Union will need to choose a random sample of at least 65 wages to be 90% confident that its estimate of the mean hourly wage of foodservice workers is within $0.45 of the true population mean.
What is the minimum sample size needed?To calculate the minimum sample size needed for the union to be 90% confident within $0.45 of the true population mean, we can use the formula which states n = (Z^2 * σ^2) / E^2
Z = 90% = 1.645
σ = $2.20
E = $0.45
Substituting the values, we get:
n = (1.645^2 * 2.20^2) / 0.45^2
n = 13.097161 / 0.2025
n = 64.6773382716
n = 64.678
n = 65
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The perimeter of a rectangle is 21.2 m, and its area is 23.68 m².
Find its length and width.
length: m
width: m
Construct a 95% confidence interval of the mean pulse rate for adult males ___bpm
The 95% confidence interval of the mean pulse rate for adult females is 68.2 bpm < μ < 76.4 bpm
For a 95% confidence interval, the Z-score is 1.96. Plugging in the values we have for the sample mean, sample standard deviation, and sample size, we get:
Confidence interval = 75.8 ± (1.96 × (3.7 / √50))
Simplifying the expression, we get:
Confidence interval = 71.5 bpm < μ < 80.2 bpm
This means that we can be 95% confident that the true population mean pulse rate for adult females falls within this range.
Now let's construct a confidence interval for adult males. We are given that the sample mean pulse rate for adult males is 72.3 bpm, and the sample standard deviation is 4.0 bpm. Using the same formula and Z-score as before, we can calculate the confidence interval as follows:
Confidence interval = 72.3 ± (1.96 × (4.0 / √50))
Simplifying the expression, we get:
Confidence interval = 68.2 bpm < μ < 76.4 bpm
This means that we can be 95% confident that the true population mean pulse rate for adult males falls within this range.
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the table below shows different make of cars own by teacher in a certain school. work out the angles and percentage then illustrate the information using a pie chart.
Toyota -- 12
Nissan --- 8
Datsun --- 8
Volvo --- 2
Peugeot -- 10
The angles and percentages have been calculated as shown below.
A pie chart for the information about the different make of cars is shown below.
How to determine the angles and percentage?For the total number of car makes, we have the following:
Total make of cars = 12 + 8 + 8 + 2 + 10
Total make of cars = 40.
Next, we would determine the angles and percentage as follows;
Toyota
12/40 × 360 = 108°
12/40 × 100 = 30%.
Nissan
8/40 × 360 = 72°
8/40 × 100 = 20%.
Datsun
8/40 × 360 = 72°
8/40 × 100 = 20%.
Volvo
2/40 × 360 = 18°
2/40 × 100 = 5%.
Peugeot
10/40 × 360 = 90°
10/40 × 100 = 25%.
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Juan catches 80% of the passes thrown to him in football. If the quarterback throws to him 15 times during a game, what is the probability he will catch atleast 10 of them?
the probability that Juan will catch at least 10 passes out of 15 is approximately 0.987.
The binomial distribution, which models the number of successful trials (catches) in a certain number of independent trials (passes thrown), can be used to solve this problem.
The likelihood of not catching a pass is 0.2, but the likelihood of catching one is 0.8. The likelihood of catching at least 10 passes out of 15 can be calculated as follows:
P(X >= 10) equals P(X = 10) plus P(X = 11). + ... + P(X = 15)
where X is how many of the 15 passes were intercepted.
The probability of catching precisely k passes out of n can be calculated using the binomial distribution formula:
P(X = k) = (n choose k) × p²k × (1 - p)²(n-k)
where (n choose k) is the binomial coefficient, which represents the number of ways to choose k items from a set of n distinct items.
Plugging in the values for n = 15, p = 0.8, and k = 10, 11, 12, 13, 14, and 15, we get:
P(X >= 10) = P(X = 10) + P(X = 11) + ... + P(X = 15)
= (15 choose 10) × 0.8²10 × 0.2²5 + (15 choose 11) × 0.8²11 × 0.2²4 + ... + (15 choose 15) × 0.8²15 × 0.2²0
≈ 0.987
Therefore, the probability that Juan will catch at least 10 passes out of 15 is approximately 0.987.
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If a case of 24 water bottles is $8 per case, how much are you paying for each bottle?
Emilio took a random sample of n=12 giant Pacific octopi and tracked them to calculate their mean lifespan. Their lifespans were roughly symmetric, with a mean of x= 4 years and a standard deviation of sx=0.5 years. He wants to use this data to construct a t interval for the mean lifespan of this type of octopus with 90% confidence.
What critical value t* should Emilio use?
Emilio can find that the critical value t* for a 90% confidence level and 11 degrees of freedom is approximately 1.796.
Define standard deviation?To construct a t interval for the mean lifespan with 90% confidence, Emilio needs to use a t-distribution with n-1 degrees of freedom. The confidence interval for the population is given by:
confidence interval = x ± t × (s·x/√n)
Where x is the sample mean, s·x is the sample standard deviation, n is the sample size, and t is the critical value of the t-distribution.
Since the sample size is n=12, the degrees of freedom for the t-distribution will be (n-1) = 11. To find the critical value t* for a 90% confidence level and 11 degrees of freedom, Emilio can use a t-distribution table or a statistical software.
Using a t-distribution table or calculator, Emilio can find that the critical value t* for a 90% confidence level and 11 degrees of freedom is approximately 1.796.
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Hannah is working in England for 3 months on a project for her company. One weekend Hannah decides to go to France with her car on the ferry, then explore the French countryside. In England, speed limit signs are posted in miles per hour (mph) and Hannah's rental car only shows the speed in miles per hour. In France, speed limit signs are posted in kilometers per hour (kph). Hannah looks up the conversion and learns that 1 kph = 0.62 mph.
On the road that Hannah is currently on, the posted speed limit is 130 kilometers per hour. What is the maximum whole-number speed, in miles per hour, that Hannah can drive without exceeding the speed limit?
A. 82 mph
B. 79 mph
C. 209 mph
D. 80 mph
Answer:
To convert kilometers per hour to miles per hour, we need to multiply by 0.62. Therefore, to find the maximum speed that Hannah can drive without exceeding the speed limit of 130 kilometers per hour, we can multiply 130 by 0.62:
130 km/h * 0.62 = 80.6 mph
Since Hannah needs to stay within the speed limit, the maximum whole-number speed she can drive is 80 mph, which is option D.
Step-by-step explanation:
A bag contains 5 blue marbles, 7 white marbles, and 4 yellow marbles. If two different marbles are drawn from the bag, what is the probability of drawing first a blue marble and then a yellow marble?
Answer: The probability of drawing a blue marble and then a yellow marble is 1/12 or 0.0833.
Step-by-step explanation:
There are 16 marbles in the bag. To calculate the probability of drawing a blue marble and then a yellow marble, we can use the formula:
P(blue and yellow) = P(blue) x P(yellow|blue)
The probability of drawing a blue marble on the first draw is 5/16. After one blue marble has been drawn, there are 15 marbles left in the bag, so the probability of drawing a yellow marble on the second draw, given that the first marble was blue, is 4/15.
P(blue and yellow) = (5/16) x (4/15) = 1/12 or 0.0833
Elisa finished her math assignment in 1/2 hours. Then she completed her chemistry assignment in 1/5 hours. What was the tot amount of time Elsa spent doing these two assignments? Write your answer as a fraction in simplest form.
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8-6: MathXL for School: Practice & Problem Solving
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The circumference of the hub cap of a tire is 83.90 centimeters. Find the area of this hub cap. Use 3.14 for x. Use pencil and paper. If the circumference
were smaller, explain how this would change the area of the hub cap.
The area of this hub cap is about 560 square centimeters.
(Round the final answer to the nearest whole number as needed. Round all intermediate values to the nearest thousandth as needed.)
It can be seen that if the circumference were smaller, the area would decrease, as it is proportional to the square of the radius.
How to solveGiven the circumference (C) of the hub cap as 83.90 cm, we can find the radius (r) using the formula C = 2 * π * r,
where π = 3.14.
Thus, r ≈ 13.363 cm.
To find the area (A), use the formula A = π * r^2, yielding A ≈ 560.509 cm². Rounded, the area is about 561 cm².
Therefore, it can be seen that if the circumference were smaller, the area would decrease, as it is proportional to the square of the radius.
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Need help with this problem
The sales tax on 250 dollars purchase is: $3865
How to find the equation model?We are told that sales tax is directly proportional to retail price. Thus:
S ∝ p
Any item that sells for 158 dollars has a sales tax of 10.22 dollars. Thus:
158 = 10.22k
where k is constant of proportionality
Thus:
k = 158/10.22
k = 15.46
Thus, the equation is:
S = 15.46p
Sales tax on 250 dollars purchase is:
S = 15.46 * 250
S = $3865
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what is the difference between the square of the sum and the square of a difference?
Answer:
The product of the sum and difference of the same two terms is always the difference of two squares; it is the first term squared minus the second term squared.
Step-by-step explanation:
Thus, this resulting binomial is called a difference of squares.
Answer:
Step-by-step explanation:
Square of the sum
square means you are multiplying something twice and looks like:
ex. [tex]x*x=x^{2}[/tex]
sum is the addition of numbers
so square of the sum looks like:
(a+b)²
Square of the difference
difference means subtraction of numbers
so square of the difference looks like:
(b-a)²
Answer:
The product of the sum and difference of the same two terms is always the difference of two squares; it is the first term squared minus the second term squared.
Step-by-step explanation:
Thus, this resulting binomial is called a difference of squares.
Answer:
Step-by-step explanation:
Square of the sum
square means you are multiplying something twice and looks like:
ex. [tex]x*x=x^{2}[/tex]
sum is the addition of numbers
so square of the sum looks like:
(a+b)²
Square of the difference
difference means subtraction of numbers
so square of the difference looks like:
(b-a)²
What is the surface area of this cylinder?
Use ≈ 3.14 and round your answer to the nearest hundredth.
1 mm
1 mm
square millimeters
Answer:
13.56 mm²
Step-by-step explanation:
surface area = 2 circle area + the side
circle = π r² = 3.14
2 of them = 6.28
side = circumference * 1 = 2πr *1 = 6.28
total 6.28*2 = 13.56 mm²
A bag has 30 cards it in. There are 10 red cards, 10 blue cards, and 10 yellow cards. What is the probability that you reach in without looking and pick a red card?
Betty has 30 mls of cough medicine with breakfast.
She drinks half of her 4 ounce orange juice, and 25% of her 8 oz cup of coffee. How many mls total
did she consume?
Betty consumed a total of 148.294 milliliters of liquid with her breakfast.
To solve this problemWe can change the volumes of the coffee and orange juice to milliliters so that all of the measurements are in the same unit:
4 ounces = 4 * 29.5735, = 118.294 ml.
8 ounces = 8 x 29.5735, = 236.588 ml.
Half of Betty's 4-ounce glass of orange juice, or:
1/2 * 118.294 mls = 59.147 mls
She consumed 25% of her 8-ounce coffee, which is :
0.25 * 236.588 mls = 59.147 mls.
So, in total, Betty consumed:
30 mls of cough medicine + 59.147 mls of orange juice + 59.147 mls of coffee = 148.294 mls
Therefore, Betty consumed a total of 148.294 milliliters of liquid with her breakfast.
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suppose a scatterplot is created from the points in the following table. when x=7, what is the second coordinate in a scatterplot of the linearized data? round your answer to the tenths place. im so lost honestly.
Okay, let's break this down step-by-step:
From the table, we know the x-values are 1, 3, 5, 7, and 9.
And the y-values are 4, 6, 8, ?, 12.
So at x=7, there is a missing y-value that we need to determine.
To find this, we need to look at the linear relationship between the points. Some clues:
1) There are 5 points total.
2) The x-values increase by 2 each time.
3) The y-values also seem to be increasing by 2 each time.
So the linear relationship is: y = mx + b (where m is the slope and b is the y-intercept)
In this case, the slope is 2 (because y increases by 2 for every increase of 1 in x).
And the y-intercept is 4 (because when x = 1, y = 4).
So the equation is: y = 2x + 4
Plugging in x = 7:
y = 2(7) + 4
y = 14 + 4
y = 18
Therefore, when x = 7, the second coordinate in the scatterplot is 18.
Rounded to the tenths place: 1.8
Does this help explain the steps? Let me know if you have any other questions!
3 A system of two linear equations is graphed on a coordinate plane. If the system of
equations has infinitely many solutions, which statement must be true?
a. On the graph, there are no points (x, y) that satisfy both equations.
b. On the graph, there is exactly one point (x, y) that satisfies both equations.
c. On the graph, any point (x, y) that satisfies one of the equations cannot satisfy the
other equation.
d.
On the graph, any point (x, y) that satisfies one of the equations must also satisfy
the other equation.
Answer:
d. On the graph, any point (x, y) that satisfies one of the equations must also satisfy the other equation.----------------------
If the system of linear equations has infinitely many solutions, it means the two lines overlap.
In other words, each point of one of the lines also belongs to the second line.
Choices a, b, c give us one or no solutions and therefore not the answer.
Choice d is reflecting the infinitely many solutions and hence is the correct one.
The equation for a projectile's height versus time is h(t)=-16t^2+Vt+h. A tennis ball machine serves a ball vertically into the air from a height of 2 feet, with an initial speed of 110 feet per second. Which equation correctly models the ball’s height as a function of time?
The maximum height at the moment is 191.0625 ft.
What is the projectile's height?
Let's find out the projectile's maximum height now that we know what it is. The highest vertical location along the object's flight is considered to be its maximum height. The range of the bullet is defined as its horizontal displacement.
Here, we have
Given: The equation for a projectile's height versus time is h(t)=-16t²+Vt+h. A tennis ball machine serves a ball vertically into the air from a height of 2 feet, with an initial speed of 110 feet per second.
The equation for a projectile's height versus time is
h(t) = -16t²+Vt+h
h = 2
V = 110
Substitute these values into the function
h(t) = -16t²+110t+2
Take the first derivative
h'(t) = -32t + 110
Equate the derivative with zero h'(t) = 0
0 = -32t + 110
110 = 32t
t = 110/32
t = 3.4375
Find the maximum height at the moment
t = 3.4375 (s)
h(3.4375) = -16(3.4375)² + 110(3.4375) + 2
h(3.4375) = -189.0625 + 378.125 + 2
h(3.4375) = 191.0625 ft
Hence, the maximum height at the moment is 191.0625 ft.
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Question
Each answer choice below represents a relation by a set of ordered pairs. In which of the answer choices is the relation a function?
Select all correct answers.
Select all that apply:
{(2,−5),(−2,0),(−3,6),(2,−4)}
{(−1,5),(−4,8),(−4,14),(2,6)}
{(1,3),(−2,−1),(4,3),(8,1)}
{(−2,−5),(7,1),(7,−3),(4,−1)}
{(8,8),(4,1),(1,6),(−5,6)}
Answer:
(c) {(1,3),(−2,−1),(4,3),(8,1)}(e) {(8,8),(4,1),(1,6),(−5,6)}Step-by-step explanation:
You want the lists of ordered pairs that represent a functional relation.
FunctionA function maps an input value to exactly one output value. A set of ordered pairs will represent a function if no input (x-value) is repeated.
We only need to look at the first values of the ordered pairs.
(a) 2 is repeated
(b) -4 is repeated
(c) a function
(d) 7 is repeated
(e) a function
Answer:
(c) {(1,3),(−2,−1),(4,3),(8,1)}(e) {(8,8),(4,1),(1,6),(−5,6)}Step-by-step explanation:
You want the lists of ordered pairs that represent a functional relation.
FunctionA function maps an input value to exactly one output value. A set of ordered pairs will represent a function if no input (x-value) is repeated.
We only need to look at the first values of the ordered pairs.
(a) 2 is repeated
(b) -4 is repeated
(c) a function
(d) 7 is repeated
(e) a function
Tyrone factored the polynomial completely. What is the value of B?
12x4+30x3+4x2+10x
Ax(Bx2+1)(2x+5)
2
3
5
6
Answer:
the value of B is 3
Step-by-step explanation:
We can start by factoring out the greatest common factor of the polynomial, which is 2x:
2x(6x3 + 15x2 + 2x + 5)
Now, we can factor the expression inside the parentheses by grouping:
2x[(6x3 + 2x) + (15x2 + 5)]
2x[2x(3x + 1) + 5(3x + 1)]
2x(2x + 5)(3x + 1)
Comparing this expression to the given expression:
Ax(Bx2+1)(2x+5)
We see that A = 2, B = 3, and the factor (2x + 5) is the same in both expressions. Therefore, the value of B is 3.
the angle of elevation from the horizontal to the sun is 38°. How long of a shadow would a 32 foot tree make at this time?
The length of the shadow would be approximately 41.7 feet if the angle of elevation from the horizontal to the sun is 38° at this time.
If the angle of elevation from the horizontal to the sun is 38°, then the tangent of that angle is equal to the opposite side (the height of the tree) divided by the adjacent side (the length of the shadow).
Therefore, we can set up the equation using trigonometric function tangent as,
tan(38°) = height of tree / length of shadow
Solving for the length of the shadow, we get:
length of shadow = height of tree / tan(38°)
Plugging in the given height of the tree (32 feet) and using a calculator to find the tangent of 38°, we get:
length of shadow = 32 / tan(38°) = 41.7 feet (rounded to one decimal place)
Therefore, the length of the shadow would be approximately 41.7 feet at this time.
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To compare the dry braking distances from 30 to 0 miles per hour for two makes of automobiles, a safety engineer conducts braking tests for 35 models of Make A and 35 models of Make B.
The mean braking distance for Make A is 42 feet. Assume the population standard deviation is 4.6 feet.
The mean braking distance for Make B is 45 feet. Assume the population standard deviation is 4.3 feet.
At α = 0.10, can the engineer support the claim that the mean braking distances are different for the two makes of automobiles?
Assume the samples are random and independent, and the populations are normally distributed.
(a) Identify the claim and state H_0 and H_a
(The mean braking distance is different for the two makes of automobiles.)
What are H_0 and H_a?
(b) Find the critical value(s) and identify the rejection region(s).
(c) Find the standardized test statistic z for μ_1 - μ_2
z = _____
(d) Decide whether to reject or fail to reject the null hypothesis.
(e) Interpret the decision in the context of the original claim.
Upper Critical Value; 1.645
p-Value; 0.0814
Reject the null hypothesis
How to solvea).
claim: A. The mean breaking distance is different for the two makes of automobiles
H0 and Ha.: E
[tex]\ H_0: \mu_1 = \mu_2 \ \ \ H_a: \mu_1 \neq \mu_2[/tex]
b).
critical values are (-1.645, 1.645)
Rejection region: E. z < -1.645 , z >1.645
c)
test statistic z= -1.743
d).
C. Reject H0. The stat statistic falls in the rejection region.
e).
At the 10% significance level, there is sufficient evidence to support the claim that means breaking distance of make A is different from mean breaking distance of making B.
m 2
M1
7t
Z Test for Differences in Two Means
Data
Hypothesized Difference
0
Level of Significance
0.1
Population 1 Sample
Sample Size
35
Sample Mean
42
Population Standard Deviation
4.9
Population 2 Sample
Sample Size
35
Sample Mean
44
Population Standard Deviation
4.7
Intermediate Calculations
Difference in Sample Means
-2
Standard Error of the Difference in Means
1.1477
Z Test Statistic
-1.7427
Two-Tail Test
Lower Critical Value
-1.645
Upper Critical Value
1.645
p-Value
0.0814
Reject the null hypothesis
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A triangle with an area of 40 in.² has a height that is four less than six times the base. Find the base and height of the triangle.
Answer: 9.32 inches.
Step-by-step explanation:
what is the value of the expression shown below
2 3/5 - 1 3/5
^ ^
TWO THREE-FIFTHS MINUS ONE THREE-FIFTHS
THE NUMBERS ARE MIXED FRACTIONS
Answer:
1
Step-by-step explanation:
1. One way to do this is converting both into improper fractions. To do this, multiply the whole number by the denominator and add that to the numerator.
2 3/5 --> 2*5 is 10 --> 10+3 is 13. --> 13/5
2. This leaves us with 13/5 - 8/5
3. Subtract the numerators
13/5 - 8/5 = 5/5
4. Simplify. If the numerator is the same number as the denominator, it's a whole number.
5/5 = 1
Several years ago, the average earnings for male workers between the ages of 25 and 34 with a high school diploma was $31,680. Comparing this value in
constant dollars to the average earnings 21 yr later showed that the average earnings have decreased to $27,900. Find the average rate of change in dollars
year for this time period.
[ Hint: Use the ordered pairs (0, 31,680) and (21, 27,900).]
Answer:
For 25- to 34-year-olds who worked full time, year round, higher educational attainment was associated with higher median earnings.
Step-by-step explanation:
This pattern was consistent for each year from 2010 through 2020. For example, in 2020, the median earnings of those with a master’s or higher degree were $69,700, some 17 percent higher than the earnings of those with a bachelor’s degree ($59,600). In the same year, the median earnings of those with a bachelor’s degree were 63 percent higher than the earnings of those who completed high school ($36,600).
Two mountain peaks are known to be 17 kilometers apart. A person located at a vista point such that a right angle is spanned when he looks from one peak to the other
is told that the distances from the vista point to each peak differ by 7 kilometers. How far is the vista point from each mountain peak?
The person is looking at each peak on a leg of a right triangle. The hypotenuse is the distance between the mountains.
How far is the vista point from each mountain peak?The distance is determined by
x^2+(x+5)^2=25^2
x^2+x^2+10x+25=625
2x^2+10x-600=0
x^2+5x-300=0
(x+20)(x-15)=0
only positive root is x=15
x+5=20
The vista point is 15 miles from one mountain peak and 20 miles from the other.
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resoudre l inequation (5x-4)(4x+3)<5(4x²-1)
Answer:
This shows the step by step process of rhetorical reduction of the question given
Suppose a company wanted to find out whether a new highlighter lasted less than their original highlighters lasted.
The value of t= -1.946; p = 0.029; Reject the null hypothesis; there is strong evidence to suggest that the highlighters last less than 14 hours.
To test the hypothesis that the highlighters last less than 14 hours, we will use a one-sample t-test. The null hypothesis for this test is that the mean continuous writing time for the highlighters is equal to or greater than 14 hours. The alternative hypothesis is that the mean continuous writing time for the highlighters is less than 14 hours.
In this problem, we are given that x = 13.6 hours and s = 1.3 hours. The sample size is n = 40. Substituting these values into the formula for the test statistic, we get:
t = (13.6 - 14) / (1.3 / √(40)) = -1.946
The p-value for the test can be found using a t-distribution table or a statistical software program. The p-value is the probability of observing a t-value as extreme as the one we calculated, assuming the null hypothesis is true. In this problem, the p-value is 0.029.
To make a decision about the null hypothesis, we compare the p-value to the significance level, which is typically set at 0.05. If the p-value is less than the significance level, we reject the null hypothesis. If the p-value is greater than the significance level, we fail to reject the null hypothesis.
In this problem, the p-value is less than 0.05, so we reject the null hypothesis. This means there is strong evidence to suggest that the highlighters last less than 14 hours. We can conclude that the manufacturer's claim that their highlighters can write continuously for 14 hours is not supported by the sample data.
Hence the correct option is (c).
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Complete Question:
Solve the problem. Suppose a consumer product researcher wanted to find out whether a highlighter lasted less than the manufacturer's claim that their highlighters could write continuously for 14 hours. The researcher tested 40 highlighters and recorded the number of continuous hours each highlighter wrote before drying up. Test the hypothesis that the highlighters wrote for less than 14 continuous hours. Following are the summary statistics:
x =13.6 hours,
s =1.3 hours
Report the test statistic, p-value, your decision regarding the null hypothesis, and your conclusion about the original claim. Round all values to the nearest thousandth.
a) z = 1.946; p = 0.029; Reject the null hypothesis; there is strong evidence to suggest that the highlighters last less than 14 hours.
b) t = -1.946; p = 0.029; Fail to reject the null hypothesis; there is not strong evidence to suggest that the highlighters last less than 14 hours. o
c) t= -1.946; p = 0.029; Reject the null hypothesis; there is strong evidence to suggest that the highlighters last less than 14 hours.
d) z = 1.946; p = 0.974; Fail to reject the null hypothesis; there is not “strong evidence to suggest that the highlighters last less than 14 hours.
P is a point on the terminal side of 0 in standard position. Find the exact value of the six trigonometric functions for 0 where P (-5, 5)
We can use the coordinates of point P (-5, 5) to find the values of the trigonometric functions for the angle formed between the positive x-axis and the line passing through the origin and point P.
First, we can find the distance from the origin to point P using the Pythagorean theorem:
r = sqrt((-5)^2 + 5^2) = sqrt(50)
Next, we can use the fact that the sine of an angle is equal to the y-coordinate of a point on the unit circle and the cosine of an angle is equal to the x-coordinate of a point on the unit circle. Since the radius of the unit circle is 1, we need to divide the x and y coordinates of point P by sqrt(50) to get the values for sine and cosine:
sin(θ) = y/r = 5/sqrt(50) = (5/10)sqrt(2) = (1/2)sqrt(2)
cos(θ) = x/r = -5/sqrt(50) = -(5/10)sqrt(2) = -(1/2)sqrt(2)
Next, we can use the fact that the tangent of an angle is equal to the sine of the angle divided by the cosine of the angle:
tan(θ) = sin(θ)/cos(θ) = (1/2)sqrt(2)/(-(1/2)sqrt(2)) = -1
Similarly, we can use the reciprocal identities to find the values of the other three trigonometric functions:
csc(θ) = 1/sin(θ) = sqrt(2)
sec(θ) = 1/cos(θ) = -sqrt(2)
cot(θ) = 1/tan(θ) = -1
Therefore, the exact values of the six trigonometric functions for the angle formed by the line passing through the origin and point P (-5, 5) are:
sin(θ) = (1/2)sqrt(2)
cos(θ) = -(1/2)sqrt(2)
tan(θ) = -1
csc(θ) = sqrt(2)
sec(θ) = -sqrt(2)
cot(θ) = -1
IG:whis.sama_ent
According to Masterfoods, the company that manufactures M&M’s, 12% of peanut M&M’s are brown, 15% are yellow, 12% are red, 23% are blue, 23% are orange and 15% are green. You randomly select five peanut M&M’s from an extra-large bag of the candies. (Round all probabilities below to four decimal places; i.e. your answer should look like 0.1234, not 0.1234444 or 12.34%.) Compute the probability that exactly three of the five M&M’s are green. Compute the probability that three or four of the five M&M’s are green. Compute the probability that at most three of the five M&M’s are green. Compute the probability that at least three of the five M&M’s are green. If you repeatedly select random samples of five peanut M&M’s, on average how many do you expect to be green? (Round your answer to two decimal places.) green M&M’s With what standard deviation? (Round your answer to two decimal places.) green M&M’s
The standard deviation of the number of green M&M's in a sample of 5 is 0.91
What is standard deviation?Standard deviation is a measure of the amount of variation or dispersion of a set of data values. It is calculated by finding the square root of the variance, which is the average of the squared differences from the mean.
According to given information:To solve this problem, we can use the binomial probability formula:
[tex]P(X=k) = C(n,k) * p^k * (1-p)^{(n-k)[/tex]
where:
X is the number of green M&M's in the sample
k is the number of green M&M's we are interested in (3 or 4 or at most 3 or at least 3)
n is the sample size (5)
p is the probability of getting a green M&M in one trial
We can use the given percentages to calculate the probability of getting a green M&M:
p = 0.15
Now we can calculate the probabilities for the different scenarios:
Probability that exactly three of the five M&M's are green:
[tex]P(X=3) = C(5,3) * 0.15^3 * 0.85^2 = 0.0883[/tex]
Probability that three or four of the five M&M's are green:
[tex]P(X=3\ or\ X=4) = P(X=3) + P(X=4) = C(5,3) * 0.15^3 * 0.85^2 + C(5,4) * 0.15^4 * 0.85^1 = 0.1527[/tex]
Probability that at most three of the five M&M's are green:
P(X≤3) = [tex]P(X=0) + P(X=1) + P(X=2) + P(X=3) = C(5,0) * 0.15^0 * 0.85^5 + C(5,1) * 0.15^1 * 0.85^4 + C(5,2) * 0.15^2 * 0.85^3 + C(5,3) * 0.15^3 * 0.85^2 = 0.9053[/tex]
Probability that at least three of the five M&M's are green:
P(X≥3) [tex]= P(X=3) + P(X=4) + P(X=5) = C(5,3) * 0.15^3 * 0.85^2 + C(5,4) * 0.15^4 * 0.85^1 + C(5,5) * 0.15^5 * 0.85^0 = 0.2413[/tex]
To find the expected number of green M&M's in a sample of size 5, we can use the formula:
E(X) = n * p
where E(X) is the expected value of X.
E(X) = 5 * 0.15 = 0.75
Therefore, on average we expect 0.75 green M&M's in a sample of 5.
To find the standard deviation, we can use the formula:
SD(X) = sqrt(n * p * (1-p))
SD(X) = sqrt(5 * 0.15 * 0.85) = 0.9138 (rounded to two decimal places)
Therefore, the standard deviation of the number of green M&M's in a sample of 5 is 0.91
To know more about standard deviation visit:
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