Answers
The value for the A³ matrix will be [tex]A^{3} = \left[\begin{array}{ccc}75&0 \\0&1\end{array}\right][/tex]
In the given question, it is stated that A is a given matrix. We have to find out the values of A³. This can be done by product of A*A*A. The product should follow the properties of the Matrix. First, we will find out the value of A². So calculating, we get:
=> [tex]A^{2} = \left[\begin{array}{ccc}-5&-1\\0&1\end{array}\right] * \left[\begin{array}{ccc}-5&-1\\0&1\end{array}\right][/tex]
=> [tex]A^{2} = \left[\begin{array}{ccc}-25+0 &1 -1\\0+0&0 + 1\end{array}\right][/tex]
=> [tex]A^{2} = \left[\begin{array}{ccc}-25 &0\\0&1\end{array}\right][/tex]
Now we will calculate the value of A³. We can calculate the value of A³ by using the values of A² because we know that A³ = A².A. So, after calculating we get:
=> [tex]A^{3} = \left[\begin{array}{ccc}-25&0\\0&1\end{array}\right] * \left[\begin{array}{ccc}-5&-1\\0&1\end{array}\right][/tex]
=> [tex]A^{3} = \left[\begin{array}{ccc}75+0&0 + 0\\0+0&0+1\end{array}\right][/tex]
=> [tex]A^{3} = \left[\begin{array}{ccc}75&0 \\0&1\end{array}\right][/tex]
Hence we get value for [tex]A^{3} = \left[\begin{array}{ccc}75&0 \\0&1\end{array}\right][/tex]
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Related Questions
Keandre wants to buy a new pair of shoes that costs $220. In order to earn money for this, Keandre babysits his neighbor for $10 an hour. He also has saved up his monthly allowance which totals $50. What is the minimum number of hours he should babysit in order to be able to afford the shoes?
Answers
Answer:
Step-by-step explanation:
$220=$10x+$50
x= hours
subtract $50 from both sides making sure to cancel the right side
$220-$50=$10x
$170=$10x
Divide both sides by $10 to leaving x by itself on the right side
$170/$10=x
17hrs=x
The minimum number of hours is 17 hours to babysit in order to be able to afford the shoes.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Cost of new pair of shoes = $220
In order to earn money for this, Keandre babysits his neighbor for $10 an hour.
And, He also has saved up his monthly allowance which totals $50.
Now,
Let number of minimum hours = x hour
So, We can formulate;
⇒ $10x + $50 = $220
Solve for x as;
⇒ $10x + $50 = $220
Subtract 50 both side, we get;
⇒ $10x + $50 - $50 = $220 - $50
⇒ $10x = $170
Divide by 10 both side, we get;
⇒x = 17
Thus, The minimum number of hours is 17 hours to babysit in order to be able to afford the shoes.
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Cars enter a car wash at a mean rate of 4 cars per half an hour. What is the probability that, in any hour, exactly 4 cars will enter the car wash? Round your answer to four decimal places.
Answers
The probability that, in any hour, exactly 5 cars will enter the car wash is P(x = 5) = 0.0920.
This can be modeled as a Poisson random variable.
The mean rate is the parameter of the Poisson distribution:
λ = 4 cars/30 mins
λ = 8 cars/hr
The probability that exactly k cars will enter the car wash can be calculated as:
P(x = k) = ([tex]8^{k}[/tex] × [tex]e^{-8}[/tex]) ÷ k!
Then, the probability that exactly 5 cars will enter the car wash for k=5 is:
P(5) = ([tex]8^{5}[/tex] × [tex]e^{-8}[/tex]) ÷ 5!
P(5) = (32768 × 0.0003) ÷ 120
P(5) = 0.0920
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The value of a baseball player's rookie card began to increase once the player retired. When he retired in 1997 his card was worth $6.36. The value has increased by $1.93 each year since then. Express the relationship relating the value of the card y in dollars and the number of years x the player has been in retirement with an equation. Is the relationship between x and y proportional? What was the value of the card in 2007
?
