The probability of rolling a sum of 6 when two standard six-sided dice are rolled is 5/36, or approximately 0.139.
What is probability?The probability of an event occurring is defined by probability. There are many instances in real life where we may need to make predictions about how something will turn out.
There are 36 possible outcomes when two standard six-sided dice are rolled. Each die has 6 possible outcomes, so the total number of outcomes is 6 x 6 = 36.
To find the probability of rolling a sum of 6, we need to count the number of ways we can get a sum of 6. There are five possible ways to get a sum of 6:
- Roll a 1 on the first die and a 5 on the second die
- Roll a 2 on the first die and a 4 on the second die
- Roll a 3 on the first die and a 3 on the second die
- Roll a 4 on the first die and a 2 on the second die
- Roll a 5 on the first die and a 1 on the second die
So, the probability of rolling a sum of 6 is 5/36.
Therefore, the probability of rolling a sum of 6 when two standard six-sided dice are rolled is 5/36, or approximately 0.139.
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Let f be a differentiable function such that f (2) = 4, f(4) = 6, f'(2) = -4, and f'(6) = -3. f 6 . The function g is differentiable and g(x) = f-1(x) for all x. What is the value of g'(4) =
The value of g'(4) is -1/3 if f is a differential function such that f (2) = 4, f(4) = 6, f'(2) = -4, and f'(6) = -3.
First, let's use the information given to find the equation of the tangent line to f at x=2. We know that f(2) = 4 and f'(2) = -4, so the equation of the tangent line at x=2 is
y - 4 = -4(x - 2)
Simplifying, we get
y = -4x + 12
Now let's use the fact that g(x) = f-1(x) for all x. This means that g(f(x)) = x for all x. We want to find g'(4), which is the derivative of g at x=4.
Using the chain rule, we have
g'(4) = [g(f(4))]'
Since f(4) = 6 and g(f(4)) = g(6) (since g(x) = f-1(x)), we can rewrite this as
g'(4) = [g(6)]'
Now we can use the fact that g(x) = f-1(x) to rewrite g(6) as f-1(6)
g'(4) = [f-1(6)]'
Now we need to find the derivative of f-1(x) with respect to x. To do this, we can use the fact that f(f-1(x)) = x for all x. Differentiating both sides with respect to x using the chain rule, we get
f'(f-1(x)) * (f-1)'(x) = 1
Solving for (f-1)'(x), we get
(f-1)'(x) = 1 / f'(f-1(x))
Now we can plug in x=6 and use the information given to find f'(f-1(6)). Since f(4) = 6, we know that f-1(6) = 4. Therefore
f'(f-1(6)) = f'(4)
Using the tangent line equation we found earlier, we know that f(2) = 4 and f'(2) = -4. Therefore, the slope of the line connecting (2,4) and (4,6) is
(6 - 4) / (4 - 2) = 1
Since the line connecting (2,4) and (4,6) is the tangent line to f at x=2, we know that this slope is equal to f'(2). Therefore
f'(4) = f'(f-1(6)) = f'(4)
Now we can plug in x=6 and f'(4) into our expression for (f-1)'(x)
(f-1)'(6) = 1 / f'(4)
Substituting this into our expression for g'(4), we get
g'(4) = [f-1(6)]' = (f-1)'(6) = 1 / f'(4)
Plugging in f'(4) = f'(f-1(6)) = f'(4), we get
g'(4) = 1 / f'(4) = 1 / (-3) = -1/3
Therefore, g'(4) = -1/3.
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Use the differential dz to approximate the change that will be
observed in z = f (x, y) = 5/x^2 + y^2 as x changes from −1 to
−0.93 and y changes from 2 to 1.94.
To approximate the change in z = f(x, y) as x changes from −1 to −0.93 and y changes from 2 to 1.94, we can use the differential dz.
