We want to find different ways of selecting and ordering elements. The answers are:
A) C = 395
B) combinations = 479,001,600
C) combinations = 239,500,800
First, we know that Rebecca has 12 photos.
A) She wants to choose 8 of these 12 photos, we want to see in how many ways she can choose these 8 photos.
Remember that for a set of N elements, the number of different combinations of K elements (such that K is smaller than N) is given by:
[tex]C(N, K) = \frac{N!}{(N - K)!*K!}[/tex]
Here we have N = 12 and K = 8, then:
[tex]C(12, 8) = \frac{12!}{(12 - 8)!*8!} = \frac{12!}{4!*8!} = \frac{12*11*10*9}{4*3*2*1} = 495[/tex]
So there are 495 different ways of choosing 8 photos out of the 12.
B) Now we want to see in how many ways she can arrange all 12 photos.
The first photo can be any one of the 12, so there we have 12 options.The second photo can be any one of the remaining 11 (so we have 11 options).The third photo can be any one of the remaining 10, and so on.The total number of combinations is just the product between the numbers of options, we got:
[tex]combinations = 12*11*10*9*8*7*6*5*4*3*2*1 = 479,001,600[/tex]
C) Now we must combine the two things we did before, first, we select 10 out of the 12 photos, and then we want to find in how many ways we can arrange these 10 photos.
[tex]C(12, 10) = \frac{12!}{(12 - 10)°*10°} = \frac{12*11}{2} = 66[/tex]
And we multiply this by the total number of arrangements of these 10 photos, that is just given by 10!, so we get:
[tex]c = 66*10! = 66*(10*9*8*7*6*5*4*3*2*1) = 239,500,800[/tex]
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the 7th term of a Gp is 192 and it common ratio is 2 find the first term
[tex]n^{th}\textit{ term of a geometric sequence} \\\\ a_n=a_1\cdot r^{n-1}\qquad \begin{cases} a_7=\stackrel{7^{th}\ term}{192}\\ 7=\textit{term position}\\ a_1=\textit{first term}\\ r=\stackrel{\textit{common ratio}}{2} \end{cases} \qquad \qquad a_7=a_1\cdot 2^{7-1} \\\\\\ 192=a_1\cdot 2^6 \implies 192=64a_1\implies \cfrac{192}{64}=a_1\implies \boxed{3=a_1}[/tex]
Which is the correct solution for the following inequality: 9 ≤ 4x + 1 < 21
2 < x < 5
2 < x < 5
2 < x < 5
2 , <, x < 5
2 < x < 5
Answer:
2<=x<5
Step-by-step explanation:
first subtract one from all pieces, then divide by four. because you never divide by a negative so switching of sides is needed. Two is less than or equal to x which is less than five.
Please hurry will mark brainliest if you answer correctly
i need help on this math problem
El primer término de una progresión geométrica es 3 y el séptimo 12 288. Hallar la suma de los siete términos.
Answer:
16383
Step-by-step explanation:
El primer término de la progresión geométrica es 3 y lo llamaremos [tex]a[/tex].
Se tiene que una progresión geométrica es de la forma:
[tex]a, ar, ar^2, ar^3, ar^4, \cdot \cdot \cdot[/tex]
Donde [tex]r \neq 0[/tex] y es la proporción es común. Por lo tanto si el séptimo número de la sucesión es 12.288 este se puede re-escribir como:
[tex]ar^6 = 12.288[/tex]
Si se resuelve la ecuación para hallar [tex]r[/tex] se tiene
[tex]r = \sqrt[6]{\frac{12.288}{a} } = \sqrt[6]{\frac{12.288}{3} } = \sqrt[6]{ 4096} = 4[/tex]
Ahora se halla cada número de la progresión geométrica entre 1 y 7 para finalmente sumarlos
[tex]ar^0+ar^1+ar^2+ar^3+ar^4+ar^5+ar^6[/tex]
[tex]3+12+48+192+768+3072+12288[/tex] = 16383
Por lo tanto la sumatoria de los primeros [tex]7[/tex] términos de la sucesión son 16383
trevin puts 8 gallons of
Answer:
24.75 is answer
Step-by-step explanation:
Answer:
That was a good start, but we need the rest of the question.
Step-by-step explanation:
4
b(x) = 16.22 – 25
bx)
Use the drop-down menus to factor the expression and find the zeros of b(x).
Answer:
1) (4x)² - (5)²
2) (4x + 5) (4x -5)
3) Zeros of b are [tex]\frac{5}{4}[/tex] and [tex]\frac{-5}{4}[/tex] (can also be 1.25 and -1.25)
7k -2(k+4) What is this answer?
5−8
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PLEASE HELP WITH THIS QUESTION
Answer:
which question can I help you
1) f(x) = x² + 2x + 1
2) g(x) = x² + 6x + 5
3) h(x) = x² - 12x + 36
4) g(x) = 9x² + 6x + 2
5) g(x) = x² + 6x + 4
Answer:
(X+1)(X+1) (X+5)(X+1)3. (X-6)(X-6)
Solve for the missing variable
Answer:
x = 7.5.
