The Given statement "If a distribution is normal, then it is not possible to randomly select a value that is more than 4 standard deviations from the mean" is a true statement.
A normal distribution is a bell-shaped curve that represents how data is spread out around an average value. About 99.99% of the data in a normal distribution falls within 4 standard deviations from the average.
This means that it is very rare to find a data point that is more than 4 standard deviations away from the average. Therefore, if a distribution is normal, it is not possible to randomly select a value that is more than 4 standard deviation from the mean.
The answer is true.
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write the force equation for the following system b and b are the coefficient of viscious friction and force case by this friction is
The force equation for the system is F = bV - bF, where F is the force of friction, V is the velocity of the object, and b is the coefficient of viscous friction.
Viscous friction is a force that acts to oppose the motion of an object moving through a fluid or solid. The amount of friction experienced is determined by the coefficient of viscosity, which is a measure of how easily the two surfaces move against each other. In this equation, bV is the force generated by the object's motion, and b
F is the opposing force of friction. Together, these two forces determine the net force acting on the object.
Viscous friction can be very important in understanding the behavior of a system. It helps us to understand how much energy is needed to move objects, as well as how quickly they will accelerate.
Viscous friction can also cause objects to slow down over time, as the energy it takes to move them is continually being lost to friction. Understanding the force equation for a system helps us to better predict and understand its behavior.
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janna scored 77 on her history test, on which the class average was 72.7 with a standard deviation of 6.1. maria made 89 on her biology test, where the class average was 82.6 with a standard deviation of 5.6. find the standardized (z) scores for janna and maria. round to 2 decimal places. janna has a standardized score of ____ on her test. maria has a standardized score of ____on her test. made the best score. type 1 for janna or 2 for maria. 1. janna 2. maria
Maria has the highest standardized score of 2.13, making her the one who made the best score.
Janna's standardized score is 0.80, and Maria's is 2.13.
Janna scored 77 on her history test, while the class average was 72.7 with a standard deviation of 6.1. To find the standardized score, the formula is (score - average) / standard deviation. Therefore, the standardized score for Janna is [tex](77-72.7)/6.1[/tex]= 0.80.
Maria scored 89 on her biology test, while the class average was 82.6 with a standard deviation of 5.6. To find the standardized score, the formula is (score - average) / standard deviation. Therefore, the standardized score for Maria is [tex](89-82.6)/5.6[/tex]= 2.13.
Maria has the highest standardized score of 2.13, making her the one who made the best score.
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4Interpreting z-scores: Complete the following statements using your knowledge about z-scores.
a. If the data is weight, the z-score for someone who is overweight would be
zero
positive
negative
b. If the data is IQ test scores, an individual with a negative z-score would have a
average IQ
high IQ
low IQ
c. If the data is time spent watching TV, an individual with a z-score of zero would
watch the average amount of TV
watch very little TV
watch a lot of TV
d. If the data is annual salary in the U.S and the population is all legally employed people in the U.S., the z-scores of people who make minimum wage would be
positive
negative
zero
a. If the data is weight, the z-score for someone who is overweight would be positive.
b. If the data is IQ test scores, an individual with a negative z-score would have a low IQ.
c. If the data is time spent watching TV, an individual with a z-score of zero would watch the average amount of TV.
d. If the data is annual salary in the U.S and the population is all legally employed people in the U.S., the z-scores of people who make minimum wage would be negative.
The z-score represents how far a data point is from the mean in terms of standard deviations. If someone is overweight, their weight would be above the mean weight, so their z-score would be positive.
Again, the z-score represents how far a data point is from the mean in terms of standard deviations. If someone has a negative z-score for IQ test scores, it means their score is below the mean score, so their IQ would be low.
A z-score of zero means the data point is exactly at the mean, so someone with a z-score of zero for time spent watching TV would watch the average amount of TV.
Again, the z-score represents how far a data point is from the mean in terms of standard deviations. If someone is making minimum wage, their salary would be below the mean salary, so their z-score would be negative.
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Find the 8th term of the arithmetic sequence x + 1 x+1, 8 x − 3 8x−3, 15 x − 7 ,
Answer: 50x - 27
Step-by-step explanation:
To find the 8th term of the arithmetic sequence, we need to first find the common difference between consecutive terms:
Common difference (d) = second term - first term
d = (8x - 3) - (x + 1)
d = 7x - 4
Now, we can use the formula to find the nth term of an arithmetic sequence:
an = a1 + (n - 1)d
where a1 is the first term, d is the common difference, and n is the term number we want to find.
Plugging in the values, we get:
a8 = (x + 1) + (8 - 1)(7x - 4)
a8 = x + 1 + 7(7x - 4)
a8 = x + 1 + 49x - 28
a8 = 50x - 27
Therefore, the 8th term of the arithmetic sequence x + 1, 8x - 3, 15x - 7 is 50x - 27.
given the speeds of each runner below, determine who runs the fastest. stephanie runs 8 feet per second. stephanie runs 8 feet per second. katie runs 463 feet in 32 seconds. katie runs 463 feet in 32 seconds. jessica runs 1 mile in 555 seconds. jessica runs 1 mile in 555 seconds. noah runs 728 feet in 1 minute. noah runs 728 feet in 1 minute.
Katie runs the fastest at 14.469 ft/s
To compare the speeds of each runner, we need to convert all the measurements to the same units. Let's convert them all to feet per second:
Stephanie runs 8 feet per second (8 ft/s)Katie runs 463 feet in 32 seconds, so her speed is (463 ft / 32 s) = 14.469 feet per second (14.469 ft/s)Jessica runs 1 mile in 555 seconds, which is equivalent to 5,280 feet in 555 seconds. Her speed is (5,280 ft / 555 s) = 9.514 feet per second (9.514 ft/s)Noah runs 728 feet in 1 minute, which is equivalent to (728 ft / 60 s) = 12.133 feet per second (12.133 ft/s)Therefore, in order of fastest to slowest runner:
Katie (14.469 ft/s)
Noah (12.133 ft/s)
Stephanie (8 ft/s)
Jessica (9.514 ft/s)
Hence, Katie runs the fastest
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Please give me the right answer, no people who just want to take points.
Answer:
Do C.
Step-by-step explanation:
A box of chocolates has 8 red, 12 blue, 5 green and 10 yellow. Express the number of chocolates as
ratios in their lowest terms.
a. red: yellow
b.green: yellow
c. red: total chocolates
Answer:
a. red: yellow
[tex]8:10=4:5[/tex]
There are 4 reds for every 5 yellows.
b. green: yellow
[tex]5:10=1:2[/tex]
There is 1 green for every two yellows.
c. red: total
[tex]8:35[/tex]
There are 8 reds out of 35 chocolates.
Hope this helps
Simplify 2a÷a- 1 - a^2 +3÷ a^2 - 1
suppose that each day the price of a stock moves up 1/8th of a point with probability 1/3 and moves down 1/8th of point with probability 2/3. if the price fluctuations from one day to another are independent, what is the probability that after 6 days the stock has its original price?
After 6 days, the probability that the stock has its original price is 5/16.
There are two possible scenarios that can take place when the stock price fluctuates from one day to the next. Either the price goes up by 1/8th of a point with probability 1/3 or it goes down by 1/8th of a point with probability 2/3.
The price of the stock after six days can be denoted as S6. The price of the stock after the first day can be represented as S0.
Since the price fluctuates either up or down by 1/8th of a point on each day, the price after six days can be represented as follows:S6 = S0 + (up, up, up, up, up, up), (up, up, up, up, up, down), (up, up, up, up, down, up), ... , (down, down, down, down, down, down)
In order to return to the original price, the stock must go up and down by the same amount. As a result, there must be an equal number of ups and downs in the six-day period.
As a result, we must calculate the probability of obtaining an equal number of ups and downs over six days.
Let's represent an increase in the stock price as 'U' and a decrease as 'D.'
The total number of ways in which the stock can go up and down over six days is [tex]2^6 = 64[/tex].
The total number of ways in which the stock can return to its original price can be calculated as follows: [tex]N(UUUDDD) = 6! / (3! * 3!) = 20[/tex]
The probability of the stock returning to its original price after six days can be calculated as:
[tex]P = N(UUUDDD) / 64 = 20 / 64 = 5 / 16[/tex]
Therefore, the probability that after 6 days the stock has its original price is 5/16.
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Find the height of an open cylinder of radius of 8cm given that it has a curved surface area of 1000cm²
The height of an open cylinder of radius of 8cm given that it has a curved surface area of 1000 cm² is equals to the 159.24 cm.
The area obtained after substracting the circular area from the total area of the cylinder is called as curved surface area. Curved surface area is calculated by formula, 2πrh
where r --> radius of cylinder
h --> height of cylinder
π --> math special constant
We have an open cylinder with the following dimensions,
Radius of cylinder, r = 8 cm
Curved surface area of cylinder, A = 1000 cm². We have to calculate the height of this open cylinder. Let the height of an open cylinder be 'h cm' . Using the above formula, height of cylinder, h = curved Area/ 2πr
=> h = A/2π
=> h = 1000/2 ( 3.14)
=> h = 1000/6.28
=> h = 159.24
Hence, required value of height is 159.24 cm.
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The hanger image below represents a balanced equation.
Write an equation to represent the image
HELP THIS IS DUE TODAY
Answer:
2 + r = 6
Step-by-step explanation:
2 + r = 6
r = 6 - 2 = 4
6 on the left balanced by 2 plus r on the right
7. (x³ +7x² + 2)÷(x-1)
Answer:
(x³ + 7x² + 2)÷(x-1) = x² + 8x + 15 + 8/(x-1).
I need help please show your work
Answer:
The 2nd equation is false.
Step-by-step explanation:
You don't even have to solve. DE is not 58, it's 40.
The 2nd equation is false.
2 numbers add together to make -4 but subtract to make 8 what are the 2 numbers
Answer:
x=2 and y= ‐6
Step-by-step explanation:
Let the two numbers be 'x' and 'y'
Here, it says two numbers add up to make -4
So,
x+y= ‐4 .....equation (i)
Also, its says two numbers subtract to make 8
So,
x‐y=8 .....equation (ii)
We have,
x+y= ‐4 .....equation (i)
x‐y=8 .....equation (ii)
Subtracting equation (i) from equation (ii)
x‐y=8
x+y=‐4
-----------
‐2y=12
y=12/‐2
y= ‐6
Now, replacing value of x in equation (i)
x+y= -4
4x+(‐6) = -4
4x‐6= ‐4
x= -4+6
x= 2
Therefore the unknown numbers are 2 and ‐6
I need help asap I just need atleast one of these explained and I can do the rest
The factοred fοrm οf a pοlynοmial is
1. 30b³- 54b² = 6b²(5b−9)
2. 3y⁵ - 48y³ = 3y³(y −4)(y + 4)
3. x³ + 8 = (x + 2) (x² – 2x + 2²)
4. y³ - 64 = (y - 4) (y² – 4y + 4²)
5. 8c³ + 343(2c + 7)(4c² − 14c + 49)
What dοes a pοlynοmial functiοn in factοred fοrm lοοk like?The factοred fοrm οf a pοlynοmial is represented as a³ + b³ = (a + b) (a² – ab + b²). All equatiοns are cοmpοsed οf pοlynοmials. Earlier we've οnly shοwn yοu hοw tο sοlve equatiοns cοntaining pοlynοmials οf the first degree, but it is οf cοurse pοssible tο sοlve equatiοns οf a higher degree.
One way tο sοlve a pοlynοmial equatiοn is tο use the zerο-prοduct prοperty. If yοu remember frοm earlier chapters the prοperty οf zerο tells us that the prοduct οf any real number and zerο is zerο.
We will use the formula
a³ + b³ = (a + b) (a² – ab + b²)
And
a³ - b³ = (a - b) (a² – ab + b²)
1. [tex]30b^3-\ 54b^2[/tex]
⇒ 6b²(5b−9)
2. 3y⁵ - 48y³
⇒ 3y³( y² - 16y)
⇒ 3y³( y² - 4 + 4 - 16y)
⇒ 3y³(y −4)(y + 4)
3. x³ + 8
⇒ x³ + 2³
Using a³ + b³ = (a + b) (a² – ab + b²)
⇒ x³ + 2³
⇒ (x + 2) (x² – 2x + 2²)
4. y³ - 64
⇒ y³ - 4³
Using a³ - b³ = (a - b) (a² – ab + b²)
⇒ y³ - 4³
⇒ (y - 4) (y² – 4y + 4²)
5. 8c³ + 343
Using a³ + b³ = (a + b) (a² – ab + b²)
2c + 7
(2c + 7)(4c² − 14c + 49)
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On Monday, Elise walked 9. 9 kilometres. On Tuesday, she walked 0. 7 kilometres less than she had walked on Monday. How far did Elise walk on Tuesday?
Elise walked a distance of 9.2 kilometers on Tuesday.
To solve the problem, we need to first understand the information provided.
On Monday, Elise walked a distance of 9.9 kilometers.
On Tuesday, she walked a distance that was 0.7 kilometers less than what she walked on Monday.
This means that we need to subtract 0.7 kilometers from the distance that she walked on Monday to find the distance she walked on Tuesday.
To do this, we can use subtraction. We start by writing down the distance Elise walked on Monday, which is 9.9 kilometers, and then subtract 0.7 kilometers from it.
9.9 km - 0.7 km = 9.2 km
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What is the solution to -1/2 [x-1] =0?
x=1
x=-1 or x=1
x=1 or x=2
No solutions exists
Answer:
x=1
Step-by-step explanation:
Ashed is shaped like a rectangular prism. The base of the shed has an area of 64 square feet. The volume of the shed is 576 cubic feet.
What is the height of the shed? Enter the answer in the box.
The value height of the shed is 9 feet.
The area of the shed = 64 square feet
The volume of the shed = 576 cubic feet.
The area occupied inside a rectangular prism is referred to as the volume of the prism. A polyhedron with two pairs of congruent and parallel bases is referred to as a rectangular prism. It is a result of the intersection of equal cross-sections, identical bases, and flat faces.
Calculating the volume of the rectangular prism
The volume of rectangular prism = area of base x height
Substituting the values -
576 = 64 x h
h = 576 / 64
h = 9
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CAN SOMEONE HELP WITH THIS ASAP I’LL GIVE YOU POINTS
10+
Answer:
9/12
Step-by-step explanation:
To determine which fraction is not equivalent to 2/3, we can simplify each fraction and compare it to 2/3. If a fraction is simplified to a different value than 2/3, then it is not equivalent.
16/24 simplifies to 2/3, so it is equivalent to 2/3.
6/9 simplifies to 2/3, so it is equivalent to 2/3.
12/18 simplifies to 2/3, so it is equivalent to 2/3.
9/12 simplifies to 3/4, which is not equivalent to 2/3.
10/15 simplifies to 2/3, so it is equivalent to 2/3.
Therefore, the fraction that is not equivalent to 2/3 is 9/12.
Answer:
9/12 is not equal to 2/3
Step-by-step explanation:
To find which fractions are equivalent and which are not, we must make sure they are proportional.
To do this, we must make sure the denominators can multiply and divide with each other, and the same for the numerators.
12 divided by 3 is 4,
but 4 times 2 is not 9
Therefore, the answer is 9/12
A triangle has vertices at (-4, 0), (2, 8), and (8, 0). Complete the table. Write answers as decimals
rounded to the nearest hundredth, when necessary.
The coordinate of centroid of the triangle is (2, 8/3), the coordinate of the circumcenter is (-7/32, 121/24) and the coordinate of orthocenter is (2, 9/2)
What is the coordinate of the centroid?a. To find the centroid of a triangle, we take the average of the x-coordinates and the average of the y-coordinates of the vertices. Therefore, the x-coordinate of the centroid is:
(x₁ + x₂ + x₃) / 3 = (-4 + 2 + 8) / 3 = 2
Similarly, the y-coordinate of the centroid is:
(y₁ + y₂ + y₃) / 3 = (0 + 8 + 0) / 3 = 8/3
So the coordinate of the centroid is (2, 8/3).
b. The circumcenter of a triangle is the point where the perpendicular bisectors of the sides of the triangle intersect. To find the circumcenter, we can find the equations of the perpendicular bisectors of any two sides of the triangle and solve for their intersection point.
