You launch an object off a 55-foot cliff. If the object was launched at 85 feet/second, 64.23 feet/second long it will take for the object to hit the ground below. This can be solved using the concept of law of conservation of energy.
What is law of conservation of energy?Three fundamental quantities all maintain their original values. Energy, momentum, and angular momentum are these. Energy is a conserved quantity, which could surprise you if you've read instances in previous pages, such the kinetic energy of charging elephants. The first law of thermodynamics, generally known as the law of conservation of energy, stipulates that the energy of a closed system must remain constant and cannot rise or fall on its own without external intervention.
Given that,
Height of the cliff, h= 55 Foot
Initial speed of the projectile, u = 85 m/s
Let, the projectile hit the ground with velocity "v"
Applying the law of conservation of energy,
mgh + 1/2 mu² = 1/2 mv²
or, m (gh + 1/2 u²) = 1/2 mv²
or, (gh + 1/2 u²) = 1/2 v²
or, 10 × 55 + (1/2 × (55)²) = 1/2 v²
or, 550 + 1512.5 = 1/2 v²
or, 2062.5 = 1/2 v²
or, 4125 = v²
or, v = 64.23 feet/second
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PLEASE ANSWER I WILL MARK YOU AS BRAINLIEST
Oz Jeans has factories in Medney and Selbourne. At the Mydney factory, fixed costs are $28 000 per month and the cost of producing each pair of jeans is $30. At the Selbourne factory, fixed costs are $35 2000 per month and the cost of producing each pair of jeans is $24. During the next month Oz Jeans must manufacture 6000 pairs of jeans. Calculate the production order for each factory, if the total manufacturing costs for each factory are to be the same.
The total manufacturing costs for each factory are to be the same is M = 3318.52.
Let's denote the number of pairs of jeans produced at the Medney factory as M, and the number of pairs of jeans produced at the Selbourne factory as S.
We can set up the following system of equations based on the given information:Total cost of production at the Medney factory = Total cost of production at the Selbourne factory
28000 + 30M = 35200 + 24S
Total number of pairs of jeans produced = 6000
M + S = 6000
We can solve for M and S by using substitution or elimination. Here, we will use substitution:
M + S = 6000 (from equation 2)
M = 6000 - S (subtracting S from both sides)
28000 + 30M = 35200 + 24S (from equation 1)
Substituting M = 6000 - S:
28000 + 30(6000 - S) = 35200 + 24S
180000 - 30S = 35200 + 24S
180000 = 54S + 35200
54S = 144800
S = 2681.48
So the number of pairs of jeans produced at the Selbourne factory is approximately 2681.48. To find the number of pairs of jeans produced at the Medney factory, we can substitute this value of S back into equation 2:
M + S = 6000
M + 2681.48 = 6000
M = 3318.52
So the number of pairs of jeans produced at the Medney factory is approximately 3318.52.
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es-Ratios-
<
Question 12, 5.5.3
>
Caroline can sketch 6 cartoon strips in two hours. How long will it take her to
sketch 9 strips?
It would take Caro-line 3 hours to sketch 9 cartoon str-ips.
What is a ratio?
A ratio in mathematics demonstrates how many times one number is present in another. For instance, if a dish of the fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six.
We are given that, Caro-line can sketch 6 car-toon str-ips in two hours.
And we are asked that how much time it would require for Caro-line to sketch 9 str-ips
Now let the time required be x
Hence, the ratio becomes
6/2=9/x
x= (9*2)/6
x= 3
Hence, It would take Caroline 3 hours to sketch 9 cartoon str-ips
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We have graph, 5 points on the graph , and need to answer on question b(ii) b(iii), and c) it is connected .The rest of the questions are answered. So an not go separately . Thank you
The evaluation of the cubic function represented by the graph can be presented as follows;
a. The equation of the function, S = a·t³ + b·t² + c·t + d, indicates that the equation is a cubic equation
b. i. d = -5
ii. The three equations are;
a + b + c = 8...(1)
8·a + 4·b + 2·c = 4...(2)
27·a + 9·b + 3·c = 0...(3)
iii. a = 2, b = -12, and c = 18
c. The student is expected to be in debt for 2 years, 4 months and 3 days
What is a cubic function?A cubic function is a degree three polynomial that can be expressed in the form; f(x) = a·x³ + b·x² + c·x + d.
The specified function can be presented as follows;
S = a·t³ + b·t² + c·t + d
a. A feature of the graph that indicates that a cubic equation is the appropriate model, is the largest power of the input time variable t in the function is 3, which is the same as the power of a cubic function.
b. i. The value of d can be found by plugging in t = 0, in the function; S = a·t³ + b·t² + c·t + d
From the table in the question, we get;
At t = 0, S = -5
Therefore;
S = a×0³ + b×0² + c×0 + d = -5
d = -5
The value of d = -5
b. ii. The simultaneous equations can be obtained by plugging in the values of t from the table into the function for S as follows;
S = a·t³ + b·t² + c·t + d
S = a·t³ + b·t² + c·t - 5
When t = 1, we get;
S = a·1³ + b·1² + c·1 - 5 = 3
a + b + c - 5 = 3
a + b + c = 3 + 5 = 8
a + b + c = 8...(1)When t = 2, we get;
S = a·2³ + b·2² + c·2 - 5 = 3
8·a + 4·b + 2·c - 5 = -1
8·a + 4·b + 2·c = -1 + 5 = 4
8·a + 4·b + 2·c = 4...(2)When t = 3, we get;
S = a·3³ + b·3² + c·3 - 5 = 3
27·a + 9·b + 3·c - 5 = -5
27·a + 9·b + 3·c = -5 + 5 = 0
27·a + 9·b + 3·c = 0...(3)iii. Solving the system of equations using a graphing calculator, indicates that we get;
a = 2, b = -12, and c = 18c. Plugging in the values into the specified equation, we get;
S = 2·t³ - 12·t² + 18·t - 5
The solution of the above equation can be found as follows;
2·t³ - 12·t² + 18·t - 5 = 0
Based on an online tool, the Newton Raphson method indicates that a solution of the equation is; t ≈ 0.35821, which indicates that a factor of the equation, 2·t³ - 12·t² + 18·t - 5 = 0 is; (x - 0.35821)
(2·t³ - 12·t² + 18·t - 5) ÷ (x - 0.35821) ≈ 2·t² - 11.28356·t + 13.95804
The other solutions are therefore;
t ≈ 1.83, and t ≈ 3.81
The student is expected to be in debt at time t = 0, and from the graph, cross the x-axis out of depth first at time, t ≈ 0.35821 of a year
The student will be in dept again between t ≈ 1.83 and t ≈ 3.81
The total time the student is expected to be in debt is therefore;
∑t = 0.35821 + (3.81 - 1.83) ≈ 2.33821 years ≈ 2 years 4 months and 3 daysLearn more on cubic functions here: https://brainly.com/question/2456468
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(Score for Question 2: of 5 points)
-
2. Explain how to calculate 7% of 250 by first calculating 1% of 250.
Answer:
Math
Answer:
Note that 0.01 is the decimal form of 1%, so 0.01 multiplied by 7 yields 7%. So, if we were to find 1% of 250, which is 2.5, we can multiply the value by 7, which is 17.5.
Therefore, 7% of 250 is 17.5
an actor invests some money at 9% and 29000 more than four times the amount at 11% the total annual interest earned from the investment is 55130. how much did he invest at each amount?
A building has two elevators that both go above and below ground. At a certain time of day, the travel time it takes elevator A to reach height in meters is seconds. The travel time it takes elevator B to reach height in meters is seconds. what is the height of each elevator at this time
The height of each elevator at this time is, -2.5 m, negative means below ground level.
What is the relation between time, distance & speed ?The distance covered by the object is equal to the product of the speed at which the object is moving and time taken for covering the distance.
Distance = Time × Speed
To find how long it would take each elevator to reach ground level, we can set h = 0 in the given expressions for their travel times:
Elevator A:
= 0.8h + 16
= 0.8(0) + 16
= 16 seconds
Elevator B:
= -0.8h + 12
= -0.8(0) + 12
= 12 seconds
Therefore, elevator A would take 16 seconds and elevator B would take 12 seconds to reach ground level at this time.
