Answer:
the Inverse of the matrix is; A⁻¹
[tex]= \left[\begin{array}{ccc}\frac{-3}{(2k)} &\frac{1}{k}&\frac{15}{(2k)}\\\frac{-3k+15}{(10k)}&\frac{-1}{k}&\frac{-75+13k}{(10k)}\\\frac{1}{2}&0&\frac{-5}{2}\end{array}\right][/tex]
Step-by-step explanation:
Given the data in the question;
Matrix A = [tex]\left[\begin{array}{ccc}-25&-25&-13\\k&0&3\\-5&-5&-3\end{array}\right][/tex]
To find the Inverse of matrix A
A⁻¹ = Adj.A / det.A
so
Determinant of the matrix A will be
|A| = -25( 0 + 15) + 25( -3K + 15 ) - 13( -15K + 0 )
= -375 - 75K + 375 + 65K
= -10K
Now, the adjoin of matrix A will be
Adj.A = [tex]\left[\begin{array}{ccc}15&-10&-75\\3k-15&10&75-13k\\-5k&0&25k\end{array}\right][/tex]
The Inverse of the matrix is;
A⁻¹ = Adj.A / det.A
[tex]= \frac{1}{-10k} \left[\begin{array}{ccc}15&-10&-75\\3k-15&10&75-13k\\-5k&0&25k\end{array}\right][/tex]
[tex]= \left[\begin{array}{ccc}\frac{15}{-10k} &\frac{-10}{-10k}&\frac{-75}{-10k}\\\frac{3k-15}{-10k}&\frac{10}{-10k}&\frac{75-13k}{-10k}\\\frac{-5k}{-10k}&\frac{0}{-10k}&\frac{25k}{-10k}\end{array}\right][/tex]
[tex]= \left[\begin{array}{ccc}\frac{-3}{2k} &\frac{1}{k}&\frac{15}{2k}\\\frac{-3k+15}{10k}&\frac{-1}{k}&\frac{-75+13k}{10k}\\\frac{1}{2}&0&\frac{-5}{2}\end{array}\right][/tex]
[tex]= \left[\begin{array}{ccc}\frac{-3}{(2k)} &\frac{1}{k}&\frac{15}{(2k)}\\\frac{-3k+15}{(10k)}&\frac{-1}{k}&\frac{-75+13k}{(10k)}\\\frac{1}{2}&0&\frac{-5}{2}\end{array}\right][/tex]
Therefore the Inverse of the matrix is; A⁻¹
[tex]= \left[\begin{array}{ccc}\frac{-3}{(2k)} &\frac{1}{k}&\frac{15}{(2k)}\\\frac{-3k+15}{(10k)}&\frac{-1}{k}&\frac{-75+13k}{(10k)}\\\frac{1}{2}&0&\frac{-5}{2}\end{array}\right][/tex]
least common multiple of 35 and 15
Find the perimeter of the following shape:
Answer:
itas niot hard. its 10+10+7+7. the 9 is meaning if it was a striaghjt line, and that is the length of the straight line.
Step-by-step explanation:
Susan subscribed to a video game rental service. She pays the same
amount for each video game she rents plus a monthly fee to subscribe to
the service. The cost for different numbers of video game rentals are
shown in the graph.
Answer:
C
Step-by-step explanation:
Answer: C. $6.00 monthly fee and $1.25 per video game
Step-by-step explanation:
I did the test
find the value of x
A wildlife biologist is doing research on chronic wasting disease and its impact on the deer populations in northern Colorado. To estimate the difference between the proportions of deer with chronic wasting disease in two different regions, a random sample of 200 deer was obtained from one region and a random sample of 197 deer was obtained from the other region. The biologist checked for the following.
(200)(0.06)≥10
(200)(0.94)≥10
(197)(0.086)≥10
(197)(0.914)≥10
Which of the following conditions for inference was the biologist checking?
a. The population of deer within each region is approximately normal.
b. It is reasonable to generalize from the samples to the populations.
c. The samples are independent of each other.
d. The observations within each sample are close to independent.
e. The sampling distribution of the difference in sample proportions is approximately normal.
Answer:e. The sampling distribution of the difference in sample proportion is approximately normal.
Step-by-step explanation:
(200) (0.06) >= 10
(200) (0.94) >=10
(197)(0.086) >=10
(197)(0.914) >= 10
We test the sample proportions of it is normal :
Deer population 1:
Sample size, n1 = 200
Proportion, p1 = 0.06
q = 1 - p = 1 - 0.06 = 0.94
n1 * p = 200 * 0.06 = 12
n1 * q = 200 * 0.94 = 188
Deer population 2:
Sample size, n2 = 197
Proportion, p = 0.086
q = 1 - p = 1 - 0.086 = 0.914
n2 * p = 197 * 0.086 = 16.94
n2 * q = 197 * 0.914 = 180.06
Since for samples and proportions ;
n*p and nq ≥ 10 ;
We cm conclude that the sampling distribution of the difference in sample mean is appropriately normal.
The sampling distribution of the difference in sample proportions is approximately normal because samples and proportions are greater than or equal to 10.
Given :
A wildlife biologist is doing research on chronic wasting disease and its impact on the deer populations in northern Colorado. A random sample of 200 deer was obtained from one region and a random sample of 197 deer was obtained from the other region.For dear population 1, the sample size is 200 and proportion is 0.06.
[tex]\rm q_1 = 1-p_1=1-0.06=0.94[/tex]
[tex]\rm n_1p_1=200\times 0.06=12\\[/tex]
[tex]\rm n_1q_1=200\times 0.94 = 188[/tex]
Now, for dear population 2, the sample size is 197 and the proportion is 0.086.
[tex]\rm q_2 = 1-p_2=1-0.086=0.914[/tex]
[tex]\rm n_2p_2=197\times 0.086=16.94[/tex]
[tex]\rm n_2q_2=197\times 0.914 = 180.06[/tex]
Therefore, from the above calculations, it can be concluded that the sampling distribution of the difference in sample proportions is approximately normal because samples and proportions are greater than or equal to 10.
So, the correct option is e).
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(-7. + 3 + x) - (=6 - 7.3 + 2.)
Rotate 90° counterclockwise about the origin.
M (3.2), N'(5,5), P'(4,5), Q'(2, 2)
M"1-2.3). N'(-5,5), P'(-5.4), (-2,2)
M(-2,-3). N'(-5.-5), P'(-5.-4). Q'-2,-2)
M*2.3). N'(5,5), P75,4), Q (2.2)
Answer:
it should be the second one
How do I find the correct Domain.
Answer:
The domain of a function is the set of all possible inputs for the function. For example, the domain of f(x)=x² is all real numbers, and the domain of g(x)=1/x is all real numbers except for x=0. We can also define special functions whose domains are more limited.
Step-by-step explanation:
Another way to identify the domain and range of functions is by using graphs. Because the domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the x-axis. The range is the set of possible output values, which are shown on the y-axis.
hope this helps a little
Order these numbers from least to greatest.
3.027, 3.2742, 3.27, 3.3
Answer:
3.027, 3.27, 3.2742, 3.3
Step-by-step explanation:
Hi! When we have these types of problems we always look at the first number. Is it less than the others? Since they are all 3, we have to look at the decimal place. 0 is less than 2 and 3, so we put 3.027 first. Since the others have 3.27 as the first point, we look at the one with the most decimal placements after 3.27 (3.2742) as being greater than 3.27. 3.27 goes before 3.2742. 3.3 is greater than all of them, so it goes last.
Answer:
3.027, 3.27, 3.2742, 3.3
Step-by-step explanation:
First list the numbers:
3.027
3.2742
3.27
3.3
Add the zero to the numbers without 4 decimal places so that they are equal.
Now you have:
3.0270
3.2742
3.2700
3.3000
Look at the number with the lowest number on the first decimal place, which is 3.0270. This becomes the lowest number. Then move on to the next decimal place. 3.2700 and 3.2742 both have the same digits on the first two decimal places. Look at the third decimal place between the two and you can see that 0 (on 3.2700) is lower than 4 (on 3.2742).
So now we have:
3.0270, 3.2700.
Then looking at the last two you have 3.2742 and 3.3000. In this case it's clear that 3.2742 is smaller so we put it as the third.
The order is as follows:
3.0270 (3.027)
3.2700 (3.27)
3.2742 (3.2742)
3.3000 (3.3)
Thirty percent of the students in a high school face a disciplinary action of some kind before they graduate. Of those students, 40% go on to college. Of the 70% who do not face a disciplinary action, 60% go on to college. What percent of the students from the high school go on to college
Answer:
54% of the students from the high school go on to college
Step-by-step explanation:
We have these following percentages:
30% of the students from a high school face a disciplinary action of some kind before they graduate. Of those, 40% go on to college.
70% do not face action, and of those, 60% go to college.
What percent of the students from the high school go on to college?
Sum of 40% of 30%(face disciplinary action) and 70% of 60%(do not
face disciplinary action). So
[tex]0.4*0.3 + 0.7*0.6 = 0.12 + 0.42 = 0.54[/tex]
54% of the students from the high school go on to college
Complete the following statements.
A soda bottle contains 2 liters of liquid. Therefore:
The soda bottle contains fluid ounces of liquid.
The soda bottle contains gallons of liquid.
A milk jug contains 2 gallons of milk. Therefore:
The milk jug contains quarts of milk.
The milk jug contains liters of milk.
Answer:
A soda bottle contains 2 liters of liquid. Therefore:
The soda bottle contains 67.62 fluid ounces of liquid.
The soda bottle contains 0.525 gallons of liquid.
2) A milk jug contains 2 gallons of milk. Therefore:
The milk jug contains 8 quarts of milk.
The milk jug contains 7.6 liters of milk.
Step-by-step explanation:
We need to complete the statements.
1)
A soda bottle contains 2 liters of liquid. Therefore:
The soda bottle contains ------- fluid ounces of liquid.
Converting Liters to fluid ouncesWe know that 1 liter = 33.81 fluid ounces
So, 2 liter = 2 x 33.81 = 67.62 fluid ounces
The soda bottle contains 67.62 fluid ounces of liquid.
The soda bottle contains gallons of liquid.
Converting liters to gallonsAs, we are not given direct conversion from liters to gallons, first we convert liter to quarts and then convert quarts to gallons
We know that
1 liter = 1.05 quarts
2 liters = 2 x 1.05 = 2.1 quarts
4 quarts = 1 gallon
1 quarts = 1/4 gallon
2.1 quarts = 1/4 * 2.1 = 0.525 gallon
The soda bottle contains 0.525 gallons of liquid.
2)
A milk jug contains 2 gallons of milk. Therefore:
The milk jug contains -------- quarts of milk.
Converting gallons to quartsWe know:
1 gallon = 4 quarts
2 gallons = 2 x 4 = 8 quarts
The milk jug contains 8 quarts of milk.
The milk jug contains ------ liters of milk.
Converting gallons to litersWe know:
1 gallon = 4 quarts
2 gallon = 8 quarts
1.05 quarts = 1 liter
1 quarts = 1/1.05 liter
8 quarts = 1/1.05 * 8 = 7.6 liter
The milk jug contains 7.6 liters of milk.
Kaylee and Josiah are reading the same book. At the beginning of the month, Kaylee was on page 24 and Josiah was on page 50. Kaylee will read 16 pages per day and Josiah will read 14 pages per day. Let K K represent the page of the book that Kaylee is on at the end of t t days into the month, and let J J represent the page of the book that Josiah is on at the end of t t days into the month. Write an equation for each situation, in terms of t , t, and determine what page Kaylee and Josiah will be on on the day they are both on the same page.
Answer:
They'll be on page 72
Step-by-step explanation:
Kaylee:
Current page = 24
Page per day = 16
Page, K, Kaylee is on at end of t days
K = current page + (page per day * Number of days)
K = 24 + 16t
Josiah:
Current page = 50
Page per day = 14
Page, J, Josiah is in at the end of t days
J = current page + (page per day * Number of days)
J = 50 + 14t
To be on the same page ;
K = J
24 + 16t = 50 + 14t
24 - 50 = 14t - 16t
- 26 = - 2t
t = 13
After 13 days, they'll be on same page :
K = 24 + 16(13)
K = 24 + 48
K =72
They'll be on page 72
Move words to the blanks and equations to the boxes to prove that vertical angles <1 and <3 are congruent
Answer:
Because linear pairs are supplementary. m∠1 + m∠2 = 180° and m∠2 + m∠3 = 180°.
Because angles that are supplementary to the same angle are congruent. It can be concluded that ∠1 ≅ ∠3.
Step-by-step explanation:
A linear pair is a pair of adjacent angles formed when two lines intersect. The two angles of a linear pair are always supplementary (that is they add up to 180°).
Therefore m∠1 and m∠2 are linear pairs, also m∠2 and m∠3 are linear pairs.
Hence:
m∠1 + m∠2 = 180°
m∠2 + m∠3 = 180°
Using substitution property:
m∠1 + m∠2 = m∠2 + m∠3
subtracting m∠2 from both sides:
m∠1 + m∠2 - m∠2 = m∠2 + m∠3 - m∠2
m∠1 = m∠3
∠1 and ∠2 are congruent
Because linear pairs are supplementary. m∠1 + m∠2 = 180° and m∠2 + m∠3 = 180°.
Because angles that are supplementary to the same angle are congruent. It can be concluded that ∠1 ≅ ∠3.
I NEED HELP PLEASE PLEASE HELP ME I WILL THANK YOU A LOT
Answer:
$8.50
Step-by-step explanation:
First, you would look at all the prices. If you have 8 tickets and they cost $62 after discount, what is the discount amount? That is 75 cents. Then, you would divide $62 by 8 tickets to get the price of each ticket. That would be $7.75 for each ticket. You would then add the discount of 75 cents to get the original price of $8.50 for each ticket.
3/5 of the students in a classroom are girls. If there are ten boys in the class, how many total students are there?
