help me please a.) Use the table below to calculate the average percent change in population in California from 2000-2009.
b.) If California's population in 2009 was 37,000,000 and the population trend were to continue, what would the population be in the year 2015?
Answers
the solution is: population in 2015 will be 40,115,896
What is exponential?The exponential function is an illustration of a mathematical function that may be used to identify if something is increasing or decreasing exponentially. An exponential function employs exponents, as suggested by its name.
But, you should be aware that an exponential function does not have a constant base and a variable exponent (if a function has a variable as the base and a constant as the exponent then it is a power function but not an exponential function).
the median population change in California from 2000 to 2009 in percentage terms.
Given that there are 9 years, add up all the percentages, and then divide by 9.
1.97+1.71+1.65+1.42+1.22+1.02+1.07+1.22+0.93/9 = 1.3567%
From 2009 through 2015, there were six different time periods.
In the future, 37,000,000 x (1 + 0.013567) x 6 = 40,115,896.06
Hence, the solution is: population in 2015 will be 40,115,896
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Related Questions
The graph of y= 3 + 2x - x^2 What are the coordinates of the root of the equation
Answers
Answer:
To find the coordinates of the root of the equation y = 3 + 2x - x^2, we need to find the values of x where y = 0 (because the root is the point where the function intersects the x-axis). So we can set y equal to 0 and solve for x:
0 = 3 + 2x - x^2
Rearranging, we get:
x^2 - 2x - 3 = 0
We can factor the quadratic equation by finding two numbers that add up to -2 and multiply to -3. These numbers are -3 and 1, so we can write:
(x - 3)(x + 1) = 0
This equation is true when either x - 3 = 0 or x + 1 = 0. So the roots of the equation are:
x = 3 or x = -1
Therefore, the coordinates of the roots of the equation y = 3 + 2x - x^2 are (3, 0) and (-1, 0).
zearn homework got 10 lessons to catch up on i will give some points if u help me with all my work
Answers
1/3x36in
how do you graph y=5x+2
Answers
The graph of the linear equation, y = 5x + 2, is shown below in the attachment.
How to Graph a Linear Equation?To graph the linear equation, y = 5x + 2, first plot the y-intercept at (0, 2) on the coordinate plane. Then, use the slope of 5 to move up 5 units and right 1 unit from the y-intercept to find another point on the line.
Continue this process to plot several more points, and then connect the points with a straight line to complete the graph of the equation. The resulting graph will be a straight line with a positive slope of 5 and y-intercept of 2.
See the attachment below for the graph.
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HELPPPPPP EASY 15 POINTSSSSSSSS HELP A GIRL OUT GUYS!!!!!
Answers
All of the functions have a constant rate of change since they are linear functions with a slope (rate of change) that is equal to the coefficient of the independent variable. Therefore, all functions have a constant rate of change of their slope.
Option A: y = 6(2) = 12 has a slope of 6, which means it increases by 6 for every unit increase in x.
Option B: y = 2(3) = 6 has a slope of 2, which means it increases by 2 for every unit increase in x.
Option C: y = 3(4) = 12 has a slope of 3, which means it increases by 3 for every unit increase in x.
Option D: y = 4(2) = 8 has a slope of 4, which means it increases by 4 for every unit increase in x.
Therefore, option A has the most rapid rate of change with a slope of 6.
Answer:
the ans the last person gave is very correct
If
two balanced dice are rolled, what is the probability that the sum
of the two numbers that appear will be even?
Answers
The probability of the sum of the two numbers being even can be calculated using the formula for the probability of independent events.
The formula for the probability of independent events is: P(A and B) = P(A) x P(B
In this case, A represents the first die and B represents the second die.
To calculate the probability of the sum being even, we need to consider the possible outcomes for each die that would result in an even sum.
For the first die, there are three possible outcomes that would result in an even sum: 1, 3, and 5. The probability of any of these outcomes occurring is 3/6, or 1/2.
For the second die, there are also three possible outcomes that would result in an even sum: 2, 4, and 6. The probability of any of these outcomes occurring is also 3/6, or 1/2.
Using the formula for the probability of independent events, we can calculate the probability of the sum being even:
P(A and B) = P(A) x P(B) = (1/2) x (1/2) = 1/4
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Find the coordinates of the reflection: B (1, 3) is reflected over the x-axis B’=?
Answers
B' is the reflection of the x-axis at position B(1,3) (1,-3) as a consequence of B (1, 3) being reflected over the x-axis.
what is coordinate ?A coordinate is a group of integers used to describe a point's location in space in mathematics. Cartesian coordinates are the most widely used form of coordinates. They are made up of an ordered pair of numbers (x, y) that represent a point's horizontal and vertical distances from a constant point of reference known as the origin. The y-coordinate indicates the point's vertical distance from the origin, while the x-coordinate represents the point's horizontal distance from it.
given
The x-coordinate remains constant while the sign of the y-coordinate varies when a point is reflected over the x-axis.
Therefore, we only need to alter the sign of the y-coordinate of B in order to determine the reflection B' of the point B(1,3) over the x-axis.
B' is the reflection of the x-axis at position B(1,3) (1,-3) as a consequence of B (1, 3) being reflected over the x-axis.
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ctions: Factor each expression. Be sure to check for a GCF first. Use x for the val 5. 9m^(2)-49
Answers
the factored form of the expression 9m^(2)-49 is (3m+7)(3m-7).
To factor the expression 9m^(2)-49, we need to use the difference of squares formula.
The difference of squares formula states that a^(2)-b^(2)=(a+b)(a-b).
In this case, we can see that 9m^(2) is a perfect square and 49 is also a perfect square. So, we can write the expression as (3m)^(2)-(7)^(2).
Using the difference of squares formula, we get:
(3m)^(2)-(7)^(2)=(3m+7)(3m-7)
So, the factored form of the expression 9m^(2)-49 is (3m+7)(3m-7).
Therefore, the answer is (3m+7)(3m-7).
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A company makes Poppy label pins. Each of them costs £1. 10 to make. In october it made 1000 label pins. 35% of them are given to charities. The rest are sold in two formats: 60% of them are sold at £3. 00 each
40% of them are sold at £5. 00 for 2
Assuming that all the label pins will be sold by the end of November, work out the percentage profit that the company will make. Give your answer to 1 decimal place
Answers
A company will make a profit of 63.9%
Here, the cost of making pins = £1.10
the number of pins = 1000
Using unitary method, the total cost for making 1000 pins would be,
= Cost of each pin × Number of pins
= 1.10 × 1000
= £1110
Now we find the number of pins that sold in charities.
35 percent of pins in charities.
Using percentage formula, we find 35% of total number of pins.
= 35% of 1000
= (35/100) × 1000
= 350 pins
This means that 350 pins were sold in charities.
So, the number of pins left = 1000 - 350
= 650 pins
Out of these remaining pins, 60% are sold at £3. 00 each
So, the number of pins sold at £3.00:
= 60% of 650
= (60/100) × 650
= 390
And the selling price of these 390 pins would be:
= 390 × £3.00
= £1170 .................(1)
40% of 650 pins were sold at £5. 00 for 2
So, using percentage formula the number of pins sold at £5.00 for 2 would be:
= 40% of 650
= (40/100) × 650
= 260
These 260 pins were sold in pairs for £5.
Therefore, number of pairs sold
= 260/2
= 130 pairs
The selling price of these 130 pairs of pins would be,
= 130 × 5.00
= £650 ...............(2)
Therefore, from (1) and (2) the total selling price would be,
= £1170 + £650
= £1820
So, the Profit would be:
= Selling price - Cost price
= 1820 - 1110
= £710
Now using we find the profit percentage:
= Profit × 100 / Total cost price
= 710 × 100 / 1110
= 63.9%
Therefore, the required percentage profit = 63.9%
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I. Linear functions - Complete the table by writing the Slope-Intercept form, identifying the slope, and finding the
y
-intercept for each equation given. Indicate if an answer does not exist.
