is x+5 a facotr of f(x)=x3-4x2+3x+7 explain

The area of the shaded region of the semicircle is 108π mm²

Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.

Given that, a semicircle with a diameter of 24 mm, a circle is fitted in it, we need to find the measurement of the area which is shaded.

The diameter of the smaller circle = radius of semicircle.

Therefore,

Radius of smaller circle = 24/4 = 6 mm

To find the area of shaded region, we will subtract the area of the smaller circle from the area of semicircle.

Area of a circle = π × radius² {area of semicircle is just half of it}

Area of shaded region = π × 12² - π × 6²

= π(144-36)

= 108π

Hence, the area of the shaded region of the semicircle is 108π mm²

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Answer:

Each person gets .36 quarts of vegetable soup.

Step-by-step explanation:

If Suzie makes 9 quarts of vegetable soup to serve among 25 people, you must divide 25 by 9, doing so you get .36 .

Answer:

Step-by-step explanation:

The volume of a solid obtained by rotating a two-dimensional region about an axis can be found using the method of cylindrical shells.

The region in question is bounded by the parabolic curve y = x^2, the vertical line x = 5, and the x-axis. We can find the volume of the solid obtained by rotating this region about the x-axis by adding up the volumes of an infinite number of infinitely thin cylindrical shells with radius equal to the distance from the axis to the boundary of the region at each y-value.

The formula for the volume of a cylindrical shell is given by V = 2 * pi * y * dV, where y is the distance from the x-axis to the boundary of the region at each y-value, and dV is the incremental volume at that y-value.

To find the volume, we need to find the incremental volume dV, and integrate the cylindrical shell formula over the region bounded by y = x^2 and x = 5. The incremental volume is given by dV = pi * (R^2 - r^2)dy, where R is the outer radius, r is the inner radius, and dy is the incremental change in y.

In this case, the outer radius R is equal to the value of x = 5 when y = x^2, and the inner radius is equal to zero. Thus, the incremental volume is given by: dV = pi * (5^2 - 0^2)dy = 25 * pi * dy.

The bounds of the integration are from 0 to 5^2 = 25. Integrating the cylindrical shell formula over this range, we find that the volume of the solid obtained by rotating the region bounded by y = x^2, x = 5, and y = 0 about the x-axis is:

V = 2 * pi * integral from 0 to 25 of (y * 25 * pi)dy = 2 * pi * (25^2 * 25 / 2) = 15625 * pi cubic units.

So, the volume of the solid is approximately 49,093 cubic units.

The probability that in an hour there will be at least 10 requests for parts is P(X ≥ 10) = 1 - P(X < 10) = 1 - (Σ P(X = k) for k = 0 to 9) . The probability that the 10th request in the morning requires at least 2 hours of waiting time is P(time until the 10th request ≥ 2 hours) = 1 - P(time until the 10th request < 2 hours) .

i) Poisson Distribution: The Poisson distribution can be used to model the number of requests for parts in a given time period, assuming that the average rate of requests is constant. The Poisson distribution with parameter λ is given by the following formula:

P(k requests in a time period) = (e^-λ * λ^k) / k! , where k is the number of requests, e is the mathematical constant approximately equal to 2.71828, and λ is the average rate of requests.

a) Using Poisson distribution, the probability that in an hour there will be at least 10 requests for parts is given by:

P(X ≥ 10) = 1 - P(X < 10) = 1 - (Σ P(X = k) for k = 0 to 9)

b) To find the probability that the 10th request in the morning requires at least 2 hours of waiting time, we need to find the distribution of the time between requests. Since the requests are modeled as a Poisson process, the time between requests is modeled as an exponential distribution with parameter λ.

ii) Gamma Distribution: The gamma distribution is a continuous probability distribution that can be used to model the sum of k independent and identically distributed exponential random variables. In this case, the distribution of the time between requests is exponential, and the sum of 10 independent exponential random variables gives us the distribution of the time until the 10th request.

a) To find the probability that in an hour there will be at least 10 requests for parts using the gamma distribution, we need to first find the distribution of the number of requests in an hour.The sum of 10 independent exponential random variables with rate λ follows a gamma distribution with shape parameter k = 10 and scale parameter 1/λ.

Using the cumulative distribution function of the gamma distribution, the probability that in an hour there will be at least 10 requests for parts is given by:

P(number of requests ≥ 10) = 1 - P(number of requests < 10)

b) Using Gamma distribution, the probability that the 10th request in the morning requires at least 2 hours of waiting time is given by:

P(time until the 10th request ≥ 2 hours) = 1 - P(time until the 10th request < 2 hours) , where the cumulative distribution function of the gamma distribution can be used to calculate the probability.

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The expression (8+√12) / (5+√3) in the form of (a+√3) / b is given by (18 + √3) / 11, where a = 18 and b = 11

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Given that, an expression (8+√12) / (5+√3) we need to convert it into

(a+√3) / b, where, a and b are integers.

The given expression is (8+√12) / (5+√3)

Rationalizing the expression by multiplying the numerator and denominator by changing the sign of the denominator, (5-√3)

Therefore, (8+√12) / (5+√3)

= (8+√12) / (5+√3) × (5-√3) / (5-√3)

= (40 - 8√3 + 5√12 - √36) / 5²-√3²   [a²-b² = (a+b)(a-b)}

= (40 - 8√3 + 5× 2√3 - 6) / (25-3)

= (40 - 8√3 + 10√3 - 6) / 22

= (36 + 2√3) / 22

= (18 + √3) / 11

Hence, the expression (8+√12) / (5+√3) in the form of (a+√3) / b is given by (18 + √3) / 11, where a = 18 and b = 11

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On dilating the point X(6,5) with scale factor of -2, the value is obtained as X(-12,-10).

What is dilation?

Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. The initial shape should be stretched or contracted during a dilatation.

The coordinate point for X is given as X(6,5).

The dilation is centered at the origin (0,0).

The dilation scale factor is given as -2.

To find the value of X' use the formula -

X(a,b) → X[(a×(-2)) , (b×(-2))]→ X'

Substitute the values in expression -

X(6,5) → X[(6×(-2)) , (5×(-2))]

X(6,5) → X'(-12,-10)

Therefore, the coordinate point is X'(-12,-10).

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The length of the dashed diagonal line is drawn from one vertex of the base to the opposite vertex of the same base is 10

The length of the dashed diagonal line is drawn from one vertex of the base to the opposite vertex of the other base is 14.87

The interior diagonal is solved using the Pythagoras theorem is applicable to right angle triangle.  the formula of the theorem is

hypotenuse² = opposite² + adjacent²

For same base

opposite = 6

adjacent = 8

plugging the values as in the problem

let x be the required distance

x² = 6² + 8²

x² = 36 + 64

x² = 100

x = √100

x = 10

dashed diagonal line is drawn from one vertex of the base to the opposite vertex of the other base

opposite = 11

adjacent = 10

let y be the required distance

y² = 10² + 11²

y² = 100 + 121

y² = 221

y = √221

y = 14.87

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The table that represents a proportional relationship is given as follows:

x −3 0 3

y −2 0 2

(which is the last option).

A proportional relationship is defined as follows:

y = kx.

In which k is the constant of proportionality.

From the definition, we have that a proportional relationship is a linear function with an intercept of zero, meaning that when x = 0, y = 0.

The last option is the only option for which the intercept of zero condition is satisfied, hence it is the correct option.

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Answer:

the answer is 330000

Step-by-step explanation:

just do 22,000 divided by 4 and that 5, 500 so its 5,500 miles a month and then do 5,500 x 60= 330000

The most appropriate measure of spread for this data is standard deviation, because the boxplot is skewed to the right.

The most appropriate measure of spread for this data is standard deviation. The data is represented by a boxplot, which is a graphical representation of the data that shows the median, quartiles, and range of the data. In this case, the boxplot is skewed to the right, meaning that the data is not normally distributed. When the data is not normally distributed, the standard deviation is the best measure of spread to use. Standard deviation measures the spread of data by calculating the distance between each data point and the mean, and then taking the average of these distances. This allows us to accurately measure the spread of data that is not normally distributed. Therefore, standard deviation is the most appropriate measure of spread for this data.

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The probability that after servicing twelve of these phones, phones of only two of the three types remain to be serviced can be calculated using combinatorics.

The number of ways to choose two types of phones out of three and the number of ways to arrange twelve phones of these two types need to be determined. The probability can then be calculated as the number of favorable outcomes divided by the total number of possible outcomes. This method can help determine the likelihood of a specific event happening in a given scenario.

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Using proportions, if a contractor hired 18 workers to complete the construction of a road in 60 days, to complete the construction work 15 days earlier, the additional workers he should hire is 6.

We can use proportions to determine the number of workers needed to complete the work 15 days earlier, which is in 45 days.

Proportions are ratios equated to one another.

The number of workers needed to complete a road construction in 60 days = 18

If the contractor wants to complete the work 15 days earlier, he must complete it in 45 days (60 - 15).

The number of workers needed to complete the construction in 1 day = 1,080 (60 x 18)

The number of workers needed to complete the construction in 45 days = 24 (1,080/45)

The difference between completing the work in 60 days and 45 days = 6 workers (24 - 18).

Thus, proportionately, it will take 6 additional workers to complete the construction work 15 days earlier.

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Answer:

10

Step-by-step explanation:

Use the pythagorean theorem/distance formula.

AB = \sqrt{(4-(-2))^2+(7-(-1))^2} = \sqrt{36+64} = \sqrt{100} = 10

Answer:

4 inches

Step-by-step explanation:

Let b = base length

h = height

A = area

[tex]A = \dfrac{1}{2}\cdot b \cdot h\\\\[/tex]

Multiply throughout by 2

[tex]2 \cdot A = 2\cdot \dfrac{1}{2}\cdot bh\\\\2A = bh\\\\h = \dfrac{2A}{b}[/tex]

We are given A = 16 in² and b = 8 inches

So, h = 2(16)/8 = 32/8 = 4 inches

Check to see if this is correct

A = (1/2)(8)(4) = (4)(4) = 16

The cost of carpeting a rectangular floor measuring 9 feet by 18 feet is 18 square yards x 12.75 = 228.50.  If needed, this can be rounded to the nearest penny, which is 228.50.

The formula to calculate the cost of carpeting a rectangular floor is Area of the floor x Cost of carpet per square yard.

The area of the floor is calculated by multiplying the length and the width, which in this case is 9 feet x 18 feet = 162 square feet.

To convert 162 square feet into square yards, divide 162 square feet by 9, which equals 18 square yards.

Therefore, the cost of carpeting a rectangular floor measuring 9 feet by 18 feet is 18 square yards x 12.75 = 228.50.  If needed, this can be rounded to the nearest penny, which is 228.50.

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The perimeter of the trapezoid is 50 cm.

A trapezoid, commonly referred to as a trapezium, is a quadrilateral or a polygon with four sides. It has a set of parallel opposing sides and a set of non-parallel sides. The bases and legs of the trapezoid are known as the parallel and non-parallel sides, respectively.

Given the trapezoid,

let us consider ABCD be the trapezoid,

so given angle B = 90°

AB = 12 cm, AD = 10 cm, and BC = 15 cm

let us draw a perpendicular from D on BC parallel to AB

which forms the right triangle DEC

from the Pythagorean theorem, from the figure attached in the image.

DC² = DE² + EC²

DC² = 12² + 5²

DC² = 144 +25

DC² = 169

DC = 13 cm

perimeter is the sum of all sides,

P = AB + BC + AD + DC

P = 12 + 15 + 10 + 13

P = 50 cm

Hence perimeter is 50 cm.

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The required correct answer is A. the five-number summary.

A box and whisker plot, often known as a box plot, shows a data set's five-number summary. The minimum, first quartile, median, third quartile, and maximum make up the five-number summary. A box is drawn from the first quartile to the third quartile in a box plot. At the median, a vertical line passes through the box.

The correct answer is A. the five-number summary. A boxplot is a graphical representation of the distribution of a set of data, and it provides information about the shape, spread, and skewness of the data. The five-number summary is used to construct a boxplot and includes the minimum value, first quartile (Q1), median, third quartile (Q3), and maximum value.

The boxplot uses these five values to display the range of the data and highlight any outliers or unusual observations. Knowing the five-number summary is sufficient to create a boxplot, while knowing all of the individual observations or the mean and standard deviation is not necessary.

Final answer: A. the five-number summary.

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Answer:

length=9

width=4m

Step-by-step explanation:

Let the width of the rectangle be, x and the length be, x+5

perimeter=2(L+W)

26 m=2(x+5+x)

26=2x+10+2

26-10=4x

16=4x

x=

length=9m

width=4m

If Judy's refund is $535, to pay for furniture worth $800, she will have to come up with $265, which is the difference.

The difference is the result of the subtraction operation.

The subtraction operation is one of the four basic mathematical operations.

Subtraction operations involve the minuend, subtrahend, the subtraction operator (-), the difference, and the equal symbol (=).

The cost of furniture = $800

Expected credit refund = $535

The difference between the cost and refund = $265 ($800 - $535)

Thus, Judy will bring $265 to make up for the purchase of the furniture.

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Equation can use to find the number of water balloons w in the bin before Naomi trips is w - 13 = 15.

As per the given data, Naomi's carries a bin of water balloons outside for the balloon toss, she trips and breaks 13 balloons.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The number of water balloons w in the bin before Naomi trips.

She counts the remaining water balloons, and there are 15 left.

According to the question, the equation is

w - 13 = 15

⇒ w = 15 + 13

⇒ w = 28

Hence, equation which is used to find the number of water balloons w in the bin before Naomi trips is w - 13 = 15.

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Answer: Tony

Step-by-step explanation: What I did is I took the 7.02 and multiplied it by 4 to make the 50 200 and I got 28.08 so since the time for Simon is larger than the time for Tony, tony went faster because it look him less time. Hope this helps!

Answer: Tony was faster

Step-by-step explanation: To find who ran faster we multiply Tony's time by 4. If it took Tony 7.02 seconds for 50 yards we can multiply that by for to find how long it would have taken him at that speed to run 200 yards.

7.02 x 4 = 28.08

The given statement: The standard deviation is a resistant measure of spread is true.

Standard deviation is the measure of how spread out numbers are. It is a measure that is used to quantify the amount of variation or dispersion of a set of data values.

The standard deviation is a metric that reveals how much variance from the mean there is, including spread, dispersion, and spread. A "typical" variation from the mean is shown by the standard deviation. Because it uses the data set's original units of measurement, it is a well-liked measure of variability. When data points are closely spaced from the mean, there is a little variation, and when they are far spaced from the mean, there is a large variation. The standard deviation determines how much the data deviate from the mean.

When outliers are included, resistant statistics don't change (or vary very little). Resistance does not imply that anything is immobile; that would be "immovable." It implies that your results could fluctuate a bit, but not much.

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The total sales in week 20 after the beginning of the advertising campaign was $3297.03

An equation is an expression that shows the relationship between numbers and variables using mathematical expressions. Equations are classified based on degree as linear, quadratic, cubic

Her sales in the first week were $86. After starting an online advertising campaign, her sales increased 20% the following week. This expression can be represented in the form of an exponential function:

y = abˣ

Where a is the initial value and b is the multiplication factor

Let y represent the total sales after x weeks. Comparing with the expression:

a = $86, b = 100% + 20% = 1.2. Hence:

y = 86(1.2)ˣ

After 20 weeks:

y = 86(1.2)²⁰ = 3297.03

The total sales was 3297.03

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The first five terms will be -4, 3, 10, 17 and 24.

The 34th term will be 227

An arithmetic sequence is one in which each phrase grows by adding or removing a certain constant, k. The difference between consecutive terms in an arithmetic series is always the same and is known as the common difference d.

Based on the information, it should be noted that the AP is given as An = - 11 + 7b

First term = -11 + 7(1) = -4

Second term = -11 + 7(2) = 3

Third term = -11 + 7(3) = 10

Fourth term = -11 + 7(4) = 17

Fifth term = 24

The 34 term will be:

= -11 + 7(34)

= 227

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Given the explicit formula for an arithmetic sequence find the first five terms and the term named in the problem. An=-11+7b. Find a34

Para encontrar el equivalente decimal de una fracción, divide el numerador por el denominador. Debido a que el número en el numerador es más pequeño que el número en el denominador, debe colocar el punto decimal después y agregar ceros.

Un número decimal es un número formado por números enteros y fraccionarios, que al escribirse entre enteros y fracciones se separan por una coma, lo que se denomina punto decimal.

En números enteros, estamos familiarizados con los términos miles, centenas, decenas y unidades. Sin embargo, estos números aún pueden continuar con números más pequeños, a saber, décimas, centésimas, milésimas, etc.

En los números decimales, la parte cuyo valor es menor que el número de la unidad se coloca a la derecha de la coma, siempre que el número a la derecha del decimal sea un número de décimas, y cada número a la derecha sea una décima menor que el anterior.

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The estimates that is led from the data from a poll conducted by Travelocity , then the percentages are "computed from a sample"  .

The Data from the poll conducted by Travelocity was computed from a sample of travelers and was used to estimate the proportion of travelers

The travelers have certain habits or behaviors, such as checking work email (44%) taking a cell phone (32%) , or bringing a laptop computer on vacation (26%) .

The sample estimates are used to make inferences about the population.

Therefore , the given percentages are that they were  "computed from a sample" .

The given question is incomplete , the complete question is

Data from a poll conducted by Travelocity led to the following estimates:

Approximately 44% of travelers check work email while on vacation, about 32% take cell phones on vacation in order to stay connected with work, and about 26% bring a laptop computer on vacation.

Are the given percentages "population values" or were they "computed from a sample" ?

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Point that represents height after 10 years is (10 , 8.25).

A line is a one-dimensional figure, which has length but no width. A line is made of a set of points which is extended in opposite directions infinitely.

Given points

C(3, 3) and D(11, 9) are on a directed line segment that represents height of tree over 16 years.

Equation of the line segment

(y - y₁) = [(y₂ - y₁)/(x₂ - x₁)](x ₋ x₁)

(y - 3) = [(9 - 3)/(11 - 3)](x - 3)

y - 3 = (6/8)(x - 3)

y - 3 = (3/4)x - 9/4

y = (3/4)x - 9/4 + 3

y = (3/4)x + 3/4

y is height, x is number of years

In 10 years,

= (3/4)10 + 3/4

y = 30/4 + 3/4

y = 33/4 = 8.25

Point is (10 , 8.25)

Hence, (10, 8.25) is point for height of tree after 10 years.

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An outcome or collection of outcomes from a sample space is called an event.

A random experiment's sample space is the collection of all conceivable results. A random experiment's related event is a subset of the sample space. Any outcome's probability is a number between 0 and 1.

Each consequence or set of outcomes in an experiment constitutes an event.

An outcome is a potential result of an experiment or trial in probability theory. Each experiment's possible results are distinct, and alternative outcomes are mutually exclusive (only one outcome will occur on each trial of experiment).

The sample space (also known as sample description space, possibility space, or outcome space) of an experiment or random trial is a collection of all potential outcomes or results of that experiment in probability theory.

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The sphere has a volume of 113 cubic units, the sphere's radius is 2.99 units.

Volume is the quantity of space a thing occupies, whereas capacity is a measure of the substance it can store, such as a solid, a liquid, or a gas. While capacity can be measured in virtually any other unit, such as liters, gallons, pounds, etc., volume is measured in cubic units.

the sphere's diameter.

Having said that,

The sphere's volume is equal to[tex]4/3 \pi r^3.[/tex]

The volume is already known.

[tex]113 = 4/3 (3.14) r^3[/tex]

339 = 4 (3.14) r³

339/4 = 3.14 r³

84.75 = 3.14 r³

84.75/3.14 = r³

26.99 = r³

r = ∛26.99

r = 2.99

Consequently, the sphere's radius is 2.99 units.

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Complete question -

Consider a sphere whose volume is 113 cubic units what will be the radius of the mirror?

The fourth vertex of the rectangle is given as follows:

(g,g).

A rectangle is composed by two dimensions, which are given as follows:

A rectangle has four sides, meaning that two dimensions are equal, and the coordinates for this problem are given as follows:

The missing combination of one coordinate of x and one coordinate of y is given as follows:

(g,g).

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