Using the Fundamental Counting Theorem, it is found that the expression that gives the number of different 6 -character codes that are possible is:
F. 1(1)(10)(10)(10) (10)
Fundamental counting theorem:
States that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
In this problem:
For the first two digits, there is only one outcome, A and H, respectively, hence [tex]n_1 = n_2 = 1[/tex].For the next four digits, as the digits may repeat, there are ten possible outcomes for each, hence [tex]n_3 = n_4 = n_5 = n_6[/tex].Hence:
[tex]N = 1 \times 1 \times 10 \times 10 \times 10 \times 10[/tex]
And option F is correct.
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*20 POINTS*
i swear to GOD PLEASEEE HELP MEEEEEBEJEBKE I’LL GIVE BRAINLEST TO WHOEVER ANSWERS CORRECTLY FIRST
The function below has at least one rational zero. Use this fact to find ALL zeros of the function.
g(x)=5x^3+x^2-20^x-4
If there is more than one zero, separate them with commas. Write exact values, not decimal approximations.
Answer:
If you want to use the Rational Zeros Theorem, as instructed, you need to use synthetic division to find zeros until you get a quadratic remainder.
P: ±1, ±2, ±3, ±6 (all prime factors of constant term)
Q: ±1, ±7 (all prime factors of the leading coefficient)
P/Q: ±1, ±2, ±3, ±6, ±1/7, ±2/7, ±3/7, ±6/7 (all possible values of P/Q)
Now, start testing your values of P/Q in your polynomial:
f(x)=7x4-9x3-41x2+13x+6
You can tell f(1) and f(-1) are not zeros since they're not = 0Now try f(2) and f(-2):
f(2)=7(16)-9(8)-41(4)+13(2)+6
112-72-164+26+6 ≠ 0
f(-2)=7(16)-9(-8)-41(4)+13(-2)+6
112+72-164-26+6 = 0 OK!! There is a zero at x=-2
This means (x+2) is a factor of the polynomial.
Now, do synthetic division to find the polynomial that results from
(7x4-9x3-41x2+13x+6)÷(x+2):
-2⊥ 7 -9 -41 13 6
-14 46 -10 -6
7 -23 5 3 0 The remainder is 0, as expected
The quotient is a polynomial of degree 3:
7x3-23x2+5x+3
Now, continue testing the P/Q values with this new polynomial. Try f(3):
f(3)=7(27)-23(9)+5(3)+3
189-207+15+3 = 0 OK!! we found another zero at x=3
Now, another synthetic division:
3⊥ 7 -23 5 3
21 -6 -3_
7 -2 -1 0
The quotient is a quadratic polynomial:
7x2-2x-1 This is not factorable, you need to apply the quadratic formula to find the 3rd and 4th zeros:
x= (1±2√2)÷7
The polynomial has 4 zeros at x=-2, 3, (1±2√2)÷7
Step-by-step explanation:
I NEED HELP ASAPPPPPPPPPPPPPPPPPPP
Another virus starts spreading on July 1st, 2020. No one
was infected prior so there is no constant. But it does spread at a rate of 11
people per day
Write an equation to solve for the number of days it would take to reach 1,000 cases
How many days will it take to reach 1000 cases?
On what date will Gotham City reach 1000 cases?
THE PICTURE SHOWS ABOUT THE FIRST VIRUS
Answer:
1000÷11=90.9
So,29th September
Students running a food drive have collected their goal amount of canned goods. Over the weekend, volunteers collect an additional 18% of the goal. Write an expression to represent the total percentage of their goal collected in two different ways.
Answer:
[tex]Expression = x + 18x\%[/tex]
[tex]Expression = 1.18x[/tex]
Step-by-step explanation:
Given
Represent their goal with x
Additional = 18%
Required
Write two expressions to describe the total percentage
The expression is derived using:
[tex]Expression = Goal + Additional[/tex]
This gives:
[tex]Expression = x + 18\% * x[/tex]
[tex]Expression = x + 18x\%[/tex]
Solving further (Express percentage as decimal)
[tex]Expression = x + 0.18x[/tex]
[tex]Expression = 1.18x[/tex]
solve the equation
PLZ I need a good grade
answer:
p = 6
1. pull out like factors
7p - 42 = 7 • (p - 6)
2. solve it
7=0
this equation can't be solved, therefore has no solution.
simplify the expression by using distributive property and combine like terms. 4(3x - 1) -2(6+ 2x)
Answer:
8x-16
Step-by-step explanation:
multiple the 4 and the -2 by everything in the parentheses beside them then add them together to simplify
Please help! Will make brainliest !!
Answer:
5: 40.6
6: 26.57
7: 22.21
8: 66.35
Step-by-step explanation:
I am going to assume that you know
SOH CAH TOA (if you don't just ask)
For 5: we have the adjacent and opposite side, we need the angle
I think here it's easiest to use TOA
so we have
tanx=60/70
take the arctan or tan^-1 and get
arctan(60/70)=x x= 40.6
For number 6 it's just the same deal
tanx=10/20
arctan(10/20) =x =26.57
For number 7 we have the adjacent side and we need to find the oppsoite side
for this I will once again use TOA
tan(48)=x/20
20tan(48)=x=22.21
For number 8 it's the same deal as 7
tan53=x/50
50tan53=x=66.35
Each day that a library book is kept past its due date, a $0.30 fee is charged at midnight. Which ordered pair is a
viable solution if x represents the number of days that a library book is late and y represents the total fee?
O (-3,-0.90)
O(-2.5, -0.75)
O(4.5, 1.35)
O (8, 2.40)
I need the answer mate
Answer:
d
Step-by-step explanation:
The only viable solutions for the given condition are (4.5, 1.35) and (8, 2.40).
What is expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
Since the fee is charged at a rate of $0.30 per day, if a book is x days late, the total fee charged would be y = 0.30x.
We can check each ordered pair given to see if it satisfies this equation:
For (-3,-0.90), y = 0.30x = 0.30(-3) = -0.90.
This satisfies the equation, but the fee cannot be negative, so this is not a viable solution.
For (-2.5, -0.75), y = 0.30x = 0.30(-2.5) = -0.75.
Again, this satisfies the equation but the fee cannot be negative, so this is also not a viable solution.
For (4.5, 1.35), y = 0.30x = 0.30(4.5) = 1.35.
This satisfies the equation and the fee is positive, so this is a viable solution.
For (8, 2.40), y = 0.30x = 0.30(8) = 2.40.
This satisfies the equation and the fee is positive, so this is also a viable solution.
Therefore, the viable solutions are (4.5, 1.35) and (8, 2.40).
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A shoe store uses a 50
%
markup for all of the shoes it sells. What would be the selling price of a pair of shoes that has a wholesale cost of $59
?
Answer:
88.50
Step-by-step explanation:
59 divided by 2 (50%) = 29.50
59+29.50=88.50
$5200 at 7.36% for 54 months
a. Find the interest earned.
$
b. Find the balance of the account.
$
Answer:
Step-by-step explanation:
A)5200*54/12*7.36/100=5440.44
b)5200+5440.4410,640.44
Answer:
a. $1722.24 b. $6922.24
Step-by-step explanation:
for a: 5200*0.0736*54/12= 1722.24
for b: 1722.24+5200= 6922.24
Natasha rolls a fair dice 66 times.
How many times would Natasha expect to roll a number greater than 5?
Tony bought x cans of tennis balls for $3 each. He bought the same number of water bottles for $5. He also
bought a tennis racket for $42
-3x - 4y = 4
-5.2 +y = 2
Is (2, 10) a solution of the system?
Answer:
No
Step-by-step explanation:
when checking to see if a point satisfies a system of equations
plug in x and y values from your point into the system
(2, 10)
x y
-3(2) - 4(10) = 4. and. -5.2 + 10 = 2
-6-40 = 4. 4.8. = 2
-46 = 4.
invalid statement. invalid statement
therefore the point (2, 10) does not satisfy this system of equations.
pythagorean theorem. and I need to calculate the missing sides. If possible I would like an explanation but an answer is also fine.
Answer:
Step-by-step explanation:
To calculate the missing sides square the side length of the legs of the triangles( the lines that form a 90 degree angle) then add them together, then take the sqr root of that to find the hypotunse( the slanted side). In simplier terms, here how it look.
[tex]a^{2}+b^{2} =c^{2}[/tex]
where a and b are the legs, and c is the hypotunese. For example, Ill do 3. The bases are 22, and 11 so plug them in the equations.
[tex]a^{2}+b^{2} =c^{2}[/tex]
11^2+22^2=c^2
121+484=c^2
605=c^2
c=about 24.6
Dario borrows $12,000 to buy a car. He borrows the money at a yearly, or annual, simple interest rate of 4.2%. How much more interest will Dario owe if he borrows the money for 5 years instead of 1 year?
ITS URGENT HURRY!!!!!
Answer:
$2016 moreStep-by-step explanation:
Borrowed amount = $12000Interest rate = 4.2% per year simpleInterest in 1 year:
$12000*4.2/100 = $504Interest in 5 years:
$12000*4.2*5/100 = $2520The difference between 1-year interest and 5-year interest:
$2520 - $504 = $2016Need help ASAP
Will mark you brainlist
Kelly has 7 days to read 60 pages of a book for school. She plans to read 8 pages a night for 6 nights.What percent of the assigned pages will she have left to read on the last night?
Answer:
20 percent left
Step-by-step explanation:
Answer:
20%
Step-by-step explanation:
The diagram shows a piece of cheese in the shape of the triangular prism.Work out the area of the cling film needed to cover the cheese
Answer:
488.4 cm²
Step-by-step explanation:
Area of cling film needed = surface area of the triangular prism = 2(B.A) + P×H
Where,
B.A = triangular base area = ½*base*height
height = 10.5 cm
base = √(13.7² - 10.5²) = √77.44 = 8.8 cm
B.A = ½*8.8*10.5 = 46.2 cm²
P = perimeter of the triangular base = 10.5 + 13.7 + 8.8 = 33
H = height of prism = 12 cm
Surface area of triangular prism = 2(46.2) + 33*12
= 92.4 + 396
= 488.4 cm²
pls help asap!!!!!!!!!!!
Answer:
I can not see it well
Step-by-step explanation:
i don't see what your asking but thanxs for the points
i'll give you free point about 40 just look asap because people may snag it
in each bouquet of flowers there are four roses and 6 white carnations complete the table to find how many roses and carnations you still are in four bouquets of flowers
Answer:
so i hope im understanding this. for every 1 bouqet there is 4 roses 6 white carnations so the amount of roses in total you will need for the 4 bouques is 16 and the amount of carnations is 24
Step-by-step explanation:
1 b= 4r an 6c r= roses c=carnations
sooo 4+4+4+4=16 6+6+6+6= 24
1b= 4r 6c
1b= 4r 6c
1b= 4r 6c
1b= 4r 6c
What is the standard algorithm
How do you get from 4 to 4/3
Answer:
- 8/3
Step-by-step explanation:
Simply subtract 4 from 4/3
4/3 - 4 = 4/3-12/3=-8/3
Lets check of our answer is correct:
4 - 8/3 = 12/3 - 8/3 = 4/3. So our answer is correct.
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Score
Which term best describes the savings account that Isabel has set up, given its purpose?
Select the correct answer.
es
Comments
O emergency fund
O mutual fund
Orainy-day fund
sinking fund
Answer:
Emergency Fund
Step-by-step explanation:
Isabel has setup fund for her emergency needs. She has started saving with named as emergency fund so that she can use her savings when she is in severe needs. Isabel has saved money and then she is now saving her money in saving accounts in the bank.
Ayana received some gift cards for music and movie downloads for her birthday. Using one of them, she downloaded 20 songs and 3 movies, which cost a total of $73. Using another, she purchased 5 songs and 17 movies, which cost a total of $197. How much does each download cost?
20s + 3m = 73
5s + 17m = 197
Eliminate s terms: Multiply second equation by -4, then add to first equation:
-20s - 68m = -788
20s + 3m = 73
—————————-
-65m = -715
m = (-715)/(-65) = 11
20s + 3(11) = 73
20s = 40
s = 2
A movie download costs $11. A song download costs $2
A right triangle has an area of 72 square feet. If the lengths of the sides are multiplied by 6, what is the area of the new triangle?
Answer:
The answer is 2592 ft squared
Step-by-step explanation:
Brainliest?
Answer:
The answer is 2592:)
Step-by-step explanation:
Which pair of triangles can be proven congruent by SAS?
Answer:
SAS postulate says that if two sides and the included angle of a triangle are equal to two sides and the included angle of another triangle, then the two triangles are said to be congruent.
Exercise 1.6.3: Translating mathematical statements in English into logical expressions. info About Consider the following statements in English. Write a logical expression with the same meaning. The domain is the set of all real numbers. (a) There is a number whose cube is equal to 2. (b) The square of every number is at least 0. (c) There is a number that is equal to its square. (d) Every number is less than or equal to its square..
Answer:
a) Эx ∈ R ⊇ x³ = 2
b) ∀x ∈ R, x² ≥ 0
c) Эx ∈ R ⊇ x³ = x
d) ∀x ∈ R, x ≤ x²
Step-by-step explanation:
Given the data in the question;
let us first go through some symbols and their possible meanings;
Э ⇒ there exists
∀ ⇒ for all
∈ ⇒ belongs to or set membership or element of the set
⊇ ⇒ such that
now;
a) There is a number whose cube is equal to 2
let x represent the number; so
Эx ∈ R ⊇ x³ = 2
b) The square of every number is at least 0
x² ≥ 0, ∀x ∈ R
∀x ∈ R, x² ≥ 0
c) There is a number that is equal to its square
Эx ∈ R ⊇ x³ = x
d) Every number is less than or equal to its square.
x ≤ x², ∀x ∈ R
∀x ∈ R, x ≤ x²
Find 110.9% of 419.Round to the nearest hundredth.
Answer:
400
Step-by-step explanation:
When you are rounding to the nearest hundred you
You round the number up to the nearest hundred if the last two digits in the number are 50 or above.
Then, round the number down to the nearest hundred if the last two digits in the number are 49 or below and if the last two digits are 00, then you don't have to do any rounding, because it is already to the hundred.
In gym class, the sixth graders walk 3 laps for every 2 laps they run. If the students run 6 laps, how many laps will they walk?
(p.s whoever types it fast and correct i will friend you. i like to do these brain stretches for people to have fun :D
Answer:
They walk 9 laps
Step-by-step explanation:
If the run for 6 laps you need to multiply how many times they walked when they ran for 2 laps by 3 (3*3) which should give you 9
Answer:
5
Step-by-step explanation:
The answer is 873.17
Answer:
wat
Step-by-step explanation:
Answer:
To what exactly...?
Step-by-step explanation: