The inverse of the matrix A by getting its determinant value is equal to [tex]A^{-1} = \left[\begin{array}{ccc}1&-1\\\frac{-3}{2} &2\end{array}\right][/tex]
The matrix is equal to,
A = [tex]\left[\begin{array}{ccc}4&2\\3&2\end{array}\right][/tex]
To find the inverse of a matrix,
we first need to calculate its determinant of the matrix A we have,
|A| = [tex]\left|\begin{array}{ccc}4&2\\3&2\end{array}\right|[/tex]
⇒ |A| = 4(2) - 2(3)
= 8 - 6
= 2
Now we can proceed to find the inverse of A.
Set up the matrix of cofactors.
The matrix of cofactors C is obtained by replacing each element of A with its corresponding cofactor,
which is the determinant of the submatrix obtained by deleting the row and column that contain that element.
For our matrix A, we have,
C = [tex]\left[\begin{array}{ccc}2&-3\\-2&4\end{array}\right][/tex]
Transpose the matrix of cofactors.
The transpose of a matrix is obtained by flipping its rows and columns. For our matrix C, we have.
[tex]C^{T} = \left[\begin{array}{ccc}2&-2\\-3&4\end{array}\right][/tex]
Divide by the determinant.
The inverse of A is obtained by dividing the transpose of the matrix of cofactors by the determinant of A.
For our matrix A, we have,
A⁻¹ = [tex]C^{T}[/tex] / |A|
[tex]C^{T} = (1/2)\left[\begin{array}{ccc}2&-2\\-3&4\end{array}\right][/tex]
[tex]C^{T} = \left[\begin{array}{ccc}1&-1\\\frac{-3}{2} &2\end{array}\right][/tex]
Therefore, the inverse of the matrix A is equal to [tex]A^{-1} = \left[\begin{array}{ccc}1&-1\\\frac{-3}{2} &2\end{array}\right][/tex]
learn more about inverse of a matrix here
brainly.com/question/12537023
#SPJ1
PLS HELP WITH THIS MATH PROBLEM! The problem is attached to this problem.
The quintic equation has integer coefficients for x = - 5 / 3.
How to find the values of the missing coefficients of a quintic equation
In this question we need to determine the missing coefficients of a quintic equations, that is, a polynomial of grade 5, on the basis that the coefficients are integers.
First, we evaluate on each case:
x = - 5 / 3
12 · (- 5 / 3)⁵ + a · (- 5 / 3)³ + b · (- 5 / 3)² - 3 · (- 5 / 3) + 15 = 0
- 12500 / 81 - (125 / 27) · a + (25 / 9) · b + 5 + 15 = 0
- (125 / 27) · a + (25 / 9) · b = 10880 / 81
- (5 / 3) · a + b = 2176 / 45
b = (5 / 3) · a + 2176 / 45
x = - 4 / 3
12 · (- 4 / 3)⁵ + a · (- 4 / 3)³ + b · (- 4 / 3)² - 3 · (- 4 / 3) + 15 = 0
- 4096 / 81 - (64 / 27) · a + (16 / 9) · b + 4 + 15 = 0
- (64 / 27) · a + (16 / 9) · b = 2557 / 81
- (4 / 3) · a + b = 2557 / 144
b = (4 / 3) · a + 2557 / 144
x = 3 / 5
12 · (3 / 5)⁵ + a · (3 / 5)³ + b · (3 / 5)² - 3 · (3 / 5) + 15 = 0
2916 / 3125 + (27 / 125) · a + (9 / 25) · b - 9 / 5 + 15 = 0
(27 / 125) · a + (9 / 25) · b - 2709 / 3125 + 46875 / 3125 = 0
(27 / 125) · a + (9 / 25) · b + 44166 / 3125 = 0
(27 / 125) · a + (9 / 25) · b = - 44166 / 3125
(3 / 5) · a + b = - 14722 / 375
b = - (3 / 5) · a - 14722 / 375
x = 6 / 5
12 · (6 / 5)⁵ + a · (6 / 5)³ + b · (6 / 5)² - 3 · (6 / 5) + 15 = 0
12 · (7776 / 3125) + (216 / 125) · a + (36 / 25) · b - 18 / 5 + 15 = 0
93312 / 3125 + (216 / 125) · a + (36 / 25) · b - 18 / 5 + 15 = 0
82062 / 3125 + (216 / 125) · a + (36 / 25) · b + 15 = 0
(216 / 125) · a + (36 / 25) · b = - 128937 / 3125
(6 / 5) · a + b = - 3223425 / 112500
(6 / 5) · a + b = - 644685 / 22500
(6 / 5) · a + b = - 128937 / 4500
b = - (6 / 5) · a - 128937 / 4500
After using a graphing tool, we conclude that x = - 5 / 3 can be found by using the following integers:
(a₁, b₁) = (19, 80), (a₂, b₂) = (31, 100), (a₃, b₃) = (79, 180)
To learn more on polynomials: https://brainly.com/question/29205091
#SPJ1
A cylindrical can of vegetables has a label wrapped around the outside, touching end to end. The only parts of the can not covered by the label are the circular top and bottom of the can. If the area of the label is 66π square inches and the radius of the can is 3 inches, what is the height of the can?
22 inches
11 inches
9 inches
6 inches
If a cylindrical can of vegetables has a label wrapped around the outside, touching end to end. The height of the can is: A. 22 inches.
How to find the height?
Let's call the height of the can "h". The total surface area of the cylinder is given by 2πr² + 2πrh
where:
r = radius of the cylinder.
The label covers all of the cylinder except for the top and bottom circles, which have a combined area of 4πr². So the area of the label is equal to 2πr² + 2πrh - 4πr² = 2πrh.
Set up the equation to solve for h:
2π × 2 ×h = 88π
Dividing both sides by 2π× 2:
h = 44/2
Therefore the height of the can is 22 inches.
To know more about height visit:
brainly.com/question/10726356
#SPJ1
0.15
11A) Suppose a 2 is rolled on a number cube with sides numbered 1, 2, 3, 4, 5, and 6.
Which outcome(s) make up the complement of this event? Select all that apply.
rolling a 1
rolling a 2
rolling a 3
rolling a 4
☐ rolling a 5
rolling a 6
11B) What is the probability of the complement written as a fraction in simplest form?
6
A. rolling a 1,3,4,5,6
B. The probability of the complement event is 5/6.
What is a complement event?An experiment's probability of an event occurring is measured by its probability of occurring. When there are only two outcomes, or complement, we can say that it is the complete opposite of an event.
11(A ) Rolling any number other than 2 on the number cube is the complement of rolling a 2. Therefore, the complement's outcomes are as follows: rolling a one, a three, a four, a five, and a six
So, the correct answers are:
☐ rolling a 1
☐ rolling a 3
☐ rolling a 4
☐ rolling a 5
☐ rolling a 6
11B) Since there is only one favorable outcome (rolling a 2) out of six possible outcomes, the probability of rolling a 2 is 1/6. By deducting the probability of rolling a 2 from 1, the probability of the complement event (rolling any number other than 2) can be determined:
P(complement) = 1 - P(rolling a 2) = 1 - 1/6 = 5/6
Therefore, the probability of the complement event is 5/6.
know more about probability visit :
https://brainly.com/question/30034780
#SPJ1
In the problems below, f(x) = log2x and
g(x) = log10x.
How are the graphs of f and g similar? Check all that apply.What happens to the value of f(x) = log4x as x approaches +∞?
When the value of f(x) = log4x as x approaches +∞ Both have an asymptote of x = 0 and Both have a domain of all real numbers. Hence, option B and D are correct.
The graphs of f(x) = log2x and g(x) = log10x are similar in shape, both being increasing and concave down. As x approaches +∞, the value of f(x) = log4x approaches +∞ as well, since log4x grows without bound as x gets larger and larger.
The correct options are B and D. The graphs of f(x) = log2x and g(x) = log10x are similar in that both increase from left to right and have a domain of all real numbers. Both have an asymptote of x = 0. As x approaches +∞, the value of f(x) = log4x approaches +∞ as well.
To know more about logarithmic functions, visit,
https://brainly.com/question/13473114
#SPJ1
Complete question - In the problems below, f(x) = log2x and
g(x) = log10x.
How are the graphs of f and g similar? Check all that apply. What happens to the value of f(x) = log4x as x approaches +∞?
A. Both have a y-intercept of 1.
B. Both increase from left to right.
C. Both have an asymptote of x = 0.
D. Both have a domain of all real numbers.
In a grid of the swimming area at a beach, the vertices are (1,-1),(1,5),(-4,5) and (-4,-1). Find the perimeter of the swimming area in meters.
In a grid of the swimming area at a beach, the vertices are (1,-1),(1,5),(-4,5) and (-4,-1). Find the perimeter of the swimming area in meters.
The perimeter of the swimming area in meters is 24 meters.
To find the perimeter of the swimming area, we need to calculate the distance between each pair of consecutive vertices and add them up.
Using the distance formula, we can calculate the distance between each pair of consecutive vertices:
Distance between (1,-1) and (1,5):
d = √[(1-1)² + (5-(-1))²] = √(0² + 6²) = 6 meters
Distance between (1,5) and (-4,5):
d = √[(-4-1)² + (5-5)²] = √((-5)² + 0²) = 5 meters
Distance between (-4,5) and (-4,-1):
d = √[(-4-(-4))² + (-1-5)²] = √(0² + (-6)²) = 6 meters
Distance between (-4,-1) and (1,-1):
d = √[(1-(-4))² + (-1-(-1))²] = √(5² + 0²) = 5 meters
Therefore, the perimeter of the swimming area is:
6 + 5 + 6 + 5 = 22 meters
Can someone help me do the working for the answer to this question? Urgently needed!!
They have enough money for the flights, as they are bringing 1600 euros, while the total cost is of 1136 euros.
How to obtain the total amount spent?The total amount spent on the flight, in Euros, is obtained applying the proportions in the context of the problem.
Their daughter is 11 years old, hence she is not charged for the flight.
The costs are given as follows:
October 29th: 2 flights at 283 euros each.November 6th: 2 flights at 285 euros each.Hence the total amount spent is given as follows:
2 x (283 + 285) = 1136 euros.
Hence they have enough money for the flights, as they are bringing 1600 euros, while the total cost is of 1136 euros.
More can be learned about proportions at https://brainly.com/question/24372153
#SPJ1
If the space in her entertainment center is 19.87 inches high and 42 long, will the tv for in her entertainment center ? Yes or no
The 43-inch TV will fit in Susan's entertainment center.
To determine if the 43-inch TV will fit in Susan's entertainment center, we need to make sure that the height, width, and diagonal of the TV are all smaller than or equal to the corresponding measurements of the entertainment center.
Since the entertainment center has a height of 19.87 inches, the 43-inch TV will fit in terms of height if its height is 19.87 inches or smaller.
Similarly, since the entertainment center has a length of 42 inches, the 43-inch TV will fit in terms of length if its length is 42 inches or smaller. Since the length of the TV is 37.41 inches, it will fit.
Finally, we need to check the diagonal. The diagonal of a rectangle can be found using the Pythagorean theorem. If we let a be the height and b be the length, then the diagonal d is given by:
d = sqrt(a² + b²)
For the entertainment center, this gives a diagonal of approximately 45.53 inches. Since the diagonal of the TV is 43 inches, it will also fit.
Therefore, the 43-inch TV will fit in Susan's entertainment center.
To learn more about Pythagorean theorem here
https://brainly.com/question/14930619
#SPJ1
Its about fractions please help me
The times the 7 in the Susan's scores is greater than Sarah's score is 100 times
How many times is the 7 in the scores greater than the otherFrom the question, we have the following parameters that can be used in our computation:
Susan = 87, 325
Sarah = 46, 175
The values of the 7's in their scores are
Susan = 7, 000
Sarah = 70
So, we have
Number of times = 7000/70
Evaluate
Number of times = 100
Hence, the number of times is 100
Read more about fractions at
https://brainly.com/question/17220365
#SPJ1
A large toiletry distributor claims that 35% of all individuals who purchase toilet paper from the stores that carry its product choose original toilet paper, 28% choose sensitive toilet paper, 20% choose ultra-strong toilet paper, and 17% choose ultra-soft toilet paper. To investigate this claim, researchers collected data from a random sample of customers in a large city. The results were 170 packages of original, 105 sensitive, 80 ultra-strong, and 45 ultra-soft toilet paper purchases. Are the data from the sample consistent with the distributor's claim? Conduct an appropriate statistical test at the 5% significance level to support your conclusion. Make sure to include parameters, check conditions, and show calculations before formulating a conclusion.
__________________________________
No, The Data From The Sample Is Not Consistent With The Distributor's Claim.CLAIM:Original: 35%Sensitive: 28%Ultra-Strong: 20%Ultra-Soft: 17%= 35% + 28% + 20% + 17%= 100%DATA: Original: 170 PacksSensitive: 105 PacksUltra-Strong: 80 PacksUltra-Soft: 45 Packs= 170 Packs + 105 Packs + 80 Packs + 45 Packs= 400 PacksOriginal = 170 ÷ 400 × 100 = 42.5%Sensitive = 105 ÷ 400 × 100 = 26.25%Ultra-Strong = 80 ÷ 400 × 100 = 20% Ultra-Soft = 45 ÷ 400 × 100 = 11.25%= 42.5% + 26.25% + 20% + 11.25%= 100%_________________________________
evaluate the expression
(2t+4)/r^3, for r =-2 and t=-4
Answer:
64Step-by-step explanation:
(2t+4)^4/r^2 when,
t = -4r=-2[tex]\mathrm{\cfrac{\left(2t+4\right)^4}{r^2}}[/tex]
[tex]\mathrm{\cfrac{(2(-4)+4)^4}{(-2)^2}}[/tex][tex]\mathrm{(2(-4)+4)^4=\bf 256}[/tex][tex]\mathrm{\left(-2\right)^2=\bf 4}[/tex][tex]\mathrm{\cfrac{256}{4}}[/tex][tex]\mathrm{64}[/tex]____________________
Hope this helps!
Jack’s grandfather gave his
parents a check to start a college
savings account. They opened the account
with the check, and then deposited
$175 per month since. After 5 years,
there is $13,000 in the account.
(This does not include interest).
Jack's parents initially deposited $2,500 into the college savings account.
To determine the initial amount deposited by Jack's parents, we can subtract the accumulated monthly deposits from the total amount in the account after 5 years.
Total amount in the account after 5 years = $13,000
Monthly deposit = $175
Number of months = 5 years * 12 months/year = 60 months
Total accumulated deposits = Monthly deposit * Number of months
= $175 * 60
= $10,500
Initial amount deposited = Total amount in the account after 5 years - Total accumulated deposits.
= $13,000 - $10,500
= $2,500.
For similar question on initial amount.
https://brainly.com/question/11271432
#SPJ11
When keith had 5 years left in college, he took out a student loan for $14,342. The student loan has an annual interest rate of 2.7%. Keith graduated 5 years after acquiring the loan and began repaying the loan immediately upon graduation What was his subsided monthly payment
Keith's subsidized monthly payment upon graduation would be approximately $135.65.
Keith took out a student loan for $14,342 with an annual interest rate of 2.7%. He had 5 years left in college before he began repaying the loan. To find his subsidized monthly payment, we need to first calculate the total amount he owes after 5 years and then divide that by the number of months in the repayment period.
1. Convert the annual interest rate to a decimal: 2.7% ÷ 100 = 0.027
2. Calculate the interest for one year: $14,342 × 0.027 = $387.234
3. Calculate the total interest for 5 years: $387.234 × 5 = $1,936.17
4. Add the interest to the principal amount: $14,342 + $1,936.17 = $16,278.17
5. Assume a standard repayment period of 10 years (120 months) after graduation.
6. Divide the total amount owed by the number of months in the repayment period: $16,278.17 ÷ 120 = $135.65
To know more about monthly payment here:
https://brainly.com/question/26192602
#SPJ1
mr sanchez´s driveway is 0.25 kilometer long.how many centimeters is this
Answer:
25000
Step-by-step explanation:
to convert from kilometres to centimetres you have to times by one hundred thousand so it would look like
0.25x100000=25000
(b) One of the worst nuclear disasters in history occurred on April 26, 1986 when the Chernobyl nuclear power plant (located in what is now known as Ukraine) exploded scattering radioactive material over parts of Asia and Europe. One radioactive element involved was cesium-137, which has a half-life of 30 years. It is almost 37 years since the Chernobyl disaster. Let Ao be the amount of cesium-137 present near the disaster site at the time of the explosion. What percentage of cesium-137 is still near the disaster site today (after 37 years)? Your answer will be a percentage of Ao. Make sure to leave k in exact form in your calculation. Round your answer to 2 decimal places.
