The value of variance Var(X) is 2
We know that the mean is nothing but the central value of the data and the variance represents the deviation of the data from the mean.
As we know Var(X) = E(X²) − (E(X))²
So, Var(X²) would be,
Var(X²) = E((X²)²) − (E(X²))²
Var(X²) = E(X⁴) − (E(X²))²
Substitute the values Var(X²) = 5 and E(X⁴) = 14 in above equation.
5 = 14 - (E(X²))⁴
(E(X²))² = 14 - 5
(E(X²))² = 9
E(X²) = 3
Now we subatitute the values E(X²) = 3 and E(X) = 1 in equation Var(X) = E(X²) - (E(X))²,
Var(X) = 3 - (1)²
Var(X) = 3 - 1
Var(X) = 2
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The complete question is:
You are told that E(x) = 1 Var(x²) = 5,and E(x⁴) = 14.What is Var(x) (the answer is an integer)?
a car is travelling at 84 km/h how far can a car travel in 45 mins?
it will go far as 231 km in 45 mins
I’ve always been terrible at geometry. I’m supposed to find the area of the triangle on top, then also the area of the square on the bottom. Then the area of both together. I attached a screenshot of the figure
Answer: The triangle on top is [tex]32m^2[/tex]. The square on the bottom is [tex]64m^2[/tex]. Both together is [tex]96m^2[/tex]
Which of the following are true about Principal Component Analysis (PCA)? (2 correct answers)a) PCA is intended for use with categorical variablesb) The idea of PCA is to find a linear combination of the two variables that contains most, even if not all, of the information, so that this new variable can replace the two original variables.c) PCA is intended for use with quantitative variablesd) Normalization (= standardization) is usually performed in PCA when analysis is conducted on covariances
Principal Component Analysis (PCA) is a statistical technique used to reduce the number of variables in a dataset.
It is used to transform a set of correlated variables into a smaller set of uncorrelated variables, called principal components, which capture the most variance in the data. The formula for PCA can be written as:
X' = ΣX - μ
Where X is the original data, X' is the transformed data, μ is the mean of the original data, and Σ is the covariance matrix of the original data.
To calculate PCA, the mean of the original data is first subtracted from each of the observations. This is then multiplied by the covariance matrix, which is a matrix of the variances and covariances of the original data. The resulting product is the transformed data, which is a matrix of uncorrelated principal components. The principal components are the linear combinations of the original variables that capture most of the variance in the data. The amount of variance captured by each component is determined by the eigenvalues of the covariance matrix. The eigenvectors of the covariance matrix are the principal components.
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Susan Meyer likes to study personality types. The personality types are broadly defined according to four main preferences. Do individuals usually choose similar or different personality types as their friends? The following data gives an indication. Use the data to estimate the probability that a student will have at least 3 similar personality traits in common. Round to four decimal places when necessary.0.40090.31600.35380.0472
The probability that a student will have at least 3 similar personality traits in common with their friends is 0.8802 or 87.98%.
The probability of having at least 3 similar personality traits in common is calculated by taking into account the probability of having 3, 4 or all 4 traits in common.
To do this, Susan uses the formula for finding the probability of a complement event, which is 1 minus the probability of not having at least 3 traits in common.
The probability of not having at least 3 traits in common is found by adding up the probabilities of having 0, 1, or 2 traits in common. This gives us a total probability of
=> 0.4009 + 0.316 + 0.3538 + 0.0472 = 0.1198.
The probability of having at least 3 traits in common is then found by subtracting this value from 1, which gives us a probability of
=> 1 - 0.1198 = 0.8802.
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Comment on any apparent relationship between these two variables.For midsized cars, all driving speeds seem to yield about the same miles per gallon.For midsized cars, there seems to be no relationship between driving speeds and fuel efficiency. For midsized cars, lower driving speeds seem to yield higher miles per gallon.For midsized cars, lower driving speeds seem to yield lower miles per gallon.
The statement "For midsized cars, lower driving speeds seem to yield lower miles per gallon" indicates a negative relationship between driving speed and fuel efficiency.
This statement means that as the driving speed increases, the fuel efficiency decreases and vice versa. This relationship is likely due to the increase in air resistance and engine drag as driving speed increases, which leads to a decrease in fuel efficiency.
This relationship can be seen in the context of the physics of motion and energy, where energy is conserved, and an increase in one form of energy, such as kinetic energy, is accompanied by a decrease in another form of energy, such as thermal energy.
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43. At the beginning of the month, Emika had $24 in her school cafeteria account. The table below
shows how her account balance changed over the course of three weeks. (Positive change means
money she added into her account, while negative change means money she spends.)
1.
2
Week
1
2
3
Beginning
Balance
($)
24
8
-18
Final
Balance
($)
8
-18
Change
($)
16
26
-12
Expression to show your work
24-16 = 8
8-26-18
-18--12-6
Complete the table for weeks 2-3.
How much would Emika have to deposit into the account during week 4 so that the final
balance is positive?
Answer:
$6
Step-by-step explanation:
Week 4 Beginning Balance: -6
Final Balance: ?
Change: ?
Emika would need to deposit at least $6 into her account during week 4 in order for the final balance to be positive.
Determine the intercepts of the line. − 7 x − 6 y = − 15
The intercepts of the linear function in this problem are defined as follows:
x - intercept: (15/7, 0).y - intercept: (0, 5/2).How to obtain the intercepts of a function?The function for this problem is defined as follows:
-7x - 6y = -15.
The x-intercept of the function is the value of x when y assumes a value of 0, hence:
-7x = -15
7x = 15
x = 15/7
x = 2.1429.
The y-intercept of the function is the value of y when x assumes a value of 0, hence:
-6y = -15
6y = 15
y = 15/6
y = 5/2
y = 2.5.
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What is the answer to -40-24u
The simplification of the expression -40-24u is -8(3u+5)
What is simplification?Making something simpler is the definition of simplify. Simplifying an expression, fraction, or mathematical problem is referred to as simplification in mathematics. Through calculations and problem-solving, it simplifies the issue.
As you are aware, simplifying mathematical problems improves test scores and is also used in daily life. For example, in malls, you can receive a 35% discount, a flat discount, or a 20% discount up to Rs 100. To solve equations in this section, you only need to apply the most basic simplification rules.
Therefore, simplifying an expression entails applying various techniques to make it into a simpler version. The operations necessary to simplify things are carried out according to a predetermined procedure called BODMAS.
-40-24u
= -24u-40
= -8(3u+5)
The answer is -8(3u+5)
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Rodrigo is an ichthyologist, or a scientist who studies fish. When he first started monitoring the sturgeon population of Lavender Lake, he estimated there were 600 sturgeon in the lake. One year later, Rodrigo estimated the population had decreased to 510. He expects the sturgeon population to continue decreasing each year. Write an exponential equation in the form y = a(b) that can model the estimated sturgeon population, y, in x years. Use whole numbers, decimals, or simplified fractions for the values of a and b.
An exponential equation in the form y = a(b)ˣ that can model the estimated sturgeon population, y, in x years, is y = 600(1-3/20)ˣ.
What is exponential decay?
An exponential function's curve is created by a pattern of data called exponential decay, which exhibits higher decreases over time.
Given:
Rodrigo is an ichthyologist, or a scientist who studies fish.
When he first started monitoring the sturgeon population of Lavender Lake, he estimated there were 600 sturgeon in the lake.
One year later, Rodrigo estimated the population had decreased to 510. He expects the sturgeon population to continue decreasing each year.
The exponential decay function:
y = A₀(1-r)ˣ, where y = Final amount, A₀ = Initial amount, r = Rate of decay in decimal form, x = Time.
So, y = 600(1 - r)ˣ.
One year later,
510 = 600(1-r)
r = 3/20
So, the function is y = 600(1 - 3/20)ˣ
Therefore, the function is y = 600(1 - 3/20)ˣ
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Answer:
600(0.85)^x
step by step explanation
Problem 4. As a cold front passed through Denver, the temperature changed at the same
rate of 6 hours. The total change in temperature was -42 degrees. What was the change in
temperature each hour?
The change in temperature in each hour would be = -7 degrees/ hour
What is temperature?Temperature is defined as the degree of how hot or cold a body is which can be measured in degree Celsius or degree Fahrenheit.
As the individual passed through Denver the time for total temperature change = 6 hours.
The total temperature changes = -42 degrees
If 6 hours = -42 degrees
1 hour = × degrees
make X the subject of formula;
X = -42/6
X = -7 degrees/hour
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A family buys 4 airline tickets online. The family buys travel insurance that costs $19 per ticket. The total cost is $752. Let x represent the price of one ticket. What is the price of one ticket?
The price of the ticket is $169.
Travel insurance
$19 per ticket
Total cost
$752
x = price of the ticket
Equation for the total cost
752 = 4(x+19)
x + 19 = 752/4
x + 19 = 188
x = 188 - 19
x = $169
Find each hyperbola’s general form.
For the hyperbola [(x - 3)²/16 - (y + 1)²/4] = 1 -
The general form - x² - 6x - 4y² - 8y - 11 = 0
Centre - (3,-1)
Vertices - (7,-1) and (-1,-1)
Foci - (3 + 2√5 , -1) and (3 - 2√5 , -1)
Asymptotes - (x - 3)/2 - 1 and -(x - 3)/2 - 1
What is a hyperbola?
One sort of smooth curve that lies in a plane is called a hyperbola, and it has two connected components or branches that are mirror reflections of one another and seem like two infinite bows. A set of points is referred to as a hyperbola if the difference between their distances from two foci is constant.
The given equation is - [(x - 3)²/16 - (y + 1)²/4] = 1
The equation of a hyperbola is [(x - h)²/a² - (y - k)²/b²] = 1, where (h,k) is the centre, a and b are the lengths of the semi-major and the semi-minor axes.
In the equation h = 3, k = -1, a = 4 and b = 2.
The standard form is [(x - 3)²/4² - (y + 1)²/2²] = 1.
The vertex form is [(x - 3)²/16 - (y + 1)²/4] = 1.
The general form is x² - 6x - 4y² - 8y - 11 = 0.
The vertices of hyperbola is given as (h+a,k) and (h-a,k) which are the two bending points of the hyperbola with centre (h,k).
Vertices = (3+4,-1) and (3-4,-1)
Vertices = (7,-1) and (-1,-1)
For a right-left facing hyperbola, the Foci (focus points right) are defined as (h+c,k) and (h-c,k) where c = √(a² + b²) is the distance from the center (h,k).
c = √(4² + 2²)
c = √16 + 4
c = √20
c = 2√5
So the foci is -
Foci = (3 + 2√5 , -1) and (3 - 2√5 , -1).
The asymptotes are the lines the hyperbola tends to at ±∞.
For right-left hyperbola the asymptotes are y = ± b/a(x - h) + k.
y = ± 2/4(x - 3) + -1.
y = (x - 3)/2 - 1 and -(x - 3)/2 - 1
Therefore, the graph for the hyperbola is plotted.
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c7h14o ir peak wavenumbers functional group
C7H14O is likely an alcohol with IR peaks due to C-O and O-H bond stretching vibrations around 1050-1300 cm^-1 and 3000-3600 cm^-1.
What is atom ?
The smallest part of a substance that cannot be broken down chemically. Each atom has a nucleus (center) made up of protons (positive particles) and neutrons (particles with no charge). Electrons (negative particles) move around the nucleus.
The C7H14O molecule is likely to be an alcohol, as the functional group for alcohols includes a hydroxyl (-OH) group, which contains an oxygen atom bonded to a hydrogen atom.
The wavenumber of an IR peak corresponds to the frequency of a vibration in the molecule. In the case of an alcohol, the IR peaks of interest are typically due to the stretching vibrations of the C-O and O-H bonds. The IR peaks for these vibrations typically occur at wavenumbers in the range of 1050-1300 cm^-1 and 3000-3600 cm^-1, respectively.
C7H14O is likely an alcohol with IR peaks due to C-O and O-H bond stretching vibrations around 1050-1300 cm^-1 and 3000-3600 cm^-1.
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1. (3 points) is the following a valid argument or fallacy? if it is sunday, then the store is closed. the store is closed. therefore, it is sunday. you must explain your answer.
According to a conclusion, therefore, the answer is palace now deductive argument form that is contra position.
consider part 1 here, since the store may be closed on other days. According to a conclusion, therefore, the answer is palace now
consider part 2 deductive argument form that is contra position.
Third, here, the even number of the form 2 n for all k belongs to a natural number and odd numbers are of form 2n+1 where n belongs to the natural number. So the product of the ordinem number that is 2(n+1), is equal to 2 into 2 n+1 that is, of the form of 2 n. Therefore, the product is even
part 4. Here let us take contra positively that, if is odd, integral then n is of the form 2 k plus 1, where k belongs to integral implies. N square is equal to 2 k plus 1 whole square, that is, equals to 4 k square plus 4 k plus 1. That is equal to 2 into 2 k square plus 2. K plus 1 is the odd integer. So if n square is an even integer, then is an even integer now
consider part 5. Here we have given that 2 n plus 1 is greater than equal to 33 implies 2 is greater than equal to 32, which implies n is greater than equal to 16. Point proves the existence of integer hope.
The complete question is:-
Is the following a valid argument or fallacy? If it is Sunday, then the store is closed. The store is closed. Therefore, it is Sunday. You must explain your answer.
2. Name the argument form of the following argument: Dogs eat meat. Fluffy does not eat meat. Therefore, Fluffy is not a dog.
3. Prove directly that the product of an even and an odd number is even.
4. Prove by contraposition for an arbitrary integer n that if n2 is even, then n is even.
5. Prove that there is a positive integer n that satisfies 2n + 1 ≥ 33. Do
not overthink this problem. Do not write more than logically necessary to
prove existence.
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The power of the statistical test is zero (0) when the mean is 52, the sample size is 25, and the standard deviation is 2, and the probability of committing Type II error when P 55 is one (1) (previous problem).TrueFalse
The probability of committing a Type II error when the mean difference is 55 is 1.
The concept of power in statistical testing is important for understanding the reliability of results. When the power of a statistical test is zero, it means that the test is unable to detect the difference between the means of two groups, even if there is a real difference.
In the given scenario, the mean is 52, the sample size is 25, and the standard deviation is 2.
This means that if the true mean difference between two groups is 55, there is a 100% chance that the test will not detect it. The probability of committing a Type II error is directly related to the power of a statistical test.
The higher the probability of committing a Type II error, the lower the power of the test.
Therefore, it is important to consider the power of a statistical test when interpreting results.
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in a study to determine whether miles driven is a good predictor of trade-in value, 11 cars of the same age, make, model, and condition were randomly selected. the following scatterplot shows trade-in value and mileage for those cars. five of the points are labeled a, b, c, d, and e, respectively. the figure represents a scatter plot in the coordinate plane with 11 data points, several of which are labeled with the letters a through e. the vertical axis is labeled miles driven, in thousands, and the numbers 50 through 100, in increments of 10, are indicated. the vertical axis is labeled value, and the numbers 4000 dollars through 6500 dollars, in increments of 500, are indicated. the values represented by the data points are as follows. note that all values are approximate. point 1, which is labeled as point a. 51 comma 6200.point 2. 60 comma 5700.point 3. 61 comma 6400.point 4, which is labeled as point b. 62 comma 5700. point 5, which is labeled as point c. 68 comma 5400.point 6. 72 comma 5800.point 7, which is labeled as point d. 83 comma 4700.point 8. 98 comma 4600.point 9. 99 comma 4400.point 10. 92 comma 4200.point 11, which is labeled as point e. 96 comma 6500. which of the five labeled points is the most influential with respect to a regression of trade-in value versus miles driven?
Step-by-step explanation:
and a line going from the point 0 comma 100 through the point 2 comma 120
Question 6(Multiple Choice Worth 2 points)
(Graphing Linear Equations MC)
Which graph represents the equation y equals one half times x minus 1?
graph of a line passing through the points negative
PLS HURRY ASAP SHOW SOLVING STEPS WILL MARK BRAINLIEST IF CORRECT
The fixed fee for Company 1 is equal to $5.5.
The fixed fee for Company 2 is equal to $9.15625.
A statement which is true is: A. Company 1's rate per pound is twice the rate per pound of Company 2.
How to determine the value of the constant rate of change?In Geometry, the rate of change of any straight line simply refers to its gradient or slope and it can be calculated by using this mathematical expression;
Rate of change (slope), m = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Rate of change (slope), m = (y₂ - y₁)/(x₂ - x₁)
Based on the weight of the package for Company 1, the constant rate per pound is given by:
Rate of change (slope), m = (14.50 - 9.25)/(6 - 2.5)
Rate of change (slope), m = 5.25/3.5
Rate of change (slope), m = 1.5.
At data point (2.5, 9.25), an equation for the fixed fee for Company 1 can be calculated in point-slope form as follows:
y - y₁ = m(x - x₁)
y - 9.25 = 1.5(x - 2.5)
y = 1.5x - 3.75 + 9.25
y = 1.5x + 5.5
Therefore, the fixed fee is $5.5.
Based on the weight of the package for Company 2, the constant rate per pound is given by:
Rate of change (slope), m = (7.25 - 6.5)/(2 - 1)
Rate of change (slope), m = 0.75/1
Rate of change (slope), m = 0.75.
At data point (1, 6.5), an equation for the fixed fee for Company 1 can be calculated in point-slope form as follows:
y - y₁ = m(x - x₁)
y - 6.5 = 0.75(x - 1)
y = 0.75x - 0.75 + 6.5
y = 0.75x + 5.75
Therefore, the fixed fee is $5.75.
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a population consists of 400 elements. we want to draw a simple random sample of 40 elements from this population. on the first selection, the probability of an element being selected is
The probability of an element being selected is 0.1 or 1/10 or 10%.
Probability is a mathematical concept that describes the likelihood of an event occurring. It is a value between 0 and 1, where 0 indicates that an event is impossible, 1 indicates that an event is certain, and values between 0 and 1 indicate the degree of uncertainty or likelihood of an event occurring.
In simple random sampling, each element in the population has an equal chance of being selected, and the probability of any given element being selected is equal to the sample size divided by the population size.
In this case, the sample size is 40, and the population size is 400, so the probability of any given element being selected is 40/400 = 1/10.
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Anna baked 3 batches of cookies with c cookies in each batch. She then ate 8 cookies!
Answer:
[tex]t=3c-8[/tex]
Step-by-step explanation:
It seems like your question is incomplete, so I will assume it is asking for an expression that represents how many cookies Anna has left.
Let t represent the total number of cookies left. Let's build this expression. If each batch contains c cookies, and there are 3 batches, the total number of cookies baked is 3 times c. Since she ate 8 cookies, 8 must be subtracted from that total. Therefore:
[tex]t=3c-8[/tex]
Hope this helps!
Please answer this: !! (50 points)
Answer: Lower bound: 25°C
Upper bound: 26°C
Step-by-step explanation:
PLS MARK BRAINLIEST IF U CAN !!
A chain of gyms has 3.5×105 members throughout the U.S. Their total annual revenue from membership fees is 4.2×107 dollars. Assuming each member pays the same amount, what is the annual membership fee per person?
Write your answer in standard form. Do not use exponents.
The annual membership fee per person is 120 dollars.
What is scientific notation?In scientific notations numbers are written in the form of a base that is
0 ≤ b < 10 and multiplied by 10ⁿ where n represents integers.
We write large standard numbers in scientific form in a compact manner.
Given, A chain of gyms has 3.5×10⁵ members throughout the U.S. Their total annual revenue from membership fees is 4.2×10⁷ dollars.
Therefore, The annual membership fee per person is,
= (4.2×10⁷)/(3.5×10⁵).
= 1.2×10².
= 1.2×100
= 120 dollars.
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2√5x-4-3= -11
Is there roots or no roots?
While packing , Goerge and harri did a number of foolih and funny thing. Name any five
The true statements are (i),(iii),(iv),(vi),(vii), and (ix).
While packing the hamper, George and Harris do a number of foolish and funny things. The true statements are as follows:
(i) They started with breaking a cup.
(iii) They squashed a tomato.
(iv) They trod on the butter.
(vi) They put things behind them and couldn't find them.
(vii) They stepped on things.
In the descriptions, it appears that George and Harris were not very skilled at packing and ended up making a lot of mistakes, such as breaking dishes, squashing food, losing items, and stepping on things. So, statement (ii), (v), (viii) is false because they did not pack the pictures well, and statement (x) is false because they were not very good at packing.
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--The given question is incomplete; the complete question is
"While packing the hamper, George and Harris do a number of foolish and funny things. Tick the statements that are true.
(i) They started with breaking a cup.
(ii) They also broke a plate.
(iii) They squashed a tomato.
(iv) They trod on the butter.
(v) They stepped on a banana.
(vi) They put things behind them and couldn't find them.
(vii) They stepped on things.
(viii)They packed the pictures at the bottom and put heavy things on top.
(ix) They upset almost everything.
(x) They were very good at packing."--
im just trying get this over with haha dont guess please, if you dont know the answer then dont answer
We can see here that:
1. x-y=3
3x + y = 1 - One solution
2. y = 5x-4
y=5x+13 - No solutions
3. 4g + r = 12
8g= -2r+24 - Infinite number of solutions
4. 3y+ 15x = -1
y = 4-5x - No solutions
What is a system of equation?A system of equations is a set of two or more equations that are related to each other and must be solved simultaneously to find the values of the variables involved. A system of equations represents a situation in which multiple unknowns are related to each other in a specific way, and finding a solution requires finding the values of all the unknowns that satisfy all the equations in the system.
Solving:
x-y=3 ----eq. 1
3x + y = 1 ----eq. 2
Thus, x = 3+y --- eq. 3
Substituting it into eq. 2, we have:
3( 3+y ) + y = 1
9 + 3y + y = 1
9 + 4y = 1
4y = 1-9
4y = -8
y = -8/4 = -4
Substituting y in eq. 1, we have:
x - (-4) = 3
x + 4 = 3
x = 3 - 4 = -1.
Thus, one solution.
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if multiple events have a 20% probability, what is the chance that two or more will happen simultaneously
The probability of two or more events happening simultaneously is 0.36.
The probability of two or more events happening simultaneously depends on the number of events and the type of relationship between them. If the events are independent, meaning that the occurrence of one event does not affect the probability of the other event happening.
The probability of two or more events happening simultaneously can be calculated using the formula for the sum of probabilities:
P(A or B) = P(A) + P(B) - P(A and B)
Where A and B are two events. If we have n independent events with the same probability of 20%, the probability of two or more events happening simultaneously can be calculated as follows:
P = 1 - P(none of them happen) = 1 - (1 - 0.2)ⁿ
For n = 2, we have:
P = 1 - (1 - 0.2)² = 1 - 0.64 = 0.36
So, the chance that two events with a 20% probability will happen simultaneously is 36%. The chance for three or more events is even higher.
It's important to note that if the events are dependent, the calculation will be different. The relationship between the events can significantly impact the final probability.
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what the answer for 18k+22p-10
Answer:
92
Step-by-step explanation:
In the figure, ABC is a right angled triangle and angle BAC = 90°. If AD perpendicular to BC and BD=DC then prove that BC² = 4AD².
2
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a trapezoid has an area of 100 square units. what scale factor would be required to dilate the trapezoid to have each area?
A dilation of a figure is a transformation that changes the size of a figure but not its shape. To find the scale factor required to dilate a trapezoid to have a different area, we need to know the formula for the area of a trapezoid and the desired area. In this conext, the area would be 100 * scale factor^2
The formula for the area of a trapezoid is:
Area = (base1 + base2) * height / 2
Let's say the original trapezoid has an area of 100 square units and the desired area is "A" square units.
The scale factor required to dilate the trapezoid to have an area of "A" square units is given by the equation: 100 = (base1 + base2) * height / 2
100 * 2 / (base1 + base2) = height
200 / (base1 + base2) = height
To find the new area:
A = (base1 + base2) * height / 2
A = (base1 + base2) * 200 / (2 * (base1 + base2))
A = 200 * height / 2
A = 100 * scale factor^2
So, the scale factor required to dilate the trapezoid to have an area of "A" square units is given by the equation:
Scale factor = sqrt(A/100)
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What is the slope of line a?
(I didnt mean to click the -3/4 it was by accident)
Answer: it is 3/4
Step-by-step explanation:
(0,1) and (4,4) are the two points.
slope = (4-1)/(4-4) = 3/ 4
Harry had 25 marbles. For his birthday, his grandmother gave him m more marbles. Which expression shows the total number of marbles Harry has now?
Answer:
Step-by-step explanation:
If Harry has 25 marbles, and his grandmother gave him m more marbles we can say that harry has 25+m amount of marbles.
