The number of k-element subsets of a set of n elements is given by
... C(n, k) = n!/(k!(n-k)!)
a) C(100, 99) = 100!/(99!×1!) = 100
b) C(100, 98) = 100!/(98!×2!) = 100*99/2 = 4950
c) C(100, 2) = 100!/(2!×98!) = 4950 . . . . same as (b)
The circle below is centered at the point (4, -3) and has a radius of length 3. What is its equation?
Answer:
(x-4)² + (y+3)² = 9
Step-by-step explanation:
The equation of a circle of radius r centered at (h, k) is ...
... (x-h)² + (y-k)² = r²
Subsituting your given values gives ...
... (x -4)² +(y -(-3))² = 3²
... (x -4)² +(y +3)² = 9
1. The creek festival charges and entry fee plus $1.25 per ticket needed for the rides. Jennifer spent her money only on ride tickets and festival admission. The price of the festival admission is the same for everyone. Use y to represent the total cost and x to represent the number of ride tickets.
(a) Jennifer spent a total of $30.75 on the entry fee plus 15 ride tickets. How much did Jennifer pay for the entry fee?
(b) James has $22 he can spend at the festival on the entry fee and tickets. How many tickets can James buy?
(c) Let x represent the number of ride tickets purchased and y represent the total cost of festival entry fee and ride tickets. Write an equation to calculate the total cost of the entry fee and festival admission for a person who purchases x tickets.
please show all of your work than you so much i will give brainiest answer as well thank you so much have a good day.
(a) entry fee cost
(b) the number of ride tickets James can buy (after he pays the entry fee)
(c) an equation for total cost y for purchase of x tickets
Solution(a) We know the total cost is the cost of entry fee and ride tickets. For Jennifer, this is ...
... 30.75 = (entry fee) + 15×1.25
... 30.75 -18.75 = (entry fee)
entry fee = 12.00 . . . dollars
(b) If James spends his entire budget on entry fee and x rides, the number of ride tickets he can buy is given by ...
... 22 = 12 + 1.25x
... 10 = 1.25x
... 10/1.25 = x = 8
James can buy 8 ride tickets.
(c) The equation for total cost that we have been using is ...
... total cost = entry fee + (cost per ticket)×(number of tickets)
... y = 12 + 1.25x
Can someone please help with number 3 and 4 thank you
Answer:
Step-by-step explanation:
3) Purchase price of the home is $585000
Cash down payment is $ 175000
Amount to taken for loan
[tex] = 585000-175000 = $410000[/tex]
Therefore, loan to value ratio will be
[tex]= \frac{loan amount}{value}[/tex]
[tex] =\frac{410000}{585000}[/tex]
On solving
[tex]=\frac{410}{585}[/tex]
On simplifying
[tex] =\frac{82}{117}[/tex]
The loan to value ratio will be [tex]82:117[/tex]
4) it is given that
Fixed monthly expences i.e. debt [tex]=$1836[/tex]
Total income per month [tex] =$4934[/tex]
Therefore debt to income ratio will be
[tex]= \frac{debt}{income}[/tex]
[tex]= \frac{1836}{4934}[/tex]
On simplifying we get
[tex]=\frac{918}{2467}[/tex]
Therefore debt to income ratio will be
[tex]918:2467[/tex]
A person who is 6.2 feet tall is standing in a pool. The top of the person's head is 2.8 feet above the surface of the water. How deep is the pool?
Answer:
3.8 feet
Step-by-step explanation:
Given that the person is standing in a pool. That means he is keeping his feet at the bottom level of the pool. His height is 6.2 ft.
Top of the person head above the surface of water= 2.8 feet.
Hence height of the person= Top of the person head above the surface of water+depth of the pool
6.2 = 2.8+depth of pool
Depth of pool = 6.2-2.8 = 3.4 feet.
the pool is four feet deep
Bobby built twice as many forts as his brother. If his brother built 6 forts , how many did bobby build?
Bobby built 12 forts
Answer:
12 forts
Step-by-step explanation:
6x2=12
19,20,21,?,?,26,28,32,33,40 which two numbers should replace on the question mark?
The two numbers that should replace the question marks on the given sequence are; 22 and 24
We are given the series;
19,20,21,?,?,26,28,32,33,40
From the given sequence, we see that there are two interwoven sequences.
Between 19 and 21 the difference is +2Between 21 and second question mark, the difference is +3
Between second question mark and 28, the difference is +4
Between 28 and 33, the difference is +5
Similarly;Between 20 and first question mark the difference will be +2
Between the first question mark and 26, the difference is +4
Between 26 and 32 the difference is +6.
Thus our missing numbers are 22 and 24
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Which of the following must be given to prove that ΔABC is similar to ΔDBA?
a. Segment AD is an altitude of ΔABC.
b. Segment CB is a hypotenuse.
c. Segment CA is shorter than segment BA.
d. Angle C is congruent to itself.
Answer:
The correct answer is option A.
Step-by-step explanation:
For the given triangles to be similar the segment AD must be an altitude of ΔABC.
We can provide a theorem for the same:
If we draw an altitude from the right angle of any right triangle, then the two triangles formed are similar to the original triangle.
Also all the three triangles are similar to each other.
Like here, in the triangle ABC, we draw an altitude from A to the side BC, thus forming 2 triangles; ΔDBA and ΔDAC. These both will be similar to ΔABC.
So, by the theorem it is proven that ΔABC is similar to ΔDBA.
Therefore, option A is correct.
the number 3456 is divisible by wich single-digit number?
I'm assuming what you mean is what can you divide 3456 by to get a natural number.
First of all every number is divisible by 1.
Every even number is divisible by 2, so since 3456 is an even number, it can be divided by 2. That would equal 1728.
2456 can also be divided by 3, to get 1782.
You can also divide it by 4, to get 865.
Divided by 6, it's 576.
Divided by 8, it's 432.
And lastly, 3456 divided by 9 is 384.
So, there isn't just one single-digit number you can divide 3456 by to get a natural number. You can divide it by 1,2,3,4,6,8, and 9.
Hope that helps!
The rectangular floor of a classroom is 36 feet in length and 32 feet in width. A scale drawing of the floor has a length of 9 inches. What is the area, in square inches, of the floor in the scale drawing?
Answer:
Area of the Scale drawing is [tex]72[/tex] square inches.
Step-by-step explanation:
First we need to convert feet and inches to a common unit. For that lets convert feet into inches.
1 feet = 12 inches
Therefore,
The length of the floor in inches:
[tex]36[/tex] feet = [tex]36*12[/tex] inches
=[tex]432[/tex] inches
The width of the floor in inches:
[tex]32[/tex] feet = [tex]32*12[/tex] inches
=[tex]384[/tex] inches
Now lets calculate by how many times the length has been scaled down:
432 inches of length has been reduced to 9 inches.
[tex]\frac{432}{9}=48[/tex]
So the length has been scaled down 48 times.
Now lets scale down the width 48 times:
[tex]\frac{384}{48} =8[/tex]
So the width of the Scale drawing is 8 inches.
Area of the Scale drawing = Scaled down length * Scaled down width
=[tex]9*8[/tex]
=[tex]72[/tex] square inches
Answer:
72 square inches.
Step-by-step explanation:
Convert feet and inches.
36 feet = 36*12 inches
=432 inches
Width of the floor; Converted from feet to inches:
32 feet = 32*12 inches
= 384 inches
Calculate how many times the length (l) has been scaled down.
432 inches of length has been reduced to 9 inches.
[tex]\frac{432}{9}=48[/tex]
Now the length has been scaled down 48 times.
Scale down the width (w) 48 times.
[tex]\frac{384}{48} =8[/tex]
The width of the scale drawing = 8 in
Area of the Scale drawing = Scaled down length * Scaled down width
[tex]=9*8 =72in^{2}[/tex]
Graph this compound inequality 2.5 is equal to or less than x is equal to or less than 4.5
Graph this compound inequality 2.5 is equal to or less than x is equal to or less than 4.5
2.5 <= x < = 4.5
We graph this inequality using number line.
Here x lies between 2.5 and 4.5
While graphing, we start with closed circle at 2.5 because we have equal symbol .
Then shade till 4.5. Use closed circle at 4.5.
The graph is attached below.
Answer:
its c
Step-by-step explanation:
for the rest of the question when it asks "which scenario fits the compound inequality?"
Select all the points that represent a solution to the linear inequality −2x − 3y ≥ 8.
