When rolling a standard die and another die with faces having either 0 or 6 spots, the possible total values y range from 1 to 12, excluding the numbers 5 and 6 twice due to the unique nature of the second die.
Explanation:The question asks about the possible values for the total number of spots y on the up-faces when you roll two nonstandard dice: a standard six-sided die with faces having 1, 2, 3, 4, 5, and 6 spots, and another die with three faces having 0 spots and three faces having 6 spots. To find y, we need to consider all the possible outcomes of rolling these two dice and summing the numbers of spots on the up-faces.
If the standard die shows a 1, y can be 1+0=1 or 1+6=7.If it shows a 2, y can be 2+0=2 or 2+6=8.If it shows a 3, y can be 3+0=3 or 3+6=9.If it shows a 4, y can be 4+0=4 or 4+6=10.If it shows a 5, y can be 5+0=5 or 5+6=11.If it shows a 6, y can be 6+0=6 or 6+6=12.Therefore, the possible values for y are 1, 2, 3, 4, 5, 5, 7, 8, 9, 10, 11, and 12.
Suppose that water is pouring into a swimming pool in the shape of a right circular cylinder at a constant rate of 7 cubic feet per minute. if the pool has radius 5 feet and height 8 feet, what is the rate of change of the height of the water in the pool when the depth of the water in the pool is 5 feet?
The rate of change of the height of the water in the pool when the depth is 5 feet is approximately 0.089 feet per minute.
Explanation:To find the rate of change of the height of the water in the pool, we can use the formula for the volume of a cylinder.
The volume of a cylinder is given by the formula V = πr^2h, where r is the radius and h is the height.
So, when the depth of the water is 5 feet, we can find the rate of change of the height by differentiating the volume equation with respect to time.
Let's calculate it:
V = π(5^2)(h)
dV/dt = π(25)(dh/dt)
Since the volume is increasing at a constant rate of 7 cubic feet per minute, we have dV/dt = 7.
Substituting the given values, we have:
7 = π(25)(dh/dt)
dh/dt = 7/π(25)
So, the rate of change of the height of the water in the pool when the depth is 5 feet is approximately 0.089 feet per minute.
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To find the rate of change of the height of the water in the pool, we can use the concept of related rates. The rate of change is approximately 0.089 cubic feet per minute.
Explanation:To find the rate of change of the height of the water in the pool, we can use the concept of related rates. Let's call the height of the water in the pool 'h' and the rate of change of the height 'dh/dt'. We know that the volume of water in the pool is flowing at a constant rate of 7 cubic feet per minute, therefore the rate of change of the volume of water in the pool is also constant at 7 cubic feet per minute. The volume of a cylinder is given by V = πr^2h, where r is the radius of the pool and h is the height of the water. We can differentiate this equation with respect to time to find the rate of change of the volume.
dV/dt = πr^2(dh/dt)
Since the radius of the pool is constant at 5 feet and the rate of change of the volume is 7 cubic feet per minute, we can substitute these values into the equation and solve for dh/dt.
7 = π(5^2)(dh/dt)
dh/dt = 7/(π(5^2))
Therefore, the rate of change of the height of the water in the pool when the depth of the water is 5 feet is approximately 0.089 cubic feet per minute.
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MATH HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The equation 1.5r+15=2.25r1.5r+15=2.25r represents the number rr of movies you must rent to spend the same amount at each movie store. How many movies must you rent to spend the same amount at each movie store?
Brody is purchasing some tools for his workshop. He has a budget of $120 and needs to buy at least 14 tools. Each hammer costs $10, and each wrench costs $6.
Answer:
The graph in the attached figure
Step-by-step explanation:
Let
x------> the number of hammers
y------> the number of of wrenches
we know that
[tex]10x+6y\leq 120[/tex] -----> inequality A
[tex]x+y\geq 14[/tex] -----> inequality B
using a graphing tool
The solution of the system of inequalities is the shaded area
see the attached figure
Determine if conjecture: True or False
The difference between two negative numbers is always negative
False, because the difference between two negative numbers is not always negative.
Here,
Given that, The difference between two negative numbers is always negative.
We have to prove this statement is true or false.
What is Negative number?
In the real number system, a negative number is a number that is less than zero.
Now,
We can prove it false with a counter example.
Let two negative number -6 and -8.
Hence, difference between -6 and -8 is,
⇒-6 - ( -8 )
⇒-6 + 8
⇒2
it is not negative number.
Hence, the difference between two negative numbers is not always negative.
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The sum of two trinomials ________.
