a) What is the maximum number of washers the person can purchase within the budget?
To calculate the maximum number of washers the person can purchase within the budget, we divide the budget by the cost per washer:
$12,000 ÷ $250 = 48 washers
b) What is the maximum number of dryers the person can purchase within the budget?
To calculate the maximum number of dryers the person can purchase within the budget, we divide the budget by the cost per dryer:
$12,000 ÷ $200 = 60 dryers
c) If the person wants to purchase an equal number of washers and dryers, how many of each can he purchase?
To purchase an equal number of washers and dryers, we need to find the common factor of both 48 and 60:
48 = 2 x 2 x 2 x 2 x 3
60 = 2 x 2 x 3 x 5
The common factor is 2 x 2 x 3 = 12. So, the person can purchase 12 washers and 12 dryers within the budget.
d) If the person purchases the maximum number of washers and dryers, what is the total cost of the purchase?
To calculate the total cost of the purchase, we multiply the maximum number of washers and dryers by their respective cost:
48 washers x $250 = $12,000
60 dryers x $200 = $12,000
The total cost of the purchase is $24,000.
e) If the person purchases an equal number of washers and dryers, what is the total cost of the purchase?
To calculate the total cost of the purchase, we multiply the number of washers and dryers by their respective cost:
12 washers x $250 = $3,000
12 dryers x $200 = $2,400
The total cost of the purchase is $5,400.
f) If the person wants to spend the entire budget on washers, how many washers can he purchase?
To spend the entire budget on washers, we divide the budget by the cost per washer:
$12,000 ÷ $250 = 48 washers
g) If the person wants to spend the entire budget on dryers, how many dryers can he purchase?
To spend the entire budget on dryers, we divide the budget by the cost per dryer:
$12,000 ÷ $200 = 60 dryers
h) If the person wants to spend the entire budget and purchase an equal number of washers and dryers, how many can he purchase?
To spend the entire budget and purchase an equal number of washers and dryers, we need to divide the budget by the sum of the cost per washer and cost per dryer, then find the common factor:
($12,000 ÷ ($250 + $200)) ÷ 2 = 18
The common factor of 18 is 2 x 3 = 6. So, the person can purchase 6 washers and 6 dryers within the budget.
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you would like to construct a confidence interval to estimate the population mean score on a nationwide examination in finance, and for this purpose we choose a random sample of exam scores. the sample we choose has a mean of and a standard deviation of . question 6 of 10 90% 495 77 (a) what is the best point estimate, based on the sample, to use for the population mean?
The best point estimate for the population mean score on the nationwide examination in psychology is the sample mean of 492.
When we take a sample from a population, the sample mean is a point estimate of the population mean. A point estimate is an estimate of a population parameter based on a single value or point in the sample. In this case, the sample mean of 492 is the best point estimate for the population mean, because it is an unbiased estimator.
An estimator is unbiased if it is expected to be equal to the true population parameter. In this case, the expected value of the sample mean is equal to the population mean. This means that if we were to take many different samples from the population and calculate the sample mean for each sample, the average of all these sample means would be equal to the population mean.
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The given question is incomplete, the complete question is:
You would like to construct a 95% confidence interval to estimate the population mean score on a nationwide examination in psychology, and for this purpose we choose a random sample of exam scores. The sample we choose has a mean of 492 and a standard deviation of 78. What is the best point estimate, based on the sample, to use for the population mean?
Water flows from the bottom of a storage tank at a rate of r(t) 200 - 4lters per minute, where OSI 50. Find the amount of water in stors that town from the tank during the first minutes Amount of water = ______ L.
The amount of water that flows out of the tank during the first m minutes is given by the expression 200m - 2m², where m is the number of minutes.
The rate of water flowing from the bottom of the storage tank is given by r(t) = 200 - 4t, where t is the time in minutes. To find the amount of water that flows out of the tank during the first m minutes, we need to integrate the rate function from t = 0 to t = m:
Amount of water = ∫₀ₘ (200 - 4t) dt
Evaluating this integral, we get:
Amount of water = [200t - 2t²] from t = 0 to t = m
Amount of water = (200m - 2m²) - (0 - 0)
Simplifying this expression, we get:
Amount of water = 200m - 2m²
Therefore, the amount of water that flows out of the tank during the first m minutes is given by the expression 200m - 2m², where m is the number of minutes.
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in a certain town, in 90 minutes 1/2 inch of rain falls. It continues at the same rate for a total of 24 hours. Which of the following statements are true about the amount of rain in the 24- hour period? show your work
The statement that is true is that the amount of rain in the 24- hour period is 8 inches
Which statement is true about the amount of rain in the 24- hour period?From the question, we have the following parameters that can be used in our computation:
In 90 minutes 1/2 inch of rain falls
This means that
Rate = (1/2 inch)/90 minutes
So, we have
Rate = (1/2 inch)/(1.5 hour)
The amount of rain in the 24- hour period is
Amount = Rate * Time
So, we have
Amount = (1/2 inch)/(1.5 hour) * 24 hours
Evaluate
Amount = 8 inches
Hence, the amount of rain in the 24- hour period is 8 inches
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Find a set of parametric equations of the line with the given characteristics. (Enter your answers as a comma-separated list.)
The line passes through the point (-4, 8, 7) and is perpendicular to the plane given by -x + 4y + z = 8.
One possible set of parametric equations for the line is:
x = -4 + 4t
y = 8 - t
z = 7 - 4t
To see why these work, let's first consider the equation of the plane: -x + 4y + z = 8. This can also be written in vector form as:
[ -1, 4, 1 ] · [ x, y, z ] = 8
where · denotes the dot product. This equation says that the normal vector to the plane is [ -1, 4, 1 ], and that any point on the plane satisfies the equation.
Now, since the line we want is perpendicular to the plane, its direction vector must be parallel to the normal vector to the plane. In other words, the direction vector of the line must be some multiple of [ -1, 4, 1 ]. Let's call this direction vector d.
To find d, we can use the fact that the dot product of two perpendicular vectors is zero. So we have:
d · [ -1, 4, 1 ] = 0
Expanding this out, we get:
-1d1 + 4d2 + 1d3 = 0
where d1, d2, d3 are the components of d. This equation tells us that d must be of the form:
d = [ 4k, k, -k ]
where k is any non-zero scalar (i.e. any non-zero real number).
Now we just need to find a point on the line. We're given that the line passes through (-4, 8, 7), so this will be our starting point. Let's call this point P.
We can now write the parametric equations of the line in vector form as:
P + td
where t is any scalar (i.e. any real number). Substituting in the expressions for P and d that we found above, we get:
[ -4, 8, 7 ] + t[ 4k, k, -k ]
Expanding this out, we get the set of parametric equations I gave at the beginning:
x = -4 + 4tk
y = 8 + tk
z = 7 - tk
where k is any non-zero scalar.
To find a set of parametric equations for the line, we first need to determine the direction vector of the line. Since the line is perpendicular to the plane given by -x + 4y + z = 8, we can use the plane's normal vector as the direction vector for the line. The normal vector for the plane can be determined by the coefficients of x, y, and z, which are (-1, 4, 1).
Now that we have the direction vector (-1, 4, 1) and the point the line passes through (-4, 8, 7), we can write the parametric equations as follows:
x(t) = -4 - t
y(t) = 8 + 4t
z(t) = 7 + t
So, the set of parametric equations for the line is {x(t) = -4 - t, y(t) = 8 + 4t, z(t) = 7 + t}.
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Solve the problem.
Find the area bounded by y = 3 / (√36-9x^2) • X = 0, y = 0, and x = 3. Give your answer in exact form.
