Using the method of mathematical induction, we show that the inequality σ(n) > H(n) holds for all n≥1. Thus, the inequality n≥1 is true for all n≥1.
What is mathematical induction?It is a a technique used in mathematics to prove that a statement is true for every positive integer or natural number. It consists of two steps:
Base case: Prove that the statement is true for the first positive integer (usually 1).Inductive step: Assume that the statement is true for some arbitrary positive integer k, and then prove that it must also be true for the next positive integer (k+1).We can calculate like this:
Base case: Show that the inequality holds for n=1.
When n=1, we have σ(1) = 1 and H1 = 1, so the inequality 1 ≤ 2^(σ(1)/H1) becomes 1 ≤ 2^(1/1), which is true.Inductive hypothesis: Assume that the inequality holds for some arbitrary positive integer k, i.e., k ≤ 2^(σ(k)/Hk).
Inductive step: Show that the inequality also holds for k+1. Consider σ(k+1) and H(k+1). We can express them as σ(k+1) = σ(k) + k+1 and H(k+1) = H(k) + 1/(k+1).
Using the inductive hypothesis, we have:
k ≤ 2^(σ(k)/Hk),So, we can raise both sides to the power of (k+1)/(kH(k+1)) to get:
k^(1/(kH(k+1))) ≤ 2^((k+1)/(kH(k+1)) * σ(k)/Hk).By the AM-GM inequality, we know that σ(k+1)/k+1 ≥ H(k+1), so we can replace the denominator (kH(k+1)) with H(k+1) and simplify to get
k^(1/H(k+1)) ≤ 2^(σ(k+1)/H(k+1)).Therefore, we have shown that k+1 ≤ 2^(σ(k+1)/H(k+1)), which means the inequality holds for all positive integers n by mathematical induction.
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XYZ Software employed three different salespeople last year. Person 1
earned $4700 in the first quarter, Person 2 earned $19,800 in the first quarter,
and Person 3 earned $6500 in the first quarter. What are the maximum FUTA
deductions for the first quarter?
OA. $291.40
OB. $1227.60
C. $403.00
D. $1128.40
The maximum FUTA deductions for the first quarter is $1092.Because none of the given options correspond to this result, the correct answer is not listed.
The Federal Unemployment Tax Act (FUTA) tax rate is 6% on the first $7,000 paid to each employee in a calendar year. Therefore, the maximum FUTA deduction for each employee is $420 ($7,000 x 0.06).
Person 1 earned $4700, so the FUTA deduction for Person 1 is $282 ($4700 x 0.06).
Person 2 earned $19,800, but only the first $7,000 is subject to FUTA. Therefore, the FUTA deduction for Person 2 is $420.
Person 3 earned $6500, so the FUTA deduction for Person 3 is $390 ($6500 x 0.06).
The total FUTA deduction for the first quarter is the sum of the FUTA deductions for each employee:
$282 + $420 + $390 = $1092
Therefore, the maximum FUTA deductions for the first quarter is $1092.Because none of the given options correspond to this result, the correct answer is not listed.
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need help please thanks
Answer:
a)
[tex]y = 7( {1.03}^{t} )[/tex]
[tex]y = 7( {1.03}^{5} ) = 8.11[/tex]
There were about 8.11 billion subscribers in 2019.
b)
[tex]7( {1.03}^{t}) = 7.5[/tex]
[tex]t = 2.33 \: years \: after \: 2014[/tex]
sometime in 2016
You paid $6.99 for a shirt that was 70% off; what was the original price of the shirt?
Answer:
$23.30
Step-by-step explanation:
We Know
You paid $6.99
The shirt was 70% off
$6.99 = 30%
What was the original price of the shirt?
We Take
(6.99 ÷ 30) x 100 = $23.30
So, the original price is $23.30
1. What is Maxwell's filing status?
a. Single
b. Married filing jointly
c. Head of household
d. Dependent
Maxwell's filing status can be described as: b. Married filing jointly.
What is a filing status?A filing status is a category that defines your tax-filing status based on your marital status and family situation. The filing status determines tax rate and standard deduction, as well as the eligibility for certain credits, deductions, and exemptions.
Maxwell can be described as married filing jointly because he and his spouse combined their income, deductions, and credits on one tax return. This status generally results in lower tax rates and a larger standard deduction compared to filing separately.
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Based on the information in the table, what
was the approximate value of this item in
1980?
Answer:
B) 4,700
Step-by-step explanation:
6000 - 4000 = 2000
2000 in 15 year, find how much for each year
2000/ 15 = 133.3333333
133.3333333 estimated = 133
133 approximately for each year
1975 to 1980 is five years
133 x 5 = 665
4000 + 665 = 4665
4665 rounded the the nearest hundred
4700
raph the image of △BCD after a dilation with a scale factor of
1/3, centered at the origin.
Therefore, The dilated image's vertices are as follows:B'(2 , 3) C'(3 , 3) D'(1 , 3)
dilated image definition ?It is not necessary for the dilation's center to be inside the form. It might be the polygon's vertices. The preimage is still a square in this case, but the center of the dilatation is at the top-left vertex, which is shared by both of the dilated pictures (one smaller and one larger).
To get the vertices of the dilated image, multiply each vertex's coordinate by a factor of three.
B(6,9)⇒B'(1/3×6,1/3×9) = B'(2 , 3)
C(9,9)⇒C'(1/3×9 , 1/3×9) = C'(3 , 3)
D(3,9)⇒D'(1/3×3 ,1/3×9) = D'(1 , 3)
The dilated image's vertices are as follows:
B'(2 , 3) C'(3 , 3) D'(1 , 3)
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What is the length of the diagonal from P to Q ?
Step-by-step explanation:
Use a modified Pythagorean theorem for 3 -D
diagonal = sqrt ( 9^2 + 12^2 + 8^2 ) = sqrt(289) = 17 units
A movie theater has a seating capacity of 257. The theater charges $5.00 for children, $7.00 for
students, and $12.00 of adults. There are half as many adults as there are children. If the total ticket
sales was $ 1870, How many children, students, and adults attended?
The attendance at the movie theatre is;
Children = 142
Students = 44
Adults = 71
What is arithmetic?
Arithmetic is an elementary part of mathematics that consists of the study of the properties of the traditional operations on numbers—addition, subtraction, multiplication, division, exponentiation, and extraction of roots.
Here, we have
Given:
Seating capacity = 257
Charges: Children = $5.00; Students = $7.00; Adults = $12.00
Total sales of ticket = $1870
A number of children, students, and adults were present in the theatre.
Let A, C, and S represent adults, children, and students respectively.
There are half as many adults as there are children; this means that
A = ½C
If the total seat capacity is 257, then
A + C + S = 257
Also, if the total sales of tickets are $1870, then
12A + 7S + 5C = 1870
So, we have two equations to be solved simultaneously.
A + C + S = 257 --- (1)
12A + 7S + 5C = 1860 --- (2)
Substitute ½C for A in (1) and (2)
½C + C + S = 257
Multiply both sides by 2
2(½C + C + S) = 2 * 257
C + 2C + 2S = 514
3C + 2S = 514 ----- (3)
12(½C) + 7S + 5C = 1870
6C + 7S + 5C ,= 1870
6C + 5C + 7S = 1870
11C + 7S = 1870 --- (4)
Make S the subject of the formula in (3)
2S = 514 - 3C
S = ½(514 - 3C)
S = 257 - 1.5C
Substituton 257 - 1.5C for S in (4)
11C + 7(257- 1.5C) = 1870
11C + 1799 - 10.5C = 1870
Collect like terms
11C - 10.5C = 1870 - 1799
0.5C = 71
Multiply both sides by 2
2 * 0.5C = 2 * 71
C = 142
Recall that
S = 257 - 1.5C
S = 257 - 1.5(142)
S = 257 - 213
S = 44
Also, recall that
A = ½C
A = ½ * 142
A = 71
Hence, the attendance at the movie theatre is;
Children = 142
Students = 44
Adults = 71
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find the gcf of 8a^3b^2 and 12ab^4
Answer:
To find the greatest common factor (GCF) of 8a^3b^2 and 12ab^4, we need to factor each term into its prime factors and then find the common factors.
8a^3b^2 can be written as:
8a^3b^2 = 2^3 * 2 * a * a * a * b * b
12ab^4 can be written as:
12ab^4 = 2^2 * 3 * a * b * b * b * b
The common factors are 2, a, and b^2.
Therefore, the GCF of 8a^3b^2 and 12ab^4 is:
2 * a * b^2 = 2ab^2
The 8th grade math team is having a bake sale as a fundraiser. Alan can make 5 cookies in 2 minutes. Abigail can make 8 cookies in 3 minutes. However, Katie eats 1 cookie every 6 minutes. How many minutes will it take to make 5 dozen cookies.
Answer: B. 12
Step-by-step explanation:
1) Alan can make 2.5 cookies per min
2) Abi can make 8/3 which is 2.7.
3) overall, 5.2 cookies per minute can be made.
multiple 5.2 x 6 and you get around 31.5?
then subtract =1. you have 30.5, now add onto that number 31.5, which is another 6 minutes. since you're still only subtracting 1, the answer would be above 60, which is 5 dozen, and it only took 12 mins
Working alone, Lisa can pick forty bushels of apples in 13 hours. One day her friend Cody helped and it only took them 4.8 hours to do it together. Find out how long it would take Cody to do it alone.
it would take Cody 40 bushels / 5.26 bushels per hour = 7.61 hours to pick 40 bushels of apples alone.
How to find Lisa's individual work?To begin, let's determine Lisa's individual work rate, or the amount of work she can complete in an hour.
The work formula states that the amount of work completed is equal to the product of the work rate and the amount of time spent working. Lisa's work rate is 40 bushels divided by 13 hours equals 3.08 bushels per hour.
Let C represent Cody's work rate, and let t represent the amount of time it takes him to pick 40 bushels on his own.
At the point when Lisa and Cody cooperate, they pick 40 bushels, so we can compose:
Lisa's work + Cody's work = Total work
3.08 bushels/hour * 4.8 hours + C * 4.8 hours = 40 bushels
14.78 + 4.8C = 40
4.8C = 25.22
C = 5.26 bushels per hour
Consequently, it would take Cody 40 bushels/5.26 bushels each hour = 7.61 hours to pick 40 bushels of apples alone.
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Help pls! Average winter temperatures in 45 states were recorded and divided by geographical region.
Choose True or False.
A: The mean of Region 2 is 5.8 greater than the mean of Region 1.
B: The data of Region 2 has greater variability than the data of Region 3 because the data are clustered around a greater average temperature
C: The difference of the means of Region 2 and Region 3 is about twice the MAD of Region 3
D: The average of the means of the three regions is closest to the mean of Region 3
pls show work
The correct answer is a. True, b. False, c. True, d. True
How to find the mean of regions?The mean of Region 1 is 31+ (32+33+34)×3+35×4+36/15 = 33.6°CThe mean of Region 2 is 36+ 37+ 2x38+ (39+41)x3 +40x4+42/15 = 39.4°C
(The mean = all temperature of region divided by the number of states )
So, 39.4- 33.6 = 5.8 True
The data of Region 2 is more concentrated, So its variability is weaker than Region 3.So False (variability is comparing the density)
The mean of Region 3 is (32+ 2x (34+35+37+38)+ 36x3+ 39+ 40] ÷15 = 33.8°CThe difference is 39.4 - 33.8= 5.6
The MAD of Region 3 is (32 - 33.8) +2 x (34 -33.8) + 2x (35 - 33.8) + 4x (36-33.8) + 2x (37-33.8) + 2x (38-33.8) + (39-33.8) + (40-33.8) ÷ 15 = 2.64
2-64 × 2 = 5.28, so true
The average of mean is 33.6+ 39.4+ 33.8/3 = 35.633.8 is closest to 35.6, so true.
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the combined sales tax rate for your country 7.25%
Answer: The California state sales tax rate is 7.25%. This rate is made up of a base rate of 6%, plus California adds a mandatory local rate of 1.25% that goes directly to city and county tax officials.
Step-by-step explanation:
Hope this helped! :)
Y can represent the distance Frog B hopped as y=x+ 8/3 x. Now rewrite the equation using the distributive property.
The rewritten expression of y = x + 8/3x using the distributive property is y = x(1 + 8/3)
Rewriting the equation using the distributive property.From the question, we have the following parameters that can be used in our computation:
Y can represent the distance Frog B hopped as y=x+ 8/3 x.
This means that
y = x + 8/3x
Factor out x from the equation
So, we have
y = x(1 + 8/3)
The above equation has been rewritten using the distributive property.
Hence, the rewritten expression using the distributive property is y = x(1 + 8/3)
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If a 95% confidence interval for is calculated to be (21.4 , 27.9) , what would be the result of a hypothesis test at a 5% significance level performed on the set of hypotheses?
H0: mean = 27
Ha: mean different 27
PLEASE ANSWER!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
OMG PLS NOBODY ANSWERS
YOU GET 100 POINTS
PLS PLS PLS PLS PLS PLS
Answer:
11
Step-by-step explanation:
You want the degree of the monomial -3q⁴rs⁶.
DegreeThe degree of a variable expression is its exponent. The degrees of the variables in the given expression are ...
q: 4
r: 1
s: 6
The degree of their product is the sum of the exponents:
monomial degree = 4 + 1 + 6 = 11
The degree is 11.
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Music streaming services are the most popular way to listen to music. Data gathered over the last 12 months show Apple Music was used by an average of 1.81 million households with a sample standard deviation of 0.47 million family units. Over the same 12 months Spotify was used by an average of 2.21 million families with a sample standard deviation of 0.32 million. Assume the population standard deviations are not the same. Using a significance level of 0.02, test the hypothesis of no difference in the mean number of households picking either service.
a. Compute the test statistic.
b. Compute the p-value.
PLEASE HELP ON QUESTION!(if answer and explanation is correct I'll rate you five stars a thanks and maybe even brainly. Also your very smart!)
What is value of x in this equation:
4x+15=33-2x
Answer: Simplifying
4x + 15 = 33 + -2x
Reorder the terms:
15 + 4x = 33 + -2x
Solving
15 + 4x = 33 + -2x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '2x' to each side of the equation.
15 + 4x + 2x = 33 + -2x + 2x
Combine like terms: 4x + 2x = 6x
15 + 6x = 33 + -2x + 2x
Combine like terms: -2x + 2x = 0
15 + 6x = 33 + 0
15 + 6x = 33
Add '-15' to each side of the equation.
15 + -15 + 6x = 33 + -15
Combine like terms: 15 + -15 = 0
0 + 6x = 33 + -15
6x = 33 + -15
Combine like terms: 33 + -15 = 18
6x = 18Divide each side by '6'.
x = 3
Simplifying
x = 3
so X=3 is your answer
Three fair coins are tossed. How many different outcomes will
there be?
Answer:
just 2 outcomes
Step-by-step explanation:
no matter how often you throw it, there are only two sides available
What is 5a^2b + 15ab^2 factories fully
Answer:
[tex]5 {a}^{2} b + 15a {b}^{2} = [/tex]
[tex]5ab(a + 3b)[/tex]
Can you write equation in conic form?
The equation x = 1/16y² - 1/8y + 17/16 in conic form is (y - 1)² = 16(x - 1)
Writing the equation in conic form?From the question, we have the following parameters that can be used in our computation:
x = 1/16y² - 1/8y + 17/16
Multply through the equation by 16
S, we have
16x = y² - 2y + 17
Rewrite as
16x - 17 = y² - 2y
Add the square of half the coefficient of y to both sides
So, we have
16x - 17 + 1 = y² - 2y + 1
Evaluate and express as perfect squares
16x - 16 = (y - 1)²
Factor out 16
16(x - 1) = (y - 1)²
Rewrite as
(y - 1)² = 16(x - 1)
The above equation is an equation of a parabola whose inverse has been calculated
Hence, the conic equation is (y - 1)² = 16(x - 1)
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In this 30°-60°-90° right triangle, the length of the long leg is 9√3
What is the measure of the hypotenuse n and the short leg m?
30°
9√3
n
m
Answer:
30°
Step-by-step explanation:
Answer:
9
Step-by-step explanation:
In a 30°-60°-90° right triangle, the sides are always in the ratio of 1: √3:2, where 1 is the length of the short leg opposite the 30° angle, √3 is the length of the long leg opposite the 60° angle, and 2 is the length of the hypotenuse opposite the 90° angle1234.
In this case, we are given that the long leg is 9√3, so we can use this value to find the other sides by setting up a proportion:
short leglong leg=13
short leg93=13
Cross-multiplying and solving for the short leg, we get:
short leg=393×1=9
Similarly, we can use another proportion to find the hypotenuse:
long leghypotenuse=32
93hypotenuse=32
Cross-multiplying and solving for the hypotenuse, we get:
hypotenuse=32×93=18
Therefore, the measure of the hypotenuse n is 18 and the measure of the short leg m is 9.
if L(x) =sinx-cosx, then dxy=? A. cosx+sinx B. cosx-sinx C. sin²x+cosx D. none
Answer: To find d(L(x))/dx, we need to differentiate L(x) with respect to x using the derivative rules.
d(L(x))/dx = d/dx (sinx - cosx)
= cosx + sinx
Therefore, the correct answer is option A, cosx+sinx.
Step-by-step explanation:
The sales tax for an item was 11.70 and it cost 390 before tax.
Find the sales tax rate. Write your answer as a percentage.
The sales tax rate for the item is 3%.
How to find the sales tax rate?To find the sales tax rate, we can divide the sales tax amount by the original cost of the item, and then multiply by 100 to express the result as a percentage.
Given:
Sales tax amount = $11.70
Original cost of item = $390
Sales tax rate = (Sales tax amount / Original cost of item) x 100
Plugging in the given values:
Sales tax rate = (11.70 / 390) x 100
Calculating:
Sales tax rate = 0.03 x 100
Final result:
Sales tax rate = 3%
So, the sales tax rate for the item is 3%.
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PLEASE HELP!!!!!!!!!!!!!!!!!!!!!!
Find the probability of drawing a green, then yellow, with replacement.
A bag has 4 green blocks, 6 red blocks, 7 blue and 3 yellow.
The probability of drawing a green block followed by a yellow block with replacement is 0.03, or 3%.
What is probability?The probability of an event is calculated by dividing the total number of possible outcomes by the number of possible outcomes.
The likelihood of drawing a green block on the main draw is:
P(green) = (number of green blocks) / (total number of blocks)
P(green) = 4 / (4 + 6 + 7 + 3)
P(green) = 4 / 20
P(green) = 0.2
Since the blocks are replaced after each draw, the probability of drawing a yellow block on the second draw is still:
P(yellow) = (number of yellow blocks) / (total number of blocks)
P(yellow) = 3 / (4 + 6 + 7 + 3)
P(yellow) = 3 / 20
P(yellow) = 0.15
To find the probability of both events happening, we multiply the probabilities:
P(green, then yellow) = P(green) * P(yellow)
P(green, then yellow) = 0.2 * 0.15
P(green, then yellow) = 0.03
As a result, replacing a yellow block with a green one has a chance of 0.03, or 3%, being drawn.
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A hard drive has enough storage space left for 7 1/2 hours of TV programmes. How many programmes each lasting 5/6 of an hour can be recorded on the hard drive?
Answer:
9
Step-by-step explanation:
7 1/2 divided by 5/6 would equal 9.
first step: convert the mixed number into an improper fraction.
7 1/2 = 15/2
2nd step: change the operation. (KCF)
keep the first term - change the operation - flip the second term
so, 15/2 x 6/5 =.
15x6=90
2x5=10
90/10 = 9
hope it helps!
Find the surface area of the triangular prism. The base of the prism is an isosceles triangle.
The answer of the given question based on the Rectangular prism is , the surface area of the given triangular prism is 3360 cm².
What is Rectangular prism?A rectangular prism is a three-dimensional geometric shape with six rectangular faces. It is also known as rectangular parallelepiped or cuboid. A rectangular prism has a length (l), width (w), and height (h) and the formula for the volume of a rectangular prism is given as V = l * w * h.
To find the surface area of a triangular prism, we need to add up the areas of all of its faces. A triangular prism has two identical triangular bases and three rectangular faces.
First, let's find the area of the triangular base. We know that it is an isosceles triangle with a perpendicular height of 35 cm and base of 24 cm, and the length of the two equal sides is 37 cm. We can use the formula for the area of a triangle:
Area of base = (1/2) * base * height
Area of base = (1/2) * 24 cm * 35 cm
Area of base = 420 cm²
Since there are two identical bases, we can multiply this by 2 to get the total area of the triangular bases:
Total area of bases = 2 * 420 cm²
Total area of bases = 840 cm²
Now, let's find the area of the three rectangular faces. We know that the height of the prism is 35 cm, and the length of each rectangular face is equal to the base of the triangular base, which is 24 cm. To find the width of each rectangular face, we need to use the Pythagorean theorem to find the length of the altitude of the triangular base:
a² + b² = c²
where a and b are the two equal sides of the triangular base, and c is the base.
Substituting the given values, we get:
a² + b² = c²
37² + 12² = c²
1369 + 144 = c²
c² = 1513
c = √1513
c = 38.95 cm
Therefore, the altitude of the triangular base is approximately 35 cm, and we can use this value as the width of each rectangular face. So, area of each rectangular face is given:
Area of each rectangular face = length*width
Area of each rectangular face = 24 cm * 35 cm
Area of each rectangular face = 840 cm²
Since there are three identical rectangular faces, we can multiply this by 3 to get the total area of the rectangular faces:
Total area of rectangular faces = 3 * 840 cm²
Total area of rectangular faces = 2520 cm²
Finally, we can find the total surface area of the prism by adding the areas of the two triangular bases and the three rectangular faces:
Total surface area = Total area of bases + Total area of rectangular faces
Total surface area = 840 cm² + 2520 cm²
Total surface area = 3360 cm²
Therefore, the surface area of the given triangular prism is 3360 cm².
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Which of these is an accurate way to measure the volume of a rectangular prism
A. Fill it with water and then weigh the water.
B.Trace each face of the prism on centimeter grid paper, and then count the number of squares it comprises.
C. Measure the length and the width, and then multiply the two values.
D. pack it with unit cubes, leaving no gaps or overlaps, and count the number of unit cubes.
The correct option is (D) if unit cubes are packed into a rectangular prism without any gaps or overlaps, the volume of the prism can be calculated by counting the number of unit cubes.
What is a rectangular prism?A rectangular prism is a polyhedron in geometry that has two parallel and congruent bases.
It also goes by the name cuboid.
Six faces, each with a rectangle shape and twelve edges, make up a rectangular prism.
It is referred to as a prism because of the length of its cross-section.
There are 6 faces, 8 vertices, and 12 edges on a rectangular prism.
A rectangular prism's volume can be determined by packing unit cubes into it without any gaps or overlaps, then counting the number of unit cubes.
A rectangular prism's surface area is equal to the sum of the areas of each of its faces.
It can be calculated using the formula 2(lw+ wh+ hl).
Therefore, the correct option is (D) if unit cubes are packed into a rectangular prism without any gaps or overlaps, the volume of the prism can be calculated by counting the number of unit cubes.
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What is the slope intercept of -2 and y-intercept (0,2)?
Answer:
The slope-intercept form of the equation of a line is:
y = mx + b
where m is the slope and b is the y-intercept.
We are given that the y-intercept is (0,2), which means that the value of b is 2.
We are also given that the slope is -2, which means that the value of m is -2.
Substituting these values into the slope-intercept form, we get:
y = -2x + 2
Therefore, the slope-intercept form of the equation of the line is y = -2x + 2.
Step-by-step explanation:
Answer:
that is correct just to give you feedback on that
Mackenzie answered 72 questions correctly on her multiple choice math final that had a total of 160 problems. What percentage of questions did Mackenzie answer correctly on the final exam?
Answer:
45%
Step-by-step explanation:
72/160 = 0.45
0.45 x 100 = 45%