The result, when rounded to two decimal places, is 23.87%.
What is a decimal ?In algebra, a decimals is one of the number types that has a full integer and a fractional component divided by a point that is decimal. 34.5 is an illustration of a decimal number.
The formula A = Ao * (1/2)(t/30) can be used to determine how much cesium-137 is still present after t years, where Ao is the initial amount and t is the amount of time in years.
After simplifying and replacing t=37, we obtain:
A = Ao * (1/2)^(37/30)
A = Ao * (1/2)^(37/30)
After 37 years, there is a proportion of cesium-137 left, which is:
% is equal to (A/Ao) * 100 = (Ao * (1/2)(37/30)/Ao) * 100 = (1/2)(37/30) * 100.
Calculating (1/2)(37/30) yields the result: (1/2)(37/30) 0.2387
Consequently, the percentage of cesium-137 still present in the area now is about equal to: percentage 0.2387 * 100 23.87%
The result, when rounded to two decimal places, is 23.87%.
To know more about decimal visit - https://brainly.com/question/29018620
#SPJ1
About 21.44% of cesium-137 is still near the disaster site today.
What is algebra?
Algebra is a branch of mathematics that deals with mathematical operations and symbols used to represent numbers and quantities in equations and formulas.
The amount of cesium-137 present near the disaster site at the time of the explosion is Ao.
The half-life of cesium-137 is 30 years. This means that after 30 years, half of the initial amount will have decayed, leaving us with 1/2 of the initial amount. After another 30 years, half of the remaining amount will have decayed, leaving us with 1/4 of the initial amount.
Since it is almost 37 years since the Chernobyl disaster, we can calculate the percentage of cesium-137 that is still near the disaster site today as follows:
Amount of cesium-137 present today = Ao * (1/2)^(37/30)
Percentage of cesium-137 present today = (Amount of cesium-137 present today / Ao) * 100
= (Ao * [tex](1/2)^{(37/30)}[/tex] / Ao) * 100
= [tex](1/2)^{(37/30)}[/tex]) * 100
= [tex](1/2)^{(37/30)}[/tex]) * 100%
≈ 21.44%
Therefore, about 21.44% of cesium-137 is still near the disaster site today.
To learn more about algebra from the given link:
https://brainly.com/question/24875240
#SPJ1
WILL GIVE 100 POINTS FOR CORRECT ANSWER AND WILL GIVE BRAINLIEST I will report you if you try to just get the points instead of helping me and getting points
Answer: e, f, c, a
Step-by-step explanation:
1. If you follow the chart, students that didn't get hired and CS major was 102 and total applicants were 234. so your percent comes from 102/234=.4358 move decimal over 2 places or multiply by 100
=e. 43.5%
2. 74/234 = .3162
=f. 31.6
3. 58/160 =.3625
=c. 36.2
4. 36/74=.4864
=a. 48.6
The following histogram shows the exam scores for a Prealgebra class. Use this histogram to answer the questions.
Using the histogram, we can see that the upper-class limit of the second class is given to be 80.5.
Define histogram?A collection of rectangles with bases and the spaces between class boundaries can be referred to as a histogram. Each rectangular bar represents some type of data, and every rectangle is next to another. Rectangle heights are inversely correlated with matching frequencies for both similar and dissimilar groups.
A bar graph is used to represent data in a histogram. It is a visualisation of several outcomes organised into columns along the x-axis. The y-axis of the same histogram represents the number count or multiple occurrences in the data for each column. It is the simplest method for visualising data distributions.
Using the histogram, we can see that the upper-class limit of the second class is given to be 80.5.
To know more about histogram, visit:
https://brainly.com/question/30354484
#SPJ1
Answer B ONLY!!!
Please I need help with this
If 453 teenagers were surveyed, the number of teenagers who would receive a weekly allowance is approximately 263.
Given that,
According to a survey,
Percent of teenagers who will receive a weekly allowance for doing household chores = 58%
So, if the number of teenagers surveyed is 453,
Number of teenagers who will receive a weekly allowance for doing household chores = 58% × 453
= (58/100) × 453
= 0.58 × 453
= 262.74 ≈ 263
Hence the number of teenagers who will receive a weekly allowance for doing household chores is approximately 263.
Learn more about Percentage here :
https://brainly.com/question/13466731
#SPJ1
David’s taxable income is $36,480. He is filing as married filing jointly, and he has already paid $4047 in federal taxes.
What will he receive or pay after he figures his taxes for the year?
Use the tax table sample to answer a question.
Responses
He will receive a refund of $554.
He will receive a refund of $1102.
He will pay $554.
He will pay $1102.
.
Answer:
(c) He will pay $554
Step-by-step explanation:
You want to know whether David will receive a refund or pay additional tax on his taxable income of $36,480 when he files as "married filing jointly" after he as paid $4047.
Tax tableDavid's tax is found on the line of the table that begins 36,450 36,500. In the column titled "Married filing jointly" the tax listed on that line is 4,601.
The amount due is found from ...
amount paid + amount due = tax
4047 + amount due = 4601
amount due = 4601 -4047 = 554
He will pay $554, choice C.
<95141404393>
[tex]10000 \times 2.0000581 = [/tex]
[tex]254 \div 506[/tex]
[tex]800 - 6595[/tex]
[tex]9871 + 2840[/tex]
Then you add all the answer
According to the information, the result of these mathematical operations are: 200,005.81, 0.50, -5,795, 12,711.
How to solve the mathematical operations?To solve the different mathematical operations we have several alternatives. However, the easiest is to use a calculator to help us find the solution more quickly.
In the case of multiplication, we must understand that an operation in which a number is repeated several times and added and that would be the result, for example:
5 * 5 = 25
5 + 5 + 5 + 5 + 5 = 25
In the case of division, it is when a number is divided into another in equal parts, for example:
15 / 5 = 3
that is to say that there are 3 sets of 5 units each.
A subtraction is an operation in which we remove some units from a number, for example:
10 - 2 = 8
In this case, we subtract 2 units from the 10 and a number 8 remains.
An addition is the opposite of subtraction, in this we increase the value of a number by adding another value, for example:
10 + 10 = 20
In this case we added 10 units and the result was 20.
Then, the answers of the operations would be:
200,005.81 multiplication0.50 division-5,795 remainder12,711 sumLearn more about operations in: https://brainly.com/question/29949119
#SPJ1
1) Which of the following statements can be expressed as an inequality? (Select all that apply.)
A) 9 less than the product of 4 and y
B) x decreased by 4 is less than 9
C) x is decreased by the product of 4 and y
Using inequalities, we can find that x - 4 < 9 is an inequality.
Option B is correct.
Define inequality?The two sides of a mathematical equation having an inequality must be equal. We compare two values via inequality rather than equations. The equal-sign is replaced by the signs less than (or less than or equal to), greater than (or greater than or equal to), or not equal to.
Here in the question,
A) 9 less than the product of 4 and y is given.
Let the number be x.
So,
x = 4y - 9
So, this is not an inequality.
B) x decreased by 4 is less than 9 is given.
So,
x - 4 < 9
This is an inequality.
C) x is decreased by the product of 4 and y is given.
So,
x - 4y.
This is not an inequality.
Hence, x - 4 < 9 is an inequality.
Option B is correct.
To know more about inequality, visit:
https://brainly.com/question/30231190
#SPJ1
Pls hurry quick answer now
Which details from the poster suggest that giving women the vote will destroy home life?
Step-by-step explanation:
the fourth one
...
.
.
...
..
Answer:
O.D) The broken plate, the creaming children, and the boiling tea kettle.
No explanation needed.A certain drug is made from only two ingredients: compound A and compound B. There are 3 milliliters of compound A used for every 5 milliliters of compound
B. If a chemist wants to make 728 milliliters of the drug, how many milliliters of compound A are needed?
? milliliters of compound A
The chemist will need 273 ml of compound A to make 728 ml of the drug.
