The cars should be rented at a rate of $30 per day to produce the maximum income of $13200 per day.
To solve this problem, we can use the following steps:
Define the variables.
Let x be the number of cars rented per day and y be the rate per day.
Write down the equation for the revenue.
The revenue is equal to the number of cars rented multiplied by the rate per day. Therefore, the equation for the revenue is:
R = x * y
Write down the equation for the decrease in demand. For each $1 increase in rate, 10 fewer cars are rented. Therefore, the equation for the decrease in demand is:
D = -10 * (y - 30)
Set the revenue equal to the maximum value. The revenue is maximized when the derivative of the revenue function is zero. Therefore, we set the derivative of the revenue function equal to zero and solve for y.
R' = x = 0
x = 440
y = 30
Calculate the maximum revenue. The maximum revenue is equal to the number of cars rented multiplied by the rate per day. Therefore, the maximum revenue is:
R = 440 * 30 = $13200
Therefore, the cars should be rented at a rate of $30 per day to produce the maximum income of $13200 per day.
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What’s the value of Y?
Answer:
44
Step-by-step explanation:
if 88 is the right angle degree, that means the acute angle would be half of 88.
88÷2=44
Add a cell phone assembly plant, 80% of the cell phone keypad pass inspection. A random sample of 181 keypads is analyzed. Find the probability that less than 76 in the sample keypads pass inspection.
Answer:
0% probability that less than 76 in the sample keypads pass inspection.
Step-by-step explanation:
I am going to use the normal approximation to the binomial to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
In this problem, we have that:
[tex]n = 181, p = 0.8[/tex]
So
[tex]\mu = E(X) = np = 181*0.8 = 144.8[/tex]
[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{181*0.8*0.2} = 5.38[/tex]
Find the probability that less than 76 in the sample keypads pass inspection.
Using continuity correction, this is [tex]P(X < 76 - 0.5) = P(X < 75.5)[/tex], which is the pvalue of Z when X = 75.5.
So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{75.5 - 144.8}{5.38}[/tex]
[tex]Z = -12.88[/tex]
[tex]Z = -12.88[/tex] has a pvalue of 0
0% probability that less than 76 in the sample keypads pass inspection.
Two functions are shown in the table below.
~
Complete the table on your own paper, then select the value that is a solution to f(x) = g(x). (2 points)
Group of answer choices
A. x = 2
B. x = 3
C. x = 5
D. x = 6
Answer:
D
Step-by-step explanation:
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A relation is a special type of function.
A. True
B. False
(30) points
A group of statistics students conducted a survey about smoking habits on campus to determine the proportion of students who believe that smoking hookah (a water pipe) is less harmful than smoking cigarettes. Of the 50 students surveyed, 45 think that smoking hookah is less harmful than smoking cigarettes.
Which of the following is a reason that this group of students should not calculate a confidence interval for the proportion of all students who believe that smoking hookah is less harmful than smoking cigarettes? Check all that apply.
a) The sample needs to be random but we don’t know if it is.
b) The actual count of students who believe that smoking hookah is less harmful than smoking cigarettes is too small.
c) The actual count of students who do not believe that smoking hookah is less harmful than smoking cigarettes is too small.
d) n(p^) is not greater than 10.
e) n(1 - p^) is not greater than 10.
Answer:
The answer is A, C and D
Step-by-step explanation:
a
c
d
The correct answer is a) The sample needs to be random but we don’t know if it is.
Calculate success by multiplying the sample % by the sample size to make sure the sample size is adequate.
Why is it necessary to satisfy the random condition?The situation at random we receive impartial population data from random sampling. It might be dangerous to draw conclusions about a community from data that was not randomly chosen samples since such data typically contains some type of bias.
Calculate success by multiplying the sample % by the sample size to make sure the sample size is adequate, and calculate failure by multiplying one less than the sample percentage by the sample size. The condition is satisfied if both of these items are larger than ten.
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Hector took out a loan of $900 for 18 months at a rate of 5.5% annually. How much will he pay in interest on the loan?
Answer:
Hector will pay $74.25 interest on the loan.
Step-by-step explanation:
Hector took out a loan of $900 for 18 months at a rate of 5.5% annually.
Principal amount = $900
Rate of interest = 5.5%
Time = 18 months = 1.5 years
Formula for interest :
[tex]I=\frac{P\times R\times T}{100}[/tex]
[tex]=\frac{900\times 5.5\times 1.5}{100}[/tex]
= 74.25
Hector will pay $74.25 interest on the loan.
The ordered pairs in the table below represent a linear function.
What is the slope of the function?
One-fourth
One-half
2
4
Answer:
2Step-by-step explanation:
The ordered pairs are
x | y 2 | 3 5 | 9The slope is:
m = (y2 - y1)/(x2 - x1) m = (9 - 3)/(5 - 2)= 6/3 = 2Answer is 2
Answer:
4
Step-by-step explanation:
The graph is:
x y
1/4 2
1/2 4
Slope formula is (y2-y1/x2-x1)
4-2/0.5-0.25
2/0.25
4
Best of Luck!
What is the volume of the square pyramid with base edges 32 mm and slant height 34 mm?
9,920 mm3
10,010 mm3
7,680 mm3
10,240 mm3
Answer:
V = 10,240mm^3
Step-by-step explanation:
The volume of pyramid is given by the following formula:
[tex]V=\frac{1}{3}bh[/tex] (1)
b: base of the pyramid = (32mm)^2
h: height
Thus, it is necessary to find the value of h, by using the Pitagoras's theorem, one half of the base and the slant height (which forms a rectangle triangle with h):
[tex]h=\sqrt{(34)^2-(16)^2}=30mm[/tex]
by replacing in (1) you obtain:
[tex]V=\frac{1}{3}(32mm)^2(30mm)=10,240\ mm^3[/tex]
hence, the volume is 10240mm^3
What are the quotient and remainder of (3x^4+ 2x^2 - 6x + 1) = (x + 1)
Answer: Im 75% sure the answer is A. Its either A or B.
Step-by-step explanation:
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I am going to assume 10.42 is 10 minutes 42 secons.
10 min * 60 seconds / per minute, = 600 seconds
600 + 42 = 642 seconds starting
-
8 min * 60 seconds / per minute, = 480 seconds objective
To solve for how long this will take set up an equation,
642 - 1.6t = 480
162 = 1.6t
t = 101.25 days
Since time has a decial, it needs to be rounded up in order for her to be fully below 8 minutes.
Therefore the answer is 102 days.
What is the surface area of this cylinder? Use 3.14 and round your answer to the nearest hundredth.
Two components in a rocket operate independently, and the probability that for every component to fail on a launch is p. Let X denote the number of launches required to have a failure of the first component, and let Y denote the number of launches required to have a failure of the second component, X, Y
Answer: p = X/(1-X)X + Y/(1-Y)Y
Step-by-step explanation:
Which best explains why the expression plus or minus StartRoot b squared minus 4 a c EndRoot cannot be rewritten as b plus or minus StartRoot negative 4 a c EndRoot during the next step?
Answer:
Step-by-step explanation:
let the quadratic eq. be ax²+bx+c=0
or x²+b/a x+c/a=0
or x²+b/ax=-c/a
to complete the square add both sides (b/2a)²or b²/4a²
x²+b/a x+(b/2a)²=b²/4a² -c/a
(x+b/2a)²=(b²-4ac)/(4a²)
taking square root
[tex]x+\frac{b}{2a} =\pm \frac{\sqrt{b^2-4ac} }{2a} \\or\\x=-\frac{b}{2a} \pm\frac{\sqrt{b^2-4ac} }{2a} \\or\\x=\frac{-b \pm\sqrt{b^2-4ac} }{2a}[/tex]
now you must know why -b and not +b
Final answer:
The expression ± √(b² - 4ac) in the quadratic formula refers to the discriminant and cannot be rewritten as b ± √(-4ac) because it would incorrectly separate b from the discriminant and alter the expression's meaning, leading to incorrect solutions.
Explanation:
The student is asking about the quadratic formula, which is used to find the solutions to a quadratic equation of the form at² + bt + c = 0. The formula for the solutions is given by:
-b ± √(b² - 4ac) / 2a
The term ± √(b² - 4ac) cannot be rewritten as b ± √(-4ac) because it alters the original expression's meaning. The square root is taken of the entire expression b² - 4ac, which represents the discriminant of the quadratic equation. It provides information on the nature and number of roots of the equation. Separating b from the discriminant before taking the square root would calculate a different value and therefore lead to incorrect solutions.
Example:
When you substitute the given values, say a = 1, b = 0.0211, and c = -0.0211, into the quadratic formula, you will get:
-0.0211 ± √((0.0211)² - 4(1)(-0.0211)) / (2(1))
Changing the formula to b ± √(-4ac) incorrectly suggests that you can separate b from the discriminant and take the square root of -4ac alone, which would not yield a correct solution.
What is the interquartile range of the data ? 0,2,4,0,2,3,8,6
(arrange the data set from least to greatest)
0, 0, 2, 2, 3, 4, 6, 8
(find the median: *the middle number*)
Median: 2.5
Lower quartile: 1
Upper quartile: 5
Interquartile range : upper quartile - lower quartile = answer
Interquartile range: 5 - 1 = 4
So the IQR or interquartile for the following data set is 4.
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I WILL MARK AS BRANLIEST!!
16 POINTS!!
Answer:
y = 1.8x + 32
or
y = 9/ 5x + 32
Step-by-step explanation:
Used a slope calculator
Birdseed costs $0.52 a pound and sunflower seeds cost $0.82 a pound. Angela Leinenbachs' pet store wishes to make a 40-pound mixture of birdseed and sunflower seeds that sells for $0.72 per a pound. How many pounds of each type of seed should she use?
Answer: she should use 13 pounds of birdseed and 27 pounds of sunflower seeds.
Step-by-step explanation:
Let x represent the number of pounds of birdseed that she should use.
Let y represent the number of pounds of sunflower seeds that she should use.
Angela Leinenbachs' pet store wishes to make a 40-pound mixture of birdseed and sunflower seeds. It means that
x + y = 40
Birdseed costs $0.52 a pound and sunflower seeds cost $0.82 a pound. If the mixture would sell for $0.72 per a pound, then the total cost of the mixture would be 0.72 × 40 = $28.8
The equation would be
0.52x + 0.82y = 28.8- - - - - - - - - -1
Substituting x = 40 - y into equation 1, it becomes
0.52(40 - y) + 0.82y = 28.8
20.8 - 0.52y + 0.82y = 28.8
- 0.52y + 0.82y = 28.8 - 20.8
0.3y = 8
y = 8/0.3 = 27
x + y = 40
x + 27 = 40
x = 40 - 27
x = 13
Find the arc length of the shaded region. Multiply through by #(3.14) Round solution to
tenth place. Ex. 1.2
90°
Given:
The radius of the circle is 12 units.
The central angle of the shaded region is 90°
We need to determine the arc length of the shaded region.
Arc length:
The arc length of the shaded region can be determined using the formula,
[tex]Arc \ length=(\frac{\theta}{360} ) 2 \pi r[/tex]
substituting [tex]\theta=90[/tex] and r = 12, we get;
[tex]Arc \ length=(\frac{90}{360} ) 2 (3.14)(12)[/tex]
Multiplying the terms, we have;
[tex]Arc \ length=\frac{6782.4}{360}[/tex]
Dividing, we get;
[tex]Arc \ length=18.84[/tex]
Rounding off to the nearest tenth, we get;
[tex]Arc \ length =18.8[/tex]
Thus, the arc length of the shaded region is 18.8 units.
A grain silo is shaped like a cylinder with a cone-shaped top. The cylinder is 30 feet tall. The volume of the silo is 1152 cubic feet. Find the radius of the silo.
Answer:
The radius of the silo is 3.49 m.
Step-by-step explanation:
We have,
Height of the cylinder, h = 30 ft
Volume of cylindrical shaped grain silo, [tex]V=1152\ ft^3[/tex]
It is required to find the radius of silo. The formula of volume of cylinder is given by :
[tex]V=\pi r^2h[/tex]
r is radius
[tex]r=\sqrt{\dfrac{V}{\pi h}} \\\\r=\sqrt{\dfrac{1152}{\dfrac{22}{7}\times 30 }} \\\\r=3.49\ m[/tex]
So, the radius of the silo is 3.49 m.
A right triangle whose hypotenuse is StartRoot 18 EndRoot18 m long is revolved about one of its legs to generate a right circular cone. Find the radius, height, and volume of the cone of greatest volume that can be made this way.
Answer:
V = [tex]\frac{1}{3}[/tex]π(8 - [tex]\frac{8}{3}[/tex])[tex]\sqrt{\frac{8}{3} }[/tex] = 9.11 [tex]m^{3}[/tex]
r = 4[tex]\frac{\sqrt{3} }{3}[/tex]
h = [tex]\sqrt{\frac{8}{3} }[/tex]
Step-by-step explanation:
Given that the right triangle whose hypotenuse is [tex]\sqrt{8}[/tex]
Let r is the radius of the cone Let h is the height of the coneWe know that:
[tex]r^{2} + h^{2} = 8[/tex]
<=> [tex]r^{2} = 8 - h^{2}[/tex]
The volume of the cone is:
V = π[tex]r^{2} \frac{1}{3} h[/tex]
<=> V = π[tex]\frac{1}{3}(8 - h^{2} )h[/tex]
Differentiate w.r.t h
[tex]\frac{dV}{dh}[/tex] = π [tex]\frac{1}{3}[/tex] (8 - [tex]3h^{2}[/tex])
For maximum/minimum: [tex]\frac{dV}{dh}[/tex] = 0
<=> π [tex]\frac{1}{3}[/tex] (8 - [tex]3h^{2}[/tex]) = 0
<=> [tex]h^{2}[/tex] = [tex]\frac{8}{3}[/tex]
<=> h = [tex]\sqrt{\frac{8}{3} }[/tex]
=> [tex]r^{2}[/tex] = [tex]\frac{16}{3}[/tex]
<=> r = 4[tex]\frac{\sqrt{3} }{3}[/tex]
So the volume of the cone is:
V = [tex]\frac{1}{3}[/tex]π(8 - [tex]\frac{8}{3}[/tex])[tex]\sqrt{\frac{8}{3} }[/tex] = 9.11 [tex]m^{3}[/tex]
What is the surface area of this square pyramid
Answer 144 ft2
Step-by-step explanation:
Answer:
The surface area is 81 feet squared
Step-by-step explanation:
IM SO SORRY! the answer is 33 feet squared
How many one-third cubes are needed to fill the gap in the prism shown below?
A. 4
B. 8
C. 16
D. 24
The one-third cubes which are needed to fill the gap in the prism shown below are [tex]976[/tex].
What is cube ?Cube is a [tex]3D[/tex] solid object bounded by six square faces, facets or sides, with three meeting at each vertex.
Here we have,
Length [tex]=4\frac{2}{3}[/tex]
Breadth [tex]=4[/tex]
Height [tex]=2[/tex]
Here, we have the side of cube [tex]=\frac{1}{3}[/tex],
So, Total volume of the prism [tex]=l*b*h[/tex]
[tex]=2*4*4\frac{2}{3}[/tex]
[tex]=\frac{112}{3}[/tex]
Volume of a cube [tex]= a^{3}[/tex]
[tex]=(\frac{1}{3} )^{3}=\frac{1}{27}[/tex]
Total number of cubes [tex]= \frac{\frac{112}{3}}{\frac{1}{27} } =1008[/tex]
Volume of given cubes in prism [tex]= 32*\frac{1}{27} =\frac{32}{27}[/tex]
So, the gap left in the prism [tex]=\frac{112}{3} -\frac{32}{27} =\frac{976}{27}[/tex]
So, the number of cubes required [tex]=\frac{\frac{976}{27} }{\frac{1}{27} }=976[/tex]
Hence, we can say that the one-third cubes which are needed to fill the gap in the prism shown below are [tex]976[/tex].
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Answer:
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The probability that Linda receives spam e-mail is 4 percent. If she receives 520 e-mails in a week, about how many of them can she expect to be spam?
Answer:21 (2 sf)
Step-by-step explanation:
10%0f 520=52
1%0f 520=52 divide by 10 =5.2
5.2x4=20.8
=21 to 2sf
Use the two-point form of the linear equation. Fill in the missing blanks using (1, 1) for (x1, y1). You will need both points to determine the slope, y2 − y1 x2 − x1 . y − 1 = − 2 3 − 1 6 − 1 x −
Answer: (-2, 3)
Step-by-step explanation:
Answer:
The point-slope form of a linear equation is a formula that allows a person to calculate the slope and point of intercept of a line, and then once you calculate the linear equation, you can calculate the x and y coordinate of any point on the line!
1. Choose two points on a line.
2. Indicate the y1 (the y coordinate of the first point) and y2 (the y coordinate of the second point).
3. Indicate the x1 (the x coordinate of the first point) and the x2 (the x coordinate of the second point)
4. Plug the previously identified variables into the slope formula where the slope is equal to (y2-y1)/(x2-x1)
5. Subtract y2 and y1.
6. Subtract x2 and x1.
7. Divide the quantity in #5 by the quantity in #6. This is your slope.
8. Observe the equation: y=mx+b where "m" is the slope calculated in #7.
9. Plug in the slope for "m"
10. Using one of the points identified earlier, plug in y1 into "y" and x1 into "x". Rearrange and solve for b.
11. Then plug in the value "b" into y=mx+b. Make sure to leave the unknown variables "x" and "y", but make sure to still plug in the "m" calculated earlier!
2.
1. A small town's population is growing at
an exponential rate. In 2010, there were
700 residents in the town. In 2011 there
were 770 residents and in 2012, there
were 847 residents. What equation can
be used to determine p, the number of
residents in 2018?
Answer:
[tex]P(8)=700\cdot(1.1)^8\approx 1500[/tex], where t is the number of years since 2010.
Step-by-step explanation:
See my attached image for an explanation!
The wait times in line at a grocery store are roughly distributed normally with an average wait time of 7.6 minutes and a standard deviation of 1 minute 45 seconds. What is the probability that the wait time is less than 7.9 minutes
Answer:
[tex]0.56749[/tex].
Step-by-step explanation:
We have been given that the wait times in line at a grocery store are roughly distributed normally with an average wait time of 7.6 minutes and a standard deviation of 1 minute 45 seconds. We are asked to find the probability that the wait time is less than 7.9 minutes.
First of all, we will convert 45 seconds into minutes by dividing by 60 as:
[tex]45\text{ Seconds}=\frac{45}{60}\text{ minutes}=0.75\text{ minutes}[/tex]
So 1 minute 45 seconds will be equal to 1.75 minutes.
Now, we will find z-score corresponding to 7.9 minutes using z-score formula.
[tex]z=\frac{x-\mu}{\sigma}[/tex]
z = z-score,
x = Random sample score,
[tex]\mu[/tex] = Mean,
[tex]\sigma[/tex] = Standard deviation.
[tex]z=\frac{7.9-7.6}{1.75}[/tex]
[tex]z=\frac{0.3}{1.75}[/tex]
[tex]z=0.17142\approx 0.17[/tex]
Now we will use normal distribution to find area under normal curve that corresponds to a z-score of 0.17 that is [tex]P(z<0.17)[/tex].
[tex]P(z<0.17)=0.56749[/tex]
Therefore, the probability that wait time is less than 7.9 minutes would be 0.56749.
A woman puts $1 million dollars into a savings account that she is not going to touch. She isn’t going to work either but she will live off the interest. If the rate of interest on the account is 6 1/2% what is the amount she will make in interest? If her totally expenses last year is $47,000 will she be able to live off the interest? Justify your answer
Answer:
i. The amount made in interest is $65,000.
ii. Yes, because her expenses is lesser that her interest.
Step-by-step explanation:
i. The woman puts $1,000,000 in a savings account with an interest rate of 6[tex]\frac{1}{2}[/tex]%.
Interest rate = 6[tex]\frac{1}{2}[/tex]% = [tex]\frac{13}{200}[/tex]
The amount she would make in interest = [tex]\frac{13}{200}[/tex] × 1,000,000
= 65,000
The amount made in interest is $65,000.
ii. The total of her expenses last year is $47,0000 which is lesser than the amount made in inerest.
After her total expenses, should would have a remainder of;
= $65,000 - $47,0000
= $18,000
Therefore, she would be able to live off the interest.
Suppose Frances is a researcher at Beaded Gemsz, a company that makes beaded jewelry. She wants to evaluate whether using better equipment during the current year has increased jewelry-making productivity. The company's reporting team estimated an average daily production yield of 105 units per store from previous years. Frances conducts a one-sample z - test with a significance level of 0.08 , acquiring daily unit yield data from each of the stores' databases for 45 randomly selected days of the year. She obtains a P -value of 0.06 . The power of the test to detect a production increase of 12 units or more is 0.85 . What is the probability that Frances concludes that the new equipment increases the average daily jewelry production when in fact the new equipment has no effect
Answer:
There is 8% (P=0.08) that Frances concludes that the new equipment increases the average daily jewelry production when in fact the new equipment has no effect.
Step-by-step explanation:
We have one-sample z-test with a significance level of 0.08 and a power ot the test of 0.85.
In this test, the null hypothesis will state that the new equipment has the same productivity of the older equipment. The alternative hypothesis is that there is a significative improvement from the use of new equipment.
The probability that Frances concludes that the new equipment increases the average daily jewelry production when in fact the new equipment has no effect is equal to the probability of making a Type I error (rejecting a true null hypothesis).
The probability of making a Type I error is defined by the level of significance, and in this test this value is α=0.08.
Then, there is 8% that Frances concludes that the new equipment increases the average daily jewelry production when in fact the new equipment has no effect.
Hayden is 59 inches tall and is standing on top of a ladder that is 2 yards y’all in inches what is the distance from the top of Hayden’s head to the ground
Answer:
131 inches
Step-by-step explanation:
1 yard = 36 inches
36 x 2 = 72
72 + 59 = 131
c:
Of the 100 students enrolled at the dance studio, 50 take ballet and 24 take tap dancing. Eight of the students who take ballet also take tap dancing. If a student at the studio is chosen at random, find the probability that they take ballet, if it is known that they do not take tap dancing
Answer:
42 over 100
Step-by-step explanation:
Answer:21/38
Step-by-step explanation: