Matching each scenario with the amount of simple interest after 6 months:
$1,000 invested at 5% annual interest -> $25
$400 invested at 12% annual interest -> $24
$300 invested at 20% annual interest -> $30
$800 invested at 7% annual interest -> $28
To calculate the simple interest for each scenario after 6 months, we will use the formula:
Simple Interest = Principal * Rate * Time
$1,000 invested at 5% annual interest:
Principal = $1,000
Rate = 5% = 0.05
Time = 6 months = 0.5 years
Simple Interest = $1,000 * 0.05 * 0.5 = $25
$400 invested at 12% annual interest:
Principal = $400
Rate = 12% = 0.12
Time = 6 months = 0.5 years
Simple Interest = $400 * 0.12 * 0.5 = $24
$300 invested at 20% annual interest:
Principal = $300
Rate = 20% = 0.20
Time = 6 months = 0.5 years
Simple Interest = $300 * 0.20 * 0.5 = $30
$800 invested at 7% annual interest:
Principal = $800
Rate = 7% = 0.07
Time = 6 months = 0.5 years
Simple Interest = $800 * 0.07 * 0.5 = $28
Matching each scenario with the amount of simple interest after 6 months:
$1,000 invested at 5% annual interest -> $25
$400 invested at 12% annual interest -> $24
$300 invested at 20% annual interest -> $30
$800 invested at 7% annual interest -> $28
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Please help I’m stuck and keep getting the wrong answer
The time spent higher than 26 meters above the ground is 0.42 minutes. Answer: 0.42
A Ferris wheel is 30 meters in diameter and boarded from a platform that is 4 meters above the ground.
The six o'clock position on the Ferris wheel is level with the loading platform.
The wheel completes 1 full revolution in 2 minutes.
We have to find how many minutes of the ride are spent higher than 26 meters above the ground.
So, let's start with some given data,Consider the height of a person at the six o'clock position = 4 meters
So, the height of a person at the highest point = 4 + 15 = 19 meters (since the diameter is 30 meters, the radius will be 15 meters)
Also, the height of a person at the lowest point = 4 - 15 = -11 meters
Therefore, the Ferris wheel completes one cycle from the lowest point to the highest point and back to the lowest point.
So, the total distance travelled will be = 19 + 11 = 30 meters.
Also, we are given that the wheel completes 1 full revolution in 2 minutes.
We need to calculate the time spent higher than 26 meters above the ground.
So, the angle between the 6 o'clock position and 2 o'clock position will be equal to the angle between the 6 o'clock position and the highest point.
This angle can be calculated as follows:
Angle = Distance travelled by the Ferris wheel / Circumference of the Ferris wheel * 360 degrees
Angle = 30 / (pi * 30) * 360 degrees
Angle = 360 degrees / pi
= 114.59 degrees
So, the total angle between the 6 o'clock position and the highest point is 114.59 degrees.
Now, we need to find out how much time is spent at an angle greater than 114.59 degrees.
This can be calculated as follows:
Time = (Angle greater than 114.59 degrees / Total angle of the Ferris wheel) * Total time taken
Time = (180 - 114.59) / 360 * 2 minutes
Time = 0.42 minutes
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I need some statistics help
True or False
____ 6. If the obtained sample data (test statistic value) is inside the critical region, then we have provided support for the researcher's hypothesis
____ 7. When the Z-test statistic, obtained from the sample data, falls inside the critical region, we reject the null hypothesis
____ 8. If the obtained sample data (test statistic value) are not in the critical region, the correct statistical decision is "fail to reject the null hypothesis."
____ 9. If you fail to reject the null hypothesis, it means that the data do not provide sufficient evidence to say that the treatment has an effect: the independent variable had an effect on the dependent variable
____ 10. Whenever the statistical decision is to fail to reject the null hypothesis, there is a probability that the decision is incorrect and this probability is known as Type I error
True 6. If the obtained sample data (test statistic value) falls inside the critical region, it provides support for the researcher's hypothesis.
True 7. When the Z-test statistic, obtained from the sample data, falls inside the critical region, it indicates that the observed result is unlikely to have occurred by chance alone under the assumption of the null hypothesis. Therefore, we reject the null hypothesis and accept the alternative hypothesis.
True 8. If the obtained sample data (test statistic value) is not in the critical region, it means that the observed result is likely to have occurred by chance under the assumption of the null hypothesis. hypothesis.
True 9. Failing to reject the null hypothesis means that the data do not provide sufficient evidence to conclude that the treatment or independent variable had a significant effect on the dependent variable.
True 10. Whenever the statistical decision is to fail to reject the null hypothesis, there is a possibility of making a Type I error.
6. The critical region is determined based on the desired level of significance and contains the extreme values that would lead to rejecting the null hypothesis.
7. When the Z-test statistic, obtained from the sample data, falls inside the critical region, it indicates that the observed result is unlikely to have occurred by chance alone under the assumption of the null hypothesis. Therefore, we reject the null hypothesis and accept the alternative hypothesis.
8. In this case, we do not have sufficient evidence to reject the null hypothesis, and the correct statistical decision is to "fail to reject" the null
9. It does not necessarily mean that the treatment had no effect, but rather that the evidence in the sample is not strong enough to support such a claim.
10. Type I error refers to rejecting the null hypothesis when it is actually true. The probability of committing a Type I error is denoted by the significance level (usually denoted as alpha) and is predetermined before conducting the statistical test.
In summary, the statements are all true. The critical region plays a crucial role in hypothesis testing, and the decisions made based on the test statistic falling inside or outside the critical region determine whether the null hypothesis is rejected or failed to be rejected.
Failing to reject the null hypothesis does not provide sufficient evidence to support the researcher's hypothesis and there is always a possibility of making a Type I error when conducting hypothesis tests.
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Can I please get some help I’ve been stuck on this question for a while!
Using the radius of the Ferris wheel and the angle between the two positions, the time spent on the ride when they're 28 meters above the ground is 12 minutes
How many minutes of the ride are spent higher than 28 meters above the ground?The radius of the Ferris wheel is 30 / 2 = 15 meters.
The highest point on the Ferris wheel is 15 + 4 = 19 meters above the ground.
The time spent higher than 28 meters is the time spent between the 12 o'clock and 8 o'clock positions.
The angle between these two positions is 180 degrees.
The time spent at each position is 10 minutes / 360 degrees * 180 degrees = 6 minutes.
Therefore, the total time spent higher than 28 meters is 6 minutes * 2 = 12 minutes.
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Need answers please help if you can
The area to the right of z = 1.51 under the standard normal curve is approximately 0.0655 or 6.55% (rounded to four decimal places).
To find the area to the right of z = 1.51 under the standard normal curve, we need to calculate the probability of obtaining a z-value greater than 1.51.
The standard normal distribution has a mean of 0 and a standard deviation of 1. The area under the entire standard normal curve is equal to 1. Since we want to find the area to the right of z = 1.51, we need to calculate the area from 1.51 to positive infinity.
Using a standard normal distribution table or a statistical software, we can find that the cumulative probability associated with a z-value of 1.51 is approximately 0.9345. This means that the area to the left of z = 1.51 is 0.9345.
Since the total area under the curve is 1, we can subtract the area to the left of z = 1.51 from 1 to find the area to the right of z = 1.51:
Area to the right of z = 1.51 = 1 - 0.9345 = 0.0655
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Exercise 1.2
A person has G¢60 to spend on two goods, X and Y, whose respective prices are GH¢6 and GH¢4.
(a) Draw a budget line showing all the different combinations of the two goods that can be bought within the given budget.
(b) What happens to the original budget line if the budget is increased by 20%?
(c) What happens to the original budget line if the price of X is halved?
(a) The maximum combination of X and Y is (10, 15).
(b). The new maximum combination of X and Y is (12, 18).
(c). The new maximum combination of X and Y is (20, 15).
To draw the budget line, we need to determine the different combinations of goods X and Y that can be bought within the given budget.
The budget line represents all the possible combinations of X and Y that can be purchased with G¢60.
Let's assume the quantity of good X is represented on the x-axis and the quantity of good Y is represented on the y-axis.
The combinations, we can start with the maximum quantity of each good that can be purchased with the given budget.
Given that the price of X is GH¢6 and the price of Y is GH¢4, we can calculate:
Maximum quantity of X = G¢60 / GH¢6 = 10
Maximum quantity of Y = G¢60 / GH¢4 = 15
Now, we can plot the budget line connecting this point with the origin (0, 0).
The budget line represents all the combinations of X and Y that can be purchased with G¢60.
|
15 +---------------------
|
|
|
10 + /
| /
| /
| /
Y | /
| /
5 + /
| /
| /
| /
0 +-----------------------
0 5 10 15 X
(b) If the budget is increased by 20%, the new budget will be 120% of the original budget.
New budget = 120% of G¢60 = 1.2 × G¢60
= G¢72
To draw the new budget line, we repeat the steps from part (a) using the new budget of G¢72.
Maximum quantity of X = G¢72 / GH¢6 = 12
Maximum quantity of Y = G¢72 / GH¢4 = 18
Plotting the new budget line:
|
18 +---------------------
|
|
|
12 + /
| /
| /
| /
Y | /
| /
6 + /
| /
| /
| /
0 +-----------------------
0 6 12 18 X
(c) If the price of X is halved, the new price of X will be GH¢6 / 2 = GH¢3.
To draw the new budget line, we keep the budget and the price of Y the same as in the original scenario.
Only the price of X changes.
Maximum quantity of X = G¢60 / GH¢3 = 20
Maximum quantity of Y = G¢60 / GH¢4 = 15
Plotting the new budget line:
|
15 +---------------------
|
|
|
20 + /
| /
| /
| /
Y | /
| /
5 + /
| /
| /
| /
0 +-----------------------
0 5 10 15 X
Note that the slope of the budget line changes in both cases, reflecting the changes in the budget and the price of X.
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The graph of the function f(x) = (x-4)(x + 1) is shown
below.
Which statement about the function is true?
O The function is increasing for all real values of x
where
x < 0.
O The function is increasing for all real values of x
where
x < -1 and where x > 4.
O The function is decreasing for all real values of x
where
-1
O The function is decreasing for all real values of x
where
x < 1.5.
The statement that is true regarding the function f(x) = (x-4)(x + 1) is that the function is increasing for all real values of x where x < -1 and where x > 4. So, the option is: O The function is increasing for all real values of x where x < -1 and where x > 4.
Explanation: Given function is:f(x) = (x - 4) (x + 1). The graph of the given function is shown below: As it is visible from the graph, the function is decreasing for all real values of x where x lies between -1 and 4 (inclusive).
The turning point of the function is x = -0.5, which is the x-coordinate of the vertex of the parabola. Also, we see that the vertex is the minimum point of the parabola and the y-coordinate of the vertex is -4.25. This means that f(x) ≥ -4.25 for all x. The function is increasing for all real values of x where x < -1 and where x > 4.
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Which set does square root of 3 belong to
The square root of 3 belongs to the set of irrational numbers.
What are irrational numbers?In mathematics, an irrational number is a real number that cannot be expressed as a simple fraction or ratio of two integers.
The square root of 3 is an example of an irrational number because it cannot be expressed as a fraction or a terminating or repeating decimal.
It is an infinite, non-repeating decimal: approximately 1.73205080757.
Thus, the square root of 3 belongs to the set of irrational numbers.
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Find HCF of 78,52,23 by division Method
The highest common factor of the following numbers 78 , 52 and 23 by division method is 1
In this question The prime factorization of
78 = 2 X 3 X 13
52 = 2 X 2 X 13
= [tex]2^{2}[/tex] X 13
and 23 = 1 x 23
23 is a prime number and there it cannot have any factor other than 1
Thus the HCF of 78,52 and 23 is 1
Also , In Division method
We divide 78 by 52 and get
[tex]\frac{78}{52}[/tex] = 1 as quotient and 26 as remainder
Dividing further
[tex]\frac{52}{26}[/tex] = 2
But 23 is a prime number and cannot be divided with any number other than 1 .
HCF of the following numbers 78, 52 and 23 is 1
The highest common factor of the following numbers 78 , 52 and 23 by division method is 1 .
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I’m have three shops and I’m making $10,000 a year one shop is open six days a week the other shop is open two days a week and the last shop is open three days a week the first shop is open from 10 AM to 1800 the other shop is open from 9 AM to 1700 and the last shop is open from 11 AM to 1800 how much clientele am I getting in each shop in the in the year
Without specific information about the average number of customers, it is not possible to determine the clientele for each shop in a year accurately.
Let's calculate the clientele for each shop:
Shop 1: Open six days a week from 10 AM to 6 PM (8 hours per day).
Number of operating hours per week: 6 days * 8 hours = 48 hours
Number of operating hours per year: 48 hours/week * 52 weeks = 2,496 hours
Assuming an average of 4 clients per hour, the total clientele for Shop 1 is:
2,496 hours * 4 clients/hour = 9,984 clients per year.
Shop 2: Open two days a week from 9 AM to 5 PM (8 hours per day).
Number of operating hours per week: 2 days * 8 hours = 16 hours
Number of operating hours per year: 16 hours/week * 52 weeks = 832 hours
Assuming an average of 3 clients per hour, the total clientele for Shop 2 is:
832 hours * 3 clients/hour = 2,496 clients per year.
3. Shop 3: Open three days a week from 11 AM to 6 PM (7 hours per day).
Number of operating hours per week: 3 days * 7 hours = 21 hours
Number of operating hours per year: 21 hours/week * 52 weeks = 1,092 hours
Assuming an average of 5 clients per hour, the total clientele for Shop 3 is:
1,092 hours * 5 clients/hour = 5,460 clients per year.
Therefore, the estimated clientele for each shop over the course of a year is as follows:
- Shop 1: 9,984 clients per year
- Shop 2: 2,496 clients per year
- Shop 3: 5,460 clients per year.
It's important to note that these numbers are based on assumptions about the average number of clients per hour and the operating hours. The actual clientele may vary depending on various factors such as location, competition, marketing efforts, and customer demand.
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Solve for X, Answer options
A.77
B.9
C.35
D.11
The value of x for measure of the angle m∠RQS subtended by the arc SR at the circumference is equal to 11. Option D. 11 is correct
What is angle subtended by an arcThe angle subtended by an arc of a circle at it's center is twice the angle it substends anywhere on the circles circumference. Also the arc measure and the angle it subtends at the center of the circle are directly proportional.
arc SR = 2(m∠RQS)
Also arc SR = 190°
190°° = 2(18 + 7x)°
18 + 7x = 190/2 {divide through by 2}
18 + 7x = 95
7x = 95 - 18 {collect like terms}
7x = 77
x = 77/7 {divide through by 7}
x = 11
Therefore, the value of x for measure of the angle m∠RQS subtended by the arc SR at the circumference is equal to 11
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Evaluate x^y, when x=-2 and y=3
Answer:
- 8
Step-by-step explanation:
given
[tex]x^{y}[/tex] ( substitute x = - 2 and y = 3 )
= [tex](-2)^{3}[/tex]
= - 2 × - 2 × - 2
= 4 × - 2
= - 8
The answer is:
-8
Explanation:
Plug in the value of each variable.
[tex]\sf{x^y}[/tex]
[tex]\sf{-2^3}[/tex]
Multiply -2 by itself 3 times. Remember, the exponent tells us how many times the base should be multiplied by itself:
[tex]\sf{-8}[/tex]
Hence, the answer is -8.
I’m having a hard time with this problem
Cara used the order of operations to evaluate the expression below.
What was Cara’s first error?
Cara did not evaluate 7-13.
Cara did not evaluate (Negative 4) squared.
Cara subtracted 2 from 6 incorrectly.
Cara multiplied 2 and 4 incorrectly.
Cara's first error was not 7 - 13, leading to an incorrect result of -32.
Cara's first error was that she did not evaluate (Negative 4) squared.
The expression in question is not provided, so let's assume it is "6 - 2 × (-4)² + 7 - 13".
According to the order of operations (PEMDAS/BODMAS), we evaluate operations inside parentheses first, then exponents, followed by multiplication and division from left to right, and finally addition and subtraction from left to right.
To evaluate the expression correctly, we follow the order of operations:
Evaluate the exponent (-4)².
Since (-4) squared is positive, (-4)² = 16.
Multiply 2 and 16.
2 × 16 = 32.
Evaluate the addition and subtraction from left to right.
6 - 32 + 7 - 13.
At this point, we see that Cara did not evaluate 7 - 13.
Therefore, her first error was not evaluating the subtraction correctly.
Continuing the evaluation:
6 - 32 + 7 - 13 = -32.
So, Cara's first error was not evaluating 7 - 13, leading to an incorrect result of -32.
It's important to carefully follow the order of operations to ensure accurate evaluations of mathematical expressions.
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Use the function f(x) to answer the questions:
fx) = 2x2-3x-5
Part A: What are the x-intercepts of the graph of f(x)? Show your work. (2 points)
Part B: Is the vertex of the graph of f(x) going to be a maximum or a minimum? What are the coordinates of the vertex? Justify your answers and show your work. (3 points)
Part C: What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part A and Part B to draw the graph. (5 points)
***15 points to make it easy for me to type!!***
Part A: The x-intercepts of the graph of f(x) are x = 2.5 and x = -1.
Part B: The vertex of the graph of f(x) is a minimum, and its coordinates are (3/4, -67/8).
Part C: Steps to graph f(x):
Plot the x-intercepts: (2.5, 0) and (-1, 0).
Plot the vertex: (3/4, -67/8).
Determine the shape (upward-opening parabola).
Plot additional points using the equation.
Connect the points to create a smooth curve.
Using the answers from Parts A and B, we have the key points needed to accurately graph f(x) and justify the shape of the curve.
Part A: To find the x-intercepts of the graph of f(x), we set f(x) equal to zero and solve for x.
Given f(x) = 2x^2 - 3x - 5, we set f(x) = 0:
2x^2 - 3x - 5 = 0
To solve this quadratic equation, we can either factor it or use the quadratic formula. Let's use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
For our equation, a = 2, b = -3, and c = -5. Substituting these values into the quadratic formula:
x = (-(-3) ± √((-3)^2 - 4(2)(-5))) / (2(2))
x = (3 ± √(9 + 40)) / 4
x = (3 ± √49) / 4
x = (3 ± 7) / 4
This gives us two possible x-intercepts:
x1 = (3 + 7) / 4 = 10 / 4 = 2.5
x2 = (3 - 7) / 4 = -4 / 4 = -1
Therefore, the x-intercepts of the graph of f(x) are x = 2.5 and x = -1.
Part B: To determine whether the vertex of the graph of f(x) is a maximum or a minimum, we can look at the coefficient of the x^2 term. If the coefficient is positive, the parabola opens upward, and the vertex is a minimum. If the coefficient is negative, the parabola opens downward, and the vertex is a maximum.
In our equation, the coefficient of the x^2 term is 2, which is positive. Therefore, the parabola opens upward, and the vertex is a minimum.
To find the coordinates of the vertex, we can use the formula:
x = -b / (2a)
Substituting the values from our equation:
x = -(-3) / (2(2))
x = 3 / 4
To find the y-coordinate, we substitute this x-value back into the equation:
f(x) = 2(3/4)^2 - 3(3/4) - 5
f(x) = 18/16 - 9/4 - 5
f(x) = 9/8 - 36/8 - 40/8
f(x) = -67/8
Therefore, the coordinates of the vertex are (3/4, -67/8).
Part C: The steps to graph f(x) can be summarized as follows:
Plot the x-intercepts obtained in Part A: x = 2.5 and x = -1. These points lie on the x-axis.
Plot the coordinates of the vertex obtained in Part B: (3/4, -67/8). This point represents the minimum point of the parabola.
Determine the shape of the graph. Since the coefficient of the x^2 term is positive, the parabola opens upward.
Determine additional points on the graph. We can choose other x-values and calculate the corresponding y-values using the equation f(x) = 2x^2 - 3x - 5.
Connect the plotted points with a smooth curve, following the upward opening shape of the parabola.
By following these steps, we can graph f(x) accurately, incorporating the x-intercepts and the vertex obtained in Parts A and B, respectively.
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Please help me solve this
The quadrant that the angle of 1166º terminates is given as follows:
First quadrant.
How to obtain the quadrant of the angle?The angle in this problem is given as follows:
1166º.
The remainder of the division operation of 1166º by 360º is given as follows:
86.
This means that the equivalent angle to the angle of 1166º is of 86º, which is on the first quadrant, as 0 < 86 < 90º.
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Find the value of b if = 2.
The value of b is 7/4
How to determine the valueTo determine the value, we have that the index forms are written as;
[tex](2/5)^7^-^b[/tex] × [tex](5/2)^2^+^4^b[/tex] = [tex](2/5)^ 3^b^-^5[/tex]
Now, take the inverse of the exponent, we have;
[tex](2/5)^7^-^b[/tex] × [tex](2/5)^-^2^-^4^b[/tex] = [tex](2/5)^ 3^b^-^5[/tex]
take the exponent of the value, we have;
7 - b + (-2 - 4b) = 3b - 5
expand the bracket
7 - b - 2 - 4b= 3b - 5
collect the like terms, we have;
-8b = -5 - 7 - 2
-8b = -14
b = 7/4
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The complete question:
find the value of b if (2/5)ki power 7-b multiple by (5/2)ki power 2+4b equal to (2/5) ki power 3b-5
I WILL MARK BRAINLIEST PLS HELP ME
calculate the area and perimeter
The area and perimeter of the composite figure are:
Area = 360 mm²
Perimeter = 134 mm
How to find the area and Perimeter of the composite figure?The formula for the area of a rectangle is:
Area = Length * Width
Formula for area of parallelogram is:
Area = Base * perpendicular height
Thus:
Area of composite figure = (30 * 5) + (21 * 8) + (14 * 3)
Area of composite figure = 360 mm²
Perimeter = 30 + 5 + 14 + 10 + 8 + 21 + 8 + 14 + 19 + 5
Perimeter = 134 mm
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Jane wants to win a prize by drawing 2 red marbles from a pot that contains 7 marbles
There are 21 possible ways that Jane can win a prize by drawing two red marbles from the pot.
Jane wants to win a prize by drawing two red marbles from a pot containing seven marbles. She can do this in several ways. However, we will solve the problem by using the combination formula.The combination formula gives us the number of possible ways to choose r items from a group of n items without considering the order.
The formula is given by:[tex]C(n,r) = n! / r!(n-r)![/tex]where n is the total number of items and r is the number of items to be selected.To solve Jane's problem, we will find the number of possible ways to choose two red marbles from seven marbles. The number of red marbles in the pot is not given;
we assume that all marbles in the pot are of different colors.Since Jane wants to draw two red marbles, we will consider only the red marbles. We have to find the number of combinations of two red marbles from the total number of red marbles in the pot.
Therefore, n = total number of red marbles in the pot and r = 2 (the number of red marbles to be selected).Thus, using the combination formula;[tex]C(n,r) = n! / r!(n-r)!C(n,2) = n! / 2!(n-2)![/tex]We have n = total number of red marbles in the pot = [tex]7C(n,2) = 7! / 2!(7-2)!C(n,2) = 7! / 2!5!C(n,2) = (7 x 6 x 5!)/ (2!5!)C(n,2) = 21[/tex].
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Find the value of L that Will Maximize the profit Q=L²e^0.01L
The minimum profit occurs at L = 0, where Q = 0.
To find the value of L that maximizes the profit Q = L²[tex]e^{(0.01L)[/tex].
We need to differentiate Q with respect to L and find the critical points where the derivative equals zero.
Then we can determine whether each critical point is a maximum or a minimum by examining the second derivative.
Testing for critical points:Q = L²[tex]e^{(0.01L)[/tex]
Q' = [tex]2Le^{(0.01L)[/tex] + [tex]0.01 L^2e^{(0.01L)[/tex]
= 0(2L + 0.01L²) [tex]e^{(0.01L)[/tex]
= 0L (critical point) or 200 [tex]e^{(0.01L)[/tex]
= 0 (extraneous, ignore)
2L + 0.01L² = 0L(2 + 0.01L) = 0L = 0 or L = -200 (extraneous, ignore)
The only critical point is at L = 0.
Testing for maximum or minimum:Q'' = [tex]2e^{(0.01L)[/tex] + 0.02Le^(0.01L) + 0.0001L²[tex]e^{(0.01L)Q''(0)[/tex]
= [tex]2e^{(0)[/tex] = 2Since Q''(0) > 0,
The critical point at L = 0 is a minimum.
Therefore, there is no value of L that maximizes the profit.
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The values of L that will maximize the profit are 0 and -200
Finding the value of L that will maximize the profitFrom the question, we have the following parameters that can be used in our computation:
[tex]Q = L\²e^{0.01L[/tex]
Differentiate the function
So, we have
[tex]Q' = \frac{L \cdot (L + 200) \cdot e^{0.01L}}{100}[/tex]
Set the equation to 0
[tex]\frac{L \cdot (L + 200) \cdot e^{0.01L}}{100} = 0[/tex]
Cross multiply
[tex]L \cdot (L + 200) \cdot e^{0.01L} =0[/tex]
When expanded, we have
L = 0, L + 200 = 0 and [tex]e^{0.01L} =0[/tex]
When solved for L, we have
L = 0 and L = -200
Hence, the values of L are 0 and -200
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If x = 2, y = 3 and z = -5, find the value of square root of x + y squared + z squared
The value of square root of x + y squared + z squared is 30
How to solve algebra?x = 2, y = 3 and z = -5
[tex]( \sqrt{x + y} )^{2} + z ^{2} [/tex]
substitute the value of x, y and z
[tex] = ( \sqrt{2 + 3} )^{2} + - 5 ^{2} [/tex]
simplify the square root and square
[tex] = (2 + 3) + 25[/tex]
[tex] = 5 + 25[/tex]
[tex] = 30[/tex]
Ultimately, x + y squared + z squared is 30
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Recall the equation for a circle with center (h,k) and radius r. At what point in the first quadrant does the line with equation y=x+4 intersect the circle with radius 3 and center (0, 4)?
Step-by-step explanation:
the circle equation is
r² = (x - h)² + (y - k)²
in our case
3² = (x - 0)² + (y - 4)²
9 = x² + y² - 8y + 16
x² + y² - 8y + 7 = 0
this intersects with
y = x + 4
that means we have
x² + (x + 4)² - 8(x + 4) + 7 = 0
x² + x² + 8x + 16 - 8x - 32 + 7 = 0
2x² - 9 = 0
2x² = 9
x² = 9/2
x = 3/sqrt(2) = 2.121320344...
y = 3/sqrt(2) + 4 = 6.121320344...
the point is
(3/sqrt(2), 3/sqrt(2) + 4) = (2.121320344..., 6.121320344...)
¿Cuál es la línea recta que representa la siguiente ecuación?
y
=
2
The graph of the line is on the image at the end.
Which line represents the equation?Here we have the following equation:
y = 2
This is a line that has the y-value consantly equal to 2, so all the points in this line are of the form:
(x, 2).
So this will be an horizontal line that covers all the values of x, but where the value of y is always 2, the graph of this line can be seen in the image at the end.
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the value of the 2 in 204.75 is how many times the value of the 2 in 103.52
Answer: 10,000 times.
Step-by-step explanation:
In 204.75, the 2 is in the hundreds place. The value of the 2 is 200.
In 103.52, the two is in the hundredths place. The value of the 2 is 0.02.
Now, we can simply divide 200 by 0.02. 200/0.02 = 10,000.
Another way you could do this is to move the 0.02 in 103.52 a number of places to the left to match the place where the 200 of 204.7 is. We would move it four times to the left to get it to the hundreds place, and then we identify the power of 10 that has 4 zeros for the 4 places we moved: [tex]10^{4\\[/tex]
[tex]10^4 = 10,000.[/tex]
Hope this helps!
Select the correct answer. In which direction must the graph of f(x) = x be shifted to produce the graph oSelect the correct answer.
In which direction must the graph of f(x) = x be shifted to produce the graph of g(x) = f(x) - 4?
A.
left and down
B.
right and up
C.
down
D.
upf g(x) = f(x) - 4? A. left and down B. right and up C. down D. up
Answer:
A. down
Step-by-step explanation:
The parent graph is
f(x)=x
If this graph is transformed to obtain
g(x)=f(x)−4
The subtracttion means the graph will shift downward vertically
The graph of g(x) is obtained by shifting f(x) down by 4 unit.
Therefore the direction is down.
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Question 4
Use the given conditions to write an equation for the line in the indicated form.
Passing through (2, -4) and parallel to the line whose equation is y = -8x + 3;
slope-intercept form?
A)y=-8x + 12
B)y=-8x-12
C)y=-1/8x-3/2
D)y=8x-16
Answer:
A) y = -8x + 12
Step-by-step explanation:
Given equation: y = -8x + 3
Parallel lines have the same slope, so the slope of our desired line is also -8.
Point-slope form equation: y - y1 = m(x - x1)
Substitute the coordinates of the given point (2, -4): y - (-4) = -8(x - 2)
Simplify: y + 4 = -8x + 16
Rewrite in slope-intercept form: y = -8x + 12
Final equation: y = -8x + 12
f(x)
10
6
2.
146 +3₂
4.
-19-
g(x)
246810
What is the equation of the translated function, g(x), if
f(x)=x²?
O g(x) = (x + 5)² + 2
O g(x) = (x + 2)² +5
O g(x) = (x - 2)² +5
O g(x) = (x - 5)² + 2
Answer:
93666 .83766,739+836!83726298
Type < or > to make this statement true -a___-b
The comparisons that are true are 11. -5 < 0 12. 9 > -8 14. 55 > -75 15. -32 < -24 16. 89 > 73 17. -58 < -51 19. 17 < 23 20. 18 > -36 and that is not true are 13. -7 = -7 (not true) 18. -32 > 4 (not true)
To make each statement true, write < or >. We need to compare two values for each statement to determine whether it is true or false.
To indicate that the first value is less than the second value, write <.
Alternatively, to indicate that the first value is greater than the second value, write >.
Below are the comparisons: 11. -5 < 0 12. 9 > -8 13. -7 > -7 14. 55 > -75 15. -32 < -24 16. 89 > 73 17. -58 < -51 18. -32 > 4 19. 17 > 23 20. 18 > -36
To determine the direction of inequality, we need to compare the values.
We used inequality signs such as > (greater than) or < (less than) to indicate which value is larger or smaller than the other.
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The correct question would be as
Write > or < to make each statement true.
11. -5 0
12. 9 -8
13. -7 7
14. 55 -75
15. -32 -24
16. 89 73
17. -58 -51
18. -32 4
19. 17 23
20. 18 -36
Find the value of 35÷c when c= 7.
Answer:
5
Step-by-step explanation:
when c = 7,
substitute 7, into 35÷c
35 ÷ 7 = 5
How much has the value of y changed between the points (-8, 4) and (8,-4)?
A. 1
units
B. 2 units
C. 8 units
D. 16 units
Answer:
The answer is C.
Step-by-step explanation:
Given, two points are (-8, 4) and (8, -4).
We have to find the change in the value of y.
We know that
Change in the value of y = 4 - (-4) = 8 units
Therefore, the change in the value of y is 8 units.
I didn't feel like writing an explanation myself so I found this one on Cuemath
Select the correct answer from each drop down menu
Central angle ∠C and circumscribed angle ∠S intersect the same arc, so the angles are supplementary. Central angle ∠C and inscribed angle ∠R intersect the same arc, so m∠R is half the measure of central angle ∠C.
What makes the angles supplementary?Central angles are angles that have their vertex at the center of the circle. Circumscribed angles are angles that are formed by two tangents to a circle that intersect at a point outside the circle. Inscribed angles are angles that are formed by two chords in a circle that intersect at a point inside the circle.
The measures of central angles and circumscribed angles are always supplementary, which means that their measures add up to 180 degrees. Inscribed angles, on the other hand, are always half the measure of the central angle that intersects the same arc.
In the diagram, central angle ∠C and circumscribed angle ∠S intersect the same arc, so they are supplementary. Central angle ∠C and inscribed angle ∠R also intersect the same arc, so m∠R is half the measure of central angle ∠C.
Therefore, the correct answers are supplementary and half.
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