In a study of government financial aid for college students, it becomes necessary to estimate the percentage of full-time college students who earn a bachelor's degree in four years or less
find the sample size needed to estimate that percentage. use a 0.01 margin of error and use a confidence level of 95%. assume that nothing is known about the percentage to be estimated
Answers
A sample size of 9604 is needed to estimate the percentage of full-time college students who earn a bachelor's degree in four years or less, with a 95% confidence level and a margin of error of 0.01.
To find the sample size needed to estimate the percentage of full-time college students who earn a bachelor's degree in four years or less, we can use the following formula:
n = [Z^2 * p * (1 - p)] / E^2
where:
Z is the z-score associated with the desired confidence level (95%), which is 1.96
p is the estimated proportion of students who earn a bachelor's degree in four years or less (since we don't have any prior knowledge, we can use 0.5 as a conservative estimate)
E is the margin of error, which is 0.01
Plugging in the values, we get:
n = [(1.96)^2 * 0.5 * (1 - 0.5)] / (0.01)^2
n = 9604
Therefore, a sample size of 9604 is needed to estimate the percentage of full-time college students who earn a bachelor's degree in four years or less, with a 95% confidence level and a margin of error of 0.01.
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Related Questions
evaluate the line integral ∫cf⋅dr, where f(x,y,z)=5xi−yj+zk and c is given by the vector function r(t)=⟨sint,cost,t⟩, 0≤t≤3π/2.
Answers
We have
\(\displaystyle \int_C \vec f \cdot d\vec r = \int_0^{\frac{3\pi}2} \vec f(\vec r(t)) \cdot \dfrac{d\vec r}{dt} \, dt\)
and
\(\vec f(\vec r(t)) = 5\sin(t) \, \vec\imath - \cos(t) \, \vec\jmath + t \, \vec k\)
\(\vec r(t) = \sin(t)\,\vec\imath + \cos(t)\,\vec\jmath + t\,\vec k \implies \dfrac{d\vec r}{dt} = \cos(t) \, \vec\imath - \sin(t) \, \vec\jmath + \vec k\)
so the line integral is equilvalent to
\(\displaystyle \int_C \vec f \cdot d\vec r = \int_0^{\frac{3\pi}2} (5\sin(t) \cos(t) + \sin(t)\cos(t) + t) \, dt\)
\(\displaystyle \int_C \vec f \cdot d\vec r = \int_0^{\frac{3\pi}2} (6\sin(t) \cos(t) + t) \, dt\)
\(\displaystyle \int_C \vec f \cdot d\vec r = \int_0^{\frac{3\pi}2} (3\sin(2t) + t) \, dt\)
\(\displaystyle \int_C \vec f \cdot d\vec r = \left(-\frac32 \cos(2t) + \frac12 t^2\right) \bigg_0^{\frac{3\pi}2}\)
\(\displaystyle \int_C \vec f \cdot d\vec r = \left(\frac32 + \frac{9\pi^2}8\right) - \left(-\frac32\right) = \boxed{3 + \frac{9\pi^2}8}\)
Algo) Cost Behavior; Contribution Format Income Statement [LO1-4, LO1-6] Harris Company manufactures and sells a single product. A partially completed schedule of the company's total costs and costs per unit over the relevant range of 54,000 to 94,000 units is given below: Required: 1. Complete the schedule of the company's total costs and costs per unit as given in the relevant tab below. 2. Assume that the company produces and sells 84,000 units during the year at a selling price of $8.43 per unit. Prepare a contribution format income statement for the year. Complete this question by entering your answers in the tabs below. Complete the schedule of the company's total costs and costs per unit as given in the relevant tab below. (Round the per unit variable cost and fixed cost to 2 decimal places.) Exercise 1-11 (Algo) Cost Behavior; Contribution Format Income Statement [LO1-4, LO1-6] Harris Company manufactures and sells a single product. A partially completed schedule of the company's total cost and costs per unit over the relevant range of 54,000 to 94,000 units is given below: Required: 1. Complete the schedule of the company's total costs and costs per unit as given in the relevant tab below. 2. Assume that the company produces and sells 84,000 units during the year at a selling price of $8.43 per unit. Prepare a contribution format income statement for the year. Complete this question by entering your answers in the tabs below. Assume that the company produces and sells 84,000 units during the year at a selling price of $8.43 per unit. Prepare a contribution format income statement for the year. Note: Round your intermediate calculations to 2 decimal places.
Answers
Calculate variable cost per unit using the change in costs divided by the change in units. Subtract variable costs to find fixed costs. Prepare income statement by subtracting fixed costs from the contribution margin.
To complete the schedule of the company's total costs and costs per unit, we need to calculate the variable cost per unit and total fixed costs. The relevant range is given as 54,000 to 94,000 units. We calculate the change in costs by subtracting the total costs at the low point from the total costs at the high point. Similarly, we calculate the change in units. Dividing the change in costs by the change in units gives us the variable cost per unit.
To find the fixed costs, we subtract the total variable costs at the high point from the total costs at the high point. The fixed costs remain constant within the relevant range.
Next, assuming the company produces and sells 84,000 units at a selling price of $8.43 per unit, we can prepare a contribution format income statement. We multiply the number of units sold by the selling price per unit to calculate the sales revenue. From this, we subtract the total variable costs (found in the schedule) to obtain the contribution margin. Finally, subtracting the total fixed costs from the contribution margin gives us the net income for the year.
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To complete the company's total costs and costs per unit schedule, calculate the fixed cost per unit and variable cost per unit. Then, use the given selling price and quantity to prepare a contribution format income statement for the year.
Explanation:The student is given a partially completed schedule of the company's total costs and costs per unit over a relevant range of units. The goal is to complete the schedule and then use that information to prepare a contribution format income statement for the year based on a given selling price and quantity.
To complete the schedule, the student needs to calculate the fixed cost per unit and variable cost per unit. These can be found by subtracting the total cost at the low end of the relevant range from the total cost at the high end of the relevant range, and then dividing the difference by the change in units.
Once the schedule is complete, the student can use the selling price and quantity information to calculate the total revenue and variable cost. The contribution margin can be found by subtracting the variable cost from the total revenue, and the fixed cost can be subtracted from the contribution margin to find the net income.
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if two population distributions are normal and the population variances σ12 and σ22 are not known, then the sampling distribution used for inferences about μ1-μ2 is:
Answers
The sampling distribution used for inferences about μ1-μ2 is the Student's t-distribution.
The Student's t-distribution is used when the population variances are unknown and assumed to be equal. It is a probability distribution that arises from the hypothesis testing of small sample sizes. When the sample sizes are large, the t-distribution approaches a normal distribution.
The t-distribution is symmetric and bell-shaped, like the normal distribution, but has heavier tails. The shape of the t-distribution depends on the degrees of freedom, which is calculated based on the sample sizes and is used to determine the critical values for hypothesis testing.
In summary, the Student's t-distribution is used for inferences about the difference between two population means when the population variances are unknown and assumed to be equal.
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It is suggested that an incompressible fluid flows with the velocity field v = (cos (xyzt), y²t,0) (i) (ii) (iii) Dv Determine expressions for, and D Dt at Explain in a few sentences the difference between and Is physically acceptable? State your reasoning. Dv Dt dv at
Answers
dv at is the local acceleration, while Dv Dt is the total acceleration. dv at is physically acceptable as it represents the acceleration of the fluid at a particular point in space.
(i) The velocity field given is v = (cos (xyzt), y²t,0). This field represents the velocity of an incompressible fluid.
(ii) Expression for Dv Dt at is as follows:
The derivative of the velocity field with respect to time t is given by, Dv Dt = (∂v/∂t) + v · ∇v ...(1)
Here, v · ∇v = dot product of the velocity vector and gradient of the velocity vector.
Taking the dot product of v and ∇v and simplifying, we get,
v · ∇v = (cos (xyzt)· (-xyz sin (xyzt)), y²t· 2y, 0)
= (-xyz² sin (xyzt), 2y³t, 0)
On substituting the dot product in equation (1), we get,
Dv Dt = (∂v/∂t) + v · ∇v
= ((0, 2yt, 0)) + ((-xyz² sin (xyzt), 2y³t, 0))
= (-xyz² sin (xyzt), 2y³t + 2yt, 0) ...(2)
(iii) The expression for Dv is as follows:
We have the velocity field as v = (cos (xyzt), y²t,0).
Differentiating each component of the velocity field w.r.t. x, y, and z, we get,
∂v/∂x = (-yzt sin (xyzt), 0, 0), ∂v/∂y = (0, 2yt, 0), ∂v/∂z = (0, 0, 0)
Using the above derivatives, the expression for Dv is given by,
Dv = (∂v/∂t) + (∂v/∂x)·i + (∂v/∂y)·j + (∂v/∂z)·k
= ((-xyz sin (xyzt), y², 0)) + ((-yzt sin (xyzt), 0, 0))·i + ((0, 2yt, 0))·j + ((0, 0, 0))·k
= (-xyz sin (xyzt) - yzt sin (xyzt))·i + 2yt·j + 0·k
= -(xyz + yz) sin (xyzt)·i + 2yt·j ...(3)
The difference between Dv Dt and dv at is that Dv Dt is the material derivative, which is the derivative of a fluid property that moves with the fluid flow.
In contrast, dv at represents the rate of change of velocity with time at a fixed point in space.
The material derivative considers changes at a particular point in space as well as changes in time.
On the other hand, the acceleration vector dv at only considers the instantaneous change in velocity at a particular point in space.
Thus, dv at is the local acceleration, while Dv Dt is the total acceleration. dv at is physically acceptable as it represents the acceleration of the fluid at a particular point in space.
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Given 1 || m , find the value of %.
(7x - 1)
125"
m
Find x
Answers
We know that 7x - 1 must equal 125 because of Alternate interior angles. Now, let's solve for x.
Step-by step solution:=> 7x - 1 = 125=> 7x = 126=> x = 126 ÷ 7=> x = 18Conclusion:Therefore, we can conclude that x = 18.
Hoped this helped.
\(BrainiacUser1357\)
\(\\ \tt\Rrightarrow 7x-1=125\)
\(\\ \tt\Rrightarrow 7x=125+1\)
\(\\ \tt\Rrightarrow 7x=126\)
\(\\ \tt\Rrightarrow x=126/7\)
\(\\ \tt\Rrightarrow x=18\)
Identify the antecedent and the consequent for each of the following conditional sentences. Assume that a, b, and f represent some fixed sequence, integer, or function, respectively.
(a) If squares have three sides, then triangles have four sides.
(b) If the moon is made of cheese, then 8 is an irrational number.
(c) b divides 3 only if b divides 9.
(d) The differentiability of f is sufficient for f to be continuous.
(e) A sequence a is bounded whenever a is convergent.
(f) A function f is bounded if f is integrable.
(g) 1 + 2 = 3 is necessary for 1 + 1 = 2.
(h) The fish bite only when the moon is full.
(i) A time of 3 minutes, 48 seconds or less is necessary to qualify for the Olympic team.
Answers
(a) Antecedent: Squares have three sides
Consequent: Triangles have four sides
(b) Antecedent: The moon is made of cheese
Consequent: 8 is an irrational number
(c) Antecedent: b divides 3
Consequent: b divides 9
(d) Antecedent: The differentiability of f
Consequent: f is continuous
(e) Antecedent: A sequence a is convergent
Consequent: a is bounded
(f) Antecedent: A function f is integrable
Consequent: f is bounded
(g) Antecedent: 1 + 2 = 3
Consequent: 1 + 1 = 2
(h) Antecedent: The moon is full
Consequent: The fish bite
(i) Antecedent: Time of 3 minutes, 48 seconds or less
Consequent: Qualification for the Olympic team
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1) If total costs for a product are given by C(x) = 1760 + 8x + 0.6x2 and total revenues are given by R(x) = 100x -0.4x2, find the break-even points. =
2) If total costs for a commodity are given by C(x) = 900 +25x and total revenues are given by R(x) = 100x - x2, find the break-even points. 3) Find the maximum revenue and maximum profit for the functions described in Problem #2.
