The points the blue marble should be worth for the game to be fair is given by: Option C: 8
How to calculate the probability of an event?Suppose that there are finite elementary events in the sample space of the considered experiment, and all are equally likely.
Then, suppose we want to find the probability of an event E.
Then, its probability is given as
[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text{Number of total cases}} = \dfrac{n(E)}{n(S)}[/tex]
where favorable cases are those elementary events who belong to E, and total cases are the size of the sample space.
How to calculate the expectation of a discrete random variable?Expectation can be taken as a weighted mean, weights being the probability of occurrence of that specific observation.
Thus, if the random variable is X, and its probability mass function is given : f(x) = P(X = x), then we have:
[tex]E(X) = \sum_{i=1}^n( f(x_i) \times x_i)[/tex]
(n is number of values X takes)
For the game to be fair, the expected number of points that one can loose should be equal to the expected number of points one can gain.
Now, probability of getting any specific colored marble = 1/5 = 0.2 (since there is one way to choose a specified colored marble, but there are 5 ways to choose a single (no color specified) marble out of 5 marbles.
The game would be fair if there is equal chance of winning and loosing.
Let we have:
Then we need E(X) = expectation of X = 0 (since the negative points of loosing would equate to positive point of winning, thus, making the expected overall score 0, thus, making game fair.
Values of X = -2(if lost, or say chose any four colored marble except blue marble), or p(if won, or say chose blue colored marble)
P(X = -2) = P(choosing non-blue marble) = 4/5P(X = p) = P(choosing blue marble) = 1/5(its because choosing one marble from 5 marbles can be done in 5 ways, so n(S) = 5, and choosing 1 blue marble out of 5 different colored marble can be done in 1 way, and choosing 1 non-blue marble out of 5 different colored marble can be done in 4 ways)
Thus, we get:
[tex]E(X) = -2 \times P(X = -2) + p \times P(X = p)\\E(X) = -2 \times 4/5 + p \times 1/5\\0 = -8/5 + p/5\\0 = -8 + p\\p = 8[/tex]
Thus, the points the blue marble should be worth for the game to be fair is given by: Option C: 8
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D=xlx is a whole number)
E = {xlx is a perfect square between 1 and 9)
F={xlx is an even number greater than or equal to 2 and less than 9)
Which of the following is an element of D n (E n F)?
16
3
6
4
Answer:
Option (4)
Step-by-step explanation:
D = {x| x is a whole number}
D = {1, 2, 3, 4..........}
E = {x | x is a perfect square between 1 and 9}
E = {4}
F = {x | x is an even number greater than 2 and less than 9}
F = {2, 4, 6, 8}
(E ∩ F) = Set of common numbers of E and F
= {4}
D ∩ (E ∩ F} = Set of common numbers in the sets of D and (E ∩ F)
= {4}
Therefore, Option (4) will be the answer.
Ellen has $75 in her savings account she deposits 25 every week her father also deposit 35 into the account every time Ellen most salon
Answer:
She have 345$ in her account.
Step-by-step explanation:
Given that,
Ellen has $75 in her savings account she deposits 25 every week her father also deposit 35 into the account every time Ellen most salon
Suppose, her savings account balance can be shown with the following expression:
75 + 25w + 35m
If Ellen saves for 8 weeks and most the salon 2 times, how much will she have in her account.
We know that,
When the numbers appear with variables it called coefficients.
When the numbers appear without variables it called constant.
Alphabets in an expression are called variables.
According to question,
25 and 35 are the coefficients and the number 75 appear without variables.
We need to calculate the balance in her account
Using expression
[tex] 75 + 25w + 35m [/tex]
Put the value in the expression
[tex]75+25\times8+35\times2[/tex]
[tex]=345$[/tex]
Hence, She have 345$ in her account.
The distributions of X and of Y are described here. If X and Y are independent, determine the joint probability distribution of X and Y.
Answer:
The joint probability distribution of X and Y is shown below.
Step-by-step explanation:
The distributions of X and of Y are described as follows:
X : 0 1
P (X) : 0.23 0.77
Y : 1 2 3
P (Y) : 0.40 0.22 0.38
It is provided that X and Y are independent.
That is:
P (X ∩ Y) = P (X) × P (Y)
Compute the joint probability distribution of X and Y as follows:
[tex]P(X=0,Y=1)=P(X=0)\times P(Y=1)=0.23\times 0.40=0.92\\\\P(X=0,Y=2)=P(X=0)\times P(Y=2)=0.23\times 0.22=0.0506\\\\P(X=0,Y=3)=P(X=0)\times P(Y=3)=0.23\times 0.38=0.0874\\\\P(X=1,Y=1)=P(X=1)\times P(Y=1)=0.77\times 0.40=0.308\\\\P(X=1,Y=2)=P(X=1)\times P(Y=2)=0.77\times 0.22=0.1694\\\\P(X=1,Y=3)=P(X=1)\times P(Y=3)=0.77\times 0.38=0.2926[/tex]
X 0 1
Y
1 0.9200 0.3080
2 0.0506 0.1694
3 0.0874 0.2926
plsss help asap!!!!1
Math To Do, -Ready
Home Jefferson County School X
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Which unit would you most likely use to measure the capacity of a mug?
Answer:
fluid ounces
hope it helps;)
The most likely unit to measure the capacity of a mug is fluid ounces (fl oz).
What is capacity?The maximum amount that something can contain or hold is referred to as its capacity. It is useful for determining the volume of a container, such as a mug or a bucket. Capacity measurement units vary, but common ones include millilitres, litres, fluid ounces, and gallons.
Capacity is a measurement of how much fluid or material a container can hold, and it is usually expressed in ounces, millilitres, litres, or gallons.
Because a mug is a container that holds liquids, the appropriate unit of measurement to use when determining how much liquid a mug can hold is capacity.
Thus, the answer is fluid ounces.
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find the slope and the y intercept of the line y=-5/4x+9
Answer:
-5/4
Step-by-step explanation:
the slope is the variable in front of x
y = mx + b
m = slope
b = y-int
Answer:
-5/4
Step-by-step explanation:
using slope intercept form, the slope is -5/4
m= -5/4
Use the commutative and associative properties as needed to simplify the expression. (12+a)+14
Answer:
26+a
Step-by-step explanation:
(12+a)+14
(12+14)+a
26+a
Write the slope-intercept form of the line passing through (–8, –5) and (4, 4).
Answer:
[tex]\Huge \boxed{y=\frac{3}{4} x+1}[/tex]
[tex]\rule[225]{225}{2}[/tex]
Step-by-step explanation:
We can find the slope through two points.
m = (y2 - y1)/(x2 - x1)
m = (4 - -5)/(4 - -8)
m = 9/12 = 3/4
The slope of the line is 3/4.
Slope-intercept form of a line is y=mx+b. Where m is the slope and b is the y-intercept.
y = 3/4x + b
A point on the line is (4, 4). x = 4 and y =4.
4 = 3/4(4) + b
4 = 3 + b
b = 1
The y-intercept is 1.
[tex]\rule[225]{225}{2}[/tex]
Answer:
[tex]\huge\boxed{y = \frac{3}{4}x+1}[/tex]
Step-by-step explanation:
Finding the slope (m) first:
Given the coordinates (-8 , -5) and ( 4 , 4 )
Slope = [tex]\sf \frac{Rise}{Run}[/tex]
Slope = [tex]\sf \frac{y2-y1}{x2-x1}[/tex]
Slope = [tex]\frac{4 + 8}{4+5}[/tex]
Slope = [tex]\frac{12}{9}[/tex]
Slope = m = [tex]\frac{3}{4}[/tex]
Finding y - intercept (b) :
Taking a coordinate say (4,4)
And putting it in slope intercept form along with b
y = mx+b
Where y = 4 , m = 3/4 and x = 4
4 = (3/4)(4) + b
4 = 3+b
4-3 = b
1 = b
So,
b = 1
Putting m and b now in slope-intercept equation:
y = mx+b
[tex]y = \frac{3}{4}x+1[/tex]
Steve spent $40 at the grocery store. He bought bottled water, soda, and sandwiches. A bottle of water costs $1.50, a bottle of soda costs $2, and a sandwich costs $3. If he bought 10 bottles of water and 5 bottles of soda, how many sandwiches did he buy?
Answer:
5 sandwiches.
Step-by-step explanation:
$15 for the water, $10 for the soda. So if you add 15 and 10 that's 20. 40-25 = 15 on sandwiches. If each sandwich is $3, then that's 5 sandwiches.
