Answer:
Final answer is [tex]\sqrt[3]{x^1}\cdot\sqrt[3]{x^2}=x[/tex].
Step-by-step explanation:
Given problem is [tex]\sqrt[3]{x}\cdot\sqrt[3]{x^2}[/tex].
Now we need to simplify this problem.
[tex]\sqrt[3]{x}\cdot\sqrt[3]{x^2}[/tex]
[tex]\sqrt[3]{x^1}\cdot\sqrt[3]{x^2}[/tex]
Apply formula
[tex]\sqrt[n]{x^p}\cdot\sqrt[n]{x^q}=\sqrt[n]{x^{p+q}}[/tex]
so we get:
[tex]\sqrt[3]{x^1}\cdot\sqrt[3]{x^2}=\sqrt[3]{x^{1+2}}[/tex]
[tex]\sqrt[3]{x^1}\cdot\sqrt[3]{x^2}=\sqrt[3]{x^{3}}[/tex]
[tex]\sqrt[3]{x^1}\cdot\sqrt[3]{x^2}=x[/tex]
Hence final answer is [tex]\sqrt[3]{x^1}\cdot\sqrt[3]{x^2}=x[/tex].
The original expression ∛x * ∛[tex]x^2[/tex] simplifies to x.
This means that the cube root of x times the cube root of [tex]x^2[/tex] is equal to x.
To simplify the expression ∛x * ∛[tex]x^2[/tex], we can apply the rules of exponents and radicals.
The cube root of x is equivalent to raising x to the power of 1/3.
Similarly, the cube root of [tex]x^2[/tex] is equivalent to raising [tex]x^2[/tex] to the power of 1/3.
So, we have:
∛x = [tex]x^{(1/3)[/tex]
∛[tex]x^2 = (x^2)^{(1/3)} = x^{(2/3)[/tex]
Now, let's multiply these two expressions:
[tex]x^{(1/3)}\times x^{(2/3)[/tex]
To simplify, we add the exponents when multiplying like bases:
[tex]x^{(1/3 + 2/3)} = x^{(3/3)} = x^1[/tex]
So, the simplified expression is just x.
For similar question on original expression.
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True or False: Validity of data refers to whether the data doesn’t measure what it claims to measure. True False
Answer:
It's False
Step-by-step explanation:
It does refer to whether the data measures what it claims to measure.
Hope i helped you!
NEED HELP ASAP!! Drag the tiles to the boxes to form the correct pairs. Not all tiles will be used. Match the function to its inverse. (See attachment below)
QUESTION 1
We have [tex]f(x)=\frac{2x-1}{x+2}[/tex]
Let [tex]y=\frac{2x-1}{x+2}[/tex]
Interchange x and y.
[tex]x=\frac{2y-1}{y+2}[/tex]
Solve for y.
First, cross multiply;
[tex]x(y+2)=2y-1[/tex]
Expand now:
[tex]xy+2x=2y-1[/tex]
Group the y-terms on the LHS
[tex]xy-2y=-2x-1[/tex]
Factor y on the left hand side;
[tex](x-2)y=-2x-1[/tex]
Divide both sides by (x-2).
[tex]y=\frac{-2x-1}{x-2}[/tex]
[tex]f^{-1}(x)=\frac{-2x-1}{x-2}[/tex]
[tex]\boxed{f(x)=\frac{2x-1}{x+2}\to f^{-1}(x)=\frac{-2x-1}{x-2}}[/tex]
QUESTION 2
Given: [tex]f(x)=\frac{x-1}{2x+1}[/tex]
Let [tex]y=\frac{x-1}{2x+1}[/tex]
Interchange x and y.
[tex]x=\frac{y-1}{2y+1}[/tex]
Solve for y
[tex]x(2y+1)=y-1[/tex]
[tex]2xy+x=y-1[/tex]
[tex]2xy-y=-x-1[/tex]
[tex](2x-1)y=-x-1[/tex]
[tex]y=\frac{-x-1}{2x-1}[/tex]
[tex]f^{-1}(x)=\frac{-x-1}{2x-1}[/tex]
[tex]f^{-1}(x)=\frac{-x-1}{2x-1}[/tex]
[tex]\boxed{f(x)=\frac{x-1}{2x+1}\to f^{-1}(x)=\frac{-x-1}{2x-1}}[/tex]
QUESTION 3
Given : [tex]f(x)=\frac{2x+1}{2x-1}[/tex]
We let [tex]y=\frac{2x+1}{2x-1}[/tex]
Interchange x and y.
[tex]x=\frac{2y+1}{2y-1}[/tex]
Solve for y;
[tex]x(2y-1)=2y+1[/tex]
[tex]2xy-x=2y+1[/tex]
[tex]2xy-2y=x+1[/tex]
[tex](2x-2)y=x+1[/tex]
[tex]y=\frac{x+1}{2x-2}[/tex]
[tex]f^{-1}(x)=\frac{x+1}{2(x-1)}[/tex]
[tex]\boxed{f(x)=\frac{2x+1}{2x-1}\to f^{-1}(x)=\frac{x+1}{2(x-1)}}[/tex]
Answer:
Step-by-step explanation:
Kevin says that lines p and m will eventually intersect.
Is Kevin correct?
Answer:
no because they are parallel
Step-by-step explanation:
The table below represents a linear function f(x) and the equation represents a function g(x):
x f(x)
−1 −7
0 −1
1 5
g(x)
g(x) = 5x − 4
Part A: Write a sentence to compare the slope of the two functions and show the steps you used to determine the slope of f(x) and g(x). (6 points)
Part B: Which function has a greater y-intercept? Justify your answer. (4 points)
(10 points)
Answer:
A.
⇒The slope of the function f(x) is greater than the slope of the function g(x).
This is so because using the slope intercept form equation, the slope of f(x) is 6 while that of g(x) is 5
B.
⇒The function f(x) has a greater y-intercept than the function g(x)
⇒The y intercept for the function f(x) is -1 where as that of the function g(x) is -4
Step-by-step explanation:
This question is on the standard equation of a linear function using the slope-intercept form
y=m x+c----------where m is the gradient/slope of the line and c is the y-intercept.
Given the values in function f(x) we can identify the points in the line as;
(-1,-7), (0,-1) , (1,5)............plot the points to obtain the graph as indicated in the attachment.
Find the gradient of the graph ;
m₁=Δy/Δx
m₁= 5--1/1-0 =6/1 =6
Equation of line will be;
y-5/x-1 = 6
y-5=6(x-1)
y-5=6x-6
y=6x-1.........................m₁=6 and c₁= -1
Given that;
g(x)=5x-4.........................m₂=5 c₂= -4
⇒The slope of slope of the function f(x) is greater than the slope of the function g(x).
This is so because using the slope intercept form equation, the slope of f(x) is 6 while that of g(x) is 5
B.
⇒The function f(x) has a greater y-intercept than the function g(x)
⇒The y intercept for the function f(x) is -1 where as that of the function g(x) is -4
In the attached graph;
Red line graph, y=5x-4
Blue line graph, y=6x-1
Answer:
g(x) = y=5x-4
f(x) =. y= 6x-1
I know the slope of f(x) is greater than the slope of g(x) since the slope of f(x)=6 and g(x)=5 and 6>5.
I also know that the y-intercept of f(x) is greater because f(x)=-1 and g(x)=-4 and -1>-4.
Step-by-step explanation:
First, I will put both functions into slope-intercept form.
Next, I will use by picking two points on the table. and
this equals or 6.
So, I know the slope is 6.
To find the y-intercept I have to do, -7=6(-1)+b
So, the y-intercept is -1.
From this, I know the slope of f(x) is greater than the slope of g(x) since the slope of f(x)=6 and g(x)=5 and 6>5.
I also know that the y-intercept of f(x) is greater because f(x)=-1 and g(x)=-4 and -1>-4.
Solve x2 + 8x = 33 by completing the square. Which is the solution set of the equation? {–11, 3} {–3, 11} {–4, 4} {–7, 7}
Answer:
The solution of the equation are 3 , -11
Step-by-step explanation:
* Lets revise how to make the completing square
- The form of the completing square is a(x - h)² + k, where a , h , k
are constant
- The general form of the quadratic is ax² + bx + c, where a , b , c
are constant
- To change the general form to the completing square form equate
them and find the constant a , h , k
* Now lets solve the problem
∵ x² + 8x = 33 ⇒ subtract 33 from both sides
∴ x² + 8x - 33 = 0
- lets change the general form to the completing square
∴ x² + 8x - 33 = a(x - h)² + k ⇒ solve the bracket of power 2
∴ x² + 8x - 33 = a(x² - 2hx + h²) + k ⇒ multiply the bracket by a
∴ x² + 8x - 33 = ax² - 2ahx + ah² + k ⇒ compare the two sides
∵ x² = ax² ⇒ ÷ x²
∴ a = 1
∴ -2ah = 8 ⇒ substitute the value of a
∴ -2(1)h = 8 ⇒ -2h = 8 ⇒ ÷ (-2)
∴ h = -4
∵ ah² + k = -33 ⇒ substitute the value of a and h
∴ (1)(-4)² + k = -33
∴ 16 + k = -33 ⇒ subtract 16 from both sides
∴ k = -49
∴ x² + 8x - 33 = (x + 4)² - 49
* Now lets solve the completing square
∵ (x + 4)² - 49 = 0 ⇒ add 49 to both sides
∴ (x + 4)² = 49 ⇒ take square root for both sides
∴ (x + 4) = ± 7
∵ x + 4 = 7 ⇒ subtract 4 from both sides
∴ x = 3
∵ x + 4 = -7 ⇒ subtract 4 from both sides
∴ x = -11
* The solution of the equation are 3 , -11
Answer:
{-11, 3}
Step-by-step explanation:
The price of a gallon of unleaded gas was $2.83 yesterday. Today, the price rose to $2.88 . Find the percentage increase. Round your answer to the nearest tenth of a percent.
The percentage increase from yesterday's gas price to today's price is 1.8%.
Explanation:To find the percentage increase from yesterday's price to today's price, we need to calculate the difference between the two prices, divide it by the original price, and then multiply by 100.
The difference between $2.88 and $2.83 is $0.05. Dividing $0.05 by $2.83 gives us 0.0176. Multiplying by 100 gives us 1.76%. Rounding to the nearest tenth of a percent, the percentage increase is 1.8%.
On Friday, a local hamburger shop sold a combined total of 420 hamburgers and cheeseburgers. The number of cheeseburger sold was three times tge number of hamburgers sold. How many hamburgers were sold on Friday?
Answer:
315 hamburgers
Step-by-step explanation:
Because 3 times the amount of hamburgers were sold than the cheeseburgers, it is fair to say that 420 burgers is 4 times the amount of cheeseburgers sold.
That means that 420/4 = 105 cheeseburgers were sold.
That means that 105 * 3 = 315 hamburgers were sold.
The total number of hamburgers sold on Friday is 105
How to find the number of hamburgers sold on Friday?Number of Hamburgers sold = h
Number of Cheeseburgers sold = c
h + c = 420
c = 3*h
substitute the value of c in ( h + c = 420 )
h + 3h = 420
4h = 420
h = [tex]\frac{420}{4}[/tex]
h = 105
The number of hamburgers sold is 105
To learn more about solving an equation using the substitution method, refer to:
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Steve leaves the beach at 3p.m. and drives along the highway at 55 mph. One hour later, his friend leaves the same beach, and drives along the same highway at 65 mph.
How many hours will it take his friend to catch up to Steve?
10 hours
5.5 hours
8.5 hours
55 hours
It will take Steve's friend 6.5 hours to catch up to Steve.
The correct answer is:
e) 6.5 hours.
To calculate this, let's first determine the time it takes for Steve's friend to catch up to him after he starts driving.
Steve's speed = 55 mph
Steve's friend's speed = 65 mph
Relative speed = Speed of Steve's friend - Speed of Steve
Relative speed = 65 mph - 55 mph = 10 mph
Now, since Steve's friend starts one hour later, Steve has already traveled for one hour at 55 mph before his friend starts.
Distance traveled by Steve in one hour = Speed × Time
Distance = 55 mph × 1 hour = 55 miles
Now, when Steve's friend starts driving, he needs to catch up this initial distance of 55 miles.
