Answer:
c.is the average value for the random variable over many repeats of the experiment.
Step-by-step explanation:
Expected value of a discrete random variable:
To find the expected value of a discrete random variable, we multiply each outcome of the variable by it's probability, which over many repeats of the experiment, will give the average value, and thus, the correct answer is given by option c.
Even though a discrete random variable takes only discrete values, the mean can be a continuous(decimal) value.
What is the value of cot ø= 2/3 what is the value of csc ø
Answer:
Step-by-step explanation:
cotθ = cosθ/sinθ = 2/3
sinθ = 3/√(2²+3²) = 3/√13
cscθ = 1/sinθ = √13/3
A survey of 77 teenagers finds that 30 have 5 or more servings of soft drinks a week. a. Give a 90% confidence interval for the proportion of teenagers who have 5 or more servings of soft drinks a week. b. In the general population, 30% have 5 or more servings of soft drinks a week. Is there evidence that a higher proportion of teenagers have 5 or more servings of soft drinks a week than the general population
Answer:
a) The 90% confidence interval for the proportion of teenagers who have 5 or more servings of soft drinks a week is (0.2982, 0.481).
b) 30% = 0.3 is part of the confidence interval, which means that there is no evidence that a higher proportion of teenagers have 5 or more servings of soft drinks a week than the general population.
Step-by-step explanation:
Question a:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
A survey of 77 teenagers finds that 30 have 5 or more servings of soft drinks a week.
This means that [tex]n = 77, \pi = \frac{30}{77} = 0.3896[/tex]
90% confidence level
So [tex]\alpha = 0.1[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.3896 - 1.645\sqrt{\frac{0.3896*0.6104}{77}} = 0.2982[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.3896 + 1.645\sqrt{\frac{0.3896*0.6104}{77}} = 0.481[/tex]
The 90% confidence interval for the proportion of teenagers who have 5 or more servings of soft drinks a week is (0.2982, 0.481).
Question b:
30% = 0.3 is part of the confidence interval, which means that there is no evidence that a higher proportion of teenagers have 5 or more servings of soft drinks a week than the general population.
Any help would be very appreciated
Answer:
21
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan theta = opp/ adj
tan 60 = x / 7 sqrt(3)
7 sqrt(3) tan 60 = x
7 sqrt(3) sqrt(3) = x
7*3 = x
21 = x
CAN SOMEONE PLEASE HELP??????
Maintaining your balance may get harder as you grow older. A study was conducted to see how steady the elderly is on their feet. They had the subjects stand on a force platform and have them react to a noise. The force platform then measured how much they swayed forward and backward, and the data is in table #7.3.10 ("Maintaining balance while," 2013). Do the data show that the elderly sway more than the mean forward sway of younger people, which is 18.125 mm? Test at the 5% level.
Table #7.3.10: Forward/backward Sway (in mm) of Elderly Subjects
19
30
20
19
29
25
21
24
50
Answer:
Reject H0 and conclude that adults sway more than the mean forward sway for younger people.
Step-by-step explanation:
H0 : μ = 18.125
H0 : μ > 18.125
Sample data: 19 30 20 19 29 25 21 24 50
Sample size, n = 9
Sample mean, xbar = Σx / n = 237 / 9 = 26.333
Sample standard deviation, s = 9.772 (calculator)
The test statistic :
(xbar - μ) ÷ (s/√(n))
T = (26.333 - 18.125) ÷ (9.772/√(9))
T = 8.208 / 3.2573333
T = 2.519 = 2.520
Decison :
Reject H0 ; If Pvalue < α
The Pvalue :
Degree of freedom, df = n - 1 ; df = 9 - 1 = 8
Pvalue(2.520; 8) = 0.0179
Since 0.0179 < 0.05 ; WE reject H0 and conclude that adults sway more than the mean forward sway for younger people.
help with num 4 please.
Answer:
y=1/2(x-1)
Step-by-step explanation:
If x=t^2 and t>0, then t=sqrt(x).
If t=sqrt(x) or x^(1/2) and y =1-1/t, then y=1-x^(-1/2).
The x-intercept is when y=0.
So we need to solve 0=1-x^(-1/2) to find point P.
Add x^(-1/2) on both sides: x^(-1/2)=1.
Raise both sides to -2 power: x=1
So point P is (1,0).
Let's find tangent line at point (1,0).
We will need the slope so let's differentiate.
y'=0+1/2x^(-3/2)
y'=1/(2x^(3/2))
The slope at x=1 is y'=1/(2[1]^(3/2))=1/(2×1)=1/2.
Recall point-slope form is y-y1=m(x-x1).
So our line we are looking for is y-0=1/2(x-1)
Let's simplify left hand side y=1/2(x-1)
The function above models hhh, the height of a flower pot in meters, ttt seconds after it falls from a fourth floor balcony. What is the height of the flower pot, in meters, 333 seconds after it falls
Answer:
See explanation
Step-by-step explanation:
The question is incomplete, as the function is not given.
However, I will give a general rule.
From the question, we understand that the question requires the value of h(3)
Assume:
[tex]h(t) = 20 - 4t[/tex]
Then:
[tex]h(3) = 20 - 4*3[/tex]
[tex]h(3) = 20 - 12[/tex]
[tex]h(3) = 8[/tex]
A tank has the shape of an inverted circular cone with height 8 m andbase radius 2 m. It is filled with water to the top. Find the integralfor the work required to empty the tank by pumping all of the waterto the top of the tank. DoNOTcompute the integral. (The densityis 1000 kg/m3.)
Answer:
Step-by-step explanation:
I'll try to make this make as much sense as possible. If we have a cone with a liquid in it, this liquid takes up volume. Therefore, our main equation, at least at first, is to find the volume. This is because if we pump the liquid out of the tank, the thing that changes is the amount of liquid in the tank which is the tank's volume. The formula for the volume of a circular cone is
[tex]V=\frac{1}{3}\pi r^2h[/tex] and here's what we know:
r = 2 and h = 8. The formula for volume has too many unknowns in it, so let's get the radius in terms of the height and sub that in so we only have one variable. The reason I'm getting rid of the radius is because in the problem we are being asked how much work is done by pumping the liquid to the top of the tank, which is a height thing. Solve for r in terms of h using proportions:
[tex]\frac{r}{2}=\frac{h}{8}[/tex] and solve for r:
[tex]r=\frac{2}{8}h =\frac{1}{4}h[/tex] so we will plug that in and rewrite the equation:
[tex]V=\frac{1}{3}\pi(\frac{1}{4}h)^2h[/tex] and simplify it til it's a simple as it can get.
[tex]V=\frac{1}{3}\pi(\frac{1}{16}h^2)h[/tex] and
[tex]V=\frac{\pi}{48}h^3[/tex] and since the volume is what is changing as we pump liquid out, we find the derivative of this equation.
[tex]\frac{dV}{dt}=\frac{\pi}{48}*3h^2\frac{dh}{dt}[/tex] and of course this simplifies as well:
[tex]\frac{dV}{dt}=\frac{\pi}{16}h^2\frac{dh}{dt}[/tex]
Work is equal to the amount of force it takes to move something times the distance it moves. In order to find the force it takes to move this liquid, we need to multiply the amount (volume) of liquid times the weight of it, given as 1000 kg/m³:
F = [tex]1000(\frac{\pi}{16}h^2\frac{dh}{dt})[/tex] and the distance it moves is 8 - h since the liquid has to move the whole height of the tank in order to move to the top of the 8-foot tank. That makes the whole integral become:
[tex]W=\int\limits^8_0 {1000(\frac{\pi}{16}h^2(8-h)) } \, dh[/tex] and we'll just simplify it down all the way:
[tex]W=62.5\pi\int\limits^8_0 {8h^2-h^3} \, dh[/tex] and you're done (except for solving it, which is actually the EASY part!!)
Which equation could represent a linear combination of the systems?
9514 1404 393
Answer:
(b) 0 = -78
Step-by-step explanation:
Subtracting 6 times the first equation from the second will give ...
(4x +15y) -6(2/3x +5/2y) = (12) -6(15)
0 = -78
Answer:
the answer is b
Step-by-step explanation:
The mean examination mark of a random sample of 1390 students is 67% with a standard deviation of 8.1%.
How many students scored above 80%? (Round to the nearest student)
Answer:
76 students scored above 80%.
Step-by-step explanation:
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.
The mean examination mark of a random sample of 1390 students is 67% with a standard deviation of 8.1%.
This means that [tex]\mu = 67, \sigma = 8.1[/tex]
Proportion above 80:
1 subtracted by the p-value of Z when X = 80, so:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{80 - 67}{8.1}[/tex]
[tex]Z = 1.6[/tex]
[tex]Z = 1.6[/tex] has a p-value of 0.9452.
1 - 0.9452 = 0.0548.
Out of 1390 students:
0.0548*1390 = 76
76 students scored above 80%.
Which equation is true?
f of negative 10 = 1
f of 2 = negative 10
f of 0 = 6
f of 1 = negative 10
Answer:
f(0) = 6
Step-by-step explanation:
Complete question:
The function f (x) is given by the set of ordered pairs 1,0 (-10,2), (0,6) (3,17) (-2,-1) which equation is true
f(-10)=1
f(2)=-10
f(0)=6
f(1)=-10
Given the coordinate (x, y). This shows that the input function is x and the output function is y, i.e. f(x) = y
From the pair of coordinates given, hence;
f(1) = 0
f(-10) = 2
f(0) = 6
f(3) = 17
f(-2) = -1
From the following options, this shows that f(0) = 6 is correct
Answer:
f(0) = 6
Step-by-step explanation:
EDGE
About 9% of the population has a particular genetic mutation. 400 people are randomly selected. Find the mean for the number of people with the genetic mutation in such groups of 400
Answer:
36 people
Step-by-step explanation:
The expected value E(X) = mean of sample = np
Where, p = population proportion, p = 9% = 0.09
n = sample size, = 400
The mean of the number of people with genetic mutation, E(X) = np = (400 * 0.09) = 36
36 people
Rectangle QRST with vertices Q(-3,2), R(-1,4), S(2,1), and T(0,-1)) in the x-axis
Answer:
D
Step-by-step explanation:
The coordinate of the new rectangle after the reflection across will be Q'(-3, -2), R'(-1, -4), S'(2, -1), and T'(0, 1). Then the correct option is D.
What is a transformation of a point?A spatial transformation is each mapping of feature space to itself and it maintains some spatial correlation between figures.
The reflection does not change the shape and size of the geometry. But flipped the image.
Rectangle QRST with vertices Q(-3, 2), R(-1, 4), S(2, 1), and T(0, -1).
The coordinate of the new rectangle after the reflection across is given as,
Q' = (-3, -2)
R' = (-1, -4)
S' = (2, -1)
T' = (0, 1)
The coordinate of the new rectangle after the reflection across will be Q'(-3, -2), R'(-1, -4), S'(2, -1), and T'(0, 1). Then the correct option is D.
More about the transformation of a point link is given below.
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write √3 x √6 in the form b√2 where b is an integer
Answer:
[tex]3 \sqrt{2} [/tex]
Step-by-step explanation:
[tex] \sqrt{(9 \times 2)} [/tex]
Take the square root of 9 out of the square root and leave the 2 in.
Answer:
3[tex]\sqrt{2}[/tex]
Step-by-step explanation:
Using the rules of radicals
[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex] , then
[tex]\sqrt{3}[/tex] × [tex]\sqrt{6}[/tex]
= [tex]\sqrt{3(6)}[/tex]
= [tex]\sqrt{18}[/tex]
= [tex]\sqrt{9(2)}[/tex]
= [tex]\sqrt{9}[/tex] × [tex]\sqrt{2}[/tex]
= 3[tex]\sqrt{2}[/tex]
after adjusting the number of servings in a recipe Charlotte determine that she will need 53 tbsp of flour one cup is equivalent to 16T . how much cups of flour will be required
Answer:
3.31 cups
Step-by-step explanation:
1/× =16/53
16x = 53
x = 53/16
x = 3.3125
The temperature at 5 a.m. was −7.4°C. By 9 a.m., the temperature was −4.7°C. How much warmer was the temperature at 9 a.m.?
Answer:
2.7°C.
Step-by-step explanation:
If it was -7.4°C. at 5 am, then -4.7°C. at 9am, then the temperature rose by 2.7°C.
Proof:
-7.4
-4.7
--------
2.7
Which of the following answer choices correctly shows the graph of y=−2x+5?
The graph of the linear function y = -2x + 5 is attached below.
Graph of Linear FunctionA linear function is a type of function that describes a relationship between two variables in which the output of the function is directly proportional to the input. It is a type of function that follows a straight-line pattern when graphed. Linear functions can be expressed in the form of an equation, such as y = mx + b, where m is the slope of the line, and b is the y-intercept.
The linear function given is y = -2x + 5
In this function, the slope of the line is -2 and the y-intercept is 5
This shows that the graph will pass through the y-axis at 5 which is a straight line.
Kindly find attached graph below.
Learn more on graph of linear function here;
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Solve the system of equations below using the inverse of matrix
Answer:
(x, y) = (4,-3)
Step-by-step explanation:
...............
.
.
.
.
Simplify to the extent possible:
(logx16)(log2 x)
Answer:
Step-by-step explanation:
Use the change-of-base rule.
What is the m∠ACB?
10°
50°
90°
180°
Answer:
The total sum of angles in a triangle is 180, thus the value of ∠ACB will be obtained as follows:
Given that the triangle is a right triangle, the sum of angles will be:
(4x)°+(7x-20)°+90=180
simplifying and solving for x we get:
4x+7x-20+90=180
11x=180+20-90
11x=110
dividing both sides by 11 we get:
(11x)/11=110/11
this gives us
x=10°
Thus substituting the value of x in:
∠ACB=(7x-20)°
=(7*10-20)
=70-20
=50°
Answer: 50°
Answer:
50
Step-by-step explanation:
Which of the following describes an angle with a vertex at Z?
which of the following tables represents an inverse variation between x and y
Answer:
I think that d is the answer
I need help with this
Answer:
D. Rotation reflection is the right answer
Answer:
Rotation, reflection
Step-by-step explanation:
R and I are equal so if you rotate clockwise you'll see I is in the top left and R would be in the bottom left. By reflecting, it's like flipping a pancake. R will now be in the in the top left on top of I.
(It's kind of weird to explain) Sorry if that was confusing.
Question 7(Multiple Choice Worth 1 points)
(07.02 MC)
Jason has two bags with 6 tiles each. The files in each bag are shown below
1
2
3
4
5
6
Without looking, Jason draws a file from the first bag and then a file from the second bag What is the probability of Jason drawing the file numbered 5 from the first bag and an odd file from the second bag?
0
영
o
Answer:a.3/6
Step-by-step explanation:
Because there’s a total of 12 files in each bag which is 6 in each
This is a list of the heights ( each nearest cm ) of 12 children
150 134 136 139 131 141
132 134 136 137 150 146
Select the type of the data.
Discrete
Continuous
Categorical
Qualitative
choose one
NO FAKE ANSWERS
FIRST MARKED BRAINLIST
qualitative
Step-by-step explanation:
b cos the question is in quality format
Answer:
cutee!
SUP???
Hiii friend :]
cuteee~!
prettyyy
1. Which expression is equivalent to 9k + 16? Explain why.
A 4 + 5k + 10 +6
B 4 + 3k + 2k + 10 +6
C2k +7 + 10 + 6
D 3k + 4k + 2k + 10 +6
Answer:
D
Step-by-step explanation:
3k +4k+2k+10+6
Collect like terms
9k +16
Answred Gauthmath
Answer:
D 3k + 4k + 2k + 10 +6
Step-by-step explanation:
A 4 + 5k + 10 +6 Combine like terms
5k+ 20 not equal
B 4 + 3k + 2k + 10 +6 Combine like terms
5k +20
C 2k +7 + 10 + 6 Combine like terms
2k + 23
D 3k + 4k + 2k + 10 +6 Combine like terms
9k+ 16
Please help me solve log3(2x+5)=3
Answer:
x = -2
Step-by-step explanation:
Divide both sides by 3
3 (2x + 5)/3 = 3/3
Simplify
2x + 5 = 1
Subtract 5 from both sides
2x + 5 - 5 = 1 - 5
Simplify
2x = -4
Divide both sides by 2
2x/2 = -4/2
Simplify: 2x/2
Divide the numbers: 2/2 = 1
= x
Simplify: -4/2
Apply the fraction rule: -1/b = -a/b
= - 4/2
Divide the numbers: 4/2 = 2
= -2
x = -2
In another state, all license plates consist of 6 symbols chosen from the 26 letters of the alphabet and the digits 0-9. How many license plates are possible if no repetitions are allowed and there must be exactly 3 letters followed by 3 numbers
Answer:
11,232,000 license plates are possible.
Step-by-step explanation:
The order in which the symbols are chosen is important(ABC is a different plate than BAC), which means that the permutations formula is used to solve this question.
Permutations formula:
The number of possible permutations of x elements from a set of n elements is given by the following formula:
[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]
In this question:
3 letters from a set of 26.
3 digits from a set of 10. So
[tex]T = P_{26,3}P_{10,3} = \frac{26!}{23!} \times \frac{10!}{7!} = 11232000[/tex]
11,232,000 license plates are possible.
round 8 5/6 to the nearest whole number
Answer:
9
Step-by-step explanation:
8 5/6
5/6 is close to 1 so it will round up
8+1 = 9
8 5/6 rounds to 9
Answer:
[tex]9[/tex]
Step-by-step explanation:
Step 1: Round [tex]8\frac{5}{6}[/tex] to the nearest whole number
In order to round up, the fraction needs to be either 1/2 or greater than 1/2. In our case, it is greater than half therefore we will round up to 9.
Answer: [tex]9[/tex]
A G.P is such that the 3rd term minus a first term is 48. The 4th term minus 2nd term 144. Find: (i) Common ratio ii) The first term (ii) 6th term of the sequence
Answer:
Step-by-step explanation:
r is the common ratio.
Third term minus first term is 48.
a₃ - a₁ = 48
a₃ = a₁r²
a₁r² - a₁ = 48
a₁(r²-1) = 48
r²-1 = 48/a₁
Fourth term minus second term is 144.
a₄ - a₂ = 144
a₂ = a₁r
a₄ = a₁r³
a₁r³ - a₁r = 144
a₁r(r²-1) = 144
r²-1 = 144/(a₁r)
48/a₁ = 144/(a₁r)
r = 3
:::::
r²-1 = 48/a₁
a₁ = 6
:::::
a₆ = a₁r⁵ = 1458
(i) The common ratio for the given condition is 3.
ii) The first term of the sequence is 6.
iii) The 6th term of the sequence is 1458.
What is a sequence?It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.
Divergent sequences are those in which the terms never stabilize; instead, they constantly increase or decrease as n approaches infinity,
It is given that a is a geometric progression such that the 3rd term minus a first term is 48. The 4th term minus the 2nd term 144.
Each number following the first in a geometric sequence is multiplied by a particular number, known as the common ratio.
As the third term minus the first term is 48.
a₃ - a₁ = 48
a₃ = a₁r²
a₁r² - a₁ = 48
a₁(r²-1) = 48
r²-1 = 48/a₁
The fourth term minus the second term is 144.
a₄ - a₂ = 144
a₂ = a₁r
a₄ = a₁r³
a₁r³ - a₁r = 144
a₁r(r²-1) = 144
r²-1 = 144/(a₁r)
48/a₁ = 144/(a₁r)
r = 3
r²-1 = 48/a₁
a₁ = 6
a₆ = a₁r⁵ = 1458
Thus the common ratio for the given condition is 3, the first term of the sequence is 6 and the 6th term of the sequence is 1458.
Learn more about the sequence here:
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a pit is 7m long, 5m wide,and 8m deep how many cubic meter of sand will fill the pit?
Answer:
280
Step-by-step explanation:
7 x 5 x 8
