The inverse of the equation y = - 4x + 3 is y = (3 - x)/4.
What is an inverse function?First to be an inverse function that function needs to one to one function, meaning every different preimage must correspond to a different image.
We can obtain the inverse of a function by switching the variables x and y with their respective positions and solving for y in terms of x.
Given, An equation y = - 4x + 3.
To find the inverse we'll first solve for 'x'.
Therefore,
y = - 4x + 3.
4x = 3 - y.
x = (3 - y)/4.
Now, we'll interchange the positions of 'x' and 'y'.
Therefore,
x = (3 - y)/4 becomes,
y = (3 - x)/4.
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rewrite each expression without using absolute value notation |7m-56| if m<8
Considering the definition of the absolute value function, the expression is written as -7m + 56.
What is the definition of the absolute value function?The absolute value function is defined as follows:
[tex]|x| = x, x \geq 0[/tex].[tex]|x| = -x, x < 0[/tex]That is, where the expression is negative, it is multiplied by -1, while where it is not negative the expression is kept.
In this problem, the expression is:
|7m - 56|
For m < 8, we have that one example is m = 0:
7(0) - 56 = -56.
The expression is negative, hence the signal is changed, that is:
|7m - 56| = -(7m - 56) = -7m + 56.
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Firm valuation schultz industries is considering the purchase of arras manufacturing. arras is currently a supplier for schultz, and the acquisition would allow schultz to better control its material supply. the current cash flow from assets for arras is $8 million. the cash flows are expected to grow at 9 percent for the next five years before leveling off to 6 percent for the indefinite future. the cost of capital for schultz and arras is 13 percent and 11 percent, respectively. arras currently has 3 million shares of stock outstanding and $25 million in debt outstanding. what is the maximum price per share schultz should pay for arras? (do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) price per share $
Based on the calculations, the maximum price per share that Schultz should pay for Arras is approximately equal to $53.00.
How to calculate the maximum price per share?First of all, we would determine the cash flows for the company until the growth rate changes at a constant perpetual rate:
Year 1: $8,000,000(1 + 0.09) = $8,720,000.
Year 2: $8,720,000(1 + 0.09) = $9,504,800.
Year 3: $9,504,800(1 + 0.09) = $10,360,232.
Year 4: $10,360,232(1 + 0.09) = $11,292,652.88.
Year 5: $11,292,652.88(1 + 0.09) = $12,308,991.6392.
Year 6: $12,308,991.6392(1 + 0.06) = $13,047,5311.137552.
Next, we would calculate the terminal value in Year 5:
TV₅ = CF₆/(RWACC - g)
TV₅ = CF₆/(0.11 - 0.06)
TV₅ = $12,308,991.6392/0.05
TV₅ = $246,179,832.784.
By using Arras' cost of capital, we would determine its present value:
V₀ = $8,720,000/(1 + 0.11) + $9,504,800/(1 + 0.11)² + $10,360,232/(1 + 0.11)³+ $11,292,652.88/(1 + 0.11)⁴+ ($12,308,991.6392 + $246,179,832.784)/(1 + 0.11)⁵.
V₀ = $8,720,000/(1.11) + $9,504,800/(1.11)² + $10,360,232/(1.11)³+ $11,292,652.88/(1.11)⁴+ ($12,308,991.6392 + $246,179,832.784)/(1.11)⁵.
V₀ = 7,855,855.8559 + 7,714,308.9035 + 7,575,312.3467 + 7,438,820.2323 + 153,400,536.1422.
V₀ = $183,984,855.4806.
For the market value of the equity, we have:
S = 183,984,855.4806 - 25,000,000
S = $158,984,855.4806.
Now, we can find the maximum price per share:
Maximum price per share = 158,984,855.4806/3,000,000
Maximum price per share = $52.9949 ≈ $53.00.
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You have fifteen blankets that each take up 557 cubic inches of space. How many blankets could you pack into a 14-inch moving box
You have fifteen blankets that each take up 557 cubic inches of space. In a 14-inch moving box, we can pack approximately 5 blankets.
The Volume that can take up by single blanket is 557 cubic inches.
The dimension of the moving box = 14 × 14 × 14
Hence, the volume of the moving box = 2744 cubic inches
The total number of blankets that can be packed in the given moving box = 2744/557 = 4.92 ≅ 5
Therefore, in a 14-inch moving box, there can be 15 blankets with 557 cubic inches of space of each can be packed.
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If AH=13mm, A F=15mm, and FC=37mm, what would be the distance between A and D? Round your answer to two decimal places if necessary.
The measure of segment AD in the similar triangle is 45.07 mm
What are similar triangles?Two triangles are said to be similar if they have the same shape and the ratio of their corresponding sides are in the same proportion. Also, their corresponding angles are congruent.
Triangle FEA and triangle ABC are similar triangles by the angle angle similarity postulate, therefore:
13/AD = 15 / (15 + 37)
AD = 45.07 mm
The measure of segment AD in the similar triangle is 45.07 mm
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The figure shows lines r, n, and p intersecting to form angles numbered 1, 2, 3, 4, 5, and 6. All three lines lie in the same plane.
not to scale
Based on the figure, which of the individual statements would provide enough information to conclude that line r is perpendicular to line
p?
Select all that apply.
A m2 3 = m/6
OB. m2 3+m/4= 90°
Answer:
B.
Step-by-step explanation:
If the measures of angles 3 and 4 add to 90, then lines r and p meet at right angles making them perpendicular.
Answer: B.
Answer:
Step-by-step explanation:
The solution of the cubic function f(x) are −4,53, and 1. Identify a factor of this function.
Select one:
a. 3x+5
b. 5x+3
c. x+1
d. x+4
A factor of the polynomial function is (d) x + 4
How to determine the factor of the function?The solution of the cubic function f(x) are given as:
−4, 5/3, and 1.
This means that:
x = -4, x = 5/3 and x = 1
Set the above equations to 0
x + 4 = 0, x - 5/3 = 0 and x - 1 = 0
From the list of options, we have
(d) x + 4
Hence, a factor of the polynomial function is (d) x + 4
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help im in a rush!!!!!!!
Answer:
Your answer should be 52!!
Step-by-step explanation:
Work included on the picture below.
Last year, nicholas started babysitting to earn extra spending money. over the summer, he tracked how much money he earned at each babysitting job. this box plot shows the results.
The percent of the time Nicholas earned is the percent of the time 25%
The 5 values of the given box plot are;
The minimum fee = 20
In the first quartile, the 25th percentile point, Q₁ = 25
In the median or second quartile, the fiftieth percentile factor, Q₂ = 30
The 1/3 quartile, the 75th percentile point, Q₃ = 40
The maximum value = 55
The range = The most value - The minimal fee
The range = 55 - 20 = 35
We are aware that Nicholas earned $25 or less from the minimum value up to the first quartile, Q₁, which is the 25th percentile point, in which we've got 25 percent of the statistics points.
Consequently, the percentage of the time Nicholas earned $25 or much less is 25 percent of the time.
In mathematics, a percentage is a variety of ratios that can be expressed as a fraction of 100. If we have to calculate the percent of various, divide the wide variety by way of the whole and multiply by way of a hundred. For this reason, the shared approach is a component in line with a hundred. The phrase according to cent means in keeping with one hundred.
A relative cost indicates the hundredth component of any amount. One percent (symbolized 1%) is the hundredth part; for this reason, a hundred percent represents the whole lot and two hundred percent specifies two times the given amount.
Multiply the entire number amount through the decimal equal to the proportion. The end result is the share portion quantity. (consequently, this answers the question “How a whole lot is 24 percentage of 500,” you examine that 24 percent of 500 is a hundred and twenty).
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Brian is 8 and his brother is twice his age. How old will his brother be when brian is 11?.
Hence, the age of his brother when brain is [tex]11[/tex] is [tex]19.[/tex]
What is the simplification?
Simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving.
Here given that,
Brian is [tex]8[/tex] and his brother is twice his age.
As age of brain is [tex]8[/tex].
His brother is twices than his age is [tex]8(2)=16[/tex]
When the age of brain is [tex]11[/tex] then [tex]3[/tex] added to his present age.
Then the age of his brother is [tex]16+3=19[/tex]
Hence, the age of his brother when brain is [tex]11[/tex] is [tex]19.[/tex]
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Which of the following correlation coefficients expresses the weakest relationship between two variables
The correct option is a) -0.15.
The weakest correlation relationship between two variables is given by -0.15.
What is correlation?With the aid of correlation, the strength of the relationship between two variables can be determined. We can tell from this study whether there is no correlation, weak correlation, or a strong correlation between the two variables.
Two different types of correlation exist:
positive correlation: Two variables that move together, or in the same direction, are said to have a positive correlation. When one variable rises while the other rises or when one variable falls while the other falls, there is a positive correlation.negative correlation: When two variables are correlated negatively, the other variable's value falls as the value of the first variable rises. The correlation coefficient, which expresses correlation on a scale from +1 to -1, is used. Values less than 0 indicate a negative connection.The correlation value (r) always lies between -1 and 1.
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The complete question is -
Which of the following is the weakest correlation relationship between two variables?
a) -0.15
b) 0.27
c) -0.70
d) 0.55
A group of scientists is conducting an experiment on the effects of media on children. they randomly select 100 children and randomly assign each child to one of four treatment groups. each treatment group has a specific amount of screen time during a one-week time frame. the first group has no screen time, the second group has two hours of screen time, the third group has four hours of screen time, and the fourth group has six hours of screen time. after the first week, the scientists conduct the same experiment, with the same subject groups, for three more weeks so that each group experiences each of the four treatments. which statements about this study are true?
The statements that are true about this study are
This study uses random samplingThis study uses a control groupThis study uses a repeated measures designThis is further explained below.
What is an experiment?Generally, a scientific technique is used to create a discovery, test a theory or show an established truth.
In conclusion, The following are accurate claims concerning this study:
Random sampling is used in this investigation. In this investigation, a control group is used. Repeated measurements are employed in this investigation.
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If you apply the changes below to the quadratic parent function, f(x) = x²
what is the equation of the new function?
• Shift 3 units right.
• Vertically stretch by a factor of 4.
• Reflect over the x-axis.
A. g(x) = -4(x+3)²
B. g(x) = -4(x-3)²
C. g(x) = (-4x - 3)²
D. g(x) = 4x²+3
The equation of the unique function exists g(x) = -4(x-3)².
What is a quadratic equation?The polynomial of degree two exists named a quadratic polynomial and the equation corresponding to a quadratic polynomial P(x) exists named a quadratic equation.
Given: F(x) = x²
The vertical stretch by a factor of 4 exists can be satisfied by (b)
if we use a vertical stretch, it transforms the y-values which causes it to seem skinnier when graphed.
Multiply 4 by f(x) which provides 4x².
As the reflection over the x-axis, so multiply it by -1 to f(x), which results in -4x².
Shift the graph right 3 which exists by moving it right, so by adjusting the x values indicating use f(x-3), to obtain this subtract the value from x when you move right, and add the value to x when you move left.
Hence, the unique graph would be g(x) = -4(x-3)²
Therefore, the correct answer is option B. g(x) = -4(x-3)².
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a. Find the linear approximating polynomial for the following function centered at the given point a. b. Find the quadratic approximating polynomial for the following function centered at the given point a. c. Use the polynomials obtained in parts a. and b. to approximate the given quantity. -1/1.06
The required answers are:
a. The linear approximating polynomial at a = 1: P₁(x) = x - 2
b. The quadratic approximating polynomial at a = 1: P₂(x) = -3 + 3x - x²
c. Appromating the given quantity -1/1.06 for P₁(x) and P₂(x): -3.06 and -7.30 respectively.
Using Taylor polynomial series, the required approximating polynomials are calculated.
What is the Taylor polynomial series?The Taylor polynomial series is
Pₙ(x) = ∑ [tex]\frac{f^n(a)}{n!}[/tex](x - a)ⁿ; limits from 0 to n
Where fⁿ(a) is the nth derivation of f(x) at a
The first order(linear) Taylor polynomial series is
P₁(x) = f(a) + [tex]\frac{f'(a)}{1!}[/tex](x - a)¹
The second order(quadratic) Taylor polynomial series is
P₂(x) = f(a) + [tex]\frac{f'(a)}{1!}[/tex](x - a) + [tex]\frac{f''(a)}{2!}[/tex](x - a)²
Calculation:The given function is f(x) = -1/x at a = 1
f(a) = f(1) = -1
f'(x) = -(-1/x²) = 1/x²; f'(a) = f'(1) = 1
f''(x) = -2/x³; f''(a) = f''(1) = -2
a. Linear approximating polynomial:
From the Taylor series, we have
P₁(x) = f(a) + [tex]\frac{f'(a)}{1!}[/tex](x - a)¹
On substituting,
P₁(x) = -1 + (1/1!)(x - 1)¹
= -1 + (x - 1)
= x - 2
b. Quadratic approximating polynomial:
From the Taylor series, we have
P₂(x) = f(a) + [tex]\frac{f'(a)}{1!}[/tex](x - a) + [tex]\frac{f''(a)}{2!}[/tex](x - a)²
On substituting,
P₂(x) = f(1) + (1/1!)(x - 1) + (-2/2!)(x - 1)²
= -1 + (x - 1) - (x - 1)²
= -1 + x - 1 - (x² - 2x + 1)
= x - 2 - x² + 2x - 1
= -3 + 3x - x²
c. Approximating the given quantity -1/1.06:
Substituting x = -1.06 in P₁(x) and P₂(x),
P₁(x) = x - 2
⇒ P₁(-1.06) = (-1.06) - 2 = -3.06
P₂(x) = -3 + 3x - x²
⇒ P₂(-1.06) = -3 + 3(-1.06) - (-1.06)² = -7.30
Therefore, the approximating polynomials are calculated by using Taylor polynomial series.
Disclaimer: The given question is incomplete. Here is the complete question.
Question:
a. Find the linear approximating polynomial for the following function centered at the given point a.
b. Find the quadratic approximating polynomial for the following function centered at the given point a.
c. Use the polynomials obtained in parts a. and b. to approximate the given quantity.
f(x) = -1/x , a = 1; approximate -1/1.06
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Read the excerpt from The Land.
"I'm ready to start getting to know him," I answered. "Not ready to mount him yet."
"Now, what you mean by that? Get on that horse."
"No, sir, I can't. You need to give me some time with him first."
"Well, I don't have none of that."
"It's important. Now, I said I'd ride your horse, Mister Sutcliffe, but I've got my own way of dealing with horses. You want me to win, then I've got to deal with this grey my way."
Based on this dialogue, which word best describes Paul’s approach to riding a new horse?
overbearing
carefree
methodical
informal
From the conversation it can be inferred that Paul's approach to getting on the horse is methodical (option c).
What is methodical behavior?A methodical attitude or behavior refers to the preference of people to use an organized method and sequences to perform an activity correctly.
According to the above, it can be inferred that Paul behaves in a methodical manner because he prefers to relate to the horse slowly and in a controlled manner before proceeding to mount it.
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A bookshelf is 4-3/4 feet wide. how many 3-inch-wide books will fit on the shelf?
19 books can fit into a bookshelf that has a width of 19/4 feet
What is an equation?An equation is an expression that shows the relationship between two or more number and variables.
The bookshelf is 4 3/4 feet wide = 19/4 feet
1 ft = 12 in, hence:
19/4 feet = 19/4 feet * 12 in per feet = 57 inches
Number of books = 57 inches / 3 in = 19
19 books can fit into a bookshelf that has a width of 19/4 feet
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The table shows data from a survey about the number of times families eat at restaurants during a week. The families are either from Rome, Italy or New York, New York:
Maximum Minimum Q1 Q3 IQR Median Mean σ
Rome 16 0 3 13 10 8.5 8 5.4
New York 20 1 4.5 6 1.5 5.5 7.25 5.4
Which of the choices below best describes how to measure the center of this data? (5 points)
Group of answer choices
Both centers are best described with the mean.
Both centers are best described with the median.
The Rome data center is best described by the mean. The New York data center is best described by the median.
The Rome data center is best described by the median. The New York data center is best described by the mean.
It's NOT C "The Rome data center is best described by the mean. The New York data center is best described by the median." already tried, its incorrect.
The best description on measurement of the center of this data is; C. The Rome data center is best described by the mean. The New York data center is best described by the median.
How to find the center of the data?If we make the box and whisker plot of the Rome and New York data, we will see that there will clearly be an outlier in the New York data.
Thus;
Due to the fact that the data set for New York has an outlier and the mean is skewed, it means that we would use the median.
Finally, we see that the Rome data set is symmetrical because it has no outlier, and as such we can use the mean.
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Which point is a solution to the inequality shown in this graph? (urgent)
Answer: D
Step-by-step explanation:
sorry if its wrong
Diamond went to lunch with her friends. The total bill came to $32.20. If Diamond tipped 19%, how much tip did she leave?
$6.12
Step-by-step explanation:A percentage is some portion of a whole number. Multiple methods can be used to find percentages.
Multiplication to Find Percentages
One of the easiest ways to find percentages is to multiply the original number by a decimal. To do this, one first needs to turn the percentage into a decimal.
For example,
19% = 0.19To convert a percentage to a decimal, just move the decimal point 2 places to the left.
Then, multiply this decimal by the whole number, and the answer, in this case, will be the tip.
19% of $32.20
Now, to solve we can just multiply.
0.19 * 32.20 = 6.118The exact answer is 6.118. However, since we are using money, we are going to round to the nearest hundredth place. This gives the final answer of $6.12.
The graph of F(x) shown below resembles the graph of G(x) = x4, but it has
been changed somewhat. Which of the following could be the equation of
F(x)?
Using translation concepts, the equation of F(x) is:
A. [tex]F(x) = \frac{1}{3}x^4 - 2[/tex]
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
The parent function is:
[tex]G(x) = x^4[/tex]
For function F(x), we have that:
It was shifted down 2 units, hence F(x) = G(x) - 2.It was vertically compressed by a factor of 3, hence [tex]F(x) = \frac{1}{3}G(x) - 2[/tex]Then the equation is:
A. [tex]F(x) = \frac{1}{3}x^4 - 2[/tex]
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If $2000 is invested at 4% per annum compounded semiannually, how much is in the account after 8 years?
A pile of cards contains 3 diamonds,
4 hearts, and 2 spades. Marianna randomly
selects two cards without replacing the
first. What is P(hearts, then spades)?
F. 8/81
G. 1/9
H. 2/3
J. 1/18
Answer:G
Step-by-step explanation:
4/9 times 2/8= 1/9
Answer:
G 1/9
Step-by-step explanation:
add all of the cards together that will get you 9 then you take the hearts overing it by total then times it by 2 overing by 8 or
4/9x2/8
Two friends are planning for a gathering. The food budget is modeled by 1/2(x-120)=10,where x is the amount spent on food. What are the least and greatest amounts that the two friends could spend on food
The least and greatest amounts that the two friends could spend on food are 100 and 140 respectively
Functions and values
Functions are expressions written in terms of letters known as variables. Given the equation that represents the food budget of two friends as shown;
1/2(x-120)=10
where x is the amount spent on food.
In order to determine the least and greatest amounts that the two friends could spend on food,
For the least amount
-(x-120) = 20
-x+120 = 20
x = 100
For the greatest amount
(x-120) = 20
x = 140
Hence the least and greatest amounts that the two friends could spend on food are 100 and 140 respectively
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A yard with a tree is to be concreted. The owner wants to concrete the whole yard, but keep the tree in place and so concretes around the tree to its circumference. The tree has a circular cross section, with a diameter of 1 m. The yard is a rectangle, with sides of length 3 m and 4 m. What is the area of concrete required (to 1 d.p.)?
Answer:
11.2 square meters
Step-by-step explanation:
This is a very simple question. Basically, it's the area of a rectangle with the area of a circle subtracted. The area of a circle is calculated with the following formula:
[tex]\pi \times r^{2} [/tex]
Where r is the radius. We know the diameter is 1m, so we can simply halve this value to find the radius of 0.5m. Substituting in this value, we find the area of the circle to be:
[tex]\pi \times {0.5}^{2} \approx0.78539816339744830961566[/tex]
Now let's calculate the area of the rectangle, which is simply 3x4=12. Subtracting our earlier value from 12, we are left with an answer of 11.2 (to 1 d.p)
is flipped ten times, and he is asked to predict in advance the outcome. Our individual gets seven out of ten correct. What is the probability he would have done at least this well if he had no ESP
The required probability is 0.171.
What is probability?
Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.
We can find required Probability as shown:
From 10 coins we choose 7 he guessed correct with probability of each 1/2. For three remaining coins he failed to predict the outcomes of the flip with the probability of 1/2 for each. Similarly for 8,9 or 10 successive trials. Let X denote number of successive trials
[tex]P(X\geq 7)= \tbinom{10}{7}.\frac{1}{2^{10}}+\tbinom{10}{8}.\frac{1}{2^{10}} +\tbinom{10}{9}.\frac{1}{2^{10}}+\tbinom{10}{10}.\frac{1}{2^{10}}[/tex]
[tex]=120.\frac{1}{2^{10}} +45.\frac{1}{2^{10}} +10.\frac{1}{2^{10}} +.\frac{1}{2^{10}}[/tex]
[tex]=\frac{120+45+10+1}{2^{10}}[/tex]
[tex]=\frac{176}{1024}[/tex]
=0.171
Hence, the required probability is 0.171.
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Given question is incomplete. This is complete question:
A man claims to have extrasensory perception. As a test, a fair coin is flipped 10 times and the man is asked to predict the outcome in advance. He gets 7 out of 10 correct. What is the probability that he would have done at least this well if he had no ESP?
Total slack is calculated by ____
Total slack is calculated by the late finish minus early finish and the late start minus the early start
What is the total slack?Total slack is simply the amount of time taken for a task to be delayed before the project finish date is delayed. It can be positive or negative.
It is calculated as the calculated as the value of the Late Finish minus the Early Finish field, and the Late Start minus the Early Start field.
Total slack = Late finish - early finish + late start - early start
Thus, the total slack is calculated by the late finish minus early finish and the late start minus the early start.
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Use the function f(x) = 5x² + 2x-3 to answer the questions.
Part A: Completely factor f(x). (2 points)
Part B: What are the x-intercepts of the graph of f(x)? Show your work. (2 points)
Part C: Describe the end behavior of the graph of f(x). Explain. (2 points)
Part D: What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part B and Part C to draw the graph. (4 points)
A)f(x)=3/5 and -1.
B)f(x)=(3/5, 0) and (-1, 0).
C)f(x)=(-0.2, -3.2)
D)f(x)= = -0.2.
What is factorization and example?Factorization in mathematics is dividing a large number into smaller ones that, when multiplied together, give you the original number. Factorization is the division of a number into its factors or divisors.For instance, the factorization of the integer 12 might appear as 3 times 4.Function: f(x) = 5x² + 2x-3.
a) Completely factor f(x)
f(x) = 5x² + 2x-3.
= 5x² + 5x-3x − 3
= 5x(x+1)-3(x+1)
=(5x-3)(x+1)
f(x)=3/5 and -1.
b)The x-intercepts of the graph of f(x):
f(x) = 5x² + 2x-3.
At f(x) = 0, the x-intercepts are present.
Therefore, x-intercepts are (3/5, 0) and (-1, 0).
c) The end behavior of the graph of f(x):
f(x) = 5x² + 2x-3.
The middle of the zeros is the vertex's x-coordinate.
=-0.2
Find the y-coordinate of the vertex, and substitute the found value of x into the given equation:
f(-0.2)= 5(-0.2)² + 2(-0.2) − 3
=-3.2
d)The steps you would use to graph f(x):
The axis of symmetry is the x value of the vertex.
Therefore, the graph is symmetrical at about x = -0.2.
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The cost of a flight is related to the distance traveled:
Miles 225 1,100 1,375 1,675 1,950 2,250
Cost ($) 50.3 111 143 187 214 196
Find the linear regression equation that models this data.
The linear regression equation that models the cost of a flight in function of the distance traveled is given as follows:
C(m) = 0.08316m + 31.36331
How to find the equation of linear regression using a calculator?To find the equation, we need to insert the points (x,y) in the calculator.
For this problem, the points (x,y) are given as follows:
(225, 50.3), (1100, 111), (1375, 143), (1675, 187), (1950, 214), (2250, 196).
Hence, inserting these points in the calculator, the linear regression equation that models the cost of a flight in function of the distance traveled is given as follows:
C(m) = 0.08316m + 31.36331
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What is the image point of (-8, 3) after the transformation R2700 0 T-2,-1?
The transformation of the coordinate (-8, -3) R 270° and T-2,-1 is (-5, -9)
What is transformation?Transformation is the change of the coordinates of a shape either by rotation, reflection or translation.
Analysis:
When coordinates (x, y) rotate 270° the resulting coordinates become (-y, x)
so coordinates (-8, -3) after 270° rotation becomes ( 3, -8)
When it is translated 2 units to the left and 1 unit down, that is -3 + -2 = -5 and -8 + -1 = -9
Therefore the transformed coordinate becomes (-5, -9)
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The projectile motion of an object can be modeled using s(t) = gt2 + v0t + s0, where g is the acceleration due to gravity, t is the time in seconds since launch, s(t) is the height after t seconds, v0 is the initial velocity, and s0 is the initial height. The acceleration due to gravity is –4.9 m/s2.
An object is launched at an initial velocity of 19.6 meters per second from an initial height of 24.5 meters. Which equation can be used to find the number of seconds it takes the object to hit the ground?
A. 0 = –4.9t2 + 19.6t + 24.5
B 0 = –4.9t2 + 24.5t + 19.6
C. 19.6 = –4.9t2 + 24.5t
D. 24.5 = –4.9t2 + 19.6t
Answer: 0=-4.9t²+19.6t+24.5
Step-by-step explanation:
[tex]s(t)=gt^2+v_0t+s_0\\v_0=19,6\ \frac{m}{s} \ \ \ \ s_0=24,5\ m\ \ \ \ g=-4,9\ \frac{m}{s^2} \ \ \ \ S(t)=0\ (the\ object \ hitts\ the \ ground)\ \Rightarrow\\0=-4,9t^2+19,6t+24,5.[/tex]
What's the difference between sampling with replacement and sampling without replacement? How should you account for this
using TI-84's or the "hat method"?
When sampling with replacement is used, an element that has already been chosen is put back into the sample frame and given the chance to be chosen again.
In the case of sampling without replacement, an element is eliminated from the sample frame after it has been chosen.
In this question, we are supposed to state the differences between sampling with replacement and sampling without replacement.
Generally speaking, sampling without replacement is more effective than producing representative samples using replacement sampling. It prevents the inclusion of the same population element in the sample several times.
By "drawing from a hat" or by using a computer program that simulates the same process, you select the sample at random using the lottery method.
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