Rising or growing steadily and quickly: a city in exponential expansion. noun. Mathematics the value of the constant e raised to the power of a given expression, represented as the exponential of 3x, e3x. something that is positive and raised in power.
Explain exponential functions?In the biological sciences, exponential functions are frequently employed to simulate the evolution of a certain quantity over time, such as population number. Experimental data graphs are often created with the quantity on the y-axis and the time on the x-axis.
The development of bacteria is an illustration of an exponential function. Some germs multiply by two per hour. After x hours, you will have twice as much germs if you start with one and it doubles every hour. F(x) = 2x can be used to express this.
The values of f(x) and g(x) in the table for various values of f(x) = 9x + 7 and g(x) = 5x
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What is the input value for which f(x) = -3?
a university found that 14% of its students withdraw without completing the introductory statistics course. assume that 20 students registered for the course. if required, round your answer to four decimal places. (a) compute the probability that 2 or fewer will withdraw
The Probability that 2 or fewer will withdraw without completing the introductory statistics course is 0.4547 .
The Binomial Distribution formula is
P(X=x) = C(n,x)*pˣ*qⁿ⁻ˣ
where ,
n is the number of trials
x is the number of times success occurs
p is the probability of success
q is the probability of failure .
In the given question ;
it is given that
students that are registered for the course = 20
so , n=20
Let x denote the number of students that withdraw without completing the course .
given that 14 % students withdraw without completing the course ,
hence p = 14% = 0.14
So , q= 1-p = 1-0.14 = 0.86
the probability that 2 or fewer will withdraw from the course is denoted by P(X ≤ 2) and is calculated using
the formula , P(X≤2)=P(X=0)+P(X=1)+P(X=2) ...(i)
using Binomial Probability we get
P(X=x) = C(n,x)*pˣ*qⁿ⁻ˣ
P(X=0) = C(20,0)*(0.14)⁰*(0.86)²⁰⁻⁰
= C(20,0)*(0.14)⁰*(0.86)²⁰
= 1*1*(0.0489)
= 0.0489
So , P(X=0)=0.0489 ...(ii)
P(X=1) = C(20,1)*(0.14)¹*(0.86)¹⁹
= 20*0.14*0.0569
= 0.1593
So , P(X=1)=0.1593 ...(iii)
P(X=2) = C(20,2)*(0.14)²*(0.86)¹⁸
= 190*0.0196*0.0662
= 0.2465
So , P(X=2)=0.2465 ...(iv)
Substituting the values of (ii) , (iii) and (iv) in (i) , we get
P(X≤2)=P(X=0)+P(X=1)+P(X=2)
P(X ≤ 2) = 0.0489 + 0.1593 + 0.2465
= 0.4547
Therefore , the Probability that 2 or fewer will withdraw without completing the introductory statistics course is 0.4547 .
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Find the slope of the line through (-3,2) and (6,2)
If there are 200 people in a cinema and the probability of choosing a person eating popcorn is 0.25, how many people in the cinema are eating popcorn?
800 people in the cinema are eating popcorn by probability.
What does math probability mean?
Probability is the study of possible outcomes of events, along with their comparative probabilities and distributions.Probability is the measure of how probable something is to happen. As an illustration, since there is only one way to get a head and a total of two potential outcomes, the probability of flipping a coin and getting heads is one in two. a tail or a head. We write P(heads) = 12 here.Total people in cinema = 200
probability of choosing a person eating popcorn is = 0.25
people in the cinema are eating popcorn = 200/0.25
people in the cinema are eating popcorn = 800
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Want 10 points? 2+2 = ? im so confused on this one!
Answer:
2 + 2 is 5
Step-by-step explanation:
everyone knows that
Answer:
Obviously its 22
Step-by-step explanation:
list prime numbers between 5420
Answer:
(1-5420)
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997, 1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087, 1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, 1153, 1163, 1171, 1181, 1187, 1193, 1201, 1213, 1217, 1223, 1229, 1231, 1237, 1249, 1259, 1277, 1279, 1283, 1289, 1291, 1297, 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373, 1381, 1399, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451, 1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511, 1523, 1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583, 1597, 1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657, 1663, 1667, 1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733, 1741, 1747, 1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811, 1823, 1831, 1847, 1861, 1867, 1871, 1873, 1877, 1879, 1889, 1901, 1907, 1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987, 1993, 1997, 1999, 2003, 2011, 2017, 2027, 2029, 2039, 2053, 2063, 2069, 2081, 2083, 2087, 2089, 2099, 2111, 2113, 2129, 2131, 2137, 2141, 2143, 2153, 2161, 2179, 2203, 2207, 2213, 2221, 2237, 2239, 2243, 2251, 2267, 2269, 2273, 2281, 2287, 2293, 2297, 2309, 2311, 2333, 2339, 2341, 2347, 2351, 2357, 2371, 2377, 2381, 2383, 2389, 2393, 2399, 2411, 2417, 2423, 2437, 2441, 2447, 2459, 2467, 2473, 2477, 2503, 2521, 2531, 2539, 2543, 2549, 2551, 2557, 2579, 2591, 2593, 2609, 2617, 2621, 2633, 2647, 2657, 2659, 2663, 2671, 2677, 2683, 2687, 2689, 2693, 2699, 2707, 2711, 2713, 2719, 2729, 2731, 2741, 2749, 2753, 2767, 2777, 2789, 2791, 2797, 2801, 2803, 2819, 2833, 2837, 2843, 2851, 2857, 2861, 2879, 2887, 2897, 2903, 2909, 2917, 2927, 2939, 2953, 2957, 2963, 2969, 2971, 2999, 3001, 3011, 3019, 3023, 3037, 3041, 3049, 3061, 3067, 3079, 3083, 3089, 3109, 3119, 3121, 3137, 3163, 3167, 3169, 3181, 3187, 3191, 3203, 3209, 3217, 3221, 3229, 3251, 3253, 3257, 3259, 3271, 3299, 3301, 3307, 3313, 3319, 3323, 3329, 3331, 3343, 3347, 3359, 3361, 3371, 3373, 3389, 3391, 3407, 3413, 3433, 3449, 3457, 3461, 3463, 3467, 3469, 3491, 3499, 3511, 3517, 3527, 3529, 3533, 3539, 3541, 3547, 3557, 3559, 3571, 3581, 3583, 3593, 3607, 3613, 3617, 3623, 3631, 3637, 3643, 3659, 3671, 3673, 3677, 3691, 3697, 3701, 3709, 3719, 3727, 3733, 3739, 3761, 3767, 3769, 3779, 3793, 3797, 3803, 3821, 3823, 3833, 3847, 3851, 3853, 3863, 3877, 3881, 3889, 3907, 3911, 3917, 3919, 3923, 3929, 3931, 3943, 3947, 3967, 3989, 4001, 4003, 4007, 4013, 4019, 4021, 4027, 4049, 4051, 4057, 4073, 4079, 4091, 4093, 4099, 4111, 4127, 4129, 4133, 4139, 4153, 4157, 4159, 4177, 4201, 4211, 4217, 4219, 4229, 4231, 4241, 4243, 4253, 4259, 4261, 4271, 4273, 4283, 4289, 4297, 4327, 4337, 4339, 4349, 4357, 4363, 4373, 4391, 4397, 4409, 4421, 4423, 4441, 4447, 4451, 4457, 4463, 4481, 4483, 4493, 4507, 4513, 4517, 4519, 4523, 4547, 4549, 4561, 4567, 4583, 4591, 4597, 4603, 4621, 4637, 4639, 4643, 4649, 4651, 4657, 4663, 4673, 4679, 4691, 4703, 4721, 4723, 4729, 4733, 4751, 4759, 4783, 4787, 4789, 4793, 4799, 4801, 4813, 4817, 4831, 4861, 4871, 4877, 4889, 4903, 4909, 4919, 4931, 4933, 4937, 4943, 4951, 4957, 4967, 4969, 4973, 4987, 4993, 4999, 5003, 5009, 5011, 5021, 5023, 5039, 5051, 5059, 5077, 5081, 5087, 5099, 5101, 5107, 5113, 5119, 5147, 5153, 5167, 5171, 5179, 5189, 5197, 5209, 5227, 5231, 5233, 5237, 5261, 5273, 5279, 5281, 5297, 5303, 5309, 5323, 5333, 5347, 5351, 5381, 5387, 5393, 5399, 5407, 5413, 5417, 5419
Step-by-step explanation:
Situation: A DJ will play music. The DJ charges $20 per hour plus a $50 appearance fee. Represent the relationship between the number of hours the DJ works and the total cost of hiring the DJ.
Answer:total cost= 20x+50 x= number of hours
Step-by-step explanation: Gooooooooooooogle
Find the equation of the line of best fit for the points ( − 4 , 10 ) , ( − 1 , 5 ) , ( 2 , − 1 ) , ( 3 , − 6 ) , and ( 5 , − 7 ) .
The equation of the line of best fit for the points is y = -2x + 3
Equation of line of best fitThe distance between two points is referred to as a line. The standard equation of a line in slope-intercept form is expressed according to the equation
y = mx + b
where:
m is the slope
b is the intercept
Using the coordinate points (-1, 5) and. (5, -7)
Slope = -7-5/5-(-1)
Slope = -12/6
Slope = -2
Find the y-intercept
-7 = -2(5) + b
-7 = -10 + b
b. = 3
Determine the equation
y = mx + b
y = -2x + 3
This gives the required equation of line of best fit.
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Enter the correct answer in the box.
Simplify the expression (6^2)4.
answer; 6^8
explanations;
power rule for exponent; 2 x 4 = 8
Find the value of the missing angle x.
A. 45 degrees
B. 90 degrees
C. 135 degrees
D. 180 degrees
Answer:
.............. ................
two hundred and fifty six x^4 minus one thousand two hundred and ninety six y^4
The expression two hundred and fifty six x^4 minus one thousand two hundred and ninety six y⁴ will be 16(4²x⁴ - 9²y⁴)
How to explain the expression?It should be noted that expressions simply means one or more number or variables that are used to represent a data or a particular information.
It should be noted that two hundred and fifty six x⁴ minus one thousand two hundred and ninety six y^4 will be expressed as:
256x⁴ - 1096y⁴
In this case, there's a common factor between 256 and 1096. This will give a result as:
= 16(16x⁴ - 81y⁴)
= 16(4²x⁴ - 9²y⁴)
= 16[(4x)² - (9y²)²][(4x²)² + (9y²)²]
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[8a squared b]\frac{x}{y}[/2ab squared]
The quotient [8a squared b]/[2ab squared] is simplified to 16/b
What are algebraic expressions?Algebraic expressions are simply known as arithmetic expressions which are made up of constants, variables, terms, factors and coefficients.
They are also made up of certain operations, arithmetic, mathematical which includes;
DivisionMultiplicationAdditionSubtractionParenthesesBracket, etcGiven the expression;
[8a squared b] = x
[2ab squared] = y
Take the quotient of the values
(8a)²b/(2ab)²
Expand the bracket
64a²b/4a²b²
Now, divide the common terms, we have
16/b
Hence, the value is 16/b
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The LCM of 700 and N, is 2^2x3x5^2x7^2.
Find the lowest possible value for N.
The lowest possible value for N is 21.
What is LCM?The smallest positive integer that is divisible by both a and b is known as the least common multiple (lcm), lowest common multiple (lcm), or smallest common multiple of two numbers a and b in mathematics and number theory. The smallest number that can be divided by both numbers is the LCM of two numbers. Finding the lowest common denominator (LCD) of two or more fractions is a key application of LCM. It is crucial when combining, dividing, and contrasting two or more fractions.
Given Data
LCM of 700 and N
is 2²x3x5²x7²
700 and N = 2²x3x5²x7²
700 and N = 14700
N = [tex]\frac{14700}{700}[/tex]
N = 21
The lowest possible value for N is 21.
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A basketball team wants to see if its fans like its new uniforms. Which description represents a population?
children who root for the team
season ticket holders
employees who work for the basketball team
fans of the basketball team
Answer:
Step-by-step explanation:
What are the slope and the Y-Intercept of the linear function y=5X-2
slope = 5 or 5 rise over 1 run.
y-intercept = (0,-2)
You roll a fair 6-sided die twice. Find the probability of getting the same number.
The probability of getting the same number is 1/6.
The ratio of good outcomes to all possible outcomes of an event is known as the probability.
utilizing two ethical six-sided dice.
The likelihood that the dice will produce the same number must be determined.
36 total outcomes were obtained.
The positive results are (1,1), (2,2), (3,3), (4,4), (5,5), and (6,6).
6 good outcomes total.
Therefore, the likelihood of an event is equal to the ratio of good outcomes to all possible outcomes.
Changing the values
Event probability is 6/36, or 1/6.
As a result, there is a 1/6 chance that both dice will reveal the same number.
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Justin has $56.05 and needs to go downtown. For the cab ride, there is an initial fee of $3.19 with a $0.44 charge for every half mile.
If m represents every half mile, which equation could determine exactly how far can Justin travel?
A
B
D
56.05 = 3.19 +0.44m
56.05 = 3.19m +0.44
0.44m 56.05 + 3.19
3.19 = 56.05 + 0.44m
Complete both transformations
below.
Then enter the final coordinates of the figure.
New coordinate systems on the plane are frequently defined via coordinate transformations. The transformation's curves are representations of horizontal lines with the form v - constant and vertical lines with the form u - constant, respectively.
Answer the below figure
1. Reflect across y-axis
2.<4,5>
Answer:
B'''(6, -15), C'''(-3, -12) (-3, -12)
Detailed explanation:
Point B concerns
As for point C,
In order to reflect a point across the x-axis, keep the x coordinate
constant while changing the y coordinate to its opposite.
<1, -3> the following translations: Add 1 to x, take 3 away from y.
Add 3 to both x and y to dilate k=3.
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The graph of y=-2x² + 1 is shown.
The relative maximum point is point D.
The relative maximum point is determined by the slope.
Here the slope is represented by tan theta.
If we draw a tangent at every point of the curve then we observe that A has a positive curse and point D has a increasing curve which is almost equal to 90° and tan 90 is 1. Point B and C however have a steady curve and tan 0 is 0.
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A = {Prime numbers between 10 and 16} B = {Multiples of 3 between 10 and 16}
(a) List the members of AUB.
(b) What is AB?
(c) Is it true that 11 € B?
Part (a)
A = {prime numbers between 10 and 16}
A = {11, 13}
B = {multiples of 3 between 10 and 16}
B = {12, 15}
A U B = union of set A with set B
A U B = {set of stuff from A or B or both}
A U B = {11, 12, 13, 15}
=================================================
Part (b)
I'm assuming that you meant to write [tex]A \cap B[/tex]
If so, then this is the set of values inside set A and set B at the same time.
Since there is no common overlap between the sets A and B, we say that the answer is the empty set. We write the empty set as a pair of curly braces with nothing inside. Not even zero is a member of the empty set.
[tex]A \cap B = \{ \ \}[/tex]
we could also write the empty set using the symbol [tex]\varnothing[/tex]
So,
[tex]A \cap B = \varnothing[/tex]
=================================================
Part (c)
Answer: FalseReason:
The weird looking E symbol in this context means "is inside" or "is part of"
In other words, a statement like [tex]11 \in B[/tex] translates to "11 is part of set B", which is a false statement. Recall that B = {12, 15}
If we said [tex]11 \in A[/tex], then it would be true since A = {11, 13} which shows 11 as one of the values of set A.
What is the slope of the line?
Answer:
-2
Step-by-step explanation:
find two points on the line. You go down 2 units and 1 unit to the right.
Let’s imagine a ball being thrown up in the air by the wind, meaning that it started on the ground. If we were to graph how the ball’s height changes relative to time, we would get a parabola or a what looks like or a curve that is upside down (sort of like the smile of sad face or upside down smiley face). In what quadrant or quadrants could the curve fall?
Answer:
Quadrant I
Step-by-step explanation:
Time and height must both be positive.
On a clearance rack, t-shirts cost $10 and shorts cost $13. You have $25 to spend. Write an equation that models the possible combinations of t-shirts t, and shorts, s, you can buy.
The equation that models the situation is 10t + 13s = 25
How to model equation?T-shirts cost $10 and shorts cost $13.
The shorts cost $13.
The total amount to be spend is $25.
let
t = number of T-shirt
s = number of shorts
The equation that models the possible combinations of T-shirt t, and shorts s, is as follows:
An equation is a mathematical statement that shows that two mathematical expressions are equal.
Hence,
10t + 13s = 25
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Yosef drops a basketball from his bedroom window, which is 3m off the ground. After each bounce,
the basketball comes back to 75% of its previous height. If it keeps on bouncing forever, what
vertical distance, to the nearest metre, will it travel?
After the sixteenth bounce, the basketball would be nearest which is 0.01 meters.
Height after dropping from a height = 3m
Bounce up rate = 75%
Height in first bounce = 2.25m (3 x 0.75)
Height in second bounce = 1.68m (2.25 x 0.75)
Height in third bounce = 1.26m (1.68 x 0.75)
Height in fourth bounce = 0.70m (0.94 x 0.75)
Height in fifth bounce = 0.525m (0.70 x 0.75)
Height in sixth bounce = 0.39m (0.52 x 0.75)
Height in seventh bounce = 0.29m (0.39 x 0.75)
Height in eighth bounce = 0.21m (0.29 x 0.75)
Height in ninth bounce = 0.15m (0.21 x 0.75)
Height in tenth bounce = 0.11m (0.15 x 0.75)
Height in eleventh bounce = 0.08m (0.11 x 0.75)
Height in twelfth bounce = 0.06m (0.08 x 0.75)
Height in thirteenth bounce = 0.04m (0.06 x 0.75)
Height in fourteenth bounce = 0.03m (0.04 x 0.75)
Height in fifteenth bounce = 0.02m (0.03 x 0.75)
Height in sixteenth bounce = 0.01m (0.02 x 0.75)... so on
After the sixteenth bounce, the basketball would be nearest.
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Triangle A'B'C' is the image of ABC under a dilation with a scale factor of 2.
What is the length of segment
——
A’B’?
After dilation, the length of line segment A'B' is 6 units.
What is dilation?Resizing an object uses a transformation called dilation. Dilation is used to enlarge or contract objects. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. A dilation in mathematics is a function f from a metric space M into itself that, for all points x, y in M, satisfies the identity d=rd, where d is the distance between x and y and r is some positive real number. Such a dilation is a similarity to the space in Euclidean space.So, the length of line segment AB:
We would multiply a figure by 2 when dilating it by its length.The length of AB is 3 units.After dilation:
3 × 2 = 6 unitsTherefore, after dilation, the length of line segment A'B' is 6 units.
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What’s the answer pls
The length of the side marked x is 10.2 cm.
What is the missing side?We know that it is possible to solve the right angle triangle by the use of the Pythagoras theorem. Also, we could make use of the trigonometric ratios when we have to solve the right angled triangle.
The task here id to find the angle that has been marked x in the image that was shown above.
We are going to use the trigonometric ratios here;
Given that;
Cos θ = adjacent/ hypotenuse
θ = 40 degrees
Adjacent = x
Hypotenuse = 13.4 cm
adjacent = cos 40 * 13.4 cm
adjacent = 10.2 cm
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Eight avocados cost 4$
How much do 16 avocados cost
Answer:
8 dollars
Step-by-step explanation:
Describe each transformation of the parent function y + |x|. Then, graph each function.
33. y = |x| - 4
35. y = -|x + 4| + 3
PLEASE HELP
The correct transformation include
Transformation 1: Shifted down by 4 unitsTransformation 2: Shifted left by 4 units, reflected across the x-axis and shifted up by 3 unitsHow to determine the transformation of the graph?The equation of the function is given as
y = |x|
The transformed functions are given as
y = |x| - 4
y = -|x + 4| + 3
The transformation 1
Here, we have
y = |x|
y = |x| - 4
This can be represented as
y = f(x) - 4
The description of the above transformation is:
The function y = |x| is shifted down by 4 units
The transformation 2
Here, we have
y = |x|
y = -|x + 4| + 3
This can be represented as
y = -f(x + 4) + 3
The description of the above transformation is as follows
The function y = |x| is shifted left by 4 unitsThe function is then reflected across the x-axisThe function y = |x| is shifted up by 3 unitsNext, we graph the functions where the blue line represents y = |x|, the green line represents y = |x| -4 and the orange line represents y = -|x + 4| + 3
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Are the ratios 5:3 and 6:4 equivalent?
Answer:
I believe so but I'm nor 100% sure
The ratios 5:3 and 6:4 are not equivalent.
What are ratios?A ratio in mathematics illustrates how many times one number contains another. For example, if a dish of fruit contains eight oranges and six lemons, the orange-to-lemon ratio is eight to six. Similarly, the lemon to orange ratio is 6:8, while the orange to total fruit ratio is 8:14.
Equivalent ratios are those that are the same when compared. Two or more ratios can be compared to determine whether they are equal. For example, the ratios 1:2 and 2:4 are equal.
The given two ratios are 5:3 and 6:4. We can write them as 5/3 and 6/4
Let us apply subtraction, if we get 0 then these are equivalent.
6/4-5/3
The LCM of 4 and 3 is 12
=(18-20)/12
The value of 18-20 is -2
=-2/12
We have to divide 2 by 12 we get -1/6.
=-1/6 not equal to 0
Therefore, it can be concluded that the ratios 5:3 and 6:4 are not equivalent.
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What fraction of an hour is 24 minutes?
Give your answer in its simplest form
Answer:
Step-by-step explanation:
I hour = 60 minutes
So x hours = 24 minutes
to find x-->
Using the ratio method,
[tex]\frac{1}{60}[/tex] = [tex]\frac{x}{24}[/tex]
where x is the unknown number of hours we have to find.
After solving it, we get 60 * (x) = 24
we get x= 24/60
x= 0.4 hours
Hence, 24 mins is 4/10 of an hour.
In the simplest form--> x= 2/5