Let's take the sides formed by vertices (-4, 0) and (2, 8), and vertices (-4, 0) and (8, 0). The midpoint of the first side is ((-4+2)/2, (0+8)/2) = (-1, 4), and the slope of the line passing through the two points is (8-0)/(2-(-4)) = 8/6 = 4/3. Therefore, the equation of the perpendicular bisector passing through (-1, 4) is:
y - 4 = (4/3)(x + 1)
Simplifying this equation, we get:
y = (4/3)x + 13/4
Similarly, the midpoint of the second side is ((-4+8)/2, (0+0)/2) = (2, 0), and the slope of the line passing through the two points is (8-0)/(2-8) = -8/6 = -4/3. Therefore, the equation of the perpendicular bisector passing through (2, 0) is:
y = -(4/3)(x - 2)
To find the intersection point of these two lines, we can set the equations equal to each other and solve for x:
(4/3)x + 13/4 = -(4/3)(x - 2)
x = -7/32
Substituting x = -7/32 into either of the equations, we get:
y = (4/3)(-7/32 + 1) + 4 = 121/24
So the coordinate of the circumcenter is (-7/32, 121/24).
c. The orthocenter of a triangle is the point where the altitudes of the triangle intersect. An altitude of a triangle is a line segment from a vertex of the triangle perpendicular to the opposite side.
Let's take vertex (-4, 0) and find the equation of the line passing through this vertex and perpendicular to the opposite side formed by vertices (2, 8) and (8, 0). The slope of the opposite side is (0-8)/(8-2) = -8/6 = -4/3, so the slope of the line we want is the negative reciprocal of this, which is 3/4. Therefore, the equation of the altitude passing through (-4, 0) is:
y - 0 = (3/4)(x + 4)
Simplifying this equation, we get:
y = (3/4)x + 3
Let's now take vertex (2, 8) and find the equation of the altitude passing through it. The slope of the opposite side formed by vertices (-4, 0) and (8, 0) is (0-0)/(8-(-4)) = 0, which means the altitude passing through (2, 8) is a vertical line passing through (2, 0). Therefore, the equation of this altitude is:
x = 2
Now we need to find the intersection point of these two altitudes. Substituting y = (3/4)x + 3 into the equation x = 2, we get:
y = 9/2
The coordinate of the orthocenter is (2, 9/2)
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What is the measure of angle C? Enter your answer as a decimal in the box. Round only your final answer to the nearest hundredth. m∠C= ° Right triangle A B C, with right angle C B A. Side A B is three centimeters, side B C is four centimeters, and side C A is five centimeters.
The measure of angle C is 53.13 degrees.
What are trigonometric functions?
Trigonometric functions are a set of mathematical functions used to relate the angles of a right triangle to the lengths of its sides. There are six trigonometric functions: sine, cosine, tangent, cosecant, secant, and cotangent. Each function represents a ratio of two sides of a right triangle.The tangent function, denoted as tan(x), is a trigonometric function that represents the ratio of the length of the opposite side to the length of the adjacent side in a right triangle.
Calculating the value of angle C :
The three sides of the given right triangle are 3 cm, 4 cm, and 5 cm.
To find the measure of angle C, we can use the trigonometric function called inverse tangent, or arctan, which gives the ratio of the length of the opposite side to the length of the adjacent side.
Using the Pythagorean Theorem, we can verify that the given triangle is a right triangle:
[tex]5^2 = 3^2 + 4^2[/tex]
[tex]25 = 9 + 16[/tex]
[tex]25 = 25[/tex]
So, the triangle is a right triangle.
To find the measure of angle C, we can use the arctan function:
[tex]tan(C) =opposite/adjacent = 3/4[/tex]
[tex]C = arctan(3/4) \approx 53.13[/tex] degrees
Therefore, the measure of angle C is 53.13 degrees (rounded to the nearest hundredth).
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Find the probability of
drawing a spade, then
drawing a face card out of a
deck
[tex]\huge\underline{\red{A}\green{n}\blue{s}\purple{w}\pink{e}\orange{r} →}[/tex]
P of spade = 1/4
P of face cards = 3/13
{P = probability}
Step-by-step explanation:
•Total cards in a deck = 52
No. of spade cards in the deck = 13
therefore,
Probability of drawing a spade out of a deck of cards = 13/52 = 1/4
No. of face cards in a deck = 3×4 = 12 (joker,king,queen)
therefore,
Probability of drawing a face card out of a deck of cards = 12/52 = 3/13
Hope it helps you ~4. The total cost of a group of friends to go on vacation includes $500 in airfare per person and $5600 for the Airbnb. The total cost will be split evenly amongst the number of people going. Let C represent the cost per person and x represent the number of people attending.
a. Write an equation that models the cost per person.
b. How much would the vacation cost per person if 10 people decided to go?
Using equations the answers to both subparts are shown:
(A) The equation: (500x + 5600)/x = C
(B) Cost per person (C) = $1,060
What is an equation?A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.
A mathematical equation is a statement that two amounts or values are equal, such as 6 x 4 = 12 x 2. 2.
When two or more components must be taken into account collectively in order to comprehend or describe the overall situation, this is known as an equation.
So, (A) the equation would be:
C is the cost per person and x is the number of people.
(500x + 5600)/x = C
(B) Cost per person if 10 people are traveling.
x = 10
(500x + 5600)/x = C
(500*10 + 5600)/10 = C
(5000 + 5600)/10 = C
10600/10 = C
$1,060 = C
Therefore, using equations the answers to both subparts are shown:
(A) The equation: (500x + 5600)/x = C
(B) Cost per person (C) = $1,060
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The height of a rectangle is multiplied by 4. Which of the following describes the effect of this change on the area?The area is multiplied by 16.The area is multiplied by 8.The area is multiplied by 4.The area is multiplied by 2.
The correct option is: The area is multiplied by 4.
The height of a rectangle is multiplied by 4. This change in the area is that the area is multiplied by 4. The rectangle is a geometrical shape that is defined as a four-sided polygon with four right angles. Rectangle has two pairs of parallel sides, so opposite sides are equal and the diagonals bisect each other at the centre of the rectangle.
The formula for the area of a rectangle is: Area of rectangle = Length × Width, or A = L × W as the height of a rectangle is multiplied by 4. Therefore, the new height of the rectangle is four times its initial value or h = 4h. The area of the rectangle can now be calculated using the above formula, which is:
New Area of rectangle = length x 4h = 4 × (length x h) = 4 x Area of rectangle
The effect of increasing the height of the rectangle by 4 times is that the area of the rectangle is multiplied by 4.
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Victor spent $61 on some sandpaper for his model
cars. He bought 2 packages of the smallest-grain
sandpaper and spent the rest on the largest-grain
sandpaper. How many packages of the largest-
grain sandpaper did he buy?
Victor bought 10 packages of the largest-grain sandpaper.
What does "spent 50 balance 51" mean?Total money spent (20+15+9+6) = 50; total money left over (30+15+6+0) = 51. Balance plus spent always equals 50, but balance added to balance does not always equal 50. So, it is always necessary to include simply the amount spent or the expenditure rather than the balance.
Thus, we know how much he spent:
2S + (61 - 2S) = 61 - S
$1 on sandpaper with the biggest grit. We can condense this phrase as follows:
61 - S = 61 - 2S
Adding S to both sides, we get:
S = 0
Then we know that he spent:
2L + Ly = 61
Spending money on sandpaper. Additionally, since he purchased two packages of the finest sandpaper, the price of those two packages is:2S = 2L
We can substitute 2L for 2S in the first equation:
2L + Ly = 61
Simplifying, we get:
2L + L(2/3)L = 61
Multiplying both sides by 3/2, we get:
3L² = 91.5
Taking the square root of both sides, we get:
L ≈ 5.27
determine how many packages of the coarsest sandpaper Victor purchased:
2L + Ly = 61
2(5.27) + 5.27y = 61
10.54 + 5.27y = 61
5.27y = 50.46
y ≈ 9.56
Rounding to the nearest whole number, we get:
y = 10
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Center of Mass Suppose R is the region bounded by the graphs of f(x) = = sin x and g(x) = cos x over the interval [**, ]. Find the center of mass of the region. Assume that the region has a constant density d. (x,y) = Note: your answer should be an ordered pair.
The center of mass of the region R, bounded by the graphs of
[tex]f(x) = sin x[/tex] and [tex]g(x) = cos x[/tex]over the interval [**, ], is (x,y) = (π/4, 0.8540). This can be calculated by taking the area-weighted average of the region's two boundaries.
The area of R can be calculated using the formula: A = [tex]∫f(x) - g(x)dx.[/tex] Then, the x-coordinate of the center of mass is calculated using the formula: x = [tex](1/A) * ∫x * [f(x) - g(x)]dx.[/tex]
Finally, the y-coordinate of the center of mass is calculated using the formula:
y = [tex](1/A) * ∫y * [f(x) - g(x)]dx[/tex]. With the given boundary equations and constant density d, the center of mass can be determined to be (x,y) = (π/4, 0.8540).
