The expected value of the sum when rolling a pair of 7-sided dice is 8.
Explanation:When rolling a pair of 7-sided dice, each die has numbers 1 through 7 on its faces. To find the expected value of the sum, we need to calculate the average of all possible sums.
The first die can have 7 possible outcomes, and for each outcome, the second die can also have 7 possible outcomes. This gives us a total of 7*7=49 possible outcomes. The sums of these outcomes range from 2 (1+1) to 14 (7+7).
To find the expected value, we multiply each sum by its probability and sum them up. Since each sum has an equal probability of occurring (1/49), we can simplify the calculation:
Expected value = (2*1/49) + (3*1/49) + (4*1/49) + ... + (14*1/49) = 8
Therefore, the expected value of the sum when rolling a pair of 7-sided dice is 8.
if the circumference of a circle measures 3π cm, what is the area of the circle in terms of π?
The area of the given circle, in terms of pi, is:
A = (9/4)pi cm^2
How to find the area of the circle?We know that for a circle of radius R, the circumference is:
C = 2*pi*R
And the area is:
A = pi*R^2
In this case, we know that:
C = 3pi cm = 2pi*R
Then we must have:
3cm = 2R
(3/2)cm = R
Now we can replace this on the area equation:
A = pi*((3/2)cm)^2 = pi*(9/4) cm^2
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rebekah's baby brother wights 7.71 pounds. Her newborn kitten weights 0.24 pound. How much more does tebekah's baby brother weight that her kitten?
On the map of a town, 1 cm represents 6 miles. Find the distance represented by 4.5 cm. A) 4.5 miles B) 6 miles C) 17 miles D) 27 miles
Maritza is buying a multipack of 3 pairs of socks for $25.98. She will save $6.24 by buying the multipack instead of buying 3 individual pairs of the same socks.
If each pair of socks costs the same amount, how much does each pair of socks cost when bought individually?
write the integer 9 as m/n in simplest form where m and n are integers
The height of the pyramid in the diagram is three times the radius of the cone. The base area of the pyramid is the same as the base area of the cone. What is the expression for the volume of the pyramid in terms of the radius r of the cone?
The volume of the pyramid is πr³ cubic units. Then the correct option is A.
What is the volume of the pyramid?Suppose the base of the pyramid has length = L units, width = W units, slant height = K units, and the height of the pyramid is of H units.
Then the volume of the pyramid will be
V = (A × H) / 3
V = (L × B × H) / 3
Where, A is the base area of the pyramid.
Let r be the radius of base circle of the cone.
The height of the pyramid in the diagram is three times the radius of the cone.
Then the height of the pyramid will be 3r.
The base area of the pyramid is the same as the base area of the cone.
Base area of pyramid = Base area of cone
Base area of pyramid = πr²
Then the volume of the pyramid will be
Volume of pyramid = (1/3) x πr² x (3r)
Volume of pyramid = πr² x r
Volume of pyramid = πr³ cubic units
The volume of the pyramid is πr³ cubic units.
Then the correct option is A.
Complete question is attached below.
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a sheep breeding farm counted a total of 40 sheep on their grounds after one year the number of sheep doubled then in the next year the number of sheep doubled again if this trend continues which of the following options represents the number of sheep on the farm by then end of each year
£850 is invested for 2 years at 6% per annum compound interest. a) Work out the total interest earned over the first 2 years.
Answer:
6% annum for 850 would be 955
f=11gh solve the formula for the variable h.
The formula f=11gh can be solved for h by dividing both sides of the equation by 11g. This will give h = f / (11g), where h is isolated on one side of the equation.
Explanation:To solve the formula f=11gh for the variable h, we need to isolate h on one side of the formula. The current formula tells us that the value of f is equal to the result of 11 times g times h.
As our goal is to solve for h, we can do this by dividing both sides of the equation by 11g. In doing so, the 11g on the right side of the equation will cancel out, leaving us with just h on one side.
So the formula solved for h will look like this:
h = f / (11g).
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Tell what each of the residual plots below indicates about the appropriateness of the linear model
Residual plots can indicate the appropriateness of a linear model by examining patterns and deviations of the residuals.
Explanation:A residual plot is a graph that shows the difference between the observed and predicted values in a linear regression model. It helps to assess the appropriateness of the linear model by examining the patterns and deviations of the residuals. In the first graph, there seems to be a systematic pattern and non-randomness in the residuals, indicating that the linear model may not be appropriate. However, in the second graph, the residuals are randomly scattered around zero with no evident pattern, suggesting that the linear model is more appropriate.
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HELP ME PLEASEEEEEEEEEEEEEEEEEE
Can you please help me ?
The human population doubles approximately every 50 years. If there were 2.5 million people in 1950, how many people are forecasted to populate the earth in 2050?
Is the quotient of 5 and 1 / 2 greater than or less than 5? Explain your answer.
The quotient of 5 divided by 1/2 is greater than 5 because dividing by a number less than 1 results in a larger number. In this case, it is equivalent to multiplying 5 by 2, yielding 10.
To determine if the quotient of 5 and 1/2 is greater than or less than 5, we consider the operation of division. Dividing by a number less than 1 will result in a larger number, while dividing by a number greater than 1 will result in a smaller number. The number 1/2 is less than 1, so when 5 is divided by 1/2, the quotient is greater than 5. It is equivalent to multiplying 5 by 2 (since dividing by a fraction is the same as multiplying by its reciprocal), which is 10. Therefore, 5 divided by 1/2 equals 10, which is greater than 5.
What is the correct solution for the arithmetic expression (2+8)/2*9/3 using the order of operations employed by oracle 12c when solving equations??
The order of operations is the steps used to simplify any mathematical expression. Order of operations refers to which operations should be performed in what order and it is denoted by PEMDAS, This means that you should do what is possible within parentheses first, then exponents, then multiplication and division (from left to right), and then addition and subtraction (from left to right). If parentheses are enclosed within other parentheses, work from the inside out.
[tex] (2+8)/2*9/3\\ Performing \; the \; operation\; in\; Parenthesis\; first\\ \\ 10/2 *9/3\\ Dividing \; 10/2\; from\; left\; to\; right\\ \\ 5*9/3\\ Multiply\; from\; left\; to\; right\\ \\ 45/3\\ Divide \; to\; get\; final\; answer\\ \\ 15 [/tex]
Conclusion:
The correct solution for the arithmetic expression (2+8)/2*9/3 using the order of operations is 15
Alice has 1/5 as many miniature cars as Sylvester has Sylvester has 35 miniature cars how many miniature cars does alic have?
Final answer:
Alice has 1/5 as many miniature cars as Sylvester, who owns 35. By multiplying 35 cars by 1/5, we find that Alice has 7 miniature cars.
Explanation:
The student's question is about finding the number of miniature cars Alice has if she has 1/5 as many as Sylvester, who has 35 miniature cars. To solve this, we use the following mathematical operation:
Alice's miniature cars = 1/5 of Sylvester's miniature cars
Sylvester's miniature cars = 35 cars
To find out how many miniature cars Alice has, multiply the number of Sylvester's miniature cars by 1/5:
35 cars x 1/5 = 7 cars
Therefore, Alice has 7 miniature cars.
Which list of decimals is ordered from least to greatest? A) 0.11, 0.101, 0.21 B) 0.27, 0.35, 0.41 C) 0.35, 0.056, 4.2 D) 1.09, 0.91, 1.90. I need it quick
What is the exact value of 400,000x200
Answer:
80,000,000
Step-by-step explanation:
We can rewrite this expression as:
(4 x 10⁵) x (2 x 10²)
To solve this, we multiply first 4 x 2 = 8 and then we multiply the powers of ten using law of exponents:
10⁵x10²= 10₇.
Therefore, the answer is: 8 x 10⁷. If we write it in decimal form we would have:
80,000,000
Solve the system of equations using the substitution method.
{y=−3x+7
x=−2y−16
Enter your answers in the boxes.
x=
y=
ANSWER
[tex]x = 6[/tex]
[tex]y = - 11[/tex]
EXPLANATION
The given system of equations is
[tex]y = - 3x + 7...(1)[/tex]
and
[tex]x = - 2y - 16...(2)[/tex]
We substitute equation (1) into equation (2) to get;
[tex]x = - 2( - 3x + 7) - 16[/tex]
[tex]x = 6x - 14- 16[/tex]
We group similar terms
[tex]x - 6x = - 14 - 16[/tex]
[tex] - 5x = - 30[/tex]
Divide both sides by -5.
[tex]x =6[/tex]
Put x=6 into equation (1).
[tex]y = - 3(6) + 7[/tex]
[tex]y = - 18 + 7[/tex]
[tex]y = - 11[/tex]
Answer:
x = 6 and y = -11
Step-by-step explanation:
Given : System of linear equation
y=−3x+7
x=−2y−16
We have to solve the system of equations using the substitution method.
In substitution method, we substitute the value of one variable in term of other and solve for it.
Consider the given system of linear equation
y = −3x + 7 ...(1)
x = −2y − 16 .....(2)
Substitute, (2) in (1), we get,
y = -3(-2y - 16) + 7
Simplify , we get,
y = 6y + 48 + 7
6y - y = - 55
5y = -55
y = -11
Substitute y = -11 in (2), we get,
x = −2(-11) − 16 = 22 - 16 = 6
thus, x = 6
Thus , x = 6 and y = -11
Measure the length of the top of your desk in centimeters.describe how you found the length
Which is the graph of g(x) = 2x – 1 + 3?
Answer:
The graph given can be further simplified as follows:
[tex]g(x)=2x+2[/tex]
I have drawn and attached the graph with the answer.
Step-by-step explanation:
The graph given can be further simplified as follows:
[tex]g(x)=2x-1+3[/tex]
[tex]g(x)=2x+2[/tex]
Slope of the graph is 2 as x has a coefficient of 2 and intercept is 2.
To graph the above substitute several values to x and calculate the corresponding g(x) values.
[tex]g(1)=2*1+2\\g(1)=4[/tex]
So when x=1, g=4
[tex]g(3)=2*3+2\\g(3)=8[/tex]
So when, x=3, g=8
Calculate several values in the same way and then plot the values is a Cartesian plane, x values in x axis and take g(x) values as y axis.
Then you will get a few dots in a straight line, join those dots with a line and that is the graph.
I have drawn and attached the graph with the answer.
Answer:
The graph is shown below.
Step-by-step explanation:
The given function is
[tex]g(x)=2^{x-1}+3[/tex]
It is an exponential function.
The given exponential function is defined for all real numbers. So, the domain of given function is all real numbers.
Domain = { x | x ∈ R }
Domain = (-∞,∞)
We know that
[tex]2^{x-1}>0[/tex]
Add 3 on both sides.
[tex]2^{x-1}+3>0+3[/tex]
[tex]g(x)>3[/tex]
Range of the function is
Range = (3,∞)
Table of values is
x y
0 3.5
1 4
2 5
Plot these point on a coordinate plane.
The graph of given function is shown below.
Find a ⋅ b.
a = 7i - 4j, b = 4i + 3j
A) <28, -12>
B) 16
C) -40
D) <11, -1>
Answer:
B) 16
Step-by-step explanation:
The dot product of a pair of vectors is the sum of the products of their corresponding parts. It is a scalar.
... a · b = (7i -4j) · (4i +3j) = 7·4 + (-4)·3
... = 28 -12 = 16
what is 5/10 + 25/100
The formula for the volume of a sphere is V=4/3 3.14r^3. What is the formula solved for r?
One number is 33 more than another number. The quotient of the larger number and smaller number is 5 and the remainder is 1. Find the numbers.
Final answer:
The two numbers in question are 8 and 41.
Explanation:
Step-by-Step Solution to Find the Two Numbers
Let the smaller number be x. Thus, the larger number would be x + 33. According to the problem, the larger number divided by the smaller number gives a quotient of 5 and a remainder of 1. We can represent this information using the following equation:
(x + 33) = 5x + 1
This equation states that when the larger number is divided by the smaller number, we obtain a quotient of 5 and a remainder of 1.
Now, let's solve the equation for x:
Subtract 5x from both sides of the equation: (x + 33) - 5x = 1Simplify the equation: -4x + 33 = 1Subtract 33 from both sides: -4x = -32Divide both sides by -4: x = 8Since we have found the smaller number to be 8, the larger number is:
8 + 33 = 41
Therefore, the two numbers are 8 and 41.
The modulus operator would confirm our solution since 41 % 8 does indeed yield a remainder of 1, as stated in the problem.
When constructing an inscribed equilateral triangle, how many arcs will be drawn on the circle?
a. 3
b. 4
c. 5
d. 6
it rained 3/8 of a inch each day for 3 days straight how much rain fell altogether
What are the zeros of the function f(x)=3x^2-3x-6
tim has 30 grapes. he keeps 9 grapes for himself. then he gives 7 grapes each to some of his friends. to how many friends does tim give grapes?
[x÷(y–1)](−4)–[xy+(−3)]÷(−1) if x=−5, y=−2
Answer:
94
Step-by-step explanation:
1 89
2321
33
214