Answers
a) The break-even points for the given cost and revenue functions are approximately x = 16.526 and x = 6.474.
b) The break-even points for the given cost and revenue functions are approximately x = 12.225 and x = 62.775.
c) The maximum profit for the given cost and revenue functions is approximately $843.75.
a) To find the break-even points, we need to determine the values of x where the total costs (C(x)) equal the total revenues (R(x)). We set C(x) = R(x) and solve for x:
C(x) = R(x)
1760 + 8x + 0.6x² = 100x - 0.4x²
Combining like terms and rearranging the equation, we get:
1x² - 92x + 1760 = 0
Solving this quadratic equation, we find two solutions for x:
x ≈ 16.526
x ≈ 6.474
b) Similarly, we set C(x) = R(x) and solve for x:
900 + 25x = 100x - x²
Rearranging the equation, we get:
x² - 75x + 900 = 0
Solving this quadratic equation, we find two solutions for x:
x ≈ 12.225
x ≈ 62.775
c) To find the maximum revenue, we need to determine the vertex of the revenue function R(x) = 100x - x². The x-coordinate of the vertex is given by x = -b / (2a), where a and b are the coefficients of the quadratic equation.
In this case, a = -1 and b = 100. Plugging in the values, we get:
x = -100 / (2 * -1) = 50
Substituting this value back into the revenue function, we find:
R(50) = 100(50) - (50)² = 5000 - 2500 = 2500
Therefore, the maximum revenue for the given cost and revenue functions is $2500.
To find the maximum profit, we need to subtract the total costs from the total revenues. Given that the cost function is C(x) = 900 + 25x, the profit function is P(x) = R(x) - C(x). Substituting the revenue and cost functions, we have:
P(x) = (100x - x²) - (900 + 25x)
P(x) = -x² + 75x - 900
To find the maximum profit, we need to determine the vertex of the profit function. Using the same formula as before, we find:
x = -75 / (2 * -1) = 37.5
Substituting this value back into the profit function, we find:
P(37.5) = -(37.5)² + 75(37.5) - 900 ≈ 843.75
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Helppp!!!!!!!!!!!!!!!!!!!!!
Answers
The value of x is equal to 15°
How to determine the value of x?In Mathematics and Geometry, the sum of the exterior angles of both a regular and irregular polygon is always equal to 360 degrees.
Note: The given geometric figure (regular polygon) represents a pentagon and it has 5 sides.
By substituting the given parameters, we have the following:
3x + 4x + 8 + 5x + 5 + 6x - 1 + 5x + 3 = 360°.
3x + 4x + 5x + 6x + 5x + 8 + 5 - 1 + 3 = 360°.
23x + 15 = 360°.
23x = 360 - 15
23x = 345
x = 345/23
x = 15°.
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There are 10 number cards, numbered 1 - 10, what is the probability of randomly selecting an even number from the cards? Determine the likelihood of this event.
Answers
The likelihood of the event is 1/2
Somebody pleassseee tell me if I’m doing this right or wrong Pleassee
Answers
Answer:
-4.5
Step-by-step explanation:
\(6x+5.5=3x-8\\\)
\(6x-3x=-8-5.5\)
\(3x=-13.5\)
\(x=\frac{-13.5}{3}\)
\(x=-4.5\)
. if it is assumed that all poker hands are equally likely, what is the probability of being dealt a. a flush? (a hand is said to be a flush if all 5 cards are of the same suit.) b. one pair? (this occurs when the cards have denominations where and are all distinct.)
Answers
a) The probability of being dealt a flush is approximately 0.00198, or about 0.2%.
b) The probability of being dealt one pair is approximately 0.422, or about 42.2%.
a. To find the probability of being dealt a flush, we need to first determine how many possible flush hands there are, and then divide that by the total number of possible hands. There are 4 suits in a deck of cards, so there are 4 ways to choose which suit the flush will be in.
Once we have chosen a suit, there are 13 cards of that suit, and we need to choose 5 of them. The number of ways to choose 5 cards from 13 is given by the combination formula: C(13,5) = 1287. Therefore, there are 4 x 1287 = 5148 possible flush hands.
The total number of possible hands is given by the combination formula for choosing 5 cards from a deck of 52: C(52,5) = 2598960. Therefore, the probability of being dealt a flush is 5148/2598960, which simplifies to approximately 0.00198, or about 0.2%.
b. To find the probability of being dealt one pair, we need to first determine how many possible one pair hands there are, and then divide that by the total number of possible hands. There are 13 denominations in a deck of cards, so there are 13 ways to choose which denomination will form the pair.
Once we have chosen a denomination, there are 4 cards of that denomination, and we need to choose 2 of them. The remaining 3 cards must each be a different denomination from the pair, so there are 12 denominations left to choose from, and 4 cards of each denomination.
We need to choose 3 of these 12 denominations, and then 1 card from each of those 3 denominations. The number of ways to choose 2 cards from 4 is given by the combination formula: C(4,2) = 6. The number of ways to choose 3 denominations from 12 is given by the combination formula: C(12,3) = 220.
The number of ways to choose 1 card from each of 3 denominations is 4 x 4 x 4 = 64. Therefore, the total number of possible one pair hands is 13 x 6 x 220 x 64 = 1,098,240. Dividing this by the total number of possible hands gives us the probability of being dealt one pair, which is 1,098,240/2598960, or approximately 0.422, or about 42.2%.
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PLEASE HELP!!! MATH FINAL
Answers
Answer:
He Won 26 Box trolls and 11 Pikachus
Step-by-step explanation:
You subtract 37-11 which would get you 26
a
=
8.4
rounded to 1 DP
b
=
6.19
rounded to 2 DP
Find the minimum of
a
−
b
Answers
Answer:
8,6.2 8÷6. 2=1.3
Step-by-step explanation:
13 because I rounded off the answer to 2 dp
The minimum value of a - b is around 2.2 with a = 8.4 rounded to one decimal place and b = 6.19 rounded to two decimal places.
Given that, a = 8.4 rounded to 1 decimal place and b = 6.19 rounded to 2 decimal places.
We must first subtract b (lower bound) from a (upper bound) to determine the least value of a - b,
which is equal to 8.4 - 6.19 = 2.21. 2.21 is the difference between a and b.
However, the question requests that we round off this number to the nearest tenth.
We remove the first decimal point because 1 is less than 5, giving us 2.2.
Hence the minimum value of a -b to the nearest decimal is found to be 2.2.
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The complete question is:
Given a = 8.4 rounded to 1 decimal place and b = 6.19 rounded to 2 decimal places, find the minimum value of a - b rounded to 1 decimal place.
Find the sum or type
“impossible"
Help Resources
[1 -2 1] + [4 -5 -6]
Skip
[[?]
Enter
![Find the sum or typeimpossible"Help Resources[1 -2 1] + [4 -5 -6]Skip[[?]Enter](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/TgypNiBscvvl9iBjjzuwZMmkWkcqPmN7.png)
Answers
Answer:
-7
Step-by-step explanation:
looked on photomath
since the mode is the most frequently occurring data value, it group of answer choices is always larger than the mean can never be larger than the mean none of these alternatives is correct. is always larger than the median
Answers
Since the mode is the most frequently occurring data value so -
Option D : None of the alternatives is correct.
What is mode?
A mode is described as the value in a group of values that occurs more frequently. The value that appears the most frequently is called mode.
The distribution of the mean, median, and mode values will depend on how skewed the distribution is.
The total dependency of mean, median and mode of data is on the asymmetric form of the data.
As a result, mean or mode may be larger than or less than mode.
Therefore, the mode is neither large than mean or median and can never be larger than mean.
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Find ABC (GRADE 9 MATH)
Answers
B = 2k
A = k√3
C = k
\( \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \)
The total cost of buying two potatoes and a half pound of hamburger at the grocery store is $3.00. Lisa buys one potato and two pounds of hamburger and pays $8.50. Find the price for each potato and each pound of hamburger.
doing test rn need help asap
Answers
Answer:
buuuuuuuuuuuuuu
Step-by-step explanation:
A prestigious program accepts 2 out of every 9 applicants per yer. If the program accepted 360 applicants, how many applicants were NOT accepted?
A.1260
B.1620
C.2520
D.3240
E.3600
Answers
The density of a fish tank is 0.2 fish over feet cubed . There are 8 fish in the tank. What is the volume of the tank?
Answers
Answer: 16 feet cubed
Step-by-step explanation:
Answer:
The answer is 40 ft³
Step-by-step explanation:
I took the test. Simple as that
What is the approximate radius of a sphere with a surface area of 65π inches
Answers
\(\textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ V=65\pi \end{cases}\implies 65\pi =\cfrac{4\pi r^3}{3}\implies \cfrac{3}{4\pi}\cdot 65\pi =r^3 \\\\\\ \cfrac{195}{4}=r^3\implies \sqrt[3]{\cfrac{195}{4}}=r\implies 3.65\approx r\)
Find the critical numbers of f(x)=x3+3x2+3x−6.
Answers
Answer:
x = -1
Step-by-step explanation:
\(f(x)=x^3+3x^2+3x-6\\f'(x)=3x^2+6x+3\\\\0=3x^2+6x+3\\0=x^2+2x+1\\0=(x+1)^2\\0=x+1\\x=-1\)
Therefore, the only critical number of f(x) is x=-1
after paying $9 for the pie Sally has $99 left how much money did she have before buying the pie
Answers
Sally pays $9 for a pie and has $99 left. Then, the money before buying the pie is represented by the sum of $9+$99
\(\begin{gathered} \text{money before the pie=\$9+\$99} \\ \text{money before the pie}=\text{\$}108 \end{gathered}\)Therefore, she had $108 before buying the pie.
Could you guys help meee
Answers
1. y= 2x
2. (0, 5)
3. y = 3x + 12
What is Algebra?Algebra is the part of mathematics that helps represent problems or situations in the form of mathematical expressions.
1. let us take (0,0) and (1, 2)
m= 2-0/1-0
m= 2
So equation of line
y- 0 = 2(x-0)
b
2. y= 3x+5
passes through (0, 5)
3. y= 3x+5
m = 3
We need the equation of a line with slope 3 that passes through point (0, 12).
y - y1 = m(x - x1)
y - 12 = 3(x - 0)
y - 12 = 3x
y = 3x + 12
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273.23÷36 step by step
Answers
The division of the numbers 273.23÷36 yields the value 7.589.
What is long division?Long division in mathematics is a strategy for breaking down complicated division problems into a series of simpler steps. It is the approach that division-based issues are often solved with. Much like the usual division questions, the dividend is divided by the divisor which yields a result known as the quotient, and occasionally it gives a remainder too.
The given expression is:
273.23÷36
Divide the number 273.23 with 36 and write the remainder at the bottom.
Again, divide the remainder with 36, until further reduction is not possible.
Hence, the division of the numbers 273.23÷36 yields the value 7.589.
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lynne has \$8.00$8.00dollar sign, 8, point, 00 to spend on apples and oranges. apples cost \$0.65$0.65dollar sign, 0, point, 65 each, and oranges cost \$0.75$0.75dollar sign, 0, point, 75 each. if there is no tax on this purchase and she buys 555 apples, what is the maximum number of whole oranges she can buy?
Answers
Lynne can buy 5 apples and 6 oranges with her $8.00.
The first thing to do is determine how much money Lynne spends on the apples. Since she is buying 5 apples,
we can multiply the price of each apple ($0.65) by 5: $5 * 0.65 = $3.25
Therefore, Lynne has $8 - $3.25 = $4.75 to spend on oranges.
Now we need to determine the maximum number of whole oranges that she can buy with $4.75. We can do this by dividing $4.75 by the price of each orange ($0.75): $4.75 ÷ $0.75 = 6.33.
Since we can't buy a fraction of an orange, the maximum number of whole oranges Lynne can buy is 6. Therefore, Lynne can buy 5 apples and 6 oranges with her $8.00.
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What is a correlation? Give three examples of pairs of variables that are correlated. Select the correct answer below. A. A correlation is when one variable causes another variable. B. A correlation exists between two variables when higher values of one variable consistently go with higher or lower values of another variable. C. A correlation is only when two variables tend to change in opposite directions, with one increasing and one decreasing. D. A correlation is only when two variables tend to increase or decrease together. Give three examples of pairs of variables that are correlated. Select the correct answer below. A. the Superbowl winner and the performance of the stock market, amount of smoking and lung cancer, per capita personal income and the percent of the population below the poverty level B. production cost of movies and gross receipts of movies, per capita personal income and the percent of the population below the poverty level, height and weight of people C. amount of smoking and lung cancer, height and weight of people, price of a good and demand of the good D. production cost of movies and gross receipts of movies, inflation and unemployment, the Superbowl winner and the performance of the stock market
Answers
1. Option B. A correlation exists between two variables when higher values of one variable consistently go with higher or lower values of another variable
2. Option C. Amount of smoking and lung cancer, height and weight of people, price of a good and demand of the good
What are the examples of correlation?Examples of pairs of variables that are correlated:
The amount of exercise a person gets and their overall physical fitness level - as the amount of exercise increases, the person's physical fitness level tends to increase as well.The number of hours a student studies and their grade point average (GPA) - as the number of hours of studying increases, the student's GPA tends to increase as well.The amount of rainfall and crop yield - as the amount of rainfall increases, the crop yield tends to increase as well.Read more on correlation here:https://brainly.com/question/4219149
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Let X1, X2, X3, and X4 be four independent random variables, each with pdf f(x) = 3(1 – x)?, 0 < x < 1, zero elsewhere. If Y is the minimum of these four variables, find the cdf and the p
Answers
The cumulative distribution function (CDF) for the minimum of four independent random variables with the given probability density function (PDF) f(x) = 3(1 - x), 0 < x < 1, zero elsewhere, can be expressed as (1 - 3(1 - y) + (3/2)(1 - y)^2)^4. To find the probability P(Y = y), subtract the CDF values at y and the previous value.
The CDF of Y is obtained by calculating the probability that all four variables (X1, X2, X3, and X4) are greater than a threshold value y. Using the properties of independent random variables, we can derive the CDF formula by substituting the given PDF into the equation.
To find the probability P(Y = y), subtract the CDF values at y and the previous value. This represents the probability of Y taking on a specific value y.
By applying these formulas, you can determine the CDF and probabilities for specific values of Y.
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What is the equation of the line?
Answers
Answer:
y = 1/2x + 2
Step-by-step explanation:
The y-intercept is 2 because it passes through the y axis at (0,2) and the slope if 1/2
Hope that helps and have a great day!
Answer:
\(y=\frac{1}{2}x+2\)
Step-by-step explanation:
To find the equation for the line, lets try to find the slope and y-intercept of the line.
From looking at the graph, we can see that the line intersects the y-axis at y = 2. So the y-intercept would be 2.
The slope of the line would be the rise divided by the run. Looking at the graph, we can see that for every 2 the line moves in the x-direction, it moves 1 in the y-direction. This means that the rise is 1 and the run is 2. So the slope would be 1/2.
So we now know that the slope is 1/2 and the y-intercept is 2, we can now plug the information into the slope-intercept form.
Slope-intercept form is:
y = mx + b
where m is the slope and b is the y-intercept.
Plugging in we get
\(y=\frac{1}{2}x+2\)
And now we have the equation of the line.
I hope you find my answer and explanation to be helpful. Happy studying.
Find the volume of the cone. Use 3.14 for pi. Round your answer to the nearest tenths
place.
Answers
The volume of the cone is approximately 37.7 cubic units
What is volume?
A volume is simply defined as the amount of space occupied by any three-dimensional solid. These solids can be a cube, a cuboid, a cone, a cylinder, or a sphere. Different shapes have different volumes.
To find the volume of a cone, we use the formula:
V = (1/3) * π * r² * h
where π is the constant pi, r is the radius of the base of the cone, and h is the height of the cone.
Plugging in the given values, we get:
V = (1/3) * 3.14 * 3² * 4 ≈ 37.7
Therefore, the volume of the cone is approximately 37.7 cubic units (rounded to the nearest tenth).
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Given a normal distribution with u = 100 and o= 10, complete parts (a) through (d).
a. What is the probability that X> 85? The probability that X> 85 is_____(Round to four decimal places as needed.) b. What is the probability that X<80? The probability that X < 80 is ____(Round to four decimal places as needed.) c. What is the probability that X<90 or X> 130? The probability that X<90 or X> 130 is ____ (Round to four decimal places as needed.) d. 99% of the values are between what two X-values (symmetrically distributed around the mean)? 99% of the values are greater than __ and less than _(Round to two decimal places as needed.)
Answers
To solve the given problems, we'll use the properties of the normal distribution with mean μ = 100 and standard deviation σ = 10.
a. Probability that X > 85:
To find this probability, we need to calculate the area under the normal curve to the right of 85. We can use the standard normal distribution table or a calculator to find the corresponding z-score and then use the z-table to find the probability.
First, let's calculate the z-score:
z = (X - μ) / σ
z = (85 - 100) / 10
z = -15 / 10
z = -1.5
Using the z-table or a calculator, we find that the probability of Z > -1.5 is approximately 0.9332.
Therefore, the probability that X > 85 is 0.9332 (rounded to four decimal places).
b. Probability that X < 80:
Similarly, we'll calculate the z-score for X = 80:
z = (X - μ) / σ
z = (80 - 100) / 10
z = -20 / 10
z = -2
Using the z-table or a calculator, we find that the probability of Z < -2 is approximately 0.0228.
Therefore, the probability that X < 80 is 0.0228 (rounded to four decimal places).
c. Probability that X < 90 or X > 130:
To calculate this probability, we'll find the individual probabilities of X < 90 and X > 130, and then subtract the probability of their intersection.
For X < 90:
z = (90 - 100) / 10
z = -10 / 10
z = -1
Using the z-table or a calculator, we find that the probability of Z < -1 is approximately 0.1587.
For X > 130:
z = (130 - 100) / 10
z = 30 / 10
z = 3
Using the z-table or a calculator, we find that the probability of Z > 3 is approximately 0.0013.
Since these events are mutually exclusive, we can add their probabilities:
P(X < 90 or X > 130) = P(X < 90) + P(X > 130)
P(X < 90 or X > 130) = 0.1587 + 0.0013
P(X < 90 or X > 130) = 0.1600
Therefore, the probability that X < 90 or X > 130 is 0.1600 (rounded to four decimal places).
d. 99% of the values are between what two X-values (symmetrically distributed around the mean)?
To find the two X-values, we need to find the corresponding z-scores for the cumulative probabilities of 0.005 and 0.995. These probabilities correspond to the tails beyond the 99% range.
For the left tail:
z = invNorm(0.005)
z ≈ -2.576
For the right tail:
z = invNorm(0.995)
z ≈ 2.576
Now we can find the corresponding X-values:
X1 = μ + z1 * σ
X1 = 100 + (-2.576) * 10
X1 = 100 - 25.76
X1 ≈ 74.24
X2 = μ + z2 * σ
X2 = 100 + 2.576 * 10
X2 = 100 + 25.76
X2 ≈ 125.76
Therefore, 99% of the values are greater than 74.24 and less than 125.76 (rounded to two decimal places).
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