The comparison between the distance he biked and swam is 3 : 1.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
From the given information the comparison of the distance he swam to the distance he biked can be represented in the form of ratios.
Given, He rode his bike 3/4 miles and swam for 1/4 mile.
Therefore, The ratio of biking : swimming = 3/4 : 1/4.
Now, Multiplying by 4 to get rid of the denominator we have,
Biking : Swimming = 3 : 1.
As the days in both comparisons increase in the same manner the ratio will remain the same.
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Sux less than two times a number is no more than 17
The mathematical statement οf given statement Sux less than twο times a number is nο mοre than 17 is 2x - 6 ≤ 17.
What is mathematical statement?A mathematical statement is a sentence that can be either true οr false and cοntains mathematical expressiοns οr variables, such as numbers, variables, οperatiοns, relatiοns, οr lοgical cοnnectives.
Mathematical statements can take many fοrms, such as equatiοns, inequalities, geοmetric theοrems, and lοgical prοpοsitiοns. Fοr example, "2 + 2 = 4" is a mathematical statement that is true, while "1 + 1 = 3" is a mathematical statement that is false.
Nοw,
Given statement can be written as
Twο times=2x
six less than 2 times=2x-6
is nο mοre than 17= 2x-6≤17
where x is the number.
Hence,
The mathematical statement οf given statement Sux less than twο times a number is nο mοre than 17 is 2x - 6 ≤ 17.
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Could use some help problem is in picture thanks!!
The equation that quickly reveals the y-intercept is f(x) = 3x²+ 36x + 33 and the y- intercept is 33
What are intercepts?The x-intercept is the point where a line crosses the x-axis, and the y-intercept is the point where a line crosses the y-axis.
This shows that the y-intercept is gotten when x is 0
Therefore amongst the equation above equation 1 is the equation that easily shows the y-intercept.
The equation f(x) = 3x²+ 36x + 33 is presented in a standard form of quadratic equation.
when x= 0
f(x) = 3x²+ 36x + 33
f(x) = 3(0)²+ 36(0) + 33
f(x) = 0+ 0+ 33
= 33
therefore the y-intercept is 33
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Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms. (Assume all variables are positive)
The expression can be expanded as a difference of two logarithms:
[tex]ln(\sqrt\frac{x^2}{y^5})[/tex] = [tex]2 ln(x) - (5/2) ln(y)[/tex]
What is the logarithms?
Logarithms are mathematical functions that help to simplify the representation of very large or very small numbers. They are the inverse functions of exponential functions.
We can use the properties of logarithms to expand the expression as follows:
[tex]ln(\sqrt\frac{x^2}{y^5})[/tex] = [tex]ln(x^2) - ln(y^5/2)[/tex]
Next, we can simplify each logarithm using the property that log(a^b) = b log(a):
[tex]ln(x^2) - ln(y^5/2)[/tex] = [tex]2 ln(x) - (5/2) ln(y)[/tex]
Hence, the expression can be expanded as a difference of two logarithms:
[tex]ln(\sqrt\frac{x^2}{y^5})[/tex] = [tex]2 ln(x) - (5/2) ln(y)[/tex]
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(a) Find all solutions for x =
[[
x1
x2
x3
]] of the equation system Ax = 3x
where
A =[
[
3 4 3
2 5 3
0 2 6
]]
(b) What is the dimension of the solution set of Ax = 3x?
Note that, in order to answer this question you need first to argue
why it is allowed to speak about the dimension of the solution set
of Ax = 3x
In the following question, among the various parts to solve- a- "x = [[3/2x3-3/2x3x3]]", b- the dimension of the solution set of Ax = 3x is 1.
(a) To find all solutions of the equation system Ax = 3x, we need to solve the following system of linear equations:
(3 4 3) (x1) (3x1)
(2 5 3) (x2) = (3x2)
(0 2 6) (x3) (3x3)
This can be written as (A - 3I)x = 0, where I is the identity matrix. To find the solutions, we need to find the null space of A - 3I.
(A - 3I) = [[0 4 3 2 2 3 0 2 3]]
To find the null space of this matrix, we row-reduce it to obtain:
[[1 0 -3/2 0 1 3/2 0 0 0]]
The last row tells us that x3 is a free variable, while the first two rows give us:
x1 = (3/2)x3
x2 = (-3/2)x3
Therefore, the general solution to Ax = 3x is:
x = [[3/2x3-3/2x3x3]]
where x3 is any real number.
(b) We can speak about the dimension of the solution set of Ax = 3x because it is a linear homogeneous equation. In this case, the solution set is a subspace of the vector space R^3, and the dimension of this subspace is the number of linearly independent solutions. Since we have one free variable in the solution, the set of solutions is a line in R^3, and its dimension is 1. Therefore, the dimension of the solution set of Ax = 3x is 1.
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Pls
Assistance and steps
What is the inverse of y = 3/2x?
Answer:
option (1)
Step-by-step explanation:
rearrange making x the subject, then x is the inverse
y = [tex]\frac{3}{2}[/tex] x ( multiply both sides by 2 to clear the fraction )
2y = 3x ( isolate x by dividing both sides by 3 )
[tex]\frac{2}{3}[/tex] y = x
change y back into terms of x , then inverse is
[tex]f^{-1}[/tex] (x) = [tex]\frac{2}{3}[/tex] x , or
y = [tex]\frac{2}{3}[/tex] x
the sum of two numbers is 149 and the difference is 31.
Answer:
The two numbers are 90 and 59
Step-by-step explanation:
Let's call the two numbers x and y.
From the problem statement, we know that:
x + y = 149 (the sum of two numbers is 149)
x - y = 31 (the difference of the two numbers is 31)
To solve for x and y, we can use the method of elimination. Adding the two equations together eliminates the y term:
(x + y) + (x - y) = 149 + 31
2x = 180
x = 90
Substituting x = 90 into one of the original equations, we can solve for y:
x + y = 149
90 + y = 149
y = 59
Therefore, the two numbers are 90 and 59.
I dont know what the answer is and well im quite confused.
Answer:
C
Step-by-step explanation:
They are not proportional
If 3 pie cost $12, one pie will be $4
If 10 pie cost $25, then 1 pie is $2.5
$4 is not proportional to $2.5
Hence 12/3 is not proportional to 25/10
What difference in inches are there in 7 3/4 and 8 wholes
The difference in inches between 7 3/4 and 8 whole numbers is 1/4 inch.
What is Subtraction?
One of the four arithmetic operations, along with addition, multiplication, and division, is subtraction, which is denoted by the minus sign. The operation of subtraction represents the removal of items from a collection. In the adjacent image, for instance, there are 5 2 peaches, which means 5 peaches with 2 subtracted, making a total of 3 peaches.
As a result, 5 minus 2 equals 3, or the difference between 5 and 2. Although subtraction is most often used in mathematics with natural numbers, it can also be used with other types of objects, such as negative numbers, fractions, irrational numbers, vectors, decimals, functions, and matrices, to remove or decrease physical and abstract quantities.
The difference in inches between 7 3/4 and 8 whole numbers is 1/4 inch.
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9 of 119 of 11 Items
Question
Jillian and Jacob are playing a game where they have to collect blue and yellow tokens. Blue and yellow tokens are worth a different amount of points. Jillian has collected 4 blue tokens and 7 yellow tokens and has 95 points. Jacob has collected 4 blue tokens and 3 yellow tokens and has 75 points. How many points are a blue token and a yellow token worth?
Using the unitary method, we found that one yellow token is worth 13.57 points and one blue token is worth 8.57 points.
Let's first find the value of one yellow token. We know that Jillian has collected 7 yellow tokens and has a total of 95 points. Therefore, the value of 1 yellow token can be found using the unitary method as follows:
1 yellow token = 95 / 7
1 yellow token = 13.57
Therefore, one yellow token is worth 13.57 points.
Therefore, the value of 4 blue tokens can be found using the unitary method as follows:
4 blue tokens = 75 - (3 x 13.57)
4 blue tokens = 34.29
Now, we know that 4 blue tokens are worth 34.29 points. To find the value of one blue token, we can use the unitary method again as follows:
1 blue token = 34.29 / 4
1 blue token = 8.57
Therefore, one blue token is worth 8.57 points.
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The temperature in Astralia one morning wa 5° at 03:00 and increased by 2° every hour until 12:00 what will the temperature be at 11:30
Answer:
21.5
Step-by-step explanation:
Table A tracks the date when 100 players played a game, where one row corresponds to a player id and the date they opened and played the game. The same player id can have multiple rows if they have played the game across multiple days. In Table A, 90 played for 1 day and 10 played across 2 days. Table B tracks the install date of 99 players who were in Table A for the same game. In Table B, one row corresponds to a player id and the date they installed the game. The same player id can have multiple rows if they have installed the game multiple times. Of the 90 players who played for 1 day, 82 installed once, 7 installed twice and 1 was not in Table B. Of the 10 players who played across 2 days, 9 installed once and 1 installed twice. How many rows would the resulting table have if you took Table A and left (outer) joined with Table B using the player id?
According to the question the resulting table would have 109 rows.
What is table?Table is a piece of furniture with a flat top and one or more legs, used as a surface for working at, eating from or on which to place things. Tables come in a variety of materials, shapes, and sizes and are used in many different settings, including homes, offices, and commercial establishments.
This is because all 90 players who played for 1 day would be joined, plus the 10 players who played across 2 days. Of the 90 players who played for 1 day, 82 would have 1 row each from the join, 7 would have 2 rows from the join, and 1 would have 0 rows from the join (since it was not in Table B). Of the 10 players who played across 2 days, 9 would have 1 row each from the join, and 1 would have 2 rows from the join. This adds up to a total of 109 rows.
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Han bought a chest of drawers for $210 and sold it 4 years later for $139. Calculate his loss as a percentage of the original price correct to 2 decimal places.
Therefore, Han's loss amounts to 33.81% of the original cost because he spent $210 on a chest of drawers before selling it for $139 four years later.
what is percentage ?A figure can be expressed as a fraction of 100 using a percentage. It is frequently utilised to compare two values or to convey a portion of a whole. "%," which stands for "per hundred," is the symbol used to indicate percentages. 50%, for instance, is 50/100, or 50 out of 100. Calculating percentages involves dividing a portion by a whole and multiplying the result by 100. For instance, if a bag contains 75 blue spheres and 25 red balls, the proportion of red balls is as follows:
(Number of red balls / Total Number of Balls) times 100% equals the percentage of red balls.
Red ball percentage equals (25/100) times 100%
25% of the balls are crimson.
given
You can compute the cost as follows:
Loss is calculated as Initial Price - Selling Price ($210 - $139).
Loss = $71
We must divide the loss by the initial price and multiply by 100 to determine the percentage loss:
(Loss / Original price) times 100 equals the percentage of loss.
($71 / $210) times 100 equals the percentage loss.
Loss as a percentage: 33.81%
Therefore, Han's loss amounts to 33.81% of the original cost because he spent $210 on a chest of drawers before selling it for $139 four years later.
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Can somebody tell me If this is right or wrong because I don’t know.
The simple interest values are all wrong
What is simple interest?Simple Interest (S.I) is a method of charging or yielding a specific percentage on the principal amount borrowed/deposited in a particular period. It is calculated using the formula
SI = (Principal*Rate*Time)/100,
a) SI = (450*25.2*3)/100,
SI = %70.2
2) SI = (Principal*Rate*Time)/100,
SI = (250*3.75*5)/100,
$46.875
(3) SI = (Principal*Rate*Time)/100,
SI = (1800*2.1*2)/100,
SI = $75.6
4) SI = (Principal*Rate*Time)/100,
SI = (1500*2.9*2)/100,
SI = $87
5) SI = (Principal*Rate*Time)/100,
SI = (50*1.9*10)/100,
SI =$9.5
6) SI = (Principal*Rate*Time)/100,
SI = (8*0.7*300)/100,
SI = $16.8
7) SI = (Principal*Rate*Time)/100,
SI = (125*2.03*4)/100,
SI = $10.15
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Skydiving, anyone? A humor piece published in the British Medical Journal ("Parachute use to prevent death and major trauma related to gravitational challenge: Systematic review of randomized control trials," Gordon, Smith, and Pell, BMJ, 2003:327) notes that we can’t tell for sure whether parachutes are safe and effective because there has never been a properly randomized, double-blind, placebo-controlled study of parachute effectiveness in skydiving. (Yes, this is the sort of thing statisticians find funny. . . .) Suppose you were designing such a study:
a) What is the factor in this experiment?
b) What experimental units would you propose?10
c) What would serve as a placebo for this study?
d) What would the treatments be?
e) What would the response variable be?
f) What sources of variability would you control?
a) The factor in this experiment would be the use of a parachute during skydiving.
b) The experimental units would be individuals who are participating in skydiving.
c) A placebo for this study would be a dummy or fake parachute that is identical in appearance to a real parachute, but does not actually function as a parachute.
d) The treatments would be the use of a real parachute and the use of the placebo or fake parachute.
e) The response variable would be the incidence of injury or death during the skydiving experience.
f) Some sources of variability that would be controlled include
the location of the skydiving activitythe weather conditionsthe experience level of the individuals participating in the study,the safety measures or precautions during skydiving experience.Read more about experiment
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I Need Help!!
Write a rule for this function
[tex]y =ax+b[/tex]
[tex]x = 0 \iff a(0) + b = 3 \implies b = 3[/tex]
[tex]x = 1 \iff a(1) + 3 = 5 \implies a = 2\\[/tex]
[tex]\implies \bf y = 2x + 3[/tex]
___________
[tex]x = 2 \iff 2(2) + 3 = 4 + 3 = 7[/tex]
[tex]x = 3 \iff 2(3) + 3 = 6 + 3 = 9[/tex]
So far in this course, you have solved single-variable equations like 3x+7=-x-3. Consider this change to that equation: 3(x+7)=-x-3. What is different about the equations? How will the changes made to the original equation change the steps needed to solve the equation?
Answer below
Step-by-step explanation:
For the first 3x+7=-x-3 you will get 4x=-10 and the final answer is x=-5/2
The second is 3(x+7)=-x-3 which is different since it will equal 3x+21=-x-3 then 4x=-24 and you get x=-6
Solve, use a table: If 5 pounds of a baking mixture "A" that is20%powdered sugar is added to 11 pounds of another mixture "B" to make 16 pounds of a mixture that is24%powdered sugar, then what percent powdered sugar was mixture "B" ?
The percent of powdered sugar in mixture B is 25.82%.
To solve this problem, we can use a table to organize the information and find the percent of powdered sugar in mixture B.
MixturePoundsPercent Powdered SugarPounds of Powdered SugarA520%1B11x%0.11xTotal1624%3.84
From the table, we can create an equation to find the percent of powdered sugar in mixture B:
1 + 0.11x = 3.84
Solving for x:
0.11x = 2.84
x = 25.82%
Therefore, the percent of powdered sugar in mixture B is 25.82%.
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Two values of x that would make this inequality true.
Answer:-12&-8
Step-by-step explanation:
since 3x is negative the -12 and -8 become positive to combine with 5 to either become 41 or 37
A boat traveled 34 miles in two hours. At this rate , how many miles would the boat travel in 6 hours
An item on sale costs 5% of the origional price.origional price was $75.00. Find the sale price.
Answer:
If it costs 5% of $75 it would be $3.75
If it is 5% off $75 it would be $71.25
How we find the answer.
To find 10% of an item you move the decimal point once to the right
If we do this to 75.00 it would be 7.500
We can remove the two 0's
7.5
We are not looking for 10% though we are looking for 5%
Half of 10 = 5 so half 7.5
3.75 is 5% of 75
---------------------------------------
Now if we want to find out 5% off of 75 we subtract
75.00 - 3.75
71.25
Hope i could help
Answer:
$3.75
Step-by-step explanation:
If the item was on sale and cost 5% of its original price, to find the answer we would have to find 5% of 75 and to do this we have to do 5 ÷ 100 × 75
5 ÷ 100 = 0.050.05 × 75 = 3.75This means that the price would be $3.75
Hope this helps, have a lovely day! :)
2.2616161 using bar notation
To show that a pattern repeats indefinitely, a bar is put over it. For example, 2.2616161 in bar notation is: 2.26¯.
what is significant figures ?The meaningful numbers in a number are known as significant figures, also known as significant digits. They are the digits that indicate the level of measurement uncertainty and add to the precision of a number. In other words, important figures are one digit that is either uncertain or estimated in addition to the digits that are known for sure.
given
Repeating digits are represented using the bar notation.
We must recognise the repetitive pattern in the decimal before we can represent 2.2616161 as a repeating decimal using bar notation.
The repetitive pattern is 6161, as can be seen by looking at the decimal. As a result, we can write 2.2616161 as:
2.26 16161...
To show that a pattern repeats indefinitely, a bar is put over it. For example, 2.2616161 in bar notation is: 2.26¯.
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The median price of a single family home in a given town is $250,000 in 2018. A real estate broker believes the price value of homes has increased since then. State the null and alternative hypothesis for the scenario using math symbols and words.
Null hypothesis (H0): The population median price of single-family homes in the town has not changed since 2018.
H0: μ = $250,000
Alternative hypothesis (Ha): The population median price of single-family homes in the town has increased since 2018.
Ha: μ > $250,000
What is represent the null hypothesis?The null hypothesis assumes that there has been no change in the median price since 2018, while the alternative hypothesis assumes that the median price has increased. The alternative hypothesis is one-sided, as the broker is interested in testing whether the price has increased, rather than testing whether there has been any change (i.e., a two-sided test).
The null and alternative hypotheses for the scenario can be stated as follows:
Null hypothesis (H0): The population median price of single-family homes in the town has not changed since 2018.
H0: μ = $250,000
Alternative hypothesis (Ha): The population median price of single-family homes in the town has increased since 2018.
Ha: μ > $250,000
In the above hypotheses, μ represents the population median price of single-family homes in the town.
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10 points if someone gets right
Given the percentage of 2/5 %.
What is its value as a decimal? What is its value as a fraction?
Step-by-step explanation:
remember,
100% = 1
1% = 100%/100 = 1/100 = 0.01
as decimal
2/5 % = 1% × 2/5 = 0.01 × 0.4 = 0.004
as fraction
1% × 2/5 = 1/100 × 2/5 = 2/500 = 1/250
I'd really like some help with this. Please...Please! What's the probability that the point ends in the shaded region?
Answer: 29%
Step-by-step explanation:
109/360=.294 Then move the decimal to make it a percent
Jack is sick and takes a flu medication every hour. He takes 100 mg initially and each dosage drops by
20%. If he keeps taking the medication forever, how much will he have taken? Jill is also sick. Each
dosage of hers drops by 30%. If she ends up taking half the amount of medication that Jack eventually
took, what was her original dosage?
The dosage of Jack and Jill is obtained using geometric series formula which is 500 mg and 225 mg respectively.
What is geometric series?
A geometric series is a collection of terms in mathematics that have an unlimited number and a fixed ratio between each term. A geometric series is typically expressed as a + ar + ar² + ar³ + ..., where r is the common ratio between neighbouring terms and a is the coefficient of each term.
Let's start by finding the amount of medication that Jack takes in total.
Each hour, Jack takes a dosage that is 80% of the previous dosage (since it drops by 20%).
So his dosages form a geometric sequence with first term 100 and common ratio 0.8 -
100, 80, 64, 51.2, 40.96, ...
The sum of an infinite geometric series with first term a and common ratio r (where |r| < 1) is given by -
sum = a / (1 - r)
In this case, a = 100 and r = 0.8, so the sum is -
sum = 100 / (1 - 0.8) = 500
Therefore, Jack takes a total of 500 mg of medication.
Now let's find the original dosage for Jill.
If Jill takes half the amount of medication that Jack eventually took, then she takes -
500 / 2 = 250 mg
Let's call Jill's original dosage x.
Then her dosages form a geometric sequence with first term x and common ratio 0.7 (since it drops by 30%).
The sum of this sequence must be 250.
x + 0.7x + 0.49x + 0.343x + ... = 250
This is an infinite geometric series with first term x and common ratio 0.7, so we can use the formula for the sum of an infinite geometric series -
sum = x / (1 - 0.7) = x / 0.3
Simplifying the equation from before -
x / 0.3 × (1 + 0.7 + 0.49 + 0.343 + ...) = 250
x / 0.3 × (1 / (1 - 0.7)) = 250
x / 0.3 × 3.333... = 250
x = 250 / 1.111... = 225
Therefore, Jill's original dosage was 225 mg.
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I need help with these point + brainliest if 80% of them are anwered
Answer:Answer:
1) SA = 2(wl + hl + hw) = 2(12*2 + 12*6 + 6*2) = 2(24 + 72 + 12) = 2(108) = 216
2) SA = (6*4)/2 + 6*11 + 2(5*11) = 12 + 66 + 110 = 188
3) SA = 2(6*12 + 14*12 + 6*14) = 648
4) (9*12)/2 + 15*6 + 9*6 + 12*6 = 54 + 90 + 54 + 72 = 270
5) 2(16*9 + 4*9 + 16*4) = 488
6) SA = 2πrh+2πr^2 = 2*3.14*10*16 + 2*3.14*10^2 = 1004.8 + 628 = 1632.8
7) SA = 2(7*7 + 14*7 + 7*14) = 490
8) SA = 2πrh+2πr^2 = 2*3.14*7*11 + 2*3.14*7^2 = 483.56 + 307.72 = 791.28
9) (12*10)/2 + 2(14*13) + 14*10 = 60 + 364 + 140 = 564
Step-by-step explanation:
Kim Chung worked for his uncle during the summer. He was paid $2,897 but no
withholding tax was deducted. He earned $57 in interest on his savings account.
He has no adjustments to his income and his parents claim him on their tax
return. How much does he owe in federal income taxes?
Kim Chung owes $176 in federal income taxes.
What is the interest?
In finance, interest refers to the fee that a borrower pays to a lender for the use of money or assets. It is a cost of borrowing money, usually expressed as a percentage of the principal amount borrowed (or invested).
To calculate the federal income tax owed by Kim Chung, we need to first determine his taxable income.
Kim Chung's taxable income is calculated as follows:
Total Income = $2,897 (wages) + $57 (interest) = $2,954
Adjustments = $0
Adjusted Gross Income (AGI) = Total Income - Adjustments = $2,954 - $0 = $2,954
Since Kim Chung's parents claim him as a dependent, his standard deduction for tax year 2022 is $1,150.
Taxable Income = AGI - Standard Deduction = $2,954 - $1,150 = $1,804
To determine the federal income tax owed, we need to use the tax tables provided by the IRS for tax year 2022.
According to the tax tables, the tax on $1,804 of taxable income is $176.
Therefore, Kim Chung owes $176 in federal income taxes.
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Based upon extensive data from a national high school educational testing program, the mean score of national test scores for mathematics was found to be 606 and the standard deviation of national test scores for mathematics was found to be 187 points. What is the probability that a random sample of 289 students will have a mean score of more than 621? Less than 595? The probability that a random sample of 289 students will have a mean score of more than 621 is ____
(Round to four decimal places as needed) The probability that a random sample of 289 students will have a mean score of less than 595 is ______
(Round to four decimal places as needed.)
The probability that a random sample of 289 students will have a mean score of more than 621 is 0.0869. The probability that a random sample of 289 students will have a mean score of less than 595 is 0.1597.
To answer this question, we need to use the central limit theorem. The central limit theorem states that the distribution of sample means approaches a normal distribution as the sample size increases. In this case, the sample size is 289 students.
First, we need to calculate the standard error of the mean. The standard error of the mean is the standard deviation of the distribution of sample means. It is calculated as:
SE = σ/√n
Where σ is the standard deviation of the population and n is the sample size. In this case, σ = 187 and n = 289. So, the standard error of the mean is:
SE = 187/√289 = 11.04
Next, we need to calculate the z-score for each of the two scenarios. The z-score is a measure of how many standard deviations away from the mean a data point is. It is calculated as:
z = (x - μ)/SE
Where x is the data point, μ is the population mean, and SE is the standard error of the mean. In the first scenario, x = 621, μ = 606, and SE = 11.04. So, the z-score is:
z = (621 - 606)/11.04 = 1.36
In the second scenario, x = 595, μ = 606, and SE = 11.04. So, the z-score is:
z = (595 - 606)/11.04 = -0.996
Now, we can use the z-score to find the probability. The probability that a random sample of 289 students will have a mean score of more than 621 is:
P(z > 1.36) = 0.0869
The probability that a random sample of 289 students will have a mean score of less than 595 is:
P(z < -0.996) = 0.1597
So, the probability that a random sample of 289 students will have a mean score of more than 621 is 0.0869 (rounded to four decimal places) and the probability that a random sample of 289 students will have a mean score of less than 595 is 0.1597 (rounded to four decimal places).
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Let A, B, and C be 3x3 matrices such that det(A) =2, det(C) = 4,
and 2A^TB^-1 = C. Find det(B)
Let A, B, and C be 3x3 matrices such that det(A) =2, det(C) = 4, and 2A^TB^-1 = C the determinant of matrix B is 4.
To find the determinant of matrix B, we can use the property of determinants that states that det(AB) = det(A)det(B). We can rearrange the given equation 2A^TB^-1 = C to get B = 2A^T C^-1. Then, we can take the determinant of both sides to get det(B) = det(2A^T C^-1).
Using the property of determinants, we can expand the right side of the equation to get det(B) = det(2)det(A^T)det(C^-1). Since the determinant of a scalar multiple of a matrix is the scalar multiple of the determinant, det(2) = 2^3 = 8. Also, the determinant of the transpose of a matrix is the same as the determinant of the original matrix, so det(A^T) = det(A) = 2.
Finally, the determinant of the inverse of a matrix is the reciprocal of the determinant of the original matrix, so det(C^-1) = 1/det(C) = 1/4.
Substituting these values back into the equation, we get det(B) = 8*2*(1/4) = 4. Therefore, the determinant of matrix B is 4.
det(B) = 4.
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The equation �=112�y=1\frac{1}{2}xy=1
2
1
x represents the number of cups of dried fruit, y, needed to make x pounds of granola. Determine whether each point would be on the graph of this proportional relationship.
Choose Yes or No for each point.
The coordinates (2,1) will be on graph but (1,3) is not on graph.
What is a coordinate?
A coordinate is a set of two or more numbers or variables that identify the position of a point, line, or plane in a space of a given dimension. Coordinates are used to pinpoint a particular location, such as a specific point on a map or a specific point in a mathematical equation.
This means that for every 1.5 cups of dried fruit, there is 1 pound of granola. The graph of this proportional relationship would be a line that goes through the origin and has a slope of 1.5. For the point (2,1), the x-coordinate (2) is exactly 1.5 times the y-coordinate (1). This means that if you used 2 cups of dried fruit, you would get 1 pound of granola. Therefore, this point would be on the graph of the proportional relationship, so the answer is Yes. However, for the point (1,3), the x-coordinate (1) is not 1.5 times the y-coordinate (3). This means that if you used 1 cup of dried fruit, you would not get 3 pounds of granola.
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