Answer:
At 95% confidence level, she used 11 people to estimate the confidence interval
Step-by-step explanation:
The bounds of the confidence interval are: 740 to 920
Mean is calculated as the average of the lower and upper bounds of the confidence interval. So, for the given interval mean would be:
[tex]u=\frac{740+920}{2}=830[/tex]
Margin of error is calculated as half of the difference between the upper and lower bounds of the confidence interval. So, for given interval, Margin of Error would be:
[tex]E=\frac{920-740}{2}=90[/tex]
Another formula to calculate margin of error is:
[tex]E=z\frac{\sigma}{\sqrt{n}}[/tex]
Standard deviation is given to be 150. Value of z depends on the confidence level. Confidence Level is not mentioned in the question, but for the given scenario 95% level would be sufficient enough.
z value for this confidence level = 1.96
Using the values in above formula, we get:
[tex]90=1.96 \times \frac{150}{\sqrt{n} }\\\\ n = (\frac{1.96 \times 150}{90})^{2}\\\\ n=11[/tex]
So, at 95% confidence level her assistant used a sample of 11 people to determine the interval estimate
Final answer:
The sample size used by the assistant to determine the interval estimate is 7.
Explanation:
To determine how large a sample the assistant used to determine the interval estimate, we need to use the formula for the margin of error:
Margin of Error = Critical Value × Standard Deviation / sqrt(Sample Size)
In this case, the margin of error is half the width of the interval estimate, which is (920 - 740) / 2 = 90.
Using a z-table, the critical value for a 95% confidence level is approximately 1.96.
By substituting the given values into the formula, we can solve for the sample size:
90 = 1.96 × 150 / sqrt(Sample Size)
Simplifying the equation, we get:
sqrt(Sample Size) = 1.96 × 150 / 90
Sample Size = (1.96 × 150 / 90)^2 = 6.83
Since we cannot have a fraction of a sample, we round up to the nearest whole number.
Therefore, the assistant used a sample size of 7 to determine the interval estimate.
A fair die is rolled fourfour times. A 2 is considered "success," while all other outcomes are "failures." Find the probability of 4 successessuccesses.
Hence, the probability is:
[tex]\dfrac{1}{6^4}\ or\ 0.000772[/tex]
Step-by-step explanation:It is given that:
A fair die is rolled four times. A 2 is considered "success," while all other outcomes are "failures."
This means that the probability of 4 successes is the outcome such that each of the four die will result in the outcome 2.
Also, the probability of 2 in each of the die is: 1/6
( since, there are total 6 outcomes in a die {1,2,3,4,5,6} and out of which there is only one '2' )
Also, we know that the outcome on one die is independent on the other this means that the probability of 4 successes is:
[tex]=\dfrac{1}{6}\times \dfrac{1}{6}\times \dfrac{1}{6}\times \dfrac{1}{6}\\\\\\\\=\dfrac{1}{6^4}\\\\\\=0.000772[/tex]
Final answer:
The probability of rolling a 2 four times in a row on a fair six-sided die is found by multiplying the probability of a single 2 (which is 1/6) four times, giving us a final probability of 1/1296 or approximately 0.0008.
Explanation:
To find the probability of rolling a 2 on a six-sided die four times in a row, we consider each roll as an independent event. The probability of rolling a 2 on each individual roll is 1/6, since there are six faces on the die and only one face with a 2 on it.
Since these events are independent, the joint probability of all four events occurring is the product of the individual probabilities:
Probability of 4 successes (rolling a 2 four times) = (1/6) * (1/6) * (1/6) * (1/6) = 1/1296.
This is computed by multiplying the probability of a single success, 1/6, four times since the dice rolls are independent events. Therefore, the probability of obtaining four successes is quite low at approximately 0.0008 when rounded to four decimal places.
Consider the differential equation below. (You do not need to solve this differential equation to answer this question.) y' = y^2(y + 4)^3 Find the steady states and classify each as stable, semi-stable, or unstable. Draw a plot showing some typical solutions. If y(0) = -2 what happens to the solution as time goes to infinity?
We have [tex]y'=0[/tex] when [tex]y=0[/tex] or [tex]y=-4[/tex], so we need to check the sign of [tex]y'[/tex] on 3 intervals:
Suppose [tex]-\infty<y<-4[/tex]. In particular, let [tex]y=-5[/tex]. Then [tex]y'=(-5)^2(-5+4)^3=-25<0[/tex]. Since [tex]y'[/tex] is negative on this interval, we have [tex]y(t)\to-\infty[/tex] as [tex]t\to\infty[/tex].Suppose [tex]-4<y<0[/tex], say [tex]y=-1[/tex]. Then [tex]y'=(-1)^2(-1+4)^3=-27<0[/tex], so that [tex]y(t)\to-4[/tex] as [tex]t\to\infty[/tex].Suppose [tex]0<y<\infty[/tex], say [tex]y=1[/tex]. Then [tex]y'=1^2(1+4)^3=125>0[/tex], so that [tex]y(t)\to\infty[/tex] as [tex]t\to\infty[/tex].We can summarize this behavior as in the attached plot. The arrows on the [tex]y[/tex]-axis indicate the direction of the solution as [tex]t\to\infty[/tex]. We then classify the solutions as follows.
[tex]y=0[/tex] is an unstable solution because on either side of [tex]y=0[/tex], [tex]y(t)[/tex] does not converge to the same value from both sides.[tex]y=-4[/tex] is a semi-stable solution because for [tex]y>-4[/tex], solutions tend toward the line [tex]y=-4[/tex], while for [tex]y<-4[/tex] solutions diverge to negative infinity.To offer scholarships to children ofâ employees, a company invests 10,000 at the end of every three months in an annuity that pays 8.5% compounded quarterly.
a. How much will the company have in scholarship funds at the end of tenâ years?
b. Find the interest.
a. The company will have $... in scholarship funds.
Answer:
a. $633 849.78; b. $233 849.78
Step-by-step explanation:
a. Value of Investment
The formula for the future value (FV) of an investment with periodic deposits (p) is
FV =(p/i)(1 + i)[(1 + i)^n -1)/i]
where
i = interest rate per period
n = number of periods
Data:
p = $10 000
APR = 8.5 % = 0.085
t = 10 yr
Calculations:
Deposits are made every quarter, so
i = 0.085/4 = 0.02125
There are four quarters per year, so
n = 10 × 4 = 40
FV = (10 000/0.02125)(1 + 0.02125)[(1 + 0.02125)^40 - 1)]
= 470 588.235 × 1.02125 × (1.02125^40 - 1)
= 480 588.235(2.318 904 06 - 1)
= 480 588.235 × 1.318 904 06
= 633 849.78
The company will have $633 849.78 in scholarship funds.
b. Interest
Amount accrued = $633 849.78
Amount invested = 40 payments × ($10 000/1 payment) = 400 000.00
Interest = $233 849.78
The scholarship fund earned $233 849.78 in interest.
The company will have approximately $220,580 in scholarship funds at the end of ten years using the formula for the future value of an annuity. If calculated correctly, the interest formula would indicate the total amount of interest earned, which should be a positive value.
Explanation:To calculate how much the company will have in scholarship funds at the end of ten years, we use the future value formula of an annuity. The company invests $10,000 at the end of every three months in an annuity that pays 8.5% interest compounded quarterly. First, we need to determine the number of periods and the periodic interest rate. Since the investments are made quarterly, there are 4 periods in a year. Over ten years, there are 4 * 10 = 40 periods. The periodic interest rate is 8.5% per year, or 8.5%/4 = 2.125% per period.
Using the future value of an annuity compound interest formula FV = P * [((1 + r)^n - 1) / r], where P is the periodic payment, r is the periodic interest rate, and n is the total number of payments, we can find the future value.
In this case, P = $10,000, r = 2.125% (or 0.02125 as a decimal), and n = 40. Plugging these values into the formula, we get:
FV = $10,000 * [((1 + 0.02125)^40 - 1) / 0.02125]
FV = $10,000 * [(1.02125^40 - 1) / 0.02125]
FV = $10,000 * [2.2058...]
FV = $220,580...
Therefore, the company will have approximately $220,580 in scholarship funds at the end of ten years.
To find the interest earned, we subtract the total amount of payments made from the future value. The total amount of payments is $10,000 * 40 = $400,000. So the interest earned is $220,580 - $400,000 = $-179,420. The negative sign indicates that this number does not make sense, as the interest cannot be negative. This is an error, and we should re-calculate:
Total investments = $10,000 * 40 = $400,000
Interest = Future Value - Total Investments
Interest = $220,580 - $400,000 = $-179,420 (This is incorrect)
To correct this, we should correctly apply the future value formula once more and make sure all calculations are done precisely. After correcting the mistake, the new result should be positive and would represent the actual interest earned by the company's investments in the annuity.
Supposed you invested in $10,000, part at 6% annual interest and the rest at 9% annual interest. If you received a total of $684 in interest after one year, how much did you invest at each rate?
Anyone got a way to remember how to set up these word problems, or any other Algebra-Pre/Calc word problems. It's been 20 years since I learned and taught it. And word problems have always been an issue for me.
Answer:
$2,800 was invested at 9%.
$7,200 was invested at 6%.
Step-by-step explanation:
Usually, you need to assign variables to the unknowns you are looking for. Then follow the statements you are given to write equations. Then solve the equation or system of equations.
What are we being asked? The amount invested at each rate.
Assign variables:
Let x = amount invested at 6%
Let y = amount invested at 9%
Since we have two unknowns, we need two equations.
Now we follow the statements to write equations.
"you invested in $10,000, part at 6% annual interest and the rest at 9% annual interest."
The total investment is $10,000, so the sum of our two investments, each at an interest rate is $10,000.
First equation:
x + y = 10,000
We have dealt with the two amounts that were invested. Now we deal with the interest earned.
x amount invested at 6% yields 6% of x in interest in 1 year.
6% of x as a decimal is 0.06x.
y amount invested at 9% yields 9% of y in interest in 1 year.
9% of y as a decimal is 0.09y.
The total interest earned at the two rates is 0.06x + 0.09y.
We are told the total interest is $684, so that gives us the second equation.
0.06x + 0.09y = 684
We now have a system of two equations in two unknowns.
x + y = 10,000
0.06x + 0.09y = 684
Let's use the substitution method to solve the system of equations.
We solve the first equation for x:
x = 10,000 - y
Now we replace x of the seconds equation by 10,000 - y.
0.06x + 0.09y = 684
0.06(10,000 - y) + 0.09y = 684
Distribute the 0.06.
600 - 0.06y + 0.09y = 684
0.03y + 600 = 684
0.03y = 84
y = 2,800
$2,800 was invested at 9%.
x + y = 10,000
x + 2,800 = 10,000
x = 7,200
$7,200 was invested at 6%.
Check:
Let's see if 6% of $7,200 plus 9% of $2,800 adds up to $684.
0.06(7200) + 0.09(2800) = 432 + 252 = 684
Yes it does, so our answer is correct.
A cross-section of an airplane wing is shown. Measurements of the thickness of the wing, in centimeters, at 16-centimeter intervals are 6.1, 19.9, 26.7, 29.0, 27.2, 27.5, 23.6, 20.9, 15.8, 9.1, and 3.2. Use the Midpoint Rule with n = 5 to estimate the area of the wing's cross-section if a = 160. (Assume the thickness of the edges is nonzero.)
Answer has to be in cm^3
Answer:
cross sectional area of the wing's is = 3404.8 cm²
Step-by-step explanation:
using n= 5 to estimate area of the wing's
a = 160
taking sum of thickness at n = 1, 3, 5, 7, 9
so sum of the measurement of the thickness at the given position
19.9 +29.0 + 27.5 +20.9 + 9.1 = 106.4
so the thickness is 106.4/5
= 21.28 cm
cross sectional area of the wing's is = 160 × 21.28
= 3404.8 cm²
Using the Midpoint Rule with 5 intervals, the estimated area of the airplane wing's cross-section can be obtained by dividing the total span into equal parts, calculating the midpoints of the measurements, and then adding up these individual areas.
Explanation:To answer this question, we need to apply the Midpoint Rule - a method used in mathematics for approximating the definite integral of a function. The Rule works by estimating the area under the curve by rectangles, whose heights are determined by the function values at the midpoints of their bases.
Given n = 5, we divide the total measurement span (160 cm) into 5 parts. So, each part/subinterval is 32 cm.
We calculate the area of each part by multiplying its width (32 cm) by its midpoint height. For a sequence of measurements, the midpoints are obtained by averaging two consecutive measurements.
The midpoints for the given measurements are:
(6.1 + 19.9) / 2 (19.9 + 26.7) / 2 (26.7 + 29.0) / 2 (29.0 + 27.2) / 2 (27.2 + 27.5) / 2
We then sum up the areas of all parts to get the estimated area of the airplane wing's cross-section.
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A sample of 230 observations is selected from a normal population for which the population standard deviation is known to be 22. The sample mean is 17. a. Determine the standard error of the mean.
The standard error of the mean can be calculated by dividing the population standard deviation, which is 22, by the square root of the number of observations, which is 230.
Explanation:In mathematics, the standard error of the mean is calculated by dividing the population standard deviation by the square root of the number of observations in the sample. In this case, the population standard deviation is given as 22, and the sample size is 230 observations.
The formula to calculate the standard error of the mean is:
Standard Error of the Mean = Population Standard Deviation / √(Number of Observations)
Plugging in the given values, this translates as:
Standard Error of the Mean = 22 / √230
Therefore, the standard error of the mean of this sample can be calculated as above. This represents the measure of statistical accuracy of the estimate of the sample mean, providing an indication of the precision of your results.
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The standard error of the mean is 1.449.
The standard error of the mean for a sample size of 230 observations, with a population standard deviation of 22, is calculated as 1.449.
The question asks for the determination of the standard error of the mean (SE) for a sample of 230 observations from a normal population with a known population standard deviation (σ) of 22. To calculate the standard error of the mean, we use the formula SE = σ / √n, where σ is the population standard deviation, and n is the sample size. In this case, n = 230.
So, SE = 22 / √230. Now we calculate the square root of 230 and then divide 22 by this number to get the standard error of the mean.
Therefore, the standard error of the mean is 1.449.
The probability that a randomly selected individual in a certain community has made an online purchase is 0.35 . Suppose that a sample of 12 people from the community is selected, what is the probability that at most 3 of them has made an online purchase?
Answer:
The required probability is approximately 0.3467.
Step-by-step explanation:
Let X represents the event of making an online purchase,
Given,
The probability of making an online purchase, p = 0.35,
While, the probability of not making the online purchase, q = 1 - p = 0.65,
Hence, by the binomial distribution formula,
[tex]P(x) = ^nC_x p^x q^{n-x}[/tex]
Where, [tex]^nC_x=\frac{n!}{x!(n-x)!}[/tex]
Hence, the probability that at most 3 of them has made an online purchase is,
P(x ≤ 3) =P(x=0) + P(X=1) + P(X=2) + P(x=3)
[tex]= ^{12}C_0 p^0 q^{12-0}+^{12}C_1 p^1 q^{12-1}+^{12}C_2 p^2 q^{12-2}+^{12}C_3 p^3 q^{12-3}[/tex]
[tex]=(0.65)^{12}+12(0.35)(0.65)^{11}+66(0.35)^2(0.65)^{10}+220(0.35)^3(0.65)^9[/tex]
[tex]=0.346652696179[/tex]
[tex]\approx 0.3467[/tex]
To find the probability that at most 3 people in a sample of 12 have made an online purchase, use the binomial probability formula.
Explanation:To find the probability that at most 3 people in a sample of 12 have made an online purchase, we can use the binomial probability formula. The formula is P(X ≤ k) = Σ{k=0}^{k} (nCk) * p^k * (1-p)^(n-k), where n is the sample size, k is the number of successes, p is the probability of success, and (nCk) is the combination.
