The results of the matrix operations are:
-2A = [-4 0 2; -8 6 -4]B - 2A = [11 -5 -1; 9 -10 1]AC = undefinedCD = [1 13; -7 -6]To compute each matrix sum or product, we first need to determine if the operation is defined. Then, we can use the rules of matrix arithmetic to find the result.
-2A is defined, since we can multiply a matrix by a scalar. To find the result, we simply multiply each element of A by -2:
-2A = [-2(2) -2(0) -2(-1); -2(4) -2(-3) -2(2)] = [-4 0 2; -8 6 -4]
B - 2A is defined, since both matrices have the same dimensions. To find the result, we first compute -2A as shown above, then subtract each corresponding element of B and -2A:
B - 2A = [7 -5 1; 1 -4 -3] - [-4 0 2; -8 6 -4] = [7-(-4) -5-0 1-2; 1-(-8) -4-6 -3-(-4)] = [11 -5 -1; 9 -10 1]
AC is undefined, since the number of columns in A (3) does not match the number of rows in C (2).
CD is defined, since the number of columns in C (2) matches the number of rows in D (2). To find the result, we multiply each row of C by each column of D and sum the products:
CD = [(1)(3)+(2)(-1) (1)(5)+(2)(4); (-2)(3)+(1)(-1) (-2)(5)+(1)(4)] = [1 13; -7 -6]
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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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Find the volume of a right circular cone that has a height of 2.5 ft and a base with a diameter of 8 ft. Round your answer to the nearest tenth of a cubic foot
Answer:
41.9 cubic feet
Step-by-step explanation:
V = 1/3πr^2h,
r=radius
h=height.
V = 1/3πr^2h
= 1/3π4^2 * 2.5
= 40π/3 cubic feet
so the answer would be 41.9 cubic feet
Review Question Simplify the expression. (8d^((3)/(2))*7h^((5)/(6)))(7h^((3)/(2))*8d^((5)/(6)))
To simplify the expression (8d^((3)/(2))*7h^((5)/(6)))(7h^((3)/(2))*8d^((5)/(6))), we need to use the distributive property and the laws of exponents.
First, we can distribute the 8d^((3)/(2)) and 7h^((5)/(6)) to the 7h^((3)/(2)) and 8d^((5)/(6)):
= (8d^((3)/(2))*7h^((3)/(2)))*(7h^((5)/(6))*8d^((5)/(6)))
Next, we can use the laws of exponents to simplify the expressions with the same base:
= (8^2*d^((3)/(2)+(5)/(6))*7^2*h^((5)/(6)+(3)/(2)))
= (64*d^((11)/(6))*49*h^((9)/(6)))
Finally, we can simplify the exponents and multiply the constants:
= (3136*d^((11)/(6))*h^((3)/(2)))
Therefore, the simplified expression is 3136*d^((11)/(6))*h^((3)/(2)).
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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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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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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:
Suppose you have 22 units of Virtual Currency and John takes 21 of them. How many units of Virtual Currency would you need to purchase Bloxburg on the rablax platform?
a. 1 unit of Virtual Currency (insufficient for Bloxburg purchase)
b. 25 units of Virtual Currency (sufficient for Bloxburg purchase)
c. 1 extra large unit of Virtual Currency (sufficient for Bloxburg purchase)
d. 62 units of Virtual Currency (insufficient for Bloxburg purchase)
In response to the aforementioned query, we may say that The right equation response is b. 25 virtual currency units (sufficient for Bloxburg purchase).
What is equation?A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.
You presently have 22 units of virtual currency, and John takes 21, according to the facts provided. You now only have 1 unit of virtual currency.
Consequently, to acquire Blox , you would require an additional 24 units of virtual currency.
The right response is b. 25 virtual currency units (sufficient for Bloxburg purchase).
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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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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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You have a Poisson process with rate parameter λ = 2.
i. Let Xk be the waiting time for k occurences. Write down the probability
distributions for X1, X2, X3, and X5, and calculate the expected waiting
time E[Xk], the standard deviation σXk, and draw these four probability
distributions for the interval 0 ≤x ≤7. You do not need to include values
on the vertical axis.
ii. Let Yt ∼ ft(x) be the number of occurences in the span of t time units.
Draw the three probability distributions ft(x) (for t = 13, t = 12, t = 1.2)
for x = 0,1,2,3,4,5. Include values on the vertical axis.
