The probability of choosing two green balls without replacement is 111, and the probability of choosing one green ball is 13.What is the probability of drawing a second green ball, given that the first ball is green?
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SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given probabilities
[tex]\begin{gathered} Pr(2\text{ greens\rparen}=\frac{1}{11} \\ Pr(one\text{ green\rparen}=\frac{1}{3} \end{gathered}[/tex]STEP 2: Write the probability formula for probability of second green given first green
[tex]\begin{gathered} Pr(G2|G1)=\frac{Pr(2\text{ greens\rparen}}{Pr(one\text{ green\rparen}} \\ =\frac{1}{\frac{11}{\frac{1}{3}}}=\frac{1}{11}\div\frac{1}{3}=\frac{1}{11}\times\frac{3}{1}=\frac{3}{11} \end{gathered}[/tex]Hence, the answer is 3/11
Related Questions
ima just send the pic
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Answer:
r = -27/16
Step-by-step explanation:
We have:
8r - 3/2 = -15
To find r, we have to isolate the term which contains this variable. Then, we can use the least common multiple:
[tex]\begin{gathered} 8r-\frac{3}{2}=-15 \\ 8r=-15+\frac{3}{2} \\ 8r=\frac{-15\cdot2+3}{2} \\ 8r=\frac{-30+3}{2} \\ 8r=-\frac{27}{2} \\ \text{Dividing both sides by 8, we have:} \\ \frac{8r}{8}=-\frac{27}{2\cdot8} \\ r=-\frac{27}{16} \end{gathered}[/tex]So,
r = -27/16
I have to describe the end behaviors by matching the correct sine to the blank your answer + or -
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The left and right sides of the graph are the negative and positive sides of x respectively. When the values of x continues endlessly to the left, it tends towards negative infinity and if it continues endlessly to the right, it tends towards positive infinity.
The bottom and top sides of the graph are the negative and positive sides of f(x) or y respectively. When the values of f(x) continues downwards, it tends towards negative infinity and if it continues endlessly upwards, it tends towards positive infinity.
Considering the given graph,
As x tends towards negative infinity(the left), f(x) tends towards positive infinity(upwards)
As x tends towards positive infinity(the right), f(x) tends towards negative infinity(downwards)
1.The area of Triangle B is 8 square units. Find the length of b. Show your reasoning.2The area of Triangle C is 545 square units. What is the length of h? Show your reasoning.
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Given:
The area of the triangle B is 8 square units. And height of the triangle is 8/3 unit.
[tex]\begin{gathered} A=8unit^2 \\ h=\frac{8}{3}unit \end{gathered}[/tex]Required:
To find the value of b.
Explanation:
The formula for area of triangle is
[tex]A=\frac{bh}{2}[/tex]Now
[tex]\begin{gathered} 8=\frac{1}{2}\times\frac{8}{3}\times b \\ \\ 8=\frac{8}{6}b \\ \\ b=8\times\frac{6}{8} \\ \\ b=6unit \end{gathered}[/tex]Final Answer:
The value of b is
[tex]b=6unit[/tex]an amount of $24,000 is borrowed for 13 years at 5.5% interest compounded annually if the loan is paid in full at the end of the period how much must be paid back?
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Given:
P = $ 24, 000
r = 5.5 % = 0.055
t = 13 years
n = 1 (compounded annually)
Required: Amount of the loan if paid in full after 13 years, A
Solution
[tex]\begin{gathered} A=P(1+\frac{r}{n^{}})^{nt} \\ A=24,000(1+\frac{0.055}{1})^{(1)(13)} \\ A=48,138.57 \end{gathered}[/tex]Answer:
$ 48,138.57 much must be paid back in full at the end of the period
which of the following is equivalent to i⁹A. i²⁷/i³B. (i⁴) (i⁵)C. (i³)²D. iE. (i • i) x (i•i•i•i) x (i•i•i) F. (i³)³(there could be more than one answer)
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Options B, D, E, and F are correct
In a raffle where 7000 tickets are sold for $2 each, one prize of $2900 will be awarded. What is the expected value of a single ticket in the raffle?
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• The expected value of a single ticket in the raffle here is as follows:
1. E= -cost of ticket + expected payout,
where cost of ticket = $2
expected payout = 1(/7000) * 2900= 2/7
substituting this to the above formula we will have
E = -2 + 2/7
= -12/7 = -1.714
Therefore -$1.714 is the expected value of a single ticket in the raffle here.
find the solution of this system of equationsx+3y=-33-4x+5y=-38
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Answer:
The solution to the system is:
x = -63
y = 10
Explanation:
Given the pair of equations:
x + 3y = -33 ......................................................(1)
-4x + 5y = -38 ...................................................(2)
Multiply (1) by 4
4x + 12y = -132 ..................................................(3)
Add (2) and (3)
-4x + 4x + 5y + 12y = -38 - 132
17y = 170
Divide both sides by 17
y = 170/17 = 10
Substitute y by 10 in (1)
x + 3(10) = -33
x + 30 = -33
Subtract 30 from both sides
x = -33 - 30
x = -63
Therefore,
x= -63, y = 10
Which transformations map the strip pattem onto itself? (I'll send pic of problem)1) a horizontal translation only 2)a horizontal translation, a reflection across a vertical line, a reflection across a horizontal line, a glide reflection, and a 180 rotation3) a horizontal translation and a 180° rotation only4) a horizontal translation, a reflection across a horizontal line, and a glide reflection only
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Notice that the strip has the first triangle translated horizontally, and then rotated 180°, then the second triangle is translated horizontally again and given another rotation of 180°, therefore, the correct option is 3
Anmol took a house loan this year. He borrowed 6 lakh from the bank at a rate of interest of 10% per annum.The interest is compounded annually.How much money will Anmol owe to the bank after two years?
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Compound Interest
We'll use the formula:
[tex]{\displaystyle A=P\mleft(1+{\frac{r}{n}}\mright)^{nt}}[/tex]Where:
A=final amount
P=initial principal balance
r=interest rate
n=number of times interest applied per time period
t=number of time periods elapsed
The problem describes the situation where that Anmol took a house loan and borrowed P=6 lakh at a rate of r=10%. Converting to decimal r=10/100=0.1.
It's also given the interest is compounded annually, thus n=1. In t=2 years:
Applying the formula
[tex]{\displaystyle A=6(1+{\frac{0.1}{1}})^{1\cdot2}}[/tex]Calculating:
[tex]{\displaystyle A=6(1.1)^2=7.26}[/tex]Anmol will owe 7.26 lakh to the bank after two years
TotalUniversity DataReceiving Not ReceivingFinancial Aid Financial Aid42223898Undergraduates8120Graduates18797312610Total6101462910730What is the probability that a given student is onfinancial aid, given that he or she is a graduate?Rounded to the nearest percent, [? ]%
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Let's define
A: a student is on financial aid
B: a student is a graduate
We want to find P(A|B), that is, the probability of A given B, which is computed as follows:
[tex]P(A|B)=\frac{P(A\cap B)}{P(B)}[/tex]P(A∩B) means the probability of A and B at the same time. In this case, the probability that a student is on financial aid and is a graduate. From the table:
[tex]P(A\cap B)=\frac{1879}{10730}[/tex]The probability that a student is a graduate is:
[tex]P(B)=\frac{2610}{10730}[/tex]Finally, the probability that a student on financial aid given that is a graduate is:
[tex]P(A|B)=\frac{\frac{1879}{10730}}{\frac{2610}{10730}}=\frac{1879}{10730}\cdot\frac{10730}{2610}=\frac{1879}{2610}=0.72\text{ or 72\%}[/tex]The probability distribution of a random variable is given below.
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Step 1:
Write the range of the probability of any event
[tex]\begin{gathered} \text{Probability of any event is in the range of } \\ 0\leq\text{ P(event) }\leq\text{ 1} \\ \text{Total probability = 1} \end{gathered}[/tex]Step 2
[tex]\begin{gathered} \sum ^3_0\text{ p(x) = }0\text{ + a + 4a + 9a = 14a} \\ 14a\text{ = 1} \\ \text{a = }\frac{1}{14} \end{gathered}[/tex]Step 3:
[tex]\begin{gathered} \text{Expected value } \\ =\sum ^3_0x\mathrm{}p(x) \\ =\text{ 0}\times0\text{ + }1\times a\text{ + 2}\times4a\text{ + 3}\times9a \\ \text{= 0 + a + 8a + 27a} \\ =\text{ 36a} \\ =\text{ 36}\times\text{ }\frac{1}{14} \\ =\frac{36}{14} \\ =\text{ 2.57} \end{gathered}[/tex][tex]\begin{gathered} Final\text{ answer} \\ \frac{1}{14}|2.57 \end{gathered}[/tex]Option C
y=-2x +13x-2y=5how to solve the system equations algebraically?
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The given equations are:
[tex]\begin{gathered} y=-2x+1 \\ 3x-2y=5 \end{gathered}[/tex]So from the first equation, we have the value for y. Now we can substitute that value in the second equation for y. We have,
[tex]\begin{gathered} 3x-2(-2x+1)=5 \\ 3x+4x-2=5 \\ 7x=5+2 \\ 7x=7 \\ x=\frac{7}{7}=1 \end{gathered}[/tex]Now we can substitute the value of x in the equation for y,
[tex]y=-2\times1+1=-2+1=-1[/tex]Hence, x = 1 and y = -1.
can you pls help m e
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Number of Classes = 4
Number of Students per class = 19
Thus, total number of students = 4 x 19 = 76
Each table can display highest of 6 projects, so we divide 76 (total number of projects since each student = 1 project) by 6 and get:
76 / 6 = 12 remainder 4
We need 12 tables + 1 table to display the remaining 4 projects.
That's a total of 12 + 1 = 13 tables
Correct Answer
BGiven the equation below graph the polynomial. On the graph indicate x and y intercepts multiplicity and end behavior.
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Given the polynomial function h(x) defined as:
[tex]h(x)=(x+3)^2(x-2)[/tex]The y-intercept is the value of the function at x = 0. Then, evaluating h(0):
[tex]\begin{gathered} h(0)=(0+3)^2(0-2)=3^2\cdot(-2)=-9\cdot2 \\ \Rightarrow h(0)=-18 \end{gathered}[/tex]The y-intercept is a unique value, so its multiplicity is 1. On the other hand, the x-intercepts are those x-values such that h(x) = 0. Then, solving the polynomial equation for x:
[tex](x+3)^2(x-2)=0[/tex]This equation is 0 for:
[tex]\begin{gathered} (x+3)^2=0\Rightarrow x+3=0\Rightarrow x=-3 \\ (x-2)=0\Rightarrow x=2 \end{gathered}[/tex]The first equation has a square exponent, so the multiplicity is 2. The multiplicity of the second equation is 1 because it is linear.
Summarizing:
x-intercepts:
i) -3, multiplicity 2
ii) 2, multiplicity 1
y-intercept:
i) -18, multiplicity 1
And the graph of the function looks like this:
For the end behavior, we need to analyze the limits for +∞ and -∞:
[tex]\begin{gathered} \lim _{x\to+\infty}(x+3)^2(x-2)=\infty^2\cdot\infty=+\infty \\ \lim _{x\to-\infty}(x+3)^2(x-2)=(-\infty)^2\cdot(-\infty)=\infty\cdot(-\infty)=-\infty \end{gathered}[/tex]So the function tends to infinite when x tends to infinite, and to minus infinite when x tends to minus infinite.
Hey I need help with this question this question has two parts to it
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The Solution:
Given:
We are asked to find the vertical height (x) of the cone.
Applying the Pythagorean Theorem on the right angle triangle AOB, we get:
[tex]\begin{gathered} x^2+6^2=10^2 \\ \\ x^2=10^2-6^2 \\ \\ x^2=100-36 \\ \\ x^2=64 \end{gathered}[/tex]Taking the square root of both sides, we get:
[tex]\begin{gathered} x=\sqrt{64}=8\text{ inches.} \\ \text{ So, the height of the cone is 8 inches.} \end{gathered}[/tex]Therefore, the correct answer is 8 inches
If the temperature outside is 16.87 degrees below zero in the mid-morning and drops by 3.47 degrees by nighttime, what is the temperature outside in the nighttime?
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The temperature at nighttime would be
-16.87 - 3.47 = - 20.34 degrees.
what is the equation when dealing with the question, "What is the equation of a line that goes through a point"
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h(t) = 2t + 1g(t) = 2t + 2Find (h - g)(t)
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hello
to solve this problem, let's identify the functions first
[tex]h(t)=2t+1[/tex][tex]g(t)=2t+2[/tex][tex]h-g(t)=\text{ ?}[/tex][tex]\begin{gathered} h-g(t)=(2t+1)-(2t+2)_{} \\ h-g(t)=2t+1-2t-2 \\ h-g(t)=0-1 \\ h-g(t)=-1 \end{gathered}[/tex]the answer to this question is -1
Consider the graph of f shown in the figure below.Estimate the average rate of change from x=1 to x=4Enter your estimate as a decimal number (not as a fraction), rounded to one decimal place.
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The formula to calculate the average rate of change is given to be:
[tex]AROC=\frac{f(b)-f(a)}{b-a}[/tex]where a and b are the values of x and f(a) and f(b) are the corresponding values of y.
The image below shows the values of f(a) and f(b) when a and b are 1 and 4 respectively:
Therefore, we have the following parameters:
[tex]\begin{gathered} a=1 \\ b=4 \\ f(a)=5 \\ f(b)=3.5 \end{gathered}[/tex]Therefore, we can calculate the average rate of change is calculated to be:
[tex]\begin{gathered} AROC=\frac{3.5-5}{4-1}=\frac{-1.5}{3} \\ AROC=-0.5 \end{gathered}[/tex]The average rate of change is -0.5.
Part 1: Buying Supplies DeMarcus and Catalina need to buy 2 of each item. Use the information in the left-hand column to figure out the unit price of each item. Then multiply it by 2 to find how much the will spend for two of that item. Finally, add to find the total amount of money they wil spend. The first one is done for you as an example. Item Unit Price Total for Two Water $6 for 4 bottles Apples 10 apples for $5 Nuts $15 for 5 bags Juice 12 boxes for $9 Helmets 3 helmets for $45 Locks $35 for 5 locks
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To find the unit price of each product you have to divide the price by the number of units in the information. For example
Water: $6 for 4 bottles. We have to divide the total price ($6) by the amount of bottles (4). 6/4 is 1.5, so each bottle will cost $1.5
Apples: 10 apples for $5 ---> 5/10 = 0.5, each apple costs $0.5
Nuts: $15 for 5 bags ---> 15/5 = 3, each bag of nuts costs $3
Juice: 12 boxes for $9 ----> 9/12 = 0.75, each box of juice costs $0.75
Helmets: 3 helmets for $45 ---> 45/3 = 15, each helmet costs $15
Locks: $35 for 5 locks ---> 35/5 = 7, each lock costs $7
Those are the unit prices for each product. Now you just have to fill in the center column with these results. To find the results to fill in the right hand column you have to multiply these costs by 2.
Finally, to find how much they'll spend, you sum up all the results in the right hand column
write a equation dor each line in slope intercept form
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Answer
y = (4x/3) - 1
Explanation
The slope and y-intercept form of the equation of a straight line is given as
y = mx + b
where
y = y-coordinate of a point on the line.
m = slope of the line.
x = x-coordinate of the point on the line whose y-coordinate is y.
b = y-intercept of the line.
For the slope of a straight line, the slope of the line can be obtained when the coordinates of two points on the line are known. If the coordinates are (x₁, y₁) and (x₂, y₂), the slope is given as
[tex]Slope=m=\frac{Change\text{ in y}}{Change\text{ in x}}=\frac{y_2-y_1}{x_2-x_1}[/tex]For this question,
(x₁, y₁) and (x₂, y₂) are (0, -1) and (3, 3)
[tex]\text{Slope = }\frac{3-(-1)}{3-0}=\frac{3+1}{3}=\frac{4}{3}[/tex]While the y-intercept is the point where the line crosses the y-axis.
b = y-intercept = -1
Recall
y = mx + b
m = (4/3)
b = -1
y = (4x/3) - 1
Hope this Helps!!!
Stuck with this one, I'm doing the correction for extra points.
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the correct answer id D because if we made a rotation clockwise of 90º about the origin the coordinates wil change like this:
[tex]\begin{gathered} W\to(-3,3)\Rightarrow(3,3) \\ Z\to(-6,3)\Rightarrow(2,6) \\ Y\to(-6,5)\Rightarrow(5,6) \\ X\to(-3,6)\Rightarrow(6,3) \end{gathered}[/tex]And then if we made the replection over the x axis
[tex]\begin{gathered} (3,3)\Rightarrow(3,-3) \\ (2,6)\Rightarrow(2,-6) \\ (5,6)=(5,-6) \\ (6,3)=(6,-3) \end{gathered}[/tex]that are the coordinates of the final figure
imma just send the pic
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SOLUTION:
(i)
[tex]\begin{gathered} \text{12x = -36} \\ \frac{12x}{12}=\frac{-36}{12} \\ \\ x\text{ = -3} \end{gathered}[/tex](ii)
[tex]\begin{gathered} -2x\text{ = -14} \\ \frac{-2x}{-2}\text{ = }\frac{-14}{-2} \\ \\ x\text{ = 7} \end{gathered}[/tex](iii)
[tex]\begin{gathered} \frac{x}{-3}=\text{ 9} \\ \\ x\text{ = -3 X 9} \\ x\text{ = -27} \end{gathered}[/tex](iv)
[tex]\begin{gathered} \frac{5}{x}=\text{ 10} \\ \\ \frac{5}{x}=\frac{10}{1} \\ \\ 10x\text{ = 5} \\ \frac{10x}{10}=\frac{5}{10} \\ \\ x\text{ = }\frac{1}{2} \end{gathered}[/tex]The diagram shows a square of length 6cm and two quarter circular arcs of radius 6 cm. Find the area of the shaded region, leaving your answer in terms of \pi and surds.
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Answer:
this is a 24cm...............
Which of the binomials below is a factor of this trinomial? x^2-10x-39A. x-13B. x-6C. x+6D. x^2+13
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we have the equation
[tex]x^2-10x-39[/tex]Rewrite the given quadratic equation in factored form
[tex]x^2-10x-39=(x+3)(x-13)[/tex]therefore
The answer is the option AA military plane is flying directly toward an air traffic control tower, maintaining an altitude of 12 miles above the tower. Theradar detects that the distance between the plane and the tower is 20 miles and that it is decreasing at a rate of770 mph. What is the ground speed of the plane? Round your answer to two decimal places if necessary.
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Solution:
Consider the following diagram of the situation:
By the Pythagorean theorem, we obtain the following equation:
[tex]d^2=x^2+12^2[/tex]this is equivalent to:
[tex]d^2=x^2+144[/tex]now, when d = 20, we get:
[tex]20^2=x^2+144[/tex]this is equivalent to:
[tex]400=x^2+144[/tex]solving for x, we get:
[tex]x^{}=\sqrt[]{400-144}=\text{ }\sqrt[]{256}=16[/tex]On the other hand, consider again the following equation:
[tex]d^2=x^2+144[/tex]Deriving implicitly, we get:
[tex]2xx^{\prime}=2dd^{\prime}^{}[/tex]solving for the derivative of x, we get:
[tex]x^{\prime}=\frac{dd^{\prime}}{x}[/tex]note that in this case, the derivative of d is 770, d=20, and x=16, so :
[tex]x^{\prime}=\frac{(20)(770)^{}}{16}=962.5[/tex]so that, we can conclude that the solution is:
[tex]962.5[/tex]You put the letters SCHOOL into a bag. What is the probability that you pull a Lout on your first pick, set it aside, and then pull a vowel? answer choices: 1/18 1/15 3/11 1/10
Answers
Let's begin by identifying key information given to us:
Total number of letters = 6
Number of letter "L" = 1
Number of vowels = 2
The probability that you pull an "L" out on your first pick is:
[tex]\begin{gathered} P(L)=\frac{no\mathrm{}of\mathrm{}LetterL}{Total.no} \\ P(L)=\frac{1}{6} \end{gathered}[/tex]The probability that you pull a vowel afterwards is:
[tex]\begin{gathered} P(vowel)=\frac{no\mathrm{}of\mathrm{}vowels}{Total\mathrm{}letters.left} \\ P(vowel)=\frac{2}{6-1}=\frac{2}{5} \\ P(vowel)=\frac{2}{5} \end{gathered}[/tex]The total probability of this event is given by the product of P(L) & P(vowel):
[tex]\begin{gathered} P(Total)=P(L)\cdot P(vowel) \\ P(Total)=\frac{1}{6}\cdot\frac{2}{5}=\frac{1\cdot2}{6\cdot5} \\ P(Total)=\frac{2}{30}=\frac{1}{15} \\ P(Total)=\frac{1}{15} \end{gathered}[/tex]Hence, the probability of this event is 1/15
Graph the inequality on a plane. (Click to shade a region below or above the line).2x – y > 4Pls look at the pictures because the last sign is supposed to be y is greater than or equal to 4
Answers
Answer:
Explanation:
Given the below inequality;
[tex]2x-y\ge4[/tex]The slope-intercept form of the equation of a line is generally given as;
[tex]y=mx+b[/tex]where m = slope of the line
b = y-intercept of the line
Let's go ahead and rewrite the given inequality in slope-intercept form by subtracting 2x from both sides, multiplying both sides by -1, and reversing the inequality sign;
[tex]\begin{gathered} 2x-2x-y\ge-2x+4 \\ -y\ge-2x+4 \\ -1(-y)\ge-1(-2x+4) \\ y\leq2x-4 \end{gathered}[/tex]If we compare the slope-intercept equation with the above inequality, we can see that the graph of the inequality will have a slope(m) of 2 and a y-intercept(b) of -4.
Since the inequality has both an inequality sign and an equality sign, the line will be a solid line.
Since the inequality has a less than sign, we'll shade the region below the line.
See below the graph of the given inequality with the shaded region;
uestion 2 of 50The function f(x) = 3 has a vertical asymptote atx+3OA. T=0B. z = 3C. z = 1OD. x = -3
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ANSWER
D. x = -3
EXPLANATION
The vertical asymptotes of a rational function are given by the zeros of the denominator. So, to find the vertical asymptote, we have to solve:
[tex]x+3=0\text{ }\Rightarrow\text{ }x=-3[/tex]Hence, this function has a vertical asymptote at x = -3.
What is the parallel of 2x+4y=16
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QUESTION: What is the parallel to 2x+4y=16?
CHOICES:
A. y = 2x + 5
B. y = -1/2x + 4
C. y = -1/2x + 8
D. y = -2x + 5
SOLUTION:
We will use the slope-intercept form with the formula:
[tex]\begin{gathered} y\text{ =mx + b} \\ Where\colon \\ \begin{cases}m=\text{slope} \\ b=y\text{ - intercept}\end{cases} \end{gathered}[/tex]NOTE: Equations with the same slope are said to be parallel.
Let's get the slope-intercept form of the question.
[tex]\begin{gathered} 2x\text{ +4y =16} \\ \cdot\text{Transpose 2x to the other side of the equation and change the sign. } \\ 4y\text{ =-2x+16} \\ \cdot\text{Divide both sides by 4.} \\ \frac{4y}{4}=\frac{-2x+16}{4} \\ y=-\frac{1}{2}x+4^{} \end{gathered}[/tex]ANSWER: y = -1/2x +4
Among the choices, it is the letter B.