The values of x that make the expression (x - 6)(x + 2) equal to zero are -2 and 6. This is based on the Zero Product Property in Mathematics, which states that if the product of two factors is zero, then at least one of the factors must equal zero.
Explanation:In Mathematics, the Zero Product Property states that if the product of two factors is zero, then at least one of the factors must be zero. Applying this property in the expression (x - 6)(x + 2) = 0, one can conclude that either (x - 6) = 0 or (x + 2) = 0.
The expression (x−6)(x+2) equals 0 when either (x−6)=0 or (x+2)=0. Solving each equation separately:
For (x−6)=0, add 6 to both sides to get x=6.
For (x+2)=0, subtract 2 from both sides to get x=−2.
So, the values of x that make (x−6)(x+2)=0 are x=−2 and x=6.
Solving both equations, we get two possible solutions, x = 6 or x = -2. So, the values of x that would result in the expression being equal to zero are -2 and 6, listed in order from least to greatest.
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What does 3(8)+8 equal
Answer: 32
Step-by-step explanation: You need to use PEMDAS. First, multiply the two numbers.
3(8) = 24
Then, add 8.
24 + 8 = 32
32 is your answer.
Find P(not rolling 1, 3, 4, or 5) with one number cube.
The event "not rolling 1, 3, 4, or 5" is the same event as "rolling 2 or 6".
Since the possible outcomes of a number cube have the same probability, the probability of rolling 2 or 6 is given by
[tex]\dfrac{\text{\# of good outcomes}}{\text{\# of possible outcomes}}=\dfrac{2}{6}=\dfrac{1}{3}[/tex]
If f(1) = 160 and f(n + 1) = –2f(n), what is f(4)?
Answer:
-1280
Step-by-step explanation:
There are 2 ways you could do this. You could just do the question until you come to the end of f(4). That is likely the simplest way to do it.
f(1) = 160
f(2) = - 2 * f(1)
f(2) = -2*160
f(2) = -320
f(3) = -2 * f(2)
f(3) = -2 * - 320
f(3) = 640
f(4) = - 2 * f(3)
f(4) = - 2 * 640
f(4) = - 1280
I don't know that you could do this explicitly with any real confidence.
[tex]f(1)=160\\f(n+1)=-2f(n)\\\\f(2)=-2\cdot 160=-320\\f(3)=-2\cdot(-320)=640\\f(4)=-2\cdot 640=-1280[/tex]
(-b3 + 3b2 + 8) – ? - 5b2 – 9) = 5b3 +852 +17
Let's solve for x.
−b3+3b2+8−x−5b2−9=5b3+852+17
Step 1: Add b^3 to both sides.
−b3−2b2−x−1+b3=5b3+869+b3
−2b2−x−1=6b3+869
Step 2: Add 2b^2 to both sides.
−2b2−x−1+2b2=6b3+869+2b2
−x−1=6b3+2b2+869
Step 3: Add 1 to both sides.
−x−1+1=6b3+2b2+869+1
−x=6b3+2b2+870
Step 4: Divide both sides by -1.
−x
−1
=
6b3+2b2+870
−1
x=−6b3−2b2−870
Answer:
x=−6b3−2b2−870
Answer:
the answer is the first option -6b^3
Step-by-step explanation:
yup
can You show how to graph this
Answer:
The graph in the attached figure
Step-by-step explanation:
we have that
[tex]f(x)=x-4[/tex] ------> For [tex]x < 2[/tex]
[tex]f(x)=-2x+2[/tex] ------> For [tex]x\geq2[/tex]
To graph this piece wise- defined function
In the interval (-∞,2) ----> graph the line [tex]f(x)=x-4[/tex]
In the interval [2,∞) ----> graph the line [tex]f(x)=-2x+2[/tex]
The function is continue -----> the domain is all real numbers
using a graphing tool
see the attached figure
Find the remainder when f(x) is divided by (x - k).
f(x) = 7x4 + 12x3 + 6x2 - 5x + 16; k = 3
Answer:
946
Step-by-step explanation:
To find just the remainder when dividing a polynomial by x-3, you could just plug in 3 into that polynomial.
If you were dividing by x+3, the remainder would just be the polynomial evaluated at x=-3.
Anyways plugging in 3 gives
7(3)^4 + 12(3)^3 + 6(3)^2 - 5(3) + 16
Just put this into your nearest calculator .
It should output 946.
You could use synthetic division or even long.
Synthetic Division.
We put 3 on outside because we are dividing by x-3.
3. | 7. 12. 6. -5. 16
| 21. 99. 315. 930
________________________
7. 33. 105. 310. 946
The remainder is the last number in the last column.
The plugging in and the synthetic division will always work when dividing by a linear expression.
Find the value of 10!/(10-2)!
A) 720
B)80
C)90
D)45
Answer:
[tex]\huge \boxed{90}[/tex]
Step-by-step explanation:
First thing you do is subtract.
10-2=8
[tex]\displaystyle \frac{10!}{8!}[/tex]
Then you cancel the factorials.
[tex]\displaystyle \frac{10!}{8}=10\times9[/tex]
Multiply numbers from left to right to find the answer.
[tex]\displaystyle 10\times9=90[/tex]
[tex]\huge \textnormal{90}[/tex], which is our answer.
Hope this helps!
Final answer:
The value of 10!/(10-2)! simplifies to 90 after canceling out the common factorial terms, hence the correct answer is option C (90).
Explanation:
The expression 10!/(10-2)! represents a calculation involving factorials. The factorial of a number n is denoted n! and means the product of all positive integers from 1 up to n.
So, to simplify this expression, we can expand both factorials:
10! means 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1,
and (10-2)! or 8! means 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1.
When we divide 10! by 8!, the terms 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 (which is 8!) cancel out, leaving us with:
10 x 9 = 90.
Therefore, 10!/(10-2)! simplifies to 90, which is option C.
Select one answer choice For part A and select one answer choice for part B
[tex]\bf \qquad \qquad \qquad \textit{discriminant of a quadratic} \\\\\\ \stackrel{\stackrel{a}{\downarrow }}{1}x^2\stackrel{\stackrel{b}{\downarrow }}{+6}x\stackrel{\stackrel{c}{\downarrow }}{+9}=0 ~~~~~~~~ \stackrel{discriminant}{b^2-4ac}= \begin{cases} 0&\textit{\underline{one real solution}}~~\textit{\Large \checkmark}\\ positive&\textit{two real solutions}\\ negative&\textit{no solution} \end{cases} \\\\\\ 6^2-4(1)(9)\implies 36-36\implies 0[/tex]
There are 86,400 frames of animation in 1 hour of anime. How many frames are there per second? There are 3600 seconds in 1 hour. (PLZZ HELP!)
Answer:
There are 86,400 / 3,600 = 24 frames/second
Step-by-step explanation:
Since there are 60 minutes in an hour and 60 seconds in a minute, in an hour you have 60 x 60 = 3,600 seconds.
You have 86,400 frames of animation in 1 hour.
Divide 86,400 by 3,600 to get the number of frames per second.
There are 86,400 / 3,600 = 24 frames/second
To solve, make a simple equation.
86400/3600=x
In order to get x, divide 86400 by 3600 and which x will be 24.
You can either divide the long way or the short way.
Algorithm, mental.
Get rid of the two 0s.
Then you'll get 864/36. .... 24... x=24
So 24 is the answer.
Hope this helps:)
Please help, it'd be greatly appreciated.
I keep failing this, it's my last resort.
Answer:
the measure of angle 4 should be 45
Step-by-step explanation:
since angle 2 and 4 are congruent, 2x+15 = x + 30
so x = 15
15 + 30 = 45
Identify the zeros of f(x) = (x + 1)(x − 8)(5x + 2).
1, 2 over 5, 8
−1, −2 over 5,−8
−1, 2 over 5, −8
−1, −2 over 5,8
Answer:
The zero's are -1, -2/5, 8
Step-by-step explanation:
f(x) = (x + 1)(x − 8)(5x + 2)
We can use the zero product property
0 = (x + 1)(x − 8)(5x + 2)
0 = x+1 0 = x-8 0 =5x+2
x=-1 x=8 -2 =5x
x=-1 x=8 -2/5 =x
The zero's are -1, -2/5, 8
Which expression is equivalent to log3 c/9
log3c + logz(9)
log;(9) + log3
log3c - log3(9)
logg (9) - log:)
Answer:
log3c-log3(9) i.e. [tex]log_{3}c-log_{3}9[/tex]
Step-by-step explanation:
As per logarithmic relation
[tex]log_{base}\frac{A}{B}=log_{base}A-log_{base}B[/tex]
Now, in the given question base value is 3. Therefore
[tex]log_{3}\frac{c}{9}=log_{3}c-log_{3}9[/tex]
Hence the correct answer is third option.
