Answer:
The expected value of the game is $0.33.
Step-by-step explanation:
There are N = 36 outcomes of rolling two 6-sided fair dice.
The sample for the sum of two numbers to be 7 is:
S = {(1, 6), (2, 5), (3, 4), (4, 3), (5, 2) and (6, 1)}
n (S) = 6
It is provided that there is a 7 to 1 odds against rolling a sum of 6 with the roll of two fair dice.
That is, you win $7 if you succeed and you lose $1 if you fail.
Compute the expected value of the game as follows:
[tex]E(X)=\sum x\cdot P (X=x)[/tex]
[tex]=[\$(7)\times \frac{6}{36}]+[\$(-1)\times \frac{30}{36}]\\\\=\frac{7}{6}-\frac{5}{6}\\\\=\frac{7-5}{6}\\\\=\frac{1}{3}\\\\=\$0.33[/tex]
Thus, the expected value of the game is $0.33.
The pressure applied to a leverage bar varies inversely as the distance from the object. If 150 pounds is required for a distance of 10 inches from the object how much pressure is needed for a distance of 3 inches
Answer:
500 pounds
Step-by-step explanation:
Let the pressure applied to the leverage bar be represented by p
Let the distance from the object be represented by d.
The pressure applied to a leverage bar varies inversely as the distance from the object.
Written mathematically, we have:
[tex]p \propto \dfrac{1}{d}[/tex]
Introducing the constant of proportionality
[tex]p = \dfrac{k}{d}[/tex]
If 150 pounds is required for a distance of 10 inches from the object
p=150 poundsd=10 inches[tex]150 = \dfrac{k}{10}\\\\k=1500[/tex]
Therefore, the relationship between p and d is:
[tex]p = \dfrac{1500}{d}[/tex]
When d=3 Inches
[tex]p = \dfrac{1500}{3}\\\implies p=500$ pounds[/tex]
The pressure applied when the distance is 3 inches is 500 pounds.
A rectangle's length and width are in a ratio of 10:1. The perimeter is 66 feet. What are the length and width?
hii
Step-by-step explanation:
length-10x
width-x
perimeter-2(l+b)
66=2(10x+x)
66-2=10x+x
64=11x
x=11/64
lenght-11
width-64
Select the correct answer.
Estimate the solution to the following system of equations by graphing.
3x + 5y=14
6x - 4y=9
Answer:
y = 19/14 and x = 25/42
Step-by-step explanation:
Answer:
(5/2, 4/3)
Step-by-step explanation:
the solution is the point (2.41,1.36)
x=5/2
y=4/3
he math team wraps gifts as a way to raise money for traveling to competitions. They offer two choices: a plain wrapping or a decorative wrapping with bows. The table represents the money raised over a busy shopping weekend.
The team charged $2 to wrap a gift with no bow and $3 to wrap a gift with a bow.
Answer:
The answer above is correct B
Step-by-step explanation:
Took the Unit Test Review on edg 2020 correct
tje mean of 12 scores is 8.8 what is the sum of tue 12 scores
Answer:
105.6
Step-by-step explanation:
If the mean is 8.8, than that means that in total the sum must be (8.8 * 12) which equals 105.6.
This is because the sum of all the numbers in a list divided by the amount of numbers in a list equals the mean.
The value of x that will make L and M
Greetings from Brasil...
Here we have internal collateral angles. Its sum results in 180, so:
(6X + 8) + (4X + 2) = 180
6X + 4X + 8 + 2 = 180
10X + 10 = 180
10X = 180 - 10
10X = 170
X = 170/10
X = 17What is the square root of nine?
Answer:
3 or -3
Step-by-step explanation:
sqrt(9)
What number multiplied by itself will give you 9
3*3 =9
-3 * -3 =9
The square root of 9 is 3 or -3
From a population that is not normally distributed and whose standard deviation is not known, a sample of 6 items is selected to develop an interval estimate for the mean of the population (μ).
a. The normal distribution can be used.
b. The t distribution with 6 degrees of freedom must be used.
c. The sample size must be increased.
d. The t distribution with 5 degrees of freedom must be used.
Answer:
d) The t-distribution with 5 degrees of freedom must be used
Step-by-step explanation:
For cases of Normal Distribution where the variance is unknown and the sample size n is smaller than 30, we must use the t-student distribution.
The shape of the curve for t-student is bell-shape (flatter and with wider tails than the bell shape of normal distribution.
Actually, when we deal with t-student distribution we are dealing with a family of curves that will become closer and closer to the bell shape of the normal distribution as the degree of freedom increases. From values of n =30( and bigger), we can assume that the curve of t-student is the same as for normal distribution
An hourglass consists of two sets of congruent composite figures on either end. Each composite figure is made up of a cone and a cylinder, as shown below: Hourglass with sand measuring 45 millimeters high © 2011 Jupiterimages Corporation Each cone of the hourglass has a height of 15 millimeters. The total height of the sand within the top portion of the hourglass is 45 millimeters. The radius of both cylinder and cone is 6 millimeters. Sand drips from the top of the hourglass to the bottom at a rate of 10π cubic millimeters per second. How many seconds will it take until all of the sand has dripped to the bottom of the hourglass? (4 points) Select one: a. 126 b. 108 c. 18 d. 29
Answer:
126
Step-by-step explanation:
Total volume of sand = pi/3*(6^2)*(15) + pi*(6)^2*(30) = 1260*pi mm^3
So it will therefore take 1260*pi/10*pi = 126 seconds for all of the sand from the top hourglass to drip down to the bottom hourglass.
i will give 50 points and brainliest
Answer:
Hey there!
0.5(8.4)(h)=69.3
4.2h=69.3
h=16.5
Hope this helps :)
Answer:
[tex] \boxed{\sf Height \ of \ the \ triangle = 16.5 \ mm} [/tex]
Given:
Area of the triangle = 69.3 mm²
Base of the triangle = 8.4 mm
To Find:
Height of the triangle
Step-by-step explanation:
[tex]\sf \implies Area \ of \ the \ triangle = \frac{1}{2} \times Base \times Height \\ \\ \sf \implies 69.3 = \frac{1}{2} \times 8.4 \times Height \\ \\ \sf \implies 69.3 = \frac{1}{ \cancel{2}} \times \cancel{2} \times 4.2 \times Height \\ \\ \sf \implies 69.3 = 4.2 \times Height \\ \\ \sf \implies 4.2 \times Height = 69.3 \\ \\ \sf \implies Height \times \frac{ \cancel{4.2}}{ \cancel{4.2}} = \frac{69.3}{4.2} \\ \\ \sf \implies Height = \frac{16.5 \times \cancel{4.2}}{ \cancel{4.2}} \\ \\ \sf \implies Height = 16.5 \: mm[/tex]
The snowfall from this snowstorm above covered most of IA, northern IL, northern IN, and southern MI. While some locations in that swath saw over a foot of snow, let’s assume the average depth of the snow over this area was 8 inches. If the total area covered by the 8 inch average depth was 72,150 square miles, what percentage of the volume of the Grand Canyon would this amount of snow fill?
Answer:
Percentage volume of the Grand Canyon filled by the snow = 0.911 %
Step-by-step explanation:
This question is incomplete; please find the complete question in the attachment.
Given :
Area of the snow cover = 72150 square miles
Depth of the snow = 8 inches
Volume of the Grand Canyon = 4.166 × 101² m³
Solution:
Area of the snow cover = 72150 square miles
≈ 72150 × 2589988 square meter
≈ 1.868 × 10¹¹ square meter
Depth of the snow = 8 inches ≈ 0.2032 m
Volume of the snow on this area = Area × depth of the snow
= 1.868 × 10¹¹ × 0.2032
= 3.796 × 10¹⁰ m³
Volume of the Grand Canyon = 4.166 × 10¹² m³
Percentage volume of the Grand Canyon filled by the snow
= [tex]\frac{\text{Volume of the snow}}{\text{Volume of the Grand Canyon}}\times 100[/tex]
= [tex]\frac{3.796\times 10^{10} }{4.166\times 10^{12} }\times 100[/tex]
= 0.911%
which is greater 7.955 or 7.95
Answer:
[tex]\boxed{7.955>7.95}[/tex]
Step-by-step explanation:
7.95 can also be written as 7.950 .
So, we'll compare 7.955 and 7.950.
All the digits in ones, tenths, hundredths place are equal so we'll look at the thousandths place.
5 is in the thousandths place of 7.955 and 0 is in the thousandths place of 7.950. Since 5 is greater than 0 so 7.955 is greater than 7.95. It can also be written as:
7.955 > 7.950
A personnel director interviewing 12 senior engineers for five job openings has scheduled seven interviews for the first day and five for the second day of interviewing. Assume that the candidates are interviewed in a random order.
(a) What is the probability that x of the top four candidates are interviewed on the first day?
h(N; 5, 5, 12)
h(x; 5, 12, 5)
h(N; 7, 12, 5)
h(x; 7, 5, 12)
(b) How many of the top four candidates can be expected to be interviewed on the first day? (Round your answer to two decimal places.)
Answer:
a) h(x; 7, 5, 12) = (⁵Cₓ)( ⁷C₇₋ₓ) / (¹²C₇)
b) 2.92
Step-by-step explanation:
a)
Here
Number of interviewees = N = 12
Number of job openings = M = 5
Interviews schedules for the first day = n = 7
N − M = 12 - 5 = 7
Using hypergeometric distribution:
Let X be the no. top four candidates interviewed on first day.
The probability mass function of X:
P(X = x) = [tex](^{M} C_{x})[/tex] [tex](^{N-M} C_{n-x})[/tex] / [tex](^{N} C_{n})[/tex]
It can be written as:
h(x; n, M, N) = [tex](^{M} C_{x})[/tex] [tex](^{N-M} C_{n-x})[/tex] / [tex](^{N} C_{n})[/tex]
= (5Cx) (7C7-x) / (12C7)
= (⁵Cₓ)( ⁷C₇₋ₓ) / (¹²C₇)
h(x; 7, 5, 12) = (⁵Cₓ)( ⁷C₇₋ₓ) / (¹²C₇)
b)
The expectation is: E(X) = np
E(X) = n * M/N
= 7 * 5/12
= 7 * 0.41667
= 2.9167
The process of using the same or similar experimental units for all treatments is called:______
a. blocking.
b. partitioning.
c. factoring.
d. replicating.
Answer:
replicating
Step-by-step explanation:
A sample of 13 small bags of the same brand of candies was selected. Assume that the population distribution of bag weights is normal. The weight of each bag was then recorded. The mean weight was 3 ounces with a standard deviation of 0.15 ounces. The population standard deviation is known to be 0.1 ounce.Required:a. Construct a 98% confidence interval for the population mean weight of the candies.b. State the confidence interval. (Round your answers to three decimal places.)c. Draw the Graph
Answer:
The answer is below
Step-by-step explanation:
Given that:
Mean (μ) = 3 ounces. standard deviation (σ) = 0.15, sample size (n) = 13 and confidence (C) = 98%
α = 1 - C = 1 - 0.98 = 0.02
α/2 = 0.02/2 = 0.01.
The z score of 0.01 (α/2) corresponds to the z score of 0.49 (0.5 - 0.01) which from the normal distribution table is 2.33.
The margin of error (E) is:
[tex]E=z_{0.01}*\frac{\sigma}{\sqrt{n} } = 2.33*\frac{0.15}{\sqrt{13} }=0.1\\[/tex]
The confidence interval = μ ± E = 3 ± 0.1 = (2.9, 3.1)
The confidence interval is between 2.9 ounce and 3.1 ounce
Evaluate the expression.
Answer:
work is shown and pictured
If 3 is added to the absolute value of the product of a number and –9, the result is 4.
Answer:
± (1 ÷ 9)
Step-by-step explanation:
Data provided in the question
Since 3 is added to the absolute value and -9
The result is 4
Now this information should be transformed in a mathematical equation
Let us assume be x so the product of the number and -9 be -9x
Fo rthe absolute value we use the mode. Thus the required expression is:
3 + |-9x|
Given that the result is 4
So, it would be
3 + |-9x| = 4
Now Solving the above equation which is given below:
|-9x| = 4-3
|-9x| = 1
here we will remove the mode by introducing ± sign which is shown below:
-9x = ± 1
-9x = 1 or -9x = -1
x = -1/9
or
x = [tex]\frac{1}{9}[/tex]
Therefore, the value of x is ± (1 ÷ 9).
Wholemark is an internet order business that sells one popular New Year greeting card once a year. The cost of the paper on the which the card is printed is $0.05 per card, and the cost of printing is $0.15 per card. The company receives $2.15 per card sold. Since the cards have the current year printed on them, unsold cards have no salvage value. Their customers are from the four areas: Los Angeles, Santa Monica, Hollywood, and Pasadena. Based on past data, the number of customers from the each of the four regions is normally distributed with mean 2,000 and standard deviation of 500. (Assume these four are independent.)
What is the optimal production quality for the card? (Use Excel's NORMSINV{} function to find the Z-score. Round intermediate calculations to four decimal places. Submit your answer to the nearest whole number.)
Answer:
The optimal production quantity is 9,322 cards.
Step-by-step explanation:
The information provided is:
Cost of the paper = $0.05 per card
Cost of printing = $0.15 per card
Selling price = $2.15 per card
Number of region (n) = 4
Mean demand = 2000
Standard deviation = 500
Compute the total cost per card as follows:
Total cost per card = Cost of the paper + Cost of printing
= $0.05 + $0.15
= $0.20
Compute the total demand as follows:
Total demand = Mean × n
= 2000 × 4
= 8000
Compute the standard deviation of total demand as follows:
[tex]SD_{\text{total demand}}=\sqrt{500^{2}\times 4}=1000[/tex]
Compute the profit earned per card as follows:
Profit = Selling Price - Total Cost Price
= $2.15 - $0.20
= $1.95
The loss incurred per card is:
Loss = Total Cost Price = $0.20
Compute the optimal probability as follows:
[tex]\text{Optimal probability}=\frac{\text{Profit}}{\text{Profit+Loss}}[/tex]
[tex]=\frac{1.95}{1.95+0.20}\\\\=\frac{1.95}{2.15}\\\\=0.9069767\\\\\approx 0.907[/tex]
Use Excel's NORMSINV{0.907} function to find the Z-score.
z = 1.322
Compute the optimal production quantity for the card as follows:
[tex]\text{Optimal Production Quantity}=\text{Total Demand}+(z\times SD_{\text{total demand}}) \\[/tex]
[tex]=8000+(1.322\times 1000)\\=8000+1322\\=9322[/tex]
Thus, the optimal production quantity is 9,322 cards.
-6(y+15)=-3y+6
what value of y makes the equation true
Answer:
y = -32
Step-by-step explanation:
-6(y+15)=-3y+6
Distribute
-6y - 90 = -3y +6
Add 6y to each side
-6y -90+6y = -3y+6y +6
-90 = 3y+6
Subtract 6 from each side
-90 -6 = 3y +6-6
-96 = 3y
Divide by 3
-96/3 = 3y/3
-32 = y
Answer:
-32 !!!!
Step-by-step explanation:
How do you make a table of value for the following equation? 3x=y
Answer:
Step-by-step explanation:
y= 3x
x y
0 0
1 3
2 6
3 9
-1 -3
-2 -6
Find the largest integer which belongs to the following interval: [−∞, 31]
Answer:
Largest integer in the interval [−∞, 31] is 31.
Step-by-step explanation:
Given the interval: [−∞, 31]
To find: The largest integer in this interval.
Solution:
First of all, let us learn about the representation of intervals.
Two kind of brackets can be used to represent the intervals. i.e. () and [].
Round bracket means not included in the interval and square bracket means included in the interval.
Also, any combination can also be used.
Let us discuss one by one.
1. [p, q] It means the interval contains the values between p and q. Furthermore, p and q are also included in the interval.
Smallest p
Largest q
2. (p, q) It means the interval contains the values between p and q. Furthermore, p and q are not included in the interval.
Smallest value just greater than p.
Largest value just smaller than q.
3. [p, q) It means the interval contains the values between p and q. Furthermore, p is included in the interval but q is not included in the interval.
Smallest value p.
Largest value just smaller than q.
4. (p, q] It means the interval contains the values between p and q. Furthermore, p is not included in the interval but q is included in the interval.
Smallest value just greater than p.
Largest value q.
As per above explanation, we can clearly observe that:
The largest integer which belongs to the following interval: [−∞, 31] is 31.
Find the dimensions of a rectangle with perimeter 68 m whose area is as large as possible. (If both values are the same number, enter it into both blanks.)
Answer:
Length is 17m and Breadth is also 17mStep-by-step explanation:
The perimeter of a rectangle is expressed as 2(L+B) where;
L is the length and B is the breadth of the triangle.
P = 2(L+B)
68 = 2(L+B)
L+B = 68/2
L+B = 34
L = 34 - B ... 1
Area of the rectangle A = LB... 2
Substituting equation 1 into 2 will give;
A = (34-B)B
A = 34B-B²
To maximize the area of the triangle, dA/dB must be equal to zero i.e
dA/dB = 0
dA/dB = 34 - 2B = 0
34-2B = 0
2B = 34
Dividing both sides of the equation by 2 we will have;
B = 34/2
B = 17
Substituting B = 17 into equation 1 to get the length L
L = 34-17
L = 17m
This shows that the rectangle with maximum area is a square since L = B = 17m
The dimension of the rectangle is Length = 17m and Breadth = 17m
The dimensions are 17m and 17m.
The perimeter of a rectangle is given as:
= 2(length + width)
Since in their case, the lengths have same values, this will be:
Perimeter = 2(l + l)
Perimeter = 4l
4l = 68
L = 68/4
L = 17m
Therefore, the dimensions are 17m and 17m.
Read related link on:
https://brainly.com/question/15366172
What is the solution to the inequality below?
x < 49
Answer: x < 7, and x > -7
Step-by-step explanation:
Simply square root both sides of the equation. The square root of x^2 is x and the square root of 49 can be 7 or -7.
Hope it helps <3
Answer:
x < 7 and x > -7
Step-by-step explanation:
x^2 < 49
Take the square root of each side, remembering to flip the inequality when we take the negative
sqrt( x^2) < + sqrt(49) and sqrt( x^2)> - sqrt(49)
x < 7 and x > -7
In a statistical experiment, we roll two die (6 sided each) and add the results. The outcomes of interest for our experiment are: A
Answer:
The highest number on a die is 6. when we roll out two die the total sum cannot be more that 12. and each sum having the same probability of showing up.
The outcome of our experiment can be 2,3,4,5,6,7,9,10,11 or 12.
Step-by-step explanation:
Statistical experiment can be simply stated as the likelihood of an an event to occur or not.
What are the dimensions of the rectangle? PLEASE HELP!!
Answer:
2(x^2 + 8x -55)
Step-by-step explanation:
Well to do the box method we first need to simplify the given equation further to,
[tex]2x^2 + 16x - 110\\[/tex],
For this quadratic the box method doesn't work so we can divide everything by 2 make make it
2(x^2 + 8x -55)
Thus,
[tex]2x^2 + 16x - 110\\[/tex] factored is 2(x^2 + 8x -55).
Hope this helps :)
Determine the domain of the function. f as a function of x is equal to the square root of two minus x.
x ≤ 2
All real numbers
x > 2
All real numbers except 2
Answer:
A. x <= 2
Step-by-step explanation:
The domain of a real function should be all real numbers. In
f(x) = sqrt(2-x)
we need 2-x to be non-negative, therefore
2-x >= 0
which implies
x <= 2
Answer:
[tex]\Huge \boxed{{x\leq 2}}[/tex]
Step-by-step explanation:
The function is given,
[tex]f(x)=\sqrt{2-x}[/tex]
The domain of a function are all possible values of x.
There are restrictions for the value of x.
2 - x cannot be equal to a negative number, because the square root of a negative number is undefined. 2 - x has to equal to 0 or be greater than 0.
[tex]2-x\geq 0[/tex]
[tex]-x\geq -2[/tex]
[tex]x\leq 2[/tex]
The domain of the function is x ≤ 2.
The shape of a garden is rectangular at the center and semicircular at the ends. Find the area and perimeter of this garden { length of the rectangle is 20 - (3.5+3.5) meters} The First, correct answer gets BRAINLIEST
Mensuration:
Mensuration is the branch of mathematics which concerns itself with the measurement of Lengths, areas & volume of different geometrical shapes or figures.
Plane Figure: A figure which lies in a plane is called a plane figure.
For e.g: a rectangle, square, a rhombus, a parallelogram, a trapezium.
Perimeter:
The perimeter of a closed plane figure is the total length of its boundary.
In case of a triangle or a polygon the perimeter is the sum of the length of its sides.
Unit of perimeter is a centimetre (cm), metre(m) kilometre(km) e.t.c
Area: The area of the plane figure is the measure of the surface enclose by its boundary.
The area of a triangle are a polygon is the measure of the surface enclosed by its sides.
A square centimetre (cm²) is generally taken at the standard unit of an area. We use square metre (m²) also for the units of area.
Circumference of a circle is the perimeter of a circle.
In a circle the radius is half of the diameter.
The approximate value of π( Pi) is= 22/7
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The function f(x) = ex is called the ---Select--- exponential function. The number e is approximately equal to . (Round your answer to five decimal places.)
Answer:
The value of e is approximately 2.71828.
Step-by-step explanation:
An exponential function is of the form:
[tex]y=a^{x}[/tex]
Here a is any value that is more than 0.
The natural form of an exponential function is:
[tex]y=e^{x}[/tex]
Here e is known as the Euler's number.
The value of e is approximately 2.71828.
can you answer this for my friend thank you
Answer:
length=16 feet and width=12 feet
Answer:
Length = 16ft, width = 12ft
Step-by-step explanation:
4:2 or 2:1
so you need to mulitply everything by 2
length = 8*2 = 16ft
width = 6*2 = 12ft
HEREEEEEEEEEEEEEElollll
Answer:
Hey there!
Your answer would be 4/50. The total times she drawed a purple tile was 4, and she drawed 50 times.
Hope this helps :)