Answer:
We do not have enough information to find the exact value of f(2.5) without additional assumptions about the nature of the exponential function. However, we can make an estimate using the given data and the properties of exponential functions.
First, we can write the general form of an exponential function as:
f(x) = a * b^x
where a is the initial value or y-intercept, and b is the base or growth factor. We can use the two given data points to set up a system of equations and solve for a and b:
f(-1) = a * b^(-1) = 18
f(5) = a * b^5 = 75
Dividing the second equation by the first equation, we get:
f(5) / f(-1) = (a * b^5) / (a * b^(-1)) = b^6 = 75 / 18 = 25 / 6
Taking the sixth root of both sides, we get:
b = (25 / 6)^(1/6) ≈ 1.472
Substituting this value of b into the first equation, we get:
a = f(-1) / b^(-1) = 18 / 1.472 ≈ 12.223
Therefore, we have the exponential function:
f(x) ≈ 12.223 * 1.472^x
Using this function, we can estimate the value of f(2.5) as:
f(2.5) ≈ 12.223 * 1.472^(2.5) ≈ 34.311
Note that this is only an estimate, and the exact value of f(2.5) may be different depending on the specific nature of the exponential function.
() Which expression is equivalent to (x^2/x^-4)^5
The expression that is equivalent to [tex](\frac{x^2}{x^-4})^5[/tex] is x³⁰
How to determine the equivalent expressionFrom the question, we have the following parameters that can be used in our computation:
[tex](\frac{x^2}{x^-4})^5[/tex]
An equivalent expression is a different way of writing the same mathematical statement using equivalent mathematical operations or properties.
Evaluate the quotients using the law of indices
So, we have the following representation
(x⁶)⁵
Remove the bracket using the law of indices
So, we have the following representation
x³⁰
Hence, the solution to the expression is x³⁰
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10 points if someone gets right
Sam believes that 1/2 % is equivalent to 50%. Is he correct? Why or why not?
Step-by-step explanation:
just ignore the % sign and answer :
is 1/2 equivalent to 50 ? yes or no ?
no, of course.
1/2 = 0.5
50 = 50
clearly they are different.
Sam is confused, because 50% = 1/2 = 0.5.
but 50% is NOT 1/2%
1/2% is half of 1%, which by itself is 1/50 of 50%.
1/2% = 1/50/2 of 50% = 1/100 of 50% =
= 0.01 × 0.5 = 0.005
The height (in feet) of a thrown ball on Neptune t seconds into flight can be described by the expression 2 + 3t - 18t2. What is the time (in seconds) the ball was in the air?
In the word problem, the time (in seconds) the ball was in the air is D)0.50 seconds.
What is word problem?
Word problems are often described verbally as instances where a problem exists and one or more questions are posed, the solutions to which can be found by applying mathematical operations to the numerical information provided in the problem statement. Determining whether two provided statements are equal with respect to a collection of rewritings is known as a word problem in computational mathematics.
Here expression which describes height is,
h(t)= [tex]-18t^2+3t+2[/tex]
Now h(t)=0 then,
=> [tex]-18t^2+3t+2=0[/tex]
=> [tex]18t^2-3t-2=0[/tex]
=> [tex]18t^2-3t=2[/tex]
=> 3t(6t-1)=2
=> 3t=2 , 6t-1=2
=> t=2/3 , 6t=3
=> t=2/3 , t=1/2
=> t= 0.5 seconds.
Hence the time (in seconds) the ball was in the air is D)0.50 seconds.
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-2y=5x-6 in standard form
Answer: 5x + 2y = 6
Step-by-step explanation:
The standard form is Ax + By = C
Subtract 5x from each side:
- 5x - 2y = - 6
The first term in the standard form must be positive, so multiply by -1 to change the sign.
5x + 2y = 6
Hope this helps!
Conduct the appropriate test of significance (z score or student’s t/t test) for a research
situation. You should be able to read a scenario and identify the test you need to conduct
as well as be able to:
a. Determine if you need to use a one-tail or a two-tailed test
b. Determine if it is a one or two sample test.
c. Select the appropriate alpha level
d. Make a decision about the test significance and interpret the results.
The difference between the two groups is likely due to chance and the two groups likely have the same mean.
To conduct the appropriate test of significance for a research situation, you must first identify whether you need to use a one-tailed or two-tailed test. A one-tailed test is used when you are looking to see if the mean of one group is greater or less than the mean of another group. A two-tailed test is used when you are testing the null hypothesis that the two groups have the same mean.
Once you have identified the type of test, you must determine if it is a one or two sample test. A one sample test is used when you are comparing the mean of one group to a known population mean, whereas a two sample test is used when you are comparing the means of two separate groups.
Next, you must select the appropriate alpha level. Alpha levels are a measure of the significance of the test and refer to the probability of rejecting the null hypothesis when it is actually true. Generally, an alpha level of 0.05 is used in research settings.
Once you have selected the appropriate test and alpha level, you can make a decision about the test significance. This is done by comparing the calculated test statistic to the critical value in the test statistic table. If the calculated test statistic is larger than the critical value, the test is statistically significant and the null hypothesis can be rejected. If the calculated test statistic is smaller than the critical value, the test is not statistically significant and the null hypothesis cannot be rejected.
Finally, you must interpret the results of the test. If the test is statistically significant, it means that the difference between the groups is not likely due to chance, and therefore the two groups are likely to have different means. If the test is not statistically significant, it means that the difference between the two groups is likely due to chance and the two groups likely have the same mean.
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Vocabulary Matching
1. apathy
2. competent
3. expectations
4. value
positive or negative
fear of failure or success
Ahmein doesn't care if he does well
or not.
Javier knows he is able to build a
birdhouse.
The correct matches for the vocabulary would be :
Apathy - Ahmein is unconcerned with his academic performance.Competent - Javier is aware that he can construct a birdhouse.Expectations - Fear of failure or success Value - Positive or negative How to explain the vocabulary ?Apathy is a lack of interest or passion for anything. The line "Ahmein doesn't care if he does well or not" describes apathy since Ahmein is apathetic about whether he succeeds or fails.
Being competent is having the knowledge and skills required to complete a task successfully which describes Javier as he is aware that he can construct a birdhouse.
Expectations are convictions or presumptions regarding future events. Value is a term used to describe something's importance or worth.
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Answer:
1. apathy = Trudy doesn't care about doing well in school.
2. competent = Javier knows he is able to build a birdhouse.
3. expectations = fear of failure or success
4. autonomy = Alfonzo likes to make choices on his own.
5. stress = Quincy feels anxious and distressed about a test.
On your last two math tests, you had scores of 81 and 94. What must you score on the next test to average exactly a 90 on all three tests?
To average a 90 on all three tests, you must score a 95 on the next test.
To find the score you need to average exactly a 90 on all three tests, you can use the formula for the mean (average) of a set of numbers:
Mean = (Sum of all numbers) / (Total number of numbers)
Let's call the score you need on the next test x. We can plug in the known values and solve for x:
90 = (81 + 94 + x) / 3
Multiply both sides by 3 to get rid of the fraction:
270 = 81 + 94 + x
Subtract 81 and 94 from both sides to isolate x:
95 = x
So, you need to score a 95 on the next test to average exactly a 90 on all three tests.
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Find The Amplitude, Asymptotes, Complete Period, Period, And Phase Shift For Each Of The Following Trigonometric Functions If Exists. A. \( F(X)=4 \Sin [5(X-\Pi)] \) B. \( G(X)=-\Sec \Left[3\Left(X-\Frac{\Pi}{2}
A. Amplitude: 4, Asymptotes: None, Complete Period: [tex]\(\frac{2\pi}{5}\)[/tex], Period: [tex]\(2\pi/5\)[/tex], Phase Shift: [tex]\(\frac{\pi}{5}\)[/tex].
B. Amplitude: 1, Asymptotes: [tex]\(x=\frac{\pi}{2}+\frac{2\pi}{3}n\)[/tex], Complete Period: [tex]\frac{2\pi}{3}\)[/tex], Period: [tex]\(2\pi/3\)[/tex], Phase Shift: [tex]\(\frac{\pi}{6}\)[/tex].
To find the amplitude, asymptotes, complete period, period, and phase shift for each of the given trigonometric functions, we need to use the standard form of the trigonometric functions:[tex]\[f(x)=A\sin(Bx+C)+D\][/tex] and [tex]\[g(x)=A\sec(Bx+C)+D\][/tex]
For function f(x), we have:
A = 4, B = 5, C = -π, and D = 0
The amplitude is |A| = |4| = 4
The period is [tex]\(\frac{2\pi}{|B|}[/tex] = [tex]\frac{2\pi}{5}\)[/tex]
The phase shift is [tex]\(-\frac{C}{B}[/tex] = [tex]-\frac{-\pi}{5}[/tex] = [tex]\frac{\pi}{5}\)[/tex]
There are no asymptotes for the sine function.
For function g(x), we have:
A = -1, B = 3, C = -π/2, and D = 0
The amplitude is |A| = |-1| = 1
The period is [tex]\(\frac{2\pi}{|B|}[/tex] = [tex]\frac{2\pi}{3}\)[/tex]
The phase shift is [tex]\(-\frac{C}{B}[/tex] = [tex]-\frac{-\pi/2}{3}[/tex] = [tex]\frac{\pi}{6}\)[/tex]
The asymptotes occur when the cosine function is equal to zero, so the asymptotes are at [tex]\(x=\frac{\pi}{2}+\frac{2\pi}{3}n\)[/tex] , where n is an integer.
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Please help me solve
The area of the hexagon is given by A = 585 units²
What is the area of a hexagon?Six equilateral triangles make create a regular hexagon, which has six congruent sides and angles. The following is the formula to get the area of a regular hexagon.
Area of a hexagon A = 3 (√3)/ 2 ) a²
where, a represent the length of a side of the regular hexagon
Given data ,
Let the area of the hexagon be represented as A
Now , the value of A is
Let the side length of the hexagon be a = 15
Now , area of a hexagon A = 3 (√3)/ 2 ) a²
On simplifying , we get
The area of hexagon A = 3 (√3)/ 2 ) ( 15 )²
The area of hexagon A = 584.56715 units²
The area of hexagon A = 585 units²
Therefore , the value of A is 585 units²
Hence , the area of the hexagon is A = 585 units²
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Use a truth table to determine whether the following two statement forms are equivalent:(p∧q)∨∼(p∨q) and (p∨∼q)∧(∼p∨q)
To determine whether the two statement forms are equivalent, we need to create a truth table for each statement form and compare the results.
First, let's create a truth table for the statement form (p∧q)∨∼(p∨q):
p
q
p∧q
p∨q
∼(p∨q)
(p∧q)∨∼(p∨q)
T
T
T
T
F
T
T
F
F
T
F
F
F
T
F
T
F
F
F
F
F
F
T
T
Next, let's create a truth table for the statement form (p∨∼q)∧(∼p∨q):
p
q
∼q
∼p
p∨∼q
∼p∨q
(p∨∼q)∧(∼p∨q)
T
T
F
F
T
T
T
T
F
T
F
T
F
F
F
T
F
T
F
T
F
F
F
T
T
T
T
T
Comparing the results of the two truth tables, we can see that the two statement forms are not equivalent. The statement form (p∧q)∨∼(p∨q) is true when both p and q are true or when both p and q are false. The statement form (p∨∼q)∧(∼p∨q) is true when both p and q are true or when both p and q are false, but it is also true when p is false and q is true. Therefore, the two statement forms are not equivalent.
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1.Solve the system of equations [8] 2x + 6y + 62 = 6 2x + 7y + z = 7 2x + 7y + 72 = 8 - using the inverse of the coefficient matrix.(Compute inverse by inversion algorithm)
The solution to the system of equations is:
x = -6.552
y = -1.655
z = 1.276
To solve the system of equations using the inverse of the coefficient matrix, we will first need to find the inverse of the coefficient matrix using the inversion algorithm. The coefficient matrix is:
A = [[2, 6, 6], [2, 7, 1], [2, 7, 7]]
To find the inverse of A, we will use the inversion algorithm:
1. Find the determinant of A:
|A| = 2(7*7 - 1*7) - 6(2*7 - 1*2) + 6(2*7 - 2*7) = 14 - 72 + 0 = -58
2. Find the matrix of minors:
M = [[(7*7 - 1*7), -(2*7 - 1*2), (2*7 - 2*7)], [-(6*7 - 6*1), (2*7 - 6*2), -(2*6 - 6*2)], [(6*1 - 7*6), -(2*1 - 7*2), (2*6 - 7*6)]]
M = [[42, -12, 0], [-36, 2, -12], [-36, 12, -30]]
3. Find the matrix of cofactors:
C = [[42, 12, 0], [36, 2, 12], [-36, -12, -30]]
4. Find the adjugate matrix:
adj(A) = [[42, 36, -36], [12, 2, -12], [0, 12, -30]]
5. Find the inverse of A:
A^-1 = (1/|A|)adj(A) = (1/-58)[[42, 36, -36], [12, 2, -12], [0, 12, -30]]
A^-1 = [[-0.724, -0.621, 0.621], [-0.207, -0.034, 0.207], [0, -0.207, 0.517]]
Now, we can use the inverse of the coefficient matrix to solve the system of equations. The system of equations can be written in matrix form as:
AX = B
Where A is the coefficient matrix, X is the matrix of unknowns, and B is the matrix of constants:
A = [[2, 6, 6], [2, 7, 1], [2, 7, 7]]
X = [[x], [y], [z]]
B = [[6], [7], [8]]
Multiplying both sides of the equation by the inverse of A, we get:
A^-1AX = A^-1B
IX = A^-1B
X = A^-1B
Substituting the values of A^-1 and B, we get:
X = [[-0.724, -0.621, 0.621], [-0.207, -0.034, 0.207], [0, -0.207, 0.517]] * [[6], [7], [8]]
X = [[-6.552], [-1.655], [1.276]]
Therefore, the solution to the system of equations is:
x = -6.552
y = -1.655
z = 1.276
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PLSSSS HELP IF YOU TURLY KNOW THISSSS
Answer:
x = 5
Step-by-step explanation:
5x - 7 = 3x + 3
- 3x -3x
2x - 7 = 3
+7 +7
2x = 10
Divide 2 from both sides
x = 5
Answer: 10
Step-by-step explanation:
2x - 7 = 3
add 7 to both sides = 2x = 10
now to solve:
once u have 2x = 10
divide both sides by 2
x=5
Does this graph show a function? Explain how you know.
O A. Yes; there are no y-values that have more than one xvalue.
O B. No; there are y-values that have more than one x-value.
O C. Yes; the graph passes the vertical line test.
O D. No; the graph fails the vertical line test.
Answer:
D
Step-by-step explanation:
The line touches the graph at 2 different points so it doesnt pass the verticle line test
Question 1: a. Suppose that f(x)=2 x^{2}-5 x-8, g(x)=9-x and ( k(x)=2 x+4 ) Perform the following combination functions, then simplify your results as much as you can: (I Mark) 1. ( 4(f+k){x}
1. 4(f+k)(x)=4(2x^2 - 5x - 8 + 2x + 4) = 8x^2 - 20x - 32.
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9. Manuel measured the distance from the top vertex of the
triangle shown to its base. He found the distance to be
5 feet. Did he measure the height? Explain your
response.
5 ft
5 ft
17 ft-
13 ft
The measure of the height of the triangle measured by Manuel is given as follows:
5 feet.
What is the height of a triangle?The height of a triangle is the perpendicular distance from the base to the vertex opposite the base, and is used to calculate the area of the triangle.
Hence, the height is measured as the distance from the top vertex of the triangle to it's base.
In this problem, it is stated that:
"Manuel measured the distance from the top vertex of the triangle shown to its base".
He found the distance to be of 5 ft, hence the height of the triangle is of:
5 ft.
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Julia's dog Toby had 5 puppies. Each pup eats 0. 13 pounds of dog food every day. How much dog food do puppies eat in 1 day?
Answer:
0.65
Step-by-step explanation:
0.13 * 5 = 0.65
In 2017, were an estimated 8,888,543 people living in New Jersey and there was a total of 74,846 deaths of NJ residents reported. Of those deaths, 1,908 were due to diabetes.
a. Calculate the crude mortality rate in NJ in 2017
b. Calculate the cause-specific mortality rate due to diabetes in NJ in 2017
c. What additional variable (piece of information) would I need to calculate the case-fatality percent of diabetes?
Answer: a. To calculate the crude mortality rate in NJ in 2017, we need to divide the total number of deaths (74,846) by the total population (8,888,543) and then multiply by 1,000 to express the result per 1,000 population.
Crude Mortality Rate = (Total deaths / Total population) x 1,000
Crude Mortality Rate = (74,846 / 8,888,543) x 1,000
Crude Mortality Rate = 8.42 per 1,000 population
b. To calculate the cause-specific mortality rate due to diabetes in NJ in 2017, we need to divide the number of deaths due to diabetes (1,908) by the total population and then multiply by 1,000 to express the result per 1,000 population.
Cause-specific Mortality Rate due to Diabetes = (Deaths due to diabetes / Total population) x 1,000
Cause-specific Mortality Rate due to Diabetes = (1,908 / 8,888,543) x 1,000
Cause-specific Mortality Rate due to Diabetes = 0.21 per 1,000 population
c. To calculate the case-fatality percent of diabetes, we would need to know the number of people diagnosed with diabetes who died during the same time period. Specifically, the case-fatality percent of diabetes would be calculated by dividing the number of people with diabetes who died (numerator) by the total number of people with diabetes (denominator) and then multiplying the result by 100 to express the percentage. Therefore, the additional variable required is the number of people with diabetes in the population.
Step-by-step explanation:
When Sarah runs the 400 meter dash, her finishing times are normally distributed with a mean of 63 seconds and a standard deviation of 1. 5 seconds. Using the empirical rule, what percentage of races will her finishing time be between 61. 5 and 64. 5 seconds?
Based on the given mean and standard deviation of Sarah's finishing times, we can estimate that approximately 68% of her races will have finishing times between 61.5 and 64.5 seconds.
The empirical rule, also known as the 68-95-99.7 rule, is a useful tool for estimating the percentage of data that falls within a certain number of standard deviations from the mean in a normal distribution.
In this case, Sarah's finishing times in the 400-meter dash are normally distributed with a mean of 63 seconds and a standard deviation of 1.5 seconds. To use the empirical rule, we need to first calculate the z-scores for the lower and upper bounds of the range we're interested in.
For the lower bound of 61.5 seconds:
z = (61.5 - 63) / 1.5 = -1
For the upper bound of 64.5 seconds:
z = (64.5 - 63) / 1.5 = 1
These z-scores tell us how many standard deviations are away from the mean each time. Using the empirical rule, we know that approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations.
Since the range we're interested in is within one standard deviation of the mean, we can estimate that approximately 68% of Sarah's finishing times will be between 61.5 and 64.5 seconds.
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#2:
2
10-8 F6 F4 F2
649
4x+3y s 24
5x+By z 40
4x+3y <24
5x+By > 40
SENT
2
-4
Which system of inequalities describes the graph?
-B
10
4x + 3y 2 24
5x+By s 40
4x + 3y - 24
5x+8y <40
The system of inequalities that describes the graph is given as follows:
4x + 3y ≥ 24.5x + 8y ≤ 40.How to define the linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
m is the slope, representing the rate of change.b is the intercept, representing the value of y when x = 0.For the lower bound of the inequality, we have that:
The line has an intercept of 8, as when x = 0, y = 8.The line has a slope of -4/3, as when x increases by 6, y decays by 8.Hence:
y ≥ -4/3x + 8
4x/3 + y ≥ 8
4x + 3y ≥ 24.
For the upper bound of the inequality, we have that:
The line has an intercept of 5, as when x = 0, y = 5.The line has a slope of -5/8, as when x increases by 8, y decays by 5.Hence:
y ≤ -5x/8 + 5
5x/8 + y ≤ 5
5x + 8y ≤ 40.
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45. SAT/ACT Practice Triangle QRS has sides of lengths 14, 19, and t, where t is the length of the longest side. If t is the cube of an integer, what is the perimeter of the triangle? A 41 B 58 C 60 D
The perimeter of triangle QRS 60. Therefore, the correct answer is C: 60.
The perimeter of a triangle is the sum of the lengths of its sides. Therefore, the perimeter of triangle QRS is 14 + 19 + t.
Since t is the cube of an integer, we can write t as x³, where x is an integer. The perimeter of the triangle is then 14 + 19 + x³.
We also know that t is the longest side of the triangle, so it must be greater than both 14 and 19. This means that x³ must be greater than 19, so x must be greater than or equal to 3.
If x is 3, then t is 3³, or 27. The perimeter of the triangle is then 14 + 19 + 27, or 60.
Therefore, the correct answer is C: 60.
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What is the value of 6 = 3 × 2³? 2/03/0 16 64
The value of 6 = 3 × 2³ is 24 by using PEMDAS operations, the correct option is (d).
To understand why, we can simplify the equation using the order of operations, which is PEMDAS (parentheses, exponents, multiplication/division, addition/subtraction). To evaluate the expression 3 x 2³, we first need to simplify the exponent, which means multiplying 2 by itself three times:
2³ = 2 x 2 x 2
2³ = 8
Now we can substitute the value of 2³ into the original expression:
3 x 2³ = 3 x 8
3 x 2³ = 24
However, the value of 6 = 3 x 2³, is equal to 24 the correct option is (d).
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The complete question is:
What is the value of 6 = 3 × 2³?
a. 16
b. 64
c. 42
d. 24
Compute the inverseA−1of the following matrices (a)A=[111−4](b)A=211312−13−1Verify thatA−1A=IandAA−1=I
We have verified that A^-1A = I and AA^-1 = I for both matrices.
To compute the inverse of a matrix, we can use the formula: A^-1 = 1/det(A) * adj(A), where det(A) is the determinant of the matrix A and adj(A) is the adjoint of the matrix A.
(a) A = [1 1; 1 -4]
det(A) = (1*-4) - (1*1) = -4 - 1 = -5
adj(A) = [-4 -1; -1 1]
A^-1 = 1/-5 * [-4 -1; -1 1] = [4/5 1/5; 1/5 -1/5]
(b) A = [2 1 1; 3 1 2; -1 3 -1]
det(A) = (2*(1*-1) - 1*(2*3) + 1*(-1*3)) - (1*(1*-1) - 1*(2*-1) + 1*(3*3)) = -6 - 3 - 3 - 9 = -21
adj(A) = [-1 -2 7; 5 1 -8; 2 5 -7]
A^-1 = 1/-21 * [-1 -2 7; 5 1 -8; 2 5 -7] = [1/21 2/21 -7/21; -5/21 -1/21 8/21; -2/21 -5/21 7/21]
To verify that A^-1A = I and AA^-1 = I, we can simply multiply the matrices and check if the result is the identity matrix.
For (a):
A^-1A = [4/5 1/5; 1/5 -1/5] * [1 1; 1 -4] = [1 0; 0 1] = I
AA^-1 = [1 1; 1 -4] * [4/5 1/5; 1/5 -1/5] = [1 0; 0 1] = I
For (b):
A^-1A = [1/21 2/21 -7/21; -5/21 -1/21 8/21; -2/21 -5/21 7/21] * [2 1 1; 3 1 2; -1 3 -1] = [1 0 0; 0 1 0; 0 0 1] = I
AA^-1 = [2 1 1; 3 1 2; -1 3 -1] * [1/21 2/21 -7/21; -5/21 -1/21 8/21; -2/21 -5/21 7/21] = [1 0 0; 0 1 0; 0 0 1] = I
Therefore, we have verified that A^-1A = I and AA^-1 = I for both matrices.
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Repost
Simplify.
4x^3 - 12x^2
__________
4x^2 + 7x - 2
__________
2x^2 - 6x
__________
5x^2 + 11x + 2
Answers:
A. 2x(5x-1)
_____
4x-1
B. 2x(5x+1)
_____
4x-1
C. x(5x+1)
_____
4x-1
D. x(5x+1)
_____
2(4x-1)
Answer:
the answer is B. 2x(5x+1)
Use synthetic division to find the quotient and remainder when -x^(4)+6x^(3)+7x^(2)+3 is divided by x-7
The quotient and remainder when -x⁴+6x³+7x²+3 is divided by x-7 is 12 and 73, respectively.
Using synthetic division, the quotient and remainder when -x⁴+6x³+7x²+3 is divided by x-7 is 12 and 73, respectively.
To solve this problem, start by writing out the synthetic division form, with the coefficients in the same order as the original problem:
|-7 |6 7 3
|1 -7
|0 12
|-73
Take the first coefficient of the divisor (-7) and multiply it by the first coefficient of the dividend (-1). The result is 7. Place this number at the top of the first column of the table.
Take the divisor’s first coefficient (-7) and add it to the dividend’s second coefficient (6). Place the result (–1) in the second column of the table.
Take the first coefficient of the divisor (-7) and multiply it by the second coefficient of the dividend (6). Place the result (-42) in the third column of the table.
Now add the first two numbers in the second column of the table (7 and -1). Place the result (6) in the fourth column.
The last number in the table (-73) is the remainder. The second number in the table (12) is the quotient.
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what is 1/2 shaded in 8 pieces
Answer:
4
Step-by-step explanation:
8 + (9-1) ÷ 4 =? 10 or 4
Answer:
10
Step-by-step explanation:
Answer:
10
Step-by-step explanation:
Lucky Duck
What is the probability you will choose each duck described below?
Write the answer as a fraction in lowest terms and place it in the appropriate
box (certain, likely, unlikely, impossible).
The ducks are
numbered from one
through 12!
Lucky duck probabilities include:
4. Impossible, 0/12.5. Likely, 1/6.6. Certain, 1.7. Likely, 1/12.8. Impossible, 0/129. Likely, 1/1210. Certain, 1/2.11. Likely, 1/2.12. Impossible, 0/12.13. Likely, 2/3.14. Certain, 1.15. Likely, 7/12.16. Likely, 1/3.How to determine probability?A duck with a number:
Every duck has a number, so the probability of choosing a duck with a number is certain (1/1 or 100%).
A duck with a number greater than 10:
is 2/12 or 1/6, since there are 2 ducks with numbers greater than 10 out of a total of 12 ducks.
Duck number 4:
There is only one duck with the number 4, so the probability of choosing this duck is 1/12.
A duck with sunglasses:
There are no ducks with sunglasses so the probability is impossible.
A duck with a hat:
We don't know how many ducks wear hats, so we cannot determine the probability.
An even-numbered duck:
There are 6 even-numbered ducks (2, 4, 6, 8, 10, 12) out of 12 ducks in total, so the probability of choosing an even-numbered duck is 6/12, which simplifies to 1/2.
A duck with a number less than 7:
There are 6 ducks with a number less than 7 (1, 2, 3, 4, 5, 6) out of 12 ducks in total, so the probability of choosing a duck with a number less than 7 is 6/12, which simplifies to 1/2.
A duck with a mustache:
There are no ducks with mustaches, so the probability of getting a duck with a mustache is impossible, 0.
A duck with a bow tie:
Ducks with bowties are 8, so the probability of choosing a duck with bowtie is likely 8/12, 2/3
A duck with a number lower than 25:
All ducks have a number lower than 25, so the probability of choosing a duck with a number lower than 25 is certain (1).
A duck with a number greater than 5:
There are 7 ducks with a number greater than 5 (6, 7, 8, 9, 10, 11, 12) out of 12 ducks in total, so the probability of choosing a duck with a number greater than 5 is 7/12.
A duck with number that's a multiple of 3:
There are 4 ducks with a number that's a multiple of 3 (3, 6, 9, 12) out of 12 ducks in total, so the probability of choosing a duck with a number that's a multiple of 3 is 4/12, which simplifies to 1/3.
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The scatter plot shows the selling price versus area (in square feet) for 20 homes that
recently sold in a neighborhood.
The equation of the least squares regression line is given as:
Predicted Selling Price = 68,115 + 122.2 Area
Use the drop-down menus to complete the statements below about what this linear
model tells you about the selling price of homes in this neighborhood.
30 Points!!!
Answer: Your welcome!
Step-by-step explanation:
This linear model tells us that, on average, for every additional square foot of area in a home, the selling price increases by 122.2 dollars. Therefore, this model suggests that the larger the area of a home, the higher the selling price of the home will be.
Answer:
Step-by-step explanation:
Identify the factor pair of ac you could use to rewrite b to factor the trinomial by grouping. 2x^(2)+7x-4
To factor the trinomial 2x²+7x-4, you could rewrite it as 2x²+8x-2x-4, and then factor by grouping. The factor pairs of ac are (x+4), (2x-1).
To factor the trinomial 2x²+7x-4 by grouping, we need to find a factor pair of ac that sums to b. In this case, ac = (2)(-4) = -8 and b = 7.
The factor pair of -8 that sums to 7 is 8 and -1. Therefore, we can rewrite the trinomial as follows:
2x²+7x-4 = 2x²+8x-x-4
Next, we can group the first two terms and the last two terms:
(2x²+8x)+(-x-4)
Now, we can factor out the greatest common factor from each group:
2x(x+4)-1(x+4)
Finally, we can factor out the common factor of (x+4):
(x+4)(2x-1)
Therefore, the factored form of the trinomial 2x²+7x-4 is (x+4)(2x-1).
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Math part 2 question 5
The solution of the function f(h.g)(x) will be 6x³ -3x² + 5. The correct option is C.
What is an expression?In mathematics, expression is defined as the relationship of numbers, variables, and functions using mathematical signs such as addition, subtraction, multiplication, and division.
The given functions are,
h(x) = 3x +5
g(x) = 2x³ - x ²
The value of the function f(h.g)(x) will be calculated as,
f(h.g)(x) = 3 ( 2x³ - x² ) + 5
f(h.g)(x) = 6x³ - 3x² + 5
Therefore, the solution of the function f(h.g)(x) will be 6x³ -3x² + 5. The correct option is C.
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