a) There are 128 subsets of A with 8 elements. This is because the number of subsets of a set with n elements is 2 ^ n. Therefore, the number of subsets of A with 8 elements is 2 ^ 8 = 128.
b) There are 82 subsets of A with 8 elements that have only numbers. This is because there are 10 numbers in A and each of these numbers can be included or excluded from the subset of 8 elements. Therefore, the number of subsets of A with 8 elements that have only numbers is 2 ^ 10 = 1024.
c) There are 46 subsets of A with 8 elements that have only letters. This is because there are 6 letters in A and each of these letters can be included or excluded from the subset of 8 elements. Therefore, the number of subsets of A with 8 elements that have only letters is 2 ^ 6 = 64.
d) There are 28 subsets of A with 8 elements that have 2 letters. This is because there are 6 letters in A and each of these letters can be included or excluded from the subset of 8 elements twice. Therefore, the number of subsets of A with 8 elements that have 2 letters is 2 ^ 12 = 4096.
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Find the gradients of lines A and B.
B
-2
6
O
-21
Fet
A
4
72%
X
The gradient of line A is 4 and the gradient of line B is -2.
What is graph?Graph is a data structure that consists of nodes (or vertices) connected by edges. It is a way of representing data in a structured form and can be used to represent any type of real-world relationship. It can be used to represent geographical relationships between cities, social networks, and even computer networks. Graphs are often used in computer science, mathematics, and engineering to represent relationships between data points.
To calculate the gradient of a line, the formula is rise/run. Thus, the gradient of line A can be calculated as rise/run = 72/4 = 18. On the other hand, the gradient of line B can be calculated as rise/run = 6/-2 = -3
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(1 point) If the 100th term of an arithmetic sequence is 783, and its common difference is 8, then its first term a = 9 its second term Q2 = its third term az = (1 point) Express the following sum i
The first term is 9, the second term is 17, and the third term is 25.
The 100th term of an arithmetic sequence is given by the formula:
Tn = a + (n-1)d
Where Tn is the nth term, a is the first term, n is the number of terms, and d is the common difference.
In this case, the 100th term is 783, the common difference is 8, and the first term is 9.
Plugging in the values into the formula, we get:
783 = 9 + (100-1)8
Solving for the first term, we get:
783 = 9 + 792
783 = 801
a = 9
The second term, Q2, can be found by adding the common difference to the first term:
Q2 = a + d
Q2 = 9 + 8
Q2 = 17
The third term, az, can be found by adding the common difference to the second term:
az = Q2 + d
az = 17 + 8
az = 25
the first term is 9, the second term is 17, and the third term is 25.
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Pls help :(
where are the vertical asymptotes for y = 7tan(0. 4x)?
Answer:
x = 3.92699081 + 7.85398163n where n is an integer
Ok so we are supposed name each pair of angels this is due tomorrow so please help me :D
Answer:See below
Step-by-step explanation:
answers from top left to top right, then bottom left to bottom right.
First one is alternate interior, because they are on the inside, and are on opposite sides.
the second one is supplementary, because they supplement each other, or add up to 180 degrees.
the third one is alternate exterior, because they are opposite to each other on the outside.
the last one is corresponding, because they are in the same position on each side, and are almost like a copy and paste.
I found a few images on the internet to help you understand.
Hope this helped!
I need help on this asap!!
If Bici expects to produce more than 500 bikes, then they should follow the second plan, and if they expect to produce fewer than 500 bikes, then they should follow the first plan.
How to analyze the plans ?Under the first plan, the total cost to design and build a prototype bicycle is $125,000, and the combined materials and labor costs for each bike made under this plan will be $225. This means that for each bike produced, the total cost will be $125,000 + $225 = $125,225.
Under the second plan, the total cost to design and build a prototype bicycle is $100,000, and the combined materials and labor costs for each bike made under this plan will be $275. This means that for each bike produced, the total cost will be $100,000 + $275 = $100,275.
To determine which plan is more cost-effective, we need to consider the breakeven point where the costs of both plans intersect:
125, 000 + 225x = 100, 000 + 275x
50x = 25, 000
x = 500 bicylces
If Bici Bicycle Company plans to produce more than 500 bikes, then the second plan would be more cost-effective. However, if Bici plans to produce fewer than 500 bikes, then the first plan would be more cost-effective.
