A bag contains 3 black balls and 5 white balls. Paul picks a ball at random from the
and replaces it back in the bag. He mixes the balls in the bag and then picks another
ball at random from the bag.
a) Construct a probability tree of the problem.
b) Calculate the probability that Paul picks:
i) two black balls
ii) a black ball in his second draw
Answers
Answer:
(a) Tree (see diagram)
(b) (i) 9/64 (ii) 3/8
Step-by-step explanation:
3 black, 5 white, picks two at random with replacement.
SEE DIAGRAM FOR EXPLANATIONS
(a) Tree (see diagram)
(b)
(i) 9/64
(ii) 3/8
In the given problem we have 3 black ball and 5 white ball, the probability tree be constructed as per ball picks from bag.
(a) Refer the attached figure for the probability tree.
(b)
(i) The probability that Paul picks two black balls is [tex]\dfrac{9}{64}[/tex].
(ii) The probability that Paul picks a black ball in his second draw is [tex]\dfrac{3}{8}[/tex].
Given:
The bag contain 3 black and 5 white balls.
(a)
Refer the attached figure for the construction of probability tree.
(b)
(i)
Since the getting two black ball are independent event so multiply the branch B ( refer attached figure)
[tex]P(\rm two\: black)=\dfrac{3}{8}\times\dfrac {3}{8}\\P(\rm two\: black)=\dfrac{9}{24}[/tex]
Thus, the probability that Paul picks two black balls is [tex]\dfrac{9}{64}[/tex].
(ii)
There should be two outcomes either (B,B) or (W, B).
From the attached figure,
[tex]P(\rm B,B)=\dfrac{9}{64}[/tex]
[tex]P(\rm W, B)=\dfrac{15}{64}[/tex]
Calculate the probability of second ball black.
[tex]P(\rm second\: ball\: black)=P(B, B) + P(W, B)\\P(\rm second\: ball\: black)=\dfrac{9}{64}+\dfrac{15}{64}\\P(\rm second\: ball\: black)=\dfrac{3}{8}[/tex]
Thus, the probability that Paul picks a black ball in his second draw is [tex]\dfrac{3}{8}[/tex].
Learn more about probability here:
https://brainly.com/question/11234923
Related Questions
Rico can walk 3 miles in the same amount of time that Donna can walk 2 miles. Rico walks at a rate 2 miles per hour faster than Donna. At that rate, what is the number of miles that Rico walks in 2 hours and 10 minutes?
Answers
Answer:
[tex]13[/tex]
Step-by-step explanation:
Donna's Rate is [tex]R[/tex]
Rico's Rate is [tex]R+2[/tex]
[tex]\frac{R}{R+2}=\frac{2}{3}[/tex]
Cross-Multiply
[tex]2(R+2)=32[/tex]
[tex]2R+4=3R[/tex]
[tex]4=R[/tex]
Donna's Rate is [tex]R=4[/tex]
Rico's Rate is [tex]R+2=6[/tex]
[tex]\frac{6(130)}{60} = \frac{130}{10}=13[/tex]
George would like to build a garden this year, George measure out his proposed garden and would like to know how many square feet of space he will have to use . Calculate the area of the garden from the picture below
Answers
Answer:
The area is 105.5ft^2
Step-by-step explanation:
Required
The area of the composite figure
The figure can be divided to 2 shapes
(1) Rectangle: Length = 6ft and Width = 8ft
(2) Trapezoid: Height = 5ft (i.e. 8 - 3), Parallel sides = 9ft and 14ft (i.e. 20 - 6)
The area of the rectangle is:
[tex]Area = 6 * 8 = 48[/tex]
The area of the trapezoid is:
[tex]Area = \frac{1}{2}(9 + 14) * 5[/tex]
[tex]Area = \frac{1}{2}(23) * 5[/tex]
[tex]Area = 11.5 * 5[/tex]
[tex]Area = 57.5[/tex]
So, the area of the garden is:
[tex]Total = 48 + 57.5[/tex]
[tex]Total = 105.5[/tex]
Suppose an test consisted of 10 multiple choice problems, each with five possible responses (A-E), only 1 of which is correct. If a student randomly guesses the answers to each question then what is the probability that a student guesses the correct answer to exactly 7 questions?
Answers
Answer:
Step-by-step explanation:
[tex]10C_{7}\times (0.2)^{7} \times (0.8)^{3}\\[/tex]
The probability that a student guesses the correct answer to exactly 7 questions is 0.004.
What is binomial probability?The probability of exactly x successes on n repeated trials in an experiment which has two possible outcomes is called binomial probability.
Binomial probability formula[tex]P_{x} =nC_{x} P^{x} q^{n-x}[/tex]
where,
P is binomial probability
x is number of times for a specific outcome within n trials
[tex]nC_{x}[/tex] number of combinations
p is probability of success on a single trial
q is probability of failure on a single trial
n is number of trials
According to the given question.
A test consisted of 10 multiple choices.
⇒ Number of trials, n = 10
The student have to give exactly 7 correct answers.
⇒ x = 7
The probability of being correct in one trial, p = [tex]\frac{1}{5}[/tex]
(only one option is correct among fives)
So, the probability of being incorrect/wrong in one trial, q = [tex]1-\frac{1}{5} =\frac{4}{5}[/tex]
Therefore, the probability that a student guesses the correct answer to exactly 7 questions is given by
[tex]P_{x} = 10C_{7} (\frac{1}{5}) ^{7} (\frac{4}{5} )^{3}[/tex]
⇒ [tex]P_{x} = \frac{10!}{7!3!} (0.2)^{7}( 0.8)^{3}[/tex]
⇒[tex]P_{x} = 120(0.0000128)(0.512)[/tex]
⇒ [tex]P_{x} =0.004[/tex]
Hence, the probability that a student guesses the correct answer to exactly 7 questions is 0.004.
Find out more information about binomial probability here:
https://brainly.com/question/12474772
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In parallelogram HJKL if HM=12 find HK.
K
M
M
H
L
Answers
Answer:
HK = 24
Step-by-step explanation:
HK and JL are diagonals of the parallelogram.
Recall that diagonals of a parallelogram bisect each other. This implies that, they divide each other into equal parts.
Therefore,
HK = 2(HM)
HM = 12
Thus,
HK = 2(12)
HK = 24
The ratio of girls to boys in a particular classroom is 4: 3. What fraction of the total number of students are boys?
The ratio of boys to the total number of students in a particular classroom is
Answers
Answer:
3 : 7
Step-by-step explanation:
The ratio of girls to boys = 4 : 3
Since there are only two possible genders :
Then the total fraction of student is the sum of the ratio = (4 + 3)
Since,
Boys = 3
The ratio of boys to the total number of student in the class will be :
Boys : Total
3 : 7
SOLVE THIS PROBLEM PLEASE 20 POINTS
Answers
Answer:
x=5
y=0
Step-by-step explanation:
KL = JM
3x-y = 15
and JK = LM
4x -4y = 20
Divide this equation by 4
x-y= 5
Multiply by -1
-x+y =-5
Add this to the first equation
3x-y = 15
-x+y =-5
-----------------
2x = 10
Divide by 2
2x/2 = 10/2
x =5
x-y = 5
5-y = 5
-y = 0
y =0
Answer:
x=5,y=0
Step-by-step explanation:
KL=JM [Opposite sides of rectangle are equal]
3x-y=15-> eq 1
JK=LM
4x-4y=20
=>4(x-y)=20
=>x-y=5-> eq 2
From eq 1 and 2,
3x-y=15
x-y=5
=>2x=10
=>x=5
x-y=5
y=x-5
=>y=5-5
=>y=0
Solve the homogeneous linear system corresponding to the given coefficient matrix. (If there is no solution, enter NO SOLUTION. If the system has an infinite number of solutions, set x4 = t and x2 = s and solve for x1 and x3 in terms of t and s.)
[1 0 0 1]
[0 0 1 0]
[0 0 0 0]
(x1, x2, x3, x4) = _________
Answers
Answer:
[tex]x_1 = -t[/tex]
[tex]x_2 = s[/tex]
[tex]x_3 = 0[/tex]
[tex]x_4 = t[/tex]
Step-by-step explanation:
Given
[tex]\left[\begin{array}{cccc}1&0&0&1\\0&0&1&0\\0&0&0&0\end{array}\right][/tex]
Required
Determine x1 to x4
First, we write the augmented matrix
[tex]\left[\begin{array}{cccc}1&0&0&1\\0&0&1&0\\0&0&0&0\end{array}\right] = \left[\begin{array}{c}0&0&0\end{array}\right][/tex]
Taking the position of each column, we have:
[tex]x_1 + 0 + 0 +x_4 = 0[/tex]
[tex]0 + 0 + x_3 +0 = 0[/tex]
[tex]0 + 0 + 0 + 0 = 0[/tex]
There is no explicit equation for [tex]x_2[/tex]
So: [tex]x_2 = s[/tex] ----- arbitrary variable
[tex]x_1 + 0 + 0 +x_4 = 0[/tex] implies that:
[tex]x_1 + x_4 = 0[/tex]
[tex]0 + 0 + x_3 +0 = 0[/tex] implies that
[tex]x_3 = 0[/tex]
[tex]0 + 0 + 0 + 0 = 0[/tex] implies that
[tex]0 = 0[/tex]
So, we have:
[tex]x_1 + x_4 = 0[/tex]
[tex]x_3 = 0[/tex]
[tex]x_1 + x_4 = 0[/tex] becomes
[tex]x_1 = -x_4[/tex]
Let
[tex]x_4 = t[/tex]
So:
[tex]x_1 = -x_4[/tex]
[tex]x_1 = -t[/tex]
Where t , s are real numbers
Consider the following conditional statement. Determine the contrapositive
of the statement and then determine if the contrapositive is true or false.
If two angles are not complements, then their measures do not add up to 180°.
The contrapositive of the statement is true.
The contrapositve of the statement is false.
Answers
Answer:
The contrapositive of the statement is true.
Step-by-step explanation:
For a general statement:
p ⇒ q
The contrapositive statement is:
¬q ⇒ ¬p
where:
¬q is the negation of the proposition q.
Here we have the statement:
If two angles are not complements, then their measures do not add up to 180°
So we have:
p = two angles are not complements
q = their measures do not add up to 180°
Then the negations are:
¬p = two angles are complements
¬q = their measures do add up to 180°
The contrapositive statement is:
"if for two angles their measures do add up to 180°, then the two angles are complements"
This is true, if for two angles the sum of their measures is equal to 180°, then these angles are complementary.
Then: The contrapositive of the statement is true.
please answer yes i give brainliest
A.
B .
C.
OR
D.
Answers
Explanation:
Linear functions are those whose graph is a straight line.
Answer:
D. its the only straight line
Step-by-step explanation:
by the way, they are all functions
Determine which data are qualitative and which data are quantitative. Explain your reasoning
a. The yearly salaries of the employees at a school district. (9)
b. The employee numbers of the employees at an accounting firm.
c. The area codes of a sample of 350 residents of nursing homes. (2)
d. The ages of a sample of 350 residents of nursing home. (eta)
e. The answers to a survey of 5000 people about how likely is it that the US will enter a 1930s-like depression. The answers are: Very likely, somewhat likely, not very likely, not at all likely. (20)
f. The IQ index of the students in a statistics class.
What are the levels of measurement of data in question 4? Justify
a. Yearly salaries: (20)
b. Employee numbers: (ca)
c. Area codes: (eca)
d. The ages:
e. Survey answers: (ca)
f. IQ index: (en)
Answers
Answer:
1. A. Quantitative data
B. Quantitative data
C. Qualitative data
D. Quantitative data
E. Qualitative data
F. Quantitative data
2.a. Yearly salaries: interval or ratio data
b. Employee numbers: interval or ratio data
c. Area codes : nominal data
d. The ages: interval or ratio data
e. Survey answers: ordinal data
f. IQ index: interval or ratio data
Explanation:
Qualitative data is data in the form of a quality such as a characteristic. It is usually a noun, such as whether a person is fair or dark in complexion. Quantitative data is data in form of quantity such as the amount in dollars of one's salary.
There are four levels of data measurement. They are: nominal data, ordinal data, interval data, and ratio data. Nominal and ordinal data are qualitative data while interval and ratio data are quantitative data.
los tornillos vienen en bolsa de 100. cada 10 bolsas se empaqueta una caja. las cajas se embalan de a 10 en cajones y los cajones se guardan de a 10 en un contenedor para ser transportados. ¿ cuantos tornillos lleva un contenedor?
Answers
Answer:
lleva 10 000 tornillos un contenedor
Step-by-step explanation:
Find the area of the following circle.
plz I need this fast!
------11m------
379.94 m 2
34.54 m 2
94.985 m 2
17.27 m 2
Answers
Answer:
[tex]A=379.94\ m^2[/tex]
Step-by-step explanation:
Given that,
The radius of a circl is 11 m
We need to find the area of the circle. The forcemula for the area of a crcle is given by :
[tex]A=\pi r^2[/tex]
Put all the values,
[tex]A=3.14\cdot11^{2}\\A= 379.94\ m^2[/tex]
So, the area of the circle is equal to [tex]379.94\ m^2[/tex].
Answer:94.985 m 2
Step-by-step explanation:
the radius of a circle in cm ,with area 77 over 2 cm square is
Answers
Answer:
7/√2 cm
Step-by-step explanation:
Area of circle = 77 cm^2
=> π(r)^2 = 77
=> (22/7) x (r)^2 = 77
=> (r)^2 = (77 x 7) / 22
=> (r)^2 = 49/2
=> (r) = 7/√2 cm
Shawna reduced the size of a rectangle to a
height of 2 in. What is the new width if it
was originally 24 in wide and 12 in tall?
Answers
Answer: 10 in
Step-by-step explanation:
Suppose you have a regular hexagon with all side lengths equal to1. Prove that if you pick seven points from the interior of the hexagon, there is a pair of two points that are distance at most 1 apart.
Answers
Answer:
Proved
Step-by-step explanation:
Given
[tex]n = 6[/tex] --- sides of hexagon
[tex]l = 1[/tex] --- side length
Required
Prove that for 7 points picked from the interior, 2 points are at most 1 unit apart
1. Draw a hexagon (see attachment)
2. Divide the hexagon into 6 triangles
3. Select 7 points on the hexagon
You will notice that at least 2 points will be in one of the triangle.
The maximum distance between these two points is 1 unit. This is because
1. The triangle is equilateral (all sides equal)
2. The length of each is 1 unit (in other words, the distance between points, cannot exceed the side length)
In a mathematics each correct answer gains 5 marks - However, 1 mark is deducted for each incorrect answer. Mary answered 30 questions for a total of 78 marks Determine the number of correct and incorrect questions Mary answered.
Answers
Answer:
Correct answers= 18
Incorrect answers=30-18= 12 answers
Step-by-step explanation:
total questions=30
correct answers= x
incorrect answers= 30-x
given: 5 marks for each correct answer
therefore, marks for correct answers = 5*x = 5x
Given: 1 mark deducted for every incorrect answer
therefore, marks deducted = 1(30-x) = 30-x
Total marks scored= 78
★ The Difference of Marks scored for Correct Answers and Marks deducted for Incorrect Answers should be equal to 78
5x- (30-x) =78
5x-30+x=78
5x+x=78+30
6x= 108
x=108/6 = 18
Correct answers= 18
Incorrect answers=30-18= 12 answers
if ABCD is a cyclic quadrilateral and A,B,C,D are its interior angles , then prove that
tanA/2+tanB/2=cotC/2+cotD/2
answer the question plz
dont spam or else i will report that
Answers
9514 1404 393
Explanation:
In a cyclic quadrilateral, opposite angles are supplementary. This means ...
A + C = 180° ⇒ A/2 +C/2 = 90° ⇒ C/2 = 90° -A/2
B + D = 180° ⇒ B/2 +D/2 = 90° ⇒ D/2 = 90° -B/2
It is a trig identity that ...
tan(α) = cot(90° -α)
so we have ...
tan(A/2) = cot(90° -A/2) = cot(C/2)
and
tan(B/2) = cot(90° -B/2) = cot(D/2)
Adding these two equations together gives the desired result:
tan(A/2) +tan(B/2) = cot(C/2) +cot(D/2)
14x^4y^6/7x^8y^2 assume the denominator does not equal zero
Answers
Answer:
(y/x)⁴
Step-by-step explanation:
14x^4y^6/7x^8y^2
= 2x^(-4)/2y^(-4)
= (y/x)⁴
Answer:
2y^4/x^2
Step-by-step explanation:
4x^4y^6 ÷ 7x^8y^2
you will find the GCF of the equation which is: 7x^4y^2 . Then, you will divide both of the equation by the GCF and it will become
14x^4y^6 ÷ 7x^4y^2 = 2y^4
7x^8y^2 ÷ 7x^4y^2 = x^2
then you'll get the answer 2y^4/x^2
If i Bahraini dinar = £2.13, convert 4000 dinar to pounds. show your working.
Answers
Answer:
£8520
Step-by-step explanation:
1 Bahraini dinar = £2.13
Multiply both sides of the equation by 4000.
4000 * 1 Bahraini dinar = 4000 * £2.13
4000 Bahraini dinar = £8520
Ahmed packs 8 text books each of mass x grams. And two dictionaries each mass y grams into a box of mass 250 grams. What is total mass of the box now?
Answers
Answer:
8x + 2y + 250 grams
Step-by-step explanation:
The box contains
8 text books each with a mass of x grams = 8x
2 dictionaries each with a mass of y grams = 2y
1 box = 250 grams
Total = 8x + 2y + 250
90 dollars ratio in 1:2:3
Answers
Answer:
3:6:9
Step-by-step explanation:
1/1+2+3 × 90 = 15
2/1+2+3 × 90 = 30
3/1+2+3 × 90 = 45
The following dot plot shows the number of chocolate chips in each cookie that Shawn has. Each dot represents a different cookie. Which of the following is a typical amount of chocolate chips in one of Shawn's cookies?
Choose 1 answer:
Please help me!!!!
Answers
Using the dot plot, it is found that a typical amount of chocolate chips in one of Shawn's cookies is around 4.56.
What is a dot plot?The dot plot is a graph shows the number of times each measure appears in the data-set.
Researching this problem on the internet, the dot plot states that:
2 cookies have 2 chips.2 cookies have 3 chips.5 cookies have 4 chips.4 cookies have 5 ships.3 cookies have 6 ships.2 cookies have 7 chips.The mean is given by:
M = (2 x 2 + 2 x 3 + 5 x 4 + 4 x 5 + 3 x 6 + 2 x 7)/(2 + 2 + 5 + 4 + 3 + 2) = 4.56.
Hence, a typical amount of chocolate chips in one of Shawn's cookies is around 4.56.
More can be learned about dot plots at https://brainly.com/question/24912483
Answer:
5 chocolate chips
Step-by-step explanation:
did on khan
Identify the vertex, focus, and directrix of the graph. Which of the following equations represents the parabola in the graph?
need help with this, i’ll mark you brainliest!!
Answers
Answer:
Equation: [tex](x-2)^2=16(y-2)[/tex]
Vertex: [tex](2,2)[/tex]
Directrix: [tex]y=-2[/tex]
Focus: [tex](2,6)[/tex]
Step-by-step explanation:
Standard Form of Vertical Parabola:
Equation -> [tex](x-h)^2=4p(y-k)[/tex] where [tex]p\neq 0[/tex]Vertex -> [tex](h,k)[/tex]Directrix -> [tex]y=k-p[/tex]Focus -> [tex](h,k+p)[/tex]We know that our vertex is [tex](h,k)[/tex] -> [tex](2,2)[/tex], therefore, we can determine the value of [tex]p[/tex] by selecting a point from the parabola as [tex](x,y)[/tex]:
[tex](x-h)^2=4p(y-k)[/tex]
[tex](x-2)^2=4p(y-2)[/tex]
[tex](6-2)^2=4p(3-2)[/tex]
[tex](4)^2=4p(1)[/tex]
[tex]16=4p[/tex]
[tex]4=p[/tex]
Therefore:
Directrix -> [tex]y=k-p[/tex] -> [tex]y=2-4[/tex] -> [tex]y=-2[/tex]Focus -> [tex](h,k+p)[/tex] -> [tex](2,2+4)[/tex] -> [tex](2,6)[/tex]Conclusion:
Equation -> [tex](x-2)^2=16(y-2)[/tex]Vertex -> [tex](2,2)[/tex]Directrix -> [tex]y=-2[/tex]Focus -> [tex](2,6)[/tex]Review the graph for a visual
4(x+9)=2x-6
Solve for x
Answers
Answer:
-21
Step-by-step explanation:
4(x+9) = 4x+36
4x+36 = 2x-6
-36 -36
minus 36 from both sides
4x = 2x-42
2x = -42
-42/2 = -21
x = -21
Hi there!
We are given the equation below:
[tex] \large \boxed{4(x + 9) = 2x - 6}[/tex]
1. Expand 4 in the expression.
When expand in the expression, it is like multiply everything in the expression. So when we expand 4 in x+9, it becomes 4(x)+9(4).[tex] \large{(4 \times x) + (9 \times 4) = 2x - 6} \\ \large{(4x) + (36) = 2x - 6}[/tex]
Cancel the brackets.
[tex] \large{4x + 36 = 2x - 6}[/tex]
2. Isolate x-term and solve for the variable.
Think it easy. If you want to isolate x-term then what should you do? Well simply swap sides, and change the operator/sign.[tex] \large{4x - 2x = - 6 - 36}[/tex]
Finally, combine like terms.
[tex] \large{2x = - 42}[/tex]
Then divide both sides by 2 so we can finally leave only x-term.
[tex] \large{ \frac{2x}{2} = \frac{ - 42}{2} } \\ \large \boxed{x = - 21}[/tex]
3. Check the solution if it is right or wrong.
This step is optional but if you are not confident on your answer, this step is recommended.To check the answer, we simply substitute the value of x which is -21 in the equation and see if both sides are equal or not. If both sides are equal then the answer is correct, if not then the answer is wrong. Therefore,
[tex] \large{4(x + 9) = 2x - 6 \longrightarrow 4( - 21 + 9) = 2 ( - 21) - 6} \\ \large{4( - 12) = - 42 - 6} \\ \large{ - 48 = - 48}[/tex]
Since both sides are equal when substitute in x = -21.
4. Answer
Hence, the answer for this equation is x = -21.I hope this helps and let me know if you have any doubts!
a basketball team playd 64 games they won 28 more than they lost
Answers
how would I classify a triangle which has a angle of 49 and 82, acute, right, or obtuse?
Answers
9514 1404 393
Answer:
acute
Step-by-step explanation:
The third angle is ...
180° -49° -82° = 49°
So, the triangle has two angles the same, 49°. When two angle are the same, the triangle is an isosceles triangle.
The largest angle, 82°, is less than 90°, so is an acute angle. The classification acute, right, or obtuse is based on the measure of the largest angle.
The triangle is an acute isosceles triangle.
Find the following list of data calculate a demean be the maid and see mode or mothers for the following numbers listed in the picture above above
Answers
Answer:
Mean = 4.8875
Median = 4.6
Mode = 4.5 and 7.7
Step-by-step explanation:
Mean is the sum of total of data divided by the sample size
Sum total = 1.5 + 4.7 + 6 + 7.7 + 7.7 + 4.5 + 2.5 + 4.5
Sum total = 39.1
Sample size = 8
Mean = 39.1/8
Mean = 4.8875
To get the median we need to first rearrange
1.5, 2.5, 4.5, 4.5, 4.7, 6, 7.7, 7.7
Median = 4.5 + 4.7/2
Median = 4.6
Hence the median is 4.6
Mode is the value occuring the most. Since 4.5 and 7.7 both occurs twice, hence the mode of the data is 4.5 and 7.7
Help!!
f is a quadratic function where f(2) = 0, f(-2) = 0, and f(0) = -0.12. Find an algebraic equation for
f(u).
Answers
Answer:
bad gvkvkgcnhvvjzadhljang
v
gjddkfzutwdjtabkf
f(0) = k x -2 x 2 = -0.12
so k = -0.12 / -4 = 0.03
f(u) = 0.03(u - 2)(u + 2)
sammy is on level 40 , which is five times as much as rocky.what islevel rocky on
Answers
Answer:
8
Step-by-step explanation:
40÷5=8
Hope this helps! :)
Natural logs can be written as _______.
Answers
Answer:
Step-by-step explanation:
The natural logarithm of x is generally written as ln x, loge x, or sometimes, if the base e is implicit, simply log x.
Answer:
Ln x as opposed to log x
Step-by-step explanation: