Answer:
The sequence has common difference 3, and its general nth term can be written as:
[tex]a_n=3\,n-1[/tex]
Step-by-step explanation:
In order to define the sequence, we recall the formula for the nth term of an arithmetic sequence as:
[tex]a_n=a_1+(n-1)\,d[/tex]
where "d" is the common difference for the sequence (our unknown in this case), and the nth term is our fourth term (n = 4) which equals 11, and the first term is 2:
[tex]a_n=a_1+(n-1)\,d\\11=2+(4-1)\,d\\9=3\,d\\d=9/3\\d=3[/tex]
Therefore our sequence has common difference 3, and its general nth term can be written as:
[tex]a_n=2+(n-1)3\\a_n=3\,n-1[/tex]
2(x-3)+3=6x-5 help
How many gallons of a 90% antifreeze solution must be mixed with 80 gallons of 25% antifreeze to get a mixture that is 80% antifreeze?
Answer:
x=440 gaL 90 % Antifreeze II
Step-by-step explanation:
In the problem, there are two types of antifreeze
antifreeeze I and
antifreeze II
antifreeze I 25 ----80 gal
Antifreeze II 90 ----- x gal
Total 80 ---------------- (80 + x ) gal
(25*80)+(90*x)=80(80+x)
2000+90x=6400+80x
90x-80x=6400-2000
10x=4400
divide both sides by 10 we have
x= 440
x=440 gaL 90 % Antifreeze II
write a context story for the equation 32 divided by 5
find the missing value 1/2 equals 28 over X
Answer:
x = 56
Step-by-step explanation:
cross multiply. 28 times 2 and 1 times x. set them equal to each other and solve for x to get 56.
graph of the
equation f(x) = 1x-2
I used desmos which is an online graphing calculator and I got this
According to a study done by a university student, the probability a randomly selected individual will not cover his or her mouth when sneezing is 0.267. Suppose you sit on a bench in a mall and observe people's habits as they sneeze.
A) What is the probability that among 12 randomly observed individuals exactly 8 do not cover their mouth when sneezing?
B) What is the probability that among 12 randomly observed individuals fewer than 5 do not cover their mouth when sneezing?(
C) Would you be surprised if, after observing 12 individuals, fewer than half covered their mouth when sneezing? Why?
Answer:
A
[tex]P(X = 8 ) = 0.0037[/tex]
B
[tex]P(X < 5) = 0.805[/tex]
C
I will not be surprised because the probability that fewer than half covered their mouth when sneezing is less than 0.5
Step-by-step explanation:
From the question we are told that
The probability a randomly selected individual will not cover his or her mouth when sneezing is [tex]p = 0.267[/tex]
The probability a randomly selected individual will cover his or her mouth when sneezing is
[tex]q = 1 -p[/tex]
[tex]q = 1 -0.267[/tex]
[tex]q = 0.733[/tex]
Generally the probability that among 12 randomly observed individuals exactly 8 do not cover their mouth when sneezing is mathematically represented as
[tex]P(X = 8 ) = \left 12 } \atop {}} \right. C_8 * p^8 * q^{12-8}[/tex]
[tex]P(X = 8 ) = 495 * (0.267)^8 * (0.733)^{12-8}[/tex]
[tex]P(X = 8 ) = 0.0037[/tex]
Generally the probability that among 12 randomly observed individuals fewer than 5 do not cover their mouth when sneezing is mathematically represented as
[tex]P(X < 5 ) = P[ P(X = 0) + \cdots + P(X = 4)][/tex]
=> [tex]P(X < 5) = \left 12 } \atop {}} \right. C_0 * (0.267)^0 * (0.733)^{(12- 0) }+\cdots + \left 12 } \atop {}} \right. C_4 * (0.267)^0 * (0.733)^{(12- 4) }[/tex]
=> [tex]P(X < 5) = 0.805[/tex]
Give that half of 12 is 6 then
The probability that fewer than half covered their mouth when sneezing is mathematically represented as
[tex]P(X > 6) = 1 - P( X \le 6 )[/tex]
=> [tex]P(X > 6) = 1 - [P(X = 0 ) +\cdots+P(X = 6) ][/tex]
=> [tex]P(X > 6) = 1 - [\left 12 } \atop {}} \right. C_0 *(0.267)^0 * (0.733)^{12 - 0 } +\cdots + \left 12 } \atop {}} \right. C_6 * (0.267)^6 * (0.733)^{12-6}][/tex]
=> [tex]P(X > 6) = 0.0206[/tex]
Anyone know how to solve this...
Answer:
see below
Step-by-step explanation:
D = 1 - ∑(4/125)²
D = 1 - (2/5³)²
D = 1 - 2²
5³ ²
D ≅ 0.99974
6 x 10^4 please help me I just don’t want to do the math right now I’m so tired
Answer:
6,000
Step-by-step explanation:
1) Which ratio of cups of fruit to cups of
almond milk is shown on the double
number line?
4/3 1/2
How much fruit does Faith use per cup
of almond milk?
cup(s) of fruit per cup of almond milk
Answer:
8/3 or 2 2/3, but I used 8/3
Step-by-step explanation:
got it right :)
Answer:
The answer is 2 2/3 but the fastest way to do it is 8/3.