15
25
16
20
Answer:
25
Step-by-step explanation:
15=Girls
10=Boys
25 =The total of the number of students
Given that P=x+y. Find P when: x=−5 and y=−3
Answer:
P = - 8
Step-by-step explanation:
Given
P = x + y ← substitute x = - 5 and y = - 3
P = - 5 + (- 3) = - 5 - 3 = - 8
What is the range? The range is __
Answer:
8
Step-by-step explanation:
Take the biggest value and smallest value, and subtract the smallest value from the biggest value:
9-1=8
The range is 8
The numbers provided are 1, 2, 3, 4, and 9. Subtract the greatest from least,
9 - 1, and your answer is 8
(1, 1), (–1,5)
find slope
Answer:
slope = 0MARK ME AS A BRAINLIST AND FOLLOW MEHal rolls a fair six-sided die 60 times. What is the best prediction of the number of times Hal will roll a 3 or a 6?
exactly 20 times
roughly 20 times
exactly 30 times
roughly 30 times
Answer:
roughly 20 times
Step-by-step explanation:
2/6 = 1/3 is the probability he will roll a 3 or a 6
1/3 * 60 = 20.
It's not exact because you can't predict exactly what will happen, so it's roughly 20 times.
The measures of the angles of a triangle are shown in the figure below. Solve for x.
(6x+4)
41°
81°
A study of a population of 3600 dogs found that 6 out of every 90 dogs have brown fur. Based on the results of this study, how many dogs in the population DO NOT have brown fur?
7. Mangoes are sold at 5 for $4.00 and oranges are sold at 3 for $10.50. Mother bought 8
mangoen and 7 oranges. How much did she pay in all for the Items?
working
Answer:
hi hahahah
Step-by-step explanation:
A DVD normally costs $22. This week it is on sale for 25% off the original price. What is the sale price of the DVD?
Answer:
$16.5
Step-by-step explanation:
25 % of 22 is 5.5
22 - 5.5 = 16.5
The sale price of the DVD in this week on sale for 25% off on the original price is $16.5.
Given that the original price of a DVD is $22, that means the cost of the DVD is $22.
This week the sale on the original price of a DVD. The sale is that 25% off on the original price of a DVD, that is 25% off on $22.
Here, calculate the discount on the original price of a DVD.
[tex]Discount=22\times25 \%\\Discount=22\times\frac{25}{100}\\Discount=\frac{22}{4} \\Discount=\$5.5[/tex]
The discount is $5.5 on the original price of a DVD.
Therefore, the sale price of a DVD on this week after the discount:
[tex]Sale\ price= \$22-$5.5\\Sale\ price=\$16.5[/tex]
Thus, the sale price of a DVD is $16.5.
Learn more about Discount here:
https://brainly.com/question/5182397
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Is the expression 3(x+1 1/2)-3 equivalent to 3x+ 1 1/2
Answer:
Yes
Step-by-step explanation:
3(x+5.50)-3
3x+16.50)-3
-3(3x+16.50)
HELP IM TIMES FOR 20 MINUTES! IVE BEEN ON THIS FOR THE LONGEST!
Answer:
Point d
Step-by-step explanation:
because the x is -2 and the y is 3 so you look for the x and then the y
Which expressions are equivalent to 74-x-3)? Select two options.
X )? .
0-54x-21
0-72x-713)
63x-21
067x-4
3
071-x)+7(3)
Answer:
A,EStep-by-step explanation:
Edge 2021
The expressions that are equivalent to 7(-¾x - 3) are:
A. -5¼x - 21
E. 7(-¾x) -7(3)
What are Equivalent Expressions?Equivalent expressions are expressions that have the same values when evaluated or simplified.
Given:
7(-¾x - 3)
Open the bracket
7(-¾x) -7(3)
-5¼x - 21
Therefore, the expressions that are equivalent to 7(-¾x - 3) are:
A. -5¼x - 21
E. 7(-¾x) -7(3)
Learn more about equivalent expressions on:
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Find the slope of the two coordinates:
(2, 4) and (4, 14)
Write the equation of the line in Point-Slope Form
using the first coordinate.
Answer:
3,6
Step-by-step explanation:
what are the factors of 15
Answer:
[tex]factors \: of15 = 3 , 1\: and \: 5[/tex]
Write the equation of the line passing through the points (-4,7) and (-7,4)
Answer:
y=x+11
Step-by-step explanation:
The triangle with lines through it designates a no parking zone. What is the value of x?
2x
45°
+o
GO
Answer:
45°
Step-by-step explanation:
A triangle is a polygon that has three sides and three angles. There are different types of triangles such as equilateral triangle, isosceles triangle, scalene triangle, right angled triangle.
All the three angles in a triangle add up to 180°.
From the question:
x + 2x + 45 = 180° (sum of angles in a triangle)
Adding alike terms:
3x + 45 = 180
Subtract 45 from both sides:
3x + 45 - 45 = 180 - 45
3x = 135
Divide both sides of the equation by 3 to find x:
3x / 3 = 135 / 3
x = 45°
Therefore:
The value of x is 45°