It is given that 8 parts of drug are made by using 2 parts of compound A and 5 parts of compound B.
So the proportion (ml of compound A)/(ml of drug) = 3/8
Suppose the chemist needs x ml of compound A to make 728 ml of the drug.
So we have, [tex]\frac{x}{728} = \frac{3} {8}[/tex]
So , [tex]x = \frac{(728)(3)}{8} = 273\,\,ml.[/tex]
How do we solve ratio and proportion questions.
How do we solve ratio and proportion questions.Consider this question?
Suppose every project team will have equal no of boys and girls. Suppose a particular team will have 10 members. How many boys will be in this team. To answer this question we find the the key proportionality or ratio in the problem. it is #boys/#girls = 1/1. So #boys/#team members = 1/(1+1)=1/2. So if the team size is 10. then #boys = (1/2)(10) = 5. This is the way we solve problems in ratio and proportion.
To know more about proportionality, visit:
https://brainly.com/question/30657439
#SPJ1
Enter the ordered pairs for the equation provided.
-2x + y = 85
There are an infinite number of ordered pairs that satisfy the equation -2x + y = 85. Some are (0, 85),(-10, 65)
What do you mean by Linear Equation in one variable ?The linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution. For example, 2x+3=8 is a linear equation having a single variable in it.
To find the ordered pairs for the equation -2x + y = 85, we can assign a value to one variable and solve for the other. Here are a few ordered pairs that satisfy the equation:
When x = 0, y = 85:
(0, 85)
When x = -10, y = 65:
(-10, 65)
When x = 20, y = 45:
(20, 45)
When x = -42.5, y = -8:
(-42.5, -8)
And so on. There are an infinite number of ordered pairs that satisfy the equation -2x + y = 85.
Learn more about integers here
https://brainly.com/question/15276410
#SPJ1
The accompanying table shows the value of a car over time that was purchased for
15700 dollars, where x is years and y is the value of the car in dollars. Write an
exponential regression equation for this set of data, rounding all coefficients to the
nearest hundredth. Using this equation, determine the value of the car, to the nearest
cent, after 9 years.
Years (x)
0
1
2
3
4
5
6
Value in Dollars (y)
15700
14220
13060
11446
10927
9140
8418
Answer:
To write an exponential regression equation for this set of data, we can use the formula y = ab^x, where y is the value of the car in dollars, x is the number of years since purchase, a is the initial value of the car, and b is the rate of depreciation.
To find the values of a and b, we can use the first two data points:
y = ab^x
14220 = ab^1
Solving for a, we get:
a = 14220 / b
Now, we can substitute this expression for a into the first data point:
y = ab^x
15700 = (14220 / b) * b^0
Simplifying, we get:
15700 = 14220
This is not a valid equation, so we need to adjust our estimate for the rate of depreciation, b. One way to do this is to take the average of the depreciation rates between each pair of consecutive data points:
b = (14220/15700)^(1/6)
b = 0.9497
Now, we can use this value of b to find the value of a:
a = 14220 / b
a = 14955.15
Therefore, the exponential regression equation for this set of data is:
y = 14955.15 * 0.9497^x
To find the value of the car after 9 years, we can substitute x = 9 into the equation:
y = 14955.15 * 0.9497^9
y = 7327.78
Therefore, the value of the car, to the nearest cent, after 9 years is $7327.78.
If all data points on its scatter plot are on one line, then the correlation coefficient is equal to?
If all of the points on the scatter plot are directly on a straight line with a negative slope, the product-moment correlation coefficient is a negative one.
What is a Scatter Plot?A scatter chart, also known as a scatter plot, is a graph that shows the relationship between two variables. They are a powerful chart type that allows readers to see a relationship or trend that would be impossible to see in almost any other format.
Accordingly, when all of the points on a scatter plot fall on a straight line, the connection between the two variables is perfect linear. The correlation coefficient (r) will be either +1 or -1 in this scenario.
Learn more about scatter plot here: https://brainly.com/question/6592115
#SPJ1
I don’t know ♀️. Question below
The experimental probability of making both free throws is given as follows:
0.4.
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
For an experimental probability, the outcomes are considered from previous trials.
From the table, we have that out of 10 sets of free throws, 4 are (Y,Y), representing both made, hence the probability is given as follows:
p = 4/10 = 0.4.
More can be learned about probability at https://brainly.com/question/24756209
#SPJ1
Awanita is placing items on a shelf that is 200 cm above the ground. She exerts a force of 20 N to lift a box from the floor to the shelf. She does this in 5 s.
What is Awanita’s power output?
4 W
8 W
40 W
800 W
Awanita's power output is 8 W.
The following formula must be used to determine Awanita's power output:
power = work/time
where work is the quantity of energy that is transmitted and time is the length of time that the transfer takes place.
In this instance, Awanita's work is calculated as the product of her force and the height of the box she lifts:
Work = force x distance, or 20 N x 200 cm = 4000 J.
The distance must be changed to meters:
2 metres = 200 centimetres.
As a result, Awanita's work is as follows:
work = 20 N x 2 m = 40 J.
Now that we know her power output, we can:
Work = Time * Power = 40 J * 5 s * 8 W
Therefore, Awanita's power output is 8 W as a result.
Learn more about force here:
https://brainly.com/question/13191643
#SPJ1
Two numbers are in the ratio of 3 to 4. If 9 is subtracted from each, they are in a ratio of 3 to 5. Find the two numbers.
The two numbers in the ratio are 18 and 24
Finding the two numbers.From the question, we have the following parameters that can be used in our computation:
Two numbers are in the ratio of 3 to 4. If 9 is subtracted from each, they are in a ratio of 3 to 5.Let the numbers be x and y
So, we have
x : y = 3 : 4
x - 9 : y - 9 = 3 : 5
So, we have
4x = 3y
Also, we have
(x - 9)/(y - 9) = 3/5
When solved using a graphing tool, we have
x = 18 and y = 24
Hence, the numbers are 18 and 24
Read more about ratio at
https://brainly.com/question/12024093
#SPJ1
4.Sarah wants to give her friend a fish tank for her birthday.
The tank is a cylinder that measures 10 inches high and has a
diameter of 8 inches.
a.What is the minimum amount of wrapping paper Sarah will
need to cover the present? (Please show your work for credit)
Please help me
The minimum amount of wrapping paper Sarah will need to cover the present is; 351.68 square inches and one gallon of filtered water is not enough because the capacity of fish tank will be 2.17 gallons.
WE are Given that, the dimensions of cylindrical fish tank are height=10 inches and radius = 8/2 = 4 inches.
Now the total surface area of a cylinder is 2πr(r + h).
Here, the required wrapping paper = 2×3.14 ×4(4+10)
= 2×3.14×4×14
= 351.68 square inches
We know that, the volume of cylinder = πr²h
= 3.14 × 4² × 10
= 502.4 cubic inches
Thus, 1 gallon is equal to 231 cubic inches
Number of gallons of filtered water required = 502.4/231
= 2.17 gallons
To learn more about the volume visit:
brainly.com/question/13338592.
#SPJ1
In Exercises 11 and 12, solids A and B are similar. Use the given information and scale factor k from solid A to solid B
to find the surface area of solid B.
11. The surface area of pyramid A is
72 square centimeters and k =
12. The surface area of cone A is
150# square meters and k =
5
The surface area of solid B is 3,750 square meters.
How to calculate the surface area of solid?Since the solids are similar with a scale factor k from solid A to solid B, the ratio of their surface areas is k². Therefore, the surface area of solid B is:
Surface area of solid B = Surface area of solid A * k²
Substituting the given values, we get:
Surface area of solid B = 72 * 12²
Surface area of solid B = 10368 square centimeters.
Therefore, the surface area of solid B is 10,368 square centimeters.
Following the same approach as above:
Surface area of solid B = Surface area of solid A * k²
Substituting the given values:
Surface area of solid B = 150 * 5²
Surface area of solid B = 3750 square meters
Therefore, the surface area of solid B is 3,750 square meters.
Learn more about the surface area at brainly.com/question/15476432
#SPJ1
