The kinetic energy T units of a motion body (of constant mass) varies as the square of its speed v m/s. If kinetic energy T = 800 units when speed v= 20m/s: Calculate V when T= 1800.
If T=1800 then V=30m/s.
kinetic energy is nothing but The energy an object has as a result of motion is known as kinetic energy.
Given that,
If T = 800 units when v= 20m/s
Kinetic energy formula is
[tex]T=\frac{1}{2}mv^{2}[/tex]
Here, T is kinetic energy , m is mass and v is speed
Now,
[tex]800=\frac{1}{2}m(20)^{2} \\800\times2=m(400)\\\frac{1600}{400}=m\\ m=4[/tex]
We got mass m as 4
Now, when T= 1800 find v=?
[tex]1800=\frac{1}{2}\times4\times v^{2} \\1800\times2= v^{2} \\ v^{2} =900\\v=30[/tex]
Therefore, we got speed v=30m/s when the kinetic energy T=1800.
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Which number line shows the solution the inequality
greatest common factor 2a and 4ab
Answer: [tex]2a[/tex]
Step-by-step explanation:
So let's say you're adding [tex]2a+4ab[/tex] and you want to factor that...
well you can take a 2 out of that...
[tex]2(a+2ab)[/tex]
Next, you can take an "a" out of that..
[tex]2a(1+2b)[/tex]
So the greatest monomial factor is 2a... Hope this helps!! Please rate it 5 stars!
A group of 25 students participated in a science competition. Their scores are below.
Score (points) 30-39 40-49 50-59 60-69 70-79
Number of Students
5
7
6
4
3
Would a dot plot or a histogram best represent the data presented here? Why?
O Histogram, because a large number of scores are reported as ranges
O Histogram, because a small number of scores are reported individually
O Dot plot, because a large number of scores are reported as ranges
O Dot plot, because a small number of scores are reported individually
The best graphical representation used to represent the score of 25 students is option A " Histogram, because a large number of scores are reported as ranges "
Histogram is the graphical representation of distribution of numerical data. The histogram look like a bar graph in appearance, but the frequency of numerical data using rectangles.
In histogram the range is the width of the rectangular bar along the x-axis. The range in the histogram is an approximate value.
In the given data, there are large number of scores are reported. So the given data will be represented in histogram. Therefore correct option is option A "Histogram, because a large number of scores are reported as ranges
Hence, the best graphical representation used to represent the score of 25 students is option A " Histogram, because a large number of scores are reported as ranges "
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PLS HELP!! MIDDLE SCHOOL 8TH GRADE MATH QUESTION!! The school cafeteria serves portions of fried rice that are 140 grams each.
A. If 64 portions of rice are served, how many grams of rice would that be?
B. Write an expression for the total weight in grams of rice needed for p portions.
C. One day, the total weight of rice served was 11,340 grams. How many portions were served that day?
D. Write an expression for the number of portions served if the total rice weighed t grams.
Answer:
a: 8960
b: I suck at proportions even though im in hs. srry i cant answer that.
c: 177.1875, if you have to round than 177.
d: im so srry lol
Step-by-step explanation:
Using long division what is the quotient of this expression
3x^4-2x^3-x-4
———————-
X^2+2
3x² - 2x -6 is quotient in polynomial after long division .
What in mathematics is a polynomial?
Sums of terms of the form kxn, where k is any number and n is a positive integer, make up polynomials. For instance, the polynomial 3x+2x-5. a description of polynomials. The concepts degree, standard form, monomial, binomial, and trinomial are all covered in this video.A polynomial is a mathematical expression that solely uses the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables. It is made up of indeterminates (also known as variables) and coefficients. x2 4x + 7 is an illustration of a polynomial with a single indeterminate x.[tex]\frac{3x^{4} - 2x^{3} - x - 4 }{x^{2} + 2}[/tex]
after long division we get quotient - 3x² - 2x -6 .
Divide using long division: standard [tex]3x^{2} + \frac{3x + 8 }{x^{2} + 2} - 2x - 6[/tex]
quotient - 3x² - 2x -6
remainder - 3x + 8
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Answer:
see image
Step-by-step explanation:
Plato/Edmentum
Can someone help me with these 2 problem
Answer:
Step-by-step explanation:
volume of small cuboid=5×2×4=40 cm³
volume of one small cube=(1/2)³=1/8
so number of cubes=40÷1/8=40×8=320
now width of bigger cuboid=9-5=4 cm
volume of bigger cuboid=4×2×12=96
number of small cubes in this cuboid=96÷1/8=96×8=768
total cubes=768+320=1088
Suppose the average yearly salary of an individual whose final degree is a master's is $40 thousand less than twice that of an individual whose final degree is a bachelor's. Combined, two people with each of these educational attainments earn $113 thousand. Find the average yearly salary of an individual with each of these final degrees.
In linear equation 109333.2 dollars is the average yearly salary of an individual with each of these final degrees .
What is a linear equation ?
There are only one or two variables in a linear equation. No variable can be multiplied by a number larger than one or used as the denominator of a fraction in a linear equation. All of the points fall on the same line when you identify the values that together make a linear equation true and plot those values on a coordinate grid.let x be the salary of individual with bachelor degree
Then the average salary of individual with Masters degree is:
(2x-40000)
the combined of two salaries is 130000:
x+(2x-40000)=130000
3x-40000=130000
3x=130000+40000
x=170000/3
x = 56,666.66
x= 56,666.6 dollars ( the average salary of bachelor degree)
the average salary of Masters degree = 2x - 40000
2(56666.6)-40000 = 109333.2 dollars
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A parachutist's rate during a free fall reaches 70 meters per second. What is this rate in feet per second? At this rate, how many feet will the parachutist fall during 2 seconds of free fall? In your computations, assume that 1 meter is equal to 3.3 feet. Do not round your answers.
The rate of feet per second is 231 ft/sec and parachutists will fall 462 ft in 2 seconds.
What do we mean by speed?The definition of speed is The rate at which an object's position changes in any direction. Speed is defined as the ratio of distance traveled to time spent traveling. Because it has only one direction and no magnitude, speed is a scalar quantity.So, let's assume that y70m/s is the terminal velocity.
As 1 meter = 3.3 feetThen, 70 meters = 70 × 3.3 = 231 ft/secParachutist will fall at what rate in 2 seconds: 462 ft/secTherefore, the rate of feet per second is 231 ft/sec and parachutists will fall 462 ft in 2 seconds.
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Evaluate if k=3
K^2 + 5 =
Answer:
k2+5=?
3²+5=?
9+5=14......
4.30. An internet service provider has two connection lines for its customers. Eighty percent of
customers are connected through Line I, and twenty percent are connected through Line II.
Line I has a Gamma connection time with parameters a = 3 and λ = 2 min-¹. Line II has
a Uniform(a, b) connection time with parameters a = 20 sec and b = 50 sec. Compute the
probability that it takes a randomly selected customer more than 30 seconds to connect to
the internet.
Using the uniform distribution, there is a 0.6667 = 66.67% probability that it takes a randomly selected customer more than 30 seconds to connect to the internet.
What is the uniform probability distribution?It is a distribution with two bounds, given by a and b, in which each possible outcome is equally as likely.
The probability of finding a value above x is:
[tex]P(X > x) = \frac{b - x}{b - a}[/tex]
For this problem, the connection time has parameters a = 20 sec and b = 50 sec, as stated in the problem.
The probability that it takes a randomly selected customer more than 30 seconds to connect to is P(X > 30).
Hence, applying the formula, with the bounds, we have that:
P(X > 30) = (50 - 30)/(50 - 20) = 2/3 = 0.6667.
The measure above is the desired probability.
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A pool cleaner uses 3/5 pound of liquid chlorine for each pool she services. She has 5 pounds of liquid chlorine available. Determine how many whole pools can be serviced with the available liquid chlorine.
Answer:
8 pools
Step-by-step explanation:
5 ÷ 3/5
5 x 5/3 = 35/3 = 8 1/3
PLEASE HELP FIND FOR X QUICK PLEASE!!!!
Greetings from Brasil...
Assuming that the line segments CE and FH are parallel, then:Angle W
Here we have Opposite Angles by Vertex, so
W = 14
According to the attached figure, the angle W is also corresponding, so in the triangle CEG one of the angles will be 14°
Angle Z
The sum of the interior angles of a triangle is 180°, so for triangle CEG:
Z + W + 78 = 180
Z + 14 + 78 = 180
Z = 88
Angle X
Z and 4X are complementary angles, then
Z + 4X = 180
88 + 4X = 180
X = 23
___________________________________
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The quotient of x^2 − 16/ x − 4 is x+4 .
Compute each quotient using the identities you discovered in this module.
The quotient of x^3 − 64/x − 4 is x^2+
.
The quotient of x^4 − 256/x − 4 is x3+
.
The quotient of x^5 − a^5/x − a is x4+
The quotient of x³ - 64/x - 4 is (x² + 4x + 16).
The quotient of x⁴ − 256/x − 4 is (x³ + 4x² + 16x + 64).
The quotient of x⁵ - a⁵ /x - a is (x⁴ + ax³ + a²x² + a³x + a⁴).
What is Division method?
Division method is used to distributing a group of things into equal parts.
We have to given that;
The quotient of x² − 16/ x − 4 is x + 4.
Now, We have compute each quotient as;
The quotient of x³ - 64/x - 4 is;
[tex]\frac{x^{3} - 64}{x-4} = \frac{x^{3} - 4^{3} }{x-4} = \frac{(x-4) (x^{2} +4x+16)}{(x-4)} = (x^{2} +4x+16)[/tex]
Hence, The quotient of x³ - 64/x - 4 is (x² + 4x + 16).
And, The quotient of x⁴ − 256/x − 4 is;
[tex]\frac{x^4-4^4}{x-4} = \frac{((x^2)^2-(4^2)^2)}{(x-4)} = \frac{(x^{2} -4^4) (x^{2} + 4^2)}{(x-4)} = \frac{(x-4)(x+4)(x^{2} +4^2)}{(x-4)} = (x+4)(x^{2} + 16)[/tex]
[tex](x+4)(x^{2} + 16) = x^{3} + 4x^{2} +16x + 64[/tex]
Hence, The quotient of x⁴ − 256/x − 4 is (x³ + 4x² + 16x + 64).
The quotient of x⁵ - a⁵ /x - a is;
_______
x - a ) x⁵ - a⁵ ( x⁴ + ax³ + a²x² + a³x + a⁴
x⁵ - ax⁴
- +
-------------------
ax⁴ - a⁵
ax⁴ - a²x³
- +
-------------------
a²x³ - a⁵
a²x³ - a³x²
- +
-----------------
a³x² - a⁵
a³x² - a⁴ x
- +
--------------------------
a⁴ x - a⁵
a⁴ x - a⁵
- +
-----------------------
0
Hence, The quotient of x⁵ - a⁵ /x - a is (x⁴ + ax³ + a²x² + a³x + a⁴).
Therefore, The quotient of x³ - 64/x - 4 is (x² + 4x + 16).
The quotient of x⁴ − 256/x − 4 is (x³ + 4x² + 16x + 64).
The quotient of x⁵ - a⁵ /x - a is (x⁴ + ax³ + a²x² + a³x + a⁴).
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Juliana is taking out an $8,700, 3-year loan with an APR of 2.31%. What will be the monthly payment for this loan? Round to the nearest cent.
Answer: $250.37
Step-by-step explanation: no clue teacher told me because she doesn't know
What is the reciprocal of -2/3
A. -3/2
B. -2/3
C. 1/3
D. 1/2
Which numbers have a digit in the ones place that is 1/10 the value of the digit in the tens place? select all that apply
a. 6,044.7
b 6,339.99
c. 8,101.13
d. 8,066.51
e. 9,777.1
The numbers having a digit in the ones place that is 1/10 the value of the digit in the tens place are 6,044.7, 8,066.51 and 9,777.1 . Option A, D , E
What is place value?The place value of a number can be defined as the position of the number is a digit.
Given the digits, we have to determine the numbers of digits in the ones that is 1/10 the value of the digit in the tens place.
⇒ 6044. 7
The ones digit is 4
The tens digit is 40
Take ratio = 4/ 40 = 1/ 10
⇒ 8
The ones digit is 8
The tens digit is 80
Take ratio = 8/ 80 = 1/ 10
⇒ 9,777.1
The ones digit is 7
The tens digit is 70
Take ratio = 7/ 70 = 1/ 10
Thus, the numbers having a digit in the ones place that is 1/10 the value of the digit in the tens place are 6,044.7, 8,066.51 and 9,777.1 . Option A, D , E
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Grandpa Mayowa and Grandma Quetta gave money to their 5 grandchildren to divide evenly among themselves. Grandpa Mayowa gave 500 dollars and Grandma Quetta gave d dollars. How much money did each grandchild receive? Write your answer as an algebraic expression.
(URGENT) Lines a & m are parallel. Using the diagram below, what is the degree measure of angle 3?
Enter the numerical answer only. Example, if the answer is 12 degrees, only enter 12.
The value of angle 3 is 127 degrees.
How to find angles formed by parallel lines?Parallel lines are those lines that are equidistant from each other and never meet.
Parallel lines cut by a transversal, forms different angle relationship like alternate angles, corresponding angles, etc.
The line a and m are parallel lines.
The parallel lines are cut by a transversal y.
The angles formed are 1, 2, 3, 4, 5, 6, 7, 127 degrees etc.
This angles are related by alternate rule or corresponding rule.
Therefore,
∠3 is an alternate angle to 127 degrees.
Hence, alternate angles are congruent.
Therefore,
∠3 = 127 degrees.
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Unknown Numbers
Consider the following problem.
One number is 3 less than 6 times a second number.
Their sum is 46. Find the numbers
If × represents the second number, which equation is
correct for solving this problem?
Step-by-step explanation:
y is the second number. This means we can define it as the following equations where x is the second number:
y=6x-3
y+x=46
we have a system of equations, let's move all x to the right side
y=6x-3
y=46-x
this means that 6x-3=46-x
6x+x=46+3
7x=49
x=7
now that we know x we can calculate the y through one of the equations above:
y=39
6. The Edwards's Theater chain has studied its movie customers to determine how much money they spend on concessions. The study revealed that the spending distribution is approximately normally distributed with a mean of $4.11 and a standard deviation of $1.37. What percentage of customers will spend less than $3.00 on concessions? a. 2.09% b. 20.9% c. 81.0% d. 209.0%
The percentage of customers will spend less than $3.00 on concessions is which is option (d).
Z-scores can be placed on a normal distribution curve. Z-scores range from -3 standard deviations (leftmost part of normal distribution curve) to +3 standard deviations (rightmost part of normal distribution curve). To use the z-score, we need to know the mean μ and the population standard deviation σ. A Z-score is a way to compare results to a "normal" population. Test or poll results have thousands of possible outcomes and units. These results often seem meaningless. A sample basic Z-score formula is z = (x - μ) / σ ...(1)It is given that mean is $4.11 , standard deviation is $1.37 and value is $3.00
Putting above values in equation (1) , we get
[tex]z=\frac{3-4.11}{1.37} \\\\z=-0.810[/tex]
P(x<3) = 0.20891
Percentage will be 209. %
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Which of the following shows the correct solution steps and solution to
7x-4--18?
O A.
7x-4 =-18
7x-4-4 = -18-4
7x = −14
7x
-14
7
7
=
-
x = -2
The solution for the equation 7x-4 = -18 is x = -2
The equation given is, 7x - 4 = -18.
We will try to solve this equation using elimination method in the following steps.
7x-4= -18
⇒ 7x-4+4 = -18+4
⇒7x = -14
⇒7x/7 = -14/7
⇒x = -2 is the solution for the given equation.
In the first step, we added 4 on both sides to eliminate -4 on the left side.
In the next step, we divided the both sides by 7 to eliminate the 7 on the left side. Finally, we got the solution as x = -2.
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Which of these is not a technique that can be used to randomly assign
students to a treatment group?
OA. Flipping a coin
B. Winning an election for class president
C. Rolling a die
D. Choosing a card from a fair deck
What is 9 divided 2.43
If f(x) = 4x² -3 and g(x) = x+1, find (f - g)(x)
The value of (f - g)(x) = 4x² - x - 4.
Function - A function is a relationship or expression involving one or more variables. It has a set of input and outputs. Each input has only one output. The function is the description of how the inputs relate to the output.
We have been given that -
f(x) = 4x² - 3
g(x) = x + 1
Find out (f - g)(x) = ?
(f - g)(x) = 4x² - 3 - (x + 1)
(f - g)(x) = 4x² - 3 - x - 1
Output of
(f - g)(x) = 4x² - x - 4
Hence , for the given function f(x) = 4x² - 3 and g(x) = x + 1 the relationship of (f - g)(x) is 4x² - x - 4.
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eight to the fourth power increased by six
Answer: 4102
Step-by-step explanation:
8^4 + 6=
4096+6=4102
you have a $3125 student loan. suppose you pay the loan off in two and a half years(30 months). estimate your monthly payment by ignoring interest and rounding down the amount owed. (round your answer to the nearest dollar.)
The monthly payment by ignoring intrest and rouning down the amount owed is $104
Given that "you have a $3125 student loan. suppose you pay the loan off in two and a half years(30 months)" and asked to find out the monthly payment by ignoring the intrest and round off the amount to nearest integer.
Total loan=$3125 .
Total time given= two and a half years(30 months)
The monthly payment=[tex]\frac{3125 }{30}[/tex]
The monthly payment=$104
To complete the student loan monthly payment of $104 is required.
Therefore,The monthly payment by ignoring intrest and rouning down the amount owed is $104
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Given the function: f(x) = 2x³-3/2x, find f(-4).
Order the square root of 70, negative 8.2 repeating, twenty five thirds, and negative eight and four sevenths from least to greatest. negative eight and four sevenths, negative 8.2 repeating, square root of 70, twenty five thirds negative eight and four sevenths, negative 8.2 repeating, twenty five thirds, square root of 70 negative 8.2 repeating, negative eight and four sevenths, twenty five thirds, square root of 70 negative 8.2 repeating, negative eight and four sevenths, square root of 70, twenty five thirds
Answer:
[tex]\textsf{B)} \quad -8 \frac{4}{7} \quad -8.\.{2} \quad \dfrac{25}{3} \quad \sqrt{70}[/tex]
Step-by-step explanation:
Given:
[tex]\sqrt{70} \quad -8.\.{2} \quad \dfrac{25}{3} \quad -8 \frac{4}{7}[/tex]
Convert the given numbers into decimals:
[tex]\sqrt{70}=8.366...[/tex]
[tex]-8.\.{2} =-8.222...[/tex]
[tex]\dfrac{25}{3}=8.333...[/tex]
[tex]-8 \frac{4}{7}=-8.571...[/tex]
Order the decimals from least to greatest:
[tex]-8.571... < -8.222... < 8.333... < 8.366...[/tex]
Therefore:
[tex]-8 \frac{4}{7} < -8.\.{2} < \dfrac{25}{3} < \sqrt{70}[/tex]
Answer:
negative eight and four sevenths, negative 8.2 repeating, twenty five thirds, square root of 70
Can you use absolute value when subtracting two negatives?
- 2 1/2 - (-1 2/3)
or does it only work when one number is negative?
Yes, it is possible to use absolute value when subtracting two negatives and as such it does not only work when one number is negative.
How to Interpret Absolute Values?
When adding two negative numbers, add the absolute value of the numbers and keep the negative sign.
For example -1 + -2 = - (||-1| + |-2||), which is -(1 + 2) or -3
The absolute value when subtracting two negatives is -2¹/₂ - (-1²/₃) is possible because when subtracting, we will change the subtraction to addition and change the sign of the number being taken away.
Thus, we can conclude that it is possible to use absolute value when subtracting two negatives.
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If Ef bisects CD, CG = 9x - 4, GD = 2x + 31, EF = 4x - 1, and GF = 7, find EG
The value of EG is 12
In geometry, the term line segment is defined as the part of a line segment used to join two points in a plane. When segments join the midpoints of two sides of a triangle, the segments are parallel to the other side and represent one half of it.Given equations of line are :
CG = 9x -4
GD = 2x+31
EF = 4x-1
GF = 7
We are asked to find the length of EG. We can start by analyzing the bisector, CD. Since the segment is the bisector, So CG = GD.
CG = GD
9x -4 = 2x+31
7x = 35
x = 5
Analyzing EF
EF = EG + GF
4x-1 = EG +7
20 - 1 -7 = EG
EG = 12
The value of EG is 12
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