The equation of the curve is y = x2 + 4.
To solve this problem, we need to use the fact that the curve y = ax2 + bx + c passes through the point (2, 12) and is tangent to the line yat at the origin.
First, we know that the tangent to the curve at the origin is the line y = 0x + c = c. Since the curve is tangent to this line at the origin, we know that the derivative of the curve at x = 0 is equal to 0.
Taking the derivative of y = ax2 + bx + c, we get y' = 2ax + b. Setting x = 0, we get y' = b. Since y' = 0 at x = 0, we know that b = 0.
So now we have y = ax2 + c. We can use the fact that the curve passes through the point (2, 12) to solve for a and c.
Substituting x = 2 and y = 12 into the equation y = ax2 + c, we get 12 = 4a + c.
Since we know that a = 4, 6, or 1, we can substitute each of these values into the equation and solve for c.
When a = 4, we get 12 = 4(4)(2) + c, which simplifies to 12 = 32 + c. Solving for c, we get c = -20.
When a = 6, we get 12 = 4(6)(2) + c, which simplifies to 12 = 48 + c. Solving for c, we get c = -36.
When a = 1, we get 12 = 4(1)(2) + c, which simplifies to 12 = 8 + c. Solving for c, we get c = 4.
So the values of a, b, and c are:
a = 1
b = 0
c = 4
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or
Hazel bought 4 souvenirs during 2 days of vacation. How many days will Hazel have to spend on vacation before she will have bought a total of 8 souvenirs? Assume the relationship is directly proportional.
Suppose the length of voicemails (in
seconds) is normally distributed with a mean
of 40 seconds and standard deviation of 10
seconds. Find the probability that a given
voicemail is between 20 and 50 seconds.
10
20
30
40
50
60
P = Г?1%
Hint: Use the 68 - 95 - 99.7 rule
70
Enter
The probability that a given voicemail is between 20 and 50 seconds is 0.8185, or 81.85%.
How to find the the probability that a given voicemail is between 20 and 50 seconds.To find the probability that a voicemail is between 20 and 50 seconds, we need to standardize the values and use a standard normal distribution table.
First, we find the z-scores for 20 seconds and 50 seconds:
z1 = (20 - 40) / 10 = -2
z2 = (50 - 40) / 10 = 1
Using a standard normal distribution table, we can find the area to the left of each z-score:
Area to the left of z1 = 0.0228
Area to the left of z2 = 0.8413
To find the probability between 20 and 50 seconds, we subtract the area to the left of z1 from the area to the left of z2:
P(20 < x < 50) = P(-2 < z < 1)
= 0.8413 - 0.0228
= 0.8185
Therefore, the probability that a given voicemail is between 20 and 50 seconds is 0.8185, or 81.85%.
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Express (x+5)^2(x+5)
2
as a trinomial in standard form
x² + 10x + 25 is the expression of (x+5)^2 in trinomial in standard form
What is the trinomial ?A trinomial is a polynomial that consists of three terms. It is a type of algebraic expression that contains three algebraic terms separated by either plus or minus signs.
For example, the expression 2x^2 + 5x - 3 is a trinomial because it has three terms: 2x^2, 5x, and -3. Similarly, the expression 4a^3 - 7a^2 + 2a is also a trinomial because it has three terms: 4a^3, -7a^2, and 2a.
We have to expand this
x² + 2(x)(5) + 5²
= x² + 10x + 25
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Mr Mensah starts a job with an
annual salary of € 6400. 00 which increases by
€ 240. 00 every year After working for eight years
Mr Mensah is promoted to a new post with an
annual salary of ¢ 9500. 00 which increases by
€ 360. 00 every year Calculate
i) Mr. Mensah's Salary in the fifteenth year of service
ii) Mensah's total earnings at the end the fifteenth
year of service
Mr. Mensah's total earnings at the end of the fifteenth year of service is €1920.00 + €2520.00 = €4440.00.
To calculate Mr. Mensah's salary in the fifteenth year of service, we need to determine the pattern of salary increase over the years.
We know that Mr. Mensah's salary starts at €6400.00 and increases by €240.00 every year for the first eight years. After that, he is promoted to a new post with an annual salary of €9500.00, which increases by €360.00 every year.
Let's break it down:
For the first eight years, the salary increases by €240.00 per year:
After 1 year: €6400.00 + €240.00 = €6640.00
After 2 years: €6640.00 + €240.00 = €6880.00
...
After 8 years: €6400.00 + (8 * €240.00) = €6400.00 + €1920.00 = €8320.00
From the ninth year onwards, the salary increases by €360.00 per year:
After 9 years: €9500.00 + €360.00 = €9860.00
After 10 years: €9860.00 + €360.00 = €10220.00
...
After 15 years: €9500.00 + (7 * €360.00) = €9500.00 + €2520.00 = €12020.00
Therefore, Mr. Mensah's salary in the fifteenth year of service is €12,020.00.
To calculate Mr. Mensah's total earnings at the end of the fifteenth year of service, we need to sum up his salaries from year 1 to year 15.
For the first eight years, the total earnings can be calculated as follows:
Total earnings = (Salary in year 1 + Salary in year 2 + ... + Salary in year 8) = 8 * €240.00 = €1920.00
From the ninth year onwards, the total earnings can be calculated as follows:
Total earnings = (Salary in year 9 + Salary in year 10 + ... + Salary in year 15) = 7 * €360.00 = €2520.00
Therefore, Mr. Mensah's total earnings at the end of the fifteenth year of service is €1920.00 + €2520.00 = €4440.00.
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Will give brainliest if right
aabc ~ def. what sequence of transformations will move aabc onto adef?
d. a dilation by scale factor of 2, centered at the origin, followed by a reflection over the y-axis
AABC is transformed onto ADEF by a dilation by a scale factor of 2, centered at the origin, followed by a reflection over the y-axis.
The sequence of transformations that will move AABC onto ADEF is a dilation by a scale factor of 2, centered at the origin, followed by a reflection over the y-axis.
Firstly, dilation is a transformation that changes the size of an object but not its shape.
The dilation factor is multiplied by each coordinate, so when the dilation is centered at the origin, the new coordinates will be twice the original coordinates.
Therefore, AABC will be enlarged to A'BC', and DEF will be enlarged to D'E'F, both with double the size.
Then, reflection is a transformation that flips an object over a line of reflection. In this case, the line of reflection is the y-axis.
When we reflect A'BC' over the y-axis, we get A''B''C'', and when we reflect D'E'F over the y-axis, we get D''E''F''.
Therefore, AABC is transformed onto ADEF by a dilation by a scale factor of 2, centered at the origin, followed by a reflection over the y-axis.
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the function g(x) = x2 is transformed to obtain function h: h(x) = g(x) + 1. Which statement describes how the graph of h is different from the graph of g? A. The graph of h is the graph of g horizontally shifted right 1 unit. B. The graph of h is the graph of g vertically shifted up 1 unit. C. The graph of h is the graph of g vertically shifted down 1 unit. D. The graph of h is the graph of g horizontally shifted left 1 unit.
The statement that describes how the graph of h is different from the graph of g is: B. The graph of h is the graph of g vertically shifted up 1 unit.
Which statement describes how the graph of h is different from the graph of g?The function h(x) = g(x) + 1 is obtained by adding a constant (1) to the output of the function g(x) = x^2. This means that the graph of h(x) will be the same as the graph of g(x), except that every point on the graph of h(x) will be shifted vertically upward by 1 unit.
Therefore, the correct statement is: B. The graph of h is the graph of g vertically shifted up 1 unit.
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The potters want to buy a small cottage costing $118,000 with annual insurance and taxes of $710. 00 and $2800. 0. They have saved $14,000. 00 for a down payment, and they can get a 5%, 15 year mortgage from a bank. They are qualified for a home loan as long as the total monthly payment does not exceed $1000. 0. Are they qualified?
The potters are qualified for the home loan as their total monthly payment is $831.02, which is less than $1000.00.
The total cost of the cottage along with the annual insurance and taxes is $118,000 + $710 + $2800 = $121,510.
The down payment made by the potters is $14,000. Therefore, the amount to be financed through a mortgage is $121,510 - $14,000 = $107,510.
Using the formula for the monthly payment of a mortgage, which is given by:
M = P [ i(1 + i)^n ] / [ (1 + i)^n - 1]
where P is the principal (amount to be financed), i is the monthly interest rate, and n is the total number of monthly payments.
For a 5%, 15-year mortgage, the monthly interest rate is 0.05/12 = 0.0041667, and the total number of monthly payments is 15 x 12 = 180.
Plugging in the values, we get:
M = $107,510 [ 0.0041667 (1 + 0.0041667)^180 ] / [ (1 + 0.0041667)^180 - 1 ]
M = $831.02
Therefore, the total monthly payment for the mortgage and the annual insurance and taxes is $831.02 + $59.17 + $233.33 = $1123.52, which is more than the maximum allowed payment of $1000.00. Hence, the potters are qualified for the home loan.
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A researcher asked 933 people what their favourite type of TV programme was: news, documentary, soap or sports. They could only choose one answer. As such, the researcher had the number of people who chose each category of programme. How should she analyse these data?
a. T-test
b. One-way analysis of variance
c. Chi-square test
d. Regression
The researcher should analyze the data obtained from 933 people who were asked about their favorite type of TV program, with the condition that they could only choose one answer. The appropriate statistical test to analyze these data is c. Chi-square test.
The Chi-square test is used for analyzing categorical data, which is the case in this scenario where individuals have to choose among news, documentary, soap, or sports. The test will help the researcher determine if there is a significant difference in preferences for TV program types among the respondents.
The specific techniques and statistical tests used may vary depending on the goals of the research and the nature of the data.
Therefore option c is correct.
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Sergey is solving 5x2 + 20x – 7 = 0. Which steps could he use to solve the quadratic equation by completing the square? Select three options
The quadratic equation where the squares had been completed is:
(x + 2)² = 27/5
How to complete squares?Remember the perfect square trinomial:
(a + b)² = a² + 2ab + b²
now we have the quadratic equation:
5x² + 20x - 7 = 0
If we divide it all by 5, we will get.
x² + 4x - 7/5 = 0
Now we can rewrite this as:
(x² + 2*2*x ) - 7/5 = 0
Now we need to add 2² in both sides, we will get:
(x² + 2*2x + 2²) - 7/5 = 2²
(x + 2)² = 4 + 7/5
(x + 2)² = 27/5
There the square is completed.
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Write a polynomial function of least degree with integral coefficients that has the given zeros.
-5, -3-2i
Answer:
[tex]f(x)=x^3+11x^2+43x+65[/tex]
Step-by-step explanation:
If a polynomial function has a complex zero, then the conjugate of that complex zero is also a zero of the polynomial.
So, if (-3 - 2i) is a zero of the polynomial, then its conjugate (-3 + 2i) is also a zero of the polynomial.
Therefore, the three zeros of the polynomial function are:
-5(-3 - 2i)(-3 + 2i)The zero of a polynomial f(x) is the x-value when f(x) = 0.
According to the factor theorem, if f(a) = 0 then (x - a) is a factor of the polynomial f(x).
Therefore, the polynomial function in factored form is:
[tex]\begin{aligned}f(x) &= (x - (-5))(x-(-3-2i))(x-(-3+2i))\\&= (x +5)(x+3+2i)(x+3-2i)\end{aligned}[/tex]
Expand the brackets to write the polynomial in standard form.