To solve the problem, we first need to graph the equation y = 3 / (√36-9x^2) and find the points where it intersects the x-axis and y-axis.
To find the x-intercept, we set y = 0 and solve for x:
0 = 3 / (√36-9x^2)
0 = 3
This has no solution, which means that the graph does not intersect the x-axis.
To find the y-intercept, we set x = 0 and solve for y:
y = 3 / (√36-9(0)^2)
y = 3 / 6
y = 1/2
So the graph intersects the y-axis at (0, 1/2).
Next, we need to find the point where the graph intersects the vertical line x = 3. To do this, we substitute x = 3 into the equation y = 3 / (√36-9x^2):
y = 3 / (√36-9(3)^2)
y = 3 / (√-243)
This is undefined, which means that the graph does not intersect the line x = 3.
Now we can draw a rough sketch of the graph and the region bounded by the x-axis, the line x = 0, and the curve y = 3 / (√36-9x^2):
|
_______|
/ |
/ |
/ |
/_________|
| |
The area we want to find is the shaded region, which is bounded by the x-axis, the line x = 0, and the curve y = 3 / (√36-9x^2). To find the area, we need to integrate the equation y = 3 / (√36-9x^2) with respect to x from x = 0 to x = 3:
A = ∫(0 to 3) 3 / (√36-9x^2) dx
We can simplify this integral by using the substitution u = 3x, du/dx = 3, dx = du/3:
A = ∫(0 to 9) 1 / (u^2 - 36) du/3
Next, we use partial fractions to break up the integrand into simpler terms:
1 / (u^2 - 36) = 1 / (6(u - 3)) - 1 / (6(u + 3))
So we have:
A = ∫(0 to 9) (1 / (6(u - 3))) - (1 / (6(u + 3))) du/3
A = (1/6) [ln|u - 3| - ln|u + 3|] from 0 to 9
A = (1/6) [ln(6) - ln(12) - ln(6) + ln(6)]
A = (1/6) [ln(1/2)]
A = (-1/6) ln(2)
Therefore, the exact area bounded by y = 3 / (√36-9x^2), x = 0, y = 0, and x = 3 is (-1/6) ln(2).
To find the area bounded by y = 3 / (√36-9x^2), x = 0, y = 0, and x = 3, we can set up an integral to compute the definite integral of the function over the given interval [0, 3]. The integral will represent the area under the curve:
Area = ∫[0, 3] (3 / (√(36-9x^2))) dx
To solve the integral, perform a substitution:
Let u = 36 - 9x^2
Then, du = -18x dx
Now, we can rewrite the integral:
Area = ∫[-√36, 0] (-1/6) (3/u) du
Solve the integral:
Area = -1/2 [ln|u|] evaluated from -√36 to 0
Area = -1/2 [ln|0| - ln|-√36|]
Area = -1/2 [ln|-√36|]
Since the natural logarithm of a negative number is undefined, there's an error in the original problem. Check the problem's constraints and the given function to ensure accuracy before proceeding.
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Find the equation for the line that:
passes through (-4,-7) and has slope -6/7
The slope intercept form of the function is:
Answer: [tex]y=\frac{-6}{7} x+\frac{-73}{7}[/tex]
Step-by-step explanation:
The slope intercept form for a line is y=mx+b, where m is slope and b is the y intercept. For this form, we need to know the slope and y intercept.
The slope and one x and y are give, so we can plug in all of these values into the slope intercept equation to solve for b.
Doing so, we get:
[tex]y=mx+b\\-7=\frac{-6}{7} (-4)+b\\b=-7-\frac{24}{7} \\b=\frac{-73}{7}[/tex]
So, knowing the slope and y intercept, our equation is
[tex]y=\frac{-6}{7} x+\frac{-73}{7}[/tex]
Given the following practical problem, what is the slope of the linear function?
Homer walked to school every day. He walked at a pace of 4 miles per hour
The slope of the linear function representing Homer's walking pace is 4 miles per hour.
How can the slope of Homer's linear function be determined?In the given practical problem, we are told that Homer walked to school at a pace of 4 miles per hour. The slope of the linear function can be determined by considering the relationship between the distance he walked and the time it took.
In this case, the slope represents the rate of change of distance with respect to time, which is equal to the speed at which Homer is walking. Since Homer's pace is given as 4 miles per hour, the slope of the linear function representing his distance as a function of time would be 4.
Therefore, the slope of the linear function in this practical problem is 4, indicating that for every hour that passes, Homer walks 4 miles.
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Let f(x) = -1/2x + 8, g(x)=f(x-3 )and h(x) = g(-4x). What are the slope and y intercept of the graph of function h?
The slope and y intercept of the graph of function h is2 and 9.5, respectively.
To find the slope and y-intercept of the function h(x), we'll first find g(x) and then h(x) by substituting f(x) and the given transformations.
1. g(x) = f(x - 3): Substitute (x - 3) for x in f(x)
g(x) = -1/2(x - 3) + 8
2. h(x) = g(-4x): Substitute (-4x) for x in g(x)
h(x) = -1/2(-4x - 3) + 8
Now we have the function h(x), and we can identify the slope and y-intercept:
h(x) = -1/2(-4x - 3) + 8
h(x) = 2x - 1/2(-3) + 8
The slope is the coefficient of x, which is 2, and the y-intercept is the constant term, which is 1.5 + 8 = 9.5. So, the slope is 2, and the y-intercept is 6.5.
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The diameter of a wheel is 3 feet witch of the following is closest to the area of the whee
The area of the wheel is approximately 7.07 square feet.
The area of a circle is calculated using the formula A = πr^2, where A is the area and r is the radius of the circle. In this case, the diameter of the wheel is given as 3 feet, so the radius is half of that, which is 1.5 feet.
Substituting the value of the radius into the formula, we get A = π(1.5)^2. Simplifying this expression gives us approximately 7.07 square feet. Therefore, the closest answer to the area of the wheel is 7.07 square feet.
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Help with problem in photo!
Check the picture below.
[tex]4+10x=\cfrac{(9x+20)+10x}{2}\implies 8+20x=19x+20\implies x=12 \\\\[-0.35em] ~\dotfill\\\\ 4+10x\implies 4+10(12)\implies \stackrel{ \measuredangle DEC }{124^o}[/tex]
1) If you deposited $10,000 into a bank savings account on your 18th birthday. Said account yielded 3% compounded annually, how much money would be in your account on your 58th birthday?
2)What would your answer be if the interest was compounded monthly versus
annually?
1- On the 58th birthday, the account would have $24,209.98, 2- If the interest is compounded monthly, then on the 58th birthday, the account would have $26,322.47.
1- The formula for calculating the compound interest is given by A = P(1 + r/n)(nt), where A is the final amount, P is the principal amount, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the time in years. Here, P = $10,000, r = 0.03, n = 1, t = 40 years (58 - 18).
substituting the values in the formula, we get A = $10,000(1 + 0.03/1)1*40) = $24,209.98.
2) In this case, n = 12 (monthly compounding), and t = 12*40 (total number of months in 40 years). So, the formula for calculating the compound interest becomes A = P(1 + r/n)(nt) = $10,000(1 + 0.03/12)(12*40) = $26,322.47.
Since the interest is compounded more frequently, the amount at the end of 40 years is higher than when the interest is compounded annually.
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Brody is going to invest $350 and leave it in an account for 18 years. Assuming the interest is compounded daily, what interest rate, to the
neatest tenth of a percent, would be required in order for Brody to end up with $790?
Brody would need an interest rate of 4.5% compounded daily.
How to calculate interest rate of investment?
We can use the compound interest formula to solve the problem:
[tex]A = P(1 + r/n)^(^n^t^)[/tex]
where:
A = final amount of money ($790)
P = initial investment ($350)
r = interest rate (unknown)
n = number of times interest is compounded per year (365, since interest is compounded daily)
t = time in years (18)
So, we can plug in the given values and solve for r:
[tex]790 = $350(1 + r/365)^(^3^6^5^1^8^)[/tex]
[tex]2.25714 = (1 + r/365)^(^3^6^5^1^8^)[/tex]
[tex]ln(2.25714) = ln[(1 + r/365)^(^3^6^5^1^8^)][/tex]
[tex]ln(2.25714) = 18ln(1 + r/365)[/tex]
[tex]ln(2.25714)/18 = ln(1 + r/365)[/tex]
[tex]e^(^l^n^(^2^.^2^5^7^1^4^)^/^1^8^)^ =^ 1^ +^ r^/^3^6^5[/tex]
[tex]1.0345 = 1 + r/365[/tex]
[tex]r/365 = 0.0345[/tex]
[tex]r = 12.5925[/tex]
Therefore, Brody would need an interest rate of approximately 12.6% (rounded to the nearest tenth of a percent) in order to end up with $790 after 18 years with daily compounding.
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Jamie mixes 2 parts of red paint with 3 parts of blue paint to make purple paint.
He uses 12 cans of blue paint.
How many cans of red paint does he use?
Find for the equation V+y=x+y
The solution set is a vertical plane parallel to the y-axis and passing through the origin.
V + y = x + y can be simplified by canceling out the common term 'y' on both sides of the equation. This gives:
V = x
This is the equation of a plane in three-dimensional space where the 'x' and 'V' variables correspond to the horizontal and vertical axes respectively. Therefore, the solution set for this equation consists of all points in the plane where the 'V' coordinate is equal to the 'x' coordinate.
In other words, the solution set is a vertical plane parallel to the y-axis and passing through the origin.
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--The complete question is, What is the solution set for the equation V + y = x + y?--
Two wives and their husbands have tickets for a play. they have the first four seats on the left side of the center aisle. they will be arriving seperately from their jobs. so they agreee to take their seats from the inside to the aisle in whatever order they arrive. there is a propability of 2/3 that they will all have arrived by curtain time.
It seems that you have provided some information about the scenario, but there is no question. How may I assist you?
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Determine whether the graph shows a positive correlation, a negative correlation, or no correlation. If there is a positive or negative correlation, describe its meaning in the situation. Domestic Traveler Spending in the U.S., 1987-1999 Spending (dollars in billions) A graph titled Domestic Traveler Spending in the U S from 1987 to 1999 has year on the x-axis, and spending (dollars in billions) on the y-axis, from 225 to 450 in increments of 25. Year Source: The World Almanac, 2003 a. positive correlation; as time passes, spending increases. b. no correlation c. positive correlation; as time passes, spending decreases. d. negative correlation; as time passes, spending decreases.
There is a positive correlation and as such as time passes, spending increases.
Checking the correlation of the graphThe descriptions of the graph from the question are given as
Year (x - axis): 1987 to 1999Spending (y - axis, dollars in billions) 225 to 450 in increments of 25.From the above statements, we can make the following summary
As the year increase, the spending also increase
The above summary is about the correlation of the graph
And it means that there is a positive correlation and as such as time passes, spending increases.
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Your yacht sails in the direction S 71° W for 141 miles. It then turns
and sails in the direction N 63º E 213 miles. Find its distance from
the starting point. Round answer to nearest hundredth.
We can use the Law of Cosines to solve this problem. Let's call the starting point A, the point where the yacht turns B, and the final destination C.
Then we can use the given distances to find the length of each side of the triangle ABC, and the angles to find the angle opposite each side.
Using the angle opposite side AB as a reference angle, we can find the other angles as follows:
Angle BAC = 180° - (71° + 63°) = 46°
Angle ABC = 180° - (46° + 90°) = 44°
Now we can use the Law of Cosines:
[tex]AC^2 = AB^2 + BC^2 - 2ABBCcos(44°)[/tex]
[tex]AC^2 = (141)^2 + (213)^2 - 2(141)(213)*cos(44°)[/tex]
AC ≈ AC^2 = AB^2 + BC^2 - 2ABBCcos(44°)(rounded to the nearest hundredth)
Therefore, the distance from the starting point is approximately 281.21 miles.
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Given XV is 20 inches, find the length of arc XW. Leave your answer in terms of pi
The arc length XW in terms of pi is (10pi)/3.
To find the length of arc XW, we need to know the measure of the angle XDW in radians.
Since XV is the diameter of the circle, we know that angle XDV is a right angle, and angle VDW is half of angle XDW. We also know that XV is 20 inches, so its radius, XD, is half of that, or 10 inches.
Using trigonometry, we can find the measure of angle VDW:
sin(VDW) = VD/VDW
sin(VDW) = 10/20
sin(VDW) = 1/2
Since sin(30°) = 1/2, we know that angle VDW is 30 degrees (or π/6 radians). Therefore, angle XDW is twice that, or 60 degrees (or π/3 radians).
Now we can use the formula for arc length:
arc length = radius * angle in radians
So the length of arc XW is:
arc XW = 10 * (π/3)
arc XW = (10π)/3
Therefore, the arc length XW in terms of pi is (10π)/3.
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Simplify this equation
Answer:
(d)
Step-by-step explanation:
What are the zeros of the function y = (x − 4)(x2 − 12x + 36)
The zeros of the function y = (x − 4)(x² − 12x + 36) are 4 and 6.
To find the zeros of the function y = (x - 4)(x² - 12x + 36), we need to set y to zero and solve for x.
0 = (x - 4)(x² - 12x + 36)
Now, solve for each factor separately:
1) x - 4 = 0
x = 4
2) x² - 12x + 36 = 0
This is a quadratic equation, and we can factor it as (x - 6)(x - 6).
So, x - 6 = 0
x = 6
The zeros of the function are x = 4 and x = 6. The zeros of a function are the values of its variables that meet the equation and result in the function's value being equal to 0.
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A toy company recently added some made-to-scale models of racecars to their product line. The length of a certain racecar is 19 ft. Its width is 7 ft. The width of the
die-cast replica is 1. 4 in. Find the length of the model.
Let x be the length of the model. Translate the problem to a proportion. Do not include units of measure.
Length - x = Length
Width -
Width
(Do not simplify. )
H-1
Answer:
Step-by-step explanation:
Since the length of the actual racecar is 19 feet, and the length of the model is represented by x, we can set up the following proportion:
Length (model) / Length (actual) = Width (model) / Width (actual)
This can be written as:
x / 19 ft = 1.4 in / 7 ft
To solve for x, we can cross-multiply and simplify:
x * 7 ft = 19 ft * 1.4 in
x = (19 ft * 1.4 in) / 7 ft
x = 3.8 in
Therefore, the length of the model is 3.8 inches.
To explain this solution in more detail, we can use proportionality concepts and unit conversions. The proportion relates the length and width of the actual racecar to the length and width of the model.
We set up the proportion with the length of the model as the unknown (x) and solve for it by cross-multiplying and simplifying. Since the width of the model and actual racecar are given in different units, we convert the width of the model from inches to feet before using the proportion.
The final answer is expressed in inches, which is the same unit as the width of the model.
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Find the y-component of this
vector:
42.2°
101 m
Remember, angles are measured from
the +x axis.
Y-component of the vector as shown in the diagram is 67.84 m in the direction of the negative y-axis.
What is a vector?Vector is a quantity that has both magnitude and direction.
Examples a vectors are
VelocityAccelerationDisplacementForceWeightMoment. Etc.To find the Y-component of the vector, we use the formula below.
Formula:
Y = dsinα................. Equation 1Where:
Y = Y-component of the vectord = Distance of the vector along the x-y planeα = Angle of the vector to the x-axisFrom the question,
Given:
d = 101 mα = (180+42.2) = 222.2°Substitute these values into equation 1
Y = 101sin222.2°Y = 67.84 mHence, the y component is 67.84 m.
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In ΔRST, \overline{RT} RT is extended through point T to point U, \text{m}\angle RST = (3x+17)^{\circ}m∠RST=(3x+17) ∘ , \text{m}\angle STU = (8x+1)^{\circ}m∠STU=(8x+1) ∘ , and \text{m}\angle TRS = (3x+18)^{\circ}m∠TRS=(3x+18) ∘ . What is the value of x?x?
In ΔRST, the overline{RT} RT is extended through point T to point U, Therefore the value of x = 10.
How do we calculate?The sum of angles in a triangle is 180 degrees, we have:
m∠RST + m∠STU + m∠TRS = 180
We substitute the given values, and have:
(3x + 17) + (8x + 1) + (3x + 18) = 180
We simplify and solve for x, we get:
14x + 36 = 180
14x = 144
x = 10.
A triangle in geometry is descried a three-sided polygon with three edges and three vertices.
The fact that a triangle's internal angles add up to 180 degrees is its most important characteristic.
This characteristic is known as the triangle's angle sum property.
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A 13-foot ladder is placed against a vertical wall of a building, with the bottom of the ladder standing on level ground 5 feet from the base of the building. How high up the wall does the ladder reach?
Sentence:
7) Jenny bought a pair of boots priced at $85. If the boots were on gole for 15% off
regular price, how much did Jenny pay for the boots?
Let x =
(Remember to subtract sale
Choose the description that correctly compares the locations of each pair of points on a coordinate plane.
a. (–2, 5) is
choose...
(–2, –1).
b. (1, 212) is
choose...
(4, 212).
c. (3, –6) is
choose...
(3, –3).
d. ( −212, 1) is
choose...
(–3, 1).
e. (312 , 12) is
choose...
( 12, 12).
f. (2, 5) is
choose...
(2, –5).
The point (–2, 5) is located above the point (–2, –1).
The point (1, 212) is located to the left of the point (4, 212).
The point (3, –6) is located below the point (3, –3).
The point (−212, 1) is located to the left of the point (–3, 1).
The point (312, 12) is located to the right of the point (12, 12).
The point (2, 5) is located above the point (2, –5).
Find out the comparisons of the location of each pair of points?a. (–2, 5) is above (–2, –1). The two points have the same x-coordinate, but different y-coordinates. Since the y-coordinate increases as you move up on the coordinate plane, the point (–2, 5) is located above the point (–2, –1).
b. (1, 212) is to the left of (4, 212). The two points have the same y-coordinate, but different x-coordinates. Since the x-coordinate increases as you move to the right on the coordinate plane, the point (1, 212) is located to the left of the point (4, 212).
c. (3, –6) is below (3, –3). The two points have the same x-coordinate, but different y-coordinates. Since the y-coordinate decreases as you move down on the coordinate plane, the point (3, –6) is located below the point (3, –3).
d. (−212, 1) is to the left of (–3, 1). The two points have the same y-coordinate, but different x-coordinates. Since the x-coordinate decreases as you move to the left on the coordinate plane, the point (−212, 1) is located to the left of the point (–3, 1).
e. (312, 12) is to the right of (12, 12). The two points have the same y-coordinate, but different x-coordinates. Since the x-coordinate increases as you move to the right on the coordinate plane, the point (312, 12) is located to the right of the point (12, 12).
f. (2, 5) is above (2, –5). The two points have the same x-coordinate, but different y-coordinates. Since the y-coordinate increases as you move up on the coordinate plane, the point (2, 5) is located above the point (2, –5).
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M
what is the rate of return when 30 shares of stock
a. purchased for $20/share, are sold for $720? the
commission on the sale is $6.
rate
return = [?] %
give your answer as a percent rounded to the
nearest tenth.
The rate of return is 19%, rounded to the nearest tenth.
Given that a purchased for $ 20/share, are sold for $ 720. $ 6 is the commission on the sale. We need to calculate the total cost of the investment and the total proceeds from the sale, and then use the formula for rate of return.
The total value should be
= 20 × 30
= $ 600
Since, it is sold for $ 720 along with commission of $6 so final money should be
= 720 - 6
= $ 714.
Now rate of return is
= (714 - 600)/714*100
= 114/600*100
= 19%
Therefore, the rate of return is 19%, rounded to the nearest tenth.
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The volume of a sphere is 14.13 cubic centimeters. What is the radius of the sphere? Use 3.14 for π.
The correct answer is 904.78 cm2
evaluate : 20-[5+(9-6]
Answer:
12
Step-by-step explanation:
20-(5+(9-6)) = 20-(5+(3)) = 20-(8) = 12.
Alternatively, rewrite the question without parenthesis.
20-(5+(9-6)) = 20-(5+9-6) = 20-5-9+6 = 12.
A power Ine is to be constructed from a power station at point to an island at point which is 2 mi directly out in the water from a point B on the shore Pontis 6 mi downshore from the power station at A It costs $3000 per milo to lay the power line under water and $2000 per milo to lay the ine underground. At what point S downshore from A should the line come to the shore in order to minimize cost? Note that could very well be Bor At The length of CS is 14) 5 miles from (Round to two decimal places as needed)
To minimize cost, we need to determine whether it's cheaper to lay the power line underground from A to S and then underwater from S to B, or to lay it underwater directly from A to B.
Let CS = x miles. Then AS = 6 - x miles and SB = 8 + x miles.
The cost of laying the power line underground from A to S is $2000 per mile for a distance of AS, or 2000(6-x) dollars. The cost of laying the power line underwater from S to B is $3000 per mile for a distance of SB, or 3000(8+x) dollars. So the total cost C(x) is:
C(x) = 2000(6-x) + 3000(8+x)
C(x) = 18000 - 2000x + 24000 + 3000x
C(x) = 42000 + 1000x
The power line should come to the shore at point S that is 5 miles downshore from A to minimize cost.
To minimize cost, we need to find the value of x that minimizes C(x). To do this, we take the derivative of C(x) with respect to x and set it equal to zero:
C'(x) = 1000
0 = 1000
x = -42
This doesn't make sense since x represents a distance and cannot be negative. So we know that this is not the minimum.
Alternatively, we can check the endpoints of our interval (0 ≤ x ≤ 6) to see which one gives the minimum cost. When x = 0, the cost is:
C(0) = 42000
When x = 6, the cost is:
C(6) = 44000
When x = 5, the cost is:
C(5) = 43000
To minimize the cost of constructing the power line, we need to find the point S on the shore where the combined cost of laying the underground line from A to S and the underwater line from S to B is minimized.
Let x be the distance from A to S, then the distance from S to B is (6 - x) miles.
Using the Pythagorean theorem, the underwater line's length from S to C is √((6 - x)^2 + 2^2) = √(x^2 - 12x + 40).
The cost of the underground line from A to S is 2000x, and the cost of the underwater line from S to C is 3000√(x^2 - 12x + 40). The total cost is:
Cost = 2000x + 3000√(x^2 - 12x + 40)
To minimize this cost, we can find the derivative of the cost function with respect to x and set it to zero, then solve for x. The optimal x value will give us the point S downshore from A that minimizes the cost.
After calculating the derivative and solving for x, we find that the optimal value of x is approximately 4.24 miles. Therefore, the point S should be approximately 4.24 miles downshore from A to minimize the cost of constructing the power line.
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