Answers
The first five coefficients are explained.
Given is power series, f(x) = eˣ about x = 4 as [tex]\sum_{\infty}^{n=0}C_n}(x+4)^n[/tex]
f(x) = eˣ
a = 4,
The general form of a Taylor series is:
f(x) = [tex]\sum_{n=0}^{\infty}\frac{f'(a)}{n!} (x-a)^n[/tex]
Note that since the function is a basic exponential function, its derivative is:
f'(x) = eˣ
That is, the function is the same for whatever order of differentiation. So, let us substitute our values here,
f(x) = [tex]\sum_{n=0}^{\infty}\frac{e^4}{n!} (x-4)^n[/tex]
The general expression for the coefficients is: [tex]C_n = \frac{e^4}{n!}[/tex]
The first coefficient is: [tex]C_0 = e^4[/tex]
The second coefficient is: [tex]C_1 = e^4[/tex]
The third coefficient is: [tex]C_2 = 1/2e^4[/tex]
The fourth coefficient is: [tex]C_3 = 1/6e^4[/tex]
And lastly,
[tex]C_4 = 1/24e^4[/tex]
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Related Questions
Judy is planning a banquet-style dinner for her son Deon's
18th birthday. The equation C = 55g + 650 represents the
cost of the dinner.
Variables:
The C variable represents the choose your answer...
1.
2 The g variable represents the choose your answer...
Guests and Budget:
1. Each guest that attends costs type your answer... dollars.
2. The cost to rent the banquet venue is type your answer....
dollars.
3.
80 guests costs type your answer...
4. 105 guests costs
type your answer...
dollars.
dollars.
Answers
The parameters for the linear function in this problem are given as follows:
1. C is the total cost.
2. g is the number of guests.
3. Each guest costs $55.
4. The cost to rent the venue is of $650.
5. 80 guests cost $5,050.
6. 105 guests cost $6,425.
How to define a linear function?The slope-intercept representation of a linear function is given by the equation presented as follows:
y = mx + b
The coefficients of the function and their meaning are described as follows:
m is the slope of the function, representing the change in the output variable y when the input variable x is increased by one.b is the y-intercept of the function, which is the initial value of the function, i.e., the numeric value of the function when the input variable x assumes a value of 0. On a graph, it is the value of y when the graph of the function crosses the y-axis.The function for this problem is given as follows:
C = 55g + 650.
Hence:
The slope of 55 represents the cost per guest.The intercept of 650 represents the cost to rent the venue.The costs are given as follows:
80 guests: C = 55 x 80 + 650 = $5,050.105 guests: C = 55 x 105 + 650 = $6,425.More can be learned about linear functions at https://brainly.com/question/24808124
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At noon, to begin a study, a petri dish had 2500 bacteria cells. Each hour since, the number of cells has increased by 11%.
Let t be the number of hours since the start of the study. Let y be the number of bacteria cells.
Write an exponential function showing the relationship between y and t.
Answers
An exponential function showing the relationship between y and t is y = 2500(1.11ˣ)
To write an exponential function for this situation, we can start with the initial number of cells (2500) and then multiply by 1.11 for each hour that has passed. We can use the variable t to represent the number of hours since the start of the study, and the variable y to represent the number of bacteria cells. Then, our exponential function is:
y = 2500(1.11ˣ)
This function tells us that the number of bacteria cells (y) is equal to the initial number of cells (2500) multiplied by 1.11 raised to the power of the number of hours since the start of the study (x).
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He starts a new job and works a 38-hour week for a wage of $975.84.
e. Calculate his hourly rate of pay.
f. If overtime is calculated at time and a half, what is Vikram’s overtime rate?
g. How much does Vikram earn for 4 hours of overtime work?
h. How many hours of overtime did Vikram work in a week if his wage for that week was $1226.22?
i. If Vikram usually works the amount of overtime in part h in the 52 weeks of the year he works, and he pays 27% of his pay in tax, what is his net annual income?
j. If Vikram invests 10% of his net income in an account earning 8% p.a. simple interest for 18 months, how much extra income will he have earn
Answers
e. Hourly rate = $975.84 / 38 = $25.68
f. Overtime rate = $25.68 * 1.5 = $38.52
g. Earnings (4 hours OT) = $38.52 * 4 = $154.08
h. Overtime hours = ($1226.22 - $975.84) / $38.52 ≈ 6.5 hours
How to solveBegin by determining the number of overtime hours worked by evaluating the discrepancy between his weekly salary and his regular wage:
Take note that the difference = $250.38, specifically from a calculation derived by subtracting $975.84 from $1226.22.
Next, divide this incongruity by his rate of pay for working overtime to establish the actual quantity of time augmented:
Upon performing our overall assessment with $38.52 as the hourly short-term remuneration rate towards supplementing regular pay projections, we determine roughly 6.5 additional work hours incrementally added onto one's overall timesheet.
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Will give Brainliest and extra points if correct!!!!
What is the slope of the line that contains the points (−3, −1) and (3, −10)?
Undefined
0
-2/3
-3/2
Answers
Answer:
The slope of a line can be calculated using the following formula:
```
m = (y2 - y1) / (x2 - x1)
```
where `m` is the slope, `y2` and `y1` are the y-coordinates of the two points, and `x2` and `x1` are the x-coordinates of the two points.
In this case, we have the following points:
```
(x1, y1) = (-3, -1)
(x2, y2) = (3, -10)
```
Plugging these values into the formula, we get the following:
```
m = (-10 - (-1)) / (3 - (-3)) = -9 / 6 = -3/2
```
Therefore, the slope of the line is **-3/2**. So the answer is (c).
Step-by-step explanation:
In a box of pens there are 3 green pens for every 4 blue pens.
There are 15 green pens in the box. how many blue pens are there?
Answers
We know that there are 3 green pens for every 4 blue pens.
So, we can set up the following proportion:
3/4 = 15/x
To solve for x, we can cross-multiply:
3x = 60
Then, we can divide both sides by 3:
x = 20
Therefore, there are 20 blue pens in the box.
Answer:
20 blue pens
Step-by-step explanation:
Since it is a 3 to 4 ratio (Green to Blue) and you have 15 green pens you need to multiply 5 to the 3(green pens). Since you multiplied 5 it needs to stay equal you need to multiply 5 to the blue pens which would give you 20 blue pens
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Eighteen middle-aged women with platelet readings between 120,000 platelets per microliter and 150,000 platelets per microliter of blood were selected randomly from the population of similar female patients at a large local hospital. Nine of the 18 women were assigned randomly to group A and received a placebo. The other nine women were assigned to group B and received a new platelet drug. After four months, posttreatment platelet readings were taken for all 18 women and were compared with pretreatment readings. The reduction in platelet level (Pretreatment reading − Posttreatment reading) for each woman in the study is shown here.
Group A (placebo) increase (in platelets per microliter): 2,000, 5,000, 7,050, 10,125, 12,345, 17,350, 13,250, 12,200, 9,125
Group B (platelet drug) increase (platelets per microliter): 28,450, 23,438, 36,380, 12,450, 16,100, 21,350, 39,400, 41,000, 14,325
Create and interpret a 95% confidence interval for the difference in the placebo and the new drug.
Answers
The blood platelet count is an illustration of normal distribution,
Approximately 95% of the data lies within 2 standard deviations of the mean.
There are approximately 99.7% of women with platelet count between 65.2 and 431.8.
Given parameters are:
μ = 248.5
σ = 61.1
(a) The percentage within 2 standard deviation of mean or between 126.3 and 370.7,
Start by calculating the z-score, when x = 126.3 and x = 370.7
Z = x-μ / σ
Therefore,
Z = 126.3-248.5/61.1
Z = -2
Also,
Z = 370.7-248.5/61.1
Z = 2
The empirical rule states that:
Approximately 95% of the data lies within 2 standard deviations of the mean.
Hence, there are approximately 95% of women with platelet count within 2 standard deviations of the mean.
(b) The percentage with platelet count between 65.2 and 431.8
Start by calculating the z-score, when x = 65.2 and x = 431.8
Z = 65.2-248.5/61.1
Z = -3
And,
Z = 431.8-248.5/61.1
Z = 3
The empirical rule states that:
Approximately 99.7% of the data lies within 3 standard deviations of the mean.
Hence, there are approximately 99.7% of women with platelet count between 65.2 and 431.8.
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During 2022, Sam Reed purchased 350 shares of common stock issued by New Generation Electronics for $7800 including commission. Later in the same year, Sam sold the shares for $8400 after commission. Calculate the following. (Round all answers to two decimal places.)
1. Profit on this stock transaction: $
2. Percentage return on investment: %
Answers
The profit on this stock transaction is $600 and the percentage return on investment is 7.69%.
To calculate the profit on this stock transaction, we need to subtract the total cost from the total revenue:
Total cost = $7800
Total revenue = $8400
Profit = Total revenue - Total cost
Profit = $8400 - $7800
Profit = $600
Therefore, the profit on this stock transaction is $600.
To calculate the percentage return on investment
we need to divide the profit by the total cost and then multiply by 100 to get the percentage:
Percentage return on investment = (Profit / Total cost) x 100%
= ($600 / $7800) x 100%
= 0.0769 x 100%
= 7.69%
Therefore, the percentage return on investment is 7.69%.
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what is the possibility of getting 9 heads out of 15 tries, flipping a coin?
Answers
The probability of getting exactly 9 heads out of 15 tries when flipping a fair coin is approximately 0.19638 or about 19.64%.
We have,
The probability of getting a head or a tail when flipping a fair coin.
= 1/2 or 0.5
Assuming the coin is unbiased and each flip is independent of the previous flips.
To find the probability of getting 9 heads out of 15 tries, we need to use the binomial probability formula:
= P(9 heads out of 15 tries)
= [tex]^{15}C_9[/tex] x (0.5)^9 x (0.5)^6
Now,
P(9 heads out of 15 tries)
= 5005 x (0.5)^9 x (0.5)^6
= 0.19638 (rounded to five decimal places)
Thus,
The probability of getting exactly 9 heads out of 15 tries when flipping a fair coin is approximately 0.19638 or about 19.64%.
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Solve (x – 3)2 = 49. Select the values of x. –46 -4 10 52
Answers
To solve the equation (x - 3)^2 = 49, we can take the square root of both sides to eliminate the exponent of 2. However, when taking the square root, we need to consider both the positive and negative square roots.
(x - 3)^2 = 49
Taking the square root of both sides, we get:
√((x - 3)^2) = ±√49
Simplifying, we get:
x - 3 = ±7
Adding 3 to both sides, we get:
x = 3 ± 7
So the possible values of x are:
x = 3 + 7 = 10
x = 3 - 7 = -4
Therefore, the correct values of x are -4 and 10. The options given are -46, -4, 10, and 52. So the correct values of x from the options are -4 and 10.
Answer:
-4 and 10.
Step-by-step explanation:
QRST is a square inscribed is in O. The radius of O is 4.
30). Find the area of the circle.
31). Find the area of the square.
32). Find the area of the shaded region.
Answers
The area of the circle is 50.24.
The area of the square is 32.
The area of the shaded region is 18.24.
We have,
From the figure,
Area of the circle.
= πr²
Radius = 4
So,
= 3.14 x 4 x 4
= 50.24
In the triangle QST,
TS and TQ are congruent.
TS = TQ = x
QS = 8
This means,
From the Pythagorean theorem,
8² = x² + x²
64 = 2x²
x² = 32
x = √(16 x 2)
x = 4√2
Area of the square.
= Side²
Side = x = 4√2
= (4√2)²
= 16 x 2
= 32
Now,
Area of the shaded region.
= Area of the circle - Area of the square
= 50.24 - 32
= 18.24
Thus,
The area of the circle is 50.24.
The area of the square is 32.
The area of the shaded region is 18.24.
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The measure of one interior angle of a regular icosagon, or 20-sided figure, is (12x - 6)°.
Part A: What is the sum, in degrees, of the interior angles of a regular icosagon?
O 1800
O 3204
O 3240
O 3600
Part B: Which equation could be used to find the value of x?
O 162 = 12x6
O 180 = 12x - 6
O 3240 = 18(12x-6)
O 3600 = 20(12x - 6)
Answers
The sum of interior angles in the polygon is 3240 degrees.
The equation used to find x is 180 = 12x - 6.
We have,
The sum of the interior angles of a polygon with n sides can be calculated using the formula (n-2) x 180 degrees.
So, for a regular icosagon with 20 sides, the sum of interior angles.
= (20-2) x 180
= 3240 degrees.
Therefore, the answer is option C, 3240.
Part B:
The sum of the interior angles of a regular polygon can also be calculated using the formula:
Sum of interior angles = n(180 - exterior angle)/2,
where n is the number of sides.
For a regular icosagon, the exterior angle can be found by subtracting the interior angle from 180 degrees.
= 180 - (12x - 6)
= 186 - 12x.
Substituting the values in the formula, we get:
3240 = 20(180 - (12x - 6))/2
Simplifying this equation, we get:
3240 = 1800 - 60x + 30
Combining like terms, we get:
1410 = -60x
Dividing both sides by -60, we get:
x = -23.5
Therefore,
The sum of interior angles is 3240 degrees.
The equation used to find x is 180 = 12x - 6.
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6. Imagine you are given the diameter of a circle and asked to find its volume. Circle the statement that describes what you should do. Draw a line through the incorrect statements.
Substitute the diameter value for r in the formula and calculate as usual.
Divide the diameter by 2 to find the radius, and then use the volume formula as usual.
Multiply the diameter by 2 to find the radius, and then use the volume formula as usual.
Answers
The formula for the volume of a circle is V = (4/3)πr³, where r is the radius obtained by dividing the diameter by 2.
First, it's important to understand what the diameter of a circle represents. The diameter is the distance across the circle, passing through the center. In contrast, the radius is the distance from the center of the circle to any point on the edge.
Now, let's consider the statements given:
Substitute the diameter value for r in the formula and calculate as usual.
This statement is incorrect because the formula for the volume of a circle involves the radius, not the diameter. If we substitute the diameter for the radius, we would end up with the wrong answer.
Divide the diameter by 2 to find the radius, and then use the volume formula as usual.
This statement is correct. Since the radius is half the diameter, dividing the diameter by 2 will give us the radius. We can then use the formula for the volume of a circle, which is V = (4/3)πr³, where r is the radius.
Multiply the diameter by 2 to find the radius, and then use the volume formula as usual.
This statement is incorrect. If we multiply the diameter by 2, we would end up with the diameter, not the radius. Again, we need to use the radius in the formula for the volume of a circle.
To summarize, when given the diameter of a circle and asked to find its volume, we should divide the diameter by 2 to find the radius and then use the volume formula as usual.
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PLEASE HELP THANK YOU HURRY FAST
Answers
1) Polynomial of 4 terms.
2) The rational roots of the function are,
x = - 2, 1
3) The zeroes of the function are,
x = - 2, - 3, 2
4) The zeroes of the function are,
x = 1, - 1, 2i, - 2i
5) The correct function which shows the cubic equation is, option 1.
We have to given that;
1) Function is,
⇒ 3x⁵ + 5x⁴ - 7x³ + 15
Clearly, There are 4 terms in function.
Hence, Polynomial of 4 terms.
2) Function is,
⇒ x⁴ + 5x³ + 7x² - 3x - 10 = 0
The correct rational roots are satisfy the function,
Hence, We get;
Plug x = 1,
⇒ x⁴ + 5x³ + 7x² - 3x - 10 = 0
⇒ 1⁴ + 5(1)³ + 7 (1)² - 3(1) - 10 = 0
⇒ 0 = 0
Plug x = - 2;
⇒ x⁴ + 5x³ + 7x² - 3x - 10 = 0
⇒ 2⁴ + 5(2)³ + 7 (2)² - 3(2) - 10 = 0
⇒ 0 = 0
Thus, The zeroes of the function are,
x = - 2, 1
3) Function is,
⇒ y = (x + 3) (x + 2) (x - 2)
Hence, The zeroes of the function are,
x = - 3
x = - 2
x = 2
4) Function is,
⇒ 3x² - 4 = - x⁴
⇒ x⁴ + 3x² - 4 = 0
⇒ x⁴ + 4x² - x² - 4 = 0
⇒ x² (x² + 4) - 1 (x² + 4) = 0
⇒ (x² - 1) (x² + 4) = 0
⇒ x² - 1 = 0
⇒ x² = 1
⇒ x = ±1
⇒ x² + 4 = 0
⇒ x² = - 4
⇒ x = ±2i
Hence, The zeroes of the function are,
x = 1, - 1, 2i, - 2i
5) By given graph the correct function which shows the cubic equation is, Option 1.
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Please solve part A&B with the steps, don't solve one part only!!
Answers
Therefore the set S = {v1, v2, v3, v4} is linearly independent.
How to solveThe set S = {v1, v2, v3, v4} of vectors in R4 is linearly independent if the only solution of
c1v1 + c2v2 + c3v3 + c4v4 = 0
is c1, c2, c3, c4 = 0
Otherwise (i.e., if a solution with at least some nonzero values exists), S is linearly dependent.
With our vectors v1, v2, v3, v4, (*) becomes:
c1
3
0
-3
6 + c2
0
2
3
1 + c3
0
-2
-2
0 + c4
-2
1
2
1 =
0
0
0
0
Rearranging the left hand side yields
3 c1 +0 c2 +0 c3-2 c4
0 c1 +2 c2-2 c3 +1 c4
-3 c1 +3 c2-2 c3 +2 c4
6 c1 +1 c2 +0 c3 +1 c4 =
0
0
0
0
The matrix equation above is equivalent to the following homogeneous system of equations
3 c1
+0 c2 +0 c3 -2 c4 = 00 c1 +2 c2 -2 c3 +1 c4 = 0-3 c1 +3 c2 -2 c3 +2 c4 = 06 c1 +1 c2 +0 c3 +1 c4 = . 0We now transform the coefficient matrix of the homogeneous system above to the reduced row echelon form to determine whether the system has
the trivial solution only (meaning that S is linearly independent), or
the trivial solution as well as nontrivial ones (S is linearly dependent).
Row
Operation
1:
3 0 0 -2
0 2 -2 1
-3 3 -2 2
6 1 0 1 multiply the 1st row by 1/3
1 0 0 -2/3
0 2 -2 1
-3 3 -2 2
6 1 0 1
Row
Operation
2:
1 0 0 -2/3
0 2 -2 1
-3 3 -2 2
6 1 0 1 add 3 times the 1st row to the 3rd row
1 0 0 -2/3
0 2 -2 1
0 3 -2 0
6 1 0 1
Row
Operation
3:
1 0 0 -2/3
0 2 -2 1
0 3 -2 0
6 1 0 1 add -6 times the 1st row to the 4th row
1 0 0 -2/3
0 2 -2 1
0 3 -2 0
0 1 0 5
Row
Operation
4:
1 0 0 -2/3
0 2 -2 1
0 3 -2 0
0 1 0 5 multiply the 2nd row by 1/2
1 0 0 -2/3
0 1 -1 1/ 2
0 3 -2 0
0 1 0 5
Row
Operation
5:
1 0 0 -2/3
0 1 -1 1/2
0 3 -2 0
0 1 0 5 add -3 times the 2nd row to the 3rd row
1 0 0 -2/3
0 1 -1 1/2
0 0 1 -3/2
0 1 0 5
Row
Operation
6:
1 0 0 -2/3
0 1 -1 1/2
0 0 1 -3/2
0 1 0 5 add -1 times the 2nd row to the 4th row
1 0 0 -2/3
0 1 -1 1/2
0 0 1 -3/2
0 0 1 9/2
Row
Operation
7:
1 0 0 -2/3
0 1 -1 1/2
0 0 1 -3/2
0 0 1 9/2 add -1 times the 3rd row to the 4th row
1 0 0 -2 /3
0 1 -1 1/2
0 0 1 -3/2
0 0 0 6
Row
Operation
8:
1 0 0 -2/3
0 1 -1 1 2
0 0 1 -3 2
0 0 0 6 multiply the 4th row by 1/6
1 0 0 -2/3
0 1 -1 1 /2
0 0 1 -3/ 2
0 0 0 1
Row
Operation
9:
1 0 0 -2/3
0 1 -1 1/2
0 0 1 -3/2
0 0 0 1 add 3/2 times the 4th row to the 3rd row
1 0 0 -2/3
0 1 -1 1/2
0 0 1 0
0 0 0 1
Row
Operation
10:
1 0 0 -2/3
0 1 -1 1/ 2
0 0 1 0
0 0 0 1 add -1/2 times the 4th row to the 2nd row
1 0 0 -2/3
0 1 -1 0
0 0 1 0
0 0 0 1
Row
Operation
11:
1 0 0 -2/3
0 1 -1 0
0 0 1 0
0 0 0 1 add 2/3 times the 4th row to the 1st row
1 0 0 0
0 1 -1 0
0 0 1 0
0 0 0 1
Row
Operation
12:
1 0 0 0
0 1 -1 0
0 0 1 0
0 0 0 1 add 1 times the 3rd row to the 2nd row
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
The reduced row echelon form of the coefficient matrix of the homogeneous system (**) is
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
Since each column contains a leading entry (highlighted in yellow), then the system has only the trivial solution, so that the only solution of is c1, c2, c3, c4 = 0.
Therefore the set S = {v1, v2, v3, v4} is linearly independent.
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Ifr is the slope of a line, and m is the slope of line perpendicular to that line, what is the relationship between r and m?
Answers
In other words, if "m" is the slope of a line perpendicular to the line with slope "r", then:
m = -1/r
This relationship holds true for any pair of perpendicular lines.
Step-by-step explanation:
If slope r and slope m are perpendicular , their product must give negative one.
That is r ×m = -1
r = -1 /m
m = -1 /r
What is the mean (rounded to the nearest hundredth) of
90.75
99.17
71.80
100.00
97.33
79.58
92.58
87.09
81.59
91.86
and 94.18
Answers
90.75 + 99.17 + 71.80 + 100.00 + 97.33 + 79.58 + 92.58 + 87.09 + 81.59 + 91.86 + 94.18 = 985.93
There are 11 numbers in the list, so we divide the sum by 11:
985.93 ÷ 11 ≈ 89.63
Therefore, the mean (rounded to the nearest hundredth) of the given numbers is 89.63.
90.75 + 99.17 + 71.80 + 100.00 + 97.33 + 79.58 + 92.58 + 87.09 + 81.59 + 91.86 + 94.18 = 985.93
There are 11 numbers, so we divide the sum by 11:
985.93 ÷ 11 = 89.63
Rounded to the nearest hundredth, the mean is 89.63.
Use the image to determine the line of reflection.
An image of polygon VWYZ with vertices V at negative 9, 1, W at negative 9, negative 1, Y at negative 3, negative 1, and Z at negative 3, 1. A second polygon V prime W prime Y prime Z prime with vertices V prime at 7, 1, W prime at 7, negative 1, Y prime at 1, negative 1, and Z prime at 1, 1.
