Answer:
a) Null and alternative hypothesis:
[tex]H_0: \pi=0.1\\\\H_a:\pi>0.1[/tex]
b) A Type I error is made when a true null hypothesis is rejected. In this case, it would mean a conclusion that the proportion is significantly bigger than 10%, when in fact it is not.
c) The consequences would be that they would be more optimistic than they should about the result of the investment, expecting a proportion of students that is bigger than the true population proportion.
d) A Type II error is made when a false null hypothesis is failed to be rejected. This would mean that, although the proportion is significantly bigger than 10%, there is no enough evidence and it is concluded erroneously that the proportion is not significantly bigger than 10%
e) The consequences would be that the investment may not be made, even when the results would have been more positive than expected from the conclusion of the hypothesis test.
Step-by-step explanation:
a) The hypothesis should be carried to test if the proportion of students that would eat there at least once a week is significantly higher than 10%.
Then, the alternative or spectulative hypothesis will state this claim: that the population proportion is significantly bigger than 10%.
On the contrary, the null hypothesis will state that this proportion is not significantly higher than 10%.
This can be written as:
[tex]H_0: \pi=0.1\\\\H_a:\pi>0.1[/tex]
What is the greatest common factor of the polynomial below 12x^2-9x
Answer:
the greatest common factor of this is 3
Please help!!!!! I'm on a timerrrrrrrrrrrrrr!
Step-by-step explanation:
6
[tex]6 \sqrt{6} [/tex]
Answer:
6√6is the exact answer
Find the surface area of each prism. Round to the nearest tenth if necessary while doing your calculations as well as in your final answer. 360 units2 586 units2 456 units2 552 units2
Answer:
correct answer is 456 sq units.
Step-by-step explanation:
Let us have a look at the formula for Surface Area of a prism:
[tex]A =p \times h+2 \times B[/tex]
Where p is the perimeter of base
h is the height of prism
and B is the base area of prism.
Given that:
h = 7.5 units
Hypotenuse of prism's base = 20 units
One of the Other sides = 12 units
Pythagorean theorem can be used to find the 3rd side of right angled base.
Square of hypotenuse = Sum of squares of other two sides
[tex]20^2=12^2+side^2\\\Rightarrow 400=144+side^2\\\Rightarrow side =\sqrt{256}\\\Rightarrow side =16\ units[/tex]
Area of base = area of right angled triangle:
[tex]B = \dfrac{1}{2} \times \text{Base Length} \times \text{Perpendicular Length}\\\Rightarrow B = \dfrac{1}{2} \times 16\times 12 = 96\ sq\ units[/tex]
Perimeter [tex]\times[/tex] height = (12+20+16) [tex]\times[/tex] 7.5 = (48) [tex]\times[/tex] 7.5 = 360 sq units
Now putting the values in formula:
Surface area, A = 360+96 = 456 sq units
So, correct answer is 456 sq units.
The number of bacteria, B(h), in a certain population increases according to the following
function, where time, h, is measured in hours:
B(h) = 1425 e ^0.15h
How many hours will it take for the bacteria to reach 3300?
Round your answer to the nearest tenth, and do not round any intermediate
computations.
Please helpppp!!!
Answer:
It will take 5.6 hours to get the given population (3300) of the bacteria.
Step-by-step explanation:
A function that defines the population increase of a bacteria is,
B(h) = [tex]1425e^{0.15h}[/tex]
where h = duration or number of hours for bacterial growth
B(h) = Final population
If the final bacterial population is 3300,
3300 = [tex]1425e^{0.15h}[/tex]
By taking log on both the sides of the equation,
ln(3300) = [tex]ln(1425e^{0.15h})[/tex]
8.10168 = ln(1425) + [tex]ln(e^{0.15h})[/tex]
8.10168 = 7.261927 + 0.15h
h = [tex]\frac{8.10168-7.261927}{0.15}[/tex]
h = 5.5983
h ≈ 5.6 hours
Therefore, it will take 5.6 hours to get the given population (3300) of the bacteria.
The World Issues club has decided to donate 60% of all their fundraising activities this year to Stephen Lewis
Foundation. This foundation was created to help ease the pain of HIV/AIDS in Africa Lewis, a Canadian
works for the United Nations trying to determine ways to stop the spread of this deadly disease from crippling
an entire continent
a. Choose a variable to represent the money earned during fundraising activities and the revenue generated
for the foundation
b. Use these variables to create an equation that will determine the amount of money the foundation will
receive
c. In their latest bake sale, the club raised $72. Calculate the amount the foundation will receive
d. At the end of the year, the World Issues Club mailed a cheque to the foundation for $850. How much
money did they fundraise in total?
Answer:
a. Let the variable be [tex]x[/tex] for the fundraising activities and [tex]M[/tex] as the revenue for foundation.
b. [tex]M =0.60x[/tex]
c. $43.2
d. $1416.67
Step-by-step explanation:
Given that:
The World Issues club donates 60% of the total of their fundraising activities.
Answer a.
Let us choose the variable [tex]x[/tex] to represent the money earned during fundraising activities and [tex]M[/tex] for the revenue generated for foundation.
Answer b.
Foundation will receive 60% of the total of the fundraising activities.
Equation to determine the money that will be received by foundation:
[tex]M = 60\%\ of\ x\\OR\\M = 0.6x[/tex]
Answer c.
Given that x = $72, M = ?
Putting the value of x in the equation above:
[tex]M = 0.6 \times 72\\\Rightarrow \$43.2[/tex]
Answer d.
Given that M = $850, x = ?
Putting the value of M in the equation above to find x:
[tex]850= 0.6 \times x\\\Rightarrow x = \dfrac{850}{0.6}\\\Rightarrow x = \$ 1416.67[/tex]
So, the answers are:
a. Let the variable be [tex]x[/tex] for the fundraising activities and [tex]M[/tex] as the revenue for foundation.
b. [tex]M =0.60x[/tex]
c. $43.2
d. $1416.67
A Norman window has the shape of a rectangle surmounted by a semicircle. (Thus the diameter of the semicircle is equal to the width of the rectangle.) If the perimeter of the window is 30 ft, find the dimensions of the window so that the greatest possible amount of light is admitted.
The dimensions of the Norman window that admit the greatest possible amount of light are approximately:
Width (w) ≈ 11.72 ft
Height (h) ≈ 2.91 ft
To find the dimensions of the Norman window that admit the greatest possible amount of light, we need to maximize the area of the window. The window consists of a rectangle and a semicircle, so the area is the sum of the areas of both shapes.
Let's assume the width of the rectangle is "w" and the radius of the semicircle is "r".
Since the diameter of the semicircle is equal to the width of the rectangle, the radius "r" is half of "w".
Area of the rectangle = w * h, where h is the height of the rectangle.
Area of the semicircle = (1/2) * π * r²
The perimeter of the window is given as 30 ft, which can be written as:
Perimeter = 2 * (w + h) + π * r + w
Since r = w/2, we can rewrite the perimeter equation as:
Perimeter = 2 * (w + h) + (π/2) * w + w
Perimeter = 2w + 2h + (π/2 + 1) * w
Given that the perimeter is 30 ft, we have:
30 = 2w + 2h + (π/2 + 1) * w
Now, we can express "h" in terms of "w" using the perimeter equation:
h = (30 - 2w - (π/2 + 1) * w) / 2
Next, let's express the area "A" of the window in terms of "w" using the formulas for the area of the rectangle and the semicircle:
Area (A) = Area of rectangle + Area of semicircle
A = w * h + (1/2) * π * r²
A = w * ((30 - 2w - (π/2 + 1) * w) / 2) + (1/2) * π * (w/2)²
A = w * ((30 - 2w - (π/2 + 1) * w) / 2) + (1/2) * π * (w² / 4)
Now, we want to maximize the area "A."
To find the maximum value, we take the derivative of "A" with respect to "w" and set it equal to zero:
dA/dw = (30 - 2w - (π/2 + 1) * w) / 2 + (π/4) * w = 0
Solving for "w":
(30 - 2w - (π/2 + 1) * w) / 2 + (π/4) * w = 0
(30 - 2w - (π/2 + 1) * w) + (π/2) * w = 0
(30 - (2 + π/2) * w) + (π/2) * w = 0
30 - (2 + π/2) * w + (π/2) * w = 0
(30 - 2w) + (π/2 - π/4) * w = 0
30 - 2w + (π/4) * w = 0
(π/4) * w - 2w = -30
w ((π/4) - 2) = -30
w = -30 / ((π/4) - 2)
w ≈ 11.72 ft
Now that we have the value of "w," we can find the value of "h" using the perimeter equation:
Perimeter = 2w + 2h + (π/2 + 1) * w
30 = 2(11.72) + 2h + (π/2 + 1) * (11.72)
30 = 23.44 + 2h + (π/2 + 1) * 11.72
2h = 30 - 23.44 - (π/2 + 1) * 11.72
2h = 6.56 - (π/2 + 1) * 11.72
h = (6.56 - (π/2 + 1) * 11.72) / 2
h ≈ 2.91 ft
So, the dimensions of the Norman window that admit the greatest possible amount of light are approximately:
Width (w) ≈ 11.72 ft
Height (h) ≈ 2.91 ft.
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Find the magnitude of side R. Show work please!
Answer:
21.7 metres (assuming the triangle is a right triangle)
Step-by-step explanation:
Assuming this is a right triangle, we can simply use the Pythagorean Theorem, which states that in a right triangle with legs a and b and hypotenuse c:
a² + b² = c²
Here, a = 20, b = 8.5, and R = c. Plug these in:
a² + b² = c²
20² + 8.5² = R²
400 + 72.25 = R²
472.25 = R²
R = √472.25 ≈ 21.7 m
Thus, R is about 21.7 metres.
~ an aesthetics lover
About 16.6% of Americans can speak Spanish. We obtain a random sample of seventy-five Americans and determine the proportion in the sample who speak Spanish. Find the probability that 25% or more in the sample speak Spanish.
Answer:
The probability that 25% or more in the sample speak Spanish is 76%.
Step-by-step explanation:
Sample of 75 Americans
If 25% or more in the sample speak Spanish, it can be deduced that 24% do not speak Spanish.
The proportion of those who do not speak Spanish is 18 (24% of 75)
Therefore, the proportion of those who speak Spanish is 57 (75 - 19)
This implies that 57/75 x 100 = 76% of the sample speak Spanish.
This 76% of the sample who speak Spanish is equal to the 25% or more who do speak Spanish in the sample.
Probability is the chance that an event may occur from many other events that could have occurred. It is an educated guess or estimate of something or one event happening when all the events in the set are given an equal chance.
Please answer this correctly
Answer:
9/49
Step-by-step explanation:
The probability of landing on an even number is 3/7.
Because there are only 3 numbers even out of 7 total numbers.
[tex]3/7 \times 3/7[/tex]
[tex]= 9/49[/tex]
10) BRAINLIEST & 10+ Points!
Answer:
20Solution,
Complement of 70°
=90°-70°
=20°
hope this helps...
Good luck on your assignment..
Answer:
20°
Step-by-step explanation:
Complement of 70° is 90°-70°= 20°
To determine the complement, subtract the given angle from 90.
Which graph represents the function?
the answer is the bottom left option
Solve for x in the equation 3 x squared minus 18 x + 5 = 47.
Answer:
x = -1.796, 7.796
Step-by-step explanation:
3x² - 18x + 5 = 47
3x² - 18x - 42 = 0
use quadratic equation
x = -1.796, 7.796
Answer:
x = 3 +/- √23
Step-by-step explanation:
got it right on edg
The state of Wisconsin would like to understand the fraction of its adult residents that consumed alcohol in the last year, specifically if the rate is different from the national rate of 70%. To help them answer this question, they conduct a random sample of 852 residents and ask them about their alcohol consumption.
Answer:
The answer is below
Step-by-step explanation:
What we should do is the following:
First, from the random sample of 852 researchers, it is necessary to obtain the number of adult residents who consumed alcohol in the past year.
After the above, we must calculate the proportion of adult residents who consumed alcohol in the last year by dividing the number of adult residents who consumed alcohol in the last year by 852.
After this, we must compare if the proportion is exactly 70% or different from it.
We have the following hypotheses:
Null Hypothesis: The proportion of adult residents who consumed alcohol in the last year in the state of Wisconsin is exactly 70%
Alternative hypothesis: The proportion of adult residents who consumed alcohol in the last year in the state of Wisconsin is not equal to 70%
Consider a normal population with the mean of 40 and standard deviation of 10. A random sample of was selected: 39.2, 45.7, 27.4, 25.9, 25.1, 46.3, 42.9, 49.0, 40.6, 47.0. What is the bias of this the estimated mean for this sample
Answer:
[tex]\bar X = \frac{\sum_{i=1}^n X_i}{n}[/tex]
And replacing we got:
[tex]\bar X= 38.91[/tex]
And we can find the bias with this formula:
[tex] Bias= \bar X -\mu[/tex]
And replacing we got:
[tex] Bias = 38.91 -40 = -1.09[/tex]
Step-by-step explanation:
For this problem we know that the random variable of interest follows this distribution:
[tex]X \sim N(\mu =40, \sigma= 10)[/tex]
And we have the following random sample given:
39.2, 45.7, 27.4, 25.9, 25.1, 46.3, 42.9, 49.0, 40.6, 47.0
And we can calculate the sample mean with the following formula:
[tex]\bar X = \frac{\sum_{i=1}^n X_i}{n}[/tex]
And replacing we got:
[tex]\bar X= 38.91[/tex]
And we can find the bias with this formula:
[tex] Bias= \bar X -\mu[/tex]
And replacing we got:
[tex] Bias = 38.91 -40 = -1.09[/tex]
The prize in a raffle is a flat-screen TV valued at $350, and 1,000 tickets are sold for a dollar each. Let’s find the expected value if you buy 1 ticket. Find the expected value. Round your answer to two decimal places. Remember a gain would be posit
Answer:
the expected value EV = −$0.65
Step-by-step explanation:
Expected value EV = expected gain - expected loss
Given;
Cost of a ticket L = $1
Probability of losing the ticket P(L)= 999/1000 = 0.999
Cost of a flat screen TV = $350
Expected gain G = $350 - $1 = $349
Probability of winning the TV P(G) = 1/1000 = 0.001
EV = G × P(G) - L × P(L)
Substituting the values;
EV = $349 × 0.001 - $1 × 0.999
EV = −$0.65
the expected value EV = −$0.65
Emily and George had a farm with a new barn.
True
False
Answer:
true
Step-by-step explanation:
it is so because they are brother and sister
And in the chapter there is that they had farm with a new barn
if in your book lesson there is that they had no farm with a new barn then there will be false
Now did you understood?
Answer:
True
Step-by-step explanation:
The scores from a state standardized test have a mean of 80 and a standard deviation of 10. The distribution of the scores is roughly bell shaped. to find the percentage of scores that lie between 60 and 80.
Answer:
47.5%.
Step-by-step explanation:
60 is 2 standard deviations below the mean.
According to the emperical rule, there is approximately 90% of normally distributed data within 2 standard deviations of the mean. Your interval is half of that because it is the data between the mean and two standard deviations
below the mean. therefore, the answer is 47.5%.
The percentage of scores that lie between 60 and 80 is 47.75%
Z score is used to determine by how many standard deviations the raw score is above or below the mean. The z score is given by:
[tex]z=\frac{x-\mu}{\sigma} \\\\where\ x=raw\ score,\mu=mean, \sigma=standard\ deviation[/tex]
Given that:
μ = 80, σ = 10
[tex]For\ x=60:\\\\z=\frac{60-80}{10} =-2\\\\For\ x=80:\\\\z=\frac{80-80}{10} =0[/tex]
P(60 < x < 80) = P(-2 < z < 0) = P(z < 0) - P(z < -2) = 0.5 - 0.0228 = 47.75%
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At an international conference, flags from 8 different countries will be displayed. Of these flags, 4 are from the continent of Africa and 4 flags are from the continent of Europe. The flags will be displayed in a row, alternating between continents. A flag from Africa will be in the first position. In how many ways can the flags be displayed?
Answer:
96 ways
Step-by-step explanation:
Let´s call flags of countries from Africa as A₁, A₂, A₃, A₄, and from Europe as E₁, E₂, E₃ and E₄
We have to display the flags always beginning with one flag from Africa let´s take A₁
For that flag, we have 4! possibilities Then 4! is:
4*3*2*1 = 24
As we have 4 different Flags from Africa, we will have
4*24 = 96 possibilities
Someone help me please pls pls pls
Answer:
There is 9 on each pace and 3 on a row
Step-by-step explanation:
54/6=9
if there is 9 on each side and the same on each side, then it has to be 3 in each row and column. Also, this is a Rubix cube
Please give me brainliest, it really helps! :)
Have a good day!
Example of a 3rd degree polynomial in standard form?
