Answer:
If the value of our test statistics is less than the critical value of t at 7 degrees of freedom at a 10% level of significance for the right-tailed test (which is 1.415), then we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region.
If the value of our test statistics is more than the critical value of t at 7 degrees of freedom at a 10% level of significance for the right-tailed test (which is 1.415), then we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.
Step-by-step explanation:
We are given that the means of two populations using paired observations. Suppose that [tex]\bar D[/tex] = 3.125, [tex]s_D[/tex] = 2.911, and n = 8, and that you wish to test the hypothesis below at the 10% level of significance.
Let D = difference between the two paired observations.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu_D[/tex] = 0
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu_D[/tex] > 0
The test statistics that would be used here is Paired t-test for dependent samples;
T.S. = [tex]\frac{\bar D-\mu_D}{\frac{s_d}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar D[/tex] = 3.125, [tex]s_D[/tex] = 2.911, and n = 8
The decision rule for rejecting the null hypothesis in the given hypothesis test would be;
If the value of our test statistics is less than the critical value of t at 7 degrees of freedom at a 10% level of significance for the right-tailed test (which is 1.415), then we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region.If the value of our test statistics is more than the critical value of t at 7 degrees of freedom at a 10% level of significance for the right-tailed test (which is 1.415), then we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.what is the cross section if i Move the intersecting plane of a cylinder parallel to the verticle axis
Answer:
A horizontal cross-section is obtained when the plane that passes through the solid object is parallel to its base. On the other hand, a vertical cross section is found when the intersecting plane is perpendicular to the base of the solid. These are known as a parallel cross-section and perpendicular cross section.
Step-by-step explanation:
What is the missing term that makes these ratios equivalent? 1.5:3, 31.5:____
=========================================
Work Shown:
1.5/3 = 31.5/x
1.5x = 3*31.5 cross multiply
1.5x = 94.5
x = 94.5/1.5 dividing both sides by 1.5
x = 63
-----------
An alternative equation to solve is
1.5/31.5 = 3/x
1.5x = 31.5*3
1.5x = 94.5
The remainder of the steps are the same as in the previous section above.
Biologists stock a lake with 160
160
fish, and estimate the carrying capacity of the lake to be 9100
9100
fish. The number of fish tripled in the first year.
(a) Assuming that the fish population satisfies logistic growth, the fish population can be modeled by:()=/[1+55.875−1.13506]
From the given information about this population, determine the constant
that completes the model.
Answer:
[tex]P ( t ) = \frac{9100.024}{1 + 55.875e^-^1^.^1^3^5^0^6^*^t}[/tex]
Step-by-step explanation:
Solution:-
- We are given a logistic growth model of the fish population cultured. The logistic growth of fish population is modeled by the following equation:
[tex]P ( t ) = \frac{c}{1 + 55.875e^-^ 1^.^1^3^5^0^6^t}[/tex]
Where, c: the constant to be evaluated.
- We are given the initial conditions for the model where at t = 0. The initial population was given to be:
t = 0 , Po = 160
N ( carrying capacity ) = 9100
- After a year, t = 1. The population was tripled from the initial value. That is P ( 1 ) = Po*3 = 160*3 = 480.
- We will use the given logistic model and set P ( 1 ) = 480 and determine the constant ( c ) as follows:
[tex]P ( 1 ) = \frac{c}{1 + 55.875e^-^ 1^.^1^3^5^0^6^*^1} = 480\\\\c = 480* [ 1 + 55.875e^-^ 1^.^1^3^5^0^6]\\\\c = 9100.024[/tex]
- The complete model can be written as:
[tex]P ( t ) = \frac{9100.024}{1 + 55.875e^-^1^.^1^3^5^0^6^*^t}[/tex]
Find the exact values of sin 2θ and cos 2θ for cos θ = 6/13
Answer:
Step-by-step explanation:
cos^-1(6/13)=62.5136°
sin(2*62.5136°)=0.8189
cos(2*62.5136°)=-0.5740
Drag each tile to the correct box. Order the expressions from least value to greatest value . -3 3/10 - ( -7/20 ), 5/-1.6, 5 6/15 + ( -2 4/5 ), -4.5 x -2.3
Answer:
B A C D
Step-by-step explanation:
Your calculator can tell you the values of these expressions. In the order given, they are ...
-3 3/10 -(-7/20) = -2.955/-1.6 = -3.1255 6/15 +(-2 4/5) = 2.6-4.5×-2.3 = 10.35We hope you have no trouble recognizing that swapping the first two expressions will put them all in increasing order.
-3 3/10 -(-7/20) = -2.95
5/-1.6 = -3.125
5 6/15 +(-2 4/5) = 2.6
-4.5×-2.3 = 10.35
Recall the scenario about Eric's weekly wages in the lesson practice section. Eric's boss have been very impressed with his work. He has given him a $2 raise and now Eric earns $12 an hour. His boss also has increased Eric's hours to 10 to 25 hours per week. The restrictions remain the same; he needs to work a full-hour in order to get the hourly wage working 1.5 hour does not pay him for 1.5 hours but for one hour. Tasks: Consider the scenario and restrictions and interpret the work hour and potential earning relation as a function. Express the relation in the following formats: 1. Function equation 2. Domain of the function in the set notation (Would domain (work hours) be infinite?(write the domain in the set notation) 3. Range of the function in the set notation (Would the range (weekly wage) be infinite(write the range in the set notation) 4. Sketch the function and plot the points for his earnings.
Answer:
[tex]1)\quad f(x)=\bigg\{\begin{array}{ll}12x&0\leq x <9\\18x-48&9\leq x \leq 24\end{array}[/tex]
2) D: x = [0, 24]
3) R: y = [0, 384]
4) see graph
Step-by-step explanation:
Eric's regular wage is $12 per hour for all hours less than 9 hours.
The minimum number of hours Eric can work each day is 0.
f(x) = 12x for 0 ≤ x < 9
Eric's overtime wage is $18 per hour for 9 hours and greater.
The maximum number of hours Eric can work each day is 24 (because there are only 24 hours in a day).
f(x) = 18(x - 8) + 12(8)
= 18x - 144 + 96
= 18x - 48 for 9 ≤ x ≤ 24
The daily wage where x represents the number of hours worked can be displayed in function format as follows:
[tex]f(x)=\bigg\{\begin{array}{ll}12x&0\leq x <9\\18x-48&9\leq x \leq 24\end{array}[/tex]
2) Domain represents the x-values (number of hours Eric can work).
The minimum hours he can work in one day is 0 and the maximum he can work in one day is 24.
D: 0 ≤ x ≤ 24 → D: x = [0, 24]
3) Range represents the y-values (wage Eric will earn).
Eric's wage depends on the number of hours he works. Use the Domain (given above) to find the wage.
The minimum hours he can work in one day is 0.
f(x) = 12x
f(0) = 12(0)
= 0
The maximum hours he can work in one day is 24 (although unlikely, it is theoretically possible).
f(x) = 18x - 48
f(24) = 18(24) - 48
= 432 - 48
= 384
D: 0 ≤ y ≤ 384 → D: x = [0, 384]
4) see graph.
Notice that there is an open dot at x = 9 for f(x) = 12x
and a closed dot at x = 9 for f(x) = 18x - 48
f(x)= x^2– 3x + 9
g(x) = 3x^3+ 2x^2– 4x – 9
Find (f - g)(x).
Answer:
[tex]\large \boxed{\sf \ \ -3x^3-x^2+x+18 \ \ }[/tex]
Step-by-step explanation:
Hello, please consider the following.
[tex](f-g)(x)=f(x)-g(x)=x^2-3x+9-(3x^3+2x^2-4x-9)\\\\=x^2-3x+9-3x^3-2x^2+4x+9\\\\=\boxed{-3x^3-x^2+x+18}[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
When 394 Beach Boys fans were surveyed, 113 said that California girls was their fav song. Find a point estimate for the true proportion of BB fans who favor that song??
1. 0.713
2. 113
3. 0.287
4. 0.95
5. None of the above
Answer: 3. 0.287
Step-by-step explanation:
Let p be the true proportion of BB fans who favor that song.
As per given, Sample size for survey of Beach Boys fans = 394
Number of Beach Boys fans said that California girls was their fav song = 113
Then, the sample proportion of BB fans who favor that song: [tex]\hat{p}=\dfrac{113}{394}[/tex]
[tex]=0.286802030457\approx0.287[/tex]
Since sample proportion is the best estimate for the true proportion.
Hence, a point estimate for the true proportion of BB fans who favor that song is 0.287.
So, the correct option is 3. 0.287 .
Tom determines that the system of equations below has two solutions, one of which is located at the vertex of the parabola. Equation 1: (x – 3)2 = y – 4 Equation 2: y = -x + b In order for Tom’s thinking to be correct, which qualifications must be met?
Answer:
b=7
Step-by-step explanation:
Answer:
b must equal 7 and a second solution to the system must be located at the point (2, 5).
Step-by-step explanation:
i got it right on the test
What is the value of s in the equation 3 r equals 10 plus 5 s, when r equals 10? 4 8 100 200
Answer
4Step-by-step explanation:
Given,
r = 10
Let's create an equation,
[tex]3r = 10 + 5s[/tex]
plugging the value of r
[tex]3 \times 10 = 10 + 5s[/tex]
Multiply the numbers
[tex]30 = 10 + 5s[/tex]
Move 5s to L.H.S and change its sign
Similarly, Move 30 to R.H.S and change its sign.
[tex] - 5s = 10 - 30[/tex]
Calculate
[tex] - 5s = - 20[/tex]
The difference sign ( - ) should be cancelled on both sides
[tex]5s = 20[/tex]
Divide both sides of the equation by 5
[tex] \frac{5s}{2} = \frac{20}{5} [/tex]
Calculate
[tex]s = 4[/tex]
The value of s is 4.
Hope this helps..
Best regards!!
Answer:
A. 4 (on edgenuity)
Step-by-step explanation:
The population of Oak Forest is increasing at a rate of 4% per year. If the population is 74,145 today, what will it be in three years?
Answer:
83,403
Step-by-step explanation: Take 74,145 and multiply it by 4%. Then take that number and add it to the 74,145 and that'll give you year one. For year 2 you'll take your total from year 1 and multiply it by the 4% growth rate then you'll add the 4% to what your ending from year 1 and that'll give you your total growth after 2 years. Then you'll take your ending total from year 2 and multiply it by 4% and then you'll add that 4% to the total end from year 2 and that'll give you your total growth of 4% every year for 3 consecutive years.
Hope this helps!
solve the inquality 1/2*<10
Answer:
[tex]\boxed{x<20}[/tex]
Step-by-step explanation:
[tex]\frac{1}{2} x<10[/tex]
Multiply both sides by 2.
[tex]x<20[/tex]
a scale drawing of a rectangular playground has a length of 20 inches and a width of 10 inches as shown below. the scale is 1 inch = 4 feet. what is the area of the actual playground? *
Answer:
3,200 ft²
Step-by-step explanation:
first you want to convert the sides from inches to feet so 20* 4= 80, and 10* 4= 40 then you multiply the sides to get the area which is 80*40= 3,200 ft²
Monica’s school band held a car wash to raise money for a trip to a parade in New York City. After washing 125 cars, they made $775 from a combination of $5.00 quick washes and $8.00 premium washes. This system of equations models the situation. x + y =125 5x + 8y = 775
Answer:
[tex] x+y = 125[/tex] (1)
[tex] 5x+8y = 775[/tex] (2)
We can solve for y from equation (1) and we got:
[tex] y = 125-x[/tex] (3)
And replacing (3) into (2) we got:
[tex] 5x +8(125-x) = 775[/tex]
And solving for x we got:
[tex] 1000-3x = 775[/tex]
[tex] 3x= 225[/tex]
[tex] x=75 [/tex]
And solving for y from (3) we got:
[tex] x= 125-75 =50[/tex]
And the solution would be x = 50 and y =75
Step-by-step explanation:
For this problem we have the following system of equations:
[tex] x+y = 125[/tex] (1)
[tex] 5x+8y = 775[/tex] (2)
We can solve for y from equation (1) and we got:
[tex] y = 125-x[/tex] (3)
And replacing (3) into (2) we got:
[tex] 5x +8(125-x) = 775[/tex]
And solving for x we got:
[tex] 1000-3x = 775[/tex]
[tex] 3x= 225[/tex]
[tex] x=75 [/tex]
And solving for y from (3) we got:
[tex] x= 125-75 =50[/tex]
And the solution would be x = 50 and y =75
Solve the system for x. x+y+z=5 2x-y-z=-2 2x=10
Answer:
x = 1.
Step-by-step explanation:
x + y + z = 5
2x - y - z = -2
3x = 3
x = 1
Hope this helps!
The simple interest on a sum of money invested at 5% per annum for 3 years was $90. The sum of money invested was
Answer:
Sum of money = $600
Step-by-step explanation:
X = sum of money
Simple interest means that its the same percentage of interest for a given number of years.
The interest per annum is 5% for 3 years, so 5% x 3 = 15%
15% = 0.15 (as a decimal)
Now, we can put this into an equation:
0.15x = 90
x = 90 / 0.15
x = 600.
sum of money invested = $600
Identify the CRITICAL VALUES(S) used in a hypothesis test of the following claim and sample data:
Claim: "The proportion of defective tablets manufactured in this factory is less than 6%."
A random sample of 500 tablets from this factory is selected, and it is found that 20 of them were defective. Test the claim at the 0.05 significance level.
a. -1.883
b. -1.645
c. -1.96
d. -0.102
Answer:
-1.96
Step-by-step explanation:
Significance level or alpha level is the probability of rejecting the null hypothesis when null hypothesis is true. It is considered as a probability of making a wrong decision. It is a statistical test which determines probability of type I error. If the obtained probability is equal of less than critical probability value then reject the null hypothesis. In this question the sample of 500 defective tablets is under test. 20 tablets found to be defective so the null hypothesis is accepted as less than 6% of tablets are defective.
What is the vertex, domain and the range? PLEASE HELP I’m really stuck!
Answer:The vertex, or turning point, is at (1, 4). From the graph, you can see that f(x) ≤ 4. Answer. The domain is all real numbers, and the range is all real numbers f(x) such that f(x) ≤ 4.
Step-by-step explanation:
I really hope this helped! :)
Which is steeper: a road with a 12% grade or a road with a pitch of 1 in 8?
Answer:
A road with a pitch of 1 in 8 is steeper.
Step-by-step explanation:
Let us convert these to the same units so that we can better compare them.
[tex]\frac{1}{8} = 0.125[/tex]
0.125=12.5 %
As 12.5% is greater than 12%, the road with a pitch of 1 in 8 will be steeper.
someone could help me?
Answer:
Step-by-step explanation:
From 6 to 9 is 3 units, the horizontal distance between C and D. From 4 to 5 is 1 unit, the vertical distance between C and D.
Using the Pythagorean Theorem (or the closely related distance formula), we find the distance between C and D as follows:
distance between C and D: sqrt(3^2 + 1^2) = sqrt(10)
What is the list price of an article that is subject to discounts of 334 %, 10%, and 2%
if the net price is $564.48?
A record club has found that the marginal profit, Upper P prime (x ), in cents, is given by Upper P prime (x )equals negative 0.0008 x cubed plus 0.35 x squared plus 45.5 x for x less than or equals 400, where x is the number of members currently enrolled in the club. Approximate the total profit when 240 members are enrolled by computing the sum
Answer:
The total profit when 240 members are enrolled is:
3,587,212.8 cents
Step-by-step explanation:
First of all, the total profit function is gotten by integrating the marginal profit function.
Integrate thus:
Total Profit = P(x) = [-0.0008x^4 ÷ 4] + [0.35x^3 ÷ 3] + [45.5x^2 ÷ 2]
P(x) = 0.0002x^4 + 0.1167x^3 + 22.75x^2
Next, substitute 240 for x, in the total profit function.
P(x) = 0.0002[240]^4 + 0.1167[240]^3 + 22.75[240]^2
P(x) = 663552 + 1613260.8 + 1310400
P(x) = 3,587,212.8 cents
Equivalent to $35,872.128
Help with finding the slope of the line and graph find the slope 1.) (1, 6) (3,8) 2.) (7,10) (5,6) 3.) (1,-2) (3,4) 4.) (10,5) (4,7) 5.) (-2,6) (0,5) 6.) (-9,9) (7,5) 7.) (-3, 5) (0,0) (8, 10) (-7, 14) 9.) (-12, -5) (0, -8)
Answer:
1 is 1.
2 is 2.
3 is 3. (this is not a joke, keep going)
4 is -1/3.
5 is -1/2.
6 is -1/4.
7 is -5/3.
8 is -4/15, if you meant that the points are (8,10) and (-7,14). You might have typed wrong.
9 is -1/4.
10 is 1/3. Take a look at it. It goes up by 1 and it goes over 3. 1 divided by 3 is 1/3.
11 is 1. It rises 2 and goes across by 2. 2 divided by 2 is 1.
12 is -3/4, because it goes down 3 and over 4.
13 is -3/2. Do you see why?
14 is 1. It's super easy, since it only goes up 1 and over 1.
15 is easy. You have to figure this one out, but I'll give you a hint. It goes down by 3 .
Please answer this correctly without making mistakes
Answer:
14.3 km
Step-by-step explanation:
Using the paths shown, we would need to add the path length from Belmont to Yardley and Yardley to Oxford. When we add 8.5 and 5.8, we get 14.3 km.
Hence,
the distance from Belmont to Oxford is 14.3 km.
Hope this helps!!! PLZ MARK BRAINLIEST!!!
Help me with this please anyone
Answer:
B. [tex] -3x [/tex]
Step-by-step explanation:
In algebra, a term could be a single negative or positive number (constant), a variable or a variable with a coefficient. It could also be 2 variables multiplied together.
The algebraic expression [tex] -3x - 7(x + 4) [/tex] , can be expanded and expressed as:
[tex] -3x - 7(x) -7(+4) [/tex]
[tex] -3x - 7x - 28 [/tex]
The three terms are: [tex]-3x, - 7x, -28[/tex]
Therefore, from the given answer choices, the term that is a term in the expression, [tex] -3x - 7(x + 4) [/tex] , is B. [tex] -3x [/tex]
SOMEONE PLEASE HELP ME!!! I REALLY NEED SOME HELP!!!
Which of the following points is a solution of the inequality y < - lxl?
A. (1, -2)
B. (1, -1)
C. (1, 0)
Answer:
A. (1, -2)
Step-by-step explanation:
We can substitute the variables of x and y into the inequality of [tex]y < -|x|[/tex].
Let's start with A, -2 being y and 1 being x.
[tex]-2 < - |1|[/tex]
The absolute value of 1 is 1, and negating that gets us -1.
[tex]-2 < -1[/tex]
Indeed, -2 is less than -1! So A is a solution to the inequality.
Let's test the rest of them, just in case.
For B:
[tex]-1 < -|1|[/tex]
Absolute value of 1 is 1, negating it is -1.
[tex]-1<-1[/tex]
-1 is EQUAL to -1, not less than it, so is not a solution to the inequality.
Let's try C.
[tex]0 < -|1|[/tex]
Absolute value of 1 is 1, negating it is -1.
[tex]0 < -1[/tex]
0 is GREATER than -1, so that is not a solution to the inequality.
Hope this helped!
Need answers ASAP!!!! (due today)
Answer:
6. 156.6 cm
7. 687.7’
Step-by-step explanation:
45 cm and 150 cm are the legs of one triangle.
The longest side is the hypotenuse.
Apply Pythagorean theorem, since the two triangles are right triangles.
a² + b² = c²
a and b are the legs, c is the hypotenuse.
45² + 150² = c²
24525 = c²
√24525 = c
c = 156.604597634...
c ≈ 156.6
Brain hang-glided from a 520’ high cliff. He landed 450’ away from the base of the cliff. Create a right triangle and apply Pythagorean theorem. The distance he travelled is the hypotenuse of the triangle. The 520’ and 450’ are the legs.
a² + b² = c²
450² + 520² = c²
c² = 472900
c = √472900
c = 687.677249878...
c ≈ 687.7
Answer: 6) =approx 156.60 cm
7) =approx 687.68'
Step-by-step explanation:
6. Let the shortest side of the triangle is AB=45 cm ( ∡A=90° so ABCD is a rectangle). The middle side AD=150 cm. The longest side is BD
The length of BD can be calculated using Phitagore theorem because triangle BAD ia right angle.
BD=sqrt(AD²+AB²)=sqrt(2025+22500)=approx 156.60 cm
7. So we can create the model of the situation described in this problem.
The model is right-angle triangle ABC with side AB=520' ,side AC=450', right angle is A. So we have to find the length of side BC .
BC is hypotenuse of triangle ABC. We can find it using Phitagore theorem again.
BC=sqrt(AC²+AB²)=sqrt(450²+520²)=sqrt(472900)=approx 687.68'
For the following information, determine whether a normal sampling distribution can be used, where p is the population proportion, is the level of significance, p is the sample proportion, and n is the sample size.
Claim: p >=0.28; α:0.08. Sample statistics: p=0.20, n= 180
Required:
If a normal sampling distribution can be used, decide whether to reject or fail to reject the null hypothesis and interpret the decision.
Answer:
The Central Limit Theorem says that if the sample size is more than 30, the data follows a normal sampling distribution. Since the sample size is 180, and that is more than 30, a Normal sampling distribution can be used.
Since a normal sampling distribution can be used, we should FAIL TO REJECT the null hypothesis because p = 0.20, which is more than the significance level of α = 0.08. There is NOT sufficient evidence to suggest that the alternative hypothesis is true.
Hope this helps!
The triangles are similar. Write a similarity statement for the triangles.
Answer:
Option (2)
Step-by-step explanation:
In the two triangles ΔWVZ and ΔYXZ,
If the sides WV and XY are parallel and the segments WY and VX are the transverse.
∠X ≅ ∠V [Alternate angles]
∠W ≅ ∠Y [Alternate angles]
Therefore, ΔWVZ ~ ΔYXZ [By AA postulate of the similarity]
Option (2) will be the answer.
You have 50 each of the following kinds of jellybeans: red, orange, green, yellow. The jellybeans of each color are identical. How many different handfuls of 12 jellybeans are possible?
Answer:
There are 455 different handfuls of 12 jellybeans possible
Step-by-step explanation:
From the given information;
we are told that there exist 50 kinds of jellybean for each of these colors (red, orange, green, yellow)
Also the jellybeans of each color are identical.
i.e Let say y represent the color of the jellybean.
Then y₁ = y₂ = y₃ = y₄ corresponds to each of these colors (red, orange, green, yellow)
The objective is to determine how many different handfuls of 12 jellybeans are possible?
So;
y₁ + y₂ + y₃ + y₄ = 12
Therefore; the number of different handfuls of 12 jellybean possible can be computed by using the formula:
[tex]C(r+k-1,r) = \dfrac{(r+k-1)!}{r! (k-1)!}[/tex]
where;
r =12 jellybeans
k = 4 types of colors
[tex]C(12+4-1,4) = \dfrac{(12+4-1)!}{12! (4-1)!}[/tex]
[tex]C(15,4) = \dfrac{15!}{12! (3)!}[/tex]
[tex]C(15,4) = \dfrac{15\times 14 \times 13 \times 12!}{12! (3)!}[/tex]
[tex]C(15,4) = \dfrac{15\times 14 \times 13 }{3!}[/tex]
[tex]C(15,4) = \dfrac{15\times 14 \times 13 }{3 \times 2 \times 1}[/tex]
[tex]C(15,4) =5\times 7 \times 13[/tex]
[tex]C(15,4) =455[/tex]
There are 455 different handfuls of 12 jellybeans possible
There are [tex]455[/tex] different handfuls of [tex]12[/tex] jellybeans that are possible.
Probability:
Probability is termed as the possibility of the outcome of any random event. The meaning of this term is to check the extent to which any event is likely to happen. The probability formula is determined as the possibility of an event to happen is equal to the ratio of the number of outcomes and the total number of outcomes.
Given information are:
There are exist of [tex]50[/tex] kinds of jellybean of different colors i.e. red, orange, green, yellow.
The jellybeans of each color are identical.
i.e Let say [tex]y[/tex] represent the color of the jellybean.
Then [tex]y_1=y_2=y_3=y_4[/tex] corresponds to each of these colors (red, orange, green, yellow)
So,
[tex]y_1+y_2+y_3+y_4=12[/tex]
Therefore, the number of different handfuls of [tex]12[/tex] jellybean possible can be computed by using the formula:
[tex]C\left ( r+k-1,r \right )=\frac{\left (r+k-1 \right )!}{r!\left ( k-1 \right )!}[/tex]
where,
[tex]r=12[/tex] jellybeans
[tex]k=4[/tex] types of colors
[tex]C\left ( 12+4-1,4 \right )=\frac{\left (12+4-1 \right )!}{12!\left ( 4-1 \right )!} \\ C(15,4)=\frac{15!}{12!(3)!} \\ C\left ( 15,4 \right )=\frac{15\times 14\times 13\times 12!}{12!(3!)} \\ C(15,4)=\frac{15\times 14\times 13}{3!} \\ C(15,4)=\frac{15\times 14\times 13}{3\times2\times1} \\ C(15,4)=5\times7\times13 \\ C(15,4)=455[/tex]
So, the possibility are [tex]455[/tex] different handfuls of [tex]12[/tex] jellybeans.
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