In the diagram below, FG is parallel to CD. If the length of CD is the same as the length of FE, CE = 26, and FG = 11, find the length of FE. Figures are not necessarily drawn to scale. State your answer in simplest radical form, if necessary.

The value of x that makes the line containing (1,2) and (5,3) perpendicular to the line containing (x,4) and (3,0) is x = 2.

To determine the value of x such that the line containing (1,2) and (5,3) is perpendicular to the line containing (x,4) and (3,0), we need to find the slope of both lines and apply the concept of perpendicular lines.

The slope of a line can be found using the formula:

slope = (change in y) / (change in x)

For the line containing (1,2) and (5,3), the slope is:

slope1 = (3 - 2) / (5 - 1) = 1 / 4

To find the slope of the line containing (x,4) and (3,0), we use the same formula:

slope2 = (0 - 4) / (3 - x) = -4 / (3 - x)

Perpendicular lines have slopes that are negative reciprocals of each other. In other words, if the slope of one line is m, then the slope of a line perpendicular to it is -1/m.

So, we can set up the equation:

-1 / (1/4) = -4 / (3 - x)

Simplifying this equation:

-4 = -4 / (3 - x)

To remove the fraction, we can multiply both sides by (3 - x):

-4(3 - x) = -4

Expanding and simplifying:

-12 + 4x = -4

Adding 12 to both sides:

4x = 8

Dividing both sides by 4:

x = 2

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No, the inference is not valid because it excluded those who were not online and so did not see the poll.

To improve the poll, the news show could have conducted it in a more representative manner by surveying a larger sample of people from a variety of backgrounds

The poll's results may have been influenced by various factors, including but not limited to the order in which the comedians were presented, the demographics of the respondents, and the fact that it was conducted online, possibly excluding those without internet access. Overall, the poll's representative accuracy is questionable.

To enhance the accuracy of the survey, the broadcast could have implemented a more inclusive method by polling a wider range of individuals from diverse backgrounds. An alternate method for conducting the poll would have been by personal or telephonic means, enabling individuals without internet connectivity to participate.

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Answer:

b. R-square must be greater than 1.0

Step-by-step explanation:

For a least square regression fit, Assumptions include : Absence of heteroscedasticity, which is the variation must not occur in the variance of the error term. That is the variance between error term and each observation is consistent.

Also, Lack of correlation between observations of the error term and also between independent variables and the error term. It is highly recommended that error term be randomized and normally distributed variable.

The value of R - squared being greater Than 1 is. not an assumption of the least square principle for fitting a regression line.

Answer:

28.52

Step-by-step explanation:

105.87 - 77.35 = 28.52

The percent decrease in the number of ponds that support brook trout would be approximately 47.37%.

To calculate the percent decrease in the number of ponds that support brook trout, we need to determine the difference between the initial number of ponds and the final number of ponds, and then express that difference as a percentage of the initial number of ponds.

Initial number of ponds: 19

Final number of ponds: 10

To calculate the percent decrease, we can use the following formula:

Percent Decrease = (Difference / Initial Value) * 100

Let's apply this formula to the given data:

Difference = Initial number of ponds - Final number of ponds

Difference = 19 - 10

Difference = 9

Percent Decrease = (9 / 19) * 100

Now, let's calculate the percent decrease:

Percent Decrease = (9 / 19) * 100

Percent Decrease ≈ 47.37%

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Answer:

The slops is -4

Step-by-step explanation:

Given

x: -1   1    3   5

y: 10   2   -6   -14

Required

The slope

Pick any pair of x and y

\((x_1,y_1) = (-1,10)\)

\((x_2,y_2) = (1,2)\)

The slope is:

\(m = \frac{y_2 - y_1}{x_2 -x_1}\)

\(m = \frac{2 -10}{1 --1}\)

\(m = \frac{-8}{2}\)

\(m = -4\)

Answer:

Happy New Years sir it is 12:00 in the morning.

Step-by-step explanation:

yes

Answer:80 miles

Step-by-step explanation:

Answer:

24

Step-by-step explanation:

I just did it in class. it was hard but you just have to think about the question

A pair of corresponding angles, alternate interior angles, and alternate exterior angles include the following:

Corresponding angles: ∠1 ≅ ∠5.

Alternate interior angles: ∠4 ≅ ∠6.

Alternate exterior angles: ∠2 ≅ ∠8

In Mathematics, corresponding angles can be defined as a postulate (theorem) which states that corresponding angles are always congruent when the transversal intersects two (2) parallel lines:

∠1 ≅ ∠5

By applying the alternate interior angles theorem to parallel lines m and n, we have the following congruent angles:

∠4 ≅ ∠6

By applying the alternate exterior angles theorem to parallel lines m and n, we have the following congruent angles:

∠2 ≅ ∠8

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Answer:

this list

Step-by-step explanation:

1×12000=12000

2×6000=12000

3×4000=12000

4×3000=12000

5×2400=12000

6×2000=12000

8×1500=12000

10 ×1200=12000

12 ×1000=12000

Answer:

D as 32 divided by 8 is 4

Step-by-step explanation:

A quotient is a result obtained by dividing one quantity by another.

Answer:

The second choice is the correct answer. d/8=4

Step-by-step explanation:

if something is a quotient it means it is the solution of a division problem. So we know it cant be the first. the last one doesn't make sense because it says that 8 and a number d equals 4 so it cant be that 8*4=d. that also goes for the third problem because it has to equal 4 and that equals d not 4.

To find this out we see that because it is the quotient of a number and 8 is 4, that means that we have to have a number divided by 8, the only one with that is the second one.

Step-by-step explanation:

7! = 5040 ways

Answer:

Step-by-step explanation:

BAD = 42

x + 103 + 42 = 180

x = 180 - 145

x = 35

The probability that a randomly selected point within the circle would fall in the red- shaded area is 45. 833 %

The arc that is covered by the red - shaded area in the circle has a degree measure of 165 degrees. This is out of the total circle angle measure of 360 degrees.

This therefore means that the probability that a randomly selected point within the circle would fall in the red- shaded area can be found to be :

= Angle measure of red - shaped area / Total area x  100 %

= 165 / 360 x 100 %

=0. 45833 x 100 %

= 45. 833 %

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Answer:

$839.20

Step-by-step explanation:

To find the finance charge, we need to first calculate the total amount financed, which is the price of the snow thrower minus the down payment.

The down payment is 20% of $1,501, which is:

0.20 x $1,501 = $300.20

So the total amount financed is:

$1,501 - $300.20 = $1,200.80

The total amount of the 12 monthly payments is:

12 x $170 = $2,040

The finance charge is the difference between the total amount of the payments and the amount financed:

$2,040 - $1,200.80 = $839.20

Therefore, the finance charge is $839.20.

Answer:

As points, A and B move, the slope of the two lines change but remain equal to each other. As point C moves, the slope does not change but remains equal to each other since the line through C is drawn parallel to AB.

I can canclude that slope of any two parallel lines are equal

Step-by-step explanation:

The net area of the paper needed is 4.125 square feet.

A cuboid is a three-dimensional closed figure which has volume along with surface area.

The volume of a cuboid is the product of its length, width, and height.

The total surface area of a cuboid is 2(lw + wh + wl) and the lateral surface area is 2(l + w)×h.

Given, The gift is 1.5 feet tall and one of the bases is 9 inches = 0.75 by 0.5 feet.

Therefore the total surface area is,

= 2(1.5×0.5 + 1.5×0.75 + 0.75×0.5).

= 2(0.75 + 1.125 + 0.375).

= 2(2.25).

= 4.5 square feet.

Now, She left one of the bases uncovered which have an area of 0.375 square feet.

Therefore, the net amount of paper needed is = 4.5 - 0.375.

= 4.125 square feet.

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The mean value is 1.19

x           p(x)        x*p(x)        X^2p(x)
1           0.1            0.1               0.1
2           0.15         0.3               0.6
3           0.4          1.2                3.6
4          0.25          1                   4
5           0.1           0.5               2.5
Sum        1            3.1                 10.8

Mean =Σx * p(x)

u=3.1

Variance=σ^2

=Σx*p(x)-u^2

=10.8-(3.1)^2 =1 .19    

A probability distribution is a frequency distribution that has been idealised. A frequency distribution is a description of a particular sample or dataset. It is the number of times each possible variable value appears in the dataset.

The probability of occurrence determines how many times a value appears in a sample. Probability is a number between 0 and 1 that indicates the likelihood of an event occurring:


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Answer:

8(2m+5)

Step-by-step explanation:

GCF: 8

Factor 8 out of 16 and 40 giving you 2 and 5

DON'T FORGET TO CARRY THE M

1) Number of participants whose headache remained is: 62

2) The probability of randomly selecting an individual whose headache remained is: 0.4133

3) The probability of randomly selecting an individual whose headache remained and took a placebo is: 0.2933

From the table, we have the parameters as:

Number of participants that took medicine and headache went away = 120

Number of participants that took placebo and headache went away = 68

Number of participants that took and headache remained = 18

Number of participants that took placebo and headache remained = 44

1) Number of participants whose headache remained = 18 + 44 = 62

2) The probability of randomly selecting an individual whose headache remained is:

62/(62 + 120 + 68)

= 62/150

= 0.4133

3) The probability of randomly selecting an individual whose headache remained and took a placebo is:

44/150 = 0.2933

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To get the total number of points Brendan scored

Since we have been given the number of arrows shot to obtain different points, we will sum the points as follow

The next step will be to add the points together

The answer is 134 points

Answer: The width of the rectangular window is 53 cm.

Step-by-step explanation:

We know that the area of a rectangle is given by the formula:

Area = Length x Width

Substituting the given values, we have:

3816 cm² = 72 cm x Width

To solve for the width, we can divide both sides by 72 cm:

Width = 3816 cm² ÷ 72 cm

Width = 53 cm

Therefore, the width of the rectangular window is 53 cm.

Answer:

3 /4

Step-by-step explanation:

The probability that selected person is a female Given she is married :

This is a conditional probability in the form ; A given B

P(A|B) = P(AnB) / P(B)

Let, Female = F ; Married = M

P(F|M) = P(FnM) / P(M) = 150 / 200 = 3 / 4

To find equivalent expression in math is the fractions with distinct numerators and denominators but the same value are said to be equivalent fractions.

In mathematics, equivalent fractions are those with the same denominator and differing numerators.

The multiplicity of a member of a multiset in mathematics is the number of times the member appears in the multiset. The multiplicity of a root, for instance, is how many times a given polynomial has a root at a particular point.

It's crucial to understand the concept of multiplicity in order to correctly count without mentioning exceptions (for example, double roots counted twice). Thus, "counted with multiplicity" is used.

This can be highlighted by counting the number of different elements, as in "the number of separate roots," if multiplicity is disregarded. However, multiplicity is always taken into account when a set (as opposed to a multiset) is established, therefore the word "different" is not necessary.

For instance, if we simplify 5/15, we get a fraction that is equal to 1/3, which is equal to 5/15.

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The ratio of diameter to height that minimizes the surface area of a cylindrical can while holding a specific volume is: diameter/height = 2r/h

= 2(√(V/2π))/(2√(V/2π)) = 1

What is area ?

Area is a measure of the size of a two-dimensional surface or shape. It is the amount of space inside a closed boundary, such as a square, rectangle, circle, or any other shape.

A = 2πrh + 2πr²

where r is the radius of the can, h is the height of the can, and π is a constant (approximately equal to 3.14).

The volume of the can is given by:

V = πr²h

We want to find the ratio of diameter to height that minimizes the surface area of the can while holding a specific volume. We can use the volume formula to solve for one variable in terms of the other:

h = V/πr²

Substituting this expression for h into the surface area formula, we get:

A = 2πr(V/πr²) + 2πr²

Simplifying, we get:

A = 2V/r + 2πr²

To minimize the surface area, we need to find the value of r that makes the derivative of A with respect to r equal to zero:

dA/dr = -2V/r² + 4πr

Setting this equal to zero, we get:

-2V/r² + 4πr = 0

Solving for r, we get:

r = √(V/2π)

Substituting this value of r back into the expression for h, we get:

h = 2√(V/2π)

Therefore, the ratio of diameter to height that minimizes the surface area of a cylindrical can while holding a specific volume is: diameter/height = 2r/h = 2(√(V/2π))/(2√(V/2π)) = 1

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