Answer: A) 1716 B) 1235520
Step-by-step explanation:
If order doesn't matter , then we use combinations, where the number of combinations of selecting r things from n is given by :-[tex]^nC_r=\dfrac{n!}{r!(n-r)!}[/tex]
If order matters , then we use permutations, where the number of permutations of selecting r things from n is given by :-[tex]^nP_r=\dfrac{n!}{(n-r)!}[/tex]
Given, Total distinct letters = 13
To choose = 6 letters
A) Number of ways to choose (if order does not matter)=[tex]^{13}C_6[/tex]
[tex]=\dfrac{13!}{6!7!}=\dfrac{13\times12\times11\times10\times9\times8\times7!}{(720)\times 7!}\\\\= $$1716[/tex]
B) Number of ways to choose (if order matters)=[tex]^{13}P_6[/tex]
[tex]=\dfrac{13!}{7!}=\dfrac{13\times12\times11\times10\times9\times8\times7!} 7!}\\\\= $$1235520[/tex]
Hence, A) 1716 B) 1235520
A finite geometric series is the sum of a sequence of numbers. Take the sequence 1, 2, 4, 8, … , for example. Notice that each number is twice the value of the previous number. So, a number in the sequence can be represented by the function f(n) = 2n–1. One way to write the sum of the sequence through the 5th number in the sequence is ∑5n-12n-1. This equation can also be written as S5 = 20 + 21 + 22 + 23 + 24. If we multiply this equation by 2, the equation becomes 2(S5) = 21 + 22 + 23 + 24 + 25. What happens if you subtract the two equations and solve for S5? Can you use this information to come up with a way to find any geometric series Sn in the form ∑an-1bn-1?
hope this helps you alot
mm
a
Solve this system of equations using substitution:
y = 2x-4
x + 2y = 10
Step 1: Substitute for hin the second equation. Which is
the resulting equation?
2x - 4 = 10
x + 2x - 4 = 10
x + 2(2x - 4) = 10
Answer:
x + 2(2x-4) = 10
Step-by-step explanation:
Here in this question, we want to select which is the correct answer if we substitute for the value of y in the second equation, using the first.
In the first, we have;
y = 2x -4
Now, let’s input this value of y into the second equation.
By direct substitution, what we have is the following;
x + 2y = 10
—-> x + 2(2x -4) = 10
waht is the gcf of 4x^5 + 7x^3
Answer:
Step-by-step explanation:
4x^5 + 7x^3
x^3(4x^2 + 7)
The GCF is x^3
Please answer this question now
Answer:
48°
Step-by-step explanation:
arc BC = 136(2) -145 = 127
arc DC = 83(2) - 127 = 39
arc AD = 360 - 145- 127 - 39 = 48
Answer:
49 degrees
Step-by-step explanation:
Measure of arc ABC = 116*2 = 232 degrees.
Measure of arc BC = 232-145 = 87 degrees.
Measure of arc BCD = 83*2 = 166 degrees.
Measure of arc DC = 166-87 = 79 degrees.
Measure of arc AD = 360 - (145+87+79) = 360 - 311 = 49 degrees
need help will give you a good rating
Explanation : As you can see, [tex]\sqrt{-16}[/tex] is not a real number, and hence should be expressed as 4[tex]i[/tex], [tex]i[/tex] being an imaginary number. Respectively [tex]\sqrt{-64}[/tex] will be 8[tex]i[/tex]. Therefore this expression boils down to [tex]\left(3+4i\right)\left(6-8i\right)[/tex]. All we have to do from now on is expand this expression.
Apply the rule [tex]\left(a+bi\right)\left(c+di\right)=\left(ac-bd\right)+\left(ad+bc\right)i[/tex], in this case where [tex]a=3,\:b=4,\:c=6,\:d=-8[/tex],
[tex]\left(3\cdot \:6-4\left(-8\right)\right)+\left(3\left(-8\right)+4\cdot \:6\right)i[/tex]
Let's simplify each part, [tex]3\cdot \:6-4\left(-8\right)[/tex] and [tex]3\left(-8\right)+4\cdot \:6[/tex]. Afterwards we can add [tex]i[/tex], and refine.
[tex]3\cdot \:6-4\left(-8\right) = 50[/tex] ; [tex]3\left(-8\right)+4\cdot \:6 = 0[/tex]
Therefore our simplified expression will be [tex]50+0i[/tex], otherwise known as just 50. That is our solution.
Answer:
Step-by-step explanation:
The row-echelon form of the augmented matrix of a system of equations is given. Find the solution of the system. FYI it’s not b
Answer:
c.
Step-by-step explanation:
From the last row in the matrix z = 1.
From the second row:
y + 5z = -4
y = -4 -5(1) = -9.
From the first row:
x + -1 = -3
x = - 3 + 1
x = -2.
To get from home to work, Felix can either take a bike path through the rectangular park or ride his bike along two sides of the park. How much farther would Felix travel by riding along two sides of the park than he would by taking the path through the park?
Answer:
c=5.9/6(G)
Step-by-step explanation:
first find the 2 distances.
a^2+b^2=c^2 c=2.4+.7
7^2+2.4^2=c^2 c=3.1
.49+5.85=c^2
c^2=6.34
c=√6.34
c=2.51.
next subtract the two distances to find the difference.
c=2.51-3.1
c=.59
so the distance would be .59 which can be rounded up to .60/G
explanation on how I knew the answer.
Im reviewing for the math 8th grade staar.
The graph of y=√x is translated 5 units to the left and 7 units up. What is the equation of the graph that results from this translation?
Answer:
y = [tex]\sqrt{x+5}[/tex] + 7
Step-by-step explanation:
Given the graph of f(x) then f(x + k) is a horizontal translation of f(x)
• If k > 0 then a shift to the left of k units
• If k < 0 then a shift to the right of k units
Thus a translation of 5 units to the left
y = [tex]\sqrt{x+5}[/tex]
Given the graph of f(x) then f(x) + c is a vertical translation of f(x)
• If c > 0 then shift up by c units
• If c < 0 then shift down by c units
Thus
y = [tex]\sqrt{x+5}[/tex] + 7 ← translated equation
A room in the shape of a cube has a floor area of 20.25 square metre what is its height ? what is its volume ?
Answer:
Height= 4.5 Volume= 91.125
Step-by-step explanation:
Which equation does the graph of the systems of equations solve? 2 linear graphs. They intersect at 1,4
Answer:
See below.
Step-by-step explanation:
There is an infinite n umber of systems of equations that has (1, 4) as its solution. Are you given choices? Try x = 1 and y = 4 in each equation of the choices. The set of two equations that are true when those values of x and y are used is the answer.
Question 3 Multiple Choice Worth 2 points)
04.04
The swimming team has competed in 45 races this season. They have won 30 races so far. How many races will the team need to win today for the team to have a 75%
Success rate?
8
10
12
15
Answer:
Total number of matches need to win = 15
Step-by-step explanation:
Given:
Total number of race completed = 45
Total races win = 30
Success rate = 75% = 0.75
Find:
Total number of matches need to win
Computation:
Assume, extra number of matches = y
Extra number of win matches = x
So,
(30 + x) / (45 + y) = 0.75
Assume y = x
So,
(30 + x) / (45 + x) = 0.75
30 + x = 33.75 + 0.75 x
x = 15
Total number of matches need to win = 15
The sum of two numbers is negative thirty. One number is five times the other
Answer:
-25, -5
Step-by-step explanation:
Let's write a system of equations. Lets call x and y the numbers, where x is 5 times y.
x + y = -30
x = 5y
Plugging this in, we get:
5y + y = -30
y = -5
Since y = -5, we can plug this in, and see that x = -25.
Answer:
-5 & -25
Step-by-step explanation:
1st number=x
2nd number=5x
x+5x=-30
6x=-30
x=-5
5x=-25
So the numbers are -5 & -25
After Marshall's alarm went off, he spent 3/4 hr getting ready for school. He walked 1/6 hr to the bus stop, waited 1/12 hr, rode1/4 hr, and arrived at school at 8:30 A.M..What time did his alarm go off?
Answer:
7:15 am
Step-by-step explanation:
1. Add the times together by finding a common denominator
3/4 = 9/12
1/6 = 2/12
1/12 = 1/12
1/4 = 3/12
9/12 + 2/12 + 1/12 + 3/12 = 15/12
It took him 15/12 of an hour in total.
2. Convert to hours
15/12 = 1 3/12
3/12 = 1/4
1/4 of an hour is 15 minutes.
I took him a total of 1 hour and 15 minutes.
3. Subtract 1 hour and 15 minutes from 8:30
8:30 - 1:15 = 7:15
Find the value of x.
ASAP!!
Answer:
x = 80
Step-by-step explanation:
Tangent Chord Angle =1/2 Intercepted Arc
40 = 1/2 x
80 = x
Find the distance across the lake. Assume the triangles are similar.
