Answer:
A"( - 3, 2), B"( - 6, 0), and C"( - 6, 2)
Step-by-step explanation:
Rotation of 90° clockwise rule :
(x, y) ----> ( y , - x )
A(2, 3), B(0, 6), and C(2, 6)
A'(- 2, - 3), B'(0, - 6), and C'( - 2, - 6)
A"( - 3, 2), B"( - 6, 0), and C"( - 6, 2)
Last year Mr Peterson had a fence all the way around his garden. He can reuse all of the fence he had around the garden last year but he needs to buy more fencing to go around this years garden. How many more meters of fencing is needed for this years garden than last years?
Complete Question:
Last year Mr. Petersen’s rectangular garden had a width of 5 meters and an area of 20 square meters. This year he wants to make the garden three times as long and two times as wide.
Last year, Mr. Petersen had a fence all the way around his garden. He can reuse all of the fence he had around the garden last year, but he needs to buy more fencing to go around this year’s garden.
How many more meters of fencing is needed for this year’s garden than last year’s?
Answer:
26 meters of fencing needed
Step-by-step explanation:
Given
Last Year:
\(Width = 5m\)
\(Area = 20m^2\)
This Year:
\(Length = 3\ times\ longer\)
\(Width = 2\ times\ wider\)
Required
Determine how many more meters is needed
Represent last year's length of Fence with L and last year's width with W
First, we need to calculate L
\(Area = L * W\)
Where
\(Area = 20m^2\)
\(W = 5m\)
\(20m^2 = L * 5m\)
Divide both sides by 5m
\(\frac{20m^2}{5m} = \frac{L * 5m}{5m}\)
\(\frac{20m^2}{5m} = L\)
\(L = \frac{20m^2}{5m}\)
\(L = 4m\)
So, we have that:
For Last Year
\(Length = 4m\) and \(Width = 5m\)
For this year:
\(Length = 3\ times\ longer\)
\(Length = 3 * 4m\)
\(Length = 12m\)
\(Width = 2\ times\ wider\)
\(Width = 2 * 5m\)
\(Width = 10m\)
So, for this year, we have:
\(Length = 12m\) and \(Width = 10m\)
Next, we calculate perimeter of fencing in both years.
\(Perimeter = 2 * (Length + Width)\)
Last Year:
\(Perimeter = 2 * (4m + 5m)\)
\(Perimeter = 2 * 9m\)
\(Perimeter = 18m\)
This Year:
\(Perimeter = 2 * (12m + 10m)\)
\(Perimeter = 2 * 22m\)
\(Perimeter = 44m\)
To get the meters of fencing needed this year, we simply calculate the difference in the calculated perimeters.
\(Difference = 44m - 18m\)
\(Difference = 26m\)
Hence, there are 26 meters of fencing needed
Traffic speed: The mean speed for a sample of cars at a certain intersection was kilometers per hour with a standard deviation of kilometers per hour, and the mean speed for a sample of motorcycles was kilometers per hour with a standard deviation of kilometers per hour. Construct a confidence interval for the difference between the mean speeds of motorcycles and cars at this intersection. Let denote the mean speed of motorcycles and round the answers to at least two decimal places. A confidence interval for the difference between the mean speeds, in kilometers per hour, of motorcycles and cars at this intersection is ________.
Construct the 98% confidence interval for the difference μ 1-y 2 when x 1 475.12, x 2-32134, s 1-43.48, s 2-21.60, n 1-12, and n 2-15. Use tables to find the critical value and round the answers to two decimal places. A 98% confidence interval for the difference in the population means is ________.
Answer:
Step-by-step explanation:
Hello!
X₁: speed of a motorcycle at a certain intersection.
n₁= 135
X[bar]₁= 33.99 km/h
S₁= 4.02 km/h
X₂: speed of a car at a certain intersection.
n₂= 42 cars
X[bar]₂= 26.56 km/h
S₂= 2.45 km/h
Assuming
X₁~N(μ₁; σ₁²)
X₂~N(μ₂; σ₂²)
and σ₁² = σ₂²
A 90% confidence interval for the difference between the mean speeds, in kilometers per hour, of motorcycles and cars at this intersection is ________.
The parameter of interest is μ₁-μ₂
(X[bar]₁-X[bar]₂)±\(t_{n_1+n_2-2}\) * \(Sa\sqrt{\frac{1}{n_1} +\frac{1}{n_2} }\)
\(t_{n_1+n_2-2;1-\alpha /2}= t_{175; 0.95}= 1.654\)
\(Sa= \sqrt{\frac{(n_1-1)S_1^2+(n_2-1)S_2^2}{n_1+n_2-2} } = \sqrt{\frac{134*16.1604+41*6.0025}{135+42-2} } = 3.71\)
[(33.99-26.56) ± 1.654 *(\(3.71*\sqrt{\frac{1}{135} +\frac{1}{42} }\))]
[6.345; 8.514]= [6.35; 8.51]km/h
Construct the 98% confidence interval for the difference μ₁-μ₂ when X[bar]₁= 475.12, S₁= 43.48, X[bar]₂= 321.34, S₂= 21.60, n₁= 12, n₂= 15
\(t_{n_1+n_2-2;1-\alpha /2}= t_{25; 0.99}= 2.485\)
\(Sa= \sqrt{\frac{(n_1-1)S_1^2+(n_2-1)S_2^2}{n_1+n_2-2} } = \sqrt{\frac{11*(43.48)^2+14*(21.60)^2}{12+15-2} } = 33.06\)
[(475.12-321.34) ± 2.485 *(\(33.06*\sqrt{\frac{1}{12} +\frac{1}{15} }\))]
[121.96; 185.60]
I hope this helps!
a survey has to be taken to estimate the proportion of voters who favored stem cell research among the
The proportion of voters who favor stem cell research can be estimated by taking a survey and calculating (Number of voters who favor stem cell research / Total Number of voters) x 100.
Proportion of favor stem cell research = (Number of voters who favor stem cell research / Total Number of voters) x 100
In order to estimate the proportion of voters who favor stem cell research, a survey has to be taken. Suppose the survey results indicate that out of a total of 500 voters, 300 of them favor stem cell research. Then, the proportion of favor stem cell research would be calculated as follows: Proportion of favor stem cell research = (300/500) x 100 = 60%. This means that 60% of the total voters favor stem cell research.
The proportion of voters who favor stem cell research can be estimated by taking a survey and calculating (Number of voters who favor stem cell research / +++Total Number of voters) x 100.
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a. Define a relation with four ordered pairs
such that the first element is a university
and the second element is its mascot.
Write the quotient
6+8i
2i
The quotient when 6+8i is divided by 2i is given by -3i+4.
We know that, complex number \(i^1=-1\).
Given the divisor is = 2i and dividend is = 6+8i
Dividing the dividend by divisor we get,
(6+8i)/2i = 6/2i + 8i/2i = 3/i + 4 \(=\frac{3i}{i^2}+4\) = 3i/(-1)+4 = -3i+4
Hence the quotient is = -3i+4.
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woman bought 1.8 kg of chicken and 1.6 kg of meat. The chicken cost N5.40 and the meat cost #6.40. If she had bought 2.4 kg of chicken and 2 kg of meat, how much would she have had to pay?
The amount the women would pay for 2.4 kg of chicken and 2 kg of meat in total is $15.2
What is the unit price?The meaning of unit price is a price quoted in terms of so much per agreed or standard unit of product or service
Given that, a woman bought 1.8 kg of chicken and 1.6 kg of meat. The chicken cost $5.40 and the meat cost $6.40,
We need to find, if she had bought 2.4 kg of chicken and 2 kg of meat, how much would she have had to pay,
To find the same, we will first find the unit price of each,
Unit price = total price / total quantity
Since, 1.8 kg of chicken costs $5.40,
Therefore, 1 kg will cost = 5.40 / 1.8 = $3
Similarly,
If 1.6 kg of meat costs $6.40,
Therefore, 1 kg will cost = 6.40 / 1.6 = $4
Now, to find the cost of 2.4 kg of chicken and 2 kg of meat, we will multiply the unit prices to the required quantities,
Therefore,
2.4 kg of chicken will cost = 2.4 x 3 = $7.2
2 kg of meat will cost = 2 x 4 = $8
In total, she had to pay = 8+7.2 = $15.2
Hence, the amount the women would pay for 2.4 kg of chicken and 2 kg of meat in total is $15.2
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What’s the correct answer answer asap for brainlist
Answer: serbia
Step-by-step explanation:
Solve |x + 1| = 3
Question 5 options:
A)
x = 4
B)
x = 3 or x = 2
C)
No solutions
D)
x = –4 or x = 2
Answer:
D) x = - 4, x = 2
Step-by-step explanation:
\( |x + 1| = 3 \\ \\ x + 1 = \pm \: 3 \\ \\ x + 1 = 3 \: or \: x + 1 = - 3 \\ \\ x = 3 - 1 \: or \: x = - 3 - 1 \\ \\ x = 2 \: or \: x = - 4 \\\\
x = - 4, \: x = 2\)
express this formula as a probabilistic relationship between poisson and gamma random variables. math.stackexchange
The gamma as well as Poisson distributions have an intriguing link. For each x, P(X x) = P(Y x), (1) where Y Poisson(x/), if X is a gamma(x, y) random variable and x is an integer.