Select one or more:
A. (-9, 8)
B. (-4, 0)
C. (-2, 5)
D. (0, -3)
E. (7, -1)
F. (-3, -2)
B, D and F
to test for a solution, substitute the coordinates of the given point and if the inequality is true then the point is a solution
A(- 9, 8 ) : 18 - 24 = - 6 < 8 not a solution
B(- 4, 0 ) : 8 - 0 = 8 = 8 hence a solution
C(- 2, 5) : 8- 15 = - 7 not a solution
D(0, - 3 ) : 0 + 9 = 9 hence a solution
E(7, - 1 ) : - 14 + 3 = - 11 not a solution
F(- 3, - 2 ) : 6 + 6 = 12 hence a solution
Answer:
B, D and F
Explanation:
A(- 9, 8 ) : 18 - 24 = - 6 < 8 not a solution
B(- 4, 0 ) : 8 - 0 = 8 = 8 is a solution
C(- 2, 5) : 8- 15 = - 7 not a solution
D(0, - 3 ) : 0 + 9 = 9 is a solution
E(7, - 1 ) : - 14 + 3 = - 11 not a solution
F(- 3, - 2 ) : 6 + 6 = 12 is a solution
For how many minutes did Lynn ru at a greater speed than kael?
Answer:
28 minutes.
Step-by-step explanation:
We can see from our graph that 12 minutes after starting the race Lynn left Kael behind and he ran at a greater speed till the race ended after 40 minutes.
To find total number of minutes Lynn ran faster than Kael we will subtract 12 from 40.
[tex]40-12=28[/tex]
Therefore, Lynn ran at a greater speed than Kael for 28 minutes.
Answer:
28 minutes
Step-by-step explanation:
please help me with A B and C
(a)
the equation of a quadratic in vertex form is
y = a(x - h)² + k
where (h, k ) are the coordinates of the vertex and a is a multiplier
here the vertex = (6, - 2 ) and a = 1
y = (x - 6 )² - 2 ← in vertex form
(b)
to find the zeros let y = 0
(x - 6 )² - 2 = 0 ( add 2 to both sides )
(x - 6 )² = 2 ( take the square root of both sides )
x - 6 = ±√2 ← ( note plus or minus )
add 6 to both sides
x = 6 ±√2 ← zeros
(c)
to obtain standard form expand the vertex form of the equation
y = x² - 12x + 36 - 2
y = x² - 12x + 34 ← in standard form
Given the point (-1, 8), answer the questions below: After that point was translated 5 units right and 4 units up, the coordinates of this particular point would be ( , ). If this point is a part of a linear function, the parent function f(x)=x would be transformed into an equation that looks like this: g(x) = .
a) x=4 is 5 units to the right of x=-1.
y=12 is 4 units up from y=8.
Your point (-1, 8) is translated to (4, 12).
___
b) If the parent function f(x) = x is translated so it goes through (4, 12), the translated function can be written ...
... g(x) = f(x-4) +12 = (x -4) +12
... g(x) = x +8
there is a photo attached
You can use the sum of angles identities, then rearrange to put the result in the form of tangents.
[tex]\displaystyle\frac{\sin{(x+y)}}{\sin{(x-y)}}=\frac{\sin{(x)}\cos{(y)}+\cos{(x)}\sin{(y)}}{\sin{(x)}\cos{(y)}-\cos{(x)}\sin{(y)}}\\\\=\frac{\left(\frac{\sin{(x)}\cos{(y)}+\cos{(x)}\sin{(y)}}{\cos{(x)}\cos{(y)}}\right)}{\left(\frac{\sin{(x)}\cos{(y)}-\cos{(x)}\sin{(y)}}{\cos{(x)}\cos{(y)}}\right)}\\\\=\frac{\tan{(x)}+\tan{(y)}}{\tan{(x)}-\tan{(y)}}[/tex]
Write the 2-digit number that matches the clues.my number has a ten s digit that is 8 more than the ones digit. Zero is not one of my digits
There are two pairs of digits such that one is 8 more than the other: 0, 8 and 1, 9.
Since 0 is not one of the digits of the number in question, that number must be ...
... 91
Which is the most accurate way to estimate 33% of 52?
1/3 x 51 or 1/3 x 53?
The most accurate way to estimate 33% of 52 is explained as follows:
To find a percentage, we calculate it as follows:
a% of b [tex]=\frac{a}{100} \times b[/tex]
Now, lets convert 33% into fraction first:
33% [tex]=\frac{33}{100} =0.33[/tex]
Now,
[tex]0.33 \times 52=17.16 \approx 17[/tex]
We have two ways to calculate the same so we will compare the values of them and figure out which gives a value nearer to our actual value:
So, [tex]\frac{1}{3} \times51=17[/tex] and [tex]\frac{1}{3} \times 53=17.66[/tex]
We can see that the first method gives us a value which is far closer to the actual value.
Therefore, [tex]\frac{1}{3} \times 51[/tex] is the most accurate way to estimate 33% of 52.