Answers
Part a: The relationship between x and y can be represented as y = 6.36 + 1.93x
Part b: The relationship between x and y is proportional
Part c: The value of the card in 2007 will be $25.66
Worth of the card in 1997 = $6.36
Increase in value each year = $1.93
Let x be the number of years the player has been in retirement and y be the value of the cards in dollars
Formulating the equations we get the following:
Value of the card = Worth of the card in 1997 + Increase in value each year*Number of years the player has been in retirement
Part a:
y = 6.36 + 1.93x
Part b:
The relationship between x and y is proportional as the increase in the value each year leads to an increase in the worth of the card
Part c:
Value of the card in 2007:
The number of years the player has been retired will be 10 years in this case
Formulating the equation we get the following:
y = 6.36 + 1.93(10)
= 25.66
So, the value will be $25.66
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given AC=XZ and AB=XY prove BC=YZ
Answers
Find the expected value of the winningsfrom a game that has the followingpayout probability distribution:Payout ($) 1 2 5 8 10Probability 0.35 0.2 0.1 0.2 0.15Expected Value = [?]Round to the nearest hundredth.
Answers
On the frequency table, you can see the payouts of the lottery and the corresponding probabilities for every payout. To determine the expected payout, you have to multiply each possible price by its corresponding probability and add the results, following the formula:
[tex]E(X)=\sum ^{10}_{n\mathop=1}x_i\cdot P(x_i)[/tex][tex]\begin{gathered} E(X)=(1\cdot0.35)+(2\cdot0.20)+(5\cdot0.10)+(8\cdot0.20)+(10\cdot0.15) \\ E(X)=0.35+0.4+0.5+1.6+1.5 \\ E(X)=4.35 \end{gathered}[/tex]The expected payout for the lottery is $4.35
A triangle can be formed by drawing line segments on a map of Texas connecting the cities of Dallas, Houston, and San Antonio (see figure).
If the actual distance from San Antonio to Houston is approximately 192 miles, use the lengths of the line segments indicated in the figure along with similar triangles to approximate
a. the actual distance from Dallas to Houston.
b. the actual distance from Dallas to San Antonio.
Answers
a. The actual distance from Dallas to Houston is 0.058 mi. b. The actual distance from Dallas to San Antonio is 0.064 mi
What is the scale factor?The ratio between comparable measurements of an item and a representation of that thing is known as a scale factor in arithmetic.
Given that the actual distance from San Antonio to Houston is approximately 192 miles.
The scale factor from the map to the real world is;
(actual)/( map) = (192mi)/(3 in) = 64 mi/in
Then the actual distance from Dallas to Houston will be;
(3.75 in)(64 mi/in) = 0.058 mi
And from Dallas to San Antonio, the distance will be;
(4.125 in)(64 mi/in) = 0.064 mi
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Bharat types 20 words/min. How many words can he type in each length of time? a) 5 min b) 30 min c) 23 min
Answers
Bharat can type words in lengths of time as 100 words, 600 words, and 460 words in 5 minutes, 30 minutes, and 23 minutes respectively.
What are Arithmetic operations?Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.
* Multiplication operation: Multiplies values on either side of the operator
For example 12×2 = 24
Bharat types 20 words per minute which are given in the question.
To determine the number of words can he type in each length of time
We have to multiply the time by his typing speed.
The number of words that can be typed by Bharat in 5 minutes :
⇒ 20 × 5
⇒ 100
The number of words that can be typed by Bharat in 30 minutes :
⇒ 20 × 30
⇒ 600
The number of words that can be typed by Bharat in 23 minutes :
⇒ 20 × 23
⇒ 460
Therefore, He can type words in lengths of time as 100 words, 600 words, and 460 words in 5 minutes, 30 minutes, and 23 minutes respectively.
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Ward is planning to install a new counter top in kitchen, as shown in the figure. Determine the area of the countertop.
Answers
What is the slope of the line?
*2
*1/2
*-1/2
*-2
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The answer is 2 m = -4 / -2 = -2 / -1 = 2
Composition of Functions and Inverses:Question 7Which expression represents f(f(x)) if f(x) = x2 – 1? A. 2x ^2-2 B. X^4-2x^2+1C. XD. X^4-2x^2
Answers
To solve the question, we will follow the steps below:
[tex]f(x)=x^2-1[/tex]To find f(f(x)), we will simply replace x by x² - 1 in the function x² - 1
That is:
f((fx)) = (x²-1)² - 1
Then we open the parenthesis
f(f(x)) = (x² - 1)(x² -1) - 1
=x²(x²-1)-1(x²-1) - 1
= x⁴ - x² - x² + 1 - 1
= x⁴ - 2x²
So the correct option is option D. which is x⁴ - 2x²
A clothing designer is selecting models to walk the runway for her fashion show.
