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Difference of two exponential random variables
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Difference of two exponential random variables
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Is it possible to remove ten unit cubes from a 3 by 3 by 3 cube made from 27 unit cubes so that the surface area of the remaining solid is the same as the surface area of the original 3 by 3 by 3 cube? In how many different ways can this be done?
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I removed all eight corners, leaving the total area unchanged.
I removed the central cube of the top surface obtaining an increase of the surface area with four units.
I removed one cube from the middle of an edge at the top (any of the four remaining) and I arrived at a figure with ten cubes less then the original one but with the same surface area.
https://nrich.maths.org/787/solutionThe cube can be removed from the top middle and from the center if a 3 by 3 by 3 cube is made from 27 unit cubes.
What is surface area?An object's surface area refers to the overall space that its surfaces occupy.
Given:
The dimensions of the cube are 3 by 3 by 3
Calculate the surface area of the cube as shown below,
Surface area = 6 × side²
Surface area = 6 × 3²
Surface area = 6 × 9
Surface area = 54
I eliminated each of the eight corners, leaving the entire space untouched.
I deleted the top surface's central cube to increase the surface area by four units.
I started with a shape that was ten cubes smaller than the original one but had the same surface area after removing one cube from the center of one of the top edges (any of the four still there).
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Bonita is testing prototype model rocket engines. To be considered a successful launch, the rocket must reach a height of at least 24 ft and must go a horizontal distance of no more than 10 ft. The vertical height must be at least three times as high as the horizontal distance. No rocket should go higher than 33 ft.
The graph shows the feasible region, where x represents the horizontal distance and y represents the vertical distance.
Which ordered pairs meet all the constraints for a successful launch and make sense in context of the situation?
Select each correct answer.
1. (4, 36)
2. (0, 33)
3. (4.8, 30.5)
4. (2, 22)
5. (9, 26)
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A public park is in the shape of a triangle. the side of the park that forms the base of the triangle is 22 yd long and the area of the park is 7500 yd 2 what is the length of the side of the park that forms the height of the triangle
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1/2 (22h)=7500
22h=15000
h=15000/22=681.8181 yds
(3a) ^ 3 =
This expression without exponents is 3aaa 3 • 3 • 3a 3a3a3a 3 • 3 • 3a 3
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answer
3a x 3a x 3a
Answer: The correct option is (C) [tex]3a.3a.3a.[/tex]
Step-by-step explanation: We are given to select the correct representation of the following exponent expression :
[tex]E=(3a)^3.[/tex]
We will be using the following property of exponents :
[tex]a^n=a.a.a.~.~.~.~(n~times).[/tex]
So, for the given expression, we get
[tex]E=(3a)^3=3a.3a.3a.[/tex]
Thus, the correct representation is [tex]3a.3a.3a.[/tex]
Option (C) is CORRECT.
divide -2x^3-5x^2+4x+2 by x+2
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Final answer:
The detailed answer explains how to divide a polynomial by another using long division method.
Explanation:
To divide -2x³-5x²+4x+2 by x+2, we will perform polynomial long division:
-2x³-5x²+4x+2 / x+2
Start by dividing the leading terms: -2x³ / x = -2x². Multiply x+2 by -2x² to get -2x³-4x². Subtract this from -2x³-5x² to get x². Bring down the 4x next. Continue the process and you will get a quotient of -2x²+x-2 with a remainder of 6.
What is the missing term? (10x-4x^2)-(7x+?)=3x-6x^2
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Because everything on the right of the minus sign will turn negative
The given problem is =
[tex]( 10x-4x^{2} )-(7x+?)=3x-6x^{2}[/tex]
Lets suppose the missing term to be T
So equation becomes:
[tex]10x-4x^{2} -7x-T=3x-6x^{2}[/tex]
[tex]T=10x-4x^{2} -7x-3x+6x^{2}[/tex]
[tex]T=2x^{2}[/tex]
Hence, the missing term is [tex]2x^{2}[/tex]
How many different outcomes are possible when a nickel,a quarter and a penny are flipped at the came time? Solve by applying the counting principle
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he value of an autographed baseball from 2017 is $300. The value of the baseball exponentially increases by 5% each year after 2017. Write a one-variable inequality that could be used to solve for the number of years, x, it would take for the baseball to be worth at least $650. Do not use any dollar signs in the inequality. Write the inequality in standard form.
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fv=300*(1+.05)^t, where fv is future value. So:
300*(1.05)^t=650
1.05^t=2.166667
t=15.85 years
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Answer:
[tex]300(1.05)^x\geq 650[/tex]
Step-by-step explanation:
Since, the initial value of the basketball = $ 300
Annual rate of interest = 5 %
Let the basket ball after x years is worth at least $ 650,
⇒ The cost of basketball after x years ≥ 650
[tex]\implies 300(1+\frac{5}{100})^x\geq 650[/tex]
[tex]\implies 300(1+0.05)^x\geq 650[/tex]
[tex]\implies 300(1.05)^x \geq 650[/tex]
Which is the required inequity.
Consider the equation 3p – 7 + p = 13. What is the resulting equation after the first step in the solution?
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So the resulting equation AFTER the first step would be 4p = 13 + 7.
that's all you can do in one step, and it calls combine like terms. On the next step you use the addition property of equality to add 7 on both side and it would gives you 4p=20.
if they asked to solve for P then you can use the division property of equality to divide 4 on both side.
p=5
Convert the mixed number to a decimal. 4 6/25 A. 4.12 B. 4.24 C. 4.25 D. 4.625
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4 6/25 = 106/25 = 4.24
confused on this question
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since WZ is a bisector of the quadrilateral, that means, it makes two equal halves at the vertex Z and W, that means each triangle gets of those twin angles, so those two angles are the same for both triangles.
now, notice, the segment WZ is shared by both triangles, and thus the tickmark, is the same length for both.
so, you have on Angle and then a Side and then another Angle, two angles and the side between them equal in each triangle, thus congruents by ASA.
The graph of y=-4x+7 is:
A. a line that shows the set of all solutions to the equation.
B. a point that shows one solution to the equation.
C. a point that shows the y-intercept.
D. a line that shows only one solution to the equation.
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Answer:
A. A line that shows the set of all solutions to the equation
Step-by-step explanation:
Question 12 information reference tables look at each expression. is it a factor of 8x4 + 2x2 – 45 when this expression is fully factored? select yes or no for expressions a –
d.
a. 2x2 + 3 yes no
b. 2x2 + 5 yes no
c. 2x – 3 yes no
d. 4x2 – 9 yes no
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(a) 2x^2 + 3....no
(b) 2x^2 + 5...yes
(c) 2x - 3....yes
(d) 4x^2 - 9)...no...not when it is fully factored
Apply THe ORder of operations to simplify the expression
90/ [10+(3² - 4)]
most with best answer gets brainliest please help.
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PEMDAS
Parentheses, exponents, multiplication, division, addition, subtraction
First, we would solve what's in the parentheses. However, since we have more than one set of parentheses and a value in the parentheses has an exponent, we'll do that first. Then, we can do the addition inside the parentheses.
90/(10+(9-4))
90/(10+(5))
90/(10+15)
90/(25)
Now, we can finish the problem by doing division.
90/25
18/5
3.6
Please write the function
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What does it mean for a set of financial records to be comprehensive?
a. Comprehensive records are protected against theft and fire.
b. The records must contain sufficient information to cover all of your financial plan. c. At least two people must be able to view and assess the records.
d. The records must contain every one of your financial files, such as pay stubs and receipts.
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Answer:
B. The records must contain sufficient information to cover all of your financial plan.
Step-by-step explanation:
For a set of financial records to be comprehensive, means - The records must contain sufficient information to cover all of your financial plan.
One should prepare all the strategies before hand and all the details of ones financial plans should be thoroughly examined , before implementing any plan.
Calculate the value of the area between the function f(x)=x^2-4f(x)=x2−4 and the x-axis on the interval from x = 0 to x = 2. round your answer to one decimal place.
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f(x) = x² - 4
Differentiating,
f'(x) = 2x
Then, we officially have 2.
f'(2) = 2(2) = 4
f'(0) = 2(0) = 0
To determine the area, subtract the given answer to get 4 units squared.
Answer: 4 units/guarrantee
[tex] A = \int\limits^2_0 {(x^{2}-4) } \, dx [/tex]
A = [x³/3 - 4x]lim 0->2
A = (2³/3 - 4(2)] - (0³/3 - 4(0)]
A = 16/3 - 0
A = 16/3 ≈ 5.3 sq. units
Fatimah works two shifts per day at the pizza shop. During her storefront shift, she sells her pizzas at a rate of 6 pizzas per hour. During her delivery shift, she sells 20 pizzas per night. Write an equation in slope-intercept form that represents the number of pizzas that Fatimah sells in one day if she works x hours.
A-y=1/6x-20
B-y=20x+6
C-y=6x+20
D-y=-6x+20
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If a memory cell whose address is 5 contains the value 8, what is the difference between writing the value 5 into cell number 6 and moving the contents of cell number 5 into cell number 6?
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The required difference is value 5 is put in cell 6 and in the second case value of cell 5 is transferred to cell number 6.
Given that,
If a memory cell whose address is 5 contains the value 8, what is the difference between writing the value 5 into cell number 6 and moving the contents of cell number 5 into cell number 6 is to specify.
Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in set of y. x is the independent variable while Y is a dependent variable.
Here,
If a memory cell whose address is 5 contains the value 8
implies at cell number 5 the entry is 8
Similarly,
writing the value 5 into cell number 6
While in the case of moving the contents of cell number 5 into cell number 6, Implies 8 is transferred to cell number 6.
Thus, the required difference is value 5 is put in cell 6, and in the second case value of cell 5 is transferred to cell number 6.
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Dennis has 30 plums and 42 apricots. he wants to put the fruit in bag so that each bag has the same number of like fruit. how many pieces of fruit can he put in each bag
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Solve.
Mr. Madison picked 80 pieces of fruit on Thursday.Add.
042412+ 4080Given an int variable n that has been initialized to a positive value and, in addition, int variables k and total that have already been declared, use a do...while loop to compute the sum of the cubes of the first n whole numbers, and store this value in total. thus if n equals 4, your code should put 1*1*1 + 2*2*2 + 3*3*3 + 4*4*4 into total. use no variables other than n, k, and total.
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Which number can each term of the equation be multiplied by to eliminate the decimals before solving? –m + 0.02 + 2.1m = –1.45 – 4.81m A)0.01
B)0.1
C)10
D)100
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since the 2 in 0.02 is in the hundredths place, you need to multiply that by 100 to eliminate the decimal, then you would need to multiply the other numbers by 100 as well
Answer is D) 100
The decimals place in a number can be shifted right or left by multiplying or dividing by powers of 10 respectively
The option which gives the number that will multiply each term of the equation -m + 0.02 + 2.1·m = -1.45 - 4.81·m to eliminate the decimals before solving, is option D)
D) 100
Reason:
The given expression is presented as follows;
-m + 0.02 + 2.1·m = -1.45 - 4.81·m
The number that can multiply the terms to eliminate the decimals before solving
Solution;
The number of decimal places to which the coefficient and constant values are given = 2 decimal places
Therefore, to eliminate the decimal places, the decimal point of each term has to be moved two places to the right
To move decimal points to the right x number of places is given by multiplying the number by 10ˣ
Therefore, to move the decimal point two places to the right so as to eliminate the decimal point, by multiplicative property of equality, we have;
10² × (-m + 0.02 + 2.1·m) = 10² × (-1.45 - 4.81·m)
10² = 100, therefore, we have;
100 × (-m + 0.02 + 2.1·m) = 100 × (-1.45 - 4.81·m)
-100·m + 2 + 2,100·m = -145 - 481·m
Therefore, the number the equation, -m + 0.02 + 2.1·m = -1.45 - 4.81·m, is to be multiplied by is 100
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Find ONLY the areas of the polygons
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11.
area for lower left = 52*62 = 3224
area for upper right = 68*54 = 3672
total area = 3224 + 3672 = 6896 square yards
12.
area of upper left = 57-69 = 3933
area of lower right = 24*37 = 888
total area = 3933 +888 = 4821 square feet
Taylor made 5 1⁄4 cups of iced tea. How many 10 ounce glasses can he fill to the brim with iced tea?
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4
Explanation:
Word problems like this are always a bit tricky to get to the bottom to.
But to put it simply, this question is asking how many times can 10 oz be taken out of 5 1/4 cups. This is also shown as:
5 1/4 cups ÷ 10 ounces
First, make both numbers the same units. Since ounces are smaller, convert 5 1/4 cups into ounces.
5 1/4 cups
5 cups = 40 ounces
1/4 cup = 2 ounces
40 + 2 = 42 ounces.
so now do this:
42 ÷ 10 = 4.2
So Taylor can fill 4 full glasses with iced tea.
Complete the inequality statement with the symbol that makes it true.
1.67 ___ 16.7
>
<
=
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Answer:
The symbol in the blank space would be '<'
Step-by-step explanation:
Since, in inequality,
'>' = greater than,
'<' = less than,
'≥' = greater than equal to,
'≤' = less than equal to,
Now, 1.67 × 10 = 16.7
⇒ 16.7 is 10 times of 1.67,
That is,
1.67 is less than 16.7
⇒ 1.67 < 16.7
Hence, THIRD option is correct.
Alvin’s age is two times Elga’s age. The sum of their age is 60. What is Elga’s age?
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x = Elgas age
2x = Alvins age
x +2x = 60
3x =60
x = 60/3 = 20
Elga is 20 years old
Final answer:
By setting Elga's age as x and establishing an equation based on the given relationship and sum of their ages, we calculated Elga's age to be 20 years old.
Explanation:
To determine Elga's age, we will use the information given:
1. Alvin's age is two times Elga's age.
2. The sum of their ages is 60.
Let's define Elga's age as x. Then, Alvin's age would be 2x since it is two times Elga's age. The sum of their ages can be written as the following equation:
x + 2x = 60
This simplifies to 3x = 60. To find Elga's age, we divide both sides by 3:
3x / 3 = 60 / 3
x = 20
Therefore, Elga's age is 20 years old.
A restaurant offers a $12 dinner special that has 77 choices for an appetizer, 1010 choices for an entrée, and 44 choices for a dessert. how many different meals are available when you select an appetizer, an entrée, and a dessert?
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Choose the correct transformation of the graph f(x) = |x + 8| - 3.
The graph of f(x) = x| is shifted to the left 8 units, down 3 units.
The graph of f(x) = x| is shifted to the right 8 units, down 3 units.
The graph of f(x) = x| is shifted to the left 8 units, up 3 units.
The graph of f(x) = x| is shifted to the right 8 units, up 3 units.
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Answer:
A. The graph of f(x) = |x| is shifted to the left 8 units, down 3 units.
Step-by-step explanation:
We are given,
The transformed function is [tex]f(x)=|x+8|-3[/tex].
Now, the parent function is [tex]f(x)=|x|[/tex].
So, we have,
When the parent function is shifted 8 units to the left, the function is [tex]|x+8|[/tex].
This function when translated 3 units downwards gives [tex]f(x)=|x+8|-3[/tex].
Thus, we get,
The parent function f(x)=|x| is translated 8 units to the left and 3 units downwards.So, option A is correct.
In the given right triangle, find the missing length to the nearest tenth.
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a^2 + b^2 = c^2
a = 11
b = 17
c = We don't know yet so I'll call it x
11^2 + 17^2 = c^2
121 + 289 = c^2
410 = c^2
c = √410
c = 20.2
Thus, the answer is B.
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