Answer:
18/95
Step-by-step explanation:
What is probability?
Probability is simply the chances of something occuring.
As a formula, I like to say that formula = # of favorable outcomes / total # of outcomes
Where favorable outcomes is what we want to happen and total # of outcomes is the total number of possibilities.
In order to find the probability of the occurrence of something in a row, we multiply the individual probabilities of each action
Understanding the question
Here we are given that caleb has 7 black caps 4 yellow caps and 9 blue caps in his wardrobe and given this we want to find the probability of Caleb randomly selecting 2 blue caps without replacing it the first being drawn.
So here # of favorable outcomes = # of blue caps = 9
and
total number of outcomes = total # of caps = 7 + 4 + 9 = 20
Finding the probability
For first draw
First let's find the probability that caleb will select a blue cap the first time.
We know that probability = # of favorable outcomes / total # of outcomes
We also know that # of favorable outcomes = 9 and total # of outcomes = 20
Plugging this in, we get that the probability of Caleb randomly selecting a blue cap on the first draw is 9/20
For second draw
Because it says that caleb will not replace the cap when drawn it's important to subtract 1 from both the # of caps and # of blue caps
This results us in having # of favorable outcomes as 8 and total # of outcomes as 19
Plugging this in we get that the probability of Caleb drawing a blue cap the second time is 8/19
Finally to find the total probability of him selecting two blue caps in a row without replacing the first cap, we multiply the individual probabilities
From doing so we acquire 9/20 * 8/19 = 18/95
Answer:
18/95
Step-by-step explanation:
Probability Formula :
Probability (Event) = Number of outcomes with Event / Total outcomes
=============================================================
Given :
⇒ 7 black caps
⇒ 4 yellow caps
⇒ 9 blue caps
===========================================================
Solving :
P (1st cap is blue) :
⇒ Number of blue caps / Total caps
⇒ 9 / 7 + 4 + 9
⇒ 9/20
It mentions the cap is not replaced. Hence, when taking the probability of the 2nd cap, subtract a blue cap from the number of blue caps and the total.
P (2nd cap is blue) :
⇒ Number of blue caps - 1 / Total caps - 1
⇒ 9 - 1 / 20 - 1
⇒ 8/19
P (both caps are blue) :
⇒ P (1st cap blue) × P (2nd cap blue)
⇒ 9/20 × 8/19
⇒ 9/5 × 2/19
⇒ 18/95
wyatt has a square garden. he adds 3 feet to one side and 1 foot to the other and now it is a rectangle with an area of 24 ft^2 what are the new dimensions of the garden
The new dimension of the rectangle are as follows;
6 ft4 ftHow to find the new dimension of the rectangle?The new dimension of the rectangle can be found as follows;
The sides of a square are equal.
Therefore,
let the side of the square = x
Hence,
length = x + 3
width = x + 1
area of rectangle = lw
where
l = lengthw = widthTherefore,
24 = (x + 3)(x + 1)
24 = x² + x + 3x + 3
24 = x² + 4x + 3
x² + 4x + 3 - 24
x² + 4x - 21 = 0
(x - 3)(x + 7)
Therefore,
x = 3 or -7
It can't be negative. Hence, x = 3 ft
Therefore, the new dimension of the rectangle are as follows;
x + 3 = 3 + 3 = 6 ftx + 1 = 3 + 1 = 4 ftlearn more on rectangles here: https://brainly.com/question/17562456
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Use vectors to find the interior angles of the triangle with the given vertices. (Enter your answers as a comma-separated list. Enter your answers in terms of degrees. Round your answers to two decimal places.) (−6,-9), (2,7),(7,2)
Answer:
23.20°, 71.57°, 85.24°
Step-by-step explanation:
The angle between two vectors can be found by making use of the definition of the dot product. The computed angle is the angle between the vectors when they are placed tail-to-tail.
__
setupvector definition
The second attachment shows the given points plotted as A, B, C in the order given. In the diagram, the vectors a, b, c are defined as BA, CB, AC, respectively. That is, the vector a is ...
a = A -B = (-6, -9) -(2, 7) = (-6-2, -9-7) = (-8, -16)
The vectors are defined in counterclockwise order around the triangle, though that makes no difference to the calculation.
dot product definition
The definition of the dot product of vectors A and B is ...
