Find the gcf of X^2-5x

Answer:

x = -5

Step-by-step explanation:

3 (2x + 4) = 2x - 8

6x + 12 = 2x - 8

- 2x         - 2x

4x + 12 = -8

    - 12     - 12

4x = -20

/ 4    / 4

x = -5

We get the age of Jack is 29 years and the age of Jill is 16 years.

We are given that the sum of Jack's age and Jill's age is 45 years.

Let Jack's age be x.

Let Jill's age be y.

x + y = 45

x = 45 - y

Now, we are also given that jack's age next year will be twice Jill's age last year.

Jack's age next year = x + 1

Jill's age last year = y - 1

ATQ, We get the equation as:

x + 1 = 2( y - 1)

x + 1 = 2 y - 2

x = 2 y - 2 - 1

x = 2 y - 3

We get that:

45 - y = 2 y - 3

2 y + y = 45 + 3

3 y = 48

y = 48 / 3

y = 16 years.

x + y = 45

x + 16 = 45

x = 45 - 16

x = 29 years.

Therefore, we get the age of Jack is 29 years and the age of Jill is 16 years.

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Based on the formula of the quadratic function y=-x^2+6x-5, we know that its graph is a downward-facing parabola that opens wide, with a vertex at (3,-14), and an axis of symmetry at x=3.

Based on the formula of the quadratic function y=-x^2+6x-5, we can determine several properties of its graph, including its shape, vertex, and axis of symmetry.

First, the negative coefficient of the x-squared term (-1) tells us that the graph will be a downward-facing parabola. The leading coefficient also tells us whether the parabola is narrow or wide. Since the coefficient is -1, the parabola will be wide.

Next, we can find the vertex using the formula:

Vertex = (-b/2a, f(-b/2a))

where a is the coefficient of the x-squared term, b is the coefficient of the x term, and f(x) is the quadratic function. Plugging in the values for our function, we get:

Vertex = (-b/2a, f(-b/2a))

= (-6/(2*-1), f(6/(2*-1)))

= (3, -14)

So the vertex of the parabola is at the point (3,-14).

Finally, we know that the axis of symmetry is a vertical line passing through the vertex. In this case, it is the line x=3.

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Answer:

applying transformation 2 (only once) bottom LH corner

Step-by-step explanation:

We need to calculate the 8% of $45

The total charge will be

ANSWER

The total charge is $48.60

Answer:To get the graph of the given parabola, we will use the equation of the parabola to check if given points in options are lying on that parabola or not. If they lie on the graph of parabola,  then they would satisfy the equation, else not. We will use vertex form of parabola to get its vertex.

Thus, by below shown calculations, we have

Option A: On a coordinate plane, a parabola opens up. It goes through (-6, 0), has a vertex at (-2, -8), and goes through (2,0)

Answer:

its the 3rd graph

Step-by-step explanation:

c

(10 3/4 + 3 1/2) − (8 1/4 + 2 1/4) simplifies to 3 1/2. To simplify (10 3/4 + 3 1/2) − (8 1/4 + 2 1/4), we can start by adding the whole numbers separately and then adding the fractions separately.  

10 + 3 − 8 − 2 = 3

3/4 + 1/2 − 1/4 − 1/4 = 1/2

Therefore, (10 3/4 + 3 1/2) − (8 1/4 + 2 1/4) simplifies to 3 1/2.

One way to think about this is by imagining you have a certain number of objects (the whole numbers) plus part of another object (the fractions). If you add and subtract these quantities separately, you can get the total number of objects and their corresponding parts.

In this case, we had 10 whole objects, added 3 more, and subtracted 8 and 2 separately. We ended up with 3 whole objects. For the fractions, we combined 3/4 and 1/2, and subtracted 1/4 and 1/4 separately. This gave us 1/2.

Overall, we can conclude that (10 3/4 + 3 1/2) − (8 1/4 + 2 1/4) is equal to 3 1/2.

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The answer is , it would take Mrs. Adam 24 number of days to use up all the water if she camps alone.

Let x be the number of days it would take Mrs. Adam to use up all the water if she camps alone.

Therefore, Mr. Adam uses 1/12 of the water in one day and Mrs. Adam and Mr. Adam together use 1/8 of the water in one day.

Separately, Mrs. Adam uses 1/x of the water in one day.

Thus, the equation would be formed as;

1/12 + 1/x = 1/8

Multiply through by the LCM of 24x.

The LCM of 24x is 24x.

Thus, we have;

2x + 24 = 3x

Solve for x to get;

x = 24

Therefore, it would take Mrs. Adam 24 days to use up all the water if she camps alone.

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The norm of the partition P={-1.8, -0.9, -0.6, 0.1, 0.5, 1) is 0.9.

To calculate the norm of P, firstly take the absolute values of each element in the partition. This leaves us with |-1.8| = 1.8, |-0.9| = 0.9, |-0.6| = 0.6, |0.1| = 0.1, |0.5| = 0.5, and |1| = 1. Then, find the largest absolute value in the set, which is 1.8. The norm of P is therefore 1.8.

In general, the norm of a partition P is the largest absolute value of all the elements in the partition. The norm is denoted as ||P||. This is also known as the infinity norm or the supremum norm.

To calculate the norm, simply take the absolute values of each element in the partition and find the largest absolute value in the set. The norm of the partition is the largest absolute value.

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Every month, the number of people who receive the email is multiplied by a factor of 8.

We have the following information is:

Venera sent a chain letter to her friends, asking them to forward the letter to more friends.

The relationship between the elapsed time t, in months, since Venera sent the letter, and the number of people, P(t), who receive the email is modeled by the following function:

\(P(t) =2^\\3t+7\)

Every month, the number of people who receive the email is multiplied by a factor will be

For t = 2, we have

P(2) = 2³⁽²⁾ ⁺⁷

P(2) = 2¹³

For t = 3, we have

P(3) = 2³⁽³⁾⁺⁷

P(3) = 2¹⁶

Calculate the \(\frac{P(3)}{P(2)}\)

⇒ \(\frac{P(3)}{P(2)}\)

⇒ 2¹⁶ / 2¹³

⇒ 2³

⇒ 8

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Complete question is:

Venera sent a chain letter to her friends, asking them to forward the letter to more friends.

The relationship between the elapsed time t, in months, since Venera sent the letter, and the number of

people, P(t), who receive the email is modeled by the following function:

3t+7

P(t) = 2

Complete the following sentence about the monthly rate of change in the number of people who receive

the email.

Round your answer to two decimal places.

Every month, the number of people who receive the email is multiplied by a factor of

Answer:

2x3x7

Step-by-step explanation:

The 90% confidence interval for the slope β is approximately (0.079 to 0.106), which is option b.

Part I:
The slope of the least-squares regression line is 0.092498, which is option b.

Part II:
To find the confidence interval for the slope β, we use the formula:
β ± t* (s/√n)
where t is the t-value for a 90% confidence interval with (n-2) degrees of freedom, s is the standard error of the estimate, and n is the sample size.
From the output, we have s = 466.2 and n = 19.
To find the t-value, we can use a t-distribution table or a calculator. For a 90% confidence interval with 17 degrees of freedom, the t-value is approximately 1.734.
Substituting the values, we get:
0.092498 ± 1.734 * (466.2/√19)
Simplifying, we get:
0.092498 ± 0.099
Therefore, the 90% confidence interval for the slope β is approximately (0.079 to 0.106), which is option b.

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Answer:

200 pounds

Step-by-step explanation:

Peter's bill = 3 * 54.50 = 163.50

He received changes = 36.50

Money which he gave to shop assistant: 163.50 + 36.50 = 200

Answer:

Slope: 9/10

Step-by-step explanation:

We need to find the slope of the line that passes through the coordinates given.

To find the slope, we would use the slope formula: m = y2-y1/x2-x1

Plug in your coordinates and solve:

m = 4-(-5)/4-(-6)

m = 4+5/4+6

m = 9/10

Since we can't simplify further, the slope of the line would be 9/10.

The equation of the trend line is given as follows:

y = 1.33x + 20.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

The coefficients m and b represent the slope and the intercept, respectively, and are explained as follows:

Two points on the line in this problem are given as follows:

(0, 20) and (15, 40).

When x = 0, y = 20, hence the intercept b is given as follows:

b = 20.

When x increases by 15, y increases by 20, hence the slope m is given as follows:

m = 20/15

m = 1.33.

Hence the function is given as follows:

y = 1.33x + 20.

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A firm experiences increasing returns to scale if inputs are doubled and output more than doubles.

