Given the polynomial 4x3 − 3x2 + 16x − 12, rewrite the polynomial as a product of binomials. a. (x2 − 4)(4x + 3) b. (x2 − 4)(4x − 3) c. (x2 + 4)(4x − 3)
d. (x2 + 4)(4x + 3)

The probability of drawing 1 red marble and 1 blue marble from the given boxes is 2/7.

The probability of drawing 1 red marble and 1 blue marble from the given boxes can be calculated using the concept of probability and sample space. The probability can be defined as the ratio of the number of favorable outcomes to the total number of possible outcomes. The sample space can be defined as the set of all possible outcomes.

Given, a box contains 4 white marbles and 3 red marbles. A second box has 3 white marbles and 6 blue marbles. If one marble is drawn from each box, the probability that 1 red marble and 1 blue marble will be drawn can be calculated as follows:

The total number of possible outcomes is given by the product of the number of marbles in each box:

Total number of possible outcomes = 7 × 9 = 63

The number of favorable outcomes can be calculated by considering all possible cases where one red marble is drawn from the first box and one blue marble is drawn from the second box.

The number of ways to draw one red marble from the first box = 3

The number of ways to draw one blue marble from the second box = 6

Therefore, the number of favorable outcomes = 3 × 6 = 18

Hence, the probability of drawing 1 red marble and 1 blue marble can be given as follows:

Probability = Number of favorable outcomes / Total number of possible outcomes

Probability = 18/63

The probability of drawing 1 red marble and 1 blue marble from the given boxes is 2/7.

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complete question:

a box contains 4 white marbles and 3 red marbles. a second box has 3 white marbles and 6 blue marbles. if one marble is drawn from each box, what is the probability that 1 red marble and 1 blue marblle will be drawn

The minimum IQ score required to be considered as a part of the 2% is approximately 68.25, obtained by converting the score into a standard normal distribution and using the z-score for the 2nd percentile

A percentile is a measure used in statistics to indicate the percentage of data values that fall below a particular value in a distribution, often used to describe test scores, rankings, and other quantitative data.

The standard normal distribution is a specific normal distribution with a mean of 0 and a standard deviation of 1, used to standardize any normal distribution to compare and analyze data from different sources.

According to the given information:

To find the minimum IQ score required to be considered as a part of the 2%, we need to use the standard normal distribution table.

First, we need to convert the given distribution with a mean of 100 and a standard deviation of 15 into a standard normal distribution with a mean of 0 and a standard deviation of 1. We can do this by using the formula:

z = (x - μ) / σ

where x is the IQ score, μ is the mean (100), and σ is the standard deviation (15).

Substituting the values, we get:

z = (x - 100) / 15

Now, we need to find the z-score corresponding to the 2nd percentile, which is the value below which 2% of the scores fall. From the standard normal distribution table, the z-score for the 2nd percentile is approximately -2.05.

Substituting this value into the formula:

-2.05 = (x - 100) / 15

Solving for x, we get:

x = -2.05 x 15 + 100

x ≈ 68.25

Therefore, the minimum IQ score required to be considered as a part of the 2% is approximately 68.25.

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The IQR is the best measure of variability, and it equals 4.

We have a box plot.

From the box plot, we can see that the box extends from 17 to 21 on the number line, with a line at 19 inside the box.

Then, Q1 is 17 and Q3 is 21.

Now, Interquartile range

= Q3 - Q1

= 21 - 17

= 4

Thus, The IQR is the best measure of variability, and it equals 4.

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Answer:  Thus, the width of the second park is 92.5 yards, and its length is also 92.5 yards.

Step-by-step explanation:  The perimeter of the first rectangular park is:

P = 2L + 2W

P = 2(110 yds) + 2(75 yds)

P = 220 yds + 150 yds

P = 370 yds

Since the second rectangular park has the same perimeter as the first, its perimeter is also 370 yards. Let's call its width "x" and its length "y".

Then, we have:

2x + 2y = 370

Simplifying this equation, we get:

x + y = 185

The area of the second park is:

A = xy

To find the dimensions of the second park with the largest area, we need to maximize this expression subject to the constraint x + y = 185.

One way to do this is to use the method of Lagrange multipliers. However, in this case, we can use a simpler approach based on the fact that the area of a rectangle is maximized when its sides are equal. Therefore, we can set x = y = 185/2 = 92.5.

The equation of a line passing through (3, -1) and is perpendicular to x+4y=10 is y = 4x - 13.

Given that a line is passing through (3, -1) and is perpendicular to x+4y=10,

We need to find the equation of the line,

The slope-intercept of a line is, y = mx+c, where m is the slope.

Converting the given line into its slope-intercept form =

x + 4y = 10

4y = -x + 10

y = -x/4 + 5/2

Therefore, the slope is -1/4.

We know that the slopes of two perpendicular lines are negative reciprocal of each other.

So, the slope of the asked line is 4.

Therefore, the equation in form of c is =

y = 4x+c

To find c put x = 3, y = -1 in the equation above,

-1 = 4(3) + c

-1 = 12 + c

c = -13

Now, the equation is y = 4x - 13.

Hence the equation of a line passing through (3, -1) and is perpendicular to x+4y=10 is y = 4x - 13.

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Answer:

Step-by-step explanation:

ince right triangle ABC is graphed in the xy-coordinate plane with vertices at (0,0), (5,0) and (5,12), we can use the coordinates of the vertices to find the lengths of the sides of the triangle.

The length of side AB is 5 units, the length of side BC is 12 units, and the length of side AC is given by the Pythagorean theorem:

AC^2 = AB^2 + BC^2

AC^2 = 5^2 + 12^2

AC^2 = 169

AC = 13

Therefore, right triangle ABC is a 5-12-13 triangle.

The angle at the origin is opposite to the side of length 12, so it is the angle opposite to the side BC. We can find this angle using the inverse tangent function:

tan(theta) = opposite / adjacent

tan(theta) = 12 / 5

theta = tan^-1(12/5) ≈ 68.2°

Since cos(pi + theta) = -cos(theta), we have:

cos(pi + theta) = -cos(theta) = -cos(tan^-1(12/5))

Using the identity cos(arctan(x)) = 1 / sqrt(1 + x^2), we can simplify this expression:

cos(tan^-1(12/5)) = 1 / sqrt(1 + (12/5)^2) = 5 / 13

Therefore, cos(pi + theta) = -cos(theta) = -cos(tan^-1(12/5)) = -5/13.

The components of the vector with initial point (7,−6) and a terminal point at (6,−3) are:

The components of a vector are the vectors that makes up the resultant as described in the problem to have starting point (7,−6) and terminal point (6,−3).

This can be gotten by plotting these points and getting the coordinates of the points that makes the initial point and the terminal point the hypotenuse of the triangle

From the graph, the coordinates are:

component 1: (6, -6) to (3, -6)

component 2: (7, -6) to (6, -6)

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Answer:

Do 1:6 150x =6x5

Step-by-step explanation:

it wouuld be 2/6*150=50

where's thw graph? what we have to show?

Answer:

Step-by-step explanation:

The situation involving testing a claim about a single population proportion is: "The head of health services at Goodheart University suspects that the proportion of smokers may be lower there."

In this situation, the researcher is interested in testing a claim about the proportion of smokers in a single population, namely the population of college students at Goodheart University. The researcher suspects that the proportion of smokers at Goodheart University may be lower than the estimated proportion of 20% for all college students in the United States.

To test this claim, the researcher would conduct a hypothesis test for a single population proportion, where the null hypothesis would be that the proportion of smokers at Goodheart University is equal to 20%, and the alternative hypothesis would be that the proportion is less than 20%.

Based on the sample data, the researcher would then either reject or fail to reject the null hypothesis, and make conclusions about whether there is evidence to support the claim that the proportion of smokers at Goodheart University is lower than the national average.

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Answer: No solution.

Step-by-step explanation:

     To solve, we will substitute the first equation into the second equation for the value of y.

Given:

     y = 1 - 2x

     4x + 2y = 0

Substitute:

     4x + 2(1 - 2x) = 0

Distribute:

     4x + 2 - 4x = 0

Subtract 2 from both sides of the equation:

     4x - 4x = -2

     0 = -2

     We see that the variables cancel out each other, and now we have nothing to solve or continue moving forward within our solution. This means that there are no solutions to this system of equations.

     This means that the lines are parallel. We can also see this when we graph the system, see attached. This becomes more clear when we change both of the equations into slope-intercept form. 4x + 2y = 0 becomes y = -2x, which has the same slope as the first equation (again, parallel lines). If they also had the same y-intercept there would be infinitely many solutions, however, they do not.

The coordinates of the rectangle are (3,-3), (3, -7), (7, -7) and (7, -3).

We also know that the distance between the left and right sides of the rectangle is 4 (since the x-coordinate of the right side is 7 and the x-coordinate of the left side is 3). So we have the equation:

4x = 16

Solving for x, we get x = 4. This means that the length of the top and bottom sides of the rectangle is 4 units. The height of the rectangle is 16/4 = 4 units.

Now that we know the length and height of the rectangle, we can draw it on the coordinate plane.

The left side starts at (3, -3) and ends at (3, -7). The right side starts at (7, -3) and ends at (7, -7).

The top side starts at (3, -3) and ends at (7, -3). The bottom side starts at (3, -7) and ends at (7, -7).

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Step-by-step explanation:

1) We can start by finding the adjacent and opposite sides of the right triangle using the Pythagorean theorem. Let x be the length of the adjacent side, then:

tan θ = (3-√3)/9

tan θ = opposite/adjacent

(3-√3)/9 = opposite/x

opposite = (3-√3)x/9

Using Pythagorean theorem:

(adjacent)^2 + (opposite)^2 = (hypotenuse)^2

x^2 + [(3-√3)x/9]^2 = (hypotenuse)^2

x^2 + (9-6√3+3)x^2/81 = (hypotenuse)^2

(82-54√3)x^2/81 = (hypotenuse)^2

We can simplify this expression to find the hypotenuse:

(hypotenuse)^2 = [(82-54√3)/81]x^2

hypotenuse = sqrt[(82-54√3)/81]x

Now we can find the other trig ratios:

cos θ = adjacent/hypotenuse = x/sqrt[(82-54√3)/81]x

cos θ = 1/sqrt[(82-54√3)/81]

cos θ = sqrt[(82+54√3)/81] / [(82-54√3)/81]

cos θ = sqrt(82+54√3) / (82-54√3)

sin θ = opposite/hypotenuse = (3-√3)x/9 / sqrt[(82-54√3)/81]x

sin θ = (3-√3) / sqrt(82-54√3)

2) To find the other trig ratios, we need to first find the adjacent and hypotenuse sides of the right triangle. Let x be the length of the adjacent side, then:

sin θ = opposite/hypotenuse = 8/10

opposite = (8/10)hypotenuse = 0.8hypotenuse

Using Pythagorean theorem:

(adjacent)^2 + (opposite)^2 = (hypotenuse)^2

x^2 + (0.8hypotenuse)^2 = hypotenuse^2

x^2 + 0.64h^2 = h^2

x^2 = 0.36h^2

x = 0.6h

Now we can find the other trig ratios:

cos θ = adjacent/hypotenuse = 0.6h/h = 0.6

tan θ = opposite/adjacent = (8/10)/0.6 = 4/3

cot θ = 1/tan θ = 3/4

Based on the corresponding sides, the calculated value of x in the similar triangles is x = 7.5

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

The similar triangles

As a general rule, the corresponding sides of similar triangles are in proportions

Using the ratio of corresponding sides, we have

x : 10 = 6 : 8

Express as fraction

This gives

x/10 = 6/8

Multiply both sides by 10

x = 60/8

Divide

x = 7.5

Hence, the value of x in the similar triangles is x = 7.5

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Stratified sampling is a technique where the sample is split into exclusive groups proportional to the population and then simple random sampling is employed within those groups. So, option B is correct.

This sampling technique involves dividing the population statistics into smaller subgroups on certain given characteristics and then selecting a random sample of solution from each stratum based on the requirement.

This technique is best suitable when the type of population is heterogeneous with respect to characteristics of interest. This sampling uses Proportionate sampling which takes an equal stratum with population size. The output of data is identical to the entire population size.

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Answer:

-8xy^4 -3x -3y+ 15

The solution to the system of equations is (-3, 1).

The system of equation is given as:

y = –3x – 8       ....(i)

4x – 3y + 15 = 0   ....(i)

Substitute the value of equation (i) into (ii):

4x – 3(–3x – 8) + 15 = 0

4x + 9x + 24 + 15 = 0

13x = - 24 - 15

13x = -39

Divided by 13 both sides of the equation,

x = -3

Substitute the value of x = -3 into equation (i),

y = –3(-3) – 8

y = 9 - 8

y = 1

Thus, the solution to the system of equations is (-3, 1).

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The complete question is as follows:

Find the solution to the system of equations:

y = –3x – 8       ....(i)

4x – 3y + 15 = 0   ....(i)

Answer: i got no answer.

Step-by-step explanation:

lol sorry im just putting this for the points

Answer:

For finding 4 rational numbers between two numbers we just multiply the numerator and denominator 

Rational numbers -1 and -1/2 are -1/4,-1/8,-1/12,-1/16

This means the four rational numbers are -1/4,-1/8,-1/12,-1/16

The complete answers are:

Right angles are angles that are equal to 90 degrees.

A triangle that includes a right angle is known as a right-angled triangle.

Congruent angles are angles that are equal in size or measure. For example, the right angles in two or more right-angled triangles are congruent.

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(a) The probability distribution of the number of machines not running, and the mean of this distribution is 0.899.

(b)The expected fraction of time that the repair technician will be busy is 88.9% of the time.  

(a) Let X be the number of machines not running. At that point, X can take on values 0, 1, 2, 3, or 4. We will discover the likelihood conveyance of X as takes after:

P(X = 0) = P(all machines are running) = [tex]e^(-84)^4[/tex]/4! = 0.302

P(X = 1) = P(one machine isn't running) = (4)([tex]e^(-84)^3[/tex]/3!) = 0.393

P(X = 2) = P(two machines are not running) = (6)([tex]e^(-84)^2[/tex]/2!) = 0.236

P(X = 3) = P(three machines are not running) = (4)([tex]e^(-84)^1[/tex]/1!) = 0.067

P(X = 4) = P(all machines are not running) = [tex]e^(-8*4)^0[/tex]/0! = 0.002

The cruel(mean)  of this dispersion is E(X) = (0)(0.302) + (1)(0.393) + (2)(0.236) + (3)(0.067) + (4)(0.002) = 0.899.

(b) Let Y be the division of time that the repair specialist is active. At that point, Y can be communicated as

Y = T/(T + R),

where T is the full time that machines are not running

and R is the entire time that went through on repairs.

We know that

T has an Erlang dispersion with parameters

n = 4 and λ = 1/8 (since the running time of each machine has exponential dissemination with cruel 8 hours).

Subsequently, the anticipated esteem of T is E(T) = n/λ = 32 hours.

Additionally, R has an exponential dispersion with cruel 4 hours,

so E(R) = 4 hours. In this way, we have:

E(Y) = E(T/(T + R))

= E(T)/E(T + R)

= 32/(32 + 4)

= 0.889.

In this manner, ready to anticipate the repair professional to be active around 88.9% of the time. 

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The amount he will receive as his salary in the 18th year of working at this job will be $107,500

What is Rate?

A rate in arithmetic is a ratio that contrasts two separate values with various unit systems. For instance, if John types 50 words per minute, that means he types 50 words per minute. We are dealing with a rate because the word "per" is there. The symbol "/" can be used in place of the word "per" in issues.When two or more similar amounts or numbers are being compared using the same units, a ratio is utilized.

The amount of money Jamar made in his first year= $48,000

The salary rise per year = $3,500

The amount of money he will make for the extra 17 years is

= 17 × $3,500

= $59,500

he will receive as his salary in the 18th year working at this job = $48,000 + $59,500 = $107,500

Therefore the amount he will receive as his salary in the 18th year of working at this job will be $107,500

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The solution to the equation 83x + 1 = 16, rounded to the nearest thousandth, is x = 0.181, the key features of the function f(x) = 83x + 1 are; y-intercept; (0, 1), and Asymptote; None.

To solve 83x + 1 = 16, we need to isolate x on one side of the equation. We can do this by subtracting 1 from both sides and then dividing by 83;

83x + 1 - 1 = 16 - 1

83x = 15

x = 15/83

Rounded to the nearest thousandth, x is approximately 0.181.

Therefore, the solution to the equation 83x + 1 = 16, rounded to the nearest thousandth, is x = 0.181.

The function f(x) = 83x + 1 is a linear function in the form y = mx + b, where m is the slope and b is the y-intercept. Therefore;

The y-intercept is (0, 1), since b = 1.

The function does not have an asymptote, since it is a linear function and it does not approach any particular value as x increases or decreases.

So the key features of the function f(x) = 83x + 1 are;

y-intercept; (0, 1)

Asymptote; None.

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The correct pairing of DNA bases is: A with T, and C with G. The Option C is correct.

The correct pairing of DNA bases is established by the rules of base pairing in DNA structure which is known as Chargaff's rules.

According to the rule, the adenine (A) pairs with thymine (T) and cytosine (C) pairs with guanine (G); these pairing are based on the complementary nature of the DNA bases where adenine forms two hydrogen bonds with thymine, and cytosine forms three hydrogen bonds with guanine.

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Faye can sort 22,200 recyclable items in 444 minutes, based on the ratio shown in the double number line.

To determine how many recyclable items Faye can sort in 444 minutes, we need to use the ratio shown in the double number line. We can do this by finding the slope of the line, which is the ratio of the change in items to the change in time.

To find the slope, we start at the point (0,0) on the number line and move to the point (150,3). The change in items is 150 - 0 = 150, and the change in time is 3 - 0 = 3. Therefore, the slope is:

slope = change in items / change in time

slope = 150 / 3

slope = 50

This means that Faye can sort 50 recyclable items in one minute. To find out how many items she can sort in 444 minutes, we simply multiply the number of minutes by the rate of 50 items per minute:

items sorted = rate x time

items sorted = 50 x 444

items sorted = 22,200

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Answer:

C and D both represent angle relationships in the figure.

C represents the relationship between the angles labeled x, y, and z. We know that the sum of the angles in a triangle is 180 degrees, so we can set 6x+14 (angle x), 33 (angle y), and 180-(7x-9) (angle z) equal to 180 and solve for x.

D represents the relationship between the angles labeled w, x, y, and z. We know that the sum of the angles in a quadrilateral is 360 degrees, so we can set 33+(5x-10)+(7x-9)+w equal to 360 and solve for x.

15 ounces of wax Cindy use for each candle.

To find out how many ounces of wax Cindy uses for each candle, we need to divide the total amount of melted wax by the number of candles.

First, let's find the total amount of melted wax:

6 bags * 20 ounces/bag = 120 ounces

Cindy melted 120 ounces of wax in total.

Now, let's divide the total amount of melted wax by the number of candles to find out how many ounces of wax Cindy used for each candle:

120 ounces / 8 candles = 15 ounces/candle

Therefore, Cindy used 15 ounces of wax for each candle.

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Answer: B

Step-by-step explanation:

It bounces off of x=3   take opposite sign when you put in parenthesis

(x-3)²   the bounce makes it squared on outside

(x-1)   goes through 1

(x+2) goes through -2

put it togehter

(x-3)²(x-1)(x+2)    B