The regression equation y = –0.414x + 106.55 approximates the percent of people in an audience who finish watching a documentary, y, given the length of the film in minutes, x. Which is the best prediction for the percent of people in an audience who will finish watching a documentary that is 70 minutes long?
Answer:
77.57
If we round.
78
Step-by-step explanation:
To solve this, just plugin 70 where the x is located in the equation:
y = -0,414x + 106.55
y = -0,414(70) + 106.55 = 77.57
The best prediction for the percentage of people would be 78 % in an audience finish watching a documentary that is 70 minutes long.
What is the equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
The regression equation is given by:
y = -0.414x + 106.55
Here y represents the percentage of people in an audience who finish watching a documentary.
and x represents the length of the film in minutes.
We have to determine the value of y when the value of x is: 70
Substitute the value of x = 70 in the equation,
y = -0.414x + 106.55
y = -0.414(70) + 106.55
y = 77.57
Therefore, the best prediction for the percentage of people would be 78 % in an audience finish watching a documentary that is 70 minutes long.
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Write the equation of line in slope-intercept form. Line parallel to y=−2x+3 that passes through the point (−100,−100)
When you want a parallel line through a given point (h, k), you can start with the equation you have and do the following:
eliminate the constant termreplace x with (x-h)replace y with (y-k)Here, that looks like
... (y-(-100)) = -2(x-(-100))
... y = -2x -200 -100 . . . . . eliminate parentheses, add -100
... y = -2x -300 . . . . the equation you want.
Answer:
y = - 2x - 100
Step-by-step explanation:
Remark
The line we want is a line parallel to y = - 2x + 3
That means it has the same slope as the given line. The given line has a slope of -2
y = -2x + b is what you have so far. Now you have to use the point to get b
y = - 100
x = - 100
Solve for b
-100 = -2(-100) + b
-100 = 200 + b Notice the sign change. Two minus's make a plus. Subtract 200 from both sides.
- 100 - 200 = b
- 300 = b
Answer
y = - 2x - 100
PLEASEE HELPPP!!!!
What is the equation of a line that passes through the point (5, −4) and is parallel to the line whose equation is 2x + 5y = 10?
Enter your answer in the box
y = - [tex]\frac{2}{5}[/tex] x - 2
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y-intercept )
rearrange 2x + 5y = 10 into this form
subtract 2x from both sides
5y = - 2x + 10 ( divide all terms by 5 )
y = - [tex]\frac{2}{5}[/tex] x + 2 ← point- slope form with slope m = - [tex]\frac{2}{5}[/tex]
Parallel lines have equal slopes hence
y = - [tex]\frac{2}{5}[/tex] x + c is the partial equation of the parallel line
to find c, substitute ( 5, - 4 ) into the partial equation
- 4 = - 2 + c ⇒ c = - 4 + 2 = - 2
y = - [tex]\frac{2}{5}[/tex] x - 2 ← equation of parallel line
The equation of the line that is parallel to 2x + 5y = 10 and passes through the point (5, -4) is y + 4 = (-2/5)x + 2.
Explanation:To find the equation of a line that is parallel to another line, we need to use the fact that parallel lines have the same slope. First, let's write the given equation in slope-intercept form (y = mx + b), where m represents the slope:
2x + 5y = 10
5y = -2x + 10
y = (-2/5)x + 2
Since the given line has a slope of -2/5, the parallel line will also have a slope of -2/5. Now, we can use the point-slope form of a line (y - y1 = m(x - x1)) to find the equation. Plugging in the coordinates of the point (5, -4):
y - (-4) = (-2/5)(x - 5)
y + 4 = (-2/5)(x - 5)
y + 4 = (-2/5)x + 2
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given the function f(x)=3x -2 and g(x)= x+2/3 complete parts A and B.
A. Find f(g(x)) and g(f(x)). Include your work in your final answer.
B. Use complete sentence's to explain the relationship that exists between the composition of the functions. F(g(x)) and g(f(x)).
First, I should point out that g(x) should be written as g(x)=(x+2)/3, otherwise the problem is confusing.
[tex]f(x)=3x-2 \enspace g(x)=\frac{x+2}{3}[/tex]
(A) [tex]f(g(x))=3(\frac{x+2}{3})-2=x\\g(f(x))=\frac{3x-2+2}{3}=x[/tex]
(B) Since [tex]f(g(x))=x[/tex] and [tex]g(f(x))=x[/tex], it holds that
[tex]f(g(x))=g(f(x))[/tex] for all x. This means the composed functions are *identical*
A
f(g(x)) = f([tex]\frac{x+2}{3}[/tex]) = 3([tex]\frac{x+2}{3}[/tex]) - 2 = x + 2 - 2 = x
g(f(x)) = g(3x - 2) = [tex]\frac{3x-2+2}{3}[/tex] = [tex]\frac{3x}{3}[/tex] = x
B
Since both composite functions f(g(x)) and g(f(x)) equal x
This indicates that the functions f(x) and g(x) are inverse functions
What is 0.523 divided by 10 exponent 2 ?
WILL MARK BRAINIEST y=4 times x + 8 y=3 times x + 2 tell me how you solved by using the subduction method
Complete the equation of the line through (-1,6) (7,-2)
Like Y= ??
Find the slope first, use the formula (y₁-y₂)/(x₁-x₂)
[6-(-2)]/(-1-7) = 8/-8 -> -1 Therefore your slope (mx) is -x.
To find the y-intercept, you use one of the points and substitute it in the slope intercept formula: y=mx+b, using the slope you just found.
-2=-1(7)+b
-2=-7+b -> -2+7=b
b=5
In conclusion, your equation will be y=-x+5. I hope this helped ;)
Math Write the number 63 in four different ways.
63 = 0.63×10² = 126/2 = 3×21 = √3969 = 77₈
The last is as a base-8 number.
63=60+3=31.5*2=63/100
If the area of a circle measures 25π cm2, what is the circumference of the circle in terms of π? A) 5π cm B) 10π cm C) 50π cm D) 100π cm
the answer to the question is a.) 5rr cm because 5rr is right on brainly i've had it
What is the graph of 3x + 5y = –15? Image for option 1 Image for option 2 Image for option 3 Image for option 4
The "intercept form" of the equation for a line is ...
... x/a + y/b = 1
where a and b are the x- and y-intercepts, respectively.
Dividing by -15 will put your equation into this form:
... 3x/-15 + 5y/-15 = 1
... x/(-5) + y/(-3) = 1
Your graph will go through the points (-5, 0) and (0, -3).
a square has a side lengths of 9, use the pythagorean theorem to find the length of the diagonal
diagonal = 9√2 ≈ 12.73
the diagonal splits the square into 2 right triangles with the hypotenuse being the diagonal of the square
using Pythagoras' identity
d = √(9² + 9²) = √162 = 9√2 ≈ 12.73 ( to 2 dec. places )
To find the diagonal of a square with side lengths of 9 inches, use the Pythagorean theorem, yielding a diagonal length approximately equal to 9√2 inches.
To calculate the diagonal of a square, you can use the Pythagorean theorem for a right triangle formed by two adjacent sides of the square and the diagonal. The formula for the diagonal (d) of a square with side length (s) is given by d = s√2. Therefore, the diagonal of the square is:
d = 9√2
d = 9 × 1.414 (approx)
d = 12.726 inches (approx)
Rounded to the nearest whole number or given options, the length of the diagonal is closer to 9√2 inches.
The complete question is:
A square has a side lengths of 9, use the pythagorean theorem to find the length of the diagonal of the square.
WILL GIVE BRAINLIEST The sequence 7 21 63 189......shows the number of jumping jacks justin did each week, starting with the first week of him working out.
A. is the sequence arithmetic or geometric? how do you know?
B. What is the recursive rule for the sequence?
C. what is the iterative (explicit) rule for the sequence.
A
this is a geometric sequence since there exists a common ratio r between the terms
r = [tex]\frac{21}{7}[/tex] = [tex]\frac{63}{21}[/tex] = [tex]\frac{189}{63}[/tex] = 3
B
to obtain the next term in the sequence multiply the previous term by 3
[tex]a_{n+1}[/tex] = 3 [tex]a_{n}[/tex] ← recursive rule
C
the n th term of a geometric sequence is
[tex]a_{n}[/tex] = [tex]a_{1}[/tex] [tex]r^{n-1}[/tex]
where [tex]a_{1}[/tex] is the first term in the sequence
[tex]a_{n}[/tex] = 7 × [tex]3^{n-1}[/tex] ← explicit rule
100 pts please help
What is the value of x?
1. x/4 - 5 = 6
Answer:
x = 44
Step-by-step explanation:
This is a 2-step linear equation. Add the opposite of the constant (the one on the side with the variable term), then multiply by the inverse of the coefficient of the variable.
Add 5, then multiply by 4.
x/4 -5 = 6 . . . . . given
x/4 = 11 . . . . . . . add 5
x = 44 . . . . . . . . multiply by 4
Answer:
x=44
Step-by-step explanation: