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We have proven that ∠BEC ≅ ∠BCE by using the alternate interior angles theorem

From the question, we are to write a proof to prove that ∠BEC ≅ ∠BCE

From the given information, we have that

BC || EF

Note that line DE is a transversal

Thus, by the alternate interior angles theorem, we have that

∠BCE ≅ ∠FEC

Also, we were given that line EC bisects ∠BEF

That is,

Line EC divides ∠BEF into two equal angles.

Therefore,

∠BEC ≅ ∠FEC

By the substitution property of equality, we get

∠BEC ≅ ∠BCE

Hence, we have proven that ∠BEC ≅ ∠BCE by using the alternate interior angles theorem

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Hello, the solution of the problem is in this photo.

If the graph of the line falls from left to right, then the slope is negative.

The area of the shape is 84.78 square units

The formula for calculating the area of a circle is expressed as:

A = πr²

where

r is the radius of a circle

Given the following

r = 6 units

pi = 3.14

Substitute

A = 3.14 * 6²

A = 113.04 square units

If the figure is 3/4 of a circle, the area of the shape will be:

A = 3/4 * 113.04

A = 84.78 square units

Hence the area of the shape is 84.78 square units

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Answer:

2

Step-by-step explanation:

Nguyen saves 15% of his income

The given parameters are:

Savings = $120

Income = $800

The percentage saved is calculated as:

Percentage = Savings/Income * 100%

This gives

Percentage = 120/800 * 100%

Evaluate

Percentage = 15%

Hence, Nguyen saves 15% of his income

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table 1, and table 2 are the answers.

we know that any function is increasing when for an increase in x-values, y-value should also increase

we will verify each table

table-1:

we can see that

x increase as -3, -2, -1 , 0, 1,2

y is also increasing -6,-3,-1,1,3,6

so, this is increasing

table-2:

we can see that

x increase as -3, -2, -1 , 0, 1,2

but it is asking between -2 to 1

y-values are -4,-1,1,4.....which is increasing

so, this is  increasing

table-3:

we can see that

x increase as -3, -2, -1 , 0, 1,2

but y changes from -3 to -5 .....which is decreasing

so, this is not increasing

table-4:

we can see that

x increase as -3, -2, -1 , 0, 1,2

but y changes from 7 to 1 .....which is decreasing

so, this is not increasing

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For Part A the probability is 0.0095 and for Part B the probability is

0.0043.

Probability of defect is perhaps the most important indicator of a manufacturing process's quality. It's a statistical technique used to indicate how often a product will fail during its lifespan, which in turn allows you to estimate the likelihood that an item will result in customer dissatisfaction.

Part A:

The number of rivets=22 rivets

Probability that no rivet is defective= [tex](1-p)^{22}[/tex]

The probability that at least one rivet is defective=1-[tex](1-p)^{22}[/tex]

For 19% of all seams need reworking, probability that a rivet is defective is given by

1-[tex](1-p)^{22}[/tex] = 0.19

[tex](1-p)^{22} = 1-0.19\\(1-p)^{22} = 0.81\\ p=1-\sqrt[22]{0.81} \\p=0.0095[/tex]

Part B:

For 9% of all seams need reworking, probability of a defective rivet is:

1-[tex](1-p)^{22}[/tex] = 0.09

[tex](1-p)^{22} = 1-0.09\\(1-p)^{22} = 0.91\\ p=1-\sqrt[22]{0.91} \\p=0.0043[/tex]

Hence, For Part A the probability is 0.0095 and for Part B the probability is 0.0043.

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To solve a triangle means to obtain al the missing parts of the triangle.

To solve a triangle means to obtain al the missing parts of the triangle. Now we have the following information;

<ABC = 51°

c = 8

a = 11

Then;

b^2 = a^2 + c^2 - 2acCos B

b^2 = (11)^2 + (8)^2 - [2 * 11 * 8 * cos 51]

b^2 = 121 + 64 - 55.38

b = 11.39

Now;

a/sinA = b/sinB

asinB = bsinA

sinA = asinB/b

sinA = 11 * sin 51/11.39

A = 48.6 or 49°

C = 180 - (49 + 51)

C = 80°

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The concept of factoring quadratic equations simply is one of the ways to solve for the zeroes of the quadratic equation.

