The value of t for which (4, 6, 3, t) is a linear combination of (1, 3, - 4, 1), (2, 8, - 5, - 1) and (- 1, - 5, 0, 2) is equal to 13.
How to find a vector as a linear combination of other vectors
In this question we must solve for t such that (4, 6, 3, t) is a linear combination of vectors (1, 3, - 4, 1), (2, 8, - 5, - 1) and (- 1, - 5, 0, 2), which means that non-zero coefficients have to be found by algebraic handling:
(4, 6, 3, t) = α₁ · (1, 3, - 4, 1) + α₂ · (2, 8, - 5, - 1) + α₃ · (- 1, - 5, 0, 2)
Which is equivalent to this system of linear equations:
α₁ + 2 · α₂ - α₃ = 4
3 · α₁ + 8 · α₂ - 5 · α₃ = 6
- 4 · α₁ - 5 · α₂ = 3
α₁ - α₂ + 2 · α₃ - t = 0
Whose solution is (α₁, α₂, α₃, t) = (38, - 31, - 28, 13). The value of t for which (4, 6, 3, t) is a linear combination of (1, 3, - 4, 1), (2, 8, - 5, - 1) and (- 1, - 5, 0, 2) is equal to 13.
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Among two congruent angles ,one has measure 69⁰,then the measure of other angle is
Answer:
Your answer is
Congruent means similar.
Other angle is 69°
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Sampson has a list of items that are on sale to pick up at the store. The sale items are the following:
Ice cream – $1.89
Sweet corn – 3 for $1
Bananas – $0.49 per pound
Sampson buys 1 carton of ice cream, 4 ears of corn, and 2.5 pounds of bananas. His receipt is shown below.
Swt corn 2 3/$1 $0.67
Bananas 2.5 lb 0.49 $1.23
Ice crm 1 2.49 $2.49
Store discount for ice crm $0.60 -$0.60
Swt corn 2 3/$1 $0.67
Determine if Sampson's receipt is correct.
a.
Yes, Sampson's receipt is correct.
b.
No, Sampson paid too much for corn.
c.
No, Sampson paid too much for ice cream.
d.
No, Sampson paid too much for bananas.
The Answer is A
Answer:
the answer is A) Yes, Sampson's receipt is correct.
Step-by-step explanation:
Answer:
A
Step-by-step explanation: edge
SOLVE the EXPRESSION
Evaluate 6s - 3t If s=4 and t=-2
Answer:
30
Step-by-step explanation:
6(4) - 3(-2) =
24 + 6 =
30
A random sample of 250 juniors majoring in psychology or communication at a large university is selected. These students are asked whether or not they are happy with their majors. Assume that none of these 250 students is majoring in both areas. There are a total of 100 majoring in psychology and only 80 of those majoring in psychology are happy while 35 students majoring in communication are unhappy.
If one student is selected at random from this group, find the probability that this student is:________
i. happy with the choice of major
ii. a psychology major
iii. a communication major given that the student is happy with the choice of major
iv. unhappy with the choice of major given that
Solution :
It is given that :
Number of students in a random sample majoring in communication or psychology at an university = 250
Total number of students majoring in psychology = 100
Number of students majoring in psychology those who are happy = 80
So number of students majoring in psychology those who are not happy = 20
Total number of students majoring in communication = 250 - 100 = 150
Number of students majoring in communication those who are happy = 115
So number of students majoring in psychology those who are not happy = 35
a). Probability of the students happy with their major choices are
[tex]$=\frac{80+115}{250}$[/tex]
= 0.78
b). Psychology major [tex]$=\frac{80+20}{250}$[/tex]
= 0.4
c). Probability of the students who are happy with the communication as the choice of major = [tex]$\frac{115}{250}$[/tex] = 0.46
d). Students unhappy with their choice of major given that the student is psychology major = [tex]$\frac{20}{250}$[/tex] = 0.018
a) Probability of the students happy with their major choices is 0.78.
b) Probability of Psychology major is 0.4
c) Probability of the students who are happy with the communication as the choice of major is 0.46.
d) Students unhappy with their choice of major given that the student is psychology major is 0.018
Given:
Number of students in a random sample majoring in communication or psychology at an university = 250
Total number of students majoring in psychology = 100
Number of students majoring in psychology those who are happy = 80
So, number of students majoring in psychology those who are not happy = 20
Total number of students majoring in communication = 250 - 100 = 150
Number of students majoring in communication those who are happy = 115
So, number of students majoring in psychology those who are not happy = 35
a). Probability of the students happy with their major choices are
[tex]=\frac{80+115}{250} =0.78[/tex]
b). Psychology major
[tex]\frac{80+20}{250} =0.4[/tex]
c). Probability of the students who are happy with the communication as the choice of major =[tex]\frac{115}{250} =0.46[/tex]
d). Students unhappy with their choice of major given that the student is psychology major =[tex]\frac{20}{250} =0.018[/tex]
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5(y+25)=-13 i need help explaining
Answer:
y=-138/5=-27 3/5 = -27.6
Step-by-step explanation:
5(y+25)=−13
Divide both sides by 5.
y+25=-13/5
Subtract 25 from both sides.
y=-13/5−25
Convert 25 to fraction 125/5
y=-13/5-125/5
Since -13/5 and 125/5 have the same denominator, subtract them by subtracting their numerators.
y=-13 - 125/5
Subtract 125 from −13 to get −138.
y=-138/5
In the diagram, JK is congruent to GI. Solve for x if HJ = 3x, HK = 2x, KI = 6x, and JG = 18 units.
Su is baking 5 batches each of cookies and cupcakes. The cookies use 2 cups of sugar per batch and the cupcakes use 3 cups of sugar per batch. Write two equivalent expressions using the Distributive Property. Then find how many total cups of sugar are needed.
I know the answer is 25 but how would I write the expression.
Answer:x=25 divided by 5
Step-by-step explanation:
Geometric mean of 45 and 15
Answer:
30
Step-by-step explanation:
[tex]\frac{45+15}{2}[/tex] equals 30.
Answer:
45 + 15 = 60 divided by 2 is 30
Solve for m.
m
2
= 13
Answer:
m=6.5
Step-by-step explanation:
13 divided by 2= 6.5
consider the two functions. which statement is true?
Answer:
The right answer is D
Step-by-step explanation:
The slope of the first function is 2.5, the slope of the second function is 3, so function 2 has a greater rate of change by [tex]\frac{1}{2}[/tex].
If (y + 1) varies directly as square root of x and y =14 when x = 27, find the value of y when
x = 64 without finding the variation constant.
Answer:
22.1 or 22
Step-by-step explanation:
Y + 1 varies√x
Y + 1 = K√x ( k is costant)
so we solve for K
given: 14 + 1 = K√27
15 = K√27
divide both sides by √27
15/√27 = K
to find the value of y
y + 1 = 15/√27 (8) : substitute K for 15/√27
Y + 1 = 120/√27
i.e Y = 120/√27 - 1
Y = 23.1 - 1
Y = 22.1 or 22
Your mom loves to walk. She walks 4 miles each day. If
she wants to walk a total of 56 miles, how many days
should she walk?
Answer:
14 Days
Step-by-step explanation:
Your mom walks 4 miles each day and wants to walk a total of 56 miles.
You have to divide 56 by 4 and you'll get 14 days.
If you would like to check your answer, you can multiply 14 by 4 and you'll get 56 miles!
suppose that rectangle ABCD is dilated to A'B'C'D using the origin as the center and a mangnitude of 2. What are the coordinates of C'?
Answer:
-8,-8
Step-by-step explanation:
Hope u get it right! :D
Tina buys a briefcase online for 62.95. If shipping and handling are an additional 20% of the price, how much shipping and handling will Tina pay?
Answer:
Tina will pay $12.95 for shipping and handling.
Step-by-step explanation:
Because you literally just have to multiply $62.95 by .2 and you have your answer.
[7TH GRADE MATH] Can someone please explain how to round a square root to the tenth place without using a calculator.
(I WILL BE GIVING BRAINLIEST!!!!)
Answer:
Step-by-step explanation: To find a decimal approximation to, say √2, first make an initial guess, then square the guess, and depending how close you got, improve your guess. Since this method involves squaring the guess (multiplying the number times itself), it uses the actual definition of square root, and so can be very helpful in teaching the concept of square root.
Example: what is square root of 20?
You can start out by noting that since √16 = 4 and √25 = 5, then √20 must be between 4 and 5.
Then make a guess for √20; let's say for example that it is 4.5. Square that, see if the result is over or under 20, and improve your guess based on that. Repeat this process until you have the desired accuracy (amount of decimals). It's that simple and can be a nice experiment for students!
Answer:
The number’s square root is a number that, when multiplied by itself, equals the first number. Another way of saying this is: “What can we multiply by itself to get the number in question?”
Step-by-step explanation:
For example, the square root of 1 is 1 because 1 multiplied by 1 equals 1 (1X1=1). However, the square root of 4 is 2 because 2 multiplied by 2 equals 4 (2X2=4). Think of the square root concept by imagining a tree. A tree grows from an acorn. Thus, it’s bigger than but related to the acorn, which was at its root. In the above example, 4 is the tree, and 2 is the acorn.
Thus, the square root of 9 is 3 (3X3=9), of 16 is 4 (4X4=16), of 25 is 5 (5X5=25), of 36 is 6 (6X6=36), of 49 is 7 (7X7=49), or 64 is 8 (8X8=64), of 81 is 9 (9X9=81), and of 100 is 10 (10X10=100).[1]
pls help 100 points helphelp
Answer:
Some kind of evadence
Step-by-step explanation:
Answer:
Im pretty sure it would be C.
Step-by-step explanation:
Sine a signature, photograph and quotes are all pieces of evidence, you can rule them out and infer that c would be the most reliable answer.
In a survey, 150 seventh graders said that they had been to a foreign country. That number represented 20% of the students who were surveyed. How many students were surveyed?
Answer:
750
Step-by-step explanation:
150/2=7.5
7.5*100=750
750*0.2=150
Select all the correct answers.
A group of scientists is conducting an experiment on the effects of media on children. They randomly select 100 children and randomly assign each child to one of four treatment groups. Each treatment group has a specific amount of screen time during a one-week time frame. The first group has no screen time, the second group has two hours of screen time, the third group has four hours of screen time, and the fourth group has six hours of screen time.
After the first week, the scientists conduct the same experiment, with the same subject groups, for three more weeks so that each group experiences each of the four treatments.
Which statements about this study are true?
the study uses blocking
this study uses random sampling
this study uses blinding
this study uses a control group
this study uses a repeated measures design
Answer:
this study uses random sampling
this study uses a control group
this study uses a repeated measures design
Step-by-step explanation:
plato/edmentum
Correct answers bolded and italicized and underlined
the study uses blocking
this study uses random sampling
this study uses blinding
this study uses a control group
this study uses a repeated measures design
Step-by-step explanation:
no :)
Use the graph of f to describe the transformation that results in the graph of g. Then sketch the graphs of g and f. f(x) = ; g(x) =
Answer:
Di ko alam
Step-by-step explanation:
Hirap niyan eh
absolute value of x=5
what is x
Answer:
5
Step-by-step explanation:
5 = 5
Imagine you are a financial analyst at an investment bank. According to your research of publicly-traded companies, 60% of the companies that increased their share price by more than 5% in the last three years replaced their CEOs during the period. At the same time, only 35% of the companies that did not increase their share price by more than 5% in the same period replaced their CEOs. Knowing that the probability that the stock prices grow by more than 5% is 4%, find the probability that the shares of a company that fires its CEO will increase by more than 5%.
Answer:
0.0667 = 6.67% probability that the shares of a company that fires its CEO will increase by more than 5%.
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this problem:
Event A: Company fires the CEO
Event B: Shares increase by more than 5%.
Probability of a company firing it's CEO:
35% of 100 - 4 = 96%(shares did not increase by more than 5%).
60% of 4%(shared did increase by more than 5%).
So
[tex]P(A) = 0.35*0.96 + 0.6*0.04 = 0.36[/tex]
Intersection of events A and B:
Fires the CEO and shared increased by more than 5%, is 60% of 4%. So
[tex]P(A \cap B) = 0.6*0.04 = 0.024[/tex]
Probability that the shares of a company that fires its CEO will increase by more than 5%.
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.024}{0.36} = 0.0667[/tex]
0.0667 = 6.67% probability that the shares of a company that fires its CEO will increase by more than 5%.
One end of a ramp is raised to the back of a truck 5 feet above the ground. 1 point
If the length of the ramp is 8 feet, what is the approximate measure of the
angle the ramp makes with the ground? Round your answer to the nearest
tenth of a degree.
38.7°
58.0°
32.0
51.3
Answer:
38.7°
Step-by-step explanation:
You are basically looking at a triangle with a 90° angle (check picture).
Since we are looking for the ramp's angle and are given the length of the opposite and the hypothenuse, we have to solve the following equation:
[tex]sin (\alpha) = opposite / hypothenuse= 5 ft/8ft[/tex]
which is equivalent to
[tex]\alpha = sin^{-1}(5/8)\approx 38.7\deg[/tex]
given 1/cot x - sec x/ csc x= cos x find a numerical value of one trigonometric function of x
Answer:
what's is supposed to be going on here what the the option
Answer:
Step-by-step explanation:
c on edge
I ready volume with fractional length
Answer:
im here to help.
Step-by-step explanation:
yup
Adrienne’s lunch cost $13.16. She hands the cashier $20. About how much change does Adrienne receive?
Answer:
Use long subtraction to evaluate.
6.84
Step-by-step explanation:
Plz help! I don’t know how to do these!
4. x= 40
plz mark my answer as brainlist plzzzz.
hope this will be helpful to you .
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Common ratio of 1/2,1,2,4,8
Step-by-step explanation:
common ratio (r) = second term÷first term
Which set of numbers below DO NOT make a triangle?
7,7,7
6, 3, 3
3,4,5
5, 11,7
Answer:
6, 3, 3 (B)
Step-by-step explanation:
Two sides of a triangle must be greater than the remaining side
A way to think about this is like this:
The two shortest sides of a triangle must be greater than the final side
Go through this process for each option and find the B does not work
Help me I’m stuck and please can someone explain this to me
Answer:
84 degrees
Step-by-step explanation:
3x = 4x - 28. Reason: Alternate Exterior Angle are congruent
X=28 Reason: Algebra
Y+4x-28= 180 Reason: Straight angles = 180 degrees
Y=84. Reason: Algebra
1+1 impossible sooooooooooooo hard
Answer:
2 is my answer im sureeee
Step-by-step explanation:
1+1=1
Answer: ok so these are my guesses 1+1=11, 1+1=Window ,100+1=lol last guess 1+1=2 ldk soooooo complicated
Step-by-step explanation: