Answer:
matrices can be added together if both have the same order
Addition is both commutative and associative
matrices can be multiplied together if the number of column in the right hand matrix equals the number of row in the left hand matrix
Question 24: [1 + 1 + 1 + 1= 4 points]
Let X be a discrete random variable with the following
x 0.2 0.4 0.5 0.8 1
P(x) 0.1 0.2 0.2 0.3 0.2 (a) Find () , the range of the random variable X
Considering the given discrete probability distribution, the range of the variable X is given by:
Range(X) = {0.2, 0.4, 0.5, 0.8, 1}.
What is the range of a random variable?The range of a random variable is the set of all values that the variable can assume.
From the table, we have that X can assume the values of 0.2, 0.4, 0.5, 0.8 and 1, hence the range of the variable X is given by:
Range(X) = {0.2, 0.4, 0.5, 0.8, 1}.
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how many decimal places does 22.22105 have
Answer:
5
Step-by-step explanation:
where there is the decimal point,you count the numbers after the decimal point
Consider the line 3x - 4 y = 7.
What is the slope of a line perpendicular to this line?
What is the slope of a line parallel to this line?
Answer:
The slope of a line perpendicular to this line is -1/3. The slope of a line parallel to this line would be 3.
Step-by-step explanation:
Perpendicular lines have opposite(sign) and reciprocal slopes.
Parallel lines have the same slope.
Zachary's weight is 130% of Noah's weight. If Noah weighs 75 pounds, what does Zachary weigh?
Answer:
Zachary weights 95.7 pounds
Claire buys a condo for $350,000. The value of the condo appreciates on average 5% per year where she
bought the condo
If you know the rest of the problems on the page then that would help;)
1. The best way that we can represent the condo that Claire bought is by option B. [tex]350000(1.05)^{t}[/tex]
How to determine the functionTo determine the function, we would have to do so by making use of the given equation that we have here.
This is given as
Ct = [tex]A(1+r)^t[/tex]
Where a is the principal
r is the rate of interest and
t is the time
2. we have 70 = 30(1.03)^t
70/30 = (1.03)^t
We have to take the log of the function above in order to find the value of t
t = 28.665
This is approximated to 29
Hence the answer here is option A after 29 weeks.
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How to Convert 11010112 to base 10?
Answer:
So this is all you need to do!
Hope it helped you:)
Devon is young and has just graduated college with her associate’s degree. She plans to start saving money for retirement as soon as she starts her new job. By taking 10% of her monthly gross income, Devon is able
to contribute (a) $__________ each month to a retirement plan. The account is expected to earn interest with an APR of 5.25% compounded monthly. Round answers to two decimal places.
a. How much money will be in Devon’s retirement account if she continues to make the same monthly
.
investment for 40 years?
b. Overall, Devon contributed how much of her own money into the retirement account?
c. What percent of the final balance in Devon’s retirement account was interest?
You may not ask for help from others or give help to others on specific project questions.
Part 1: Continued
2. Later in life, Devon convinces her friend Taylor to start saving for retirement as well. Even though Taylor is the same age as Devon, she hasn’t started saving for retirement yet. With only 20 years left until they both plan to retire, Taylor decides she needs to invest at least twice as much as Devon each month to try to catch up to Devon’s retirement plan. Taylor opens a similar retirement account to Devon’s that also has an APR
5.25% compounded monthly. She will invest (b) $__________ per month. Round answers to two decimal places.
a. How much money will be in Taylor’s retirement account if she continues to make the same monthly
investment for 20 years?
b. By the time she retires, Taylor will have contributed how much of her own money overall?
c. What percent of the final balance in Taylor’s retirement account will be interest?
3. Write complete sentences that identify which person had the higher amount and by how much. Round answers to two decimal places.
a. Who had more money in their retirement account when they planned to retire? How much more?
b. Who contributed more to their retirement account? How much more?
Part 1: Devon is able to contribute (a) $450 each month to a retirement plan.
a. The amount in Devon's retirement account if she makes the same monthly investment for 40 years is $733,253.26.
b. Overall, Devon's total contribution of her own money into the retirement account is $216,000.
c. The percent of the final balance in Devon's retirement account that was interest was 70.5%.
Part 2: Taylor will invest (b) $1,733.00 per month.
a. The amount that will be in Taylor's retirement account if she makes the same monthly investment for 20 years is $733,253.26.
b. By the time that Taylor retires, she will have contributed $415,920 of her own money into the account.
c. The percent of the final balance in Taylor's retirement account that will be interest is 43.3%.
3. Both Devon and Taylor had the same amount, $733,253.26, in their retirement accounts when they planned to retire.
a. None had more money at their retirement.
b. Taylor contributed more to her retirement account by $199,920 ($414,920 - $216,000).
Data and Calculations:Devon's Investments:Gross monthly income = $4,500
APR = 5.25% compounded monthly
N (# of periods) = 480 months (12 x 40 years)
I/Y (Interest per year) = 5.25%
PV (Present Value) = $0
PMT (Periodic Payment) = $450 ($4,500 x 10%)
Results:
FV = $733,253.26 ($517,253.26 + $216,000)
Sum of all periodic payments = $216,000 ($450 x 480)
Total Interest = $517,253.26
Percentage of interest out of the FV = 70.5% ($517,253.26/$733,253.26 x 100)
Taylor's Investment:N (# of periods) = 240 months (12 x 20 years)
I/Y (Interest per year) = 5.25%
PV (Present Value) = $0
FV (Future Value) = $733,253.26
Results:
PMT = $1,733.00
Sum of all periodic payments = $415,920 ($1,733 x 240
Total Interest = $317,333.26
Percentage of interest out of the FV = 43.3% ($317,333.26/$733,253.26 x 100)
Thus, based on the time value of money of investments, it is more profitable to start investing early.
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Three books are what percent of four books?
If four books are 100%, then 3 books are how much percent of total books?
[tex]\frac{3}{4}[/tex] × 100 = 3 × 25 = 75%
Hope it helps!
The answer is 75%.
To find the percentage, divide the number of given books by total books and multiply by 100%.
(3 ÷ 4) × 100%0.75 × 100%75%A company that produces dog food claims that its bags contain 11 kg of food. From
prior experimentation, it is known that the weight of the dog food in these bags is normally
distributed with a standard deviation of 0.6 kg. From a random sample of 25 bags, the mean
weight of the dog food was 10.6 kg. We are concerned that the company is exaggerating how
much dog food they put in their bags. Test at the 5% significance level.
By testing the hypothesis we can conclude that the bag does not contain 11 kg of food.
Given mean of 10.6 kg, population standard deviation of 0.6 and sample size of 25.
We are required to find whether the company is right in saying that their bags contain 11 kg of food.
First we have to make hypothesis.
[tex]H_{0}[/tex]:μ≠11
[tex]H_{1}[/tex]:μ=11
We have to use t statistic because the sample size is less than 30.
t=(X-μ)/s/[tex]\sqrt{n}[/tex]
We will use s/[tex]\sqrt{n}[/tex]=0.6 because we have already given population standard deviation of weights.
t=(11-10.6)/0.6
=0.4/0.6
=0.667
Degree of freedom=n-1
=25-1
=24
T critical at 0.05 with degree of freedom 24=2.0639
T critical at 0.05 with degree of freedom is greater than calculated t so we will accept the null hypothesis.It concludes that the bags donot contain 11 kg of food.
Hence by testing the hypothesis we can conclude that the bag does not contain 11 kg of food.
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If the diameter of a circular pond is x meter, what is the its circumference?
Answer:
piex
Step-by-step explanation:
the circumference of a circle is pie times the diameter of the circle.
Find the area between the following curves.
y=x^3-x^2+x+8 ; y=5x^2-7x+8
Find where the two curves meet.
[tex]x^3 - x^2 + x + 8 = 5x^2 - 7x + 8 \\\\ \implies x^3 - 6x^2 + 8x = 0 \\\\ \implies x (x-2) (x - 4)= 0 \implies x=0, x=2, x=4[/tex]
The area between the curves is
[tex]\displaystyle \int_0^4 \left|\left(x^3-x^2+x+8\right) - \left(5x^2 - 7x + 8\right)\right| \, dx = \int_0^4 \left|x(x-2)(x-4)\right| \, dx[/tex]
When [tex]x[/tex] is between 0 and 2, [tex]x(x-2)(x-4)[/tex] is positive; when [tex]x[/tex] is between 2 and 4, [tex]x(x-2)(x-4)[/tex] is negative. So we split the integral at [tex]x=2[/tex] to get
[tex]\displaystyle \int_0^2 x(x-2)(x-4) \, dx - \int_2^4 x(x-2)(x-4)\,dx[/tex]
In the second integral, substitute [tex]y=x-2[/tex] to get
[tex]\displaystyle \int_0^2 x(x-2)(x-4) \, dx - \int_0^2 (y+2)y(y-2)\,dy[/tex]
[tex]\displaystyle \int_0^2 x(x-2) \bigg((x-4) - (x+2)\bigg) \, dx[/tex]
[tex]\displaystyle -6 \int_0^2 x(x-2) \, dx[/tex]
[tex]\displaystyle 6 \int_0^2 \left(2x - x^2\right) \, dx[/tex]
[tex]\displaystyle 6 \left(x^2 - \frac13x^3\right)\bigg|_0^2 = \boxed{8}[/tex]
For a certain company, the cost function for producing x items is C(x)=50x+100 and the revenue function for selling x items is R(x)=−0.5(x−100)2+5,000 . The maximum capacity of the company is 120 items.
The profit function P(x) is the revenue function R(x) (how much it takes in) minus the cost function C(x) (how much it spends). In economic models, one typically assumes that a company wants to maximize its profit, or at least make a profit!
Answers to some of the questions are given below so that you can check your work.
Assuming that the company sells all that it produces, what is the profit function?
P(x)=
Assuming that the company sells all that it produces, The profit function is: P(x)=-x^/2+50x -100 or P(x)=-0.5x²+50x -100.
Profit functionProfit = R-C = -(x-100)^2/2 +5000 - 50x -100 =
-(x^2 -200x +10000)/2 -50x +4900 =
-x^2/2 +100x -5000 +5000 -50x +4900
Collect like terms
-x^/2+50x -100
Hence,
Profit function = P(x)=-0.5x²+50x -100
Maximum profit generating output can be determine by taking the derivative and setting it equal to zero
R-C = -x^2/2 + 50x -100
R'-C' = -x + 50 =0
P(0)x = 50
Maximum profit can be determine by substituting x=50 into the original profit equation, R-C
P(50) =-(1/2)(50)^2 +50(50) -100
P(50)= -1250 + 2500 -100
P(50) = $1150 profit
P(120) =-(1/2)(120)^2 +50(120) -100
P(120)= -3600 + 6000 -100
P(120) = $2300 profit
Therefore the profit function is: P(x)=-x^/2+50x -100 or P(x)=-0.5x²+50x -100.
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Write an equation of the line that passes through (3,-2) and is parallel to the line y = 2x + 4.
Answer: [tex]y+2=2(x-3)[/tex]
Step-by-step explanation:
Parallel lines have the same slope, so substituting into point-slope form, the equation is
[tex]y+2=2(x-3)[/tex]
The price of a train ticket consists of an initial fee plus a constant fee per stop. The table compares the number of stops and the price of a ticket (in dollars). Stops Price (dollars) 333 6.506.506, point, 50 777 12.5012.5012, point, 50 111111 18.5018.5018, point, 50 What is the fee per stop?
Based on the task content given; the initial fee and the fee per stop is $2 and $1.5 respectively.
Equationlet
Initial fee = xFee per stop = yx + 3y = 6.50
x + 7y = 12.50
Subtract both equation to eliminate x7y - 3y = 12.50 - 6.50
4y = 6
y = 6/4
y = 1.5
Substitute y = 1.5 intox + 3y = 6.50
x + 3(1.5) = 6.50
x + 4.5 = 6.50
x = 6.50 - 4.5
x = 2
Therefore, the initial fee and the fee per stop is $2 and $1.5 respectively.
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The legs of a 45-45-90 triangle has lengths of 21. What is the length of the hypotenuse?
Answer:
[tex]21 \sqrt{2} [/tex]
Step-by-step explanation:
See attached image.
PLEASE HELP ME WITH THIS QUESTION
6
Answer:
45
Step-by-step explanation:
Assuming this is a trapezoid,
[tex]\frac{29+WZ}{2}=37 \\ \\ 29+WZ=74 \\ \\ WZ=45[/tex]
Combined, Tanya and Sanjay have 40 pens. If Tanya has four times as many pens as Sanjay, how many pens does Sanjay have?
Answer:Sanjay has 8
Step-by-step explanation: Because 8x4 equals 32 so thats how much tanya has a 32+8 equals 40. This is what I did I knew 10x4 is 40 so that couldn't be it so then I tried 8 because nine x four is 36 which would be to high so I tried 8 and it was perfect hope this helps.
If Combined, Tanya and Sanjay have 40 pens. If Tanya has four times as many pens as Sanjay, then Sanjay have 8 pens.
What is Equation?Two or more expressions with an equal signs is called as Equation.
Given that Tanya and Sanjay have 40 pens. If Tanya has four times as many pens as Sanjay, We need to find how many pens sanjay has.
Let sanjay has x number of pens.
Tanya has four times as many pens as Sanjay
So 4 times means four multiple of sanjay pens.
Tanya has four times as many pens as Sanjay can be write as 4x.
Combined of tanya and sanjay has 40 pens.
Combined means adding.
x+4x=40
Add the like terms
5x=40
Divide both sides by 5.
x=8
So Sanjay has eight pens and Tanya has 4(8)=32 pens.
Hence Sanjay have eight pens.
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The letters of "EAGLES" should be evenly spaced across a 70-inch-wide banner, with no margins. Each letter is 10 inches wide. How many inches (x) should exist between each pair of letters
Answer:
2 Inches or ~1.43 Inches
Step-by-step explanation:
2 Inches if it's not including the spacing before the first "E" and after the "S", ~1.43 Inches if it's including the spacing.
You would get 2 Inches since if each letter is 10 inches (total 6 letters), that would be 60 inches. There are 5 total spaces in between all the letters. 70 Inches(Banner size) - 60 Inches (total letter size) = 10 Inches, divided equally within the 5 spaces. That would equal 2 :)
You also get ~1.43 Inches by doing the same process as the one shown above^ (that is if you're including the spacing before and after the word)
:)
IF THE ODDS AGAINST A PARTICULAR CANDIDATE WINNING AN ELECTION ARE 9
TO 5, WHAT IS THE PROBABILITY THAT THE CANDIDATE WILL WIN?
The probability that the candidate will win is P = 0.357
How to find the probability?
We know that the odds against the particular candidate are 9 to 5.
The the odds for the candidate are 5 to 9, this means that in 5 cases the candidate will win, and in 9 cases the candidate will lose.
Then the candidate wins in 5 out of 14 cases, then the probability that the particular candidate wins the elections is given by the quotient:
P = 5/14 = 0.357
The probability that the candidate will win is P = 0.357
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Complete the statement below with the appropriate term. According to John Locke, is how we acquire basic knowledge. Choose the best answer.
Which of the following explains why, in many of the problems, historical data is used?
Information changes rapidly.
It is an opportunity to study history at the same time.
Better math problems can be made from historical data.
Up-to-date information is difficult to find.
According to John Locke, Experience is how we acquire basic knowledge.
What explains why, in many of the problems, historical data is used is; Information changes rapidly.
What is the theory of John Locke?1) John Locke's theory simply means that all knowledge comes exclusively through experience. He argues that at birth the mind is a tabula rasa, that humans fill with ideas as they experience the world through the five senses.
Thus, the missing word in the question is "Experience".
2) The reason why historical data is used in may problems is because Information changes rapidly. The information being circulated currently may be different from that circulated 100 years ago.
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I need help please yall
use orders of operation and simplify
Answer: [tex]\large\boxed{12x^3-30x+3=0}[/tex]
Step-by-step explanation:
[tex]Solve:\\\ 6(2x^2-5)x=-3\\\\Use\ distributive\ property\ first\\\\(12x^2-30)x=-3\\\\Now\ multiply\ the\ terms\ in\ ()\ by\ 'x'\\\\12x^3-30x=-3\\\\\large\boxed{12x^3-30x+3=0}[/tex]
create a pattern of 6 numbers by multiplying a number by 5 to get the next number.starts with 4
Answer:
45 405 415 425 435 445
Step-by-step explanation:
this are the pattern of 6 numbers multiplying by number 5 to get the number starts with 4
Answer:
4,20,100,500,1500,8500.
Step-by-step explanation:
can someone help me with this, it's urgent!
1. D
2. B
3. E
4. C
5. B
Concept:From the three examples at the top of the page, the sum of the bottom two parts of the triangle equals to six times the value of the part at the top.
For example, the first one: 20, 10, 5 (Tip)
20 + 10 = 305 × 6 = 30For example, the second one: 4, 14, 3 (Tip)
4 + 14 = 183 × 6 = 18Solve:Question 1
Given information
Tip = 15
Bottom = ?, 51
Determine the sum
15 × 6 = 90
Find the other bottom part
90 - 51 = 39
[tex]\Large\boxed{D.~39}[/tex]
Question 2
Given information
Tip = 9
Bottom = 21, ?
Determine the sum
9 × 6 = 54
Find the other bottom part
54 - 21 = 33
[tex]\Large\boxed{B.~33}[/tex]
Question 3
Given information
Tip = ?
Bottom = 60, 60
Determine the sum
60 + 60 = 120
Find the tip
120 ÷ 6 = 20
[tex]\Large\boxed{E.~20}[/tex]
Question 4
Given information
Tip = ?
Bottom = 18, 30
Determine the sum
18 + 30 = 48
Find the tip
48 ÷ 6 = 8
[tex]\Large\boxed{C.~8}[/tex]
Question 5
Given information
Tip = 12
Bottom = ?, 38
Determine the sum
12 × 6 = 72
Find the other bottom part
72 - 38 = 34
[tex]\Large\boxed{B.~34}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
We will start with a string which is pulled tight enough to vibrate at 288 Hertz when
plucked. Let the length of the string be 1 unit. We can find additional nice sounding
notes by using a string of a smaller length with the same amount of tension. To find
the string lengths, we need to use fractions whose numerators are powers of 2 and
whose denominators are powers of 3 (which are larger than ½, but smaller than 1).
The first few fractions are given below. Determine the remaining fractions:
The series of fractions is 1, 2/3, 8/9, 16/27, 64/81, 128/243, 512/729, 2048/2187, 4096/6516, 16384/19683, 32768/59049, 131072/177147.
The string lengths are fractions whose numerators are powers of 2 and denominators are powers of 3, and the fractions are larger than 1/2 but smaller than 1.
Some powers of 2 are:
2⁰ = 1, 2¹ = 2, 2² = 4, 2³ = 8, 2⁴ = 16, 2⁵ = 32, 2⁶ = 64, 2⁷ = 128, 2⁸ = 256, 2⁹ = 512, 2¹⁰ = 1024, 2¹¹ = 2048, 2¹² = 4096, 2¹³ = 8192, 2¹⁴ = 16384, 2¹⁵ = 32768, 2¹⁶ = 65536, and 2¹⁷ = 131072.
Some powers of 3 are:
3⁰ = 1, 3¹ = 3, 3² = 9, 3³ = 27, 3⁴ = 81, 3⁵ = 243, 3⁶ = 729, 3⁷ = 2187, 2⁸ = 6561, 3⁹ = 19683, 3¹⁰ = 59049, and 3¹¹ = 177147.
The fractions, for which the numerator is a power of 2, the denominator is a power of 3, and the value is between 1/2 and 1 are:
2/3, 8/9, 16/27, 64/81, 128/243, 512/729, 2048/2187, 4096/6516, 16384/19683, 32768/59049, 131072/177147.
Thus, the series of fractions is 1, 2/3, 8/9, 16/27, 64/81, 128/243, 512/729, 2048/2187, 4096/6516, 16384/19683, 32768/59049, 131072/177147.
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Identify the discrete data.
A. the length of a caterpillar during a week
B. the number of dogs you take for a walk each day
C. the wind speed during a particular day
D. the temperature of the water in the local river during the day
Discrete data exists as a numerical kind of data that contains total, concrete numbers with clear and fixed data values specified by counting.
Therefore, the correct answer is option B. the number of dogs you take for a walk each day.
What is discrete data?Discrete data exists as a numerical kind of data that contains total, concrete numbers with clear and fixed data values specified by counting. Discrete data exists a count that involves integers only a limited number of values exists possible. This kind of data cannot be subdivided into distinct parts. Discrete data contains discrete variables that exist in finite, numeric, countable, and non-negative integers.
Therefore, the correct answer is option B. the number of dogs you take for a walk each day.
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2x² + 5x +2can you please give me the answer of 2x + 5 x + 2
Answer:
you better give me brainliest
Step-by-step explanation:
2x +5x+2 = 7x+2
Some of the steps in the derivation of the quadratic formula are shown. Step 4: StartFraction negative 4 a c + b squared Over 4 a EndFraction = a ( x + StartFraction b Over 2 a EndFraction) squared Step 5: (StartFractio.n 1 Over a EndFraction) StartFraction b squared minus 4 a c Over 4 a EndFraction = (StartFraction 1 Over a EndFraction) a (x + StartFraction b Over 2 a EndFraction) squared Step 6: StartFraction b squared minus 4 a c Over 4 a squared EndFraction = ( x + StartFraction b Over 2 a EndFraction) squared Step 7: StartFraction plus or minus StartRoot b squared minus 4 a c EndRoot Over 2 a EndFraction = x + StartFraction b Over 2 a EndFraction Which best explains why the expression plus or minus StartRoot b squared minus 4 a c EndRoot cannot be rewritten as b plus or minus StartRoot negative 4 a c EndRoot during the next step? Negative values, like −4ac, do not have a square root. The ± symbol prevents the square root from being evaluated. The square root of terms separated by addition and subtraction cannot be calculated individually. The entire term b2 − 4ac must be divided by 2a before its square root can be determined.
The reason why we used plus or minus when taking the square root is because; The square root of terms separated by addition and subtraction cannot be calculated individually.
How to use the quadratic formula?
The general formula for a quadratic equation is;
ax² + bx + c = 0
Now, the steps to derive quadratic formula to find the roots of this equation are as follows;
Step 1; Divide both sides of the equation by a to get;
x² + (b/a)x + c/a = 0
Step 2; Transpose the quantity c/a to the right side of the equation to get; x² + (b/a)x = -c/a
Step 3; Complete the square by adding b²/4a² to both sides of the equation to get; x² + (b/a)x + b²/4a² = -c/a + b²/4a²
Step 4; Factor the left side and combine the right side to get;
(x + (b/2a))² = (b² - 4ac)/(4a²)
Step 5: Extract the square-root of both sides of the equation to get;
x + (b/2a) = ±(√(b² - 4ac))/2a
The reason why we used plus or minus when taking the square root is because The square root of terms separated by addition and subtraction cannot be calculated individually.
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2. Brynn borrowed $25,000 at 1% per month from a family friend to start her entrepreneurial venture on December 2, 2011. If she paid back the loan on June 16, 2012, how much simple interest did she pay?
She paid a simple interest of $3,125.00 on the borrowing of $25,000
What is simple interest?
The simple interest on a loan or an investment can be determined as the principal multiplied by interest multiplied by the number of periods.
This is quite different from compound interest where the interest earned previously would earn interest in the future alongside the principal
I=PRT
I=interest on loan=unknown
P=amount borrowed=$25,000
R=interest rate=1% per month
T=12.5 months( from December 2 2011 to December 1 2012 makes one year and from December 1-16 gives 15 days, which is 0.5 of one month)
I=$25,000*1%*12.5
I=$3,125.00
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Directions: Find the missing side of each triangle. Round your answers to the nearest tenth if necessary.
Answer:
1) 13m, 2) 10ft, 3) 11.4ft, 4) 12.7m
Step-by-step explanation:
Since all of these triangles are right triangles, we can use the Pythagorean Theorem: a^2+b^2 = c^2
1) 5^2+12^2 = c^2 = 25+144 = c^2 = 169 = c^2 = 13 = c
2) 6^2+8^2 = c^2 = 36+64 = c^2 = 100 = c^2 = 10 = c
3) 5^2+10.3^2 = c^2 = 25+106.09 = c^2 = 131.09 = c^2 = 11.4494541 = 11.4 = c
4) 8.6^2+9.4^2 = c^2 = 73.96+88.36 = c^2 = 162.32 = c^2 = 12.7404866 = 12.7 = c
Find the area of the trapezoid 19 12.6 29.2 14.5
Answer:
303.66 in²
Option 4 is the correct answer
