Answer:
Step-by-step explanation:
A, use three_digite rounding arithmetic to compute 13- 6 and determine the absolute,relative ,and percentage errors.
tepeat part (b) using three – digit chopping arithmetic.
Q1. An industry analyst wants to compare the average salaries of two firms, both to each other and to the industry. Firm A's average salary is 93% of the industry average, Firm B's average salary is $58,000, and the industry average salary is 96% of Firm B's average salary. a. Determine the industry average salary. b. Determine Firm A's average salary. c. Express Firm B's average salary as a percentage of Firm A's average salary. Round the percentage to two decimals.
a.The Industry Average Salary is $55,680. b.The Firm A's Average Salary is $51,718.40 .c. Firm B's average salary is approximately 112.27% of Firm A's average salary.
a. To determine the industry average salary, we can use the information that the industry average salary is 96% of Firm B's average salary. Firm B's average salary is $58,000. Therefore, we can calculate the industry average salary as follows:
Industry Average Salary = 96% of Firm B's Average Salary
= 0.96 * $58,000
= $55,680
b. Firm A's average salary is stated as 93% of the industry average salary. To calculate Firm A's average salary, we can multiply the industry average salary by 93%:
Firm A's Average Salary = 93% of Industry Average Salary
= 0.93 * $55,680
= $51,718.40
c. To express Firm B's average salary as a percentage of Firm A's average salary, we can divide Firm B's average salary by Firm A's average salary and multiply by 100:
Percentage = (Firm B's Average Salary / Firm A's Average Salary) * 100
= ($58,000 / $51,718.40) * 100
≈ 112.27%
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Find the periodic payment R required to accumulate a sum of S dollars over t years with interest earned at the rate of r%/year compounded m times a year. (Round your answer to the nearest cent.)
S = 50,000, r = 6, t = 8, m = 2
$
The periodic payment required to accumulate a sum of $50,000 over 8 years with an interest rate of 6% compounded semiannually is approximately $79,466.27.
To find the periodic payment required to accumulate a sum of S dollars over t years with interest earned at the rate of r% per year compounded m times a year, we can use the formula for the future value of an ordinary annuity:
R = S / (((1 + r/m)^(m*t)) - 1)
Given the values:
S = 50,000 (sum to accumulate)
r = 6 (interest rate in percentage)
t = 8 (number of years)
m = 2 (compounding frequency per year)
Substituting these values into the formula, we get:
R = 50,000 / (((1 + 6/100/2)^(2*8)) - 1)
Simplifying further:
R = 50,000 / (((1 + 0.06/2)^(16)) - 1)
R = 50,000 / (((1.03)^(16)) - 1)
Using a calculator, we find that (1.03)^16 is approximately 1.62989494.
R = 50,000 / (1.62989494 - 1)
R = 50,000 / 0.62989494
R ≈ $79,466.27
Therefore, the periodic payment required to accumulate a sum of $50,000 over 8 years with an interest rate of 6% compounded semiannually is approximately $79,466.27.
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what is the range of the inverse of the given function?
f(x)=√x-2
(infinity, 2]
(2, infinity]
[-2, infinity)
[2, infinity)
The range of the inverse of the function is [2, ∝)
What is the range of the inverse of the function?From the question, we have the following parameters that can be used in our computation:
f(x) = √x - 2
Set the radicand greater tahn or equal to 0
So, we have
x - 2 ≥ 0
When evaluated, we have
x ≥ 2
This means that
[2, ∝)
Hence, the range of the inverse of the function is [2, ∝)
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Find the third, fourth, and fifth terms of the sequence defined by
a1 = 1, a2 = 3,
and
an = (−1)nan − 1 + an − 2
for
n ≥ 3.
The third term (a3) of the sequence is -8, the fourth term (a4) is 35, and the fifth term (a5) is -183. These values are obtained by applying the given formula recursively and substituting the previous terms accordingly. The calculations follow a specific pattern and are derived using the provided formula.
The sequence is defined by the following formula:
a1 = 1, a2 = 3,
and
an = (-1)nan - 1 + an - 2 for n ≥ 3.
To find the third term (a3), we substitute n = 3 into the formula:
a3 = (-1)(3)(a3 - 1) + a3 - 2.
Next, we simplify the equation:
a3 = -3(a2) + a1.
Since we know a1 = 1 and a2 = 3, we substitute these values into the equation:
a3 = -3(3) + 1.
Simplifying further:
a3 = -9 + 1.
Therefore, the third term (a3) is equal to -8.
To find the fourth term (a4), we substitute n = 4 into the formula:
a4 = (-1)(4)(a4 - 1) + a4 - 2.
Simplifying the equation:
a4 = -4(a3) + a2.
Since we know a2 = 3 and a3 = -8, we substitute these values into the equation:
a4 = -4(-8) + 3.
Simplifying further:
a4 = 32 + 3.
Therefore, the fourth term (a4) is equal to 35.
To find the fifth term (a5), we substitute n = 5 into the formula:
a5 = (-1)(5)(a5 - 1) + a5 - 2.
Simplifying the equation:
a5 = -5(a4) + a3.
Since we know a4 = 35 and a3 = -8, we substitute these values into the equation:
a5 = -5(35) + (-8).
Simplifying further:
a5 = -175 - 8.
Therefore, the fifth term (a5) is equal to -183.
In summary, the third term (a3) is -8, the fourth term (a4) is 35, and the fifth term (a5) is -183.
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Please answer this picture
your picture is not so clear can you upload again
(1.85)x + 2.55
Question 3
(3a) The equation that can be used to determine the cost, C is C = 2.55 + 1.85x.
(3b) The cost of 3 miles taxi ride is $8.1.
What is the solution of question 3?(3a) The equation that can be used to determine the cost, C is calculated by applying the following equation as follows;
C = f + nx
where
f is the fixed chargex is the number of milesn is the charge per milesC = 2.55 + 1.85x
(3b) The cost of 3 miles taxi ride is calculated as follows;
C = 2.55 + 1.85x
where;
x is the number of milesC = 2.55 + 1.85 (3)
C = $8.1
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Which TWO inferences about the interaction between Anna and Mrs. Morgan are supported by the information in paragraphs 7 and 8 (“She spoke . . . behind her”) ? Responses
Inferences about the interaction between Anna and Mrs. Morgan are supported by the information in paragraphs 7 and 8 are as follows: Mrs. Morgan is not very patient with Anna and is trying to get rid of her.Mrs. Morgan thinks Anna is lying and is not telling the truth.
Mrs. Morgan appears to be strict and unkind towards Anna, as well as being skeptical about her intentions. She is not really interested in Anna's concerns and is rather impatient and dismissive, trying to get rid of her as soon as possible. Additionally, Mrs. Morgan doesn't believe Anna, thinking she is lying and hiding something from her.
This suggests that Mrs. Morgan might not be a trustworthy person and has a negative impression of Anna without even knowing her well.
The textual evidence used to support these inferences is the description of Mrs. Morgan's tone and behavior towards Anna as well as her verbal responses, such as the abruptness of her question about the purse and her insistence on Anna leaving.
These actions suggest that Mrs. Morgan is not open to listening to Anna's story and is only interested in getting her out of the way, as well as indicating that she doesn't believe Anna's story.
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simplify 1200×1260÷800 leaving your answer in standard form
The simplified form of the expression 1200 × 1260 ÷ 800 in standard form is 1890.
To simplify the given expression, we perform the multiplication and division operations according to the order of operations (PEMDAS/BODMAS).
First, we perform the multiplication: 1200 × 1260 = 1,512,000.
Next, we perform the division: 1,512,000 ÷ 800 = 1890.
The result, 1890, is in standard form.
In standard form, a number is expressed as a product of a number between 1 and 10 (inclusive) and a power of 10. In this case, 1890 is already in the appropriate format and does not require any further modification.
Therefore, the simplified form of the expression 1200 × 1260 ÷ 800 is 1890 in standard form.
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HELP PLEASE AS SOON AS POSSIBLE WILL GIVE U BRAINLIST
Answer:
The table represents a nonlinear function because the rate is not constant.
Step-by-step explanation:
As shown in the picture below, the x side of the table has the same rate of change of +1. However, due to the fact that the y side does not have the same rate of change, +6 and +3, the table represents a non linear function. If the rate on the y side of the table were all the same, then this would be a Linear function.
2(x+5)-5 x 12 example pls
When x = 3, the expression 2x - 50 evaluates to -44.
To demonstrate an example using the expression 2(x + 5) - 5 × 12, let's simplify it step by step:
Start with the given expression.
2(x + 5) - 5 × 12
Apply the distributive property.
2x + 2(5) - 5 × 12
Simplify within parentheses and perform multiplication.
2x + 10 - 60
Combine like terms.
2x - 50
The simplified form of the expression 2(x + 5) - 5 × 12 is 2x - 50.
Let's consider an example for substituting a value for the variable x:
Suppose we want to evaluate the expression when x = 3. We substitute x = 3 into the simplified expression:
2(3) - 50
Now, perform the calculations:
6 - 50
The result is -44.
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Question
evaluate the expression 2(x+5)-5 x 12.
Answer the following questions about the function whose derivative is given below.
a. What are the critical points of f?
b. On what open intervals is f increasing or decreasing?
c. At what points, if any, does f assume local maximum or minimum values?
a. The critical points of f are x = π/2, x = 2π/3, and x = 4π/3.
b. f is increasing on the intervals (0, π/2) and (2π/3, 2π).
f is decreasing on the interval (π/2, 2π/3) and (4π/3, 2π).
c. f assumes a local maximum at x = π/2 and x = 4π/3.
f assumes a local minimum at x = 2π/3.
Understanding Derivativesa. The critical points of f occur where the derivative f'(x) equals zero or is undefined.
Note that the derivative is defined for all values of x in the given interval:
0 ≤ x ≤ 2π
Therefore, we need to find the values of x where f'(x) = 0:
f'(x) = (8 sin x - 8)(2 cos x + 1) = 0
Setting each factor equal to zero gives us:
8 sin x - 8 = 0 ==> sin x - 1 = 0 ==> sin x = 1
x = π/2 + 2πk,
where k is an integer.
2 cos x + 1 = 0 ==> cos x = -1/2
x = 2π/3 + 2πk or x = 4π/3 + 2πk,
where k is an integer.
Therefore, the critical points of f are x = π/2, 2π/3, and 4π/3.
b. To determine where f is increasing or decreasing, we can examine the sign of the derivative f'(x) within different intervals. The intervals can be defined by the critical points we found in part (a):
Interval (0 ≤ x < π/2):
In this interval, sin x and cos x are positive. Thus, both factors in f'(x) are positive, resulting in f'(x) > 0.
Therefore, f is increasing on this interval.
Interval (π/2 < x < 2π/3):
In this interval, sin x is positive, but cos x is negative. Thus, the first factor in f'(x) is positive, while the second factor is negative, resulting in f'(x) < 0.
Therefore, f is decreasing on this interval.
Interval (2π/3 < x < 4π/3):
In this interval, sin x and cos x are negative. Both factors in f'(x) are negative, resulting in f'(x) > 0.
Therefore, f is increasing on this interval.
Interval (4π/3 < x ≤ 2π):
In this interval, sin x is negative, but cos x is positive. The first factor in f'(x) is negative, while the second factor is positive, resulting in f'(x) < 0.
Therefore, f is decreasing on this interval.
c. To find the points where f assumes local maximum or minimum values, we need to consider the critical points we found in part (a) and check the behavior of the function around these points.
At x = π/2: Since f'(x) changes from positive to negative as we move from the left side of π/2 to the right side, this implies that f has a local maximum at x = π/2.
At x = 2π/3: Since f'(x) changes from negative to positive as we move from the left side of 2π/3 to the right side, this implies that f has a local minimum at x = 2π/3.
At x = 4π/3: Since f'(x) changes from positive to negative as we move from the left side of 4π/3 to the right side, this implies that f has a local maximum at x = 4π/3.
Therefore, the function f has local maximum values at x = π/2 and 4π/3, and a local minimum value at x = 2π/3.
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A video posted on social media is gaining views among female users aged 25-30. The number of views, in thousands, is modeled by f(t)=70001+35000e−0.2t where time, t, is measured in hours.
How many views, in thousands, are predicted among this demographic after 24 hours? Round your answer to the nearest whole number.
Answer:
After 24 hours 24 thousand views are predicted.
Step-by-step explanation:
To find the number of times the video is predicted to be viewed after 24 hours, we evaluate f(24) for the function f(t)=7000/1+35000e−0.2t
f(24)=7000/1+35000e^(−0.2⋅(24))
f(24)=7000/1+35000e^−4.8
f(24)≈24.21800522
After 24 hours, 24 thousand views are predicted.
The number of views that the video would get after 24 hours based on the function is 24 thousand
What is an exponential function?An exponential function is a mathematical function of the form:
f(x) =[tex]a^x[/tex]
where "a" is a positive constant called the base, and "x" is the exponent, representing the power to which the base is raised. The exponent "x" can be any real number, making exponential functions quite versatile in describing a wide range of phenomena.
We have that;
=7000/1+35000[tex]e^{-0.2t[/tex]
Where t = 24 hours
=7000/1+35000[tex]e^{-0.2 * 24[/tex]
= 24
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Drag each shape and value to the correct location on the image. Not all labels will be used.
The tower has a base that is 24 meters wide. The height is shown for the separate sections of the tower.
What is an appropriate shape to model each section of the tower? What is an approximate surface area if each of those shapes?
The appropriate shape to model each section of the tower are the cone and the cylinder.
The approximate surface area of each shape would be =
For cone = 1,041.27m²
For cylinder = 3,543.72m².
How to calculate the surface area of each shape given above?The first shape is a cone and the formula for the surface area = A = πr(r+√h²+r²)
where;
Radius = 24/2 = 12
height = 10m
Area = 1,041.27m²
For cylinder:
A = 2πrh+2πr²
where:
r = 12m
h = 35m
A = 3,543.72m²
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find the value of x and the mesasurement of angle axc
Answer:
x = 4 , ∠ AXC = 150°
Step-by-step explanation:
∠ 1 and ∠ 2 form the angle AXC , that is
∠ AXC = ∠ 1 + ∠ 2 , then
6(6x + 1) = 102 + 10x + 8
36x + 6 = 10x + 110 ( subtract 10x from both sides )
26x + 6 = 110 ( subtract 6 from both sides )
26x = 104 ( divide both sides by 26 )
x = 4
Then by substituting x = 4
∠ AXC = 6(6x + 1) = 36x + 6 = 36(4) + 6 = 144 + 6 = 150°
I need some statistics help (this question got deleted)
A researcher hypothesizes that zylex, a new antidepressant, will affect concentration. It is known that scores on a standardized concentration test is normally distributed with a μ= 50 and a σ= 12. A random sample of n=16 participants, aged 19-35, are chosen from the State of New Jersey. The sample is put on a six month dosage plan of zylex. After six months, all the participants are given a standardized concentration test. The researcher records the data and calculates a sample mean of M=56. Are the data sufficient to conclude that the drug, zylex, does have an effect on concentration?
Based on the above research scenario, please answer the following questions:
1. Name the population: ____________________________________
2. Name the sample: _______________________________
3. What is the independent variable? ________________
4. What is the dependent variable? _
_______________________
5. What is the appropriate hypothesis test? __________________
6. What two means are you comparing in this test? ____________________________
7. Please calculate the appropriate hypothesis test using all four steps:
Step 1:
Step 2:
Step 3:
Step 4: _______________________________
Write the statistical statement for your results: __________________________________
Interpret your results (relating back to the hypothesis): _____________________________________________________________________________ _____________________________________________________________________________ _____________________________________________________________________________
Is there a probability of Type I error? Yes ______ No ______ If yes, what is the probability of a Type I error? ________
Is yes, how could you have decreased that probability? __________________________________
Is there a probability of Type II error? Yes____ _ No______
If it is appropriate, please calculate effect size: Answer:________
Function f is modeled by the equation f(x)=-(x-1)^2+4 . Function g is created by moving the vertex of function f 4 units to the right and 2 units down. Which statement is true about the zeros of function g?
The statement about the zeros of function g is that they are located at x = 5 + √2 and x = 5 - √2.
When the vertex of function f is moved 4 units to the right and 2 units down, the equation of function g can be represented as g(x) = -(x-5)^2 + 2.
To determine the statement about the zeros of function g, we need to find the x-values where g(x) equals zero.
Setting g(x) = 0 and solving for x:
[tex]0 = -(x-5)^2 + 2[/tex]
Adding (x-5)^2 to both sides:
[tex](x-5)^2 = 2[/tex]
Taking the square root of both sides (considering both positive and negative roots):
x - 5 = ±√2
Adding 5 to both sides:
x = 5 ± √2
Therefore, the zeros of function g are x = 5 + √2 and x = 5 - √2.
In summary, the statement about the zeros of function g is that they are located at x = 5 + √2 and x = 5 - √2.
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c) A company is considering expanding its business. The expansion will cost 350million initially for the premises and a further sh150 million to refurbish the premises with new equipment. Cash flow projections from the project show the
following cash flows over the next six years.
Year Net cash flows
Sh 000
1 70000
2 70000
3 80000
4 100000
5 100000
6 120000
The equipment will be depreciated to a zero resale value over the same period and after the sixth year, it is expected that the new business could be sold for sh350 million.
Required:
Calculate:
i. The payback period for the project. (5 marks)
ii. The accounting rate of Return (ARR) , using the average investment method.
(5 marks)
iii. The net present value (NPV) of the project. Assume the relevant cost of capital is 12%.
(5 marks)
iv. The internal Rate of Return (IRR) of the project. (5 marks)
i. The payback period for the project is 6 years.
ii. The accounting rate of return (ARR) using the average investment method is 21.18%.
iii. The net present value (NPV) of the project is -165,143.
iv. The internal rate of return (IRR) of the project is approximately 19.61%.
i. The payback period for the project:
To calculate the payback period, we need to determine how long it takes for the cumulative net cash flows to equal or exceed the initial investment of 350 million + 150 million.
Year 1: 70,000, Year 2: 70,000, Year 3: 80,000, Year 4: 100,000, Year 5: 100,000, Year 6: 120,000.
Cumulative Cash Flow:
Year 1: 70,000
Year 2: 70,000 + 70,000 = 140,000
Year 3: 140,000 + 80,000 = 220,000
Year 4: 220,000 + 100,000 = 320,000
Year 5: 320,000 + 100,000 = 420,000
Year 6: 420,000 + 120,000 = 540,000.
The cumulative cash flows exceed the initial investment of 500 million (350 million + 150 million) in Year 6.
So, the payback period for the project is 6 years.
ii. The accounting rate of return (ARR) using the average investment method:
ARR = Average Annual Profit / Average Investment
Average Annual Profit = Sum of Net Cash Flows / Number of Years
Average Annual Profit = (70,000 + 70,000 + 80,000 + 100,000 + 100,000 + 120,000) / 6
Average Annual Profit = 540,000 / 6
Average Annual Profit = 90,000
Average Investment = (Initial Investment + Residual Value) / 2
Average Investment = (500 million + 350 million) / 2
Average Investment = 425 million.
ARR = 90,000 / 425,000 = 0.2118 or 21.18%
iii. The net present value (NPV) of the project:
To calculate NPV, we discount each cash flow to its present value using the cost of capital of 12%.
NPV = (Net Cash Flow1 / [tex](1 + r)^1)[/tex] + (Net Cash Flow2 / [tex](1 + r)^2)[/tex] + ... + (Net Cash Flow6 / (1 + r)^6) - Initial Investment.
[tex]NPV = (70,000 / (1 + 0.12)^1) + (70,000 / (1 + 0.12)^2) + (80,000 / (1 + 0.12)^3) + (100,000 / (1 + 0.12)^4) + (100,000 / (1 + 0.12)^5) + (120,000 / (1 + 0.12)^6) -[/tex] (350 million + 150 million)
Calculating each term and summing them up:
NPV = 54,017 + 48,234 + 54,497 + 62,313 + 55,631 + 60,165 - 500 million
NPV = -165,143
Therefore, the net present value (NPV) of the project is -165,143.
iv. The internal rate of return (IRR) of the project:
To calculate the IRR, we find the discount rate that makes the NPV equal to zero. Using a financial calculator or Excel, we can determine that the IRR for this project is approximately 19.61%.
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Which of the following is the prime factorization of 15?
1x15
3x5
2x2x5
5x2
Answer: The prime factorization of 15 is 3x5.
Select an expression that is equivalent to V(6x²). (6x5)
A. 32/6x7/5
B. 32/37/3
C. 62/37/3
D. 62/6x7/5
The expression that is equivalent to x√6 is option C, 62/37/3.The correct choice is C. 62/37/3.
To find an expression that is equivalent to √(6x²), we need to simplify the square root.
Using the properties of square roots, we know that the square root of a product is equal to the product of the square roots. Therefore, we can simplify the expression as follows:
√(6x²) = √6 * √(x²)
The square root of x² is simply x, and the square root of 6 cannot be simplified further. Therefore, the expression can be simplified as:
√(6x²) = x√6
Among the given options, the expression that is equivalent to x√6 is option C, 62/37/3.
Therefore, the correct choice is C. 62/37/3.
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PLEASE HELP AS SOON AS POSSIBLE
Answer:
B
Step-by-step explanation:
Yes, because for each input there is exactly one output. You can have two of the same x values but you cannot have 2 of the same y values. if you have two of the same y values, it is not a function as it doesn't pass the vertical line test.
Given rhombus QRST, find the
perimeter if QU = 3 and RU equals 4.
Q
R
T
U
X
S
The perimeter of the rhombus in this problem is given as follows:
19.8 units.
What is the perimeter of a polygon?The perimeter of a polygon is given by the sum of all the lengths of the outer edges of the figure, that is, we must find the length of all the edges of the polygon, and then add these lengths to obtain the perimeter.
The diagonal length can be obtained as follows:
QU = US = 3.RU = UT = 4.RU + UT = 7.
Applying the Pythagorean Theorem, the side length is obtained as follows:
x² + x² = 7²
2x² = 49
[tex]x = \sqrt{\frac{49}{2}}[/tex]
x = 4.95.
Then the perimeter is given as follows:
P = 4 x 4.95
P = 19.8 units.
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6 minutes 20 seconds into seconds.
Answer:
380 seconds
Step-by-step explanation:
Convert 6 minutes to seconds by multiplying 6 times 60, because there are 60 seconds per minute.
6 x 60 = 360
Now add the 20 seconds.
360 + 20 = 380
6 minutes and 20 seconds are equal to 380 seconds.
Use logarithms to solve the problem.
How long will it take $12,000 to grow to $17,000 if the investment earns interest at the rate of 4%/year compounded monthly? (Round your answer to two decimal places.)
yr
Answer:
[tex]12000 ( {1 + \frac{.04}{12}) }^{12t} = 17000[/tex]
[tex] {( \frac{301}{300}) }^{12t} = \frac{17}{12} [/tex]
[tex]12t (ln(301) - ln(300) ) = ln(17) - ln(12) [/tex]
[tex]t = \frac{ ln(17) - ln(12) }{12( ln(301) - ln(300) )} = 8.72 \: years[/tex]
Select the correct answer. If function g has the factors (x − 7) and (x + 6), what are the zeros of function g? A. -7 and 6 B. -6 and 7 C. 6 and 7 D. -7 and -6
Answer:
-6 and 7.
Step-by-step explanation:
If we have a function called g, and we know that it has two factors: (x - 7) and (x + 6), then we can find the values of x that make g equal to zero. We call those values the "zeros" of the function g. To find the zeros, we just need to solve the equation (x - 7)(x + 6) = 0. The answer is that the zeros of g are -6 and 7.
A cell phone company charges an initial price of $500 for a new phone and then $60 each month after the purchase. If C (t) is a rational function that represents the average monthly cost of owning the cell phone, what is the range of the function?
The range of the rational function is the set of all real numbers larger than 60 but less than 560, therefore;
Range; [60, 560]
What is a rational function?A rational function, f(x) is a function that can be expressed in the form f(x) = p(x)/q(x), where the functions p(x) and q(x) are polynomial functions.
The initial fee charged by the cell phone company = $500
The monthly charge after purchase = $60
The total cost of owning the cell phone = $500 + $60·t
The average monthly cost of owning a cell phone is therefore;
C(t) = (500 + 60·t)/t
The range of the function is the set of all possible values o C(t), which can be frond from the limit of the function, as follows;
[tex]\lim\limits_{x\to\infty}C(t) = \lim\limits_{x\to\infty}\frac{500 + 60\cdot t}{t} = \lim\limits_{x\to\infty}(\frac{500 }{t} + 60)[/tex] = 60
The limit of the average monthly cost indicates that the range of the function approaches $60 as t approaches infinity.
When t = 1, we get; C(1) = (500 + 60 × 1)/1 = 560
The range of the function is therefore, the set of all real numbers, larger than $60 but less than $560
The range of the function is therefore; [60, 560]
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How many gallons of a 50% antifreeze solution must be mixed with 70 gallons of 10% antifreeze to get a mixture that is 40% antifreeze?
Answer: 180 gallons needed
Step-by-step explanation:
Zykeith,
Assume x gallons of 50% antifreeze is needed
Final mixture is x + 60 gallons
Amount of antifreeze in mixture is 0.4*(x+60)
Amount of antifreeze added is .5x + .1*60 = .5x + 6
so .5x + 6 = .4(x + 60)
.5x -.4x = 24 -6
.1x = 18
x = 180
Let x be the number of gallons of the 50% antifreeze solution needed. We know that the resulting mixture will be 70 + x gallons. To get a 40% antifreeze mixture, we can set up the following equation:
[tex]{\implies 0.5x + 0.1(70) = 0.4(70 + x)}[/tex]
Simplifying the equation:
[tex]\qquad\implies 0.5x + 7 = 28 + 0.4x[/tex]
[tex]\qquad\quad\implies 0.1x = 21[/tex]
[tex]\qquad\qquad\implies \bold{x = 210}[/tex]
[tex]\therefore[/tex] We need 210 gallons of the 50% antifreeze solution to mix with 70 gallons of 10% antifreeze to get a mixture that is 40% antifreeze.
[tex]\blue{\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}[/tex]
A marble is rolling up an inclined plane. The distance (in cm) the marble has rolled after t seconds is given by s(t)=100t/t+1
a. What is the initial velocity of the marble?
b. How fast is the marble rolling at time 4 seconds?
c. At what time is the velocity 50 cm/s?
d. How fast is the marble rolling when it is 90 cm from its starting point?
e. Find and interpret lim s(t) t-> infinity and lim v(t) lim t-> infinity. Do you think this model is valid for large values of t?
Explain.
a. The initial velocity of the marble is 0 cm/s.
b. The marble is rolling at a speed of 80 cm/s at 4 seconds.
c. The velocity is 50 cm/s at approximately t = 2√2 - 1 seconds.
d. The marble is rolling at a speed of 90 cm/s when it is 90 cm from its starting point at t = 9 seconds.
e. lim s(t) as t approaches infinity is 100 cm and lim v(t) as t approaches infinity is 0 cm/s; the model may not be valid for large values of t as it assumes the marble is rolling up an inclined plane without considering other factors such as friction.
a. To find the initial velocity of the marble, we need to calculate the limit of the function s(t) as t approaches 0:
lim (t->0) s(t) = lim (t->0) (100t / (t + 1))
By substituting 0 into the expression, we get:
lim (t->0) (0 / (0 + 1)) = 0 / 1 = 0.
Therefore, the initial velocity of the marble is 0 cm/s.
b. To find the speed of the marble at time 4 seconds, we substitute t = 4 into the expression for s(t):
s(4) = 100(4) / (4 + 1) = 400 / 5 = 80 cm/s
The marble is rolling at a speed of 80 cm/s at 4 seconds.
c. To find the time at which the velocity is 50 cm/s, we set s'(t) (the derivative of s(t)) equal to 50 and solve for t:
s'(t) = 50
[tex](100 / (t + 1))^2 = 50[/tex]
100 / (t + 1) = ±√50
100 = ±√50(t + 1)
±√50(t + 1) = 100
t + 1 = 100 / ±√50
t + 1 = ±2√2
Since time cannot be negative, we take t + 1 = 2√2:
t = 2√2 - 1
The velocity is 50 cm/s at approximately t = 2√2 - 1 seconds.
d. To find the speed of the marble when it is 90 cm from its starting point, we need to solve the equation s(t) = 90 for t:
100t / (t + 1) = 90
100t = 90(t + 1)
100t = 90t + 90
10t = 90
t = 9
The marble is rolling at a speed of 90 cm/s when it is 90 cm from its starting point, which occurs at t = 9 seconds.
e. The limit of s(t) as t approaches infinity (lim s(t) as t->∞) is calculated by considering the dominant term in the numerator and denominator:
lim (t->∞) (100t / (t + 1))
≈ lim (t->∞) (100t / t)
= lim (t->∞) 100
= 100
Therefore, lim s(t) as t approaches infinity is 100 cm.
Similarly, the limit of v(t) (velocity) as t approaches infinity (lim v(t) as t->∞) can be found by taking the derivative of s(t) and evaluating the limit:
[tex]v(t) = s'(t) = 100 / (t + 1)^2[/tex]
lim (t->∞) v(t) = lim (t->∞) (100 / [tex](t + 1)^2)[/tex]
≈ lim (t->∞)[tex](100 / t^2)[/tex]
= lim (t->∞) [tex](100 / t^2)[/tex]
= 0.
The limit of v(t) as t approaches infinity is 0 cm/s.
As for the validity of the model for large values of t, it is important to note that the given model assumes that the marble is rolling up an inclined plane.
However, without further information about the nature of the inclined plane (e.g., its slope, frictional forces), it is difficult to determine the accuracy.
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Triangle JKL has vertices at J(−1, −5), K(−2, −2), and L(2, −4). Determine the translation direction and number of units of the image of triangle JKL if vertex J′ is at (−3, −5).
4 units down
4 units up
2 units to the right
2 units to the left
A triangle JKL has vertices at J(−1, −5), K(−2, −2), and L(2, −4) and J′ at (−3, −5). The translation direction is 2 units to the left. The number of units of the image of triangle JKL is 2 units to the left only.
Given that a triangle JKL has vertices at J(−1, −5), K(−2, −2), and L(2, −4) and J′ at (−3, −5). We have to determine the translation direction and the number of units of the image of triangle JKL. Let's first find the translation direction to determine the image of triangle JKL.
Seeing the position of J and J', we can determine that the translation was made in the left direction because J has moved from the point (-1,-5) to (-3,-5). Thus, the translation direction is 2 units to the left. Now, let's calculate the number of units of the image of triangle JKL.
Let's draw a rough sketch of the triangle JKL and locate its vertices J(-1,-5), K(-2,-2), and L(2,-4).To find the number of units of the image of triangle JKL, we need to find the horizontal and vertical distances between the vertices of the original triangle and its image.
We can use the horizontal distance between J and J′ as a reference to calculate the remaining distances. J has moved 2 units to the left, so the horizontal distance between J and J′ is 2. Now, let's calculate the vertical distance between J and J′. The coordinates of J and J′ are (-1,-5) and (-3,-5), respectively.
The difference between the y-coordinates of J and J′ is 0, which means that J and J′ are on the same horizontal line. Therefore, the vertical distance between J and J′ is 0. Hence, the image of the triangle JKL has moved 2 units to the left and 0 units vertically. Thus, the number of units of the image of triangle JKL is 2 units to the left only.
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Damien repairs furniture. He recorded the total fee for renting a truck and the number of miles he drove
for the last 5 times he rented a moving van for deliveries in the table below. What is the best description of the fees he is charged for renting or the cost per mile?
*
He is charged about $0.70 per mile.
He is charged $80 for renting the van and $0.30 per mile.
He is charged $45 for renting the van and $0.50 per mile.
He is charged $50 for renting the van and $0.07 per mile.
He is charged an initial rate of $55.60 for renting the van.
Answer:im not sure
Step-by-step explanation:
An individual needs a daily supplement of at least 380 units of vitamin C and 170 of vitamin E and agrees to obtain this supplement by eating two foods, I and II. Each ounce of food I contains 76 units of vitamin C and 10 units of vitamin E, while each ounce of food II contains 38 units of vitamin C and also 20 units of vitamin E. The total supplement of these two foods must be at most 22 ounces. Unfortunately, food I contains 10 units of cholesterol per ounce and food II contains 16 units of cholesterol per ounce. Find the appropriate amounts of the two food supplements so that cholesterol is minimized. Find the minimum amount of cholesterol.
The minimum amount of cholesterol is 350 units.
To minimize cholesterol intake while meeting the daily supplement requirements, we need to find the optimal amounts of foods I and II to consume. Let's denote the amount of food I as x ounces and the amount of food II as y ounces.
We have the following constraints:
- The total supplement of the two foods must be at most 22 ounces: x + y ≤ 22
- The daily vitamin C requirement is at least 380 units: 76x + 38y ≥ 380
- The daily vitamin E requirement is at least 170 units: 10x + 20y ≥ 170
To minimize cholesterol intake, we need to minimize the amount of cholesterol from both foods. Food I contains 10 units of cholesterol per ounce, so the cholesterol from food I is 10x. Food II contains 16 units of cholesterol per ounce, so the cholesterol from food II is 16y. Therefore, the total cholesterol is 10x + 16y.
Now, let's solve this problem using linear programming:
Step 1: Rewrite the constraints in terms of x and y:
x + y ≤ 22
76x + 38y ≥ 380
10x + 20y ≥ 170
Step 2: Graph the feasible region determined by these constraints.
Step 3: Identify the corner points of the feasible region.
Step 4: Substitute the corner points into the objective function 10x + 16y and find the minimum value.
After performing these steps, we find that the minimum amount of cholesterol is 350 units.
The values for x and y that correspond to the minimum cholesterol intake may vary, so it is important to verify the optimal solution by substituting the values into the constraints to ensure they satisfy all the requirements.
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