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3. Find the slope of each of the lines.
4. Find the slope of the line that passes through the points: a. (−2, 3) and (0, 0) b. (2, 5) and (−2, 2)
5. Find the equation of the line parallel to the x-axis passing through the point (2, 3).
The line passes through the point (2, 3), the equation of the line is y = 3.
3. To find the slope of a line, you can use the formula slope = (y2 - y1)/(x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.
4. a. The slope of the line that passes through the points (−2, 3) and (0, 0) is (0 - 3)/(0 - (-2)) = -3/2 = -1.5.
b. The slope of the line that passes through the points (2, 5) and (−2, 2) is (2 - 5)/(-2 - 2) = -3/-4 = 0.75.
5. The equation of a line parallel to the x-axis is y = b, where b is the y-coordinate of any point on the line. Since the line passes through the point (2, 3), the equation of the line is y = 3.
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Cooper decides to estimate the volume of a grapefruit by modeling it as a sphere. He measures its radius as 6.7 cm. Find the grapefruit's volume in cubic centimeters. Round your answer to the nearest tenth if necessary.
Step-by-step explanation:
Refer to pic............
One kilogram is how many times one nanogram?
Answer:
1 trillion times larger
Step-by-step explanation:
One kilogram (kg) is equal to 1,000,000,000,000 (1 trillion) nanograms (ng).
Therefore, one kilogram is 1 trillion times larger than one nanogram.
Gina buys 7 tacos for $4.20 how much does each taco cost
Answer: $29.4
Step-by-step explanation: one taco cost 4.20 so multiply the price of the tacos times the amount of tacos gina buys and you should get your answer which is 29.4
In order to solve the inequality 100 - 3x>= -50, Makayla solves the equation 100 - 3x = -50 and gets x = 50. What is the solution to the inequality?
The solution to the inequality is x <= 50. This means that any value of x less than or equal to 50 will satisfy the inequality.
To solve the inequality 100 - 3x >= -50, we want to find the values of x that satisfy this inequality.
Makayla solved the equation 100 - 3x = -50 and got x = 50. This equation is not the same as the inequality we want to solve, but we can check whether Makayla's solution is a valid solution to the inequality.
Substituting x = 50 into the inequality, we get:
100 - 3x >= -50
100 - 3(50) >= -50
100 - 150 >= -50
-50 >= -50
This is a true statement, so x = 50 is a valid solution to the inequality.
However, we also need to check whether there are any other values of x that satisfy the inequality. We can do this by rearranging the inequality to isolate x:
100 - 3x >= -50
100 + 50 >= 3x
150 >= 3x
50 >= x
Therefore, the solution to the inequality is calculated to x <= 50.
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In ΔWXY, WY is extended through point Y to point Z, m∠YWX=(3x+17) , m
Angle, when two straight lines or rays intersect at a single endpoint, then an angle is created.
What is Exterior angle?The exterior angle of a triangle equals the sum of opposite interior angles. The angle between any side of a shape and a line that extends from the next side is known as the exterior angle.
∠XYZ = ∠YWX + ∠WXY
10x - 5 = 3x + 17 + 3x + 2
10x - 5 = 6x + 19
10x - 6x = 24
4x = 24
x = 6
∠WXY = 3x + 2
= 3*6 + 2
= 20°
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Who many times larger is f(x)=-2.5x^2+2.5x+5 than g(x)=-x^2+6x+2
f(x) is 5/2 times larger than g(x) for large positive or negative values of x, except at the two values x = 3 ± √7 where the expression is undefined.
What is a function?A relation is a function if it has only One y-value for each x-value.
To find out how many times larger f(x) is than g(x), we need to divide the value of f(x) by the value of g(x).
Then we simplified the expression and found that it is always larger than g(x) except at two values of x where it is undefined.
To determine how much larger f(x) is than g(x), we looked at their leading coefficients and found that f(x) is always larger than g(x) for large positive or negative values of x.
Finally, we took the limit of f(x) / g(x) as x approaches infinity or negative infinity and found that it approaches -5/2.
Hence, f(x) is 5/2 times larger than g(x) for large positive or negative values of x, except at the two values x = 3 ± √7 where the expression is undefined.
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Ruth sell oranges. Her average sale for three days was 45 bags. How many bags of oranges does she need to sell on day four to have an average of 50?
The number of bags of oranges that Ruth needs to sell on day 4 to have an average of 50 bags is 65.
Let the number of bags to be sold on day four be = x,
To have an average of 50 bags over 4 days,
The total number of bags Ruth sells in four days must be,
⇒ 4 days × 50 bags/day = 200 bags,
The total number of bags of oranges she sells in 3 days is,
⇒ 3 days × 45 bags/day = 135 bags,
So, to reach a total of 200 bags in 4 days, she needs to sell x bags on the fourth day, which is in equation form as :
⇒ x + 135 = 200
⇒ x = 200 - 135
⇒ 65
Therefore, Ruth needs to sell 65 bags on day four.
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A biologist is trying to find the optimal salt concentration for the growth of a certain species of mollusk. She begins with a brine solution that has 10 g/L of salt and increases the concentration by 14% every day. Let C0 denote the initial concentration and Cn the concentration after n days.
Find a recursive formula for Cn. Write your answer in terms of Cn-1. You will need to use an underscore to make the subscript and parentheses to write the n-1 in the subscript.
Find the salt concentration after 11 days.
After 11 days, the concentration is __________ g/L.
After 11 days, the concentration is 42.4 g/L.
The recursive formula for Cn can be written as Cn = Cn-1 + 0.14Cn-1. This formula shows that the concentration after n days is equal to the concentration after n-1 days plus 14% of the concentration after n-1 days.
To find the salt concentration after 11 days, we can use the recursive formula and plug in the values for C0 and n.
C0 = 10 g/L
C1 = C0 + 0.14C0 = 10 + 0.14(10) = 11.4 g/L
C2 = C1 + 0.14C1 = 11.4 + 0.14(11.4) = 13 g/L
C3 = C2 + 0.14C2 = 13 + 0.14(13) = 14.8 g/L
C4 = C3 + 0.14C3 = 14.8 + 0.14(14.8) = 16.9 g/L
C5 = C4 + 0.14C4 = 16.9 + 0.14(16.9) = 19.3 g/L
C6 = C5 + 0.14C5 = 19.3 + 0.14(19.3) = 22 g/L
C7 = C6 + 0.14C6 = 22 + 0.14(22) = 25.1 g/L
C8 = C7 + 0.14C7 = 25.1 + 0.14(25.1) = 28.6 g/L
C9 = C8 + 0.14C8 = 28.6 + 0.14(28.6) = 32.6 g/L
C10 = C9 + 0.14C9 = 32.6 + 0.14(32.6) = 37.2 g/L
C11 = C10 + 0.14C10 = 37.2 + 0.14(37.2) = 42.4 g/L
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Three friends, Jessa, Tyree, and Ben, are collecting canned food for a culinary skills class. Their canned
food collection goal is represented by the expression 7x? - 4xy + 6. The friends have already collected
the following number of cans:
Jessa: 2x2
Tyree: 3x2 - 4
Ben: 3xy + 6
Part A: Write an expression to represent the amount of canned food collected so far by the three
friends. Show all your work. (5 points)
Part B: Write an expression that represents the number of cans the friends still need to collect to meet
their goal. Show all your work. (5 points)
Answer: Your welcome!
Step-by-step explanation:
Part A: 2x^2 + 3x^2 - 4 + 3xy + 6 + 6 = 7x^2 - 4xy + 6
Part B: 0 = 7x^2 - 4xy + 6 - (2x^2 + 3x^2 - 4 + 3xy + 6 + 6)
= 0 = 5x^2 - 4xy
A) The expression that represents the amount of canned food collected by the three friends is [tex]5x^2 + 3xy + 2[/tex].
B) The expression that represents the number of cans the friends still need to collect to meet their goal is [tex]2x^2 - 7xy + 4[/tex].
Given: Number of cans collected
Jessa: 2x²
Tyree: 3x² - 4
Ben: 3xy + 6
Goal : [tex](7x^2 - 4xy + 6)[/tex]
A) The total amount collected:
Total = Jessa + Tyree + Ben
= [tex]2x^2 + (3x^2 - 4) + (3xy + 6)[/tex]
= [tex]2x^2 + 3x^2 - 4 + 3xy + 6[/tex]
= [tex](2x^2 + 3x^2 + 3xy) + (-4 + 6)[/tex]
= [tex]5x^2 + 3xy + 2[/tex]
Therefore, the expression is [tex]5x^2 + 3xy + 2[/tex].
B) The number of cans the friends still need to collect to meet their goal is
Cans still needed = Goal - Total
[tex]= (7x^2 - 4xy + 6) - (5x^2 + 3xy + 2)[/tex]
[tex]= 7x^2 - 4xy + 6 - 5x^2 - 3xy - 2[/tex]
[tex]= (7x^2 - 5x^2) + (-4xy - 3xy) + (6 - 2)[/tex]
[tex]= 2x^2 - 7xy + 4[/tex]
Therefore, the expression is [tex]2x^2 - 7xy + 4[/tex].
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100 points hurry and mark brainly
Jennifer bought three of the same shirt and paid $63 after the 30% discount. What was the original price of each shirt? Show your work or explain in words how did you get the answer.
Step-by-step explanation:
The price is $30.
please make me brainalist and keep smiling dude
Tommy and Kim share some grapes in the ratio 5:6
Tommy eats half of his grapes.
Kim eats 4 more than Tommy.
They now have the same number of grapes.
How many grapes did they share to begin with?
Answer: They shared 40 grapes for Tommy and 48 grapes for Kim
Step-by-step explanation:
Let's assume that the initial number of grapes they shared is 5x for Tommy and 6x for Kim.
After Tommy eats half of his grapes, he will have 5x/2 grapes left.
Kim eats 4 more grapes than Tommy, so she will have 5x/2 + 4 grapes.
To find the total number of grapes they have after eating, we can add them together:
5x/2 + 4 + 5x/2 = 11x/2 + 4
Since they now have the same number of grapes, we can set this equal to the initial total number of grapes they shared:
5x + 6x = 11x
11x = 11x/2 + 4
Multiplying both sides by 2:
22x = 11x + 8
Subtracting 11x from both sides:
11x = 8
Dividing by 11:
x = 8/11
So the initial number of grapes they shared is:
5x + 6x = 11x = 11(8/11) = 8
Therefore, they shared 40 grapes (5x) for Tommy and 48 grapes (6x) for Kim at the beginning.
helppp pls is urgent
The value of x, considering the angle addition postulate, is given as follows:
x = -5.
What does the angle addition postulate state?The angle addition postulate states that if two angles share a common vertex and a common angle, forming a combination, the larger angle will be given by the sum of the smaller angles.
The larger angle in this problem is QRS, hence the equation to obtain the value of x is given as follows:
3x + 93 + 66 + x = -x + 134
4x + 159 = -x + 134
5x = -25
x = -25/5
x = -5.
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From the plots of porosity and permeability vs depth given in Question 2,what can you say about variability of porosity and permeability? Calculate the coefficient of variation for both porosity and permeability, For comparison, the Vdp for the plug permeability is given as 0.46 -3834 -3835 -3836 Core depth (m) -3837 -3838 -3839 -3840 10 15 25 30 20 Porosity (%) -3834 -3835 -3836 Core depth (m) -3837 -3838 -3839 -3840 0 600 100 200 300 400 500 Horizontal Permeability (mD) 4. From the plots of porosity and permeability vs depth given in Question 2,what can you say about variability of porosity and permeability? Calculate the coefficient of variation for both porosity and permeability, For comparison, the Vdp for the plug permeability is given as 0.46
The Vdp for the plug permeability is given as 0.46, which indicates that the variability of permeability in the plug is lower than that of the porosity and permeability in the core samples.
From the plots of porosity and permeability vs depth given in Question 2, we can say that both porosity and permeability have a certain degree of variability as they change with depth. However, the variability of permeability appears to be greater than that of porosity as the values of permeability change more drastically with depth compared to the values of porosity.
To calculate the coefficient of variation for both porosity and permeability, we can use the formula:
Coefficient of Variation (CV) = (Standard Deviation / Mean) * 100
For porosity:
Mean = (10 + 15 + 25 + 30 + 20) / 5 = 20
Standard Deviation = √[(10 - 20)² + (15 - 20)² + (25 - 20)² + (30 - 20)² + (20 - 20)²] / 5 = 7.07
CV = (7.07 / 20) * 100 = 35.35%
For permeability
Mean = (0 + 600 + 100 + 200 + 300 + 400 + 500) / 7 = 300
Standard Deviation = √[(0 - 300)² + (600 - 300)² + (100 - 300)² + (200 - 300)² + (300 - 300)² + (400 - 300)² + (500 - 300)²] / 7 = 200
CV = (200 / 300) * 100 = 66.67%
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Determine whether the function is even, odd, or neither. Then describe the symmetry. g(s)=8s^2/3
o even o odd o neither
Symmetry: o no symmetry o y-axis symmetry o x-axis symmetry o origin symmetry o x=y symmetry
The function g(s) = 8s²/3 is an even function and its symmetry is y-axis symmetry.
The given function satisfies the condition g(-s) = g(s) which makes it an even function. This means that if we plug in the opposite value of s into the function, we will get the same result. For example, g(-2) = 8(-2)^2/3 = 8(4)/3 = 32/3 and g(2) = 8(2)^2/3 = 8(4)/3 = 32/3.
The symmetry of an even function is y-axis symmetry. This means that the graph of the function is symmetric with respect to the y-axis. In other words, if we fold the graph along the y-axis, the two halves will match up perfectly.
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I need the answer to this
Answer:130
Step-by-step explanation:
2×5+3= 13
10×13=130
Answer:
130/5
Step-by-step explanation:
10x13=130
130/5
ghyhf f yyhgf
Write a general form of an explicit function for what the nth term of any arithmetic sequence would be in terms of a and d. Use the form below to write your function. Type the correct answer in the box.
The general form of an explicit function for what the nth term of any arithmetic sequence would bean = a + (n-1)*d
What is explicit function?An explicit function is a mathematical function containing only the independent variable or variables —opposed to an implicit function which is written in terms of both dependent and independent variables
The general arithmetic progression can be written as:
T₁ , T₂, T₃, T₄, ......, Tn.
Where n is any term
Now since a = 1 and d = common difference, The general arithmetic progression can be written as:
a, a+d, a+2d, a+3d, a+4d, a+(n-1)*d
Thus, the explicit function becomes a+(n-1)*d
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What is the area of this triangle?
Enter your answer as a decimal in the box. Round only your final answer to the nearest hundredth.
The area of the triangle is approximately 6.696 square feet.
What is Area of Triangle?
The area of a triangle is the amount of space enclosed by the three sides of the triangle
To find the area of a triangle with two sides and the included angle, we can use the following formula:
Area = (1/2) x a x b x sin(C)
where "a" and "b" are the lengths of the two sides and "C" is the angle between them.
Substituting the given values, we get:
Area = (1/2) x 3.2 ft x 4.7 ft x sin(62 degrees)
Using a calculator, we can evaluate sin(62 degrees) to be approximately 0.88.
So, Area = (1/2) x 3.2 ft x 4.7 ft x 0.88
= 6.696 ft²
Therefore, the area of the triangle is approximately 6.696 square feet.
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Answer:
The answer is 6.64 ft^2
Step-by-step explanation:
Please help! :>
Jason works at least 16 hours but not more than 24. He earns $15.00 per hour. The function f(t)=15t represents the money he earns for working t hours. What is the practical domain? What is the practical range? Show all your work!
Thanks!!
The practical range is: $76.50 ≤ f(t) ≤ $153
How to solve thisThe minimum number of hours is 5 hours, so the minimum money earned is:
minimum money = 15.30 * 5 = $76.50
The maximum number of hours is 10 hours, so the maximum money earned is:
maximum money = 15.30 * 10 = $153
2. Since the words “at least” and “not more than” are used, hence this is inclusive.
3. The practical range is: $76.50 ≤ f(t) ≤ $153
The domain is the number of hours he worked. It says that he works at least 16 hours, but not more than 24.
This means that the number of hours he worked can be any number between 16 and 24, including 16 and 24 as a possible number of hours.
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Find (fo) (fog )(x) and (gof )(x) and the domain of each. f(x)=x+1,g(x)=7x^(2)-6x-1
(fo)(fog)(x) = 7x^(2)-6x+1
(gof)(x) = 7x^(2)+8x
Domain is a real number.
The first step in finding (fo)(fog)(x) and (gof)(x) is to substitute the functions into each other. For (fo)(fog)(x), we will substitute g(x) into f(x) for x:
(fog)(x) = f(g(x))
= f(7x^(2)-6x-1)
= (7x^(2)-6x-1) + 1
= 7x^(2)-6x
Now we will substitute (fog)(x) into f(x) for x:
(fo)(fog)(x) = f((fog)(x))
= f(7x^(2)-6x)
= (7x^(2)-6x) + 1
= 7x^(2)-6x+1
For (gof)(x), we will substitute f(x) into g(x) for x:
(gof)(x) = g(f(x))
= g(x+1) = 7(x+1)^(2)-6(x+1)-1
= 7x^(2)+14x+7-6x-6-1
= 7x^(2)+8x
The domain of each function is the set of all real numbers, since there are no restrictions on the values of x. Therefore, the domain of (fo)(fog)(x) and (gof)(x) is all real numbers.
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If you apple these changes to the linear parent function, f(x) = x, what is the equation of the new function?
Answer:
C) g(x) = 1/5x + 7-----------------------------------
Vertical compression of a function by a factor of a is:
f(x) → a f(x), where a is between 0 and 1Vertical compression of a function by a factor of 5 is:
g(x) = 1/5 f(x)Shifting up by b units is:
f(x) → f(x) + bIf we apply both transformations we get:
g(x) = 1/5x + 7Option C is correct.
The following figure is made of
1
11 triangle and
1
11 rectangle.
Find the area of each part of the figure and the whole figure.
Figure Area (square units)
Triangle A
Rectangle B
Whole figure
Answer:
Step-by-step explanation:
Find the HCF. 6. ( 26, 32 )=2 7. (32, 58 )= 8. (25, 37 )= 9. (158, 200 ) = 10. (49, 98 )=
The Answers are:
6. HCF is equal to 2
7. HCF is equal to 2
8. HCF is equal to 1
9. HCF is equal to 2
10. HCF is equal to 49
What is HCF?Highest Common Factor is the full form for this term. The highest factor that may divide two integers evenly is known as the HCF of two numbers. HCF can be assessed using two or more numbers.
To find the HCF of the following:
HCF of (26, 32):
2 | 26, 32
| 13, 16
HCF is equal to 2.
HCF of (32, 58)
2 | 32, 58
| 16, 29
HCF is equal to 2.
HCF of (25, 37)
No common divisor except 1.
HCF is equal to 1.
HCF of (158, 200)
2 | 158, 200
| 79, 100
HCF is equal to 2.
HCF of (49, 98)
49 | 49, 98
| 1, 2
HCF is equal to 49.
Hence, 6. HCF is equal to 2
7. HCF is equal to 2
8. HCF is equal to 1
9. HCF is equal to 2
10. HCF is equal to 49
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1. The two graphs show models characterized by exponential decay representing the
area covered by two different algae blooms, in square yards, w weeks after different
chemicals were applied.
The algae bloom that is covered a larger area when the chemicals were applied is the red arrow.
The algae population that is decreasing more rapidly is the blue dot.
What is a population?A population in statistics is a group of comparable objects or occurrences that are relevant to a particular topic or experiment.
A statistical population can be a collection of real things or a hypothetical, possibly limitless collection of objects derived from experience.
It should be noted that the red arrow represents a larger area that is covered by algae.
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what is an equilvalent expression to 15x + 10
Answer:
5 (3x+2)
Step-by-step explanation:
Hope this helps! :)