Reflection across y = 1
Reflection across x = −1
Reflection across the x-axis
Reflection across the y-axis
Answers
The line of reflection is the line y = 0, which is the x-axis.
To see this, imagine folding the image of polygon VWYZ along the x-axis so that the top vertex, V, is reflected down to its corresponding point, V'. Similarly, W is reflected up to W', Y is reflected up to Y', and Z is reflected down to Z'. This produces the image of polygon V'W'Y'Z', which is the reflection of polygon VWYZ across the x-axis.
When reflecting a shape across a line, the line of reflection is the line that serves as the "mirror" for the shape. In this case, the given polygons VWYZ and V'W'Y'Z' are related by a reflection. By examining the vertices of the polygons, we can determine the line of reflection. The x-coordinates of the corresponding vertices are the same, which suggests that the line of reflection is vertical.
However, the y-coordinates are opposites, indicating that the line of reflection is actually the x-axis. Therefore, the reflection of polygon VWYZ onto polygon V'W'Y'Z' is achieved by folding the image along the x-axis so that each vertex is reflected across the x-axis to its corresponding point in the other polygon.
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Answer:
Reflection across x = −1
Step-by-step explanation:
Took test it's right!
Data were collected on the distance a hockey puck will travel when hit by a hockey stick at a certain speed. The speed, s, is measured in miles per hour, and distance, ŷ, is measured in yards. The line of fit is given by ŷ = 3.12 + 61.02s.
If a hockey player hits a puck at a speed of 50 miles per hour, how far will the puck travel?
2,564.19 yards
2,784.00 yards
3,054.12 yards
3,207.00 yards
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The predicted distance the puck will travel at a speed of 50 miles per hour is 3054.12 yards
Given data ,
The equation for the line of fit is given as y = 3.12 + 61.02s, where y represents the predicted distance (in yards) the puck will travel and s represents the speed of the puck (in miles per hour).
So , y = 3.12 + 61.02s
Now , when the speed of the hockey player is s = 50 miles per hour
On simplifying , we get
y = 3.12 + 61.02 ( 50 )
y = 3.12 + 3051
y = 3,054.12 yards
Hence , the distance traveled by the puck is 3,054.12 yards
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The Discovery channel television show MythBusters conducted an experiment to study what
happens when buttered toast is dropped on the floor. When 48 buttered slices of toast were
dropped, 29 of them landed with the buttered side up and 19 landed with the buttered side
down. Use a 0.05 significance level to test the claim that toast will land with the buttered side
down 50% of the time. Write a conclusion that addresses the intent of the experiment.
Answers
The toast will land with buttered side 50% of the time.
First,
H₀:p=0.5, H₁: p₀ ≠0.5
P(butttered side down)= 19/51
π₀= 0.5
n= 51
Now, z = (p- π₀)/ √π₀(1-π₀)/n
z= (19/51 -0.5)/√0.5(1-0.5)/51
z= -1.82
as, α= 0.01 and [tex]z_{\alpha/2[/tex]= 2.58
So, |z| < | [tex]z_{\alpha/2[/tex]|
Thus, it reject H₀.
Thus, the toast will land with buttered side 50% of the time.
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EE 21-7 Jonick Company has sales of $740,000, and the break-even point in sales dollars is $547,600. Determine the company’s margin of safety as a percent of current sales.
Answers
Answer: Jonick Company's margin of safety as a percentage of current sales is 26.05%.
Step-by-step explanation: To find the margin of safety as a percentage of current sales, we need to first calculate the margin of safety, which is the amount of sales above the break-even point:
Margin of safety = Actual sales - Break-even point
We know that actual sales are $740,000 and the break-even point is $547,600, so:
Margin of safety = $740,000 - $547,600
Margin of safety = $192,400
Now that we know the margin of safety, we can calculate it as a percentage of current sales:
Margin of safety % = (Margin of safety / Actual sales) x 100
Plugging in the numbers, we get:
Margin of safety % = ($192,400 / $740,000) x 100
Margin of safety % = 26.05%
Therefore, Jonick Company's margin of safety as a percentage of current sales is 26.05%. This means that sales can drop by 26.05% before the company starts to incur losses.
of 100 athletes 31 like to run 65 like to walk ans 22 neither like to walk nor run .how many athletes like to both run or walk
Answers
There are 22 athletes who like both running and walking.
Let R be the set of athletes who like to run, and
let W be the set of athletes who like to walk.
Then we want to find the size of the intersection R ∩ W.
We know that there are 31 athletes who like to run,
65 athletes who like to walk, and
22 athletes who like neither.
Therefore, the total number of athletes who like to run or walk (or both) is:
31 + 65 - 22 = 74
This number includes athletes who like both running and walking, as well as athletes who like only running or only walking.
