Answer:
Answer is 5
Step-by-step explanation:
x+2x+3x=30
6x=30
x=5
Suppose that the distribution of IQ's of North Catalina State University's students can be approximated by a normal model with mean 130 and standard deviation 8 points. Also suppose that the distribution of IQ's of Chapel Mountain University's students can be approximated by a normal model with mean 120 and standard deviation 10 points.
Required:
What is the probability that the mean IQ of the 3 North Catalina students is at least 5 points higher than the mean IQ of the 3 Chapel Mountain students?
Answer:
0.7517 = 75.17% probability that the mean IQ of the 3 North Catalina students is at least 5 points higher than the mean IQ of the 3 Chapel Mountain students
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Subtraction of normal variables:
When we subtract normal variables, the mean is the subtraction of the means, while the standard deviation is the square root of the sum of the variances.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
North Catalina:
Population has mean 130 and standard deviation 8 points. Sample of 3. This means that:
[tex]\mu_{N} = 130, s_{N} = \frac{8}{\sqrt{3}} = 4.6188[/tex]
Chapel Mountain:
Population has mean 120 and standard deviation 10 points. Sample of 3. This means that:
[tex]\mu_{C} = 120, s_{C} = \frac{10}{\sqrt{3}} = 5.7735[/tex]
What is the probability that the mean IQ of the 3 North Catalina students is at least 5 points higher than the mean IQ of the 3 Chapel Mountain students?
We want that: [tex]N - C > 5[/tex]
Distribution N - C:
The mean is:
[tex]\mu = \mu_N - \mu_C = 130 - 120 = 10[/tex]
The standard deviation is:
[tex]s = \sqrt{s_N^2+s_C^2} = \sqrt{4.6188^2+5.7735^2} = 7.3937[/tex]
This probability is 1 subtracted by the pvalue of Z when X = 5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{5 - 10}{7.3937}[/tex]
[tex]Z = -0.68[/tex]
[tex]Z = -0.68[/tex] has a pvalue of 0.2483
1 - 0.2483 = 0.7517
0.7517 = 75.17% probability that the mean IQ of the 3 North Catalina students is at least 5 points higher than the mean IQ of the 3 Chapel Mountain students
Which equation describes the line with the slope 2/3 that passes through the given point on the graph?
Answer: y=2/3x-2
Step-by-step explanation:
Slope intercept form is: y=mx+b
m=slope
b= y-intercept
slope is 2/3
Ella ran 6 times around her school building. Then she ran 4 miles home.
Her phone told her that she ran 7 miles total.
Select an equation that represents this situation
A. 6+4x=7 B. 6x+4=7 C. 6 (x+4) =7
Determine the value of x.
Answer:
B.6x+4=7
Step-by-step explanation:
x represents how many miles is around her school building which she did 6 times, 4 miles is for the amount she ran home and 7 miles is the combination of the 6 times the miles around her school, 6x and the miles she ran home 4
making the equation 6x+4=7
Please help me with my hw thank you so much
Answer: d
Step-by-step explanation:
Please help due soon.
Helping to give out points!! Whoever solves the math riddle correctly with a brief explanation will get brainliest and a thanks (the other answers will just get a thanks).
Riddle: I have a big family. I am 16 years old. My sister Reina is 22 years old. The twins are 14 years old. Susana is 10 years old and my brother Robert is 7 years old. If the total number of our ages added together is 100, how old is Albert?
Answer:
Robbert is 7
Step-by-step explanation:
because you already said it
Four teams will receive prize money based on their ticket sales. The total prize amount to be apportioned is $63. Determine the standard divisor based on the ticket sales. The ticket sales are: Applejacks: 66 tickets sold Broncos: 769 tickets sold Colts: 652 tickets sold Deers: 556 tickets sold Calculate the standard divisor to two decimal places.
Answer:
32.43
Step-by-step explanation:
To get the standard divisor
We sum up the tickets sold
Applejack's = 66 tickets
Broncos = 769 tickets
Colts = 652 tickets
Deers = 556 tickets
The total prize amount = $63
Total tickets = 66 + 769 + 652 + 556 = 2043
Standard divisor = 2043/63
= 32.43
The standard divisor to two decimal places is 32.43
Can someone please help me with these 2 problems
Answer:
uhururfjfhfufjfjfjfjfjfif
Answer:
I believe the first one is 250
the second one I haven't got a clue
How many solutions does the equation 6a − 3a − 6 = −2 + 3 have?
Two
None
One
Infinitely many
Answer: There is only one solution
6a - 3a - 6 = -2 + 3
3a - 6 = 1
3a = 7
is 29.6 = 29.600 true or false???
Answer:
true
Step-by-step explanation:
this is the decimal helps shorten up 29.600
Given the geometric sequence tn with t1=96 and r=−1/4, find t4.
Give your answer as a fraction, if necessary. Do not include "t4=" in your answer. For example, if you found t4=9, you would enter 9.
Answer:
3/2
Step-by-step explanation:
Given
[tex]t_1 = 96[/tex]
[tex]r = \frac{1}{4}[/tex]
Required
Find t4
The nth term of a geometric sequence is calculated as:
[tex]t_n = t_1 * r^{n-1[/tex]
So:
[tex]t_4 = t_1 * r^{4-1[/tex]
[tex]t_4 = t_1 * r^3[/tex]
This gives:
[tex]t_4 = 96 * \frac{1}{4}^3[/tex]
[tex]t_4 = 96 * \frac{1}{64}[/tex]
Express as a single fraction
[tex]t_4 = \frac{96}{64}[/tex]
[tex]t_4 = \frac{3}{2}[/tex]
Hence, the 4th term is 3/2
Bryce grew
33 inches each year for the past 4 years. How many inches total has Bryce grown in the
past 4 years ?
Answer:
132 inches
Step-by-step explanation:
33 x 4 = 132 inches
This Question: 1 pt
17 of 29
Emma has $160 cash to spend at a music store. How much can she spend on items if there is a 7% sales tax?
Emma can spend on items.
(Round to the nearest cent as needed.)
Answer:
i would say $148.80
Step-by-step explanation:
tax would amount to 11.20 so when you subyract that from the total then the rest is what she can spend.
Find the next number in the pattern.
4, 6, 11, 19, 30, ______
Answer: 44
Step-by-step explanation:
help? :’) on math:
Which equation would you use to solve the following situation?
If everybody on the team scores 6 points, and the team has a total of 42 points, how many people are on the team?
1. 6 p = 42
2. 7 p = 42
3. 6 + p = 42
or 4. 42 - p = 6
what number ??
Answer:
yeppy the answer should be 1. 6p=42 :)
Whichever answer is correct will get brainliest!
Find the value of x. Round to the nearest tenth. 35 12. х x = [?] Enter
Answer:
Round to the nearest tenth. 35 12. х x = [?] Enter
Step-by-step explanation:
The Hiking Club is taking another trip. The hike leader's watch shows that they gained 296 feet in altitude from their starting position.
Their altitude is now 285 feet, but there is no record of their starting altitude.
Write and solve an equation to represent this situation and find their starting altitude.
Answer:
Step-by-step explanation:
The required equation is x+295=285 , where x= starting altitude( in feet).
The starting altitude is -11 feet.
Let x be the starting altitude( in feet) .
Given: The Hiking Club is taking another trip. The hike leader's watch shows that they gained 296 feet in altitude from their starting position.
Then, the altitude is now = x+ 296
Since their altitude is now 285 feet.
So the required equation is x+296=285
Subtract 296 from both sides, we get
x= -11
divide 4 questions
Answer:
huh
Step-by-step explanation:
Helpp with math!!!!!!!!
I think the area is 63. Sorry if it is incorrect.
