3.7 suppose you roll two ordinary dice. calculate the expected value of their product.
The expected value of the product of the given ordinary dice is 2.528.
To calculate the expected value of the product of two dice, we need to first find the probability of each possible outcome. There are 36 possible outcomes when rolling two dice, each with a probability of 1/36. The product of the dice can range from 1 (when both dice are 1) to 36 (when both dice are 6).
To find the expected value, we multiply each possible product by its probability and add them up.
E(product) = (1/36)*1 + (2/36)*2 + (3/36)*3 + ... + (6/36)*36
Simplifying this expression, we get:
E(product) = (1/36)*(1 + 4 + 9 + 16 + 25 + 36)
E(product) = (1/36)*91
E(product) = 2.528
Therefore, the expected value of the product of two dice is 2.528.
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2. Find the missing side length
of the right triangle below.
24 ft.
25 ft.
Step-by-step explanation:
Since it's a right triangle, you can use Pythagoras
a^2 + b^2 = c^2
We have b and c, we just need a, so let's plug it in
\( {x}^{2} + {24}^{2} = {25}^{2} \)
\( {x}^{2} + 576 = 625\)
\( {x}^{2} = 49\)
\(x = 7\)
Answer: 7ft
Step-by-step explanation:
hypotenuse (h) = 25
perpendicular (p) = 24
base (b) = ?
We know by using Pythagoras theorem
b = √h² - p²
= √ 25² - 24²
= √ 49
= 7 ft
Find f′(x) and f′(c) Function Value of c f(x)=(x3+3x)(7x2+8x−2)c=0 f′(x)= f′(c)=
We have found f'(x) and f'(c), which represent the derivative of the function and the derivative evaluated at the specific value c, respectively. The final expressions are :\(f'(x) = [(x^3 + 3x)(14x + 8)] + [(7x^2 + 8x - 2)(3x^2 + 3)] f'(c) = [(c^3 + 3c)(14c + 8)] + [(7c^2 + 8c - 2)(3c^2 + 3)]\)
To find the derivative of the function \(f(x) = (x^3 + 3x)(7x^2 + 8x - 2)\), we can use the product rule. The product rule states that if we have two functions u(x) and v(x), the derivative of their product is given by [u(x)v'(x) + v(x)u'(x)]. Applying the product rule to our function, we have:\(f'(x) = [(x^3 + 3x)(d/dx)(7x^2 + 8x - 2)] + [(7x^2 + 8x - 2)(d/dx)(x^3 + 3x)]\)Now, we need to find the derivative of each term separately. Taking the derivative of\((x^3 + 3x)\)gives us \(3x^2 + 3\), and taking the derivative of \((7x^2 + 8x - 2)\)gives us 14x + 8. Plugging these derivatives into our previous equation, we have:\(f'(x) = [(x^3 + 3x)(14x + 8)] + [(7x^2 + 8x - 2)(3x^2 + 3)]\)
Now, to find f'(c), we substitute c into our derivative expression:\(f'(c) = [(c^3 + 3c)(14c + 8)] + [(7c^2 + 8c - 2)(3c^2 + 3)]\)
At this point, we have found f'(x) and f'(c), which represent the derivative of the function and the derivative evaluated at the specific value c, respectively. The final expressions are : \(f'(x) = [(x^3 + 3x)(14x + 8)] + [(7x^2 + 8x - 2)(3x^2 + 3)] f'(c) = [(c^3 + 3c)(14c + 8)] + [(7c^2 + 8c - 2)(3c^2 + 3)]\)
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Solve this problem. Reduce to lowest terms.
John worked in his garden for 4 3/4hours on Saturday and 2 1/2 hours on Sunday. How
many hours did he work in all?
6 hours
O 74 hours
4 hours
5 hours
Answer:
7 1/4
Step-by-step explanation:
4 3/4 + 2 1/2 =
4 3/4 +2 2/4 =7 1/4
Answer:
7 1/4 hours
Step-by-step explanation:
4 3/4 + 2 1/2
Get a common denominator
4 3/4 + 2 2/4
6 5/4
Rewriting as
6 + 4/4 + 1/4
6 + 1 + 1/4
7 1/4 hours
The sum of 4 and Janelle's height is 88
Answer:
So her height would be 84
Step-by-step explanation:
HELP!!!! PLEASE!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer: red hot= $4
gummies=$9
Step-by-step explanation:
3r+1g=21
-(3r+3g=39)
3r+1g=21
-3r-3g=-39
-2g=-18
g=9
3r+1(9)=21
3r=12
r=4
Given two points which represent the endpoints of the diameter of a circle, which of the following statements is true?
A.
The x-coordinate of the center of the circle must be the same as at least one of the x-coordinates of the given endpoints of the diameter.
B.
The center of the circle is the midpoint of the given endpoints of the diameter.
C.
The center of the circle cannot be found without additional information.
D.
The y-coordinate of the center of the circle must be the same as at least one of the y-coordinates of the given endpoints of the diameter.
The correct statement is B. The center of the circle is the midpoint of the given endpoints of the diameter.
In a circle, the center is located at the midpoint of any diameter. A diameter is a line segment that passes through the center of the circle and has its endpoints on the circle. Therefore, if we are given the endpoints of a diameter, we can determine the center of the circle by finding the midpoint of these endpoints. This means that the x-coordinate of the center will be the average of the x-coordinates of the endpoints, and the y-coordinate of the center will be the average of the y-coordinates of the endpoints.
Option A is not necessarily true because the x-coordinate of the center may or may not be the same as the x-coordinates of the given endpoints.
Option C is incorrect because the center of the circle can be found by determining the midpoint of the diameter.
Option D is not necessarily true because the y-coordinate of the center may or may not be the same as the y-coordinates of the given endpoints.
Therefore, the correct statement is B. The center of the circle is the midpoint of the given endpoints of the diameter.
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What is 604,000,000 expressed in scientific notation?
A. 6.04 x 109
B. 0.604 109
C. 6.04 x 10-8
D. 6.04 x 108
Answer:
D would be your answer
Hope this helped
IMMIDEATE HELP what is the slope of a line perpendicular to the line of whose equation is 3x-5y=45 fully simplified
Answer:
y= -6x+3 (The 3 can be any number other than -9)
Step-by-step explanation:
3x-5y=45
+5y to each side:
3x=5y+45
-45 to each side:
3x-45=5y
Divide by 5
.6x-9=y: y=.6x-9
Perpendicular is opposite sign, resiprecol, (I know, I cant spell)
y= -6x-9
The y-intercept can be any number other than -9
y= -6x+3
PLEASE CORRECT ME IF I MADE A MISTAKE!!!!
Someone please help me out with this one. If LM=XY, then LM-GH=
LM=XY, then LM-GH= XY - GH and this illustrates the subtraction property of equality.
How to illustrate the information?It should be noted that the subtraction property of equality simply implies that when the same number is subtracted form both sides, then the two sides will still remain equal.
In this case, when LM=XY, then LM-GH= XY - GH. This illustrates the subtraction property.
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Given that YZ bisects VW, and VX = 46, find XW
Answer:
XW = 134
Step-by-step explanation:
The fact that YZ bisects VW means that the angles VX and XW are supplementary, that is, they add to 180º. So
VX + XW = 180
We have that VX = 46. So
46 + XW = 180
XW = 134
how to do this question plz
Answer:
y=6
Step-by-step explanation:
divide the total area by 5 to get the area of the square
180/5= 36 cm²
the area of a square is y²
so y²=36⇒ y= 6
easy 10 points, math underline. photo below
Answer:
4
Step-by-step explanation:
Answer:
4
Step-by-step explanation:
A number, one-fourth of that number, and one-third of that number are added. The result is 38. What was the oringnal number?
Answer:
24
Step-by-step explanation:
x + (1/4)x + (1/3)x = 38
multiply both sides by 12 to clear the fractions
12x + 3x + 4x = 456
19x = 456
Divide both sides by 19
x = 24
Answer:
24
Step-by-step explanation:
x+1/4x+1/3x=38
x+7/12x=38
19/12x=38
x=38*12/19=24
the table layout and relationship structure of a relational database is called its:
The table layout and relationship structure of a relational database is called its schema.
A schema in a relational database refers to the overall structure and organization of tables, their attributes (columns), and the relationships between them. It defines the blueprint for how the data is organized and stored in the database.
The schema includes information such as the table names, column names, data types, constraints, and the relationships established through keys (such as primary keys and foreign keys). It provides a logical representation of the database structure and helps ensure data integrity and consistency.
The schema serves as a guide for creating, modifying, and querying the database tables. It defines the structure that enforces rules and relationships between tables, facilitating data manipulation and retrieval.
By designing a well-defined schema, database administrators and developers can establish the foundation for efficient data storage, retrieval, and management within a relational database system.
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Which of the following operators in R2 are linear? = A. L(x) = (0,10x2) B.L(x) = (6x1 + x2, -21) OC. L(x) = (x1 +8, 22) OD. L(x) = (7x1, 9)T
B. L(x) = (6x1 + x2, -21), C. L(x) = (x1 + 8, 22), D. L(x) = (7x1, 9)^T are linear operators.
In order to determine which of the given operators in R2 are linear, we need to check if they satisfy the properties of linearity.
An operator is linear if it satisfies two conditions:
1. Additivity: L(a + b) = L(a) + L(b)
2. Homogeneity: L(c * a) = c * L(a)
Let's go through each option to determine if it is linear:
A. L(x) = (0, 10x^2)
This operator is not linear because it does not satisfy the additivity property. If we take a = (1, 1) and b = (2, 2), we have L(a + b) = L(3, 3) = (0, 10(3^2)) = (0, 90). However, L(a) + L(b) = (0, 10(1^2)) + (0, 10(2^2)) = (0, 10) + (0, 40) = (0, 50), which is not equal to (0, 90).
B. L(x) = (6x1 + x2, -21)
This operator is linear because it satisfies both the additivity and homogeneity properties. For example, if we take a = (1, 2) and b = (3, 4), we have L(a + b) = L(4, 6) = (6(4) + 6, -21) = (30, -21). And L(a) + L(b) = (6(1) + 2, -21) + (6(3) + 4, -21) = (8, -21) + (22, -21) = (30, -42), which is equal to (30, -21).
C. L(x) = (x1 + 8, 22)
This operator is linear because it satisfies both the additivity and homogeneity properties. For example, if we take a = (1, 2) and b = (3, 4), we have L(a + b) = L(4, 6) = (4 + 8, 22) = (12, 22). And L(a) + L(b) = (1 + 8, 22) + (3 + 8, 22) = (9, 22) + (11, 22) = (20, 44), which is equal to (12, 22).
D. L(x) = (7x1, 9)^T
This operator is linear because it satisfies both the additivity and homogeneity properties. For example, if we take a = (1, 2) and b = (3, 4), we have L(a + b) = L(4, 6) = (7(4), 9) = (28, 9). And L(a) + L(b) = (7(1), 9) + (7(3), 9) = (7, 9) + (21, 9) = (28, 18), which is equal to (28, 9).
In summary, options B, C, and D are linear operators, while option A is not linear.
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Khan Academy
layer 1
layer 2
layer 3
surface
layer 4
layer 1 and layer 4
layer 2 and layer 6
layer 3 and layer 5
layer 5
layer 6
surface
Which two layers are approximately the same age?
Layer 1 and Layer 4 are approximately the same age.
The geological structure of the earth's crust can be analyzed by studying the layers of sedimentary rocks. These layers represent various geological periods in the history of the Earth and provide information on the events that have occurred throughout time.
The Khan Academy is an online platform that offers various courses and lessons on different subjects, including geology. The different layers of the earth's crust are named and classified according to their age, composition, and position in the crust. The layers of the earth's crust are as follows:
Layer 1: The surface layer or the soil. It is the layer that contains the organic matter that supports plant growth.
Layer 2: The subsoil, which is composed of partially decomposed organic matter and clay.
Layer 3: The layer of weathered rock. It is the layer that has been altered by the action of water and wind.
Layer 4: The solid bedrock that is composed of igneous, metamorphic or sedimentary rocks. This layer is considered to be the oldest layer of the earth's crust.
Layer 5: The asthenosphere, which is a semi-solid layer of the upper mantle.
Layer 6: The mantle, which is the thickest layer of the earth's crust. The two layers that are approximately the same age are layer 1 and layer 4. Layer 1, which is the surface layer or the soil, is relatively young and is formed by the accumulation of organic matter.
On the other hand, layer 4 is the solid bedrock that is composed of igneous, metamorphic or sedimentary rocks. This layer is considered to be the oldest layer of the earth's crust.
Therefore, layer 1 and layer 4 are approximately the same age.
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Is the line x=-3 parallel to the line y=1/3
Answer:
No, The line x = 3 is not parallel to the line y = 1/3
Step-by-step explanation:
Here's What the graph looks like on Demos graphing calculator.
High Hopes^^
Barry-
David drove 20 miles in 5 mins. Sean drove 45 miles in 9 mins. Who drove at a faster rate? Explain.
3. A leaking tap drips water at 0,5 ml/sec. Convert this rate to l/h.
Answer: 1.8 L/h
Step-by-step explanation:
To convert the rate of water dripping from a tap from millilitres per second (ml/sec) to litres per hour (L/h), we need to use conversion factors.
Step 1:
First, let's convert the rate from millilitres per second to litres per second.
There are 1000 millilitres in a litre, so we can divide the rate in millilitres per second by 1000 to get the rate in litres per second:
\(\LARGE \boxed{\textsf{0.5 ml/sec $\div$ 1000 = 0.0005 L/sec}}\)
Step 2:
We can convert the rate from litres per second to litres per hour. There are 3600 seconds in an hour, so we can multiply the rate in litres per second by 3600 to get the rate in litres per hour:
\(\LARGE \boxed{\textsf{0.0005 L/sec $\times$ 3600 = 1.8 L/h}}\)
Therefore, the rate of water dripping from the tap is 1.8 L/h.
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in problems 13–20, solve the given initial value problem. 13. y′′ 2y′-8y = 0; y102 = 3, y′102 = -12
The solution to the initial value problem is:
y(t) = (-3/4) * e^(-4t+4) + (3/8) * e^(2t+8)
To solve a second-order linear homogeneous differential equation the equation is y′′ 2y′-8y = 0.
Given initial conditions: y(102) = 3 and y′(102) = -12.
To solve this differential equation, we can use the characteristic equation: r^2 + 2r - 8 = 0
Factoring this equation, we get: (r + 4)(r - 2) = 0
So the roots of the characteristic equation are r = -4 and r = 2.
The general solution to the differential equation is:
y(t) = c1 * e^-4t + c2 * e^2t
To find the values of c1 and c2, we can use the initial conditions.
We know that y(102) = 3, so we can substitute t = 2 into the general solution:
3 = c1 * e^-8 + c2 * e^4
We also know that y′(102) = -12, so we can take the derivative of the general solution and substitute t = 2:
y′(t) = -4c1 * e^-4t + 2c2 * e^2t
y′(102) = -4c1 * e^-8 + 2c2 * e^4 = -12
Solving for c1, we get:
c1 = (-3/4) * e^4 + (3/4) * e^-8
Solving for c2, we get:
c2 = (3/8) * e^8 - (3/8) * e^-4
Therefore, the solution to the initial value problem is:
y(t) = (-3/4) * e^(-4t+4) + (3/8) * e^(2t+8)
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can yall pls help me on this
Click on the origine i.e. (0,0)
HOPE IT HELPS
PLEASE MARK ME BRAINLIEST ☺️
what’s the area and the perimeter and of the triangle?
an exponential function passes through the points (0, 10000) and (2, 3600). what are the values of and ?
An exponential function has the form f(x) = ab^x, where a and b are the values you're looking for. Given the points (0, 10000) and (2, 3600), we can set up two equations:
1) f(0) = ab^0 = 10000
2) f(2) = ab^2 = 3600
Now, we can substitute the value of a in the second equation:
10000 * b^2 = 3600 ⇒ b^2 = 0.36
⇒ b = sqrt(0.36) = 0.6
So, the values of a and b for this exponential function are a = 10000 and b = 0.6.
To solve this problem, we need to use the formula for an exponential function:
y = a(b^x)
where a is the initial value, b is the growth factor, x is the input variable (usually time), and y is the output variable (usually the value of the function at a given time).
Using the two given points, we can set up two equations:
10000 = a(b^0)
3600 = a(b^2)
Simplifying the first equation, we get:
10000 = a
Substituting this into the second equation, we get:
3600 = 10000(b^2)
Dividing both sides by 10000, we get:
0.36 = b^2
Taking the square root of both sides, we get:
b = 0.6 or b = -0.6 (but we reject this value since exponential functions always have positive growth)
So the values of a and b are:
a = 10000
b = 0.6
Therefore, the exponential function that passes through the points (0, 10000) and (2, 3600) is:
y = 10000(0.6^x)
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Please help me will mark brainliest
Answer:
-10
Step-by-step explanation:
Steven has $150. John has J dollars. Steven has 30 less than 2 times the amount John has. How much does John have?
Answer:
J = 90
John has 90 dollars.
Step-by-step explanation:
We need to find how much money John has. To find how much J equals we need to break it down.
We already know that Steven has 150 dollars. We also know that he has 30 less than two times the amount John has.
Steven has 30 less than two times the amount John has.
So 150 + 30 = 180
180 is two times the amount John has.
Because 180 is two times the amount John has we need to divide by two.
180 ÷ 2 = 90.
J = 90. Therefore John has 90 dollars.
This question was tricky! I hope I helped a little! Have a great day!!
Find the largest six digits number which is divisible by 120 exactly.
Answer:
999,960
Step-by-step explanation:
let x be a multiple of 120
120x ≤ 999,999
999,999 / 120 = 8333.325
8333 ≤ x ≤ 8334
8333(120) = 999,960
8334(1200) = 1,000,080 this is a 7-digit number
Therefore, the largest 6-digit number that is exactly divisible by 120 is 999,960
Tom and rosie are designing a game. In each turn, a player rolls five 666-sided dice and adds the numbers showing on each face to determine how many points they get that turn. For example, the lowest number of points in a given turn is 1+1+1+1+1=51+1+1+1+1=51, plus, 1, plus, 1, plus, 1, plus, 1, equals, 5 points, and the highest is 6+6+6+6+6=306+6+6+6+6=306, plus, 6, plus, 6, plus, 6, plus, 6, equals, 30 points.
Rosie's statement about expecting a total of about 175 points over 100 turns is accurate.
Based on the expected value, Rosie's statement is correct.
The expected value, denoted as E(X), represents the average or mean value of a random variable, in this case, the sum of points in a given turn when rolling the five dice.
Tom's statement, "A player will most likely get 17.5 points in any given roll," is not accurate. The expected value of 17.5 points does not necessarily mean that a player is most likely to get exactly 17.5 points in any single roll. Instead, it indicates that over many rolls, the average value of points earned in a turn is 17.5 points.
On the other hand, Rosie's statement, "Over 100 turns, we can expect a total of about 175 points," is correct. Since the expected value is 17.5 points per turn, over 100 turns, we can expect the total sum of points to be approximately 100 turns × 17.5 points/turn = 1750 points.
In summary, the expected value of 17.5 points represents the average outcome over multiple rolls, and based on this value, Rosie's statement about expecting a total of about 175 points over 100 turns is accurate.
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The complete question:
Tom and Rosie are designing a game. In each turn, a player rolls five 6-sided dice and adds the numbers showing on each face to determine how many points they get that turn. For example, the lowest number of points in a given turn is 1+1+1+1+1=5 points, and the highest is 6+6+6+6+6=30 points.
They let X represent the sum in a given turn, and they find the expected value of X is E(X) = 17.5 points.
Tom says, "A player will most likely get 17.5 points in any given roll."
Rosie says, "Over 100 turns, we can expect a total of about 175 points."
Whose statement is correct based on the expected value?
Given the speeds of each runner below, determine who runs the fastest.
\text{Frank runs 9 feet per second.}
Frank runs 9 feet per second.
\text{Tony runs 299 feet in 34 seconds.}
Tony runs 299 feet in 34 seconds.
\text{Zach runs 1 mile in 396 seconds.}
Zach runs 1 mile in 396 seconds.
\text{Will runs 675 feet in 1 minute.}
Will runs 675 feet in 1 minute.
Zach runs with 14.31 feet per second speed and faster than other runners.
What is Speed?Speed is measured as the ratio of distance to the time in which the distance was covered
Given that Frank runs 9 feet per second.
Speed=Distance /time
=9 feet/ 1 second
=9 feet per second.
Tony runs 299 feet in 34 seconds
Speed=299/34
=8.794 feet per second.
Zach runs 1 mile in 396 seconds.
We know that 1 mile =5280 feet
Speed=5280/369
=14.31 feet per second.
Will runs 675 feet in 1 minute
1 minute is 60 seconds
Speed=675/60
=11.25 feet per second.
Hence, Zach runs with 14.31 feet per second speed and faster than other runners.
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Find all 3 solutions: 3 − 42 − 4 + 5 = 0
Answer:
Step-by-step explanation:
If you mean 3x^3 - 42x^2 - 4x + 5 = 0 you can graph it manually or with technology
The roots are 14.09, 0.30 and -0.39 to nearest hundredth.