What does the word "Poisson" mean?The probability density function f(x)=e−μμxx!, which approximates the binomial distribution and is frequently employed as a mathematical model of something like the number of outcomes acquired in an appropriate period of time and space, has a mean equal to its variance.
What is the purpose of Poisson?A Poisson distribution can be used to forecast or explain how many events will take place over a specific period of time or space. "Events" might include anything from illness occurrences towards to customer purchases to meteor strikes. Any defined period of time or area, such as 10 days or 5 square inches, can be used as the interval.
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Does this procedure describe a completely randomized design for this experiment?
Answer:
Yes
Step-by-step explanation:
Which number is a counterexample to the following statement? All numbers that are divisible by 2 are divisible by 4.
A. 0
B. 12
C. 28
D. 42
Using divisibility concepts, a counterexample to the statement is given by option the number 42, option D.
-------------
If the remainder of the division of A by B is 0, it is said that A is divisible by B.-------------
In option A, 0 is divisible by both 2(0/2 = 0) and 4(0/4 = 0), so it is not a counterexample.In option B, 12 is divisible by both 2(12/2 = 6) and 4(12/4 = 3), so it is not a counterexample.In option C, 28 is divisible both by 2(28/2 = 14) and 4(14/2 = 7), so it is not a counterexample.In option D, 42 divided by 4 is 10 with a remainder of 2, thus 42 is not divisible by 4, being a counterexample to the statement.A similar problem is given at https://brainly.com/question/24354438
the volume of a pyramid is given by the formula V=1/, where B is the area of the base and h is the height?
Answer:
Step-by-step explanation:
The volume of this pyramid in cubic inches is 16.
Given that,
The base and height is 8 and 6.
Based on the above information, the calculation is as follows:
The volume is
= 16
FIRST RIGHT ANSWER GETS BRAINLIEST!!!!
Madison Middle School spends $750 per year on club activities. They spend at least twice that amount on after-school activities. Write an inequality that represents how much they spend on after-school activities.
Answer:
x ≥ 1500
Step-by-step explanation:
Multiply the product
(m+3)(m-3)
Answer:
The answer to (m+3)(m-3) is m^2-9.
Step-by-step explanation:
We will use distributive law to solve this question.
m(m-3)+3(m-3)
= m^2-3m+3m-9
= m^2-9 (since, 3m-3m=0)
As an alternative method, we can use the direct rule learned in algebra: (a+b)(a-b)=a^2-b^2.
so, here a=m and b=3.
(m+3)(m-3)
=m^2-3^2
=m^2-9
solve the following inequality |2x-6|<10
Answer:
Absolute Value Inequality entered : |2x-6|<10
Step by step solution :STEP 1:Rearrange this Absolute Value InequalityAbsolute value inequalitiy entered |2x-6| < 10 STEP 2:Clear the
Absolute Value BarsClear the absolute-value bars by splitting the equation into its two cases, one for the Positive case and the other for the Negative case.
The Absolute Value term is |2x-6| For the Negative case we'll use -(2x-6) For the Positive case we'll use (2x-6) STEP 3:Solve the Negative Case -(2x-6) < 10 Multiply -2x+6 < 10 Rearrange and Add up -2x < 4 Divide both sides by 2 -x < 2 Multiply both sides by (-1) Remember to flip the inequality sign x > -2
Which is the solution for the Negative Case
STEP 4:Solve the Positive Case (2x-6) < 10 Rearrange and Add up 2x < 16 Divide both sides by 2 x < 8 Which is the solution for the Positive Case
STEP 5:Wrap up the solution -2 < x < 8 Solution in Interval Notation (-2,8) Solution on the Number Line
One solution was found : -2 < x < 8
Step-by-step explanation:
mark me brainliest!!
Tina's Treats charges a $4.35 fee for each delivery. Which table best represents the relationship between f, the amount made from the delivery fee, and d, the number of deliveries made in a day?
Answer:
Is there any answer choices? If not I would think its 5$
5$
4$
Step-by-step explanation:
hi please help! ill give u a good 5 starz :)
Answer:
Option C and D!
Step-by-step explanation:
Option C because:-When 9 is placed in the box after 7, we get:-
7 ÷ 9 = \(\frac{7}{9}\) which is correct!
7 ÷ 9 can also be written as \(\frac{7}{9}\). So, this Option is right since the equation is correct when 9 is placed in the box!
Option D is also correct because,When we place 9 in the box before \(\frac{1}{9}\), we get:-
9 ÷ \(\frac{1}{9}\) = 81
9 ÷ \(\frac{1}{9}\) equals 9 x 9 (take the reciprocal of \(\frac{1}{9}\))
9 x 9 equals 81 which means the equation is correct when 9 is placed in the box!
What is the approximate area of the circle shown below
Answer:
the approximate area of corcle is 3848
\(diameter = 70in \\ radius = \frac{70}{2} \\ = 35in \\ area = \pi \: r {}^{2} \\ = \pi \: 35 {}^{2} \\ = 3848.45in {}^{2} \)
Find the area of the shaded region?
3x + 1
3x + 1
Round 51.78 to the greatest place
Answer:
51.78 is rounded to 52
Answer:
it would be rounded up to 52
! 20 points to those who give me the answer!
The surface area of two similar figures are given. The volume of the larger figure is given. Find the volume of the smaller figure.
S.A (Smaller figure) = 567
S.A (Larger figure) = 1575
V (Larger figure) = 2500
Answer:
1575 is the answer
Step-by-step explanation:
a gas tank which can hold a total of 41 liters contains only 5 liters of gas when the driver stops to refuel. If it takes 3 minutes to fill up the tank, what is the rate in liters per minute
Answer:
12 liters per minute.
Step-by-step explanation:
41litres-5litres=36
If 36litres are filled up within 3 min,how many litres will be filled within 1 min
1/3×36=12
=12 litres per min
Borrowed N$20000 AT 5% for three and half years. she wants to pay N$8000 ON MATURITY . TO ACHIEVE THIS SHE IS PLANNING TO PAY 2000 IN 10 MONTHS, AND 5000 IN 16 MONTHS FROM NOW. HOW MUCH SHOULD SHE PAY IN TWO AND HALF YEARS FROM NOW TO MEET HER OBLIGATION?
She needs to pay N $8378.31 in two and a half years from now to meet her obligation.
What are the basic arithmetic operations?
The four basic mathematical operations are Addition, subtraction, multiplication, and division.
Let's first calculate the total interest on the loan for three and a half years:
Interest = Principal × Rate × Time
Interest = 20000 × 0.05 × 3.5
Interest = 3500
So, the total amount she needs to pay back on maturity is:
20000 + 3500 = N$23500
Now, let's subtract the amount she plans to pay in the next 10 months and 16 months:
N$23500 - N$2000 - N$5000 = N$16500
So, she needs to pay N$16500 in two and a half years from now to meet her obligation.
Alternatively, we can also calculate the present value of the remaining payments using the formula for present value of an annuity:
PV = \(PMT \times (1 - (1 + r)^{(-n)}) / r\)
where PV is the present value, PMT is the payment amount, r is the interest rate per period, and n is the number of periods.
Using this formula, we get:
PV = \(2000 \times (1 - (1 + 0.05/12)^{(-10})) / (0.05/12) + 5000 \times x (1 - (1 + 0.05/12)^{(-16)}) / (0.05/12)\)
PV = N$13658.80
So, the amount she needs to pay in two and a half years from now to meet her obligation is the present value of the remaining payments:
PV = \(PMT \times (1 + r)^{(-n)}\)
N$13658.80 = \(PMT \times (1 + 0.05/12)^{(-30)}\)
PMT = N$8378.31
Hence, she needs to pay N$8378.31 in two and a half years from now to meet her obligation.
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What is the total length of all meteors that are 1 6/8 inches?
3 4/8
3 5/8
4 7/8
3 7/8
Anwser: Hitler was the first person to get a 100 bomb IRL
Explenation: Took me 900 years to figure this out
solve the inequality 1/3h≤7
Answer:
h ≤ 21
Step-by-step explanation:
Simply just divide both sides by 1/3 to isolate x and you should get your answer!
Answer:
h ≤ 21
Step-by-step explanation:
1/3h ≤ 7
Multiply 1/3 on both sides of the inequality.
1/3(1/3h) ≤ 1/3(7)
h ≤ 1/3(7)
Reciprocal 1/3.
h ≤ 7(3/1)
h ≤ 21
QUESTION IN PICTURE
Please explain your answer in steps, thank you.
We can complete the blanks with the following ratios:
(7.5 mi/1) * (1 mi/ 5280 ft) * (400ft/1 yd) * (3 ft/1 ft) =33 flags
Since we do not need a flag at the starting line, then 32 flags will be required in total.
How to obtain the number of flagsTo solve the problem, we would first convert 400 yds to feet and miles.
To convert to feet, we multiply by 3. This gives us: 400 yd * 3 = 1200 feet.
To convert to miles, we would have 0.227 miles.
Now, we divide the entire race distance by the number of miles divisions.
This gives us:
7.5 mi /0.227 mi
= 33 flags
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Solve for x. Round to the nearest tenth, if necessary.
X
H
In this problem we are given an angle and two sides. Therefore, we should use a trigonometric function to solve for x.
Trigonometric Functions: SOH-CAH-TOA
Looking from the 23 degree angle, we have the adjacent side and the opposite side. Therefore, we should use the tangent function.
tan(23) = x / 2
x = tan(23) * 2
x = 0.8489
x = 0.8
Hope this helps!
Step-by-step explanation:
ATTACHED IS THE SOLUTION!what is the value of 2.57 1.75
Answer:
2.57 - 1.75 = 0.82
Step-by-step explanation:
Let us assume that we need to find the value of 2.57 - 1.75 i.e. we need to subtract 1.75 from 2.57. It can be done as follows :
The first number is 2.57 and other no is 1.75.
In 2.57, 2 is in ones place, 5 is in tenths place and 7 is in hundredths place.
In 1.75, 1 is in ones place, 7 is in tenths place and 5 is in hundredths place.
Subraction :
2.57
- 1.75
= 0.82
Hence, the value of 2.57 - 1.75 is 0.82
A washer and a dryer cost $857 combined. The washer costs $93 less than the dryer. What is the cost of the dryer?
Answer:
Dryer cost $475; Washer cost $382
Step-by-step explanation:
For this problem, we will simply set up a system of equations to find the value of each the washer (variable x) and the dryer (variable y).
We are given the washer and dryer cost $857 together.
x + y = 857
We are also given that the washer cost $93 less than the dryer.
x = y - 93
So to find the cost of the dryer, we simply need to find the value of y.
x + y = 857
x = y - 93
( y - 93 ) + y = 857
2y - 93 = 857
2y = 950
y = 475
So now we have the value of the dry to be $475. We can check this by simply plugging in the value and see if it makes sense.
x + y = 857
x + 475 = 857
x = 382
And check this value:
x = y - 93
382 ?= 475 - 93
382 == 382
Therefore, we have found the values of both the washer and the dryer.
Cheers.
The cost of the dryer is $475 and the cost of the washer is $382.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given that, a washer and a dryer cost $857 combined.
Let the cost of dryer be x.
The washer costs $93 less than the dryer.
Then, the cost of washer will be x-93
So, x+x-93=857
2x=857+93
2x=950
x=$475
x-93=475-93
= $382
Hence, the cost of the dryer is $475.
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Which function graph represents the following scenario?
The number of students per classroom can be represented by the equation y = 22x.
Question 9 options:
Answer:
The third graph
Step-by-step explanation:
We can immediately eliminate the 1st and last graphs because they are decreasing, not increasing. It wouldn't make sense that the more classrooms there are, the fewer students. Y = 22x would be increasing in the graph.
Let's plug some x values into the equation first, to see where our points are at.
Plug 1 into x
Y = 22(1)
Y= 22
(1,22)
Plug 2 into x
Y = 22(2)
Y = 44
(2,44)
Plug 3 into x
Y = 22(3)
Y = 66
(3,66)
Plug 4 into x
Y = 22(4)
Y = 88
(4,88)
The second graph matches the coordinates, so it works, but it isn't a complete function graph. A function graph needs a line drawn through the points. The second graph isn't your answer.
Let's look at the third graph. The coordinates also match up with the graph and it has a line drawn through the points. It's an accurate function graph representing this scenario. Therefore, the third graph is your answer.
Have a lovely day! :)
Answer: the 2nd graph is what i got right on the test
Step-by-step explanation: