A bag contains 4 black, 5 red, and 6 pink balls. If 3 balls are selected one after the other without replacement, what is the probability that 3 red balls are chosen?
Answer:
The probability that 3 red balls are chosen is: 2.2%
Step-by-step explanation:
A bag contains 4 black, 5 red, and 6 pink balls.
Total balls in the bag= 4+5+6= 15 balls in the bag
We need to know what is the probability that 3 red balls are chosen without replacement?
[tex]P_r=\frac{R_b}{T_b}*\frac{R_b-1}{T_b-1}*\frac{R_b-2}{T_b-2}[/tex]
Where:
[tex]P_r:[/tex] Probability that 3 red balls are chosen
[tex]R_b:[/tex] Number of red balls
[tex]T_b:[/tex] Number of total balls
[tex]P_r=\frac{5}{15}*\frac{5-1}{15-1}*\frac{5-2}{15-2}\\P_r=\frac{5}{15}*\frac{4}{14}*\frac{3}{13}\\P_r=\frac{1}{3}*\frac{4}{14}*\frac{3}{13}\\P_r=\frac{2}{91}\\P_r=0.022[/tex]
[tex]P_r=0.022=2.2[/tex]%
The probability that 3 red balls are chosen is: 2.2%
Which are names of points drawn in the figure?
Choose all answers that are correct.
A.
K
B.
v
C.
M
D.
h
Julia can type 150 words in five minutes at this rate how many words can she type in one minute
Julia can type 30 words per minute.
Julia can type 150 words in five minutes.
To find out how many words she can type in one minute, divide 150 by 5, which equals 30.
[tex]\frac{150}{5} = 30[/tex]
So she can type 30 words per minute.
Evaluate the formula V=BH/3 for B = 9 in.2 and h = 32 in.
Integer is a special name for _____. positive whole numbers. positive or negative whole numbers. negative whole numbers. positive whole or mixed numbers.
Rewrite the equation of the circle in vertex form.
x2 + y2 - 2y - 15 = 0
Final answer:
The equation of the circle x² + y² - 2y - 15 = 0 is rewritten in vertex form by completing the square for the y terms, resulting in x² + (y - 1)² = 4², indicating a center at (0, 1) and a radius of 4.
Explanation:
To rewrite the equation of the circle in vertex form, you want to complete the square for both the x and y terms. The equation given is x² + y² - 2y - 15 = 0. First, we need to isolate the x and y terms:
x² + y² - 2y = 15Since there's no x-term to complete the square with, we can leave the x² term as it is. For the y-terms, add and subtract (1/2 * coefficient of y)2, which is (1/2 * -2)² = 1:
x² + (y² - 2y + 1) - 1 = 15Now the equation inside the parentheses is a perfect square trinomial and can be factored as (y - 1)². After adjustment, we get:
x² + (y - 1)² = 15 + 1x² + (y - 1)² = 16So the circle in vertex form is x² + (y - 1)² = 4², with the center at (0, 1) and a radius of 4 units.
two equivalent fractions for 1/3
How do you solve C=Q/V for V.
To solve for V in the equation C = Q/V, you need to multiply both sides of the equation by V and then divide both sides by C.
Explanation:To solve the equation C = Q/V for V, we need to isolate V on one side of the equation. We can do this by multiplying both sides of the equation by V. This gives us CV = Q. To solve for V, we divide both sides of the equation by C. Therefore, V = Q/C.
what is 4 divided by 2
Let f be the function defined by f(x) = 3x^5-5x^3+2
a) On what intervals is f increasing
b) On what intervals is the graph of f concave upward.
c) Write the equation of each horizontal tangent line to the graph of f.
Please provide some detail to your response. ...?
Answer:
a) [-1, ∞-) and [1, ∞+)
b) (√2/2,∞) and (0,-√2/2)
c) y=0, y=2 and y=4
Step-by-step explanation:
a) On what intervals is f increasing?
We need to proceed some steps, to answer it properly. What are the critical points? So
1) Differentiate the original function
[tex]f(x)=3x^{5}-5x^3+2\\ f'(x)=15x^4-15x^{2}[/tex]
2) Turn this into an equation
[tex]15x^4-15x^2=0\\ u=x^{2} and \\u^{2}=x^{4} \\ Then\\ 15u^{2} -15u=0\\ \\15u(u^2 -1)=0\\Therefore\\u=0,u=1[/tex]
Substitute back to x
[tex]x^{2} =u\\ x^{2} =u^4\\ x^{2}=1\\ x= 1,x=-1\\ x^{2} =0\\ x=0[/tex]
Those are x-coordinates of the critical points of [tex]f(x)=3x^{5}-5x^3+2[/tex]
Using the critical points x, to find y-coordinates of those critical points: namely, maximum point, saddle point and minimum point
x=-1 [tex]y=3x^{5}-5x^3+2[/tex]
[tex]y=3(-1)^{5}-5(-1)^3+2[/tex]
y=4
(-1,4) Maximum point
--
x=0 [tex]y=3x^{5}-5x^3+2[/tex]
[tex]y=3(0)^{5}-5(0)^3+2[/tex] y=2
(0,2) Saddle Point
--
x=1 [tex]y=3x^{5}-5x^3+2[/tex]
[tex]y=3(1)^{5}-5(1)^3+2[/tex]
(1,0) Minimum point
f(x) increases when any value of x ∈ (-∞, -1] and x ∈ [1, ∞+) is plugged in the function. Or we can rewrite as x[tex]x\leq -1\\ \\x\geq 1[/tex]
-------------------------------------
b)On what intervals is the graph of f concave upward?
To find out which intervals are these, we need to calculate the 2nd derivative.
[tex]f(x)=3x^{5}-5x^3+2\\ f(x)'=15x^4-15x^{2} \\f(x)''=60x^3-30x\\[/tex]
Since we want the concave upward
f(x)''>0
Then:
[tex]60x^3-30x>0\\ 30x(2x^2-1)>0\\[/tex]
Rewriting
[tex]30x(\sqrt{2x}-1)[/tex]
Then
x=0, x=[tex]\frac{\sqrt{2}}{2} \\-\frac{\sqrt{2}}{2}[/tex]
Studying the sign
The intervals >0, when the graph is concave upwards.
are (√2/2,∞) and (0,-√2/2)
c) Write the equation of each horizontal tangent line to the graph of f.
Generally, every time somebody ask for a tangent line of any given function, they provide an information. A specific point.
But when they do not? Like in this case?
We have to look for where the 1st function's derivative is zero.
As we 've done previously in letter a. x=-1, x=0, x=1
Let's plug them back to the original function
[tex]y=3x^{5}-5x^{3}+2\\ y=3(-1)^{5}-5(-1)^{3}+2\\ y=-3-5+2\\ y=-8+2\\ y=4\\ \\y=3x^{5}-5x^{3}+2\\ y=3(0)^{5}-5(0)^{3}+2\\ y=2\\\\ y=3x^{5}-5x^{3}+2\\ y=3(1)^{5}-5(1)^{3}+2\\ y=0[/tex]
So each horizontal tangent line, tangents the maximum, saddle and the minimum point.
The average score on a recent test was 75%. One of the students earned a grade of 93% while another student earned a grade of 78%. A total of 23 students took the test. Find the average grade of the remaining 21 students.
You are told that having a college education increases a person's earnings by 30% over their lifetime. a non-college graduate earns about $30,000 per year. how much more will you earn with a college education over a 40 year career?
Answer: 360,000
See for yourself
If 800 feet of fencing is used to enclose a rectangular plot of land that borders a river, what is the maximum area that can be enclosed? Answer to the nearest square foot without commas. For example, if the answer is 1,000, write 1000.
Answer:
80000
Step-by-step explanation:
The maximum area that can be enclosed with 800 feet of fencing and the river bordering one side is 0 square feet.
Explanation:To find the maximum area that can be enclosed with 800 feet of fencing, we need to maximize the area of the rectangular plot. A rectangle with one side bordering the river will have two sides of equal length and two sides of different length. Let's denote the length of the side parallel to the river as x and the length of the other side as y. Since there are two sides of equal length, the total length of those two sides would be 2x. The other two sides would be y each, giving a total length of 2y. The equation we can form based on the given information is:
2x + y + y = 800
Simplifying the equation, we get:
2x + 2y = 800
Dividing both sides by 2, we have:
x + y = 400
Now, we need to express one of the variables in the equation in terms of the other variable. Let's solve for x:
x = 400 - y
To find the maximum area, we need to express it in terms of a single variable. The area of a rectangle is given by length multiplied by width. So, the area A can be expressed as:
A = x * y = (400 - y) * y
To find the maximum value of A, we can use calculus. Let's take the derivative of A with respect to y:
A' = -y + 400
Setting A' to 0 and solving for y, we get:
0 = -y + 400
y = 400
Substituting this value back into the expression for A, we have:
A = (400 - 400) * 400 = 0
Therefore, the maximum area that can be enclosed is 0 square feet.
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over the last 50 years, the average temperature has increased by 2.5 degrees worlwide
Cassie has 15 yards of ribbon to make bows for birthday packages . How many ribbons will she if she wants to use 1/3 yards length of ribbon for each bow?
Answer:45
Step-by-step explanation:
The sides of a square are three to the power of two sevenths inches long. What is the area of the square?
H(n) = −2n 2 4; find h(4)
The Probability that one bulb is red and one is yellow?
27 Bulbs contains 11 red, 9 yellow and 7 purple
The probability of choosing one red bulb and then one yellow bulb from 27 bulbs (11 red, 9 yellow, and 7 purple) is calculated by multiplying the chance of picking a red bulb first and a yellow bulb second. This results in approximately 1 in 7.1, or roughly 0.14.
Explanation:The question you are asking is about finding the probability that one bulb is red and one is yellow out of a total of 27 bulbs, with a distribution of 11 red, 9 yellow, and 7 purple bulbs. To calculate this probability, we use the following steps:
First, the probability of selecting a red bulb is the number of red bulbs divided by the total number of bulbs, so P(Red) = 11/27.Next, since one bulb has already been chosen, we have 26 bulbs left. The probability of choosing a yellow bulb after picking a red one is the number of yellow bulbs divided by the remaining total bulbs, so P(Yellow | Red) = 9/26.To find the combined probability of both events occurring in sequence (one red, then one yellow), we multiply the probabilities of each individual step: P(Red then Yellow) = P(Red) × P(Yellow | Red) = (11/27) × (9/26).Using the multiplication rule of probability, we get:
P(Red then Yellow) = (11/27) × (9/26) = 99/702 = 1/7.1 (approximately).
So the probability that one bulb is red and one is yellow is about 1 in 7.1, or approximately 0.14.
102 is what percent of 225
Kellies mom takes a 400 gm dose of aspirin . Each hour the amount of aspirin in a persons system decreases by about 29%. How much aspirin is left in her system after 6 hours
A quadratic equation is shown below:
9x2 - 36x + 36 = 0
Part A: Describe the solution(s) to the equation by just determining the discriminant. Show your work. (3 points)
Part B: Solve 2x2 - 9x + 7 = 0 using an appropriate method. Show the steps of your work and explain why you chose the method used.(4 points)
Simplify fully:
4d² - 6d² + 5d²
and
7x + 5y - 3x - 8y
Consider this equation: –3x – 5 2x = 6which is an equivalent equation after combining like terms?
transform the equation to isolate x. ax= bx+1. how is the value of x related to the differenace of a and b? answer
The equation ax = bx + 1 is the same as x = 1/(a - b) when solved for x. This means that x is equal to the reciprocal of the difference of a and b. This is the answer from the sample response.
Answer:
The equation ax = bx + 1 is the same as x = 1/(a - b) when solved for x. This means that x is equal to the reciprocal of the difference of a and b. This is the answer from the sample response.
Step-by-step explanation:
A cube has a surface area of 181.5 sq. in. What is the length of its sides?
4c-7.8 Evaluate the expression if c=4
How does tap enable transport proteins to move ions across a cell membrane?
how many times can 18 go into 357
#1: How many meters are in 0.05 kilometers?
A. 50
B. 500
C. 5,000
D. 50,000
Answer:
50 meters
A is correct
Step-by-step explanation:
Given: 0.05 kilometers
As we know, In 1 km = 1000 m
So, multiply 0.05 km to 1000 to change into meter
[tex]\Rightarrow 0.05\ km\times \dfrac{1000\ m}{1\ km}[/tex]
[tex]\Rightarrow \dfrac{5}{100}\times 1000[/tex]
[tex]\Rightarrow 50\ km[/tex]
Hence, In 0.05 km is 50 meters.
The meter equivalent of 0.05 km is 50 .
Given,
0.05 kilometers
As we know, In 1 km = 1000 m
So, multiply 0.05 km to 1000 to change into meter
0.05 * 1000
= 50 m
Hence, In 0.05 km is 50 meters.
Thus option A is correct .
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multiply (3x+2)(x-3)
The product is 3x² - 7x - 6 after combining like terms.
The student asked to multiply the binomials (3x+2) and (x-3). To do this, we use the FOIL method, which stands for First, Outside, Inside, Last. This refers to the elements in each binomial we need to multiply together.
First, we multiply the first terms in each binomial: (3x) and (x), which gives 3x².
Next, we multiply the outside terms: (3x) and (-3), which gives -9x.
Then we multiply the inside terms: (2) and (x), which produces +2x.
Last, we multiply the last terms of each binomial: (2) and (-3), yielding -6.
Finally, we combine the like terms to get the expanded product - 3x² - 7x - 6.