Answer:
f⁻¹(-2)=3
f⁻¹(1)=0
Step-by-step explanation:
inverse function flips x any coordinate into y and x
whats an"an amount, shared equally with 4 people "
well if that's in a math problem then its division. Because you are sharing equally.
GD Simpinying Radicals Simplify the number into simplest radical form. Use the factor tree to help determine the factors. √96 Warm-Up √6 O 2√6 0 4√6 0 4√3 Intro O Select a composite number to break into factors. Continue factoring until all factors are prime. 96 Done GD Simpinying Radicals Simplify the number into simplest radical form . Use the factor tree to help determine the factors . √96 Warm - Up √6 O 2√6 0 4√6 0 4√3 Intro O Select a composite number to break into factors . Continue factoring until all factors are prime . 96 Done
Answer:
Step-by-step explanation:
Select the logical expression that is equivalent to:¬∀x∃y(P(x)∧Q(x,y))
Group of answer choices
A. ∃y∀x(¬P(x)∨Q(x,y))
B. ∀y∃x(¬P(x)∨¬Q(x,y))
C. ∃x∀y(¬P(x)∨¬Q(x,y))
D. ∀x∃y(¬P(x)∨¬Q(x,y))
The logical expression that is equivalent to ¬∀x∃y(P(x)∧Q(x,y)) is ∀x∃y(¬P(x)∨¬Q(x,y)) i.e., the correct option is option D.
To determine the equivalent logical expression, we need to apply De Morgan's laws and quantifier negation rules.
Starting with the given expression ¬∀x∃y(P(x)∧Q(x,y)), let's break it down step by step:
Apply the negation of the universal quantifier (∀x) to get ∃x¬∃y(P(x)∧Q(x,y)).
This step changes the universal quantifier (∀x) to an existential quantifier (∃x) and negates the following expression.
Apply the negation of the existential quantifier (∃y) to get ∃x∀y¬(P(x)∧Q(x,y)).
This step changes the existential quantifier (∃y) to a universal quantifier (∀y) and negates the following expression.
Apply De Morgan's law to the negation of the conjunction (P(x)∧Q(x,y)) to get ∃x∀y(¬P(x)∨¬Q(x,y)).
This step distributes the negation inside the parentheses and changes the conjunction (∧) to a disjunction (∨).
Therefore, the equivalent logical expression is option D. ∀x∃y(¬P(x)∨¬Q(x,y)).
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suppose the vertical distance between the points (0, a) and (0, b) is 5. if her wealth increased from $1,050 to $1,350, then a. britney's subjective measure of her well-being would increase by more than 5 units. b. britney would change from being a person who is not risk averse into a risk-averse person. c. britney would change from being a risk-averse person into a person who is not risk averse. d. britney's subjective measure of her well-being would increase by less than 5 units.
The correct answer is d. Britney's subjective measure of her well-being would increase by less than 5 units.
We have, The vertical distance between points (0, a) and (0, b) is 5.
Her wealth increased from $1,050 to $1,350.Britney's subjective measure of her well-being would increase by less than 5 units. Option (d) is correct. Because the vertical distance between the points (0, a) and (0, b) is 5.
If the horizontal distance is the same as the vertical distance, then the slope is 1.
The slope of the straight line joining two points is given by;
\(\displaystyle m=\frac{y_2-y_1}{x_2-x_1}\)
Where the points are \((x_1,y_1), (x_2,y_2)\)
Let's assume the two points are \((0, a) \ and \ (0, b)\).
The slope of the line connecting these two points is;
\(\displaystyle m=\frac{b-a}{0-0}=\frac{b-a}{0}\)
This is undefined as we cannot divide by 0.Hence, there is no horizontal distance, and there is no slope.
Therefore, if the vertical distance between two points is 5, and there is no horizontal distance, then she will experience less than 5 units of well-being.
Therefore, Britney's subjective measure of her well-being would increase by less than 5 units.
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(Comparing Data MC)
The data given represents the number of gallons of coffee sold per hour at two different coffee shops.
Coffee Ground
1.5 20 3.5
12 2 4
11 7 2.5
9.5 3 5
Perks A Lot
10 3.5 3
5 2.5 7
8 5.5 9.5
6 9 4.5
Compare the data and use the correct measure of center to determine which shop typically sells the most amount of coffee per hour. Explain.
Perks A Lot, with a mean value of 6.125 gallons
Perks A Lot, with a median value of 6.125 gallons
Coffee Ground, with a mean value of 6.75 gallons
Coffee Ground, with a median value of 6.75 gallons
The data shows that Coffee Ground typically sells the most amount of coffee per hour.
How to explain the informationThe mean value of the number of gallons of coffee sold per hour at Coffee Ground is 6.75 gallons, while the mean value at Perks A Lot is 6.125 gallons. The median value of the number of gallons of coffee sold per hour at Coffee Ground is also 6.75 gallons, while the median value at Perks A Lot is 6.125 gallons.
The mean is calculated by adding up all of the values in a set of data and dividing by the number of values. The median is calculated by finding the middle value in a set of data after the values have been arranged in order from least to greatest.
In this case, the mean and median values are both higher for Coffee Ground than for Perks A Lot
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Which is bigger -7/11 or -2/3
Answer:
-2/3
Step-by-step explanation:
You are shopping for single-use cameras to hand out at a party. The daylight cameras cost $2.75 and the flash cameras cost$4.25. You must buy exactly 20 cameras and you want to spend between $65 and$75, inclusive. Write and solve a compound inequality for this situation. Then list all the solutions that involve whole numbers of cameras.
The compound inequality for the given situation is $2.75x + $4.25y ≥ $65 and $2.75x + $4.25y ≤ $75, where x represents the number of daylight cameras and y represents the number of flash cameras.
To solve this compound inequality, we need to find the values of x and y that satisfy both conditions. The inequality $2.75x + $4.25y ≥ $65 represents the lower bound, ensuring that the total cost of the cameras is at least $65. The inequality $2.75x + $4.25y ≤ $75 represents the upper bound, making sure that the total cost does not exceed $75.
To list the solutions involving whole numbers of cameras, we need to consider integer values for x and y. We can start by finding the values of x and y that satisfy the lower bound inequality and then check if they also satisfy the upper bound inequality. By trying different combinations, we can determine the possible solutions that meet these criteria.
After solving the compound inequality, we find that the solutions involving whole numbers of cameras are as follows:
(x, y) = (10, 10), (11, 8), (12, 6), (13, 4), (14, 2), (15, 0), (16, 0), (17, 0), (18, 0), (19, 0), (20, 0).
These solutions represent the combinations of daylight and flash cameras that fulfill the requirements of buying exactly 20 cameras and spending between $65 and $75.
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point) The number of Drosophila fruit flies in controlled experiment assumes the following growth pattern when the food source is limited: 600 N(t) 1+ Me-0.3t where measured in days. A. How many fruit files were there in the beginning? What is the limiting number of fruit flies 600 C.At what time was the population increasing most rapidly? D. At what rate is the number of fruit flies increasing after days? 600/(1+11e
time was the population increasing most rapidly. At rate is the number of fruit flies increasing after days A. 600 B. 600 C. t=0 D. 0.09
The equation 600/(1+Me-0.3t) is a model for the population of Drosophila fruit flies, with time representing the number of days the experiment has gone on for. A. The population of fruit flies in the beginning is given by the equation as 600. B. The limiting number of fruit flies is also given by the equation as 600. C. The population is increasing most rapidly when t=0. D. After days, the number of fruit flies is increasing at a rate of 0.09, which can be calculated by taking the derivative of the equation with respect to t.
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As the number of baseball cards increases, what happens to the money spent in dollars?
Answer:
decreases
Step-by-step explanation:
a rectangular wall with a height of 7 1/2 ft has a perimeter of 46 ft. What is the area of the wall?
Answer:
116.25 ft²
Step-by-step explanation:
Height = 7.5ft
Perimeter : 2(7.5)ft + 2x ft = 46ft
Length = x ft
15+2x = 46ft
31 ft = 2x ft
x = 15.5 ft
7.5 x 15.5 = 116.25 ft²
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A company wants to test the claim that their batteries last more than 42 hours. Using a simple random sample of 18 batteries yielded the following battery life:
35 54 36
50 53 42
37 51 37
40 55 45
45 42 52
45 39 47
Test this claim using a significance level of 0.05.
To test the claim that the batteries last more than 42 hours, a hypothesis test can be conducted using the given sample data. With a significance level of 0.05, t
We can set up the hypotheses as follows:
Null hypothesis (H0): The true mean battery life is 42 hours.
Alternative hypothesis (Ha): The true mean battery life is greater than 42 hours.
To conduct the hypothesis test, we calculate the sample mean and sample standard deviation from the given data. The sample mean is found to be 44.111 hours.
Next, we calculate the test statistic using the formula:
t = (sample mean - hypothesized mean) / (sample standard deviation / sqrt(sample size))
Plugging in the values, we get:
t = (44.111 - 42) / (sd /\(\sqrt{18}\))
With the given sample data, the sample standard deviation is calculated to be approximately 6.247.
Calculating the test statistic gives us t = 1.420.
We then compare the test statistic to the critical value from the t-distribution with n-1 degrees of freedom and a significance level of 0.05. If the test statistic is greater than the critical value, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.
Looking up the critical value for a one-tailed test at a 0.05 significance level and 17 degrees of freedom, we find it to be approximately 1.740.
Since the test statistic (1.420) is less than the critical value (1.740), we fail to reject the null hypothesis. Therefore, based on the given data, there is not sufficient evidence to support the claim that the batteries last more than 42 hours.
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Suppose you have a job that pays $13.50 per hour and you work anywhere from 10 to 40 hours per week. a. Write an equation, with a restriction on the variable I, that gives the amount of money, y, you will earn for working 2 hours in one week. y = _____ , Preview with ____ <= x <= ____ b. Use the function rule you have written in part a. to find the y values for the given z values: x = 10, y = ___ x = 20, y= ___
x = 30, y = ____. x = 40, y = ____ c. Construct a line graph from the information found in b. 520+ -480+ 440+ 400- 360 320- 280- 240 200 160+ 120+ 80- 40+ 10 20 30 40 Clear All Draw: Line Dot Open Dot d. State the domain and range of this function. Domain: ____ <= x <= ______
Range: <= y <= _____
e. What is the minimum amount you can earn in a week with this job? You'll earn at least $ ______.
What is the maximum amount? You can earn up to $ ____.
The maximum amount you can earn is $540
a. y = 13.50x , 10 <= x <= 40
b. x = 10, y = 135; x = 20, y= 270; x = 30, y = 405; x = 40, y = 540
c. Domain: 10 <= x <= 40; Range: 0 <= y <= 540
d. The minimum amount you can earn in a week with this job is $135. The maximum amount you can earn is $540.
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-16x-10>14-10x
hi can u please help me with this
Answer:
x < -4
General Formulas and Concepts:
Pre-Algebra
Equality PropertiesStep-by-step explanation:
Step 1: Define inequality
-16x - 10 > 14 - 10x
Step 2: Solve for x
Add 16x to both sides: -10 > 14 + 6xSubtract 14 on both sides: -24 > 6xDivide 6 on both sides: -4 > xRewrite: x < -4Here we see that any value x that is less than -4 would work as a solution.
Answer:
Step-by-step explanation:
Let's solve your inequality step-by-step.
−16x−10>14−10x
Step 1: Simplify both sides of the inequality.
−16x−10>−10x+14
Step 2: Add 10x to both sides.
−16x−10+10x>−10x+14+10x
−6x−10>14
Step 3: Add 10 to both sides.
−6x−10+10>14+10
−6x>24
Step 4: Divide both sides by -6.
−6x
−6
>
24
−6
x<−4
Answer:
x<−4
There are four students named A,B,C, and D. All four of them are loss averse over money, with the same value function for money: v(x dollars )={√x x ≥ 0
{-2√-x x < 0
All three of them are also loss averse over mugs, with the same value function for mugs:
v(y mugs)={3y y ≥ 0
{4y y < 0
Total utility is the sum of the gain/loss utility for mugs and the gain/loss utility for money. The reference point is the status quo, that is, a person's initial endowment. Student A owns a mug and is willing to sell it for a price of a dollars or more. Student B does not own a mug and is willing to pay up to b dollars for buying it. Student C does not own a mug and is indifferent between getting a mug and getting c dollars. Student D is indifferent between losing a mug and losing d dollars.
1. Solve for a,b,c, and d.
2. Instead, suppose A, B, C, and D are only loss averse over mugs, but not over money. That is, their value function for money is instead:
v(x dollars)={√x x ≥ 0
{-√-x x < 0
and their value function for mugs remains:
v(y mugs)={3y y ≥ 0
{4y y < 0
Solve for a,b,c, and d.
3. Instead, suppose A,B,C, and D are not loss averse:
v(x dollars)={√x x ≥ 0
{-√-x x < 0
and v(y mugs)=3y
Solve for a,b,c, and d.
4. Suppose A, B, C, and D are not loss averse (as in the previous question), but their value for a mug varies with ownership. Specifically, the value of the mug is 3 for someone who does not currently own the mug, and 4 for someone who currently owns a mug. Solve for a,b,c, and d.
As per the question, All four students A, B, C, and D are loss-averse over money and have the same value function as below:v(x dollars)={√x x ≥ 0 {-2√-x x < 0They are also loss averse over mugs and have the same value function.
v(y mugs)={3y y ≥ 0
{4y y < 0
Now, we have to find the values of a, b, c and d as below:
- Student A owns a mug and is willing to sell it for a price of a dollars or more. i.e v(a) = v(0) + v(a-A), where A is the initial endowment of A. According to the given function, v(0) = 0, v(a-A) = 3, and v(A) = 4.
So, a ≥ A+3/2
- Student B does not own a mug and is willing to pay up to b dollars for buying it. i.e v(B-b) = v(B) - v(0), where B is the initial endowment of B. According to the given function, v(0) = 0, v(B-b) = -4, and v(B) = -3.
So, b ≤ B+1/2
- Student C does not own a mug and is indifferent between getting a mug and getting c dollars. i.e v(c) = v(0) + v(c), where C is the initial endowment of C. According to the given function, v(0) = 0, v(c) = 3.
So, c = C/2
- Student D is indifferent between losing a mug and losing d dollars. i.e v(D-d) = v(D) - v(0), where D is the initial endowment of D. According to the given function, v(0) = 0, v(D-d) = -3.
So, d = D/2
2) In this case, value function for money changes to:v(x dollars)={√x x ≥ 0
{-√-x x < 0
However, the value function for mugs remains the same:v(y mugs)={3y y ≥ 0
{4y y < 0
Therefore, values for a, b, c, and d will remain the same as calculated in part (1).
3) In this case, students are not loss-averse. Value function for money:v(x dollars)={√x x ≥ 0
{-√-x x < 0
Value function for mugs:v(y mugs)={3y y ≥ 0
The reference point is the status quo, i.e initial endowment. So,
- Student A owns a mug and is willing to sell it for a price of a dollars or more. The value of mug for A is 3 initially and he would sell it for 3 or more.
So, a ≥ A+3/2
- Student B does not own a mug and is willing to pay up to b dollars for buying it. The value of mug for B is 3 initially and he would buy it for 3 or less.
So, b ≤ B+3/2
- Student C does not own a mug and is indifferent between getting a mug and getting c dollars. The value of the mug for C is 3 initially.
So, c = 3
- Student D is indifferent between losing a mug and losing d dollars. The value of the mug for D is 3 initially.
So, d = 3
4) In this case, value function for money:v(x dollars)={√x x ≥ 0
{-√-x x < 0
Value function for mugs: Mug will have a value of 4 for someone who owns it and 3 for someone who does not own it.
The reference point is the status quo, i.e initial endowment. So,
- Student A owns a mug and is willing to sell it for a price of a dollars or more. The value of mug for A is 4 initially and he would sell it for 4 or more.
So, a ≥ A+2
- Student B does not own a mug and is willing to pay up to b dollars for buying it. The value of mug for B is 3 initially and he would buy it for 3 or less.
So, b ≤ B+3/2
- Student C does not own a mug and is indifferent between getting a mug and getting c dollars. The value of the mug for C is 3 initially and he would like to buy it for 3.
So, c = 3
- Student D is indifferent between losing a mug and losing d dollars. The value of the mug for D is 3 initially.
So, d = 3.
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Try solving the equation 2x + 20 = 12x
Answer:
x = 2
Step-by-step explanation:
2x + 20 = 12x
First, we have to put our exponent on the same side of our equation
2x + 20 = 12x
-2x -2x
20 = 10x
Now, we have to divide by 10 on both sides to get our exponent on its own (x)
20 = 10x
÷10 ÷10
2 = x or x =2
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3. Suppose g(t) = [0.5sinc²(0.5 t) cos(2 t)], where the sinc function is defined as (3.17) on p. 100 of the textbook. (a) Apply Parseval's Theorem to determine the 95% energy bandwidth (B) of this signal, where we define the 95% energy bandwidth as:
(b) Gf²df = 0.95Eg. What is the 95% energy bandwidth of g(2t) in terms of the value of B determined in Part a. Please provide full justification for your answer.
To determine the 95% energy bandwidth (B) of the signal g(t) = [0.5sinc²(0.5 t) cos(2 t)], we can apply Parseval's Theorem. Parseval's Theorem states that the total energy of a signal in the time domain is equal to the total energy of the signal in the frequency domain. Mathematically, it can be expressed as:
∫ |g(t)|² dt = ∫ |G(f)|² df
In this case, we want to find the frequency range within which 95% of the energy of the signal is concentrated. So we can rewrite the equation as: 0.95 * ∫ |g(t)|² dt = ∫ |G(f)|² df
Now, we need to evaluate the integral on both sides of the equation. Since the given signal is in the form of a product of two functions, we can separate the terms and evaluate them individually. By applying the Fourier transform properties and integrating, we can find the value of B.
For part (b), when we consider g(2t), the time domain signal is compressed by a factor of 2. This compression results in a corresponding expansion in the frequency domain. Therefore, the 95% energy bandwidth of g(2t) will be twice the value of B determined in part (a). This can be justified by considering the relationship between time and frequency domains in Fourier analysis, where time compression corresponds to frequency expansion and vice versa.
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How do you write 2.15 in two different ways using whole numbers 2.15 or 1._5
2.15 can also be written as 1._5, where the blank space represents the digit 1.
2.15 can be written as 215/100, in fraction form. This can also be simplified as 43/20. Two different ways of writing 2.15 using whole numbers are:215 as 215 is already in whole number form, hence it's the first way of writing 2.15 using whole numbers. To get the second way of writing 2.15 using whole numbers, one can multiply both the numerator and denominator of the fraction 43/20 by 10. This gives 430/200, which simplifies to 21/10. Therefore, 2.15 can also be written as 1._5, where the blank space represents the digit 1.
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Be sure to SHOW YOUR WORK!!! 1.) You oversee the community garden. You have 3 teams who want plots in your garden, and all gardens are in the shape of a square. Team A wants a plot which is 36 square meters, Team B wants a plot which is 64 square meters and Team Cwants a plot which is 49 square meters. You need to determine the length and width of your garden. You also need to determine which team gets which plot.) a.) Qotline the dimensions of the garden and insert the plots for the 3 teams. b.) Calculate the dimensions of each side and show your work Team A A Team B: Team C: b.) What are the minimum dimensions of your garden plot? Length: Width:
hello
to solve this problem, we need to draw the
Find value of X.. round to the tenth place if needed
Identify the graph of the solution set of 13 > 5 + 4x.
The requried graph of the solution of a set of given inequality 13 > 5+ 4x is shown.
Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.
here,
Given inequality,
13 > 5 + 4x
Simplify the above expression,
Subtract -5 from both sides,
13 - 5 > 5 - 5 + 4x
8 > 4x
Divide by 4 into both sides
2 > x
The graph of the solution to the given inequality is less than 2, and line x = 2 will be a dotted line [value no included in x < 2]
Thus, the graph of the inequality has been shown.
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Explain how two samples can have the same mean but different standard deviations. Draw a bar graph that shows the two samples, their means, and standard deviations as error bars.
Two samples can have the same mean but different standard deviations due to the spread of data around the mean. Standard deviation is a measure of how much the data values differ from the mean. The greater the deviation of the data points from the mean, the greater the standard deviation.
Two samples can have the same mean but different standard deviations because standard deviation is a measure of the spread of data around the mean. If the data values are tightly clustered around the mean, the standard deviation will be small. If the data values are spread out around the mean, the standard deviation will be large. Therefore, two samples can have the same mean but different standard deviations because the spread of data around the mean can be different for each sample.
Two samples can have the same mean but different standard deviations because the spread of data around the mean can be different for each sample. For example, consider two samples of test scores. Sample A has a mean score of 80 and a standard deviation of 5. Sample B has a mean score of 80 and a standard deviation of 10. The scores in Sample B have more variability than the scores in Sample A.In a bar graph, the means of the two samples can be represented by two bars with the same height. The standard deviations of the two samples can be represented by error bars on each bar. The error bars show the variability of the data in each sample. The length of the error bars for Sample B would be longer than the length of the error bars for Sample A.
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"liabilities whose book values and fair values difered.
of \( \$ 100,000 \) during that year. Muliplechoce 52000000 \( 52,05,000 \)
liablities whose book values and fair values differed:"
The liabilities whose book values and fair values differed by \$100,000 during that year are:
What is the explanation for the difference between book values and fair values of liabilities?The difference between book values and fair values of liabilities arises due to various factors. Book value refers to the value of a liability as recorded on the balance sheet, which is based on historical cost and may not reflect the current market conditions. Fair value, on the other hand, represents the estimated value of a liability in the current market.
There are several reasons why the book values and fair values of liabilities may differ.
Changes in interest rates, creditworthiness of the debtor, market conditions, and the passage of time can all contribute to these differences. If interest rates have changed since the liability was initially recorded, the fair value may be higher or lower depending on the prevailing rates.
Similarly, if the creditworthiness of the debtor has changed, the fair value may be adjusted to reflect the increased or decreased risk associated with the liability.
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The ______________ probability of an outcome is obtained by dividing the frequency of occurrence of an event by the number of trials of the experiment
Answer:
Empirical probability
Step-by-step explanation:
Empirical probability is data collected from experiment and real-life situation.
The "empirical probability" of an outcome is obtained by dividing the frequency of occurrence of an event by the number of trails of the experiment.
\(\Longrightarrow: \sf{P(E)=\dfrac{\text{number of times event occured}}{\text{number of trails}}\)
Therefore, the correct answer is empirical probability.I hope this helps you! Let me know if my answer is wrong or not.
Find the equation for the
following parabola.
Vertex (2, -1)
Focus (2, 3)
Answer:
(x−2)^2=16(y+1)
Step-by-step explanation:
The equation for the parabola is (x - 2)² = 16(y + 1) if the vertex of the parabola is (2, -1) and focus of the parabola is (2, 3) option (D) is correct.
What is a parabola?It is defined as the graph of a quadratic function that has something bowl-shaped.
We have:
The vertex of the parabola = (2, -1)
The focus of the parabola = (2, 3)
As we know, the vertex form of the parabola is given by:
(x - h)² = 4a(y - k)
(h, k) is the vertex of the parabola:
(x - 2)² = 4a(y - (-1))
(x - 2)² = 4a(y + 1)
The value of a can be found using the formula:
a = √[(c-h)² + (d-k²]
(c, d) is the focus of the parabola:
(c, d) = (2, 3)
a = √[(2-2)² + (3-(-1))²]
a = √ (3+1)²]
a = 4
(x - 2)² = 4(4)(y + 1)
(x - 2)² = 16(y + 1)
Thus, the equation for the parabola is (x - 2)² = 16(y + 1) if the vertex of the parabola is (2, -1) and focus of the parabola is (2, 3) option (D) is correct.
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I NEED HELP PLEASEEEE HELP ME
Answer:
pi r^2
Step-by-step explanation:
that's the answer for question 13
rationalize the denominator of $\frac{2}{\sqrt[3]{4} \sqrt[3]{32}}$. the answer can be written in the form of $\frac{\sqrt[3]{a}}{b}$, where $a$ and $b$ are positive integers. find the minimum possible value of $a b$.
The original expression \($\frac{2}{\sqrt[3]{4} \sqrt[3]{32}}$\) was rationalized by multiplying both numerator and denominator by \($\sqrt[3]{4} \sqrt[3]{2}$\), and then dividing numerator and denominator by \($\sqrt[3]{4}$\).
\($\frac{2}{\sqrt[3]{4} \sqrt[3]{32}} = \frac{\sqrt[3]{8}}{4}$\)
Minimum possible value of \($ab = 32$\)
\(= \frac{\sqrt[3]{4} \sqrt[3]{8}}{\sqrt[3]{4} \sqrt[3]{4} \sqrt[3]{2}}$= \frac{\sqrt[3]{8}}{\sqrt[3]{4} \sqrt[3]{2}}$= \frac{\sqrt[3]{8}}{4}$\)
We start with the given expression, \($\frac{2}{\sqrt[3]{4} \sqrt[3]{32}}$\), which is in the form \($\frac{p}{qr}$\). To rationalize the denominator, we need to multiply both numerator and denominator by qr (which is \($\sqrt[3]{4} \sqrt[3]{2}$\) in this case). This gives us\($\frac{\sqrt[3]{4} \sqrt[3]{8}}{\sqrt[3]{4} \sqrt[3]{4} \sqrt[3]{2}}$\). We can simplify this expression further by dividing both numerator and denominator by \($\sqrt[3]{4}$\), giving us \($\frac{\sqrt[3]{8}}{\sqrt[3]{2} \sqrt[3]{4}}$\). Finally, we can simplify the denominator further by multiplying both numerator and denominator by \($\sqrt[3]{2}$\), giving us the final result of \($\frac{\sqrt[3]{8}}{4}$\). The minimum possible value of ab is 32.
The original expression \($\frac{2}{\sqrt[3]{4} \sqrt[3]{32}}$\) was rationalized by multiplying both numerator and denominator by \($\sqrt[3]{4} \sqrt[3]{2}$\), and then dividing numerator and denominator by \($\sqrt[3]{4}$\). The final result was\($\frac{\sqrt[3]{8}}{4}$\), and the minimum possible value of ab was 32.
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Omg, I need help! A builder is buying property where she can build new houses. The line plot shows the sizes for each house. 1/6 has 6 X's 1/3 has 3 X's and 1/2 has 6 X's. Help anyone?
Answer:
Average size of the lots = ⅓ acre
Step-by-step explanation:
The question incomplete without specifying what we are to determine.
Question:A builder is buying property where she can build new houses. The line plot shows the sizes for each house. 1/6 has 6 X's 1/3 has 3 X's and 1/2 has 6 X's. Organize the information in a line plot. What is the average size of the lots? _________ acre
Help anyone?
Solution:
We are asked to organize the information in a line plot. See attachment for the line plot.
Given: 1/6 has 6 X's 1/3 has 3 X's and 1/2 has 6 X'sIn no particular order, the sizes of the lots are:1/6, 1/6, 1/6, 1/6, 1/6, 1/6, 1/3, 1/3, 1/3, 1/2, 1/2, 1/2, 1/2, 1/2 and 1/2 acre.
Let's count the number of lot for each size given.
For 1/6: there are 6 X's on the line plot of 1/6 number of lot for 1/6
= the lot × number of times it occurs
= (1/6) × 6 = 6/6 = 1 acre
For 1/3: there are 3 X's on the line plot of 1/3 number of lot for 1/3 = the lot × number of times it occurs
= (1/3) × 3 = 3/3 = 1 acre
For 1/2: there are 6 X's on the line plot of 1/2 number of lot for 1/2
= the lot × number of times it occurs
= (1/2) × 6 = 6/2= 3 acres
To find average size of the lots, we would sum all lot for each given size then divide by the total number of lots given.Sum of all lot for each given size = 1+1+3
Sum of all lot for each given size = 5
The total number of lots given = 15
Average size of the lots = 5/15 = 1/3
Average size of the lots = ⅓ acre
A jogging track has a length of 1144 yards yd. How long is this in miles mi? First fill in the blank on the left side of the equation using one of the ratios. Then write your answer on the right side of the equation.
Answer:
length=0.65 mi
length in yr= 0.65x1760=1144
The length of the jogging track is 0.65 miles.
To convert the length of the jogging track from yards (yd) to miles (mi), use the ratio between yards and miles.
1 mile = 1760 yards
Now, set up the equation to convert the length:
Length in miles (mi) = Length in yards (yd) / Conversion ratio
Length in miles (mi) = 1144 yd / 1760 yd/mi
Now, perform the calculation:
Length in miles (mi) = 1144 / 1760 ≈ 0.65 miles (rounded to the nearest hundredth)
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Find the length of diagonal AC in the rectangle
at the right
show you’re work plss
Answer:
26
Step-by-step explanation:
Let 10 be a, and 24 be b, and the undefined hypotenuse be c.
\(a^2 + b^2 = c^2\)
\(10^2 + 24^2 = c^2\)
100 + 576 = c
c = 676
\(\sqrt{100} + \sqrt{576} = \sqrt{676}\)
\(10^2 + 24^2 = 26^2\)
c = 26
The value of the undefined line is 26.
Let M −1
=[ 1
2
1
1
]. Then (2M T
) −1
= [ 4
−2
1
5
] [ 4
1
−2
5
] None of the mentioned [ 1
5
4
−2
]
The correct option for the equation is is [1/5 4/5 / -2/5 2/5].
To find (2MT)-1,
First, we need to find 2MT.
(2MT) = 2 * [ 1 2 / 1 1 ]T = 2 * [1 1 / 2 1] = [2 2 / 4 2]
Now, let's find the inverse of (2MT).
To find the inverse of (2MT), we can use the formula:
(AB)-1 = B-1 A-1
Here, A = [4 -2 / 1 5] and B = [4 1 / -2 5]
We need to find (2MT)-1 = [4 -2 / 1 5] -1 [4 1 / -2 5] -1
On solving, we get(2MT)-1 = [1/5 4/5 / -2/5 2/5]
Therefore, the correct option is [1/5 4/5 / -2/5 2/5].
The answer is: (D) [ 1/5 4/5 / -2/5 2/5 ]
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