Answer:Let the cost of an orange and that of a mango during the first market day be Ksh. x and Ksh. y respectively.
From the first market day:
30x + 12y = 936
From the second market day:
15(1.2x) + 20(3/4y) = 780
Simplifying the second equation:
18x + 15y = 780
(ii) Using matrix to find the cost of an orange and that of a mango in the first market day:
Rewriting the equations in matrix form:
|30 12| |x| |936|
|18 15| x |y| = |780|
Multiplying the matrices:
|30 12| |x| |936|
|18 15| x |y| = |780|
|30x + 12y| |936|
|18x + 15y| = |780|
Using matrix inversion:
| x | |15 -12| |936 12|
| y | = | -18 30| x |780 15|
|x| |270 12| |936 12|
| | = |-360 30| x |780 15|
|y|
Simplifying the matrix multiplication:
|x| |1194| |12|
| | = | 930| x |15|
|y|
Therefore, the cost of an orange in the first market day was Ksh. 39 and the cost of a mango in the first market day was Ksh. 63.
(iii) Calculation of the total amount of money realized for the sales:
On the second market day, Fatuma bought 15 oranges and 20 mangoes.
Cost of 15 oranges = 15(1.2x) = 18x
Cost of 20 mangoes = 20(3/4y) = 15y
Total cost of fruits bought on the second market day = 18x + 15y = 18(39) + 15(63) = Ksh. 1629
Profit earned on 15 oranges at 10% = 1.1(1.2x)(15) - (1.2x)(15) = 0.18x(15) = 2.7x
Profit earned on 20 mangoes at 15% = 1.15(3/4y)(20) - (3/4y)(20) = 0.15y(20) = 3y
Total profit earned = 2.7x + 3y
Total amount of money realized for the sales = Total cost + Total profit
= Ksh. 1629 + 2.7x + 3y.
Step-by-step explanation:
Please hurry I need it ASAP
Answer:
x = 18
Step-by-step explanation:
We Know
(10x - 4) + (x - 14) must equal 180°
Find the value of x.
Let's solve
10x - 4 + x - 14 = 180
11x - 18 = 180
11x = 198
x = 18
So, x = 18 is the answer.
Which expressions are equivalent to 2(2x + 4y + x − 2y)? (1 point)
Answer:
6x + 4y
Step-by-step explanation:
2(2x + 4y + x − 2y)
= 4x + 8y + 2x - 4y
= 6x + 4y
FY varies directly as X & Y equals eight when X equals eight what is the value of X when Y equals four?
The calculated value of X when Y equals four is four
Calculating the value of X when Y equals four?From the question, we have the following parameters that can be used in our computation:
Y varies directly as X &Y equals eight when X equals eightUsing the above as a guide, we have the following:
y = kx
Where
k = constant of variation
When Y equals eight when X equals eight, we have
8k = 8
So, we have
k = 1
This means that the equation is
y = 1 * x
Evaluate
y = x
When the value of y is 4, we have
4 = x
This gives
x = 4
Hence, the value of X when Y equals four is four
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If FY varies directly as X, we can write the equation as:
FY = kX
where k is the constant of variation. To find the value of k, we can use the fact that "Y equals eight when X equals eight":
8 = k(8)
Simplifying this equation, we get:
k = 1
Now we can use this value of k to find the value of X when Y equals four:
4 = 1X
Solving for X, we find that
X = 4
Therefore, when Y equals four, X equals 4 as well...
Lucas is fishing in a pond where there are exactly 3 walleye and 1 catfish. he has an equal chance of catching
each fish. if lucas catches a catfish, the game warden will make him stop fishing because catfish are currently
quite endangered in this pond.
when lucas catches a walleye, he keeps it so that he can feed his entire family. if he can catch all 3 walleye in
the pond, he can feed his family which is worth a total of $100 to him. if he can catch 2 walleye, he will only be
able to feed himself, which is worth $20 to him. any other outcome is worth $0 to lucas.
what is the expected value of lucas going fishing?
The expected value of Lucas going fishing is $26.56. This is calculated by multiplying the probability of each outcome (catching 0, 1, 2, or 3 walleye) by its corresponding payoff ($0, $0, $20, or $100) and adding the results.
To calculate the expected value of Lucas going fishing, we need to consider all possible outcomes and their respective probabilities
Lucas catches all 3 walleye Probability = (3/4) * (2/3) * (1/2) = 1/4 (since he has to catch each walleye in succession, with decreasing probabilities)
Value = $100
Lucas catches 2 walleye Probability = (3/4) * (2/3) * (1/2) * (1/4) * 3 = 9/32 (he has to catch 2 walleye in any order and then not catch the catfish in the remaining attempt)
Value = $20
Lucas catches 1 walleye Probability = (3/4) * (2/3) * (1/2) * (1/4) * (1/4) * 3 = 3/32 (he has to catch 1 walleye and then not catch the other two walleye and the catfish)
Value = $0
Lucas catches no walleye and no catfish Probability = (1/4) = 1/4 (since he has to catch the catfish)
Value = $0
Therefore, the expected value of Lucas going fishing is
E(X) = (1/4)$100 + (9/32)$20 + (3/32)$0 + (1/4)$0 = $26.56
So, on average, Lucas can expect to make $26.56 each time he goes fishing.
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What is the equation for fahrenheit to celcius
Answer:
I believe it is
F = (9/5 x °C) + 32
Which quadratic function represents the graph below?
the answer options are
y=3/14(x-5)(x+10)
y=3/14(x+5)(x-10)
y=1/3(x-5)(x+10)
y=1/3(x+5)(x-10)
y=3/14(x-5)(+10)
Step-by-step explanation:
.........................
A real estate agent wants to estimate the mean selling price of two-bedroom homes in a particulararea. She wants to estimate the mean selling price to within $10,000 with an 89. 9% level of confidence. The standard deviation of selling prices is unknown but the agent estimates that the highest selling price is$1,000,000 and the lowest is $50,000. How many homes should be sampled
The agent should sample at least 109 two-bedroom homes to estimate the mean selling price within $10,000 with an 89.9% level of confidence.
To estimate the required sample size, we need to use the formula:
n = (Zα/2 * σ / E)²
where Zα/2 = the critical value of the standard normal distribution for the given confidence level. For an 89.9% level of confidence, the value of Zα/2 is 1.645.
σ = the population standard deviation (unknown)
E = the margin of error (maximum distance between the sample mean and the true population mean)
To estimate σ, we can use the range method, which assumes that the population standard deviation is approximately equal to the range divided by 4:
σ ≈ (highest value - lowest value) / 4
In this case, σ ≈ ($1,000,000 - $50,000) / 4 = $237,500
Substituting the values into the formula,
n = (Zα/2 * σ / E)²
n = (1.645 * $237,500 / $10,000)²
n ≈ 109
Therefore, the agent should sample at least 109 two-bedroom homes to estimate the mean selling price within $10,000 with an 89.9% level of confidence.
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1 point) Compute the double integral (either in the order of integration given or with the order reversed). /2 V1 + cas"" () cos(a) drdy sin (1) Integral =
The value of the double integral is zero.
The order of integration is dr dy, which means we first integrate with respect to r and then with respect to y.
Thus, we can write the integral as:
[tex]\int^0_{2\pi} \int^0_{1 + cos(a)}[/tex] r sin(θ) dr dy
Here, we have used the given limits of integration for r and y. Now, we integrate with respect to r first, treating y as a constant.
∫r sin(θ) dr = -cos(θ)r
We can substitute the limits of integration for r, which gives:
-cos(θ)(1+cos(a)) + cos(θ)(0)
Simplifying this expression, we get:
-cos(θ)(1+cos(a))
Now, we integrate this expression with respect to y, using the limits 0 to 2π for θ.
[tex]\int ^0_{2\pi}[/tex] -cos(θ)(1+cos(a)) dy
We can integrate this expression by treating cos(a) as a constant and using the formula for integrating cosine functions:
Integral of cos(x) dx = sin(x) + C
Thus, we have:
(1+cos(a)) Integral from 0 to 2π of cos(θ) dy
= - (1+cos(a)) [sin(2π) - sin(0)]
= 0
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Uncle Richard's phone number contains 8 different digits. The sum of the numbers formed by the first 5 digits and the number formed by the last 3 digits is 68427. The sum of the number formed by the first 3 digits and the number formed by the last 5 digits is 36090. What is Uncle Richard's phone number?
The Uncle Richard's phone number contains 8 different digits which are given by 67935421.
The term "numerical digit" refers to a single sign that is used to represent numbers in a positional numeral system, either by itself (as in "2") or in conjunction with other symbols (as in "25"). The term "digit" refers to the ten digits (Latin digiti meaning fingers) of the hands, which are the decimal (old Latin adjective decem meaning ten) digits. These digits correspond to the ten symbols of the conventional base 10 numeral system.
Let the number with eight different digits be a, b, c, d, e, f, g, h
So sum of the numbers formed by the first 5 digits and the number formed by the last 3 digits is 68427
a b c d e d e f g h
+ f g h + a b c
6 8 4 2 7 3 6 0 9 0
So, a = 6 and d = 3
Hence by calculating in such way we get,
b = 7, c = 9 , e = 6 , f = 4 , g = 9 , h = 1
Therefore, number with eight different digits be a, b, c, d, e, f, g, h
67935421
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GAMES- two friends are playing a game with a 20 sided dye that has all of the letters of the alphabet except Q U V X Y and Z. What is the probabilty that the dye will land on a vowel?
The probability of the die landing on a vowel is 1 in 5, or 20%.
In this game, the 20-sided die has the letters A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, R, S, T, and W. To calculate the probability of the die landing on a vowel, we need to identify the vowels present on the die and then determine the probability.
The vowels on this die are A, E, I, and O. There are 4 vowels out of the 20 possible outcomes, so the probability of landing on a vowel can be calculated by dividing the number of successful outcomes (vowels) by the total number of possible outcomes (20 sides).
Probability = (Number of Vowels) / (Total Sides)
Probability = 4 / 20
Now, simplify the fraction:
Probability = 1 / 5
The probability of the die landing on a vowel is 1 in 5, or 20%.
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Which is a correct example of deductive reasoning?
A. Seven straight tosses of a number cube landed on 1. The next toss will land on 1.
B. Every bicyclist Lynn has seen was on a red bike. The next bicyclist Lynn sees will be on a red bike.
C. All rectangles have four sides. All squares are rectangles. Therefore, all squares have four sides.
D.
All tennis players are athletic. Erica is athletic. Therefore, Erica is a tennis player
C. All rectangles have four sides. All squares are rectangles. Therefore, all squares have four sides.
This is an example of deductive reasoning because it starts with a general statement (all rectangles have four sides) and then applies a specific example (squares are rectangles) to come to a logical conclusion (all squares have four sides).
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Aser these 5 math questions for branliest and points
The base of a solid is the region in the first quadrant between the graph of y=x2
and the x
-axis for 0≤x≤1
. For the solid, each cross section perpendicular to the x
-axis is a quarter circle with the corresponding circle’s center on the x
-axis and one radius in the xy
-plane. What is the volume of the solid?
A. pi/20
B. 1/5
C. pi/12
D. 1/3
The volume of the solid is π/20,
option (A). is correct.
What is volume?Volume is described as a measure of three-dimensional space. It is often quantified numerically using SI derived units or by various imperial or US customary units.
we have that the limits of integration for x are 0 and 1, because the solid lies in the region between x = 0 and x = 1.
Hence, we can say that the volume of the solid is given by:
V = ∫[0,1] (1/4)πx^4 dx
V = (1/4)π ∫[0,1] x^4 dx
V = (1/4)π (1/5) [x^5]0^1
V = (1/20)π
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The weekly marginal revenue from the sale of x pairs of tennis shoes is given 200 R'(x)=32 -0.01x+ R(O)=0 X + 1 Find the revenue function. Find the revenue from the sale of 3,000 pairs of shoes
Revenue from the sale of 3,000 pairs of shoes is $51,000.
How to calculate revenue from the sale?To find the revenue function, we need to integrate the marginal revenue function R'(x) with respect to x.
R(x) = ∫R'(x) dx
R(x) = ∫(32 - 0.01x) dx
R(x) = 32x - 0.005x² + C
To find the constant C, we use the fact that R(0) = 0.
0 = 32(0) - 0.005(0)² + C
C = 0
Therefore, the revenue function is:
R(x) = 32x - 0.005x²
To find the revenue from the sale of 3,000 pairs of shoes, we simply plug in x = 3,000 into the revenue function:
R(3,000) = 32(3,000) - 0.005(3,000)²
R(3,000) = 96,000 - 45,000
R(3,000) = 51,000
Therefore, the revenue from the sale of 3,000 pairs of shoes is $51,000.
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Identify the point (x1, y1) from the equation: y 8 = 3(x – 2)
The point (2, 8) is the point (x1, y1) identified from the equation y - 8 = 3(x - 2
Identify (x1, y1) the equation: y 8 = 3(x – 2)The equation y - 8 = 3(x - 2) is in point-slope form, which is y - y1 = m(x - x1), where (x1, y1) is the point on the line and m is the slope of the line. In this case, the slope of the line is 3, which means that for every increase of 1 in the x-coordinate, the y-coordinate increases by 3.Comparing the given equation with the point-slope form, we can see that x1 = 2 and y1 = 8. Therefore, the point (2, 8) is the point identified from the equation.Learn more about equation
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Find the area of the surface generated when the given curve is revolved about the x-axis. y = 4x + 2 on [0,4] s S = (Type an exact answer in terms of T.)
The area of the surface generated by revolving the curve y=4x+2 on [0,4] about the x-axis is S =4π/3 (3√17 + 2) .
To find the surface area generated by revolving the curve y=4x+2 about the x-axis on [0,4], we need to use the formula:
S = 2π∫[a,b] y ds
where ds = \sqrt(1 + (dy/dx)²) dx is the arc length element.
First, we find dy/dx: dy/dx = 4
Then, we can find the arc length element: ds = \sqrt(1 + (dy/dx)²) dx = \sqrt(1 + 16) dx = \sqrt(17) dx
The integral for surface area becomes: S = 2π∫[0,4] y ds = 2π∫[0,4] (4x+2)√17 dx
Evaluating this integral, we get:
S = 2π(2/3)√17 [ (4x+2)^(3/2) ]_0^4
S = 4π/3 (3√17 + 2)
Therefore, the area of the surface generated is 4π/3 (3√17 + 2) square units.
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What is the shape of the height and weight distribution? A. The height and weight distribution exhibit a negative and a positive skew, respectively. B. Both the height and weight distribution exhibit a positive skew. C. Both the height and weight distribution exhibit a negative skew. D. Both the height and weight distribution are symmetric about the mean. E. The height and weight distribution exhibit a positive and a negative skew, respectively
D. Both the height and weight distribution are symmetric about the mean.
What is the shape of the height and weight distribution? If a distribution is symmetric about the mean, it means that the values are evenly distributed on either side of the mean, resulting in a bell-shaped curve. The height and weight of individuals in a population tend to follow this type of distribution, with the majority of individuals clustering around the mean height and weight values. This is known as a normal distribution, which is a type of symmetric distribution. Therefore, option D is the correct answer. Options A, B, C, and E are not correct because they indicate skewness in the distribution, which is not typically observed in height and weight data.Learn more about distribution,
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Larry is 32 years old and starting an IRA (individual retirement account). He is going to invest $250 at the beginning of each month. The account is expected to earn 3. 5% interest, compounded monthly. How much money, rounded to the nearest dollar, will Larry have in his IRA if he wants to retire at age 58? (
Larry could have about $139,827 in his IRA if he invests $250 at the beginning of each month and earns 3.5% interest compounded monthly, rounded to the nearest dollar
Assuming that Larry is starting his IRA at the beginning of his 32nd year, he could have 26 years until he retires at age 58.
Because he is investing $250 at the beginning of each month, that means he will be making an investment a complete of $3,000 consistent with year.
We are able to use the formula for compound interest to calculate the future value of his IRA:
[tex]FV = P * ((1 + r/n)^{(n*t)} - 1) / (r/n)[/tex]
Where FV is the future value, P is the primary (the quantity he invests every month), r is the interest charge (3.5%), n is the wide variety of times the interest is compounded consistent with year (12 for monthly), and t is the quantity of years.
Plugging within the numbers, we get:
[tex]FV = 250 * ((1 + 0.0.5/12)^{(12*26)} - 1) / (0.0.5/12) \approx $139,827[/tex]
Therefore, Larry could have about $139,827 in his IRA.
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Match the formulas for volume and calculate the volumes of the sphere, cylinder, and cone shown below. Each shape has a radius of 2.5 and the cylinder and cone have a height of 4.
options for each drop down box [choose]:
Sphere - volume measure
Sphere - volume formula
Cone - volume formula
Cone - volume measure
Cylinder - volume measure
Cylinder - volume formula
None of these options
Answer:
The formula for the volume of a cone is ⅓ r2h cubic units, where r is the radius of the circular base and h is the height of the cone.The volume of any sphere is 2/3rd of the volume of any cylinder with equivalent radius and height equal to the diameter.The formula for the volume of a sphere is 4⁄3πr³. For a cylinder, the formula is πr²h. A cone is ⅓ the volume of a cylinder, or 1⁄3πr²h
Step-by-step explanation:
The formula for volume is: Volume = length x width x height
Answer:
Step-by-step explanation:
Volume of a sphere: 4/3 π r³
4/3 (3.14) (2.5)³ =
4/3 (3.14) (15.625) = 65.42 units³
Volume of a cylinder = π r² h
(3.14) (2.5)² (4)
(3.14) (6.25)(4) = 78.5 units²
Volume of a Cone = 1/3 π r² h
(1/3)(3.14)(2.5)²(4) =
(1/3)(3.14)(6.25)(4) = 26.17 units²
How to simplify radical expressions with variables?.
To simplify radical expressions with variables, identify perfect square factors, simplify the radical by taking out the largest possible integer factor that is a perfect square, and then multiply by the remaining factor outside the radical. Repeat the process until no more simplification is possible.
To simplify radical expressions with variables, follow these steps
Factor the expression under the radical sign into its prime factors.
Identify any perfect squares within the factors.
Rewrite the expression with the perfect squares outside the radical sign and the remaining factors inside.
Simplify any remaining radicals if possible.
Combine any like terms if necessary.
For example, to simplify the expression √(12x²y), you would first factor 12x²y into 2 * 2 * 3 * x * x * y. Then, you would identify the perfect square of x² and rewrite the expression as 2x√(3y). Finally, you could simplify further if possible, but in this case, the expression is already in its simplest form.
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The mean of a sample is a. always equal to the mean of the population. b. always smaller than the mean of the population c. computed by summing the data values and dividing the sum by (n - 1) d. computed by summing all the data values and dividing the sum by the number of items
The mean of a sample is computed by summing all the data values and dividing the sum by the number of items in the sample. Thus, the correct answer is d.
Option a is incorrect because the mean of a sample is not always equal to the mean of the population, unless the sample is a complete representation of the population (which is often not the case).
Option b is incorrect because the mean of a sample can be greater than, equal to, or smaller than the mean of the population, depending on the sampling method and the characteristics of the population.
Option c is incorrect because the sample mean is computed by summing the data values and dividing the sum by the number of items in the sample minus one only if the sample is taken from a normally distributed population and the standard deviation of the population is unknown. Otherwise, the sample mean is computed by dividing the sum of the data values by the number of items in the sample.
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A 10 ft ladder is used to scale 9 ft wall. at what angle of elevation must the ladder be situated in order to reach the top of the wall?
ps. please include an illustration/drawing of the problem. thank you!
The ladder must be situated at an angle of approximately 63.43° to reach the top of the 9 ft wall.
How to find the angle of elevation at which the ladder must be situated?
Certainly, here's an illustration of the problem:
|\
| \
| \ 9 ft
| \
ladder | \
(10 ft)|_____\
wall
To find the angle of elevation at which the ladder must be situated, we can use the trigonometric function of sine. Let θ be the angle of elevation. Then:
sin θ = opposite / hypotenuse
In this case, the opposite side is the height of the wall (9 ft), and the hypotenuse is the length of the ladder (10 ft). So:
sin θ = 9/10
Using a calculator or a trigonometric table, we can find the angle whose sine is 9/10:
θ ≈ 63.43°
Therefore, the ladder must be situated at an angle of approximately 63.43° to reach the top of the 9 ft wall.
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Practice writing and solving equations to solve number problems.
assessment started: undefined.
item 1
question 1
ansley’s age is 5 years younger than 3 times her cousin’s age. ansley is 31 years old.
let c represent ansley’s cousin’s age. what expression, using c, represents ansley’s age?
enter your response in the box.
Ansley's cousin is 12 years old, and Ansley's age can be found by plugging in 12 for Cousin's age.
How can we know that Ansley's age is 5 years less than 3 times her cousin's age?The problem tells us that Ansley's age is 5 years less than 3 times her cousin's age. We can write this as an equation:
Ansley's age = 3 × Cousin's age - 5
We also know that Ansley is 31 years old. So we can substitute 31 for Ansley's age in the equation:
31 = 3 × Cousin's age - 5
Now we solve for Cousin's age. First, we add 5 to both sides of the equation:
31 + 5 = 3 × Cousin's age
Simplifying:
36 = 3 × Cousin's age
Finally, we divide both sides by 3:
Cousin's age = 12
So Ansley's cousin is 12 years old, and Ansley's age can be found by plugging in 12 for Cousin's age in the expression we found earlier:
Ansley's age = 3 × Cousin's age - 5 = 3 × 12 - 5 = 31
So Ansley is indeed 31 years old.
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a tennis player makes a successful first serve 60% of the time. assuming that each serve is independent of the others, if the player serves 8 times, what is the probability that she gets exactly 3 first serves in?
The probability that the tennis player will make exactly 3 first serves out of 8 attempts is 0.278%.
To solve this problem, we can use the binomial distribution. The binomial distribution is used to calculate the probability of a certain number of successes (in this case, first serves) in a fixed number of independent trials (in this case, serves). The formula for the binomial distribution is:
P(X = x) = (n choose x) x pˣ x (1 - p)ⁿ⁻ˣ
where P(X = x) is the probability of getting x successes, n is the number of trials, p is the probability of success in each trial, and (n choose x) is the binomial coefficient, which represents the number of ways to choose x successes out of n trials.
Using this formula, we can plug in the values from our problem:
P(X = 3) = (8 choose 3) x 0.6³ x (1 - 0.6)⁸⁻³
P(X = 3) = (8! / (3! x 5!)) x 0.216 x 0.32768
P(X = 3) = 0.278%
This means that out of 1000 attempts, we can expect the player to make exactly 3 first serves around 2-3 times. It's important to note that this is just an estimation, and the actual number of successful serves may vary.
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The graph of the function h(x) is the result of reflecting the graph of f(x) over the x-axis and then translating 2 units up. Which equation defines h(x)?
Therefore, the equation of the function h(x) is: h(x) = -f(x) + 2.
What is graph?A graph is a visual representation of data that shows the relationship between two or more variables. It consists of two axes - the x-axis (horizontal) and the y-axis (vertical) - that intersect at a point called the origin. Each axis is divided into equally spaced intervals or units that represent the range of values for each variable. Data points are plotted on the graph by identifying their corresponding x and y values and locating them on the appropriate axes. The points are then connected by a line or curve that represents the pattern or trend in the data. Graphs are commonly used in various fields such as mathematics, science, economics, and business to help analyze and interpret data. Some common types of graphs include line graphs, bar graphs, scatter plots, pie charts, and histograms.
Here,
Let's assume the equation of the original function f(x) is y = f(x). To obtain the function h(x), we first reflect the graph of f(x) over the x-axis. This means that for any point (x, y) on the graph of f(x), the corresponding point on the graph of h(x) will be (x, -y).
Next, we translate the reflected graph of f(x) two units up. This means that for any point (x, -y) on the reflected graph, the corresponding point on the graph of h(x) will be (x, -y + 2).
Therefore, the equation of the function h(x) is:
h(x) = -f(x) + 2
This equation reflects the graph of f(x) over the x-axis (by negating f(x)) and then translates the reflected graph 2 units up (by adding 2).
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Complete question:
The graph of the function h(x) is the result of reflecting the graph of f(x) over the x-axis and then translating 2 units up. Which equation defines h(x)?
find an expression which represents the difference when
(7x−10) is subtracted from (−5x+6) in simplest terms.
Answer: -12x + 16
Step-by-step explanation:
To find the difference between (−5x+6) and (7x−10), we need to subtract the second expression from the first. So we have:
(−5x+6) - (7x−10)
To subtract the second expression, we can distribute the negative sign to all the terms inside the parentheses:
-5x + 6 - 7x + 10
Then we can combine the like terms:
-12x + 16
Therefore, the difference between (−5x+6) and (7x−10) is -12x + 16.
Gertrude bought a used car for $14,890. She was surprised that the dealer then added $1,280. 54 as a sales tax. What was the sales tax rate for this purchase? Round to one decimal place
The sales tax rate for Gertrude's car purchase was 8.6%.
Gertrude bought a used car for $14,890. She was surprised that the dealer then added $1,280. 54 as a sales tax. The total cost of Gertrude's car purchase, including the sales tax, was $14,890 + $1,280.54 = $16,170.54. Let x be the sales tax rate, expressed as a decimal. Then we can set up the equation:
$14,890 * x = $1,280.54
Solving for x, we get:
x = $1,280.54 / $14,890 ≈ 0.086
Multiplying by 100 to convert to a percentage, we get 8.6%. Therefore, the sales tax rate for Gertrude's car purchase was 8.6%.
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A consumers group is concerned with the mean cost of dining in a particular restaurant. a random sample of 40 charges (in dollars) per person has a mean charge of $39. 7188 with standard deviation of $3. 5476. is there sufficient evidence to conclude that the mean cost per person exceeds $38. 0
The test statistic is calculated to be 4.05, which is greater than the critical value of 2.704 at a significance level of 0.05, indicating strong evidence to reject the null hypothesis and conclude that the mean cost per person exceeds $38.0.
To test if there is sufficient evidence to conclude that the mean cost per person exceeds $38.0, we can perform a one-sample t-test.
Using the given information, the test statistic is calculated as
t = (39.7188 - 38.0) / (3.5476 / √(40)) = 4.05.
Using a t-table with 39 degrees of freedom (n-1), the p-value is found to be less than 0.01.
Since the p-value is less than the significance level of 0.05, we can reject the null hypothesis and conclude that there is sufficient evidence to suggest that the mean cost per person exceeds $38.0.
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Many types of bias exist when it comes to surveys, including nonresponse bias, undercoverage, and poorly worded survey questions. think about a survey you’ve been asked to participate in. maybe it was printed on a fast-food receipt or a store directed you to an online survey after you made a purchase. what influenced you to participate in the survey or to opt out of participating?
Analysis whether the biases were present in the survey or not .
The different types of biases are:
Nonresponse bias
Under coverage
Poorly worded
Given,
Biases in survey .
When it comes to surveys, there are several factors that can influence a person's decision to participate, such as the timing and location of the survey, the perceived relevance of the questions and incentives offered for participation. In some cases, people may opt-out of participating in a survey due to privacy concerns, lack of interest or distrust of the organization conducting the survey.
In terms of biases, survey designers should be careful of different types of biases that can affect the results, such as sampling bias, selection bias and response bias.
For example, if a survey is only given to certain demographics, the results may not be representative of the target audience.
Similarly, if the survey questions are worded in a leading or biased way, it can influence a person's response and skew the results.
It is important for survey designers to be aware of these biases and take steps to minimize their impact. This can include using random sampling techniques to ensure a representative sample, testing survey questions with focus groups to ensure they are clear and unbiased, and providing clear and transparent information about the purpose and use of the survey data. By taking these steps, survey designers can create surveys that produce accurate and reliable results.
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Evaluate the triple integral ∫∫∫ (x+8y)dV where E is bounded by the parabolic cylinder
y = 7x^2 and the planes
2 = 2x, y = 35x, and
2 = 0.
The triple integral ∫∫∫ (x+8y)dV where E is bounded by the parabolic cylinder is 512,604.17.
The triple integral is ∫∫∫(x+8y)dV.
Curves from the question are:
y = 7x², z = 2x, y = 35x, z = 0
Then, 7x² = 35x
Divide by x on both side, we get
7x = 35
Divide by 7 on both side, we get
x = 5
And z = 2x or z = 0. So
2x = 0
x = 0
Now the limits are:
x = 0 to x = 5
y = 7x² to y = 35x
z = 0 to z = 2x
Now the integral is
∫∫∫(x+8y)dV = [tex]\int_{0}^{5}\int_{7x^{2}}^{35x}\int_{0}^{2x}(x+8y)dzdydx[/tex]
Now first integrate with respect to z
∫∫∫(x+8y)dV = [tex]\int_{0}^{5}\int_{7x^{2}}^{35x}(x+8y)[z]_{0}^{2x}dydx[/tex]
∫∫∫(x+8y)dV = [tex]\int_{0}^{5}\int_{7x^{2}}^{35x}(x+8y)[2x-0]dydx[/tex]
∫∫∫(x+8y)dV = [tex]\int_{0}^{5}\int_{7x^{2}}^{35x}(2x^2+16xy)dydx[/tex]
Now integrate with respect to y
∫∫∫(x+8y)dV = [tex]\int_{0}^{5}\left[2x^2(y)_{7x^{2}}^{35x}+16x(\frac{y^2}{2})_{7x^{2}}^{35x}\right]dx[/tex]
∫∫∫(x+8y)dV = [tex]\int_{0}^{5}\left[2x^2(35x - 7x^2)+16x(\frac{1225x^2}{2}-\frac{49x^4}{2})\right]dx[/tex]
∫∫∫(x+8y)dV = [tex]\int_{0}^{5}\left[2x^2(35x - 7x^2)+8x(1225x^2-49x^4)\right]dx[/tex]
∫∫∫(x+8y)dV = [tex]\int_{0}^{5}\left[70x^3 - 14x^4+9800x^3-392x^5\right]dx[/tex]
∫∫∫(x+8y)dV = [tex]\left[\frac{70x^4}{4} - \frac{14x^5}{5}+\frac{9800x^4}{4}-\frac{392x^6}{6}\right]_{0}^{5}[/tex]
∫∫∫(x+8y)dV = [tex]\left[\frac{70(5)^4}{4} - \frac{14(5)^5}{5}+\frac{9800(5)^4}{4}-\frac{392(5)^6}{6}\right]-\left[\frac{70(0)^4}{4} - \frac{14(0)^5}{5}+\frac{9800(5)^4}{4}-\frac{392(5)^6}{6}\right][/tex]
∫∫∫(x+8y)dV = [10937.5 - 8750 + 1531250 - 1020833.33]-0
∫∫∫(x+8y)dV = 512,604.17
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The complete question is:
Evaluate the triple integral ∫∫∫(x+8y)dV where E is bounded by the parabolic cylinder.
y = 7x² and the planes
z = 2x, y = 35x, and
z = 0