The answer is 90 elves.
Here's how to find it
100 giants = 100/160 or 5/8
3/8 is left for the elves
3/8 x 240 = 90
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]
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:
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]
15) f(x) = 3x + 5
g(x)=-4x + 3
Find f(x) + g(x)
17) f(x) = 2x +4
g(x)= x - 5
Find f(x) - g(x)
how do u solve these equations?
Answer:
15) f(x) + g(x) = -x + 8
17) f(x) - g(x) = x + 9
Step-by-step explanation:
15)
f(x) = 3x + 5
g(x)= - 4x + 3
Find f(x) + g(x)
f(x) + g(x) = 3x + 5 + ( - 4x + 3 )
f(x) + g(x) = 3x + 5 - 4x + 3
f(x) + g(x) = -x + 8
17)
f(x) = 2x +4
g(x)= x - 5
Find f(x) - g(x)
f(x) - g(x) = 2x +4 - (x - 5 )
f(x) - g(x) = 2x +4 - x + 5
f(x) - g(x) = x + 9
[tex]
f(x)=3x+5 \\
g(x)=-4x+3 \\
(f+g)(x)=f(x)+g(x)=(3x+5)+(-4x+3) \\
3x+5-4x+3=\boxed{-x+8} \\ \\
f(x)=2x+4 \\
g(x)=x-5 \\
(f-g)(x)=f(x)-g(x)=(2x+4)-(x-5) \\
2x+4-x+5=\boxed{x+9}
[/tex]
Hope this helps.
r3t40
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.
What percentage kf the rolls are greater than 3?
Add the total number of rolls that were greater than 3.
This would be the number 4, 5 and 6.
8 + 11 + 10 = 29 rolls higher than 3.
Now divide the number of rolls higher than 3 by the total number of rolls which is given as 50:
29 / 50 = 0.58
Multiply by 100 to get the percent:
0.58 x 100 = 58% of the rolls were higher than 3.
I need answers for both please!!
1 = a
2 = h
have a good day
The circumference of a circle is 15centimeters. What is the area of the circle in terms of?
I can’t put the sign but it’s in the picture
A 0.53
B is wrong
C 56.25
D is wrong
Answer: 56.25
Step-by-step explanation:
You just need to use common sense.
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!!
Lydia bought a car for $20,000. It is expected to depreciate at a continuous rate. What will be the value of the car in 2 years? Use k = 0.105 and round to the nearest dollar.
Answer:
[tex]\$16,021[/tex]
Step-by-step explanation:
we know that
The formula to calculate the depreciated value is equal to
[tex]V=P(1-k)^{x}[/tex]
where
V is the depreciated value
P is the original value
k is the rate of depreciation in decimal
x is Number of Time Periods
in this problem we have
[tex]P=\$20,000\\k=0.105\\x=2\ years[/tex]
[tex]V=\$20,000(1-0.105)^{2}=\$16,020.50[/tex]
round to the nearest dollar
[tex]\$16,020.50=\$16,021[/tex]
the value of the car after 2 years will be approximately $16,212.
To find the value of the car after 2 years with continuous depreciation, we will use the formula for continuous exponential decay:
[tex]V(t) = V_0 \times e^{-kt}[/tex]
Where V(t) is the value after time t V_0 is the initial value, k is the decay constant and t is time
Plugging in the values:
[tex]V(2) = 20000 \times e^{-0.105 \times 2}[/tex]
Simplifying the exponent:
[tex]V(2) = 20000 \times e^{-0.21}[/tex]
[tex]V(2) = 20000 \times 0.8106 \approx 16212[/tex]
Thus, the value of the car after 2 years will be approximately $16,212.
solve for K thanks!!!
4.5 + 1.5k = 18 - 3k
Bring -3k to the other side by adding 3k to both sides
4.5 + (1.5k + 3k) = 18 + (-3k + 3k)
4.5 + 4.5k = 18 + 0
4.5 + 4.5k = 18
Bring 4.5 to the other side by subtracting it to both sides
(4.5 - 4.5) + 4.5k = 18 - 4.5
0 + 4.5k = 13.5
4.5k = 13.5
Isolate k by dividing 4.5 to both sides
4.5k / 4.5 = 13.5 / 4.5
k = 3
Hope this helped!
~Just a girl in love with Shawn Mendes
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!
FACTOR: 36−(5+2a)^2
QUICKLY PLS!
36-(4+2a)^2=0
36-16+4a^2=0
4a^2+20=0
a^2+5=0 <— Factored form
A student pulls out a marble from a pag containing blue, green, and red marbles. He records the color and places it back into the bag The table below shows the frequency of
each color after 100 marbles are pulled out
Color of Marbles Blue Green Red
Number of Draws 13 29 58
How many green draws can you expect if the marbles are pulled out 1,000 times?
Answer:
Answer is B - 290.
Step-by-step explanation:
The idea here is that we're assuming the frequency each colour is drawn is a reflection of the proportion of marbles in the bag that are that colour. The more of a particular colour you have, the more likely you are to draw it, and vice versa.
Therefore we can assume the proportion of blue, gree, and red marbles is 13%, 29%, and 58% respectively based on the first 100 draws.
These percents should stay relatively similar as more draws are done, approaching the true proportions of each colour better the higher the number of draws. That means 29%, or 290, of the 1000 draws will be green.
Answer: 290
Step-by-step explanation:
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]
6. Mr Wade works for 5 straight
hours when he opens his stand
After a 1 hour break he works
6 hours and 15 minutes before
Closing at 6:10p.m. What time
does Mr Wade open his stand
5:55am
Start by finding how long the stand was open. Add 5 hours + 1 hour + 6 hours 15 minutes to get 12 hours 15 minutes.
Now, just find the time that is 12 hours and 15 minutes before 6:10pm. Start by subtracting 12 hours, which just switches the time from a.m. to p.m. This brings you to 6:10am. Finally, subtract the 15 minutes to get 5:55am.
Which line is the line of best fit for this scatter plot?
The last one. It goes and touches the most points.
The 4th line is the line of best fit for this given scatter plot.
What is a scatter plot?"A scatter plot is a type of plot or mathematical diagram using Cartesian coordinates to display values for typically two variables for a set of data. If the points are coded, one additional variable can be displayed."
Here, 4 different lines are drawn for a given scatter plot.
We know, a line drawn on a scatter plot fits it the best is the line that is closer to most of the points.
Here, the 4th line is closer to most of the points on the scatter plot.
Therefore, 4th line is the best fit.
Learn more about scatter plot here: https://brainly.com/question/19741330
#SPJ2
Kevin says that lines p and m will eventually intersect.
Is Kevin correct?
Answer:
no because they are parallel
Step-by-step explanation:
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:
https://brainly.com/question/11745624
#SPJ2
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
A total of 430 dogs and people attend a fundraising dog walk. Altogether, 1210 legs participated in the walk. How many dogs were there?
1210÷4=302.5 and u can have a half of a dog so there would be 302
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...
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.
Which statement describes the speed of the remote control car over time?
Answer:
Step-by-step explanation:
D
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:
Determine the total annual FICA tax for an annual salary of $165,000. Use $106,800 for maximum taxable earnings.
Answer:
FICA Tax =$8170.2
Step-by-step explanation:
Given
Total income=$165000
Taxable income=$106800
FICA tax includes Social security tax and medicare tax.
Medicare tax is 1.45% of the taxable wage and social security tax is6.2% of the taxable wage.
1.45% of medicare is paid by the employer and similarly 6.2% social security tax is paid by the employer.
0.9% of medical surtax is deducted if the employee earns more than $200000
So,
Medicare Tax=Taxable income*1.45/100
=106800*0.0145
=$1548.6
Social Security Tax=Taxable Income*6.2/100
=106800*0.062
=$6621.6
As the income of the employee is less than $200000, so there will be no medical surtax.
Total FICA tax=$1548.6+$6621.6
=$8170.2
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:
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.
The radius of a circle is three meters. What is the circle’s diameter
The diameter of a circle is the radius times 2.
Diameter = 3 x 2 = 6 meters.
Answer:
6 is the answer.
3 x 2 = 6
Step-by-step explanation:
Find the volume of the figure. Round your answer to the nearest hundredth, if necessary.
Answer:
Step-by-step explanation:
3.14 x 10.6^2= 352.81 pi
Answer is...
Volume = 4988.92
See attached photo