Is x2(2x+1) fully factored?

Answer:

x³ -6x² +11x-6

Step-by-step explanation:

as there are three zeros visible, we assume the function is cubic. It can be written in the form ax³ +bx²+cx +d. Another form of writing a function is by making the brackets (x-x0), where x0 is the zero of the function (the value of the function for x0 is equal zero):  a(x-1)(x-2)(x-3) (I assumed a is 1). By multiplying the brackets, you got the answer.

We must raise the $1,190 starting rent by 1.7% in order to determine the monthly rent after a year.

We can begin by figuring out how much the rise will be:

Amount of increase: 1.7% of $1,190 multiplied by 0.017 times equals $20.23. (rounded to the nearest cent)

We must multiply the initial rent by this sum in order to determine the new monthly rate:

New rate is $1,190 plus $20.23 per month, or $1,210.23. (rounded to the nearest cent)

As a result, the rate will be $1,210 per month after a year.

When the input parameter value is 0, the output of a function is its starting value, or 0. The first number would be the amount of money you had to start with on day 0 if your function, for instance, was tracking the sum of money you earned over a specific period of time.

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The monthly rent after 1 year will be $1,210.

"Amount" is a general term that refers to the quantity, value, or total of something. It can be used in different contexts to refer to different things.

To calculate the monthly rent after 1 year, we need to find the 1.7% increase and add it to the initial rent.

First, we need to calculate the amount of the increase:

Increase = 1.7% of $1,190

Increase = 0.017 × $1,190

Increase = $20.23 (rounded to two decimal places)

Next, we can find the new monthly rent by adding the increase to the initial rent:

New rent = $1,190 + $20.23

New rent = $1,210.23 (rounded to two decimal places)

Therefore, the monthly rent after 1 year will be $1,210.

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The statement represented by Sk+1 in the induction proof is that (k+1)! is divisible by 10.

When using mathematical induction to prove a statement, we typically follow the steps of establishing a base case and then proving the inductive step.

In this case, let's assume the statement Sk is that k! is divisible by 10. The base case would be to show that S1 is true, meaning that 1! is divisible by 10.

After establishing the base case, we proceed to the inductive step. In the inductive step, we assume that Sk is true for some arbitrary positive integer k, which means that k! is divisible by 10. Then we need to prove that Sk+1 is also true, which means that (k+1)! is divisible by 10.

So, Sk+1 represents the statement that (k+1)! is divisible by 10 in the induction proof. This is the statement we aim to prove based on the assumption that Sk is true for some value of k.

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Answer:

0.6293

Step-by-step explanation:

The \(z\) score for $24000 is \(\frac{24000-25000}{3000} \approx 0.333\).

\(P(z<0.333)=0.6293\)

The area of the sector is 16π square inches.

To find the area of a sector of a circle, we need to use the formula:

Area of sector = (central angle/360) x \(\pi r^2\)

where r is the radius of the circle.

In this case, the radius is given as 8 inches.

We are also given that the central angle measures from 60 to 150 degrees. To calculate the area of the sector, we need to find the size of the central angle first.

To do this, we subtract the smaller angle from the larger angle:

150 - 60 = 90 degrees

So, the central angle is 90 degrees.

Now, we can substitute the values into the formula:

Area of sector = (90/360) x \(\pi 8^2\)

Area of sector = (1/4) x π(64)

Area of sector = 16π square inches

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Answer: Let us call the centers of the four circles C1, C3, C5, and C7, respectively, where the subscript refers to the radius of the circle. Without loss of generality, we can assume that the tangent point A lies to the right of all the centers, as shown in the diagram below:

                 C7

          o-----------o

       C5 /             \ C3

         /               \

        o-----------------o

                C1

                |

                |

                | l

                |

                A

Let us first find the coordinates of the centers C1, C3, C5, and C7. Since all the circles are tangent to line l at point A, the centers must lie on the perpendicular bisector of the line segment joining A to the centers. Let us denote the distance from A to the center Cn by dn. Then, the coordinates of Cn are given by (an, dn), where an is the x-coordinate of point A.

Using the Pythagorean theorem, we can write the following equations relating the distances dn:

d1 = sqrt((d3 - 2)^2 - 1)

d3 = sqrt((d5 - 4)^2 - 9)

d5 = sqrt((d7 - 6)^2 - 25)

We can solve these equations to obtain:

d1 = sqrt(16 - (d7 - 6)^2)

d3 = sqrt(4 - (d7 - 6)^2)

d5 = sqrt(1 - (d7 - 6)^2)

Now, let us consider the region S that lies inside exactly one of the four circles. This region is bounded by the circle of radius 1 centered at C1, the circle of radius 3 centered at C3, the circle of radius 5 centered at C5, and the circle of radius 7 centered at C7. Since the circles are all tangent to line l at point A, the boundary of region S must pass through point A.

The maximum possible area of region S occurs when the boundary passes through the centers of the two largest circles, C5 and C7. To see why, imagine sliding the circle of radius 1 along line l until it is tangent to the circle of radius 3 at point B. This increases the area of region S, since it adds more points to the interior of the circle of radius 1 without removing any points from the interior of the other circles. Similarly, sliding the circle of radius 5 along line l until it is tangent to the circle of radius 7 at point C also increases the area of region S. Therefore, the boundary of region S must pass through points B and C.

Using the coordinates we obtained earlier, we can find the x-coordinates of points B and C as follows:

x_B = a - 2 - sqrt(9 - (d7 - 6)^2)

x_C = a + 6 + sqrt(9 - (d7 - 6)^2)

To maximize the area of region S, we want to maximize the distance BC. Using the distance formula, we have:

BC^2 = (x_C - x_B)^2 + (d5 - d3)^2

Substituting the expressions we derived earlier for d3 and d5, we get:

BC^2 = 32 - 2(d7 - 6)sqrt(9 - (d7 - 6)^2)

To maximize BC^2, we need to maximize the expression inside the square root. Let y = d7 - 6. Then, we want to maximize:

f(y) = 9y^2 - y^4

Taking the derivative of f(y) with respect to y and setting it equal to zero, we get:

f'(y) = 18y - 4y^3 = 0

This equation has three solutions: y = 0, y = sqrt(6)/2, and y = -sqrt(6)/2. The only solution that gives a maximum value of BC^2 is y = sqrt(6)/2, which corresponds to d7 = 6 + sqrt(6)/2.

Substituting this value of d7 into our expressions for d1, d3, and d5, we obtain:

d1 = sqrt(16 - (sqrt(6)/2)^2) = sqrt(55/2)

d3 = sqrt(4 - (sqrt(6)/2)^2) = sqrt(19/2)

d5 = sqrt(1 - (sqrt(6)/2)^2) = sqrt(5/2)

Using these values, we can compute the coordinates of points B and C as follows:

x_B = a - 2 - sqrt(9 - (sqrt(6)/2)^2) = a - 2 - sqrt(55)/2

x_C = a + 6 + sqrt(9 - (sqrt(6)/2)^2) = a + 6 + sqrt(55)/2

The distance between points B and C is then:

BC = |x_C - x_B| = 8 + sqrt(55)

Finally, the area of region S is given by:

Area(S) = Area(circle of radius 5 centered at C5) - Area(circle of radius 7 centered at C7)

= pi(5^2) - pi(7^2)

= 25pi - 49pi

= -24pi

Since the area of region S cannot be negative, the maximum possible area is zero. This means that there is no point that lies inside exactly one of the four circles. In other words, any point that lies inside one of the circles must also lie inside at least one of the other circles.

Step-by-step explanation:

Answer:

8. adjacent 9. vertical 10. adjacent

Step-by-step explanation:

Answer:

answer might be 128 degrees because it is an opposite angle

Step-by-step explanation:

he will be 17. he is going to grow 1.5 inch per year, if we do 1.8×8= 12.0 or 1 ft so it will take him 8 years to be 6feet

Answer:

3.3 x 10^-4

Step-by-step explanation:

It's 3.3 x 10^-4 because 3.3 x 10^-4 would be 0.00033 and 8.0 x 10^0 would be 1 so 0.00033 x 1 = 0.00033. Then when we plug 0.00033 into scientific notation we will get 3.3 x 10^-4

Respuesta:

a = 82; b 164

Explicación paso a paso:

a = 1 / 2b - - - (1)

a gana 66 = a + 66

b = b - 90

a = 2b

a + 66 = 2 (segundo - 90) - - - (2)

Ponga a = 1 / 2b en (2)

1 / 2b + 66 = 2 (b-90)

0.5b + 66 = 2b - 180

0.5b - 2b = - 180 - 66

-1,5b = - 246

b = 164

a = 1 / 2b

a = 1/2 * 164

a = 82

Step-by-step explanation:

To solve the equation, factor x

2

+x−56 using formula x

2

+(a+b)x+ab=(x+a)(x+b). To find a and b, set up a system to be solved.

a+b=1

ab=−56

Since ab is negative, a and b have the opposite signs. Since a+b is positive, the positive number has greater absolute value than the negative. List all such integer pairs that give product −56.

−1,56

−2,28

−4,14

−7,8

Calculate the sum for each pair

−1+56=55

−2+28=26

−4+14=10

−7+8=1

The solution is the pair that gives sum 1.

a=−7

b=8

Rewrite factored expression (x+a)(x+b) using the obtained values.

(x−7)(x+8)

To find equation solutions, solve x−7=0 and x+8=0.

x=7

x=−8

Answer: 430 cm

Step-by-step explanation:

Answer:

430 cm

Step-by-step explanation:

43 multiplied by 10 is 430

Answer:

(5w-1) (w-1)

Steps:

5w^2-w-5w+1

w(5w-1)-(5w-1)

(5w-1) (w-1)

(5w-1) (w-1)

Answer:

x^3y^2

there are 3 X multiplied together and 2 y multiplied together

Answer:

-10, -8, -3, 2,6,9

will you be my friend

Answer:

-10, -8, -3, 2, 6, 9

Step-by-step explanation:

Hope this helps!

The answer is 24π square feet per second, which means that the area inside the ripple is increasing at this rate when the ripple is 8 feet in diameter.

To solve this problem, we need to use the formula for the area of a circle, which is A = πr². We know that the diameter of the ripple is 8 feet, so the radius is 4 feet (half of the diameter).
Next, we need to find the rate of change of the area with respect to time. This is given by the formula dA/dt = 2πr(dr/dt), where dr/dt is the rate at which the radius is changing (in this case, the speed of the ripple).

We are given that the speed of the ripple is 3 ft/sec. Therefore, dr/dt = 3 ft/sec.

Substituting the values we have, we get dA/dt = 2π(4)(3) = 24π.

So the area inside the ripple is increasing at a rate of 24π square feet per second when the ripple is 8 feet in diameter.

In more than 100 words, we have used the formula for the area of a circle, as well as the formula for the rate of change of the area with respect to time, to solve this problem. The speed of the ripple, which is given, is used to find the rate at which the radius is changing. Finally, we substitute the values we have into the formula to find the rate of change of the area. The answer is 24π square feet per second, which means that the area inside the ripple is increasing at this rate when the ripple is 8 feet in diameter.

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From the rate of change in area, the increasing rate of area inside the ripple with diameter 8 feet and ripple rate 3 ft/sec is equals to 24π.

We have a pebble is dropped into a pond. Rate or speed of ripple travelling in pond = 3 ft/sec

We have to determine the rate of the area inside the ripple increasing when the ripple is 8 feet in diameter.

Let area and radius be A and r of the ripple respectively. Both are changing with time, so, \(\frac{ dr}{dt} = 3 ft/sec\). Area of circular ripple is written as,

A = πr² --(1)

Differentiating the above equation with respect to time,t, \(\frac{dA}{dt}= 2πr \frac{dr}{dt } \).

Now, for obtaining the increase rate of area inside the ripple, substitute r = d/2

= 4 feet and \(\frac{ dr}{dt} = 3\)

in above expression

=>\( \frac{dA}{dt} = 2π (4)(3) \)

= 24π

Hence, required value is 24π .

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The expression that can be used to find profit is 20x – 50 and that profit when 75 pairs of jeans are sold is 1,450.

Let R represents the revenue function and C represents the cost function, the two functions can be stated correctly as follows:

R = 2x^2+17x−175

C = 2x^2−3x−125

Let P represents the expression that can be used to find profit, we therefore have:

P = R – C

P = 2x^2+17x−175 – (2x^2−3x−125)

P = 2x^2+17x−175 – 2x^2 + 3x + 125

P = 2x^2 – 2x^2 + 17x + 3x – 175 + 125

P = 20x – 50

The profit when 75 pairs of jeans are sold can therefore be calculated as follows:

P = (20 * 75) – 50

P = 1,450

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Answer:

-34

Step-by-step explanation:

All you have to do is subtract by 4 until you count to 15 which then leads you to the number -34

The minimum sample size which is need to to create the given confidence interval is equal to 467.

Sample size n

z = z-score for the desired confidence level

From attached table,

For 85% confidence level, which corresponds to a z-score of 1.44.

Maximum error or margin of error E = 0.06

Population standard deviation σ = 0.9

Minimum sample size required to construct a 85% confidence interval with an error of no more than 0.06,

Use the formula,

n = (z / E)^2 × σ^2

Plugging in the values, we get,

⇒ n = (1.44 / 0.06)^2 × 0.9^2

⇒ n = 466.56

Rounding up to the next integer, we get a minimum sample size of 467.

Therefore, the minimum sample size required to construct a 85% confidence interval with an error of no more than 0.06 is 467.

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Answer:

Length of the segment of a secant 'x' is 4 cm.

Step-by-step explanation:

If a secant and a tangent are drawn from a point outside the circle, then the product of the segments of the secant is equal to the square of the length of the tangent.

By this property,

\(4\times x = 8^2\)

\(4x = 64\)

\(x=\sqrt{16}\)

\(x=4\) cm

Therefore, length of the segment of a secant 'x' is 4 cm.

a. \(r^2 = 0.1024\): Approximately 10.24% of the variance in the dependent variable can be explained by the independent variable(s).

b. \(r^2 = 0.0169\): Only about 1.69% of the variance in the dependent variable can be explained by the independent variable(s).

c. \(r^2 = 0.1600\): Approximately 16% of the variance in the dependent variable can be explained by the independent variable(s).

d. \(r^2 = 0.8649\): About 86.49% of the variance in the dependent variable can be explained by the independent variable(s).

What is variance?

In statistics, variance is a measure of the spread or dispersion of a set of data points around the mean. It quantifies the average squared deviation of each data point from the mean.

The coefficient of determination, denoted as \(r^2\), represents the proportion of the variance in the dependent variable that can be explained by the independent variable(s). It ranges between 0 and 1, where 0 indicates no linear relationship, and 1 indicates a perfect linear relationship.

To determine the coefficient of determination, we square the linear correlation coefficient (r) to find \(r^2\).

Let's calculate the coefficient of determination for each given linear correlation coefficient:

\(a. r = -0.32\\\\r^2 = (-0.32)^2 = 0.1024\)

The coefficient of determination, \(r^2\), is approximately 0.1024. This means that about 10.24% of the variance in the dependent variable can be explained by the independent variable(s).

\(b. r = 0.13\\\\r^2 = (0.13)^2 = 0.0169\)

The coefficient of determination, \(r^2\), is approximately 0.0169. This means that only about 1.69% of the variance in the dependent variable can be explained by the independent variable(s).

\(c. r = 0.40\\\\r^2 = (0.40)^2 = 0.1600\)

The coefficient of determination, \(r^2\), is 0.1600. This means that approximately 16% of the variance in the dependent variable can be explained by the independent variable(s).

\(d. r = 0.93\\\\r^2 = (0.93)^2 = 0.8649\)

The coefficient of determination, \(r^2\), is approximately 0.8649. This indicates that about 86.49% of the variance in the dependent variable can be explained by the independent variable(s).

In summary:

a. \(r^2 = 0.1024\): Approximately 10.24% of the variance in the dependent variable can be explained by the independent variable(s).

b. \(r^2 = 0.0169\): Only about 1.69% of the variance in the dependent variable can be explained by the independent variable(s).

c. \(r^2 = 0.1600\): Approximately 16% of the variance in the dependent variable can be explained by the independent variable(s).

d. \(r^2 = 0.8649\): About 86.49% of the variance in the dependent variable can be explained by the independent variable(s).

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Answer:

1.

$9,000 x ((1+0.0435)^3) = $10,226.33

$3,000 x ((1+0.0375)^3) = $3,350.31

(($4,000 x (1+0.08))x (1-0.04)) x (1+0.06) = $4,396.03

$4,000 x ((1+0.029)^3) = $4,358.19

2.

$22,330.87 - $20,000 = $2,330.87

3.

$4,000 x ((1+0.0435)^3) = $4,545.04

$3,000 x ((1+0.0375)^3) = $3,350.31

(($9,000 x (1+0.08))x (1-0.04)) x (1+0.06) = $9,891.07

$4,000 x ((1+0.029)^3) = $4,358.19

Total Gain on new split: $22,144.61 - $20,000 = $2,144.61

Option with highest yield: 40% Treasury Bonds, 20% stocks

Step-by-step explanation:

Answer:

Step-by-step explanation:

34

Answer:

(+8×5) + (-6)

(+40) + (-6)

(+40-6)

(+34)

Answer:

(5,1)

Step-by-step explanation:

2x-y=9

(5,1)

There are many ordered pairs you could choose. For instance if x=0, then y=9. So you have the pair (0,9). If y=0, then 2x=9, so x=4.5. So you have the pair (4.5,0). You can keep making pairs by plugging in different values!

Answer:

18.8

Step-by-step explanation:

Answer:

  3n

Step-by-step explanation:

The number of raised fingers is 3 for each hand, so is 3 times the number of hands.

For n hands, the number of raised fingers is ...

  3n

Answer:

It appears that you are trying to find a quadratic function in standard form that models the number of guests at the large resort as a function of the number of months since the beginning of the year.

To do this, you can use the given data points to solve for the constants a, b, and c in the standard form of the quadratic function f(x) = ax^2 + bx + c.

To find the values of a, b, and c, you will need to have at least three data points. You can then use these data points to solve a system of three equations with three variables.

For example, using the data points (0, 10), (2, 15), and (4, 18), you can set up the following system of equations:

f(0) = 10 = a(0)^2 + b(0) + c

f(2) = 15 = a(2)^2 + b(2) + c

f(4) = 18 = a(4)^2 + b(4) + c

Solving this system of equations will give you the values of a, b, and c that you can use to write the standard form of the quadratic function that models the data.

I hope this helps! Let me know if you have any questions or need further assistance.

Step-by-step explanation:

The drama club ordered 150 short-sleeved shirts and 100 long-sleeved shirts.

Let S represent the number of short-sleeved shirts and L represent the number of long-sleeved shirts the drama club ordered.

Given that the price of each short-sleeved shirt is $5, so the revenue from selling all the short-sleeved shirts is 5S.

Similarly, the price of each long-sleeved shirt is $10, so the revenue from selling all the long-sleeved shirts is 10L.

The total revenue from selling all the shirts should be $1,750.

Therefore, we can write the equation:

5S + 10L = 1750

Now, let's use the information from the first week of the fundraiser:

They sold one-third of the short-sleeved shirts, which is (1/3)S.

They sold one-half of the long-sleeved shirts, which is (1/2)L.

The total number of shirts they sold is 100.

So, we can write another equation based on the number of shirts sold:

(1/3)S + (1/2)L = 100

Now, you have a system of two equations with two variables:

5S + 10L = 1750

(1/3)S + (1/2)L = 100

You can solve this system of equations to find the values of S and L. Let's first simplify the second equation by multiplying both sides by 6 to get rid of the fractions:

2S + 3L = 600

Now you have the system:

5S + 10L = 1750

2S + 3L = 600

Using the elimination method here.

Multiply the second equation by 5 to make the coefficients of S in both equations equal:

5(2S + 3L) = 5(600)

10S + 15L = 3000

Now, subtract the first equation from this modified second equation to eliminate S:

(10S + 15L) - (5S + 10L) = 3000 - 1750

This simplifies to:

5S + 5L = 1250

Now, divide both sides by 5:

5S/5 + 5L/5 = 1250/5

S + L = 250

Now you have a system of two simpler equations:

S + L = 250

5S + 10L = 1750

From equation 1, you can express S in terms of L:

S = 250 - L

Now, substitute this expression for S into equation 2:

5(250 - L) + 10L = 1750

Now, solve for L:

1250 - 5L + 10L = 1750

Combine like terms:

5L = 1750 - 1250

5L = 500

Now, divide by 5:

L = 500 / 5

L = 100

So, the drama club ordered 100 long-sleeved shirts. Now, use this value to find the number of short-sleeved shirts using equation 1:

S + 100 = 250

S = 250 - 100

S = 150

So, the drama club ordered 150 short-sleeved shirts and 100 long-sleeved shirts.

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Complete question:

The drama club is selling short-sleeved shirts for $5 each, and long-sleeved shirts for $10 each. They hope to sell all of the shirts they ordered, to earn a total of $1,750. After the first week of the fundraiser, they sold StartFraction one-third EndFraction of the short-sleeved shirts and StartFraction one-half EndFraction of the long-sleeved shirts, for a total of 100 shirts.

Answer: y=4x-5     y=4x

Step-by-step explanation:

first we find the slope by using

(y2-y1)/(x2-x1)

(-1-3)/(3-2)

-4/1

-4

so we know the slope is -4

y=4x+b

now we can use either point but ill use (2,3)

we substitute to find b

3=4(2)+b

3=8+b

-5=b

so now we know that the y intercept is -5

so put it together

y=4x-5

if it passes through the origin

it would have the y-intercept of 0

so that equation just be

y=4x

and it keeps the same slope

because they are parallel

hope this helped

1) The statement is False

2) correct answer is a. Underestimated learning effects may cause overestimation of capacity needs.

3) The statement is False

Q1: False

The process capability index (Cpk) can be greater than the process capability ratio (Cp) when the process is centered within the tolerance limits.

Q2: a. Underestimated learning effects may cause overestimation of capacity needs.

This statement highlights the potential impact of underestimating the learning effects on capacity needs, which can lead to overestimation.

Q3: b. False

Activities that take place closer to the customer are called downstream activities, not upstream activities. Upstream activities refer to processes that occur earlier in the production or service delivery process.

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