To find the value of x when (fog)(x) = -8, we first need to find the composition of f and g, which is given by (fog)(x) = f(g(x)). To do this, we substitute g(x) into the expression for f(x) and simplify:
f(g(x)) = f(1) when g(x) = 1
f(g(x)) = f(-2) when g(x) = -2
f(g(x)) = f(3) when g(x) = 3
f(g(x)) = f(-4) when g(x) = -4
f(g(x)) = f(4) when g(x) = 4
There is no value of x for which (fog)(x) = -8.
Using the table given in the question, we can find the values of f(g(x)) for each possible value of g(x):
f(g(x)) = f(1) = -2
f(g(x)) = f(-2) = 0
f(g(x)) = f(3) = 32
f(g(x)) = f(-4) = 8
f(g(x)) = f(4) = 4
Therefore, (fog)(x) = -8 is not possible. The closest value we can get to -8 is by setting g(x) = -4, which gives f(g(x)) = f(-4) = 8. Thus, there is no value of x for which (fog)(x) = -8.
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What is 7-12 problems. The image is attached.
The number of bases, faces, edges and vertices are;
7. 2, 4, 6, 6
8. 6, 5, 10, 10
9. 1, 4, 5, 5
10. 1, 5, 7 , 7
11. 1, 5, 7, 7
12. 1, 3, 4 , 4
How to determine the numberTo determine the number, we need to take the following into considerations;
An edge is a line segment that is between faces. Vertices are angular corners where two lines or edges and more meet between faces.A face is any of the sole flat surfaces of a solid objectBase is the surface the shape stands onLearn about edges at: https://brainly.com/question/22735873
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Can you help me with part C? Please
Answer: -40
Step-by-step explanation:
Rate of change is calculated as the slope. The formula for Slope is:
S = [tex]\frac{x_{1}-x_{2} }{ y_{1}-y_{2}}[/tex]
The two points we have are when x = 3 and 6.
the points are (3, 120) and (6, 0), as we can see.
plugging into the slope formula:
S = [tex]\frac{120-0 }{ 3-6}[/tex]
S = 120/-3
S = -40
Which hopefully makes sense, because the slope is negative, (the graph is falling).
Find the smallest number of terms of the series ∑ n = 1 (-1)^n+1/2^n you need to be certain that the partial sum Sn is within 1/100 of the sum.n=2 n=4 n=6 n=8 n=7
We need at least 7 terms of the series to be certain that the partial sum Sn is within 1/100 of the sum.
We want to find the smallest value of n such that the absolute value of the difference between the sum of the first n terms and the sum of the entire series is less than 1/100.
The sum of the first n terms of the series is given by:
Sn = ∑_(k=1[tex])^n[/tex] (-1[tex])^(k+1)[/tex]/[tex]2^k[/tex]
We can write the sum of the entire series as:
S = ∑_(k=[tex]1)^∞[/tex] (-1[tex])^(k+1)[/tex]/[tex]2^k[/tex]
The absolute value of the difference between the sum of the first n terms and the sum of the entire series is:
|S - Sn| = |∑_(k=n+1[tex])^∞[/tex] [tex](-1)^(k+1)/2^k|[/tex]
We want to find the smallest value of n such that |S - Sn| < 1/100.
Let's start by evaluating the sum of the series:
S = ∑_(k=1) (-1[tex])^(k+1)[/tex]/[tex]2^k[/tex] = 1/2 - 1/4 + 1/8 - 1/16 + ...
This is a geometric series with first term a = 1/2 and common ratio r = -1/2. The sum of the series is:
S = a/(1-r) = (1/2)/(1+1/2) = 1/3
Now we can write:
|S - Sn| = |∑_(k=n+1[tex])^∞[/tex] (-1[tex])^(k+1)[/tex]/[tex]2^k|[/tex] <= 1/[tex]2^(n+1)[/tex]
The last inequality is true because the terms of the series are decreasing in absolute value, and we are summing an infinite number of terms.