The concept of factoring quadratics is a technique which is characterized by expressing the quadratic equation ax2 + bx + c = 0 as a product of its associated linear factors as (x - f)(x - g), in which case, f and g are the roots of the quadratic equation ax2 + bx + c = 0.

Factoring is an important concept that helps express equations of any type in simpler forms The mode of operation of the factoring works such that, the polynomial is rewritten in a simpler form and consequently, expressed as a product of it's linear factors.

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Answer:

Total cost is $177.50.

Step-by-step explanation:

Rackets:

Divide the cost for racket by 6 to find the cost per racket.

186÷6=31

Multiply 31 by 5 to find the cost for 5 rackets.

31×5=155

$155

Tubes of balls:

Divide 27 by 6 to find the cost per a tube of balls.

27÷6=4.50

Multiply 4.50 by 5 to find the cost for 5 tubes of balls.

4.50×5=22.50

$22.50

Add the amounts for rackets and tubes of balls to find the total cost.

155+22.50=177.50

The total cost is $177.50.

Hope this helps!

Answer:

76.25

Step-by-step explanation:

Check the picture below, so the parabola looks more or less like so, with the vertex half-way from the focus point and the directrix.

Now, the distance from the directrix to the focus point is only 1 unit, so half that, or namely the "p" distance is 1/2 unit, and since the parabola is opening downwards, "p" is negative, so

[tex]\textit{vertical parabola vertex form with focus point distance} \\\\ 4p(y- k)=(x- h)^2 \qquad \begin{cases} \stackrel{vertex}{(h,k)}\qquad \stackrel{focus~point}{(h,k+p)}\qquad \stackrel{directrix}{y=k-p}\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix}\\\\ \stackrel{"p"~is~negative}{op ens~\cap}\qquad \stackrel{"p"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\begin{cases} h=0\\ k=-\frac{1}{2}\\[1em] p=-\frac{1}{2} \end{cases}\implies 4\left( -\frac{1}{2} \right)\left( ~~y-\left( -\frac{1}{2} \right) ~~ \right)~~ = ~~(x-0)^2 \\\\\\ -2\left( y+\frac{1}{2} \right)=x^2\implies y+\cfrac{1}{2} =\cfrac{x^2}{-2}\implies y = -\cfrac{1}{2}x^2-\cfrac{1}{2}[/tex]

now, we could also write that as either

[tex]y = -\cfrac{1}{2}(x^2+1)\qquad or\qquad y = \cfrac{1}{2}(-x^2-1)[/tex]

Answer:

H. 10 h

Step-by-step explanation:

40.50-5.5 = 35

35/3.5 = 10 hours

The researcher is using a within-subjects factorial design.

According to statement

A researcher conducts an experiment to determine whether the type of car and color of the car impact how fast people drive.

This can be done by within-subjects factorial design.

In a within-subjects factorial design, all of the independent variables are manipulated within subjects. This would mean that each participant was tested in all conditions.

Another common example of a within-subjects design is medical testing.

So, The researcher is using a within-subjects factorial design.

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Answer:

Step-by-step explanation:

Cylinder volume formula:

Given:

The first cylinder, has base radius - r and height - h. Its volume is:

The second cylinder has:

Its volume is:

Substitute the value of the first cylinder:

Answer:

x = -9, y = 8

or,

(-9, 8)

Explanation:

Equation 1: 2x + 3y = 6

Equation 2: 4x - y = -44

To solve by substitution, make y subject for equation 2.

4x - y = -44

-y = -44 - 4x

y = 4x + 44

Substitute this y value into equation 1.

2x + 3(4x + 44) = 6

2x + 12x + 132 = 6

14x = 6 - 132

14x = -126

x = -9

Now, find y value:

y = 4x + 44

y = 4(-9) + 44

y = 8

To check for solution, insert x and y value in either equations.

2x + 3y = 6

insert values

2(-9) + 3(8) = 6

6 = 6

Hence, the solution is correct as both sides equal.

Therefore x = -9 and y = 8.

Substitution method

Equation (1) ——— 2x + 3y = 6

Equation (2) ——— 4x - y = -44

When using substitution method , make x the subject of equation (1).

2x + 3y = 6

2x = 6 - 3y

x = 3 - 3y/2

Substitute the value of x in equation (2) to find y.

4(3 - 3y/2) - y = -44

12 - 6y - y = -44

Subtract 12 from both sides.

12 - 12 - 7y = -44 - 12

-7y = -56

y = 8

Substitute the value of y in equation (1) to find x.

2x + 3y = 6

2x + 3(8) = 6

2x +24 = 6

Subtract 24 from both sides.

2x + 24 - 24= 6 - 24

2x = -18

x = -9

Therefore x = -9 and y = 8.

To check out the solution.

Equation (1) 2x + 3y = 6 , x = -9 , find y.

Substitute the value of x

2(-9) + 3y = 6

-18 + 3y = 6

Add 18 to both sides.

-18 + 18 + 3y = 6 + 18

3y = 24

y = 8

Substitute the value of y in equation (1) .

2x +3(8) = 6

2x + 24 = 6

Subtract 24 from both sides.

2x + 24 - 24 = 6 -24

2x = -18

x = -9

As you can see when you substitute the value of x and y in the equation(1) , you get the same value of x and y ,which is -9 and 8 respectively. So the solution is correct.

Answer: this is the solutions

The rotation about 90 degrees clockwise from the origin would give H'( -2, 3) , I' (1 , -1) and J' (-4, 0)

Note that rotation about in clockwise 90 degrees direction when M(h , k) rotated about the origin, the new rotation coordinates would be in the form M' (k , -h)

Coordinates of the preimage were given as;

H ( -3, -2)

I ( 1, 1 )

J ( 0, -4)

The coordinates after a 90 degrees rotation about the origin, would be

For H ( -3, -2)

h = - (-3) = 3

k = -2

H' = ( -2, 3)

For I ( 1, 1)

h = - (1) = -1

k = 1

I' = ( 1, -1)

For J ( 0, -4)

h = - (0) = 0

k = -4

J' = ( -4, 0 )

Thus, the rotation about 90 degrees clockwise from the origin would give H'( -2, 3) , I' (1 , -1) and J' (-4, 0)

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The time that the first train would get to Oakengats is 08:15.

The time of arrival of the first train can be gotten from the table.

The first entry has a blank space. This would have been the time of arrival for the train.

After the blank space, the next time is when the fits train got to this destination. That is at 08:15

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Answer:

None of the answers

Step-by-step explanation:

There are 60 minutes in one hour so to find the number of minutes in two hrs we multiply 2 by 60: 2*60 = 120 minutes

We then add the extra 20 minutes: 120+20 = 140 minutes

None of the answers include 140 minutes.

Using the combination formula, the probability that a person with one combination of five numbers will win is:

[tex]\frac{1}{1,221,759}[/tex]

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

For this problem, 5 numbers are taken from a set of 45, hence the number of combinations is:

[tex]C_{45,5} = \frac{45!}{5!40!} = 1,221,759[/tex]

Hence the probability is:

[tex]\frac{1}{1,221,759}[/tex]

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The coordinates of the focus and the equation of the directrix is option B: focus: (0, one-half); directrix: y = negative one-half.

Since we were given Parabola x² = 2 y

Then one has to compare and and so it will be  x² = 4 a y

                                                                               4 a = 2

Make a the subject of the formula:

a = 2/4

= 1/2

Therefore,   Focus ( 0,a) = (0, 1/2 )

To solve for directrix:

Note that the equation of the directrix is:

y = -a or y +a=0

Then the equation of the directrix is:

y = - 1/2 or

y = + 1/2 = 0

Then the equation of the directrix will be 2 y +1 =0.

Therefore, The coordinates of the focus and the equation of the directrix is option B: focus: (0, one-half); directrix: y = negative one-half.

See full question below

A parabola can be represented by the equation x2 = 2y. What are the coordinates of the focus and the equation of the directrix? focus: (0,8); directrix: y = –8 focus: (0, one-half); directrix: y = negative one-half focus: (8,0); directrix: x = –8 focus: (one-half, 0); directrix: x = negative one-half

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Answer:

x/8 gallons.

Step-by-step explanation:

The 8 containers have the larger capacity as the 2 totals are x and the other containers are 16 in total.

Capacity of each of the large containers = x/8 gallons.

quick answer (A)

ALL real numbers less than or equal to 8

Answer: y=8x+6

Step-by-step explanation:

The slope is

[tex]\frac{70-54}{8-6}=\frac{16}{2}=8[/tex]

So, the slope is 8.

Since the y-intercept is 6, the equation is y=8x+6.

