Answer:
(a) The best answer for residuals plot (a) is:
A. The fanned pattern indicates that the linear model is not appropriate. The model's predicting power decreases as the values of the explanatory variable increases.
A fanned pattern in the residuals plot suggests that the linear model is not appropriate because the variability of the residuals increases as the values of the explanatory variable increases. This indicates that the linear model is not capturing all the important features of the data and may not be the best fit for the data.
(b) The best answer for residuals plot (b) is:
B. The curved pattern in the residuals plot indicates that the linear model is not appropriate. The relationship is not linear.
A curved pattern in the residuals plot suggests that the linear model is not appropriate because the relationship between the variables is not linear. This indicates that the linear model is not capturing all the important features of the data and may not be the best fit for the data.
I’m wondering if it’s correct and if it’s not, I give u 20 points
20 POINTS
Using percentage,
18. 78/100 of earth's atmosphere is made up of nitrogen.
19. 0.21 part of earth's atmosphere is made up of oxygen.
20. 100% of earth's atmosphere is here represented by the graph.
21. 1/100 of earth's atmosphere is made up of other gases.
Define percentage?The denominator of a percentage (also known as a ratio or fraction) is always 100. Sam, for instance, would have received 30 out of a possible 100 points if he had received 30% on his maths test. In ratio form, it is expressed as 30:100 and in fraction form as 30/100. In this case, the percentage symbol "%" is read as "percent" or "percentage."
This percent symbol can always be changed to a fraction or decimal equivalent by substituting "divided by 100."
Here in the graph as we can see,
Nitrogen = 78%
Oxygen = 21%
Other gases = 1%
Total = 100%
Fraction of nitrogen gas means, 78% in fraction = 78/100
Now, decimal of oxygen gas means, 21% in decimal = 0.21
The total percentage represented by graph = 100%
Other gases make up for 1/100 fraction of the total earth's atmosphere.
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Technology In 2002, there were approximately 544,000,000 Internet users
worldwide. Write this number in scientific notation.
mplify.
Answer: 5.44 x 10 to the power of 8
Step-by-step explanation:
At sunrise the distance from the top of the Great Sphinx in Egypt to the end of its shadow is measured to be 220 ft. The distance from the top of the head of a 6 ft-tall person who is standing next to the Sphinx to end of their shadow is measured to be 20 ft. How tall is the Great Sphinx?
54. 5ft
The Great Sphinx in Egypt is 66 ft tall, based on measurements of its shadow and a 6 ft-tall person's shadow at sunrise.
Let's denote the height of the Sphinx as "h".
At sunrise, the angle of elevation from the tip of the Sphinx to the top of the sun is 90 degrees. This means that the triangles formed by the Sphinx, its shadow, and the sun are all similar.
Using this fact, we can set up a proportion between the height of the Sphinx and the length of its shadow:
h/220 = 6/x
where "x" is the length of the shadow of the 6 ft-tall person.
Solving for "x", we get:
x = (220*6)/h
We also know that the length of the shadow of the person is 20 ft, so we can set up another proportion:
h/220 = 6/20
Solving for "h", we get:
h = (220*6)/20 = 66 ft
Therefore, the height of the Great Sphinx is 66 ft.
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The complete question is:
The Great Sphinx in Egypt's shadow extends 220 feet below the summit of the structure at sunrise. An someone who is 6 feet tall and standing close to the Sphinx has a shadow that extends 20 feet from the top of their head. The Great Sphinx's height is how tall?
a) 70.0 ft
b) 66.0 ft
c) 733.3 ft
d) 54.5ft
whats the answer to d??
Answer:
I think the answer is 4 tell me if it wasn't
(X-3)(x+3)
Solve this polynomial plss
Answer: x^2 - 9
Step-by-step explanation:
I WILL GIVE 15 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS PLEASE
Answer:
B, $305.11
Step-by-step explanation:
since it is in annual interest, 36 months = 3 years.
use the formula for simple interest, which is x = Prt
278 * 0.0325 * 3 = 27.105
that is the interest that you gained.
then, add the original amount that you had, which was 278.
27.105+278 = 305.105
this rounds to $305.11, which is answer choice B
Melissa is tracking the progress of her plants growth. She measures the plant and finds that it is 5. 5 inches tall. The plant then is measured every day for the next few days and she finds it is growinf at a constant rate of 1. 4 inches per day. What is the y-intercept
The y-intercept is 5.5 inches, which is the initial height of the plant before it started growing.
We can use the slope-intercept form of a linear equation, y = mx + b, where m is the slope and b is the y-intercept, to solve the problem.
Since the plant is growing at a constant rate of 1.4 inches per day, the slope of the line that represents its growth is 1.4.
Let y be the height of the plant after x days. We know that the plant was 5.5 inches tall on day 0, so we have the point (0, 5.5) on the line.
Using the point-slope form of a linear equation, we get:
y - 5.5 = 1.4x
Simplifying, we get:
y = 1.4x + 5.5
Comparing the equation to the slope-intercept form, we see that the y-intercept is 5.5.
Therefore, the y-intercept is 5.5 inches.
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Find the mean and median of the given data: 6, 3, 4, 9, 13
Step-by-step explanation:
mean is all the numbers added together, which is 35 and divide by the amount of numbers so 35 divide 5 is 7. Mean= 7
Medial is the number in the middle so 4 is the medial. Because it is in the middle of all the numbers.
Hope this helps.
Karla’s dad is planning to change the fencing around his backyard. The area of the yard and the length is given by (8x+5) ft.is (8x^2+13x+5) ft^2If the fence is along the length and two widths of the yard, determine how many feet of fencing he will need
Answer:
(16x^2 + 46x + 20)/(4x + 5) ft
Step-by-step explanation:
he area of the yard is given by (8x^2+13x+5) ft^2. The length of the yard is (8x+5) ft. The width of the yard is (8x^2+13x+5)/(8x+5) ft.
The fence is along the length and two widths of the yard. Therefore, the length of the fence is 2(8x+5) ft and the width of the fence is 2(8x^2+13x+5)/(8x+5) ft.
The total length of the fence is the sum of the length and width of the fence.
Therefore, the total length of the fence is 2(8x+5) + 2(8x^2+13x+5)/(8x+5) ft.
Simplifying the expression, we get:
2(8x+5) + 2(8x^2+13x+5)/(8x+5) = (16x^2 + 46x + 20)/(4x + 5) ft.
Therefore, Karla’s dad will need (16x^2 + 46x + 20)/(4x + 5) ft of fencing.
real estate ads suggest that 60% of homes for sale have garages, 30% have swimming pools, and 18% have both features. what is the probability that a home for sale has garage but no pool?
The probability of a home for sale having a garage but no pool is 0.42.
To do this, we need to use some probability rules. One useful rule is the formula for calculating the probability of an event not occurring. This is given by:
P(not A) = 1 - P(A)
where A is the event we are interested in, and not A is the event of A not occurring.
In this case, we are interested in the probability of a home having a garage but no pool. Let's call this event GNP (short for garage no pool). Using the information given, we know that 60% of homes have garages and 18% have both garages and pools. We can use this information to calculate the probability of a home having a garage but no pool as follows:
P(GNP) = P(G) - P(G and P)
where G is the event of a home having a garage and P is the event of a home having a pool.
Substituting the values we have:
P(GNP) = 0.6 - 0.18
P(GNP) = 0.42
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Choose scales for the coordinate plane shown so that you can graph the points J(20, 3), K(25, 3), L(15, −3), M(−5, 5), and N(−5, −4). On the x−axis, use a scale of unit(s) for each grid square. On the y−axis, use a scale of unit(s) for each grid square. Complete the explanation for using using these scales for each axis. The x−coordinates range from to , and the y−coordinates range from _ to _ PLS HURRY!!!
The x-coordinates range from -5 to 25, and the y-coordinates range from -4 to 5.
To choose appropriate scales for the coordinate plane, first, observe the range of x and y coordinates for the given points J(20, 3), K(25, 3), L(15, -3), M(-5, 5), and N(-5, -4).
The x-coordinates range from -5 to 25, and the y-coordinates range from -4 to 5.
For the x-axis, we can use a scale of 5 units for each grid square.
This scale will allow us to cover the entire range of x-coordinates.
The grid will have 6 squares in the positive x-direction and 2 squares in the negative x-direction.
For the y-axis, we can use a scale of 1 unit for each grid square.
This scale will allow us to cover the entire range of y-coordinates.
The grid will have 5 squares in the positive y-direction and 4 squares in the negative y-direction.
In summary, use a scale of 5 units for each grid square on the x-axis, and a scale of 1 unit for each grid square on the y-axis.
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Using completing the square method solve : 3x^2+5x+2=0
Answer:
Step-by-step explanation:
Finally got it right. lol
By which axiom AABC and ADEF shown in the figure are congruent? Also, write a pair of corresponding angles.
The axiom AABC and ADEF shown in the figure are congruent by SAS axiom.
What is SAS?The SAS (Side-Angle-Side) axiom, also known as the SAS postulate or SAS congruence criterion, states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.
In other words, if you have two triangles with the same angle between two sides of equal length, then those triangles are congruent.
This can be written mathematically as:
If triangle ABC is congruent to triangle DEF by SAS axiom, then:
AB = DE
AC = DF
angle BAC = angle EDF
angle ABC = angle DEF
angle ACB = angle DFE
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Given the relation of this table:
What is the rule for this relation?
The rule for this relation could be S = n² + 1.
What is relation rule?
A relation rule is a description of how two or more quantities or variables are related to each other. A relation rule can take various forms, depending on the nature of the relation and the variables involved.
For example, a relation rule can be expressed as an equation, a formula, a table, a graph, or a verbal description. In each case, the relation rule specifies the conditions under which the variables are related, and how they vary in relation to each other.
Based on the given table:
n: 1, 0, 2
S: 1, 0, 3
We can observe that when n=1, S=1; when n=0, S=0; and when n=2, S=3.
There are different possible rules that can describe this relation, but one possible rule is:
S = n² + 1
Using this rule, we can verify that it matches the given table:
When n=1, S = 1² + 1 = 2, which matches the given value of S=1.When n=0, S = 0² + 1 = 1, which matches the given value of S=0.When n=2, S = 2² + 1 = 5, which matches the given value of S=3.Therefore, the rule for this relation could be S = n² + 1.
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PLS HELPP ILL MARK U BRAINLIST and explain ur choice
Answer:
A.
Step-by-step explanation:
Because If you are simplifying then -3 would become -1 and -5 would become -3 and -4 would become -2 so your basically just simplifying
The value, y, in dollars of a painting after x years can be represented by the function y=6000(1.25)x.
How much is the painting worth after 6 years to the nearest dollar?
Answer:22,888
Step-by-step explanation: replace x with 6 and use calculator :)
need help with this question
[tex](5x^8y^4)/(15x^3y^8) = (x^5/y^4) * (1/3)[/tex] is the fully simplified expression using only positive exponents.
To simplify [tex](5x^8y^4)/(15x^3y^8)[/tex], we can start by dividing the numerator and denominator by their greatest common factor, which is[tex]5x^3*y^4[/tex]:
[tex](5x^8y^4)/(15x^3y^8) = (x^8/x^3) * (y^4/y^8) * (1/3)[/tex]
Now we can simplify each term separately. First, [tex]x^8[/tex] divided by [tex]x^3[/tex] equals [tex]x^5[/tex], because when we divide two terms with the same base, we subtract their exponents:
[tex]x^8/x^3 = x^(8-3) = x^5[/tex]
Similarly, [tex]y^4[/tex]divided by[tex]y^8[/tex] equals [tex]1/y^4[/tex], because when we divide two terms with the same base, we subtract their exponents and change the sign:
[tex]y^4/y^8 = y^(4-8) = 1/y^4[/tex]
Finally, 1/3 is already in its simplest form. Putting it all together, we get:
[tex](5x^8y^4)/(15x^3y^8) = (x^5/y^4) * (1/3)[/tex]
This is the fully simplified expression using only positive exponents.
We can state that the original equation represents a fraction, where the numerator is the product of 15, the third power of x, and the eighth power of y, and the denominator is the product of 5, the eighth power of x, and the fourth power of y.
We then determined the numerator and denominator's largest common factor, which is 5x*3*y*4, in order to condense the formula. Using the exponentiation principles, we divided the numerator and denominator by this factor before simplifying each term. The end result is a fraction with x raised to the fifth power as the numerator, y raised to the fourth power as the denominator, and 3 as the common factor.
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A family wants to make an addition to a deck that extends off the back of their home. The current deck is 400 ft2. The addition will be 18.75 ft in length and 15 ft wide. What will be the total area of the deck once the addition is complete? 681.25 ft2 433.75 ft2 281.25 ft2 118.75 ft2
Answer:
681.25 ft2.
Step-by-step explanation:
Answer:
Step-by-step explanation: answer is option b
. The table shows how many books students
in a class read each week for two months.
Graph the data.
Week 1 2 3
Books
Read
10 9
7
4 5 6
8
7 8
9
67
4
What is the difference between the greatest numb
books read and the least number of books read?
The difference between the greatest and least number of books read is 6.
