The value of x', the image point with respect to an axis rotated 60 is 3/2 + 4√3
How to determine the x' coordinate?The point is given as:
(x, y) = (3, 8)
The angle of rotation is given as:
θ = 60
The image of rotation is calculated using:
x = x'cosθ - y'sinθ
y = x'sinθ + y'cosθ
So, we have:
3 = x'cos(60) - y'sin(60)
8 = x'sin(60) + y'cos(60)
Evaluate cos(60) and sin(60)
3 = 1/2x' - y'√3/2
8 = x'√3/2 + 1/2y'
Multiply the second equation by √3
8√3 = 3/2x' + √3/2y'
Add this equation and the first equation to eliminate y'
3 + 8√3 = 1/2x' + 3/2x'
Evaluate the sum
3 + 8√3 = 2x'
Divide through by 2
x' = 3/2 + 4√3
Hence, the value of x' is 3/2 + 4√3
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Why is the average approaching 3.5?
There are no remaining rolls, and the average approaching 3.5 is simply the current average of 3.51.
What is a mean?It is the average value of the set given.
It is calculated as:
Mean = Sum of all the values of the set given / Number of values in the set
We have,
To find the average approaching 3.5, we need to use the concept of the mean or expected value.
The expected value of a random variable is the long-run average value that we would expect to get if we repeat an experiment many times.
In this case, we can consider each roll of a die as an experiment, and the value of the die as the random variable.
Assuming that the die is fair and has six equally likely outcomes, each with a value between 1 and 6, the expected value of the die is:
E(X) = (1 + 2 + 3 + 4 + 5 + 6)/6 = 3.5
Therefore, if we roll the die many times, we would expect the long-run average value to be 3.5.
Now, if we have rolled the die 3200 times and the average so far is 3.51, we can calculate the sum of all the values rolled so far as:
Sum = (Average so far) x (Number of rolls) = 3.51 x 3200 = 11232
To find the average approaching 3.5, we need to calculate the average of the remaining rolls. Let's call the number of remaining rolls "n". Then we have:
Average approaching 3.5 = (Sum of remaining rolls) / n
We know that the total number of rolls is 3200, so the number of remaining rolls is:
n = 3200 - (number of rolls already rolled)
n = 3200 - 3200 = 0
Therefore,
There are no remaining rolls, and the average approaching 3.5 is simply the current average of 3.51.
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Pls help fast will give brainliest
Answer:
y= -2x+ 5
Step-by-step explanation:
parallel with y= -2x+ 1 means the lines have the same slope m= -2
from point (-1, 7) we go with a slope of -2 until we find the y-intercept (0, 5)
y= mx+b is the general formula
y= -2x+ 5
Find the area of the figure.
Answer:
The answer is 28.5
Step-by-step explanation:
Right triangle: 4.5
Top triangle: 6
Rectangle: 18
Your welcome :)
HELP HELP HELPH EPLHEPLHEPLHEPLHEPLEP
Answers:
1a) y=-10/3x+90
1b) 20
1c) -18
2a) 2.8
2b) How much the heights of five basketball players vary from the average height.
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Explanations:
1a) The trend line is linear, so we just need to find the slope and y-intercept to find an equation for it. Our y-intercept is (0,90), or 90, and our slope is -10/3. Our equation is now y=-10/3x+90.
1b) To find when x=21, we plug 21 into our equation where the x is. Now we do the math.
y=-10/3(21)+90 (plug in)
y=-70+90 (simplify by multiplying -10/3 by 21)
y=20 (simplify by adding -70 to 90)
Therefore, we can predict that when x is 21, y is 20.
1c) To find when y=150, we plug 150 into our equation where the y is. Now we do some more math.
150=-10/3x+90 (plug in)
60=-10/3x (subtract 90 from both sides
-18=x (divide both sides by -10/3)
Therefore, we can predict that when y is 150, x is -18.
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2a) The mean absolute deviation (or MAD for short) of a data set is calculated as such:
Step 1) Find the mean (average) by finding the sum of the data values, then dividing the sum of the data values by the number of data values. In this case, we have the numbers 65, 58, 64, 61, and 67, which add up to 315. The data set has 5 numbers, so we divide our sum of 315 by 5 to get 63. Therefore, our mean is 63.
Step 2) Find the absolute value of the distance between each data value and the mean. In this case, we find out how far away each data value is from 63, our mean. To do this, we subtract 63 from each number.
65-63=2
58-63=-5
64-63=1
61-63=-2
67-63=4
Some of these values are negative, but we're using absolute value so they all become positive. We now have a new set of values: 2, 5, 1, 2, and 4.
Step 3) Finally, we calculate the mean of our new set of values. In this case, we will add up 2, 5, 1, 2, and 4 to get 14 and divide by 5 to get our MAD of 2.8. Therefore, the MAD (and the answer to problem 2a) is 2.8.
2b) Now we just find out what the MAD means in this context. The MAD always is a measure of variance in a data set. In this context, it's describing how much the heights (in inches) of five people on a basketball team vary from the average height.
Hope this helps!
Marco is reconstructing his expenses for the past two weeks. Here are the records of his expenses:
Transaction
Cost ($)
T-shirt
20
Gas
22
Movie
13
Video game
39
Jeans
34
Hat
15
Books
31
Marco’s bank statement says that he has an ending balance of $81. What is Marco’s starting balance?
Answer:
255 - A
Step-by-step explanation:
81+31+15+34+39+13+22+20=255
Find the Difference: 0.325-0.01
Answer:
= 0.315
Step-by-step explanation:
hope this helps :)
The function r(n) = 5n² + 1 represents the value of the nth term in a sequence.
What is the sum of the 1st and 3rd terms of the sequence?
Step-by-step explanation:
a_n=5n²+1
➜a_1=5(1)²+1
➜5×1+1
➜5+1
➜6➜a_3=5(3)²+1
➜5×9+1
➜45+1
➜46Write a sentence in which the relative frequency of the letter E (or e) is exactly 10%.
Answer:
I'd try to do that, but it cannot be done.
Step-by-step explanation:
The above sentence contains 30 letters, including 3 "e"s, so the frequency of e is 3/30 = 0.1 = 10%
9. The quotient of n and -4 is 5. What is the
value of n?
Answer:
n=-20
Step-by-step explanation:
Answer:
n = -20
Step-by-step explanation:
n/-4 = 5
n/-4 (-4) = 5(-4)
n = -20
-20/-4 = 5
Sonia has a hat collection. The ratio of white hats to
blue hats in her hat collection is 10:9. Which ratio is
equivalent to 10:9?
Answer:
20:18 30:27 40:36 etc..
Step-by-step explanation:
To find equivalent ratios you multiply both 10 and 9 by the same number to find equivalent ratios.
Logan inherited $8,000 from his grandmother. He split the money and placed the amounts in the two accounts below. Find the total amount of money he will have in the accounts combined after 5 years. x Account A: earns 7% interest compounded quarterly x Account B: earns 5.5% interest compounded annually
Answer:
What i got was 3000 please mark wrong if it not right
Step-by-step explanation:
Question b quick 10 points
BJ purchased five candy bars ($.79 each) three sodas ($.169)each and four bags of chips ($.89 each). What percent of the total order was spent on sodas? 
Answer:
12.0%
Step-by-step explanation:
Nico practiced drums 1.5 fewer hours than he practiced piano. If Nico practiced the piano for 4 hours, how many hours did Nico practice the drums
Answer:
2.5 hours
Step-by-step explanation:
4 - 1.5 = 2.5
You must subtract 1.5 from the amount of hours he plays piano, which is 4. This is because he spends 1.5 hours less playing drums than he does playing piano.
Find the missing lengths of the leg AND the hypotenuse in simpilest radical form.
Answer:
Above picture is the solution for your question
Step-by-step explanation:
Use relation of trignometric ratios
What is the equation of a circle with a radius of 6 and a center at ( -2 , 3 )?
Answer:
Solution given:
centre(h,k)=(-2,3)
radius(r)=6 units
we have
equation of a circle is:
(x-h)²+(y-k)²=r²
(x+2)²+(y-3)²=6²
(x+2)²+(y-3)²=36 is required equation of a circle.
Which of the following shows the quadratic formula correctly used to solve the
polynomial equation 3x^2 - 2 =11x
[tex]3{x}^{2} - 2 = 11x \\ + 11x \: \: \: \: \: \: + 11x \\ 3 {x}^{2} + 11x- 2 = 0 \\ quadratic \: formula \: goes \: fom \: this \: : a {x}^{2} + bx + c = 0 \\ to \: this : x = \frac{- b \ \frac{ + }{ \: } \: \sqrt{ {b}^{2} - 4ac } }{2a} [/tex]
so now you just plug in the numbers to their corresponding letter:
[tex]x = \frac{ - 11 \frac{ + }{ \: } \sqrt{ {11}^{2} - 4(3)( - 2)} }{2(3)} [/tex]
one side of a triangle is 50 and the other side is 120 what is the length of the third side?
this is exterior angle theorem.
I think it 10
Hope that helps
What is the length of the hypotenuse
Answer:
15
Step-by-step explanation:
The Pythagorean's Theorem states that a^2 + b^2 = c^2, so 81 + 144 = 225, and 225 square rooted is 15.
Answer:
15
Step-by-step explanation:
So, to find the hypotenuse you must use the pythagreons theorm:
A^2+B^2=C^2
Now, we knowt hat A and B is the side lengths.(9 and 12)
The hyoptenuse is C.
So, lets plug in our values for A and B, and find C:
A^2+B^2=C^2
=
9^2+12^2=C^2
Now lets square each number except for C, since its a unknown value:
81+144=C^2
Now combine the 144 and 81:
225=C^2
Finally, square root both sides so C^2 becomes C:
15=C
So the answer for the hyotenuse is 15!
Hope this helps!
There are 3 liters of orange juice at a school party. 10 students want to drink all of the orange juice, and they all want to get exactly the same amount. How much orange juice can each get? (enter your answer as a fraction or mixed number)
Write a number sentence that represents the problem.
Answer:
0.3
Step-by-step explanation:
yushhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh
Answer:
0.3
Step-by-step explanation:
djdjwinqwp9dejnedm
Which statement accurately describes the economic characteristics of modern
Texas?
A. Texas has one of the strongest and most diverse economies in the country.
B. Texas has a fairly strong economy, but growth has slowed since 2004.
C. Texas has a stable economy, but lacks industrial diversity.
D. Texas has a strong oil industry, but all other sectors have struggled recently.
Answer:
D
Step-by-step explanation:
sorry if incorrect
Answer:
The answer is A. Texas has one of the strongest and most diverse economies in the country.
Step-by-step explanation:
Texas is a densely populated state with numerous successful industries and businesses. It has many different cultures and ways of life. Texas has grown and adapted in order to succeed and not only remain stable and functioning, but also climb the ladder of achievement and keep its position (there). (Modern) Texas has a diverse economy that continues to thrive.
Edgar pay $67.86 for 7.8 pounds of fertilizer. What is the price per pound of fertilizer?
(Write in dollars & cents.)
Answer:
He pays $8.70
Step-by-step explanation:
You would do $67.86 divided by 7.8 lbs
which model represents the expression
Answer:
C, there are 4 groups of 5/12 on the numberline. They are jumping 4 times whilst each of those jumps are 5/12.
HELP MEEEEEEEEEEEEEEE!
Answer: go
Step-by-step explanation:
Please help! I will give points for helpng.
Answer:
Should Be 19 students
Step-by-step explanation:
HELP ME I will give brainliest to whoever is RIGhT
Answer:
B)
Step-by-step explanation:
PLEASE ANSWER PLZ PLZ
Answer:
Your answer is -5/2.
Step-by-step explanation:
Use the slope equation. (Refresh if you cant see below.)
[tex]\frac{y_2-y_1}{x_2-x_1}\\\text{Substitute two points into the equation. We can use the first two, (3, 5), and (5, 0).}\\\frac{0-5}{5-3}\\\text{Subtract.}\\-\frac{5}{2}[/tex]
Which expressions represent rational numbers? Check all that apply.
Answer:
The answer is 1.2 or 5
Step-by-step explanation:
Answer:
B,D,E
Step-by-step explanation:
Which ordered pair is a solution of the equation? −7x+3y=2
Answer:
(-2/7,2/3)
Step-by-step explanation:
Let's solve for x.
−7x+3y=2
Step 1: Add -3y to both sides.
−7x+3y+−3y=2+−3y
−7x=−3y+2
Step 2: Divide both sides by -7.
−7x/ −7 = −3y+2/ −7
x= 3/ 7 y+ −2/ 7
Answer:
x= 3/ 7 y+ −2/ 7
Let's solve for y.
−7x+3y=2
Step 1: Add 7x to both sides.
−7x+3y+7x=2+7x
3y=7x+2
Step 2: Divide both sides by 3.
3y/ 3 = 7x+2/ 3
y= 7/ 3 x+ 2/ 3
Answer:
y= 7/ 3 x+ 2/ 3
Noah wrote the expression 10m - 2c to represent the following scenario.
A bakery sells muffins for $2 each and cakes for $10 each. Write an expression that gives the amount of money, in
dollars, the bakery makes from selling m muffins and c cakes.
Explain why Noah's expression is incorrect. Provide the correct expression that represents the scenario.
Answer:
Noah's expression is wrong because he used the wrong coefficients for the variables, and he used a subtraction sign instead of an addition sign.
The correct expression is 2m + 10c
Step-by-step explanation:
Noah is incorrect because he used the wrong coefficients for both of the variables in the expression.
Since muffins are $2 each, and m is the number of muffins, the amount of money made from the muffins is 2m, not 10m.
Similarly, since cakes are $10 each, and c is the number of cakes, the amount of money made from the cakes is 10c, not 2c.
Noah is also incorrect because he used a subtraction sign instead of an addition sign. The amounts made from the muffins and cakes have to be added together.
Putting all of this together, the correct expression is 2m + 10c.