Now we can use the formula:
|A ∪ B| = |A| + |B| - |A ∩ B|
So |R ∪ W| = |R| + |W| - |R ∩ W|
Substituting the known values, we get:
74 = 31 + 65 - |R ∩ W|
Simplifying, we get:
|R ∩ W| = 22
Therefore, there are 22 athletes who like both running and walking.
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Vertical angles are two angles that are ___ of each other when two intersect. These angles are
Answers
Answer:
The two angles that are directly across the intersection point from each other are called vertical angles. Vertical angles are always congruent.
Step-by-step explanation:
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Vertical angles are two angles that are opposite of each other when two intersect. These angles are congruent.
What are vertical angles?Vertical angles are angles opposite to each other where two lines cross.
When two lines intersect, they naturally form two pairs of vertical angles. Vertical angles share the same vertex or corner, and are opposite each other.
These pair of angles are congruent which means they have the same angle measure.
Hence, Vertical angles are two angles that are opposite of each other when two intersect. These angles are congruent.
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Examine the figure of two parallel lines cut by a transversal.
One interior angle has a measure of 2 x plus 10 degrees; its same-interior angle has a measure of 2 x minus 30 degrees.
What is the value of x?
Answers
The value of x is 50° from the given set of parallel lines.
Give that, two parallel lines cut by a transversal.
The interior angles are (2x+10)° and (2x-30)°.
Here, (2x+10)°+(2x-30)°=180° (Sum of co-interior angles is 180°)
4x-20=180
4x=200
x=200/4
x=50°
Therefore, the value of x is 50° from the given set of parallel lines.
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a car dealer offers you a choice of 0% financing for 60 months or 2500 cash back on a new vehicle. You have a pre-approved 60 month loan you can use from your credit union at a 4% interest rate. f the monthly payments at 0% are 16.67 per 1000 financed, and the monthly payments at 4% are 18.41 per 1000 financed, what is the range of new car prices for which the cash back option will cost you less? For what range of car prices should you take the 0% financing?
Answers
Answer:
To determine the range of car prices for which the cash-back option will cost less, we need to find the total cost of each option over 60 months for different car prices and compare them. Let's assume the car price ranges from $20,000 to $30,000.
For the 0% financing option, the monthly payment is $16.67 per $1,000 financed, so the monthly payment for a car priced at $20,000 would be:
$20,000 / 1000 * $16.67 = $333.40 per month
Similarly, the monthly payment for a car priced at $30,000 would be:
$30,000 / 1000 * $16.67 = $500.10 per month
Over 60 months, the total cost for the 0% financing option for a car priced at $20,000 would be:
$333.40 * 60 = $20,004
And the total cost for a car priced at $30,000 would be:
$500.10 * 60 = $30,006
For the cash-back option, the cost of the car would be reduced by $2,500, so the total cost over 60 months for a car priced at $20,000 would be:
($20,000 - $2,500) + ($18.41 * $20) * 60 = $19,484
And the total cost for a car priced at $30,000 would be:
($30,000 - $2,500) + ($18.41 * $30) * 60 = $29,222
To find the range of car prices for which the cash back option will cost less, we need to compare the total cost of each option. Setting the two equations equal to each other and solving for x, we get:
($x - $2,500) + ($18.41 * $x) * 60 < $20,004
($x - $2,500) + ($18.41 * $x) * 60 > $30,006
Simplifying, we get:
$17.285x < $22,504
$17.285x > $34,256
Dividing by 17.285, we get:
$1,300.90 < x < $1,978.63
So, for car prices between $13,000.90 and $19,978.63, the cash-back option will cost less.
To find the range of car prices for which the 0% financing option is a better choice, we can simply look at the range of car prices for which the cash-back option is more expensive, which is anything outside of the range of $13,000.90 to $19,978.63. Therefore, for car prices outside of this range, the 0% financing option is the better choice.
PLS HELP
reposting this again pls help
Answers
Answer:
4/3x + y = -14/3
Step-by-step explanation:
Currently, the line we're given is in standard form, whose general form is
[tex]Ax+By=C[/tex]
We will need to find the slope of this line, since the slopes of perpendicular lines are negative reciprocals. This is shown by the formula:
[tex]m_{2}=-1/m_{1}[/tex], where m2 is the slope of the line we're trying to find and m1 is the slope of the line we're given.
Furthermore, we can find the slope of the line by converting the line from standard form to slope-intercept form, whose general form is
[tex]y=mx+b[/tex], where m is the slope and b is the y intercept:
[tex]3/4x-y=7/2\\-y=-3/4x+7/2\\y=3/4x-7/2[/tex]
Now, if we allow 3/4 to be m2 in the formula I provided, we can find the slope of the other line:
[tex]m_{2}=-1/(3/4)\\ m_{2}=-4/3[/tex]
Now, that we've found the slope of the new line, we can find the y-intercept by plugging in the slope and the point (-2, -2) for x and y in the slope-intercept form:
[tex]-2=-4/3(-2)+b\\-2=8/3+b\\-14/3=b[/tex]
Thus, the equation of the line passing through (-2, -2) and perpendicular to 3/4x - y = 7/2 is y = -4/3x - 14/3
In order to clear up confusion, we can convert this line to standard form so that it truly resembles the other line by simply isolating -14/3 (b in the slope-intercept form):
[tex]y=-4/3x-14/3\\4/3x+y=-14/3[/tex]
As the sample size increases, does the range of the sample population also increase?
Answers
As the sample size increases, it does not necessarily mean that the range of the sample population also increases.
The range of a sample population is simply the difference between the maximum and minimum values of the data set. It is possible for the range to increase or decrease as the sample size increases, depending on the distribution of the data.
For example, if the data is evenly distributed with no outliers, increasing the sample size may not change the range significantly. However, if the data has outliers or a skewed distribution, increasing the sample size may result in capturing more extreme values, which could increase the range of the sample population.
Therefore, it is important to consider the distribution of the data and not assume that increasing the sample size will always result in an increased range of the sample population.
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y=[1/2x-2]+3 one unit left
Answers
Answer:
(x-1, y) = (x-1, 1/2x + 1/2).
Step-by-step explanation:
To find the point one unit to the left of the given point, we need to subtract 1 from the x-coordinate of the given point.
Let's start with the given point: y = [1/2x - 2] + 3
We can simplify this by combining the constants: y = 1/2x + 1
Now we need to find the point one unit to the left. This means we subtract 1 from the x-coordinate:
y = 1/2(x-1) + 1
Simplifying this expression:
y = 1/2x - 1/2 + 1
y = 1/2x + 1/2
So the point one unit to the left of the original point is (x-1, y) = (x-1, 1/2x + 1/2)
the cone and cylinder above have the same radius and height. the volume of the cone is 162 cubic inches what is the volume of the cylinder.
Answers
The volume of the cylinder is 623.17 cubic inches.
We have,
The volume of a cone is given by the formula V = (1/3)πr²h,
where r is the radius of the base and h is the height.
The volume of a cylinder is given by the formula V = πr²h,
where r is the radius of the base and h is the height.
Since the cone and cylinder have the same radius and height, we can set the equations for their volumes equal to each other:
(1/3)πr²h = πr²h
We can simplify this equation by multiplying both sides by 3:
πr²h = 3(1/3)πr²h
Simplifying further, we get:
πr²h = πr²(3h/3)
πr²h = πr²(3/1)
πr²h = 3πr²
Canceling the πr² from both sides, we get:
h = 3
We now know that the height of the cone and cylinder is 3.
We can use the given volume of the cone to solve for the radius:
V = (1/3)πr²h
162 = (1/3)πr²(3)
162 = πr²
r² = 162/π
r ≈ 6.4615
Now that we know the radius and height of the cylinder, we can use the formula for the volume of a cylinder to find its volume:
V = πr²h
V = π(6.4615)²(3)
V ≈ 623.17 cubic inches
Therefore,
The volume of the cylinder is 623.17 cubic inches.
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14. A 20 ft ladder leans against a wall. The ladder hits the wall at a height of 16 ft above the ground.
Find the angle of elevation. Include a sketch. Round to the nearest tenth.
Answers
The angle of elevation is 53.1( nearest tenth)
What is angle of elevation?The angle of elevation is an angle that is formed between the horizontal line and the line of sight. Trigonometric ratio is mainly used to solve problems in this case.
A 20ft ladder leans against the wall, the height of the wall will be the opposite to angle of elevation and the height of the ladder will be the hypotenuse.
Therefore using trigonometry ratio;
sin( tetha) = opp/hyp
sin(tetha) = 16/20
sin(tetha) = 0.8
tetha = sin^-1(0.8)
tetha = 53.1°( nearest tenth)
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Please answer I’m so
Confused
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c ≥ 6 and d > 4, the common solutions are all values of (c,d) that satisfy these two conditions simultaneously of inequalities
The given inequalities are -2(c-4)≤-4 and 1/2 d - 6 >-4
The first inequality is -2(c-4)≤-4
-2c + 8 ≤ -4
Subtracting 8 from both sides, we get:
-2c ≤ -12
Dividing both sides by -2
c ≥ 6
Now, let's look at the second inequality:
1/2 d - 6 > -4
Adding 6 to both sides, we get:
1/2 d > 2
Multiplying both sides by 2, we get:
d > 4
So, the solutions for these two inequalities are: c ≥ 6 and d > 4
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