AB = [1 0] is the 2x2 identity matrix so, AB=I.
[0 1]
To find a 3x2 matrix B such that AB=I, we need to solve the equation:
A × B = I
where I is the 2x2 identity matrix. We can use the hint given to us to find the columns of B.
Let B1 and B2 be the columns of B. Then we have:
A × B1 = I1
A × B2 = I2
where I1 and I2 are the columns of the 2x2 identity matrix I.
We can solve for B1 and B2 by setting up and solving the following systems of linear equations:
For B1:
1 × B1[1] + 1 × B1[2] = 1
2 × B1[1] + 1 × B1[2] = 0
1 × B1[1] + 1 × B1[2] = 0
For B2:
1 × B2[1] + 1 × B2[2] = 0
2 × B2[1] + 1 × B2[2] = 1
1 × B2[1] + 1 × B2[2] = 0
Solving these systems of equations, we get:
B1 = [-1, 1]
B2 = [1, -1]
Therefore, the 3x2 matrix B that satisfies AB=I is:
B = [-1 1]
[ 1 -1]
[ 0 0]
We can verify that AB is indeed equal to the 2x2 identity matrix I:
A × B = [1 2 1] × [-1 1 0] = [(-1)+2 (1)+(-1) 0+0] = [1 0]
[1 1 1] [ 1 -1 0] [ 1+1 (1)+(-1) 1+0] [0 1]
Therefore, AB = I:
AB = [1 0]
[0 1]
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The question is -
For the given matrix A find a 3x2 matrix B such that AB=I, where I is the 2x2 identity matrix. [Hint: If B1 and B2 are the columns of B, then ABj = Ij.]
A = 1 2 1
1 1 1
Rewrite in simplest radical form
130 estimated to the nearest integer is
130 estimated to the nearest integer is 130 itself as 130 itself is an integer.
What are Integers?Integers are numbers which includes the set of natural numbers, 0 and the negatives of all those natural numbers.
Set of integers are usually denoted as Z.
A number is normally rounded to the nearest integer when it is decimal.
First we have to look at the tenths place.
When the digit in the tenths place is 5 or numbers greater than 5, then increase digit in the ones place by 1.
If the digit in tenths place is less than 5, then leave the ones place as such.
Suppose that the number is 1.30.
Then the digit in tenths place is 3, less than 5. So leave the digit in one place which is 1, as such.
So 1.30 rounded to the nearest integer is 1.
Here 130 itself is an integer.
Hence 130 rounded to nearest integer is 130.
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Jack works at a party supply store. He sold 750 balloons in the last 15 days. What was his selling rate in balloons per day
his selling rate is: 750 balloons / 15 days = 50 balloons per day . To calculate Jack's selling rate in balloons per day, we need to divide the total number of balloons he sold by the number of days he worked.
This means that Jack sold an average of 50 balloons per day over the last 15 days. This information is useful for several reasons. For example, the party supply store might use this information to evaluate Jack's performance and determine whether he is meeting their expectations. It might also be useful for forecasting future sales, since if Jack continues to sell balloons at a rate of 50 per day, we can estimate how many balloons he will sell in a future period of time by multiplying the number of days by 50. In this case,
Jack sold 750 balloons in 15 days, so his selling rate is: 750 balloons / 15 days = 50 balloons per day
It's important to note that the selling rate of 50 balloons per day is an average, and it's possible that Jack's sales varied from day to day. For example, he might have sold more balloons on some days and fewer on others. However, by calculating the average selling rate, we get a general sense of how many balloons Jack sold per day over the course of the last 15 days.
In conclusion, Jack's selling rate in balloons per day over the last 15 days was 50 balloons. This information provides insight into Jack's performance and can be used to make informed decisions about future sales.
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How many books with spines that are 1 1/4 inches wide can fit on each shelf
We can fit 33 books on a 42-inch shelf if each book is 1 1/4 inches wide.
Using a unitary method, we can easily solve problems that involve proportional relationships between different units. In this problem, we used the unitary method to determine how many books can fit on a shelf based on its length and the width of one book.
To find out how many books can fit on a 42-inch shelf, we need to divide the length of the shelf by the width of one book. In this case, each book is 1 1/4 inches wide. However, it's important to convert this fraction to a decimal so we can do the math more easily. To do this, we can divide 1 by 4 and add it to 1 1/4:
1/4 = 0.25
1 1/4 = 1 + 0.25 = 1.25
Now that we know each book is 1.25 inches wide, we can use the unitary method to find how many books can fit on the shelf:
1 book = 1.25 inches
x books = 42 inches
To solve for x, we can cross-multiply:
1 book * 42 inches = 1.25 inches * x books
42 = 1.25x
Finally, we can divide both sides by 1.25 to isolate x:
42 / 1.25 = x
33.6 = x
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Starting with the number 10, build a sequence of 5 numbers.
Answer:
Step-by-step explanation:
To build a sequence, you have to create a rule. For example, if the rule is +2, then you add 2 to 10 to get 12, and then you add 2 to 12 to get 14, and so on. Your sequence would then be 10, 12, 14, 16, 18.
Which of the following rational functions is graphed below?
-5
OA. F(x)=
O C. F(x) =
1
B. F(x) = (x+2)(x-3)
OD. F(x) =
5
x(x - 2)
(x-2)
(x + 3)
1
(x-2)(x+3)
5
The graph of the function f(x) = x(x + 5)(x - 2) have x intercepts at x = 0, -5 and 2
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
An equation is an expression that shows the relationship between two or more numbers and variables.
Given the equation:
f(x) = x(x + 5)(x - 2)
x(x + 5)(x - 2) = 0
x = 0, x + 5 = 0, x - 2 = 0
x = 0, -5 and 2
The graph of the function f(x) = x(x + 5)(x - 2) have x intercepts at x = 0, -5 and 2
Hence, the graph of the function f(x) = x(x + 5)(x - 2) have x intercepts at x = 0, -5 and 2
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Louise is planning to renovate her house. She intends to spend no more than $30 000. She has
$20 000 to invest in an account that pay 4.28% compounded monthly. How long will it take
Louise to meet her goal? Show your work. Round your answer to the nearest tenth of a year.
Answer:
Step-by-step explanation:
To determine how long it will take for Louise to reach her goal of $30,000, we can use the formula for compound interest:
A = P * (1 + r/n)^(nt)
where:
A is the amount of money Louise will have after "t" years,
P is the initial investment of $20,000,
r is the annual interest rate of 4.28%,
n is the number of times the interest is compounded per year (12 times per year), and
t is the number of years.
We can rearrange this formula to solve for t:
t = (log(A/P)) / (log(1 + r/n))
Plugging in the values:
t = (log(30000/20000)) / (log(1 + (0.0428/12)))
t = 5.97 years
Rounding to the nearest tenth of a year, Louise will need to wait 6.0 years in order to reach her goal of $30,000.
Greta has two pet lizards, Draco and Lizzy. For every 11 crickets Greta feeds Draco, she always feeds Lizzy 8 crickets. Last week, Greta fed Draco 77 crickets.
Greta feeds Lizzy 56 crickets when she feeds Draco 77.
What do you understand by Proportion?Proportion, in general is referred to as a part, share or number considered in comparative relation to a whole.
According to proportion, if two sets of given numbers are increasing or decreasing in the same ratio, then the ratios are said to be directly proportional to each other.
The ratio is a way of comparing two quantities of the same kind by using division. The ratio formula for two numbers a and b is given by a: b or a/b
Given:
For every 11 crickets Greta feeds Draco, she always feeds Lizzy 8 crickets.
Let solve it by an equality
[tex]\frac{11}{8} = \frac{77}{x}[/tex]
We want to solve for x.
We can do so by finding how much larger the second fraction is than the first.
In this case, 77 is 7 times larger than 11.(77/11 = 7)
So, we know that x must be 7 times larger then 8( because the fractions are proportinal)
Since x is 7 times larger than 8, we can use 7 times 8 to find the value.
7 times 8 i s56
56 crickets for Lizzy.
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x is 7 times larger than 8, we can use 7 times 8 to find the value, 7 times 8 is 56. Greta feeds Lizzy 56 crickets while she feeds Draco 77.
What is the Proportion?
Proportion, in general, is referred to as a part, share, or number considered in comparative relation to a whole.
According to proportion, if two sets of given numbers are increasing or decreasing in the same ratio, then the ratios are said to be directly proportional to each other.
The ratio is a way of comparing two quantities of the same kind by using division. The ratio formula for two numbers a and b is given by a: b or a/b
Given:
For every 11 crickets Greta feeds Draco, she always feeds Lizzy 8 crickets.
Let solve it with an equality
11/8 = 77/x
We want to solve for x.
We can do so by finding how much larger the second fraction is than the first.
In this case, 77 is 7 times larger than 11.(77/11 = 7)
So, we know that x must be 7 times larger than 8( because the fractions are proportional)
Hence, x is 7 times larger than 8, we can use 7 times 8 to find the value.
7 times 8 is 56.
56 crickets for Lizzy.
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Is (x + 2) a factor of the polynomial:x4 +
x³ - 2x² + 3x + 7, and what was the
remainder?
Answer:no
Step-by-step explanation:
help this is dew soon!
Answer:
Step-by-step explanation:
so 1in is 2.5ft.
6.4 times 2.5 is 16.
4.8 times 2.5 is 12.
16+16+12+12
is 24+32.
which is 56.
answer: B
14) For y=-7, when x = -35, what is the constant of variation and what is the direct-variation equation?
A 35-year-old woman purchases a $100,000 term life insurance policy for an annual payment of $360. Based on a period life table for the U.S. government, the probability that she will survive the year is 0.999057. Find the expected value of the policy for the insurance company.
The expected value of the policy for the insurance company: $359.38
What is probability?Probability is a mathematical term, which can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. The possibility that an event will occur is measured by probability.
Probability of Event = Favorable Outcomes/Total Outcomes = X/n
The expected value of the policy for the insurance company can be calculated as follows:
Expected value = (Probability of survival) x (Annual payment)
= 0.999057 x $360
= $359.38
So, the expected value of the policy for the insurance company is $359.38.
It's important to note that this is just an estimate based on statistical probabilities and does not guarantee the outcome. The actual value could be higher or lower than this estimate, depending on the actual lifespan of the policyholder.
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bearing is measured from reference line clockwise or counter-clockwise. group of answer choices true false
Bearing is measured from reference line clockwise or counter-clockwise - FALSE.
A bearing is an angle that is calculated clockwise from the north.
The vertical angle between an object's direction and either north or another object is known as a bearing or azimuth in navigation. You can specify the angle value in a number of different angular units, including degrees, mils, and grad.
Angles are measured in comportments clockwise from north.
The direction of north must be identified before taking a bearing measurement.
The math exam question will typically include this north direction. The required angle is then measured in a clockwise fashion. Since all bearings must be reported in three figures, we must begin the three-figure bearing with zero if the angle measured is less than 100 degrees.
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ari thinks the perfect milkshake has 5 55 scoops of ice cream for every 3 33 spoonfuls of caramel. freeze zone makes batches of milkshakes with 10 1010 scoops of ice cream and 7 77 spoonfuls of caramel. what will ari think about the amount of caramel in freeze zone milkshakes?
Ari will likely think that the amount of caramel in Freeze Zone milkshakes is too high, since the ratio of ice cream to caramel is much higher than her ideal ratio.
Ari's ideal ratio of ice cream to caramel for a milkshake is 5 scoops of ice cream for every 3 spoonfuls of caramel. Freeze Zone's milkshakes, however, have a ratio of 10 scoops of ice cream for every 7 spoonfuls of caramel, which is significantly higher than Ari's ideal ratio. Therefore, Ari will likely think that the amount of caramel in Freeze Zone milkshakes is too high. The higher ratio of ice cream to caramel means that the milkshake will be sweeter, and may not have the desired balance of flavors that Ari prefers. Ari may also think the milkshake is too heavy or overly sweet, since the extra caramel creates a consistency that is different from what she is used to. Ultimately, Ari will likely think that the amount of caramel in Freeze Zone's milkshakes is too high for her liking.
