The probability that he weighs more than 81 kg given that he is above the average weight is 0.4532.
(a) Probability that male is heavier than 81 kg can be found using the z-score formula;
z = (x - μ) / σ = (81 - 75) / 8 = 0.75P(z > 0.75) = 1 - P(z < 0.75)
Now referring to z-tables, we find that P(z < 0.75) = 0.7734
Therefore, P(z > 0.75) = 1 - P(z < 0.75) = 1 - 0.7734 = 0.2266
Thus, the probability that the male is heavier than 81 kg is 0.2266.
(b) Let X be the weight of female and Y be the weight of male. We know that X ~ N(52, 6) and Y ~ N(75, 8)
Let Z = X - Y then, Z ~ N(52 - 75, sqrt(6^2 + 8^2)) = N(-23, 10)
Now, we need to find the probability that X > Y. i.e P(X - Y > 0)P(X - Y > 0) can be written as P(Z > -23/10)
Now, referring to the z-tables, we can find that P(Z > -2.3) = 0.9893
Therefore, P(X > Y) = P(X - Y > 0) = 0.9893.
(c) Given that male weight is above average weight, we need to find the probability that he weighs more than 81 kg i.e. P(Y > 81 | Y > 75)
This is conditional probability and can be found using Bayes' Theorem:
P(Y > 81 | Y > 75) = P(Y > 75 | Y > 81) * P(Y > 81) / P(Y > 75)
Now, P(Y > 75 | Y > 81) = 1, P(Y > 81) can be found as:
P(Y > 81) = P(Z > (81 - 75) / 8) = P(Z > 0.75) = 1 - P(Z < 0.75) = 1 - 0.7734 = 0.2266
Also,P(Y > 75) = P(Z > 0) = 0.5Therefore,P(Y > 81 | Y > 75) = 1 * 0.2266 / 0.5 = 0.4532
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The given information is that weights of females are normally distributed with mean 52kg and standard deviation 6kg. Weights of males are normally distributed with mean 75kg and standard deviation 8kg. One male and one female are chosen at random.
The probability that the male is heavier than 81kg is 0.2266.
The probability that the female is heavier than the male is 0.0107.
If the male is above average weight(75kg),then the probability that he is heavy than 81kg is 0.2266.
a) The weight of males is normally distributed with a mean of 75kg and a standard deviation of 8kg. The probability that the male is heavier than 81kg can be calculated as follows: z = (81 - 75) / 8
= 0.75P(Z > 0.75)
= 0.2266
Therefore, the probability that the male is heavier than 81 kg is 0.2266.
b) If X and Y are independent Normal random variables, then, for every ab e R, aX + bY has a Normal distribution. The weights of males and females are independent, normally distributed random variables with means of 75kg and 52kg and standard deviations of 8kg and 6kg respectively. Therefore, the difference in weights of the male and the female is a normally distributed random variable with mean μ = 75 - 52 = 23kg and standard deviation σ = √(8² + 6²) = √(100) = 10kg. Let Z be a standard normal variable. The probability that the female is heavier than the male can be calculated as follows:
P(X < Y) = P(X - Y < 0) = P[(X - Y - μ)/σ < (-23)/10] = P(Z < -2.3) = 0.0107
Therefore, the probability that the female is heavier than the male is 0.0107.
c) If the male is above average weight, then we can assume that he weighs 75 kg. The probability that he is heavier than 81 kg can be calculated as follows:
z = (81 - 75) / 8 = 0.75P(Z > 0.75) = 0.2266
Therefore, the probability that the male is above average weight and heavier than 81 kg is 0.2266.
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the base of the cylinder? Use 3.14 for n and round the answer
to the nearest hundredth.
h-13 in
r =
in.
Answer:
r = 7
Step-by-step explanation:
Volume of a cylinder:
V = πr²h
Given:
V = 2000
h = 13
Work:
V = πr²h
r² = V/(πh)
r² = 2000/(3.14 * 13)
r² = 2000/40.82
r² ≈ 49
[tex]\sqrt{r^2} =\sqrt{49}[/tex]
r = 7
Exercises 2.17 Interpolate a cubic spline between the three
points (0, 1), (2, 2) and (4, 0).
To interpolate a cubic spline between the points (0, 1), (2, 2), and (4, 0), we can use the concept of spline interpolation. A cubic spline is a piecewise-defined function consisting of cubic polynomials, which smoothly connects the given points.
In order to construct a cubic spline, we need to determine the coefficients of the cubic polynomials for each interval between the given points. The spline should satisfy three conditions: it must pass through each of the given points, it should have continuous first and second derivatives at the interior points, and it should have zero second derivatives at the endpoints to ensure a smooth connection.
We start by dividing the interval into three subintervals: [0, 2], [2, 4]. For each subinterval, we construct a cubic polynomial that satisfies the interpolation conditions. By imposing the continuity and smoothness conditions at the interior point (2, 2), we can obtain a system of equations. Solving this system gives us the coefficients of the cubic polynomials.
Once we have the coefficients, we can express the cubic spline as a piecewise function. The resulting cubic spline will smoothly connect the given points (0, 1), (2, 2), and (4, 0) and provide an interpolation function between them. This interpolation technique ensures a smooth and continuous curve, which can be useful for approximating values between the given data points.
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I DON'T WANT A LINK I WANT AN ANSWER CAN YOU ANSWER THIS QUESTION I NEED IT DONE ASSP How large is the distance from one end of your state to the other (North to South)? What is the distance from the east coast to the west coast of your state? Your state is the ___________ largest in the United States.
My state is Virginia
A mint milk shake contains 1.25 fluid ounces of milk for every 4 ounces of ice cream. A strawberry milk shake contains 1.75 fluid ounces of milk for every 5 ounces of ice cream. Which milk shake is thicker?
Answer:
1.25/4 = 5/16
1.75/5 = 7/20
Determine which one of these fractions is bigger.
Both milkshakes have the same thickness.
Given that,
A mint milkshake contains 1.25 fluid ounces of milk for every 4 ounces of ice cream. A strawberry milkshake contains 1.75 fluid ounces of milk for every 5 ounces of ice cream. Which milkshake is thicker is to be determined.
The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.
Here,
According to the question,
A mint milkshake contains 1.25 fluid ounces of milk for every 4 ounces of ice cream.
Ratio of the milk = 1.25 / 4 = 0.35
A strawberry milkshake contains 1.75 fluid ounces of milk for every 5 ounces of ice cream.
Ratio of the milke = 1.75 / 5 = 0.35
comparing the ratio both are equal,
Thus, Both milkshakes have the same thickness.
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how can you find the diameter of this circke
Answer:
10cm
Step-by-step explanation:
pretty sure the diameter is measured by multiplying the radius twice :)
Answer:
Diameter = 10 cm
Circumference = 31.43 cm
Area = 78.57 cm²
Hey you! Would you like to promote my small pastry business??
Currently we are only selling this: UR MOM (contains: Eggs, Wheat, Milk, Extra Nuts, etc” $19.99
We take cashapp, venmo, PayPal and other types of payments
Answer: nice
Step-by-step explanation:
Sounds like a Scam though ngl
5x^2 divided by -45x
Answer: -1/9 * x.
Step-by-step explanation:
To simplify the expression (5x^2) / (-45x), we can divide the coefficients and subtract the exponents:
(5 / -45) * (x^2 / x)
Simplifying the coefficient:
-1/9 * (x^2 / x)
Now, simplify the variables:
-1/9 * x^(2-1) = -1/9 * x
Therefore, the simplified expression is -1/9 * x.
A rectangle is 29 feet long and 7 feet long. What is the area of this rectangle? 203 ft² 143 ft² 107 ft² 72 ft²
Answer:
203 ft²
Step-by-step explanation:
We need to use multiplication for the answer of this.
29 × 7 = 203
so that means that the answer in feet is 203 ft²
good luck hope this helped
-cheesetoasty
Find (a) the range and (b) the standard deviation of the data set 40,35.45,55,60. Round to the nearest hundredth if necessary.
Answer:
(a) 25
(b) 9.27
Step-by-step explanation:
Step 1
We have to rearrange the given days set from least to highest
35, 40, 45, 55, 60
(a) the range
Range = The highest number - The least number
= 60 - 35
= 25
(b) the standard deviation of the data set
35, 40, 45, 55, 60.
We find the Mean
Mean = Sum of values/Number of values
= 35+40+45+55+60/5
= 235/5
= 47
We can find the standard deviation now.
The formula =
√(x - Mean)²/n
= √(35 - 47)²+ (40 + 47)² + (45 - 47)² + (55 - 47)² + (60 - 47)²/5
= √144 + 49 + 4 + 64 +169/5
= √430/5
= √86
= 9.273618495
Approximately = 9.27
Use a normal approximation to find the probability of the indicated number of voters. In this case, assume that
108108
eligible voters aged 18-24 are randomly selected. Suppose a previous study showed that among eligible voters aged 18-24, 22% of them voted.
Probability that exactly 29 voted
The probability that exactly 29 of 108 eligible voters voted is
Using normal approximation, the probability that exactly 29 out of 108 eligible voters voted is approximately 0.2346, or 23.46%.
What is the probability that exactly 29 out of 108 eligible voters voted?To find the probability that exactly 29 out of 108 eligible voters voted, we can use a normal approximation.
First, we need to calculate the mean (μ) and standard deviation (σ) for the binomial distribution, which can be approximated using the formula:
μ = n * p
σ = √(n * p * (1 - p))
where n is the number of trials (108 in this case) and p is the probability of success (22% or 0.22).
μ = 108 * 0.22 = 23.76
σ = √(108 * 0.22 * (1 - 0.22)) = 4.3
Next, we use the normal distribution to approximate the probability of exactly 29 voters. We will use the continuity correction by considering the interval between 28.5 and 29.5.
P(28.5 < X < 29.5) ≈ P(28.5 - 0.5 < X < 29.5 + 0.5) ≈ P(28 < X < 30)
To find this probability, we calculate the z-scores for 28 and 30 using the mean and standard deviation:
z₁ = (28 - μ) / σ
z₂ = (30 - μ) / σ
Then, we use a standard normal distribution table or calculator to find the probability associated with each z-score:
P(28 < X < 30) ≈ P(z₁ < Z < z₂)
Let's calculate the z-scores and find the corresponding probabilities:
z₁ = (28 - 23.76) / 4.61 ≈ 0.92
z₂ = (30 - 23.76) / 4.61 ≈ 1.35
Using the standard normal distribution table or calculator, we find the probabilities associated with these z-scores:
P(0.92 < Z < 1.35) ≈ 0.4082 - 0.1736 = 0.2346
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An inflatable figure is a decoration on Gabriella's lawn. A rope 42 in. long secures the top of the figure to the ground at an angle of 80°. About how tall is the figure?
round to the nearest tenth of an inch
Answer:
41.4 in
Step-by-step explanation:
(sin 80) opposite = x
hypotenuse 42
x = 42 * sin (80) = 41.4 in
1. The small bag of potting soil weighs 3 1/4 pounds. The large bag weighs 3 2/3 times more than the small bag. How much does the large bag weigh?
Answer:
11 11/12 lb
Step-by-step explanation:
"3 2/3 times more than the small bag" comes out to:
(3 2/3)*(3 1/4) lb.
Convert both mixed numbers to improper fractions:
11 13 143
--- * ---- = ----------- = 11.917
3 4 12
The large bag weighs 11.917 lb, which may be converted to the mixed number 11 11/12 lb
A set of dolls is made so that the volume,V of each of them varies directly as the cube of its height h. The doll with a height of 3cm has a volume of 6.75 cm³.
A) find an equation for V in terms of H.
B) find the volume of a doll with a height of 2.5cm
Answer:
A v=2.25 H=1
b. 5.625
Step-by-step explanation:
Answer:
V = 3.90625 cm³
Step-by-step explanation:
Given that V varies directly as h³ then the equation relating them is
V = kh³ ← k is the constant of variation
To find k use the condition
V = 6.75 when h = 3 , then
6.75 = k × 3³ = 27k ( divide both sides by 27 )
0.25 = k
V = 0.25h³ ← equation of variation
(b)
When h = 2.5 , then
V = 0.25 × 2.5³ = 3.90625 cm³
A racing car is one of the many toys manufactured by Mack Corporation. The assembly time for this toy follows a normal distribution with a mean of 50 minutes and a standard deviation of 5 minutes. If one worker starts assembling a racing car, what is the probability that she will finish this job in more than 60 minutes? Find the z score? QUESTION 2 1 pol 1b. What do you get from Table A? QUESTION 3 3 point 10. What is the probability that she will finish this job in more than 60 minutos? (round to a percent with two decimals)
The probability that the worker will finish assembling the racing car in more than 60 minutes is approximately 0.1587. The z-score corresponding to 60 minutes is 2. The probability of completing the job in more than 60 minutes is 15.87%.
To find the probability that the worker will finish assembling the racing car in more than 60 minutes, we need to calculate the z-score and then find the corresponding probability from the standard normal distribution.
First, we calculate the z-score using the formula:
z = (x - μ) / σ
where x is the given time (60 minutes), μ is the mean (50 minutes), and σ is the standard deviation (5 minutes).
z = (60 - 50) / 5
z = 2
Next, we look up the probability corresponding to a z-score of 2 in Table A (standard normal distribution table). The value in the table represents the probability of a random variable being less than the given z-score. To find the probability of the worker finishing in more than 60 minutes, we subtract this value from 1.
From Table A, the probability corresponding to a z-score of 2 is approximately 0.9772.
Probability = 1 - 0.9772
Probability ≈ 0.0228
Therefore, the probability that the worker will finish assembling the racing car in more than 60 minutes is approximately 0.0228 or 2.28% (rounded to two decimal places).
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PLSSSSS HELPPP PLSSSSSSSSS PLS I NEED HELPP
Jorge takes his friends out for smoothies. He buys 5 smoothies and leaves a $3 tip,
paying a total of $23. He wants to know the price of one smoothie.
• price of 5 smoothies: 23 – 3 = 20
1) Which equation shows how to find the price of one smoothie?
20 – 5 = 15
20 : 5 = 4
23 : 5 = 4.60
23 - 5 = 18
Answer:
Each smoothie was $4
Step-by-step explanation:
Please someone help me!! Look at picture. Also write as it expression.
Answer:hi there!that same guy did that w my question too :( i’m reporting his answers. i will help u out tho ahah. the answer is 470(32-n). i hope this helps :). have a good dayyy
Step-by-step explanation:
April has 6 fruit bars.she cuts them into halves. how many 1/2 size bar pieces does she have
Answer:
12
Step-by-step explanation:
If you cut them into halves then there will be twice as many pieces.
so you do:
6 x 2
= 12
What is the solution to the following graph? Write it as an ordered pair to get credit.
Answer:
(2,6)
Step-by-step explanation:
uh someone help D:
ill make the points high
Answer:
m = 18/4 = 9/2 = 4.5
Step-by-step explanation:
Notice that the line passes through (0, 0) and (4, 18). Thus, its 'rise' is 18 - 0, or 18, and its 'run' is 4 - 0, or 4, and the slope (which is the desired constant of proportionality) is m = 18/4 = 9/2 = 4.5 This is Answer B
A coach buys a uniform and a basketball for each of the 20 players on the team. Each
basketball costs $10.40. The coach spends a total of $620 for uniforms and basketballs
What was the cost of a single uniform?
Answer:
$20.60
Step-by-step explanation:
You find how much it costs for the total amount of basketballs (10.40×20=208), then you subtract that number from the total cost of everything to get the cost of all the uniforms (620-208=412), then you divide the total costs for all uniforms by 20 to find the cost for a single uniform (412÷20=20.6). Always make sure that the decimals go until the hundredths place for USD.
Hope this helps!
What is the sign of −9⋅( 0/-3)
Answer:
hi
Step-by-step explanation:
sorry
Answer:
0
Step-by-step explanation:
The sine function of 0 is 0.
We got 0 because you multiplied -9 by 0 divided by -3. DIviding by 0 really doesn't have an answer, but it'd most logically be 0.
Ms Carr made a mistake in her checkbook. she wrote a check for $8.98 to rent a video but mistakenly recoreded it in her checkbook as an $8.98 deposit on the blank slide represent each transaction with a rational number and explain the difference between the transactions
Vera exercised for 60% of the time that Noah exercised. Vera exercised for 78 minutes. How long did Noah exercise
The time spent by Noah exercising is 130 minutes
How to determine how long did Noah exerciseFrom the question, we have the following parameters that can be used in our computation:
Vera exercised for 60% of the time that Noah exercised. Vera exercised for 78 minutes.using the above as a guide, we have the following:
Vera = 60% * Noah
So, we have
60% * Noah = 78
Divide both sides by 60%
Noah = 130
Hence, Noah exercised for 130 minutes
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Plssss help me out I really need a 87 and don’t get this wrong ❤️
Answer:
73 degrees
Step-by-step explanation:
The total number of all of the angles in a triangle added together should be 180 degrees. You know that one of the angles is 17. The other angle is 90 because it is a right triangle.
90 + 17 = 107
180 - 107 = 73
So, the other angle is 73 degrees. If this is wrong I am so sorry. Hope this helps you, let me know if it is right!
Answer:
73°
Step-by-step explanation:
A right triangle has one right angle and two acute angles.
A right angle is 90° and the question says that one of the angle are 17°.
We need to add both angles together which = 107°.
A triangle internal total angles will always add up to 180°.
So we need to do 180° - 107° to find the missing angle which = 73°.
Also, the question said that the missing angles was acute and 73° is acute.
hope this helps :)
which expression is a fourth root of -1 + i√3?
Answer:
−1+1.732051i
Step-by-step explanation:
How many toys would Louis build in 10 hours if she built 3 toys every 20 minutes?
Answer:
90 toys
Step-by-step explanation:
We should use the same unit for time. Rewrite 20 minutes as 1/3 hour.
The unit rate is then:
3 toys 9 toys
----------------- = -----------
1/3 hour hour
Multiply this unit rate by 10 hours, obtaining 90 toys
What is the measure of the other acute angle ?
Answer:
[tex]62^{o}[/tex]
Step-by-step explanation:
All the angles in a triangle add up to [tex]180^{o}[/tex]
Every right angle triangle has a right angle in it which is [tex]90^{o}[/tex]
So to find the remaining angle, you do [tex]180^{o}[/tex] - [tex]90^{o}[/tex] - [tex]28^{o}[/tex] = [tex]62^{o}[/tex]
Find the value of the variables in the simplest form
Answer:
x = 2
Step-by-step explanation:
Using Pythagoras' identity in the right triangle
x² + x² = (2[tex]\sqrt{2}[/tex] )² , that is
2x² = 8 ( divide both sides by 2 )
x² = 4 ( take the square root of both sides )
x = [tex]\sqrt{4}[/tex] = 2
Which of the statements are correct?
1. A condition for using the chi-square goodness-of-fit test is that all expected counts must be at least five.
2. The chi-square goodness-of-fit test uses 1 − n degrees of freedom.
3. A condition for using the chi-square goodness-of-fit test is the observations are based on a random sa
The chi-square goodness-of-fit test requires that all anticipated counts be at least five and observations be drawn from random sample in order to be valid. The correct statements are I and III only. Correct option is C.
I. The chi-square goodness-of-fit test requires that all anticipated counts be at least five and that observations be drawn from a random sample in order to be valid. This statement is correct. The chi-square goodness-of-fit test is based on the chi-square distribution, which approximates the sampling distribution of the test statistic.
To ensure the validity of the test, it is generally recommended that all expected counts in the cells of the contingency table have a minimum expected count of five. This guideline helps to ensure that the chi-square test statistic follows the chi-square distribution, which is approximately valid under this condition.
II. The chi-square goodness-of-fit test uses 1 − n degrees of freedom. This statement is incorrect. The number of categories being assessed determines the degrees of freedom for the chi-square goodness-of-fit test. It is equal to the total categories less one. So, if there are n categories, the degrees of freedom for the test would be n - 1, not 1 - n.
III. A condition for using the chi-square goodness-of-fit test is that the observations are based on a random sample. This statement is correct. The chi-square goodness-of-fit test assumes that the observations are obtained from a random sample or represent a random selection from a population.
This assumption is important to ensure that the test results are generalizable to the population from which the sample is drawn. If the observations are not based on a random sample, the test results may not be valid or may be biased. Therefore, random sampling is a condition for using the chi-square goodness-of-fit test.
The correct statements are I and III only. Correct option is C.
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Complete question is:
Which of the statements are correct?
I. A condition for using the chi-square goodness-of-fit test is that all expected counts must be at least five.
II. The chi-square goodness-of-fit test uses 1 − n degrees of freedom.
III. A condition for using the chi-square goodness-of-fit test is the observations are based on a random sample.
a) I only
b) II only
c) I and III only
d) II and III only
e) I, II, and III
Question 5 Multiple Choice Worth 1 points)
(05.02 MC)
Find the measure of angle x in the figure below.
52
59
X
63
O 35
O 48°
0 69
O 789
Answer:
your answer should be 48 degrees