is a difference of perfect squares, we can start by choosing two terms that are perfect squares and have a subtraction sign between them. For example, 16x² and 9y². The polynomial in standard form is:

16x² - 9y²

To write it in factored form, we can use the difference of squares formula:

(4x + 3y)(4x - 3y)

5. To create a trinomial with a factor of (y + 4) and a GCF of 3y, we can start by multiplying two terms that have 3y as a common factor. For example, 3y and 4x. To make it a trinomial with (y + 4) as a factor, we can add another term, say 12. The polynomial in standard form is:

12y + 3y² + 12 + 4xy

To write it in factored form, we can factor out the GCF 3y from the first two terms and factor out (y + 4) from the last two terms:

3y(y + 4) + 4x(y + 4)

(3y + 4x)(y + 4)

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The amount of milk left is given by A = 1.150 Liters of milk = 1150 mL

Given data ,

Let the total amount of milk be = 2 Liters = 2000 mL

Now , Tom gave Kevin 350 ml and Sold 500mL to Bob

So , the remaining amount of milk is given by A

where A = total amount of milk - 350mL - 500mL

On simplifying the equation , we get

A = 2000 - 350 - 500

A = 1150 mL

Hence , the amount of milk left is 1150 mL

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The centroid of the triangle is D and the measures of sides are solved

Given data ,

Let the triangle be represented as ΔPQR

Now , the centroid of the triangle is D

where the measure of PA = 17 units

The measure of BD = 9 units

And , the measure of side DQ = 14 units

Now , centroid of a triangle is formed when three medians of a triangle intersect

And , from the properties of centroid of triangle , we get

PA = AR

DR = DQ

AD = BD

On simplifying , we get

The measure of side AR = 17 units

PR = PA + AR = 34 units

The measure of side DR = 14 units

BR = BD + DR = 23 units

The measure of side AD = 9 units

AQ = AD + DQ = 23 units

Hence , the centroid is solved

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Answer:

3 / (7-5)

Step-by-step explanation:

"Subtract 5 from 7"

When you're subtracting from something, the reverse the order of the numbers.  So, the expression here would be "7 - 5"

"Then, divide 3 by the result."

Here, you're dividing 3 by the result, so the 3 must be in the numerator (on top of the fraction), and the "result from the previous step must be in the denominator (on the bottom of the fraction).  So, the expression here would be "3 / result"

Since order of operations forces division to happen before subtraction, we'll need parentheses around the first result to force the subtraction to happen first, as instructed.

So, the final expression would be "3 / (7-5)"

The given inequality is 3x - 12 ≤ -18. To solve for x, we can add 12 to both sides of the inequality to obtain 3x ≤ -6. Then, dividing both sides of the inequality by 3 gives x ≤ -2. Therefore, any value of x less than or equal to -2 will satisfy the inequality.

In solving the inequality, we first used the addition property of inequalities to add 12 to both sides of the inequality. This property states that if a < b, then a + c < b + c, where c is any real number. By adding 12 to both sides, we were able to isolate the variable term on one side of the inequality.

Next, we used the division property of inequalities to divide both sides of the inequality by 3. This property states that if a < b and c > 0, then a/c < b/c. By dividing both sides of the inequality by 3, we were able to solve for x.

Finally, we found that any value of x less than or equal to -2 will satisfy the inequality. This means that the solution set for the inequality is {x | x ≤ -2}. We also verified that x = -2 is a valid solution to the inequality, which confirms our solution.

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The cost for an adult is reduced by approximately 26.33% to $22.10.

The original cost for an adult ticket (X) = $30

The reduced cost for an adult ticket = $22.10

We need to find the percentage decrease (p) from the original cost to the reduced cost:

p = ((Original cost - Reduced cost) / Original cost) * 100

p = (($30 - $22.10) / $30) * 100

p = ($7.90 / $30) * 100

p ≈ 26.33 %

The fee for an adult has notably decreased by approximately 26.33%, now costing a mere $22.10.

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In May, the cost for a child is not changed. The cost for an adult is reduced by p % to $22.10. If the original cost of an adult ticket is $X, (i) calculate p, given that the original cost for an adult ticket is $30.

