To minimize the cost of the fence, the builder should use the expensive fence along the shorter side of the rectangular shape, as this will require less length of the expensive fence. Let's say the length of the rectangle is x meters and the width is y meters. Then the area of the rectangle is given by:
A = xy = 80000
And the perimeter of the rectangle is:
P = 2x + 2y
We are given that the cost of the fence along the front part of the land will cost $60 per meter, while the fence for the other three sides will cost $20 per meter. So the total cost of the fence is:
C = 60x + 20(2x + 2y)
Simplifying this expression, we get:
C = 100x + 40y
We can now use the area equation to eliminate one of the variables. Solving for y, we get:
y = 80000/x
Substituting this expression for y into the cost equation, we get:
C = 100x + 40(80000/x)
Simplifying this expression, we get:
C = 100x + 3200000/x
To minimize this function, we need to take its derivative and set it equal to zero:
dC/dx = 100 - 3200000/x^2 = 0
Solving for x, we get:
x = sqrt(32000) = 178.89
So the length of the rectangle should be approximately 178.89 meters, and the width should be:
y = 80000/178.89 = 446.68
Therefore, the amount of expensive fence needed is 178.89 meters, and the amount of cheap fence needed is:
2(178.89) + 2(446.68) - 178.89 = 893.36 meters
Finally, the length of the fence along the front part of the land that will be cost $60 per meter is simply the width of the rectangle, which is:
y = 446.68 meters (rounded to two decimal places)
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Two circles, C1 and C2, intersect at point A and B. Passes through the center O of circle C2. The point P lies on circle C2 so that the line PAT is target to circle Ci and point A. Let ∠APB =.
The value of ∠APB = 180°. It is a straight line.
Given the information, we can deduce that the line passing through the center O of circle C2 and point A also passes through point B, as AB is the intersection of the two circles.
Now, consider the line segment AP. Since PAT is tangent to circle C1 at point A, we know that ∠APT = 90°. Additionally, since AB is a diameter of circle C1, we know that ∠ABP = 90°.
Using these angles, we can see that ∠APB is equal to the sum of ∠APT and ∠ABP. Therefore,
∠APB = ∠APT + ∠ABP = 90° + 90° = 180°.
So, we have shown that ∠APB is a straight line.
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Solve for X. Round to the nearest tenth, if necessary.
The value of x to the nearest tenth is 1.4
What is trigonometric ratio?Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.
Sin(θ) = opp/hyp
cos(θ)= adj/hyp
tan( θ) = opp/adj
x is opposite side to angle F and 32 is adjascent to angle F.
therefore;
tan F = opp/adj
tan23 = x/3.2
x = tan23 × 3.2
x = 1.4
therefore the value of x to the nearest tenth is 1.4
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a mobile food vendor sells hot apple cider and ice cream at special events throughout the year. the function f(x)=500x2+10,000f(x)=500x2+10,000can be used to model the food vendor's annual revenue xx years from now.when should the food vendor expect to bring in $ 60,00060,000 in annual revenue?−3x-3x−5x-5x−2x-2x
The function f(x)=500[tex]x^2[/tex] +10,000 can be used to model the food vendor's annual revenue. The food vendor would expect to bring in $ 60,000 in annual revenue by 10 years from now.
To find out when the mobile food vendor should expect to bring in $60,000 in annual revenue using the function f(x) = 500x^2 + 10,000, follow these steps:
1. Set the function equal to 60,000: 500[tex]x^2[/tex]+ 10,000 = 60,000
2. Subtract 60,000 from both sides of the equation: 500[tex]x^2[/tex]+ 10,000 - 60,000 = 0
3. Simplify the equation: 500[tex]x^2[/tex]- 50,000 = 0
4. Divide both sides by 500:[tex]x^2[/tex] - 100 = 0
5. Add 100 to both sides: [tex]x^2[/tex] = 100
6. Find the square root of both sides: x = ±10
Since it doesn't make sense to have a negative number of years, the food vendor should expect to bring in $60,000 in annual revenue 10 years from now.
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Find the average rate of change of g (x) = 2x² - 7x from x = 1 to x = 6.
Simplify your answer as much as possible.
