A polynomial function g(x) has a positive leading coefficient. Certain values of g(x) are given in the following table.


x –4 –1 0 1 5 8 12
g(x) 0 3 1 2 0 –3 0



If every x-intercept of g(x) is shown in the table and each has a multiplicity of one, what is the end behavior of g(x)?

a
As x→–∞, g(x)→–∞ and as x→∞, g(x)→–∞.

b
As x→–∞, g(x)→ –∞ and as x→∞, g(x)→∞.

c
As x→–∞, g(x)→∞ and as x→∞, g(x)→–∞.

d
As x→–∞, g(x)→∞ and as x→∞, g(x)→∞.

The sides of the quadrilateral arranged from longest to shortest are CD, AB, DA, and BC.

We have,

To arrange the length of the sides of the quadrilateral from longest to shortest, we need to calculate the length of each side of the quadrilateral using the distance formula:

Distance Formula:

If (x1, y1) and (x2, y2) are two points in a plane, then the distance between them is given by:

d = √((x2 - x1)² + (y2 - y1)²)

Using the distance formula, we can calculate the length of each side of the quadrilateral as follows:

AB = √((4 - (-5))² + (5 - 5)²) = 9

BC = √((2 - 4)² + (0 - 5)²) = √(29)

CD = √((-5 - 2)² + (-2 - 0)²) = √(74)

DA = √((-5 - (-5))² + (5 - (-2))²) = 7

Therefore,

The sides of the quadrilateral arranged from longest to shortest are CD, AB, DA, and BC.

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Answer:

k = 7

Step-by-step explanation:

Applying,

S = (y₂-y₁)/(x₂-x₁)................ Equation 1

Where S = slope of the line.

From the question,

Given: y₂ = 10, y₁ = 4, x₂ = k, x₁ = 1, S = 1

Substitute these values into equation 1

1 = (10-4)/(k-1)

crossmultiplying,

(k-1) = (10-4)

k-1 = 6

k = 6+1

k = 7

Answer:

Mike would have -438.17, poor mike lol

Answer: x = 3; y = -2

Step-by-step explanation:

Simultaneous Equations:
3^(2x) x 3^(3y) = 3^0
2x + 3y = 0

2^(2x) x 2^(-0.5y) = 2^7
2x - 0.5y = 7

2x = -3y

-3y - 0.5 y = 7

y = -2

x = 3

Answer:

x=3 y=-2

Step-by-step explanation:

its at the bottom of the page ‍♂️‍♂️

The distance from lake b to camp is 310 km and the direction of lake b to camp is 57° S of W.

Distance is a numerical value. The length between the two points is measured by distance. The face or position of an object or person can be said by direction.

There are four cardinal directions which are the main four compass directions. The four directions are North, East, West and South. North-East, North-West, South-East and South-West also come under directions.

As per the question,

With a scale of unit 1, the vector from the base camp to the lake to the vector connecting lakes a and b is graphically represented.

Therefore, 310 km is the distance from the lake b to base camp and 57.0° south of west is the direction of the plane.

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Answer: Distance can't be negative, so it must be positive. That's the first thing you need to know. To find the distance, you take the difference between the two points.

1 - (-3) = 4

(second point on the number line) - (first point on the number line)

The null hypothesis for the alternative hypothesis "the percentage of internet users who use the internet for shopping is greater than 0.40" can be expressed as:
H0: p ≤ 0.40

Here, H0 represents the null hypothesis and p represents the proportion of internet users who use the internet for shopping.

The null hypothesis states that the percentage of internet users who use the internet for shopping is less than or equal to 40%.

In hypothesis testing, we collect data and analyze it to determine whether we can reject the null hypothesis or not.

If the data provides strong evidence against the null hypothesis, we reject it and accept an alternative hypothesis that suggests there is a significant relationship or difference.

However, if the data is not strong enough to reject the null hypothesis, we fail to reject it, but we cannot conclude that the null hypothesis is true.

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Answer:

If the cheetah sprinted at 70 mph, then the cheetah would travel 70 miles every hour.

Step-by-step explanation:

Numerical integration is a numerical analysis technique for calculating the approximate numerical value of a definite integral.

In general, integrals can be either indefinite integrals or definite integrals. A definite integral is an integral with limits of integration, while an indefinite integral is an integral without limits of integration.A numerical integration formula is an algorithm that calculates the approximate numerical value of a definite integral. Numerical integration is based on the approximation of the integrand using a numerical quadrature formula.

The numerical quadrature formula is used to approximate the value of the integral by breaking it up into small parts and summing the parts together.Equations for the calculation of integration by trapezoidal rule (1/2)h[f(x0)+2(f(x1)+...+f(xn-1))+f(xn)] where h= Δx [the space between the values], and x0, x1, x2...xn are the coordinates of the abscissas of the nodes. The basic principle is to replace the integral by a simple sum that can be calculated numerically. This is done by partitioning the interval of integration into subintervals, approximating the integrand on each subinterval by an interpolating polynomial, and then evaluating the integral of each polynomial.

Based on the given table of unequally spaced data, we are to calculate the approximate numerical value of the definite integral. To do this, we will use the integration formula as given by the trapezoidal rule which is 1/2 h[f(x0)+2(f(x1)+...+f(xn-1))+f(xn)] where h = Δx [the space between the values], and x0, x1, x2...xn are the coordinates of the abscissas of the nodes.  The table can be represented as follows:x            0.1 0.3 0.5 0.7 0.95 1.2f(x)      1 0.9048 0.7408 0.6065 0.4966 0.3867 0.3012Let Δx = 0.1 + 0.2 + 0.2 + 0.25 + 0.25 = 1, and n = 5Substituting into the integration formula, we have; 1/2[1(1)+2(0.9048+0.7408+0.6065+0.4966)+0.3867]1/2[1 + 2.3037+ 1.5136+ 1.1932 + 0.3867]1/2[6.3972]= 3.1986 (to 4 decimal places)

Therefore, the approximate numerical value of the definite integral is 3.1986.

The approximate numerical value of a definite integral can be calculated using numerical integration formulas such as the trapezoidal rule. The trapezoidal rule can be used to calculate the approximate numerical value of a definite integral of an unequally spaced table of data.

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A graph that matches the answer choice is shown in the image attached below.

In Mathematics, a piecewise-defined function can be defined as a type of function that is defined by two (2) or more mathematical expressions over a specific domain.

Generally speaking, the domain of any piecewise-defined function simply refers to the union of all of its sub-domains. By critically observing the graph of the given piecewise-defined function, we can reasonably infer and logically deduce that it is constant over the interval x ≥ 2 and increasing over the interval x < 2.

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From the given information, cholesterol level X follows the N(222, 37) distribution.

The probability of having borderline high cholesterol (between 200 and 240 mg/dl) can be calculated by using the z-score formula as follows:

z = (x - μ) / σ

For lower limit x1 = 200, z1 = (200 - 222) / 37 = -0.595

For upper limit x2 = 240, z2 = (240 - 222) / 37 = 0.486

The probability of having borderline high cholesterol (between 200 and 240 mg/dl) can be computed as

P(200 ≤ X ≤ 240) = P(z1 ≤ Z ≤ z2) = P(Z ≤ 0.486) - P(Z ≤ -0.595) = 0.683 - 0.277 = 0.406

In this population, 90% of men have a cholesterol level that is at most X90.The z-score corresponding to a cholesterol level of X90 can be calculated as follows:

z = (x - μ) / σ

Since the z-score separates the area under the normal distribution curve into two parts, that is, from the left of the z-value to the mean, and from the right of the z-value to the mean.

So, for a left-tailed test, we find the z-score such that the area from the left of the z-score to the mean is 0.90.

By using the standard normal distribution table,

we get the z-score as 1.28.z = (x - μ) / σ1.28 = (X90 - 222) / 37X90 = 222 + 1.28 × 37 = 274.36 ≈ 274

The cholesterol level of 90% of men in this population is at most 274 mg/dl.

The distributions that we can consider to be approximately normal are the sampling distribution of mean BMI for random samples of 60 adults and the sampling distribution of mean BMI for random samples of 9 adults.

The reason for considering these distributions to be approximately normal is that according to the Central Limit Theorem, if a sample consists of a large number of observations, that is, at least 30, then its sample mean distribution is approximately normal.

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Answer:

7/12

Step-by-step explanation:

3*4=12. 4/12+3/12=7/12.

Answer:

5/12

Step-by-step explanation:

you find the common factor of 12, divide 12 by the denominator, multiply the numerator by that, add the new numerators, put it on the denominator of 12, subtract it from 12/12

Answer:

I'll set it up and you can finish

Step-by-step explanation:

the axis of symmetry goes through th x-axis at x=4.

This point will be equidistant from both points that are at the x-intercepts. The distance from (-6,0) to (4,0) is

4 - (-6) = 10.

so I now you can find ? which will be in the first quadrant of the graph

Check the picture below.

\(\stackrel{\textit{left and right}}{2(8)(21)}~~ + ~~\stackrel{\textit{front and back}}{2(11)(21)}~~ + ~~\stackrel{\textit{top and bottom}}{2(11)(8)}\implies 974~in^2\)

Answer:I need help too for that :(

Step-by-step explanation:

If the level of significance is decreased, the interval for the population proportion becomes narrower.

The level of significance, denoted by α, is the probability of rejecting the null hypothesis when it is true. When the level of significance is decreased, it means that we are requiring stronger evidence to reject the null hypothesis. This leads to a narrower confidence interval.

In a confidence interval for a population proportion, the range between the lower and upper bounds represents the range of plausible values for the true population proportion. As the level of significance is decreased, the critical value associated with it becomes larger, resulting in a smaller margin of error and a narrower confidence interval.

Therefore, as the level of significance decreases, the interval for the population proportion becomes narrower, providing a more precise estimate of the true population proportion.

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The volume of the pyramid with a square base is 135.5 cubic m if the base area is 16 cubic m and the height is 25.4 m.

In geometry, it is defined as the shape having a square base with equal sides length and all the vertex of the square's joints at the top, which is perpendicular to the centre of the square.

We know the volume of the square pyramid V;

V = Bh/2

B is the base area, B = 16 square m

h is the height of the pyramid, h = 25.4 m

V = (16×25.4)/3

V = 135.46 ≈ 135.5 cubic m

Thus, the volume of the pyramid with a square base is 135.5 cubic m if the base area is 16 cubic m and the height is 25.4 m.

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Answer:

Substitute 3x - 5 for y in the second equation.

Step-by-step explanation:

Generally, to solve the system of linear equations of x and y, the first step would be trying to eliminate x (or y).

Then turn the system into the equation of only y (or x).

Next, try to solve for y (or x).

Then substitute the solved y (or x) into the original system to work out x (or y).

**********

3 options (1 addition, 2 subtractions) do not eliminate x or y (x and y still exist after manipulation).

=> Remaining option relating substitution would be a reasonable choice.

Given the dimensions of the triangle, QPR is as follows:

angle QPR =90^circle

Side QP = 8 sqrt3 units

Side PR = 8 units

To find, side QR =? units

Please refer to the attached figure for the representation of the given dimensions.

The base is side QP,

Perpendicular is side PR and

Hypotenuse is side QR.

In a right-angled triangle, the Pythagorean theorem holds i.e.

According to Pythagoras theorem:

text {Hypotenuse}^ {2} = text {Base}^ {2} + text {Perpendicular}^ {2}

=            QR^ {2} = QP^ {2} + PR^ {2}

Putting the values of QP and PR:

=           QR^ {2} = (8sqrt3) ^ {2} + 82} = QR^ {2} = 64 times 3+ 64 QR^ {2}

= 64 times 4 QR = 8 times 2 QR = 16 units.

So, the value of the length of the side QR is 16 units.  

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Answer:

I got d b and c  I am not  sure pls don't use my answers if you don't want to and don't mark brainiest again I just wanted to try to help and I couldn't fully understand if I'm wrong I apologize and god bless you

Answer:

2

Step-by-step explanation

Answer:

Answer:

$90

Step-by-step explanation:

27/.3

Answer:

2/1

is what my brother said

Step-by-step explanation:

Answer:

0.083

Step-by-step explanation:

Answer:

the value of this increase in percentage indices is 27.77%

Step-by-step explanation:

The computation of the  value of this increase in percentage indices is shown below:

Given that

The population has increase from 82,350 to 105,200

So, the increase in percentage would be

= (105,200 - 82,350) ÷ (82,350)

= 22,850 ÷ 82,350

= 27.77%

Hence, the value of this increase in percentage indices is 27.77%

Answer:

Did you mean the diagonal are equal in length and bisect each other?

In that case, it is parallelogram.

Hope this helps!

:)

Answer:

Rectangles

Step-by-step explanation:

Diagonals bisect each other for all parallelograms.

But they are equal in a few.

Note: square is also a rectangle

Answer:

0.000450 m3

Step-by-step explanation:

The probability is approximately 0.9167 or 91.67%.

To find the probability that the sum of two dice numbers does not exceed 10, we need to determine the favorable outcomes (sums less than or equal to 10) and the total possible outcomes when rolling two dice.

There are 36 possible outcomes when rolling two dice because each die has six faces (1, 2, 3, 4, 5, and 6), and the total number of outcomes is obtained by multiplying the number of outcomes for each die (6 * 6 = 36).

Now let's determine the favorable outcomes (sums less than or equal to 10):

When the sum is 2: There is only one combination (1 + 1).

When the sum is 3: There are two combinations (1 + 2 and 2 + 1).

When the sum is 4: There are three combinations (1 + 3, 2 + 2, and 3 + 1).

When the sum is 5: There are four combinations (1 + 4, 2 + 3, 3 + 2, and 4 + 1).

When the sum is 6: There are five combinations (1 + 5, 2 + 4, 3 + 3, 4 + 2, and 5 + 1).

When the sum is 7: There are six combinations (1 + 6, 2 + 5, 3 + 4, 4 + 3, 5 + 2, and 6 + 1).

When the sum is 8: There are five combinations (2 + 6, 3 + 5, 4 + 4, 5 + 3, and 6 + 2).

When the sum is 9: There are four combinations (3 + 6, 4 + 5, 5 + 4, and 6 + 3).

When the sum is 10: There are three combinations (4 + 6, 5 + 5, and 6 + 4).

Adding up the favorable outcomes, we get: 1 + 2 + 3 + 4 + 5 + 6 + 5 + 4 + 3 = 33.

Therefore, the probability that the sum of the two dice numbers does not exceed 10 is given by:

Probability = Favorable outcomes / Total outcomes = 33 / 36 = 11/12 ≈ 0.9167.

So, the probability is approximately 0.9167 or 91.67%.

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Answer:

Yes and the equation is 2y=-x-7

Step-by-step explanation:

Yes the relation is linear, the slope of the equation will be - 3/6=-1/2, the equation of line will be y=(-1/2)x-3.5. 2y=-x-7