Therefore, we need to find the smallest value of n such that 1/2^(n+1) < 1/100. This gives:
n+1 > log2(100)
n > log2(100) - 1
n > 6.64
The smallest integer value of n that satisfies this inequality is n = 7.
Therefore, we need at least 7 terms of the series to be certain that the partial sum Sn is within 1/100 of the sum.
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HELPPPP!!!!!!
Based on this information, which function best models the number of game consoles sold in millions x years since 2010?
A) g(x) = 20(1. 5)
B) g(x) = 0. 15(20)*
C) g(x) - 0. 150. 2)*
D) g(x) = 2000. 15)
The function that best models the number of game consoles sold in millions x years since 2010 is option B, g(x) = 0.15(20).
To answer this question, we need to identify the function that best models the number of game consoles sold in millions x years since 2010.
Option A can be simplified to g(x) = 30, which is a constant function. This means that it does not depend on the value of x and is not a good model for the number of game consoles sold over time.
Option B can be simplified to g(x) = 3x, which is a linear function. This means that the number of game consoles sold increases at a constant rate over time. This could be a good model for the number of game consoles sold, but we need to compare it to the other options.
Option C can be simplified to g(x) = 0.03x, which is also a linear function. However, the rate of increase is much slower than in option B. This is not a good model for the number of game consoles sold.
Option D can be simplified to g(x) = 300, which is a constant function like option A. Again, this is not a good model for the number of game consoles sold over time.
Therefore, the function that best models the number of game consoles sold in millions x years since 2010 is option B, g(x) = 0.15(20). This is a linear function that represents a constant rate of increase in the number of game consoles sold over time.
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complete question:
Based on this information, which function best models the number of game consoles
sold in millions x years since 2010?
A- g(x) = 0.15(20)^x
B- g(x) = 20(0.15)^x
C- g(x) = 20(1.5)^x
D- g(x) = 0.15(.2)^x
On Saturday mornings, Roger volunteers at the hospital. One Saturday, he answers phone calls at the information desk while the receptionist is away. Then he spends 40 minutes delivering flowers to patients' rooms. In all, Roger volunteers at the hospital for 90 minutes that day. Which equation can you use to find the amount of time t that Roger answers phone calls?
We know that by solving for t, you can find the amount of time Roger spent answering phone calls
You can use the equation t + 40 = 90, where t represents the amount of time Roger answers phone calls at the information desk.
This equation takes into account that Roger spends 40 minutes delivering flowers and the total time he volunteers at the hospital is 90 minutes.
By solving for t, you can find the amount of time Roger spent answering phone calls.
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what is an equation for the ellipse with foci (0, -5) and (0,5) and vertices (0, -9) and (0, 9)
Answer:
0,8
Step-by-step explanation:
Answer:
x^2 / 81 + y^2 / 56 = 1
Step-by-step explanation:
The center of the ellipse is at the midpoint of the foci, which is (0,0). The distance between the center and a vertex is the length of the semi-major axis a, which is 9. The distance between the center and a focus is c, which is 5. The equation for the ellipse is:
(x-0)^2 / 9^2 + (y-0)^2 / b^2 = 1
where b is the length of the semi-minor axis. To find b, you use the relationship:
b^2 = a^2 - c^2
b^2 = 9^2 - 5^2
b^2 = 56
Therefore, the equation for the ellipse is:
x^2 / 81 + y^2 / 56 = 1
Steph Curry posts a video of a puppy playing the piano and shares it with 4 of his friends. The video goes viral and the number of shares increases by a factor of 10 every minute.
a. Write an equation to model this situation.
b. What is the average rate of change for the number of shares from 2 minutes to 4 minutes?