To find at what height the elevators pass each other, we can set their travel times equal to each other and solve for h:
0.8h + 16 = -0.8h + 12
1.6h = -4
h = -2.5
Now, we can substitute value of h in the expression
Elevator A:
= 0.8(-2.5) + 16
= 14 seconds
Elevator B:
= -0.8(-2.5) + 12
= 14 seconds
Therefore, the elevators would pass each other 14 seconds after they both start moving towards each other.
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The complete question:
Elevators A building has two elevators that both go above and below ground.
At a certain time of day, the travel time it takes elevator A to reach height h in meters is 0.8h+16 seconds.
The travel time it takes elevator B to reach height h in meters is -0.8h+12 seconds.
How long would it take each elevator to reach ground level at this time? If the two elevators travel toward one another, at what height do they pass each other? How long would it take?
Their is a pair of parralle sides in the following shape 5 , 7, 6
what is the area of the shape
Answer: A = 15 units²
Step-by-step explanation:
The figure has 1 pair of parallel sides and is therefore a trapezium.
The area (A) of a trapezium is calculated as
A = h (b₁ + b₂ )
where h is the perpendicular height between bases and b₁, b₂ are bases
here h = 3, b₁ = 3 , b₂ = 7 , then
A = × 3 × (3 + 7) = 1.5 × 10 = 15 units²
In this picture B,D, and F are
midpoints. AC=50, CE=60, and
BD=35
B
AE=[? ]
The measure of the side AE would be 70 units.
What is the triangle midpoint theorem?We know that the triangle midpoint theorem says that the line segment connecting the midpoints of two sides of a triangle is parallel to the third side and is congruent to one half of the third side.
In the given triangle B, D, F are the midpoints of the triangle.
AC=50, CE=60,
BD=35
Then, in the given triangle if BD is connecting the midpoints of AC and CE then it must be parallel to AE and equal to FE ( half of AE).
⇒ BD ≅ FE= 1/2 AE
AE = 70 units
Then, the length of line segment AE = 70 units
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CIRCLES DRAG & DROP ACTIVITY 1: Drag & Drop the correct values to fill in each table below.
HELP ASAP WILL GIVE BRAINLIST!!!!!!!!!!
The radius, diameter, area and circumference of circle 1, 2, 3 and 4 are; (2, 4, 4π, 4π), (4, 8, 16π, 8π), (1, 2, 1π, 2π) and ( 8, 16, 64π, 16π) respectively.
What are the radius, diameter, area and circumference of each of the given circle?The diameter of a circle is 2 times the radius of the circle.
The area of a circle is expressed as: A = πr²
The circumference of a circle is expressed as: 2πr
For question 1)
Radius r = 2
Diameter = 2 × radius = 2 × 2 = 4
Area = πr² = π( 2 )² = 4π
Circumference = 2πr = 2 × π × 2 = 4π
For question 2)
Radius r = 4
Diameter = 2 × radius = 2 × 4 = 8
Area = πr² = π( 4 )² = 16π
Circumference = 2πr = 2 × π × 4 = 8π
For question 3)
Diameter d = 2
Radius = diameter / 2 = 2/2 = 1
Area = πr² = π( 1 )² = 1π
Circumference = 2πr = 2 × π × 1 = 2π
For question 4)
Diameter d = 16
Radius = diameter / 2 = 16/2 = 8
Area = πr² = π( 8 )² = 64π
Circumference = 2πr = 2 × π × 8 = 16π
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Which equation best represents the curve of best fit for this data?
Answer:yes
Step-by-step explanation:
Find the degree, leading coefficients, and the maximum number of real zeros of the polynomial.
f
(
x
)
=
2
x
5
−
x
3
+
x
6
−
4
Degree =
Leading Coefficient =
Maximum number of real zeros =
The degree of the polynomial is; 6.
The leading coefficient of the polynomial is; 1.
The maximum number of real zeroes is; 6.
What is the degree of the polynomial?As evident in the task content; the given polynomial is;
f (x) = 2x⁵ - x³ + x⁶ - 4.
By observation, the term with the highest power of x is; x⁶.
Therefore, the degree is; 6.
The leading coefficient is the coefficient of x⁶ which is; 1.
The maximum number of real zeroes possible is dependent on the degree of the polynomial and is; 6.
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A
15
What is the measure of ZA?
B
Enter the correct value.
C
The measure of angle A is given as follows:
<A = 60º.
What are the trigonometric ratios?The three trigonometric ratios are defined as follows:
Sine of angle = length of opposite side divided by the length of the hypotenuse.Cosine of angle = length of adjacent side divided by the length of the hypotenuse.Tangent of angle = length of opposite side divided by the length of the opposite side.For the angle A, we have that:
The opposite side is of 13.The hypotenuse is of 15.Applying the sine ratio, the angle measure is given as follows:
sin(A) = 13/15
A = arcsin(13/15)
A = 60º.
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NEED HELP FAST for 25pts
The coordinates of point C in the given right triangle ABC is (2, 2√3-2)
What is a triangle?A triangle is a three-sided polygon, which has three vertices. The three sides are connected with each other end to end at a point, which forms the angles of the triangle. The sum of all three angles of the triangle is equal to 180 degrees.
Given that, triangle ABC is a 30°-60°-90° triangle, where two vertices are A(-4, -2) and B(4, -2).
Now, AB=4-(-4)=8
AC=AB×sin60°= 8×√3/4√3
In right triangle ACD
AD=AC×cos30°
= 4√3×√3/2
= 6
Xc=6-4=2
Yc=AC×sin30°-2
= 4×3×1/2-2
= 2√3-2
The coordinates of point C(2, 2√3-2)
Therefore, coordinates of C(2, 2√3-2).
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Please help me with this question please
Answer:
51°
Step-by-step explanation:
180°-129°=51°
I hope it helps you
f(x)=
[tex]2 {x}^{2} [/tex] write down the equation of inverse of f
The equation of inverse of f is f-1(x) = √(x/2)
How to determiine the equation of inverse of fFrom the question, we have the following parameters that can be used in our computation:
f(x) = 2x^2
Express as an equation
so, we have the following representation
y = 2x^2
Swap x and y
so, we have the following representation
x = 2y^2
Divide by 2
y^2 = x/2
Take the square roots
y = √(x/2)
Hence, the inverse is f-1(x) = √(x/2)
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Please Help Me Answer!
The probability that a randomly chosen college student exercises in the morning or afternoon is B. 0. 39.
How to find the probability ?The probability that a college student chosen at random will either exercise in the morning or afternoon can be found by the formula :
= Probability that student exercises in the morning + Probability that student exercises in the afternoon
Probability that student exercises in the morning = 0. 25
Probability that student exercises in the afternoon = 0. 14
The probability would therefore be:
= 0. 25 + 0. 14
= 0. 39
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Point R is located at (1,1) on the coordinate plane. Point R is reflected over the y-axis to create point R ′ . Point R' is then reflected over the x-axis to create point R''. What ordered pair describes the location of R''?
Answer:
Step-by-step explanation:
Here's a step-by-step explanation of the reflections:
Point R is located at (1, 1) on the coordinate plane.
Reflection over the y-axis: This reflection changes the sign of the x-coordinate. In other words, if the point (x, y) is reflected over the y-axis, the reflected point will be ( -x, y). So, for point R at (1, 1), the reflection over the y-axis creates R' at (-1, 1).
Reflection over the x-axis: This reflection changes the sign of the y-coordinate. In other words, if the point (x, y) is reflected over the x-axis, the reflected point will be (x, -y). So, for point R' at (-1, 1), the reflection over the x-axis creates R'' at (-1, -1).
So the final location of R'' is at the ordered pair (-1, -1).
Ezra 1:9,10 records that King Cyrus returned thirty gold chargers, one thousand silver chargers, twenty - nine knives, thirty gold basons, four hundred ten silver basons, and one thousand other vessels. How many items did Cyrus return to Israel?
Answer:
2489
Step-by-step explanation:
it would be 30+ 1,000+29+30+400+1,000+ 2489
I really hope this helps
Proverbs 4:6-7
Do not forsake wisdom, and she will protect you; love her, and she will watch over you. The beginning of wisdom is this: Get wisdom. Though it cost all you have, get understanding. Cherish her, and she will exalt you; embrace her, and she will honor you. (just a little encouragement to keep studying hard!)
Answer:
2489
Step-by-step explanation:
Hi there please help :)
Answer:
∠ a = 30° , ∠ b = 90°
Step-by-step explanation:
∠ a and 150° are a linear pair and sum to 180° , that is
∠ a + 150° = 180° ( subtract 150° from both sides )
∠ a = 30°
------------------
the sum of the 3 angles in a triangle = 180° , that is
∠ b + ∠ a + 60° = 180°
∠ b + 30° + 60° = 180°
∠ b + 90° = 180° ( subtract 90° from both sides )
∠ b = 90°
examine whether you can construct a triangle PQR such that QR=3 cm, PQ=6 cm, PR=3 cm. Justify your answer
No, it is impossible to construct a triangle PQR such that QR=3 cm, PQ=6 cm, PR=3 cm as the dimensions defy the triangle inequality theorem.
What is the triangle inequality theorem?It follows from the triangle inequality theorem that the sum of any two side lengths of a triangle must be greater than the third side length and also, the difference of two side lengths of a triangle must be less than the third side lengths.
However, in this case, since QR + PR = PQ, it can be inferred that the two side lengths cannot possibly be used to construct a triangle.
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(6 points) Here are the data on the age for a random sample of instructors working in three different colleges. Use appropriate
99%
confidence intervals to complete the each of the following questions . Part A We are
99%
confident that the mean age of all instructors in College
A
is College B by between years old and (Round the numeric answers to 5 decimal places) Part B We are
99%
confident that the mean age of all instructors in College
A
is College C by between (Round the numeric answers to 5 decimal places) Part E We are
99%
confident that the mean age of all instructors in College B is College C by between years old and years old. (Round the numeric answers to 5 decimal places)
Part A: We are 99% confident that the mean age of all instructors in College A is between 42.79128 and 51.2088 years old.
Part B: We are 99% confident that the mean age of all instructors in College A is College C by between 37.36368 and 54.63632 years old.
Part C: We are 99% confident that the mean age of all instructors in College B is College C by between 46.24672 and 57.75328 years old.
In this question, they are asking to calculate the 99% confidence intervals for the mean age of instructors in three different colleges (A, B, and C). They want to compare the mean age of instructors in College A to College B, College A to College C, and College B to College C. The numeric answers should be rounded to 5 decimal places.
To calculate these confidence intervals, you need to find the sample mean and standard deviation of the data for each college. Then, you can use the formula for a two-sample t-test to calculate the confidence intervals. The formula is (sample mean A - sample mean B) ± t-critical value * (standard deviation of A/√nA + standard deviation of B/√nB), where nA and nB are the sample sizes for Colleges A and B, respectively.
Part A: We are 99% confident that the mean age of all instructors in College A is College B by between 20.81733 and 23.72867.
To calculate the 99% confidence interval, we must first calculate the mean and standard deviation of the sample data. The mean age of all instructors in College A is 22.273 and the standard deviation is 1.936.
Next, we must use the t-distribution to calculate the 99% confidence interval. The critical value is 2.228. The confidence interval is calculated as follows:
Lower Bound = 22.273 - (2.228 x 1.936) = 20.81733
Upper Bound = 22.273 + (2.228 x 1.936) = 23.72867
Therefore, we are 99% confident that the mean age of all instructors in College A is College B by between 20.81733 and 23.72867.
Part B: We are 99% confident that the mean age of all instructors in College A is College C by between 17.73173 and 25.71367.
To calculate the 99% confidence interval, we must first calculate the mean and standard deviation
Part C: We are 99% confident that the mean age of all instructors in College B is College C by between 46.24672 and 57.75328 years old.
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Find the average rate of change of the function on the intervals specified for a real number h F(x) =6x^2 + 5. On [ x,x+h]
Step-by-step explanation:
The average rate of change of a function on an interval [x, x + h] is given by the formula:
(F(x + h) - F(x)) / h
For the function F(x) = 6x^2 + 5, the average rate of change on the interval [x, x + h] is:
(F(x + h) - F(x)) / h = (6(x + h)^2 + 5 - (6x^2 + 5)) / h = (6(x^2 + 2xh + h^2) - 6x^2 + 5) / h = (6(2xh + h^2)) / h = (12xh + 6h^2) / h
So the average rate of change of the function on the interval [x, x + h] is (12xh + 6h^2) / h for a real number h.
Please help bro I need help solving this polynomial and terms
The expression represents a quintic polynomial with 4 terms. The constant term is -6, the leading term is x⁵/2, and the leading coefficient is 1/2.
What is a polynomial expression?A polynomial expression is a mathematical equation in which the polynomial is set to zero. The equation is made up of variables, non-negative integer exponents, coefficients, arithmetic operations, and an equal sign.
From the polynomial expression given:
[tex]\dfrac{1}{2}x^5 - 6 - x^4 -5x^2[/tex]
The degree of a polynomial is the highest degree of its terms which helps us to determine the type of polynomial (quintic polynomial). The constant term is -6.
The leading term in a polynomial is the term with the highest degree = x⁵/2. The leading coefficient of a polynomial is the coefficient of the leading term is 1/2.
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Answer:
quadrinomial, 4, -6, 1/2x^5, 1/2
Step-by-step explanation:
quadrinomials are polynomials with 4 terms
constant is the number with no variable
leading term is the term at the beginning
leading coefficient is the number at the beginning
Line AB contains points A(4, 5) and B(9, 7). What is the slope of AB?
Answer:
Step-by-step explanation:
The slope of a line can be found using the formula:
slope = (y2 - y1) / (x2 - x1)
Where (x1, y1) and (x2, y2) are the coordinates of two points on the line. In this case, we can use points A(4, 5) and B(9, 7):
slope = (7 - 5) / (9 - 4) = 2 / 5
So, the slope of line AB is 2/5.
The cost of renting a car is $75 dollars per day there is also a charge of 30 to start with a full tank of gas so that the car may be returned full or close to empty. Write a function to represent the car rental using c for cost and d for number of days
Answer:
Step-by-step explanation:
The cost of renting a car for "d" days can be represented by the following function:
c(d) = 75d + 30
where "c" is the total cost of the car rental and "d" is the number of days the car is rented for. The first term, 75d, represents the daily rental fee of $75 per day. The second term, 30, represents the flat fee for the full tank of gas that can be returned either full or close to empty.
On a standard dice, what is the probability of not landing a 3
Answer:
5/6
Step-by-step explanation:
find value of x please help
Answer:
...here is the answer...
Help me with this worksheet pls
The value of y from x= 0 to x = 3 is: y = 5(2)⁰ = 5, y = 5(2)¹ = 10, y = 5(2)² = 20, y = 5(2)³ = 40. The most rapid rate of change is: y = 7ˣ. The constant 1.20 is greater than 1 thus, the function is exponential growth.
What is exponential function?The formula for an exponential function is f (x) = axe, where x is a variable and an is a constant that serves as the function's base and must be bigger than 0. The transcendental number e, or roughly 2.71828, is the most often used exponential function basis.
The given function is:
y = 5(2)ˣ
The value of y from x= 0 to x = 3 is:
y = 5(2)⁰ = 5
y = 5(2)¹ = 10
y = 5(2)² = 20
y = 5(2)³ = 40
The most rapid rate of change as x increases beyond 0 is:
y = 7ˣ
This is observed as the graph increases rapidly with change in value of x.
3. y = (1.20)ˣ
The constant 1.20 is greater than 1 thus, the function is exponential growth.
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3. Given: RS LTS, RV LTV, and ST = VT Prove: RS RV R COMMON CORE GEOMETRY, UNIT #3-EUCLIDEAN TRIANGLE PROOF AND CONSTRUCTIONS-LESSON #9 S
A group of 500 middle school students were randomly selected and asked about their preferred television genre. A circle graph was created from the data collected.
a circle graph titled preferred television genre, with five sections labeled drama 14 percent, sports 22 percent, documentaries 24 percent, reality 20 percent, and sci-fi
How many middle school students prefer the Sci-Fi television genre?
100
80
72
20
Answer:
The answer is 100, see Step-by-step explanation:
Step-by-step explanation:
If anyone looks at the verified answer, its wrong and so are the comments under it. In the answer above it says "Sci-fi = 100-24-22-20-14=20" that is correct but the answer is not. 20 percent of 500 is 100 not 72 or 20, I don't know how anyone got those answers.
