Answer:
20 is the father's 20 is the son
Step-by-step explanation:
20+20=40
40/2=20
40-20=20
another way:
20:n= 40
40-20=20
20:20=40
Answer:
Step-by-step explanation:
let the age of son be x
x+x+20=40
2x=40-20
x=20/2
x=10
since age of a father is 20 more than his son's so,
x+20=father's age
10+20
30
therefore fathers age is thirty years and son age is 10 years
Suppose we want to choose 4 colors, without replacement, from 18 distinct colors.
(a) If the order of the choices is relevant, how many ways can this be done?
(b) If the order of the choices is not relevant, how many ways can this be done?
Answers:
(a) 73440(b) 3060=====================================================
Explanation for part (a)
Consider four slots labeled A,B,C,D.
We have
18 choices for slot A17 choices for slot B16 choices for slot C15 choices for slot DWe started at 18 and counted down until we filled the four slots. The countdown is because we cannot repeat a color. Multiply out those values to get the answer: 18*17*16*15 = 73440
You can use the nPr permutation formula as an alternative method
[tex]_nP_r = \frac{n!}{(n-r)!}[/tex]
in this case n = 18 and r = 4. The exclamation marks indicate factorial.
-----------------------------------
Explanation for part (b)
Let's say we had color labels A,B,C,... all the way up to R which is the 18th letter in the English alphabet. From those 18 letters, we can only pick four. Let's say we pick D,E,F,G.
Focusing solely on the set {D,E,F,G}, we only have one set and the order doesn't matter. So {D,E,F,G} is the same as {D,E,G,F}.
There are 4*3*2*1 = 24 ways to arrange those four items meaning that we'll need to divide the result of part (a) by 24 to get the result of part (b)
73440/24 = 3060
You could use the nCr combination formula to get the same result
[tex]_nC_r = \frac{n!}{r!(n-r)!}[/tex]
where n = 18 and r = 4 are the same from last time.
The connection between nPr and nCr is this
[tex]_nC_r = \frac{_nP_r}{r!}[/tex]
which can be rearranged into
[tex]_nP_r = r!*\left( _nC_r \right)[/tex]
these formulas are handy to help us go back and forth between nCr or nPr.
If the order of the choices is relevant, the number of ways of selecting 4 colors out of 18 distinct colors is 73440.
If the order of the choices is not relevant, the number of ways of selecting 4 colors out of 18 distinct colors is 3060.
What are combination and permutation?Combination is a way of selecting items from a collection where the order of arrangement is not relevant.
It is given by:
[tex]^nC_r[/tex] = n! / r! (n-r)!
Permutation is a way of selecting items from a collection where the order of the arrangement is relevant.
It is given as:
[tex]^nP_r[/tex] = n! / (n-r)1
We have,
Number of distinct colors = 18
Number of colors to be chosen = 4
The number of ways the four colors be chosen when the order is not relevant:
= [tex]^{18}C_4[/tex]
= 18! / 4! 14!
= 18 x 17 x 16 x 15 / 4 x 3 x 2
= 3060
The number of ways the four colors be chosen when the order is relevant:
= [tex]^{18}P_4[/tex]
= 18! / 14!
= 18 x 17 x 16 x 15
= 73440
Thus,
If the order of the choices is relevant, the number of ways of selecting 4 colors out of 18 distinct colors is 73440.
If the order of the choices is not relevant, the number of ways of selecting 4 colors out of 18 distinct colors is 3060.
Learn more about combination here:
brainly.com/question/2970011
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Which of the following are statistical questions? Select all that apply.
A.
How many goals does a high school soccer team score in each game?
B.
How long does it take a high school student to run a mile?
C.
What is the world record for the fastest time to run 1 mile?
D.
How many runs did the Georgetown Giraffes baseball team score last night?
Answer:
I think A and B
Step-by-step explanation:
• A statistical question is a question that has more than one possible answer ( and can be answered by collecting data) where there will be variability in the data. for instance an example would be " How old are the students in this room?"
• However a non statical question has only one answer for instance "How old are you?"
both a and b dont have specific answers because it's not talking about a specific high school students or a specific soccer team. i would guess those are correct, but using the information from above you can also see what you think! hope this helps :)
Handrail should be mounted 34 inches minimum and 38 inches maximum above ramps. Which inequality represents the required height?
Answer:
[tex]34 \leq x \leq 38[/tex]
Step-by-step explanation:
34 inches minimum
This means that x has to be at least 34, that is:
[tex]x \geq 34[/tex]
38 inches maximum
This means that x can be at most 38, that is:
[tex]x \leq 38[/tex]
Which inequality represents the required height?
The intersection of 34 minimum and 38 maximum is:
[tex]34 \leq x \leq 38[/tex]
Find the integration of (1-cos2x)/(1+cos2x)
Given:
The expression is:
[tex]\dfrac{1-\cos 2x}{1+\cos 2x}[/tex]
To find:
The integration of the given expression.
Solution:
We need to find the integration of [tex]\dfrac{1-\cos 2x}{1+\cos 2x}[/tex].
Let us consider,
[tex]I=\int \dfrac{1-\cos 2x}{1+\cos 2x}dx[/tex]
[tex]I=\int \dfrac{2\sin^2x}{2\cos^2x}dx[/tex] [tex][\because 1+\cos 2x=2\cos^2x,1-\cos 2x=2\sin^2x][/tex]
[tex]I=\int \dfrac{\sin^2x}{\cos^2x}dx[/tex]
[tex]I=\int \tan^2xdx[/tex] [tex]\left[\because \tan \theta =\dfrac{\sin \theta}{\cos \theta}\right][/tex]
It can be written as:
[tex]I=\int (\sec^2x-1)dx[/tex] [tex][\because 1+\tan^2 \theta =\sec^2 \theta][/tex]
[tex]I=\int \sec^2xdx-\int 1dx[/tex]
[tex]I=\tan x-x+C[/tex]
Therefore, the integration of [tex]\dfrac{1-\cos 2x}{1+\cos 2x}[/tex] is [tex]I=\tan x-x+C[/tex].
(Click on the picture to see question) please help me!
Hi there! Using one of the logarithmic property below:
[tex] \large \boxed{ log_{a}(b) = n \longrightarrow {a}^{n} = b}[/tex]
From the equation:
[tex] \large{ log_{2}(y) = x + 7}[/tex]
Therefore,
[tex] \large{ {2}^{x + 7} = y} \\ \large{y = {2}^{x + 7} }[/tex]
Answer
y = 2^(x+7) the second choice.150 round 2 decimal places
Answer:
[tex]150 = 150.00[/tex]
The midpoint of the coordinates (9, 11) and (7,8) is
Answer:
The midpoint: (8,9.5)
Step-by-step explanation:
((9+7)/2,(11+8)/2))
If p is directly proportional to q, and p = 40 when q = 15, find q when p = 64
What is the value of -(-9)?
Explain your reasoning.
Answer:
-(-9) is 9
Step-by-step explanation:
-(-9)
(when there are two negatives multiplyed with eachother, the product will be postive)
+ 9
+ 9 = 9
- ( - 9 ) =
( - 1 ) × ( - 1 × 9 ) =
( - 1 ) × ( - 1 ) × ( 9 ) =
( + 1 ) × 9 =
1 × 9 =
9
100 POINTS IF YOU GUESS RIGHT PLEASE HELP
Answer:
5 and 3Step-by-step explanation:
Let the numbers be x and y.
We have:
x + y = 8x - y = 2Sum the two and find x:
2x = 10x = 5Find y:
y = 5 - 2y = 3Let the numbers be a and b
a+b=8a-b=2Add both
2a=10a=5Put in first one
5+b=8b=3HELPP HELPPP ????pls
Answer:
B) the interquartile range of the data set is 2
Step-by-step explanation:
To find the interquartile range you have to subtract Q3-Q1. Which would be 3-1 and the answer is 2.
Hope this helped :)
Antonio is planning a birthday party for his daughter. SkateWorld charges a flat fee of $50 plus $3 per child. Roller Land charges $5 per child. If Antonio's daughter wants to invite 21 friends from school and five friends from her basketball team, which rink should Antonio use and how much would he save by doing so?
Answer:
skateworld
Step-by-step explanation:
26x3+50=128 aka skate worlds price
26x5=130 aka roller land price
Antionio should use skateworld and he would save 2$
Answer: SkateWorld. He saves $2
Step-by-step explanation:
SkateWorld:
21 *3 =63
5*3=15
63+15=78
78+50= 128
Roller Land:
21*5= 105
5*5=25
105+25=130
130-128= 2
Which expression has the same value as the one below? 87 + (-12)
Answer:
75
Step-by-step explanation:
Given data
First term= 87
Second term= -12
Hence,
87 + (-12)
open bracket
+*-= -
= 87 -12
=75
Therefore the equivalent is 75
HELP ME WITH THIS PLEASEEEEE? IM STUGGLING
Answer:
(x-5)(x+5)
Step-by-step explanation:
x^2 -25
We can rewrite this as the difference of squares
x^2 - 5^2
(x-5)(x+5)
Juan drank 3 quarts of water. Alfred drank 8 quarts. How many cups of water did they drink altogether?(no links will get brainliest)
Answer: 44 Us Cups
Step-by-step explanation:
find the value of x.
write an equivalent expression: −12(−2x+4y)
Answer:
24x-48y
hope this helps
have a good day :)
Step-by-step explanation:
Step-by-step explanation:
−12(−2x+4y) = 24x - 48y
______
Complete the comparison 5+4. A.9+1. B.10+0.C.5-4.D.15-4
Answer:
A.5+4<9+1
B. 5+4<10+0
C. 5+4>5-4
D. 5+4=15-4
Step-by-step explanation:
A. 9<10
B. 9<10
C. 9>1
D9=9
Answer:
A=10>5+4
B=10>5+4
C=1<5+4
D=11>5+4
Step-by-step explanation:
Solve each equation over the interval [0°, 360°). If a decimal approximation is necessary, round to four decimal places. cos 2x -cos x-2 = 0
Answer:earthy
Step-by-step explanation:vuinh
What is the perimeter of the triangle
Answer:
56 units
Step-by-step explanation:
add each side, you can get the hypotenuse using the formula a^2+b^2=c^2
maths question is here
9+92*12312
Answer:
it would be 101 i believe
Answer:
1,132,713
Step-by-step explanation:
9+ 92 * 12312
= 9 + 1,132,704
= 1,132,713
ABCD angles add up to 300⁰, what is the angle of B?
Answer:
I don't know im sorry I wish I could help
Answer:
75
Step-by-step explanation:
You know hat there is 4 angles. You want to divide 300 by 4 since that's the tal out of all 4 ofangles.When u divide, you 75.
This is what I would
ilang metro ang 1300 sentimetro?
a. 1metro
b. 13 metro
c. 130 metro
Answer:
1300 cm = 13 m
Step-by-step explanation:
We need to find meters in 1300 cm.
We know that,
1 m = 100 cm
1 cm = (1/100) m
It means,
[tex]1300\ cm=\dfrac{1300}{100}\ m\\\\=13\ m[/tex]
Hence, there are 13 m in 1300 cm.
Part A: Students from 4 towns attend a conference. Each town is assigned a number from 1 to 4. Drag yes or no next to the first sentence.
Yes or No
A number is drawn and replaced 6 times. Is this a fair way to pick 6 members to give each town representation? __________
Part B: What is the probability that Town 1 will have at least 1 representative after 6 number draws, to the nearest percent?
probability = __________ %
Answer:
Part A - No
Part B - 100 %
Step-by-step explanation:
Part A.
This is because, a fair chance requires that each member has the same probability of being picked.
Since there are 4 towns, a fair chance would be 1/4.That is, 1 out of every town.
Part B
The probability of at least 1 representative after 6 number draws is P(at least 1) = 1 - P(none from Town 1)
P(none from town 1) = 0
P(at least 1) = 1 - P(none from Town 1)
P(at least 1) = 1 - 0 = 1
In percentage 1 × 100 % = 100 %
EEE
What is the solution to the equation -3(h+5)+2 = 4(h+6)-9?
Oh=-4
Oh = -2
Oh = 2
Oh= 4
What is the area, in square units, of the parallelogram shown below?
21 s u
56 s u
63 s u
81 s u
Answer:
Area of parallelogram = 63 square units
Step-by-step explanation:
In the given parallelogram:
Height of parallelogram = 9 units
Base of parallelogram = 7 units
Find:
Area of parallelogram
Computation:
Using area of parallelogram;
Area of parallelogram = Height of parallelogram x Base of parallelogram
Area of parallelogram = 9 x 7
Area of parallelogram = 63 square units
Kate's dog was learning to balance a ball on his nose. The
first day he balanced the ball 6 out of 20 times; the second
day, 8 out of 25 times. Which day did he do better?
Answer:
The answer is the first day
Melissa has two coupons for shoes. Coupon A: Coupon B: 15% off of S41 shoes $10 rebate on S41 shoes Choose the coupon that gives the lower price. Then fill in the blank with the correct value.
Answer:22
Step-by-step explanation:
The complete sentence is
The price with coupon B is $10 less than the price with coupon A.
It depends on the original price of the S41 shoes.
Coupon A offers a 15% discount on S41 shoes, while Coupon B provides a $10 rebate on S41 shoes.
Let's assume the original price of the S41 shoes is P dollars.
Using Coupon A, the discounted price would be 85% of the original price = (0.85 * P) dollars.
Using Coupon B, the price after the $10 rebate = (P - $10) dollars.
Now, compare (0.85 * P) with (P - $10).
simplify the expression (0.85 * P) < (P - $10) as
0.85P < P - $10
0.85P - P < - $10
-0.15P < - $10
P > (- $10) / (-0.15)
P > $66.67
Therefore, if the original price of the S41 shoes is greater than $66.67, Coupon A (15% off) will give a lower price. If the original price is lower than $66.67, Coupon B ($10 rebate) will give a lower price.
Learn more about Inequality here:
https://brainly.com/question/20383699
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I need the answer. Please help.
===========================================================
Work Shown:
Use the tangent ratio
tan(angle) = opposite/adjacent
tan(B) = AC/AB
tan(61) = AC/1
tan(61) = AC
AC = tan(61)
AC = 1.80404775527142
AC = 1.8
The river is about 1.8 miles wide between points A and C.
Make sure your calculator is in degree mode. One way to check is to type in tan(45) and you should get 1.
Help please!!!!!!!!!!!!!!!
Answer:
-1, 5
Step-by-step explanation:
no really explanation, but its a graph and when u have agraph x goes before y. and the x in the middle of it is what its talking about and u can see the middle is on a 5 and a -1