The equation that models the objective function for the cost, C=1x+.80y. (A)
This equation is the correct model because it represents the cost, C, as a function of the number of x and y items. The cost of each x item is $1, and the cost of each y item is $0.80.
Therefore, the total cost will be the sum of the cost of x items and the cost of y items, which is represented by the equation C=1x+.80y.
In contrast, options B, C, and D do not accurately represent the cost as a function of the number of x and y items. Option B includes a subtraction of the cost of y items, which would not accurately represent the total cost.
Options C and D include incorrect coefficients for the cost of x and y items, which would also not accurately represent the total cost.
Therefore, the correct equation to model the objective function for the cost, C, is option A. C=1x+.80y.
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The total surface area of the rectangular prism is ________ square centimeters and the lateral surface area is _______ square centimeters.
Answer: surface area is _______ square centimeters.
To answer this question, I would need to know the dimensions of the rectangular prism, as both the total surface area and the lateral surface area depend on the dimensions of the prism.
Assuming the rectangular prism has length (l), width (w), and height (h), the formulas for the total surface area and the lateral surface area are:
Total surface area = 2lw + 2lh + 2wh
Lateral surface area = 2lh + 2wh
Therefore, to find the total surface area and lateral surface area of a specific rectangular prism, I would need to know its dimensions (length, width, and height) and plug them into these formulas.
Step-by-step explanation:
−2x−8y=10
2x−6y=18
−2x+9y=−4
2x+3y=−20
2x+5y=0
x + 5y = −10
−4x+y=9
−4x+9y=17
−5x−4y=−11
−4x + 4y = 20
−5x − 4y =
−15 −x + 4y = −3
3x + 2y =
−12 4x − 2y = −2
7x + 8y = 20
7x − y = 29
−3x − y = 8
−8x − y = 23
−6x − y =
−1 6x + 6y = −24
Please I need help like now I’m going to fail
The solution of the system of equation is
1) The solution to the system of equations is x = -7 and y = -2.
2) The solution to the system of equations is x = -7 and y = -2.
3) The solution to the system of equations is any point on the line 2x + 5y = 0
4) The solution to the system of equations is x = -2 and y = 1.
5) The solution to the system of equations is x = 1 and y = -16.
In mathematics, a system of equations refers to a set of two or more equations that must be solved simultaneously. Solving a system of equations involves finding the values of the variables that satisfy all the given equations. In this response, we will go through the process of solving five different systems of equations.
−2x−8y=10 and 2x−6y=18, in order to solve this system of equations, we need to eliminate one of the variables, x or y. One way to do this is to add the two equations together. When we add them, the x term cancels out, leaving us with -14y = 28. Solving for y, we get y = -2. Substituting this value of y into either equation, we get x = -7.
And then the equations, −2x+9y=−4 and 2x+3y=−20, to solve this system of equations, we can use the method of elimination again. If we add the two equations, the x term cancels out, leaving us with 12y = -24. Solving for y, we get y = -2. Substituting this value of y into either equation, we get x = -7.
Then the third one 2x+5y=0 and x + 5y = −10 is in this system of equations, we notice that the second equation is just the first equation with a constant term added. Therefore, these equations are dependent, meaning that they represent the same line. Any point that satisfies one equation will also satisfy the other equation.
And the fourth one has −4x+y=9 and −4x+9y=17, to solve this system of equations, we can use the method of substitution. We can solve the first equation for y, getting y = 4x + 9. Substituting this expression for y into the second equation, we get -4x + 9(4x + 9) = 17. Simplifying, we get 25x + 72 = 17. Solving for x, we get x = -2. Substituting this value of x into the first equation, we get y = 1.
−6x − y = 10 and −16x + 6y = −24, To solve this system of equations, we can use the method of elimination. If we multiply the first equation by -6 and the second equation by -1, we can add the two equations to eliminate y. Doing so, we get 80x = 80. Solving for x, we get x = 1. Substituting this value of x into either equation, we get y = -16.
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Complete Question:
Solve the system of equations
1) −2x−8y=10 and 2x−6y=18
2) −2x+9y=−4 and 2x+3y=−20
3) 2x+5y=0 and x + 5y = −10
4) −4x+y=9 and −4x+9y=17
5) −6x − y = 10 and −16x + 6y = −24
Given the impact of television on children’s attitudes and behavior, an important concern of behavioral scientists is the amount of time that children of various ages spend watching television. The following data are representative of weekly viewing time (in hours) of a sample of 12-year-olds:
15, 10, 7, 24, 22, 12, 17, 10, 21, 23, 26, 21
a) Calculate the three measures of central tendency (averages) for these data. (15 points)
b) Calculate the range, interquartile range, variance and standard deviation for these data. Use the definition formula for calculating the SS for the variance and standard deviation,(15 points
a) The three measures of central tendency are the 18 (mean), 14.5 (median, and 10 and 21 (mode).
(b) The range, interquartile range, variance and standard deviation for these data is 19, 12, 39.636, and 6.296, respectively.
(a) The three measures of central tendency are the mean, median, and mode.
Mean: (15 + 10 + 7 + 24 + 22 + 12 + 17 + 10 + 21 + 23 + 26 + 21)/12 = 18
Median: (12 + 17)/2 = 14.5
Mode: 10 and 21 (both appear twice in the data set)
b) Range: 26 - 7 = 19
Interquartile Range: Q3 - Q1 = 22 - 10 = 12
Variance: SS/11 = (15-18)² + (10-18)² + (7-18)² + (24-18)² + (22-18)² + (12-18)² + (17-18)² + (10-18)² + (21-18)² + (23-18)² + (26-18)² + (21-18)² / 11 = 39.636
Standard Deviation: √39.636 = 6.296
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A company produces a product for which the variable cost per unit is $8 and fixed cost is $70,000. Each unit has a selling price of $12. Determine the number of units that must be sold for the company to earn a profit of $50,000.
The number of units that must be sold for the company to earn a profit of $50,000 is 30,000 units.
To determine the number of units that must be sold for the company to earn a profit of $50,000, we need to use the following formula:
Profit = Total Revenue - Total Cost
Where Total Revenue = Selling Price × Number of Units Sold
And Total Cost = Fixed Cost + (Variable Cost × Number of Units Sold)
Plugging in the given values into the formula, we get:
$50,000 = ($12 × Number of Units Sold) - ($70,000 + ($8 × Number of Units Sold))
Simplifying the equation, we get:
$50,000 = $12 × Number of Units Sold - $70,000 - $8 × Number of Units Sold
$50,000 = $4 × Number of Units Sold - $70,000
$120,000 = $4 × Number of Units Sold
Number of Units Sold = $120,000 / $4
Number of Units Sold = 30,000
Therefore, the company must sell 30,000 units to earn a profit of $50,000.
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I NEED TO FINISH THIS TEST I HAVE ONLY 3 MINUTES LEFT!!
What is this number in standard form?
(8×10) + (2×1/100) +( 9×1/1,000)
heres the answer:
8x10=80
2x1=2/100= 0.02
9x1=9/1000= 0.002
0.002+0.02+80=
80.002!!
Create a number sequence with 5 terms involving fractions with a common difference of 1/3 from one term to the next starting from 1/3
Answer:This free number sequence calculator can determine the terms (as well as the sum of all terms) of the arithmetic, geometric, or Fibonacci sequence.
Step-by-step explanation:
Find the LU-factorization of the matrix. (Your L matrix must be unit diagonal.) 4 0 1 8 1 1 -4 10 LU = Need Help? Read It WTak to a Ttor Watch It Submit Answer Save Progress Practice Another Version
So, the LU-factorization of the given matrix is:
LU = `[1 0 0 0]` `[4 0 1 8]`
`[0.25 1 0 0]` `[0 1 -4.25 6]`
`[0 4.25 1 0]` `[0 0 1.25 -2]`
`[0 0 -1.25 1]` `[0 0 0 1]`
The LU-factorization of a matrix is a method of decomposing a matrix into a lower triangular matrix (L) and an upper triangular matrix (U). The L matrix must have a unit diagonal, meaning that all the entries on the main diagonal are equal to 1.
To find the LU-factorization of the given matrix, we can use the following steps:
1. Begin with the given matrix:
`[4 0 1 8]`
`[1 1 -4 10]`
2. Use Gaussian elimination to transform the matrix into an upper triangular matrix (U):
`[4 0 1 8]` → `[1 1 -4 10]` → `[0 1 -4.25 6]` → U = `[0 0 1.25 -2]`
3. Now, we can use the entries from the Gaussian elimination to create the lower triangular matrix (L):
L = `[1 0 0 0]`
`[0.25 1 0 0]`
`[0 4.25 1 0]`
`[0 0 -1.25 1]`
4. Finally, we can write the LU-factorization as:
LU = `[1 0 0 0]` `[4 0 1 8]`
`[0.25 1 0 0]` `[0 1 -4.25 6]`
`[0 4.25 1 0]` `[0 0 1.25 -2]`
`[0 0 -1.25 1]` `[0 0 0 1]`
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Lee wants to make at least $400 profit from selling t-shirts. The initial start up costs for making t-shirts is $125. Write an inequality that represents the amount of sales, s, that Lee must have to reach the goal.
The inequality that represents the amount of sales, [tex]s$,[/tex] that Lee must have to reach the goal is:
[tex]$$s \geq \frac{525}{p}$$[/tex]
What is profit ?In business and finance, profit refers to the monetary gain earned by a business or individual after subtracting the expenses from the total revenue. In other words, profit is the difference between the amount of money earned from selling goods or services and the total cost of producing or delivering those goods or services. Profit is often used as a key performance indicator (KPI) to measure the financial success of a business or individual.
According to given information ?Let's assume that the cost of making one t-shirt is c and Lee sells each t-shirt for p.
To make at least $400 profit, Lee's revenue from sales p must be greater than or equal to the sum of the startup costs $125 and the desired profit $400:
[tex]$$p\times s \geq 125+400$$[/tex]
We can simplify this inequality to:
[tex]$$p\times s \geq 525$$[/tex]
Therefore, the inequality that represents the amount of sales, [tex]s$,[/tex] that Lee must have to reach the goal is:
[tex]$$s \geq \frac{525}{p}$$[/tex]
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A polynomial p(x)=x^(3)-3x^(2)+4x-12 can be expressed so that p(x)=q(x)*(x-1)+R What is the value of R ?
The value of R is -10.
The polynomial p(x)=x^(3)-3x^(2)+4x-12 can be expressed as p(x)=q(x)*(x-1)+R. To find the value of R, we need to divide the polynomial p(x) by (x-1) using synthetic division.
Set up the synthetic division by writing the coefficients of the polynomial p(x) in a row and placing the divisor (x-1) to the left of the row.
1 | 1 -3 4 -12
|_____________
Bring down the first coefficient (1) and multiply it by the divisor (1) to get 1. Place this value below the second coefficient (-3) and add them to get -2.
1 | 1 -3 4 -12
| 1
|_____________
1 -2
Multiply the new value (-2) by the divisor (1) to get -2. Place this value below the third coefficient (4) and add them to get 2.
1 | 1 -3 4 -12
| 1 -2
|_____________
1 -2 2
Multiply the new value (2) by the divisor (1) to get 2. Place this value below the fourth coefficient (-12) and add them to get -10.
1 | 1 -3 4 -12
| 1 -2 2
|_____________
1 -2 2 -10
The final value (-10) is the remainder, or the value of R.
Therefore, the value of R is -10.
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Order the values from least to greatest. |-41, 10, -12, 13| A) -41, 131, 10, -12 O B) |3|, |-–4|, 10, −12 OC -12, 1-41, [3], 10 OD) -12, 131, |–4], 10 D
The order of the number from least to greatest will be -12, |3|, |-4|, 10. Then the correct option is D.
What is ascending order?It is the order of the numbers in which a smaller number comes first and then followed by the next number and then the last number will be the biggest one.
The numbers are given below.
|-4|, 10, -12, |3|
Determine the absolute value of the numbers, then we have
|-4| = 4
10 = 10
-12 = -12
|3| = 3
The order of the number from least to greatest will be given as,
-12, 3, 4, 10
-12, |3|, |-4|, 10
Thus, the correct option is D.
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In one country, 7 out of 1,000 infants die before their first birthday. Convert this figure to a percentage. Is your answer greater than or less than 1%?
PLS NOW
Answer: 0.7% < 1%
Step-by-step explanation:
Percent is out of 100 so...
7/1000 = 0.7/100 = 0.7%
0.7% < 1% so the answer is less than 1%
Hope this helped!
You are planning a vacation. The hotel you are going to stay at charges $135 per night. This can be represented by the function p(x) = 135x. The car rental company charges a $45 insurance fee plus $79 per day. This can be represented by the function p(x) = 45 + 79x. Formulate a function to represent the total charges for your hotel and car rental.
A,) p(x) = 259x
B,) p(x) = 135(79x + 45)
C,) p(x) = 45 + 214x
D,) p(x) = 45(135x + 79x)
The function to represent the total charges for your hotel and car rental is C,) p(x) = 45 + 214x
What is the equation?In other terms, an equation is a mathematical statement stating that "this is equivalent to that." It appears to be a mathematical expression on the left, an equal sign in the center, and a mathematical expression on the right.
Given that hotel, you are going to stay at charge $135 per night. It can be represented by the function p(x) = 135x.
Also, car rental company charges a $45 insurance fee plus $79 per day.
It can be represented by the function p(x) = 45 + 79x.
Daily rental fee = $135 per night,
Write the equation for the total fees
p(x) = 45 + 214x
Thus, x represents the number of days.
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In 2011, there were approximately 2.8 million nurses in a large country, with demand for nurses expected to increase by 0.044 million each year. a. Assuming the number of nurses in 2011 represents the demand for that year, express the demand for nurses in the country, D, in millions, as a function of the number of years after 2011,x. b. If the demand increases as expected, during which year will demand for nurses in the country reach 3.5 million? a. D(x)=
The demand for nurses in the country can be expressed as the function D(x) = 2.8 + 0.044x. The year in which the demand for nurses in the country will reach 3.5 million is in 2027.
a. The demand for nurses in the country can be expressed as a function of the number of years after 2011, x, by using the equation D(x) = 2.8 + 0.044x. This equation represents the initial demand in 2011 (2.8 million) plus the expected increase in demand each year (0.044 million) multiplied by the number of years after 2011 (x).
b. To find the year in which the demand for nurses will reach 3.5 million, we can set D(x) equal to 3.5 and solve for x:
3.5 = 2.8 + 0.044x
0.7 = 0.044x
x = 0.7 / 0.044
x = 15.9
Since x represents the number of years after 2011, we can add 15.9 to 2011 to find the year in which the demand will reach 3.5 million:
2011 + 15.9 = 2026.9
Therefore, the demand for nurses in the country will reach 3.5 million during the year 2027.
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What is another way to express 63+35
Answer: 35+63
The only way to label the expression without changing our numbers is 35+63. We still get the sum of 98 and the same numbers are being used, they are just in a different order.
I hope this helped and Good Luck <3!!!
Practice Makes Perfect Determine whether the ordered pairs are solutions to the given system. 3x+y=0 x+2y=-5 at (0,0) and (1,-3)
The ordered pair (1,-3) is a solution to the given system, while the ordered pair (0,0) is not
practice is a great way to help you understand how to determine whether ordered pairs are solutions to a given system. In this case, we are looking at the system:
3x+y=0
x+2y=-5
To determine whether the ordered pairs (0,0) and (1,-3) are solutions, we need to plug them into the equations and see if they make the equations true.
For the first ordered pair (0,0), we plug in x=0 and y=0 into the equations:
3(0)+(0)=0
(0)+2(0)=-5
The first equation is true, but the second equation is not. Therefore, (0,0) is not a solution to the system.
For the second ordered pair (1,-3), we plug in x=1 and y=-3 into the equations:
3(1)+(-3)=0
(1)+2(-3)=-5
Both equations are true, so (1,-3) is a solution to the system.
In conclusion, the ordered pair (1,-3) is a solution to the given system, while the ordered pair (0,0) is not.
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Which graph shows the solution to the inequality? x + 2 < -3 A) A B) B C) C D) D
Therefore , the solution of the given problem of inequality comes out to be the inequality x -5 is option B.
What does inequality imply in reality?Regardless of the equal symbol, a connection or group of numbers variables can be an inequality in mathematics. Equilibrium is always followed by equity. Inequality happens when ideals are still incompatible. Differences exist between inequality expression and fairness. We chose to utilize the most prevalent symbol because elements aren't always similar or comparable (). No mater how few or many variations there are, they can all be used to evaluate values.
Here,
Option B) B is the proper response.
We must isolate x on one side of the inequality in order to answer the inequality x + 2 -3. By taking 2 away from both edges, we arrive at:
=> x < -5
According to this inequality, x is any integer that is less than -5. Since x cannot equal -5,
we must create an open circle at this point on the number line and shade to the left of it to represent all the different values of x that could be used.
Looking at the available choices, we can see that the only graph that accurately depicts the inequality x -5 is option B) B.
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A grocery store baked three different types of
cookies to sell. The number of each type of cookie
is described below.
120 chocolate chip cookies
42 fewer oatmeal than chocolate chip cookies
3 times as many peanut butter than oatmeal cookies
What is the total number cookies that the grocery store
baked?
A 198
B 354
C 396
D 432
Answer:
D. 432
Step-by-step explanation:
To find out this question you need to find out how many cookies you have of each type. we know we have 120 chocolate chip cookies. There are 42 fewer oatmeal cookies than chocolate chip cookies so we take 120 and minus 42.
120 - 42 = 78
There are 78 oatmeal cookies. now we want to find out how many peanut butter cookies we have. There are 3 times as many peanut butter cookies than oatmeal cookies so we times 77 with 3.
78 × 3 = 234
Now we know how many cookies are in all the types, we need to find the total number of all cookies in the grocery store.
120 + 78 + 234 = 432
therefore the answer will be D. 432
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in a certain town there were 171 robberies last year . this year the number of robberies has gone down 39%. how many robberies were there this year , to the nearest whole number ?
The robberies that took place this year to the nearest whole number is 104 robberies.
What distinguishes a percent reduction from a percent difference?A value's percentage change from its initial value is expressed as a percent reduction, but the percentage difference between two values is expressed as a % change from their average.
Let us suppose the number of robberies this year = x.
Given that,
This year the number of robberies has gone down 39%.
x = 171 (1 - 39/100)
x = 171 (1 - 0.39)
x = 104.31
Hence, the robberies that took place this year is 104 robberies.
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How many ways are there to choose 4 books from a collection of 11 books? Hint... does order matter? Type your answer...
There are 330 ways to choose 4 books from a collection of 11 books.
To solve this problem, we need to use the combination formula:
C(n, r) = n! / (r! * (n-r)!)
Where n is the total number of items, r is the number of items to choose, and ! means factorial (the product of all positive integers up to that number).
In this case, we have n = 11 (the total number of books) and r = 4 (the number of books to choose). Plugging these values into the formula, we get:
C(11, 4) = 11! / (4! * (11-4)!)
= 11! / (4! * 7!)
= (11 * 10 * 9 * 8 * 7!)/ (4! * 7!)
= (11 * 10 * 9 * 8)/ (4 * 3 * 2 * 1)
= 330
So there are 330 ways to choose 4 books from a collection of 11 books.
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The price of petrol is increased from R12,58 per liter to R13,28 per liter. Determine the percentage increase in the price
a) write RS as a column vector
b) write SR as a column vector
Answer:14
Step-by-step explanation:
At a carnival, Ivan bought 14 packs of 9 tickets each. He also found 8 more tickets on the ground. How many tickets did Ivan have in all?
Answer: 134 tickets.
Step-by-step explanation:
Since we have 14 packs of 9 tickets, we can say it is 14 groups of 9. Which means we multiply. So 9 times 14 equals 126. But Ivan found 8 more tickets on the groud which means we add. so 126 plus 8 equals 134. The answer is 134 tickets.
Answer:
Step-by-step explanation:
multiply # of packs by # of tickets in each pack then add 8
14 x 9 = 126 + 8 = 134
Make x the subject of the formula x/a+y/b=1, hence, if a=4, b=1, y=2 evaluate x
When a = 4, b = 1, and y = 2, the value of x that satisfies the equation x/a + y/b = 1 is -4.
To make x the subject of the formula x/a+y/b=1, we can start by isolating x on one side of the equation. We can do this by subtracting y/b from both sides of the equation:
x/a = 1 - y/b
Next, we can multiply both sides of the equation by a to isolate x:
x = a(1 - y/b)
Now that we have a formula for x in terms of a, b, and y, we can evaluate x when a = 4, b = 1, and y = 2:
x = 4(1 - 2/1)
x = 4(1 - 2)
x = 4(-1)
x = -4
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The rational expression (20n^(2)-180)/(4n^(2)+36n+72) is not defined for any values of n for which the denominator equals zero. Find the values of n for which the denominator equals zero.
The final values of n for which the denominator equals zero are n = -3 and n = -6.
The rational expression [tex](20n^2-180)/(4n^2+36n+72)[/tex]is not defined for any values of n for which the denominator equals zero. To find the values of n for which the denominator equals zero, we need to solve the equation [tex]4n^2+36n+72 = 0.[/tex]
First, we can simplify the equation by dividing all terms by 4:
[tex]n^2+9n+18 = 0[/tex]
Next, we can use the quadratic formula to find the values of n:
n = [tex](-9 ± √(9^2-4(1)(18)))/(2(1))[/tex]
n = (-9 ± √(81-72))/2
n = (-9 ± √9)/2
n = (-9 ± 3)/2
The two values of n are:
n = (-9 + 3)/2 = -6/2 = -3
n = (-9 - 3)/2 = -12/2 = -6
So the values of n for which the denominator equals zero are n = -3 and n = -6.
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(Algebraic and graphical modelling)
please help
Ben's ball lands approximately 2.5 seconds after Andrew's ball.
How long after Andrew's does Ben's ball land?Since the value of parameter a is -5 for both balls, the height of each ball follows the equation:
h(t) = -5t² + vt + h0
where;
h(t) is the height of the ball at time t, v is the initial velocity of the ball (in meters per second), and h0 is the initial height of the ball (in meters).Let's assume that Andrew's ball is hit with an initial velocity of v1, and Ben's ball is hit with an initial velocity of v₂. We also know that Ben's ball reaches a maximum height 50% greater than Andrew's, which means that:
h_max₂ = 1.5h_max₁
At the maximum height, the velocity of the ball is zero, so we can find the time it takes for each ball to reach the maximum height by setting v = 0 in the equation for h(t):
t_max1 = v₁ / (2 x 5)
t_max2 = v₂ / (2 x 5)
Since Ben's ball reaches a maximum height that is 50% greater than Andrew's, we can write:
h_max2 = 1.5h_max1
-5(t_max2)² + v₂t_max2 + h0 = 1.5(-5(t_max1)² + v1 * t_max1 + h0)
Simplifying this equation, we get:
-5(t_max2)² + v₂t_max2 = -7.5(t_max1)² + 1.5v₁t_max1
We also know that Andrew's ball lands after 4 seconds, which means that h(4) = 0:
h(4) = -5(4)² + v1 * 4 = 0
-80 + 4v1 = 0
v1 = 80/4
v1 = 20 m/s
Solving these equations for t_max2 and v2, we get:
t_max1 = v1 / (2 x 5)
t_max1 = 20 / (2 x 5) = 2 s
t_max2 = 1.5 * t_max1 = 3 s
v2 = 1.5 * v1 = 30 m/s
To find the time it takes for Ben's ball to land, we need to find the time t2 when h(t2) = 0.
We can use the equation for h(t) with v = v2, h0 = 0, and solve for t:
-5t² + v₂t = 0
-5t² + 30 = 0
5t² = 30
t² = 30/5
t² = 6
t = √6
t = 2.5 s
Therefore, Ben's ball lands approximately 2.5 seconds after Andrew's ball.
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Consider the telephone tariff (charge) schedule by the telephone company: a. First examine the cost of an average phone call with the following charge schedule: each call is charged r for the initial period of length / (or fraction thereof). For call length exceeding !, you are charged incrementally for each subsequent period of length S(or fraction thereof), at a unit cost of p. What is the average cost of a call? (Note that it is a standard practice in the industry to assume that call duration is exponentially distributed.) b. If the cost of a call is $1 per minute, and your call is always pro-rated (as fraction of a minute) and the average call length is one minute, then the average cost of a call is just $1. If your call is rounded up to the next minute (I = S = 1), use the formula derived above to find the average cost. (Are you surprised?) c. If I = S = 0.1 (i.e., rounded up to the next 6 seconds), compute the average cost again.
The average cost of a call depends on the initial period, subsequent period, and unit cost for each subsequent period. By using the formula derived above, we can calculate the average cost of a call for different values of I, S, and p.
The average cost of a call can be calculated using the formula: Average Cost = r + p(S-1)/(S-1+1/e^S), where r is the cost for the initial period, p is the unit cost for each subsequent period, and S is the length of each subsequent period.
If the cost of a call is $1 per minute and the average call length is one minute, then the average cost of a call is just $1. However, if the call is rounded up to the next minute (I = S = 1), then the average cost can be calculated using the formula derived above: Average Cost = r + p(S-1)/(S-1+1/e^S) = $1 + $1(1-1)/(1-1+1/e^1) = $1 + $1(0)/(0+1/e) = $1.
If I = S = 0.1 (i.e., rounded up to the next 6 seconds), then the average cost can be calculated using the formula derived above: Average Cost = r + p(S-1)/(S-1+1/e^S) = $1 + $1(0.1-1)/(0.1-1+1/e^0.1) = $1 + $1(-0.9)/(-0.9+1/e^0.1) = $1.07.
Therefore, the average cost of a call depends on the initial period, subsequent period, and unit cost for each subsequent period. By using the formula derived above, we can calculate the average cost of a call for different values of I, S, and p.
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If the exponential function f(x)=((2)/(3))^(2-3x)-2 is written in the form f(x)=ka^(x)+m then 8a-27k+m is equal to:
This function 8a-27k+m is equal to -(71/27).
The exponential function f(x)=((2)/(3))^(2-3x)-2 can be rewritten in the form f(x)=ka^(x)+m by following these steps:
1. Start with the original equation: f(x)=((2)/(3))^(2-3x)-2
2. Rewrite the exponent as a product: f(x)=((2)/(3))^(2*(1-3/2)*x)-2
3. Use the property of exponents that a^(b*c)= (a^b)^c: f(x)=(((2)/(3))^2)^(1-3/2*x)-2
4. Simplify the exponent: f(x)=((4)/(9))^(1-3/2*x)-2
5. Rewrite the equation in the form f(x)=ka^(x)+m, where k=((4)/(9))^1, a=((4)/(9))^(-3/2), and m=-2: f(x)=((4)/(9))*((4)/(9))^(-3/2*x)-2
Now, we can plug in the values for k, a, and m into the expression 8a-27k+m to find the answer:
8a-27k+m = 8*((4)/(9))^(-3/2)-27*((4)/(9))-2
= (8/(4^(3/2)*9^(3/2)))-(27*(4/9))-2
= (8/(8*27))-(27*(4/9))-2
= (1/27)-(12/9)-2
= (1/27)-(4/3)-2
= -(71/27)
Therefore, 8a-27k+m is equal to -(71/27).
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13. Daniel bought some oranges and x apples. He bought twice as many oranges as apples. Each apple
cost $0. 35 and each orange cost $0. 50. Daniel paid $5. 40 in total for oranges and apples. How many
apples did he buy? Write an equation and solve it.
Daniel bought 8 apples and 16 oranges. The equation we will use to solve the problem is 0.35x + 0.5(2x) = 5.4.
We know that Daniel bought twice as many oranges as apples, so let's call the number of apples he bought "x". Therefore, the number of oranges he bought would be "2x".
We also know that each apple cost $0.35 and each orange cost $0.50, so we can write the equation:
0.35x + 0.5(2x) = 5.4
Simplifying the equation, we get:
0.35x + x = 5.4 ÷ 0.5
0.35x + x = 10.8
1.35x = 10.8
x = 8
So, Daniel bought 8 apples, which means he also bought 2x = 16 oranges.
However, we need to check if this solution makes sense hence the cost of the apples would be:
0.35 × 8 = 2.8
And the cost of the oranges would be:
0.5 × 16 = 8
Adding those together, we get:
2.8 + 8 = 10.8
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A cat weighs 814 pounds.How many ounces does the cat weigh?
Answer: 13,024
Step-by-step explanation:
used a converter
Answer:
Step-by-step explanation:
16 ounces is equal to 1 pound so to convert ounces to pounds just multiply by 16. 814 times 16 is equal to 13,024 or thirteen thousand and twenty-four.
What is the solution to the inequality x-41 <3?