First, we need to find the partial derivatives of f with respect to x and y:
∂f/∂x = -10/x³(y²)
∂f/∂y = -10(x²)/y³
Then, we can use the following formula:
dz ≈ ∂f/∂x * Δx + ∂f/∂y * Δy
where Δx and Δy are the changes in x and y, respectively.
Substituting in the given values, we have:
Δx = -0.93 - (-1) = 0.07
Δy = 1.94 - 2 = -0.06
Using the partial derivatives we calculated earlier, we get:
dz ≈ (-10/-1.037³(2²)) * 0.07 + (-10((-1)²)/1.94³) * (-0.06)
dz ≈ -0.031
Therefore, the approximate change observed in z as x changes from −1 to −0.93 and y changes from 2 to 1.94 is -0.031.
To approximate the change in z using the differential dz, we first need to find the partial derivatives of z with respect to x and y. Given z = f(x, y) = 5/(x² + y²):
∂z/∂x = -10x/(x² + y²)²
∂z/∂y = -10y/(x² + y²)²
Now, we need to find the differential dz:
dz = (∂z/∂x)dx + (∂z/∂y)dy
Since x changes from -1 to -0.93, dx = -0.93 - (-1) = 0.07. Similarly, y changes from 2 to 1.94, so dy = 1.94 - 2 = -0.06.
Now, plug in the initial values of x and y (-1, 2):
∂z/∂x = -10(-1)/((-1)² + 2²)² = -10/25
∂z/∂y = -10(2)/((-1)² + 2²)² = -40/25
Now, plug in dx and dy into the dz equation:
dz = (-10/25)(0.07) + (-40/25)(-0.06) = 0.28 - 0.096 = 0.184
So, the approximate change in z when x changes from -1 to -0.93 and y changes from 2 to 1.94 is 0.184.
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In 2015, there were roughly 1 X 10^6 high school football players and 2 X 10^3 professional football players in the United States. About how many times more high school football players are there? Explain how you know
There are approximately 500 times more high school football players than professional football players in the United States.
How to determine ratio of football players?To determine how many times more high school football players there are than professional football players in the United States, we need to divide the number of high school players by the number of professional players:
1 x 10⁶ / 2 x 10³ = 500
Therefore, there are approximately 500 times more high school football players than professional football players in the United States.
We can determine this by dividing the two numbers and finding the ratio of high school players to professional players. The result tells us how many times greater the number of high school players is than the number of professional players. In this case, the ratio is 500:1, which means that for every professional football player, there are 500 high school football players.
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Yesterday, of the coffee shop's customers ordered flavored coffee. of the
orders were for chocolate flavored coffee. What part of the coffee shop's
customers ordered chocolate flavored coffee?
67
56
14
Please upload a picture of a piece of paper with the problem worked out, and draw the graph for extra points, there will be 6 of these, so go to my profile and find the rest, and do the same, for extra points.
for questions 3 and 4, solve the system using the substitution method.
The value of X and y using substitution method for the quadratic equation given above would be = -3.6 and - 2.8 respectively.
How to calculate the unknown values using substitution method?The equations given are;
2x - 7y = 13. ----> equation 1
3x + y = 8 --------> equation 2
From equation 2 make y that subject of formula;
y = 8 - 3x
Substitute y = 8 - 3x into equation 1
2x - 7(8 - 3x) = 13
2x - 56 - 21x = 13
-19x = 13+56
-19x = 69
X = -69/19
X = - 3.6
Substitute X = -3.6 into equation 2
3(-3.6) + y = 8
y= 8 - 10.8
= - 2.8
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helppppppp please!!!!!!!
Thus, the height of cone for the given values of circumference an f volume is found as: 4 cm.
Explain about the conical shape:A tri shape that resembles a cone is what is known as a conical shape. A cone has a flat end that gradually taper towards a single point at the top known as the apex. Most commonly, a conical shape's flat end has an oval or circular shape. Conical shapes are on your mind when you imagine an ice cream cone with only a pointed end.
Volume of a cone = 1/3 * π *r²*h
r is the radiush is the height π = 3.14Given that:
circumference c = 6π Volume = 12π
using circumference c = 6π
c = 2πr (for circular base)
6π = 2πr
r = 3 cm
Now, using the volume;
Volume of a cone = 1/3 * π *r²*h
1/3 * π *3²*h = 12π
3h = 12
h = 4 cm
Thus, the height of the cone for the given values of circumference an f volume is found as: 4 cm.
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9) The profit from a business is described by the function P(x) = -3x² + 12x + 75, where xis the number of items made, in thousands, and P(x) is the profit in dollars. How many items will maximize the profit? А 1,000 4,000 B 2. 000 D 6,000
The number of items that will maximize the profit is 2000. Thus, the correct answer is option c.
To calculate the maximum profit that can be earned we have to differentiate the equation and find the value of x
dP/dx = 1/dx (-3x² + 12x + 75)
= -6x + 12
Calculating dP/dx = 0
0 = -6x + 12
6x = 12
x = 2
Next, we calculate the next differential of the equation:
It comes out to be -6
Since it is smaller than zero, the value of x calculated is the maxima.
The maxima = 2
Thus, the item that will maximize the profit comes out to be 2000 as x is the number of items made in thousand.
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A yard cleanup service charges a $254 fee plus $19. 25 per hour. Another cleanup service charges a $133 fee plus $24. 75 per hour. How long is a job for which the two companies' costs are the same?
A job that takes approximately 22 hours would result in the same cost for both yard cleanup services.
To determine when the two yard cleanup services have the same cost, you'll need to set up an equation using the given fees and hourly rates
. For the first service, the cost is $254 (fee) + $19.25 per hour (rate).
For the second service, the cost is $133 (fee) + $24.75 per hour (rate).
Let x represent the number of hours for the job.
The equation would be: 254 + 19.25x = 133 + 24.75x
To solve for x, subtract 19.25x from both sides and simplify: 121 = 5.5x
Now, divide both sides by 5.5 to find the number of hours: x ≈ 22 hours
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67 Solve for the value of x. 6x+16 12x+2 8
Answer:
x=9
Step-by-step explanation:
These 2 angles are both on a straight line, meaning that the total angle sum is 180°.
We can write an equation:
180=(6x+16)+(12x+2)
combine like terms
180=18x+18
subtract 18 from both sides
162=18x
divide both sides by 18
9=x
Hope this helps! :)
I have no congruent sides. One of my angles has a measure of 100 degrees. Answer with drawing of the triangle
I am a(n and triangle
You are an scalene triangle.
How can you identify the type of triangle when given the information that it has no congruent sides and one angle measuring 100 degrees?You are a scalene triangle.
A scalene triangle is a type of triangle where all three sides have different lengths, and no two angles are congruent. In this case, you mentioned that one of the angles has a measure of 100 degrees.
Here's a simple diagram of a scalene triangle to help illustrate:
\
\
\
\
\
\
In the diagram, the angles are not drawn to scale, but it represents a scalene triangle where one angle measures 100 degrees. The sides of the triangle would have different lengths, distinguishing it from an equilateral or isosceles triangle where at least two sides are congruent.
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Lan shuffles a standard deck of 52 playing cards and turns over the first four cards, one at a time. He records the
number of aces he observes.
Have the conditions for a binomial setting been met for this scenario?
O Yes, a success is "ace. "
O Yes, all four conditions in BINS have been met.
No, we do not know how many aces will occur in those first four cards.
O No, the cards are not being replaced, so the independence condition is not met.
Next
Submit
Save and Exit
Mark this and return
The binomial conditions are not met as the cards are not being replaced, so the independence condition is not met. So, the correct answer is D).
The conditions for a binomial setting are
there are a fixed number of trials,
the trials are independent,
there are only two possible outcomes (success or failure),
the probability of success is constant for each trial.
In this scenario, the first two conditions are met as Lan is turning over the first four cards and they are independent events. The third condition is also met as the success is defined as observing an ace and the failure is observing any other card.
However, the fourth condition is not met as the probability of success changes for each trial. After the first card is turned over, the probability of observing an ace changes for the second trial. Therefore, the scenario does not meet all the conditions for a binomial setting. So, the correct option is D).
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Which expressions are equivalent to 6\cdot6\cdot6\cdot6\cdot66⋅6⋅6⋅6⋅66, dot, 6, dot, 6, dot, 6, dot, 6 ?
The expression 6\cdot6\cdot6\cdot6\cdot66\cdot6\cdot6\cdot6\cdot66 is equivalent to 60534416.
How to simplify this expression using commutative property?The given expression is:
6\cdot6\cdot6\cdot6\cdot66\cdot6\cdot6\cdot6\cdot66
To simplify this expression we can first simplify the factors that are multiples of 6:
6\cdot6\cdot6\cdot6\cdot6\cdot6\cdot6\cdot6\cdot11\cdot11
Next, we can use the commutative property of multiplication to group the factors of 6 together:
(6\cdot6\cdot6\cdot6\cdot6\cdot6)\cdot(6\cdot6\cdot6\cdot6)
Simplifying each of these groups of factors separately, we get:
46656\cdot1296
Multiplying these two numbers together, we get the final result:
60534416
Let's break down the given expression and simplify it step by step.
The expression is:
6\cdot6\cdot6\cdot6\cdot66\cdot6\cdot6\cdot6\cdot66
We can start by simplifying the factors that are multiples of 6:
6\cdot6\cdot6\cdot6\cdot6\cdot6\cdot6\cdot6\cdot11\cdot11
Next, we can use the commutative property of multiplication to group the factors of 6 together:
(6\cdot6\cdot6\cdot6\cdot6\cdot6)\cdot(6\cdot6\cdot6\cdot6)
Simplifying each of these groups of factors separately, we get:
6\cdot6\cdot6\cdot6\cdot6\cdot6 = 46656
6\cdot6\cdot6\cdot6 = 1296
Now we can substitute these values back into the expression:
46656\cdot1296
We can multiply these two numbers together to get the final result:
60534416
The given expression is:
6\cdot6\cdot6\cdot6\cdot66\cdot6\cdot6\cdot6\cdot66
To simplify this expression, we can first simplify the factors that are multiples of 6:
6\cdot6\cdot6\cdot6\cdot6\cdot6\cdot6\cdot6\cdot11\cdot11
Next, we can use the commutative property of multiplication to group the factors of 6 together:
(6\cdot6\cdot6\cdot6\cdot6\cdot6)\cdot(6\cdot6\cdot6\cdot6)
Simplifying each of these groups of factors separately, we get:
46656\cdot1296
Multiplying these two numbers together, we get the final result:
60534416
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Find the equation of the tangent line of y=xlog(x) at the point(1,0).
The equation of the tangent line is y = x - 1.
To find the equation of the tangent line of y=xlog(x) at the point (1,0), we will first need to find the derivative of the function y=xlog(x) with respect to x.
Step 1: Find the derivative of y=xlog(x) with respect to x.
Using the product rule, (uv)' = u'v + uv', where u=x and v=log(x).
u' = derivative of x with respect to x = 1
v' = derivative of log(x) with respect to x = 1/x
Now, apply the product rule:
y' = u'v + uv' = 1*log(x) + x*(1/x) = log(x) + 1
Step 2: Find the slope of the tangent line at the point (1,0).
Evaluate y' at x=1:
y'(1) = log(1) + 1 = 0 + 1 = 1
The slope of the tangent line at (1,0) is 1.
Step 3: Find the equation of the tangent line.
We will use the point-slope form of a linear equation: y - y1 = m(x - x1), where (x1, y1) is the point (1,0) and m is the slope (1).
y - 0 = 1(x - 1)
y = x - 1
The equation of the tangent line of y=xlog(x) at the point (1,0) is y = x - 1.
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HELP ME PLEASE ANYBODY I NEED IT URGENTLY
I also have to show my work
Thank you.
P is directly proportional to (q+2)2
when q = 1, p = 1.
find p when q = 10.
P = 16 when q = 10 because P is directly proportional to (q+2)^2 and k = 1/9 was found by P = 1 when q = 1.
How to find value the of P?If P is directly proportional to (q+2)^2, we can write this as:
P = k(q+2[tex])^2[/tex]
where k is a constant of proportionality.
To find the value of k, we can use the given condition that when q = 1, P = 1:
1 = k(1+2[tex])^2[/tex]
1 = k(3[tex])^2[/tex]
1 = 9k
k = 1/9
Now we can use this value of k to find P when q = 10:
P = (1/9)(10+2[tex])^2[/tex]
P = (1/9)(12[tex])^2[/tex]
P = (1/9)(144)
P = 16
The reason for this answer is based on the given information that P is directly proportional to (q+2[tex])^2[/tex]. Using the proportionality constant k, which was determined by the condition that P = 1 when q = 1.
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Of the following options, what could be a possible first step in solving the
equation -7x- 5 = x + 3? (6 points)
Adding 7x to both sides of the equation
O Subtracting 5 from both sides of the equation
Adding x to both sides of the equation
O Combining like terms, -7x + x = - 6x
a population of 100 individuals is undergoing exponential growth with a population doubling time of 1 year. what size will this population be in 2 years?
The size of the population of 100 individuals which are undergoing exponential growth is equal to 400.
Population is undergoing exponential growth,
Use the formula of exponential ,
Nt = N0 × e^(rt)
Where,
Nt is the population size at time t
N0 is the initial population size
e is the mathematical constant, approximately 2.71828
r is the growth rate
If the population doubling time is 1 year,
Use the following formula to calculate the growth rate,
r = log(2) / t
Where t is the doubling time,
log(2) is the natural logarithm of 2 = approximately 0.693.
⇒ r = log(2) / 1 year
= 0.693 / year
Plug in the values,
Nt = N0 × e^(rt)
⇒Nt = 100 × e^(0.693 × 2)
Population size in 't' = 2 years.
Nt = 100 × e^1.386
⇒Nt = 100 × 3.998
⇒Nt = 100 ×4.000
⇒ Nt = 400
Therefore, the population will be 400 individuals in 2 years if it continues to undergo exponential growth with a population doubling time of 1 year.
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To build a triangular shaped raised bed frame for her tomato plants, chris has three pieces of lumber whose length are 4 feet 5 feet and 9 feet. can chris build her planter? explain
Chris cannot build the triangular raised bed frame with the given lumber.
How can Chris build a triangular raised bed frame?To determine if Chris can build her triangular raised bed frame, we need to check if the length of any one of the lumber pieces is greater than the sum of the other two. If this condition is not met, the pieces can be used to build the frame.
Let's check:
4 + 5 = 9 (no)
4 + 9 = 13 (no)
5 + 9 = 14 (yes)
Since the length of the 5-foot and 9-foot lumber pieces add up to be greater than the 4-foot piece, Chris can build her triangular raised bed frame. She can use the 4-foot and 5-foot pieces for the two shorter sides of the triangle and the 9-foot piece for the longer side.
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JAMIE SPUN THE SPINNER SHOWN 30 TIMES AND RECORDED THE FREQUENCY OF
EACH RESULT IN THE TABLE BELOW. USE THE TABLE TO COMPLETE THE STATEMENTS
IN THE ORANGE
If Jamie spins the spinner 60 times, we can predict 20 red, 10 blue, 20 green, and 10 yellow outcomes
How to solveFirst, calculate the probability of each color by dividing the frequency by 30 spins.
Red: 10/30 = 1/3
Blue: 5/30 = 1/6
Green: 10/30 = 1/3
Yellow: 5/30 = 1/6
Now, predict the frequency of each color if Jamie spins the spinner 60 times.
Red: (1/3) * 60 = 20
Blue: (1/6) * 60 = 10
Green: (1/3) * 60 = 20
Yellow: (1/6) * 60 = 10
So, if Jamie spins the spinner 60 times, we can predict 20 red, 10 blue, 20 green, and 10 yellow outcomes
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The Complete Question:
Jamie spun a spinner with 4 colors - red, blue, green, and yellow - 30 times and recorded the frequency of each result in the table below. Use the table to determine the probability of each color and predict the frequency of each color if Jamie spins the spinner 60 times.
Table:
Red - 10
Blue - 5
Green - 10
Yellow - 5
6. Mary Cole is buying a $225,000.00 home. Her annual housing
expenses are: mortgage payments, $14,169.20; real estate taxes,
$3,960.00; annual insurance premium, $840.00; maintenance,
$1,410.00; and utilities, $5,180.00. What is Mary's average
monthly expense?
Chapter 10 Mathematics for Business and Personal Finance
Mary's average monthly expense for housing is $2,129.93.
To find Mary's average monthly expenseWWe need to add up all her annual housing expenses and divide the total by 12 (the number of months in a year):
Total annual housing expenses = mortgage payments + real estate taxes + annual insurance premium + maintenance + utilities
Total annual housing expenses = $14,169.20 + $3,960.00 + $840.00 + $1,410.00 + $5,180.00
Total annual housing expenses = $25,559.20
Average monthly expense = Total annual housing expenses ÷ 12
Average monthly expense = $25,559.20 ÷ 12
Average monthly expense = $2,129.93
Therefore, Mary's average monthly expense for housing is $2,129.93.
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how many paths are there from point (0,0) to (90,160) if every step increments one coordinate and leaves the other unchanged and you want the path to go through (80,70)?
There are 4.097 x [tex]10^43[/tex] paths from (0,0) to (90,160) that pass through (80,70).
To calculate the number of paths from (0,0) to (90,160) while passing through (80,70), we need to break down the problem into smaller steps.
First, we can calculate the number of paths from (0,0) to (80,70) and then
multiply that by the number of paths from (80,70) to (90,160).
To go from (0,0) to (80,70), we need to take 80 steps to the right and 70 steps up, which gives us a total of 150 steps. The order in which we take these steps doesn't matter, so we can think of it as choosing 70 steps out of 150 to be up. This can be calculated using the binomial coefficient, which gives us (150 choose 70) = 2.364 x [tex]10^43[/tex]
To go from (80,70) to (90,160), we need to take 10 steps to the right and 90 steps up, which gives us a total of 100 steps. Using the same method as above, the number of paths from (80,70) to (90,160) is (100 choose 10) = 17,310,309.
Multiplying these two values together, we get the total number of paths from (0,0) to (90,160) that pass through (80,70):
(2.364 x 10^34) x (17,310,309) = 4.097 x [tex]10^43[/tex]
Therefore, there are 4.097 x [tex]10^43[/tex] paths from (0,0) to (90,160) that pass through (80,70).
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2
How much water will a cone hold that has a diameter of 6 inches and a height of 21 inches.
Use 3. 14 for 7 and round your answer to the nearest whole number.
A 66 cubic inches
B 198 cubic inches
C) 594 cubic inches
D 2374 cubic inches
The cone will hold approximately 198 cubic inches of water. The correct answer is option B.
To find how much water a cone with a diameter of 6 inches and a height of 21 inches will hold, we need to calculate the volume of the cone. We can use the formula for the volume of a cone: V = (1/3)πr^2h, where V is the volume, r is the radius, and h is the height.
1. Since the diameter is 6 inches, the radius (r) is half of that: r = 6/2 = 3 inches.
2. The height (h) is given as 21 inches.
3. Use 3.14 for π.
Now, plug the values into the formula:
V = (1/3) * 3.14 * (3^2) * 21
4. Calculate the square of the radius: 3^2 = 9
5. Multiply the values: (1/3) * 3.14 * 9 * 21 ≈ 197.64
6. Round the answer to the nearest whole number: 198 cubic inches.
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If |x+5|=, what are the possible values of x
The possible values of x that satisfy the equation |x+5| = c are x = c - 5 and x = -c - 5.
what is algebra?
Algebra is a branch of mathematics that deals with mathematical operations and symbols used to represent numbers and quantities in equations and formulas.
Assuming you meant to write |x+5|= some value, I can give you a general method to solve equations involving absolute values.
If |a| = b, then either a = b or a = -b. Thus, to solve the equation |x+5| = c, where c is some given value, we can split it into two cases:
Case 1: x+5 = c
Solving for x, we get x = c - 5.
Case 2: -(x+5) = c
Solving for x, we get x = -c - 5.
So, the possible values of x that satisfy the equation |x+5| = c are x = c - 5 and x = -c - 5.
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write a real-world example that could be solved by useing the the inequality 4x + 8 greater than 32. Then solve the inequality.
1. 8 added to four times the product of 4 and a number is greater than 32
1. x = 6
How to determine the valueIt is important to know that inequalities are expressions showing unequal comparison between number, expressions, or variables.
From the information given, we have that;
4x + 8 greater than 32.
This is represented as;
4x + 8 > 32
collect the like terms, we get
4x > 32 - 8
subtract the values
4x> 24
Divide both sides by the coefficient of x which is 4, we have;
x > 24/4
x > 6
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PLEASE HELP MEE
4 thumb drives and 1 compact disk have a total capacity of 18 gigabytes. 3 compact disks and 4 thumb drives have a total capacity of 22 gigabytes. Find the capacity of 1 thumb drive (x) and the capacity of 1 compact disk (y)
The capacity of 1 thumb drive is 4 gigabytes and the capacity of 1 compact disk is 2 gigabytes.
What is the capacity of 1 thumb drive and 1 compact disk?The first step is to form the system of equations that represent the information in the question:
4x + y = 18 equation 1
4x + 3y = 22 equation 2
The elimination method would be used to determined the required values.
Subtract equation 1 from equation 2
2y = 4
y = 4/2
y = 2
Substitute for y in equation 1: 4x + 2 = 18
4x = 18 - 2
4x = 16
x = 16/4
x = 4
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A cylinder has volume 108 cm? What is the volume of a cone with the same
radius and height? Use 3. 14 for it and be sure to add units to your answer.
The volume of the cone with the same radius and height as the cylinder is 36 cm³.
To find the volume of a cone with the same radius and height as the cylinder, we first need to find the radius and height of the cylinder.
The formula for the volume of a cylinder is V = πr^2h, where r is the radius and h is the height.
We are given that the volume of the cylinder is 108 cm^3.
So, 108 = πr^2h
To solve for r and h, we need more information. However, we can use the fact that the cone has the same radius and height as the cylinder to our advantage.
The formula for the volume of a cone is V = (1/3)πr^2h.
Since the cone has the same radius and height as the cylinder, we can substitute the values of r and h from the cylinder into the cone formula.
V = (1/3)π( r^2 )(h)
V = (1/3)π( r^2 )(108/π)
V = (1/3)( r^2 )(108)
V = 36( r^2 )
Therefore, the volume of the cone with the same radius and height as the cylinder is 36 cm³
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Find the cube of each semimajor axis length (A) by raising the value to the third power. Write your results in the table provided. Round all values to the nearest thousandth. Consult the math review if you need help with exponents
To find the cube of a semimajor axis length (A), we need to raise the value to the third power, which is simply multiplying it by itself three times. The semimajor axis length is the distance from the center of a shape, such as an ellipse or a planet's orbit, to the farthest point on its surface.
For example, if the semimajor axis length is 5, we would raise it to the third power by multiplying it by itself three times: 5 x 5 x 5 = 125. So the cube of a semimajor axis length of 5 is 125.
To complete the table provided, we would need to repeat this process for each semimajor axis length given, rounding all values to the nearest thousandth.
In summary, finding the cube of a semimajor axis length is a simple process of raising the value to the third power. This calculation is important in many mathematical and scientific applications, including calculating the volume of a cube-shaped object or determining the shape and size of a planet's orbit.
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This is the correct answer. I hope this helps!
The derivative of the function ds/dt of the function s = (tan² t - sec² t)⁵ is ...
The derivative of s with respect to t is:
ds/dt = 10(sec² t - tan t) * (tan² t - sec² t)⁴
How to find the derivative of the function?To find the derivative of s with respect to t, we will use the chain rule and the power rule of differentiation.
Let u = (tan² t - sec² t). Then, s = u⁵.
Using the chain rule, we have:
ds/dt = (du/dt) * (ds/du)
Now, we need to find du/dt and ds/du.
Using the chain rule again, we have:
du/dt = d/dt(tan² t - sec² t) = 2tan t * sec² t - 2sec t * tan t * sec t = 2sec² t * (tan t - sec t)
To find ds/du, we can simply apply the power rule:
ds/du = 5u⁴
Substituting these into the original equation for ds/dt, we get:
ds/dt = (2sec² t * (tan t - sec t)) * (5(tan² t - sec² t)⁴)
Therefore, the derivative of s with respect to t is:
ds/dt = 10(sec² t - tan t) * (tan² t - sec² t)⁴
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What is the molarity of a solution made by adding 116. 0 g of NaCl to 2. 00 L of water?
The molarity of the solution is approximately 0.9925 M.
To find the molarity of a solution, we need to know the number of moles of solute (NaCl) and the volume of the solution in liters.
First, let's calculate the number of moles of NaCl:
Number of moles of NaCl = Mass of NaCl / Molar mass of NaCl
The molar mass of NaCl is 58.44 g/mol (sodium has a molar mass of 22.99 g/mol and chlorine has a molar mass of 35.45 g/mol).
Number of moles of NaCl = 116.0 g / 58.44 g/mol = 1.985 moles
Next, let's calculate the volume of the solution in liters:
Volume of solution = 2.00 L
Finally, let's calculate the molarity of the solution:
Molarity = Number of moles of solute / Volume of solution
Molarity = 1.985 moles / 2.00 L = 0.9925 M
Therefore, the molarity of the solution is approximately 0.9925 M.
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PLEASE HELP ASAP I HAVE 10 MIN 30 PTS
A 72. 0-gram piece of metal at 96. 0 °C is placed in 130. 0 g of water in a calorimeter at 25. 5 °C. The final temperature in the calorimeter is 31. 0 °C. Determine the specific heat of the metal. Show your work by listing various steps, and explain how the law of conservation of energy applies to this situation.
The specific heat of the metal is approximately 0.392 J/g°C. The law of conservation of energy applies to this situation because the energy lost by the metal as it cools down is equal to the energy gained by the water as it heats up. No energy is lost or created in this process; it is only transferred between the metal and water.
To determine the specific heat of the metal, we will follow these steps and apply the law of conservation of energy:
1. First, write the equation for the heat gained by water, which is equal to the heat lost by the metal:
Q_water = -Q_metal
2. Next, write the equations for heat gained by water and heat lost by the metal using the formula Q = mcΔT:
m_water * c_water * (T_final - T_initial, water) = -m_metal * c_metal * (T_final - T_initial, metal)
3. Plug in the known values:
(130.0 g) * (4.18 J/g°C) * (31.0 °C - 25.5 °C) = -(72.0 g) * c_metal * (31.0 °C - 96.0 °C)
4. Solve for the specific heat of the metal (c_metal):
c_metal = [(130.0 g) * (4.18 J/g°C) * (5.5 °C)] / [(72.0 g) * (-65.0 °C)]
5. Calculate the value:
c_metal = 0.392 J/g°C
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