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1/1-p+p² + 1/1+p+p² - 2p/1-p²+p⁴
To simplify it, first factor the denominators of each fraction in eqation 1/(1-p+p²) + 1/(1+p+p²) - 2p/(1-p²+p⁴) and simplify to get simplified equation is 2(1+p)/[(1-p+p²)(1+p+p²)] .
What is factor ?
In mathematics, a factor is a number or algebraic expression that divides another number or expression without leaving a remainder.For example, the expression x^2 - 4 can be factored as (x+2)(x-2) .
What is denominator ?
denominator is a bottom part of a fraction. It represents the total number of equal parts into which a whole has been divided, and the fraction itself represents a part of that whole.For example,
in equation (x+2)/(x-2) , (x-2) is denominator .
In the given question ,
1/(1-p+p²) + 1/(1+p+p²) - 2p/(1-p²+p⁴ ) Next, we can find a common denominator for the three fractions. To do this, we need to factor the denominator of the third fraction further using the difference of squares formula as 1/(1-p+p²) + 1/(1+p+p²) - 2p/[(1-p+p²)(1+p+p²)]
Now we can find a common denominator by multiplying the first fraction by (1+p+p²)/(1+p+p²) and the second fraction by (1-p+p²)/(1-p+p²):
[(1+p+p²)/(1+p+p²)]/(1-p+p²) + [(1-p+p²)/(1-p+p²)]/(1+p+p²) - 2p/[(1-p+p²)(1+p+p²)]
= [(1+p+p²)+(1-p+p²)-2p]/[(1-p+p²)(1+p+p²)]
= [2+2p]/[(1-p+p²)(1+p+p²)]
= 2(1+p)/[(1-p+p²)(1+p+p²)]
Therefore, the simplified expression is 2(1+p)/[(1-p+p²)(1+p+p²)].
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Cake or ice cream????
Answer:
ICE CREAM
Step-by-step explanation:
These tables represent an exponential function. Find the average rate of
change for the interval from x = 8 to x = 9.
OA. 6561
B. 19,683
O C. 13,122
OD. 3
X
2456710
3
y
1
3
9
27
81
243
729
Interval
0 to 1
1 to 2
2 to 3
3 to 4
4 to 5
5 to 6
Average rate
of change
2
6
18
54
162
486
Jx3
Jx3
Jx3
Jx3
Jx3
The average rate of change for the interval from x = 8 to x = 9 is 13,122 (3⁸to 3⁹).
What is function?Function is a self-contained block of code that performs a specific task. It is used to separate logical code into separate parts and make the code more manageable. A function can accept inputs, known as parameters, and return an output, known as a return value. Functions can be reused throughout a program, making the code more efficient and easier to debug.
This can be calculated by subtracting the starting value (3⁸ = 6561) from the ending value (3⁹ = 19683) and then dividing the result by the interval (9 - 8 = 1). Mathematically, this is expressed as (19683 - 6561) / (9 - 8) = 13,122. This result shows that the rate of change for the exponential function between x = 8 and x = 9 is 13,122.
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Jake is х years old and his mother is 7x years old. If the sum of both their ages is 16x in 2036 what would their current age be in year y.
Jake is presently [tex]0[/tex] years old and the year is [tex]2036[/tex], which is not a relevant response or there may be some missing details in the question.
By year, what do you mean?A span of time that is equivalent to one year on the Calender but starts at a different period. A cycle of 365 and 366 day split into twelve month starting in January and ending in December.
In arithmetic, how much is a month?Every monthly on the calender has four complete weeks since every month has at least 28 days. A few month have a few more days, but these extra days don't add up to a full week, therefore they aren't counted.
Let's first find the current year, given that the year in which their ages will sum up to [tex]16x[/tex] is[tex]2036[/tex].
[tex]2036 - (y - 2036) = 2*2036 - y[/tex]
Simplifying this expression, we get:
[tex]2*2036 - y = 4072 - y[/tex]
[tex]2y = 4072[/tex]
[tex]y = 2036[/tex]
Now, let's find Jake's current age by subtracting his birth year from the current year [tex]y - (2036 - 7x)[/tex]
Since their ages sum up to 16x in 2036, we have:
[tex]x + 7x = 16x[/tex]
[tex]8x = 16x[/tex]
[tex]x = 0[/tex]
This means that Jake is currently [tex]0[/tex] years old, which is not a meaningful answer.
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