The expression is equivalent to log₃ (c/9) is log₃ (c) - log₃ (9).
What is Logarithm?The power to which a number must be increased in order to obtain additional values is referred to as a logarithm. The easiest approach to express enormous numbers is this manner. Numerous significant characteristics of a logarithm demonstrate that addition and subtraction logarithms can also be written as multiplication and division of logarithms.
We have,
log₃ (c/9)
We know the from the property of logarithm
logₐ (c/d) = logₐ (c) - logₐ(d)
and, logₐ (cd)= logₐ(c) x logₐ (d)
So, log₃ (c/9)
= log₃ (c) - log₃ (9)
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what is the ratio of 12 minute to 1 hour
Answer:
12:1
Step-by-step explanation:
12:1Answer:
Step-by-step explanation:
What is the truth value for the following conditional statement? p: true q: false ∼q → ∼p T F → F T T → F F T → T T F → T
Final answer:
The truth value of the conditional statement ¬q → ¬p, with p being true and q being false, is false.
Explanation:
The question is asking about the truth value of the conditional statement ¬q → ¬p, where p is true and q is false. In a conditional statement of the form 'if q then p', written symbolically as q → p, the statement is false only when q is true and p is false. Otherwise, the statement is true. In this case, ¬q means 'not q' and ¬p means 'not p'. Given that q is false, ¬q is true. Given that p is true, ¬p is false. Thus, the statement ¬q → ¬p is of the form 'true → false', which makes the entire conditional statement false.
Final answer:
The truth value for the conditional statement ¬q → ¬p when p is true and q is false is false. This is because the contrapositive of any conditional statement must have the same truth value as the statement itself, and the given condition does not maintain this logical equivalence.
Explanation:
The truth value for the following conditional statement ¬q → ¬p when p is true and q is false is what we are trying to determine. The proposition ¬q → ¬p is the contrapositive of the conditional p → q. According to logic, a conditional proposition and its contrapositive always have the same truth value. Since we are given that p is true and q is false (¬q is true), using the definitions of the logical operators, we find that the contrapositive of the original conditional should also be true if the original is true.
In this case, the contrapositive is ¬q → ¬p, which, when translated in terms of the given truth values, becomes true → false. This suggests that if ¬q is true, then ¬p is true as well; however, since we know p is true, the situation given (¬q is true, ¬p is false) is not possible because it would not uphold the truth of the original proposition. Thus, the provided sequence of truth values does not maintain the logical equivalence of the contrapositive, making it incorrect. Therefore, the truth value of ¬q → ¬p is false under the given conditions.
the slope of the line below is -4. write the equation of the line in point slope form using the coordinates of the labeled point.
Answer:
y-2=-4(x-1)
Step-by-step explanation:
point slope form is written as y-y1=m(x-x1). y1 and x1 are both the coordinates on the line. x1 is the x coordinate y1 is y coordinate. m is the slope.
two numbers have the sum of 124 and a difference of 32. find the numbers.
Answer:
78 and 46
Step-by-step explanation:
Substitution (look it up it's hard to explain lol)
please help thanks
attachment linked
Answer:
x = 150
D
Step-by-step explanation:
1 / tan(90 - x) = -√3/3 Cross multiply
3 = -√3 * tan(90 - x) Divide by -√3
3/-√3 = tan(90 - x) Rationalize the denominator
3 * √3 / (- √3 * √3 ) =tan(90-x)
3 * √3 / - 3 = tan(90 - x) Divide
- √3 = tan(90 - x) Take the inverse tan of -√3
tan-1(-√3) = 90 - x
-60 = 90 - x Add x to both sides.
x - 60 = 90 Add 60 to both sides
x = 150
Ship A receives a distress signal from the southwest, and ship B receives a distress signal from the same vessel from the north. At which location is the vessel in distress located? Describe how you arrived at your conclusion using complete sentences.
Answer:
ship B is going in a straight line north ship A is going diagonal make a straight line where each ship is moving towards and where ever they intersect will be where the ship in distress is located
hope this helped
I need help with this
Answer:
ƒ(x) = (x - 1)(x - 2)(x - 3)
Step-by-step explanation:
The graph shown is that of a cubic equation with zeros at x = 1, 2, and 3
The function in factored form must be
ƒ(x) = (x - 1)(x - 2)(x - 3).
When you solve for the zeros, the sign of the constant changes. For example
x - 1 = 0
x = 1
7+3 to the second power+(12-8) divided by 2x 4 is
[tex]\bf \stackrel{\mathbb{P~E~M~D~A~S}}{7+3^2+(12-8)\div 2\times 4}\implies 7+3^2+(\stackrel{\downarrow }{4})\div 2\times 4\implies 7+\stackrel{\downarrow }{9}+(4)\div 2\times 4 \\\\\\ 7+9+\stackrel{\downarrow }{2}\times 4\implies 7+9+\stackrel{\downarrow }{8}\implies \stackrel{\downarrow }{16}+8\implies 24[/tex]
A manufacturing machine has two processes. One of them is repeated 4 times and the second only once. The entire cycle can take no longer than 3 minutes. Which graph represents this scenario?
Answer:
The graph in the attached figure
Step-by-step explanation:
Let
x -----> time of the first process in minutes
y -----> time of the second process in minutes
we know that
The time of the first process multiplied by 4 (because is repeated 4 times) plus the time of the second process multiplied by 1 (because is repeated only once) must be less than or equal to 3 minutes
so
The inequality that represent this situation is
[tex]4x+y\leq 3[/tex]
The solution of the inequality is the shaded area below the solid line
The equation of the solid line is [tex]4x+y=3[/tex]
The y-intercept of the solid line is the point (0,3)
The x-intercept of the solid line is the point (0.75,0)
The slope of the solid line is negative m=-4
using a graphing tool
The solution is the shaded area
The graph in the attached figure
Remember that the time cannot be a negative number
Answer:
The inequality represents the situation is:
[tex]4x+y\leq 3[/tex]
And the graph is attached in the solution.
Step-by-step explanation:
Given information:
Time of first process in minutes[tex]=x[/tex]
Time of second process in minutes [tex]=y[/tex]
As we know that ,
according to the given information in the question we can write:
the inequality represents the situation is:
[tex]4x+y\leq 3[/tex]
Here, the y-intercept of the solid line is the point (0,3)
And the x-intercept of the solid line is the point (0.75,0)
And the slope is negative [tex]m=-4[/tex]
Now the graph of the above inequality can be formed as attached in the solution:
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Write an equation in slope-intercept form for the line passing through the pair of points. (–1, 2), (4, –3)
Answer:
y = - x + 1
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (- 1, 2) and (x₂, y₂ ) = (4, - 3)
m = [tex]\frac{-3-2}{4+1}[/tex] = [tex]\frac{-5}{5}[/tex] = -1, hence
y = - x + c ← is the partial equation
To find c substitute either of the 2 points into the partial equation
Using (- 1, 2), then
2 = 1 + c ⇒ c = 2 - 1 = 1
y = - x + 1 ← equation in slope- intercept form
The equation is y = –x + 1.
To find the slope-intercept form of a line passing through two points, calculate the slope using the given points and then use one point to find the y-intercept. The final equation for the line through the points (–1, 2) and (4, –3) is y = –x + 1.
To write an equation in slope-intercept form for the line passing through the points (–1, 2) and (4, –3), we first need to calculate the slope (m) using the formula
m = (y2 - y1) / (x2 - x1). Plugging in our points gives us m = (–3 – 2) / (4 – (–1)) = –5 / 5 = –1. Now that we have the slope, we can use one of the points to find the y-intercept (b). Using the point (–1, 2) and the slope-intercept formula y = mx + b, we plug in the values to get 2 = (–1)×(–1) + b, simplifying to 2 = 1 + b, which yields b = 1. Thus, the equation is y = –x + 1.
What is msu?
49°
77°
98°
161°
Answer:
77°
Step-by-step explanation:
[tex]\\ T = \frac{1}{2} (RU - SU)\\ \\ 21 =\frac{1}{2}(119 - SU)\\ \\ 42 = 119 - SU\\ SU=77[/tex]
The measure of mSU from the given diagram is 77 degrees
Circle geometryThe half of the difference of the intecepted arc is equal to the measure of the angle at the vertex
Applying this theorem to the given figure, we will havea;
1/2(119 - mSU) = 21
119 - mSU = 2(21)
119 - mSU = 42
Determine the measure of mSU
mSU = 119 -42
mSU = 77degrees
Hence the measure of mSU from the given diagram is 77 degrees
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The cost, C, to produce b baseball bats per day is modeled by the function C(b) = 0.06b2 – 7.2b + 390. What number of bats should be produced to keep costs at a minimum?
Check the picture below, that's just an example of a parabola opening upwards.
so the cost equation C(b), which is a quadratic with a positive leading term's coefficient, has the graph of a parabola like the one in the picture, so the cost goes down and down and down, reaches the vertex or namely the minimum, and then goes back up.
bearing in mind that the quantity will be on the x-axis and the cost amount is over the y-axis, what are the coordinates of the vertex of this parabola? namely, at what cost for how many bats?
[tex]\bf \textit{vertex of a vertical parabola, using coefficients} \\\\ C(b) = \stackrel{\stackrel{a}{\downarrow }}{0.06}b^2\stackrel{\stackrel{b}{\downarrow }}{-7.2}b\stackrel{\stackrel{c}{\downarrow }}{+390} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right)[/tex]
[tex]\bf \left( -\cfrac{-7.2}{2(0.06)}~~,~~390-\cfrac{(-7.2)^2}{4(0.06)} \right)\implies (60~~,~~390-216) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill (\stackrel{\textit{number of bats}}{60}~~,~~\stackrel{\textit{total cost}}{174})~\hfill[/tex]
To find the number of bats that should be produced to minimize costs, we need to find the minimum point on the cost curve given by the function C(b) = 0.06b^2 - 7.2b + 390. Using the vertex formula, we find that the minimum occurs at b = 60.
Explanation:To find the number of bats that should be produced to keep costs at a minimum, we need to determine the minimum point on the cost curve given by the function C(b) = 0.06b^2 - 7.2b + 390. The minimum point of a quadratic function can be found using the vertex formula: b = -b / (2a), where a is the coefficient of the quadratic term and b is the coefficient of the linear term. In this case, a = 0.06 and b = -7.2. Plugging these values into the formula, we get b = -(-7.2) / (2 * 0.06) = 60.
Therefore, the number of bats that should be produced to keep costs at a minimum is 60.
write the equation of a line that goes through point (4,0) and has an undefined slope
x=4
x=0
y=4
y=0
Answer:
x = 4Step-by-step explanation:
A line with undefined slope is a vertical line.
An equation of a vertical line: x = a (a - real number).
Each point on a line x = a has coordinates (a, b) (b - any real number).
We have the point (4, 0) → x = 4
The equation of the line with the following characteristics is: x = 4.
------------
Traditionally, the equation of a line is given by:
[tex]y = mx + b[/tex]
m is the slope.b is the y-intercept.However, if the slope is undefined, there is a vertical line, given by equation:
[tex]x = c[/tex]
In which c is the value of x.In this question, it goes through point (4,0), that is, [tex]c = 4[/tex], and the equation if:
[tex]x = 4[/tex].
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please help! what is the value of x when f(x)=8? The graph shows the function f(x)=2^x
Answer:
[tex]f(x) = {2}^{x } \\ f(x) = 8 \\ \\ {2}^{x} = 8 \\ \\ {2}^{x } = {2}^{3} \\ \\ x = 3[/tex]
The value of x when f(x) = 8 is 3 in f(x) = 2^x
How to determine the value of x when f(x)=8?from the question, we have the following parameters that can be used in our computation:
f(x) = 2^x
To find the value of x when f(x) = 8, we need to solve the equation 2^x = 8.
We can rewrite 8 as 2^3
So, the equation becomes:
2^x = 2^3
Since the bases are the same, we can equate the exponents:
x = 3
Hence, the value of x when f(x) = 8 is 3.
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a circular garden with a radius of 8 feet is surrounded by a circular path with a width of 3 feet. what is the approximate area of the path alone? use 3.14 for tt
Answer:
178.98 square feet
Step-by-step explanation:
Alright so we need to find two areas here and find the difference to find the area of the path.
The two shapes involved is a smaller circle inside a bigger circle.
Let's look at the smaller circle, the gardening area.
You are given is has a radius of 8 ft.
The area of a circle is [tex]\pi \cdot r^2[/tex] where r is the radius.
So the area of the smaller circle is [tex]\pi \cdot 8^2[/tex].
Now time to look at the bigger area (which will have some overlapping area with the smaller one which will subtract out to find the area of path).
The diameter of the smaller circle was (8+8)=16 feet.
What is the diameter of the bigger one. The path is 3 ft wide so we have to add a 3 before the diameter of the smaller circle to another 3 after that diameter to get the diameter of the bigger circle. So the diameter of the bigger circle is (3+16+3)=22 feet. The radius is half the diameter so the radius is 22/2=11.
The area of the bigger circle is [tex]\pi \cdot 11^2[/tex].
The area of the path=
the area of bigger circle - the area of smaller circle=
[tex]\pi \cdot 11^2-\pi \cdot 8^2[/tex]
Type this into your calculator with 3.14 instead of the [tex]\pi[/tex] button.
178.98 square feet
The answer is:
[tex]PathArea=178.98ft^{2}[/tex]
Why?To calculate the are of the path alone, we need to add the width of the path to the radius of the garden in order to know is radius, then, calculate the total area (using garden radius plus path width) and then, subtract it the area of the circular garden.
We know that the radius of the circular garden is equal to 8 feet, and the circular path has a width of 3 feet, so, the radius of the circular path will be:
[tex]CPath_{radius}=8feet+Path_{width}\\\\Path_{radius}=8feet+3feet=11[/tex]
Now, calculating the areas, we have:
Garden Area:
[tex]CircularGardenArea=\pi *radius^{2}\\\\CircularGardenRadius=\pi *8ft^{2}=3.14*64ft^{2}=200.96ft^{2}[/tex]
Total Area:
[tex]TotalArea=\pi *(8feet+3feet)^{2}=\pi *(11ft)^{2}=3.14*121ft^{2}=379.94ft^{2}[/tex]
Now, calculating the area of the path, we have:
[tex]TotalArea=CircularGardenArea+PathArea\\\\PathArea=TotalArea-CircularGardenArea\\\\PathArea=379.94ft^{2}-200.96ft^{2}=178.98ft^{2}[/tex]
Hence, we have that:
[tex]PathArea=178.98ft^{2}[/tex]
Have a nice day!
Which expression is equivalent to 30 (1/2 x - 2) + 40(3/4 y-4)
Answer:
Step-by-step explanation:
Start by removing the brackets.
Left Brackets
30(1/2 x - 2)
30*1/2 x - 30*2
15x - 60
Right Bracket
40(3/4 y - 4)
40*3/4 y - 4*40
10*3 y - 160
30y - 160
Now put these 2 results together.
15x - 60 + 30y - 160 Combine the like terms.
15x + 30y - 220 That's one answer Others are possible.
5(3x + 6y - 44)
Answer:
74
Step-by-step explanation:
Can someone please explain this for me I’m
Not sure of the steps. See photo above
[tex]\bf \cfrac{x^8}{x^{14}}\implies x^8x^{-14}\implies x^{8-14}\implies x^{-6}\implies \stackrel{\textit{using the power rule}}{-6x^{-7}\implies \cfrac{-6}{x^7}}[/tex]
Question 1:
We have the following expression:
[tex]4x ^ {-4}[/tex]
By definition of power properties we have to:
[tex]a ^ {- 1} = \frac {1} {a ^ 1} = \frac {1} {a}[/tex]
Then, rewriting the expression:
[tex]\frac {4} {x ^ 4}[/tex]
ANswer:
[tex]\frac {4} {x ^ 4}[/tex]
Question 2:
For this case we have the following expression:
[tex]\frac {x ^ 8} {x ^ {14}} =[/tex]
By definition of power properties of the same base we have:
[tex]x ^ n * x ^ m = x ^ {n + m}[/tex]
Then, we can rewrite the denominator of the expression as:
[tex]\frac {x ^ 8} {x ^ 8 * x ^ 6} =[/tex]
Simplifying terms of the numerator and denominator:
[tex]\frac {1} {x ^ 6}[/tex]
ANswer:
[tex]\frac {1} {x ^ 6}[/tex]
Given the following information, find the probability that a randomly selected student will be very short. Number of students who are very short: 45, short: 60, tall: 82, very tall: 21
Answer:
[tex]Pr=\dfrac{45}{208}\approx 0.216.[/tex]
Step-by-step explanation:
You are given the information about students:
45 students are very short;60 students are short;82 students are tall;21 students are very tall.In total, there are 45 + 60 + 82 + 21 = 208 students.
Use the definition of the probability:
[tex]Pr=\dfrac{\text{Number of favorable outcomes}}{\text{Number of all possible outcomes}}[/tex]
Number of favorable outcomes = 45
Nomber of all possible outcomes = 208,
hence,
[tex]Pr=\dfrac{45}{208}\approx 0.216.[/tex]