A bag contains 1 orange, 1 yellow, and 2 blue balls. The balls are replaced after each selection.
Draw a sample space to find the probability that the two selected balls are an orange ball and a blue ball.
Answers
The probablity that the two balls are orange and blue is 1/8
Describe Probability:
This is the chance or likelihood that an event will take place.
One orange ball, one yellow ball, and two blue balls are there in a bag.
The total number of sample space or outcome can be given as
Total outcome = 1 + 1 + 2=4
Probablity of occouring an orange ball can be given as, 1/4
Probablity of occouring a blue ball can be given as, 2/4
Probablity of an orange ball and a blue ball = 1/4 * 2/4
Probablity of an orange ball and a blue ball = 1/8
Consequently, there is a 1/8 chance that the two chosen balls are orange and blue
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Related Questions
Laplace Transform Let f be a function defined for t ≥ 0. Then the integral ℒ{f(t)} = [infinity] e−stf(t) dt 0 is said to be the Laplace transform of f, provided that the integral converges. to find ℒ{f(t)}. (Write your answer as a function of s.) f(t) = t2e−6t
Answers
Answer:
The laplace transform is \(\frac{2}{(s+6)^3}\)
Step-by-step explanation:
We will solve this problem by applying the laplace transform properties (their proofs are beyond the scope of this explanation).
Consider first the function f(t) = 1. By definition of the laplace transform, we have
\(F(s) = \int_{0}^{\infty}f(t)e^{-st}dt\)
when f(t) = 1 we get
\(F(s) = \int_{0}^{\infty}e^{-st}dt = \left.\frac{-e^{-st}}{s}\right|_{0}^{\infty} = \frac{1}{s}\)
We will apply the following properties: Define L(f) as applying the laplace transform
\(L(e^{at}f(t)) = F(s-a)\) (this means, multiplying by an exponential corresponds to a shift in the s parameter of the transform of f)
\(L(t^nf(t)) = (-1)^n\frac{d^n F}{ds^n}\) (this is, multypling by \(t^n\) is equivalent to taking the n-th derivative of the transform.
We are given the function \(g(t) = t^2e^{-6t}\cdot 1 \). Since the transform of the constant function 1 is 1/s, by applying the first property we get
\(L(e^{-6t}\cdot 1 ) = \frac{1}{s+6}\)
By applying the second property we get
\(L(g(t)) = L(t^2 e^{-6t} \cdot 1) = (-1)^2\frac{d^2}{ds^2}(\frac{1}{s+6}) = \frac{2}{(s+6)^3}\)
Please Help The question is down below.
Answers
Answer:
C. 5
Step-by-step explanation:
Becuase the left figure is just a scaled down size of the right one, 3 x 2 = 6 so 10 ÷ 2 = 5
WooHoo! Pls Brainliest! It would mean a lot! ;)
the difference of 44 and the square of n into a expression
Answers
Answer:
\(44-\sqrt{n}\)
The table below shows the number of students who are signed up for Algebra 2 and/or Chemistry next year. Find P(Algebra 2 ∩ Not Chemistry).
Answers
The probability of a student being signed up for Algebra 2 but not Chemistry is 0.54 or 54%.
What is probability?Probability is a way to gauge how likely or unlikely something is to happen. It is a number between 0 and 1, where 0 denotes an impossibility and 1 denotes a certainty for the event.
According to question:To find P(Algebra 2 ∩ Not Chemistry), we need to look at the number of students who are signed up for Algebra 2 but not Chemistry. From the table, we can see that there are 260 students who are signed up for Algebra 2 and not Chemistry.
P(Algebra 2 ∩ Not Chemistry) = number of students signed up for Algebra 2 and not Chemistry / total number of students
= 260 / 480
= 0.54
Therefore, the probability of a student being signed up for Algebra 2 but not Chemistry is 0.54 or 54%.
So the answer is 0.54.
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PLEASE HELP
Two projectiles are shot vertically upward at the same instant.
Projectile A's height in feet, f(t), is represented in the table, where t is the seconds since the projectile was shot off
Projectile B's height at any time t is modeled by the function
h (t)=-16t^2 +96t
How do the times at which the projectiles begin their descents compare?
SEE PHOTO
Answers
Projectile B begins its descent 1 seconds before Projectile A does.
What is y-intercept?In Mathematics and Geometry, the y-intercept of any graph or table such as a quadratic equation or function, generally occurs at the point where the value of "x" is equal to zero (x = 0).
By critically observing the table shown in the image attached above, we can reasonably infer and logically deduce the following y-intercept of Projectile A:
y-intercept = (0, 44).
Maximum height = (4, 300).
When t = 0, the y-intercept of Projectile B can be calculated as follows;
h(t) = -16t² + 96t
h(0) = -16(0)² + 96(0)
h(0) = 0.
For the maximum height, we have:
h(t) = -16t² + 96t
h'(t) = -32t + 96
32t = 96
t = 96/32
t = 3
Difference in time = 4 - 3
Difference in time = 1 seconds.
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King of Diamonds Industries has bonds on the market making annual payments, with 14 years to maturity, and selling for R1 482,01. At this price, the bonds yield 7%. What is the coupon rate?
Answers
The coupon rate of the bonds by King of Diamonds Industries would be 7 %.
How to find the coupon rate ?The formula for the bond price shows the coupon payment and so can be used to find the coupon rate:
= (Coupon payment x ( 1 - ( 1 + r ) ^ ( - number of years till maturity ) ) ) / r + Face value / (1 + rate )^ number of years
1,482.01 = (C x (1 - (1 + 0.07 )^ (- 14) ) ) / 0.07 + F / (1 + 0.07 ) ^ 14
103.7407 - 0.07 x (F / (1 + 0.07) ^14 ) = C x (1 - ( 1 + 0.07) ^ ( - 14) )
Using a calculator, C is $ 70.
This means that the coupon rate is:
= 70 / 1, 000
= 7 %
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the length or a rectangle is 11 centimeters less than 4 times it width its area is 20 square centimeters find the dimension of the rectangle use formula aera = length*width the width is cm
Answers
Length = 4W-11
Area = L*W = W(4W-11)
4W2 - 11W = 20
4W2 - 11W - 20 = 0
We can attempt to factor this by grouping:
Multiply the coefficient of the squared term .. 4 ..
by the constant -20... 4(-20) = -80
We need to see if there are factors of -80 that add to
the coefficient of the middle W term... -11.
The factors of -80 that add to -11 are 5(-16)
Replace -11W with -16W + 5W in our equation
4W2 - 16W + 5W - 20 = 0
4W(W-4) + 5(W-4) = 20
(4W+5)(W-4) = 0
Either 4W + 5 = 0 or W-4 = 0
4W = -5 W = 4
W = -4/5
Since the width cannot be a negative number
Our width is 4cm
The length is given by L = 4W-11
= 4(4)-11
= 16-11
= 5cm
Help help help math math
Answers
Answer:
15cm^3
Step-by-step explanation:
1^2=1
1*3=3
3*5=15
Step-by-step explanation:
Given:
\(D = 2\:\text{cm} \Rightarrow r =\frac{1}{2}D = 1\:\text{cm}\)
\(h = 5\:\text{cm}\)
Therefore,
\(V = \pi r^2 h = 3(1\:\text{cm})^2(5\:\text{cm})\)
\(\;\;\;=15\:\text{cm}^3\)
A laptop costs $1800. A shop is having a storewide 10% discount, How much does the laptop cost after the discount?
Answers
Answer:
$1620
Step-by-step explanation:
Given:
Original Cost ⇒ $1800
Discount ⇒ 10%
To Find:
How much does the laptop cost after the discount?
Solve:
$1800 × 10% = 180
$1800 - 180 = $1620 {Discount = subtract}
Hence, the Laptop cost after the discount is $1620
Kavinsky
Three potential employees took an aptitude test. Each person took a different version of the test. The scores are reported below. Tobias got a score of 74.7; this version has a mean of 61.7 and a standard deviation of 13. Norma got a score of 351; this version has a mean of 291 and a standard deviation of 25. Vincent got a score of 7.38; this version has a mean of 6.9 and a standard deviation of 0.4. If the company has only one position to fill and prefers to fill it with the applicant who performed best on the aptitude test, which of the applicants should be offered the job?
Answers
Answer:
Norma performed best on the aptitude test and should be offered the job.
Step-by-step explanation:
We are given that three potential employees took an aptitude test. Each person took a different version of the test. The scores are reported below. Tobias got a score of 74.7; this version has a mean of 61.7 and a standard deviation of 13. Norma got a score of 351; this version has a mean of 291 and a standard deviation of 25. Vincent got a score of 7.38; this version has a mean of 6.9 and a standard deviation of 0.4.
Now, to find which of the applicants should be offered the job, we have to find the z-score of each of the applicants, and the one who gets the highest z-score will get the job.
The z-score probability distribution for the normal distribution is given by;
Z = \(\frac{X-\mu}{\sigma}\) ~ N(0,1)
where, \(\mu\) = mean and \(\sigma\) = standard deviation
Firstly, we will find the z-score for Tobias;
The z-score of 74.7 = \(\frac{X-\mu}{\sigma}\)
= \(\frac{74.7-61.7}{13}\) = 1
Now, we will find the z-score for Norma;
The z-score of 351 = \(\frac{X-\mu}{\sigma}\)
= \(\frac{351-291}{25}\) = 2.4
Now, we will find the z-score for Vincent;
The z-score of 7.38 = \(\frac{X-\mu}{\sigma}\)
= \(\frac{7.38-6.9}{0.4}\) = 1.2
As we can clearly see that the z-score is highest for Norma which means that Norma performed best on the aptitude test and should be offered the job.
. A cocoa blender makes a profit of 30% be selling a super mix cocoa at Kshs.650 for 250 grams tin. He makes a super mix cocoa by blending two varieties of cocoa., A and which cost him Kshs. 1 800 and Kshs.2 400 per kg respectively. B In what proportion the cocoa types A and B mixed? were (3 marks)
Answers
Answer:
The cost price of 250 grams of super mix cocoa is Kshs.650/1.3=Kshs.500.
The cost price of 1 kg of super mix cocoa is Kshs.500*4=Kshs.2000.
If x kg of cocoa A is mixed with (1-x) kg of cocoa B, then the cost price of the mixture is Kshs.1800x+Kshs.2400(1-x).
Therefore, Kshs.1800x+Kshs.2400(1-x)=Kshs.2000.
Solving for x, we get x=2/3.
Therefore, the cocoa types A and B are mixed in the proportion 2:1.
Find P (Freshman(Girl) Hint: P(A and B)
P(B)
Classroom of Students
Boys Girls
Freshman 4 4 8
Sophomore 5 7 12
Junior 2 3 5
Senior 1
4 5
12 18
Reduce your fraction to lowest terms.
Enter the number that belongs in the green box.
Answers
Answer:
\(\sf \dfrac29\)
Step-by-step explanation:
From the table:
Total number of Girls = 18Total number of students = 30Total number of Girls who are Freshman = 4\(\sf Probability \ of \ an \ event \ occurring = \dfrac{Number \ of \ ways \ it \ can \ occur}{Total \ number \ of \ possible \ outcomes}\)
\(\sf \implies P(Girl)=\dfrac{18}{30}\)
\(\sf \implies P(Freshman \cap Girl)=\dfrac{4}{30}\)
\(\begin{aligned}\sf P(Freshman|Girl)& = \sf\dfrac{P(Freshman \cap Girl)}{P(Girl)}\\\\ & = \sf \dfrac{4}{30} \div \dfrac{18}{30}\\\\ & \sf=\dfrac{4}{30} \times \dfrac{30}{18}\\\\ & = \sf \dfrac29\end{aligned}\)
. Suppose a government agency has a monopoly in the provision of internet connections.
The marginal cost of providing internet connections is 1
2
, whereas the inverse demand
function is given by: p = 1
Answers
The government agency as a monopolist will produce and sell internet connections up to the point where the marginal cost is 1/2. The price will be set at 1, given the perfectly elastic demand function.
In the scenario where a government agency has a monopoly in the provision of internet connections and the inverse demand function is given by p = 1, we can analyze the market equilibrium and the implications for pricing and quantity.
The inverse demand function, p = 1, implies that the market demand for internet connections is perfectly elastic, meaning consumers are willing to purchase any quantity of internet connections at a price of 1. As a monopolist, the government agency has control over the supply of internet connections and can set the price to maximize its profits.
To determine the optimal pricing and quantity, the monopolist needs to consider the marginal cost of providing internet connections. In this case, the marginal cost is given as 1/2. The monopolist will aim to maximize its profits by equating marginal cost with marginal revenue.
Since the inverse demand function is p = 1, the revenue received by the monopolist for each unit sold is also 1. Therefore, the marginal revenue is also 1. The monopolist will produce up to the point where marginal cost equals marginal revenue, which in this case is 1/2.
As a result, the monopolist will produce and sell internet connections up to the quantity where the marginal cost is 1/2. The monopolist will set the price at 1 since consumers are willing to pay that price.
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f(x) = x +4
g(x) = 3x^2 – 7
Find (f.g)(x)
Answers
Answer:
(f*g)(x) = 3x³+12x²-7x-28
Step-by-step explanation:
What (f*g)(x) means is that we multiply f(x) by g(x):
f(x) = x+4
g(x) = 3x²-7
(f*g)(x) = f(x)*g(x) = (x+4)(3x²-7) = (x)(3x²)+(x)(-7)+(4)(3x²)+(4)(-7) = 3x³-7x+12x²-28 = 3x³+12x²-7x-28
10)
- If a triangle has an obtuse angle, then it cannot be equilateral
- If a triangle is not equilateral, then it is not equiangular.
What valid conjecture follows from the argument shown?
A)
If a triangle is not equilateral, then it is right
B)
If a triangle has an obtuse angle, then it is scalene.
If a triangle has an obtuse angle, then it is not right.
D)
If a triangle has an obtuse angle, then it is not equiangular
11)
The length of a room is 181 feet. If using 1 inch = 1 foot scale, what would be the length of a wall on a blueprint of a
Answers
Answer:
i think its B
Step-by-step explanation:
Write an equation in point-slope form for the line that has the given slope, m, and
that passes through the given point and graph the line.
m = -2; (-1,4)
Answers
Step-by-step explanation:
work is shown and pictured
Please help! Will give brainliest
Answers
Answer:
option A
Step-by-step explanation:
f(x)+g(x) will lead to addition of the fractions
LCM of 2x and x² is 2x²
{(2x²×½x)+(2x²×4/x²)}/2x²
x+8/2x²
Question is down below
Answers
Answer:
g(x) = -|x+12|
Step-by-step explanation:
Ummm...this confusing
Answers
Answer is 39
Kim bought a blouse for $17.16, a skirt for $28.19, and a purse for $35.14. The sales tax was 12%. If she hands the clerk a $100 bill how much will she get back?
Answers
Based on the cost of her items, if Kim hands over $100, she will get back $9.85.
The total that Kim will pay includes the cost of all three items as well as the sales tax.
The total cost of the three items is:
= Blouse + Skirt + Purse
= 17.16 + 28.19 + 35.14
= $80.49
The total including the sales tax will be:
= Cost + (Cost x Sales tax)
= 80.49 + (80.49 x 12%)
= $90.15
The change she will get is:
= 100 - 90.15
= $9.85
In conclusion, Kim will get a change of $9.85.
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- Simone calculates the volume of a cube with side length 2.3 cm to be 6.9 cm. Meiki says the volume is 12.167 cm². Who is correct, and why?
Answers
The person that calculated the volume of the cube correctly is Meiki.
How to calculate the volume?It is vital to note that the volume of a cube is simply calculated by cubing the value of the length. This will be illustrated thus in this case:
In this case, Simone calculates the volume of a cube with side length 2.3 cm. The length is w
2.3 cm.
Therefore, the volume of the cube will be:
Volume = side³
Volume = 2.3³
Volume = 12.167cm³
Therefore, Meiki calculated it correctly.
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A direct variation includes the points (2,18) and (n,9). Find n?
Answers
The value of the n is 1
In a direct variation, the relationship between two variables is of the form y = kx, where k is a constant of proportionality.
To find the constant of proportionality k in this problem, we can use the fact that the given points satisfy the equation for direct variation.
(2,18) is one of the given points, so we can substitute these values into the equation y = kx and solve for k:
18 = k(2)
k = 18/2
k = 9
Now that we have found the value of k, we can use it to find n when y = 9:
9 = 9n
n = 1
Therefore, the value of n is 1.
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The same bedroom furniture set costs $1,500 in both Florida and Alabama. The table gives a breakdown of the taxes someone would pay when purchasing the furniture set in either state. Alabama Florida State of Alabama: 4.225% County Tax: 1.375% City Tax: 3.0% State of Florida: 6.5% County Tax: 1% City Tax: 1.625% Which statement is true? A. The furniture set is cheaper in Alabama, because the amount of sales tax will be lower by about $8. B. The furniture set is cheaper in Florida, because the amount of sales tax will be lower by about $10. C. The furniture set is cheaper in Alabama, because the amount of sales tax will be lower by $10. D. The furniture set costs the same in either state, because the amount of sales tax will be the same for the two locations.
Answers
Answer:
A: True
B, C and D: False
Step-by-step explanation:
We have a total sales tax for Alabama that is:
\(T_A=4.225+1.375+3=8.6\)
The total sales tax for Florida is:
\(T_F=6.5+1+1.625=9.125\)
The total sales tax is greater in Florida than in Alabama.
A. The furniture set is cheaper in Alabama, because the amount of sales tax will be lower by about $8. TRUE
The sales tax difference in this purchase can be calculated as:
\(1500(T_F-T_A)=1500\left(\dfrac{9.125-8.6}{100}\right)=1500\cdot 0.00525=7.875\approx 8\)
B. The furniture set is cheaper in Florida, because the amount of sales tax will be lower by about $10. FALSE (it is cheaper in Alabama)
C. The furniture set is cheaper in Alabama, because the amount of sales tax will be lower by $10. FALSE (the sale tax in Alabama is $129)
The amount of sales tax in Alabama is:
\(ST_A=1500\cdot T_A=1500\cdot 0.086=129\)
D. The furniture set costs the same in either state, because the amount of sales tax will be the same for the two locations. FALSE (it is not the same in both states).
Breakfast Bar’s scrambled egg recipe uses 8 eggs to feed 5 people. How many eggs are they going to need to serve 100 people on Saturday morning?
Explain the steps you would use to solve the problem
Answers
Answer:
160
Step-by-step explanation:
If 5 people = 8 eggs
1 person = 8÷5 = 1.6 eggs
100×1.6= 160 eggs
Answer:
160 eggs
Step-by-step explanation:
First find how many sets of 5 (people) we need to get to a 100
-We know 100 divided by 5 is 20
So we need 20 sets of 5 (people)
Now, 20 times 8 is 160 OR we could say
for 20 groups of 5 people, we need 160 eggs
Solve 3(x + 2) > x.
answer
Answers
Answer:
Step-by-step explanation:
3(x + 2) > x
3x + 6 > x
3x - 3x + 6 > x - 3x
6 > -2x
6/-2 < -2x/-2
-3< x
The triangle above has the following measures.
m
a=7.5 y
Use the 45-45-90 Triangle Theorem to find the length of the hypotenuse. Include correct units.
Show all your work.
Answers
The length of the hypotenuse is 10.61 yd.
We have,
The sum of the angles in a triangle = 180
Now,
Two angles are 45.
This means,
The side opposite to angle 45 are equal.
So,
a = c
And,
a = 7.5 yd
Now,
Applying the Pythagorean theorem.
b² = a² + c²
b² = 7.5² + 7.5²
b² = 112.5
b = √112.5
b = 10.61
Thus,
The length of the hypotenuse is 10.61 yd.
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if v varies directly as w and v=8, when w=1/2, find the equation that relates v and w
Answers
Answer:
v=16w
Step-by-step explanation:
v=16w
8=16(1/2)
8=8✔
which of the following is the graph of y=(1/2)*?
Answers
The graph of function y = (1/2)ˣ is shown in figure.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
The function is,
⇒ y = (1/2)ˣ
Now, We can draw the graph of exponential function y = (1/2)ˣ.
Hence, The graph of function y = (1/2)ˣ is shown in figure
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Roger has a credit card with an APR of 19.40% and a billing cycle of 30 days. The following table shows his transactions with that credit card in the month of June.
Date
Amount ($)
Transaction
6/1
265.40
Beginning balance
6/6
90.00
Payment
6/16
43.33
Purchase
6/22
37.71
Purchase
If Roger’s finance charge for June is $3.56, which method of calculating the finance charge does Roger’s credit card company use?
a.
daily balance method
b.
adjusted balance method
c.
previous balance method
d.
there is not enough information to determine which method was used
Answers
Answer:
I got A and it was right
Step-by-step explanation:
The "Previous Balance Method" seems to be the one that aligns with the provided information.
Given that:
Beginning balance on 6/1: $265.40
Payment on 6/6: $90.00
Purchase on 6/16: $43.33
Purchase on 6/22: $37.71
They have also given the finance charge for June, which is $3.56.
The different methods according to the options are:
a. Daily Balance Method: This method calculates the finance charge based on the daily balance throughout the billing cycle. It takes into account daily changes in the balance due to transactions and payments.
b. Adjusted Balance Method: This method calculates the finance charge based on the adjusted balance at the end of the billing cycle. The adjusted balance is the beginning balance minus any payments made during the billing cycle.
c. Previous Balance Method: This method calculates the finance charge based on the previous month's balance, regardless of any payments made during the current billing cycle.
Based on the given information, we don't have the exact daily balances or the specific date of the finance charge calculation. However, we know the finance charge for the entire month of June is $3.56.
Out of the three methods, the "Previous Balance Method" seems to be the one that aligns with the provided information. It calculates the finance charge based on the previous month's balance, which would include the beginning balance on 6/1 and any outstanding balance from previous months.
So the correct answer is option C, Previous Balance Method.
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Solve the triangle. Round to the nearest tenth.
Find c aswell
Answers
Answer:
Set your calculator to Degree mode.
a² = 17² + 20² - 2(20)(17)cos(89°)
a² = 677.13236
a = 26.0 in.
sin(89°)/26.02177 = (sin B)/17
sin B = 17sin(89°)/26.02177
B = 40.8°
C = 50.2°