The general common factor (GCF) of the polynomial equation [tex]24x^9 + 21x^6 = 0[/tex] is 3x6, which, after factoring, is the common factor of the coefficients and the terms enclosed in brackets.
We must factor out the common terms from both the coefficients and the exponents in order to determine the GCF (Greatest Common Factor) for the polynomial equation 24x9 + 21x6 = 0.
The first step is to determine the coefficients' common factor, which is 3. The equation can be changed to read:
3(8x^9 + 7x^6) = 0
We now need to determine which term the parenthesized terms have in common the most. Since x is raised to a power in both terms, we may factor out x^6 to obtain:
3x^6(8x^3 + 7) = 0
The greatest common factor of the polynomial equation 24x^9 + 21x^6 = 0 is 3x^6.
We can verify this by dividing both terms in the equation by 3x^6. Doing so gives us:
(8x^3 + 7) = 0
This equation has no common factors, and we cannot factor it further. Thus, the GCF of the original polynomial equation 24x^9 + 21x^6 = 0 is 3x^6
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What does the transformation f(x)
shrinks it horizontally
shrinks it vertically
ertically
stretches it horizontally
stretches it vertically
4
f(2x) do to the graph of f(x)?
The x-coordinates of all the points on the graph of f(2x) are half the x-coordinates of the corresponding points on the graph of f(x), which results in a horizontal compression or shrinking of the graph.
What is a graph?
In computer science and mathematics, a graph is a collection of vertices (also known as nodes or points) connected by edges (also known as links or lines).
The transformation f(2x) stretches the graph of f(x) horizontally by a factor of 1/2. In other words, the graph of f(2x) will be compressed horizontally compared to the graph of f(x).
To see why this is the case, consider the effect of replacing x with 2x in the expression for f(x). If we think of f(x) as a set of points in the xy-plane, then each point (x,y) on the graph of f(x) is transformed into the point (2x,y) on the graph of f(2x).
Therefore, this means that the x-coordinates of all the points on the graph of f(2x) are half the x-coordinates of the corresponding points on the graph of f(x), which results in a horizontal compression or shrinking of the graph.
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NO LINKS!! URGENT HELP PLEASE!!!!
If x < 0 and y > 0, determine the sign of the real number.
Answer:
(a) The product xy is negative because one of the factors (x) is negative and the other factor (y) is positive. Therefore, the sign of xy is negative.
(b) The expression x^2y is also negative because x^2 is positive (the square of any real number is positive) and y is positive, so their product is positive. But since x is negative, the overall product is negative.
(c) The expression x/y + x can be written as (x/x)y + x, which simplifies to y + x. Since y is positive and x is negative, the sum y + x could be either positive or negative, depending on which absolute value is greater. If |y| > |x|, then y + x is positive. If |x| > |y|, then y + x is negative.
(d) The expression y-x is positive because y is greater than x and y is positive while x is negative. So the difference y-x is positive.
PROJECTILE A firework is launched from the ground. After 4 seconds, it reaches a
maximum height of 256 feet before returning to the ground 8 seconds after it was
launched. The height of the firework f(x), in feet, after x seconds can be modeled
by a quadratic function.
a. What are the zeros and vertex of f(x)?
b. Sketch a graph of f(x) using the zeros and vertex of the function. Interpret the
key features of the function in the context of the situation.
c. Write a quadratic function that represents the situation.
(a) The vertex is (6, 144),(b) When the fireworks are launched at time x = 0 and return to the earth at time x = 12 seconds, respectively, these times are denoted by zeros in the function,.(c) this is the quadratic function that represents the situation f(x) = -4 + 144.
How to deal with this problem?a. To find the zeros and vertex of the quadratic function, we need to first write it in the standard form:
[tex]f(x) = ax^2 + bx + c[/tex]
where a, b, and c are constants.
The vertex of the function is given by:
x = -b/2a
Since the quadratic function is symmetrical around the vertex, we know that the time it takes to reach the maximum height is halfway between the launch time and the time it hits the ground again. So, the time to reach maximum height is (4 + 8)/2 = 6 seconds.
Therefore, we can set up a system of equations using the information given:
f(4) = 0 (the firework is launched from the ground)
f(6) = 256 (the firework reaches its maximum height)
f(12) = 0 (the firework hits the ground again)
Plugging in the values of x and f(x), we get:
16a + 4b + c = 0
36a + 6b + c = 256
144a + 12b + c = 0
Solving this system of equations, we get:
a = -4
b = 48
c = 0
Therefore, the quadratic function that represents the situation is:
[tex]f(x) = -x^2 + 48x[/tex]
The zeros of the function can be found by setting f(x) = 0:
[tex]f(x) = -4x^2 + 48x[/tex]
0 = x(-4x + 48)
x = 0 (the firework is launched from the ground)
x = 12 (the firework hits the ground again)
The vertex can be found using the formula:
x = -b/2a = -48/(-8) = 6
So the vertex is (6, 144).
b. Using the zeros and vertex, we can sketch a graph of f(x):
The quadratic function's graph
Considering the function's primary characteristics in light of the circumstances:
The peak height of the fireworks, which occurs at x = 6 seconds and f(6) = 256 feet, is represented by the function's vertex.
The firework is at ground level at x = 0 (launch time) and x = 12 seconds (when it reaches the ground again), which are represented by zeros in the function.
The graph's form suggests that the firework rises before falling again, which is consistent with the scenario given.
c. The quadratic function that represents the situation is:
[tex]f(x) = -4x^2 + 48x[/tex]
This function can be simplified by factoring out -4:
[tex]f(x) = -4( x^2- 12x)[/tex]
Completing the square:
[tex]f(x) = -4( x^2- 12x + 36 - 36)[/tex]
[tex]f(x) = -4( (x^2-6)- 36)[/tex]
[tex]f(x) = -4(x^2-6) + 144[/tex]
This form of the function shows that the vertex is (6, 144), and that the maximum height is 144 feet.
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Achieve $4,000 in three years at 4.5% simple interest.
In order to achieve $4,000 in three years at 4.5% simple interest, the principal must be equal to $29,629.63.
How to calculate the simple interest and future value?In Mathematics, simple interest can be calculated by using this formula:
S.I = PRT or S.I = A - P
Where:
S.I represents the simple interest.P is the principal or starting amount.R is the interest rate.A is the future value.T represents the time measured in years.By substituting the given parameters into the simple interest formula, we have;
4,000 = P × 4.5/100 × 3
4,000 = P × 0.045 × 3
4,000 = 0.135P
Principal, P = 4,000/0.135.
Principal, P = $29,629.63
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A factory worker can make 15 products in 45 minutes. What is the workers unit rate of completion?
The required unit rate is 0.333 products per minute.
What is a product's utilisation rate?
A measurement of how much of a product a user consumes in a certain amount of time; users can be classified as heavy, moderate, or light.
Given that a factory worker can make 15 products in 45 minutes.
We are to find the unit rate.
We will be using the unitary method to solve the given problem.
In 45 minutes, the number of products made by the worker = 15
Therefore, in 1 minute, the number of products made by the worker is given by
= Number of products / Amount of time taken
= 15/45
= 0.333
Thus, the required unit rate is 0.333 products per minute.
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Miss Johnson's guests were to arrive at 6:15 P.M., but because of a bad storm they were 2/5 of an hour late. What time did they arrive for dinner?
the guests arrived for dinner at 6:39 P.M.which is solved by according to given question.
How to solve the question?
To solve this problem, we need to first convert the fraction of an hour that Miss Johnson's guests were late into minutes. We know that 1 hour is equal to 60 minutes, so we can find the number of minutes the guests were late by multiplying 2/5 by 60:
2/5 hour * 60 minutes/hour = 24 minutes
So the guests were 24 minutes late. To find out what time they arrived, we need to add 24 minutes to the original arrival time of 6:15 P.M.:
6:15 P.M. + 24 minutes = 6:39 P.M.
Therefore, the guests arrived for dinner at 6:39 P.M.
It's important to note that fractions can often be confusing when dealing with time calculations. In this case, we converted the fraction of an hour to minutes to make the calculation easier. Additionally, it's always a good idea to double-check your work to ensure that your answer makes sense in the context of the problem.
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A vending machines coin box contains nickels dimes and quarters. The total number of coins in the box is 292 the number of dimes is three times the number of nickels and quarters together at the box contains $29.95. find the number of nickels dimes and quarters that it contains.
There are 32 quarters, 225 dimes, and 53 nickels in the vending machine.
Let's denote the number of nickels by N, the number of dimes by D, and the number of quarters by Q.
From the first sentence, we know that:
N + D + Q = 292 (total number of coins)
From the second sentence, we know that:
D = 3(N + Q) (the number of dimes is three times the number of nickels and quarters together)
From the third sentence, we know that:
0.05N + 0.1D + 0.25Q = 29.95 (total value of the coins is $29.95)
Now we can substitute the second equation into the third equation to get:
0.05N + 0.1(3(N + Q)) + 0.25Q = 29.95
0.05N + 0.3N + 0.1Q + 0.25Q = 29.95
0.35N + 0.35Q = 29.95
N + Q = 85
We can now substitute this last equation into the first equation to get:
N + D + Q = 292
N + D + 85 = 292
N + D = 207
We can substitute the second equation into this last equation to get:
N + 3(N + Q) = 207
4N + 3Q = 207
We can now solve the system of equations consisting of the last two equations we derived:
N + Q = 85
4N + 3Q = 207
Multiplying the first equation by 4 and subtracting it from the second equation:
4N + 3Q - 4(N + Q) = 207 - 4*85
-N = -53
N = 53
Substituting this value into the equation N + Q = 85:
53 + Q = 85
Q = 32
Finally, we can use the equation D = 3(N + Q) from earlier to find the value of D:
D = 3(N + Q)
D = 3(53 + 32)
D = 225
Therefore, the vending machine contains 53 nickels, 225 dimes, and 32 quarters.
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.
An investment pays 14% interest compounded weekly. What percent, as a decimal, is the effective annual yield? Enter your
answer as a decimal rounded to four decimal places.
Provide your answer below:
The effective annual yield of the investment is 0.1501
What percent is the effective annual yield?To find the effective annual yield, we need to use the formula:
(1 + r/n)^n - 1
where r is the annual interest rate and n is the number of times the interest is compounded per year.
In this case, r = 0.14 (14% expressed as a decimal), and n = 52 (since interest is compounded weekly).
Plugging these values into the formula, we get:
(1 + 0.14/52)^52 - 1 = 0.1501
Therefore, the effective annual yield is 0.1501, which is equivalent to 15.01% (rounded to two decimal places).
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An amusement park has three roller coasters, the "Falcon Flyer placed at (50, 300), the "Sprinter" placed at (400, 550), and the "Air Rider" placed at (800, 250). All measurements are in meters. You are at a point half way between the "Falcon Flyer" and the "Sprinter", see a long line, and decide to take a shortcut to the "Air Rider". How far will you walk on this shortcut if it follows a straight path? Round your answer to the nearest meter
Answer: 601 meters
Step-by-step explanation:
First, let's find the midpoint between the "Falcon Flyer" and the "Sprinter".
The x-coordinate of the midpoint is (50 + 400)/2 = 225.
The y-coordinate of the midpoint is (300 + 550)/2 = 425.
So the midpoint is (225, 425).
Now we need to find the distance between the midpoint and the "Air Rider". Using the distance formula:
d = sqrt[(800 - 225)^2 + (250 - 425)^2]
d = sqrt[(575)^2 + (-175)^2]
d = sqrt[330625 + 30625]
d = sqrt(361250)
d ≈ 601.041
So the distance you will walk on this shortcut is approximately 601 meters.
1 Suppose another student says he spends $29 each
week on entertainment. Will the mean and median
increase or decrease?
decreas
2 What is the new mean when the value from problem 1
is included in the data set?
Show your work. For elementary kids
Answer:
Step-by-step explanation:
Elijah is using a ladder to hang decorations for the holidays outside. He places the ladder 4 feet from the base of tree so he can reach a branch that is 12 feet from the ground. What is the angle of elevation of the ladder?
Round to the nearest tenths place if necessary.
The angle of elevation of the ladder is approximately 71.6 degrees.
What is the angle of elevation?To find the angle of elevation of the ladder, we can use trigonometry. The ladder forms a right triangle with the ground and the tree.
The base of the triangle is 4 feet, the height is 12 feet, and the hypotenuse is the length of the ladder.
Using the trigonometric function tangent (tan), we can write:
tan(angle) = opposite/adjacent
In this case, the opposite side is the height of the tree (12 feet) and the adjacent side is the base of the triangle (4 feet).
Therefore, we can calculate the angle of elevation as follows:
tan(angle) = 12/4
angle = arctan(12/4)
Using a calculator or a trigonometric table, we can find that arctan(12/4) is approximately 71.6 degrees.
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Evaluate the indefinite integral given below.
The indefinite integral when evaluated has a solution of 2cot(2x⁵ - 5x) + C
Evaluating the indefinite integralFrom the question, we have the following parameters that can be used in our computation:
The integral of (10 - 20x⁴)csc²(2x⁵ - 5x)
³
This can be expressed as
∫(10 - 20x⁴)csc²(2x⁵ - 5x) dx
The above is a complex expression
So, we make use of a graphing tool to evaluate the solution
Using a graphing tool, we have
Step 1:
[tex]\frac{4\cos(10x)\sin(4x^5) - 4\sin(10x)\cos(4x^5)}{sin^2(4x^5) - 2\sin(10x)\sin(4x^5) + cos^2(4x5) - 2\cos(10x)\cos(4x5)+ \sin^2(10x) + \cos^2(10x)} + C[/tex]
When simplified, we get
2cot(2x⁵ - 5x) + C
hence, the solution is 2cot(2x⁵ - 5x) + C
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Write this number in standard form 3 thousands, 16 tens,7 ones
Find the intercepts and asymptotes, use limits to describe the behavior at the vertical asymptotes, and analyze and draw the graph of the given rational function. f(x)
The function has vertical asymptotes at x = -3/2 and x = 1, a horizontal asymptote at y = 0, and a y-intercept at (0, -2/3).
Describe Function?In mathematics, a function is a relation between two sets that associates each element of the first set, called the domain, with a unique element of the second set, called the range. In other words, a function maps each input value to a unique output value.
The notation used to represent a function is f(x), where f is the name of the function and x is the input value. The output value is then given by the expression f(x).
Functions can be represented in various ways, such as tables, graphs, equations, and verbal descriptions. They are used to model real-world phenomena, analyze data, and solve problems in various fields, including science, engineering, economics, and finance.
To find the intercepts of the rational function, we set the numerator equal to zero and solve for x:
2/(2x² - x - 3) = 0
2 = 0 (there is no solution for x that makes the numerator zero)
Therefore, the rational function has no x-intercepts.
To find the y-intercept, we set x = 0:
f(0) = 2/(2(0)² - 0 - 3) = -2/3
Therefore, the y-intercept is (0, -2/3).
To find the vertical asymptotes, we set the denominator equal to zero and solve for x:
2x² - x - 3 = 0
Using the quadratic formula, we get:
x = (1 ± √(1 + 24))/4
x = (1 ± 5)/4
x = -3/2, 1
Therefore, the rational function has vertical asymptotes at x = -3/2 and x = 1.
To describe the behavior at the vertical asymptotes, we can use limits. Let's consider the vertical asymptote at x = -3/2:
lim x → -3/2+ f(x) = 2/(2(-3/2)² - (-3/2) - 3) = -∞
lim x → -3/2- f(x) = 2/(2(-3/2)² - (-3/2) - 3) = +∞
This means that as x approaches -3/2 from the right, the function approaches negative infinity, and as x approaches -3/2 from the left, the function approaches positive infinity. Therefore, the function has a vertical asymptote at x = -3/2 with a vertical (or infinite) discontinuity.
Let's now consider the vertical asymptote at x = 1:
lim x → 1+ f(x) = 2/(2(1)² - (1) - 3) = +∞
lim x → 1- f(x) = 2/(2(1)² - (1) - 3) = -∞
This means that as x approaches 1 from the right, the function approaches positive infinity, and as x approaches 1 from the left, the function approaches negative infinity. Therefore, the function has a vertical asymptote at x = 1 with a vertical (or infinite) discontinuity.
To analyze and draw the graph of the rational function, we can use the intercepts, asymptotes, and behavior at the vertical asymptotes that we found earlier. We can also find the horizontal asymptote by looking at the degree of the numerator and denominator:
Degree of numerator = 0
Degree of denominator = 2
Therefore, the horizontal asymptote is y =0
As we can see from the graph, the function has vertical asymptotes at x = -3/2 and x = 1, a horizontal asymptote at y = 0, and a y-intercept at (0, -2/3). The behavior at the vertical asymptotes is a vertical (or infinite) discontinuity.
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The complete question is:
Hey can you please help me because I don’t understand this question
The area of the shaded region is 88π square inches.
What is the area of the circle?To find the area of the shaded region, we need to subtract the area of the inner circle (with a radius of 9 inches) from the area of the outer circle (with a radius of 13 inches).
The area of a circle is given by the formula A = πr^2, where r is the radius.
Area of outer circle = π * (13²) = 169π square inches
Area of inner circle = π * (9²) = 81π square inches
Area of shaded region = Area of outer circle - Area of inner circle
= 169π - 81π
= 88π square inches
So, the area of the shaded region is 88π square inches.
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See text below
A ring-shaped region is shown below. Its inner radius is 9 in, and its outer radius is 13 in.
9 in
13 in
Find the area of the shaded region.
Use 3.14 for π. Do not round your answer.
2
in2
X
G
Downtown Mathville is laid out as a 6 x 6 square grid of streets (see diagram below). Your apartment is located at the southwest corner of downtown Mathville (see point H). Your math classroom is located at the northwest corner of downtown Mathville (see point M). You know that it is a 12-block walk to math class and that there is no shorter path. Your curious roommate (we’ll call her Curious Georgia) asks how many different paths (of length 12 blocks – you don’t want to back track or go out of your way) could you take to get from your apartment to the math class. It should also be clear that no shorter path exists. Can you solve Curious Georgia’s math problem?
Answer: 924 paths
Step-by-step explanation:
Since there is no shorter path, we know that the path must consist of 6 blocks to the north and 6 blocks to the east. Thus, the problem is equivalent to finding the number of ways to arrange 6 N's (for north) and 6 E's (for east) in a sequence such that no two N's are adjacent and no two E's are adjacent.
Let's denote N by 1 and E by 0. Then the problem is equivalent to finding the number of 12-digit binary sequences (i.e., sequences consisting of 0's and 1's) such that there are no consecutive 1's or consecutive 0's.
We can solve this problem using dynamic programming. Let F(n,0) be the number of n-digit binary sequences that end in 0 and have no consecutive 0's, and let F(n,1) be the number of n-digit binary sequences that end in 1 and have no consecutive 1's. Then we have the following recurrence relations:
F(n,0) = F(n-1,0) + F(n-1,1)
F(n,1) = F(n-1,0)
with initial values F(1,0) = 1 and F(1,1) = 1.
Using these recurrence relations, we can compute F(6,0) and F(6,1), and the total number of valid sequences is F(6,0) + F(6,1) = 132. Therefore, there are 132 different paths of length 12 blocks from your apartment to the math class.
Suppose you wish to borrow $400 for five weeks and the amount of interest you must pay is $25 per $100 borrowed. What is the APR at which you are borrowing money?
If we borrowed amount of $400 for 5 weeks, then the APR at which the money is borrowed is 260.71%.
First, we calculate the total interest paid for borrowing $400 for five weeks.
The interest rate is $25 per $100 borrowed, so for $400 borrowed, the interest paid is : $25 × 4 = $100,
So, the total amount that needs to be paid-back is $400 (the original borrowed amount) plus $100 (the interest paid) = $500,
Next, we can use the APR formula to calculate, which is
⇒ APR = (Interest Paid/Amount Borrowed)/(Number of days) × 365 × 100,
In this case, the total interest paid is $100 and the total amount borrowed is $400, and
The number of days amount is borrowed is = 5×7 = 35 days,
Substituting the values,
We get,
⇒ APR = (100/400)/35 ×365 × 100 ≈ 260.71%
Therefore, the APR at which the money is being borrowed is 260.71%.
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PLEASE HELP!!!
Which one is the 10 x 8 face as the base ?
Which one is the 10 x 3 face as the base
10 x 8 face as the base for prism 1
10 x 3 face as the base for prism 2
How to find rectangular prism base?To find the area of the base, you simply multiply the length and width:
Base area = length x width = lw
Therefore, for rectangular prism 1 we get:
10 x 8
For rectangular prism 2 we get:
10 x 3
How to find triangular prism base?Similarly, if the base of the prism is a triangle, you would need to use the formula for the area of a triangle, which is:
Base area = 1/2 x base x height
where base and height are the base and height of the triangle respectively.
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20a +5,600 < 21,000 solve the following inequality and answer in interval notation
Answer: 20a +5,600 < 21,000
move the content to the right
20a < 21,000 -5600
calculate
20a<15400
20a <15400
divide both sides of the inequality by 20
a<770
Lester Hollar is vice president for human resources for a large manufacturing company. In recent years, he has noticed an increase in absenteeism that he thinks is related to the general health of the employees. Four years ago, in an attempt to improve the situation, he began a fitness program in which employees exercise during their lunch hour. To evaluate the program, he selected a random sample of eight participants and found the number of days each was absent in the 6 months before the exercise program began and in the 6 months following the exercise program. Following are the results.
Employee Before After
1 8 7
2 7 3
3 8 2
4 8 4
5 6 5
6 7 10
7 6 4
8 8 9
At the 0.050 significance level, can he conclude that the number of absences has declined?
a. Compute the test statistic.
b. Compute the p-value.
The p-value can also be calculated using a t-distribution table or a statistical software package. Using a two-tailed test with 7 degrees of freedom and a significance level of 0.05, we obtain a p-value of 0.073.
How to solve the question?
To determine whether the fitness program has had a significant effect on reducing employee absenteeism, we need to conduct a hypothesis test.
Null hypothesis: The average number of absences before and after the fitness program are the same.
Alternative hypothesis: The average number of absences after the fitness program is less than before the program.
To test this hypothesis, we can use a one-tailed paired t-test with a significance level of 0.05. We will calculate the difference between the number of absences before and after the program for each employee, and then compute the mean and standard deviation of the differences. The t-test statistic will then be calculated as the mean difference divided by the standard deviation of the differences, multiplied by the square root of the sample size.
Using the given data, we calculate the differences and obtain the following results:
Employee Before After Difference (d) d²
1 8 7 -1 1
2 7 3 -4 16
3 8 2 -6 36
4 8 4 -4 16
5 6 5 -1 1
6 7 10 3 9
7 6 4 -2 4
8 8 9 1 1
Mean difference (d-bar) = -1.25
Standard deviation of differences (s) = 3.27
Sample size (n) = 8
The t-test statistic can now be calculated as:
t = (d-bar / (s / √(n))) = (-1.25 / (3.27 / √(8))) = -1.63
The degrees of freedom for the t-test is n-1 = 7, which can be used to obtain the p-value from a t-table or calculator. Using a one-tailed test with a significance level of 0.05 and 7 degrees of freedom, the critical t-value is -1.895.
Since our calculated t-value (-1.63) is greater than the critical t-value (-1.895), we fail to reject the null hypothesis. In other words, we do not have sufficient evidence to conclude that the fitness program has resulted in a significant reduction in employee absenteeism.
The p-value can also be calculated using a t-distribution table or a statistical software package. Using a two-tailed test with 7 degrees of freedom and a significance level of 0.05, we obtain a p-value of 0.073. Since this p-value is greater than the significance level, we again fail to reject the null hypothesis.
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The function f(x) = 1.85x2 models the cost of a square carpet, where x is the length in feet. Find the average rate of change for f, to the nearest tenth, over the interval 10 ≤ x ≤ 20.
To find the average rate of change of the function f(x) = 1.85x^2 over the interval 10 ≤ x ≤ 20, we need to find the difference in the function values at the endpoints of the interval and divide by the length of the interval.
The function value at x = 10 is:
f(10) = 1.85(10)^2 = 185
The function value at x = 20 is:
f(20) = 1.85(20)^2 = 740
The length of the interval is:
20 - 10 = 10
So the average rate of change of the function over the interval 10 ≤ x ≤ 20 is:
(f(20) - f(10)) / (20 - 10) = (740 - 185) / 10 = 55.5
Rounding to the nearest tenth, the average rate of change of the function over the interval 10 ≤ x ≤ 20 is approximately 55.5.
I need help on all of them I’ll take some if not all!
Note that the angles are found using the principle of the circle theorems.
What are the measure of the angels given?The angle of the circumference is half of the angle at the center of the circle by an arc.
AB = 78°
∠5 = 39°
Angles intercepted by the same arc are equal.
∠4 = 39°
FE= 105°
∠16 =105°
ED = 27°
∠17 =27°
CD = 42°
∠10 =21°
∠3 =21°
The angle of the semi-circle is 90°.
∠2 =90°
∠8=∠9 = (180-48)/2
∠8= 66°
∠9= 66°
∠7=90°-∠8 = 90°-66°
∠7=24°
∠17 = 180°-∠15-∠16
∠17 = 180°-48°-105°
∠17 =27°
∠6=∠15/2 = 48/2
∠6=24°
∠21 = 180°-∠7-∠16
∠21 = 180°-24°-105°
∠21 =51°
∠19 =51°
∠18 = 180°-∠17-∠6
∠18 = 180°-27°-24°
∠18 = 129°
∠20 = 129°
BC = 60°
∠1 = 60/2
∠1 =30°
∠11=180°-∠1-∠2
∠11=180°-30°-90°
∠11=60°
∠13=60°
∠12=180-∠11
∠12=180°-60°
∠12=120°
∠14=120°
∠15=48°
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Can you prove that they are congruent? If so, explain how.
The correct statement regarding the congruence of the two triangles is given as follows:
Yes. We are two right triangles with congruent hypotenuses and a shared congruent side. The triangles are congruent by the HL Triangle Congruence Theorem.
What is the Pythagorean Theorem?The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
The theorem is expressed as follows:
c² = a² + b².
In which:
c is the length of the hypotenuse.a and b are the lengths of the other two sides (the legs) of the right-angled triangle.The triangles in this problem have:
A shared side.Congruent hypotenuses.Hence, applying the Pythagorean Theorem, the missing side also has the same measure for both triangles, hence they are congruent by the HL Congruence Theorem.
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O WEEK 4: QUADRATIC EQUATIONS AND FUNCTIONS
Finding intercepts of a nonlinear function give
The graph of a function is given below.
Give all y-intercepts and x-intercepts shown.
(a) y-intercept(s):
(b) x-intercept(s):
If there is more than one answer, separate them with commas.
From the graph we can conclude that the x-intercept is (-2.0) and the y-intercept is (0, -4).
Describe Graph?The graph is a logical representation of the data, to put it simply. It makes it easier for us to comprehend the facts. The numerical information gleaned via observation is referred to as data.
"Data" is derived from the Latin term datum, which means "something given."
Data are gradually gathered through observation after creating a study question. The data is then summarised, categorised, sorted, and graphically presented.
A variety of objectives are served by data and information: Data is the source of all information, whereas information can be inferred from data.
Here in the question,
From the graph we can see that the line intersects x-axis and y-axis at one point each.
So, the points where they intersect:
x-intercept is (-2.0).
y-intercept is (0, -4).
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The complete question is:
Finding intercepts of a nonlinear function give
The graph of a function is given below.
Give all y-intercepts and x-intercepts shown.
(a) y-intercept(s):
(b) x-intercept(s):
If there is more than one answer, separate them with commas.
100 points and I will give brainlist but before I get released, I have to verify answers
A simplification of the fractions (-5/8) ÷ (-3/4) is equal to: B. -20/24.
The step in which Johnetta made her error include the following: A. step 1.
What is a fraction?In Mathematics and Geometry, a fraction simply refers to a numerical quantity (numeral) which is not expressed as a whole number. This ultimately implies that, a fraction is simply a part of a whole number.
Based on the information provided above, the division can be calculated as follows;
Fraction = (-5/8) ÷ (-3/4)
Fraction = -5/8 × (-4/3)
Fraction = -20/24
For Johnetta, we have:
Fraction = 7/9 ÷ 3/8
Fraction = 7/9 × 8/3
Fraction = 56/27
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Is (-1, -10) a solution to this system of equations?
y = -8x + 7
y = 6x + 5
yes
no
Answer:
no
Step-by-step explanation:
to check if (-1,-10) is a solution to the system of equations y = -8x + 7 and y = 6x + 5, we substitute x=-1 and y=-10 into both equations and check if both equations hold true.
y = -8x + 7 -10 = -8(-1) + 7 -10 = 8 + 7 -10 ≠ 15
y = 6x + 5 -10 = 6(-1) + 5 -10 = -1
Since (-1,-10) does not satisfy both equations simultaneously, it is not a solution to the system of equations.
Finding the Mean and Median 42,5,25,2,35
The mean of the given set of numbers is 21.8. and median is 25.
Define meanIn mathematics and statistics, the mean is a measure of central tendency that represents the average value of a set of numbers. It is calculated by adding up all the numbers in the set and then dividing by the total number of values. The mean is also known as the arithmetic mean or average.
To find the mean and median of the given set of numbers, we can follow these steps:
Arrange the numbers in order from smallest to largest: 2, 5, 25, 35, 42.
To find the mean, add up all the numbers and divide by the total number of numbers:
Mean = (2 + 5 + 25 + 35 + 42) / 5
= 109 / 5
= 21.8
Therefore, the mean of the given set of numbers is 21.8.
To find the median, we need to find the middle number in the ordered list. If there is an odd number of values, the median is the middle number. If there is an even number of values, the median is the average of the two middle numbers.
In this case, there are 5 numbers, so the median is the middle number, which is 25.
Therefore, the median of the given set of numbers is 25.
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Please help if your good at (FUNCTION TABLE) and (nonlinear or liner or nor or both)
Please help ASAP look at the picture !
Answer:
Linear
Step-by-step explanation:
The table represents a consistent function and is therefore linear.
i need help with all 4 thanks
Answer: 5,8,6,1
Step-by-step explanation:
math
Can you help with me with question 3.
The experimental probability of tossing a 3 is 22% ( option D).
Experimental probability, which is also known as Empirical probability, is based on actual experiments and adequate recordings of the occurring of events. An experiment can be repeated a fixed number of times and each repetition is known as a trial. The formula for the experimental probability is defined by;
Probability of an Event P(E) = Number of times an event occurs / Total number of events
From the table it is visible that the occurrence of tossing 3 is 11 times.
So by the definition of experimental probability the possibility is 11/50
As the table given is the result for tossing a number cube 50 times.
In 50 times the possibility is 11
In 1 time the possibility is 11/50
In 100 times the possibility is (11×100)/50
= 22
Hence, the experimental probability of tossing a 3 is 22%.
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