The values on the vertical axis are the probabilities for each value of x. The probability of 0 occurrences in the span of 13 time units is f13(0) = 26^0 * e^(-26) / 0! = e^(-26) ≈ 0.0000000000000000000000000003.
The Poisson process is a type of stochastic process that counts the number of occurrences of an event in a given time interval. The rate parameter λ represents the average number of occurrences per unit time.
i. The waiting time for k occurrences in a Poisson process follows an exponential distribution with parameter λk. The probability distributions for X1, X2, X3, and X5 are given by:
X1 ∼ Exp(λ) = Exp(2)
X2 ∼ Exp(λ*2) = Exp(4)
X3 ∼ Exp(λ*3) = Exp(6)
X5 ∼ Exp(λ*5) = Exp(10)
The expected waiting time E[Xk] is given by 1/λk, and the standard deviation σXk is also given by 1/λk. Therefore, we have:
E[X1] = 1/λ = 1/2
E[X2] = 1/(λ*2) = 1/4
E[X3] = 1/(λ*3) = 1/6
E[X5] = 1/(λ*5) = 1/10
σX1 = 1/λ = 1/2
σX2 = 1/(λ*2) = 1/4
σX3 = 1/(λ*3) = 1/6
σX5 = 1/(λ*5) = 1/10
The probability distributions for the interval 0 ≤ x ≤ 7 are shown below:
ii. The number of occurrences in the span of t time units follows a Poisson distribution with parameter λt. The probability distributions ft(x) for t = 13, t = 12, and t = 1.2 are given by:
ft(x) = (λt)^x * e^(-λt) / x!
f13(x) = (2*13)^x * e^(-2*13) / x! = 26^x * e^(-26) / x!
f12(x) = (2*12)^x * e^(-2*12) / x! = 24^x * e^(-24) / x!
f1.2(x) = (2*1.2)^x * e^(-2*1.2) / x! = 2.4^x * e^(-2.4) / x!
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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
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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i need help solving this problem
Answer: A
Step-by-step explanation:
(3x ^ 2 + 4x - 7) (2x + 9)
2x (3x ^ 2 + 4x - 7) + 9 (3x ^ 2 + 4x - 7)
6x ^ 3 + 8x ^ 2 - 14x + 27x ^ 2 + 36x - 63
6x ^ 3 + 35x ^ 2 + 22x - 63
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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What lump sum must be invested at 7%, compounded monthly, for
the investment to grow to $61,000 in 13years?
The lump sum that must be invested at 7% compounded monthly for the investment to grow to $61,000 in 13 years is $25,447.09.
To find the lump sum that must be invested at 7% compounded monthly for the investment to grow to $61,000 in 13 years, we can use the formula for compound interest;
A = P(1 + r/n)^(nt)
Where:
- A is the final amount
- P is the initial principal amount
- r is the annual interest rate
- n is the number of times interest is compounded per year
- t is the number of years
Plugging in the given values, we get:
61,000 = P(1 + 0.07/12)^(12*13)
Solving for P, we get:
P = 61,000 / (1 + 0.07/12)^(12*13)
P = 61,000 / (1.00583)^156
P = 61,000 / 2.39717
P = 25,447.09
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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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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)
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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What is the remainder when f(x)=x^3+7x^2+9x-5 is divided by (x+4)
On dividing (x³ + 7x² + 9x - 5) by (x + 4), we get -
h(x) = x² + 3x - 3 + 7/(x + 4).
What is Division algorithm?Division algorithm states that -
Dividend = (Divisor x Quotient) + Remainder
Given is to find the remainder when -
(x³ + 7x² + 9x - 5) ÷ (x + 4)
We can write -
f(x) = (x³ + 7x² + 9x - 5)
g(x) = (x + 4)
So -
h(x) = f(x) ÷ g(x)
h(x) = (x³ + 7x² + 9x - 5) ÷ (x + 4)
h(x) = (x³ + 4x² + 3x² + 9x - 5)/(x + 4)
h(x) = x² + (3x² + 9x - 5)/(x + 4)
h(x) = x² + 3x + (-3x - 5)/(x + 4)
h(x) = x² + 3x - 3 + 7/(x + 4)
Therefore, on dividing (x³ + 7x² + 9x - 5) by (x + 4), we get -
h(x) = x² + 3x - 3 + 7/(x + 4).
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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
The following are body mass index (BMI) scores measured in 9 patients who are free of diabetes and participating in a study of risk factors for obesity. Body mass index is measured as the ratio of weight in kilograms to height in meters squared.
25 27 31 33 26 28 38 41 24
What is the standard deviation of BMI?
Therefore, the standard deviation of BMI for the 9 patients in the study is 5.67.
To find the standard deviation of BMI for the 9 patients in the study, we need to follow these steps:
Find the mean of the BMI scores: (25 + 27 + 31 + 33 + 26 + 28 + 38 + 41 + 24) / 9 = 29.67
Subtract the mean from each BMI score to find the deviation: -4.67, -2.67, 1.33, 3.33, -3.67, -1.67, 8.33, 11.33, -5.67
Square each deviation: 21.81, 7.13, 1.77, 11.09, 13.45, 2.79, 69.43, 128.51, 32.15
Find the mean of the squared deviations: (21.81 + 7.13 + 1.77 + 11.09 + 13.45 + 2.79 + 69.43 + 128.51 + 32.15) / 9 = 32.12
Take the square root of the mean of the squared deviations to find the standard deviation: √32.12 = 5.67
Therefore, the standard deviation of BMI for the 9 patients in the study is 5.67.
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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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Find the volume of a cone whose depth is 14 cm and base radius is 9/2cm
The volume of the cone is approximately 94.25π cubic cm.
To find the volume of a cone, we use the formula V = 1/3πr²h, where V is the volume, r is the radius of the base, and h is the height or depth of the cone. In this case, we know that the depth of the cone is 14 cm and the base radius is 9/2 cm.
First, we need to calculate the radius of the base in terms of cm, since the formula requires it. We are given that the base radius is 9/2 cm, so we can substitute this value for r:
r = 9/2 cm
Next, we need to calculate the volume of the cone using the formula. We know that the depth of the cone is 14 cm, so we can substitute this value for h:
V = 1/3πr²h
V = 1/3π(9/2)²(14)
V = 1/3π(81/4)(14)
V = 1/3π(1134/4)
V = 1/3π(283.5)
V = 94.25π
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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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Help me solve this problem please
The state income tax owed on a $40,000 per year salary is $1,500.
What is income tax?
A tax levied against people or organizations (taxpayers) in relation to their income or profits is known as an income tax. (commonly called taxable income). Tax rates multiplied by taxable income are typically used to calculate income taxes. Tax rates might change depending on the taxpayer's attributes and source of income.
To calculate the state income tax owed on a $40,000 per year salary, we need to determine which progressive tax range it falls into and apply the corresponding tax rate.
Since $40,000 falls within the range of $10,001 - $50,000, we will use the tax rate of 5% for this portion of the income.
First, we need to calculate the amount of income within this range -
$40,000 - $10,000 = $30,000
Next, we calculate the amount of tax owed on this portion of the income -
$30,000 x 0.05 = $1,500
Therefore, the value is obtained as $1,500.
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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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PLEASEEEEE ANSWERRR ANS HURRYYY
Given the box and whiskers plot with the given data, the five number summary would be :
Min - 2 Q1 = 4 Median = 8Q3 = 12Max = 15How to find the five number summary ?Arrange the numbers in order from smallest to largest:
2, 2, 3, 4, 5, 5, 8, 8, 10, 10, 11, 13, 15, 15, 15
The minimum number is therefore 2.
First Quartile Q1 = 4 :
= ( 15 + 1 ) / 4
= 4 th position
Median :
= ( 15 + 1 ) / 2
= 8 th position which is 8
Third quartile :
= ( 15 + 1 ) x 3 / 4
= 12 th position which is 13.
Maximum value is 15.
Move the box plot to correspond with these figures.
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Which of the equations has no solution? 2(x-7)=2x-14 15x-30=0,2x+1=5x-3,3(2x+1)=6x+1
The equation that has no solution is 2x+1=5x-3.
To find out which equation has no solution, we can use the process of elimination. First, let's look at the equation 2(x-7)=2x-14. If we simplify this equation, we get:
2x-14=2x-14
This equation is true for all values of x, so it has infinitely many solutions.
Next, let's look at the equation 15x-30=0. If we simplify this equation, we get:
15x=30
x=2
This equation has one solution, x=2.
Now, let's look at the equation 2x+1=5x-3. If we simplify this equation, we get:
-3x=-4
x=4/3
This equation has one solution, x=4/3.
Finally, let's look at the equation 3(2x+1)=6x+1. If we simplify this equation, we get:
6x+3=6x+1
3=1
This equation is never true, so it has no solution.
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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
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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