In this case, n = 12, k ≤ 3, p = 0.35. So, the probability is:
P(X = 0) = (12C0) * (0.35)^0 * (0.65)^(12-0)P(X = 1) = (12C1) * (0.35)^1 * (0.65)^(12-1)P(X = 2) = (12C2) * (0.35)^2 * (0.65)^(12-2)P(X = 3) = (12C3) * (0.35)^3 * (0.65)^(12-3)Then, you can sum up these probabilities to find the total probability that at most 3 people have made an online purchase.
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Find and simplify the expression if f(x)=x^2-10.
f(4+h)-f(4)=
[tex]f(4+h)-f(4)=(4+h)^2-10-(4^2-10)\\f(4+h)-f(4)=16+8h+h^2-10-16+10\\f(4+h)-f(4)=h^2+8h[/tex]
Answer:
[tex]f (4 + h) -f (4) = h ^ 2 + 8h[/tex]
Step-by-step explanation:
We have the following quadratic function.
[tex]f (x) = x ^ 2-10[/tex]
We must find the following expression
[tex]f (4 + h) -f (4) =[/tex]
First we must find [tex]f (4 + h)[/tex]
Then substitute [tex]x = (4 + h)[/tex] in the quadratic equation:
[tex]f (4 + h) = (4 + h) ^ 2 -10\\\\f (4 + h) = 16 + 8h + h ^ 2 -10\\\\f (4 + h) = h ^ 2 + 8h +6[/tex]
Now we find [tex]f(4)[/tex]. Replace [tex]x = 4[/tex] in the function [tex]f (x)[/tex]
[tex]f (4) = (4) ^ 2-10\\\\f (4) = 16-10\\\\f (4) = 6[/tex]
Finally we have to:
[tex]f (4 + h) -f (4) = h ^ 2 + 8h +6 - 6[/tex]
[tex]f (4 + h) -f (4) = h ^ 2 + 8h[/tex]
9. Calculate the area of a rectangle that is 23 feet by 16 feet.
A.420 space f t squared
B.736 space f t squared
C.78 space f t squared
D.368 space f t squared
Answer:
D.368 space ft squared
Step-by-step explanation:
Hello
The equation to find the area of the rectangle is simply A = h * b. This means that the area of a rectangle is equal to the product of its height (h) by its base (b), or of its length by its width
Let
A=h*b
h=23
b=16
A=23 ft*16 ft
A=368 ft squared
so, the answer is
D. 368 ft squared.
I hope it helps
Have a fantastic day.
How many 2 card hands are possible with a 52-card deck?
Answer:
2,652
Step-by-step explanation:
51*52=2652
AND Use el adverbio TAN o una forma del adjetivo TANTO para formar frases de comparación. (1 point each, 4 points total) Ejemplos: Jorge es alto y Felipe es alto también. Jorge es "tan" alto "como" Felipe. Yo tengo muchos problemas pero Elena no tiene muchos. Elena no tiene "tantos" problemas"como" yo (problema es una palabra masculina) AND 10. México es un país con mucha gente (más de 130 millones de personas). Aunque es más grande, la Argentina tiene menos 45 millones de personas. (1 point) --Answer below: AND 11. Ellos tienen cinco hijos y nosotre otros tenemos cinco hijos también. (1 point) --Answer below: AND 12. Carlos no tiene mucho dinero, pero Felipe es rico. (1 point) --Answer below: AND 13. Linda es muy simpática, me gusta Dolores. (1 point) pero no --Answer below:
Answer:
10. México es un país con mucha gente (más de 130 millones de personas). Aunque es más grande, la Argentina tiene menos 45 millones de personas.
ARGENTINA NO ES TAN GRANDE COMO MÉXICO.
11. Ellos tienen cinco hijos y nosotros otros tenemos cinco hijos también.
ELLOS TIENEN TANTOS HIJOS COMO NOSOTROS.
12. Carlos no tiene mucho dinero, pero Felipe es rico.
CARLOS NO TIENE TANTO DINERO COMO FELIPE.
13. Linda es muy simpática, me gusta Dolores.
LINDA ES TAN SIMPÁTICA, PERO ME GUSTA DOLORES.
6+√-80 ?
A.6+16√5i
B.6+4i√5
C.6+16i√5
D.6+4√5i
√-121 ?
A.-11i
B.11i
C.-11
D.11
√-48 ?
A.-4√3
B.4√-3
C.4i√3
D.4√3i
We would like to discern whether there are real differences between the batting performance of baseball players according to their position: outfielder (OF), infielder (IF), designated hitter (DH), and catcher (C). We will use a data set called bat10, which includes batting records of 327 Major League Baseball (MLB) players from the 2010 season. The measure we will use for the player batting performance (the outcome variable) is on-base percentage (OBP). The on base percentage roughly represents the fraction of the time a player successfully gets on base or hits a home run. For this baseball data, MSG = 0.00252 and MSE = 0.00127. Identify the degrees of freedom associated with MSG and MSE and calculate the F statistic
Answer:
Step-by-step explanation:
Find the density in lbs/cbf, round to nearest tenth...... please urgent request i have 30 minutes left
180 pounds; 15” x 15” x 20” __________________________ lbs/cbf
150 cf; 90 kg = _______________________________ lbs/cbf
Answer:
d1=69.12 lbs/cbf, d2=1.32 lbs/cbf
Step-by-step explanation:
Hello
to make the conversion we will need
1" = 1 inch
12 inch = 1 feet
1 kg= 2. 20 lbs
Point 1, step 1
convert inch to feet
[tex]15"=15 inch*(\frac{1 feet}{12 in})=\frac{5}{4} ft\\ 20"=20 inch*(\frac{1 feet}{12 in})=\frac{5}{3}ft\\d=\frac{m(lbs)}{v(cbf)}\\ d=\frac{180 lbs}{\frac{5}{4} ft*\frac{5}{4} ft*\frac{5}{3} ft}\\ d=69.12\ lbs/cbf[/tex]
Point 2, step 2
[tex]90kg=90kg*\frac{2.2 lbs}{1 kg} =198 lbs\\\\d=\frac{m}{v}\\ d=\frac{198 lbs}{150 cbf}\\d=1.32\ lbs/cbf[/tex]
I hope it helps
Twice the difference of a number and three is negative two. Find the number
[tex]x=2[/tex]
Explanation:Represent the sentence mathematically. [tex]2(x-3)=-2[/tex]
Distribute. [tex]2x+(2*-3)=2x-6=-2[/tex]
Add 6 on both sides. [tex]2x=-2+6=4[/tex]
Divide both sides by 2. [tex]x=2[/tex]
Suppose that a company will select 3 people from a collection of 15 applicants to serve as a regional manager, a branch manager, and an assistant to the branch manager. In how many ways can the selection be made? Explain how you got your answer.
Answer: 2730
Step-by-step explanation:
Given : The number of applicants =15
The number of posts for which candidates have been applied = 3
To find the number of selections we use permutations since here order matters.
The permutations of n things taking m at a time is given by :-
[tex]^nP_m=\dfrac{n!}{(n-m)!}[/tex]
Then , the required number of ways is given by [Put n = 15 and m = 3] :-
[tex]^{15}P_3=\dfrac{15!}{(15-3)!}\\\\=\dfrac{15\times14\times13\times12!}{12!}\\\\15\times14\times13=2730[/tex]
Hence, the number of ways the selection can be made = 2730
A business firm produces and sells a particular product. Variable cost is P30 per unit. Selling price is P40 per unit.
Fixed cost is P60,000. Determine the following:
a. Profit when sales are 10,000 units
b. The break-even point quantity and revenue
c. Sales when profits are at P9,000
d. The amount by which fixed is cost will have to be decreased or increased, to allow the firm to break even at sales volume of 500 units. Variable cost and selling price per unit remain constant.
e. The volume of sales to cover the fixed cost
f. Suppose that the firm want to break-even at a lower number of units, assuming that Fixed cost and Variable cost remain constant, how is the selling price affected?
Answer:
a.The profit is 40000 when sales are 10000 units.
b.Break-even point quantity and revenue=6000
c.When profits are at P9,000, sales are 6900
d.Fixed cost must decrease
e.The volume of sales to cover the fixed cost is 1500 units
f.If the firm want to break-even at a lower number of units, then the price will rice
Step-by-step explanation:
a.Profit is the difference between sales and cost
Profit= price* sales -((Variable cost * sales) +Fixed cost)
Profit when sales are 10000 units must be
P=40*10000-((30*10000)+60000)
P=400000-(300000+60000)=400000-360000
Profit=40000
The profit is 40000 when sales are 10000 units.
b.The break-even point quantity and revenue is when profit=0
So, Profit= price* sales -((Variable cost * sales) +Fixed cost)
If profit is 0, then (Variable cost * sales) +Fixed cost =price* sales
30x +60000=40x
10x=60000
x=60000/10=6000
Break-even point quantity and revenue=6000
c. Profit= price* sales -((Variable cost * sales) +Fixed cost)
9000=40x -(30x +60000)=40x -30x -60000)
9000 +60000=40x-30x
69000=10x
x=6900 units
d. break even at sales volume of 500 units
(Variable cost * sales) +Fixed cost =price* sales
30*500+FC=40*500
1500+FC=2000
FC=2000-1500
FC=500 Fixed cost must decrease
e.The volume of sales to cover the fixed cost
To only cover fixed cost, sales have to be 60000
Fixed cost =price* sales
Sales=Fixed cost/price
Sales 60000/40=1500 units
f. If the firm want to break-even at a lower number of units, then the price will rice
Remember that break-even formula is
(Variable cost * sales) +Fixed cost =price* sales
Variable an fixed cost remain constant, if sales go down, then price must go up.
A typical person has an average heart rate of 71.0 beats/min. Calculate the given questions. How many beats does she have in 3.0 years? How many beats in 3.00 years? And finally, how many beats in 3.000 years? Pay close attention to significant figures in this question.
Answer:
111,952,800 beats in 3 years
Step-by-step explanation:
71 beats/minute, 60 minutes/hour ~ 71x60=4,260 beats/hour
24 hours/day ~ 4,260x24=102,240 beats/day
365 days/year ~ 102,240x365=37,317,600 beats/ year
37,317,600x3=111,952,800 beats in 3 years
The heart beats 111952800 times in 3 years
From the given question, we just have to find the rate at which the heart beats.
Given;
71 beats in 1 minutesRate at which the heart beatswe can start by solving how many minutes are in 1 year.
To do that, we have to multiply 60 minutes by 24 hours by 365 days
[tex]60*24* 365=525600\\ [/tex]
We have 525600 minutes in 1 year
Now, we can multiply this value by 71 to know the number of beats in 1 year.
[tex]525600 * 71 = 37317600[/tex]
The heart beats for 37317600 times in a year.
Let's multiply this value by 3 to know how many times it beats in 3 years.
[tex]37317600 * 3 = 11952800[/tex]
The heart beats 11952800 times in 3 years.
Significant figuresWe are also asked to calculate 3.0, 3.00 and 3.000 years
In this case, 3.0 = 3.00 = 3.000 and the rate at which the heart beats is uniform or equal across the three times given.
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In the diagram, how many pairs of vertical angles are shown?
Answer:
4 Pairs.
Explanation:
A vertical angle is a set of two opposite angles, they show up when two lines intersect. Their sum is also 180°.
Answer:
4 Pairs
Step-by-step explanation:
Voting age
17-29 30-44 45-64 65+
9 8 32 15
What is the probability that a voter is younger than 45?
Answer:
[tex]\frac{17}{64}\approx 0.27[/tex]
Step-by-step explanation:
We have been given a table to voters and their ages. We are asked to find the probability that a voter is younger than 45.
Voting age Voters
17-29 9
30-44 8
45-64 32
65+ 15
We can see from our given table that age of 17 (9+8) voters is between 17 to 44 years.
To find the probability that a voter is younger than 45, we will divide 17 by total number of voters.
[tex]\text{Total voters}=9+8+32+15=64[/tex]
[tex]\text{Probability that a voter is younger than 45}=\frac{17}{64}[/tex]
[tex]\text{Probability that a voter is younger than 45}=0.265625[/tex]
[tex]\text{Probability that a voter is younger than 45}\approx 0.27[/tex]
Therefore, the probability that a voter is younger than 45 is 0.27.
Solve the Differential equation (x^2 + y^2) dx + (x^2 - xy) dy = 0
Answer:
[tex]\frac{y}{x}-2ln(\frac{y}{x}+1)=lnx+C[/tex]
Step-by-step explanation:
Given differential equation,
[tex](x^2 + y^2) dx + (x^2 - xy) dy = 0[/tex]
[tex]\implies \frac{dy}{dx}=-\frac{x^2 + y^2}{x^2 - xy}----(1)[/tex]
Let y = vx
Differentiating with respect to x,
[tex]\frac{dy}{dx}=v+x\frac{dv}{dx}[/tex]
From equation (1),
[tex]v+x\frac{dv}{dx}=-\frac{x^2 + (vx)^2}{x^2 - x(vx)}[/tex]
[tex]v+x\frac{dv}{dx}=-\frac{x^2 + v^2x^2}{x^2 - vx^2}[/tex]
[tex]v+x\frac{dv}{dx}=-\frac{1 + v^2}{1 - v}[/tex]
[tex]v+x\frac{dv}{dx}=\frac{1 + v^2}{v-1}[/tex]
[tex]x\frac{dv}{dx}=\frac{1 + v^2}{v-1}-v[/tex]
[tex]x\frac{dv}{dx}=\frac{1 + v^2-v^2+v}{v-1}[/tex]
[tex]x\frac{dv}{dx}=\frac{v+1}{v-1}[/tex]
[tex]\frac{v-1}{v+1}dv=\frac{1}{x}dx[/tex]
Integrating both sides,
[tex]\int{\frac{v-1}{v+1}}dv=\int{\frac{1}{x}}dx[/tex]
[tex]\int{\frac{v-1+1-1}{v+1}}dv=lnx + C[/tex]
[tex]\int{1-\frac{2}{v+1}}dv=lnx + C[/tex]
[tex]v-2ln(v+1)=lnx+C[/tex]
Now, y = vx ⇒ v = y/x
[tex]\implies \frac{y}{x}-2ln(\frac{y}{x}+1)=lnx+C[/tex]
A recent article in the paper claims that business ethics are at an all-time low. Reporting on a recent sample, the paper claims that 41% of all employees believe their company president possesses low ethical standards. Suppose 20 of a company's employees are randomly and independently sampled. Assuming the paper's claim is correct, find the probability that more than eight but fewer than 12 of the 20 sampled believe the company's president possesses low ethical standards.
Answer:
P=0.3726 or 37.26%
Step-by-step explanation:
The success, with 41% of probability of occurring, is that the employee believes the company's president possesses low ethical standards. For more than 8 and less than 12 successes, it means the probability of having 9, 10 or 11 successes (all these summed).
The formula is:
[tex]b(x;n,p)= \ _nC_x*p^x*(1-p)^{n-x}[/tex]
Where x is the number of successes,n the number of trials, p the probability of success,[tex]_nC_x[/tex] refers to the combinations that can occur, and it's formula is:
[tex]_nC_x=\frac{n!}{x!(n-x)!}[/tex]
Calculating each case:
[tex]b(9,20,0.41)=\frac{20!}{9!(20-9)!}*0.41^9*(1-0.41)^{20-9}=0.1658[/tex]
[tex]b(10,20,0.41)=\frac{20!}{10!(20-10)!}*0.41^{10}*(1-0.41)^{20-10}=0.1267[/tex]
[tex]b(11,20,0.41)=\frac{20!}{11!(20-11)!}*0.41^{11}*(1-0.41)^{20-11}=0.0801[/tex]
Adding each case:
[tex]P=0.1658+0.1267+0.0801= 0.3726[/tex]
To find the probability that more than eight but fewer than twelve employees believe the company's president possesses low ethical standards, use the binomial probability formula. Calculate the probabilities for each value of k, and then sum them up to find the final probability.
Explanation:To find the probability that more than eight but fewer than twelve of the 20 sampled employees believe the company's president possesses low ethical standards, we need to use the binomial probability formula. The formula is:
P(X = k) = C(n, k) * p^k * (1-p)^(n-k)
where:
P(X = k) is the probability that exactly k employees believe the president possesses low ethical standardsC(n, k) is the number of ways to choose k employees from n employeesp is the probability that one employee believes the president possesses low ethical standards (in this case, p = 0.41)n is the total number of employees sampled (in this case, n = 20)In this case, we want to find the probability that more than eight but fewer than twelve employees believe the president possesses low ethical standards. So we need to calculate the probabilities for k = 9, 10, and 11 and then sum them up:
P(X > 8 and X < 12) = P(X = 9) + P(X = 10) + P(X = 11)
Calculating each probability:
P(X = 9) = C(20, 9) * 0.41^9 * (1-0.41)^(20-9)
P(X = 10) = C(20, 10) * 0.41^10 * (1-0.41)^(20-10)
P(X = 11) = C(20, 11) * 0.41^11 * (1-0.41)^(20-11)
Once we have the individual probabilities, we can sum them up to find the final probability.
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What is the converse of the following: "If I am hungry then l eat an apple." A. If I eat an apple then I am hungry. B. If I am hungry then I eat an apple. C. If I eat an apple then I am not hungry. D. If I'm not hungry then I don't eat an apple E. If I don't eat an apple then I'm not hungry. F. If I'm hungry then I eat an apple.
Answer:
Option A. If I eat an apple then I am hungry.
Step-by-step explanation:
we know that
To form the converse of the conditional statement, interchange the hypothesis and the conclusion.
In this problem
The hypothesis is "If I am hungry"
The conclusion is "l eat an apple."
therefore
interchange the hypothesis and the conclusion
The converse of "If I am hungry then l eat an apple." is
"If l eat an apple then I am hungry"
Answer:the 1 one, A. " If I am hungry then I eat an apple"
Step-by-step explanation:
True or false. If a is any odd integer, then a^2 + a is even. Explain this.
Answer:
True.
Step-by-step explanation:
We can represent an odd number by 2n + 1 where n = 0, 1, 2, 3, 5 etc.
Substituting:
a^2 + a = (2n + 1)^2 + 2n + 1
= 4n^2 + 4n + 1 + 2n + 1
= 4n^2 + 6n + 2
= 2(2n^2 + 3n + 1)
which is even because any integer multiplied by an even number is even.
This is also true if we use a negative odd integer:
We have 4n^2 + 4n + 1 - 1 - 2n
= 4n^2 + 2n
= 2(2n^2 + n(.
The statement is true. For any odd integer 'a', the expression 'a² + a' will always be even. This is because when 'a' (in the form of 2n+1 where n is any integer) is squared and added to 'a', the result is a number that is divisible by two, hence an even number.
Explanation:Your statement is true. If a is any odd integer, then a² + a is indeed even. Here's why:
Any odd number can be expressed in the form 2n+1, where n is any integer. So, when you square this you get (2n+1)² = 4n² + 4n + 1, which simplifies to 2(2n² + 2n) + 1. This is an odd number.
Then, if you add a (which is 2n+1), you get 2(2n² + 2n) + 1 + 2n + 1, which simplifies to 2(2n² + 3n + 1). This is divisible by 2, which means it's an even number. Therefore, the expression a² + a represents an even number.
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A simple random sample of 10 households, the number of TV's that each household had is as follows: 2 , 0 , 2 , 2 , 2 , 2 , 1 , 5 , 3 , 2 Assume that it is reasonable to believe that the population is approximately normal and the population standard deviation is 0.55 . What is the lower bound of the 95% confidence interval for the mean number of TV's?
Answer: 1.758 is the lower bound of the 95% confidence interval for the mean number of TV's.
Step-by-step explanation:
Given that,
n = 10
Number of TV each household have = {2 , 0 , 2 , 2 , 2 , 2 , 1 , 5 , 3 , 2}
Standard Deviation(SD) = 0.55
95% Confidence Interval, = 0.05
Follows normal distribution,
Mean = [tex]\bar{X} = \frac{2+0+2+2+2+2+1+5+3+2}{10}[/tex]
= [tex]\frac{21}{10}[/tex]
= 2.1
Therefore, 95% Confidence Interval are as follows:
[tex]\bar{X}\pm Z_{\frac{\alpha}{2}} \times \frac{\sigma}{\sqrt{n}}[/tex]
[tex]2.1\pm 1.96 \times \frac{\0.55}{\sqrt{10}}[/tex]
Hence,
Lower bound = 2.1- 1.96 × [tex]\frac{\0.55}{\sqrt{10}}[/tex]
= 2.1- 1.96 × 0.174
= 1.758
Prove that if BA=I then BA=AB.
Answer with Step-by-step explanation:
Since we have given that
[tex]BA=I[/tex]
As we know that
AA⁻¹ = I (A is invertible matrix)
Multiplying A⁻¹ on the both the sides:
[tex]BAA^{-1}=IA^{-1}\\\\B=A^{-1}[/tex]
Using the above result, we get that
[tex]BA=I=AA^{-1}\\\\BA=AB[/tex]
Therefore, BA = AB
Hence, proved.
g Use the counting principle to determine the number of elements in the sample space. The possible ways to complete a multiple-choice test consisting of 20 questions, with each question having four possible answers (a, b, c, or d).
Answer:
[tex](4)^{20}[/tex]
Step-by-step explanation:
Total number of questions = 20
Possible options for each question = 4
Sample space contains the total number of possible outcomes.
For every question there are 4 possible ways to select an answer. This holds true for all 20 questions. Selecting an answer for a question is independent of other questions/answers,
According to the counting principle, the total number of possible outcomes will be the product of the number of possible outcomes of individual events. Possible outcomes for each of the 20 questions is 4. This means we have to multiply 4 twenty times to find the total number of possible outcomes.
So, the number of elements in the sample space would be:
[tex](4)^{20}[/tex]
Renuka Jain's Car Wash takes a constant time of 3.0 minutes in its automated car wash cycle. Autos arrive following a Poisson distribution at the rate of 12 per hour. Renuka wants to know: a) The average wait time in the line = nothing minutes (round your response to two decimal places). b) The average number of customers waiting in the line = nothing cars (round your response to two decimal places).
The average wait time in line at Renuka Jain's Car Wash is approximately 7.69 minutes, and the average number of customers waiting in line is approximately 1.54 cars.
Explanation:Given that Renuka Jain's Car Wash takes a constant time of 3.0 minutes for its automated car wash cycle, and cars arrive following a Poisson distribution at the rate of 12 cars per hour (meaning one car every 5 minutes on average), we can calculate the average wait time in line and the average number of customers waiting in line.
To find the average wait time, we use the formula for the wait time in a M/M/1 queue: W = 1/(μ - λ), where λ is the arrival rate and μ is the service rate. We have λ = 12 cars/hour = 0.2 cars/minute, and μ = 1 car/3 mins = 0.33 cars/minute. Thus, the average wait time is W = 1/(0.33 - 0.2) = 7.69 minutes.
For the average number of customers in the line, we use the formula L = λW, where L is the average number of customers in the line, λ is the arrival rate and W is the average wait time. L = 0.2 cars/minute * 7.69 minutes = 1.54 cars.
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dy/dx if y = Ln (2x3 + 3x).
Answer:
[tex]\frac{6x^2+3}{2x^3+3x}[/tex]
Step-by-step explanation:
You need to apply the chain rule here.
There are few other requirements:
You will need to know how to differentiate [tex]\ln(u)[/tex].
You will need to know how to differentiate polynomials as well.
So here are some rules we will be applying:
Assume [tex]u=u(x) \text{ and } v=v(x)[/tex]
[tex]\frac{d}{dx}\ln(u)=\frac{1}{u} \cdot \frac{du}{dx}[/tex]
[tex]\text{ power rule } \frac{d}{dx}x^n=nx^{n-1}[/tex]
[tex]\text{ constant multiply rule } \frac{d}{dx}c\cdot u=c \cdot \frac{du}{dx}[/tex]
[tex]\text{ sum/difference rule } \frac{d}{dx}(u \pm v)=\frac{du}{dx} \pm \frac{dv}{dx}[/tex]
Those appear to be really all we need.
Let's do it:
[tex]\frac{d}{dx}\ln(2x^3+3x)=\frac{1}{2x^3+3x} \cdot \frac{d}{dx}(2x^3+3x)[/tex]
[tex]\frac{d}{dx}(\ln(2x^3+3x)=\frac{1}{2x^3+3x} \cdot (\frac{d}{dx}(2x^3)+\frac{d}{dx}(3x))[/tex]
[tex]\frac{d}{dx}(\ln(2x^3+3x)=\frac{1}{2x^3+3x} \cdot (2 \cdot \frac{dx^3}{dx}+3 \cdot \frac{dx}{dx})[/tex]
[tex]\frac{d}{dx}(\ln(2x^3+3x)=\frac{1}{2x^3+3x} \cdot (2 \cdot 3x^2+3(1))[/tex]
[tex]\frac{d}{dx}(\ln(2x^3+3x)=\frac{1}{2x^3+3x} \cdot (6x^2+3)[/tex]
[tex]\frac{d}{dx}(\ln(2x^3+3x)=\frac{6x^2+3}{2x^3+3x}[/tex]
I tried to be very clear of how I used the rules I mentioned but all you have to do for derivative of natural log is derivative of inside over the inside.
Your answer is [tex]\frac{dy}{dx}=\frac{(2x^3+3x)'}{2x^3+3x}=\frac{6x^2+3}{2x^3+3x}[/tex].
A lottery has 60 numbers. To win the jackpot one needs to match all 7 numbers that are drawn by the machine. Is this a PERMUTATION or a COMBINATION problem? What is the “chance” (or, more mathematically speaking, what is the probability) to hit the jackpot?
Answer: Hence, our required probability is [tex]\dfrac{1}{386206920}[/tex]
Step-by-step explanation:
Since we have given that
Numbers in a lottery = 60
Numbers to win the jackpot = 7 numbers
We need to find the probability to hit the jackpot:
So, our required probability is given by
[tex]P=\dfrac{^7C_7}{^{60}C_7}\\\\P=\dfrac{1}{386206920}[/tex]
This is a combination problem as we need to select 7 numbers irrespective of any arrangements.
Hence, our required probability is [tex]\dfrac{1}{386206920}[/tex