Answers
Equation Slope-Intercept Form Slope y-Intercept
y = 2x + 5 y = 2x + 5 2 5
4x - 3y = 12 y = (4/3)x - 4 4/3 -4
x = 7 Does not exist Does not exist Does not exist
3y = 9 y = 3 0 3
For the first equation, y = 2x + 5, it is already in slope-intercept form. The slope is the coefficient of x, which is 2, and the y-intercept is the constant term, which is 5.
For the second equation, 4x - 3y = 12, we can rearrange it to get it in slope-intercept form by isolating y on one side of the equation. We can do this by subtracting 4x from both sides and then dividing by -3: 4x - 3y = 12 -3y = -4x + 12 y = (4/3)x - 4
The slope is the coefficient of x, which is 4/3, and the y-intercept is the constant term, which is -4. For the third equation, x = 7, there is no y term, so it cannot be written in slope-intercept form and the slope and y-intercept do not exist.
For the fourth equation, 3y = 9, we can rearrange it to get it in slope-intercept form by dividing both sides by 3: 3y = 9 y = 3 The slope is 0, since there is no x term, and the y-intercept is the constant term, which is 3.
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Fernando's family traveled
3
8
of the distance to his grandmother’s house on Saturday. They traveled
3
5
of the remaining distance on Sunday. What fraction of the total distance to his grandmother’s house was traveled on Sunday
Answers
The fraction of total distance that was travelled on Sunday is 3/8.
Let total distance to Fernando's grandmother's house be = D;
On Saturday, they traveled 3/8 of D,
So, the remaining distance is 5/8 of D.
On Sunday, they traveled 3/5 of the remaining distance, which is:
⇒ (3/5) × (5/8) × D = 3/8 × D,
So, on Sunday, they traveled 3/8 of D.
To find the fraction of the total distance traveled on Sunday, we divide the distance traveled on Sunday by the total distance, which is;
⇒ (3D/8)/D = 3/8
Therefore, Fernando's family traveled 3/8 of the total distance on Sunday.
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The given question is incomplete, the complete question is
Fernando's family traveled 3/8 of the distance to his grandmother’s house on Saturday. They traveled 3/5 of the remaining distance on Sunday.
What fraction of the total distance to his grandmother’s house was traveled on Sunday?
Given polynomial g(x)=x^(3)+(p-4)x^(2)+(p-9)x-4, show that the polynomial g(x)divisible by(x+1)for all values of p.
Answers
The given polynomial g(x) is g(x)=x^(3)+(p-4)x^(2)+(p-9)x-4.
To show that the polynomial g(x) is divisible by (x+1) for all values of p, we must prove that g(x) has a factor of (x+1). This can be done by expanding the given polynomial and rewriting it in a form that contains the factor (x+1).
First, we expand the given polynomial g(x):
g(x)=(x^3 + (p-4)x^2 + (p-9)x - 4)
= x^3 + px^2 - 4x^2 + px - 9x - 4
= x^3 + (p-4)x^2 + (px - 9x) - 4
= x^3 + (p-4)x^2 + (p - 9)x - 4
Now we can factor out the term (x+1) from the expression:
= (x^3 + (p-4)x^2 + (p-9)x - 4)
= (x+1)(x^2 + (p-5)x + (p-9)) - 4
Finally, we can rewrite the expression as:
g(x)=(x+1)(x^2 + (p-5)x + (p-9)) - 4
This shows that the polynomial g(x) is divisible by (x+1) for all values of p, as there is a factor of (x+1) in the expression.
Therefore, we have successfully proved that the polynomial g(x) is divisible by (x+1) for all values of p.
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What is the change in the water level per hour for Andreas swimming pool. LOOK AT IMAGE!
Answers
The rate of change is 961.37 gallons/hour. This means that the water level decreases by 961.37 gallons every hour.