Answer:
4x^3 + 2x^2 +8x -9
Step-by-step explanation:
A third degree polynomial is a is a polynomial whose highest power of x is to the power of three. Standard form is
Ax^3 + Bx^2 + Cx + D where A is non zero
An example would be
4x^3 + 2x^2 +8x -9
Find the area of the surface correct to four decimal places by expressing the area in terms of a single integral and using your calculator to estimate the integral. The part of the surface that lies above the disk x2 + y2 ≤ 81
Answer:
A(s) = 255.8857
Step-by-step explanation:
Find the area of the surface correct to four decimal places by expressing the area in terms of a single integral and using your calculator to estimate the integral. The part of the surface z = e^-x^2-y^2 that lies above the disk x2 + y2 ≤ 81.
Given that:
[tex]Z = e^{-x^2-y^2}[/tex]
By applying rule; the partial derivatives with respect to x and y
[tex]\dfrac{\partial z }{\partial x}= -2xe^{-x^2-y^2}[/tex]
[tex]\dfrac{\partial z }{\partial y}= -2ye^{-x^2-y^2}[/tex]
The integral over the general region D with respect to x and y is :
[tex]A(s) = \int \int _D \sqrt{1+(\dfrac{\partial z}{\partial x} )^2 +(\dfrac{\partial z}{\partial y} )^2 }\ dA[/tex]
[tex]A(s) = \int \int _D \sqrt{1+(-2xe^{-x^2-y^2})^2 +(-2ye^{-x^2-y^2})^2 } \ dA[/tex]
[tex]A(s) = \int \int _D \sqrt{1+4x^2({e^{-x^2-y^2})^2 +4y^2({e^{-x^2-y^2}})^2 }} \ dA[/tex]
[tex]A(s) = \int \int _D \sqrt{1+(4x^2+4y^2)({e^{-x^2-y^2})^2 }} \ dA[/tex]
[tex]A(s) = \int \int _D \sqrt{1+(4x^2+4y^2)e^{-2}({{x^2+y^2}) }} \ dA[/tex]
By relating the equation to cylindrical coordinates
[tex]A(s) = \int \int_D \sqrt{1+4r^2 e^{-2r^2} }. rdA[/tex]
The bounds for integration for the circle within the cylinder [tex]x^2+y^2 =81[/tex] is r =9
[tex]A(s) = \int \limits ^{2 \pi}_{0} \int \limits^9_0 r \sqrt{1+4r^2 e^{-2r^2} }. dr d\theta[/tex]
[tex]A(s) = {2 \pi} \int \limits^9_0 r \sqrt{1+4r^2 e^{-2r^2} }\ dr[/tex]
Using integral calculator to estimate the integral,we have:
A(s) = 255.8857
Find all values of k for which the function y=sin(kt) satisfies the differential equation y′′+16y=0. Separate your answers by commas. isn't the answer just ±4?
Answer:
0, 4, -4 and they may want you to mention formally all the kt multiples of [tex]\pi[/tex].
Step-by-step explanation:
Let's do the second derivative of the function: [tex]y(t)=sin(k\,t)[/tex]
[tex]y'(t) =k\,cos(k\,t)\\y"(t)=-k^2\,sin(kt)[/tex]
So now we want:
[tex]y"+16\,y'=0\\-k^2\,sin(kt)+\,16\,sin(kt)=0\\sin(kt)\,(16-k^2)=0\\[/tex]
Then we have to include the zeros of the binomial ([tex]16-k^2[/tex]) which as you say are +4 and -4, and also the zeros of [tex]sin(kt)[/tex], which include all those values of
[tex]kt=0\,,\,\pi\,\,,\,2\pi\, ,\,etc.[/tex]
So an extra one that they may want you to include is k = 0
If 10 is added to the maximum value and 10 is subtracted from the minimum value of a set of ages of citizens waiting in line to vote, which of the following is true? a-The mean age and median age are unchanged. b-The mean age changes but the median age does not change. c- The median age changes but the mean age does not change. d-The effect on the mean and median cannot be determined without knowing the other ages. e-None of these.
Answer:
a-The mean age and median age are unchanged.
Step-by-step explanation:
By adding the same you are subtracting, the sum of the ages remains the same. Therefore, the mean remains the same since you are dividing the same total of ages by the same number of people.
The middle number continues to be the middle number, so the median also does not change.
Try an example.
The ages are 30, 40, 50, 60, 70
Mean = (30 + 40 + 50 + 60 + 70)/5 = 250/5 = 50
Median: 50
Now add 10 to the greatest value and subtract 10 from the least value.
