The image after a dilation by a scale factor of 4 centered at the origin is (-132,-352).
What is scale factor?Scale factor is a mathematical term that refers to the ratio of two corresponding sides of similar shapes. It is used to compare the size of objects or figures by determining the size of a model in relation to its actual size. For example, if two shapes are similar, then their scale factor will be the same. This is useful in engineering and architecture when building scaled models of structures and machines. Scale factors can also be used to determine the proportions and measurements of an object in relation to similar objects.
This is because a dilation by a scale factor of 4 is the same as multiplying the original coordinates by 4. So, if the original coordinates were (-3,-8), then the new coordinates would be (-12,-32). Then, the coordinates are shifted by the center (the origin), so the new coordinates are (-132,-352).
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solve the question.
Answer: 1
\((\frac{x^{a+b} }{x^{c} }) ^{a-b}.(\frac{x^{b+c} }{x^{a} }) ^{b-c} .(\frac{x^{c+a} }{x^{b} })^{c-a}\\\\= \frac{x^{(a+b)(a-b)} }{x^{c(a-b)} }.\frac{x^{(b+c)(b-c)} }{x^{a(b-c)} }.\frac{x^{(c+a)(c-a)} }{x^{b(c-a)} }\\\\=\frac{x^{a^{2}-b^{2} } }{x^{ac-bc} }.\frac{x^{b^{2}-c^{2} } }{x^{ab-ac} }.\frac{x^{c^{2}-a^{2} } }{x^{bc-ab} } \\\\=\frac{x^{a^{2}-b^{2}+b^{2}-c^{2}+c^{2}-a^{2} } }{x^{ac-bc+ab-ac+bc-ab} }\\\\=\frac{x^{0} }{x^{0} }=1\)
Step-by-step explanation:
what is proportional to 26/13
Answer:
2 / 1
Step-by-step explanation:
26 / 13 = 2
SO any ratio or proportion that can be divided and equal to 2 would work
24 / 12
22 / 11
2 / 1
Etc..
from a consumer’s utility function alone, which of the following may be determined?
When analyzing a consumer's utility function: preferences, marginal utility, optimal consumption, and substitution and income effects.
From a consumer's utility function alone, you may determine the following:
1. Preferences: A consumer's utility function represents their preferences for different goods and services. By analyzing the function, you can determine which items the consumer prefers and how much they value them.
2. Marginal utility: The marginal utility is the additional satisfaction a consumer receives from consuming one more unit of a good or service. It can be derived from the utility function by taking its first derivative with respect to the quantity of the good or service.
3. Optimal consumption: By analyzing a consumer's utility function and taking into account their budget constraint, you can determine the optimal consumption bundle that maximizes their utility.
4. Substitution and income effects: The utility function can also help you analyze how changes in prices or income will affect a consumer's consumption choices, through the substitution and income effects.
Remember to keep these terms in mind when analyzing a consumer's utility function: preferences, marginal utility, optimal consumption, and substitution and income effects.
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2x + y - Z = 3
-X + 2y + z = 2
2x + 2y - Z = 5
Answer:
that should be 20
Step-by-step explanation:
Hope this helps!
If $600 was placed in a savings account with an interest rate of 0.5%, find the total amount in the account after 8 years and 3 months.
Answer:
$888
Step-by-step explanation:
I=P×T×R/100
=600×8.25×0.5/100 [8 year 3 months=99 months = 8.25 year ]
=1237.5/100
I =12.375
A= I +P
=600+12.375
A =612.375
hence the total amount will be $ 612.375
what is this answer 9x2000
Answer:
18,000
Step-by-step explanation:
What is the integer between 1 to 100?
The number of intergers between 1 to 100 (i.e two integers) is equals to ninty-eight in count.
The integers are collection of all positive and negative whole numbers. The positive integers are represented by adding (+) symbol in front of number and negative integers by adding (-) sign.
To calculate the number of integers between two integer using the following concept , Subtract the integers of interest i.e, if we have to calculate integer between a to b and then( b-a) and then subtract one .
As a proof of concept, calculate the number of integers that fall between 5 and 10 on a number line. We know there are 4 (6, 7, 8, 9), 10−5−1=4.
We have, to calculate the integers between 1 to 100. Using the above concept, total number of intergers between 1 to 100 are 100 - 1 -1 = 98
Hence, the number of required integers are 98.
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Solve for x
9x + 3 = 21
Hi,
9x = 21 - 3
9x = 18
x = 18/9 = 2
This is a two-step equation:
\(9x + 3 = 21\\\\9x = 18\\\\x = 2\)
In which data set is the mean greater than the median
Answer:
in 2nd figure will mean greater
Answer:
its the 4th one hopes this help
s
Step-by-step explanation:
Brianna walks around a triangular park, daily. The longest side of the park measures 75 yards
and the shortest side measures 45 yards. If she walks 3 full laps around the park, how far does she
walk in one day?
She walks 540 yards for 3 full laps around the park per day.
How to determine the distanceFrom the information given;
The longest part of the triangular park = 75 yards
The shortest part = 45 yards
Let's find the other part, using Pythagorean theorem;
a² = b² + c²
75² = 45² + c²
c² = 75² - 45²
Find the squares
c² = 5625 - 2025
c² = 3600
Make 'c' the subject
c = √3600
c = 60 yards
If she walks
75 + 60 + 45 yards per lap
180 yards per lap
For three laps, she walks
= 3 × 180
= 540 yards
Thus, she walks 540 yards for 3 full laps around the park per day.
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Given a cylinder with height = h and a diameter = d.
What is the correct application to find the volume of the cylinder?
A
V = d2∙h∙π
B
V = (2d)2∙h∙π
C
V = d∙h∙π
D
V = (d2)2∙h∙π
Answer:
V=d.h
Step-by-step explanation: I took the test i got this correct.
Rectangle A′B′C′D′ is a dilation of rectangle ABCD.
What is the scale factor?
Enter your answer in the box.
Answer:
Scale factor = 4
If you multiply by 4 the two sides of ABCD, you will get the corresponding sides of A’B’C’D’
How do you create a unique array?
Minimum Increment operations to make Array unique
Minimum Increment operations to make Array unique.Making elements distinct in a sorted array by minimum increments.Find sum of non-repeating (distinct) elements in an array.Find k closest numbers in an unsorted array.Find k closest elements to a given value.What does the unique function do in Excel?The UNIQUE function will return an array, which will spill if it's the final result of a formula. This means that Excel will dynamically create the appropriate sized array range when you press ENTER .
How does ArrayList work?ArrayList is like an array behind the scenes as it’s backed by an array of type java.lang.Object in java.
Normally arrays are fixed in size which means the number of elements that can be added are fixed and cannot be increased once created. ArrayList can dynamically increase in size once the array that backs is full so, these way we won’t encounter runtime exceptions.
When we say list.get(0), it’s equivalent to array[0]. It can be said the ArrayList is a kind of more convenient way to use dynamic arrays.
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Like other birds, emperor penguins use their lungs to
breathe air. Emperor penguins hunt for fish, squid,
and other food underwater. When an emperor
penguin dives into the water, it can hold its breath for
as long as 20 minutes.
What happens to the air that an emperor penguin breathes in? Select all that apply.
The air travels through passageways to all parts of the body.
In the lungs, oxygen from the air is absorbed into the blood.
The air travels through passageways to the lungs.
A California grower has a 50-acre farm on which to plant strawberries and tomatoes. The grower has available 300 hours of labor per week and 800 tons of fertilizer, and has contracted for shipping space for a maximum of 26 acres� worth of strawberries and 37 acres� worth of tomatoes. An acre of strawberries requires 10 hours of labor and 8 tons of fertilizer whereas an acre of tomatoes requires 3 hours of labor and 20 tons of fertilizer. The profit from an acre of strawberries is $400, and the profit from an acre of tomatoes is $300. The farmer wants to know the number of acres of strawberries and the number of acres of tomatoes to plant to maximize profit.
Formulate a linear programming model and solve this problem using POM-QM. Submit the �linear programming results� and �ranging� output from POM-QM and describe the solution by stating the values of the decision variables and the profit that can be achieved. (HINT: When you have a section of output displayed, right click and choose COPY TABLE. Then you can move to another location, like a WORD file and paste the table you copied.)
To solve this problem using linear programming, we need to formulate an objective function and constraints based on the given information.
Let:
x = number of acres of strawberries to plant
y = number of acres of tomatoes to plant
Objective function: Maximize profit
Maximize Z = 400x + 300y
Constraints:
Acres of strawberries: x ≤ 26
Acres of tomatoes: y ≤ 37
Farm size: x + y ≤ 50
Labor availability: 10x + 3y ≤ 300
Fertilizer availability: 8x + 20y ≤ 800
Using POM-QM, we can input this linear programming model and obtain the optimal solution.
The decision variables:
x = 26 (acres of strawberries)
y = 21 (acres of tomatoes)
The maximum profit achievable is:
Z = 400(26) + 300(21) = $21,800
The solution suggests that the grower should plant 26 acres of strawberries and 21 acres of tomatoes to maximize profit. The maximum profit achievable is $21,800.
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find the value of x.write answer as a fraction in simplest form or a decimal rounded to the nearest hundredth
Answer:
Step-by-step explanation:
Triangles EFG and FGH are similar.
x/15 = 36/39
x/15 = 12/13
x = 15*12/13 = 180/13 ≈ 13.8 units
The required measure of x is given as 5.8 in the given triangle.
The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should not be greater than 180°.
What are similar triangles?Similar triangles are triangle that has a relationship as of some scale factor.
here,
From the figure,
From triangle GHF and triangle EGF
x / 15 = 15 / 39
x = 225 / 39
x = 5.8
Thus, the required measure of x is given as 5.8 in the given triangle.
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(ab² + 13b - 4a) + (3ab² + a +7b)
Answer:
4ab² + 20b - 3a
Step-by-step explanation:
This question most likely asks us to simplify the expression, as factoring is not possible...
(ab² + 13b - 4a) + (3ab² + a + 7b),
ab² + 13b - 4a + 3ab² + a + 7b,
ab² + 3ab² + 13b + 7b - 4a + a,
Solution : 4ab² + 20b - 3a
if sec(∞) < 0 and the sin(∞) = 15/17 what is the exact value of cot (∞)
Lilo has 1,000 minutes per month on her cell phone plan. Write and solve an inequality showing the maximum number of minutes that Lilo can use it not be charge extra on her cell phone plan when she only used 615 minutes.
Answer:
Lilo has a maximum of 385 minutes to use on her cell phone.
A ≤ 385
Step-by-step explanation:
Let letter A represent the additional number of minutes that Lilo can talk
A + 615 ≤ 1,000
subtract 615 from both sides
A + 615 - 615 ≤ 1,000 - 615
A + 0 ≤ 385
A ≤ 385
Lilo has a maximum of 385 minutes to use on her cell phone.
A + 615 ≤ 1,000; A ≤ 385
You have taken up gardening for relaxation and have decided to fence in your new
rectangular shaped masterpiece. The length of the garden is 4 meters and 34 meters
of fencing is required to completely enclose it. What is the width of the garden?
Answer:
13 meters
Step-by-step explanation:
Adjacent sides form half the perimeter, so the sum of the unknown side and the given side is 34/2 = 17 meters.
4 meters + width = 17 meters
width = 13 meters . . . . . subtract 4 meters
8. 9 Revision Questions
Question one
James Mbuvi started a taxi business in Nairobi March 1990 under the firm name Mbuvi
Taxis. The firm had two vehicles KA and KB, which had been purchased forSh. 560,
000, and Sh. 720. 000 respectively earlier in the year.
In February 1992 vehicle KB was involved in an accident and was written off. The
insurance company paid the firm Sh. 160,000 for the vehicle. In the same year the firm
purchased two vehicles, KC and KD for Sh. 800. 000 each.
In November 1993 vehicle KC was sold for Sh. 716, 000. In January 1994 vehicle KE
was purchased for Shs. 840, 000. In March 1994 another vehicle KF was purchased for
Sh. 960. 000
The firm's policy is to depreciate vehicles at the rate of 25 per cent on cost on vehicles on
hand at the end of the year irrespective of the date of purchase. Depreciation is not
provided for vehicle disposed of during the year. The firm's year ends on 31 December
Required:
a) Calculate the amount of depreciation charged in the profit and loss account for
each of the five years.
b) Prepare the motor vehicle account (at cost).
c) Calculate the profit and loss on disposal of each of the vehicles disposed of by
the company
a) To calculate the amount of depreciation charged in the profit and loss account for each of the five years, we need to use the following formula:
Depreciation = Cost - Book Value
where Book Value is the value of the vehicle on the balance sheet at the end of the year, calculated as:
Book Value = Cost - Depreciation on Vehicles on Hand at the Beginning of the Year
For the first year, the cost of the two vehicles KA and KB is Sh. 560,000 * 2 = Sh. 1,120,000. The value of the two vehicles on the balance sheet at the end of the year is:
Book Value = 1,120,000 - 25% of 1,120,000 = 1,120,000 - 290,000 = 830,000
Therefore, the depreciation charged in the profit and loss account for the first year is:
Depreciation = 1,120,000 - 830,000 = 290,000
For the second year, the cost of vehicle KB is Sh. 720,000. The value of the three vehicles on the balance sheet at the end of the year is:
Book Value = 1,120,000 - 25% of 1,120,000 - 290,000 = 830,000 - 585,000 = 245,000
Therefore, the depreciation charged in the profit and loss account for the second year is:
Depreciation = 245,000 - 245,000 = 0
For the third year, the cost of vehicle KC is Sh. 800,000. The value of the four vehicles on the balance sheet at the end of the year is:
Book Value = 1,120,000 - 25% of 1,120,000 - 585,000 - 290,000 = 830,000 - 1,080,000 = -250,000
Therefore, the depreciation charged in the profit and loss account for the third year is:
Depreciation = 245,000 - 245,000 - 250,000 = -55,000
For the fourth year, the cost of vehicle KD is Sh. 800,000. The value of the four vehicles on the balance sheet at the end of the year is:
Book Value = 1,120,000 - 25% of 1,120,000 - 585,000 - 290,000 = 830,000 - 1,080,000 = -250,000
Therefore, the depreciation charged in the profit and loss account for the fourth year is:
Depreciation = 245,000 - 245,000 - 250,000 - 250,000 = -1,000,000
For the fifth year, the cost of vehicle KF is Sh. 960,000. The value of the four vehicles on the balance sheet at the end of the year is:
Book Value = 1,120,000 - 25% of 1,120,000 - 585,000 - 290,000 = 830,000 - 1,080,000 = -250,000
Therefore, the depreciation charged in the profit and loss account for the fifth year is:
Depreciation = 245,000 - 245,000 - 250,000 - 250,000 - 960,000 = -2,270,000
b) To prepare the motor vehicle account, we need to calculate the total depreciation charged for each year and the total value of the motor vehicles on the balance sheet at the end of each year. We also need to calculate the accumulated depreciation at the end of each year.
For the first year, the total depreciation charged is:
Depreciation = 1,120,000 - 290,000 = 830,000
The total value of the motor vehicles on the balance sheet at the end of the first year is:
Value = 1,120,000
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9. Given rectangle DEFG below, select all the true statements.
SHOW WORK!!
The true statements in the rectangle DEFG are FHE = 60 and FEH = 60
Selecting all the true statements in the rectangle DEFGFrom the question, we have the following parameters that can be used in our computation:
The rectangle DEFG
On the rectangle DEFG, we have
1.5x + 8 = 3x + 2
Evaluate the like terms
So, we have
1.5x = 6
This gives
x = 4
Also, we have the following angle measures
FHE = 180 - 120
FHE = 60
Then, we have
FEH = FHE = 60
Hence, the the true statements in the rectangle DEFG are FHE = 60 and FEH = 60
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HELP I NEED HELP ASAP
HELP I NEED HELP ASAP HELP I NEED HELP ASAP
HELP I NEED HELP ASAP HELP I NEED HELP ASAP
HELP I NEED HELP ASAP
Answer:
A (skewed to the left)
Step-by-step explanation:
28 is a much smaller number (age) than the rest of the data, so it will be a negatively skewed distributio, aka, skewed to the left.
“A left skewed distribution is sometimes called a negatively skewed distribution because it's long tail is on the negative direction on a number line.”
“A distribution skewed to the left is said to be negatively skewed. This kind of distribution has a large number of occurrences in the upper value cells (right side) and few in the lower value cells (left side).”
Consider the following regression model: Y₁ =B₁ + B₂X₂1+ B3X31 + B₂X41 +14₁ Using the model above show that the maximum likelihood estimator for the variance, var (uiX21-X31-B4X4), is biased (be sure to comment of the nature of the bias).
The maximum likelihood estimator for the variance, (ui|\(X_{2i}\), \(X_{3i}\), β₄\(X_{4i}\)), is unbiased.
To analyze the bias of the maximum likelihood estimator (MLE) for the variance, we need to consider the assumptions and properties of the regression model.
In the given regression model:
\(Y_i\) = β₁ + β₂\(X_{2i}\) + β₃\(X_{3i}\) + β₄\(X_{4i}\) + U\(_{i}\)
Here, \(Y_i\) represents the dependent variable, \(X_{2i}, X_{3i},\) and \(X_{4i}\) are the independent variables, β₁, β₂, β₃, and β₄ are the coefficients, U\(_{i}\) is the error term, and i represents the observation index.
The assumption of the classical linear regression model states that the error term, U\(_{i}\), follows a normal distribution with zero mean and constant variance (σ²).
Let's denote the variance as Var(U\(_{i}\)) = σ².
The maximum likelihood estimator (MLE) for the variance, σ², in a simple linear regression model is given by:
σ² = (1 / n) × Σ[( \(Y_i\) - β₁ - β₂\(X_{2i}\) - β₃\(X_{3i}\) - β₄\(X_{4i}\))²]
To determine the bias of this estimator, we need to compare its expected value (E[σ²]) to the true value of the variance (σ²). If E[σ²] ≠ σ², then the estimator is biased.
Taking the expectation (E) of the MLE for the variance:
E[σ²] = E[ (1 / n) × Σ[( \(Y_i\) - β₁ - β₂\(X_{2i}\) - β₃\(X_{3i}\) - β₄\(X_{4i}\))²]
Now, let's break down the expression inside the expectation:
[( \(Y_i\) - β₁ - β₂\(X_{2i}\) - β₃\(X_{3i}\) - β₄\(X_{4i}\))²]
= [ (β₁ - β₁) + (β₂\(X_{2i}\) - β₂\(X_{2i}\)) + (β₃\(X_{3i}\) - β₃\(X_{3i}\)) + (β₄\(X_{4i}\) - β₄\(X_{4i}\)) + \(U_{i}\)]²
= \(U_{i}\)²
Since the error term, \(U_{i}\), follows a normal distribution with zero mean and constant variance (σ²), the squared error term \(U_{i}\)² follows a chi-squared distribution with one degree of freedom (χ²(1)).
Therefore, we can rewrite the expectation as:
E[σ²] = E[ (1 / n) × Σ[\(U_{i}\)²] ]
= (1 / n) × Σ[ E[\(U_{i}\)²] ]
= (1 / n) × Σ[ Var( \(U_{i}\)) + E[\(U_{i}\)²] ]
= (1 / n) × Σ[ σ² + 0 ] (since E[ \(U_{i}\)] = 0)
Simplifying further:
E[σ²] = (1 / n) × n × σ²
= σ²
From the above derivation, we see that the expected value of the MLE for the variance, E[σ²], is equal to the true value of the variance, σ². Hence, the MLE for the variance in this regression model is unbiased.
Therefore, the maximum likelihood estimator for the variance, (ui|\(X_{2i}\), \(X_{3i}\), β₄\(X_{4i}\)), is unbiased.
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an initial population of 765 quail increases at an annual rate of 16%. write an exponential function to model the quail population. what will the approximate population be after 4 years?
An exponential function to model the quail population is y = 765(1+0.16)ⁿ and the approximate population be after 4 years is 1384.65 quails.
Population growth is seen to increase at an exponential rate. We use the following to model this growth.
y = A₀(1 + r)ⁿ
where
y = value at time
A₀ = original value
r = rate of growth
n = time elapsed
An exponential function that models the quail population is set up like:
y = 765(1+0.16)ⁿ
so that, for example, if we wanted to figure out the population at time (4 years), then we would set up the function as follows,
y = 765(1+0.16)⁴
y = 765(1.16)⁴
y = 765* 1.81
to get
y = 1384.65 quails after 4 year has elapsed.
Hence, an exponential function to model the quail population is y = 765(1+0.16)ⁿ and the approximate population be after 4 years is 1384.65 quails.
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i give out brainlist .write and solve the proportion in the complele statement.
1. 3 oz = _______ g
Answer:
hi its me again :3
3oz=85.048g
Step-by-step explanation:
:)
What’s the answer????????
Answer:
19.25 (tax)
294.25 (total price)
135.75 (money left)
Please mark 5 stars and brainlliest
Step-by-step explanation:
Which coordinate notation matches the description?:
3 units left and 5 units down
O (x+3y-5)
O (X-3.y-5)
O (x+3.y+5)
O (X-3.y+5)
Answer: The last one
Step-by-step explanation:
3 units left would be -3 and 5 units down would be +5
From $80 to $64 *
Percent decrease
Answer:
20%
Step-by-step explanation:
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Let g be the function with first derivative g'(x) = √x^3 + x for x > 0. If g (2) = −7, what is the value of g (5) ?
The value of g(5) can be determined by integrating the given derivative function and using the initial condition g(2) = -7. The value of g(5) is approximately 57.955.
To find the value of g(5), we need to integrate the derivative function g'(x). The antiderivative of √\(x^3\) + x with respect to x will give us the original function g(x). Let's perform the integration:
∫√\(x^3 + x dx\) = ∫\((x^(3/2) + x) dx = (2/5)x^(5/2) + (1/2)x^2 + C\)
Now, using the initial condition g(2) = -7, we can determine the constant of integration C:
\((2/5)(2)^(5/2) + (1/2)(2)^2 + C = -7\)
Simplifying the equation, we can solve for C:
(8/5) + 2 + C = -7
C = -7 - (8/5) - 2
C = -7 - (16/5) - (10/5)
C = -7 - (26/5)
C = -35/5 - 26/5
C = -61/5
Now that we have the value of C, we can substitute it back into the original function and evaluate g(5):
g(5) = \((2/5)(5)^(5/2) + (1/2)(5)^2 - (61/5)\)
Calculating this expression will give us the value of g(5).
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