Simplify. −7i⋅(−8i)
−56
−56i
56i
56
Lixin intends to buy either Gift A, which costs $10 or Gift B, which costs $8, as Christmas gifts for each of her parents, 2 siblings, 13 relatives and 10 friends. Given that she intends to spend $230, find the number of each gift she should buy
Please help !! I need someone
The distance around the outside of Cedar Park is 0.8 mile. Joanie ran 0.25 of the distance during her lunch break. How far did she run?
Answer: 0.2
Step-by-step explanation:
To calculate the distance that Joanie run during her lunch break is necessary to multiply the total distance around the outside of Cedar Park (0,8) by the 1/4 of the total distance that she ran (0,25).
So, the expression is:
0,25 . 0.8 = 0,2
Joanie run 0,2 miles during her lunch break.
A+b
A*b
A-b
A *divide sign*
Which one isn't closed
CHECK MY ANSWERS PLS!!
2m - nx = x + 4 with description
The equation 2m - nx = x + 4 is a linear equation solvable for x using algebraic manipulation. The solution is x = (2m - 4)/(nx + 1), requiring values for m and n to find x's specific value.
The given equation 2m - nx = x + 4 is a linear equation and can be solved for x by applying algebraic techniques. The question indicates that there is an element of differential equations involved, suggesting that it might be related to more advanced topics such as linear differential equations or characteristics equations. However, the provided context also mentions concepts like probability with positive and negative jumps, quadratic equations, and principles from physics, but these do not directly apply to the initial linear equation provided.
To solve for x in the given equation, we would rearrange the terms to isolate x:
2m - nx = x + 4
2m - 4 = x(nx + 1)
x = (2m - 4)/(nx + 1)
The solution for x is now expressed in terms of m and n. To find the specific value of x, values for m and n must be known.
complete a prime factorization of 54 and write it as a product of primes
For a large cooking project, Arthur needs to put 18 cups of water into a large pot. He can transport a maximum of 4 cups from the sink in a single trip. The pot already contains 5 cups of water. How many trips are required for Arthur to fill the pot to 18 cups?
In the diagram, m < ACB = 65.
m < ECA =
A. 180
B. 115
C. 65
D. 90
The measure for <ECA is 115 degree.
What is Linear Pair?When two lines cross at one point, a linear pair of angles is created. If the angles follow the intersection of the two lines in a straight line, they are said to be linear. A linear pair's total angles are always equal to 180°. These are also referred to as additional angles.
Given:
m <ACB = 65 degree
m <ECA = ?
As. <ACB and <ECA forms a linear pair.
So, m<ACB + m<ECA = 180
64 + m <ECA = 180
m <ECA = 180 - 65
m <ECA = 115
Hence, the measure of <ECA = 115 degree.
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The table shows the steps for solving the given inequality for x.
7x + 16 < −5(4 − 5x)
Select the reason for each step from the drop-down menus.
7x + 16 < − 5(4 − 5x) - Given
7x + 16 < −20 + 25x - Distributive Property
16 < −20 + 18x - (Choose)
36 < 18x - (Choose)
2 < x - (Choose)
Answer:
Subtraction (addition) property of inequalityAddition property of inequalityDivision property of inequalityStep-by-step explanation:
You want the reasons for each of the final three steps in the solution of the inequality 7x +16 < -5(5 -5x).
Steps2. 7x +16 < -20 +25x . . . . . . . given step 2
3. 16 < -20 +18x . . . . . Subtraction property of inequality
7x was subtracted from both sides4. 36 < 18x . . . . . . . . . Addition property of inequality
20 was added to both sides5. 2 < x . . . . . . . . . . . . Division property of inequality
both sides were divided by 18__
Additional comment
Subtraction of 7x is the same as adding -7x, so you can say the reason for step 3 is either of "subtraction property" or "addition property" The same would be true of step 4.
To figure this out, you compare the inequality on each line with the one before, and determine what was changed. If the same thing is done to both sides of the inequality (addition, subtraction, multiplication, division), the reason is the corresponding property of inequality.
The multiplication and division properties of inequality tell you to reverse the comparison symbol when the factor used is negative. Here, the factor is 18, a positive number, so the inequality symbol remains untouched.
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A coffee shop uses 4 liters of milk every day.If there are 15 liters of milk in the refrigerator, after how many days will more milk need to be purchased?
A function, h(x), is defined as shown.
h(x) =
Which graph represents h(x)? {image Attached)
Answer:
option B
Step-by-step explanation:
We have three different function for h(x)
[tex]h(x)= \frac{1}{4}x-4, x<=0[/tex]
WE have x<=0, so the graph starts at x=0 and goes down
Plug in 0 for x
[tex]h(0)= \frac{1}{4}(0)-4[/tex]
So h(0)= -4
When x=0, y= -4
The graph starts at (0,-4) and goes down
[tex]h(x)= \frac{1}{3}x-3, 0<x<=3[/tex]
x lies between 0 and 3, so the graph starts at x=0 and ends at x=3
Plug in 0 for x
[tex]h(0)= \frac{1}{3}(0)-3[/tex]
So h(0)= -3
When x=0, y= -4
Plug in 3 for x
[tex]h(3)= \frac{1}{3}(3)-3=-2[/tex]
When x=3, y= -2
The graph starts at (0,-4) and ends at (3, -2)
[tex]h(x)= \frac{1}{2}x-2, x>=4[/tex]
WE have x>=4, so the graph starts at x=4 and goes to the right
Plug in 4 for x
[tex]h(4)= \frac{1}{2}(4)-2[/tex]
So h(4)= 0
When x=4, y= 0
The graph starts at (4,0) and goes to the right.
SEcond graph is correct
Answer:
B
Step-by-step explanation:
Find f(2) and f(a+h) when f(x)=3x^2+2x+4
30 increased by 3 times the square of a number
The number is 30+ 3x².
What is square of a number?When an integer is multiplied by itself, the resultant number is known as its square number. Basically, a square number is a number that is obtained by the product of two same numbers. In geometry, the area of a square with 'n' as the side length (where n is an integer) is the finest example of a square number.
When an integer is multiplied by the same integer, the resultant number is known as a square number. For example, when we multiply 5 × 5 = 52, we get 25. Here, 25 is a square number. Square numbers are always positive, they cannot be negative because when a negative number is multiplied by the same negative number, it results in a positive number.
let the number be x
Now, 3 times square of a number
3x²
and, 30 increased
=30+ 3x²
Hence, the number is 30+ 3x².
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How do I do these only need to do 1 I just need to see how to do it!
Each side of this pentagon is the same length.
How many lines of symmetry does this pentagon have?
A.
0
B.
2
C.
3
D.
5
An equation has solutions of m = –5 and m = 9. Which could be the equation?
Answer:
[tex]y=m^2-4m-45[/tex]
Step-by-step explanation:
An equation has solutions of m = –5 and m = 9
WE are given with the solution. Lets write the solution as factors
When x=a is a solution then factor is (x-a)
[tex]m=-5[/tex] is a solution. change the sign of the solution while writing factor. factor is (m+5)
[tex]m=9[/tex] is a solution, factor is (m-9)
we use the factors to find the equation
[tex]y=(m+5)(m-9)[/tex]
Multiply the factors using FOIL method
[tex]y=m^2-9m+5m-45[/tex]
[tex]y=m^2-4m-45[/tex]
round to the nearest hundred 5,503,569
Final answer:
To round 5,503,569 to the nearest hundred, observe the hundreds and the following digit. Since the following digit is a 9, round the hundreds digit up to 7 and zeros follow. The rounded number is 5,503,600.
Explanation:
To round the number 5,503,569 to the nearest hundred, we need to look at the digit in the hundreds place and the digit following it. In 5,503,569, the hundreds digit is 6, and the digit to its right is 9. According to rounding rules, if the digit right after the one we are rounding is 5 or greater, we round up. Since 9 is greater than 5, we round the hundreds place up from 6 to 7 and change all the digits to the right of the hundreds place to zero.
The final answer, therefore, is 5,503,600 when 5,503,569 is rounded to the nearest hundred.
Luis can spend up to $240 buying men’s and women’s shirts for his club. Men’s shirts cost $8 each and women’s shirts cost $12 each. He needs to buy at least 3 men’s shirts and at least 8 women’s shirts. Also, the women’s shirts must be at least twice the number of men’s shirts.
The graph shows the feasible region, where x represents the number of men’s shirts and y represents the number of women’s shirts.
Which ordered pairs meet all the constraints and make sense in context of the situation?
Select each correct answer.
(4, 9)
(7, 13)
(2, 15)
(5,12)
(6, 15)
Let
x------> the number of men’s shirts
y-----> the number of women’s shirts
we know that
[tex]8x+12y \leq 240[/tex] ----> constraint A
[tex]x\geq 3[/tex] ----> constraint B
[tex]y\geq 8[/tex] ----> constraint C
[tex]y\geq 2x[/tex] ----> constraint D
using a graphing tool
see the attached figure N[tex]1[/tex]
The solution is the shaded area
Remember that
if an ordered pair meets all restrictions and makes sense in the context of the situation, then the ordered pair is a system solution
we're going to proceed to verify each pair ordered
case A) [tex](4,9)[/tex]
Substitute the value of x and y in each constraint
[tex]x=4\\y=9[/tex]
Verify constraint A
[tex]8*4+12*9 \leq 240[/tex]
[tex]140 \leq 240[/tex] -------> is true
Verify constraint B
[tex]4\geq 3[/tex] -------> is true
Verify constraint C
[tex]9\geq 8[/tex] ------> is true
Verify constraint D
[tex]9\geq 2*4[/tex]
[tex]9\geq 8[/tex] -----> is true
therefore
the ordered pair [tex](4,9)[/tex] is a system solution
case B) [tex](7,13)[/tex]
Substitute the value of x and y in each constraint
[tex]x=7\\y=13[/tex]
Verify constraint A
[tex]8*7+12*13 \leq 240[/tex]
[tex]212 \leq 240[/tex] -------> is true
Verify constraint B
[tex]7\geq 3[/tex] -------> is true
Verify constraint C
[tex]13\geq 8[/tex] ------> is true
Verify constraint D
[tex]13\geq 2*7[/tex]
[tex]13\geq 14[/tex] -----> is not true
therefore
the ordered pair [tex](7,13)[/tex] is not a system solution
case C) [tex](2,15)[/tex]
Substitute the value of x and y in each constraint
[tex]x=2\\y=15[/tex]
Verify constraint A
[tex]8*2+12*15 \leq 240[/tex]
[tex]196 \leq 240[/tex] -------> is true
Verify constraint B
[tex]2\geq 3[/tex] -------> is not true
Verify constraint C
[tex]15\geq 8[/tex] ------> is true
Verify constraint D
[tex]15\geq 2*2[/tex]
[tex]15\geq 4[/tex] -----> is true
therefore
the ordered pair [tex](2,15)[/tex] is not a system solution
case D) [tex](5,12)[/tex]
Substitute the value of x and y in each constraint
[tex]x=5\\y=12[/tex]
Verify constraint A
[tex]8*5+12*12 \leq 240[/tex]
[tex]184 \leq 240[/tex] -------> is true
Verify constraint B
[tex]5\geq 3[/tex] -------> is true
Verify constraint C
[tex]12\geq 8[/tex] ------> is true
Verify constraint D
[tex]12\geq 2*5[/tex]
[tex]12\geq 10[/tex] -----> is true
therefore
the ordered pair [tex](5,12)[/tex] is a system solution
case E) [tex](6,15)[/tex]
Substitute the value of x and y in each constraint
[tex]x=6\\y=15[/tex]
Verify constraint A
[tex]8*6+12*15 \leq 240[/tex]
[tex]228 \leq 240[/tex] -------> is true
Verify constraint B
[tex]6\geq 3[/tex] -------> is true
Verify constraint C
[tex]15\geq 8[/tex] ------> is true
Verify constraint D
[tex]15\geq 2*6[/tex]
[tex]15\geq 12[/tex] -----> is true
therefore
the ordered pair [tex](6,15)[/tex] is a system solution
therefore
the answer is
[tex](4,9)[/tex]
[tex](5,12)[/tex]
[tex](6,15)[/tex]
see the attached figure N[tex]2[/tex] to better understand the solution
Answer:
(4,9) (5,12) (6,15)
Step-by-step explanation:
Those were the correct options.
how do I factor (x^2 + 1)^1/2 +2(x^2 + 1)^1/2
Who was a Mexican american who fought for Texan independence from mexico and later became a Texas senator.
michael found a job listed in the classified ads that pays a yearly salary of $57.3k what is the weekly salary based on this annual salary
The value of the expression (2x^2)/(x) + x(100-15x) when x = 5 is
Answer:
[tex]\dfrac{2x^2}{x} + x(100-15x)[/tex] at x=5
135
Step-by-step explanation:
Given: The expression [tex]\dfrac{2x^2}{x} + x(100-15x)[/tex]
This is rational expression of variable x.
Put x=5 into the expression and then simplify
[tex]\Rightarrow \dfrac{2\cdot 5^2}{5} + 5(100-15\cdot 5)[/tex]
[tex]\Rightarrow 2\cdot 5 + 5(100-75)[/tex]
[tex]\Rightarrow 2\cdot 5 + 5\cdot 25)[/tex]
[tex]\Rightarrow 10+125[/tex] (Addition of two integer)
[tex]\Rightarrow 135[/tex]
Hence, The value of given expression is 135
O coarda a unui cerc pentru O si raza r=20 cm, are lungimea de 32cm. DIstanta de la centru cercului la coarda este: