(C) You're given a probability mass function,
[tex]P(X=x)=\begin{cases}\frac17&\text{if }x\in\{1,6,16\}\\\frac27&\text{if }x\in\{11,21\}\\0&\text{otherwise}\end{cases}[/tex]
The mean is
[tex]\displaystyle E[X] = \sum_x x\,P(X=x) = \frac{1\times1}7 + \frac{1\times6}7 + \frac{1\times16}7 + \frac{2\times11}7 + \frac{2\times21}7 = \boxed{\frac{87}7} \approx 12.43[/tex]
The variance is
[tex]\displaystyle V[X] = \sum_x x^2\,P(X=x) = \frac{1^2}7 + \frac{6^2}7 + \frac{16^2}7 + \frac{2\times11^2}7 + \frac{2\times21^2}7 = \boxed{\frac{1417}7} \approx 202.43[/tex]
The standard deviation is simply the square root of the variance:
[tex]\sqrt{V[X]} = \boxed{\sqrt{\dfrac{1417}7}} \approx 14.23[/tex]
(D) I'm not entirely sure what is being asked here, so I'm kinda guessing at the meaning. I think the question is saying there is a large set of 5000 test scores that are normally distributed with mean µ = 86 and standard deviation σ = 10.
Let X be the random variable representing these test scores. Then
(D.A)
[tex]P(96 < X < 106) = P\left(\dfrac{96-86}{10} < \dfrac{X-86}{10} < \dfrac{106-86}{10}\right) = P(1 < Z < 2)[/tex]
where Z follows the standard normal distribution with mean 0 and variance 1.
To find the remaining probability, you can use the empirical rule (68/95/99.7) which says
• approximately 68% of a normal distribution lies within 1 standard deviation of the mean; in other words, [tex]P(-1<Z<1)\approx0.68[/tex]
• approximately 95% of the distribution lies within 2 standard deviations; [tex]P(-2<Z<2)\approx0.95[/tex]
The normal distribution is also symmetric about its mean. Taking these facts together, we find
[tex]P(1<Z<2) = \dfrac{P((-2<Z<-1)\text{ or }(1<Z<2))}2 = \dfrac{P(-2<Z<2)-P(-1<Z<1)}2 \approx 0.135[/tex]
So roughly 13.5% of all test scores will fall between 96 and 106, and 13.5% of 5000 is 675. (The actual probability is closer 0.135905, and the projected test score count is closer to 679.)
(D.B) Any 50% of the distribution is still 50% of the distribution, so half of all the test scores would fall in this range. There would be 2500 test scores in that group.
(E) No choices given here...
Due to yet another road construction project in her city, Sarah must take a detour to get from work to her house. Not convinced the detour is the shortest route, Sarah decided to perform an experiment. On each trip, she flips a coin to decide which way to go; if the coin flip is heads, she takes the detour and if it's tails, she takes her alternative route. For each trip, she records the time it takes to drive from work to her house in minutes. She repeats this procedure 13 times. Sarah wants to know if the mean driving time for the alternative route is different from the mean driving time for the detour. Based on the p-value there was moderate evidence against the null hypothesis.
Select the appropriate statement for this hypothesis test.
a. There is little to no evidence to conclude the mean driving time for the alternative route is the same as the mean driving time of the detour.
b. There is little to no evidence to conclude the mean driving time for the alternative route is different from the mean driving time of the detour.
c. There is moderate evidence to conclude the mean driving time for the alternative route is the same as the mean driving time of the detour.
d. There is moderate evidence to conclude the mean driving time for the alternative route is different from the mean driving time of the detour.
Answer:
b). There is little to no evidence to conclude the mean driving time for the alternative route is different from the mean driving time of the detour.
Step-by-step explanation:
The most adequate statement to examine the proposition is that 'there is lack of adequate evidence to substantiate the claim that the mean time taken for driving through the detour and the alternative route is distinct.' This will help in testing that there is a lack of evidence to establish the validity or truth of the proposition that if the detour is actually shorter than the alternative route or not. No data has been provided to clarify that the mean driving time in both routes traveled by Sarah was varied. Hence, option b is the correct answer.
A kite is a quadrilateral with two pairs of adjacent, congruent sides. The vertex angles are those angles in between the pairs of congruent sides. Prove the diagonal connecting these vertex angles is perpendicular to the diagonal connecting the non-vertex angles. Be sure to create and name the appropriate geometric figures. This figure does not need to be submitted.
A line has a slope of -5 and
passes through the point
(0, -7). What is its equation in
slope-intercept form?
Write your answer using integers,
proper fractions, and improper
fractions in simplest form.
Diane bought new headphones originally listed for $70.99. They are 25% off. Which equation can be used to find the amount Diane will save?
Step-by-step explanation:
100% = $70.99
there is a discount of 25%.
that means 75% (100 - 25) of the original price remains.
the equation to get any x% amount of a 100% total is simply
x% amount = 100% total amount × x/100
25% = 70.99 × 25/100 = $17.75
Suppose y varies directly as the cube of x, and y = 24 when x = 2. Find y when x = 4.
Answer:
so y = 48 when x = 4
Step-by-step explanation:
if y = 24, x = 2
or, if x = 2, y = 24
so, if x = 1, y = 24/2
so, if x =1, y = 12
then if x = 4, y = 12×4 = 48
The required simplified value of the y at x = 4 is given as y = 192.
Given that,
y varies directly as the cube of x, and y = 24 when x = 2.
To determine y at x = 4.
Proportionality is defined as between two or more sets of values, and how these values are related to each other in the sense are they directly proportional or inversely proportional to each other.
here,
According to the question,
y ∝ x³
From the above property,
y₁/y₂ = [x₁ / x₂]³
Substitute the value in the equation,
24/y₂ = [2/4]³
y₂ = 64/8 × 24
y₂ = 192
Thus, the required simplified value of the y at x = 4 is given as y = 192.
Learn more about proportionality here: https://brainly.com/question/22620356
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A rectangular dance floor has a width of 12 meters and a length of 16 meters. What is the length of a diagonal of the dance floor? moters
Answer:
20
Step-by-step explanation:
The diagonal of a rectangle can be found using the formula:
[tex]\sqrt{(l^2 + w^2)}[/tex]
Find x please step by step explanation need it
Answer:
37.3
Step-by-step explanation:
19tan(63) = x = 37.289... = 37.3
Do 8 plz find OS thanks
Answer:
OS = 10
Step-by-step explanation:
We can use a ratio to solve
QP PR
----- = ------
QO OS
14 7
----- = -------
14+6 OS
14 7
----- = -------
20 OS
Using cross products
14 * OS = 7*20
14 OS = 140
Divide by 14
OS = 140/14
OS = 10
What are the x-intercepts of this quadratic function?
g(x) = -2(x - 4)(x + 1)
Answer:
4 and -1
Step-by-step explanation:
A quadratic function is given to us and we need to find the x Intercepts of the given function . The function is ,
[tex]\bf \implies g(x) = -2( x -4)(x+1)[/tex]
Step 1 : Equate the function with 0,
[tex]\bf \implies -2( x -4)(x+1) = 0 [/tex]
Step 2: Equating with 0 :-
Now equate each factors seperately with 0 , to get the x Intercepts.
Step 3: Finding the intercepts :-
[tex]\bf \implies x - 4 = 0 \\\\\implies\boxed{\bf\blue{ x = 4 }} [/tex]
Again ,
[tex]\bf \implies x + 1 = 0 \\\\\implies\boxed{ \blue{\bf x = -1}} [/tex]
Hence the x intercepts are 4 and -1 .
Answer:D (4,0) and (-1,0)
Step-by-step explanation:
a notebook and a pen together cost 11$. if the notebook costs 10 more than the pen, how much does the pen cost
Answer:
$1
Step-by-step explanation:
I assume by 10, you mean 10 dollars so you do $11 - $10 to get your answer of $1. The pen costs $1.
Hope it helps c:
The pen and the notebook together cost 11 dollars and the pen itself cost 0.5 dollars.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Given, A notebook and a pen together cost 11$.
The notebook costs 10 more than the pen.
Assuming the pen costs x dollars then the notebooks costs (x + 10) dollars.
∴ x + x + 10 = 11.
2x = 1.
x = 1/2.
So, the cost of the pen is 0.5 dollars and the cost of the notebook is 10.5 dollars.
learn more about numerical expressions here :
https://brainly.com/question/29199574
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3/4 divided by 1/2
multiple choices
2/3
1 1/4
1 1/2
3
please hurry and choose between those
Answer:
Step-by-step explanation:
how to work this problem 736.5 x .78
14 ft
3 ft
6 ft
O 873#
1313
252ft
0 262
52.31
Answer:
262.5
Step-by-step explanation:
V = l x b x h
=14x25/4x3
=262.5
Find the total surface area of this pentagon
Answer:
Step-by-step explanation:
2(lb+bh+hl) is the formula for surface area. So,
2(54+81+54) = 2(189) which is 378.
I think the surface area is 378 square inches, or 378 in^2
Will give brainliest answer
Answer:
Step-by-step explanation:
Help plzzz 60 points
Answer:
Neither lines r and s nor lines t and u must be parallel from the information given
Step-by-step explanation:
<2 and <4 are vertical angles so they are always equal
<5 and <7 are vertical angles so they are always equal
We are not given any information to tell if any of the lines are parallel
Neither lines r and s nor lines t and u must be parallel from the information given
I made a comment about this but I mean, free 30 points.
I think the answer is the last one. It only mentions <2 = <4 and <5 = <7. Nowhere does it say <2 =< 5 for example. So it can be any two lines of which don't have to be parallel to each other.
Please help
Add the following polynomials, then you place the answer in the proper location on the grid. Write your answer in descending powers of x
Answer:
5x³ - 4x + 1
Step-by-step explanation:
1.) 2x³ + 3x³ = 5x³
2.) 4x - 8x = -4x
3.) -6 + 7 = 1
4.) Line them up: 5x³ - 4x + 1
The radius of a circular disk is given as 26 cm with a maximum error in measurement of 0.2 cm. (a) Use differentials to estimate the maximum error in the calculated area of the disk. (Round your answer to two decimal places.) cm2 (b) What is the relative error
Answer:
(a) Hence the maximum error in the calculated area of the disk is 32.67[tex]cm^{2}[/tex].
(b) Hence the relative error is 1.54%.
Step-by-step explanation:
Here the given are,
The Radius of the circle r = 26cm.
The maximum error in measurement dr = 0.2 cm.
Answer:
(a) [tex]A =(4245.28\pm32.66) cm^2[/tex]
(b) [tex]\frac{dA}{A}=\frac{32.66}{4245.28}=0.0077[/tex]
Step-by-step explanation:
radius, r = 26 cm
error = 0.2 cm
(a) The area of the disc is given by
[tex]A = \pi r^2\\\\dA = 2\pi r dr\\\\dA = 2 \times 3.14\times 26\times 0.2= 32.66[/tex]
Now
A = 3.14 x r x r = 3.14 x 26 x 26 = 4245.28 cm^2
So, the area with error is given by
[tex]A =(4245.28\pm32.66) cm^2[/tex]
(b) The relative error is
[tex]\frac{dA}{A}=\frac{32.66}{4245.28}=0.0077[/tex]
Find the measure of the indicated angle to the nearest degree.
A. 46
B. 76
C. 44
D. 14
Answer:
Answer is B. 76.
Step-by-step explanation:
Let thw unknow angle be y
sin y = p/h
sin y = 32/33
y = sin‐¹(32/33)
y = 75.85888977
so y = 75.9 = 76
there are 10 crates of eggs stacked in the corner. each crate of eggs holds 20 eggs. If there is only 1 broken egg in the entire stack of crates, what percent of the crates have broken eggs in them?
Answer: 5%
Step-by-step explanation: If there is one broken egg in each crate (1/20), you would change that to5%
And if there are ten crates, then you see how many eggs there a re total.
(10 × 20 = 200)
If there are 200 eggs and for every 20 eggs there is on broken one, then there will be 10 broken eggs total. or 10/200
convert the fraction to a decimal ( 10 ÷ 200 = .05)
then convert the decimal to a percent. .05 is equal to 5%
PLEAZE RATE BRAINLIEST!!!
Someone please help me with this question
Step-by-step explanation:
cos=ROQ
Sin=QOP
HOPE THIS HELP
Now suppose that not every player can play in every position. The outfielders (left field, center field, right field) can play any outfield position, the infielders (1st base, 2nd base, 3rd base, short stop) can play any infield position, the pitchers can only pitch, and the catchers can only catch. Suppose a certain team has 20 players, of whom 3 are catchers, 4 are outfielders, 6 are infielders, and 7 are pitchers.
How many ways can the team assign field positions to 9 of the 19 players, putting each of the 9 selected players in a position he can play, and ensuring that all 9 field positions are filled?
Answer:
The team can assign field positions to 9 of the 19 players in 181,440 different ways.
Step-by-step explanation:
Since the outfielders (left field, center field, right field) can play any outfield position, the infielders (1st base, 2nd base, 3rd base, short stop) can play any infield position, the pitchers can only pitch, and the catchers can only catch, supposing a certain team has 20 players, of whom 3 are catchers, 4 are outfielders, 6 are infielders, and 7 are pitchers, to determine how many ways can the team assign field positions to 9 of the 19 players, putting each of the 9 selected players in a position he can play, and ensuring that all 9 field positions are filled, the following calculation must be performed:
3 x 7 x 6 x 5 x 4 x 3 x 4 x 3 x 2 = X
21 x 30 x 12 x 24 = X
630 x 12 x 24 = X
181,440 = X
Therefore, the team can assign field positions to 9 of the 19 players in 181,440 different ways.
Help please :c
What is the probability that a randomly selected student from your group is a 9th grader?
What is the probability that a randomly selected student from your group prefers comedy?
What is the probability that a randomly selected student does not prefer action?
What is the probability that a student prefers comedy, given that the student is in the 10th grade?
What is the probability that a student does not prefer action, given that the student is in 9th grade?
Answer:
1/4
3/8
5/8
2/5
Step-by-step explanation:
From the table :
1.)
P(9th grade) = (9th grade total / total) = 4 / 16 = 1/4
2.)
P(comedy) = (comedy total / total) = 6 / 16 = 3/8
3.)
P(not action) = 1 - P(action) = 1 - (action total / total) = (1 - 6/16) = 1 - 3/8 = 5/8
4.)
P(comefy | 10th grade) = P(comedy n 10th grade) / P(10th grade) = 2 / 5
Answer:
The answer is 12
Step-by-step explanation:
A student writes
2
pages of a report in
2
an hour. What is her unit
rate in pages per hour?
Answer:
1 page of a report per hour
Step-by-step explanation:
2/2= 1 page per hour
Lets find unit rate
[tex]\\ \sf\longmapsto \dfrac{2\dfrac{1}{2}}{2}[/tex]
[tex]\\ \sf\longmapsto \dfrac{5}{2}\div 2[/tex]
[tex]\\ \sf\longmapsto \dfrac{5}{4}[/tex]
[tex]\\ \sf\longmapsto 1.2pages/hour[/tex]
Write 20*19*18*17*16*15 in the form nPr.
Answer:
15*16*17*18*19*20 I thank it is your answer
PLEASE HELP ME AND BE CORRECT BEFORE ANSWERING
TELL ME WHERE TO PUT EACH POINT
Plz help me find sides M and N round to the nearest tenth
Answer:
44
Step-by-step explanation:
gradpoint
In a class there are 400 students. 250 of them studying Mathematics, 150 of them studying English, 100 of them studying Biology, 100 of them studying both Mathematics and English, 60 of them studying both Mathematics and Biology, 40 of them studying both English and Biology, 30 of them studying all Mathematics, English and Biology. Find
a) The number of students who are studying only Mathematics.
b) The number of students who are studying only English.
c) The number of students who are studying only Biology.
d) The number of students who are studying none of Mathematics, English and Biology.
I hope this helps and sorry if it's wrong
If angle ACB is congruent, and angle BAC=3x-10, angle ECD=45 and angle EDC=2x+10 what is x?
Answer:
x=20
Step-by-step explanation:
Since BAC and EDC are the same (ACB and DCE are congruent), 2x+10=3x-10, x=20
What is the vertex of the graph of y = 2(x + 5)2 - 2?
Answer:
The vertex is (-5, -2)
Step-by-step explanation:
y = 2(x + 5)^2 - 2
The vertex form of a parabola is
y =a(x-h)^2 +k where (h,k) is the vertex
y = 2(x - -5)^2 - 2
The vertex is (-5, -2)