85 m
X
у
20 m
60 m
Answer:
B. 255 m
Step-by-step explanation:
use similar triangle
L / 60 = 85 / 20
L = (85 * 60) / 20
L = 255 m
The distance across the lake will be 255 meters. Then the correct option is B.
What is the triangle?A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.
If the two triangles are similar, the ratio of the corresponding sides will be constant.
In an isosceles triangle, two angles and their opposite sides are equal.
The dimensions of the first triangle are L, 85, and y. And the dimensions of the second triangle are 60, 20, and x.
It is given that the triangles are similar.
Then the ratio of their corresponding sides will be
L / 60 = 85 / 20 = x / y
From first two terms, then the equation will be
L / 60 = 85 / 20
L / 60 = 4.25
L = 4.25 x 60
L = 255 m
The distance across the lake will be 255 meters.
Then the correct option is B.
More about the triangle link is given below.
https://brainly.com/question/25813512
#SPJ5
25 POINTS! FIRST TO ANSWER ****CORRECTLY**** GETS BRAINLIEST!
What number should be placed in the box to help complete the division calculation?
Numerical Answers Expected!
Answer:
The answer to your question is given below.
Step-by-step explanation:
To divide 2635 by 17 using long division method, we simply do the following:
2635 ÷ 17
17 can not go into 2. Therefore, we try 17 into 26, keeping 35 constant.
26 ÷ 17 = 1
Put the 1 on top.
Multiply 17 by 1
17 x 1 = 17
Subtract 17 from 26
26 – 17 = 9
Put the 9 in from of 35 to become 935
Next:
935 ÷ 17
17 can not go into 9. Therefore, we try 17 inot 93 keeping 5 constant.
93 ÷ 17 = 5
Put the 5 on top together with the 1 to become 15.
Multiply 17 by 5
17 x 5 = 85
Subtract 85 from 93
93 – 85 = 8
Put the 8 in front of 5 to become 85
Next:
85 ÷ 17
17 can not go into 8. Therefore, we try 85
85 ÷ 17 = 5
Put the 5 on top together with 15 to become 155
Multiply 17 by 5
17 x 5 = 85
Subtract 85 from 85
85 – 85 = 0
Since no number is remaining, we shall stop here.
Therefore,
2635 ÷ 17 = 155
Please attached photo for further details.
is the sum of any two numbers is greater than the larger of the two numbers?
Answer: Yes the sum of any two numbers is greater than the larger of the two numbers.
Step-by-step explanation:
Yes the sum of any two numbers is greater than the larger of the two numbers.
Let us assume that the two numbers are a and b and ab is the number.
a + b > a
b > a – a
b > 0
This therefore implies that b > 0.
This may however not be true when the value of b is zero(0) or a negative number.
what is 3/8 as a proportional ratio fraction
Can you please Solve for x
x - 3 = 27
add three to both sides
then x= 30
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Let's solve your equation step-by-step.
[tex]x-3=27[/tex]
Step 1: Add 3 to both sides.
[tex]x -3 + 3 = 27 +3[/tex]
[tex]x = 30[/tex]
So the answer is : [tex]x = 30[/tex]
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Hope this helped you.
Could you maybe give brainliest..?
❀*May*❀
Dell's coffee shop sells cappuccinos, mochas, and lattes. The table gives the number of servings of each beverage sold in a day.
Answer:
[tex]C. \left[\begin{array}{c}370\\228.5\\332\end{array}\right][/tex]
Step-by-step explanation:
Given the table of values for number of servings:
[tex]\begin{center}\begin{tabular}{ c c c c} & Small & Medium & Large\\ Cappuccino & 70 & 55 & 62 \\ Mocha & 42 & 34 & 39 \\ Latte & 59 & 63 & 47 \\ \end{tabular}\end{center}[/tex]
Cost of each coffee for a particular serving is same.
Cost of small serving = $1.50
Cost of medium serving = $2
Cost of large serving = $2.50
To find:
Matrix of revenue generated from sales of each coffee.
Solution:
Revenue generated by a particular coffee = Sum of (cost of each serving multiplied by number of particular servings)
So, revenue by Cappuccino = [tex]70 \times 1.5 +55 \times 2 + 62 \times 2.5 = \bold{\$370}[/tex]
So, revenue by Mocha = [tex]42\times 1.5 +34 \times 2 + 39 \times 2.5 = \bold{\$228.5}[/tex]
So, revenue by Latte = [tex]59\times 1.5 +63\times 2 + 47 \times 2.5 = \bold{\$332}[/tex]
So, the correct answer is:
[tex]C. \left[\begin{array}{c}370\\228.5\\332\end{array}\right][/tex]
Combine the radicals. 3√5-8√5+2√5
Answer: [tex]-3\sqrt{5}[/tex]
-3 times the square root of 5
=============================================
Explanation:
Let [tex]x = \sqrt{5}[/tex]
Replace all the root 5 terms with x and we go from
[tex]3\sqrt{5}-8\sqrt{5}+2\sqrt{5}[/tex]
to
[tex]3x-8x+2x[/tex]
From here, combine like terms to get
[tex]3x-8x+2x = -5x+2x = -3x[/tex]
and the last thing to do is replace the x with sqrt(5)
[tex]-3x = -3\sqrt{5}[/tex]
Meaning that,
[tex]3x-8x+2x = -3x[/tex]
[tex]3\sqrt{5}-8\sqrt{5}+2\sqrt{5} = -3\sqrt{5}[/tex]
prove the following
Answer:
Step-by-step explanation:
sin(180°-∅)=sin∅ as its in the 2nd quadrant
then tan(180°-∅)= -tan∅ as its in the 2nd quadrant and there only sin and cosec is positive and at last cos(180°-∅) = -cos∅ for the same reason
so by putting the values:
sin∅/sin∅ + -tan∅/tan∅ + -cos∅/cos∅ =1-1-1= -1
thanks ..
A weather balloon holds 2,600 cubic meters of helium. The density of helium is 0.1755 kilograms per cubic meter. How many kilograms of helium does the balloon contain?
Answer:
The balloon contains 456.3 kg of helium
Step-by-step explanation:
Density=mass / volume
Volume=2600 cubic meters of helium
Density=0.1755 kilograms per cubic meters
Mass=x
Find mass, x
Density=mass / volume
Mass=Density × volume
=0.1755 * 2600
=456.3 kg
The balloon contains 456.3 kg of helium
You are making a scaledrawing of a room using a scale of1 inch : 4 feet.a. The room is 14 feet by 18 feet. Find itsdimensions in the drawing.b. A sofa in the room has a length of 6 feet.Find the length of the sofa in thedrawing.c. You want to enlarge the scale drawing.How would you change the scale todouble the dimensions of the drawing?Explain.
Answer:
a. 3.5 inches by 4.5 inches
b. 1.5 inches
c. Divide 48 inches by 2 and multiply 1 inch by 12 to get a scale of 1 : 2
Step-by-step explanation:
A scale is a representative fraction showing the relationship between length on a drawing and actual length.
i.e scale = [tex]\frac{length on a drawing}{actual length}[/tex]
scale = 1 inch : 4 feet
a. The dimensions in the drawing can be determined as;
1 inch : 4 feet implies an inch on the drawing equates 4 feet on actual length.
[tex]\frac{14}{4}[/tex] = 3.5 inches
[tex]\frac{18}{4}[/tex] = 4.5 inches
Dimensions on drawing is 3.5 inches by 4.5 inches.
b. The length of the sofa is 6 feet, its length on the drawing is;
[tex]\frac{6}{4}[/tex] = 1.5 inches
c. To enlarge the scale so as to double the dimensions of the drawing, we have;
12 inches = 1 feet
4 feet = 4 × 12 = 48 inches
given scale = 1 inch : 48 inches
Thus, divide 48 inches by 2 and multiply 1 inch by 12.
scale = 12 inch : 24 inch
scale = 1 : 2
To double the dimensions of the drawing, the scale required is 1 : 2. This implies that a unit measure on the drawing is synonymous to 2 measures on the actual reading.
Please helpppp anyone fast
Answer:
2, 3, 4
Step-by-step explanation:
Since the question is asking which of the following are functions, lets define what it is first
Function: An equation for one answer for y for every x
This means that every x coordinate can have a y, but multiple x coordinates can have the same y coordinate
Because of this it has to be every one of them except the first one
Porfavor resolv erme esas preguntas o una :v porfis .El salón de mi clase de matemáticas mide 700 m2, cuánto mide 1/4 del salón? Cuánto mide 3/4 del salón? . Cuántos minutos son 3/5 de media hora? . Se necesitan 4/7 de litro de pintura para pintar un metro cuadrado de pared, si queremos pintar 2/5 de metro cuadrado de pared, cuánta pintura necesitaremos? . Si se necesitan 2/5 de naranja para hacer un vaso de jugo de naranja, cuántas naranjas necesitas para hacer 2 vasos y medio?
Answer:
Explained below.
Step-by-step explanation:
The question is:
Please answer me these questions or one: v please. My math class room is 700 m2, how much is 1/4 of the room? How long is 3/4 of the room? . How many minutes is 3/5 of a half hour? . It takes 4/7 of a liter of paint to paint a square meter of wall, if we want to paint 2/5 of a square meter of wall, how much paint will we need? . If it takes 2/5 of an orange to make a glass of orange juice, how many oranges do you need to make 2 and a half glasses?
(1)
Compute 1/4th of the math class room as follows:
[tex]=700\times\frac{1}{4}\\=175[/tex]
Thus, 1/4th of the math class room is 175 m².
(2)
Compute 3/4th of the math class room as follows:
[tex]=700\times\frac{3}{4}\\=525[/tex]
Thus, 3/4th of the math class room is 525 m².
(3)
Compute 3/5th of half an hour as follows:
[tex]=30\times \frac{3}[5}\\=18[/tex]
Thus, 3/5th of half an hour is 18 minutes.
(4)
A square meter of wall required 4/7 liter of paint.
Then 2/5 of a square meter will require,
[tex]=\frac{4}{7}\times \frac{2}{5}\\\\=\frac{8}{35}[/tex]
Thus, 8/35 liter of paint will be used to pain /5 of a square meter of the wall.
(5)
1 glass of orange juice can be made using 2/5 of an orange.
Then 2 and half glass will require,
[tex]=\frac{2}{5}\times 2\frac{1}{2}\\\\=\frac{2}{5}\times \frac{5}{2}\\\\=1[/tex]
Thus, 1 orange will be required to make 2 and half glass of orange juice.
Find the height of the triangle by applying formulas for the area of a triangle and your knowledge about
triangles.
9 in
9 in.
Xin
6 in
Answer:
8.5
Step-by-step explanation:
Applying pythagora's theorem,
hypotenuse^2 = opposite^2 + adjacent^2
but, hypotenuse = 9
opposite = X
adjacent = 1/2(base of triangle)= 1/2(6)
adjacent = 3
9^2 = X^2 + 3^2
X^2 = 81 - 9
X^2 = 72
X = 8.5
I need help It’s honors 7 math pls help
Answer:
411,600.000× 10^3 OR 4.11600000×10^8
Step-by-step explanation:
The expontent seems to be 3 so you move the decimal point over <this way 3
if it is 8 you move it over this way < 8
Answer:
411,600.000× 10^3 OR 4.11600000×10^8
Step-by-step explanation:
The expontent seems to be 3 so you move the decimal point over <this way 3
if it is 8 you move it over this way < 8
Please help! Urgent! Will mark Brainliest!
Answer:
[tex]x = 15[/tex]
Step-by-step explanation:
Since lines f and g are parallel, that means that the top angles will be the same, while the bottom angles will also be the same.
The angles of any quadrilaterals all add up to 360°, so we can create the equation like this:
[tex]3x + 3x + (6x + 45) + (6x+45) = 360[/tex]
Combine like terms so we can get a simpler equation:
[tex]6x + 12x + 90 = 360\\18x + 90 = 360[/tex]
Now let's solve for x!
[tex]18x + 90 - 90 = 360 - 90\\18x = 270\\18x\div18 = 270\div18\\x = 15[/tex]
So [tex]x = 15[/tex].
Hope this helped!
Answer:
15
Step-by-step explanation:
3x + 6x + 45 = 180
9x = 135
x = 15
{3, 6, 9, 12, 15, 18, 21, ...)
Answer:
Below
Step-by-step explanation:
5)
The sequence includes the terms 3,6,9,12,15.. and so on
Notice that each time we add 3.
The first term is 3.
We can see it in a different way
● 3 = 3×1
● 6 = 3×2
● 9 = 3×3
● 12 = 3×4
Let 1 be n. Notice what happens
● 3 = 3n
● 6 = 3 × (n+1)
● 9 = 3 × (n+2)
● 12 = 3 × (n+3)
So we can express it as.
● a1 = 3 × 1 =3
● a2 = 3×2 =6
● a3 = 3×3 = 9
So the third term is a3 wich is 9
● a6 = 3×6 = 18
So the sixth term is 18 .
■■■■■■■■■■■■■■■■■■■■■■■■■■
6)
the sequence is defined by:
● f(n-1) = -0.5 f(n)
Repalce n-1 with n and n with n+1
● f(n) = -0.5 f(n+1)
So to get a term you must multiply the next one by -0.5
The first term in the sequence is 120.
● 120 = -0.5 f(n+1)
● f(n+1) = 120/-0.5
● f(n+1) = -60
So the second term is -60