Mean = $ 4. 72

Median = $ 4. 5

Mode = No mode

MAD = $ 4. 8

IQR = $ 0. 5

Measure of center = $ 4. 5

Measure of variability = $ 2. 50

Given the data;

$3.50, $4.25, $6, $4.75, $5.80, $4

Mean = sum of data/ number of data values

Mean = [tex]\frac{3. 50 + 4. 25 + 6 + 4. 75 + 5. 80 + 4}{6}[/tex]

Mean = $ 4. 72

Median is the number in the center when the data is arranged in an ascending order

$3. 50, $4, $4. 25, $4. 75, $5. 80, $6

Median = [tex]\frac{4. 25 + 4. 75}{2}[/tex]

Median = $ 4. 5

Mode is the number with the highest repeats.

From the given data, none of the numbers was repeated.

Thus, there is no mode.

MAD, mean absolute deviation = |data value - mean|

MAD = [tex]|(3. 50 - 4. 72) + (4. 25 - 4. 72) + (6 - 4. 72) + (4. 75 - 4. 72) + (5. 80 - 4.72) + (4- 4. 72) |[/tex]

MAD = [tex]1. 22 + 0. 47 + 1. 28 + 0. 03 + 1. 08 + 0. 72[/tex]

MAD = $ 4. 8

IQR, interquartile range = Quartile 3 - quartile 1

IQR = 4. 75 - 4. 25

IQR = $0. 5

Note that  the mean and median are the most common measures of center.

A measure of variability is a single number that is  used to describe the spread of a data set

The measure of the center best for the data is the median = $4. 5

Measure of variability = range = highest value - lowest value = $6 - $3. 50 = $2. 50

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After 39 years, the value of this quantity is 1,023.35

Here we know that:

Then the exponential equation is:

[tex]A(t) = 570*(1 + 0.35)^{t/20}[/tex]

Where t is the time in years.

So, after 39 years, the value of this quantity is given by:

[tex]A(39) = 570*(1 + 0.35)^{39/20} = 1,023.35[/tex]

After 39 years, the value of this quantity is 1,023.35

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Answer:

d=(x^2-x^1)+(y^2-y^1)^2

Answer:

[tex]\mathfrak{Distance \: between \: two \:points}[/tex]

The distance between two points [tex]A(x_1,y_1)[/tex] and [tex]B(x_2,y_2)[/tex] is given by the formula,

[tex]AB= \sqrt{(x_2-x_1)^2+(y_2-y_1)^2 }[/tex]

Proof: Let X'OX and YOY' be the x-axis and y-axis respectively. Then, O is the origin.

Let[tex]A(x_1,y_1) [/tex] and [tex]B(x_2,y_2)[/tex]

be the given points.

Draw AL perpendicular to OX, BM perpendicular to OX and AN perpendicular to BM

Now,[tex]OL=x_1,OM=x_2,AL=y_1 \: and \: BM=y_2[/tex]

[tex] \therefore{AN=LM=(OM-OL)=(x_2-x_1)}[/tex]

[tex] \: \: \: BN=(BM-NM)=(BM-AL)=(y_2-y_1)[/tex]

In right angled triangle [tex] \triangle \: ANB[/tex],by Pythagorean theorem,

We have,

[tex] \: \: \: AB^2=AN^2+BN^2[/tex]

[tex]or,AB^2=(x_2-x_1)^2+(y_2-y_1)^2[/tex]

[tex] \therefore \: AB= \sqrt{(x_2-x_1)^2+(y_2-y_1)^2} [/tex]

Thus ,the distance between the points A(x_1,y_1) and B(x_2,y_2) is given by,

[tex] \implies \boxed{AB= \sqrt{(x_2-x_1)^2+(y_2-y_1)^2} }[/tex]

Answer:

Yes. If the squares of the 2 short sides add up to the square of the hypotenuse, the triangle contains a right angle. Hope this helped.

The number of credit hours a student have to take for the two tuition costs to be equal is 2.5 hours. Option A

c(h) = 250 + 200h

s(h) = 300 + 180h

Where,

To have equal tuition in both schools,

equate both function

250 + 200h = 300 + 180h

200h - 180h = 300 - 250

20h = 50

h = 50/20

h = 2.5 hours.

The number of credit hours a student have to take for the two tuition costs to be equal is 2.5 hours.

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