Can someone help me
Answer:
sorry sorry sorry
Step-by-step explanation:
I don't know
Please help me! I need help finding this slope.
Answer:
4/-9
Step-by-step explanation:
There are 20 pieces of fruit in a basket and 12 of them are oranges. What percentage of the pieces of fruit in the basket are oranges? Show your work in the box and circle your answer
Answer:60 percent
Step-by-step explanation: You have fraction the two numbers which will be 12/20 them you times it by 100 which equals 60 oranges.
Use the Distributive Property to
REWRITE 2/3(x - 9)
Answer:
2/3x-6
Step-by-step explanation:
a shark is located 45 feet directly below a swimmer on the surface of the water. the angle of depression from a boat nearby to the shark is 64 degrees. how far is the swimmer from the boat
Using the slope concept, it is found that the swimmer is 21.95 feet from the boat.
What is a slope?The slope is given by the vertical change divided by the horizontal change.It's also the tangent of the angle of depression.In this problem:
A shark is located 45 feet directly below a swimmer on the surface of the water, hence the vertical change is 45.The distance d is the horizontal change, which we want to find.The angle is of 64º.Hence:
[tex]\tan{64^{\circ}} = \frac{45}{d}[/tex]
[tex]d = \frac{45}{\tan{64^{\circ}}}[/tex]
[tex]d = 21.95[/tex]
The swimmer is 21.95 feet from the boat.
You can learn more about the slope concept at https://brainly.com/question/26342863
What is the slope of a line perpendicular to the line whose equation is x+3y=-12
Answer: 3
Step-by-step explanation:
Find slope of that line which is -1/3x-4
then flip its sign and the equation to get 3
What percent 39 is 26
Answer: 66.67
Step-by-step explanation:
kaylee Bryant purchased taz software that regularly sells for 74.95 but is on sale for 59.95
Answer:
well that is 15$$ off
Step-by-step explanation:
Which of the equations below could be the equation of this parabola?
(0,0)
Vertex
A. y = 1/4x²
B. x = 1/4y²
C. y = -1/4x²
D. x= -1/4y²
Answer:
B. x = 1/4y²
Step-by-step explanation:
The equation of a parabola is x = 1/4y². Therefore, option B is the correct answer.
What is the parabola?A parabola refers to an equation of a curve, such that a point on the curve is equidistant from a fixed point, and a fixed line. The fixed point is called the focus of the parabola, and the fixed line is called the directrix of the parabola.
From the graph,
x-intercept(s): (0,0)
y-intercept(s): (0,0)
Vertex is (0, 0)
Directrix, x=-1
Here, the axis of symmetry is y=0
So, the equation is x = 1/4y²
Therefore, option B is the correct answer.
To learn more about the parabola visit:
https://brainly.com/question/21685473.
#SPJ7
Find the greatest common factor of 28 and 35
Answer:
7
Step-by-step explanation:
Factors for 28: 1, 2, 4, 7, 14, and 28
Factors for 35: 1, 5, 7, and 35
A rectangular piece of metal is 30 in longer than it is wide. Squares with sides 6 in long are cut from the four corners and the flaps are folded upward to form an open
box. If the volume of the box is 1050 in3, what were the original dimensions of the piece of metal?
What is the original width? in
What is the original length in
breadth= X
L= x+30
after you cut a square with 6in from the corners, the length becomes x+30-6 =x+24 and breadth becomes x-6.
The eqn for volume of box is Length x Breadth x height
it's given that LxBxH = 1050
here height is 6, because u are folding the edge where it's been cut off and that side becomes the height.
rewrite with the given information we get
(x+24)*(x-6)*6 = 1050
divide both sides with 6
(x+25)*(x-6) = 175
distribute the brackets we get,
x^2 -18x -144 =175
x^2 -18x-319 = 0
solve for x using quadratic formula.
we get x= 29, -11
since length cannot be negative x= 29
B= 29, L=59.