The expected value of the distribution of the number of selected red balls is 0.795.
What is the expected value?The expected value of the distribution is the mean or average of the possible outcomes.
There are 12 balls in an urn, five of which are crimson. The selection of a red ball is desired and hence considered a success.
In this case, the possible outcomes are 0, 1, 2, or 3 red balls.
To calculate the expected value, we need to find the probability of each outcome and multiply it by the value of the outcome.
The probability of selecting 0 red balls is :
[tex]$\frac{7}{12} \cdot \frac{6}{11} \cdot \frac{5}{10} = \frac{105}{660}$[/tex].
The probability of selecting 1 red ball is :
[tex]$3 \cdot \frac{5}{12} \cdot \frac{7}{11} \cdot \frac{6}{10} + 3 \cdot \frac{7}{12} \cdot \frac{5}{11} \cdot \frac{6}{10} + 3 \cdot \frac{7}{12} \cdot \frac{6}{11} \cdot \frac{5}{10} = \frac{315}{660}$[/tex].
The probability of selecting 2 red balls is
[tex]:$\dfrac{5}{12} \cdot \frac{7}{11} \cdot \frac{6}{10} + \frac{7}{12} \cdot \frac{5}{11} \cdot \frac{6}{10} + \frac{7}{12} \cdot \frac{6}{11} \cdot \frac{5}{10} = \frac{105}{660}$.[/tex]
The probability of selecting 3 red balls is
[tex]$\dfrac{5}{12} \cdot \frac{4}{11} \cdot \frac{3}{10} = \frac{15}{660}$[/tex]
The expected value is then :
[tex]$0 \cdot \frac{105}{660} + 1 \cdot \frac{315}{660} + 2 \cdot \frac{105}{660} + 3 \cdot \frac{15}{660} = \frac{525}{660} = \frac{175}{220} \approx \boxed{0.795}$[/tex]
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HELP PLEASE!!!
Oak wilt is a fungal disease that infects oak trees. Scientists have discovered that a single tree in a small forest is infected with oak wilt. They determined that they can use this exponential model to predict the number of trees that will be infected after t years.
f(t)=e^0.4t
Question:
Rewrite the exponential model as a logarithmic model that calculates the # of years, g(x) for the number of infected trees to reach a value of x.
The logarithmic model is:
[tex]g(x) = \frac{\ln{x}}{0.4}[/tex]
-------------
We are given an exponential function, for the amount of infected trees f(x) after x years.To find the amount years needed for the number of infected trees to reach x, we find the inverse function, applying the natural logarithm.-------------
The original function is:
[tex]y = f(x) = e^{0.4x}[/tex]
To find the inverse function, first, we exchange y and x, so:
[tex]e^{0.4y} = x[/tex]
Now, we have to isolate y, and we start applying the natural logarithm to both sides of the equality. So
[tex]\ln{e^{0.4y}} = \ln{x}[/tex]
[tex]0.4y = \ln{x}[/tex]
[tex]y = \frac{\ln{x}}{0.4}[/tex]
Thus, the logarithmic model is:
[tex]g(x) = \frac{\ln{x}}{0.4}[/tex]
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there were 578 tickets sold for a basket all game. the activity cardholder's tickets cost $1.25 and the non-cardholders' tickets cost $2.00. the total amount of money collected was $880.00. how many of each kind of ticket were sold?
9514 1404 393
Answer:
non-cardholder: 210cardholder: 368Step-by-step explanation:
Let n represent the number of non-cardholder tickets sold. Then total revenue is ...
2.00n +1.25(578 -n) = 880.00
0.75n + 722.50 = 880.00
0.75n = 157.50 . . . . . . . . . . . subtract 722.50
n = 210 . . . . . . . . . . . . . . . divide by 0.75. Number of non-cardholder tickets
578 -n = 368 . . . . . number of cardholder tickets
368 cardholder and 210 non-cardholder tickets were sold.
What is the probability of rolling a 2 and 3 with 2 die
a number t is less than 7
Answer:
6 or 5 or 4...........
Step-by-step explanation:
Answer:
x=N :x<7
Step-by-step explanation:
123456
hope it's helpful
The math teacher and cheerleading coach have teamed up to help the students do better on their math test. The cheer coach, using dance move names for the positioning of their arms, yells out polynomial functions with different degrees.
For each position the coach yells out, write the shape by describing the position of your left and right arm.
a1. Constant Function:
a2. Positive Linear Function:
a3. Negative Linear Function:
a4. Positive Quadratic Function:
a5. Negative Quadratic Function:
a6. Positive Cubic Function:
a7. Negative Cubic Function:
a8. Positive Quartic Function:
a9. Negative Quartic Function:
When it comes time to take the test not only do the students have to describe the shape of the polynomial function, you have to find the number of positive and negative real zeros, including complex. Use the equation below:
[tex]f(x)=x^5-3x^4-5x^3+5x^2-6x+8[/tex]
b. Identify all possible rational zeros.
c. How many possible positive real zeros are there? How many possible negative real zeros? How many possible complex zeros?
d. Graph the polynomial to approximate the zeros. What are the rational zeros? Use synthetic division to verify these are correct.
e. Write the polynomial in factor form.
f. What are the complex zeros?
Step-by-step explanation:
a1. The shape will be a vertical or horizontal line.
a2. The shape will be shaped like a diagonal line increasing as we go right.
a3. The shape will be shaped like a diagonal line decreasing as we go right.
a4. The shape will be shaped like a U facing upwards.
a5.The shape will be shaped like a U facing downwards.
a6. The shape will look like a S shape and it increases as we go right.
a7. The shape will look like a S shape and it decreases as We go right.
a8. The shape look like a W shape and it facing upwards.
a9. The shape look a W shape facing downwards.
We are given function.
[tex]x {}^{5} - 3x {}^{4} - 5x {}^{3} + 5x {}^{2} - 6x + 8[/tex]
b. We can test by the Rational Roots Test,
This means a the possible roots are
plus or minus(1,2,4,8).
c. If we apply Descrates Rule of Signs,
There are 3 possible positive roots or 1 possible positive root.There are also 1 possible negative root.There is also 1 possible complex root.d. Use Desmos to Graph the Function. Some roots are (-2,1,4).
e.
[tex](x {}^{2} + 1) (x - 1)(x - 4)(x + 2)[/tex]
f. The complex zeroes are
i and -i
Polynomial [tex]f(x) = x^{5} -3x^{4} - 5x^{3} + 5x^{2} - 6x + 8[/tex] in factor form: (x-1)(x+2)(x-4)(x-i)(x+i)
What is a polynomial?A polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.
Shape of the graph for the following polynomial:
Constant function - straight line parallel to x axis.Positive linear function - straight line slanting upwards from left to right.Negative linear function - straight line slanting downwards from left to right.Positive quadratic function - U shaped curve opening upwardsNegative quadratic function - U shaped curve opening downwardsPositive cubic function - right hand curved upwards, left hand curved downwards.Negative cubic function - Left hand curved upwards, right hand curved downwards. Positive quartic function - W shaped facing upwardsNegative quartic function - W shaped facing downwardsFinding zeros of the polynomial given:
[tex]f(x) = x^{5} -3x^{4} - 5x^{3} + 5x^{2} - 6x + 8[/tex]
By factor theorem, if f(t) = 0, t is a zero of the polynomial.
Taking t = 1.
f(1) = 1 - 3 - 5 + 5 - 6 + 8 = 0
(x - 1) is a factor of the polynomial f(x).
Divide f(x) by (x-1) using long division to find the other factors.
f(x)/(x-1) = [tex]x^{4} -2x^{3}-7x^{2} -2x-8[/tex] is also a factor of f(x).
Factorizing it further:
g(x) = [tex]x^{4} -2x^{3}-7x^{2} -2x-8[/tex]
g(-2) = 16 + 16 - 28 + 4 - 8 = 0
(x + 2) is a factor of g(x) and thus f(x).
g(x)/(x+2) = [tex]x^{3} - 4x^{2} +x - 4[/tex] is a factor of f(x).
Factorizing it further:
k(x) = [tex]x^{3} - 4x^{2} +x - 4[/tex]
k(4) = 64 - 64 + 4 - 4 = 0
(x - 4) is a factor of k(x) thus of f(x).
k(x)/(x-4) = [tex]x^{2} +1[/tex]
Factorizing it further:
l(x) = [tex]x^{2} +1[/tex] = (x + i)(x - i)
Zeros of f(x) = 1, -2, 4, ±i
Rational zeros : 1, -2, 4
Positive real zeros: 1, 4
Negative real zeros: -2
Complex zeros: ±i
Polynomial in factor form: (x-1)(x+2)(x-4)(x-i)(x+i).
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The total number of branches in a tree diagram will be which of the following values?
the probability of an event occurring
the denominator of a probability
the numerator of a probability
Answer:
The total number of branches = total possibilities = the denominator of a probability.
So the second choice is correct.
Let me know if this helps!
Answer:
Step-by-step explanation: answer B (the denominator of a probability)
90units needed 8 units per case what's the #of cases & # of additional units
Answer:
# of cases: 11
Additional units: 2
Step-by-step explanation:
If each case can hold 8 units, and we want to find the total # number of cases, we have to divide the # of units (8) for one case by the total # units (90).
As you can see, after dividing by 8, we have a total of 11 cases and a remainder of 2 units. The remainder will be the # of additional units because we cannot have another case filled with 8 units.
i need help on 8-9 plss :))
Answer:
8. SU = 24
9. TU = 16√3
Step-by-step explanation:
Recall: SOH CAH TOA
8. Reference angle (θ) = 30°
Opposite = 8√3
Adjacent = SU
Apply TOA,
Tan θ = Opp/Adj
Substitute
Tan 30° = 8√3/SU
Tan 30° × SU = 8√3
SU = 8√3/Tan 30°
SU = 8√3/(1/√3) (tan 30° = 1/√3)
SU = 8√3*√3/1
SU = 8*3
SU = 24
9. Reference angle (θ) = 30°
Opposite = 8√3
Hypotenuse = TU
Apply SOH,
Sin θ = Opp/Hyp
Substitute
Sin 30° = 8√3/TU
Sin 30° × TU = 8√3
TU = 8√3/sin 30°
TU = 8√3/(½) (sin 30° = ½)
TU = 8√3 × 2/1
TU = 16√3
anyone know the answers for the final exam for part one of algebra 2 on edg?
Answer:
just show the questions i will help
Step-by-step explanation:
PLSS HELPPPP WILL GIVE BRAINLESSS A 22-foot ladder is resting against the side of a building. The bottom of the ladder is 3 feet from the building. Find the measure of the angle the ladder makes with the ground. Round your answer to the nearest tenth of a degree.
Answer:
The answer is 82.2
Step-by-step explanation
hope this helps
A factory used 99.19 kilograms of tomatoes to make 7 batches of pasta sauce. What quantity of tomatoes did the factory put in each batch?
Answer:
14.17 kilograms
Step-by-step explanation:
Find what quantity of tomatoes was in each batch by dividing the total amount of tomatoes by the number of batches:
99.19/7
= 14.17
So, the factory put 14.17 kilograms of tomatoes in each batch.
Helpp me plzzz im being timed
Which function describes this graph
Answer:
C.
Step-by-step explanation:
A P E X
1. Find the 4th term for the sequence with formula tn= n² + 1
Answer:
17
Step-by-step explanation:
T4 = 4² + 1
T4 = 4² + 1 = 17
Yip yip that's all
Start with the number 2380.
Divide by 10,
The 8 will end up in the _____ place.
The 8 will end up in the "ones place".
How can we interpret the division?When 'a' is divided by 'b', then the result we get from the division is the part of 'a' that each one of 'b' items will get. Division can be interpreted as equally dividing the number that is being divided into total x parts, where x is the number of parts the given number is divided.
We need to find the 8 will end up in which place
A negative divided by a negative is positive, then;
2380/ 10 = 238
Therefore, The 8 will end up in the _ ones_ place.
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Determine if the described set is a subspace. Assume a, b, and c are real numbers. The subset of R3 consisting of vectors of the form [a b c] , where at most one of a , b and c is non 0.
The set is a subspace.
The set is not a subspace.
If so, give a proof. If not, explain why not.
Answer:
Not a subspace
Step-by-step explanation:
(4,0,0) and (0,4,0) are vectors in R3 with zero or one entries being nonzero, but their sum, (4,4,0) has two nonzero entries.
100 x 20 + 30 help me
[tex]\boxed{\underline{\bf \: Answer}}[/tex]
[tex] \sf100 \times 20 + 30[/tex]
First multiply 100 & 20 together.
[tex] \sf= 2000 + 30[/tex]
Now add 2000 & 30. You'll get :-
[tex]= \boxed{ \bf 2030}[/tex]
____
Hope it helps.
RainbowSalt2222
[tex]\\ \rm\longmapsto 100\times 20+30[/tex]
[tex]\\ \rm\longmapsto (100\times 20)+30[/tex]
Solve bracket[tex]\\ \rm\longmapsto 2000+30[/tex]
[tex]\\ \rm\longmapsto 2030[/tex]
Police estimate that 25% of drivers drive without their seat belts. If they stop 6 drivers at random, find theprobability that more than 4 are wearing their seat belts.
Answer:
%17.80
Step-by-step explanation:
17.8% is the probability that more than 4 are wearing their seat belts.
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
Given that Police estimate that 25% of drivers drive without their seat belts.
If they stop 6 drivers at random we need to find the probability that more than 4 are wearing their seat belts.
For each driver stopped, there are only two possible outcomes. Either they are wearing their seatbelts, or they are not.
he drivers are chosen at random, which mean that the probability of a driver wearing their seatbelts is independent from other drivers.
Police estimate that 25% of drivers drive without their seat belts.
This means that 75% wear their seatbelts, so P=0.75
If they stop 6 drivers at random, find the probability that all of them are wearing their seat belts.
[tex]P(X=x)=C_{n,x} p^{x} (1-p)^{n-x}[/tex]
[tex]P(X=6)=C_{6,6} 0.75^{6} (1-0.75)^{0} =0.1780[/tex]
Hence, 17.8% is the probability that more than 4 are wearing their seat belts.
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Change the word phrase to an algebraic expression. Use x as the variable to represent the number.
16 subtracted from a number
Let x = the number.
16 subtracted from a number can be written as…
Answer:
I think the answer is
x-16
since 16 is subtracted from x.
I hope this helps
The number of hearing aids that needs to be produced and sold is??
Answer:
14.36 AND 9.89 ===> 14 or 10
Step-by-step explanation:
Y = Ax2 Bx C
Enter coefficients here >>> -4 97 -568
Standard Form: y = -4x²+97x-568
-24.25 -12.125 147.015625 -588.0625 20.0625
Grouped Form: No valid Grouping
Graphing Form: y = -4(x-12.13)²+20.06
Factored Form: PRIME
Solution/X-Intercepts: 14.36 AND 9.89
Discriminate =321 is positive, two real solutions
VERTEX: (12.13,20.06) Directrix: Y=20.13
Round 5,821 to the nearest thousands place:
Answer:
6000 hope this helps
if the question is 5,422 then the round figure is 5000
but the question is 5,821 its above 5500 will be 6000
A right pyramid with a square base has
volume of 252 cubic centimeters. The
length of one of the sides of its base is 6
centimeters. Rounded to the nearest
centimeter, what is the vertical height of
the pyramid?
Hey there!
A right pyramid with a square base just means that it isn't slanted all funny. If you create a triangle with a point on one of the edges of the base, the center of the base, and the top of the pyramid, it would be a right triangle.
To find the volume of a right pyramid, you just take the base area, multiply it by the height, and then divide by three.
However, we are looking for the height. We have been given, so we will just go backwards.
252×3=756 (multiply instead of divide)
6×6=36 (base is a square, so you just square 6. This is our base area)
756/36=21
So, the vertical height of the pyramid is 21 cubic centimeters.
Have a wonderful day! :D
Which is the answer choice to this question?
Answer:
D
Step-by-step explanation:
Graph it
In GeoGebra, display the slope of AB and the slope of the perpendicular line passing through C. Use this to verify your responses in parts B and C. Then move points A, B, and C on the grid to several different locations, and record the slopes of the two lines and the coordinates of A, B, and C.
Answer:
plato screenshot!
Step-by-step explanation:
I don't personally know *how* to find the answers, but here's the screenshot of the suggested answer on Plato
Answer:
A B Slope of C Slope of Line Through C
(−5,4) (−1,−1) −1.25 (1,2) 0.8
(−5,4) (−3, 5) 0.5 (−2, 1) −2
(−4, 1) (−3, 5) 4 (−2, −2) −0.25
(−5, −2) (−1, 1) 0.75 (−4, 3) −1.33
(−5, −2) (1, −1) 0.17 (−3, 1) −6
Step-by-step explanation:
that way you can copy and paste each one but Plato
complete the table below?
ABC = $425
Load = 0
Total Cost = $425
Sales Price = $850
Sales price ÷ total cost = 850/425
= 2%
DEF = $600
Load = $375
Total Cost = $975
Sales Price = $1200
Sales Price ÷ Total cost = 1200/975
= 1% (Nearest 1%)
Must click thanks and mark brainliest
please help me with both questions
Answer:
(b) 829 seconds
(c) 13.8 minutes
Step-by-step explanation:
(b) 2.48×10⁸/2.99×10⁵ = 829 seconds
(c) 829/60 = 13.8 minutes
What is 3.24 ( 4 repeating) as a fraction?
Answer:
81/25
Step-by-step explanation:
change 3.24 into faction
324 over 100 because there are two decimal points .
simplfy into the smallest fraction
the answer is 81 over 25
Piecewise functions alg1
Answer:
C. 0
Step-by-step explanation:
Since we are finding f(-4), we use the first function since -4 is less than -2.
f(-4) = (-4) + 4 = 0
Therefore, the answer is C.
Which graph matches the exponential function f(x) = (3)x?
Write an expression for the baseball team’s Purchase.
