Probabilities are used to determine the chance of an event. The following are the summary of the solution.
The probability that the two selected cellphones are green (without replacement) is 15/28The probability that one green and one yellow is selected (without replacement) is 3/7The probability that all three cellphones are yellow (with replacement) is 1/64The probability that the two cellphones are green (with replacement) is 9/16The probability that one green and one yellow is selected (with replacement) is 3/8Given that:
[tex]n = 8[/tex]
[tex]G = 6[/tex] --- Green
[tex]Y = 2[/tex] --- Yellow
(a) Probability that the two cellphones are green (without replacement).
Since the cellphone is not replaced, the probability is calculated as follows:
[tex]Pr = \frac Gn \times \frac{G - 1}{n-1}[/tex]
So, we have:
[tex]Pr = \frac 68 \times \frac{6 - 1}{8-1}[/tex]
[tex]Pr = \frac 68 \times \frac 57[/tex]
[tex]Pr = \frac{30}{56}[/tex]
[tex]Pr = \frac{15}{28}[/tex]
Hence, the probability that the two cellphones are green (without replacement) is 15/28
(b) Probability that one green and one yellow is selected (without replacement).
Since the cellphone is not replaced, the probability is calculated as follows:
[tex]Pr = \frac Gn \times \frac{Y}{n-1} + \frac Yn \times \frac{G}{n-1}[/tex] ---- The subtraction means the cellphones are not replaced
This gives
[tex]Pr = \frac 68 \times \frac{2}{8-1} + \frac 28 \times \frac{6}{8-1}[/tex]
[tex]Pr = \frac 34 \times \frac{2}{7} + \frac 14 \times \frac{6}{7}[/tex]
[tex]Pr = \frac 32 \times \frac17 + \frac 12 \times \frac 37[/tex]
[tex]Pr = \frac{3}{14} + \frac{3}{14}[/tex]
Take LCM
[tex]Pr = \frac{3+3}{14}[/tex]
[tex]Pr = \frac{6}{14}[/tex]
[tex]Pr = \frac{3}{7}[/tex]
Hence, the probability that one green and one yellow is selected (without replacement) is 3/7
(c) Probability that the all three cellphones are yellow (with replacement).
Since the cellphone is replaced, the probability is calculated as follows:
[tex]Pr = \frac Yn \times \frac Yn \times \frac Yn[/tex]
So, we have:
[tex]Pr = \frac 28 \times \frac 28 \times \frac 28[/tex]
[tex]Pr = \frac 14 \times \frac 14 \times \frac 14[/tex]
[tex]Pr = \frac 1{64}[/tex]
Hence, the probability that all three cellphones are yellow (with replacement) is 1/64
(d1) Probability that the two cellphones are green (with replacement).
Since the cellphone is replaced, the probability is calculated as follows:
[tex]Pr = \frac Gn \times \frac{G}{n}[/tex]
So, we have:
[tex]Pr = \frac 68 \times \frac{6}{8}[/tex]
[tex]Pr = \frac 34 \times \frac{3}{4}[/tex]
[tex]Pr = \frac{9}{16}[/tex]
Hence, the probability that the two cellphones are green (with replacement) is 9/16
(d2) Probability that one green and one yellow is selected (with replacement).
Since the cellphone is replaced, the probability is calculated as follows:
So, we have:
[tex]Pr = \frac Gn \times \frac{Y}{n} + \frac Yn \times \frac{G}{n}[/tex]
This gives
[tex]Pr = \frac 68 \times \frac{2}{8} + \frac 28 \times \frac{6}{8}[/tex]
[tex]Pr = \frac 34 \times \frac{1}{4} + \frac 14 \times \frac{3}{4}[/tex]
[tex]Pr = \frac 3{16} + \frac{3}{16}[/tex]
Take LCM
[tex]Pr = \frac {3+3}{16}[/tex]
[tex]Pr = \frac {6}{16}[/tex]
[tex]Pr = \frac {3}{8}[/tex]
Hence, the probability that one green and one yellow is selected (with replacement) is 3/8
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What number should be added to 2/8 to -1/12 get ?
Answer:
-1/3
Step-by-step explanation:
this is the best answer
What are the coordinates of the point
3
of the way from A to B?
у
4
B
2
1
+2
lo
-21
А
9514 1404 393
Answer:
(-3 1/2, 1 1/4)
Step-by-step explanation:
For some point P, we want ...
(P -A)/(B -A) = 3/4
4P -4A = 3B -3A
4P = 3B +A
P = (3B +A)/4 = (3(-3, 3) +(-5, -4))/4 = (-9-5, 9-4)/4 = (-14, 5)/4
P = (-7/2, 5/4) = (-3 1/2, 1 1/4) . . . . the desired point
Solve for x: (1/3)x = 81
Answer:
243
Step-by-step explanation:
1 /3 x=81
Step 1: Multiply both sides by 3.
3*( 1 /3 x)=(3)*(81)
x=243
The value of x for the expression (1/3)x = 81 is 243.
What is an algebraic expression?An algebraic expression is consists of variables, numbers with various mathematical operations.
The given expression is,
(1/3)x = 81
To find the value of x,
Solve the expression,
(1/3)x = 81
x = 81 x 3
x = 243
The required value of x is 243.
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Write 4 2/5 as an improper faction
Answer:
22/5
Step-by-step explanation:
4 [tex]\frac{2}{5}[/tex]
new numerator for improper fraction = (4 x 5) + 2 = 20 + 2 = 22
=> 22/5
Which of the following functions is odd?
PLZ HELP URGENT
Answer: Choice D
Explanation:
This is because all of the exponents are odd for this polynomial. It might help to think of that 4x as 4x^1.
Rewrite x2 − 6x + 7 = 0 in the form (x − a)2 = b, where a and b are integers, to determine the a and b values.
a = 4 and b = 3
a = 3 and b = 2
a = 2 and b = 1
a = 1 and b = 4
Answer:
a = 3 and b = 2
Step-by-step explanation:
From completion of squares:
[tex] {x}^{2} - 6x + 7 = 0 \\ \{ {x}^{2} - 6x + { (\frac{6}{2} )}^{2} \} + 7 - {( \frac{6}{2}) }^{2} = 0 \\ ( {x}^{2} - 6x + {3}^{2} ) = 2 \\ { \boxed {{(x - 3)}^{2} = 2}}[/tex]
a is 3
b is 2
Answer:
Answer B : a = 3 and b = 2
Step-by-step explanation:
Give man above brainlyiest he deserives it
Marissa earns $1,000 after taxes twice a month. Marissa's monthly bills are $1,200. Marissa deposits 40% of her remaining monthly income into a savings account and annually saves:
She saves $3,840 annually into savings account
1. Marissa earns $1,000 after taxes twice a month
This means Marissa earns $2,000 ($1000 x 2) after deduction of taxes
2. Marissa's monthly bills are $1,200.
The monthly bills means expenses that Marissa incurred during the month.
3. Marissa deposits 40% of her remaining monthly income into a savings account
The balance of Marissa earnings per month after deduction of his expenses (bills) is $800 ($2,000 - $1,200).
She deposits 40% of $800 into a savings account.
= 40% x $800
= $320
So, she is saving $320 out of the remaining $800 she has per month.
4. Marissa annually save?
She saves $3,840 annually ($320 x 12 months) into savings account.
However, she has a disposable income of $480 per month, equivalent to $5,760 per annum.
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12. Mitch, Miranda, and Evan added
their heights together.
They
got a total of 15 feet 3 inches.
Convert that measurement to
inches.
Answer:
183 inches.
Step-by-step explanation:
There are 12 inches in a foot.
12 * 15 = 180
Plus the 3 spare inches.
180 + 3 = 183
Answer:
Step-by-step explanation:
There are 12 inches in a foot.
The height in inches is 12 * 15 = 180
Total height = 12 * 15 + 3
Total height = 180 + 3
Total height = 183 inches
Can a set of data having two modes have two points of central tendency
Answer:
The Measure of Central Tendency are
1. Mean
2. Median and Quartiles
3. Mode
4. Geometric Mean
5. Harmonic Mean
→When all the five Measure of Dispersion are Same, it means the two data sets have Identical Variate.
→Now consider the two data sets,
A=3,4,4,5
B=1,4,4,7
Both the Data set have , same mean, median, and Mode,which is equal to 4.
→When you will consider, First three as Measure of central tendency ,then it becomes incorrect statement ,that Data Set are same.
Step-by-step explanation:
A measure of central tendency is a descriptive statistic
The correct response to the question is as follows;
Yes; A data having two modes can have two points of central tendency
The reason a dataset having two modes can have two points of central tendency is as follows:
A dataset having two modes is said to be bimodal
A dataset having three modes is said to be trimodal
A dataset having more than three modes is said to be multimodal
A measure of central tendency is a type of summary statistics that is a
single value representing the center point, or average of a set of data
thereby providing a description of the data by telling the middle value, the
average or the most common value which is the mode
As can be seen from the given example, by having two modes, a bimodal
data set describes a data that has two points of central tendency, thereby
giving a description of the data type, which for example may a collection
of the height of individuals, male and female, that have two most common
height values for each gender
Therefore, the correct response is yes, a dataset having two modes can
have two points of central tendency because the mode is a measure of
central tendency which is a descriptive statistics
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(x3)(x-5)
Fududeey
X=2
Answer:
-18 is the right answer..
Could use help on this math problem
Answer:
78
90
86
96
09
Step-by-step explanation:
80
90
90
OK LA sir I will complete my work as soon as possible LA thank you la madam My name is now signing off
State the gradient of the line 2y = 3 – 2x.
Answer:
Step-by-step explanation:
2y = 3-2x
y = -x + 3/2
Slope of line = coefficient of x = -1
HELP PLS! ;P
Find n.
A. 5√3
B. 5
C. 10√3/3
D. 10
Answer:
B
Step-by-step explanation:
tan(30)=n/(5*sqrt(3))
=> n=5
Plz help me with this
9514 1404 393
Answer:
see attached
Step-by-step explanation:
a) A table and graph are attached.
__
b) The relationship is NOT PROPORTIONAL. The line does not go through the origin (0, 0).
i’m genuinely confused, please help
Answer:
2x + 3 + 3x +12 + 90 = 180 (degree )
5x +105=180 (degree )
5x= 180-105 (degree )
5x = 75 (degree )
x = 75/5 (degree )
x = 15 #
therefore, 2x + 3= 2*15 + 3
=30+3
= 33#
3x + 12 = 3*15+12
= 45 +12
= 57#
What is the arc length of arc cd in the circle below. The circle has a radius of 6ft and an angle measure of 30
9514 1404 393
Answer:
π ft ≈ 3.14 ft
Step-by-step explanation:
The angle is 1/12 of the number of degrees in a circle, so the arc length will be 1/12 of the circumference of the circle.
C = 2πr
1/12C = 2/12π(6 ft) = π ft ≈ 3.14 ft
The arc length is about 3.14 feet.
Jungwon has $15. Notepads cost $2.50 each. How many notepads can Jungwon buy?
The midpoint of AB is (1, 2). The coordinates of A are (-3,6).Find the coordinates of B.
Midpoint has coordinates [tex](x_m,y_m)[/tex] which equal to,
[tex]x_m=\frac{x_1+x_2}{2}[/tex]
[tex]y_m=\frac{y_1+y_2}{2}[/tex]
We know the coordinates of a midpoint as well as the coordinates of [tex]A(x_1,y_1)[/tex] so we should be able to find coordinates of [tex]B(x_2,y_2)[/tex].
First solve both equations for [tex]x_2[/tex] and [tex]y_2[/tex] respectively,
[tex]x_2=2x_m-x_1[/tex]
[tex]y_2=2y_m-y_1[/tex]
Now insert the data,
[tex]x_2=2\cdot1-(-3)=\boxed{5}[/tex]
[tex]y_2=2\cdot2-6=\boxed{-2}[/tex]
The coordinates of B are therefore [tex](5,-2)[/tex].
Hope this helps :)
The midpoint of AB is (1, 2) the coordinates of A are (-3,6) coordinates of B coordinates of point B are (5, -2).
To find the coordinates of point B given that the midpoint of AB is (1, 2) and the coordinates of A are (-3, 6), use the midpoint formula:
Midpoint formula: M(x, y) = ((x1 + x2) / 2, (y1 + y2) / 2)
Given that M is the midpoint (1, 2) and A is (-3, 6), we have:
(1, 2) = ((-3 + x2) / 2, (6 + y2) / 2)
Solve for x2 and y2:
For x-coordinate:
1 = (-3 + x2) / 2
2 = -3 + x2
x2 = 2 + 3
x2 = 5
For y-coordinate:
2 = (6 + y2) / 2
4 = 6 + y2
y2 = 4 - 6
y2 = -2
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Going into the final exam, which will count as two tests, has test scores of 77 , 82, 72 , 63 and 92 What score does need on the final in order to have an average score of 80?
Answer:
you either need to score a perfect on one exam and get a 80 on the second or get two 90s on both exams.
Step-by-step explanation:
Find the value of x 3(4x+3)
3(4x+3)=12x+9
i don't know what do you need,
if roots, let 12x+9=0
the root is x=-3/4
Can someone help me solve these 3 trig identity problems? I am stuck on these last 3... I will give brainliest!
(calculators are allowed)
Answer:
1. 1,246
2. 0,545
3. 0,9539
Step-by-step explanation:
semoga membantu :)
pls help! I need the answer quickly!
Step-by-step explanation:
The correct answer is 4 (option B)
Which of the h values are solutions to the following equation?
h^2=0.36
Choose all answers that apply:
A: h= square root of 0.6
B: h = square root of -0.6
C: h = 0.18
D:h = -0.18
E: None of the above
Answer:
a:h=square root of 0.6
Step-by-step explanation:
thank you for your time today
Answer:
none of the above
Step-by-step explanation:
KHAN
How would you write 5x5x5x5x5x5 in exponential form
Answer:
5^6
Step-by-step explanation:
This is because the exponent is how many numbers are in the multiplication equation, in this case, five. Because there are six five's being multiplied together, our exponent is six.
What is Matilda's number?
Answer:
11
Step-by-step explanation:
The answer will be 11
as she is thinking of prime number so
111 is not a prime number
aswell as 77 is not a prime number
11 is a prime number and is also a multiple of 11
Answer:
11
Step-by-step explanation:
Is 0.03456 a rational number
Answer:
Yes. It is a rational number.
3. Consider the multiplication operations below and choose whether the fosuit com
be rational, Inational, or both.
Irrational
Expressions
Rational
8. VE
О
tvo. V
V3.12
о
Answer:
1st expression= rational 2nd expression= rational 3rd expression = irrational
Step-by-step explanation:
The first and second expressions are rational because they both equal whole numbers (4 and 3) while the last expression equals a decimal that goes on forever with no end, thus making it irrational.
Convert the following decimals into fraction . Do not reduce the fractions
0.25 =
Answer:
25/100
Step-by-step explanation:
0.25=25/100
Hope this helps! Thanks.
-y- 3 (-3y+5) helpppppppp
Answer:
D = 8y-15
Step-by-step explanation:
-y-9y-15 than combine -y and -9y
so = 8y-15
Two cars start at the same point. One travels north at 65 km/h and the other travels east at 50 km/h. How far are they apart after 30 minutes?
Answer:
they travel 115 km/h long