The predicted total sales for the ice-cream parlor when the average temperature is 72°F is $950.00.

You are asked to find the predicted total sales (s) for the ice-cream parlor when the average temperature (t) is 72°F, using the trend line equation s = 12.75t + 32.

Step 1: Plug the given temperature (72°F) into the trend line equation:
s = 12.75(72) + 32

Step 2: Calculate the value of 12.75(72):
12.75 * 72 = 918

Step 3: Add 32 to the result from Step 2:
918 + 32 = 950

So, the predicted total sales for the ice-cream parlor when the average temperature is 72°F is $950.00. Therefore, the correct answer is (a) $950.00.

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55 cubes I think because in the end you have to like divide it 2 times.

Answer: 110 cubes

Step-by-step explanation:

    First, we will find the volume of this prism.

V = LWH

V = (2.75 cm)(0.5 cm)(1.25 cm)

V = 1.71875 cm³

    Next, we will find the volume of the cube.

V = L³

V = (0.25 cm)³

V = 0.015625 cm³

    Next, we will divide the prism's volume by the cube's volume.

1.71875 cm³ / 0.015625 cm³ = 110 cubes

The odds in favor of the event are 1.

The probability of an event is the ratio between the total number of favorable outcomes and the total number of outcomes.

The odds in favor of an event are the ratio of the total number of favorable outcomes and the total number of unfavorable outcomes. If the probability of the event is given, we can find the odds in favor by using the formula of odds in favor:

odds in favor = probability of event/probability of not event

In this case question, the probability of an event is given as 0.5 which means that the total number of favorable outcomes is 50 out of 100

So the probability of not having an event is also 0.5 (the other half of the part.)

So, odds in favor = 0.5/0.5 = 1

The probability of the happening of an event is the same as the probability of not happening of an event. This means that the odds in favor of the event are 1 to 1, or simply 1.

Therefore,  the odds in favor of the event are 1.

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The significance level is the key indicator of whether or not a hypothesis can be supported. (option c)

In statistical analysis, there are several key indicators that are used to determine whether a hypothesis can be supported. One of these indicators is the significance level, which is denoted by the symbol alpha (α).

Another key indicator is the critical value, which is a value that is determined from a statistical distribution and is used to determine whether the observed data is statistically significant.

The test compares the observed frequencies of the categories to the expected frequencies, assuming that there is no association between the variables. The degrees of freedom refer to the number of categories minus one.

Therefore, to answer the original question, option (c)

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Kaylie earned $693 in interest on her savings account.

Kaylie deposited $900 in a savings account and earned 11% interest on it for 7 years. After the 7-year period, Kaylie earned $693 in interest, which was compounded annually.

This brought the total amount of money in her savings account to $1,593. The power of compounding interest in savings accounts can help grow your money significantly over time.

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The next time they will coincide is on November 21. when Lorena uses a social network every 8 days, Luis logs in every 6 days, and his sister and Alexa log in every 10 days.

To find the time when all three coincided, we need to find the least common multiple (LCM) of 6, 8, and 10. The LCM of 6, 8, and 10 is given as,

6 8 10 | 2

3  4  5 | 3

1   4  5 | 4

1   1  5 | 5

1   1   1

LCM = 2 × 3 × 4 × 5 = 120

if they coincided on July 24, To find the time when all three coincided we need to add 120 days to July 24 to find the next time they will coincide.  if we add 120 days to July 24 we will get the result as November 21.

Therefore, The next time they will coincide is on November 21.

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The question is,

Lorena is a student who uses a social network every 8 days. His friend Luis logs in every 6 days and his sister Alexa logs in every 10 days. If they coincided with their visit to this social network on July 24 when will they coincide next time?

The height of the flagpole is 26.0 feet.

Height is the vertical distance between two points.

To calculate the height of the flagpole, we use the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

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The bicycle mechanic should cut a strip of plastic approximately 82 inches long to place between the tube and tire of the 26-inch diameter bicycle tire.

To calculate the length of the strip of plastic needed, we first need to determine the circumference of the tire. The formula for the circumference of a circle is C=2πr, where C is the circumference, π is approximately 3.14, and r is the radius of the circle.