When the firm's output grows at a faster rate than the growth in inputs, increasing returns to scale result. In this case, the company experiences economies of scale, which makes it more effective as it grows its production.

The firm is able to boost productivity and efficiency as it expands its scale of operations if inputs are doubled and output more than doubles.

This can be ascribed to a number of things, including specialisation, labour division, the use of capital-intensive technology, discounts for bulk purchases, and spreading fixed costs over a higher output. Lower average costs per unit of output result in higher profitability and competitiveness for the company.

The firm gains a number of benefits from growing returns to scale. First off, it lets the company to benefit from cost savings brought about by economies of scale, allowing it to manufacture goods or services for less money per unit. This may enable more competitive pricing on the market or result in larger profit margins.

Second, raising returns to scale can result in better operational effectiveness and resource utilisation. As the company grows in size, it will be able to use resources more wisely and profit from production volume-related synergies.market prices that are competitive.

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Answer:

the answer would be $692.12

Answer:

4/3 is the slope

Step-by-step explanation:

Answer:

1. 12 yards.

2. 15 meters.

3. 217 centimeters.

Step-by-step explanation:

\(\frac{1}{2}\) · \(b\) · \(h\) is the formula. (for the area of a triangle.)

Hope it helped!

Answer:

a. has one solution

b. infinite solution

Step-by-step explanation:

a.

2(x - 1) + 6 = 4x - 22

2x - 2 + 6 = 4x - 22

2x - 4x = 2 - 6 - 22

-2x = -26

x = 26/2

x = 13

b.

6(2x + 1) – 2 = 12x + 4

12x + 6 - 2 = 12x + 4

12x - 12x = 4 + 2 - 6

0 = 0

Answer:

The area of the dog pen is 522 \(ft^2\).    (feet squared)

The perimeter of the dog pen is 94 feet

Step-by-step explanation:

Area

Here is the formula for the area of a rectangle.

\(A=lw\)

We are given

\(l=29\\w=18\)

Lets evaluate \(A\).

\(A=29*18\\A=522\)

Perimeter

Here is the formula for the perimeter of a rectangle.

\(P=2w+2l\)

We are given

\(l=29\\w=18\)

Lets evaluate \(P\).

\(P=2l+2w\\P=(2*29)+(2*18)\\P=58+(2*18)\\P=58+36\\P=94\)

The number of hours Natalie worked babysitting last week is 6hrs and the number of hours she worked landscaping last week is 2 hrs.

Let x be the number of hours Natalie worked babysitting and y be the number of hours she worked landscaping. Then, the total earnings were 11x + 10y = $86.

Also, x = 3y, because she worked 3 times as many hours babysitting as she did landscaping.

Substitute x = 3y into the first equation:

11(3y) + 10y = $86

Expanding the first term we get,

33y + 10y = $86

Combining terms,

43y = $86

Dividing both sides by 43 we get,

y = $2

So, Natalie worked y = 2 hours of landscaping.

To find the number of hours she worked babysitting, substitute y = 2 into x = 3y as follows -

x = 3(2) = 6

So Natalie worked x = 6 hours babysitting.

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the probability of drawing a red, then a blue, and then a white marble is \(=\frac{7}{225}\)

To find probability, we take the number of ways the specific event can occur and divide it by the number of ways any event can occur.

The probability of drawing a red marble is: (of red marbles) / (total # of marbles) = 3/(3 + 7 + 5) = 3÷15 = 1÷5.

The probability of drawing a blue marble is: ( of blue marbles) / (total # of marbles) = 5/(3 + 7 + 5) = 5÷15 = 1÷3.

The probability of drawing a white marble is: ( of white marbles) / (total # of marbles) = 7/(3 + 7 + 5) = 7÷15.

Now, we want these events to all to occur for us. So, we must multiply them by each other: (1/5) * (1/3) * (7/15)  \(=\frac{7}{225}\)

Thus, the probability is \(=\frac{7}{225}\)

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a. The unemployment rate is 20%.

b. The labor-force participation rate is 60%.

According to the question,

Working age population- 100,000

Labour force - 60,000

Unemployed - 12000 instructions

a) The unemployment rate is the percentage of the labor force that is unemployed and it is calculated as follows:

Unemployment Rate = \(\frac{Number of unemployed People}{Labor force}\) × 100

When an unemployed population is 12,000 and the labor force is 60,000,

the unemployment rate is  = \(\frac{12000}{60000}\) × 100 = 20%

b) labor force participation rate is the percentage of working adult population that participates in labor either by actively looking for a job, or working. It is calculated as follows:

Labor Force Participation Rate = \(\frac{Labor force}{working age population}\) × 100

When the labor force is 60,000 and the working-age population is 100,000

Labor Force Participation Rate = \(\frac{60000}{100000}\) × 100 = 60%

So, a. The unemployment rate is 20%.

b. The labor-force participation rate is 60 %.

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Answer:

The statement is misleading as it does not provide any context for the comparison. It does not clarify what the 74% more calories is being compared to or what amount of calories is being burned by using the product. Additionally, the advertisement does not provide any evidence to back up the claim.

The number of raisins that must cookies contain on average for the chance of a cookie containing at least one raisin to be at least 99% is λ ≥ − ln(0.01)

Assuming that a Poisson random scatters of raisins.

Let N = the number of raisins per cookie. Then If N is a Poisson random variable with a

parameter λ, then

P(N ≥ 1) = 1 − P(N = 0) = 1 − exp(−λ)

and for this to be at least 0.99, we need

λ ≥ − ln(0.01)

Recall that λ = E[N] is the average number of raisins per cookie.

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The inequality to check if Carl will take taxi or Bus to home can be written as 3 + 0.5x < 10 and Carl will take bus instead of taxi.

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

Given is a taxi that charges a flat rate of $3.00, plus an additional $0.50 per mile. Carl will only take the taxi home if the cost is under $10, otherwise he will take a bus. Carl is 15 miles from home.

We will estimate the total price it will cost Carl to take taxi. For a [x] miles distance, it will cost Carl -

C(x) = 3 + 0.5x

The inequality to check if Carl will take taxi or Bus to home can be written as -

C(x = 15) < 10

3 + 0.5 x 15 < 10

10.5 < 10

Which is false.

Hence, Carl will take bus instead of Car.

Therefore, the inequality to check if Carl will take taxi or Bus to home can be written as 3 + 0.5x < 10 and Carl will take bus instead of taxi.

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Answer:

Sample Answer

Step-by-step explanation:

Let the variable x be the number of miles. Then the problem can be modeled with the inequality 0.5x + 3 < 10,="" in="" which="">x is the number of miles. To solve, first subtract 3 from each side, then divide each side by 0.5. The solution is x < 14.="" carl="" can="" travel="" less="" than="" 14="" miles,="" but="" he="" lives="" 15="" miles="" away,="" so="" he="" will="" take="" a="" bus,="" not="" the="">

your welcome because all these others answers are wrong

Answer: The equivalent expression to Sarah's expression is:

6.25(x + y) + 242.78

This expression takes into account the total number of hours worked by James (x) and Sarah (y) and adds it to the sum of their tips, which is $242.78. The expression multiplies the total number of hours worked by 6.25, which is their hourly wage.

Step-by-step explanation:

The mean is 18.6.

Given the following information; z = 2.25, x = 22.2, and σ = 1.6, to find the mean, we have to apply the formula for z-score. z = (x - μ)/σWhere; z-score is represented by z, the value of X is represented by x, the mean is represented by μ and the standard deviation is represented by σSubstituting the values into the equation above;2.25 = (22.2 - μ)/1.6Multiplying both sides of the equation by 1.6, we have;1.6(2.25) = (22.2 - μ)3.6 = 22.2 - μ Subtracting 22.2 from both sides of the equation;3.6 - 22.2 = - μ-18.6 = - μ Multiplying both sides of the equation by -1, we have;μ = 18.6

Simply said, a z-score, also known as a standard score, informs you of how far a data point is from the mean. Technically speaking, however, it's a measurement of how many standard deviations a raw score is from or above the population mean.

You can plot a z-score on a normal distribution curve. Z-scores range from -3 standard deviations, which would fall to the extreme left of the normal distribution curve, to +3 standard deviations, which would fall to the far right. You must be aware of the mean and population standard deviation in order to use a z-score.

The z-score can show you how that person's weight compares to the mean weight of the general population.

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Answer:

210

Step-by-step explanation:

25% can also be written as .25. If you multiply .25 by 280 you get 70. 70 is 25% of 280. If you take 70 from 280 you get 210.