The solution to the exponential equation 10^(-x - 1) = 36 is given as follows:
x = -2.5563.
How to solve the exponential equation?The exponential equation in the context of this problem is defined as follows:
10^(-x - 1) = 36
The log10 operation is the inverse of the power of 10 operation, hence we can isolate the variable x as follows:
-x - 1 = log10(36)
-x - 1 = 1.5563
x = -1.5563 - 1
x = -2.5563.
Which is the solution to the exponential equation in the context of the problem.
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An ice block in the form of rectangular prism with a square base is melting at a rate of 550cm^3/min. The base length is decreasing at a rate of 1cm/min. How fast is the surface area of the ice block changning when the base length is 10cm, and height is 20cm?
The speed at which the surface area of the ice block changes when the base length is 10cm, and the height is 20cm is 180 cm^2 /min
What is the surface area of a rectangular prism?The total area or region that is covered by a rectangular prism's six faces is known as its surface area.
Solids called prisms have identical polygon bases and flat parallelogram sides. Prisms come in a variety of shapes, including triangles, squares, rectangles, pentagons, hexagons, and more.
Thus, it can be seen that the speed at which the surface area of the ice block changes when the base length is 10cm, and the height is 20cm is 180 cm^2 /min
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The data table shows the numbers of eggs laid by
individual chickens in a year
What is the median number of eggs laid in a year?
A. 231
B. 229
C. 230
D. 234,6
The value of the median number of eggs laid in a year is,
⇒ 231
We have to given that;
The data table shows the numbers of eggs laid by individual chickens in a year.
Now, We can arrange it into ascending order as;
⇒ 222, 229, 229, 231, 234, 235, 262
Since, There are 7 terms
Hence, Median is,
= (7 + 1)/2
= 4th term
= 231
Thus, The value of the median number of eggs laid in a year is,
⇒ 231
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Answer:
A. 229 is correct
answer D.231 is wrong
Arianna says that the graphs of both of these functions will grow at the same cale s
she correct? Why or why not?
She is correct They grow at the same rate because
She is not correct. The graph of grows at a faster tale
than the graph of g because each value is mutplied by 4
There is not exgh intymaton to to which graph will
grow at a fasheerale
She is not correct The graph of g grows at a faster ale
than the graph of because & greater than 2
37
Answer:She is not correct The graph of g grows at a faster rate
than the graph of because 8 greater than 2
Step-by-step explanation:
Using PEMDAS, the exponents are done first.
8^3 = 512
4*2^3 = 32
This works for every number that X can be, 3 was just an example.
The probability that a football team will win a match is 0.3. The probability that the team will draw is 0.1. Work out the probability the team will
a) not win
b) not draw
c) lose
d) not lose
The probabilities of the the team are 0.7, 0.9, 0.6 and 0.4
Working out the probabilities of the the teamGiven that
The probability that a football team will win a match is 0.3. The probability that the team will draw is 0.1a) not win
This means that
P = 1 - P(win)
So, we have
P = 1 - 0.3
P = 0.7
b) not draw
This means that
P = 1 - P(draw)
So, we have
P = 1 - 0.1
P = 0.9
c) lose
This means that
P = 1 - P(win) - P(draw)
So, we have
P = 1 - 0.3 - 0.1
Evaluate
P = 0.6
d) not lose
This means that
P = 1 - P(lose)
So, we have
P = 1 - 0.6
P = 0.4
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Write an explicit formula that represents the sequence defined by the following recursive formula:
The explicit formula for the sequence defined by the recursive formula a₁ = 150 and aₙ = -1/5 aₙ₋₁ is aₙ = 150 [tex](-1/5)^{(n-1)[/tex].
To find the explicit formula that represents the sequence defined by the given recursive formula, we need to find a pattern in the sequence and express it using a formula.
The first term in the sequence is a₁ = 150. To find the second term, we use the recursive formula: a₂ = -1/5 a₁ = -1/5(150) = -30. To find the third term, we use the recursive formula again: a₃ = -1/5 a₂ = -1/5(-30) = 6.
We can continue this process to find the fourth term: a₄ = -1/5 a₃ = -1/5(6) = -6/5, and so on.
By observing the pattern, we notice that each term is obtained by multiplying the previous term by -1/5. Therefore, the explicit formula for the sequence can be written as:
aₙ = 150 [tex](-1/5)^{(n-1)[/tex]
This formula gives the value of any term in the sequence based on its position n. It can be used to find any term in the sequence without having to recursively calculate all the previous terms.
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Write an equation then find the value of y when x =16. Show all work.
Answer:
Answer is A
Step-by-step explanation:
A) y = -1/2x represents a proportional relationship because the equation can be written in the form y = kx, where k is a constant. In this case, k = -1/2, which means that y is proportional to x with a constant of proportionality of -1/2.
B) y = 2x - 4 does not represent a proportional relationship because the equation cannot be written in the form y = kx. If we try to write it in this form, we get y/x = 2 - 4/x, which means that y/x is not constant. Therefore, y is not proportional to x with a constant of proportionality.
Give the coordinates for all three possible
locations of the fourth vertex.
Y
9
8
7
6
5
4
3
2
1
0
X
1 2 3 4 5 6 7 8 9
Answer:
To find the coordinates for all three possible locations of the fourth vertex, we need to consider the three different ways that a parallelogram can be formed on a 9 by 9 grid.
Method 1: The fourth vertex is directly below the first vertex.
In this case, the coordinates of the fourth vertex are (5, 9), as shown below:
Y 9 8 7 6 5 4 3 2 1 0
X 1 2 3 4 5 6 7 8 9
. . . . . . . . .
. . . . . . . . .
. . . . . . . . .
. . . . . . . . .
. . . . . . . . .
. . . . . . . . .
. . . . . . . . .
. . . . . . . . .
. . . . . . . . X
Method 2: The fourth vertex is directly to the right of the first vertex.
In this case, the coordinates of the fourth vertex are (1, 5), as shown below:
Y 9 8 7 6 5 4 3 2 1 0
X 1 2 3 4 5 6 7 8 9
. . . . . . . . .
. . . . . . . . .
. . . . . . . . .
. . . . . . . . .
. . . . . . . . .
X . . . . . . . . .
. . . . . . . . .
. . . . . . . . .
. . . . . . . . .
Method 3: The fourth vertex is diagonal to the first vertex.
In this case, the coordinates of the fourth vertex are (5, 5), as shown below:
Y 9 8 7 6 5 4 3 2 1 0
X 1 2 3 4 5 6 7 8 9
. . . . . . . . .
. . . . . . . . .
. . . . . . . . .
. . . . . . . . .
. . . X . . . . .
. . . . . . . . .
. . . . . . . . .
. . . . . . . . .
. . . . . . . . .
Therefore, the coordinates for all three possible locations of the fourth vertex are (5, 9), (1, 5), and (5, 5).
What is the area of the lawn of Serena's front yard, in square yards?
12 ft-
Driveway
Serena's Front Yard
72 ft
Lawn
-15 ft
Flower
Bed
15 ft
48 ft
My Progress
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3
Our square yard calculator allows you to easily find the total area of a surface. Additionally, if you wish to cover that surface with some material or to do some construction work, such as painting or gardening, it gives you an estimation of your material cost and labor cost.
The square yard calculator also allows you to use different units (imperial and metric) and seamlessly convert between the two. Want to enter your measurements in feet and get your area in square yards or square meters? We've got you covered. You can easily switch between units and get answers to questions like "How to convert from feet to yards?" or "How many square feet in a square yard?"
A car owner pays an annual premium of $780 for automobile insurance, including liability coverage of up to $100,000. The car owner pays this for seven years without needing to file a
single claim. Then the car owner causes an accident for which the other driver is claiming $32,000 in damages. How much more expensive were the costs of the accident than what the
car owner paid in premiums?
O $37,460
O $100,000
O $5,460
O $26,540
If owner of car paid $780 as annual premium, then the cost of the accident is $26540 more expensive than what car owner paid in premiums, correct option is (d).
The car owner paid a total of $780 per year for 7 years, which means that the total amount paid in premiums is:
⇒ Total premiums paid = $780 × 7 years = $5460,
When the owner caused an accident, the amount of damage claimed by other driver is $32000.
This means that cost of accident was : $32000 - $5460 = $26540 more expensive than what the "owner" had invested in his insurance policy.
Therefore, Option(d) is correct.
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The given question is incomplete, the complete question is
A car owner pays an annual premium of $780 for automobile insurance, including liability coverage of up to $100,000. The car owner pays this for seven years without needing to file a
single claim. Then the car owner causes an accident for which the other driver is claiming $32,000 in damages. How much more expensive were the costs of the accident than what the car owner paid in premiums?