What is graph?A graph is a visual representation of data that displays the relationship between two or more variables. Graphs are used in many fields, including mathematics, science, economics, engineering, and social sciences, to help researchers and practitioners analyze, interpret, and communicate data effectively.
Here,
To graph the data, we can use a bar graph or a line graph, where the x-axis represents the weeks and the y-axis represents the number of books read. Each bar or point on the graph represents the number of books read in a particular week. Using the data from the table, we can create the following line graph:
To find the difference between the greatest number of books read and the least number of books read, we need to identify the highest and lowest data points on the graph. From the graph, we can see that the highest data point is 10, which corresponds to Week 1, and the lowest data point is 4, which corresponds to Week 3. Therefore, the difference between the greatest and least number of books read is:
10 - 4 = 6
So the difference is 6 books.
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Complete question:
The table shows how many books students in a class read each week for two months. Graph the data.
Week 1 2 3
Books 10 7 9
Read 4 5 6
What is the difference between the greatest numb books read and the least number of books read?
assume that the test scores of a college entrance exam fits a normal distribution. the mean test score is 72, and the standard deviation is 5. what is the percentage of students scoring 84 or more in the exam?
The percentage of students scoring 84 or more in the exam is 99.18%.
Given, Mean test score = 72,
Standard deviation = 5.
We are supposed to find the percentage of students scoring 84 or more in the exam.
To find the percentage of students scoring 84 or more in the exam, we will use the following steps:
First, we need to find the z-score associated with 84.
Let us assume that z is the z-score corresponding to the value 84, then;
z = (84 - 72) / 5 = 2.4
Now, we have the value of z, we can find the percentage of students scoring 84 or more in the exam using the normal distribution table.
The percentage is the area under the normal distribution curve to the right of the z-score.
To find the area using the normal distribution table, we need to look for the value 2.4 in the z-table. Since 2.4 is not exactly listed in the z-table, we will use the value for 2.4 closest to it.
Using the z-table, the value closest to 2.4 is 0.9918.
Therefore, the percentage of students scoring 84 or more in the exam is;
P(Z > 2.4) = 0.9918 × 100 = 99.18%.
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PLEASE HELP ASAP!!!!!!!!
Joseph bought a pair of socks for $9, a pair of shoes for $40, and a pair of jeans for $35. The tax rate was 6%. What was the total cost of Joseph's purchases?
Responses
$78.96
$89.04
$5.04
$84.00
Answer:
$89.04
Step-by-step explanation:
PLEASE ANSWEERRR!!!
If the dimensions of the triangle in the ingrande quadrupled, what
would be the new perimeter?
Answer:
132 in
Step-by-step explanation:
You want to know the perimeter of a triangle after the dimensions are quadrupled.
Quadrupled"Quadrupled" means "multiplied by 4."
The perimeter is the sum of the lengths of the sides of the triangle:
P = 8 +10 +15 = 33 . . . . inches
If the sides are quadrupled, it is ...
P' = 4(8) +4(10) +4(15) = 4(8 +10 +15) = 4(33) = 132 . . . . inches
As you can see, if the sides are quadrupled, the perimeter is quadrupled.
The new perimeter is 132 inches.
Help me pls I will give you Brainly
Here's the tree diagram for the given scenario:
(1) The probability of getting tails and a 3 is the probability of following the path T-3, which is 1/2 x 1/4 = 1/8.
(ii) The probability of getting heads and an even number is the probability of following the path H-2 or H-4, which is 1/2 x 1/2 + 1/2 x 1/2 = 1/2.
(iii) The probability of not getting heads and an even number is the probability of following the paths T-2 or T-4, which is 1/2 x 1/2 + 1/2 x 1/2 = 1/2.
(Please could you kindly mark my answer as brainliest you could also follow me so that you could easily reach out to me for any other questions)
Help me please! I’m so stressed out.
1) To determine if the triangle is acute, obtuse, or right, we need to check if the sum of the squares of the two shorter sides is greater than, equal to, or less than the square of the longest side.
Let's first arrange the side lengths in ascending order:
28 in. < 34 in. < 42 in.
Now we can apply the Pythagorean theorem:
28² + 34² = 196 + 1156 = 1352
42² = 1764
Since 1352 is less than 1764, the sum of the squares of the two shorter sides is less than the square of the longest side. Therefore, the triangle is obtuse.
2)
We can use the tangent function to find the length of BC.
tan(B) = opposite/adjacent
We know that the opposite side of angle B is BC, and the adjacent side is AC, which is the height of the triangle. Since angle B is 45 degrees, we have:
tan(45) = BC/16
Simplifying the left side using the fact that tan(45) = 1, we get:
1 = BC/16
Multiplying both sides by 16, we get:
BC = 16
Therefore, the length of BC is 16 ft.
3)
Since the hypotenuse of each triangular quilt piece is 18 inches, we can use the Pythagorean theorem to find the length of each side. Let's call one leg of the triangle x (since the two legs will be equal), and the hypotenuse is 18. Then:
x² + x² = 18²
Simplifying:
2x² = 324
Dividing by 2:
x² = 162
Taking the square root:
x = √(162) = sqrt(2 * 3⁴)
We can simplify this by breaking it down into factors:
x = 3 * √(2) * 3
x = 9√(2)
Therefore, the length of each side of the triangular quilt piece is 9√(2) inches or 12.73 inches
4)
We can use the inverse sine function to find the angle that has a sine of 9/16. Using a calculator, we get:
sin^(-1)(9/16) ≈ 35.54°
Therefore, the missing value is approximately 35.54°
5)
We can use the inverse cosine function to find the angle that has a cosine of 7/18. Using a calculator, we get:
cos^(-1)(7/18) ≈ 61.48°
Therefore, the missing value is approximately 61.48°
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A circular pond is 21 m in diameter. It is surrounded by 3.5 m wide path. Find the
cost of constructing the path at the rate of Rs. 25 per m2.
The cost of constructing the path at the rate of Rs. 25 per m2 would be Rs. 38,465.
To find the cost of constructing the path, we need to determine the area of the path and then multiply it by the cost per square meter.
The total diameter of the pond and the path is 21m + 3.5m + 3.5m = 28m.
So the radius of the pond is half of the diameter, which is 21m/2 = 10.5m.
The radius of the pond with the path is (21m+3.5m)/2 = 12.25m.
Area of the path = Area of the outer circle - Area of the pond
[tex]= π(12.25)^2 - π(10.5)^2[/tex]
[tex]= π[(12.25)^2 - (10.5)^2][/tex]
= 3.14 x (24.5 + 10.5) x (24.5 - 10.5)
= 3.14 x 35 x 14
= 1538.6 m2 (rounded to one decimal place)
Therefore, the cost of constructing the path at the rate of Rs. 25 per m2 would be:
Cost = Area x Rate per m2
= 1538.6 x 25
= Rs. 38,465.
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which of the following random variables meets the criteria for a hypergeometric distribution? multiple choice question. suppose 30% of the population of have a graduate degree. define x to be the number of adults in a sample of 20 who have earned a graduate degree. the average number of adults who have a graduate degree is 0.7/household. let x be the number of adults in a household who have a graduate degree. out of 50 adults, 10 who have a graduate degree. a sample of 20 is taken. define x to be the number of adults in the sample with a graduate degree.
The following random variable meets the criteria for a hypergeometric distribution: Out of 50 adults, 10 who have a graduate degree. A sample of 20 is taken. Define x to be the number of adults in the sample with a graduate degree.
A hypergeometric distribution is a type of probability distribution that measures the likelihood of a particular number of successes (in this case, adults with a graduate degree) in a sample without replacement.
A random variable that meets the criteria for a hypergeometric distribution is that which meets these conditions: A sample of size n is taken from a population of size N. The population has k successes and N - k failures.
The hypergeometric distribution is used when sampling is done without replacement, where the sample size is small relative to the population size. The sample size is typically less than 10% of the population size. When you have the information of the population, you can use the hypergeometric distribution.
Out of the options provided, the random variable that meets the criteria for a hypergeometric distribution is, Out of 50 adults, 10 who have a graduate degree. A sample of 20 is taken. Define x to be the number of adults in the sample with a graduate degree.
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ten pounds of mixed birdseed sells for $8.25 per pound. the mixture is obtained from two kinds of birdseed, with one variety priced at $5.61 per pound and the other at $8.91 per pound. how many pounds of each variety of birdseed are used in the mixture?
The 2 pounds of $5.61 per pound birdseed are used in the mixture.10 - 2 = 8 pounds of $8.91 per pound birdseed are used in the mixture.
Answer:2 pounds of $5.61 per pound birdseed are used in the mixture.8 pounds of $8.91 per pound birdseed are used in the mixture.
Given information:Ten pounds of mixed birdseed sells for $8.25 per pound. The mixture is obtained from two kinds of birdseed, with one variety priced at $5.61 per pound and the other at $8.91 per pound.To find:Pounds of each variety of birdseed used in the mixture.Solution:Let 'x' be the number of pounds of the first kind birdseed used in the mixture.
Then, (10 - x) will be the number of pounds of the second kind birdseed used in the mixture.The price of the first kind of birdseed per pound is $5.61.Price of x pounds of the first kind of birdseed = 5.61x dollars.The price of the second kind of birdseed per pound is $8.91.Price of (10 - x) pounds of the second kind of birdseed = 8.91(10 - x) dollars.
The total cost of the mixture = $8.25 per pound × 10 pounds= $82.50 dollars.According to the question,$$5.61x+8.91(10-x)=82.5$$Multiply the numbers inside the brackets by multiplying with the negative sign.
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The radius r of a sphere is increasing at a rate of 3 inches per minute. a) Find the rates of changes of the volume when r = 9 inches and r = 36 inches. b) Explain why the rate of change of the volume of the sphere is not constant even though dr/dt is constant.
(a) The rates of changes of the volume are:
When r = 9 inches, dV/dt = 972π cubic inches per minute
When r = 36 inches, dV/dt = 15,552π cubic inches per minute
(b) The rate of change of the volume relates to the radius through a quadratic function not a constant function.
How to find the rates of changes of the volume?a) We know that the formula for the volume of a sphere is V = (4/3)πr³. We can take the derivative with respect to time t to find the rate of change of volume.
dV/dt = 4πr² (dr/dt)
When r = 9 inches, we have:
dV/dt = 4π(9²)(3) = 972π cubic inches per minute
When r = 36 inches, we have:
dV/dt = 4π(36²)(3) = 15,552π cubic inches per minute
b) The rate of change of the volume of the sphere is not constant even though dr/dt is constant because the rate of change of the volume relates to the radius through a quadratic function not a constant function.
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Pls solve these polynomial
(2x-4)(x+5)
(X-2^2)
(3x+1)^2
(3x-1)(2x^2+5x-4)
1- (2x-4)(x+5)
Multiplying using the distributive property, we get:
(2x-4)(x+5) = 2x(x) + 2x(5) - 4(x) - 4(5)
= 2x^2 + 10x - 4x - 20
= 2x^2 + 6x - 20
Therefore, (2x-4)(x+5) simplifies to 2x^2 + 6x - 20.
2-(x-2)^2
Expanding using the formula for the square of a binomial, we get:
(x-2)^2 = x^2 - 4x + 4
Therefore, (x-2)^2 simplifies to x^2 - 4x + 4.
3- (3x+1)^2
Expanding using the formula for the square of a binomial, we get:
(3x+1)^2 = (3x)^2 + 2(3x)(1) + (1)^2
= 9x^2 + 6x + 1
Therefore, (3x+1)^2 simplifies to 9x^2 + 6x + 1.
4- (3x-1)(2x^2+5x-4)
Using the distributive property, we can multiply each term in the first polynomial by each term in the second polynomial:
(3x-1)(2x^2+5x-4) = 3x(2x^2) + 3x(5x) - 3x(4) - 1(2x^2) - 1(5x) + 1(4)
= 6x^3 + 15x^2 - 12x - 2x^2 - 5x + 4
= 6x^3 + 13x^2 - 17x + 4
Therefore, (3x-1)(2x^2+5x-4) simplifies to 6x^3 + 13x^2 - 17x + 4.
if a snowball melts so that its surface area decreases at a rate of 2 cm2/min, find the rate at which the diameter decreases when the diameter is 11 cm.
The rate at which the diameter decreases when the diameter is 11 cm is 4 cm/min.
To solve this question, we need to use the formula for the surface area of a sphere, A = 4πr2. Since the surface area of the snowball is decreasing at a rate of 2 cm2/min, we can set up a differential equation to calculate the rate of change of the radius with respect to time: dA/dt = 2 cm2/min = 8π dr/dt.
We can rearrange this equation to find dr/dt, the rate at which the radius of the snowball is changing: dr/dt = 2 cm2/(8πmin).
We then use the equation for the diameter of a circle, d = 2r, and substitute the rate of change of the radius to get the rate of change of the diameter: dd/dt = 2(dr/dt) = 2 cm2/(4πmin).
Finally, we can plug in the given diameter, 11 cm, to find the rate of decrease in diameter: dd/dt = 11 cm/(4πmin) = 4 cm/min. Therefore, the rate at which the diameter decreases when the diameter is 11 cm is 4 cm/min.
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