A·B = |A|×|B|×cos(θ) . . . . . where θ is the angle between the vectors
Solving for the angle, we find it to be ...
[tex]\theta=\arccos\left(\dfrac{\vec{A}\cdot\vec{B}}{|\vec{A}|\,|\vec{B}|}\right)[/tex]
__
computationBecause of the way the vectors in this solution are defined, the angle between any given pair of vectors will be an exterior angle of the triangle. In order to find the measure of the interior angle, we must reverse one of the vectors. That is, the dot product used in our computation will be the opposite of the dot product of the vectors we have found.
The spreadsheet shown in the first attachment does the necessary computations.
Each vector is the difference of successive points. (x1 -x2, y1 -y2)Each dot product shown is the opposite of the dot product of successive vectors. -(x1x2 +y1y2)The magnitude is computed in the usual way: the root of the sum of the squares of the components of the vector. √(x²+y²)The cosine is the dot product of successive vectors, divided by each of the vector magnitudes.The spreadsheet shows the angle in degrees, having converted it from the radian value produced by the ACOS function.As a check, the spreadsheet shows the sum of the angle values. (The rounded values add up to 180.01°.)
The interior angles of the triangle are 23.20°, 71.57°, 85.24°.
_____
Additional comment
Another way to find the interior angles from coordinates is to consider the slope of each side of the triangle as being the tangent of the angle it makes with the x-axis. The difference of these angles can be used to find the interior angles of the triangle. Less work is involved because there is no dot-product or magnitude computation.
In a cave, a stalactite gets 44 millimeters longer each year. this year it is 72 centimeters long. how many years until it is 1 meter long?
Answer:
6.36 years (the .36 repeats), so rounded is 6.4.
Step-by-step explanation:
First, I'm going to convert all measurements to meters.
Since 1000 mm = 1 m, divide 44 by 1000.
44/1000 = 0.044 m
Since 100 cm = 1 m, divide 72 by 100.
72/100 = 0.72 m
Next, I'm going to setup an equation using y = mx + b.
b is the beginning amount which is 0.72.
m in the equation represents the rate which is 0.044.
y represents the total which is 1.
Plugin the numbers and solve for x.
1 = 0.044x + 0.72
1 - 0.72 = 0.044x + 0.72 - 0.72
0.28 = 0.044x
0.28/0.044 = 0.044x/0.044
6.36 = x
Rectangular prism A measures 2 inches by 7 inches by 8 inches. Rectangular prism B measures 1 inches by 5 inches by 10 inches.
Rectangular Prism A:
Surface Area: __inches²
Volume: __inches³
Surface Area to Volume Ratio: (Enter as an improper fraction)
Rectangular Prism B:
Surface Area: __inches²
Volume: __inches³
Surface Area to Volume Ratio: (Enter as an improper fraction)
The Volume for Rectangular prism A is 172 inches², Volume = 112 inches³
Surface Area to Volume Ratio = 43/28
Mensuration of SolidsGiven Data
Rectangular prism A
Length = 2 inches
Width = 7 inches
Height = 8 inches
Surface Area
A=2(wl+hl+hw)
A=2(7*2+8*2+8*7)
A=2(14+16+56)
A= 172 inches²
Volume
Volume = L*W*H
Volume = 2*7*8
Volume = 112 inches³
Surface Area to Volume Ratio
= 172/112
= 43/28
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What is it help pleaseee
Answer:
25.13cm
Step-by-step explanation:
formula for circumference of a circle is (2r)π with r being the radius
since the problem gave us the diameter already we can change the formula to 8π (2r is equal to the diameter since diameter is twice as long as the radius)
this gives us the circumference of 25.13
PLEASE HELP!
Which of the following statements is/are true? (5 points)
I. If f '(c) = 0, then f has a local maximum or minimum at x = c.
II. If f is continuous on [a, b] and differentiable on (a, b) and f '(x) = 0 on (a, b), then f is constant on [a, b].
III. The Mean Value Theorem can be applied to f(x) = 1/x2 on the interval [-1, 1].
I only
II only
I and III only
I and II only
I especially need help with the first statement... I think it's true in some situations, but there are some counter-examples. I don't know if this means it's true or false!!!
Both the first and second statements are true and therefore Option D is the correct answer .
What is a Function ?A function can be defined as the equation that identifies relation between a dependent variable and an independent variable.
A function always has a defined range and domain.
In the following statements
I. If f '(c) = 0, then f has a local maximum or minimum at x = c.
f'(c) = 0
It means that the slope of f(x) = 0 at x = c
If f has a local maximum or minimum at x = c It is a True statement
II. If f is continuous on [a, b] and differentiable on (a, b) and f '(x) = 0 on (a, b), then f is constant on [a, b].
If f'(x) = 0 on (a, b),
then f is neither increasing nor decreasing
and therefore is constant on [a, b]
So it is a True statement.
III. The Mean Value Theorem can be applied to f(x) = 1/x² on the interval [−1, 1].
No the theorem cannot be applied as, f is neither continuous nor differentiable at x = 0
It is a False Statement.
Therefore Option D is the correct answer.
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A mosquito has a mass of about 0.00000225 kilograms. Which of these is the measure of the mass in scientific notation?
Answer:
2.25x 10^-6
Step-by-step explanation:
In order to find out which is the scientific notation you would want to count how many zeros are in front of the number in this case it has 6 zeros before the series of numbers meaning that it would be 10^-6
Please help!!
The two-way frequency table below shows data on playing a sport and playing a musical instrument for in a class.
Answer: Check out the screenshot below for the answers
==========================================================
Explanation:
For each column, we divide the values by the sum of each column.
The sum of the first column is 6+8 = 14, and the sum of the second column is 7+3 = 10.
Column 1:
6/14 = 0.438/14 = 0.57Those values are approximate to two decimal places.
Column 2:
7/10 = 0.703/10 = 0.30Those values are exact.
The values in bold are then filled in the table as you see below.
A result like 0.43 means that 43% of those who play a sport also play an instrument. The other values are interpreted in a similar fashion.
how many Years are in 1,000
The number of years in 1000 days is = 2 . 74 years .
How many Years are in 1,000 day?Division is the arithmetic operation that is used to determine the quotient of a number. Division parts a number into equal parts with another number.
Number of years in 100 days = 1000 / 365
= 2 . 74 years
Here is the complete question:
how many Years are in 1,000 days
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A hypothesis regarding the weight of newborn infants at a community hospital is that the mean is 22.1 pounds. a sample of seven infants is randomly selected and their weights at birth are recorded as 21.1, 25.1, 26.1, 27.1, 24.1, 31.1, and 31.1 pounds. if α = 0.010, what is the critical value? the population standard deviation is unknown.
The critical value at the 0.010 significance level with 6 degrees of freedom are ±3.7074
How to determine the critical value?The dataset is given as:
21.1, 25.1, 26.1, 27.1, 24.1, 31.1, and 31.1
The sample mean is:
[tex]\bar x = 22.1[/tex]
The significance level is
α = 0.010
Start by calculating the degrees of freedom using:
df = n - 1
Where n represents the sample size (n = 7)
So, we have:
df = 7 - 1
df = 6
Using the table for t critical values for a two-tailed test, we have:
Critical value = ±3.7074
Hence, the critical value at the 0.010 significance level with 6 degrees of freedom are ±3.7074
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Evaluate
4(x+5)(x+1)
(x+3)(x-3)
for x = 5.
Answer:
3840
Step-by-step explanation:
Given expression:
4(x+5)(x+1)(x+3)(x - 3)
To:
Evaluate the expression ; for x = 5.
Solution:
4(x+5)(x+1)(x+3)(x - 3)Evaluate x = 5 :
4(5+5)(5+1)(5+3)(5 - 3)Simplify using PEMDAS rule:
P : Parentheses
E : Exponents
M : Multiplication
D : Division
A : Addition
S : Subtraction
(4)(10)(5+1)(5+3)(5−3)40(5+1)(5+3)(5−3)(40)(6)(5+3)(5−3)(240(5+3)(5−3)(240)(8)(5−3)1920(5−3)(1920)(2)3840Hence, after evaluating the given expression for x = 5 , the answer'll be 3840.
Hi student, let me help you out! :)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
We are asked to evaluate
[tex]\large\pmb{4(x+5)(x+1)(x+3)(x-3)}[/tex] for x=5.
[tex]\triangle~\fbox{\bf{KEY:}}[/tex]
Use PEMDAS. With the help of this acronym, we will not make any mistakes in the Order of Operations!Here's what PEMDAS stands for:
P=Parentheses
E=Exponents
M=Multiplication
D=Division
A=Addition
S=Subtraction
So, let's start computing...
///\\\///\\\///\\\///\\\///\\\////\\\///\\\///\\\///\\\///\\//\\\///\\\///\\\///\\\\///\\\\///\\\///\\\///\
Evaluating the expression
First, substitute 5 for x:
[tex]\star~\large\pmb{4(5+5)(5+1)(5+3)(5-3)}[/tex]
Now, use the Order of Operations.
The first operation here is:
[tex]\dag[/tex] P=Parentheses
So we need to perform the operations inside the parentheses first:
[tex]\star~\large\pmb{4(10)(6)(8)(2)}[/tex]
The next operation is multiplication, since we don't have any exponents here:
[tex]\star~\large\pmb{40\times6\times8\times2}[/tex]
Multiply!
[tex]\star~\Large\pmb{3840}~~\square\!\!\!\!\!\checkmark[/tex]
That's the value of the expression 4(x+5)(x+1)(x+3)(x-3) for x=5.
Hope it helps you out! :D
Ask in comments if any queries arise.
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Find the area of the following rhombus: A m? 52m 8m A=?m2
The area of the rhombus is 832 square m if the length of the diagonals are 104 m and 16 m.
What is a rhombus?A rhombus is a two-dimensional shape having four parallel opposite pairs of straight, equal sides. This shape resembles a diamond and is what you'd find on a deck of cards to represent the diamond suit. Rhombuses can be encountered in a variety of common situations.
We have given a rhombus with diagonals.
The length of the long diagonal p = 2×52 = 104 m
The length of the short diagonal q = 2×8 = 16 m
Area = pq/2 = (104×16)/2 = 832 square m
Thus, the area of the rhombus is 832 square m if the length of the diagonals are 104 m and 16 m.
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he triangles below are similar. Triangle Y X Z. Side Y X is 6 centimeters, X Z is 7 centimeters, and Z Y is 3 centimeters. Triangle A B C. Side A C is 14 centimeters, A B is 12 centimeters, and B C is 6 centimeters. Which similarity statement expresses the relationship between the two triangles? Triangle Z Y X is similar to triangle C A B Triangle Z Y X is similar to triangle A C B Triangle Z Y X is similar to triangle C B A Triangle Z Y X is similar to triangle A B C
And
AB=12BC=6AC=14Check
AB/YX=BC/ZY=AC/XZ12/6=6/3=14/72=2=2Hence
ABC=XYZOr
ZYX≈CBAOption C
show your working please.
Offer B is the best value for money because each kg cost is £0.61 and in offer 'A' each kg cost is £0.7.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
We have:
2 bags for £35
2 bags means 50 kg (2×25)
Each kg cost = 35/50 = £0.7 per kg
3 bags for £92.50
3 bags means 150 kg
Each kg cost = 92.50/150 = £0.61 per kg
As we can see, offer B has a low cost per kg
Thus, offer B is the best value for money because each kg cost is £0.61 and in offer 'A' each kg cost is £0.7.
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if three times a certain number is increased by 4 the result is 28
Answer:
The number is 8
Step-by-step explanation:
Let x be the number
3x+4 = 28
Subtract4 from each side
3x+4-4 = 28-4
3x= 24
Divide by 3
3x/3 =24/3
x = 8
In her free time, isabelle likes to read. she kept track of the number of pages in each book she read last summer. this box plot shows the results. what fraction of the books has 200 or fewer pages?
200 is the median (50%) of the data represented in the box plot. The fraction of the books has 200 or fewer pages is: 1/2.
What is the Median of a Data in a Box Plot?In a box plot, the median is indicated as the value marked by the vertical line that divides the rectangular box of the box plot.
The median is the middle of the data and represents the 50th percentile. That is 1/2 the data.
In the box plot given, 200 pages is the median. Therefore, the fraction of the books that have 200 or fewer pages is: 1/2.
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The speed of light is roughly 186,000 miles per second. How many minutes does it take for light to arrive from the sun, which is 93,000,000 miles away?
Answer:
8.3 minutes
Step-by-step explanation:
93,000,000 m/186,000 m/s = 500 s
500/60 = 8.333333
Calculate the mean of 1,2,3,4,5,6
Answer:
mean = 3.5
Step-by-step explanation:
the mean is calculated as
mean = [tex]\frac{sum}{count}[/tex] = [tex]\frac{1+2+3+4+5+6}{6}[/tex] = [tex]\frac{21}{6}[/tex] = 3.5
Answer:
The mean of 1 , 2 , 3 , 4 , 5 , 6 is 3.5
Given :
The observations 1 , 2 , 3 , 4 , 5 , 6
To find :
The mean of 1 , 2 , 3 , 4 , 5 , 6
Solution :
Step 1 of 2 :
Calculate sum of the observations
Here the given observations are 1 , 2 , 3 , 4 , 5 , 6
Number of observations = 6
Sum of the observations
= 1 + 2 + 3 + 4 + 5 + 6
= 21
Step 2 of 2 :
Find the mean
The required mean
what is the slope of the line through the points (-3,3) and (6,-8)
Answer:
[tex]\displaystyle \frac{-11}{9}[/tex]
Step-by-step explanation:
We will use the equation of change in y over change in x to solve for the slope of the line. Then, we will simplify.
[tex]\displaystyle \frac{y_{2}-y_1 }{x_2-x_1}[/tex]
[tex]\displaystyle \frac{-8-3}{6--3}[/tex]
[tex]\displaystyle \frac{-8-3}{6+3}[/tex]
[tex]\displaystyle \frac{-11}{9}[/tex]
Please help me with this question, it says:
Solve the equation
x to the power of 3, take away x equals to 120
Using a trial and improvement method.
You must show working out.
Answer:
x = 5.
Step-by-step explanation:
x^3 - x = 120
We first guess the value of x and calculate the left side.
Take x = 4:-
4^3 - 4 = 64-4 = 60
This is < 120 so try x = 5:
5^3 - 5 = 125 - 5 = 120.
So one solution is x = 5.
Hello Brainly, The Question is Find the Area of this Parallelogram. Please Help! Thank You!
Answer:
24 ft sq
Step-by-step explanation:
find area of triangles
6×4=24
24/2=12
add areas together
12+12=24
Fawzia randomly selected 50 plants at a nursery to test for aphids. she discovered 7 plants that had the pests. if the nursery has 780 plants. what could be the predicted number of plants with aphids?
The predicted number of plants with aphids is 109.
What is the predicted number of plants with aphids?The predicted number of plants with aphids is the ratio of the random plants with aphids to total number of random plants selected multiplied by the number of plants in the nursery.
Predicted number = (7/50) x 780 = 109.
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can someone help me with this problem? Thank you!
Answer:
152
Step-by-step explanation:
If you substitute the 6, the expression will look like this-
8( 3(6) + 1 )
You can then times 3 by 6, this makes 18. You then add the one, this equals 19.
19 times 8 = 152.
I hope this helps, have a lovely day.
triangle png What is the angle measure of angle B?
Answer:
[tex]m\angle B = 28^{\circ}[/tex]
Step-by-step explanation:
All angles in a triangle must add up to [tex]180^{\circ}[/tex]
We can solve for [tex]\angle B[/tex] using this knowledge
[tex]\angle B + 40 + 112 = 180\\\angle B + 152 = 180\\\boxed{\angle B = 28}[/tex]
That is the answer
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Fill out the chart please!
The dot plot and the box plot shown both represent Manuel’s data. Determine which visual display is more useful for answering each of the questions listed in the table, and explain your reasons.
1. Mean of the data: 8
2. Median: 8
3. IQR = 4
4. Members that use the facility 10 days a month is: 2.
See reasons below.
What is the Mean, Median, and Interquartile Range of a Data?Mean = sum of all values ÷ number of data values (easily solved using a dot plot
Median = middle value (easily found using a box plot).
Interquartile range (IQR) = Q3 - Q1 (easily found using a box plot).
1. Mean of the data: use the dot plot.
Reasoning: (3 + 3 + 5 + 6 + 6 + 7 + 8 + 8 + 8 + 9 + 10 + 10 + 11 + 12 + 14)/15 = 8
2. Median of the data set: Using the box plot, it is the value indicated by the vertical line that divides the box.
Median = 8
3. IQR = Q3 - Q1 = 10 - 6
IQR = 4
4. Members that use the facility 10 days a month, using the dot plot is: 2. 10 has 2 dots.
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Need Help ASAP
Consider the circles A, B, C, and D.
Four circles A, B, C, and D are shown. Circle A has a diameter of 8 feet. Circle B has a diameter of 10 inches. Circle C has a diameter of 2 feet. Circle D has a radius of 50 inches.
a. Without calculating, circle
has the greatest circumference.
Question 2
Explain.
Answer:
Circle D
Step-by-step explanation:
The circumference of a circle can be calculated by multiplying the diameter by π. Therefore, the circle with the greatest circumference will be the circle with the greatest diameter.
The only circle for which we have been told the radius is Circle D. The diameter of a circle is twice the radius, therefore the diameter of Circle D is 50 in × 2 = 100 in
There are 12 inches in 1 ft.
Therefore, the circumferences of the circles in order from smallest to largest is: B < C < A < D
Proof
Diameters
Circle A = 8 ft = 96 inCircle B = 10 inCircle C = 2 ft = 24 inCircle D = 2 × 50 in = 100 inIf a fair die is rolled 3 times, what is the probability, to the nearest thousandth, of getting exactly 2 ones?
[tex]\displaystyle|\Omega|=6^3=216\\A=\binom{3}{2}\cdot5=3\cdot5=15\\|A|=\dfrac{15}{216}=\dfrac{5}{72}\approx0.069[/tex]
Of the following three statements, choose the best option and write a viable argument showing how it is reflected by the cost function for wichita's factory
A viable argument showing how it is reflected by the Cost Function for Wichita’s factory is; The cost of production per unit of item produced is 1$ as long as total units produced is less than 2500. If more than 2500 units are produced than the cost per unit actually comes down to 0.8$per unit.
How to Interpret Cost Functions?
From the given options, the best statement is;
The plant’s production processes are performed primarily by robots that are able to work longer hours, when needed, at no additional cost.
A cost function is a formula used to predict the cost that will be experienced at a certain activity level. Thus, the cost function for the best option is;
The cost of production per unit of item produced is 1$ as long as total units produced is less than 2500. If more than 2500 units are produced than the cost per unit actually comes down to 0.8$per unit.
The missing options are;
___ The electricity contract with the utility company is structured so that higher daily energy usage is charged at a lower rate.
___ The plant’s production processes are performed primarily by robots that are able to work longer hours, when needed, at no additional cost.
___ Overtime wages were required to produce at levels above 25,000 units.
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A keypad has only the letters A−D. What is the total number of possible outcomes if the code has 3 letters?
Answer:
9
Step-by-step explanation:
Because 3 letter to find that just do 3 times 3 which = 9
Hope This Helped
Answer:
64
Step-by-step explanation:
There are 4 options to choose from:
ABCDEach has a 1/4 chance of being picked.
For 3 times in a row, we would multiply the chance of being picked for one option, by whatever the other option's chance is.
As they all have the same chance, and it is 3 times in a row, we would do the following:
1/4 x 1/4 x 1/4
This is:
1/16 x 1/4
Which is:
1/64
Therefore, any possible combination has a 1/64 chance of occurring, meaning that there are 64 possible combinations that could be created.
Solve 2x+6 ≤ 10 or 2x + 8 > 20.
A. x ≤2 or x>6
OB. x < 1 or x > 2
OC. x ≤ 1 or x > 6
OD.
2 and x > 2
Answer:
A. x ≤2 or x>6Step-by-step explanation:
2x+6 ≤ 10 or 2x + 8 > 20
⇔ 2x ≤ 4 or 2x > 12
⇔ x ≤ 2 or x > 6