Answer:
PQR+SQR=180°(angles in a triangle)
75°+SQR=180°
SQR=180°-75°
SQR=105°
a. A contest entrant has a 0.002 probability of winning $12,165. If this is the only prize and the fee is $35, then find the expected value of winning the contest.
b. The probability of winning a lottery is 0.125, what is the probability of winning at least once in twelve trials?
Part (a)
If you win $12165, then you really net 12165-35 = 12130 dollars when you consider the ticket fee. So this is the true amount of money you win, or take home at the end of the day. This is before taxes.
Multiply 0.002 with 12,130 to get 0.002*12130 = 24.26
We'll use this later so let A = 24.26
The chances that you don't win are 1 - 0.002 = 0.998 which multiplies with -35 to indicate you lost $35 in playing the game. So we get B = 0.998*(-35) = -34.93
Lastly, add the values of A and B to get the expected value:
A+B = 24.26 + (-34.93) = -10.67 is the expected value.
On average, you expect to lose about $10.67 for any time you play the game.
Answer: -10.67 dollars===========================================================
Part (b)
0.125 is the probability of winning so 1-0.125 = 0.875 is the probability of losing.
Let's say you get really unlucky and lose 12 times in a row. Assuming each trial (aka case when you play the game) is independent, this would mean the probability of such an event is (0.875)^12 = 0.2014172, which is approximate.
Subtract that from 1 to get the probability of winning at least once
1 - (0.875)^12 = 1 - 0.2014172 = 0.7985828
which is also approximate. If we rounded to three decimal places, then it would be 0.799; I'm picking three decimals since 0.125 is to three decimal places. Round however you need to if otherwise.
Answer: 0.799 (approximate)please help me with this on the image
Answer: For flour it is 360g
3 eggs
900ml of milk
Step-by-step explanation:
Answer:
First, find the amount of ingredient for one pancake:
240 ÷ 8 = 30g of plain flour per pancake2 ÷ 8 = 0.25 eggs per pancake600 ÷ 8 = 75 ml of milk per pancakeMultiply that amount by 12 to find the amount needed for 12 pancakes:
30 x 12 = 360g of plain flour0.25 x 12 = 3 eggs75 x 12 = 900 ml of milkIf the graphs of the linear equations in a system are the same line, what does that mean about the possible solution or solutions of the system?
A. There is exactly one solution.
В.
There is no solution.
C. There are infinitely many solutions.
D. The lines in a system cannot graph as the same line.
Answer:
C. There are infinitely many solutions.
Step-by-step explanation:
If the graphs of linear equations are the same line, then any point (solution) on one line is automatically a point on the "other" line. For example,
[tex]\begin{array}{l} x + y =10 \\ 2x + 2y =20 \end{array}[/tex]
The graphs of these "two" equations is only one line, x + y =10. The point [tex](5, 5)[/tex]is on "both" lines.
An industrial psychologist consulting with a chain of music stores knows that the average number of complaints management receives each month throughout the industry is 4, but the variance is unknown. Nine of the chain's stores were randomly selected to record complaints for one month; they received 2, 4, 3, 5, 0, 2, 5, 1, and 5 complaints. Using the .05 significance level, is the number of complaints received by the chain different from the number of complaints received by music stores in general?
1. Use the five steps of hypothesis testing.
2. Sketch the distributions involved
3. Explain the logic of what you did to a person who is familiar with hypothesis testing, but knows nothing about t tests of any kind. Be sure to explain how this problem differs from a problem with a known population variance and a single sample.
Answer: See explanation
Step-by-step explanation:
1. Use the five steps of hypothesis testing.
Step 1: The aim of the research is to conduct the five steps of hypothesis testing.
Step 2:
Null hypothesis: H0 u= 4
Population mean: H1 u = 4
Alternate hypothesis: u ≠ 4
Population mean: u ≠ 4
Step 3 and step 4 are attached.
Step 5: Based on the calculation, the calculated value of t is less than the t critical value, therefore, the null hypothesis will be failed to be rejected.
2. Sketch the distributions involved
This has been attached.
3. Explain the logic of what you did to a person who is familiar with hypothesis testing, but knows nothing about t tests of any kind.
The distribution is "t".
The means is tested by using T-test.
Chi-square is used to test the single variance.
g Let the joint probability density function of random variables X and Y. (a) Calculate the marginal probability densities of X and Y . (b) Calculate the expected values of X and Y . be given by
Answer: hello your question is incomplete attached below is the complete question
answer:
a) Fx(X) = 0 ≤ x ≤ 2, Fy(Y) = y - y^3/4
b) E(X) = 32/20 , E(Y) = 64/60
Step-by-step explanation:
a) Marginal probability density
Fx(X) = [tex]\int\limits^x_0 {\frac{xy}{2} } \, dy[/tex]
∴ probability density of X = 0 ≤ x ≤ 2
Fy(Y) = [tex]\int\limits^2_y {\frac{xy}{2} } \, dx[/tex]
∴ probability density of Y = y - y^3/4
b) Determine the expected values of X and Y
E(X) = 32/20
E(Y) = 64 /60
attached below is the detailed solution
In this graph, which transformation can produce quadrilateral A′B′C′D′ from quadrilateral ABCD?
Answer:
A reflection across the y axis and then a reflection across the x axis
Step-by-step explanation:
Answer:
An 180 degree counterclockwise rotation around the origin
Step-by-step explanation:
plato/edmuntum answer
The Smith family has
bought an above ground
pool. The manufacture
recommends that it be filled
to within 1 foot of the rim.
What is the volume of the
water at this height.
37. (V=TTr?h) (use 3.14 for TT)
a. 7536 cubic feet
b. 6280 cubic feet
c. 1570 cubic feet
d. 1884 cubic feet
Answer:
b. 6280 cubic feet
Step-by-step explanation:
Volume:
The volume of the prism, which has a cylindrical base, with radius r and height h, is given by:
[tex]V = \pi r^2h[/tex]
Radius:
The radius is 20, so [tex]r = 20[/tex]
The manufacture recommends that it be filled to within 1 foot of the rim.
Height of 6 - 1 = 5, so [tex]h = 5[/tex]
Then
[tex]V = 3.14*(20)^2*5 = 6280[/tex]
So the volume is 6280 cubic feet, and the correct answer is given by option b.
Point A lies outside of plane P, how many lines can be drawn parallel to plane P that pass through point A?
A. 0
B. 1
C. 2
D. an infinite number
Answer:
B. an infinite number
Step-by-step explanation:
Since point A lies outside of P, the number of lines that can be drawn parallel to P and passing through point A is only infinite. It is infinite because it is just one given point lying outside the plane. If there is more than one point then it will be otherwise.
Answer:
yeah
Step-by-step explanation:
Whats The Correct Answer?!
Answer: the correct answer is D 0.05
Step-by-step explanation:
Answer:
0.02 m/s
Step-by-step explanation:
42/50 meters in 26/30 minutes,
26/30 minutes = 52 seconds
so in 1 second, 42/50 ÷ 52
= 42/50 × 1/52
= 21/1300
= 0.02 (approximately)
Answered by GAUTHMATH
Write the nth term of the following sequence in terms of the first term of the sequence.
10, 20, 40,-
Answer:
10*(2)^(n-1)
Step-by-step explanation:
The common ratio of the sequence is 20/10=40/20=2.
The first term is 10 so the equation is 10*(2)^(n-1)
Answer:
10(2)^n-1
Step-by-step explanation:
Correct on Odyssey
A trough is 12 ft long and its ends have the shape of isosceles triangles that are 3 ft across at the top and have a height of 1 ft. If the trough is being filled with water at a rate of 14 ft3/min, how fast is the water level rising when the water is 4 inches deep
Answer:
[tex]\frac{dh}{dt}=0.5ft[/tex]
Step-by-step explanation:
From the question we are told that:
Length [tex]l=12[/tex]
Top length [tex]l_t=3ft[/tex]
Height [tex]h=1ft[/tex]
Rate [tex]R=14 ft3/min[/tex]
Water rise [tex]w=4[/tex]
Generally the equation for Velocity is mathematically given by
[tex]V=frac{1}{2}wh'(l)\\\\V=frac{1}{2}wh'(12)[/tex]
[tex]V=18h'^2[/tex]
Therefore
[tex]R=18(2h)(\frac{dh}{dt})[/tex]
Where
[tex]h=\frac{3}{4}[/tex]
Therefore
[tex]\frac{dh}{dt}=\frac{R}{18(2h)}[/tex]
[tex]\frac{dh}{dt}=\frac{14}{18(2.3/4)}[/tex]
[tex]\frac{dh}{dt}=0.5ft[/tex]
What is the domain and range of the graph below?
9514 1404 393
Answer:
domain: all real numbersrange: y ≥ 0Step-by-step explanation:
The domain is the horizontal extent of the graph. For a graph like this, we assume the ends extend to infinity, both horizontally and vertically. Then the horizontal extent (domain) is from -infinity to +infinity: all real numbers.
The graph does not go below y=0, so the vertical extent (range) is y ≥ 0.
A game consists of tossing three coins. If all three coins land on heads, then the player wins $75. If all three coins land on tails, then the player wins $45. Otherwise, the player wins nothing. On average, how much should a player expect to win each game
Answer:
On average, a player should expect to win $15.
Step-by-step explanation:
The expected value in an event with outcomes:
x₁, x₂, ..., xₙ
Each with probability:
p₁, ..., pₙ
is given by:
Ev = x₁*p₁ + ... +xₙ*pₙ
In this case we have 3 outcomes:
player wins $75 = x₁
player wins $45 = x₂
player does not win = x₃
Let's find the probabilities of these events.
player wins $75)
Here we must have the 3 coins landing on heads, so there is only one possible outcome to win $75
While the total number of outcomes for tossing 3 coins, is the product between the number of outcomes for each individual event (where the individual events are tossing each individual coin, each one with 2 outcomes)
Then the number total of outcomes is:
C = 2*2*2 = 8
Then the probability of winning $75 is the quotient between the number of outcomes to win (only one) and the total number of outcomes (8)
p₁ = 1/8
Win $45:
This happens if the 3 coins land on tails, so is exactly equal to the case above, and the probability is the same:
p₂ = 1/8
Not wining:
Remember that:
p₁ + p₂ + ... + pₙ = 1
Then for this case, we must have:
p₁ + p₂ + p₃ = 1
1/8 + 1/8 + p₃ = 1
p₃ = 1 - 1/8 - 1/8
p₃ = 6/8
Then the expected value will be:
Ev = $75*1/8 + $45*1/8 + $0*6/8 = $15
On average, a player should expect to win $15.
An isosceles right triangle has a hypotenuse that measures 4√2 cm. What is the area of the triangle?
Answer:
It would be B. 16 centimeters^2
Step-by-step explanation:
A, B, and C are points of tangency. CQ = 5, PQ = 10, and PR = 14. What is the perimeter
of the triangle PQR?
*see attachment for diagram
Answer:
Perimeter = 38
Step-by-step explanation:
Recall: when two tangents are drawn to meet at a point outside a circle, the segments of the two tangents are congruent.
Given,
CQ = 5
PQ = 10
PR = 14
Perimeter of ∆PQR = RC + CQ + QB + BP + PA + AR
CQ = QB = 5 (tangents drawn from an external point)
BP = PQ - QB
BP = 10 - 5 = 5
BP = PA = 5 (tangents drawn from an external point)
AR = PR - PA
AR = 14 - 5 = 9
AR = RC = 9 (tangents drawn from an external point)
✔️Perimeter of ∆PQR = RC + CQ + QB + BP + PA + AR
= 9 + 5 + 5 + 5 + 5 + 9
Perimeter = 38
Write an equation of the line that passes through a pair of points: (-5, -2), (3, -1) y=-x+ C. y=-- x - 11 11 a. 8 8 b. 11 d. y=-x+ 8 y=-x - 8 11
Answer:
y = 8x+11
Step-by-step explanation:
The coordination of the points are : (-5,-2) , (3, -1)
Then, the equation is :
[tex]\frac{y+5}{x+2} =\frac{-5-3}{-2+1} \\\\or,\frac{y+5}{x+2} = 8\\or, y+5=8(x+2)\\or, y = 8x+16-5\\y= 8x+11[/tex]
Which of the following are best described as lines that meet to form a right
angle?
A. Parallel lines
B. Lines that are coplanar
C. Perpendicular lines
D. Intersecting lines
Answer:
A line is said to be perpendicular to another line if the two lines intersect at a right angle. An angle is said to be a right angle if its measure is 90 degrees.
A certain store sells small, medium, and large toy trucks in each of the colors red, blue,green, and yellow. The store has an equal number of trucks of each possible color/sizecombination. If Stella wants a medium red truck and her mother will randomly select oneof the trucks in the store, what is the probability that the truck she selects will have atleast one of the two features that Stella wants
Answer:
The probability that the truck she selects will have at least one of the two features that Ella Stella wants is 50%.
Step-by-step explanation:
Since a certain store sells small, medium, and large toy trucks in each of the colors red, blue, green, and yellow, and the store has an equal number of trucks of each possible color / size combination, if Stella wants a medium red truck and her mother will randomly select one of the trucks in the store, to determine what is the probability that the truck she selects will have at least one of the two features that Stella wants, the following calculation must be performed:
3 sizes
4 colors
4 x 3 = 12
4 midsize cars
3 red cars
1 medium red car
4 + 3 - 1 = 6
6/12 = 0.5
Therefore, the probability that the truck she selects will have at least one of the two features that Ella Stella wants is 50%.
ASAP HELP: If a sample proportion is 0.55, which range of possible values best describes an estimate for the population parameter?
A. (0.55, 0.6)
B. (0.4, 0.7)
C. (0.4, 0.69)
D. (0.5, 0.59)
Answer:
B.(0.4,0.7)
Step-by-step explanation:
We are given that
Sample proportion
[tex]\hat{p}=0.55[/tex]
We have to find the range of possible values which describes best an estimate for the population parameter.
Estimate for the population parameter
[tex]\hat{p}\pm Z(SE)[/tex]
A.(0.55,0.6)
Difference between 0.55 and 0.55=0
Difference between 0.55 and 0.6=0.05
Difference between 0.55 and 0.55 is not equal to difference between 0.55 and 0.6.
Hence, option A is wrong.
B.(0.4,0.7)
Difference between 0.55 and 0.4=0.15
Difference between 0.55 and 0.7=0.15
Difference between 0.55 and 0.4 is equal to difference between 0.55 and 0.7.
Hence, option B is correct.
C. (0.4,0.69)
Difference between 0.55 and 0.4=0.15
Difference between 0.55 and 0.69=0.14
Difference between 0.55 and 0.4 is not equal to difference between 0.55 and 0.69.
Hence, option C is not correct.
D.(0.5,0.59)
Difference between 0.55 and 0.5=0.05
Difference between 0.55 and 0.59=0.04
Difference between 0.55 and 0.5 is not equal to difference between 0.55 and 0.59.
Hence, option D is not correct.
Find the missing length on this triangle
Answer:
Step-by-step explanation:
This is a geometric means problem where 60, the side common to both the triangles, is the geometric mean. Set it up like this:
[tex]\frac{36}{60}=\frac{60}{x}[/tex] and cross multiply to get
36x = 3600 so
x = 100
Which of the following is equivalent to the expression below?
8^11•8^x
A. 8^x-11
B. 8^11x
C. 8^11+x
D. 8^11-x
Answer:
C
Step-by-step explanation:
[tex] \sf {a}^{c} \times {a}^{b} = {a}^{b + c} \\ \sf = {8}^{11} \times {8}^{x} \\ \sf = {8}^{11 + x} (c)[/tex]
Find the missing side lengths help please?
Answer:
Step-by-step explanation:
Answer:
y=2, x=4
Step-by-step explanation:
sin60=2sqrt3/x
so x = 2sqrt3/sin60
and x=4
for the value of y, use pythagorean theorem to get
16=y^2+12
which gives you y=2
add:7ab,8ab,-10ab,-3ab
Answer:
2ab
Step-by-step explanation:
7ab+8ab+(-10ab)+(-3ab)=
=15ab-13ab= 2ab
Answer:
2ab
Step-by-step explanation:
7ab+8ab+-10ab+-3ab
Factor out ab
ab(7+8-10-3)
ab(2)
2ab
Which two values of x are roots of the polynomial below? x2 + 3x - 5
Answer:
Step-by-step explanation:
The roots are the values of x for which x² + 3x - 5 = 0.
Quadratic formula:
x = [-3±√(3²-4(1)(-5))]/(2·1) = [-3±√29]/2
Select the correct answer from the drop-down menu.
Answer:
-60 60 30 -30 one of it is answer
A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 444 gram setting. It is believed that the machine is underfilling the bags. A 41 bag sample had a mean of 440 grams with a variance of 441. Assume the population is normally distributed. A level of significance of 0.05 will be used. Specify the type of hypothesis test.
Answer:
The null hypothesis is [tex]H_0: \mu = 444[/tex]
The alternative hypothesis is [tex]H_1: \mu < 444[/tex]
The p-value of the test is 0.1148 > 0.05, which means that the sample does not give enough evidence to conclude that the machine is underfilling the bags.
Step-by-step explanation:
A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 444 gram setting.
At the null hypothesis, we test if the machine works correctly, that is, the mean is of 444. So
[tex]H_0: \mu = 444[/tex]
At the alternative hypothesis, we test if they are underfilling, that is, if the mean is of less than 444. So
[tex]H_1: \mu < 444[/tex]
The test statistic is:
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, s is the standard deviation and n is the size of the sample.
444 is tested at the null hypothesis:
This means that [tex]\mu = 444[/tex]
A 41 bag sample had a mean of 440 grams with a variance of 441.
This means that [tex]n = 41, X = 440, s = \sqrt{441} = 21[/tex]
Value of the test statistic:
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{440 - 444}{\frac{21}{\sqrt{41}}}[/tex]
[tex]t = -1.22[/tex]
P-value of the test:
Right-tailed test(test if the mean is less than a value), with 41 - 1 = 40 df and t = -1.22.
Using a t-distribution calculator, this p-value is of 0.1148
The p-value of the test is 0.1148 > 0.05, which means that the sample does not give enough evidence to conclude that the machine is underfilling the bags.
Help please Find the surface area, including the floor, of his tent.
Answer:
52.8 m. sq.
Step-by-step explanation:
2.6 x 1.5 + 1.5 (3) = 7.8 / 2 = 3.9 x 2 = 7.8 (Triangles)
3 x 5 = 15 x 2 = 30 (Side Rectangles)
5 x 1.5 + 1.5 (3) = 15
15 + 30 + 7.8 = 52.8 m. sq.
Hope this helps!
If something is wrong, please let me know.
According to The Wedding Report, Inc., the mean cost for a wedding in the United States is $28732 (as of November 2008). Suppose the cost for a wedding is normally distributed with a standard deviation of $1500, and that a wedding is selected at random. Use the appropriate Excel function to calculate each of the following. (Note - Part (e) can be done by hand.)
(a) Find the probability that the wedding costs less than $22000.
(b) Find the probability that the wedding costs more than $32000.
(c) Find the probability that the wedding costs between $25000 and $30000.
(d) Find Q1 (the 25th percentile) and Q3 (the 75th percentile).
(e) Find the IQR for the wedding costs.
(f) The top 10% of weddings cost more than how much?
Answer:
Following are the solution to the given points:
Step-by-step explanation:
[tex]X = \text{cost of wedding}\sim \text{Normal}\ (\mu = 28732, \sigma= 1500)\\\\[/tex]
For point a:
[tex]Probability\ = 0.00000359\\\\ \text{(Using Excel function:} =NORMDIST(22000,28732,1500,1)).[/tex]
For point b:
[tex]Probability \ = 0.014678\\\\\text{(Using Excel function:} =1-NORMDIST(32000,28732,1500,1))\\\\[/tex]
For point c:
[tex]Probability\ = 0.794614436 \\\\[/tex]
[tex]\text{(Using Excel function:} \\=NORMDIST (30000,28732,1500,1)-NORMDIST(25000,28732,1500,1))\\\\[/tex]
For point d:
[tex]Q_1 = 27720.26537 \\\\\text{(Using Excel function:} =NORMINV(0.25,28732,1500)) \\\\Q_3 = 29743.73463 \\\\\text{(Using Excel function:} =NORMINV(0.75,28732,1500)).[/tex]
For point e:
[tex]IQR = Q_3 - Q_1 = 29743.73463 - 27720.26537 = 2023.469251.[/tex]
For point f:
[tex]Top\ 10\% = 30654.32735 \\\\\text{(Using Excel function:} =NORMINV(0.9,28732,1500)).[/tex]
A housing official in a certain city claims that the mean monthly rent for apartments in the city is less than $1000. To verify this claim, a simple random sample of 47 renters in the city was taken, and the mean rent paid was $941 with a standard deviation of $245. Can you conclude that the mean monthly rent in the city is less than $1000
Answer:
The p-value of the test is 0.053, which is more than the standard significance level of 0.05, and thus it cannot be concluded that the mean monthly rent in the city is less than $1000.
Step-by-step explanation:
A housing official in a certain city claims that the mean monthly rent for apartments in the city is less than $1000.
At the null hypothesis, we test if the mean is of at least $1000, that is:
[tex]H_0: \mu \geq 1000[/tex]
At the alternative hypothesis, we test if the mean is less than $1000, that is:
[tex]H_1: \mu < 1000[/tex]
The test statistic is:
We have the standard deviation for the sample, so the t-distribution is used.
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, s is the standard deviation and n is the size of the sample.
1000 is tested at the null hypothesis:
This means that [tex]\mu = 1000[/tex]
To verify this claim, a simple random sample of 47 renters in the city was taken, and the mean rent paid was $941 with a standard deviation of $245.
This means that [tex]n = 47, X = 941, s = 245[/tex]
Value of the test statistic:
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{941 - 1000}{\frac{245}{\sqrt{47}}}[/tex]
[tex]t = -1.65[/tex]
P-value of the test and decision:
The p-value of the test is found using a left-tailed test(test if the mean is less than a value), with t = -1.65 and 47 - 1 = 46 df.
Using a t-distribution calculator, the p-value is of 0.053.
The p-value of the test is 0.053, which is more than the standard significance level of 0.05, and thus it cannot be concluded that the mean monthly rent in the city is less than $1000.
What is 2/11 as a decimal rounded to 3 decimal places?
Answer: The answer is 0.182
Hope this help :)