Time = Distance / Relative speed
Time = 55 miles / 10 mph = 5.5 hours
But we must remember that Steve's friend started driving one hour later than Steve. So, we add this one hour to the time calculated above to find the total time it takes for Steve's friend to catch up to Steve.
Total time = 5.5 hours + 1 hour = 6.5 hours
Therefore, it will take Steve's friend 6.5 hours to catch up to Steve.
Steve travels for one hour at 55 mph before his friend starts driving. By then, Steve's friend needs to catch up the initial distance of 55 miles at a relative speed of 10 mph. This gives us a time of 5.5 hours. However, since Steve's friend started one hour later, we add this one hour to the calculated time, resulting in a total time of 6.5 hours. Therefore, the correct answer is 6.5 hours.
Complete question:
Steve leaves the beach at 3p.m. and drives along the highway at 55 mph. One hour later, his friend leaves the same beach, and drives along the same highway at 65 mph.
How many hours will it take his friend to catch up to Steve?
a.10 hours
b.5.5 hours
c.8.5 hours
d.55 hours
e. 6.5 hours.
4x – 2y=-1
-4x + 4y = -2
you just cancel out the x variable first since 4x-4x is 0 then you bring down your y variable and solve for x then you plug x into either equation then solve for x.
In the triangles, and . Which statement correctly compares the angles? Angle G is congruent to angle P. Angle G is smaller than angle P. Angle G is larger than angle P. Angle G is congruent to angle N.
Answer:
B) Angle G is smaller than angle P.
Step-by-step explanation:
It's logic, the only way the hypotenuse could be shorter is if the angle opposite of it is more acute.
I know that's a mouthful and probably sounds really weird but just trust me.
Would appreciate brainliest, new to brainly! good luck!
The correct option is, (B) Angle G is smaller than angle P.
It's logic, the only way the hypotenuse could be shorter is if the angle opposite of it is more acute.
What is called triangle?A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices.A triangle is also a polygon.Some real-life examples of triangles include sandwiches, traffic signs, cloth hangers, and a rack in billiards.What is triangle and its types?Triangles are shapes with three sides.There are different names for the types of triangles.A triangle's type depends on the length of its sides and the size of its angles (corners).There are three types of triangle based on the length of the sides: equilateral, isosceles, and scalene.
What is triangle shape?In Geometry, a triangle is a three-sided polygon that consists of three edges and three vertices.The most important property of a triangle is that the sum of the internal angles of a triangle is equal to 180 degrees.This property is called angle sum property of triangle.
Learn more about triangle here:
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Jake is eating dinner at a restaurant. The cost of his meal, including sales tax, is m dollars. After leaving an 18% tip, the amount Jake pays at the restaurant is represented by the following expression in this expression, what does the term 0.18m represent?
m+0.18m
Answer:
It means meal cost plus the 18% tip
Step-by-step explanation:
Answer:
[tex]0.18m[/tex] represents amount of tip Jake pays to restaurant.
Step-by-step explanation:
We have been given that Jake is eating dinner at a restaurant. The cost of his meal, including sales tax, is m dollars.
Jake left an 18% tip. The amount Jake pays at the restaurant is represented by the following expression in this expression [tex]m+0.18m[/tex].
We know that Jake's total amount will be equal to cost of his meal plus 18% of the cost of meal.
[tex]\text{Total cost of dinner}=m+(\frac{18}{100}\times m)[/tex]
[tex]\text{Total cost of dinner}=m+0.18m[/tex]
Therefore, the term [tex]0.18m[/tex] represents amount of tip Jake pays to restaurant.
Find the value of x
A.
38
B.
62
C.
102
D.
150
Answer:
x=62
Step-by-step explanation:
You set the two angles equal to each other and solve. See work attached for more.
Answer:
A. 38
Step-by-step explanation:
From the diagram, [tex]s=(2x+26)\degree[/tex] because corresponding angles are equal.
[tex]s+(3x-36)\degree=180\degree[/tex]. the sum of interior angles of a triangle.
By substitution, we obtain;
[tex](2x+26)\degree+(3x-36)\degree=180\degree[/tex]
Group similar terms;
[tex]2x+3x=180+36-26[/tex]
[tex]5x=190[/tex]
Divide both sides by 5.
[tex]x=38[/tex]
a boat took 4 hours to make a trip downstream with a current of 6 kilometers/hour. The return trip against the same current took 10 hours. How far did the boat travel?
The boat traveled a distance of 80 km during the whole trip.
This question involves determining the distance a boat traveled based on its travel times with and against a current. Let's denote the speed of the boat in still water as b km/h.
Step-by-step solution:
Given data: Current speed = 6 km/h, Time downstream (with current) = 4 hours, Time upstream (against current) = 10 hours.Speed downstream = (b + 6) km/h.Speed upstream = (b - 6) km/h.The distance (d) traveled downstream is the same as upstream, so:Downstream, distance d = speed × time = (b + 6) × 4
Upstream, distance d = speed × time = (b - 6) × 10
Since the distances are equal:
(b + 6) × 4 = (b - 6) × 10
Expanding and simplifying:
4b + 24 = 10b - 60
84 = 6b
b = 14 km/h
Now, using the downstream speed to find the distance:
Distance, d = (b + 6) × 4 = (14 + 6) × 4 = 20 × 4 = 80 km.
Thus, the boat traveled a distance of 80 km.
The boat traveled 80 kilometers.
To determine how far the boat traveled, let's denote the speed of the boat in still water as B km/h. The current speed is given as 6 km/h.
When traveling downstream, the effective speed of the boat is (B + 6) km/h.When traveling upstream, the effective speed of the boat is (B - 6) km/h.Using the formula speed = distance/time, we get:
Downstream: (B + 6) = D/4Upstream: (B - 6) = D/10We now have two equations:
4(B + 6) = D10(B - 6) = DSetting the right-hand sides of these equations equal to each other:
4(B + 6) = 10(B - 6)
Simplifying this equation:
4B + 24 = 10B - 60
Bringing like terms together:
84 = 6B
Solving for B:
B = 14
Substituting B back into either distance equation, we use D = 4(B + 6):
D = 4(14 + 6) = 4(20) = 80
Therefore, the boat traveled 80 kilometers.
Question 30
Find the length of the long leg. Leave answer in simplest radical form.
Help plz
Use SOHCAHTOA. You must use sine or cosine since the hypotenuse is involved, but since you are given both angles, it does not matter which one of them you choose. We'll use sine:
sinx=O/H
sin60=O/14
√3/2=O/14
*Cross multiply*
(14√3)=2O
*Divide both sides by 2*
7√3=O
Hope this helps!!
Answer:
B
Step-by-step explanation:
Since the triangle is right we can use the sine ratio to find TI along with
the exact value of sin60° = [tex]\frac{\sqrt{3} }{2}[/tex]
sin60° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{TI}{TR}[/tex] = [tex]\frac{TI}{14}[/tex]
Multiply both sides by 14
TI = 14 × sin60° = 14 ×[tex]\frac{\sqrt{3} }{2}[/tex] = 7[tex]\sqrt{3}[/tex]
Which of these numbers is between 7 and 9?
A. √8
B. √79
C. 3√64
Answer: It has to be A. 8
Step-by-step explanation:
Daniel looks at the prices of 5 guitars. The prices are $137, $159, $127, $188 and $680. These prices contain one extreme value ($680). Which measure of center should Daniel use to describe the prices?
A. Median
B. Range
C. Mean
D. Mean absolute deviation
Answer:
A. Median
Step-by-step explanation:
Mean and median both are used to measure the central tendency of a given data while range gives us the spread of the data roughly.
Mean is even affected by a single extreme value in the data while median gives us the central value of data even when there are extreme values.
The given set of five prices has one extreme value which will affect the mean. While median is a better option to measure the central tendency of data.
So Daniel will use median to measure the central tendency to describe the prices..
Step-by-step explanation:
Answer is A. Median by jesse
SOMEONE PLEASE HELP ME ANSWER THIS
Answer: 84
Step-by-step explanation:
7 x 3 x 4 = 84
It would be 84.
Hope this helps!
Pls tell me if it is inncorrect and i will revise my answer.
7•3•4=84
How do you factor trinomials again...
Answer:
[tex]g^2+ 3g -10=(x-2)(x+5)[/tex]
Step-by-step explanation:
The trinomial is the following
[tex]g^2+ 3g -10[/tex]
Look for two numbers b and d that when multiplying them get as a result -10 and when you add up these numbers you get 3 as a result.
This is.
[tex]b * d = -10\\\\b + d = 3[/tex]
Then you can write the trinomial as the product of two factors:
[tex](x+b)(x+d)[/tex]
You can check that the numbers that meet this condition are:
[tex]b = -2\\d = 5[/tex]
Then the trinomial is written as
[tex]g^2+ 3g -10=(x-2)(x+5)[/tex]
There are 20 cups of flour in package of flour, how many muffins can i make from a package of flour if it take 1/4 cup?
Answer:
80 Muffins.
Step-by-step explanation:
There are 20 cups of flour in package
It takes [tex]\frac{1}{4}[/tex] cup to make one muffin
From a package of 20 cups of flour, you can make:
20 × 1 ÷ [tex]\frac{1}{4}[/tex] = 20 × 4 = 80 muffins
The graph below is correct for the linear equation y=-3.
True
False
Answer:
False.
Step-by-step explanation:
The graph that is shown is correct for the equation x= -3. The graph for y= -3 would run vertically, not horizontally.
Answer:
True
Step-by-step explanation:flip it and reverse it its esrever dna ti pilf
i need help im stuck on this
Hello There!
Before getting started, we should remember that the top surface and the bottom surface of any cylinder are congruent to each other.
First, we use the formula pi*radius^2 to find the area of a circle since there is always a circle in a cylinder.
Next, we multiply pi*radius^2 * height because a cylinder has a height too.
HOW TO SOLVE
First, we multiply 3.14 which is equal to pi by 25 because the radius is 5 and in the formula we used, it states radius squared so 3.14 multiplied by 25 and then multiplied by the height of our cylinder which equals 6.
Once we multiply, we get a product of 471.
Our final answer is 471.units^3
HELP!!!!!!!!!!!!!
Triangle PQR has vertices P(3,5), Q(-2,6) and R(8,-1). Give the coordinates of the vertices after the translation (x,y)——> (x+4,y - 5)
1. P’(_,_)
2.Q’ (_,_)
3.R’ (_,_)
Answer:
P'(7,0)Q'(2,1) R'(12,-6)
Step-by-step explanation:
P(3,5)------>P'(3+4,5-5)
P'(7,0)
Q(-2,6)----->Q'(-2+4,6-5)
Q'(2,1)
R(8,-1)------>R'(8+4,-1-5)
R'(12,-6)
Answer:
i think it is the third one c plz give me brainliest
Step-by-step explanation:
What is the real part of the complex number 18 - 6i?
• i
• -6i
• 18
•-6
18 is the real part of the complex number
Hope this helped!
~Just a girl in love with Shawn Mendes
Answer:
18
Step-by-step explanation:
Given a complex number z = a + bi
where a is the real part the imaginary part is b
Given
18 - 6i then 18 is the real part
Which shows one way to determine the factors of x3 – 9x2 + 5x – 45 by grouping?
x2(x – 9) – 5(x – 9)
x2(x + 9) – 5(x + 9)
x(x2 + 5) – 9(x2 + 5)
x(x2 – 5) – 9(x2 – 5)
Answer:
C
Step-by-step explanation:
x(x2 + 5) – 9(x2 + 5)
= x³ + 5x - 9x² - 45
(try to expand one by one of the answer given)
Answer:
x(x2 + 5) – 9(x2 + 5)
Step-by-step explanation:
Find the volume of the cone in terms of pi.
Answer:
how to find pi you have to add a lot of math and for a volume for the cone is V=πr2h 3
Step-by-step explanation:
i had did this all in my head.
You ask a friend to think of a
number from four to twelve. What
is the probability that his number
will be 8?
The answer is 1/9 or about 11%.
Answer:8
Step-by-step explanation: it’s right
Evaluate C(8, 8).
0
1
n
8
Answer: Second Option
C(8,8)=1
Step-by-step explanation:
We must calculate a combination
The combination [tex]C (n, r) =\frac{n!}{r!(n-r)!}[/tex]
Where n is the number of elements that you can combine and you choose "r" from them.
So
C (8, 8) is the combination of 8 in 8.
Therefore
[tex]n = 8\\r=8[/tex]
[tex]C(8,8)= \frac{8!}{8!(8-8)!}\\\\C(8,8)=\frac{8!}{8!(0)!}\\\\C(8,8)=\frac{1}{1*1}\\\\C(8,8)=1[/tex]
The answer is the second option
The value of [tex]\( C(8, 8) \)[/tex] is 1 because choosing all 8 items from 8 yields only 1 combination.
The expression [tex]\( C(8, 8) \)[/tex] represents choosing 8 items from a set of 8 items without regard to order, which is also known as a combination. Here's how we can evaluate it step by step:
Step 1: Recall the formula for combinations.
The formula for combinations is [tex]\( C(n, k) = \frac{n!}{k!(n - k)!} \),[/tex] where [tex]\( n \)[/tex] is the total number of items and [tex]\( k \)[/tex] is the number of items to choose.
Step 2: Substitute the values into the combination formula.
In this case, [tex]\( n = 8 \) and \( k = 8 \),[/tex] so the expression becomes:
[tex]\[ C(8, 8) = \frac{8!}{8!(8 - 8)!} \][/tex]
Step 3:
Simplify the expression.
[tex]\[ C(8, 8) = \frac{8!}{8!0!} \][/tex]
Step 4:
Recall that [tex]\( n! = n \times (n - 1) \times (n - 2) \times \ldots \times 1 \)[/tex] and [tex]\( 0! = 1 \).[/tex]
[tex]\[ C(8, 8) = \frac{8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1}{8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 \times 1} \][/tex]
Step 5:
Cancel out the common terms.
[tex]\[ C(8, 8) = \frac{8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1}{8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1} \][/tex]
[tex]\[ C(8, 8) = 1 \][/tex]
So, [tex]\( C(8, 8) = 1 \).[/tex]
kevin walked 3/4 of a mile in 12 minutes. assuming he walked at a constant speed the entire time, which expression can be used to determine the distance he walked each minute?
(Is it correct)
Answer:
Distance divided by time
I would say that’s correct
OOF yes it's correct...
Factor by grouping: x^3 + 3x^2 - 25x -75 Which of the following is one of the factors?
Answer:
Final factor is [tex](x + 3)(x+5)(x-5)[/tex].
Step-by-step explanation:
Given expression is [tex]x^3 + 3x^2 - 25x -75[/tex]
Now we need to factor that expression [tex]x^3 + 3x^2 - 25x -75[/tex] by grouping. So let's make group of first two terms and group of last two terms.
[tex]x^3 + 3x^2 - 25x -75[/tex]
[tex]=(x^3 + 3x^2)+( - 25x -75)[/tex]
factor each group
[tex]=x^2(x + 3)-25(x +3)[/tex]
[tex]=(x + 3)(x^2-25)[/tex]
[tex]=(x + 3)(x+5)(x-5)[/tex]
Hence final factor is [tex](x + 3)(x+5)(x-5)[/tex].
I got the Same answer
Select the correct answer. A coin is tossed 5 times in a row. What is the size of the sample space of this experiment? A. 5 B. 7 C. 10 D. 32
Answer:
32
Step-by-step explanation:
Number of times a coin is tossed up = 5
Number of possible outcomes in a toss of a coin = 2 ( Head or a Tail)
The sample space can be calculated by calculating total number of possible outcomes in 5 tosses of the coin.
Number of outcomes in 1 toss of a coin = 2
Number of outcomes in 2 tosses of a coin = 2 × 2
Number of outcomes in 3 tosses of a coin = 2 × 2 × 2
Number of outcomes in 4 tosses of a coin = 2 × 2 × 2 × 2
Number of outcomes in 5 tosses of a coin = 2 × 2 × 2 × 2 × 2
⇒ Total number of outcomes = 32
Therefore, Size of the sample space = 32
Answer:
I did the calculations and I also got 32.
Step-by-step explanation:
hope this helps!!