The average rate of change of g(x) from x = 1 to x = 6 is 7
Finding the average rate of change of g(x)The average rate of change of a function over an interval is given by the difference in the values of the function at the endpoints of the interval, divided by the length of the interval.
In this case, we want to find the average rate of change of g(x) = 2x² - 7x from x = 1 to x = 6.
The value of g(x) at x = 1 is:
g(1) = 2(1)² - 7(1) = -5
The value of g(x) at x = 6 is:
g(6) = 2(6)² - 7(6) = 30
So the difference in the values of g(x) is:
g(6) - g(1) = 30 - (-5) = 35
The length of the interval is:
6 - 1 = 5
Therefore, the average rate of change of g(x) from x = 1 to x = 6 is:
Rate = 35/5
Evaluate
Rate = 7
So, the rate is 7
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The average rate of change is 7.
We know that,
The average rate of change = (final value - initial value)/change in the value of x.
Now,
The given function is,
g(x)=2x²-7x
The initial value of x is 1 (given)
∴ The initial value of the function g(x), at x=1,
g(1)=2(1)²-7(1)=2-7
or, g(1)= -5
Now, the final value of x is 6,
∴ Finding the final value of the function g(x) at x=6,
i.e, g(6)=2(6)²-7(6)
or, g(6)=72-42 = 30
∴ The change in the value of function g(x), from x= to x=6,
= g(6)-g(1)
= 30-(-5)
= 35
Now, change in the value of x = 6-1=5
∴ The average rate of change = 35/5 = 7
Hence the average rate of change is 7.
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Make a table of values in a graph for fabian's income inexpenses the expenses e to make n cakes per month is given by the equation E = 825 + 3.25n the income I for selling n Cakes given by the equation I equals 8.20 n also graphic and make a table
The table of values in a graph for fabian's income in expenses is
n E(n)
0 825
1 828.25
2 831.5
4 838
Making a table of values in a graph for fabian's income inexpensesFrom the question, we have the following parameters that can be used in our computation:
The expenses E to make n cakes per month is given by the equation
E = 825 + 3.25n
Next, we assume values for n and calculate E
Using the above as a guide, we have the following:
E = 825 + 3.25(0) = 825
E = 825 + 3.25(1) = 828.25
E = 825 + 3.25(2) = 831.5
E = 825 + 3.25(4) = 838
So, we have
n E(n)
0 825
1 828.25
2 831.5
4 838
This represents the table of values
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In ΔSTU, t = 3. 4 cm, u = 6. 9 cm and ∠S=21°. Find the area of ΔSTU, to the nearest 10th of a square centimeter.
4.20 cm² is the area of the triangle STU to the nearest 10th of a square centimeter.
Given, t = 3.4 cm, u = 6.9 cm and ∠S = 21°
We know that the formula for the area of the triangle = 1/2 * t*u *sin(S)
Substituting the values
Area = 1/2 × 3.4 × 6.9 × sin(21°)
Area = 11.73 × sin(21°)
Area = 11.73 × 0.3583
Area = 4.2016
Rounding to the nearest 10th of a square centimeter .
Area = 4.20 cm²
Hence, 4.20 cm² is the area of the triangle STU to the nearest 10th of a square centimeter.
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Ayana played Super Star Quest, a video game that involves collecting stars and spending them on power-ups. At the end of each level, the game showed Ayana how many stars she had. Ayana created a line of best fit relating the level, x, to the number of stars, y. The equation for the line of best fit is y= 3 2 x–1. How many stars does this equation predict Ayana will have at the end of level 10?
There would be 14 stars that this equation predicts Ayana will have at the end of level 10.
In this question, we are given an equation for the line of best fit relating the level, x, to the number of stars, y. The equation is y = (3/2)x - 1.
To find the predicted number of stars at the end of level 10, we need to substitute x = 10 into the equation and solve for y.
y = (3/2)x - 1
y = (3/2)(10) - 1
y = 15 - 1
y = 14
Therefore, the equation predicts that Ayana will have 14 stars at the end of level 10.
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Complete the statements by selecting the correct answer from each-down menu. Carl's transactions for a year are given in the table. His broker charged him $5 per trade. How much does Carl pay his broker?
Carl pays his broker a total of $200 in fees for the 40 trades he made during the year.
To calculate how much Carl pays his broker, we need to first determine how many trades he made in a year. Looking at the table, we can see that Carl made a total of 40 trades - 20 buys and 20 sells. Since each trade incurs a $5 charge, we can multiply the number of trades by the cost per trade to get the total amount paid to the broker.
40 trades x $5 per trade = $200 paid to the broker in a year
It's important to note that transaction costs can have a significant impact on investment returns, especially for small accounts, so it's important to consider these costs when making investment decisions. Some brokers may offer lower transaction fees or other incentives to attract clients, so it's worth shopping around and comparing fees before choosing a broker. Additionally, it may be more cost-effective to use a robo-advisor or invest in index funds or exchange-traded funds (ETFs) that have lower fees compared to actively managed funds.
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Let z be a random variable with a standard normal distribution. Find the indicated probability. (Enter a number. Round your answer to four decimal places. )
P(z ≥ 1. 41) =
If you let z be a random variable with a standard normal distribution, the indicated probability is 0.0793. So, the probability P(z ≥ 1.41) = 0.0793
To find the probability P(z ≥ 1.41) for a standard normal distribution, you can use a Z-table or calculator to find the area to the right of z = 1.41.
Using a Z-table or calculator, you will find the value of P(z ≥ 1.41) is approximately 0.0793. So, the probability P(z ≥ 1.41) = 0.0793. Remember to round your answer to four decimal places.
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What was the average amount of books read per student according to the histogram below?
The average amount of books read per student according to the histogram is given as follows:
1.27 books.
How to calculate the mean of a data-set?The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations, which is also called the cardinality of the data-set.
The histogram shows the number of times for each observation, hence:
7 students read zero books.9 students read one book.6 students read two books.4 students read three books.Hence the mean is calculated as follows:
M = (7 x 0 + 9 x 1 + 6 x 2 + 4 x 3)/(7 + 9 + 6 + 4) = 1.27 books.
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In a survey conducted by a retail store, 58% of the sample respondents said they prefer to shop at places with loyalty cards.
96
If the margin of error is 3. 4%, the expected population proportion that prefers to shop at places with loyalty cards is between
and
%.
The expected population proportion, with 95% confidence, that prefers to shop at places with loyalty cards is between 54.6% and 61.4%.
Based on the survey results, we know that 58% of the sample respondents prefer to shop at places with loyalty cards. If the margin of error is 3.4%, we can calculate the expected range of the population proportion as follows:
Upper bound: 58% + 3.4% = 61.4%
Lower bound: 58% - 3.4% = 54.6%
Therefore, we can say with 95% confidence that the expected population proportion that prefers to shop at places with loyalty cards is between 54.6% and 61.4%.
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Kira had 3/5 acres land she planted 3/7 of it with corn. How many acres did she plant with corn?
Kira planted 9/35 acres with corn.
If Kira planted corn on 3/7 of her land total of 3/5 acres, what is the area she planted with corn?To find out how many acres planted with corn, we first need to understand that the total amount of land she had was 3/5 acres. Then, we know that she planted 3/7 of her land with corn.
To calculate the area planted with corn, we multiply the total area of her land (3/5 acres) by the fraction that represents the portion she planted with corn (3/7). This gives us:
(3/5) x (3/7) = 9/35 acres
Therefore, Kira planted 9/35 acres of her land with corn.
We can simplify the fraction by dividing both the numerator and the denominator by their greatest common factor, which is 3 in this case. This gives us:
(9/3) / (35/3) = 3/11 acres
So, Kira planted approximately 0.26 acres with corn.
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The total distance in d,in meters, traveled by an object moving in a straight line can be modeled by a quadratic function that is defined in terms of t, is the time in seconds. At a time of 10. 0 seconds the total distance is traveled by the objects is 50. 0 meters and at a time of 20. 0 seconds the total distance traveled by the object is 200. 0 meters if the object was at a distance of 0 meters when t=0 then what is the total distance traveled in meters, by the object after 30. 0 seconds
Let's denote the total distance traveled by the object as `d` and time as `t`.
We can use the given information to set up a system of equations:
When t = 10.0 seconds, d = 50.0 meters
50.0 = a(10.0)^2 + b(10.0) + c (Equation 1)
When t = 20.0 seconds, d = 200.0 meters
200.0 = a(20.0)^2 + b(20.0) + c (Equation 2)
When t = 0 seconds, d = 0 meters
0 = a(0)^2 + b(0) + c (Equation 3)
Simplifying Equation 3, we get c = 0.
Substituting c = 0 in Equations 1 and 2, we get:
50.0 = 100a + 10b (Equation 4)
200.0 = 400a + 20b (Equation 5)
We can solve Equations 4 and 5 simultaneously to get the values of `a` and `b`:
From Equation 4, we get:
10b = 50 - 100a
b = 5 - 10a
Substituting this value of `b` in Equation 5, we get:
200.0 = 400a + 20(5 - 10a)
200.0 = 400a + 100 - 200a
200.0 = 200a + 100
100.0 = 200a
a = 0.5
Substituting this value of `a` in Equation 4, we get:
50.0 = 100(0.5) + 10b
50.0 = 50 + 10b
b = 0
Therefore, the quadratic function that models the total distance traveled by the object is:
[tex]d = 0.5t^2[/tex]
To find the total distance traveled by the object after 30.0 seconds, we can substitute `t = 30.0` in the above equation:
[tex]d = 0.5(30.0)^2[/tex]
d = 450.0 meters
Therefore, the object will travel a total distance of 450.0 meters after 30.0 seconds.
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1. write the equation for each line that passes through (1, 2) and has a) slope 2/3 b) undefined slope c) m = 0 d) point (2, 3) also on the line
The equation of the line that passes through (1, 2) and (a) having a slope of 2/3 is y = (2/3)x + 4/3, (b) Having an undefined slope is x = 1, (c) having slope m = 0 is y = 2 (d) point (2, 3) also lies on the line is y = x + 1.
a) To find the equation of a line with slope 2/3 passing through (1,2), we can use the point-slope formula:
y - y1 = m(x - x1)
Substituting in the values we know, we get:
y - 2 = (2/3)(x - 1)
Expanding and simplifying:
y = (2/3)x + 4/3
So the equation of the line is y = (2/3)x + 4/3.
b) To find the equation of a line with an undefined slope passing through (1,2), we know that this line must be vertical. The equation of a vertical line passing through (1,2) can be written as:
x = 1
So the equation of the line is x = 1.
c) To find the equation of a line with slope m=0 passing through (1,2), we know that this line must be horizontal. The equation of a horizontal line passing through (1,2) can be written as:
y = 2
So the equation of the line is y = 2.
d) To find the equation of a line passing through (1,2) and (2,3), we can use the point-slope formula again:
y - y1 = m(x - x1)
Substituting in the values we know, we get:
y - 2 = (3 - 2)/(2 - 1)(x - 1)
Simplifying:
y - 2 = 1(x - 1)
y - 2 = x - 1
y = x + 1
So the equation of the line is y = x + 1.
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can someone help me answer #17 using square roots?
Answer: x = ± [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
Equation:
4x² + 10 = 11 > bring everything over to other side
> first subtract 10 from both sides
4x² = 1 > Divide by 4 on both sides
x² = [tex]\frac{1}{4}[/tex] >Take square root of both sides
> When you take square root there is a ±
x = ± [tex]\sqrt{(\frac{1}{4} )}[/tex] > take the square root of both top and bottom
x = ± [tex]\frac{1}{2}[/tex]
3) Graph polygon G(-3,-2) R(-4,4) E(0,1) A(1, -2) T(-1, -3) and it’s image G’R’E’A’T’=R (GREAT)
A graph of polygon GREAT and its image after a counterclockwise rotation of 90° around the origin is shown in the image attached below.
What is a rotation?In Mathematics and Geometry, the rotation of a point 90° about the center (origin) in a counterclockwise (anticlockwise) direction would produce a point that has these coordinates (-y, x).
By applying a rotation of 90° counterclockwise around the origin to vertices W, the coordinates of the vertices of the image ΔA'B'C' are as follows:
(x, y) → (-y, x)
Ordered pair G = (-3, -2) → Ordered pair G' = (2, -3)
Ordered pair R = (-4, 4) → Ordered pair R' = (-4, -4)
Ordered pair E = (0, 1) → Ordered pair E' = (-1, 0)
Ordered pair A = (1, -2) → Ordered pair A' = (2, 1)
Ordered pair T = (-1, -3) → Ordered pair T' = (3, -1)
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Cause then you'd only get one answer to study.
Now back to the
a collection of facts,
Numbers, measurements and things like that.
conclusion
estimate
data
A collection of information, such as numbers, measurements, or observations, is commonly referred to as data.
Data can be collected from a wide variety of sources, such as surveys, experiments, or observations, and can be analyzed to reveal patterns, trends, and relationships.
Data can be represented in many different ways, including tables, graphs, charts, or statistical summaries, and can be used to make informed decisions in a wide range of fields, including business, science, healthcare, and social sciences.
However, it is important to ensure that the data is accurate, reliable, and unbiased, and that appropriate statistical methods are used to analyze and interpret it.
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Full Question: What is a collection of information such as number measurement or observation called?
A model airplane flew the distance of 330 feet in 15 seconds. Select ALL the unit rates that are equivalent to the speed of the model airplane.
All of the unit rates that are equivalent to the speed of the model airplane are 22 feet per second, 1320 feet per minute, and 0.25 miles per minute.
To calculate the speed of the model airplane, we need to use the formula:
Speed = Distance / Time
Given that the distance covered by the model airplane is 330 feet, and the time taken is 15 seconds, we can substitute these values in the above formula to get:
Speed = 330 feet / 15 seconds
Simplifying this, we get:
Speed = 22 feet per second
To convert this unit rate to other equivalent unit rates, we need to use conversion factors. For example, to convert feet per second to feet per minute, we can multiply the unit rate by 60 (since there are 60 seconds in a minute):
22 feet per second x 60 seconds per minute = 1320 feet per minute
Similarly, to convert feet per minute to miles per minute, we can use the conversion factor 1 mile = 5280 feet:
1320 feet per minute / 5280 feet per mile = 0.25 miles per minute
Therefore, all of the unit rates that are equivalent to the speed of the model airplane are 22 feet per second, 1320 feet per minute, and 0.25 miles per minute.
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What capital letter that has more than two right angles.
Answer:
E,F,H
Step-by-step explanation:
Answer:
B = 2 (could be 4, like with this font)
E = 4
F = 3
H = 4
P = 0 (could be 3, like this this font)
R = 0 (could be 3, like with this font)
X = (could be 4)
Other right angles:
D = 0 (could be 2, like with this font)
L = 1
T = 2
Y = (could be 1)
Find the linear approximation for the following function at the given point. b. Use part (a) to estimate the given function value. f(x,y)= - 4x² + 2y² ; (3, -3); estimate f(3.1,- 3.01) a. L(x,y)= b. L(3.1, – 3.01)= (Type an integer or a decimal)
The estimate for f(3.1, -3.01) using the linear approximation is approximately -54.28.
a. To find the linear approximation of f(x,y) at the point (3,-3), we need to find the gradient of the function at that point.
∇f(x,y) = [-8x, 4y]
So, at the point (3,-3), the gradient is ∇f(3,-3) = [-24, -12].
The linear approximation is given by:
L(x,y) = f(3,-3) + ∇f(3,-3)·(x-3,y+3)
Plugging in the values, we get:
L(x,y) = -4(3)^2 + 2(-3)^2 - 24(x-3) - 12(y+3)
Simplifying, we get:
L(x,y) = -12x - 4y - 36
b. To estimate f(3.1, -3.01) using the linear approximation, we plug in the values into the equation we found in part (a):
L(3.1, -3.01) = -12(3.1) - 4(-3.01) - 36
L(3.1, -3.01) ≈ -54.28
Therefore, the estimate for f(3.1, -3.01) using the linear approximation is approximately -54.28.
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Among college students who hold part-time jobs during the school
year, the distribution of the time spent working per week is approximately normally distributed with a
mean of 20. 20 hours and a standard deviation of 2. 6 hours. Find the probability that the average time
spent working per week for 18 randomly selected college students who hold part-time jobs during the
school year is
a. Not within 1 hour of the population mean
b. 20. 0 to 20. 5 hours
c. At least 22 hours
d. No more than 21 hours
The z scοre is negative the actual probability would be
1-0.7995 = 0.2005
What is the probability?
A number that expresses hοw likely it is that an event will occur is called the probability of οccurrence. It is written as a number from 0 to 1, or frοm 0% to 100%, in percentage notation. The probability of an event occurring increases with probability.
here,
mean = 20.20
standard deviatiοn = 2.60
we knοw that,
Z scοre = (X-mean)/standard deviation
fοr X = 18:
Z scοre = (18-20.20)/2.6 = -0.8461
nοte that the z score is negative because the measured value is less than the mean value.
fοr Z score 0.8461 probability is 0.7995
and since the z scοre is negative the actual probability would be
1-0.7995 = 0.2005
a. For nοt within 1 hour of the population mean
We apply the formula here and we get the value οf P.
P(19.20>x>21.20) = P(19.20-20.20/2.60√18) > X-μ/σ√n >21.20-20.20/2.60√18
P(19.20>x>21.20) = P(-1.63>z>1.63)
Now, we find the value οf z.
P(19.20>x>21.20) = P(z>1.63) + P(z<-1.63)
P(19.20>x>21.20) = 0.0516 + 0.0516
P(19.20>x>21.20) = 0.1032
b. Fοr 20. 0 to 20. 5 hours
P(20<x<20.5) = P(20-20.20/2.60√18) < X-μ/σ√n<20.50-20.20/2.60√18
P(20<x<20.5) = P(-0.33<z<0.49)
Nοw, we find the value of the z-score and we get
P(20<x<20.5) = P(z<0.49) - P(z<-0.33)
P(20<x<20.5) = 0.6879 - 0.2707
P(20<x<20.5) = 0.3172
c. Fοr at least 22 hours
We apply the t-test fοrmula here and we get
P(x≥22) = P(X-μ/σ√n≥22-20.20/2.60√18)
Nοw, we find the value of z.
P(x≥22) = P(z≥2.94)
P(x≥22) = 0.0016
d. Fοr not more than 21 hours.
P(x<21) = P(X-μ/σ√n<21-20.20/2.60√18)
We find here the value οf P for x<21 and we get
P(x<21) = P(z<1.31)
Now, we find the value οf the z- score.
P(x<21) = 0.9049
Hence, a. 0.1032
b. 0.3172
c. 0.0016
d. 0.9049
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Complete question is,
Among college students who hold part-time jobs during the school year, the distribution of the time spent working per week is approximately normally distributed with a mean of 20.20 hours and a standard deviation of 2.60 hours. Find the probability that the average time spent working per week of 18 randomly selected college students who old part-time jobs during the school year is.
You buy a sheet with 10 stamps. Some are 45 cents and some are 30 cents. If it cost $4. 20 how many of each did you get
You bought 8 stamps that cost 45 cents each and 2 stamps that cost 30 cents each.
Let's assume you bought x stamps that cost 45 cents each and y stamps that cost 30 cents each.
From the given information, we can create two equations:
The total number of stamps is 10: x + y = 10.
The total cost is $4.20: 45x + 30y = 420 (since the cost is given in cents).
Now we can solve this system of equations to find the values of x and y.
We can multiply the first equation by 30 to eliminate y:
30x + 30y = 300.
Now we have a system of equations:
30x + 30y = 300,
45x + 30y = 420.
Subtracting the first equation from the second equation, we get:
45x + 30y - (30x + 30y) = 420 - 300,
15x = 120,
x = 120/15,
x = 8.
Substituting the value of x back into the first equation:
8 + y = 10,
y = 10 - 8,
y = 2.
Therefore, you bought 8 stamps that cost 45 cents each and 2 stamps that cost 30 cents each.
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Josie had 12 beads on her necklace. Then she added b more beads. Write an expression that shows how many beads are on the necklace in all. please write a expression like b-12 or b+?
The expression that shows how many beads are on the necklace in all is:
b + 12.
What is expression?An expression in mathematics is a combination of numbers, variables, and/or operators that represents a mathematical relationship or quantity. It may contain constants, variables, coefficients, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation. Expressions are often used to describe or represent real-world situations, and can be simplified, evaluated, or manipulated using algebraic rules and properties.
In the given question,
To write an expression that shows how many beads are on Josie's necklace in all after adding b more beads:
Start with the initial number of beads on the necklace, which is 12.
To this, add the number of beads Josie added, which is b.
Combine the two terms to form the final expression: 12 + b.
Therefore, the expression that shows how many beads are on Josie's necklace in all after adding b more beads is 12 + b.
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I need help with these questions pls
Volumes of the cylinder are given by:
(A) (1) Volume = 2486.88 cubic in.
(2) Volume = 108518.4 cubic ft.
(3) Volume = 47608.68 cubic yd.
(B) (4) Volume = 508.68 cubic ft.
(5) Volume = 8490.56 cubic yd.
(6) Volume = 43407.36 cubic in.
(7) Volume = 9420 cubic ft.
(8) Volume of cylindrical flower vase = 1105.28 cubic in.
Surface Area of the Cylinder are given by:
(1) Surface Area = 113.04 square in.
(2) Surface Area = 1444.4 square ft.
(3) Surface Area = 678.24 square yd.
(4) Surface Area = 1130.4 square yd.
(5) Surface Area = 602.88 square in.
(6) Surface Area = 1055.04 square ft.
(7) Surface Area = 1570 square ft.
(8) Surface Area = 791.28 square yd.
(9) Surface Area = 326.56 square in.
We know that the volume of a cylinder with radius 'r' and height 'h' is given by,
V = 2πr²h
(A) (1) From the figure, radius = 6 in and height = 11 in.
So the volume = 2π(6)²*11 = 2486.88 cubic in.
(2) Radius = 24 ft. and height = 30 ft.
Hence, the volume of cylinder = 2π(24)²*30 = 108518.4 cubic ft.
(3) Radius = 19 yd. and height = 21 yd.
Hence, the volume of cylinder = 2π(19)²*21 = 47608.68 cubic yd.
(B) (4) Radius = 3 ft. and height = 9 ft.
Hence, the volume of cylinder = 2π(3)²*9 = 508.68 cubic ft.
(5) Radius = 13 yd. and height = 8 yd.
Hence, the volume of cylinder = 2π(13)²*8 = 8490.56 cubic yd.
(6) Radius = 16 in. and height = 27 in.
Hence, the volume of cylinder = 2π(16)²*27 = 43407.36 cubic in.
(7) Radius = 10 ft. and height = 15 ft.
Hence, the volume of cylinder = 2π(10)²*15 = 9420 cubic ft.
(8) Cylindrical flower vase is 11 inch tall and radius of vase is 4 inches.
The volume of flower vase = 2π(4)²*11 = 1105.28 cubic in.
Now we know that the surface area of a Cylinder with radius 'r' and height 'h' is given by,
S = 2πrh + 2πr²
(1) Radius = 2 in. and Height = 7 in.
Hence the surface area = 2π*2*7 + 2π(2)² = 113.04 square in.
(2) Radius = 10 ft. and Height = 13 ft.
Hence the surface area = 2π*10*13 + 2π(10)² = 1444.4 square ft.
(3) Radius = 6 yd. and Height = 12 yd.
Hence the surface area = 2π*6*12 + 2π(6)² = 678.24 square yd.
(4) Radius = 9 yd. and Height = 11 yd.
Hence the surface area = 2π*9*11 + 2π*9² = 1130.4 square yd.
(5) Radius = 6 in. and Height = 10 in.
Hence the surface area = 2π*6*10 + 2π(6)² = 602.88 square in.
(6) Radius = 8 ft. and Height = 13 ft.
Hence the surface area = 2π*8*13 + 2π(8)² = 1055.04 square ft.
(7) Radius = 10 ft. and Height = 15 ft.
Hence the surface area = 2π*10*15 + 2π(10)² = 1570 square ft.
(8) Radius = 6 yd. and Height = 15 yd.
Hence the surface area = 2π*6*15 + 2π(6)² = 791.28 square yd.
(9) Radius = 4 in. and Height = 9 in.
Hence the surface area = 2π*4*9 + 2π(4)² = 326.56 square in.
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Which equation matches the function shown in the graph?
Answer: C
Step-by-step explanation:
The amount of money earned over a period of time is called
1. Asset
2. Fixed expense
3. Income
4. Liability
5. Net worth
6. Variable expense
The amount of money earned over a period of time is called 3. Income
Income refers to the money you receive from various sources such as salary, wages, investments, or any other means during a specific period of time.
Income is a fundamental concept in finance and accounting. It represents the inflow of money or economic benefits received by an individual, household, or organization.
It is typically measured and reported on a periodic basis, such as monthly, quarterly, or annually. Income can be derived from various sources, including salaries and wages, interest and dividends, rental income, profits from business activities, and capital gains.
It is an essential component in assessing an individual's or organization's financial health and is often used to calculate taxes, budgeting, and determining net worth. Understanding and effectively managing income is crucial for individuals and businesses to meet their financial goals and sustain their economic well-being.
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If m< a=3x and m< d=4x+6 what is the value of x?
Based on the given information that angles a and d are equal, the value of x is determined to be -6.
To find the value of x in the given scenario, we can equate the measures of the angles using the given information:
m< a = 3x
m< d = 4x + 6
Since angles a and d are stated to be equal, we can set up the equation:
3x = 4x + 6
To solve for x, we subtract 3x from both sides:
0 = x + 6
Next, we subtract 6 from both sides:
-6 = x
Therefore, the value of x is -6.
In conclusion, based on the given information that angles a and d are equal, the value of x is determined to be -6.
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Duncan's favorite park just added a statue of a badger, the state animal. The statue sits on a base shaped like a rectangular prism. The base is 5 feet long, 3 feet wide, and has a volume of 60 cubic feet. How tall is the base of the statue? Write your answer as a whole number or decimal. Do not round. PLEAS HELP â
LOL NVM
The height of the base of the statue, structured in rectangular prism shape with stated measure of dimension is 4 feet.
The volume of the rectangular prism will be given by the formula -
Volume = length × width × height
Keep the values in formula to find the value of height of the base of the statue
60 = 5 × 3 × height
Rearranging the equation in terms of height
Height = 60 × (5 × 3)
Multiplying the denominator on Right Hand Side
Height = 60/15
Divide the values
Height = 4
Hence the height is 4 feet.
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Given l||m||n, find the value of x
Answer:
x = 13
Step-by-step explanation:
We Know
(5x - 6) + (8x + 17) must equal 180°
Find the value of x.
Let's solve
5x - 6 + 8x + 17 = 180
13x + 11 = 180
13x = 169
x = 13
So, the value of x is 13.
Which ones are solutions to
7x+4y=-23
(-1,-4)
(2,6)
(-5,3)
(6,-7)
Hello!
In this question, we are asked to find which set of points are solutions to our equation: 7x + 4y = -23
In order to find which points are solutions to our equation, we will plug the values into our equation and solve. If both sides of the equation are equal, the point will be a solution.
Note: Our coordinate point is in the format of (x,y), so we will plug in the values according to its variable.
Solve:
(-1,-4):
Plug in coordinate.
7(-1) + 4(-4) = -23
Simplify.
-7 - 16 = -23
-23 = -23
Since it is equal, (-1,-4) is a solution.
(2,6):
Plug in coordinate.
7(2) + 4(6) = -23
Simplify.
14 + 24 = -23
38 = -23
Since it is not equal, making it false, (2,6) is not a solution.
(-5,3):
Plug in coordinate.
7(-5) + 4(3) = -23
Simplify.
-35 + 12 = -23
-23 = -23
Since it is equal, (-5,3) is a solution.
(6,-7):
Plug in coordinate.
7(6) + 4(-7) = -23
Simplify.
42 - 28 = -23
14 = -23
Since it is not equal, making it false, (6,-7) is not a solution.
Answer:
The solutions to the equation are: (-1,-4) and (-5,3).