Find the area of the quadrilateral with the given coordinates A(-2, 4),

B(2, 1), C(-1, -3), D(-5, 0)

Answer:

5(1+x)

Step-by-step explanation:

Hello and Good Morning/Afternoon:

Let's take this problem step-by-step:

If David buys the shirt online:

 \(\hookrightarrow \text{he gets a 25 percent discount of the list price}\)

    \(\hookrightarrow \text{he pays for 75 percent of list price}\)

If David buys the shirt in-store:

\(\hookrightarrow \text {he pays for 80 percent of the list price}\)

   \(\hookrightarrow \text{he gets a 5 percent discount of the store's price}\)        

         \(\hookrightarrow \text{he pays 95 percent of the store price}\)

             \(\hookrightarrow \text{he pays '0.95 * 80' = 76 percent of the price}\)

Thus David saves 1% if he buys the shirt online as compared to if he buys the shirt in-store.

Answer: (G) or 1%

Hope that helps!

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Answer:

B

Step-by-step explanation:

First calculate the slope. \(\frac{y2-y1}{x2-x1}\). In this case, the slope is \(\frac{4}{5}\).

If you look at all of the answer choices, they are in slope - intercept form. This makes it easier! All you have to do is find an equation with the slope 4/5 that uses the point (4,1) or (9,5).

The standard slope intercept form for a point (a,b) is

y-b = m(x-a).

Remember that two negatives equal a positive.

Substitute in the slope for m and (4,1) or (9,5) for the point (a,b).

Answer:

y=4/5x-3 - (-5, -7)

Step-by-step explanation:

So to solve this, lets just plug in each value for x, and see if the y value we get is equal to one of our answers.

So we have (-10, 5)

Well plug in -10 for 4/5x we get:

-40/5=-8

Next we take that value and solve:

y=-8-3

y=-11

The answer for this was 5, not -11.

Ill skip a few steps:

(10, -11):

Plug in 10 we get:

y=8-3 which is y=5. This is not right, for it needed to be -11.

Next we have (5, -1)

This gets us y=4-3 this is y=1 which is not -1. So thats not right.

Finally we have (-5, -7):

This gets us y=-4-3 this is y=-7. What was our y value? -7!

So the answer is (-5, -7)

I hope this helps! :)

Answer:

Step-by-step explanation:

Experimental probability is the probability of what actually happens in the given experiment.

We know that a fair six-sided cube is rolled 60 times and the outcome 2 has occurred 15 times out of 60 times.

Therefore, the experiment probability in the given experiment is:

Experimental probability of rolling 2  

\(\frac{15}{60}=\frac{1}{4}\)

Now, the theoretical probability is the probability of what is expected from the random experiment. We know that a cube has 6 sides and the theoretical probability of getting 2 is given below:

Theoretical probability of rolling a 2    

\(\frac{1}{6}\)

Therefore, the answer is:

The experimental probability of rolling a 2 is \(\frac{1}{4}\) and the theoretical probability of rolling a 2 is \(\frac{1}{6}\).

Answer:

The experimental probability of rolling a 2 is 1/4 and the theoretical probability of rolling a 2 is 1/6.

Step-by-step explanation:

the probability that none of the four non-overlapping one-half hour intervals contains any call is approximately 0.00000614.

(a) The probability of having more than three calls in one-half hour can be calculated using the exponential distribution. Since the mean of the exponential distribution is 10 minutes, the rate parameter (λ) can be calculated as λ = 1/mean = 1/10 = 0.1 calls per minute.

To find the probability of having more than three calls in one-half hour (30 minutes), we need to calculate the cumulative distribution function (CDF) of the exponential distribution up to three calls and subtract it from 1.

P(X > 3) = 1 - P(X ≤ 3)

        = 1 - (1 - e^(-λt))   [where t is the time duration in minutes]

        = 1 - (1 - e^(-0.1 * 30))

        = 1 - (1 - e^(-3))

        = 1 - (1 - 0.049787)

        = 0.049787

Therefore, the probability of having more than three calls in one-half hour is approximately 0.0498 or 4.98%.

(b) The probability of having no calls within one-half hour can be calculated using the exponential distribution as well.

P(X = 0) = e^(-λt)   [where t is the time duration in minutes]

        = e^(-0.1 * 30)

        = e^(-3)

        ≈ 0.049787

Therefore, the probability of having no calls within one-half hour is approximately 0.0498 or 4.98%.

(c) To determine x such that the probability of having no calls within x hours is 0.01, we need to solve the exponential distribution equation.

0.01 = e^(-0.1 * x * 60)

Taking the natural logarithm of both sides, we get:

ln(0.01) = -0.1 * x * 60

x = ln(0.01) / (-0.1 * 60)

  ≈ 230.26

Therefore, x is approximately 230.26 hours.

(d) The probability of having no calls within a two-hour interval can be calculated using the exponential distribution.

P(X = 0) = e^(-λt)   [where t is the time duration in minutes]

        = e^(-0.1 * 120)

        = e^(-12)

        ≈ 6.14e-06

Therefore, the probability of having no calls within a two-hour interval is approximately 6.14e-06 or 0.00000614.

(e) If four non-overlapping one-half hour intervals are selected, the probability that none of these intervals contains any call can be calculated by multiplying the individual probabilities of no calls in each interval.

P(no calls in one interval) = e^(-0.1 * 30)

                          ≈ 0.0498

P(no calls in all four intervals) = (0.0498)^4

                               ≈ 6.14e-06

Therefore, the probability that none of the four intervals contains any call is approximately 6.14e-06 or 0.00000614.

Conclusion: In this scenario with exponentially distributed call intervals, we calculated probabilities for different cases. The probability of having more than three calls in one-half hour is approximately 4.98%, while the probability of having no calls within one-half hour is also approximately 4.98%. We found that x is approximately 230.26 hours for a 0.01 probability of having no calls within x hours. The probability of having no calls within a two-hour interval is approximately 0

.00000614. Lastly, the probability that none of the four non-overlapping one-half hour intervals contains any call is approximately 0.00000614.

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Answer:

y = 7

QR = 21

Step-by-step explanation:

"bisects" means cuts in half, or that Q is exactly in the middle of PR.

PQ + QR = PR

Well, if PR is 42, then QR is 21 (that's half)

PQ = QR because the two halves are the same.

3y = 21

y = 7

The penny will fall from distance of 232 feet during the 8th second only, as it falls 960 feet in the first 8 seconds, but 728 feet in the first 8 seconds.

The distance the penny falls each second is increasing by 32 feet (16 feet + 32 feet = 48 feet, 48 feet + 32 feet = 80 feet, and so on). Therefore, during the 8th second, the distance it will fall is:

16 + 48 + 80 + ... + (8 - 1) * 32 feet

Using the formula for the sum of an arithmetic sequence, we get:

(8 / 2) * (16 + (8 - 1) * 32) feet

= 4 * (16 + 7 * 32) feet

= 4 * 240 feet

= 960 feet

So the penny will fall 960 feet during the first 8 seconds. However, we need to subtract the distance it fell during the first 7 seconds to find the distance it fell during the 8th second only. The total distance it fell during the first 7 seconds is:

16 + 48 + 80 + ... + (7 - 1) * 32 feet

= (7 / 2) * (16 + (7 - 1) * 32) feet

= 3.5 * (16 + 6 * 32) feet

= 3.5 * 208 feet

= 728 feet

Therefore, the penny will fall 960 - 728 = 232 feet during the 8th second only.

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Therefore, the measure of the central angle whose radii define the given arc is approximately 83.077 degrees.

The length of an arc on a circle is given by the formula:

Arc Length = (Central Angle / 360°) * Circumference

In this case, we know the arc length is 6π centimeters, and the radius of the circle is 13 centimeters. The circumference of the circle can be calculated using the formula:

Circumference = 2π * Radius

Substituting the radius value, we get:

Circumference = 2π * 13

= 26π

Now we can use the arc length formula to find the central angle:

6π = (Central Angle / 360°) * 26π

Dividing both sides of the equation by 26π:

6π / 26π = Central Angle / 360°

Simplifying:

6 / 26 = Central Angle / 360°

Cross-multiplying:

360° * 6 = 26 * Central Angle

2160° = 26 * Central Angle

Dividing both sides by 26:

2160° / 26 = Central Angle

Approximately:

Central Angle ≈ 83.077°

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The significance level, account for multiple testing, and recognize the limitations and context when interpreting p-values.

The p-value is a crucial concept in statistical hypothesis testing. It refers to the probability of observing a test statistic as extreme as or more extreme than the one observed, given that the null hypothesis is true.

In other words, it is the probability of obtaining the observed result by chance, assuming that there is no true effect.
There are several key guidelines that researchers need to keep in mind when interpreting p-values.

This threshold should not be taken as a hard-and-fast rule and other factors such as the study design sample size and effect size should also be considered.
Secondly, the p-value alone cannot determine the validity or importance of a research finding.

It is just one piece of evidence that needs to be considered along with other factors, such as the magnitude of the effect, the precision of the estimates, the plausibility of alternative explanations, and the practical implications of the findings.
Thirdly, the p-value can be influenced by various factors, such as the choice of statistical test, the assumptions made about the data, and the presence of outliers or influential observations.

Therefore,

Researchers should always report the assumptions and limitations of their analyses and consider conducting sensitivity analyses to test the robustness of their results.
In summary,

The key guidelines for interpreting p-values include understanding their meaning and limitations, considering other factors in addition to p-values, and being aware of the factors that can influence their interpretation.

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Roger has enough stainless steel pipe to replace the chimney liner, with a slight surplus remaining.

To determine if Roger has enough stainless steel pipe for the chimney liner, we need to convert the given measurements to a consistent unit of measurement. Since the length of the liner required is given in feet, we need to convert the 400 inches of stainless steel pipe to feet.

There are 12 inches in a foot, so 400 inches is equal to 400/12 = 33.33 feet (approximately).

Comparing this converted length of the stainless steel pipe (33.33 feet) with the length of the liner required (33 feet), we can see that Roger does indeed have enough pipe. In fact, he has slightly more than required.

Since the length of the liner required is 33 feet and Roger has 33.33 feet of stainless steel pipe available, there is a surplus of approximately 0.33 feet (about 4 inches) of pipe. This additional length is more than enough to cover any potential measurement errors or adjustments needed during the installation process.

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Answer:

Randomly assigning treatments to the farms is the best way to ensure that the results of the experiment are valid, unbiased, and accurate.

Random assignment of treatments is the best way to ensure that the results of the experiment are valid and not biased. Random assignment of treatments would ensure that the results are not affected by factors such as soil type, climate, and other environmental conditions. This is because random assignment of treatments would ensure that the farms that receive the insecticide treatment are not systematically different from those that do not receive the treatment. This is important in order to gain accurate results from the experiment.

Random assignment of treatments is accomplished using the following formula:

Treatment Assignment = (Number of Farms) x (Random Number between 0 and 1)

By randomly assigning treatments to the farms, we can be sure that the results are not skewed by external factors. This will allow us to better determine the effectiveness of different insecticides in controlling pests and their impact on the productivity of tomato plants.

Randomly assigning treatments to the farms is the best way to ensure that the results of the experiment are valid, unbiased, and accurate.

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Step-by-step explanation:

Interior angle + Exterior angle = 180°.

Size of Interior angle = 180° - 360°/n.

Question 32:

Exterior angle = 72°

Interior angle = 180° - 72° = 108°.

Therefore 180° - 360°/n = 108°, n = 5 => 5 sides.

Question 33:

Exterior angle = 36°

Interior angle = 180° - 36° = 144°.

Therefore 180° - 360°/n = 144°, n = 10 => 10 sides.

Answer: 32.) 108°. 5 sides

33.) 144°. 10 sides

Step-by-step explanation:

To find an interior angle subtract the given exterior angle from 180.

180 - 72 = 108

180 - 36 = 144

To find the number of sides of a regular polygon, divide 360 by the exterior angle.

360/72 = 5

360/36 = 10

The value of n using the concept of similar triangles is: 24

Similar triangles are defined as triangles that have the same shape, but their sizes may vary. Therefore, if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.

Since Triangle XYZ is similar to triangle PQR, then we can say that:

XY is similar to PQ

YZ is similar to QR

XZ is similar to PR

Thus:

35/28 = 30/n

cross multiply to get:

n = (30 * 28)/35

n = 24

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The equation of the plane tangent to the surface z = 3x^2 - 3y^3 at the point (2, 1, 15) is 12x - 9y + z - 30 = 0.

To find the equation of the plane tangent to the surface z = 3x^2 - 3y^3 at the point (2, 1, 15), we can use the concept of partial derivatives and the equation of a plane.

1. Compute the partial derivatives of the surface equation with respect to x and y. Taking the partial derivative with respect to x treats y as a constant, and vice versa. For the given equation, we have:

  ∂z/∂x = 6x

  ∂z/∂y = -9y^2

2. Substitute the coordinates of the point (2, 1, 15) into the partial derivatives:

  ∂z/∂x = 6(2) = 12

  ∂z/∂y = -9(1)^2 = -9

3. The normal vector of the plane is obtained by taking the coefficients of the partial derivatives:

  Normal vector = (12, -9, 1)

4. Now, we have the normal vector and a point on the plane (2, 1, 15). Using the equation of a plane, which is of the form Ax + By + Cz = D, we can substitute the values:

  12(x - 2) - 9(y - 1) + (z - 15) = 0

  12x - 24 - 9y + 9 + z - 15 = 0

  12x - 9y + z - 30 = 0

Therefore, the equation of the plane tangent to the surface z = 3x^2 - 3y^3 at the point (2, 1, 15) is 12x - 9y + z - 30 = 0.

The equation represents a plane that is tangent to the given surface at the specified point. The coefficients in the equation correspond to the components of the normal vector, and the constant term is determined by evaluating the equation at the given point.

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Answer:

75%

Step-by-step explanation:

Put the number of shots she made as to the numerator and the shots there were as the denominator: 36/48

We must reduce this fraction to the lowest terms.

36/48 ÷ 12/12 = 3/4

3/4 as a percent is the same as 75/100 or 75%

Answer: 75%

Answer:

She had missed 75%

Step-by-step explanation:

36/48 shots is equal to 75/100

which equals 75%

The statement that is not an indication of potential multicollinearity problems is  "A sign on a regression slope coefficient is negative when the sign on the correlation coefficient was positive"

The multicollinearity is defined as the theory that several independent variables in the given model is correlated. The variables that does not affected by any other variable is called independent variable

But here the independent variables will be correlated. in option b  when the sign on the correlation coefficient was positive a sign on a regression slope coefficient is negative. So the independent variables in the given statements are not correlated

In other options the independent variables are correlated

Therefore, the statement that does not shows an of potential multicollinearity problems is option B

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Answer:

Mean Absolute Deviation (MAD): 1.3125

Mean: 2.5625

Step-by-step explanation:

.

According to the perimeter of rectangle, the amount of area that the fencing does he need to go around the field is 11 3/5 miles

The general formula to calculate the perimeter of the rectangle is written as,

=> P = 2(l + b)

where l refers the length of the rectangle and b refers the width of the rectangle.

While we looking into the given question, we have identified that the following values are given in the question,

=> Length of field = 2 3/10 miles

=> Width of field = 3 1/2 miles

Now, we have to convert the mixed fraction into normal fraction, then we get,

=> Length of field = 23/10 miles

=> Width of field = 7/2 miles

Then the Perimeter is calculated as,

=> 2 (23/10 + 7/2)

=> 2 ([23 + 35)/10)

=> 2 x (58/10)

=> 2 x 5.8

=> 11.6 or 11 3/5 miles

Therefore, the length of fencing used to enclose the rectangular field is 11 3/5 miles

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The inequality that corresponds to the given graph is option C. 5x - y 1greater than or equal to 1

To determine which of the inequalities corresponds to the given graph, consider the slope-intercept form of a line's equation, which is y = mx + b, where m is the slope and b is the y-intercept.

We can see from the graph that the line passes through the points (1, 4) and (2, 9). We can use the following formula to calculate the slope:

m = (y2 - y1) / (x2 - x1) (x2 - x1)

m = (9 - 4) / (2 - 1)\sm = 5

As a result, the slope of the line is 5.

We can use one of the points and the slope to find the y-intercept:

y = mx + b 4 + b b = 5(1) + b b = -1

As a result, the y-intercept is -1.

As a result, the line's equation is y = 5x - 1.

A solid line runs through the points (1, 4) and (2, 9), with shading below the line. This implies that the inequality is y 5x - 1.

By multiplying both sides by -1 and rearranging, we can rewrite this inequality in the standard form axe + by c:

-5x + (-1y) ≥ 1

This corresponds to option C, 5x - y 1.

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The full question is: Which of the following inequalities corresponds to the graph? Inequality graph with a solid line through the points (1, 4) and (2, 9) and shading below the line.

A. greater than or equal to 5x + y

B. 5x + y must be less than or equal to 1.

C. 5x - y greater than or equal to 1

Answer:

70.05 mph

Step-by-step explanation:

A cheetah ran 300 feet in 2.92 seconds. What is the cheetah's average speed in miles per hour

--------------------------------------

(300 ft/2.92 sec)(1 mi/ 5280 ft)(3600 sec/1 hour)

= {300*1*3600 miles)/(2.92*5280*1 hour)

= 91080000 miles/15417.6 hours

= 70.05 mph

The equation of the line passing through the points (2, 11) and (-8, -18) is y = 29 / 10 x + 26 / 5

The equation of a line can be express as follows:

y = mx + b

where

Therefore, the equation of the line passes through the points (2, 11) and (-8, -18).

Hence,

m = -18 - 11 / -8 - 2

m = - 29 / - 10

m = 29 / 10

Therefore, let's find the y-intercept using (2, 11)

The equation is as follows:

11 = 29 / 10(2) + b

11 = 58 / 10 + b

b = 11 - 58 / 10

b = 110 - 58 / 10

b = 52 / 10 = 26 / 5

Therefore,

y = 29 / 10 x + 26 / 5

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Answer:

b) is correct 120π square units

Step-by-step explanation:

The sector that is not shaded froms a 300 degree angle. The area of that sector and its angle are proportional with the area of the entire circle and its angle, which is 360 degrees.

We start by computing the area of the circle. Since the radius is 12 units, then the area of the circle is 12² * π = 144π square units. Therefore, the area of the non shaded area is

144π * 300/360 = 120π square units

as option b) suggests.

Answer:

C. 120pi units^2

Step-by-step explanation:

Just took the Unit Test on Edg (2021)!!

The polynomial Identities and an example of a proof of an identity have been explained below.

Polynomial identities are defined as equations that are always true, regardless of the variable values. These polynomial identities are used while factorizing the polynomial or expanding the polynomial. These polynomial identities are;

(a + b)² = a² + b² + 2ab

(a - b)² = a² + b² - 2ab

(a + b)(a - b) = a² - b²

(x + a)(x + b) = x² + x(a + b)+ ab

Let us prove the polynomial identity (a + b)² = a² + b² + 2ab.

Now, (a + b)² is simply the product of (a + b) and (a + b).

That is; (a + b)² = (a + b) × (a + b)

This can simply be imagined to be a square whose side are (a + b) with its' area equal to (a + b)²

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If there are 22 juniors and 18 seniors, of the juniors, 12 are females, of the seniors, 11 are males, then the probability that a randomly selected student from the class is a male or a junior is 0.611 or 61.1%.

To find the probability that a randomly selected student from the class is a male or a junior, we need to add the probability of selecting a male student from the seniors and the probability of selecting a junior student, regardless of gender.

The probability of selecting a male student from the seniors is 11/18, as given in the problem.

The probability of selecting a junior student, regardless of gender, is (22/40) or (11/20), as there are 22 juniors out of a total of 40 students in the class.

To find the probability of selecting either a male student from the seniors or a junior student, we add these two probabilities:

11/18 + 11/20 = 0.611 or 61.1%

Therefore, the probability that a randomly selected student from the class is a male or a junior is 0.611 or 61.1%.

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