In this case, the tire diameter is 26 inches, so the radius is 13 inches (half of the diameter). Therefore, the circumference of the tire is: C = 2πr = 2π(13)     = 81.64 inches (rounded to two decimal places)

To ensure that the strip of plastic fits snugly between the tube and tire, it should be the same length as the circumference of the tire. Therefore, the strip of plastic should be 82 inches long (rounded to the nearest inch).

In summary, the bicycle mechanic should cut a strip of plastic that is 82 inches long to fit between the tube and tire of the 26-inch diameter bicycle tire.

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The expected cost of Bob's lunch is $8.75.

To find the expected cost of Bob's lunch, we need to determine the probability that Bob and Anna will meet at Sally's Restaurant at the same time.

There are 4 possible times for Bob and Anna to choose from: 1 PM, 2 PM, 3 PM, and 4 PM. Since they are choosing randomly, the probability of them both choosing the same time is 1/4 (one out of four choices).

Now we can calculate the expected cost of Bob's lunch. If they meet successfully, Bob's lunch will cost $5. If they do not meet, Bob's lunch will cost $10. We can find the expected cost by multiplying the probability of each outcome by its corresponding cost, and then adding these products together.

Expected cost = (Probability of meeting) * (Cost if they meet) + (Probability of not meeting) * (Cost if they don't meet)

Expected cost = (1/4) * $5 + (3/4) * $10

Expected cost = $1.25 + $7.50

Expected cost = $8.75

The expected cost of Bob's lunch is $8.75.

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Answer:

4/5

Step-by-step explanation:

In probability, if there are two events and "or" is used, we will add the probabilities of each event. Since the event that an odd number is spun does not affect whether a red number is spun, we can calculate the probability of each event separately:

Probability of spinning an odd number:

5/10        because there are 5 odd numbers possible & 10 outcomes

Probability of spinning a red number:

3/10        because there are 3 red numbers & 10 outcomes

Now add the probability of each event:

5/10 + 3/10 = 8/10 = 4/5

The percentage of the family's income that is spent on food is 25%.

Firstly, noting down the family's monthly spend on food ($550) and their total monthly income ($2,200).

Next, dividing the amount spent on food by the total income to find the ratio of the spend to income: $550 / $2,200.

Now, calculating this division: 550 ÷ 2,200 = 0.25.

Finally, finding the percentage, multiply the ratio (0.25) by 100: 0.25 x 100 = 25%.

So, the family spends 25% of their monthly income on food.

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From the given data 11 is the mean of the data set.

What is Mean ?

In statistics, the mean (also called the average) is a measure of central tendency that represents the typical value in a data set. It is calculated by adding up all the values in the data set and dividing by the number of values.

To find the value of x in the data set, we can use the formula for the mean (also called the average). The mean is calculated by adding up all the values in the data set and dividing by the number of values. In other words:

mean = (sum of all values) : (number of values)

We are given that the mean of the data set is 11, so we can write:

11 = (12 + 9 + 12.5 + 13 + x + 10 + 11 + 11 + 7 + 9) : 10

Here, we have 10 values in the data set (including the unknown value x), so we divide the sum of all the values by 10 to find the mean.

To solve for x, we can start by simplifying the right-hand side of the equation:

110 = 75.5 + x

Next, we can isolate x by subtracting 75.5 from both sides:

x = 34.5

Therefore, the value of x that makes the mean of the data set equal to 11 is x = 34.5.

In other words, if we replace the unknown value x with 34.5, the resulting data set will have a mean of 11. This means that the sum of all the values in the data set will be 110, since:

12 + 9 + 12.5 + 13 + 34.5 + 10 + 11 + 11 + 7 + 9 = 110

And when we divide this sum by 10, we get:

110 : 10 = 11

Therefore, From the given data 11 is the mean of the data set.

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The equation for the line that passes through the point ( 3,-1/2) and is perpendicular to the line y =-2x+3 is:

y = (1/2)*x - 2

Remember that two linear equations are perpendicular if the product between the slopes is -1, here we want a line perpendicular to:

y =-2x+3

Then if the slope of our line is a, we must have that:

a*-2 = -1

a = 1/2

Then our line is something like:

y = (1/2)x + b

Now we also want our line to pass through (3, -1/2), then:

-1/2 = (1/2)*3 + b

-1/2 = 3/2 + b

-1/2 - 3/2 = b

-2 = b

The linear equation is:

y = (1/2)*x - 2

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Answer:

x = 13

Step-by-step explanation:

We Know

The sum of angles of a triangle must add up to 180°

We know 2 angles, one is 60° and the other is 90°

Solve for x.

Let's solve

3x - 9 + 60 + 90 = 180

3x + 141 = 180

3x = 39

x = 13

Another possible value for j and K is (A) j = 18, k = 2

Note that in inverse variation, one of the variables increases while the other decreases.

From the information given, we have that;

j is inversely related to the cube of k,

This is represented as;

j ∝ 1/k³

Now, find the constant of variation

K = jk³

Substitute the vales

K = 3 × 6³

find the cube value

K = 648

Then, we have that;

j = 648 / 2³ = 81

For option B:

j = 648 / 3³ = 24

For option C:

j = 648 / 2³ = 81

For option D:

j = 648 / 81³ = 0.0008

For option E:

j = 648 / 2³ = 81

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The two numbers are 129 and 62, which satisfy the given conditions: their sum is 191 and their difference is 67 .

You are asked to find two numbers whose sum is 191 and whose difference is 67. Let's use the variables x and y to represent these two numbers.

We can establish the following two equations under the given conditions: 1) x + y = 191 2) x - y = 67

Now we can solve this system of linear equations to find the values of x and y.

We can start by adding both equations:

(x + y) + (x - y) = 191 + 67

2x = 258

Then we'll divide by 2 to find the value of x:

x = 129

Now, we can plug x into Equation 1 to find the value of y:

129 + y = 191

y = 191 - 129

y = 62

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Answer:

Let's solve this problem using algebra. Let x be the cost of one orange and y be the cost of one apple. Then we have the system of equations:

12x + 7y = 5.36

8x + 5y = 3.68

To solve for x and y, we can use elimination. Multiplying the second equation by 3 and subtracting it from the first equation multiplied by 5, we get:

(5*12 - 7*8)x + (5*7 - 3*5)y = 26.8 - 11.04

20x = 15.76

x = 0.788

Substituting x back into one of the equations, we can solve for y:

12(0.788) + 7y = 5.36

y = 0.308

Therefore, one orange costs $0.788 and one apple costs $0.308.

Answer: 5

Step-by-step explanation:

10 + 7h = 45

-10         -10

     7h = 35

divide by 7 to both sides

        h = 5

Step-by-step explanation:

See image for calculations:

(Note that interior angle + exterior angle = 180 degrees)

   AND  sum of exterior angles = 360     that is where the first formula comes from.

The calculated area of the rectangle is 70 + 7x

From the question, we have the following parameters that can be used in our computation:

Mario cuts out and arranged the trapezoids to form a rectangle.

Using the above as a guide, we have the following:

Area of rectangle  = base * height

In this case, we have

base = 10 + x

Where x is the length of the missing side

Next, we have

height = 7

Substitute the known values in the above equation, so, we have the following representation

Area = 7 * (10 + x)

Evaluate

Area = 70 + 7x

Hence, the area of the rectangle is 70 + 7x

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The line passes through the same point on figure A and D.

From the figure, we have the original shape to be figure E

The center point of figure E is the origin

This means that a line drawn from the origin that passes through point A must pass through the same point on the shape

From the figure, the line passes through the same point on figure A and D.

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Answer:

30%

Step-by-step explanation:

If there are only 2 categories:

Students at lunch and students studying, then the whole is 100%

100% - 70% = 30%

Helping in the name of Jesus.

The option that can be true for the function g(x) is C; g(-13) = 20

Here we know that the function g(x) has:

The domain ---> -20 ≤ x ≤ 5

The range --->  -5 ≤ g(x) ≤ 45

And g(0) = -2

       g(-9) = 6

There are two statements that could be true:

g(-13) = 20, because -13 belongs to the domain and 20 belongs to the range.

g(0) = 2  could also be true.

Now, we can see that g(-9) > g(0), then as x becomes smaller, g increases, then the option that seems to be correct is g(-13) = 20

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