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what is the order of processes that support the central dogma?
The order of processes that support the central dogma are:1.DNA replication: the process by which DNA makes a copy of itself.
2.Transcription: the process by which RNA is synthesized from a DNA template.
3.Translation: the process by which proteins are synthesized from RNA templates.
The central dogma of molecular biology describes the flow of genetic information within a biological system. The method by which DNA instructions are translated into useful products is known as the "Central Dogma." Francis Crick, who discovered the structure of DNA, first put up the idea in 1958.
The order of processes that support the central dogma are:
1.DNA replication: the process by which DNA makes a copy of itself.
2.Transcription: the process by which RNA is synthesized from a DNA template.
3.Translation: the process by which proteins are synthesized from RNA templates.
In summary, the central dogma can be described as follows: DNA is replicated to make more DNA, DNA is transcribed into RNA, and RNA is translated into proteins.
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scientists are modeling the spread of a hypothetical virus. in their computer model, there are currently 392 people infected, and the virus is spreading at a rate of 11% each day. how many people will be infected in 3 days? if necessary, round your answer to the nearest whole number.
According to the model, around 521 people will be infected in three days.
A unitary method is a mathematical technique where we use ratios and proportions to find the value of an unknown quantity.
Let's start by breaking down the problem. We know that there are currently 392 people infected and the virus is spreading at a rate of 11% each day. This means that for every 100 people, 11 people are getting infected. To calculate how many people will be infected in three days, we need to use a unitary method.
To do this, we need to calculate the total increase in the number of infected people over three days. Since the virus is spreading at a rate of 11% each day, the total increase over three days will be 33% (11% x 3). We can then use this percentage increase to calculate the total number of people infected in three days.
To find the total number of people infected in three days, we can use the following formula:
Total infected = current infected + (current infected x percentage increase)
Plugging in the values from the problem, we get:
Total infected = 392 + (392 x 0.33)
Total infected = 392 + 129.36
Total infected ≈ 521
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given f(x)=2x^{2}+4 find f(3)
Answer: 22
Step-by-step explanation:
f(x) is basically the y of the function and we sent x=3. go back to the function and plug in 3 in the x. then solve 3^2=9 2x9=18 18+4=22 BOOOM MATHH
is petid good to uniquely identify each data record of the pet relation? why does personid in the pet relation need to be a part of the primary key of the pet relation
Using petid as a primary key in the pet relation is generally a good way to uniquely identify each data record in the relation. However, in some cases, it may be necessary to include personid as part of the primary key of the pet relation.
This is because each pet should have a unique identifier, and petid is specifically designed to serve this purpose. This would be the case if a person can have more than one pet in the database, and if the same petid value is used for more than one pet (which would violate the uniqueness requirement of a primary key).
By including personid as part of the primary key of the pet relation, we ensure that each pet in the database has a unique identifier (i.e., a unique combination of petid and personid). This allows us to avoid any confusion that might arise if two or more pets in the database had the same petid value. It also allows us to link each pet to its owner via the personid attribute, which can be useful for querying and reporting on the data.
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Please find the missing side length using trig!
The length x of the right triangle is 8.66 units.
How to find the side of a right triangle?A right triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.
Therefore, the side of the right triangle can be found using trigonometric ratios as follows:
Hence,
tan 60° = opposite / adjacent
where
opposite side = x
adjacent side = 5
Therefore,
tan 60° = x / 5
cross multiply
x = 5 tan 60°
x = 5 × 1.73205080757
x = 8.66025403784
x = 8.66 units
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The basketball team averaged 68 points per game last
season and average 77 points per game this season.
What is the approximate percent of the increase?
Hi there, here's your answer:
Given, a basketball team averaged 68 points per game in the last season and averaged 77 points per game in the present season.
To find:
The approximate percentage of increase.
Solution:
If 68 points was the average last season, and 77 points was the increase this season, then the number of increase in points is 9.
Also we have that % increase = [tex]\frac{Difference}{Original}[/tex] × 100
Which is [tex]\frac{9}{68}[/tex] × 100 = 0.1323 × 100 = 13.23%
Therefore, the approximate percent increase is 13%.
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Suppose that the amount of algae in a pond doubles every 5 hours. If the pond initially contains
10 pounds of algae, how much algae will be in the pond after 20 hours?
Answer:
160 pounds of algae
Step-by-step explanation:
10 times 2 is 20 ( first 5 hours )
20 times 2 is 40 (10 hours)
40 times 2 is 80 (15 hours)
80 times 2 is 160 ( 20 hours)
there would be 160 pounds of algae
Combine the like terms to simplify this expression: ( the 2 to the right of the x, is an exponent)
10y - 14x² + 3x - 4x² + 4y - 6
Answer: -18x² + 3x +14y - 6
10y - 14x² + 3x - 4x² + 4y - 6
- 14x²- 4x² + 3x + 10y + 4y -6
-18x² + 3x +14y - 6
Work & Power: Incredibles
Must Show Work!!
Mr. Incredible can push with a force of 5000 N on a train and move it 100 meters in 100
seconds. Dash can push this tiny railcar with a force of 50 N moving it 100 meters in 1
second. Who would you say did more work? Also, who is more powerful? Explain your
answers.
Based on the information, it can be inferred that Mr. Incredible did more work than Dash moving the train car.
How to calculate the work done by Mr. Incredible and Dash?To calculate the work that Mr. Incredible and Dash did moving the train car, we must apply the following mathematical formula:
Work (Joules) = Force (N) * Distance (d)According to the above, we only have to replace the values according to each case.
J = 5,000 * 100J = 500,000J = 50 * 100J = 500According to the above, it can be inferred that Mr. Incredible made more effort than Dash because they did 500,000 J and 500 J of work respectively.
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2. Andrea and Casey work at a restaurant over the summer. Andrea gets paid $25 when they
work along with an average of $9 in tips every hour. Casey only gets $10 when they work,
but they make an average of $14 in tips every hour. Write a system of equations to determine
how many hours it takes for Andrea and Casey to make the same amount of money? How
much money is it?
Answer:
So Andrea and Casey each make $52 after working for 3 hours.
Step-by-step explanation:
Let's call the number of hours that Andrea and Casey work "x".
The amount of money that Andrea makes in a given hour can be represented as 25 + 9x.
The amount of money that Casey makes in a given hour can be represented as 10 + 14x.
We want to find the number of hours it takes for Andrea and Casey to make the same amount of money, which we can represent as:
25 + 9x = 10 + 14x
To solve for x, we can isolate x by subtracting 10 from both sides of the equation:
15 + 9x = 14x
Next, we can isolate 9x by subtracting 14x from both sides of the equation:
15 = -5x
Finally, we can divide both sides of the equation by -5 to solve for x:
-3 = x
So it takes 3 hours for Andrea and Casey to make the same amount of money. To find the amount of money, we can plug in x = 3 back into either of the equations:
Andrea's equation: 25 + 9x = 25 + 9 * 3 = 25 + 27 = 52
So Andrea and Casey each make $52 after working for 3 hours.
What is the mode of the data set 0,0,1,1,1,2,2,2,2,3
Answer:
Step-by-step explanation:
2, there are 4, making it the most.
2) g(x) = 4x + 5
f(x)=-3x²-3x
Find g(x) + f(x)
Answer:
[tex]\huge\boxed{\sf -3x\² + x + 5}[/tex]
Step-by-step explanation:
Given functions:g(x) = 4x + 5
f(x) = -3x² - 3x
Add both functionsg(x) + f(x):= 4x + 5 + (-3x² - 3x)
= 4x + 5 - 3x² - 3x
Combine like terms= 4x - 3x + 5 - 3x²
= x + 5 - 3x²
= -3x² + x + 5[tex]\rule[225]{225}{2}[/tex]
11 Jack and Sadia work for a company that
sells boxes of breakfast cereal. The
company wants to have a special offer.
Here is Jack's idea for the special offer.
Put 25% more cereal into each box and do not change the price.
Here is Sadia's idea.
Reduce the price and do not change the amount of cereal in each
box.
Sadia wants her idea to give the same value for money as Jack's idea.
By what percentage does she need to reduce the price?
Answer:
20% reduction in price
Step-by-step explanation:
Let the original price of each box be P and original quantity be Q. The unit rate is P/Q
Jack's approach
increase quantity by 25% = 0.25Q
New quantity = Q + 0.25Q = Q(1 +0.25) = 1.25Q
Unit rate = P/1.25Q
Sadia's approach
Reduce price and keep quantity same
Let price reduction be d% = d/100
Let us denote d/100 as r. This will be a decimal value. For example, a reduction of 10% means that the price is reduced by 0.10
Price reduction = P x r = Pr
New price = P - Pr = P(1-r)
Unit rate by this method =P(1-r) /Q
Both unit rates have to be the same if both values are the same
So
[tex]\dfrac{P}{1.25Q} = \dfrac{P(1-r)}{Q}\\\\\dfrac{P}{Q} \cdot \dfrac{1}{1.25} = \dfrac{P}{Q} \cdot (1-r)\\\\[/tex]
Eliminate [tex]\displaystyle {\dfrac{P}{Q}}[/tex] common factor from both sides to get
[tex]\dfrac{1}{1.25} = 1- r[/tex]
[tex]\dfrac{1}{1.25} = 0.8\\\\[/tex]
So we get
[tex]1 - r = 0.8\\\\\implies r = 1 - 0.8 = 0.2\\\\[/tex]
0.2 works out to 0.2 x 100 = 20%
So for Sadia's idea to have the same value as Jack's idea, the price should be reduced by 20%
The proof shown needs several statements and reasons filled in.
Given the angle bisector, the statements and reasons for the proof are explained.
What is an angle bisector?A bisector splits a given line or angle into two equal parts. A straight line is said to be an angle bisector if it divides a given angle into two equal measures. Such that on comparison, the sum of the angles formed is equal to the measure of the bisected angle.
The statements and reasons for the proof are given below;
STATEMENT REASONS
1. MK bisects <HKO and <HMO Given
2. m<HMK = m<OMK and m<HKM = m<OKM Definition of angle bisector
3. HK ≅ KO, and HM ≅ OM Congruent side property
4. ΔHMK ≅ ΔOMK Angle-Angle-Side theorem
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HELP!Find each percent change. Use a calculator and round answer to the nearest tenth as needed. State if it is an increase or decrease. 88 to 20
A.22.7% decrease
B.14.2% decrease
C.77.3% decrease
D.340% decrease
Answer:
C. 77.3% decrease
Step-by-step explanation:
To calculate the percent change, we can use the formula:
percent change = (new value - old value) / old value * 100
Plugging in the values, we get:
percent change = (20 - 88) / 88 * 100 = -68 / 88 * 100 = -0.772727 * 100 = -77.3
Since the new value is lower than the old value, this is a decrease, and the answer is -77.3, or 77.3% decrease.
Question is in picture - a detailed explanation would be very apricated.
Answer:
$1350.68 to nearest cent.
Step-by-step explanation:
At the beginning $500 is deposited and this accumulates interest for 3 years At the end of first year it increases to 500( 1 + r) dollars
Then at the end of the 2 years its value is
500(1+ r)(1 + r)(
and at the end of 3 years value =
500(1 + r)(1 + r)(1 + r)
= 500(1 + r)^3 dollars
and as 1 + r = x we have:
500x^3 dollars
In the same way 200 for 2 years = 200x^2
and 600 for 1 year = 600x dollars.
Total = 500x^3 + 200x^2 + 600x.
b.
So, if the interest r = 2 % (= 0.02)
and x = 1.02
Total value after 3 years
= 500(1.02)^3 + 200(1.02)^2 + 600(1.02)
= 530.604 + 208.08 + 612
= $1350.684