The designer prefers models that are no more than 3 inches away from being 5'10".
Since 5'10" is the same as 70 inches, write an inequality - in terms of inches - that
could be used to determine if a model's height is within the designer's preferred height
range.
Answers
Using proportions, the inequality that could be used to determine if a model's height is within the designer's preferred height range is of:
67 inches ≤ Height ≤ 73 inches.
What is a proportion?A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using operations such as multiplication and division, from the unit rates in the context of the problem.
One example of application of proportions is for conversion of units, as there are rates for each unit.
In the context of this problem, the rate used is:
1 feet = 12 inches.
Hence the measure of 5'10" = 5 feet and 10 inches is given by:
5 x 12 + 10 = 60 + 10 = 70 inches.
The heights that are within 3 inches of 70 inches are given by:
70 - 3 = 67 inches.70 + 3 = 73 inches.Hence the inequality that models the situation is:
67 inches ≤ Height ≤ 73 inches.
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I need help with this!!
Answers
Answer:
Step-by-step explanation:
A square has an area of 144 ft^2 what is the length of each side
Answers
Answer: 12 feet
This is because [tex]12^2 = 12*12 = 144[/tex]
Squaring a number means you multiply it with itself.
The square root goes in reverse to have [tex]\sqrt{144} = 12[/tex]
Answer:
Each side is 12 ft long.
Step-by-step explanation:
So, you have a square, which means all of the sides are going to be the same length. So, you need something times itself that equals 144. Or, you need the square root of 144 (Because when something is squared, it is multiplied by itself). And the square root of 144 is 12.
HELP PLEASE
thank youuu
Answers
Answer:
a/c
Step-by-step explanation:
Sine is always the side opposite the angle and the hypotenuse
Answer:
[tex]\large \text{Second Choice: $\dfrac{a}{c}$}[/tex]
Step-by-step explanation:
For any given triangle, the Law Of Sines states that the ratio of each side to the sine of the angle opposite that side is the same
So we have
[tex]\dfrac{a}{\sin \angle F} = \dfrac{c}{\sin \angle 90} = \dfrac{b}{\sin \angle G} \\\\[/tex]
[tex]\sin \angle 90 = 1[/tex]
So we get from the first two ratio equality,
[tex]\dfrac{a}{\sin \angle F} = \dfrac{c}{1} \\\\\\\dfrac{a}{\sin \angle F} = c\\\\\\\dfrac{a}{c} = sin \angle F\\\\[/tex]
Or, in other words,
[tex]\sin \angle F = \dfrac{a}{c}[/tex]
9y-(2y-3)=5(y-2)+2
Should equal ‘no solution’
Answers
[tex]9y - 2y + 3 = 5y - 10 + 2 \\ 7y + 3 = 5y - 8 \\ 7y - 5y = - 8 - 3 \\ 2y = - 11 \\ \frac{2y}{2} = \frac{ - 11}{2} \\ y = \frac{ - 11}{2} [/tex]
ATTACHED IS THE SOLUTION OF Y
BE AWARE THERE IS A SOLUTION FOR THE PROBLEM.
which three ordered pairs represents an input value of the function with the corresponding output value? select three answer.A.(-1,0)B.(0,1)C.(2,1)D.(2,4)E.(3,8)F.(4,2)
Answers
In order to determine the ordered pairs, look if the given points are on the curve.
Based on the graph, you can identify that the points are:
B. (0,1)
D. (2,4)
E. (3,8)
Explain how knowing the linear factor establishes that f(10) multiple of 12.
Answers
f(10) is a multiple of 12 because f(x) has a linear factor of x+2 and x+2 = 12, when x = 10
f(10) multiple of 12 is given as:
The first-degree equations that make up a polynomial's linear factors serve as the foundation stone for higher-order and more complicated polynomials. The formula for a linear factor is ax + b, and it cannot be factored further. When paired with other linear factors, each linear factor represents a separate line, resulting in several sorts of functions with progressively more intricate graphical representations.
f(10) = (10+2)(100+20+2)
= (12)(122)
= 1220+244
= 1464
Hence, f(10) is a multiple of 12
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The apartment you want has a monthly rent of $585. What does your gross monthly income range need to be for you to be able to rent this apartment? Maximum spent on rent should be 25% - 35% of your gross monthly income
Answers
The gross monthly income range to be for you to be able to rent this apartment is $1671 - $2340.
How to calculate the value?Let the monthly income be x.
Therefore, 25% of x = 585
0.25x = 585
Divide
x = 585/0.25
x = $2340
The maximum income is $2340.
The minimum income will be:
35% of x = 585
0.35x = 585
Divide.
x = 585 / 0.35
x = $1671
In this case, the minimum value is $1671 and the maximum value is $2340. This illustrates the concept for finding the range.
The range is $1671 - $2340.
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result step by step of this simple but yet hard for me exercise
Answers
Answer:
The anser is
Step-by-step explanation:
DO IT YOURSELF BRO GO LEARN AND STOP USING BRAINLY PU_$$y
What type of chart did we use to build a tornado chart?
Answers
Bar chart
For 20 charterers
I need help figuring out the measures of the missing sides
Answers
Given:
• c = 20
,• h = 15
,• j = 12
,• k = 16
Let's find the measures of the mssing sides if triangle ABC is similar to triangle JKH.
Here, the missing sides are:
Side a and Side b
Since both triangles are similar, the corresponding sides will be proportional.
To solve for the length of side a, apply the proportionality equation:
[tex]\frac{c}{h}=\frac{a}{j}[/tex]Plug in values and solve for a:
[tex]\begin{gathered} \frac{20}{15}=\frac{a}{12} \\ \\ \text{ Cross multiply:} \\ 15a=20*12 \\ \\ 15a=240 \\ \text{ } \\ \text{ Divide both sides by 15:} \\ \frac{15a}{15}=\frac{240}{15} \\ \\ a=16 \end{gathered}[/tex]Thereofore, the length of side a = 16
To solve for the length of side b, apply the equation:
[tex]\frac{c}{h}=\frac{b}{k}[/tex]Plug in the values for the variables and solve for b:
[tex]\begin{gathered} \frac{20}{15}=\frac{b}{16} \\ \\ 15b=20*16 \\ \\ 15b=320 \\ \\ b=\frac{320}{15} \\ \\ b=21.3 \end{gathered}[/tex]The length of b is 21.3
ANSWER:
• a = 16
,• b = 21.3
The Lawrence family needed to cut expenses on their cell and landline phone service, cable television service, and Internet service. Here are the best prices they found forbasic service, using different service providers: Cell Phone Service: $36.45 per month Landline Phone Service: $30.11 per month Cable TV Service: $57.43 per monthInternet Service: $37.32 per month They found a company with a package deal with all 4 services for $131.59. What is the percentage decrease by purchasing the packagedeal?15.8%16.5%17.7%18.4%None of these choices are correct
Answers
Given:
Cell Phone Service, x=$36.45 per month
Landline Phone Service, y= $30.11 per month
Cable TV Service, z=$57.43 per month
Internet Service, p= $37.32 per month
The price for a package of all services, P=$131.59.
The total price of services before purchasing the package is,
[tex]T=36.45+30.11+57.43+37.32=161.31[/tex]Now, the percentage decrease by purchasing the package is,
[tex]\begin{gathered} \text{Percentage}=\frac{T-P}{T}\times100 \\ =\frac{161.31-131.59}{161.31}\times100 \\ =18.4 \end{gathered}[/tex]Therefore, the percentage decrease by purchasing the package is 18.4%.
1/3 (x + 5) + x = 4 ( x - 4) -9
Answers
Distributing and combining similar terms
[tex]\begin{gathered} \frac{1}{3}\cdot x+\frac{1}{3}\cdot5+x=4\cdot x-4\cdot4-9 \\ \frac{1}{3}x+x+\frac{5}{3}=4x-16-9 \\ \frac{4}{3}x+\frac{5}{3}=4x-25 \end{gathered}[/tex]Subtracting 4/3x at both sides
[tex]\begin{gathered} \frac{4}{3}x+\frac{5}{3}-\frac{4}{3}x=4x-25-\frac{4}{3}x \\ \frac{5}{3}=(4-\frac{4}{3})x-25 \\ \frac{5}{3}=(\frac{4\cdot3-4}{3})x-25 \\ \frac{5}{3}=\frac{8}{3}x-25 \end{gathered}[/tex]Adding 25 at both sides:
[tex]\begin{gathered} \frac{5}{3}+25=\frac{8}{3}x-25+25 \\ \frac{5+25\cdot3}{3}=\frac{8}{3}x \\ \frac{80}{3}=\frac{8}{3}x \end{gathered}[/tex]Multiplying by 3/8 at both sides
[tex]\begin{gathered} \frac{80}{3}\cdot\frac{3}{8}=\frac{8}{3}x\cdot\frac{3}{8} \\ \frac{80}{8}=x \\ 10=x \end{gathered}[/tex]Answer:
x=10 am not sure
Step-by-step explanation:
Your lunch in the hospital cafeteria cost $6.50. How much will you spend each week if you average spending $6.50 per meal every day for your five day work week?
Answers
Use the square root property to solve the equation.x² = 36Select one:O A. (18)O B. {16}O C. {±6i}O D. {6}
Answers
Given the equation
[tex]x^2=36[/tex][tex]x=\sqrt{36}[/tex][tex]x=\pm6[/tex]Then
The Correct answer is
Option D 6
- A fireworks show starts at 9:00 P.M.
Orange rockets burst every 1.5 minutes,
green rockets burst every 30 seconds,
and silver showers burst every minute. [
What time is it when all three burst at
the same time?
A. 9:03 P.M.
C. 9:10 P.M.
BLcatc21
B. 9:05 P.M.
D. 9:25 P.M.
Answers
I hope this helps
Which two values of x are roots of the polynomial below?
4x² - 6x+1
A. x = -6-√52/16
B. x = 6+ √20/8
C. x = 6-√20/8
D. x = -8-√28/6
E. x = -8+ √28/6
F. x = -6 + √52/16
Answers
Roots are x = - 6 + √20/8 and x = - 6 - √20/8 of polynomial.
What in mathematics is a polynomial?
Sums of terms with the form kxn, where k is any number and n is a positive integer, make up polynomials. For instance, the polynomial 3x+2x-5. a description of polynomials. In this video, basic terms such terms, degrees, standard form, monomial, binomial, and trinomial are covered.4x² - 6x+1 = 0
x = -b ± √b² - 4ac/2a
x = - (6) ± √(-6)² - 4 * 4 * 1/2 * 4
x = -( 6) ± √36 - 16/8
x = - 6 ± √20/8
So, roots are x = - 6 + √20/8 and x = - 6 - √20/8
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Rewrite the expression 26 + 8 as the product of the GCF (greatest common factor) and a sum. Then, simplify the expression. Show all of your steps.
Answers
The expression 26+8 as the product of the GCF and a sum will be; 2(13+4).
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Given that we have the expression as 26+8
We have to find the greatest common factor of the numbers 26 and 8.
26 = 2 × 13
8 = 2 × 2 × 2
Then Multiply all the prime factors, both numbers share in order to determine the GCF:
Therefore, GCF = 2
Now we can write the expression as;
26 + 8
=2(13 + 4)
=2×17
=34
Hence. the required expression will be; 2(13 + 4).
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PLEASE HELP! Sharel received a bank account statement report the recent changes to her account. The statement showed an overall increase in the account balance of $4,317.59. During the time shown on the statement, Sharel was paid three times and withdrew a total of $1,230.67 to cover all her bills and expenses. How much (x) is each of Sharel's paychecks? Write an equation to represent this situation.
Answers
Write the equation of the line with a slopeof -3 that passes through (-5,20)
Answers
The equation of the line which passes through point (-5,20), with a slope of -3 is y = -3x + 5.
How yo determine the equation of line from a point and slope?The formula for equation of line is expressed as;
y = mx + b
Where m is slope and b is y-intercept.
Given the data in the question;
Slope m = -3Point ( -5,20 )
x = -5y = 20First, we find the y-intercept 'b', by plug the slope m ( -3 ) and point ( -5,20 ) into the equation of line formula and solving for b.
y = mx + b
20 = (-3)(-5) + b
20 = 15 + b
b = 20 - 15
b = 5
Now that both the slope m and y-intercept b is known, plug these into y = mx + b to determine the equation of the line.
y = (-3)x + 5
y = -3x + 5
Therefore, the linear equation of the line is y = -3x + 5.
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