(a) $37,460
(b) $100,000
(c) $5,460
(d) $26,540
Maggie bought 50 lbs of clay for her art projects. She used 15.6 lbs to make a sculpture, and 0.84 lbs for each mug. How many mugs did Maggie make if she had 19.28 lbs of clay left over? Solve on paper. Then check your work on Zearn.
The number of mugs that Maggie made with the left over clay that she had would be = 23 mugs
How to calculate the quantity of mug made by Maggie?The total quantity of clay that Maggie bought = 50lbs
The quantity she used for sculpture = 15.6lbs
The quantity of clay she used for mug = 0.84 lbs
The quantity of clay left = 19.28 lbs
If 0.84 = 1 mug
19.28 = X
make X the subject of formula:
X = 19.28/0.84
= 23 mugs
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2. An equation for a line is = 6/5 . What will the new equation of this line be after it is rotated 90° counterclockwise around the origin
If new equation of this line be after it is rotated 90° counterclockwise around the origin, the equation of the new line after rotation is y = (-5/6)x
To find the new equation of a line after it is rotated 90° counterclockwise around the origin, we need to use the following formula:
(x', y') = (-y, x)
where (x, y) are the coordinates of a point on the original line, and (x', y') are the coordinates of the corresponding point on the new line after rotation.
We can start by finding the slope of the original line, which is given by:
y = (6x/5)
Rearranging this equation, we get:
x = (5/6)y
This tells us that the slope of the original line is 5/6.
To find the equation of the new line after rotation, we need to apply the formula above to two points on the original line. Let's choose two easy points to work with, such as (0,0) and (5,6).
Using the formula, we can find the new coordinates of these points after rotation:
(0', 0') = (-0, 0) = (0,0)
(5', 6') = (-6, 5)
Now we can find the slope of the new line using these two points:
slope = (6' - 0') / (5' - 0') = 5/-6 = -5/6
In summary, to find the new equation of a line after rotating 90° counterclockwise around the origin, we can use the formula (x', y') = (-y, x) to find the new coordinates of two points on the original line, and then use these points to find the slope of the new line. In this case, the new equation of the line is y = (-5/6)x.
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if anyone could help me please? :)
The characteristics that shows that the graph is a proportional relationship is: D. The line connecting the points passes through the origin.
What is a graph of a proportional relationship?A graph of a proportional relationship is a straight line that passes through the origin (0, 0) on a coordinate plane, where the points on the line represent pairs of values that are in direct proportion to each other.
From the graph shown above, if we connect the points together, the line will pass through the origin, therefore, the correct answer is: D. The line connecting the points passes through the origin.
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The characteristics that tell you that the graph shows a proportional relationship are: A straight line can be drawn through the points and The line connecting the points passes through the origin. Option B and D are the correct answer.
A proportional relationship is a relationship between two variables where the ratio of their values is constant. This means that if we multiply one of the values by a constant, the other value also gets multiplied by the same constant.
The graph of a proportional relationship is a straight line that passes through the origin. This is because the ratio of the x- and y-values is constant, so the points can be plotted as a straight line.
The ordered pairs all have the same x- and y-values means that the two variables are perfectly correlated. This is not necessary for a proportional relationship, but it is a common characteristic.
The line connecting the points does not need to pass through the origin for the relationship to be proportional. However, if the line does pass through the origin, then the two variables are directly proportional. Option B and D are the correct answer.
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19. Two angles are complementary. The larger
angle is 36 more than the smaller angle. What
is the measure of the larger angle?
Answer:
larger angle = 63°
Step-by-step explanation:
complementary angles sum to 90°
let x be the smaller angle then larger angle is x + 36 , then
x + x + 36 = 90
2x + 36 = 90 ( subtract 36 from both sides )
2x = 54 ( divide both sides by 2 )
x = 27
Then
larger angle = x + 36 = 27 + 36 = 63°
A construction company is planning to bid on a building contract. The bid costs the company $1100. The probability that the bid is accepted is 1/10
. If the bid is accepted, the company will make $96,000 minus the cost of the bid.
What is the expected value in this situation?
Choose the statement below that best describes what this value means.
A.
In the long run, the construction company would expect to earn this amount on average per bid.
B.
In the long run, the construction company would expect to break even on average.
C.
In the long run, the construction company would expect to lose this amount on average per bid.
D.
None of the above
Answer:
The expected value in this situation can be calculated as follows:
E(X) = P(X) * V(X), where X is the random variable representing the profit of the construction company, P(X) is the probability of X, and V(X) is the value of X.
In this case, the profit of the construction company if the bid is accepted is $96,000 - $1,100 = $94,900, and the probability of the bid being accepted is 1/10. Therefore, we have:
E(X) = (1/10) * $94,900 = $9,490
The expected value of $9,490 means that in the long run, the construction company would expect to earn this amount on average per bid. Therefore, the correct answer is option A: "In the long run, the construction company would expect to earn this amount on average per bid."
I need some assistance with this ? Please
The real solution is 0, and the imaginary solution is 0.5 ± 0.866i.
What are the solutions of x?
The solutions of the equation is calculated as follows;
4x(x² - x + 1) = 0
This equation is satisfied when either 4x = 0 or x² - x + 1 = 0.
If 4x = 0, then x = 0 is a solution,
To find the solutions of x² - x + 1 = 0, we will use formula method;
x = [ -(-1) ± √((-1)² - 4(1)(1)) ] / (2(1))
x = [ 1 ± i√3 ] / 2
x = 0.5 ± 0.866i
Thus, the solutions of the cubic equation involves both real and imaginary solution.
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If the gross amount is USD 365, what is the net amount after adding 20%?
USD 438
Step-by-step explanation:If we add 20% to the gross amount of USD 365, the total amount would be:USD 365 + 20% of USD 365 = USD 365 + (0.20 * USD 365) = USD 365 + USD 73 = USD 438
If the gross amount is USD 365, then the net amount after adding 20 percent is USD 438.
Net amount refers to the final total after deductions or additions have been made whereas gross amount refers to the total amount before any deductions or additions have been made.
Us the formula:
Net Amount = Gross Amount + (Gross Amount x Percentage)
Given that,
Gross amount = $365
The given percentage = 20%
We can write 20% = 20/100
So, 20% = 0.2
Now put the values into the formula
Net amount = 365 + (365 x 0.2)
Net amount = 365 + 73
Net amount = 438
Hence,
The net amount is USD 438.
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I need help please geometry not my strong suit
The image point of (-7, -8) after the sequence of transformations is given as follows:
(-4.5, -4).
How to obtain the coordinates of the image point?The original coordinates are given as follows:
(-7, -8)
The first transformation is a dilation with a scale factor of 1/2, meaning that each coordinate is multiplied by 1/2, hence:
(-3.5, -4).
The second transformation is a translation of one unit left, meaning that one is subtracted from the y-coordinate, thus the image point after the sequence of transformations is given as follows:
(-4.5, -4).
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Solve the formula for the specified variable. V =CLS for C
Answer:
To solve for C in the formula V = CLS, we need to isolate C on one side of the equation.
Starting with the given formula:
V = CLS
Divide both sides of the equation by LS:
V/LS = C
Therefore, the formula for C is:
C = V/LS
Geometric constructions summative- need help on it.... its my end of year project
The steps for the construction are given below:
It should be noted that to begin, take a ruler and draw a straight line.Next, employ the use of a compass to draw a circle with its center at one end of said line.Maintain your compass width and place it on the opposite end of the line, drawing another circle that collides with the initial circular figure.How to explain the constructionA new line can be created connecting the points where these two circles intersect using just a simple ruler.
Now that you have succeeded in this task, feel free to experiment and manipulate the astonishing construction you've completed using the same innovative tools.
While this is only an elementary blueprint, there are numerous advanced constructions that can be produced by taking advantage of both GeoGebra and traditional paper/pencil/ruler/compass techniques.
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Is y=2x+X+1 a linear function
No, y=2x+X+1 is not a linear function because it contains a term with an exponent of 1 and a term with an exponent of 0. Linear functions are functions of the form y = mx + b, where m and b are constants, and x is the independent variable. The graph of a linear function is a straight line.
In the given function, the term X is not multiplied by a constant, so it does not have a fixed rate of change. Therefore, the graph of this function is not a straight line. Instead, it is a quadratic function, which has a parabolic graph.
g(x)
12 fy
10
88
8
6
4
4-3-2-12
-8
10
-1²1
f(x)
4 5 6 x
Which statement is true regarding the functions on the
graph?
Of(6) = g(3)
f(3) = g(3)
f(3) = g(6)
f(6) = g(6)
PLEASE HURRY IM TIMED!!!!
Answer: f(3) = g(6)
Step-by-step explanation: if you plug them in we see that f of 3 on the y axis intercept g of x so we then go up and see that g of 6 intercepts f of 3 so therefore that is the answer
Solve for the value of w.
Answer:6
Step-by-step explanation:
7w-6 + 8w+6 = 90
15w=90
w=90/15
w=6
Point A is located at (1, 2). Point B is located at (4, 6). Use this information to determine the length of the line, rounded to the nearest whole number.
If Point A is located at (1, 2) and Point B is located at (4, 6), the length of the line between points A and B is 5 units.
To determine the length of the line between points A and B, we can use the distance formula, which is a formula used to calculate the distance between two points in a coordinate plane. The distance formula is:
d = √((x₂ - x₁)² + (y₂ - y₁)²)
where (x₁, y₁) and (x₂, y₂) are the coordinates of the two points and d is the distance between them.
Using the coordinates of points A and B, we can substitute their values into the distance formula to find the length of the line between them:
d = √((4 - 1)² + (6 - 2)²)
d = √(3² + 4²)
d = √(9 + 16)
d = √25
d = 5
Rounded to the nearest whole number, the length of the line is also 5 units.
In conclusion, we can use the distance formula to find the length of the line between two points in a coordinate plane. The distance formula uses the coordinates of the two points to calculate the distance between them. The resulting distance can be rounded to the nearest whole number, if needed.
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it took people a very long time to Real like that zero is an important number. why do you think that people found difficult to accept zero as a number
Answer:
I think that people found difficult to accept zero as a number because people think that zero doesn't have any value. In a way yes Zero doesn't have value but zero is also a very important number because sometimes we need to solve some questions and we need to add value but if we need to add that particular value we should even subtract that value which makes it zero. So I think the reason is people don't think zero has any value. But in my point if view zero has many values.
Jacque is using an unopened soup can for a school project and wants to paint it. If the can is 10 cm tall and has a diameter of 9 cm, at least how many square centimeters of paint is needed? Approximate using π = 3.14.
1,073.88 cm2
635.85 cm2
621.72 cm2
409.77 cm2
The amount of paint needed for the soup can is 409.77 cm².
How to find the surface area?Jacque is using an unopened soup can for a school project and wants to paint it.
The can is 10 cm tall and has a diameter of 9 cm. Therefore, the square centimetres of paint required to paint the soup is as follows:
Therefore,
surface area of a cylinder = 2πr(r + h)
where
r = radiush = heightTherefore,
r = 9 / 2 = 4.5 cm
h = 10 cm
surface area of a cylinder = 2 × 3.14 × 4.5(4.5 + 10)
surface area of a cylinder = 28.26(14.5)
surface area of a cylinder = 409.77 cm²
Therefore,
amount of paint needed = 409.77 cm²
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Carleigh, Inc., is a pork processor. Its plants, located in the Midwest, produce several products from a common process: sirloin roasts, chops, spare ribs, and the residual. The roasts, chops, and spare ribs are packaged, branded, and sold to supermarkets. The residual consists of organ meats and leftover pieces that are sold to sausage and hot dog processors. The joint costs for a typical week are as follows: Direct materials $84,500 Direct labor 29,000 Overhead 20,000 The revenues from each product are as follows: sirloin roasts, $68,000; chops, $71,000; spare ribs, $33,000; and residual, $9,800. Carleigh’s management has learned that certain organ meats are a prized delicacy in Asia. They are considering separating those from the residual and selling them abroad for $52,000. This would bring the value of the residual down to $2,650. In addition, the organ meats would need to be packaged and then air freighted to Asia. Further processing cost per week is estimated to be $27,500 (the cost of renting additional packaging equipment, purchasing materials, and hiring additional direct labor). Transportation cost would be $12,100 per week. Finally, resource spending would need to be expanded for other activities as well (purchasing, receiving, and internal shipping). The increase in resource spending for these activities is estimated to be $3,120 per week.
Carleigh, Inc. should separate the organ meats from the residual and sell them abroad, as it would increase their total revenue by $17,150 per week.
To determine whether Carleigh, Inc. should separate the organ meats and sell them abroad, we need to calculate the incremental revenue and incremental costs associated with this decision.
The incremental revenue would be the revenue generated from selling the organ meats abroad, which is $52,000 per week. The incremental cost would include the cost of further processing ($27,500 per week), transportation cost ($12,100 per week), and the increase in resource spending for other activities ($3,120 per week).
Therefore, the incremental cost would be $42,720 per week. Subtracting this from the incremental revenue of $52,000, we get an incremental profit of $9,280 per week.
However, this decision would also decrease the value of the residual from $9,800 to $2,650 per week. Therefore, we need to subtract this decrease in value from the incremental profit. This gives us a net increase in profit of $17,150 per week ($9,280 - $7,130).
Thus, it would be beneficial for Carleigh, Inc. to separate the organ meats and sell them abroad.
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Jasper is using the following data samples to make a claim about the house values in his neighborhood:
House Value
A $150,000
B $175,000
C $200,000
D $167,000
E $2,500,000
Based on the data, should Jasper use the mean or the median to make an inference about the house values in his neighborhood? (10 points)
Group of answer choices
He should use the mean because it is in the center of the data.
He should use the median because it is in the center of the data.
He should use the median because there is an outlier that affects the mean.
He should use the mean because there are no outliers that affect the mean.
Answer:
Jasper should use the median to make an inference about the house values in his neighborhood because there is an outlier that affects the mean. The outlier in this case is the house with a value of $2,500,000, which is significantly higher than the other house values in the sample. The mean is sensitive to outliers, which means that the outlier can significantly affect the value of the mean. In contrast, the median is not affected by outliers, which makes it a better measure of central tendency for this data set. Therefore, Jasper should use the median because it is in the center of the data and is not affected by the outlier. Answer: He should use the median because there is an outlier that affects the mean.
Answer:
The answer to your problem is, C. He should use the median because there is an outlier that affects the mean. &; A & E $150,000 ‘n’ $200,000
Step-by-step explanation:
The outlier is represented as ‘ E ‘ the highest price value and lowest between, $150,000 to $200,000.
But since ‘ E ‘ is represented highest it is an outlier making ‘ E ;
$150,000 ‘n’ $200,000
So ‘ E ‘ is represented as, $150,000 ‘n’ $200,000
The second option for ‘ 10 points ‘ is He should use the median because there is an outlier that affects the mean, being the ‘ Option C ‘
Thus the answer to your problem is, C. He should use the median because there is an outlier that affects the mean. &; A & E $150,000 ‘n’ $200,000
Pls help and show how you got the answer :) I really appreciate it
In 2006, the population will reach 109 million.
The correct answer is an option (d)
Here function [tex]f(x)=100(1.0153)^x[/tex] represents the population (in millions) x years after 2000
We need to find the year x when the population will reach 109 million.
i.e., for f(x) = 109, we need to find the value of x.
Consider function f(x),
[tex]f(x)=100(1.0153)^x[/tex]
Substitute f(x) = 109
⇒ [tex]109=100(1.0153)^x[/tex]
⇒ [tex](1.0153)^x=1.09[/tex]
Taking logarithm on both the sides.
⇒ x ln(1.0153) = ln(1.09)
⇒ x = ln(1.09) / ln(1.0153)
⇒ x = 5.675
⇒ x ≈ 6
So, the required year would be,
2000 + 6 = 2006
Therefore, the correct answer is an option (d)
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Prove: 36 + 324 + 900+. . . +(12n − 6)2 = 12n(4n2 − 1)
By mathematical induction, the given formula holds for all natural numbers n:
S(n) = 36 + 324 + 900 + ... + (12n - 6)² = 12n(4n² - 1)
How to solveTo demonstrate our point, mathematical induction can be employed.
We want to prove that the given formula holds for all natural numbers n:
S(n) = 36 + 324 + 900 + ... + (12n - 6)² = 12n(4n² - 1)
Using mathematical induction:
Step 1: Base case (n=1)
S(1) = 6² = 36
12 * 1 * (4 * 1² - 1) = 36
Since S(1) holds true, the base case is proven.
Step 2: Inductive step (Assume it's true for n=k, and show it's true for n=k+1)
Assumption: S(k) = 36 + 324 + 900 + ... + (12k - 6)² = 12k(4k² - 1)
We follow the exhaustive process to prove:
= 12(4k³ + 12k² + 11k + 3)
Since both expressions for S(k+1) are equal, the inductive step is proven.
Thus, by mathematical induction, the given formula holds for all natural numbers n:
S(n) = 36 + 324 + 900 + ... + (12n - 6)² = 12n(4n² - 1)
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Is y=(1/2)X a linear function
Answer:
linear
Step-by-step explanation:
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