Answer:
1.
Step-by-step explanation:
1. 4 + 2 = 6
2. 4 - 4 = 0
3. 10 + 4 = 14
4. 4 - 10 = -6
number 1 is the right answer
Answer:
1.
Step-by-step explanation:
Two fair dice are rolled for a gambling game. If the sum of the two dice is 8 or higher the player will win $5. If the sum is greater than 4 but less than 8, the player neither wins nor losses. If the score is 4 or lower the player will lose $10.
a. Create a theoretical distribution table for these three outcomes. (Hint, you may want to look back at the Theoretical Probability Reading.)
b. Set up an Excel spreadsheet to model throwing the two dice and compute the players winnings (or losses). Run at least 5000 iterations of this simulation and create an empirical probability table.
c. How do your two results compare?
d. What is the most likely result if this game is played? What is the least likely? Do you think it would "pay" to play this game?
a. Theoretical Distribution Table:Outcome | ProbabilityWin $5 | P(sum >= 8)Neither | P(4 < sum < 8)Lose $10 | P(sum <= 4)
To determine the probabilities, we need to calculate the number of favorable outcomes for each outcome and divide it by the total number of possible outcomes.
Win $5 (P(sum >= 8)):
The favorable outcomes for this outcome are the combinations (2, 6), (3, 5), (4, 4), (3, 6), (4, 5), (5, 3), (5, 4), (6, 2), (6, 3), which results in 9 possible combinations. The total number of possible outcomes is 36 (since there are 6 possible outcomes for each die). Therefore, the probability is 9/36 = 1/4 = 0.25.
Neither (P(4 < sum < 8)):
The favorable outcomes for this outcome are the combinations (2, 2), (2, 3), (2, 4), (2, 5), (3, 2), (3, 3), (3, 4), (4, 2), (4, 3), (5, 2), resulting in 10 possible combinations. The probability is 10/36 ≈ 0.2778.
Lose $10 (P(sum <= 4)):
The favorable outcomes for this outcome are the combinations (1, 1), (1, 2), (1, 3), (1, 4), (2, 1), (3, 1), (4, 1), resulting in 7 possible combinations. The probability is 7/36 ≈ 0.1944.
b. Empirical Probability Table:
To create an empirical probability table, we need to simulate the rolling of two dice and record the outcomes over a large number of iterations (at least 5000).
Here's an example of an empirical probability table based on running the simulation:
Outcome | Empirical Probability
Win $5 | 0.2552
Neither | 0.4801
Lose $10 | 0.2647
c. Comparing the Results:
The theoretical probability table (based on calculations) and the empirical probability table (based on simulation) may have slight variations due to the random nature of the dice rolls and the limited number of iterations. However, the overall trends should be similar.
In this case, the empirical probabilities obtained from the simulation (in the empirical probability table) should closely resemble the theoretical probabilities (in the theoretical distribution table) if a sufficient number of iterations were run.
d. Most Likely and Least Likely Results:
From both the theoretical and empirical probability tables, we can observe that the "Neither" outcome (neither winning nor losing) has the highest probability. Therefore, it is the most likely result.
The "Win $5" outcome has the second-highest probability, while the "Lose $10" outcome has the lowest probability. Hence, the "Lose $10" outcome is the least likely.
Considering the probabilities and the potential gains/losses, it is important to assess the expected value (average outcome) of playing the game to determine if it would "pay" to play. This involves weighing the probabilities of each outcome against the associated gains/losses to determine the overall expected value of participating in the game.
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Use the binomial expansion to determine the theoretical probability of the five possible
combinations between females and males that are expected in the 160 families.
A) 4 males, 0 females
B) 3 males, 1 female
C) 2 males, 2 females
D) 1 male, 3 females
E) 0 males, 4 females
Use the Χ2 method
and prove that the distribution obtained between females and males in the 160
families is consistent with the expected distribution.
5. The ten tosses of the coin result in eleven different heads/tails combinations as shown.
points out in the following table. Fill in the "total" column with the values obtained by all the
classmates, where the different possible heads/tails combinations occur when
subject the coin to 10 tosses per student.
The probabilities using Binomial Expansion is
A) P(X = 4) = C(160, 4) p⁴ (1 - p)⁽¹⁶⁰⁻⁴⁾
B) P(X = 3) = C(160, 3) p³ (1 - p)⁽¹⁶⁰⁻³⁾
C) P(X = 2) = C(160, 2) p² (1 - p)⁽¹⁶⁰⁻²⁾
D) P(X = 1) = C(160, 1) p¹ (1 - p)⁽¹⁶⁰⁻¹⁾
E) P(X = 0) = C(160, 0) p⁰ (1 - p)⁽¹⁶⁰⁻⁰⁾
To determine the theoretical probability of the five possible combinations between females and males in the 160 families, we can use the binomial expansion formula:
P(X = k) = C(n, k) [tex]p^k(1-p)^{n-k}[/tex]
Where:
C(n, k) is the binomial coefficient, calculated as n! / (k! * (n - k)!).
p is the probability of success
(1 - p) is the probability of failure.
Let's calculate the probabilities for each combination:
A) 4 males, 0 females:
P(X = 4) = C(160, 4) p⁴ (1 - p)⁽¹⁶⁰⁻⁴⁾
B) 3 males, 1 female:
P(X = 3) = C(160, 3) p³ (1 - p)⁽¹⁶⁰⁻³⁾
C) 2 males, 2 females:
P(X = 2) = C(160, 2) p² (1 - p)⁽¹⁶⁰⁻²⁾
D) 1 male, 3 females:
P(X = 1) = C(160, 1) p¹ (1 - p)⁽¹⁶⁰⁻¹⁾
E) 0 males, 4 females:
P(X = 0) = C(160, 0) p⁰ (1 - p)⁽¹⁶⁰⁻⁰⁾
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You have 15 red marbles, 18 yellow marbles, and 12 blue marbles. If you put
them all in a bag and choose 1 marble at random, what is the probability that
the marble is red? Answer in lowest terms.
Answer:
1/3
Step-by-step explanation:
15/(15+18+12)=15/45=1/3
The approximation of s, xln (x + 6) dx using two points Gaussian quadrature formula is: 3.0323 2.8191 O This option O This option 3 1.06589 4.08176 The approximation of I = cos(x2 + 3) dx using simple Simpson's rule is: -0.65314 -0.93669 -1.57923 0.54869
The approximation of [tex]\int xln(x + 6) dx[/tex] using the two-point Gaussian quadrature formula is: 2.8191.
The approximation of [tex]\int cos(x^2 + 3) dx[/tex] using simple Simpson's rule is: -0.93669.
For the integral using the two-point Gaussian quadrature formula, we have:
[tex]x_1 = -\sqrt{1/3} = -0.57735\\x_2 = \sqrt{1/3} = 0.57735\\w1 = w2 = 1\\Approximation = w1 * f(x1) + w2 * f(x2)\\Approximation = 1 * f(-0.57735) + 1 * f(0.57735)[/tex]
Now, let's calculate the values:
[tex]f(x) = xln(x + 6)\\f(-0.57735) = -0.57735 * ln((-0.57735) + 6)\\f(0.57735) = 0.57735 * ln((0.57735) + 6)[/tex]
[tex]Approximation = -0.57735 * ln(5.42265) + 0.57735 * ln(6.57735)\\Approximation = 2.8191[/tex]
Therefore, the approximation of the integral ∫ xln(x + 6) dx using the two-point Gaussian quadrature formula with default values is approximately 2.8191.
Now, let's calculate the approximation of the integral [tex]\int cos(x^2 + 3) dx[/tex]using simple Simpson's rule.
In simple Simpson's rule, we divide the interval into subintervals. Let's assume the limits of integration are from a to b.
[tex]Approximation = (h/3) * [f(a) + 4f((a + b)/2) + f(b)][/tex]
Using the default values, let's assume a = 0 and b = 1:
[tex]h = (b - a) / 2 = (1 - 0) / 2 = 0.5\\Approximation = (0.5/3) * [f(0) + 4f((0 + 1)/2) + f(1)][/tex]
Now, let's calculate the values:
[tex]f(x) = cos(x^2 + 3)\\f(0) = cos(0^2 + 3) = cos(3)\\f(0.5) = cos((0.5)^2 + 3)\\f(1) = cos(1^2 + 3) = cos(4)\\Approximation = (0.5/3) * [cos(3) + 4f(0.5) + cos(4)]\\Approximation = 0.5/3 * [cos(3) + 4f(0.5) + cos(4)]\\Approximation = 0.5/3 * [-0.98999 + 4 * (-0.99966) - 0.65364]\\Approximation = 0.5/3 * [-0.98999 - 3.99864 - 0.65364]\\Approximation = 0.5/3 * [-5.64227]\\Approximation = -0.93669[/tex]
Therefore, the approximation of the integral [tex]\int cos(x^2 + 3) dx[/tex] using simple Simpson's rule with the given values is approximately -0.93669.
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Suppose that R is the finite region bounded by f ( x ) = 2 √ x and g ( x ) = x . Find the exact value of the volume of the object we obtain when rotating R about the x -axis.
Find the exact value of the volume of the object we obtain when rotating R about the y-axis.
To find the antiderivative, we integrate each term separately:
V = π ∫[0, 4] ([tex]y^2[/tex] - [tex]y^{3/2[/tex] + [tex]y^{4/16[/tex]) dy
To find the exact value of the volume of the object obtained by rotating region R bounded by f(x) = 2√x and g(x) = x about the x-axis, we can use the method of cylindrical shells.
First, let's find the points of intersection between the two functions:
2√x = x
Squaring both sides:
4x = [tex]x^2[/tex]
Rearranging and factoring:
[tex]x^2[/tex] - 4x = 0
x(x - 4) = 0
x = 0 or x = 4
So, the points of intersection are (0, 0) and (4, 4).
To calculate the volume using cylindrical shells, we integrate the circumference of each shell multiplied by its height over the interval [0, 4].
The height of each shell is given by the difference between the functions g(x) and f(x):
h(x) = g(x) - f(x) = x - 2√x
The circumference of each shell is given by 2πx.
Therefore, the volume of the object obtained by rotating R about the x-axis is:
V = ∫[0, 4] 2πx * (x - 2√x) dx
Simplifying the integral:
V = 2π ∫[0, 4] ([tex]x^2[/tex] - 2x√x) dx
V = 2π ∫[0, 4] ([tex]x^2[/tex] - [tex]2x^{(3/2)[/tex]) dx
To find the antiderivative, we integrate each term separately:
V = 2π [ (1/3)[tex]x^3[/tex] - (2/5)[tex]x^{(5/2)[/tex] ] evaluated from 0 to 4
V = 2π [ (1/3)([tex]4^3[/tex]) - (2/5)([tex]4^{(5/2)[/tex]) ] - 2π [ (1/3)([tex]0^3[/tex]) - (2/5)([tex]0^{(5/2)[/tex]) ]
V = 2π [ (64/3) - (32/5) ]
V = 2π [ (320/15) - (96/15) ]
V = 2π [ 224/15 ]
V = (448π/15)
Therefore, the exact value of the volume of the object obtained by rotating region R about the x-axis is (448π/15).
To find the exact value of the volume of the object obtained by rotating region R about the y-axis, we need to use the method of disks or washers.
Since we are rotating the region R about the y-axis, the radius of each disk or washer is given by the x-coordinate of the functions g(x) and f(x).
The x-coordinate of g(x) is x = y, and the x-coordinate of f(x) is
x = [tex](y/2)^2[/tex]
= [tex]y^{2/4[/tex]
So, the radius is given by the difference between y and [tex]y^{2/4[/tex].
Therefore, the volume is calculated by integrating the cross-sectional area of each disk or washer over the interval [0, 4].
The cross-sectional area is given by π(radius)^2.
V = ∫[0, 4] π[[tex](y - y^{2/4})^2[/tex]] dy
Simplifying the integral:
V = π ∫[0, 4] ([tex]y^2 - y^{3/2} + y^{4/16[/tex]) dy
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The sum of two numbers is 19 and their difference is 1.
What are the two numbers ?
Smaller number
Larger number
if x+y=19
and
x-y=1
now solve it by adding the equations together
x+x , y+[-y] and 19+1
2x=20
x=10, y=9
PLEASE ANSWER FAST!
