Answer:
[tex]18[/tex].
Step-by-step explanation:
Start by considering the two "[tex]\verb!P![/tex]"'s as being different from one another. That way, all five letters in this word would be distinct. With this assumption, the number of arrangements would be [tex]\left(\genfrac{}{}{0}{}{2}{1}\right) = 2[/tex] times that of the actual value.
Start by fixing the first and the last letter since they come with special requirements.
There are [tex]2[/tex] choices for the first letter (the vowel: [tex]\verb!A![/tex] and [tex]\verb!E![/tex].)
Under the assumption that the two "[tex]\verb!P![/tex]"'s are distinct, there would be [tex]3[/tex] choices for the last letter ([tex]\verb!L![/tex] and the two
After choosing the first and the last letters, there would be [tex](5 - 1 - 1) = 3[/tex] choices for the second letter, [tex](3 - 1) = 2[/tex] choices for the third, and [tex](2 - 1) = 1[/tex] for the fourth.
Thus, under the assumption that the two "[tex]\verb!P![/tex]"'s are distinct, there would be [tex](2 \times 3) \times (3 \times 2 \times 1) = 36[/tex] ways to choose the new word. Since this assumption doubles the number of arrangements, dividing the [tex]36[/tex] by [tex]\left(\genfrac{}{}{0}{}{2}{1}\right) = 2[/tex] would give the actual number of arrangements:
[tex]\begin{aligned}\frac{36}{\genfrac{(}{)}{0}{}{2}{1}} = \frac{36}{2} = 18\end{aligned}[/tex].
[tex]\begin{aligned}& 1 && \verb!APPEL!\\& 2 && \verb!APLEP!\\& 3 && \verb!APEPL!\\& 4 && \verb!APELP!\\& 5 && \verb!ALPEP!\\& 6 && \verb!ALEPP!\\& 7 && \verb!AEPPL!\\& 8 && \verb!AEPLP!\\& 9 && \verb!AELPP!\\& 10 && \verb!EAPPL!\\& 11 && \verb!EAPLP!\\& 12 && \verb!EALPP!\\& 13 && \verb!EPAPL!\\& 14 && \verb!EPALP!\\& 15 && \verb!EPPAL!\\& 16 && \verb!EPLAP!\\& 17 && \verb!ELAPP!\\& 18 && \verb!ELPAP!\end{aligned}[/tex].
What is the nth term rule of the quadratic sequence below?
8
,
16
,
26
,
38
,
52
,
68
,
86
,
.
.
.
The [tex]nth[/tex] term rule of the quadratic sequence will be [tex]n^2+5n+2[/tex] .
What is quadratic sequence ?Quadratic sequences are sequences that include [tex]nth[/tex] term. They can be identified by the fact that the differences between the terms are not equal, but the second differences between terms are equal.
Quadratic sequence [tex]=an^2+bn+c[/tex]
Here [tex]a,b,c[/tex] are constant and [tex]n[/tex] is the position of term.
First difference [tex]= 3a+b[/tex]
Second difference [tex]=2a[/tex]
We have,
Quadratic sequence [tex]8,16,26,38,52,68,86,....[/tex]
Quadratic sequence [tex]=an^2+bn+c[/tex]
so,
For [tex]n=1[/tex];
[tex]8=an^2+bn+c[/tex]
[tex]8=a+b+c[/tex] [tex]........(i)[/tex]
For [tex]n=2[/tex];
[tex]16=4a+2b+c[/tex] [tex]........(ii)[/tex]
For [tex]n=3[/tex];
[tex]26=9a+3b+c[/tex] [tex]........(iii)[/tex]
Now,
Subtract equation [tex](i)[/tex] from [tex](ii)[/tex]
we get,
[tex]8=3a+b[/tex] [tex]........(iv)[/tex]
Subtract equation [tex](ii)[/tex] from [tex](iii)[/tex] we get,
[tex]10=5a+b[/tex] [tex]........(v)[/tex]
Subtract equation [tex](iv)[/tex] from [tex](v)[/tex] we get,
[tex]2=2a[/tex] (This is second difference mentioned above)
[tex]a=1[/tex]
Putting [tex]a=1[/tex] in [tex](iv)[/tex]
⇒[tex]b=5[/tex]
Now putting values of [tex]a[/tex] and [tex]b[/tex] in equation [tex](i)[/tex]
[tex]8=1+5+c[/tex]
[tex]c=2[/tex]
Now, putting values of [tex]a[/tex] , [tex]b[/tex] and [tex]c[/tex] in,
Quadratic sequence [tex]=an^2+bn+c[/tex]
we get,
[tex]nth[/tex] term rule [tex]=n^2+5n+2[/tex]
Hence, we can say that the [tex]nth[/tex] term rule of the quadratic sequence will be [tex]n^2+5n+2[/tex].
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4. What are the last TWO DIGITS of 2^2017
a Explain how you found the last 2 digits of 2^2017
b. Show how you found the last 2 digits of 2^2017
Compute 2²⁰¹⁷ modulo 100.
From the given table,
2²² ≡ 2⁴² ≡ 2⁶² ≡ 4 (mod 100)
and we have
2017 = 32 • 62 + 33
62 = 1 • 42 + 20
Then
2²⁰¹⁷ ≡ (2⁶²)³² • 2³³ (mod 100)
2²⁰¹⁷ ≡ 4³² • 2³³ (mod 100)
2²⁰¹⁷ ≡ (2²)³² • 2³³ (mod 100)
2²⁰¹⁷ ≡ 2⁶⁴ • 2³³ (mod 100)
2²⁰¹⁷ ≡ 2⁶² • 2²² • 2¹³ (mod 100)
2²⁰¹⁷ ≡ 4² • 2¹³ (mod 100)
2²⁰¹⁷ ≡ (2²)² • 2¹³ (mod 100)
2²⁰¹⁷ ≡ 2⁴ • 2¹³ (mod 100)
2²⁰¹⁷ ≡ 2¹⁷ (mod 100)
and from the table, we get
2²⁰¹⁷ ≡ 2¹⁷ ≡ 72 (mod 100)
r^2 - 8r - 22 = 6 solve for r
Answer:
-34
Step-by-step explanation:
r^2 - 8r - 22 ( R = 6)
6^2 =36 (8r = 8*6=48)
36 - 48 = -12
-12 - 22 = -34
The angles of a triangle are in the ratio 2 : 3 : 4 . find the angles of the triangle .
don't give unwanted ans to get the points
well explained ans needed !!
spammers and plagiarism = reported
thx !!
[tex]\pink{Answer}[/tex]
The measure of ∆a = 2x The measure of ∆b = 3x The measure of ∆c = 4x[tex]\\ \sf\longmapsto2x + 3x + 4x = 180 \\ [/tex]
[tex]\\ \sf\longmapsto9x = 180 = > x = 20[/tex]
[tex]\\ \sf\longmapsto \: a = 2x = 2 \times 2 0 = 4 0 [/tex]
[tex]\\ \sf\longmapsto \: b \: = 3x = 3 \times 20 = 60[/tex]
[tex]\\ \sf\longmapsto \: c = 4x = 4 \times 20 = 80[/tex]
hence , angles of the triangle are 40 , 60 and 80
The angles of a triangle are in the ratio 2 : 3 : 4 . find the angles of the triangle .
Answer:-40° , 60° and 80°
Explanation:-We know that sum of all the angles of a triangle adds to 180° .
Let the angles be 2x , 3x and 4x
Now,
=> 2x + 3x + 4x = 180°
=> 9x = 180°
=> x = 180/9
=> x = 20°
(The value of x is 20)
2x = 2 × 20 = 40°3x = 3 × 20 = 60°4x = 4 × 20 = 80°If a = 8 and b = 36 calculate the value of a^(1/3) b^(-3/2)
Answer:
[tex]\frac{1}{108}[/tex]
Step-by-step explanation:
Using the rules of exponents
[tex]a^{\frac{m}{n} }[/tex] = [tex]\sqrt[n]{a^m}[/tex]
[tex]a^{-m}[/tex] = [tex]\frac{1}{a^m}[/tex]
[tex]a^{\frac{1}{3} }[/tex] × [tex]b^{-\frac{3}{2} }[/tex] ← substitute a = 8 and b = 36
= [tex]8^{\frac{1}{3} }[/tex] × [tex]36^{-\frac{3}{2} }[/tex]
= [tex]\sqrt[3]{8}[/tex] × [tex]\frac{1}{36^{\frac{3}{2} } }[/tex]
= 2 × [tex]\frac{1}{(\sqrt{36})^3 }[/tex]
= 2 [tex]\frac{1}{6^3}[/tex]
= 2 × [tex]\frac{1}{216}[/tex]
= [tex]\frac{1}{108}[/tex]
expess 756,000,000 in a scientific notation
Step-by-step explanation:
756000000 = 7.56×10⁸.
hope this helps you.
Answer:
7.56 x10^8
.......................................
What is the coefficient of the term 5/3 xy?
A. 5xy
B. 5/3
C. 5
D. 1/3
find the dimensions of the right circular cylinder of maximum volume that can be inscribed in a sphere of radius a
Answer:
d.
took the test
Step-by-step explanation
Help u guys plssss number 8
Answer:
27
Step-by-step explanation:
Note : -
That square like symbol at the intersection of two lines is 90°.
( 4x - 18 )° and 90° are corresponding angles.
Corresponding angles are equal since lines
a & b are parallel.
4x - 18 = 90
4x = 90 + 18
4x = 108
x = 108 / 4
x = 27
Need some help for Exponents.
1) Five squared
2) Eight to the 5th power
3) Nine cubed
4) 2 x 2 x 2 x 2
5) 7 x 7 x 7 x 7 x 7 x 7
6) 2.3 x 2.3
Find the value of each of the following:
7) 54
8) 132
9) (1.2)2
10) 180
11) 10002
12) 72 x 70
Critical Thinking Applications
13) Mali bought a new car. She drove 63 miles the first month and 64 miles the second month. How much further did she drive the second month? Explain each step.
14) Create an application problem similar to the one above. Solve your problem. Explain each step.
15) In your own words, write three or four sentences explaining what exponents are and how they are used in math.
16) Create and solve 5 problems using exponents.
Answer:
1) 25
2) 32,768
3) 729
4) 16 or 2^4
5) 117,649 or 7^6
6) 5.29 or 2.3^2
Not sure what 7-12 mean
13) 1 mile 64-63=1
14) Mali bought a new car. She drove 63 miles the first month and 100 the second month. How much further did she drive the second month? Explain each step. 37 miles 100-63=37
15) An exponet is a number raised to a power, which means that number times itself that many times. It is used because it's alot easier to go 7^6 than 7x7x7x7x7x7.
16) 8^5= 32,768 6^6= 46,656 5^7= 78,125 5^5= 3,125 4^10= 1,048,576
Step-by-step explanation:
Given: 3x < -6.
Choose the solution set.
{x | x > -2}
{x | x < -2}
{x | x > 2}
{x | x < 2}
Answer:
First divide 3 on both sides to get x by itself, now you have x < -2.
Step-by-step explanation:
Hope this helps :)
Determine the solution and the reasoning that justifies the solution to the systems of equations.
O (2,7), because this point is true for both equations
O (4, -6), because this point lies only on one of the two lines
(4, -6), because this point makes both equations true
O (2,7), because the lines intersect the x-axis at these points
Answer:
A or CStep-by-step explanation:
The system is not given to give exact answer.
Possible solution is:
A. (2,7), because this point is true for both equations
Yes, same point lies on both lines, it is their intersectionB. (4, -6), because this point lies only on one of the two lines
No, this is not a solution to both equationsC. (4, -6), because this point makes both equations true
Yes, same point lies on both lines, it is their intersectionD. (2,7), because the lines intersect the x-axis at these points
No, this is not confirming any solutionsimplify by combining like terms -(m+n)+2 (m-3n)
-(m+n)+2(m-3n)
-m+n+2m-6n
-m+2m+n-6n
m-5n
Answer:
m -7n
Step-by-step explanation:
-(m+n)+2 (m-3n), distribute in the first parenthesis the -1 and in the second parentheses the 2
-m -n + 2m -6n , group like terms
-m + 2m -n -6n , combine like terms
m -7n
Identify the indicated sum for the geometric series.
S, for 3 - 6 + 12 – 24 + .....
Answer:
Here,
3
,
(
−
6
)
,
12
,
(
−
24
)
,
...
is the geometric sequn.
w
h
e
r
e
,
1
s
t
t
e
r
m
=
a
1
=
3
and
common ratio
r
=
−
6
3
=
12
−
6
=
−
24
12
=
−
2
and
S
9
=
?
⇒
n
=
9
We know that,
The sum of first n term of Geometric series is :
S
n
=
a
1
(
r
n
−
1
)
r
−
1
Putting ,
a
1
=
3
,
r
=
−
2
and
n
=
9
S
9
=
3
[
(
−
2
)
9
−
1
]
(
−
2
)
−
1
∴
S
9
=
3
[
−
512
−
1
]
−
3
⇒
S
9
=
3
(
−
513
)
−
3
⇒
S
9
=
513
Step-by-step explanation:
Answer:
Step-by-step explanation:
c.r. r=-6/3=-2
[tex]S_{n}=3\frac{(-2)^n-1}{-2-1} =-(-2)^n+1\\let~n\rightarrow \infty\\then S_{\infty} \rightarrow \infty~or~ -\infty[/tex]
answer and please show work.
A local little league has a total of 60 players ,80% of whom are right handed how many right handed players are there?
. Add the following. Answer in feet and inches. a) (3 ft. 8 in) + (4 ft. 9 in)
Answer:
8 ft. 5 in.
Step-by-step explanation:
First, let's change everything to inches
[] 3 ft. 8 in -> 3 * 12 = 36, 36 + 8 = 44 inches
[] 4 ft. 9 in -> 4 * 12 = 48, 48 + 9 = 57 inches
Now, we can add
44 + 57 = 101 inches
Last, we will simplify
101 -> 8 feet and 5 inches
Have a nice day!
I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)
- Heather
Please help! It’s due today
Solve: 5|9 – 3x|– 7 = 38
Answer:
x = 0
Step-by-step explanation:
A you-pick blueberry farm offers 6 lbs of blueberry for $16.50.
Sketch a graph of the relationship between cost and pounds of blueberries
Answer:
Step-by-step explanation:
Lol hi
Hector watched
1
4
of a movie in the morning, and he watched some more at night. By the end of the day, he still had
2
3
of the movie left to watch. How much of the movie did Hector watch at night?
Answer:
how watched 3/4 of the movie
Step-by-step explanation:
I know this because 2 is more then half of 3 and 3 is more then half of 4 so you can come to a conclusion that he watched a total of 3/4 and 2/4 at night.
P.S when ever using a fraction when typing like 1/4 instead of doing
1
4
do 1/4
What is the value of y?
Answer:
40°
Step-by-step explanation:
We know that a triangle is equal to 180°
Since one angle is 50° we can figure out that the rest of the angles are equal to 130° (180° - 50°)
If we use 40° then 2·(40°) = 80°
and the second angle is 40° + 10° = 50°
if we add all the angles (80° + 50° + 50°) we get 180° which is correct.
Gemma made 106 beaded necklaces . Leah made 145 beaded necklaces.
At a recent craft fair, Gemma sold each of her necklaces for $14. Leah sold each of her necklaces for $10 more. Who made more money at the craft fair? How much more? ( im using my brothers acc and he is 16)
Answer: Leah made more money by 1,996 dollars more than Gemma,
Step-by-step explanation: 1484 is how much Gemma made and 3480 is how much Leah made all you had to do is multiply the total amount of necklaces they sold and the price of each so Leah made more money by 1996 dollars
I will give BRAINLIEST please help
Answer:
-2.43 then -2 2/3 then 2.045 then 2 5/9 that is from least to greatest :) hope this helps
Step-by-step explanation:
i am positive :)
just to make sure you got it i put this in your comments too !
PLS HELPP!! The table shows the progress of Carson and Jayden as they each read books. Carson Jayden Pages Minutes Pages Minutes 8 6 6 97 16 11.5 12 18 20 20 30 What TWO statements are TRUE?
Answer:
Step-by-step explanation:
How many real solutions does the function shown on the graph have?
no real solutions
one real solution
two real solutions
cannot be determined
Answer:
you can find the answer in this link bit.3ckFc
Step-by-step explanation:
no real solution ig
Janine opens a savings account with a deposit of $720. The account pays 1.4% interest, compounded daily. What is the first day's interest? Round to the nearest cent.
Answer:
The interest is $0.03
Step-by-step explanation:
($720*0.014)/365
The first day's interest will be $10.15 if Janine opens a savings account with a deposit of $720. The account pays 1.4% interest, compounded daily.
What is compound interest?It is defined as the interest on the principal value or deposit and the interest which is gained on the principal value in the previous year.
We can calculate the compound interest using the below formula:
[tex]\rm A = P(1+\dfrac{r}{n})^{nt}[/tex]
Where A = Final amount
P = Principal amount
r = annual rate of interest
n = how many times interest is compounded per year
t = How long the money is deposited or borrowed (in years)
It is given that:
Janine opens a savings account with a deposit of $720. The account pays 1.4% interest, compounded daily.
P =$720
r = 1.4% = 0.014
n = 365
t = 1 day
[tex]\rm A = 720(1+\dfrac{0.014}{365})^{365\times1}[/tex]
After solving:
A = $730.15
The interest I = A - P
I = $730.15 - 720
I = $10.15
Thus, the first day's interest will be $10.15 if Janine opens a savings account with a deposit of $720. The account pays 1.4% interest, compounded daily.
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Find: (4x2y3 + 2xy2 – 2y) – (–7x2y3 + 6xy2 – 2y)
Place the correct coefficients in the difference.
x2y3 +
xy2 +
y
Answer:
final answer: 58xy
Step-by-step explanation:
24xy + 4xy - 2y + 42xy - 12xy + 2y
(24xy + 4xy + 42xy - 2xy) + ( - 2y + 2y)
(24 + 4 + 42 - 12)x xy + ( - 2 + 2)xy
58xy + ( - 2 + 2)xy
58xy + 0y
58xy
Answer:
1st one is 11
2nd one is -4
3rd one is 0
Step-by-step explanation:
no need
you can trust me :)
Given that the zeros of a quadratic function are −2 and −5, what is the standard form of the quadratic function? A) f(x) = x2 + 5x + 10 B) f(x) = x2 + 7x + 10 C) f(x) = x2 − 5x + 10 D) f(x) = x2 − 7x + 10
Step-by-step explanation:
x = -2 and x = -5
x + 2 = 0 and x + 5 = 0
(x + 2)(x + 5) = 0
x² + 5x + 2x + 10 = 0
x² + 7x + 10 = 0
f(x) = x² + 7x + 10
The quadratic equation is x² + 7x + 10.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
We have the zeroes of Quadratic Equation as -2 and -5.
So, the factors of the equation is (x +2 ) and (x + 5).
Then, the Quadratic equation is
= (x+5)(x+2)
= x² + 5x +2x + 10
= x² + 7x + 10
Thus, the quadratic equation is x² + 7x + 10.
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hi please help with this
have a great day
Answer:
Can you explain what this is then I can help
Answer:
- 11Step-by-step explanation:
Given a = -2.9
Simplify the fraction:
(a² + a - 12)/(9 - a²) =(a² + 4a - 3a - 12)/(3 - a)(3 + a) =(a - 3)(a + 4) / - (a - 3)(a + 3) =- (a + 4) / (a + 3)Now substitute the value of a:
- (- 2.9 + 4) / (-2.9 + 3) =- 1.1 / 0.1 = - 11Given the value of cosine,
Cos 0=1/5
Find the value of sine
Sin(0)=
Answer:
25896
Step-by-step explanation: