Answer:
0% probability that the mean score for the B group will be at least five points higher than the mean score for the A group
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution, the central limit theorem, and subtraction of normal variables:
Normal probability distribution
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.
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.
Subtraction of normal variables:
When we subtract two normal variables, the mean is the subtraction of the mean of each variable, while the standard deviation is the square root of the sum of each variance.
Method A:
One student: N(75,30), so [tex]\mu = 75, \sigma = 30[/tex]
Samples of 100 students: [tex]n = 100, s = \frac{30}{\sqrt{100}} = 0.3[/tex]
Method B:
One student: N(74,40), so [tex]\mu = 74, \sigma = 40[/tex]
Samples of 100 students: [tex]n = 100, s = \frac{40}{\sqrt{100}} = 0.4[/tex]
What is the probability that the mean score for the B group will be at least five points higher than the mean score for the A group?
This is the probability that B - A >= 5. So
[tex]\mu_{B-A} = \mu_B - \mu_A = 74 - 75 = -1[/tex]
[tex]s_{B-A} = \sqrt{s_A^{2}+S_B^{2}} = \sqrt{(0.3)^2+(0.4)^2} = 0.5[/tex]
We have to find 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 - (-1)}{0.5}[/tex]
[tex]Z = 12[/tex]
[tex]Z = 12[/tex] has a pvalue of 1
1 - 1 = 0, so
0% probability that the mean score for the B group will be at least five points higher than the mean score for the A group
What is the Answer pls help
Answer:48ft
Step-by-step explanation:
In the diagram, △RST∼△R′S′T′. Determine the length of RS. Show your work.
100 points!
Answer:
RS = 6 feetStep-by-step explanation:
Use ratios of corresponding sides:
TS/T'S' = RS/R'S'Substitute and solve for x:
9/4 = (12x + 2)/(5x + 1)9(5x + 1) = 4(12x + 2)45x + 9 = 48x + 848x - 45x = 9 - 83x = 1x = 1/3Find the length of RS:
RS = 12x + 2 = 12(1/3) + 2 = 4 + 2 = 6 feetA box contains five slips of paper. These slips are marked $1, $1, $1, $10, and $25. The winner of a contest will select two slips of paper at random with replacement and will then get the larger of the dollar amounts awarded. Define a random variable W
Answer:
Random variable set is attached as image. Please see the image
Step-by-step explanation:
The random variable W consist of all possible set of selection of two reward slips
The set consists of total 20 possible outcomes
The set is given in the image attached
Another word for x-intercepts?
Answer:
X-intercepts are also called zeros, roots, solutions, or solution sets.
Another word for "x-intercepts" is "roots" or "zeros." These terms are commonly used in the context of mathematics, particularly when dealing with functions or equations.
X-intercepts, roots, or zeros of a function are the values of the independent variable (usually denoted as "x") for which the function evaluates to zero.
In other words, they are the points on the graph of the function where it intersects the x-axis, hence the name "x-intercepts."
Mathematically, for a function f(x), the x-intercepts are the solutions to the equation f(x) = 0.
Finding the x-intercepts of a function is essential in graphing, solving equations, and understanding the behavior of the function.
These points represent the locations where the function crosses or touches the x-axis, indicating where the dependent variable (usually denoted as "y") is equal to zero.
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solve for brainliest
9514 1404 393
Answer:
∠W = 130∠X = 140∠Y = 50∠Z = 40Step-by-step explanation:
Using 'y' and 'z' to represent angles with the corresponding names, we have ...
y + z = 90
(3b -1) +(2b +6) = 90 . . . . substitute the given expressions
5b +5 = 90 . . . . . . . . . . . . simplify
b +1 = 18 . . . . . . . . . divide by 5
b = 17 . . . . . . . . subtract 1
Then the angles are ...
y = 3b -1 = 3(17) -1 = 51 -1 = 50
z = 2b +6 = 2(17) +6 = 34 +6 = 40 . . . . note that these are complementary, as theys should be
Angles W and Y form a linear pair, so are supplementary:
W = 180 -Y = 180 -50 = 130
Angles X and Z form a linear pair, so are supplementary:
X = 180 -Z = 180 -40 = 140
Then the angle measures are ...
∠W = 130∠X = 140∠Y = 50∠Z = 40Cups are sold in packages of 8. Napkins are sold in packages of 6. If you want to purchase the fewest number of cups and the fewest number of napkins so there will be the same of each, how many packages of napkins will there be?
Need help! What are the coordinates of point P?
Answer:
the first circle.
Step-by-step explanation:
please mark brainliest of answers correct. have a nice day!
Answer:
A) -4,3
Step-by-step explanation:
Find the value of 2425÷45. Show your reasoning. fractions
Answer:
Step-by-step explanation:
53.8
Help plssssss it’s an emergency
Answer:
All I know is that the -3 should be there without the 1/3 because that makes no sense to me. And...
Step-by-step explanation:
3x+8=-4
Subtract 8 from both sides.
3x+8−8=−4−8
3x=−12
Step 2: Divide both sides by 3.
3x=−12
3 3
x=−4
Answer: Tyler's work is incorrect because when subtracting 8 from both sides of the equation, he didn't subtract it from -4. If he subtracted 8 from -4, it would've been 3x=-12.
The correct answer is x = -4
Step-by-step explanation:
you get x = -4 by subtracting 8 from each side of the equation, resulting in 3x = -12
then you divide both sides by 3, leaving you with x = -4
plz help me on this
hope this sheet helps :)
Answer:
It would bounce at 78 centimeters height
Step-by-step explanation:
Diana pays $33 for 12 gallons of gas. Manny pays $37.10 for 14 gallons of gas. How much less per gallon does Manny pay than
Pls help will mark brainlest
Answer:
15 bags
Step-by-step explanation:
She can fill 5 bags per each pound (because there are 5 [tex]\frac{1}{5}ths[/tex] per pound)
Since there are 3 pounds, and , again, each pound can fill 5 bags, she will need 15 bags.
Another way too look at it is to ask how many 1/5ths are in 3 pounds. To find this answer mathematically:
3 ÷ 1/5 = 15 because when we divide by a fraction, we need to flip it and then multiply (so 3 ÷ 1/5 is actually 3×5)
!!! ASAP! PLEASE ANSWER WILL GIVE A LOt OF POINTS AND MARK BRAINLIEST !!!!!
Answer:
80 minutes
35.2 km
Step-by-step explanation:
You can't give more than the 6 points you have allocated. If I am the only person answering, you have to come back to award the Brainliest -- it varies how much time. Usually 2 or 3 days. Few people do.
The answer to this question depends on you understanding that both girls will be side by side when the second one catches the first. So the distances will be equal
That means that
.44t = 35t + 7.2 Subtract 0.35t from both sides
0.44t - .35t = 7.2
0.09 t = 7.2 Divide
t = 7.2/0.09
t = 80 minutes
How far apart are they from the starting point?
d = 0.44t
d = 0.44 * 80
d = 35.2 km from the starting point.
64
4+4x U
K
36
27
72
T
96
L
Find the value of x.
The value of {x} is equivalent to 7.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given are two triangles ΔJTU and ΔJLK.
The triangles ΔJTU and ΔJLK are similar.
We can write the proportional relation as -
{JU/JK} = {JT/JL}
{- 4 + 4x/64} = {27/72}
{- 4 + 4x/64} = 3/8
- 4 + 4x = 24
4x = 28
x = 7
Therefore, the value of {x} is equivalent to 7.
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The value of x is 7.
What are similar triangles?Two triangles are similar if the angles are the same size or the corresponding sides are in the same ratio. Either of these conditions will prove two triangles are similar.
From the given figure,
Consider ΔJKL and ΔJUT
If T and U are midpoints on JL and JK, then TU is parallel to LK.
Then ∠T=∠L (Corresponding angles)
∠U=∠K (Corresponding angles)
Hence, ΔJKL is similar to ΔJUT
Now, JT/JL = JU/JK = TU/LK
27/72 = -4+4x/64 = 36/96
9/24 = -4+4x/64 = 12/32
3/8 = -4+4x/64 = 3/8
-4+4x/64 = 3/8
-4+4x=24
4x=28
x=7
Therefore, the value of x is 7.
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Jill and a friend are going hiking. They bring with them a container that holds 1/2 of a gallon of water. If they share the water equally what fraction of a gallon will each friend get?
Answer:
¼
Step-by-step explanation:
Solution,
Total quantity=½ gallon
Each friends quantity=½/2
=¼ gallon
Find the value of x.
4
X
25
10
x = [?]
Answer:
Step-by-step explanation:
Answer:
10
Step-by-step explanation:
10/4 x 25/x
Cross multiply and it will give you 100/10x
Divide and get 10
In slope-intercept form, the equation of the line with a slope of 7 and a y-intercept of (0, -8) is ________
. Do not include spaces in your answer.
Answer:
y = 7x - 8
General Formulas and Concepts:
Algebra I
Slope-Intercept Form: y = mx + b
m - slope b - y-interceptStep-by-step explanation:
Step 1: Define
Slope m = 7
y-intercept b = -8
Step 2: Write Function
Substitute in parts.
y = 7x - 8
Find the slope of the line below. Help please!
Answer:
-3/2
Step-by-step explanation:
go up 3 and left 2
Which of the following is equivalent to In 4x+5inx-in2xy
11.45 x 3.7 =
(step by step explanation pls)
What is 33/88 in simplest form?
Answer:
3/8
divide both by 11
you get 3/8
find the equation of the line passing through the point (2, -4) that is parallel to the line y=3x+2
Answer (assuming it can be put in point-slope format):
[tex]y + 4 = 3(x-2)[/tex]
Step-by-step explanation:
You can write an equation of a line when knowing its slope and a line it passes through using point slope formula, [tex]y-y_1 = m (x-x_1)[/tex].
