Consider the polynomials p(X)=21x - 4x^2 and q(X)=5 . Find the X coordinate(s) of the point(s) of intersection of these two polynomials. What is the sum of these X coordinates? (If there is only one point of intersection, give the corresponding X -coordinate.)
19/4
21/8
21/4
9
None of the above

The correlation coefficient of 0.90 indicates a strong positive linear correlation between happiness and GPA of high school students.

A correlation coefficient measures the strength and direction of the relationship between two variables. In this case, the correlation coefficient of 0.90 indicates a strong positive linear correlation between happiness and GPA of high school students.

A positive correlation means that as one variable (in this case, happiness) increases, the other variable (GPA) also tends to increase. The magnitude of the correlation coefficient, which ranges from -1 to 1, represents the strength of the relationship. A value of 0.90 indicates a very strong positive linear correlation, suggesting that there is a consistent and significant relationship between happiness and GPA.

This means that as the level of happiness increases among high school students, their GPA tends to be higher as well. The correlation coefficient of 0.90 suggests a high degree of predictability in the relationship between these two variables.

It is important to note that correlation does not imply causation. While a strong positive correlation indicates a relationship between happiness and GPA, it does not necessarily mean that one variable causes the other. Other factors or variables may also influence the relationship between happiness and GPA.

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The correct answer is (D) It is the distribution of all possible sample means from a given population.

The sampling distribution of a sample mean refers to the distribution of all possible sample means that can be obtained by taking repeated samples of the same size from a given population. The shape, mean, and standard deviation of the sampling distribution of the sample mean are determined by the properties of the population being sampled and the sample size.

In other words, if we take multiple random samples of the same size from a population, the distribution of the means of each of these samples will form a sampling distribution of the sample mean. This distribution will have a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.

Option (A) is incorrect because it only describes one aspect of the sampling distribution - the fact that it includes all possible sample means of a given size. Option (B) is incorrect because it describes a very specific scenario where the sample mean equals the population mean and the standard deviation equals zero, which is highly unlikely to occur in real-world situations. Option (C) is incorrect because it describes a graphical representation of the means of all possible samples, rather than a distribution. Option (E) is incorrect because it describes the probability distribution for each possible sample size, rather than the sampling distribution of the sample mean.

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The graph that represents the solution to the inequality is a number line with closed point at 10 with arrow pointing left

You should be aware that inequality is is a mathematical statement showing that two opposite things are not equal.  The graph is a diagram that illustrates the statement.

The given inequality is 2(b + 2) > 24

Opening the brackets to get

2b+4≥24

2b≥24-4

This implies that 2b≥20

Making b the subject

b≥20/2

b≥10

Therefore, the graph is a number line with closed point at 10 with arrow pointing left

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The area of the rectangular parking lot is 929.03 square meters.

Use the formula for the area of a rectangle to calculate the area of the rectangular parking lot, which is given as:

Area = length × width

We know that the parking lot is 67.5 ft wide and 148 ft long, the area can be calculated as follows:

Area = 67.5 ft × 148 f

t= 9990 sq. ft

However, the question asks for the area in square meters, so we need to convert square feet to square meters. 1 square foot is equal to 0.092903 square meters, so we can use this conversion factor to convert square feet to square meters.

Area in square meters = Area in square feet × 0.092903

= 9990 sq. ft × 0.092903

= 929.03 sq meters

Therefore, the area is 929.03 square meters.

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Answer:

26

Step-by-step explanation:

Because these are remote exterior angles, you set (5x-2) equal to (2x+76)

After you set them equal you solve for x

5x-2=2x+76

5x=2x+78

3x=78

x=26

Answer:

Yes, the set is a function

Step-by-step explanation:

In order to have a function, each x must pair up with exactly ONE y

That happens in this set of ordered pairs.

5 only pairs with 13

6 only pairs with 12

7 only pairs with 11

9 only pairs with 9

10 only pairs with 11

Answer:

(0,6) (0,-12)

Step-by-step explanation:

The equation y = 2x - 12 represents a linear function with a slope of 2 and a y-intercept of -12.

The equation y = 2x - 12 represents a linear function with a slope of 2 and a y-intercept of -12. This means that the graph will have a positive slope, indicating a upward trend, and it will intersect the y-axis at the point (0, -12).

To sketch the graph, you can start by plotting the y-intercept at (0, -12). From there, use the slope of 2 to determine additional points by moving 1 unit horizontally (to the right) and 2 units vertically (upward) to plot another point. Repeat this process to plot more points, then connect them to form a straight line.

Keep in mind that a visual representation is essential for accurately identifying the specific graph of y = 2x - 12.

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The perimeter of DREPFQ is 1

In an equilateral triangle, the intersection is the centroid

From the information given, we have that;

AB =√3

Then, we can say that;

AG = BG = CG = √3/3

Also, we have that D, E, and F are the midpoints of the sides of triangle Then, DE = EF = FD = √3/2.

AP = BP = CP = √3/6.

To find the perimeter of DREPFQ, we need to add up the lengths of the line segments DQ, QE, ER, RF, FP, and PD.

The perimeter of DREPFQ is √3/6 × √3/2)

Multiply the value, we get;

√3× √3/ 6 × 2

Then, we get;

3/18

divide the values, we have;

= 0.167

Multiply this by six sides;

= 1

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The complete question:

G is the centroid of equilateral Triangle ABC. D,E, and F are midpointsof the sides as shown. P,Q, and R are the midpoints of line AG,line BG and line CG, respectively. If AB= sqrt 3, what is the perimeter of DREPFQ

The table values using function rule y = -10x - 2 is (8,-2,-12,-52)

Given function

y = -10x - 2

From the table

x = -1 , 0 , 1 , 5

substitute x values in function

if x = -1

y = -10x - 2

= -10(-1) - 2

= 10 - 2

y = 8  

if x = 0

y = -10(0) -2

y = -2

if x = 1

y = -10(1) - 2

y  = -12

if x = 5

y = -10(5) -2

y = -52

y values (8,-2,-12,-52)

Table:

x      y

-1     8

0    -2

1     -12

5    -52

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Answer: No. Collin was wrong.

Step-by-step explanation:

From the question, we are informed that the answer that Collin had on his paper was −13 − (15 + 58) and the correct answer, located in the back of the book, was −13 −15 + 58.

Collin is wrong because he didn't take into cognisance the effect of minus on the bracket. Here, −13 − (15 + 58) will be equal to -13 -15 -18. This is because minus multiplied by plus equals to minus. He shouldn't have put the numbers in the bracket.

The teacher sets up 7 workstations in each classroom

Let x represent the number of workstations in each classroom.

Since an art teacher has a total of 7/8 pound of clay. The teacher puts 1/16 pound of clay at each work station . The teacher sets up an equal number of work stations in each of 2 classrooms.

Since the teacher puts 1/16 pound of clay at each work station, there are x × 1/16 pounds in each class.

So, the number of pounds ineach class is x/16.

Since there are 2 classrooms, the number of pounds of clay in both classrooms is 2x/16.

Since the total pounds of clay is 7/8, we have that

2x/16 = 7/8

So, solving for x, we have that

x = 7/8 × 16/2

x = 7/8 × 8

x = 7

So, the teacher sets up 7 workstations in each classroom

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According to the given question we have The value of k that makes the function f continuous at x = 2 is -2.

To determine the value of k that makes the function f continuous at x = 2, we need to evaluate the limit of the function at x = 2 from both sides and ensure that they are equal.

First, let's evaluate the limit as x approaches 2 from the left side (x < 2). We have:

lim (x->2-) f(x) = lim (x->2-) (x^2 - 5x + k) = 2^2 - 5(2) + k = -2 + k

Next, let's evaluate the limit as x approaches 2 from the right side (x > 2). We have:

lim (x->2+) f(x) = lim (x->2+) (4 - 4x + k) = 4 - 4(2) + k = -4 + k

For the function to be continuous at x = 2, these two limits must be equal. Therefore, we have:

-2 + k = -4 + k

Solving for k, we get:

k = -2

Therefore, the value of k that makes the function f continuous at x = 2 is -2.

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Answer:

46 cents per minute.

Explanation:

The long-distance call costs $7.36 for 16 minutes.

The goal is to determine the unit rate in cents per minute.

In order to do this, first convert the amount, $7.36 to cents.

Next, to find the unit rate, divide the number of cents by the number of minutes.

The unit rate is 46 cents per minute.

The operator S on the vector space R₁[x] is defined as S(f(x)) = -a + b + (a + 2b)x, where a and b are constants. We need to find the minimal polynomials and show that S is cyclic.

To find the minimal polynomials, we need to determine the polynomials Ns₁₁(4) and N₁,x(4).

For Ns₁₁(4), we substitute 4 for x in S(f(x)) and equate it to zero. Solving the resulting equation, we can find the minimal polynomial Ns₁₁(4).

For N₁,x(4), we need to find a polynomial f(x) such that S(f(x)) = 4f(x). By substituting S(f(x)) into the equation, we can solve for f(x) and find the minimal polynomial N₁,x(4).

To show that S is cyclic, we need to find a vector v such that the set {v, S(v), S²(v), ...} spans the entire vector space R₁[x]. This means that every polynomial in R₁[x] can be expressed as a linear combination of these vectors. By choosing an appropriate vector v, we can demonstrate that S is cyclic in R₁[x].

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Therefore, in either partial derivatives, we have u = 0 or v = 0.

The given information implies that two vectors u and v satisfy:

u * v = 0, where * denotes the dot product between vectors.

u X v = 0, where X denotes the cross product between vectors.

From the first equation, we know that the angle between u and v is either 90 degrees or 270 degrees. That is, u and v are orthogonal (perpendicular) to each other.

From the second equation, we know that the magnitude of the cross product u X v is equal to the product of the magnitudes of u and v multiplied by the sine of the angle between them. Since u and v are orthogonal, the angle between them is either 90 degrees or 270 degrees, which means that the sine of the angle is either 1 or -1. Therefore, we have:

|u X v| = |u| * |v| * sin(θ)

= 0

Since the magnitudes of u and v are non-negative, it follows that sin(θ) must be zero. This can only happen if the angle between u and v is either 0 degrees (i.e., u and v are parallel) or 180 degrees (i.e., u and v are anti-parallel).

In the case where u and v are parallel, we have:

u * v = |u| * |v| * cos(θ)

= |u|²

= 0

This implies that |u| = 0, which means that u = 0.

In the case where u and v are anti-parallel, we have:

u * v = |u| * |v| * cos(θ)

= -|u|²

= 0

This again implies that |u| = 0, which means that u = 0.

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Answer:

33.33%

Step-by-step explanation:

600/3 is 200 which means 1/3 of it is rebated

Answer: x=3 ; y=13

Step-by-step explanation:

1. isolate y from equation to substitute into the second equation

y= 16-x ---> (16-x) = 3x+4

2. move to one side and solve for x

4x=12 --> x=3

3. plug in x value to solve for y

3+y=16 or 3(3)+4

y=13

Answer:

Solve the equation for  x  by finding  a ,  b , and  c

of the quadratic then applying the quadratic formula.

x = − 2  Double roots

Answer:21-3+8=26

-14+31-6=11

Step-by-step explanation:

Answer:

You have 24

Step-by-step explanation:

Zack should use a line with one arrowhead to map an abandoned line of reasoning.

A line with one arrowhead is commonly used in diagrams to represent the direction of a process or flow of information. In the case of mapping an abandoned line of reasoning, the line can be used to show the original train of thought that was pursued but later abandoned.

The arrowhead can indicate the point at which the reasoning was abandoned or diverted. Therefore, using a line with one arrowhead would be the most appropriate shape for Zack to use. The other shapes listed (orange oval, green rectangle, red) do not provide a clear representation of a line of reasoning and would not be suitable for this purpose.

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The equation of the line with slope 4 that goes through the point (-3,0) is y = 4x + 12.

The equation of the line passing through the point (-3,0) with a slope of 4 can be found using the point-slope form of a line's equation:

y - y1 = m(x - x1)

where the provided point is (x1, y1), and m is the slope.

When we change the values, we obtain:

y - 0 = 4(x - (-3))

Making the right side simpler:

y = 4x + 12

Hence, y = 4x + 12 is the equation of the line with slope 4 passing through the point (-3,0).

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Answer:

Quotient= 70

Remainder=14

Step-by-step explanation:

Do you need explanation?

Answer:

23 goes into 1,624 70 times

The answer you are looking for is D. -5.

-5 is the answer because it's absolute value if positive 5, which has a higher value than the numbers in the answer choices.

If this helps, please mark brainliest!

Have a wonderful rest of your day!

\(\huge{ \mathfrak{  \underline{ Answer }\:  \:  ✓ }}\)

The correct option is D.)

The number having the greatest absolute value is 5

Absolute values of given numbers :

and 5 is greatest here .

_____________________________

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Answer:

D. -1.44 and 2.44

Step-by-step explanation:

\(f(x) = 2 {ax}^{2} + (3 - b)x + 7\)

is equal to:

\(g(x) = (a - 1) {x}^{2} + 2bx + 7\)

•◇•◇○◇•◇•

➡️ \( - 2 {x}^{2} + 2x + 7 = 0\)

➡️ \(Δ = {b}^{2} - 4ac = 4 - 4 \times 7 \times ( - 2) = 60 = \sqrt{Δ} = 7.746\)

➡️ \(x = \frac{ - b± \sqrt{Δ} }{2a} = \frac{ - 2± 7.746}{ - Δ} \)

➡️ \( x_{1} = \frac{ - 2 + 7.746}{ - 4} = - 1.44\)

➡️ \( x_{2} = \frac{ - 2 - 7.746}{ - 4} = 2.44\)

The forecast for the next period using the following weights: 0.3, 2, 0.5 is Option d. 421.

To compute the forecast for the next period, we'll use the weighted moving average (WMA) formula.WMA formula:

WMA = W1Yt-1 + W2Yt-2 + ... + WnYt-n

Where, WMA is the weighted moving average

W1, W2, ..., Wn are the weights (must sum to 1)

Yt-n is the demand in the n-th period before the current period

As we know Month 1 – 381, Month 2-366, and Month 3 - 348.

Weights: 0.3, 2, 0.5

We'll compute the forecast for the next period (month 4) using the data:

WMA = W1Yt-1 + W2Yt-2 + W3Yt-3WMA

= 0.3(381) + 2(366) + 0.5(348)WMA

= 114.3 + 732 + 174WMA

= 1020.3

Therefore, the forecast for the next period is 1020.3, which rounds to 421. Hence, option d is correct.

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