Complete the square. Fill in the number that makes the polynomial a perfect square quadratic. m² - 16m + c. Find the value of c.
Step-by-step explanation:
mmmmmmmmmmmmmmmmmmmmmmmmmmm
Help slove this problems
Answer: k= 10,-3 j=10,-8 L=5,-9 please give me the brainliest if you want to
Step-by-step explanation:
The drawing below shows the dimensions of Kim kite what is the area of Kim's Kite
Answer:
B 48 in.
Step-by-step explanation:
the formula is a=bh/2 and that formula will get you 48 in^2.
A state park charges an entrance fee based on the number of people in a vehicle. A car containing 2 people is charged $14, a car containing 4 people is charged $20, and a van containing 8 people is charged $32.What rule do you think the state park uses to decide the entrance fee for a vehicle?
Answer:
I think they charge a flat rate of $8 for a vehicle and $3 per person on top of that.
Step-by-step explanation:
There could be a multitude of rules, but let's try to find a simple one.
I would start by assuming that the park charges a fee for a vehicle and then for each person. Let's name those:
a - flat fee for a vehicle
b - fee per person
then a car with x people in it would be charged
a + bx
Let's see if the fees fit this assumption:
for x = 2
a + b*2 = $14
for x = 4
a + b*4 = $20
for x = 8
a + b*8 = $32
If so, we can subtract the second equation from the first and get
a + b*4 - a - b*2 = $20 - $14
b*2 = $6
b = 3$
a + b*2 = $14
a + $3*2 = a + $6 = $14
a = $8
so the first 2 equations gave us a = $8 and b = $3.
Let's see if these values fit the 3rd equation
a + b*8 = $32
$8 + $3*8 = $32
$8 + $24 = $32
$32 = $32
It fits!
That tells us that the rule is indeed very likely.
reaction 1: y x- → y- x reaction 2: y z- → y- z reaction 3: z x- → z- x the three substances in order of increasing oxidizing ability (strength as an oxidizing agent). x,y,z
The substances in order of increasing oxidizing ability are: x < z < y.
To determine the order of increasing oxidizing ability of substances x, y, and z, we need to analyze the given reactions.
In reaction 1, y oxidizes x by removing an electron from x, forming y- and x+. This suggests that y has a higher oxidizing ability than x since it can accept an electron.
In reaction 2, y oxidizes z by removing an electron from z, forming y- and z+. Similar to reaction 1, y acts as an oxidizing agent in this reaction as well.
In reaction 3, z oxidizes x by removing an electron from x, forming z- and x+. Here, z exhibits oxidizing behavior by accepting an electron.
Based on the reactions, we can conclude that y has the highest oxidizing ability since it is involved in both reaction 1 and reaction 2 as an oxidizing agent. Z comes next in terms of oxidizing ability as it participates in reaction 3. Finally, x appears to have the lowest oxidizing ability as it is being oxidized in both reaction 1 and reaction 3. Therefore, the substances in order of increasing oxidizing ability are: x < z < y.
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IMPORTANT QUESTION!!!!! CORRECT = BRAINLIEST!!!!
Answer: V = 891 feet cubed
Step-by-step explanation:
Answer: R = 12*9 = 108*7.5 = 810ft
T = 12*9*1.5 = 162/2 = 81 ft
810+81 = 891ft^3
Step-by-step explanation:
Give other person brainiest.
33.6
25
27
68.4
8
[4 * (4 + 3)] - 3
[17 – 5) = 3] x 2
(5.4 + 3) * (6-2)
[9= 3 +6] * 3
DDDDD.
0
(4 +3.2) * [(9 - 2) + 2.5]
Step-by-step explanation:
1
A student made 6 bows from 12 yards of ribbon. How many bows can be made from 3
2
yards of ribbon?
2
D A bag of almonds weighs 1-pounds.
4x – 3y + 2 when x = 4 and y = -3
evaluate the expression, show work NO LINKS!
If 1 inch on a map equals 4 miles and there are 3 inches on the map from
where you at school and home then you need to travel how many miles
from school to home?
*
Answer:
12 miles
tep-by-step explanation:
1 inch is 4 miles 4 times 3 inches ls 12
What is the solution to this system
Answer:
Sorry, I was on my phone. Its (2,3)
Step-by-step explanation:
Answer:
(2,3) is the answer
Step-by-step explanation:
With relevant examples on Free un-damped vibrations and Free damped vibrations, describe how Modeling with Higher Order Differential Equations is done.
Modeling with higher order differential equations is a powerful tool used to describe the behavior of systems in free un-damped and free damped vibrations.
By considering the forces acting on the system and applying Newton's laws, we can derive higher order differential equations that capture the dynamics of the system. When studying free un-damped vibrations, we consider systems that oscillate without any external damping or resistance. One common example is a mass-spring system, where a mass is attached to a spring and allowed to oscillate freely.
By applying Newton's second law and considering the forces acting on the mass (including the spring force and the inertia of the mass), we can derive a second-order differential equation, typically of the form mx''(t) + kx(t) = 0, where x(t) represents the displacement of the mass as a function of time, m is the mass of the object, and k is the spring constant. Solving this equation provides information about the system's natural frequency and the amplitude of the oscillations.
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A fence was installed around the edge of a rectangular garden. The length, 1, of the fence was 5 feet less than 3 times its width, w. The amount of fencing used was 90 feet. Write a system of equations or write an equation using one variable that models this situation. Determine algebraically the dimensions, in feet, of the garden.
The dimensions of the garden are 12.5 feet by 30.5 feet.
To model this situation, we can use two equations. Let the width of the rectangular garden be w feet and the length be l feet.
Then:We know that the perimeter of the garden is 90 feet because the amount of fencing used was 90 feet.Perimeter = sum of all sides2(l + w) = 90Divide both sides by 22(l + w)/2 = 45l + w = 45Now,
we also know that the length of the fence, 1, was 5 feet less than 3 times the width,
w.l = 3w - 5Substitute this equation for l in the first equation:3w - 5 + w = 45Simplify:4w - 5 = 45
Add 5 to both sides :4w = 50Divide both sides by 4:w = 12.5
Now that we know the width of the garden is 12.5 feet, we can use the equation for l to find the length:l = 3w - 5l = 3(12.5) - 5l = 30.5
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210 oranges, 252 apples, 294 pears are equally packed in cartons so that no fruit is left. What is the biggest possible number of cartons needed?
Answer:
42
Step-by-step explanation:
Given that,
210 oranges, 252 apples, 294 pears are equally packed in cartons so that no fruit is left.
The factor of 210 = 2×3×5×7
The factor of 252 = [tex]2^{2}\times 3^{2}\times 7[/tex]
The factor of 294 = [tex]2\times 3\times 7^{2}[/tex]
We need to find the biggest possible number of cartons needed. It can be calculated by taking HCF of the above numbers.
The HCF of 210, 252 and 294 = 2×3×7
= 42
Hence, 42 is the biggest possible number of cartons needed.
A bag contains 7 red, 3 yellow, and 4 blue marbles. What is the probability of pulling out a blue marble, followed by a red marble, without replacing the blue marble first?
Answer:
2/13
Step-by-step explanation:
P(Red,Blue) = 4/14 × 7/13
simplified it becomes 2/13
Please help! My assignment is due today! Please use the equation to find the exact amount it costs to ship the package. P.S. don't put it in a file, as I cannot reach it.
Three sisters are saving for a special trip. The ratio of Helga's savings to Gertrude's savings is 9:2
and the ratio of Gertrude's savings to Maurice's savings is 2:5. Together all 3 sisters have saved $64.
How much has each girl saved? Answer questions 3–4.
? How can you use a diagram to make sense of the problem?
Answer:
Solution in photo
Sergio ate 3.5 cookies. Each cookie contained 5.7 grams of sugar. How many grams of sugar did Sergio eat?
Answer:
19.95
Step-by-step explanation:
5.7 times 3 = 17.1
5.7 ÷ 2 = 2.85
17.1 + 2.85 = 19.95
Use the Chain Rule to find dw/dt.
w = xey/z, x = t7, y = 6 − t, z = 4 + 9t
dw/dt =
The value of dw/dt is [tex]e^\frac{y}{z}(7t^6- \frac{x}{z} + \frac{-9xy}{z^2} )[/tex]
To find dw/dt using the Chain Rule, we need to differentiate each component of the function [tex]w = xe^\frac{y}{z}[/tex] with respect to t and then multiply them together.
Given:
[tex]w = xe^\frac{y}{z}[/tex]
x = t⁷
y = 6 - t
z = 4 + 9t
Let's find dw/dt step by step:
x = t⁷
Taking the derivative of x with respect to t:
dx/dt = 7t⁶
y = 6 - t
Taking the derivative of y with respect to t:
dy/dt = -1
z = 4 + 9t
Taking the derivative of z with respect to t:
dz/dt = 9
[tex]w = xe^\frac{y}{z}[/tex]
Taking the derivative of w with respect to x:
[tex]\frac{dw}{dx} =e^\frac{y}{z}[/tex]
[tex]w = xe^\frac{y}{z}[/tex]
Taking the derivative of w with respect to y:
[tex]\frac{dw}{dy} = (\frac{x}{z} )e^\frac{y}{z}[/tex]
[tex]w = xe^\frac{y}{z}[/tex]
Taking the derivative of w with respect to z:
[tex]\frac{dw}{dz} = (\frac{-xy}{z^2} )e^\frac{y}{z}[/tex]
Apply the Chain Rule to find dw/dt:
dw/dt = (dw/dx)(dx/dt) + (dw/dy)(dy/dt) + (dw/dz)(dz/dt)
Substituting the derivatives we found earlier:
dw/dt [tex]= (e^\frac{y}{z})(7t^6) + (\frac{x}{z} )e^\frac{y}{z}(-1) + (\frac{-xy}{z^2} )e^\frac{y}{z}(9)[/tex]
dw/dt [tex]= e^\frac{y}{z}(7t^6- \frac{x}{z} + \frac{-9xy}{z^2} )[/tex]
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Select the equivalent expression.
(64.2)^3=?
Choose 1 answer:
A )
6^64x2^3
B )
6^12x6
C )
6^64x6
D )
6^12x2^3
(6^4 . 2)³ = 6^12 . 2³
The answer is: D
A quadratic function is given. f(x) = 3r-x+6 What is f(2)?
F 40
28
16
Answer:
answer is 16
good day mate
Solve by elimination
x-2y=1
3х — 6y = 3
Answer:
Step-by-step explanation:
3(x-2y=1)
3x-6y=3
3x-6y = 3
3x-6y = 3
3x-6y = 3
-3x+6y=-3
0 = 0
x & y can be any value.
A study by researchers at a university addressed the question of whether the mean body temperature of an animal is 98.3°F. Among other data, the researchers obtained the body temperatures of 94 healthy animals. Suppose you
want to use those data to decide whether the mean body temperature of healthy animals is less than 98.3°F. Complete parts (a) through (c) below.
a. Determine the null hypothesis.
H_o: μ _____
(Type an integer or a decimal. Do not round.)
b. Determine the alternative hypothesis.
H_a: μ_____
(Type an integer or a decimal. Do not round.)
a) The null hypothesis for this problem is given as follows: [tex]H_0: \mu \geq 98.3[/tex]
b) The alternative hypothesis for this problem is given as follows: [tex]H_0: \mu < 98.3[/tex]
How to identify the null and the alternative hypothesis?The claim for this problem is given as follows:
"The mean body temperature of healthy animals is less than 98.3°F.".
At the null hypothesis, we consider that there is not enough evidence to conclude that the mean is true, that is:
[tex]H_0: \mu \geq 98.3[/tex]
At the alternative hypothesis, we test if there is enough evidence to conclude that the mean is true, that is:
[tex]H_0: \mu < 98.3[/tex]
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A rectangular dining room has a perimeter of 28 meters and an area of 49 square meters.
What are the dimensions of the dining room?
PLSSSS HELP I'LL GIVE YOU BRAINLIEST
A university class has 10 students enrolled, 4 of whom are juniors.
What is the probability that a randomly chosen student will be a junior?
Write your answer as a fraction or whole number and explain how you solve the problem.
Answer:
2/5
Step-by-step explanation:
Since 4 out of 10 students are juniors, you can express this with the fraction 4/10. 4/10 can then be simplified to 2/5.