Answers
Hey there! I'm happy to help!
QUESTION 100
Here, we are looking for the number of permutations. A permutation is the number of possible arrangements you can make from a given set of things (order matters). If you have 6 kids standing in alphabetical order in line, that is one permutation. If you do reverse alphabetical order, that is a different permutation.
We are asked to find the number of permutations using the given format:
[tex]_{n}P_{r}\\[/tex]
This is simply a representation of what we want to find. The P means we are looking for the number of permutations. The n is the total number of objects in the set (for example, if there were 26 kids we could choose from to make this 6 person line, n would be 26). The r is the number of things chosen from the set (in our line example, the r would be six because we are choosing 6 kids).
The formula for finding the number of permutations is [tex]\frac{n!}{(n-r)!}[/tex]. The ! is factorial, it means you multiply that number by every integer counting backwards towards 1. 6! is 6×5×4×3×2×1. There is an option to do this on your calculator, though.
Let's solve this problem.
[tex]_{5}P_{4}=\frac{5!}{(5-4)!}= \frac{120}{1} =120[/tex]
This means that there are 120 permutations.
QUESTION 101
Now we have a C. This is similar to permutations but with combinations order does not matter. With our line example, having the same six kids in alphabetical order is a different permutation than having it in backwards alphabetical order. With combinations, if you have those specific six kids, it is just one combination; the order does not matter.
The formula for combinations is [tex]\frac {n!}{r!(n-r)!}[/tex]. Let's plug in our numbers and solve for this.
[tex]_{8}C_{2}=\frac{8!}{2!(8-2)!} =\frac{8!}{2!(6!)}=\frac{40320}{1440} =28[/tex]
QUESTION 102
Quick note: 0! is equal to 1. I don't really know why but there's probably proof somewhere.
[tex]_{7}C_{0}=\frac{7!}{0!(7-0)!} =\frac{7!}{7!} =1[/tex]
And I believe you already have Question 103 figured out.
4!=4×3×2×1=24
Have a wonderful day! :D
Related Questions
Which statements are true about the estimation of decimal products? Check all that apply. Estimation gives an approximate answer. Estimation always results in a product greater than the exact answer. Estimation always results in a product less than the exact answer. Estimation can be done by rounding each decimal to the nearest whole number.
Answers
Step-by-step explanation: the answers are a and d
Answer:
a d
Step-by-step explanation:
got it right
The perimeter of a basketball court is 84 meters and the length is 6 meters longer than twice the width. What is the length and width
Answers
Answer:
length: 30 meters
width: 12 meters
Step-by-step explanation:
2(a+b) = 84
a = 2b + 6
a = length
b = width
then:
2((2b+6)+b) = 84
2b + 6 + b = 84/2
3b + 6 = 42
3b = 42 - 6
3b = 36
b = 36/3
b = 12
a = 2b + 6
a = 2*12 + 6
a = 24 + 6
a = 30
Check:
84 = 2(12+30)
84 = 2*42
A countrys population in 1991 was 147 million. In 1998 it was 153 million. Estimate the population in 2017 using exponential growth formula. Round your answer to the nearest million. P=Ae to the power kt
Answers
Answer:
171 millionStep-by-step explanation:
Given the exponential growth formula expressed as [tex]P = Ae^{kt}[/tex] where P is the countrys population and t is the time.
Initially in 1991, at t= 0, P = 147 million
[tex]P = Ae^{kt}\\147 = Ae^{k(0)}\\147 = Ae^0\\147 = A(1)\\A = 147[/tex]
If by 1998 it was 153 million, this means that the population is 153 million 7 years later i.e when t = 7, P = 153. On substituting into the formula to get the constant 'k';
[tex]P = Ae^{kt}\\153 = 147e^{k(7)}\\153 = 147e^{7k}\\153/147 = e^{7k}\\e^{7k} = 1.041\\Taking \ ln \ of \ both \ sides\\lne^{7k} = ln 1.041\\7k = 0.04018\\k = 0.04018/7\\k = 0.00574[/tex]
To estimate the population in 2017, to number of years from 1991 to 2017 is 26 years. Hence we are to find the value of P given t = 27, A = 147 and k = 0.00574
[tex]P = Ae^{kt}\\P = 147e^{0.00574*26}\\P = 147e^0.14924\\P = 147*1.16095\\P = 170.659[/tex]
Hence the population in 2017 using exponential growth formula to the nearest million is 171 million.
Help please, w-5-4= -8-6w+8w?
Answers
Answer:
w = -1
Step-by-step explanation:
w-5-4= -8-6w+8w ⇒ simplifyw - 9 = - 8 + 2w ⇒ add 9 - 2w to both sidesw - 2w = - 8 + 9 ⇒ simplify-w = 1 ⇒ multiply both sides by -1w = -1 ⇒ answerAnswer:
[tex]\Huge \boxed{w=-1}[/tex]
Step-by-step explanation:
[tex]w-5-4= -8-6w+8w[/tex]
Combining like terms.
[tex]w-9= -8+2w[/tex]
Adding -w and 8 to both sides.
[tex]-9+8=2w-w[/tex]
[tex]-1=w[/tex]
Evaluate. 5(−6)= ________
Answers
The evaluation of the numeric expression is:
5(−6) = -30
How to evaluate numeric expression?A numeric expression is a mathematical statement that involves only numbers and one or more operation symbols.
Examples of operation symbols are addition, subtraction, multiplication and division. It can also be expressed in the radical symbol (the square root symbol) or the absolute value symbol.
We can evaluate 5(−6) as follow:
5(−6) = 5 * (-6)
= -30
Learn more about numeric expression on:
https://brainly.com/question/4344214
#SPJ6
What value of x will make the angle between the pottery and the arrowhead measure 57
Answers
Answer:
x = 9
Step-by-step explanation:
Take the angle of LOJ (3x) and JOK (2x+12).
LOJ + JOK = LOK.
LOK = 57.
So, 3x + 2x + 12 = 57
3x + 2x = 5x
5x + 12 = 57
57 - 12 = 45
5x = 45
x= 9
What is the solution to this equation?
X-7 = 18
A. X = 25
B. x= 35
C. x = 11
D. X = 9
Answers
Answer:
A
Step-by-step explanation:
x - 7 = 18
Adding 7 to both sides (to get rid of the -7 on the left side) gives us:
x - 7 + 7 = 18 + 7
x = 25
Answer:
25 is the correct answer
Step-by-step explanation:
i got it right on the test
Using one complete sentence give a mathmatical definition of zero
Answers
Answer:
Zero is an integer which is indicated by the symbol 0 in numbers and it is used to indicate that the count of an item when there are non of the item present which is one of the reasons zero along with the fact that it is the number between positive and negative numbers, why it is not associated with a positive or negative sign.
Step-by-step explanation:
A number which is not zero is said to be a non-zero number and the roots of a function is known as the zeros of the function.
Please help, I really would love it
Answers
Answer:
A,C, and D I believe.
Step-by-step explanation:
In the problem below, AB, CD, and EF are two-digit numbers, where A, B, C, D, E and F represent distinct digits from 1 to 9. Is F prime? A B + C D E F B and D are consecutive integers. C = 8.
Answers
Answer:
When both the conditions hold true, F is prime.
Step-by-step explanation:
AB, CD, and EF are two-digit numbers, where A, B, C, D, E and F represent distinct digits from 1 to 9.
AB
+ CD
--------
EF
1st condition, B and D are consecutive.
Adding B and D gives us F.
Possible values can be (F being the unit value after adding not considering the carry over):
B + D = F
1+2=3
2+3=5
3+4=7
4+5=9
5+6=1
6+7=3
7+8=5
8+9=7
Here F is not prime (because 9 is not prime).
Now, let us consider the 2nd condition as well.
i.e. C = 8
For the following
AB
+ CD
--------
EF
C is 8 then A must be 1 because any value other than 1 for A will make the sum of A and C greater than 9 and there will be a carry which is not the case here.
So, E = 8 + 1 = 9
Now, B and D are consecutive and can not be 1, 8 or 9.
So, possible values are:
B + D = F
2 + 3 = 5
3 + 4 = 7
Here F is prime.
So, when both the conditions hold true, F is prime.
Carrie spent 1/4 of her allowance on a shirt, 1/3 of her allowance on a skirt, and $8 on a belt. If she spent $22 in all, how much was Carrie’s allowance?
Answers
Answer:
$24
Step-by-step explanation:
1/4x + 1/3x + 8 = 22
1/4x + 1/3x = 7/12x
7/12x + 8 = 22
22 - 8 = 14
7/12x = 14
14/ 7/12
x = 24
A group of hikers keep track of their elevation as a function, E, to determine the
different elevation levels as they travel along the trail in Possum Kingdom State
Park. E(d) represents the height of elevation in feet where d is the distance the
hiker travels along the trail. What would be the most appropriate domain for the
function?
{-1,-2,0,1,2,3)
O ,-1,0, 1, 2, 3, ...)
{0,1,2,3,4,...}
C-3,0,1,2,3...
)
Answers
The mass of the part of a metal rod that lies between its left end and a point x meters to the right is 3x^2 kg. Find the linear density when is 1 m, Where is the density the highest? The lowest?
Answers
Answer
6 kg/m
Step-by-step explanation:
The linear density is said to give the way the mass is changing it's position and it's a derivatives of mass m here which is differenciated with respect to x position
Given
mass m = 3x^2.
Density ρ= dm/dx =6x
Then if we substitute x=1 into above expresion we have
ρ(1) =6 Kg/m
ρ= 6Kg/m
Hence this is how fast is the mass changing at that position.
What is the multiplicative inverse of -0.7?
Answers
Answer:
The multiplicative inverse of -0.7 is -1/0.7
hope it helps
. Find the measure of an angle which is 46° less than its complement
Answers
Answer:
Complementt angle = 44°
Step-by-step explanation:
Given:
One angle = 46°
Find:
Complementt angle
Computation:
In complement angle
∠A + ∠B = 90°
46° + ∠B = 90°
∠B = 90° - 46°
∠B = 44°
Complementt angle = 44°
Given f(x) = 3x - 40. If f(x)= 8, what is the value of x?
A. - 96
B. -16
C. 16
D. -32/3
E. 32/3
Answers
Answer:
C
Step-by-step explanation:
Given
f(x) = 3x - 40 and f(x) = 8 , then equate the right sides, that is
3x - 40 = 8 ( add 40 to both sides )
3x = 48 ( divide both sides by 3 )
x = 16 → C
Someone help!!! Tyyy
Answers
Answer:79°
Step-by-step explanation:
Given the 124° angle, the other angle formed by that line and the top side of the square must be 56°, as they are supplementary angles (they must add up to 180°). This means that the angle formed by that same line and the bottom side of the square is also 56° since it is a corresponding angle and the top and bottom sides of a square are parallel. The angle that a diagonal of a square forms with the sides of a square is always 45°.
So now we have a triangle (in red in my diagram) with angles of 45°, 56°, and x°. The sum of the angles of a triangle must always equal 180°, so we solve for x:
56 + 45 + x = 180
x = 180 - 56 - 45 = 79
So angle x must be 79°.
Please help me with this Operation: (-17+4+1-6)÷(-3)×(-1)?
Answers
Answer:
-6
Step-by-step explanation:
(-17+4+1-6)=-18
-18/-3=6
6*-1=-6
Answer:
-6
Step-by-step explanation:
(-17+4+1-6)÷(-3)×(-1)
PEMDAS
Parentheses first
(-17+4+1-6)÷(-3)×(-1)
Add and subtract inside the left parentheses
(-18)÷(-3)×(-1)
Multiply and divide from left to right
6 * -1
-6
anyone know the answers to this ?!
Answers
Answer:
Hey there!
3 x 5/4 = 3 x 5 ÷ 4 = 5 x 3 ÷ 4
5 x 4/3 = 5 x 4 ÷ 3 = 4 x 5 ÷ 3
4 x 3/5 = 4 x 3 ÷ 5 = 4 x 3 ÷ 5
Hope this helps :)
Sue has 18 sweets.
Tony also has 18 sweets.
Sue gives Tony x sweets.
Sue then eats 5 of her sweets.
Tony then eats half of his sweets.
Write expressions for the number of sweets Sue and Tony now have.
Help pleaseeeeee
Answers
Answer:
sue = 18
tony = 18
sue = 18 - x
tony = 18 + x
sue = 18 - x - 5
tony = (18 + x) / 2
sue = 13 - x
tony = (18 + x) / 2
Step-by-step explanation:
You Simplify The Equation by using PEMDAS
P: Parentheses
E: Exponents
M: Multiplication
D: Division
A: Addition
S: Subtraction
An economist wishes to conduct a survey in two different cities in the same county to determine the difference in the proportions of residents who believe that economy is improving under president Trump. A 99% confidence interval is to be constructed for the difference between the proportions. If the sample sizes for both cities are to be equal, find the minimum sample size needed for each city so that the margin of error not to exceed 6%.
Answers
Answer:
The minimum sample size needed for each city = 922
Step-by-step explanation:
From the information given:
the objective is to find the minimum sample size needed for each city so that the margin of error not to exceed 6%.
If we take a look at the question very well:
we are only given the confidence interval of 99% and the margin of error of 6%
we were not informed or given the value or estimate of any proportions>
so we assume that:
[tex]p_1 =q_ 1= p_2 = q_2 = 0.5[/tex]
At confidence interval of 0.99 , the level of significance = 1 - 0.99 = 0.01
The critical value for [tex]z_{\alpha/2} = z_{0.01 /2}[/tex]
= [tex]z_{0.005}[/tex] = 2.576
The minimum sample size needed can be calculated by using the formula :
[tex]n = \dfrac{z^2_{\alpha/2}}{E^2}(p_1q_1+p_2q_2)[/tex]
[tex]n = \dfrac{2.576^2}{0.06^2}((0.5 \times 0.5)+(0.5 \times 0.5))[/tex]
[tex]n = \dfrac{6.635776}{0.0036}(0.25+0.25)[/tex]
[tex]n =1843.271 \times (0.5)[/tex]
n = 921.63
n [tex]\simeq[/tex] 922
∴ The minimum sample size needed for each city = 922
In which number is the value of the 7 ten times the value of 7 in the number 1,273?
Answers
Answer:
1723
Step-by-step explanation:
10 x 70=700
Answer:
1723
Step-by-step explanation:
Which series represents this situation?
1 + 1 · 7 + 1 · 72 + . . . 1 · 76
1 + 1 · 7 + 1 · 72 + . . . 1 · 77
7 + 1 · 7 + 1 · 72 + . . . 1 · 76
7 + 1 · 7 + 1 · 72 + . . . 1 · 77
Answers
Answer:
1 + 1 · 7 + 1 · 72 + . . . 1 · 76
Step-by-step explanation:
bc
Answer:
1 + 1 · 7 + 1 · 72 + . . . 1 · 76
Step-by-step explanation:
Hope this helps!
Evaluate (-B)2 for A = 5, B = -4, and C = 2.
16
0 -16
Answers
Answer:
[tex] \boxed{ \boxed{ \bold{ \sf{16}}}}[/tex]Step-by-step explanation:
Given , value of b = -4
To find : ( - b )²
plug the value of b
⇒[tex] \sf{( - {( - 4))}^{2} }[/tex]
we know that ,
[tex] \sf{( - ) \times ( - ) = ( + )}[/tex]
⇒[tex] \sf{ {4}^{2} }[/tex]
Evaluate the power
⇒[tex] \sf{16}[/tex]
Hope I helped!
Best regards!!
please help on 13 and 14
Answers
Answer:
13) The planes ABF and FHG are perpendicular
14) Segments Ab and CD are parallel.
Step-by-step explanation:
13)
Planes ABF and FHG are perpendicular (they intersect along side EF)
14)
In order to find out about the segments AB and CD, let's use the formula for the slope that joins any two points [tex](x_1,y_1)\,\,\&\,\,(x_2,y_2)[/tex] on the plane:
[tex]slope=\frac{y_2-y_1}{x_2-x_1}[/tex]
Therefore, given:
A = (-3, 2)
B = (1, 4)
C = (-3, -1)
D = (1, 1)
we have for segment AB the following slope:
[tex]slope_{AB}=\frac{4-2}{1+3} =\frac{2}{4} =\frac{1}{2}[/tex]
and for segment CD the following slope:
[tex]slope_{CD}=\frac{1+1}{1+3} =\frac{2}{4} =\frac{1}{2}[/tex]
Since they show the same slope, these two segments are parallel.
what is the equivelent expression to 13a - 8a + 9b - 4b
Answers
Answer:
5a + 5b
Step-by-step explanation:
13a - 8a + 9b - 4b =
Combine like terms. 13a and -8a are like terms and can be combined.
9b and -4b are like terms and can be combined.
= 5a + 5b
Answer:
5a+5bStep-by-step explanation:
[tex]13a-8a+9b-4b\\\mathrm{Add\:similar\:elements:}\:13a-8a=5a\\=5a+9b-4b\\\mathrm{Add\:similar\:elements:}\:9b-4b=5b\\=5a+5b[/tex]
what is the answer to |3x-4|=|3x-5|
Answers
Answer:
i think this is the answer
Answer:
the answer is [tex]\frac{3}{2}[/tex] or 1.5 or 1[tex]\frac{1}{2}[/tex]
Step-by-step explanation:
Solve. Write your answer in the simplest form using integers, fractions, and natural logarithms. 9=ex
x=
Thanks!
Answers
Answer:
x = ln9
Step-by-step explanation:
Using the rule of logarithms
log [tex]x^{n}[/tex] = nlogx , lne = 1
Given
[tex]e^{x}[/tex] = 9 ( take the ln of both sides )
ln[tex]e^{x}[/tex] = ln9, thus
xlne = ln9, that is
x = ln9
Anyone help me here please!!!!
Answers
Answer:
here is a formulae
cos2A= 2cos square a -1
Step-by-step explanation:
as given cos A= 1/2 (a+1/a)
by simplifying
cosA =a²+1/2a
now by following the formulae
cos2A = 2cos²A-1
=2(a²+1/2a)² -1
=2(a⁴+2a²+1/4a²)-1
=a⁴+2a²+1/2a² -1
=a⁴+2a²+1-2a²/2a²
=a⁴+1/2a²
=1/2 (a⁴+1/a²)
=1/2(a⁴/a²+1/a²)
=1/2(a²+1/a²)
{proved}
please mark me as a brainilist...plzzz
thank uuu
Answer: see proof below
Step-by-step explanation:
Use the Double Angle Identity: cos 2A = 2cos²A - 1
Proof LHS → RHS
Given: [tex]\cos A=\dfrac{1}{2}\bigg(a+\dfrac{1}{a}\bigg)[/tex]
LHS: cos 2A
Double Angle Identity: 2(cos²A) - 1
[tex]=2\bigg(\dfrac{1}{2}\bigg(a+\dfrac{1}{a}\bigg)^2\bigg)-1[/tex]
Simplify: [tex]2\bigg(\dfrac{1}{4}\bigg(a^2+2+\dfrac{1}{a^2}\bigg)\bigg)-1[/tex]
[tex]=\dfrac{1}{2}\bigg(a^2+2+\dfrac{1}{a^2}\bigg)-1[/tex]
[tex]=\dfrac{1}{2}a^2+1+\dfrac{1}{2a^2}-1[/tex]
[tex]=\dfrac{1}{2}a^2+\dfrac{1}{2a^2}[/tex]
Factor: [tex]=\dfrac{1}{2}\bigg(a^2+\dfrac{1}{a^2}\bigg)[/tex]
[tex]\dfrac{1}{2}\bigg(a^2+\dfrac{1}{a^2}\bigg)=\dfrac{1}{2}\bigg(a^2+\dfrac{1}{a^2}\bigg)\quad \checkmark[/tex]
Can y’all help me on this I just don’t understand it’s find su and m is the midpoint
Answers
Answer:
SU = 70
Step-by-step explanation:
First, we need to find the value of x. Since M is the midpoint of SU, that means that SM = MU, therefore:
x + 15 = 4x - 45
15 = 3x - 45
60 = 3x
x = 20
We know that SU = SM + MU = (x + 15) + (4x - 45) = 5x - 30 and that x = 20 so SU = 5x - 30 = 5 * 20 - 30 = 100 - 30 = 70.