The ages now are 20, 40, 50, 60, 80
Mean = (20 + 40 + 50 + 60 + 80)/5 = 250/5 = 50
Median: 50
As you can see, both the mean and the median did not change.
Answer: a-The mean age and median age are unchanged.
Answer:
The mean age and median age are unchanged
Step-by-step explanation:
The median will not change when we alter the lowest and highest values so we can eliminate the answers that say the median changes
The mean is found by adding the values together and dividing by the number of values
If we add 10 and subtract 10, we have not changed the total value before dividing, so the mean does not change
a bag contains 6 cherry 3 orange and 2 lemon candies. You reach in and take 3 pieces of candy at random. Find the probability of all lemons
Answer:
0.181818
Step-by-step explanation:
There are total 11 candies. The possibility of combinations is 165 which is found by using computation technique 11C3. It is assumed that order does not matter. There are 3 pieces of candy are selected at random. There are 6C2 which is 15 different ways to select cherry and lemon. There are 30 ways to choose 2 cherry and a lemon combination. The probability is [tex]\frac{30}{165}[/tex] = 0.181818
Factor: 144u^2w-144w
Answer:
144w[(u - 1)(u + 1)]
Step-by-step explanation:
144w is the highest common factor of the binomial.
144u^2w - 144w = 144w(u^2 - 1) = 144w[(u - 1)(u + 1)]
What is PI times 4? HELP ASAP
Answer:
12.566370614359172953850573533118
Step-by-step explanation:
Please help me!!!!!!!!
Step-by-step explanation:
might be option c is a correct answer of your given question
18. Which function is the result of translating y = x^2 downward by 3 units and to the left by 4 units?
A) y = (x – 3)^2 + 4
B) y = (x + 3)^2 – 4
C) y = (x + 4)^2 – 3
D) y = (x – 4)^2 + 3
Answer:
C
Step-by-step explanation:
Given f(x) then f(x + k) represents a horizontal translation of f(x)
• If k > 0 then shift left by k units
• If k < 0 then shift right by k units
Here the shift is 4 units to the left, thus
y = (x + 4)²
Given f(x) then f(x) + k represents a vertical translation of f(x)
• If k > 0 then shift up by k units
• If k < 0 then shift down by k units
Here the shift is 3 units down, thus
y = (x + 4)² - 3 → C
y = (x+4)²-3 is the result of translating y = x² downward by 3 units and to the left by 4 units
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
We need to find the function is the result of translating y = x² downward by 3 units and to the left by 4 units
A translation is a movement of the graph either horizontally parallel to the -axis or vertically parallel to the axis.
To translate the graph of y = f(x) three units downward, subtract 3 from f(x) which becomes y = x²-3
To translate the graph four units to the left, replace x by x+4
y = (x+4)²-3
Hence, y = (x+4)²-3 is the result of translating y = x² downward by 3 units and to the left by 4 units
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What is the circumference of the circle below? (Round your answer to the nearest tenth.)
Hey there! :)
Answer:
75.4 cm.
Step-by-step explanation:
Formula for the circumference of a circle:
C = 2rπ
Given:
r = 12 cm
Plug this value of r into the equation:
C = 2(12)π
C = 24π
Multiply by π (3.14)
24 × 3.14 = 75.36 cm
Round to nearest tenth:
75.36 ≈ 75.4 cm.
Answer: B
Step-by Step: C=2n
r= 2•n•12= 75.39822
You round it to the nearest tenth, it would be 75.4
find the value of x given the shape
Answer:
x = 5
Step-by-step explanation:
Note: I'm assuming this shape is a trapezoid, so I'm basing a theorem of that fact. Tell me if it's not a trapezoid.
1. Identify the theorem:
There is a theorem you can use for this problem that states that the length of the meadian of a trapezoid is equal to the average of the lengths of the bases of the trapezoid.
So what I mean is:
(Base 1 Length + Base 2 Length)/2 = length of the median of a trapezoid
2. Identify:
Base 1: FC = 6x-6
Base 2: AD = 38
Median: EB = 7x-4
3. Substitute:
(Base 1 Length + Base 2 Length)/2 = length of the median of a trapezoid
(FC + AD)/2 = EB
(6x-6 + 38)/2 = 7x-4
4. Solve for x:
x = 5