An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
The number of sandwiches bought is 3.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Cost of a bottle = $1.50
Cost of a soda = $2
Cost of a sandwich = $3
Number of bottles bought = 10
Number of sodas bought = 5
Number of sandwiches bought = S
Total amount spend = $40
Now,
10 x 1.50 + 5 x 2 + 3S = 40
Simplify.
15 + 10 + 3S = 40
25 + 3S = 40
Subtract 25 on both sides.
3S = 40 - 25
3S = 15
Divide both sides by 3.
S = 15/3
S = 3
Thus,
The number of sandwiches bought is 3.
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ΔDEF is formed by lines tangent to the circle, where = 13.7, = 9, and = 14. Determine the perimeter of ΔDEF.
Question 1 options:
1)
68.4
2)
73.4
3)
73.7
4)
73.1
Answer:
Option (2)
Step-by-step explanation:
To solve this question we will use the property of tangents drawn to a circle.
"Tangents drawn from an external point to a circle are equal in length"
From the figure attached,
In ΔDEF,
DA = DC = 14 units [Equal tangents]
EA = EB = 13.7 units [Equal tangents]
FB = FC = 9 units [Equal tangents]
Therefore, DE = DA + AE = 14 + 13.7 = 27.7 units
EF = EB + BF = 13.7 + 9 = 22.7 units
DF = DC + FC = 14 + 9 = 23 units
Perimeter of ΔDEF = DE + EF + DF
= 27.7 + 22.7 + 23
= 73.4 units
Option (2) will be the answer.
Answer:73.4
Step-by-step explanation:
la empresa Delta Energy cobra a sus consumidores de energía eléctrica una tarifa de $5 por mes más $0,10 por cada kilowatt-hora. exprese el costo mensual "C" en función de la energía "E" consumida.
Answer:
C=0,10E+5
Step-by-step explanation:
De acuerdo a la información dada, la expresión debe indicar que el costo mensual "C" es igual al resultado de multiplicar la energía "E" consumida por el precio de cada kilowatt-hora y a esto se le debe sumar la tarifa por mes. De acuerdo a esto, el costo mensual se debe expresar de la siguiente forma:
C=0,10E+5
1. Use the diagram to the right to name the following.
a) Four collinear points.
b) A line that contains point M.
c) A line that contains points H and K.
d) Another name for line q.
e) The intersection of lines p and r.
Answer:
a) H,N,K and I.
b) The line p.
c) The line r.
d) The line q can be also named putting the symbol '' ↔ '' over the capital letters JL, JK or KL.
e) The point N.
Step-by-step explanation:
Let's study each item in order to answer the question :
a) Four collinear points :
We know that two or more points are called ''collinear points'' wherever they belong to the same line.
In the diagram, the only line that contains four points which have name is the line r. The four points are H,N,K and I.
b) A line that contains point M :
In this case, the only line that contains to the point M is the line p because the point M is situated over the line p.
c) A line that contains points H and K :
The only line that contains both points is the line r because the points H and K are situated over the line r.
d) Another name for line q :
Another way to name any line is putting the symbol ''↔'' over a pair of points that are situated over the line (Let's remember that we write the points with capital letters).
One possible name for the line q can be written putting ''↔'' over JL.
The other two names can be written putting ''↔'' over the capital letters JK or KL.
e) The intersection of lines p and r :
There are three cases of intersection between lines :
1 - The case in which the lines don't intersect at any point at all.
2 - The case in which the lines intersect at one point.
3 - The case in which the lines intersect at infinite points (for this case, the lines are parallel and there are superimposed).
In this case, the intersection of the lines p and r is the point N (which belongs to both lines).
The height of a triangle is 8 m more than the length of the base. The area of the triangle is 21 m^2. Find the height of the triangle
Answer:
height = 12 cmStep-by-step explanation:
Area of a triangle is given by
[tex]A = \frac{1}{2} bh[/tex]
where
b is the base
h is the height
From the question
Area = 21 m²
The statement
The height of a triangle is 8 m more than the length of the base is written as
h = 8 + b
Make b the subject
That's
b = h - 8
Substitute the expression into the above formula and solve for the height
That's
[tex]21 = \frac{1}{2} (h - 8)h[/tex]
Multiply through by 2
h² - 8h = 48
h² - 8h - 48 = 0
(h + 4)(h - 12) = 0
h + 4 = 0 h - 12 = 0
h = - 4 h = 12
Since the height cannot be a negative number we have the final answer as
height = 12 cmHope this helps you
There are 12 peaches and 8 bananas in a fruit basket. You get a snack for yourself and three of your friends by choosing of the pieces of fruit at random. 1)What is the probability that all 4 are peaches! 2)what is the probability that all 4 are bananas?
Answer:
10.2% chance
Step-by-step explanation:
There are 12 peaches and 8 bananas for a total of 20 pieces of fruit.
So we can write it:
[tex]\frac{12}{20} * \frac{11}{19} * \frac{10}{18} * \frac{9}{17}[/tex] = [tex]\frac{11880}{116,280}[/tex] = .102 or 10.2% chance
For ease multiply all numerators (top numbers) together, then multiply the denominators (bottom numbers) together, and then divide.
12 * 11 * 10 * 9 = 11880
20 * 19 * 18 * 17 = 116,280
We start with 12 peaches and 20 total fruit, as we select a peach the number of peaches and total fruit goes down by one. We do this 4 times because you draw 4 fruits. If you select 1 fruit your chances of it being a peach are 12/20, each time you select a fruit the chances of it being a peach go down because you have 1 less total fruit, and 1 less peach. This is why you multiply each probability together.
The price of a stock decreased by 60 cents one week, decreased 10 cents the next week, and decreased another 20 cents the following week. What is the average change in the price of the stock over the three weeks? –270 cents per week –90 cents per week –87 cents per week –30 cents per week
Answer:
30 cents per week
Step-by-step explanation:
The average is the sum of the numbers divided by how many there are.
60 + 10 + 20 = 90
90/3 = 30
Answer:
-30 per cents week !
Step-by-step explanation:
Solve A=1/2bh for h.
Answer:
h = 2A/b
Step-by-step explanation:
Step 1: Write out triangle formula
A = 1/2bh
Step 2: Multiply 2 on both sides to get rid of fraction
2A = bh
Step 3: Divide both sides by b to isolate h
2A/b = h
Step 4: Rearrange
h = 2A/b
Ryan is remodeling his kitchen floor, which is 110 square feet. He used
31.5 tiles in his kitchen. If Ryan wants to remodel his bathroom, which is 28
square feet, approximately how many tiles would he need?
Answer:
He will need 9 tiles
Step-by-step explanation:
Step one:
let us highlight the given parameters
Given data
the size of the kitchen floor is 110 ft^2
the size of the bathroom is 28 ft^2
he used 32.5 tiles for the kitchen
and used x tiles for the bathroom
Step two:
if he used 32 tiles for 110 ft^2 kitchen
he will use x tiles for 28 ft^2 bathroom
cross multiplying we have
x= (32*28)/110
x= 896/110
x= 8.145
Approximately he will need 9 tiles
The World Malaria Report (2008) has information on the number of reported malaria cases from 2005 and 2006 for the 10 countries listed in West Africa. The data are presented in
Answer:
The question is incomeplete, below is the completed question
The World Malaria Report (2008) has information on the number of reported malaria cases from 2005–2006 for the ten countries listed in West Africa. The data are presented in the table below:
1. The mean reported West African malaria cases in 2005 is a. less than 116,698. b. greater than 1,600,000. c. 100,000. d. greater than 200,000.
2. The median reported malaria cases in 2006 is a. around 1,000,000. b. less than 200,000. c. 100,000. d. 3,000,000.
3. If the number of reported malaria cases in Sierra Leone were mistyped and reported as 1,160,666, what would happen to the mean and median? a. Both would remain unchanged. b. The mean would change, but the median would stay the same. c. The mean and median would change. d. You cannot tell without doing the actual calculation.
Answer:
The correct answers are:
1. greater than 200,000. (d)
2. around 1,000,000 (a)
3. The mean and median would change (c)
Step-by-step explanation:
using the data in the attachment to this answer:
1.)The mean is a measure of ecntral tendency, calculated by summing the total of the values and dividing the result by the number of terms. From the data in the 2005 column, only one value is 116,698 and that value is (116,681), the rest of the 9 other values are greater than 116,698 hence option a (less than 116,698) is wrong.
b)Same reason holds for option b (greater than 1,600,000), only one value falls in this category, hence the mean cannot be more than 1,600,000.
c) since the lowest data in the dataset is 116,698, the mean cannot be 100,000, which is less than the lowest data in the dataset
d) The mean is greater than 200,000 because 8 out of 10 (80%) of the values are more than 200,000, hence this is the correct answer.
2) for the median of the 2006 data, let us arrange the values in ascending order:
160,000 266,188 566,450 861,847 1,022,592 1,105,272 1,253,408 1,555,310 2,060,867 3,511,452
For distribution with an even number of terms, the median = (sum of the two middle terms) ÷ 2
Two middle terms are 1,022,592, 1,105,272
Median = (1,022,592 + 1,105,272) ÷ 2
Median = 2127864 ÷ 2
Median = 1, 063, 932
Therefore median is around 1, 000, 000 (a)
3) mistyping the value for Sierra Leone as 1,160,666 instead of 160,666 for 2006, will increase the value by 1,000,000. Both the mean and the median will change, because the value 1,000,000 is a large number compared to the others on the list to cause a change.
Which of the following statements is true about normal distributions? the tails on the normal distribution stop at three standard deviations the tails on the normal distribution cross the x-axis after one standard deviation the tails on a normal distribution go on forever and never touch the x-axis the tails on the normal distribution cross the x-axis after three standard deviations
Answer:
The tails on a normal distribution go on forever and never touch the x-axis
Step-by-step explanation:
The normal distribution is also known as Gaussian distribution or bell shaped curve. The normal distribution is divided into two equal parts by the mean hence it is symmetrical at the mean. For a normal distribution, the height of the curve is determined by the mean while the width is determined by the standard deviation.
The two tails at both ends of the normal curve goes on and never touches the horizontal axis.
The area of a rectangular wall of a barn is 260 square feet. Its length is 6 feet longer than twice its width. Find the length and width of the wall of the barn.
Answer:
l = 26, w = 10
Step-by-step explanation:
These types of word problems always want you to use variables to find the answer. Variables are always going to represent the numbers you don't know.
This question wants you to find the length and width of the wall of the barn, so let's just use l for length (let l = length of barn wall) and w for width (let w = width of barn wall); this is called defining your variables, so that you--or anyone who looks at your work--know what the letter variable represents.
Now we use the other information we have to find what values the variables actually equal.
We know that the length is 6 feet longer than twice the width. To express this in terms of numbers and variables: l = 6 + 2w. This makes sense, right?
length = 6 + (2 * width)
If the total area of the wall is 260 square feet and we need to find the length and width, we can use the A = lw formula, which you can use for any rectangle. Since 260 is the area (A), we can put that into the formula so that we have 260 = lw.
Next, use the expression we came up with earlier (l = 6 + 2w) to help find the answer.
We have two equations now (l = 6 + 2w and 260 = lw) and we just need to put them together.
This part is the same as solving any other linear equation.
The approach I'll use is substitution:
l = 6 + 2w
260 = lw
Substitute 6 + 2w in for l:
260 = (6 + 2w) w
Distribute:
260 = 6w + 2w²
Solve:
w² + 3w - 130 = 0
w = -13, w = 10
(The width of a rectangle cannot be negative, so it has to be 10 ft.)
We're almost there. The last thing to do is to find the length. Just plug in 10 for w in the l = 6 + 2w formula:
l = 6 + 2(10) = 6 + 20 = 26
To check your work, we can double the width and add 6 to get 26, and 26 * 10 is 260.
So, the length of the wall of the barn is 26 and the width of the wall of the barn is 10.
I need help again, please.
I hope this helps you...
How many ways can the letters of the word MINUTES be arranged in a row if M and I must remain next to each other as either MI or IM
Answer:
1440 combinations ways
Step-by-step explanation:
We know that the total arrangements will be
6!= 720 because its a 6letter word
So if we take MI to be a one letter word
Same for IM
which will Also be 6!= 720
SO TOTAL possible combination will be 720+720= 1440
Answer:
1440 ways
Step-by-step explanation:
First, we must consider how many letters are in the word "minutes"
7.
This means that the word "minutes" can be arranged in 7! ways, or simply put in 5040 ways.
But then, we're interested in how many ways it can be arranged with I and M besides each other.
In how many ways can the word be arranged with the letters "MI" together
We would have, "MI, N, U, T, E, S" which happens to be 6!, or say 720 ways.
In how many ways can the word be arranged with the letters "IM" together
We would have, "IM, N, U, T, E, S"
which happens to be 6! or again, 720 ways.
Then, the number of ways it can be arranged with "IM" or "MI" together is
720 + 720, and therefore 1440 ways
Please help me. 46 points! Need this asap
Answer:
39 meters
Step-by-step explanation:
We know the bottom distance ( 20-13) = 7
And we know the height 15-0 =15
We can use the Pythagorean theorem to find the hypotenuse
a^2 + b^2 = c^2
7^2 + 15^2 = c^2
49+225 = c^2
274 = c^2
Taking the square root of each side
sqrt(274) = c
We want the perimeter
a+b+c
7+15+sqrt(274)
22+sqrt(274)
22+16.55294536
38.55294536
Rounding to the nearest meter
39 meters
Answer:
[tex]\huge \boxed{\mathrm{39 \ meters}}[/tex]
Step-by-step explanation:
The perimeter of the right triangle is required.
The base of the triangle is 7 units.
The height of the triangle is 15 units.
The hypotenuse can be found through Pythagorean theorem.
a² + b² = c²
7² + 15² = c²
49 + 225 = c²
274 = c²
c = [tex]\sqrt{274}[/tex]
Adding all the three sides of the right triangle to get the perimeter.
P = a + b + c
P = 7 + 15 + [tex]\sqrt{274}[/tex]
P = 38.552945...
The perimeter of the right triangle is 39 meters rounded to nearest meter.
what is the equivalent expression of 14n+21? I really need help with this it is due in the morning and I have no clue what I'm doing please helppppppp
Answer:
7(2n +3)Step-by-step explanation:
[tex]14n+21\\\mathrm{Rewrite\:}21\mathrm{\:as\:}7\times\:3\\\mathrm{Rewrite\:}14\mathrm{\:as\:}7\times\:2\\\\=7\times\:2n+7\times\:3\\\\\mathrm{Factor\:out\:common\:term\:}7\\=7\left(2n+3\right)[/tex]
FIND A NUMBER WITH SIX FACTORS, ALL OF WHICH ARE ODD NUMBER
Answer: 99
Step-by-step explanation:
factor of 99: 1, 3, 9, 11, 33, 99
This is 6 factors, and they are all odd number
Hope this helps!! :)
Please let me know if you have any question
2. Which of these values is the GREATEST?
63/7
450%
8.99
-22
Find the mean of the data summarized in the given frequency distribution. Compare the computed mean to the actual mean of 56.6 degrees. Low Temperature (◦F) 40−44 45−49 50−54 55−59 60−64 Frequency 2 7 9 5 2 The mean of the frequency distribution is nothing degrees.
Answer:
1. The mean of the data summarized in the given frequency distribution is 51.81 degrees
2. Comparing the computed mean (51.81 degrees) to the actual mean(56.6) degrees, the computed mean is lesser than the actual mean.
Step-by-step explanation:
1) We are given a Frequency distribution.
Mean of a frequency distribution = Fx/F
Where
Fx = Frequency × midpoint
Low Temperature (◦F) Frequency
40−44 2
45−49 7
50−54 9
55−59 6
60−64 2
F =Total Frequency
= 2 + 7 + 9 + 6 + 2
= 26
a)For low temperature 40 - 44
Frequency = 2
Midpoint (x) = 40 +44/2 = 42
Fx =42 × 2 = 84
b) For low temperature 45 - 49
Frequency = 2
Midpoint (x) = 45+49/2 = 47
Fx =47 × 7 = 329
For low temperature 50 - 54
Frequency = 2
Midpoint (x) = 50 + 54/2 = 52
Fx =52 × 9 = 468
For low temperature 55 - 59
Frequency = 6
Midpoint (x) = 55 + 59/2 = 57
Fx =57 × 6 = 342
For low temperature 60 - 64
Frequency = 2
Midpoint (x) = 60 +64/2 = 62
Fx =62 × 2 = 124
Total Fx =84 + 329 + 468 + 342 + 124
= 1347
Mean =Total Fx/ Total Frequency
= 1347/26
= 51.807692308
Approximately = 51.81 degrees
Therefore, mean of the data summarized in the given frequency distribution is 51.81 degrees
2. Comparing the computed mean (51.81 degrees) to the actual mean(56.6) degrees, the computed mean is lesser than the actual mean.
An employee earns $2,300 each pay period. He is paid on the first and fifteenth
of each month. How much does he earn in one year?
Answer:
55,200
Step-by-step explanation:
The employee is paid twice a month. There are 12 months in a year. He is paid 12x2=24 times a year.
Multiply the pay per period by the number or pay periods
=2,300x24
=55,200
Which expression is equivalent to 1/2 x + (-70) - 2 1/4 x - (-2)
Answer:
(-(7 x + 272))/4
Step-by-step explanation:
Simplify the following:
x/2 - (2 + 1/4) x - 70 - ( - 2)
Hint: | Put the fractions in 2 + 1/4 over a common denominator.
Put 2 + 1/4 over the common denominator 4. 2 + 1/4 = (4×2)/4 + 1/4:
x/2 - 9/4 x - 70 - ( - 2)
Hint: | Multiply 4 and 2 together.
4×2 = 8:
x/2 - (1/48 + 1/4) x - 70 - ( - 2)
Hint: | Add the fractions over a common denominator to a single fraction.
8/4 + 1/4 = (8 + 1)/4:
x/2 - 9/4 x - 70 - ( - 2)
Hint: | Evaluate 8 + 1.
8 + 1 = 9:
x/2 - 9 x/4 - 70 - ( - 2)
Hint: | Multiply -1 and -2 together.
-(-2) = 2:
x/2 - (9 x)/4 - 70 + 2
Hint: | Put the fractions in x/2 - (9 x)/4 - 70 + 2 over a common denominator.
Put each term in x/2 - (9 x)/4 - 70 + 2 over the common denominator 4: x/2 - (9 x)/4 - 70 + 2 = (2 x)/4 - (9 x)/4 - 280/4 + 8/4:
(2 x)/4 - (9 x)/4 - 280/4 + 8/4
Hint: | Combine (2 x)/4 - (9 x)/4 - 280/4 + 8/4 into a single fraction.
(2 x)/4 - (9 x)/4 - 280/4 + 8/4 = (2 x - 9 x - 280 + 8)/4:
(2 x - 9 x - 280 + 8)/4
Hint: | Group like terms in 2 x - 9 x - 280 + 8.
Grouping like terms, 2 x - 9 x - 280 + 8 = (2 x - 9 x) + (8 - 280):
((2 x - 9 x) + (8 - 280))/4
Hint: | Combine like terms in 2 x - 9 x.
2 x - 9 x = -7 x:
(-7 x + (8 - 280))/4
Hint: | Evaluate 8 - 280.
8 - 280 = -272:
(-272 - 7 x)/4
Hint: | Factor a minus sign out of -7 x - 272.
Factor -1 out of -7 x - 272:
Answer: (-(7 x + 272))/4
1/2 x + (-70) - 2 1/4 x - (-2) = (-(7 x + 272))/4 = True
You roll two fair dice, one green and one red. (a) Are the outcomes on the dice independent? Yes No (b) Find P(1 on green die and 5 on red die). (Enter your answer as a fraction.) (c) Find P(5 on green die and 1 on red die). (Enter your answer as a fraction.) (d) Find P((1 on green die and 5 on red die) or (5 on green die and 1 on red die)). (Enter your answer as a fraction.)
Answer:
a
Yes
b
[tex]P(1 \& 5) = \frac{1}{36}[/tex]
c
[tex]P(5 \& 1) = \frac{1}{36}[/tex]
d
[tex]P(5 \& 1 | 1\& 5 ) = \frac{1}{18}[/tex]
Step-by-step explanation:
From the question we are told that
Two fair dice, one green and one red were rolled
Generally the outcomes on the dice independent because the outcome on the first dice is not affected by the second die
Generally the probability of getting a 1 on a dice rolled is [tex]P(1) = \frac{1}{6}[/tex]
the probability of getting a 5 on a dice rolled is [tex]P(5) = \frac{1}{6}[/tex]
Generally the probability of P(1 on green die and 5 on red die) is mathematically represented as
[tex]P(1 \& 5) = \frac{1}{6} *\frac{1}{6}[/tex]
[tex]P(1 \& 5) = \frac{1}{36}[/tex]
Generally the probability of P(5 on green die and 1 on red die) is mathematically represented as
[tex]P(5 \& 1) = \frac{1}{6} *\frac{1}{6}[/tex]
[tex]P(5 \& 1) = \frac{1}{36}[/tex]
Generally the probability of P((1 on green die and 5 on red die) or (5 on green die and 1 on red die)) is mathematically represented as
[tex]P(5 \& 1 | 1\& 5 ) = \frac{1}{36} + \frac{1}{36}[/tex]
[tex]P(5 \& 1 | 1\& 5 ) = \frac{1}{18}[/tex]