1) First, find the slope of the equation. We know it has to be parallel to y = 3x + 2. Lines that are parallel have the same slope, thus the slope of y = 3x + 2 is the slope of the answer as well. y = 3x + 2 is in slope-intercept format, or [tex]y = mx + b[/tex]. The coefficient of the x term, or [tex]m[/tex], represents the slope - so, the slope must be 3.
2) Now, use point-slope formula,[tex]y-y_1 = m (x-x_1)[/tex], to write the equation. Substitute [tex]m[/tex], [tex]x_1[/tex], and [tex]y_1[/tex] for real values.
The [tex]m[/tex] represents the slope, so substitute 3 for [tex]m[/tex]. The [tex]x_1[/tex] and [tex]y_1[/tex] represent the x and y values of a point the line crosses through. The line crosses through (2, -4), so substitute 2 for [tex]x_1[/tex] and -4 for [tex]y_1[/tex]. This gives the following answer:
[tex]y - (-4) = 3 (x-(2))\\y + 4 = 3(x-2)[/tex]
The lengths of the sides of a right triangle are 10 in., 24 in., and 26 in. What is the area of the triangle?
Answer:
[tex]Solution,\\Let~a=10in.,~b=24in.~and~c=26in.\\Semiperimeter(s) = \frac{a+b+c}{2}= \frac{10+24+26}{2} = 30in.\\Now,\\Area~of~triangle = \sqrt{s(s-a)(s-b)(s-c)} \\~~~~~~~~~~~~~~~~~~~~~~~~=\sqrt{30(30-10)(30-24)(30-26)} \\~~~~~~~~~~~~~~~~~~~~~~~~=\sqrt{30(20)(6)(4)} = \sqrt{14400}=120sq.inches[/tex]
Need help with it today
Answer:
C
Step-by-step explanation:
s - 7 + 5
s - 2
In XYZ right angled at Y. find the length of the hypotenuse if the length of the other two sides is 1.6 cm and 6.3 cm.
9514 1404 393
Answer:
6.5 cm
Step-by-step explanation:
The Pythagorean theorem applies. You want c for a=1.6, b=6.3.
c² = a² +b²
c² = 1.6² +6.3² = 2.56 +36.69 = 42.25
c = √42.25 = 6.5
The length of the hypotenuse is 6.5 cm.
Adrienne has chickens and ducks on her farm. She has 48 chickens and 28 ducks. What ratio describes the number of ducks to the number of chickens?
PLS HELP!! FIND X AND Y
Answer:
x=110
y=70
Step-by-step explanation:
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please help
Professor Ivy’s students have the following scores on her Exam.
61 88 67 88 91 69 45 92 52 38 98
Find the mode value.
Answer:
88
Step-by-step explanation:
The mode is the number that occurs the most in a data set, and 88 is the only number that occurs twice.
For the pair of supply-and-demand equations, where x represents the quantity demanded in units of 1000 and p is the unit price in dollars, find the equilibrium quantity and the equilibrium price.
p = −0.3x + 6 and p = 0.05x + 2.5
equilibrium quantity
units
equilibrium price $
9514 1404 393
Answer:
(x, p) = (10, 3)
Step-by-step explanation:
Equating the expressions for p, we have ...
-0.3x +6 = 0.05x +2.5
3.5 = 0.35x . . . . . add 0.3x-2.5
10 = x . . . . . . . . . . divide by 0.35
p = -0.3(10) +6 = 3
The equilibrium quantity is 10 units.
The equilibrium price is $3.
Evaluate !! look at photo please i need help
Answer:
[tex]Sum = 832[/tex]
Step-by-step explanation:
Given
See attachment
Required
Evaluate
The expression can be expressed as:
[tex]Sum = 2n + 5;\ n=1...26[/tex]
To do this, we make use of sum of n terms of an AP.
When n = 1
[tex]2n + 5 = 2 * 1 + 5 = 7[/tex] --- T1
When n = 2
[tex]2n + 5 = 2 * 2 + 5 = 9[/tex] --- T2
When n - 26
[tex]2n + 5 = 2 * 26 + 5 = 57[/tex] --- T26
Next, we calculate d (common difference)
[tex]d = T_2 - T_1[/tex]
[tex]d = 9 - 7 = 2[/tex]
So, the sum is:
[tex]Sum = \frac{n}{2}(T_1 + T_n)[/tex]
Let n = 26
So, we have:
[tex]Sum = \frac{26}{2}(T_1 + T_{26})[/tex]
Substitute values for T1 and T26
[tex]Sum = \frac{26}{2}(7+57)[/tex]
[tex]Sum = \frac{26}{2}(64)[/tex]
[tex]Sum = 13*64[/tex]
[tex]Sum = 832[/tex]