In a right triangle, the tangent of an angle is defined as the ratio of the opposite side to the adjacent side. Therefore, for triangle ΔWXY, the tangent of ∠X is the ratio of side WY to YX, which is 8/15.
Explanation:To understand this question, we need to know that in the context of a right triangle, the tangent of an angle is defined as the ratio of the length of the opposite side to the length of the adjacent side. In ΔWXY, where the measure of ∠Y=90°, ∠X is the angle we are considering. The side opposite to ∠X is WY and the side adjacent to ∠X is YX. Therefore, the tangent of ∠X can be calculated using the formula: tan(X) = WY / YX.
In this scenario, we know that WY = 8 and YX = 15. So, the tangent of ∠X is given by: tan(X) = WY / YX = 8 / 15. Hence, the ratio that represents the tangent of ∠X is 8 / 15.
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f(x) = (x + 5)(x + 6)
Answer:(-5,0) , (-6,0)
Y= (0,30)
Step-by-step explanation:
In the illustration below, the three cube-shaped tanks are identical. The spheres in any given tank
are the same size and packed wall-to-wall. If each of the tanks are filled to the top with water, which
tank would contain the most water. Prove your answer algebraically using x to represent the edge
length of the tanks.
Answer:
Step-by-step explanation:
Let represent the edge of the tank with x and the radius of the first sphere with x/2;
The amount of the water = Volume of the tank - Volume of the sphere
= [tex]x^3 - \frac{4}{3} \pi (\frac{x}{2})^3[/tex]
on the second cube ; the radius of the sphere = [tex]\frac{x}{4} \ units[/tex] ;
Also the number of sphere here is = 8
The amount of water = [tex]x^3 -8*\frac{4}{3} \pi (\frac{x}{4})^3[/tex]
For the third figure ; the radius of the sphere is = [tex]\frac{x}{8} \ units[/tex]
Also the number of sphere here is = 64
The amount of water = [tex]x^6 -64*\frac{4}{3} \pi (\frac{x}{8})^3[/tex]
= [tex]x^3 - \frac{4}{3} \pi (\frac{x}{2})^3[/tex]
In the fourth tank ; 512 sphere illustrates that in a single row; that more than one 8 sphere is present i.e 8³ = 512
then the radius will be = [tex]\frac{x}{16}[/tex]
The amount of water = [tex]x^3 -512*\frac{4}{3} \pi (\frac{x}{16})^3[/tex]
= [tex]x^3 -\frac{4}{3} \pi (\frac{x}{2})^3[/tex]
This implies that alll the three cube shaped tanks are identical and hold equal amount of water.
A certain rare form of cancer occurs in 37 children in a million, so its probability is 0.000037. In the city of Normalville there are 74,090 children. A Poisson distribution will be used to approximate the probability that the number of cases of the disease in Normalville children is more than 2. Find the mean of the appropriate Poisson distribution (the mean number of cases in groups of 74,090 children).
Answer:
Mean = 2.7
In a group of 74090 we would expect about 3 (rounding to nearest whole number) children with the rare form of cancer.
Step-by-step explanation:
We are given that the rate of cancer in children is 37 children in 1 million. So the probability of cancer in a child is P(C) = 0.000037
Poisson distribution is used to approximate the number of cases of diseases and we have to find what will be the mean number of cases for 74,090.
In simple words we have to find the expected number of children with cancer in a group of 74,090 children.
The mean value of expected value can be obtained by multiplying the probability with the sample size. So, in this case multiplying probability of child having a cancer with total group size will give us the expected or mean number of children in the group with cancer.
Mean = E(x) = P(C) * Group size
Mean = 0.000037 x 74090
Mean = 2.7
This means in a group of 74090 we would expect about 3 (rounding to nearest whole number) children with the rare form of cancer.
Final answer:
The mean of the Poisson distribution for the number of cancer cases among 74,090 children in Normalville is approximately 2.7413 cases.
Explanation:
To find the mean of the appropriate Poisson distribution for the number of cases in groups of 74,090 children in Normalville, we multiply the probability of the disease by the number of children. Thus, the mean (μ) is:
μ = probability of one child having the disease × total number of children
μ = 0.000037 × 74,090 = approximately 2.7413
The mean of the Poisson distribution, in this case, indicates the average number of children who would have this rare form of cancer in groups of 74,090 children in Normalville.
Let the Poisson random variable U (see p. 227) be the number of calls for technical assistance received by a computer company during the firm’s nine normal work- day hours. Suppose the average number of calls per hour is 7.0 and that each call costs the company $50. Let V be a Poisson random variable representing the number of calls for technical assistance received during a day’s remaining 3.10 Order Statistics 193 fifteen hours. Suppose the average number of calls per hour is 4.0 for that time period and that each such call costs the company $60. Find the expected cost and the vari- ance of the cost associated with the calls received during a twenty-four-hour day.
Answer:
Expected cost = $6,750
Variance of the cost = $373,500
Step-by-step explanation:
During normal 9 work hours: average number of calls = 7.0
Cost of each call = $50
During 15 off hours:
average number of calls = 4.0
Cost of each call = $60
Let's take U as the number of calls during the normal 9 hours.
I.e, [tex] U = U_1+U_2+U_3+U_4....+ U_9[/tex]
Therefore,
[tex] E(U) = E(U_1)+E(U_2)+E(U_3)+E(U_4)....+E(U_9)[/tex]
= 7+7+7+7+7+7+7+7+7
= 63
In Poisson random variable, Variance= mean, thus:
[tex] Var(U) =Var(U_1)+Var(U_2).....+Var(U_9) [/tex]
= 7+7+7+7+7+7+7+7+7
=63
Let's take V as the number of calls during the day's remaining 15 hours.
E(V) = Var(V)
= 15(4)
=60
The expected cost and the variance of cost associated with the calls received during a 24 hour day:
The expected cost =
$50U + $60V
= $50(63) + $60(60)
= $3150 + $3600
= $6750
The variance of the cost :
= Var(50U + 60V)
= 50²Var(U) + 60²Var(V)
= 2500*63 + 3600*60
= $373,500
Therefore, the expected cost is $6,750 and the variance of the cost is $373,500
I NEED HELPP‼️l
Which number is farthest from 2 on the number line?
O 12.1
O √24
O 12.5
O 129
Answer:
129
Step-by-step explanation:
What is the lowest terms of 36 and -18?
Answer:
49
Step-by-step explanation:
36 minus -18 is 49
Answer:
-1/2
Step-by-step explanation:
The fraction is not reduced to lowest terms. We can reduce this fraction to lowest
terms by dividing both the numerator and denominator by 18.
S = the team's score
g = the number of goals a team has scored
Which of the variables is independent and which is dependent?
Answer:
s would be the dependent variable, and g the independent.
Step-by-step explanation:
Whatever the score is, it would depend on how many goals the team has scored.
Final answer:
The independent variable is typically the one that is manipulated, like the number of goals scored (g), and the dependent variable is the one that responds, like the team's score (S). A scatter plot can reveal patterns, and the correlation coefficient indicates the strength of the relationship. The least-squares line represents a best-fit line through the data.
Explanation:
The independent variable is typically the one that is controlled or manipulated, whereas the dependent variable is the one that responds to changes in the independent variable. In the context of a team's score (S) and the number of goals scored (g), the independent variable is usually the number of goals scored (g) because it can be controlled or affected through the team's actions. The dependent variable is the team's score (S), because it depends on the number of goals scored.
In a broader context, such as analyzing the relationship between the ranking of a state and the area of the state, the independent variable could be the ranking (since it is not influenced by the area), and the dependent variable would be the area of the state (since it could be influenced by a variety of factors, including ranking).
When creating a scatter plot, it is common to place the independent variable on the x-axis and the dependent variable on the y-axis. This scatter plot could reveal correlations or trends between the two variables. The correlation coefficient is a statistical measure that describes the strength and direction of a relationship between two variables. A correlation coefficient close to 1 or -1 indicates a strong relationship, while a number close to 0 indicates a weak relationship. The least-squares line is a regression line that minimizes the sum of the squared differences between the observed values and the values predicted by the line.
9 more than the quotient of 52 divided by 4
The solution of ''9 more than the quotient of 52 divided by 4'' is 22.
Now,
Given statement is, ''9 more than the quotient of 52 divided by 4''
What is Quotient?
A quotient is the answer a division problem. The divisor is the number of parts you divide the dividend by.
Now,
The quotient of 52 divided by 4 is,
52 ÷ 4 = 13
And, 9 more than the quotient of 52 divided by 4 is,
( 52 ÷ 4 )+ 9 = 13 + 9 = 22
Hence, The solution of ''9 more than the quotient of 52 divided by 4'' is 22.
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To solve the expression, divide 52 by 4 to get 13, then add 9 to the quotient, resulting in the final answer of 22.
Explanation:The question asks to find '9 more than the quotient of 52 divided by 4'.
First, we need to calculate the quotient of 52 divided by 4, which is done by performing the division.
So, 52 ÷ 4 equals 13. Next, we add 9 to this quotient to get the final result.
Adding 9 to 13 gives us 22.
Therefore, 9 more than the quotient of 52 divided by 4 is 22.
Simplifying each side of the equation results in x2 − 3x − 4 = x2 − 5x + 6.
Find the solution:
x + 2
3x
−
1
x − 2
=
x − 3
3x
x =
Answer:
x = 5
Step-by-step explanation:
x² -3x -4 = x² - 5x + 6.
-x² - x²
-3x -4 = -5x + 6
+3x + 3x
-4 = -2x +6
-6 -6
-10 = -2x
÷-2 ÷-2
5 = x
Hope this Helps
Answer:
x = 5
Step-by-step explanation:
hope this helps!
Average starting salaries for students using a placement service at a university have been steadily increasing. A study of the last four graduating classes indicates the following average salaries:
$60,000, $72,000, $84,500, and $96,000 (last graduating class).
(a) Predict the starting salary for the next graduating class using a simple exponential smoothing model with α = 0.25. Assume that the initial forecast was $55,000.
Given Information:
Smoothing constant = α = 0.25
Initial forecast salary = F₀ = $55,000
Actual salaries = A = $60,000, $72,000, $84,500, and $96,000
Required Information:
Forecast salaries = F = ?
Answer:
[tex]F_{1} = \$56,250\\F_{2} =\$ 60,187.5\\F_{3} = \$66,265.6\\F_{4} = \$73,699.2\\[/tex]
Step-by-step explanation:
The exponential smoothing model is given by
[tex]F_{n} = \alpha \cdot A_{n - 1} + (1 - \alpha ) F_{n - 1}[/tex]
Where
[tex]F_{n}[/tex] is the forecast salary for nth graduate class
α is the smoothing constant
[tex]A_{n-1}[/tex] is the actual salary of n - 1 graduate class
[tex]F_{n-1}[/tex] is the forecast salary of n - 1 graduate class
For n = 1
[tex]F_{1} = 0.25 \cdot A_0} + (1-0.25) \cdot F_{0}\\F_{1} = 0.25 \cdot 60,000} + (0.75) \cdot 55,000\\F_{1} = 56,250[/tex]
For n = 2
[tex]F_{2} = 0.25 \cdot A_1} + (1-0.25) \cdot F_{1}\\F_{2} = 0.25 \cdot 72,000} + (0.75) \cdot 56,250\\F_{2} = 60,187.5[/tex]
For n = 3
[tex]F_{3} = 0.25 \cdot A_2} + (1-0.25) \cdot F_{2}\\F_{3} = 0.25 \cdot 84,500} + (0.75) \cdot 60,187.5\\F_{3} = 66,265.625[/tex]
For n = 4
[tex]F_{4} = 0.25 \cdot A_3} + (1-0.25) \cdot F_{3}\\F_{4} = 0.25 \cdot 96,000} + (0.75) \cdot 66,265.625\\F_{4} = 73,699.218[/tex]
Therefore, the foretasted starting salaries are
[tex]F_{1} = \$56,250\\F_{2} =\$ 60,187.5\\F_{3} = \$66,265.6\\F_{4} = \$73,699.2\\[/tex]
Using an exponential smoothing model with α = 0.25, we sequentially calculate the forecasted starting salary for each year, then use that to estimate the starting salary for the next graduating class.
Explanation:To predict the starting salary for the next graduating class using a simple exponential smoothing model with α = 0.25 and an initial forecast of $55,000, we follow these steps:
Calculate the exponentially smoothed forecast for each year after the initial year. The formula is: Next Forecast = α(Current Actual) + (1-α)(Previous Forecast).For the class with a starting salary of $60,000: Forecast = 0.25($60,000) + 0.75($55,000) = $56,250.Continue the process using each actual salary to get the forecast for the next year, eventually reaching the forecast for the class after the $96,000 graduating class.By applying this model, we will obtain the predicted starting salary for the next class after performing these calculations for each given salary data point in sequence.
the scores on a test given to all juniors in a school district are normally distributed with a mean of 80 and a standard deviation of 8. Find the percent of juniors whose score is at least 80. The percent of juniors whose score is at or above the mean is_____% PLZ HELP!
Answer:
The percent of juniors whose score is at or above the mean is 50%
Step-by-step explanation:
Problems of normally distributed samples can be solved using 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.
In this problem, we have that:
[tex]\mu = 80, \sigma = 8[/tex]
Find the percent of juniors whose score is at least 80.
This is 1 subtracted by the pvalue of Z when X = 80. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{80 - 80}{8}[/tex]
[tex]Z = 0[/tex]
[tex]Z = 0[/tex] has a pvalue of 0.5
1 - 0.5 = 0.5
So
The percent of juniors whose score is at or above the mean is 50%
An insect population dies of exponentially and is governed by the equation p′=−µp, where µ is the mortality rate. If 1200 insects hatch, and only 70 remain after 6 days, what is the mortality rate?.
Answer:
[tex]47.36\%[/tex]
Step-by-step explanation:
The equation that governs how the insect population dies is
[tex]p' = - \mu p[/tex]
We need to solve this differential equation for p.
We separate variables to get:
[tex] \frac{p'}{p} = - \mu[/tex]
We integrate both sides to get:
[tex] \int\frac{p'}{p} dt = - \mu \int \: dt[/tex]
[tex] ln( |p| ) = - \mu \: t + ln(k) [/tex]
[tex]p = c{e}^{ \ - ut} [/tex]
If 1200 insects hatch, and only 70 remain after 6 days,
Then we have:
[tex]70 = 1200 {e}^{ - 6 \mu} [/tex]
[tex] \frac{70}{1200} = {e}^{ - 6 \mu} [/tex]
[tex] - 6 \mu = ln( \frac{7}{120} ) [/tex]
[tex] \mu = \frac{ln( \frac{7}{120} ) }{ - 6} [/tex]
[tex] \mu = 0.4736[/tex]
[tex]47.36\%[/tex]
In the United States, 41% of the population have brown eyes. If 14 people are randomly selected, find the probability that at least 12 of them have brown eyes. Is it unusual to randomly select 14 people and find that at least 12 of them have brown eyes? Why or why not?
Answer:
0.000773 is the probability that atleast 12 out of 14 will have brown eyes.
Step-by-step explanation:
We are given the following information:
We treat people having brown eyes as a success.
P(people have brown eyes) = 41% = 0.41
Then the number of people follows a binomial distribution, where
[tex]P(X=x) = \binom{n}{x}.p^x.(1-p)^{n-x}[/tex]
where n is the total number of observations, x is the number of success, p is the probability of success.
Now, we are given n = 14
We have to evaluate:
[tex]P(x \geq 12) = P(x = 12) + P(x = 13) + P(X = 14) \\= \binom{14}{12}(0.41)^{12}(1-0.41)^2 + \binom{14}{13}(0.41)^{13}(1-0.41)^1 + \binom{14}{14}(0.41)^{14}(1-0.41)^0\\= 0.0007 + 0.00007 + 0.000003\\= 0.000773[/tex]
0.000773 is the probability that atleast 12 out of 14 will have brown eyes.
Yes, it is an unusual event due to small probability values.
Jimmy bought a 5-kilogram can of peanuts for $4.50. What is the unit price?
Answer:
$0.90 per kilogram
Step-by-step explanation:
4.5/5=.9
what is the radius and diameter of the following circle
Answer:
Radius 6.5cm
Diameter 13cm
Step-by-step explanation:
Diameter ia a straight line passing from side to side through the center a circle or sphere.
Radius formula is simply derived by halving the diameter of the circle
13/2=6.5
Find the quotient. Round to the nearest tenth. 3784 divided by 18
Answer:
210.22
Step-by-step explanation:
first you need to divide 3785 divided by 18 which is 210.22222222 then u need to round to the nearest tenth which is equaled to 210.22. I hope this helped
Tiffany has a 30% chance of winning a game. She uses random numbers to simulate a series of 7 games. In her simulation, the numbers 0–2 represent a win, and the numbers 3–9 represent a loss. Select all the trials whose results show 3 wins in 7 games played. A. 8531905 B. 4963184 C. 7269108 D. 0689271 E. 7042351 F. 9094562
Answer:
C. 7269108
D. 0689271
E. 7042351
Step-by-step explanation:
If the number is 0,1 or 2, it is a win.
Otherwise, it is a loss.
Each number is a match.
A. 8531905
Two wins(0,1), 5 losses(8,5,3,9,5)
B. 4963184
One win(1), 6 losses(4,9,6,3,8,4)
C. 7269108
Three wins(2,1,0) and four losses (7,6,9,8)
D. 0689271
Three wins (0,2,1) and four losses (6,8,9,7)
E. 7042351
Three wins (0,2,1), four losses (7,4,3,5)
F. 9094562
Two wins (0,2) and five losses (9,9,4,5,6)
Answer:
C.
D.
E.
Step-by-step explanation:
PLEASE HELP ASAP!! Geometry question!! Major points
Answer:
-8 and 1
Step-by-step explanation:
the x is going by 5 and the y is going by 2
so add 5 to the x and 2 to the y
hope this help <(*__*)>
Answer:
(-7,1)
Step-by-step explanation:
(1+x/2) = -3 (-3+y/2) = -1
2(1+x/2) = -3(2) 2 (-3+y/2) = -1(2)
multiple each side by two to cancel the two's.
1+x= -6 -3+y= -2
x=-7 y= 1
Design an expression that can be used to find the surface area of tower n cubes tall
Answer: The surface is (4*n + 2)*L^2
Step-by-step explanation:
The surface of a cube is equal to 6 times the area of one of the sides.
So if the sides of the cube have a length L, we have that the area of one face is L^2, and the surface of the cube is 6*L^2
Now, if we put n of those cubes in a tower, we will have a shape were the bottom and the top still have an area of L^2, then the total area of the bottom and the top is 2*L^2
But each one of the sides has two sides of length L, and two sides of length n*L (n times the length of one of the sides), then the area of each side is equal to n*L*L = n*L^2
and we have 4 sides, then the total area of the sides is 4*n*L^2
Then the total surface of the tower is:
A = 4*n*L^2 + 2*L^2 = (4*n + 2)*L^2
Using the digits 1 to 20, at most 1 time each, fill in the boxes to create equivalent expressions.
Answer:
There are many possible solutions. For example,
(2^3)^4 = ((2^5)^12)/((2^6)^8) = 2^10 x 2^2 = (2^19)/(2^7)
(2^2)^5 = ((2^6)^11)/((2^7)^8) = 2^1 x 2^9 = (2^20)/(2^10)
Step-by-step explanation:
You need to fill in boxes with the digits 1 to 20 to create equations where both sides yield the same numerical result. This will involve understanding of basic arithmetic operations and a bit of trial and error.
Explanation:The subject of this question is Mathematics. Specifically, it relates to the concept of equivalent expressions, which are an essential component of algebra and arithmetic. First, it's crucial to understand the concept of equivalent expressions: two expressions are considered equivalent if they share the same numerical value for each possible value of their variable(s).
Now, let's make an example with the numbers 1 to 10 (just to simplify the explanation). Consider the equations: 1+2+3+4 and 5+3+2+1. Even though the order of operations is different, both expressions yield the final numerical value of 10, making them equivalent expressions.
In the context of the question, you are being asked to fill in boxes with the digits 1-20, such that the expressions on either side of the equation sign are equivalent. This might involve a combination of operations like addition, subtraction, multiplication, and division.
It's a challenging task because it involves a bit of trial and error. Start by deciding on the operations for the expressions and then fill in the numbers. Make sure you check your results by calculating the numerical value of each expression.
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Find the lateral area of the cylinder. Give answer in terms of pi. 6ft is the radius and 11ft is the height.
Answer:
[tex]132\pi[/tex]
Step-by-step explanation:
The lateral area is the area of a rectangle. Think of a soup can with the label removed and laid out flat on a table. The height of the rectangle is the same as the height of the can (cylinder). Where does the base of the rectangle come from? It's the circumference of the can "unrolled."
Area of a rectangle = base x height
Circumference of a circle [tex]C=2\pi r[/tex]
Lateral Area [tex]=2\pi r \times h[/tex] [tex]=2 \pi (6)(11) =132\pi[/tex]
A business printed 225 books on Friday. each book has 350 pages. How many pages did the business play on Friday?
Answer:
78,750 pages
Step-by-step explanation:
225 books each with 350 paged
225 x 350
78,750 pages
On a coordinate plane, a rectangle has points (4, 1), (4, negative 3), (negative 2, negative 3), (negative 2, 1).
Marina is drawing a plan for a new garden. The rectangle plotted in the coordinate plane represents the garden, measured in feet. How much soil will she need to cover the garden?
10 ft2
12 ft2
20 ft2
24 ft2
Answer:
24 feet
Step-by-step explanation:
sorry I'm so late
The daily dinner bills in a local restaurant are normally distributed with a mean of $28 and a standard deviation of $6. What is the probability that a randomly selected bill will be at least $39.10
Answer:
Probability that a randomly selected bill will be at least $39.10 is 0.03216.
Step-by-step explanation:
We are given that the daily dinner bills in a local restaurant are normally distributed with a mean of $28 and a standard deviation of $6.
Let X = daily dinner bills in a local restaurant
So, X ~ N([tex]\mu=28,\sigma^{2} =6^{2}[/tex])
The z-score probability distribution for normal distribution is given by;
Z = [tex]\frac{ X -\mu}{\sigma}[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = mean amount = $28
[tex]\sigma[/tex] = standard deviation = $6
The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) 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.
So, the probability that a randomly selected bill will be at least $39.10 is given by = P(X [tex]\geq[/tex] $39.10)
P(X [tex]\geq[/tex] $39.10) = P( [tex]\frac{ X -\mu}{\sigma}[/tex] [tex]\geq[/tex] [tex]\frac{ 39.10-28}{6}[/tex] ) = P(Z [tex]\geq[/tex] 1.85) = 1 - P(Z < 1.85)
= 1 - 0.96784 = 0.03216
Now, in the z table the P(Z [tex]\leq[/tex] x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 1.85 in the z table which has an area of 0.96784.
Hence, the probability that a randomly selected bill will be at least $39.10 is 0.03216.
The probability that a randomly selected bill will be at least $39.10 is approximately 0.0323.
First, we calculate the z-score for a bill of $39.10 using the formula:
[tex]\[ z = \frac{X - \mu}{\sigma} \][/tex]
where X is the value for which we want to find the probability, [tex]\( \mu \)[/tex] is the mean, and [tex]\( \sigma \)[/tex] is the standard deviation.
Given:
[tex]\[ \mu = 28 \] \[ \sigma = 6 \] \[ X = 39.10 \][/tex]
Plugging in the values:
[tex]\[ z = \frac{39.10 - 28}{6} \] \[ z = \frac{11.10}{6} \] \[ z \approx 1.85 \][/tex]
Now, we look up the z-score of 1.85 in the standard normal distribution table or use a calculator to find the probability of a z-score being at least 1.85. This gives us the area to the right of the z-score on the standard normal curve.
Using a standard normal distribution table or calculator, we find:
[tex]\[ P(Z \geq 1.85) \approx 0.0323 \][/tex]
Suppose cattle in a large herd have a mean weight of 1217lbs1217 lbs and a variance of 10,40410,404. What is the probability that the mean weight of the sample of cows would differ from the population mean by more than 11lbs11 lbs if 116116 cows are sampled at random from the herd? Round your answer to four decimal places.
Answer:
0.2460 = 24.60% probability that the mean weight of the sample of cows would differ from the population mean by more than 11 lbs if 116 cows are sampled at random from the herd.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation(which is the square root of the variance) [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.
In this problem, we have that:
[tex]\mu = 1217, \sigma = \sqrt{10414} = 102, n = 116, s = \frac{102}{\sqrt{116}} = 9.475[/tex]
What is the probability that the mean weight of the sample of cows would differ from the population mean by more than 11 lbs if 116 cows are sampled at random from the herd?
This is 2 multiplied by the pvalue of Z when X = 1217 - 11 = 1206. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{1206 - 1217}{9.475}[/tex]
[tex]Z = -1.16[/tex]
[tex]Z = -1.16[/tex] has a pvalue of 0.1230
2*0.1230 = 0.2460
0.2460 = 24.60% probability that the mean weight of the sample of cows would differ from the population mean by more than 11 lbs if 116 cows are sampled at random from the herd.
To calculate the probability, we can use the Central Limit Theorem. Calculate the standard error using the formula: standard error = standard deviation / sqrt(n), then use the z-score formula to find the probability.
Explanation:To find the probability that the mean weight of the sample of cows would differ from the population mean by more than 11 lbs, we can use the Central Limit Theorem. Since the sample size is large (n > 30), the distribution of sample means will be approximately normally distributed. First, we calculate the standard deviation of the sampling distribution, also known as the standard error, using the formula: standard error = standard deviation / sqrt(n). In this case, the standard error is sqrt(10404)/sqrt(116).
Finally, we can use the z-score formula to calculate the probability. The z-score is given by z = (x - mean) / standard error. We want to find the probability that the mean weight differs from the population mean by more than 11 lbs, so we calculate the z-score for both 11 and -11 and use the z-table or a calculator to find the probability of z being greater than the positive z-score and less than the negative z-score. Adding these two probabilities gives us the final answer.
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A book normally costs $21.50. Today it was on sale for $15.05. What percentage discount was offered during the sale?
Answer:
The answer is 30% off
Step-by-step explanation:
if you do 21.50 - 30% = 15.05
Click to review the online content. Then answer the question(s) below, using complete sentences. Scroll down to view additional questions. Online Content: Site 1 Online Content: Site 2 Describe how you would use the rules of exponents to simplify (7x2yz)3. You may indicate an exponent in your answer with ^. For example, 3x2 y2as 3x^2y^2. (Site 1)
Answer:
First, apply the power of a product rule by which you raise each factor to the power 3, and then multiply all the factors, to obtain:
[tex](7x^2yz)^3=7^3(x^2)^3y^3z^3[/tex]
Next, apply the power of a power rule, in virtue of which you raise the factor x² to the power 3 and obtain:
[tex]7^3(x^2)^3y^3z^3=7^3x^6y^3z^3[/tex]
Finally, compute the numerical values, doing 7³ = 7×7×7 = 343.
Therefore, the final result is:
[tex]343x^6y^3z^3[/tex]
Explanation:
The expression you have to simplify is:
[tex](7x^2yz)^3[/tex]
You have to apply two rules:
1. Power of a product2. Power of a power1. Power of a product
This rule states that the power of a product is equal to the product of each factor raised to the same exponent of the whole prduct:
For instance:
[tex](abc)^z=a^z\cdot b^z\cdot c^z[/tex]
Using this with the expression [tex](7x^2yz)^3[/tex] it is:
[tex](7x^2yz)^3=7^3\cdot (x^2)^3\cdot y^3\cdot z^3[/tex]
In complete sentences that is: raise every factor, 7, x², x, and z to the exponent 3 and, then, multiply them.
2. Power of a power:
This rule states that to raise a power to a power, you must multiply the exponents.
For instance:
[tex](a^n)^m=a^{m\times n}[/tex]
You must apply that rule to the factor [tex](x^2)^3[/tex]
That is:
[tex](x^2)^3=x^{(3\times 2)}=x^6[/tex]
3. Final result and description using complete sentences:
The first step is to apply the power of a product rule by rasing each factor to the power 3, and then multiply all the factors, to obtain:
[tex](7x^2yz)^3=7^3(x^2)^3y^3z^3[/tex]
The second step is to apply the power of a power rule, in virtue of which you raise the factor x² to the power 3, in this way:
[tex]7^3(x^2)^3y^3z^3=7^3x^6y^3z^3[/tex]
The last step is to calculate the numerical values, doing 7³ = 7×7×7 = 343.
The final result is: [tex]343x^6y^3z^3[/tex]
An online gaming site conducted a survey to determine the types of games people play online. if 1500 people participated in the study how many more would play card games than arcade games (Page 824)
Answer:
315
Step-by-step explanation:
The missing percentages of the given scenario are;
Adventure Games: 22%
Puzzles: 28%
Card Games: 30%
Arcade Games: 9%
Board Games: 11%
So in order to solve the problem, we simply use the pie chart distributions to get the result
Now if look at the percentages, we that card games percentage is 30 while arcade games is 9 so, 21 % of people play more card games.
In terms of number of people = 21/100 x 1500 = 315
Hence out of 1500, 315 people play card games more than arcade
Answer:
The number of more people that played card games than arcade games is 150 people
Step-by-step explanation:
Here we have a pie chart showing games people play in the following proportions
Assumption; Card games = 49%
Arcade games = 32%
Classic = 15%
Kids = 4%
Therefore. if 49% played card games, we have 49% of 1500 which is 735 people, while 32% that played arcade games, we have 39% of 1500 = 0.39×1500 = 585
Therefore, the number of more people that played card games than arcade games = 735 - 585 = 150 people.
How do I graph y=3 sin0+1
Repeated student samples. Of all freshman at a large college, 16% made the dean’s list in the current year. As part of a class project, students randomly sample 40 students and check if those students made the list. They repeat this 1,000 times and build a distribution of sample proportions.
(a) What is this distribution called?
(b) Would you expect the shape of this distribution to be symmetric, right skewed, or left skewed? Explain your reasoning.
(c) Calculate the variability of this distribution.
(d) What is the formal name of the value you computed in (c)?
(e) Suppose the students decide to sample again, this time collecting 90 students per sample, and they again collect 1,000 samples. They build a new distribution of sample proportions. How will the variability of this new distribution compare to the variability of the distribution when each sample contained 40 observations?
Answer:
a) p-hat (sampling distribution of sample proportions)
b) Symmetric
c) σ=0.058
d) Standard error
e) If we increase the sample size from 40 to 90 students, the standard error becomes two thirds of the previous standard error (se=0.667).
Step-by-step explanation:
a) This distribution is called the sampling distribution of sample proportions (p-hat).
b) The shape of this distribution is expected to somewhat normal, symmetrical and centered around 16%.
This happens because the expected sample proportion is 0.16. Some samples will have a proportion over 0.16 and others below, but the most of them will be around the population mean. In other words, the sample proportions is a non-biased estimator of the population proportion.
c) The variability of this distribution, represented by the standard error, is:
[tex]\sigma=\sqrt{p(1-p)/n}=\sqrt{0.16*0.84/40}=0.058[/tex]
d) The formal name is Standard error.
e) If we divided the variability of the distribution with sample size n=90 to the variability of the distribution with sample size n=40, we have:
[tex]\frac{\sigma_{90}}{\sigma_{40}}=\frac{\sqrt{p(1-p)/n_{90}} }{\sqrt{p(1-p)/n_{40}}}}= \sqrt{\frac{1/n_{90}}{1/n_{40}}}=\sqrt{\frac{1/90}{1/40}}=\sqrt{0.444}= 0.667[/tex]
If we increase the sample size from 40 to 90 students, the standard error becomes two thirds of the previous standard error (se=0.667).
Using the Central Limit Theorem, we get that:
a) Sampling distribution of sample proportions of size 40.
b) Symmetric.
c) 0.0580.
d) Standard error.
e) It would decrease.
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean and standard deviation , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean and standard erro .
For a skewed variable, we need n of 30 and greater.
For a proportion p in a sample of size n, we have that: and standard deviation .
In this problem:
Proportion of 16%, thus [tex]p = 0.16[/tex].Sample of 40 students, thus [tex]n = 40[/tex]Item a:
We are working proportions, and sample of 40, thus:
Sampling distribution of sample proportions of size 40.
Item b:
Sample size of 40, thus, by the Central Limit Theorem, approximately normal, which is symmetric.Item c:
This is the standard error, thus:
[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.16(0.84)}{40}} = 0.0580[/tex]
It is of 0.0580.
Item d:
The formal name is standard error.Item e:
The formula is:
[tex]s = \frac{\sigma}{\sqrt{n}}[/tex]
Since n is in the denominator, we can see that the standard error and the sample size are inversely proportional, and thus, increasing the sample size to 90, the variability would decrease.A similar problem is given at https://brainly.com/question/14099217