What is meant by rate?In mathematics, comparing two related quantities stated in different units is known as a rate. A rate is the ratio of two distinct values that are gauged in various ways. It is not the same as a unit rate to compare a certain number of units of the first quantity to one unit of the second. In general, the rate can be expressed as the ratio of two quantities with distinct units. With the help of rate, we can create a connection between two otherwise unconnected components. By doing this, we can gain a deeper understanding of a scenario.
Given,
The total amount of water the pool can hold = 9613.7 gallons
The time taken to drain the pool completely = 10 hours
We are asked to find the change in water level per hour of the pool.
This can be called the rate of change.
Rate of change = Total amount of water/ Time taken to drain
= 9613.7 / 10 = 961.37 gallons / hour
Therefore the rate of change is 961.37 gallons/hour. This means that the water level decreases by 961.37 gallons every hour.
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Help me please
Can someone answer number 4 please?
Will give brainlest
Answers
The measures of angles 4 and 5 are:
∠5 = 104°
∠4 =76°
How to find the measures of the angles?On the image we can see that angles 1 and 2 are next to eachother, that means that the sum of their measures must be a plane angle, that is an angle of 180°.
Then we can write the sum:
∠1 + ∠2 = 180°
(3x + 5) + (2x + 10) = 180
5x + 15 = 180
5x = 180 - 15
x = 165/5 = 33
the measure of angle 5 is the same one of angle 1 then:
∠5 = (3*33 + 5)° = 104°
And angle 4 is supplementary of angle 1, then:
∠4 + 104° = 180°
∠4 = 180 - 104= 76°
These are the measures
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A lighthouse flashes a red light every 6 minutes and a green light every 9 minutes. At 7:00 pm the lighthouse flashes red and green lights at the same time. Name the next three times that the lighthouse will flash the red and green lights at the same time.
Answers
Answer:
To calculate the time at which they flash together we need to find the least common multiple of 3 and 8.
Multiples of 3 =
3 x 1 = 3
3 x 2 = 6
3 x 3 = 9
3 x 4 = 12
3 x 5 = 15
3 x 6 = 18
3 x 7 = 21
3 x 8 = 24
3 x 9 =27
3 x 10 = 30
Multiples of 8 =
8 x 1 = 8
8 x 2 = 16
8 x 3 = 24
8 x 4 = 32
8 x 5 = 40
8 x 6 = 48
8 x 7 = 56
8 x 8 = 64
8 x 9 =72
8 x 10 = 80
So LCM of 3 and 8 = 24
So both the lights will flash next at 7:24
Step-by-step explanation:
Fun Project in Word (1) 125% A. View Zoom Statistics Fun Project I Name: The following data are the result from two classes. Class A 34,31,29,24,27,37,26,24,20,37,22,18,36 26,28,23,23,27,33,25,36,32,33,25,28,35 Class B
Answers
These statistics can help us better understand the data and make comparisons between the two classes.
The given data shows the results of two classes, Class A and Class B.
Class A: 34, 31, 29, 24, 27, 37, 26, 24, 20, 37, 22, 18, 36, 26, 28, 23, 23, 27, 33, 25, 36, 32, 33, 25, 28, 35
Class B: (no data given)
In order to analyze the data, we can use statistics. Statistics is the science of collecting, analyzing, and interpreting data. One way to analyze the data is to find the mean, median, and mode of the data set.
Mean: The mean is the average of the data set. To find the mean, add up all the numbers and divide by the total number of data points.
Mean of Class A = (34+31+29+24+27+37+26+24+20+37+22+18+36+26+28+23+23+27+33+25+36+32+33+25+28+35) / 26 = 28.42
Median: The median is the middle number in the data set. To find the median, sort the data set in ascending or descending order and find the middle number. If there are an even number of data points, the median is the average of the two middle numbers.
Sorted Class A: 18, 20, 22, 23, 23, 24, 24, 25, 25, 26, 26, 27, 27, 28, 28, 29, 31, 32, 33, 33, 34, 35, 36, 36, 37, 37
Median of Class A = (26+27) / 2 = 26.5
Mode: The mode is the number that appears most frequently in the data set.
Mode of Class A = 24, 26, 27, 33, 36, 37 (all appear twice)
These statistics can help us better understand the data and make comparisons between the two classes.
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I NEED HELP ON THIS ASAP!
Answers
Step-by-step explanation:
so u could see that the yellow cab that will take Emma to airport is much more cheaper even though the entry price is a bit expensive .
the information provided to write the vertex form equation of each par: Vertex: (10,-8), Focus: ((41)/(4),-8)
Answers
This is the vertex form equation of the parabola with the given information.
From the information provided, we can write the vertex form equation of the parabola as follows:
First, we need to determine the value of "a" in the equation y = a(x - h)^2 + k, where (h,k) is the vertex and "a" determines the width and direction of the parabola.
The distance between the vertex and the focus is equal to 1/4a, so we can use this to find "a":
1/4a = (41/4 - 10)
1/4a = 1/4
a = 1
Now we can plug in the values for the vertex and "a" into the equation:
y = 1(x - 10)^2 - 8
This is the vertex form equation of the parabola with the given information.
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Correct olve the following system of equations. If there is a solution, write -3x-4y=20 -6x-8y=38
Answers
The solution to the given system of equations is x = 2.67 and y = 5.
The given system of equations can be solved by adding the two equations together.
3x + 4y = 20
-6x - 8y = -38
Adding the two equations together, we get:
-3x - 4y = -18
Subtracting 3x from both sides, we get:
-4y = -20
y = 5
Substituting the value of y in either of the given equations, we get:
3x + 4(5) = 20
3x = 8
x = 8/3
x = 2.67
After solving system of equations is x = 2.67 and y = 5.
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How can you prove the triangle sum theorem?
Answers
The sum of angle in a triangle is 180°
What is the sum of angle in a triangle?A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC.
The sum of angle A, B and C is 180 i.e A+B +C = 180°
Also a triangle is a 3 sided polygon. The sum of of angle in a polygon is( n-2)180
How do we prove that the sum of angle in a triangle is 180°?
Since triangle is 3 sided, n= 3, because n denote the number if sides
therefore the sum of angle = (n-2) 180 = (3-2)×180
= 180°
therefore the sum of angle In a triangle is 180°
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If X ~N (0,2) Find the
probability distribution function of Y =|X| . Hence, on otherwise
Find
1.E(|X| )
2. Var(|X|)
Answers
The probability distribution function of Y = |X| is given by:
P(Y ≤ y) = P(|X| ≤ y) = P(-y ≤ X ≤ y)
Since X ~ N(0, 2), we can use the standard normal distribution to find the probability;
P(Y ≤ y) = P(Z ≤ y/√2) - P(Z ≤ -y/√2)
where Z is a standard normal random variable.
To find E(|X|), we can use the formula:
E(|X|) = √(2/π) * σ
where σ is the standard deviation of X. Since X ~ N(0, 2), σ = √2, so:
E(|X|) = √(2/π) * √2 = √(4/π)
To find Var(|X|), we can use the formula:
Var(|X|) = E(X^2) - E(|X|)^2
Since X ~ N(0, 2), E(X^2) = σ^2 = 2. And we already found E(|X|) = √(4/π), so:
Var(|X|) = 2 - (4/π) = (2π - 4)/π
Therefore, the probability distribution function of Y = |X| is P(Y ≤ y) = P(Z ≤ y/√2) - P(Z ≤ -y/√2), the expected value of |X| is E(|X|) = √(4/π), and the variance of |X| is Var(|X|) = (2π - 4)/π.
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CAN I GET SOME HELP PLS
*problem in image*
(the drawn part was some help the teacher gave us bc the image is pretty dark)
Answers
Answer:
he walks 300 meters
Step-by-step explanation:
nbsjdjsj d f f f f f f f. f f f f f f f f f f
The total surface area of the rectangular prism is ________ square centimeters and the lateral surface area is _______ square centimeters.
Answers
Answer: surface area is _______ square centimeters.
To answer this question, I would need to know the dimensions of the rectangular prism, as both the total surface area and the lateral surface area depend on the dimensions of the prism.
Assuming the rectangular prism has length (l), width (w), and height (h), the formulas for the total surface area and the lateral surface area are:
Total surface area = 2lw + 2lh + 2wh
Lateral surface area = 2lh + 2wh
Therefore, to find the total surface area and lateral surface area of a specific rectangular prism, I would need to know its dimensions (length, width, and height) and plug them into these formulas.
Step-by-step explanation:
6. Type inequality here
+
4-2 0 2 468 10 12
Answers
x≤8 is the inequality of the number line.
What is Number system?A number system is defined as a system of writing to express numbers.
A number line is a picture of a graduated straight line that serves as visual representation of the real numbers.
In the given number line the shaded dot is at 8 at the arrow is to the left side of the number line which means the value of x is decreasing from point 8.
x≤8 is the inequality
Hence, x≤8 is the inequality of the number line.
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How long of a chain can Jill make by attaching a 13 3 4 -inch chain to a 15 2 4 -inch chain? Select all the possible sums. A. 13 3 4 + 15 2 4 = 28 5 4 B. 13 3 4 + 15 2 4 = 29 1 4 C. 13 3 4 + 15 2 4 = 29 D. 13 3 4 + 15 2 4 = 117 4 E. 13 3 4 + 15 2 4 = 28 5 8 I NEED THIS ASAP
Answers
The correct option representing possible sum for the long chain is B. 13 3 4 + 15 2 4 = 29 1 4.
Firstly let us convert the mixed fraction to fraction. So, the length of first chain = (13×4)+3/4
Length of first chain = 55/4 inches
Length of first chain = 13.75 inches
Length of second chain = (15×4)+2/4
Length of second chain = 62/4
Second chain length = 15.5 inches
So, total length = length of first chain + length of second chain
Total length = 13.75 + 15.5
Total length = 29.25 inches
Converting the decimal back to mixed fraction -
Total length = 29 1/4 inches
Thus, the correct answer B. 13 3 4 + 15 2 4 = 29 1 4.
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Polly is 21 years old. Aubrey is 4 years older than Polly and 39 years younger than Colton. How old is Colton?
Answers
Answer:
60
Step-by-step explanation:
Colton is 60 because Polly is 21 and plus 39 is 60.
A. {31, 26, 21, 16, 11,...}
1. d = ?
2. The next term in the sequence would be?
B. {-45, -38, -31, -24, . . .}
1. D = ?
2. The next term in the sequence would be?
Answers
The next term in the sequence would be -31.
What is Sequence ?
A sequence is a list of numbers or objects that follow a specific pattern or rule. Each number in the sequence is called a term, and the terms can be finite or infinite.
A. {31, 26, 21, 16, 11,...}
To find the common difference (d) between consecutive terms in the arithmetic sequence, we can subtract any term from the term that comes after it. For example, we can subtract 26 from 31 to get:
31 - 26 = 5
Similarly, we can subtract 21 from 26, 16 from 21, and so on:
26 - 21 = 5
21 - 16 = 5
16 - 11 = 5
Since the differences between consecutive terms are all the same, we can conclude that the common difference is d = 5.
To find the next term in the sequence, we can add the common difference (d = 5) to the last term (11):
11 + 5 = 16
Therefore, the next term in the sequence would be 16.
B. {-45, -38, -31, -24, . . .}
To find the common difference (d) between consecutive terms in the arithmetic sequence, we can subtract any term from the term that comes after it. For example, we can subtract -38 from -45 to get:
-45 - (-38) = -7
Similarly, we can subtract -31 from -38, -24 from -31, and so on:
-38 - (-31) = -7
-31 - (-24) = -7
Since the differences between consecutive terms are all the same, we can conclude that the common difference is d = -7.
To find the next term in the sequence, we can add the common difference (d = -7) to the last term (-24):
-24 - 7 = -31
Therefore, the next term in the sequence would be -31.
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hdlppppppppppp asapppp 50 points
Answers
Answer:
5
Step-by-step explanation:
18
What can you conclude about data from its equation, y = 3x - 7? Select all that apply.
A- y causes a.
B- The data are correlated.
C- The data are not correlated.
D- You cannot determine if there is causation between x and y.
Answers
The linear equation y = 3x - 7 has a data that is correlated because it has a linear relationship and we cannot determine if there's a causation between x and y
What does the linear equation represent?A. y causes a. is not applicable in this case, as there is no variable named "a" in the equation.
B. The equation y = 3x - 7 represents a linear relationship between two variables, x and y. As the equation has a slope of 3, it indicates that as the value of x increases by 1, the value of y increases by 3. Therefore, the data are correlated positively.
C. This is incorrect. As mentioned in B, the equation represents a linear relationship between two variables, x and y, which are positively correlated.
D. This is correct. Although the equation represents a linear relationship between x and y, it does not imply causation. It is possible that x causes y, y causes x, or some other variable or variables may be influencing both x and y. Therefore, we cannot determine if there is causation between x and y based on the equation y = 3x - 7 alone
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What would be the MOST immediate effect of competition in car manufacturing?
an increase in prices of U.S. cars
an increase in U.S. car production
additional auto workers hired in the U.S.
more choices for U.S. consumers
Answers
An increase in U.S. car production would be the most immediate effect of competition in car manufacturing.
As there will be an increase in the competition in car manufacturing the manufacturer will try to produce more and more cars of different types to attract customers. More market competition will provide consumers with more options to buy whatever products they desire, which will lead to a drop in the number of devoted customers for a given product line. Competitive markets have several advantages. Businesses that must constantly compete with one another for customers and market share are motivated to do so by offering products and services that are better than those of their rivals. In this market, businesses must constantly compete with one another by offering products and services that are more innovative, superior, and affordable.
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Quadrilateral ABCD is the result of a reflection of quadrilateral EFGH over the line.
Which line segment in the image corresponds to BC¯¯¯¯¯ in the pre-image?
Responses
HE¯¯¯¯¯¯
H E with bar on top
EF¯¯¯¯¯
E F with bar on top
GH¯¯¯¯¯¯
G H with bar on top
FG¯¯¯¯¯
F G with bar on top
Quadrilateral A B C D is reflected across a line, resulting in image E F G H.
Answers
Using prοperties οf quadrilaterals, The line segment in the image that cοrrespοnds tο BC¯¯¯¯¯ in the pre-image is the line segment FG¯¯¯¯¯.
What is the quadrilateral?A pοlygοn with fοur sides and fοur vertices is called a quadrilateral (cοrners). It is a twο-dimensiοnal οbject that is flat and can take οn a number οf fοrms.
We knοw that matching sides οf the pre-image and image are identical in length since a reflectiοn maintains the size and shape οf the figure.
Since a reflectiοn preserves the shape and size οf the figure, we knοw that cοrrespοnding sides οf the pre-image and image are equal in length.
Therefοre, the line segment in the image that cοrrespοnds tο BC¯¯¯¯¯ in the pre-image is the line segment FG¯¯¯¯¯.
Tο see why, imagine fοlding the figure alοng the line οf reflectiοn sο that the pre-image and image cοincide. In this fοlded pοsitiοn, the cοrrespοnding sides οf the twο quadrilaterals will be οn tοp οf each οther. In particular, side BC¯¯¯¯¯ οf the pre-image will be οn tοp οf side FG¯¯¯¯¯ οf the image, cοnfirming that FG¯¯¯¯¯ cοrrespοnds tο BC¯¯¯¯¯ in the pre-image.
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