[tex]\begin{aligned}f(x) &=(x +5)(x+3+2i)(x+3-2i)\\&=(x+5)(x^2+3x-2xi+3x+9-6i+2ix+6i-4i^2)\\&=(x+5)(x^2+6x+9-4i^2)\\&=(x+5)(x^2+6x+9-4(-1))\\&=(x+5)(x^2+6x+9+4)\\&=(x+5)(x^2+6x+13)\\&=x^3+6x^2+13x+5x^2+30x+65\\&=x^3+11x^2+43x+65\end{aligned}[/tex]
Therefore, the polynomial function of least degree with integral coefficients that has the given zeros -5 and (-3 - 2i) is:
[tex]f(x)=x^3+11x^2+43x+65[/tex]
f(x)=x3+11x²+43x+65
Pls help me with this-
The formula for the function h(x) is given as follows:
h(x) = g(x + 5).
What is a translation?A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.
The four translation rules for functions are defined as follows:
Translation left a units: f(x + a).Translation right a units: f(x - a).Translation up a units: f(x) + a.Translation down a units: f(x) - a.The function h(x) is a translation left 5 units of the function g(x), hence it is defined as follows:
h(x) = g(x + 5).
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4. Select all the inequalities that have the same graph as x <4 a
(A.) x < 2
Bx+6 <10
C.) 5x < 20
Dx-2>2
x<8
7<4
Option (B) x + 6 < 10 and (C) 5x < 20 have same graph.
From the given set of inequalities;
(A) x < 2 represents x ∈ (-∞, 2)
(B) X + 6 < 10 ⇒ x < 4
represents x ∈ (-∞, 4)
(C) 5x < 20 ⇒ x < 4
represents x ∈ (-∞, 4)
(D) x - 2 > 2 ⇒ x > 4
represents x ∈ (4, ∞)
(E) x < 4 represents x ∈ (-∞, 8)
We can see that inequalities (B) and (C) both represents x ∈ (-∞, 4)
Thus, the graph of both inequalities are same.
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There's a roughly linear relationship between the length of someone's
femur (the long leg-bone in your thigh) and their expected height.
Within a certain population, this relationship can be expressed using
the formula h = 2. 46f + 60. 6, where h represents the expected
height in centimeters and f represents the length of the femur in
centimeters. What is the meaning of the f-value when h 128?
This means that in the population represented by the formula, someone with a femur length of 27.4 centimeters would be expected to have a height of 128 centimeters
When h is 128, we can use the formula h = 2.46f + 60.6 to solve for the corresponding value of f.
128 = 2.46f + 60.6
Subtracting 60.6 from both sides:
67.4 = 2.46f
Dividing both sides by 2.46:
f ≈ 27.4
Therefore, when h is 128, the f-value (length of the femur) is approximately 27.4 centimeters. This means that in the population represented by the formula, someone with a femur length of 27.4 centimeters would be expected to have a height of 128 centimeters.
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A gym subscription runs several promotions. Customers can choose from the following offers.
Option A: 25% off an annual subscription of $308. 00
Option B: pay $29 per month
How much will a customer save by purchasing the annual subscription over paying per month?
a
$348
b
$231
c
$79
d
$117
A customer will save $117 by purchasing the annual subscription over paying per month. So the (d) $117 is the right answer.
To determine how much a customer will save by purchasing the annual subscription over paying per month, follow these steps:
Calculate the discounted annual subscription cost:
Option A: 25% off an annual subscription of $308.00
Discount = 25% of $308 = 0.25 * $308 = $77
Discounted Annual Subscription = $308 - $77 = $231
Calculate the total cost of the monthly subscription for one year:
Option B: Pay $29 per month
Total Monthly Subscription Cost = $29 * 12 months = $348
Calculate the savings:
Savings = Total Monthly Subscription Cost - Discounted Annual Subscription
Savings = $348 - $231 = $117
So, a customer will save $117 by purchasing the annual subscription over paying per month. Your answer is d. $117.
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A mathematics professor gives two different tests to two sections of his college algebra courses. The first class has a mean of 56 with a standard deviation of 9 while the second class has a mean of 75 with a standard deviation of 15. A student from the first class scores a 62 on the test while a student from the second class scores an 83 on the test. Compare the scores. Which student performs better
The student from the first class performs better when comparing their scores using z-scores.
To compare the students' performances, we will calculate their z-scores, which show how many standard deviations away their scores are from the mean of their respective classes.
For the student from the first class:
z-score = (Score - Mean) / Standard Deviation
z-score = (62 - 56) / 9
z-score ≈ 0.67
For the student from the second class:
z-score = (83 - 75) / 15
z-score ≈ 0.53
The student from the first class has a higher z-score (0.67) compared to the student from the second class (0.53). This means the student from the first class performed better relative to their classmates.
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Khloe is a teacher and takes home 90 papers to grade over the weekend. She can
grade at â rate of 10 papers per hour. Write a recursive sequence to represent how
many papers Khloe has remaining to grade after working for n hours.
The recursive sequence representing how many papers Khloe has remaining to grade after working for n hours is given by a_n = a_{n-1} - 10, where a_0 = 90.
Let a_n denote the number of papers Khloe has remaining to grade after n hours of work. After the first hour of work, she will have 90 - 10 = 80 papers remaining. Therefore, we have a_1 = 90 - 10 = 80.
After the second hour of work, she will have a_2 = a_1 - 10 = 80 - 10 = 70 papers remaining. Similarly, after the third hour of work, she will have a_3 = a_2 - 10 = 70 - 10 = 60 papers remaining.
In general, after n hours of work, Khloe will have a_n = a_{n-1} - 10 papers remaining to grade. This is a recursive sequence, where the value of a_n depends on the value of a_{n-1}. The initial value of a_0 is given as 90, since she starts with 90 papers to grade. Therefore, the recursive sequence is given by a_n = a_{n-1} - 10, where a_0 = 90.
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The owner of a sports complex wants to carpet a hallway connecting two buildings. The carpet costs $2. 50 per square foot. How much does it cost to carpet the hallway?
If the area of the hallway is 250 square feet, it would cost $625 to carpet the hallway with $2.50 per square foot carpet.
To find the cost of carpeting the hallway, we need to know the area of the hallway first. Let's assume that the length of the hallway is 50 feet and the width is 5 feet.
The area of the hallway = length x width
= 50 feet x 5 feet
= 250 square feet
Now that we know we can find the cost of carpeting it.
Cost of carpeting = area x cost per square foot
= 250 square feet x $2.50 per square foot
= $625
Therefore, it would cost $625 to carpet the hallway with $2.50 per square foot carpet.
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write any ten ordered pairs in which the first elements is country the second element is its capital
Answer:
Sure, here are ten ordered pairs with the country as the first element and the capital as the second element:
1. (France, Paris)
2. (United States, Washington D.C.)
3. (China, Beijing)
4. (Mexico, Mexico City)
5. (Brazil, Brasília)
6. (Japan, Tokyo)
7. (Canada, Ottawa)
8. (Germany, Berlin)
9. (Australia, Canberra)
10. (India, New Delhi)
Solve the following Exact Inexact Differential Equation. If it is inexact, then
solve it by finding the Integrating Factor.
(3xy + y^2) dx + (x^2 + xy) dy = 0
The general solution to the differential equation is, |3x^4/(y(x+y))|x + |x^3| ln|y| + |x^3| ln|x+y| + h(x) = C.
The partial derivative of (3xy + y^2) with respect to y is 6xy + 2y, and the partial derivative of (x^2 + xy) with respect to x is 2x + y. Since these are not equal, the differential equation is not exact.
To make it exact, we need to find an integrating factor μ(x, y) such that μ(x, y)(3xy + y^2) dx + μ(x, y)(x^2 + xy) dy = 0 is exact. We can find μ(x, y) by using the formula:
μ(x, y) = e^(∫(∂M/∂y - ∂N/∂x)/N dx)
where M = 3xy + y^2 and N = x^2 + xy. We have:
(∂M/∂y - ∂N/∂x)/N = (6xy + 2y - 2x - y)/(x^2 + xy) = (6xy - x - y)/(x^2 + xy)
We can now find the integrating factor μ(x, y) by integrating this expression with respect to x:
μ(x, y) = e^(∫(6xy - x - y)/(x^2 + xy) dx) = e^(3ln|x| - ln|y| - ln|x+y| + C) = e^(ln|x^3/(y(x+y))| + C) = |x^3/(y(x+y))|e^C
where C is the constant of integration.
Now we multiply the original differential equation by the integrating factor μ(x, y) to obtain:
|3x^4/(y(x+y))| dx + |x^3/(y(x+y))| dy = 0
This is now an exact differential equation, and we can find its solution by integrating with respect to x or y. Integrating with respect to x, we get:
|3x^4/(y(x+y))|x + g(y) = C
where g(y) is the constant of integration. To find g(y), we integrate the coefficient of dy:
g(y) = ∫|x^3/(y(x+y))| dy = |x^3| ln|y| + |x^3| ln|x+y| + h(x)
where h(x) is another constant of integration. Substituting g(y) back into the solution, we have:
|3x^4/(y(x+y))|x + |x^3| ln|y| + |x^3| ln|x+y| + h(x) = C
This is the general solution to the differential equation.
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Cleo bought a computer for
$
1
,
495
. What is it worth after depreciating for
3
years at a rate of
16
%
per year?
The worth of the computer after depreciating for 3 years is $749.77, under the condition that a rate of 16% per year was applied.
Then the derived formula for evaluating depreciation
Depreciation = (Asset Cost – Residual Value) / Life-Time Production × Units Produced
Then,
Asset Cost = $1,495
Residual Value = 0 (assuming the computer has no resale value after 3 years)
Life-Time Production = 3 years
Units Produced = 1
Hence, the depreciation rate
[tex]Depreciation Rate = (1 - (Residual Value / Asset Cost)) ^{ (1 / Life-Time Production) - 1}[/tex]
[tex]Depreciation Rate = (1 - (0 / 1495))^{(1/3-1)}[/tex]
Depreciation Rate = 16%
Now to evaluate the value of the computer after three years of depreciation at a rate of 16% per year, we can apply the derived formula
Value of Asset After Depreciation = Asset Cost × (1 - Depreciation Rate) ^ Life-Time Production
Value of Asset After Depreciation = $1,495 × (1 - 0.16)³
Value of Asset After Depreciation = $749.77
Hence, the computer is worth $749.77 after three years of depreciation at a rate of 16% per year.
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The complete question is
Cleo bought a computer for $1,495. What is it worth after depreciating for 3 years at a rate of 16% per year?
What is the particular solution to the differential equation dy/dx = 2x/y with the initial condition y (5) = 4?
The initial condition y(5) = 4 tells us that we should use the positive square root.
To find the particular solution to the given differential equation, we can use separation of variables. First, we rearrange the equation to get:
y dy = 2x dx
Next, we integrate both sides with respect to their respective variables:
∫y dy = ∫2x dx
This gives us:
y^2/2 = x^2 + C
where C is the constant of integration. To find the value of C, we use the initial condition y(5) = 4:
4^2/2 = 5^2 + C
8 = 25 + C
C = -17
So the particular solution to the differential equation dy/dx = 2x/y with the initial condition y(5) = 4 is:
y^2/2 = x^2 - 17
or
y = ±√(2x^2 - 34)
Note that there are two possible solutions, one with a positive square root and one with a negative square root, but the initial condition y(5) = 4 tells us that we should use the positive square root.
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on a standardized test, phyllis scored 84, exactly one standard deviation above the mean. if the standard deviation for the test is 6, what is the mean score for the test?
The mean score for the test Phyllis scored 84, exactly one standard deviation above the mean is 78.
One of the statistics used in the generalised Cochran-Mantel-Haenszel tests is the mean score statistic. When the answer levels (columns) are assessed using an ordinal scale, it is applicable.
The chi-square distribution with (R-1) degrees of freedom, where R is the number of treatment groups, serves as the asymptotic distribution of the mean score statistic if the two variables are independent of one another in all strata (rows).
If the mean scores of the response differ between the treatment groups in at least one stratum, the mean score statistic tends to have larger values. The term "nonparametric ANOVA statistic" also applies to this statistic.
x = 84
[tex]\sigma=6[/tex]
since, x is 1 standard deviation above mean so,
[tex]z=\frac{x-\mu}{\sigma}[/tex]
[tex]1=\frac{84-\mu}{6}\\ \\[/tex]
[tex]\mu[/tex] = 84-6
[tex]\mu[/tex] =78.
therefore, mean = 78.
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Adding cookie dough ice cream and hot fudge to the menu next month will cost 42 dollars if your total sales remain the same would you make a profit if so how much 
If total sales remain the same and assuming a $5 profit margin per order, adding cookie dough ice cream and hot fudge to the menu could result in a profit of $58 if 20 or more orders are sold.
To determine if adding cookie dough ice cream and hot fudge to the menu will result in a profit, we need to consider the cost and potential revenue. If the cost of adding these items is $42, we need to calculate how many orders of cookie dough ice cream with hot fudge we need to sell to cover that cost and make a profit.
Assuming the profit margin on each order of cookie dough ice cream with hot fudge is $5 (for example), we would need to sell at least 9 orders (rounding up from 8.4) to cover the $42 cost and break even. If we sell more than 9 orders, we would make a profit.
Assuming we sell 20 orders of cookie dough ice cream with hot fudge, the total revenue generated would be $100 ($5 profit per order x 20 orders). Subtracting the $42 cost of adding these items, the net profit would be $58.
Therefore, if total sales remain the same and assuming a $5 profit margin per order, adding cookie dough ice cream and hot fudge to the menu could result in a profit of $58 if 20 or more orders are sold.
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given g(x)=-4x-4, find g(-2)
Answer:
g(-2) = 4.
Step-by-step explanation:
To find g(-2), we simply need to substitute -2 for x in the function g(x) and simplify:
g(-2) = -4(-2) - 4
g(-2) = 8 - 4
g(-2) = 4
Therefore, g(-2) = 4.
If it costs 0. 15 per square inch for the wood then what is the cost for design A and Design B
To calculate the cost for Design A and Design B, we need to know the size of each design in square inches. Once we have that information, we can multiply the size of each design by the cost per square inch of wood to determine the total cost.
Let's say Design A is 10 inches by 10 inches, which is a total of 100 square inches. To calculate the cost for Design A, we would multiply 100 by 0.15, which gives us a total cost of $15.
Similarly, let's say Design B is 8 inches by 12 inches, which is a total of 96 square inches. To calculate the cost for Design B, we would multiply 96 by 0.15, which gives us a total cost of $14.40.
Therefore, the cost for Design A is $15 and the cost for Design B is $14.40.
In summary, the cost of a wooden design can be calculated by multiplying the size of the design in square inches by the cost per square inch of wood. In this case, we used a cost of 0.15 per square inch and calculated the cost for Design A and Design B. It is important to know the size of the design before calculating the cost.
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Let's use Priya as an example again. The number of hairs per square cm varies from person to person, but Priya has approximately 150 hairs per square cm.
She measures the diameter of her scalp from front to back and ear to ear and she finds that it is about 28cm in both directions. Her head is round so that makes her think that she could use the area of a circle to estimate how many total hairs she has on her head.
a. What is the area of Priya's scalp?≈
≈
cm2
b. About how many strands of hair are on Priya's head? ≈
≈
strands of hair
a. The area of Priya's scalp is ≈ [tex]615.75 cm^2[/tex]. b. Priya has approximately 92,363 strands of hair on her head.
a. The area of Priya's scalp can be estimated using the formula for the area of a circle, which is A = π[tex]r^2[/tex] ,where r is the radius (half the diameter) of the circle. Since Priya's diameter is 28cm, her radius would be 14cm. So, the area of her scalp would be:
A = π[tex](14cm)^2[/tex]
A ≈[tex]615.75 cm^2[/tex]
b. To estimate how many strands of hair Priya has on her head, we can multiply the number of hairs per square cm by the total area of her scalp. So, if Priya has approximately 150 hairs per square cm and her scalp has an estimated area of 615.75 cm^2, then:
Total number of hairs ≈ [tex]150 hairs/cm^2 * 615.75 cm^2[/tex]
Total number of hairs ≈ 92,362.5 hairs
Therefore, we can estimate that Priya has approximately 92,363 strands of hair on her head.
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determine if each of the numbers below is a solution to the inequality 3x-2<2-2x
The solution set of the inequality 3x-2 < 2-2x is:
(4/5, ∞)
Which numbers are solutions for the inequality?To find this we need to isolate the variable in the inequality.
Here we have:
3x - 2 < 2 - 2x
add 2x in both sides and add 2 in both sides, then we will get:
3x + 2x < 2 + 2
5x < 4
Now we can divide both sides by 5 to get:
x < 4/5
That is the inequality solved.
Then the solution set of the inequality is:
(4/5, ∞)
The set of all real numbers larger than 4/5.
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Identify the transformations of the graph of f(x) = x^2 that result in the graph of g shown. What rule, in vertex form, can you write for g(x)?
A vertical translation (5 units up) is applied on quadratic function f(x) = x².
What kind of rigid transformation can be used to obtain an image of the quadratic function?
In this problem we find the representation of quadratic function and its image on Cartesian plane. The image is the consequence of using a vertical translation, whose definition is now introduced:
g(x) = f(x) + k
Where k is the y-coordinate of the quadratic function.
If we know that f(x) = x² and k = 5, then the image of the function is:
g(x) = x² + 5
The image is the result of a vertical translation (5 units up).
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Pls help quick
which theorem can you use to show that the quadrilateral on the tile floor is a parallelogram
To show that the quadrilateral on the tile floor is a parallelogram, you can use the opposite sides theorem, opposite angles theorem, consecutive angles theorem, and Diagonal bisector theorem.
1. Opposite sides theorem: If both pairs of opposite sides of the quadrilateral are congruent (equal in length), then it is a parallelogram.
2. Opposite angles theorem: If both pairs of opposite angles of the quadrilateral are congruent (equal in measure), then it is a parallelogram.
3. Consecutive angles theorem: If the consecutive angles of the quadrilateral are supplementary (their sum is 180 degrees), then it is a parallelogram.
4. Diagonal bisector theorem: If the diagonals of the quadrilateral bisect each other (divide each other into two equal parts), then it is a parallelogram.
Choose the most appropriate theorem based on the given information and apply it to prove that the quadrilateral is a parallelogram.
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The figure below is made up of 1 centimeters cubes, What is the volume of the figure?
Answer:
15 cubic centimeters
Step-by-step explanation:
The figure is in the shape of a rectangular and the formula for volume of such a rectangular box is
V=lwh, where V is the volume, l is the length, and h is the height.
Since each cube is 1 cm, we see that the length is 5 cm (1 cm cube * 5 = 5 cm), the width is 3 cm (1 cm cube * 3 = 3 cm), and the height is 1 cm (1 cm cube * 1 = 1 cm).
Thus, we the product of our length, width, and height will give us the volume of the figure:
V = 5 * 3 * 1
V = 15 cubic centimeters