The two lines on the side of the triangle in the screenshot show us that the two lines made are the same length. So the difference between the first two values, i.e. 22.3 and 14.9 is the same difference between 14.9 and x.
Step-by-step explanation:
hope this helps. . .<3
good luck! uωu
Answer:
Step-by-step explanation:
14.9 is the middle value of x and 22.3. So your formula looks like this.
(x + 22.3) / 2 = 14.9 Multiply both sides by 2
2(x + 22.3) / 2 = 14.9*2 Remove the brackets.
x + 22.3 = 29.8 Subtract 22.3 from both sides
x = 29.8 - 22.3
x = 7.5
PLEASE HELP WITH THIS QUESTION
Answer:
Heigh <= 63
Width <= 56
Length <= 61
Step-by-step explanation:
Height: x+7
Width: x
Length: x + 5
(x + 7) + (x) + (x + 5) <= 180 cm^3
3x + 12<= 180
3x <= 180-12
x <= 168/3
x <= 56
there are 350,000 in a warehouse predict the number of light bulbs that are likely to have no defects
Answer:
175000.(or around that number)
Step-by-step explanation:
half of 350,000 is 175000.
Phyllis invested $50,000 in two different types of stock. The first type earned 10% and the second type earned 15%. If the profit on the 15% stock was $2,500 more than the profit on the 10% stock, how much did Phyllis invest in the 15% stock?
Answer:
$ 30,000
Step-by-step explanation:
0.15(50,000 - x) - 0.1x = 2,500
7,500 - 0.15x - 0.1x = 2,500
7,500 - 2,500 = 0.15x + 0.1x
5,000 = 0.25x
5,000/0.25 = x
x =20,000
50,000 - 20,000 = 30,000
0.15 * 30,000 = $4,500
0.1 * 20,000 = $2,000
$4,500 - $2,000 = $2,500
In the ratio of 3:2:2, three brothers invested a total of 49000 pesos to a store. Find each brother's share in the investment.
Answer:
21000,14000,and14000
Step-by-step explanation:
3x+2x+2x=49000
7x=49000
x=7000
3×7000=21000
2×7000=14000
2×7000=14000
5) Mike and Mei each improved their yards by planting daylilies and shrubs. They bought their
supplies from the same store. Mike spent $70 on 5 daylilies and 5 shrubs. Mei spent $62 on 1
daylily and 5 shrubs. Find the cost of one daylily and the cost of one shrub.
Please help me out with this Math sheet. Thanks
Answer:
1. acute
2. obtuse
3. right
4. acute
5. straight
6. obtuse
7. acute
8. obtuse
9. straight
10. ∠ EAD , ∠ CED , ∠ BCE , ∠ BEA , ∠EBC
11. ∠CDA , BCD
12. ∠AED ,∠BEC
13. ∠ AEC, ∠ BED
14. ∠ EAU , ∠EUI , ∠IUO , ∠OAE
15. ∠ EUO , ∠IUA
16. ∠AUO , ∠EIO
A wall that is 12 feet high and 15 feet wide is to be painted, but the wall has two rectangular windows (which should not be painted). If each window is 3 feet by 5 feet, determine the area of the space to be painted.
Answer:Measure length of each wall including doors and windows. Find the total square feet of the wall(s) by multiplying ceiling height by total wall length.
Step-by-step explanation:
The required area that is to be painted is given as 150 square feet.
Given that,
A wall that is 12 feet high and 15 feet wide is to be painted, but the wall has two rectangular windows (which should not be painted). each window is 3 feet by 5 feet,
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
Area of the wall = 12 × 15 = 180 square feet
Area of the two windows, = 2 × 3 × 5 = 30 square feet
Area to be painteded = 180 - 30 = 150 square feet,
Thus, the required area that is to be painted is given as 150 square feet.
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A) 37.68 square inches B) 72.52 square inches C) 108.12 square inches ) D) 113.09 square inches
Answer:
The answer is D.
Step-by-step explanation:
Radius is half of diameter. So the radius of the circle is 6 in.
The formula for getting the area of circle is:
A = π[tex]r^{2}[/tex] π = 3.1416
A = (3.1416)(6)[tex]^{2}[/tex]
A = (3.1416)(36)
A = 113.09 square inches
How do you do -9-(-2)-(-6)-4?
Solve for x:
Yeah can't come in3x+7x=10x
Answer:
#happy learningStep-by-step explanation:
#brainly phWhat is the next number in the pattern?
9 4 7
—, —, — . . .
10 5 10
Answer:
3/5
The nth term of an AP = a + d(n -1)
By the looks of it, the next term in the sequence is the 4th term.
a = 9/10
d = 4/5 - 9/10 = -1/10
9/10 - 1/10(4 - 1) = 9/10 - 1/10(3)
9/10 - 3/10 = 6/10
3/5
Dylan had 300 5p coins in a box last month. He now has 360 5p coins. Find the percentage increase.
Therefore the percentage increase is 72
72Line l is a reflection in the x-axis of line k. Write an equation that represents line k.
Answer:
(-4,3)
Step-by-step explanation:
nejsjsjssjsususheheueueyeehejebebe
Answer: y = (5/3)x + -1
Step-by-step explanation:
The slope is -5/3, so since its a reflection in the x - axis, the new slope would be the opposite, 5/3. Now for the +1, you just have to find the y intercept by plotting the dots at the opposite version of the y number that is already there. For example because the point (0,1) has 1 as its y number, you make it into -1, and for example if you have the point (3,-4) since -4 is the y number you change it to 4.
Draw a square and its diaginals
Answer:
you cant draw......................
Step-by-step explanation:
Which of the following Venn diagram represents two sets with no common elements?
The Venn Diagram B, C and D, all represents two sets with common elements.
In B, the circle F is inside the circle G, so F share all of its elements with G. It is like a baby inside the belly of her mother :)
In C, F and G circles intersect and the intersection is their common space, and
the D is like the B.
But A reprents two sets F and G with no common elements. So the answer is A.
Good Luck
Part 2 out of 2
Heather's mom says that they would save more than $100 if they buy tickets for their family on opening
weekend. Do you agree or disagree with Heather's mom? Complete the explanation of how to find how
much they would save.
You ? v with Heather's mom.
The regular price tickets would cost them $80 x 4 people, which equals $
The discounted tickets would cost them $ * 4 people, which equals $224.
To find the difference subtract the discounted tickets total $224 from the regular price tickets total $
which equals $
They would save
which is less than $100.
Next
✓ Check
Next
? A
А
Question 18 of 21
Answer:
i agree I can't really explain why though sorry
Heather's mom's estimation is wrong, as they will only save $96.
What is a percentage?A percentage is a number that tells us how much out of 100 and can also be written as a decimal or a fraction.
Given that, The special price for the amusement park ticket costs $56. This is 70% of the regular price, Heather's mom says that they would save more than $100 if they bought tickets for their family on opening weekend.
Let the original price of the ticket be x,
70% of x = 56
x = 56x100/70
x = 80
That means, the regular price is $80
On a regular day, ticket will cost = 80x4 = $320
On the special ticket price cost = 56x4 = $224
The saved priced = 320-224 = $96
Hence, Heather's mom's estimation is wrong, as they will only save $96.
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The function f(t) = t2 + 4t - 14 represents a parabola.
Part A: Rewrite the function in vertex form by completing the square. Show your
work.
Part B: Determine the vertex and indicate whether it is a maximum or a minimum on
the graph. How do you know?
Part C: Determine the axis of symmetry for f(t).
Answer:
a: [tex]f(t)=(t+2)^2-18[/tex]
b: vertex: (-2, -18)
minimum
c: x = -2
Step-by-step explanation:
Completing the square is difficult to explain in words. but I'll try my best. Let me know if you need any more information.
Part A ===============
Start with the given function in this form:
[tex]f(x)=ax^2+bx+c\\t^2+4t-14[/tex]
We need an additional number, d, and we'll calculate it like this:
[tex]d=(\frac{b}{2a})^2 \\\\d=(\frac{4}{2(1)} )^2\\d=2^2\\d=4[/tex]
d needs to be added and subtracted at the same time. That way we do not change the value of the expression:
[tex]ax^2+bx+d-d+c\\\\t^2+4t+4-4-14[/tex]
And you can separate them like this to make it easier to read:
[tex](t^2+4t+4) + (-4-14)\\(t^2+4t+4)-18[/tex]
Finally, we need to factor the trinomial in the parenthesis. Because we've completed the square, it's now a perfect square trinomial. The factored form is just:
[tex](x+e)^2[/tex]
where e is half of b, or the square root of c. That looks like this in our case, and you can also expand it to make sure.
[tex](t+2)^2\\\\(t+2)(t+2)\\t^2+2t+2t+4\\t^2+4t+4[/tex]
Put that all together and you get the answer:
[tex]f(t)=(t+2)^2-18[/tex]
Part B ===============
Vertex form is this:
[tex]f(x)=a(x-h)^2+k[/tex]
where (h, k) is the vertex and a is the scale factor.
In part A, we converted the given function into vertex form. Looking at that, you can see the vertex is at (-2, -18), and the scale factor is 1. When the scale factor is positive, the parabola faces upwards. When it's negative, the parabola faces downwards.
The scale factor is a positive 1 in this case, and if you picture that in your mind, the vertex is at the very lowest point, or the minimum, of the parabola.
Part C ==============
The axis of symmetry is always on the vertex, and that is because the vertex is the exact point where the parabola changes direction from positive to negative, or negative to positive.
The vertex of this parabola is (-2, -18), so the axis of symmetry is at x = -2.
Sorry if that got too long and hard to follow, I can clarify any part of it if needed.
Round to 2 decimal places 0.966
Answer:
Step-by-step explanation:
round to 2 places 0.966: 1.00
Find the value of x.
(8x + 2)°
60°
Y
70°
Z
Here according to angle sum property all angles sum u up 180°
So,
[tex]8x + 2 + 60 + 70 = 180 \\ 8x + 132 = 180 \\ 8x = 180 - 132 \\ 8x = 48 \\ x = \frac{48}{8} \\ x = 6[/tex]
- BRAINLIEST answerer