Plot -1/4 on the horizontal and vertical number lines.
On the vertical number line, negative numbers are to the bottom of 0. Therefore, -1/4 will go one unit down from 0.
On the horizontal number line, negative numbers are to the left of 0. Therefore, -1/4 will go to the left one unit.
Best of Luck!
Suppose MQ = NR = 14 and PQ = 5NP. What is the length of NP if MR = 20?
Answer:
1 1/3
Step-by-step explanation:
Answer:
1 1/3 or 4/3 (both have the same value, but just are in different forms)
Two brothers, Mark and Walter, each inherit $20000. Mark invests his inheritance in a savings account with an annual return of 2.5%, while Walter invests his inheritance in a CD paying 6.1% annually. How much more money than Mark does Walter have after 1 year?
Answer:
$720
Step-by-step explanation:
$20000 - 100%
$x. - 2.5%
x=(20000*2.5)/100=500
20000+500=$20500 in one year (Mark)
20000 - 100
x. - 6.1
x= (20000*6.1)/100 = 1220
20000+1220= $21220 (Walter)
21220-20500= $720 more (Walter will have after 1 year)
Find the measures of the supplementary angles that satisfy each case.
The measure of the first angle is 45° more than the measure of the second.
Answer: 67.5 and 112.5 degrees
A firm gives discounts to its customers who pay their bills on time. A customer receives a ten percent discount on the next invoice when a bill is paid in full before its due date. Thirty percent of all customers use the discount. If the company sends out eight bills, what is the probability that less than three take the discount (round answers to three decimal places, for example, 0.xxx)
Answer:
0.551
Step-by-step explanation:
Let no. of people who take discount = x
Using binomial distribution, N c X. p^x. q^(n-x)
p : customer getting discount = 0.3, q : customer not getting discount = 0.7 n : no. of customers = 8
Probability that x < 3 : Prob (x=0) + Prob (x=1) + Prob (x=2)
= 8 c 0. (0.3)^0 . (0.7)^8 + 8 c 1. (0.3)^1 . (0.7)^7 + 8 c 2. (0.3)^2 . (0.7)^6
0.05764801 + 0.19765032 + 0.29647548
0.551
Simplify the expression: –5(3k − 4)
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \bold{ \sf{ - 15k + 20}}}}}}[/tex]
Step-by-step explanation:
[tex] \sf{ - 5(3k - 4)}[/tex]
Distribute -5 through the parentheses
[tex] \longrightarrow{ \sf{ - 5 \times 3k - ( - 5) \times 4}}[/tex]
[tex] \longrightarrow{ \sf{ - 15k - ( - 20)}}[/tex]
[tex] \longrightarrow{ \sf{ - 15k + 20}}[/tex]
Hope I helped!
Best regards! :D
What would be the second step to solve 5 x – 61 = 20?
Answer:Step 2: Divide both sides by 5.
Step-by-step explanation:
Answer:
divide 5 on both sidesStep-by-step explanation:
add -61 on both sides:
5x - 61 + 61 = 20 + 61
simplify
5x = 81
divide 5 on both sides:
5x = 81
5 5
x = 81
5
Find the value of x in each case:
Answer:
49 degrees
Step-by-step explanation:
its because like it's on the same line
Answer:
17 degrees
Step-by-step explanation:
what is 20x times x
Answer:
20x^2
Step-by-step explanation:
[tex]20x \times x\\\\\mathrm{Apply\:exponent\:rule}:\quad \:a^b\times \:a^c=a^{b+c}\\\\xx=\:x^{1+1}\\\\=20x^{1+1}\\\\\mathrm{Add\:the\:numbers:}\:1+1=2\\\\=20x^2[/tex]
Find the complex conjugate of 10+ 61.
a. -10 + 61
b. 10-61
C.-10-61
d. 6 - 107
Answer:
b. 10 - 61
Step-by-step explanation:
10 + 61 is 71
We need to change the addition sign to subtraction.
10 - 61= -51
We need to find an equation that is equal to -51.
a. -10 +61
That equals 51, which is not 71, which means it is not letter a.
b. 10 - 61
That equals -51, which is not 71, which means it is not letter b.
c. -10 - 61
That equals -71, which is not 71, which means it is not letter c.
d. 6- 107
That equals -101, which is not 71, which means it is not letter d.
what is the soloution to the equation 3x+4=7x-4
Step-by-step explanation:
3x+4=7x-4
add 7x to each side of equation 4x+3x+-7x=-4x+7x+-7x
combine like terms 7x+-7x=0
4+ -4x =-4 +0
4+-4x= -4
add -4 to each side of equation 4+ -4 +-4x=-4+-4
combine like terms -4 +4=0
0+ -4x = -4+ -4
combine like terms -4+-4=-8
-4x =-8
divide each side by-4
x=2
simplifying
x = 2
Composition f(g(x)) and g(f(x)) function f and g are shown on the graph. Which statements describe the composition? Check all that apply
Answer:
Step-by-step explanation:
f(g(x) = g(f(x)) for at least one value of x.
The composition of f and g is commutative.
f(g(0)) = 5 and g(f(-2.5)) = 5.
The graphs show that function composition is not commutative.
Answer:
A, C, D, and E
f(g(x)) = g(f(x)) for at least one value of x.
f(g(0)) = 5 and g(f(–2.5)) = 5.
Both f(g(x)) and g(f(x)) have the same domain.
The graphs show that function composition is not commutative.
Step-by-step explanation:
The parallelogram shown below has an area of 30units^2
30*2
60
again 2(a+b)
2(30+2)
2*32
64
Ariana rode A bicycle 7 miles and 42 minutes. Abelito road his skateboard 8 miles in 48 minutes. Who traveled at a greater average speed? Define an appropriate unit of speed and provide mathematical justification for your answer. Please i need this by TONIGHT!!
Maggie's Bakery bakes the best apple pies. If you decide to make p pies, you need a apples.
Based on this information, what are the independent and dependent variables?
A)
Both pies and apples are independent variables.
B)
Both apples and pies are dependent variables.
C)
The independent variable is pies, and the dependent variable is apples.
D)
The independent variable is apples, and the dependent variable is pies.
Im
Answer:
Option (D)
Step-by-step explanation:
When we make a pie we will need apples.
That means number of pie baked will always depend on the number of apples available or number of apples used.
So the number of apples used will be independent variable.
Since number of pie will always depend on the number of apples used,
Number of pie baked will be a dependent variable.
Therefore, Option (D) will be the answer.
Answer:No the answer is C I just took the test
Step-by-step explanation:
An NHL hockey player has 59 goals so far in a season. What are the possible numbers of additional goals the player can score to match or break the NHL record of 92 goals in a season?
Answer:
33 additional goals
Step-by-step explanation:
59+g is greater than or equal to 92 subtract 59 from both sides leaving the answer g is greater than or equal to 33
The hockey player would have to score:
33 goals to match the record 34 goals to break the recordIn order the match the record, the hockey player needs to score a certain number of goals that will take them to the record of 92. That number is:
= 92 - 59
= 33 goals
If they however want to break the record, the need to score more than 92 goals. The least number of goals they can score to do so is:
= Number of goals to match record + 1
= 33 + 1
= 34 goals
In conclusion, the player would have to score 33 goals to match the NHL record but 34 to break it.
Find out more at https://brainly.com/question/19239376.
Suppose you work as a clerk at a local retail store earning $6 per hour. The amount of your weekly paycheck (before taxes are taken out) could be written F(x) = 6x.
16. What is the independent variable in this function and what does it represent?
Answer:
x is the independent variable and it represents the number of hours worked per week by the clerk.
Step-by-step explanation:
An independent variable refers to a variable in model that is varied or changed in order to examine its effect on another variable. The other variable is called a dependent variable.
A dependent variable is a variable in a model that changes as a result of a change in the independent variable.
From the question, x is the independent variable and its represent the number of hours worked by the clerk.
F(x) represents the amount of your weekly paycheck and it is the dependent variable that changes as the number of hours worked, x, changes.
For example, since we are given:
F(x) = 6x ............................... (1)
Where;
F(x) = = depemdent variable = Amount of weekly paycheck (before taxes are taken out)
6 = coefficient of x = Earning per hour
x = Independent variable = Number of hours worked
Assuming x = 1, we can substitute this into equation (1) and have:
F(x) = 6 * 1 = $6
But when x = 2, we have:
F(x) = 6 * 2 = $12
Therefore, the dependent variable F(x) changes from $6 weekly to $12 weekly as the independent variable x changes form 1 hour to 2 hours weekly.
is 4 3/5 rational or irrational?
Answer:
It is rational
Answer:
4 and 3/5? It is irrational
Step-by-step explanation:
Its irrational because it is not a whole number, it includes a fraction, which is not a whole number.
Leo bought jet ski's a couple of years ago. He now wants to sell them. This is an example of Income.
O A. capital gains
OB. earned
OC. hourly
OD. passive
Answer:
D. passive
Step-by-step explanation:
I dont know how to do any of these problems can someone help me
Answer:
#7. JK = 1
Step-by-step explanation:
So all these problems are similar in the fact that you are given three pieces of information and you need to determine x. Let's look at #7.
We are to find the length JK but we are given it in terms of x. To find the length, we need to find x. Using the information we have about KL and JL, we can find this. Note, the value of JL is 5, and the value of KL is x + 8.
JK + KL = JL
( 2x + 9 ) + ( x + 8 ) = 5
3x + 17 = 5
3x = -12
x = -4
Now that we have the value of x, we can find the value of JK:
JK = 2x + 9
JK = 2(-4) + 9
JK = -8 + 9
JK = 1
Hence, the length of JK is 1.
Using this same basic idea, you can solve all of these problems.
Cheers.
what is the answer for 7.42 ÷ 1.75 = ______
Answer:
4.24
Step-by-step explanation:
Answer: 4.24
Step-by-step explanation:
just do 7.42/ 1.75 and ur answer is 4.24