An equation to model this situation will be S(t) = 4 * 10^(t). The average rate of change for the number of shares from 2 minutes to 4 minutes is approximately 19,800 shares per minute.
a. Let S(t) be the number of shares of the video at time t in minutes after Steph Curry shared it with his friends. The initial number of shares is 4 (the 4 friends he shared it with), and the number of shares increases by a factor of 10 every minute. Therefore, we can model this situation with the exponential function:
S(t) = 4 * 10^(t)
b. The average rate of change for the number of shares from 2 minutes to 4 minutes can be calculated by finding the slope of the line connecting the points (2, S(2)) and (4, S(4)) on the graph of S(t). Using the equation S(t) = 4 * 10^(t), we have:
S(2) = 4 * 10^(2) = 400
S(4) = 4 * 10^(4) = 40,000
The slope of the line connecting these two points is:
(S(4) - S(2)) / (4 - 2) = (40,000 - 400) / 2 = 19,800
Therefore, the average rate of change for the number of shares from 2 minutes to 4 minutes is approximately 19,800 shares per minute.
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For which values of k would be the pruduct of k/3x12 be greater than 12
The product (k/3) x 12 is greater than 12 for values of k greater than 3.
To determine the values of k for which the product (k/3) x 12 is greater than 12, follow these steps:
Step 1: Set up the inequality:
(k/3) x 12 > 12
Step 2: Simplify the inequality by dividing both sides by 12:
(k/3) > 1
Step 3: Multiply both sides by 3 to solve for k:
k > 3
So, the product (k/3) x 12 is greater than 12 for values of k greater than 3.
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Find an equation of the plane that passes through the given point and is perpendicular to the given vector or line.
Point (0, 9, 0) Perpendicular to
n = -2i ÷ 4k
To find the equation of the plane that passes through the point (0, 9, 0) and is perpendicular to the vector n = -2i ÷ 4k, we first need to find the normal vector of the plane.
Since the plane is perpendicular to the given vector, the normal vector will be parallel to it. So, we can take the given vector and multiply it by -1 to get a vector in the opposite direction, which will be normal to the plane.
n = -2i ÷ 4k = -1/2i ÷ k
Multiplying by -1 gives us:
n = 1/2i ÷ k
Now we can use the point-normal form of the equation of a plane:
r · n = d
where r is the position vector of any point on the plane, n is the normal vector, and d is the distance of the plane from the origin (since the normal vector is normalized, d will be the signed distance of the plane from the origin).
Substituting the given point (0, 9, 0) and the normal vector n = 1/2i ÷ k into the equation, we get:
(0, 9, 0) · (1/2i ÷ k) = d
0 + 9(1/2) + 0 = d
d = 4.5
So the equation of the plane is:
x/2 + z/2 = 4.5
or, multiplying by 2 to eliminate fractions:
x + z = 9
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What is the magnitude of the electrostatic force exerted by
sphere a on sphere b?
2. 0 m-
а
b
+1. 0 x 10-6c
-1. 6 x 10-60
We are not given the distance between the spheres, so we cannot calculate the force without that information.
To calculate the electrostatic force between the two charged spheres, we can use Coulomb's law, which states that the magnitude of the electrostatic force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
Mathematically, we can express this as:
F = k * (q1 * q2) / r^2
Where F is the electrostatic force, k is Coulomb's constant (9 x 10^9 N m^2/C^2), q1 and q2 are the charges of the spheres, and r is the distance between their centers.
We are given the charges of the two spheres: sphere A has a charge of +1.0 x 10^-6 C, and sphere B has a charge of -1.6 x 10^-6 C.
However, we are not given the distance between the spheres, so we cannot calculate the force without that information.
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1. Sally Rose's charge account statement showed a previous balance of $6,472. 82, a finance charge of $12. 95,
new purchases of $1,697. 08, and a payment of $4,900. 50. What is her new balance?
a. $3,454. 99
c. $3,566. 44
b. $3,282. 35
d. $3,112. 78
Sally Rose's new balance is $3,282.35, and option (b) is the correct answer.
Sally Rose's charge account statement contains information about her previous balance, finance charge, new purchases, and payment. To determine her new balance, we need to take the previous balance, add the finance charge and new purchases, and then subtract the payment.
Starting with the previous balance of $6,472.82, we add the finance charge of $12.95 and new purchases of $1,697.08 to get a total of:
$6,472.82 + $12.95 + $1,697.08 = $8,182.85
Next, we subtract the payment of $4,900.50 to get the new balance:
$8,182.85 - $4,900.50 = $3,282.35
It's important to keep track of credit card balances to avoid accumulating too much debt and paying high interest charges. When making credit card payments, it's a good idea to pay more than the minimum amount due, which can help reduce the balance faster and save money on interest charges over time. The answer is option b).
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Vanessa's team played 8 games of basketball. During those 8 games her team's score was: 68, 76, 63, 58, 64, 75, 78 and 78.
What is the mean absolute deviation?
Please help!! Please answer it correctly too!!!! Whoever gets it correct gets brainliest!! and then I will give them 154 points!!!! please!!
The mean absolute deviation is 6.25.
To find the mean absolute deviation (MAD), we first need to find the mean of the scores:
Mean = (68 + 76 + 63 + 58 + 64 + 75 + 78 + 78) / 8 = 69.5
Next, we need to find the absolute deviation of each score from the mean. The absolute deviation is the absolute value of the difference between the score and the mean.
For example, the absolute deviation of the first score (68) is:
|68 - 69.5| = 1.5
We can calculate the absolute deviation for each score:
|68 - 69.5| = 1.5
|76 - 69.5| = 6.5
|63 - 69.5| = 6.5
|58 - 69.5| = 11.5
|64 - 69.5| = 5.5
|75 - 69.5| = 5.5
|78 - 69.5| = 8.5
|78 - 69.5| = 8.5
To find the MAD, we take the average of the absolute deviations:
MAD = (1.5 + 6.5 + 6.5 + 11.5 + 5.5 + 5.5 + 8.5 + 8.5) / 8 = 6.25
Therefore, the mean absolute deviation is 6.25.
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Abc company’s budgeted sales for june, july, and august are 12,800, 16,800, and 14,800 units, respectively. abc requires 30% of the next month’s budgeted unit sales as finished goods inventory each month. budgeted ending finished goods inventory for may is 3,840 units. each unit that abc company produces uses 2 pounds of raw material. abc requires 25% of the next month’s budgeted production as raw material inventory each month.
The budgeted ending raw material inventory for May is 2,560 pounds, calculated by taking 25% of the next month's budgeted production (12,800 units) multiplied by 2 pounds per unit.
To solve this problem, we need to calculate the budgeted production and raw material inventory for June, July, and August.
For June:Budgeted production = 12,800 units + 30% * 16,800 units = 17,440 units
Raw material inventory = 25% * 17,440 units * 2 pounds = 8,720 pounds
For July:Budgeted production = 16,800 units + 30% * 14,800 units = 20,840 units
Raw material inventory = 25% * 20,840 units * 2 pounds = 10,420 pounds
For August:Budgeted production = 14,800 units + 30% * 20,840 units = 20,632 units
Raw material inventory = 25% * 20,632 units * 2 pounds = 10,316 pounds
To find the budgeted ending finished goods inventory for June, we need to subtract the budgeted sales for June from the budgeted production for June and add the budgeted ending finished goods inventory for May:
Budgeted ending finished goods inventory for June = 17,440 units - 12,800 units + 3,840 units = 8,480 units
Similarly, we can find the budgeted ending finished goods inventory for July and August:
Budgeted ending finished goods inventory for July = 20,840 units - 16,800 units + 8,480 units = 12,520 units
Budgeted ending finished goods inventory for August = 20,632 units - 14,800 units + 12,520 units = 18,352 units
Therefore, the budgeted ending finished goods inventory for June, July, and August are 8,480 units, 12,520 units, and 18,352 units, respectively. The budgeted raw material inventory for June, July, and August are 8,720 pounds, 10,420 pounds, and 10,316 pounds, respectively.
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1. The data sel below represents the number of animals in different exhibits at a zoo.
48, 86, 15, 27, 18, 52, 103
a. Write the data from least to greatest.
h. What is the minimum number of animals?
c. What is the maximum number of animals?
d. What is the median number of animals?
e. What is the median of the first half of the data? (first quartile)
f. What is the median of the second half of the data? (third quartile)
g. What is the interquartile range?
Answer:
a) 15, 18, 27, 48, 52, 86, 103
b) Minimum number = 15
c) Maximum number = 103
d) Median = 48
e) First quartile = 18
f) Third quartile = 86
g) Interquartile range = 68
Step-by-step explanation:
Part aTo write the data from least to greatest, arrange the numbers in ascending order:
15, 18, 27, 48, 52, 86, 103[tex]\hrulefill[/tex]
Part bThe minimum number in a set of data is the smallest value.
Therefore, the minimum number of animals is 15.
[tex]\hrulefill[/tex]
Part cThe maximum number in a set of data is the greatest value.
Therefore, the maximum number of animals is 103.
[tex]\hrulefill[/tex]
Part dThe median of a set of data is the middle value when all data values are placed in order of size.
[tex]\begin{array}{ccccccc}\sf 15, &\sf 18, &\sf 27, &\sf 48, &\sf 52, &\sf 86,& \sf 103\\ &&&\uparrow&&&\\&&&\sf median&&&\end{array}[/tex]
Therefore, the median is the fourth number, which is 48.
[tex]\hrulefill[/tex]
Part eThe lower quartile (Q₁) is the median of the data values to the left of the median.
[tex]\begin{array}{ccccccc}\sf 15, &\sf 18, &\sf 27, &\sf 48, &\sf 52, &\sf 86,& \sf 103\\ &\uparrow &&\uparrow&&&\\&\sf Q_1&&\sf median&&&\end{array}[/tex]
Therefore, the median of the first half of the data is 18.
[tex]\hrulefill[/tex]
Part fThe lower quartile (Q₃) is the median of the data values to the right of the median.
[tex]\begin{array}{ccccccc}\sf 15, &\sf 18, &\sf 27, &\sf 48, &\sf 52, &\sf 86,& \sf 103\\ &&&\uparrow &&\uparrow&\\&&&\sf median&&\sf Q_3&\end{array}[/tex]
Therefore, the median of the second half of the data is 86.
[tex]\hrulefill[/tex]
Part gThe interquartile range (IQR) is the difference between the third quartile (Q₃) and the first quartile (Q₁).
[tex]\begin{aligned}\sf IQR &=\sf Q_3 - Q_1 \\&= \sf 86 - 18 \\&= \sf 68\end{aligned}[/tex]
Therefore, the interquartile range is 68.
PLEASE I NEED HELP ASAP
8.4, 42, 210,....
In the sequence above, each term after the first is equal to the previous term times n. What is
the value of the next term in the sequence?
(A) 650
(B) 825
(C) 1,050
(D) 3,050
(E) 5,250
Answer:
C) 1,050
Step-by-step explanation:
We can see that to get from 8.4 to 42 and to get from 42 to 210, we have to multiply by 5.
To complete the sequence, multiply 210 by 5
210·5
=1,050
Hope this helps!
In a given diagram below, ray AB bisects angle FAE. BF = 2x + 8 and BE = 42.
A. Set up an equation to solve for "x".
B. Show your work and solve for "x".
a. The equation to solve for x is given as follows: 2x + 8 = 42.
b. The solution for x is given as follows: x = 17.
How to obtain the value of x?The value of x is obtained applying the angle bisection theorem, which divides an angle into two angles of equal measure, hence the opposite segments also have equal length.
The segments for this problem, along with their lengths, are given as follows:
BF = 2x + 8.BE = 42.Hence the equation is given as follows:
2x + 8 = 42.
The value of x is given as follows:
2x = 34
x = 17.
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What are all the possible rectangle with the perimeter 16cm,20cm,and 14cm, find the area of each rectangle
The area of a rectangle can be found by multiplying its length and width.
For perimeter 16cm: 15 cm² and 16 cm²For perimeter 20cm: 24 cm² and 25 cm²For perimeter 14cm: 12 cm²How to find area of rectangles?To find the area of rectangles with different perimeters, we need to use the formula:
Area = length x width
Perimeter = 16 cmPossible dimensions:
Length = 5 cm, Width = 3 cm
Length = 4 cm, Width = 4 cm
Area of the first rectangle = 5 cm x 3 cm = 15 cm²
Area of the second rectangle = 4 cm x 4 cm = 16 cm²
Perimeter = 20 cmPossible dimensions:
Length = 6 cm, Width = 4 cm
Length = 5 cm, Width = 5 cm
Area of the first rectangle = 6 cm x 4 cm = 24 cm²
Area of the second rectangle = 5 cm x 5 cm = 25 cm²
Perimeter = 14 cmPossible dimensions:
Length = 4 cm, Width = 3 cm
Area of the rectangle = 4 cm x 3 cm = 12 cm²
Therefore, the areas of the possible rectangles with perimeters 16cm, 20cm, and 14cm are:
For perimeter 16cm: 15 cm² and 16 cm²
For perimeter 20cm: 24 cm² and 25 cm²
For perimeter 14cm: 12 cm²
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El 91 no es un número primo porque tiene más divisores que el 1 y el 91 verdadero o falso
The statement''El 91 no es un número primo porque tiene más divisores que el 1 y el 91'' is true because 91 is not a prime number.
A prime number is a positive integer that has only two divisors, 1 and itself. To check if 91 is a prime number, we need to find its divisors. We can start by dividing 91 by 2, but we find that 2 is not a divisor of 91. Next, we can try dividing it by 3, and we get 30 with a remainder of 1. This means that 3 is not a divisor of 91 either.
We continue dividing by 4, 5, 6, and so on until we reach 13, which gives us 7 as a quotient and 0 as a remainder. Therefore, the divisors of 91 are 1, 7, 13, and 91, which means that 91 is not a prime number because it has more than two divisors. Hence, the statement is true.
91 ÷ 2 = 45 r 1
91 ÷ 3 = 30 r 1
91 ÷ 4 = 22 r 3
91 ÷ 5 = 18 r 1
91 ÷ 6 = 15 r 1
91 ÷ 7 = 13 r 0
Since 91 has more than two divisors, it is not a prime number.
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Pls help me I need it
The number of triangles formed or the interior angle sum should be matched to each regular polygon as follows;
Number of triangles formed is 4 ⇒ regular hexagonInterior angle sum is 1,440 ⇒ regular decagonInterior angle sum is 1,800 ⇒ regular dodecagonNumber of triangles formed is 6 ⇒ regular octagon.How to determine the number of triangles and interior angle sum?In Mathematics and Geometry, the sum of the interior angles of both a regular and irregular polygon can be calculated by using this formula:
Sum of interior angles = 180 × (n - 2)
1,440 = 180 × (n - 2)
1,440 = 180n - 360
180n = 1,440 + 360
n = 1,800/180
n = 10 (decagon).
Sum of interior angles = 180 × (n - 2)
1,800 = 180 × (n - 2)
1,800 = 180n - 360
180n = 1,800 + 360
n = 2,160/180
n = 12 (dodecagon).
Generally speaking, the number of triangles in a regular polygon (n-gon) can be calculated by using this formula;
Number of triangles = n - 2
4 = n - 2
n = 4 + 2 = 6 (regular hexagon).
Number of triangles = n - 2
6 = n - 2
n = 6 + 2 = 8 (regular octagon).
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A man buys a car at a cost of r60 000 from cape town and transported it to durban at a cost price of by r4 500. at what price must he sell the car to make an overall profit of 25%
He must sell the car at R80,625 to make an overall profit of 25%
To find the selling price of the car that gives a 25% profit, we need to use the following steps:
Calculate the total cost of buying and transporting the car to Durban:
Total cost = Cost of car + Cost of transportation
Total cost = R60,000 + R4,500
Total cost = R64,500
Calculate the desired profit:
Profit = 25% of total cost
Profit = 0.25 x R64,500
Profit = R16,125
Calculate the total amount that the car needs to be sold for:
Total amount = Total cost + Profit
Total amount = R64,500 + R16,125
Total amount = R80,625
Therefore, the man needs to sell the car for R80,625 to make an overall profit of 25%.
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Question 4(Multiple Choice Worth 2 points) (Identifying Transformations LC) Use the image to determine the type of transformation shown. Graph of polygon VWXYZ with W at point 3 comma negative 2. A second polygon V prime W prime X prime Y prime Z prime with W prime at point negative 3 comma negative 2. 270° counterclockwise rotation Horizontal translation Reflection across the x-axis Reflection across the y-axis
Reflection across the y-axis is the transformation used to the polygon ABCD. The type of transformation shown is a horizontal translation.
What is Polygon?A polygon is closed geometric shape that is made up of straight line segments connected end to end. It is two-dimensional shape that has three or more sides, angles, and vertices.
In a polygon, sides do not cross each other and vertices are points where two sides meet.
1) The type of transformation shown in the image is a Horizontal translation, because the second polygon A'B'C'D' is moved horizontally to the right of the original polygon ABCD while maintaining its size and shape.
2) 90° clockwise rotation
3) 90° counterclockwise rotation.
4) Reflection across the x-axis.
5) Reflection across the y-axis.
6) Reflection across the y-axis
7) the correct answer is 180° clockwise rotation.
The type of transformation shown is a horizontal translation, since the image has been shifted horizontally from the original position.
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complete question -
Para el periódico mural, los alumnos decidieron representar un pino por medio de un triángulo que tiene una superficie de 1. 5m si la base mide 1. 5 m ¿cuanto mide la altura? 
The height of the triangle is 2 meters.
How tall is triangle?Para encontrar la altura del triángulo, podemos utilizar la fórmula para calcular el área de un triángulo:
Área = (base x altura) / 2
Sabemos que el área es de 1.5 m² y que la base mide 1.5 m, por lo que podemos despejar la altura de la siguiente manera:
1.5 m² = (1.5 m x altura) / 2
Multiplicando ambos lados por 2:
3 m² = 1.5 m x altura
Despejando la altura:
altura = 3 m² / 1.5 m
altura = 2 m
Por lo tanto, la altura del triángulo que representa al pino en el periódico mural es de 2 metros.
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) Nadia buys 4 1/5 pounds of plums. Nadia used a 55 cent coupon off her entire purchase. Her total after the coupon was $3. 23. If c represents the cost per pound for the plums, create and solve an equation to determine the cost per pound for the plums
If c represents the cost per pound for the plums, the cost per pound for the plums is $0.90.
First, we need to determine the total cost of the plums before the coupon was applied.
4 1/5 pounds can be written as a mixed number:
4 1/5 = 21/5
So, the total cost of the plums without the coupon can be found by multiplying the cost per pound (c) by 21/5:
Total cost = c * 21/5
Now we can create an equation to represent the total cost after the coupon was applied:
Total cost - coupon = $3.23
Substituting the expression for total cost:
c * 21/5 - 0.55 = 3.23
To solve for c, we can start by adding 0.55 to both sides:
c * 21/5 = 3.78
Then, we can isolate c by multiplying both sides by the reciprocal of 21/5:
c = 3.78 / (21/5)
c = 0.90
Therefore, the cost per pound for the plums is $0.90.
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Two different box-filling machines are used to fill cerealboxes on the assembly line. The critical measurement influenced bythese machines is the weight of the product in the machines. Engineers are quite certain that the variance of the weight ofproduct is σ^2=1 ounce. Experiments are conducted using bothmachines with sample sizes of 36 each. The sample averages formachine A and B are xA=4. 5 ounces and xB =4. 7 ounces. Engineers seemed surprisedthat the two sample averages for the filling machines were sodifferent.
a. Use the central limit theorem to determine
P(XB- XA >= 0. 2)
under the condition that μA=μB
b. Do the aforementioned experiments seem to, in any way,strongly support a conjecture that the two population means for thetwo machines are different?
a. By central limit theorem, P(XB- XA >= 0. 2) is approximately 0.0228 under the condition that μA=μB.
b. Yes, we can conclude that the observed difference in sample means does provide evidence that the two population means for the two machines are different.
a. Using the central limit theorem, we know that the sampling distribution of the difference in means (XB - XA) is approximately normal with mean (μB - μA) and standard deviation (σ/√n), where σ is the population standard deviation (σ=1 ounce) and n is the sample size (n=36 for both machines).
So, P(XB - XA >= 0.2) can be calculated by standardizing the difference in means:
Z = (XB - XA - (μB - μA)) / (σ/√n)
Z = (4.7 - 4.5 - 0) / (1/√36)
Z = 2
Looking up the probability of Z being greater than or equal to 2 in a standard normal distribution table, we find P(Z >= 2) = 0.0228.
Therefore, P(XB - XA >= 0.2) is approximately 0.0228 under the condition that μA=μB.
b. The difference in sample means (XB - XA = 0.2) is relatively small compared to the population standard deviation (σ=1 ounce). However, the calculated probability in part a (0.0228) suggests that the observed difference in sample means is statistically significant at a significance level of 0.05 (since P(XB - XA >= 0.2) < 0.05).
Therefore, we can conclude that the observed difference in sample means does provide evidence that the two population means for the two machines are different. However, further testing or analysis may be necessary to confirm this conclusion.
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Can someone please help me ASAP? It’s due tomorrow. I will give brainliest if it’s correct.
The probability values when calculated are
P(2 numbers greater than 3) = 0.1P(2 even numbers) = 0.4P(2 cards with same numbers) = 0P(1 card is 3) = 0.3Evaluating the probability valuesFrom the question, we have the following parameters that can be used in our computation:
Cards = {1, 2, 3, 4, 5}
Selecting two cards without replacement
So, we have
P(2 numbers greater than 3) = 2/5 * 1/4
P(2 numbers greater than 3) = 0.1
P(2 even numbers) = 2/5 * 4/4
P(2 even numbers) = 0.4
P(2 cards with same numbers) = 1/5 * 0/4
P(2 cards with same numbers) = 0
P(1 card is 3) = 2 * 1/5 * 3/4
P(1 card is 3) = 0.3
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A cement walkway is in the shape of a rectangular prism. The length is 10 feet, the width is three feet and the depth is 1.5 feet. How much cubic feet of cement will they need?
The volume of cement in cubic feet that will be needed is 45 cubic feet.
What is volume?Volume is the space occuppied by an object.
To calculate the volume of cement in cubic feet that will be needed, we use the formula below
Formula:
V = lwh....................... Equation 1Where:
V = Volume of the cement that is neededl = Length of the walkwayw = width of the walkwayh = depth of the walkwayFrom the question,
Given:
l = 10 feetw = 3 feeth = 1.5 feetSubstitute these values into equation 1
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I Need help with a Math Problem (zoom in if you can’t see it) (if you can’t see it the problem is ( x degrees 49 degrees and 39 degrees) find the value of x
Answer:
Step-by-step explanation:
If there are 180 degrees in a triangle total and in this problem we know that one angle is 49 and the other is 39, we can assume that subtracting 39 and 49 from 180 will find x. In this case, x will be 92.
Answer the questions below to determine what kind of function is depicted below
Answer:
This function is an exponential function because the base is a constant and the exponent is a variable.
The path the rover travels out of the crater is a distance of 180 m and covers a vertical distance of 65 meters, determine the angle of elevation of the room to the nearest thousands of degree
The angle of elevation of the room is approximately 19.1 degrees.
To determine the angle of elevation of the room, we need to use trigonometry. The angle of elevation is the angle between the horizontal plane and the line of sight from the rover to the room. We can use the tangent function to find this angle:
tan(angle of elevation) = opposite/adjacent
In this case, the opposite side is the vertical distance of 65 meters and the adjacent side is the horizontal distance of 180 meters. So we have:
tan(angle of elevation) = 65/180
To find the angle of elevation, we can take the inverse tangent (or arctan) of both sides:
angle of elevation = arctan(65/180)
Using a calculator, we get:
angle of elevation = 19.1 degrees (rounded to the nearest thousands of degree)
Therefore, the angle of elevation of the room is approximately 19.1 degrees.
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Help give me an Explanation
Answer:
if the two angles are equal
we use sss therom to solve it
2ft/6ft=24ft/xft
x=(6*24)/2
=72