Answer:
Each cupcake cost $2.50 and each brownie cost $2.00
Step-by-step explanation:
Let x represent the price of each cupcake and let y represent the price of each brownie.
Lily and Maddie bought one cupcake and one brownie for $4.50. Hence the equation is:
x + y = 4.50 (1)
Also Jessica purchased 3 cupcakes and one brownie for $9.50. Hence the equation is given by:
3x + y = 9.50 (2)
To find the price of each cupcake and brownie, we solve equation 1 and 2 simultaneously. To find x, subtract equation 1 from equation 2:
2x = 5
x = $2.50
Put x = $2.50 in equation (1):
2.50 + y = 4.50
y = $2.00
Therefore each cupcake cost $2.50 and each brownie cost $2.00
The table below shows three special sequences (A to C) of numbers.
A 1; 4; 9; 16; 25; 36 ...
B 1:8; 27; 64; 125; 216...
C 1:3; 6; 10; 15; 21; ...
3.1 Write down the next THREE terms of the respective patterns.
3.2.
Identify the pattem (sequence of numbers) represented by each letter.
3.3
Determine the formula for the general term of each sequence.
3.4
Determine the 100 term of each respective pattern.
Answer:
3.1 A) 49; 64; and 81
B) 343; 512; and 729
C) 28; 36; and 45
3.2 A) 1²; 2²; 3²...
B) 1³; 2³; 3³...
C) 1; 1+2; 1+2+3; ...
3.3 A) aₙ = n²
B) aₙ = n³
C) aₙ = n·(n + 1)/2
3.4 A) 10,000
B) 1,000,000
C) 5,050
Step-by-step explanation:
The given sequences are;
A 1; 4; 9; 16; 25; 36...
B 1; 8; 27; 64; 125; 216...
C 1; 3; 6; 10; 15; 21;...
3.1 A) The terms, aₙ, of sequence 'A' are given as follows;
aₙ = n², where, n = 1, 2, 3,...
The next three terms of sequence 'A' are therefore;
a₇ = 7³ = 49, a₈ = 8² = 64, and a₉ = 9² = 81
The next three terms of sequence 'A' are ; 49; 64; and 81
B) The terms, aₙ, of sequence 'B' are given as follows;
aₙ = n³, where, n = 1, 2, 3,...
The next three terms of sequence 'B' are therefore;
a₇ = 7³ = 343, a₈ = 8³ = 512, and a₉ = 9³ = 729
The next three terms of sequence 'B' are; 343; 512; and 729
C) The terms, aₙ, of sequence 'C' are given as follows;
aₙ = n·(n + 1)/2, where, n = 1, 2, 3,...
The next three terms of sequence 'A' are therefore;
a₇ = 7×(7 + 1)/2 = 28, a₈ = 8×(8 + 1)/2 = 36, and a₉ = 36 + 9×(9 + 1)/2 = 45
The next three terms of sequence 'A' are ; 28; 36; and 45
3.2 A) The pattern of the numbers in sequence 'A', consists of squaring (raising to the power of 2) each number in the sequence of natural numbers
B) The pattern of the numbers in sequence 'B', consists of raising to the power of 3 each number in the sequence of natural numbers
C) The pattern is the triangular number sequence and consists of finding half the number dots that are present in a n by (n + 1) rectangle, which is given by finding the sum of the natural numbers up to the given term in the sequence
3.3 A) The formula for the general term of sequence, A, is aₙ = n²
B) The formula for the general term of sequence, B, is aₙ = n³
C) The formula for the general term of sequence, C, is aₙ = n·(n + 1)/2
3.4 A) The 100th term of sequence 'A', a₁₀₀ = 100² = 10,000
B) The 100th term of sequence 'B', a₁₀₀ = 100³ = 1,000,000
C) The 100th term of sequence 'C', a₁₀₀ = 100 × (100 + 1)/2 = 5,050.
Max drives 85 km at an average speed of 110 km/h and then 7 km at 70 km/h without stopping.
What is the average speed for the whole journey to 1 dp?
Answer:
how much time did it take him???????
Step-by-step explanation:
Pls help no links pls this is due and i need help
Answer:
angle 1=127 degree
angle 3=127 degree
angle 2=53 degree
angle 4=53 degree
angle 5=37 degree
angle 6=90 degree
angle 7=53 degree
angle 8=37 degree
angle 9=37 degree
angle 10=143 degree
angle 11=37 degree
angle 12=143 degree
Step-by-step explanation:
An amount of $45,000 is borrowed for 13 years at 6.75% interest, compounded annually. If the loan
paid back
Use the calculator provided and round your answer to the nearest dollar,
Answer:
$104850
Step-by-step explanation:
Given data
Principal= $45,000
Time = 13 years
Rate= 6.75%
the compound interest expression is
A= P(1+r)^t
A=45000(1+0.0675)^13
A= 45000(1.0675)^13
A= 45000*2.33
A= $104850
Hence the final amount will be $104850
6 = m/8
M=?
What is the answer for M?
Answer:
m =48
Step-by-step explanation:
1st step is to multiply both sides by 8
2nd step it would be 48=m
3rd step swap the sides.. m=48
someone help please I'm having a hard time understanding
Answer:
the angle shown is a straight angle value of which is equal to 180°
3x + 30. 6 = 180
3x = 180 - 30. 6
3x = 149.4
x = 49.8PLEASE HELP ME!!! ILL GIVE BRAINLIESTS IF RIGHT!
Answer:
B
Step-by-step explanation:
When you look at the model, you see that the bottom of the shape is square. So looking at the flat model, which one is thhe one with a square as a base. B does.
HELP PLEASE
identify the solution to the system of equations
Answer:
solved graphically,
it's just the point where the two lines intersect
A . What is the slope in the line of the graph ?
Answer:
0.2x+3
Step-by-step explanation:
1.) A butterfly can fly 82 feet in four seconds and a dragonfly can fly 50 feet in two seconds. Which can fly faster and by how much? *
1 point
The dragonfly is 4.5 feet per second faster.
The butterfly is 4.5 feet per second faster.
The dragonfly is 20.5 feet per second faster.
The butterfly is 32 feet per second faster.
Answer:
The dragonfly is 20.5 feet per second faster
Step-by-step explanation:
Answer:
A. The dragonfly is 4.5 feet per second faster.Step-by-step explanation:
Speed of butterfly:
82/4 = 20.5 ft/secSpeed of dragonfly:
50/2 = 25 ft/secThe difference:
25 - 20.5 = 4.5 ft/secCorrect choice is A
10 points !
what is 20% of 30 ?
Answer:
6
Step-by-step explanation:
Of means multiply
20% * 30
Change to decimal form
.20 * 30
6
Answer:
6
Step-by-step explanation:
[tex]20\% \ of \ 30 = \frac{20}{100} \times 30 = \frac{1}{5} \times 30 = 6[/tex]
41. Steven wants to buy a $535 bicycleSteven has no money saved, but will be able to deposit $30 into a savings account when he receives his paycheck each Friday. However, before Steven can buy the bike, he must give his sister $65 that he owes her. For how many weeks will Steven need to deposit money into his savings account before he can pay back his sister and buy the bike?
Answer:
17 weeks of deposits will pay for his bike and his sister
Step-by-step explanation:
PLS HELP! WILL MARK BRAINLIEST!
Mr. Smith makes a pasta sauce
He mixes tomato concentrate: olive oil at a ratio of 3: 1
How many liters of tomato concentrate does he need to mix if he adds 3 liters of olive oil?
Answer:
9 litres of tomato concentrate
What is equivalent to 5 to the third power?
Answer:
125
Step-by-step explanation:
5 to the third power is 125
[tex]20\% of gh 200 [/tex]
Answer:
answer
I think it's 40...
[tex]20\% \: \bold{of} \: 200 \\ \\ = \frac{20}{100} \times 200 \\ \\ = \frac{20}{ \cancel{100}} \times \cancel{200} \\ \\ = 20 \times 2 \\ \\ = 40[/tex]
Hope This Helps You ❤️There are 2 quarters, 1 nickel, and 2 dimes in a pocket.
What is the probability of choosing a coin, not returning it to the pocket, and then choosing another of greater value?
A ^3 10
B ^6 25
C ^4 10
D ^8 25
Answer:
C
Step-by-step explanation:
Expand the logarithm. Assume all expressions exist and are well-defined.
Write your answer as a sum or difference of common logarithms or multiples of common
logarithms. The inside of each logarithm must be a distinct constant or variable.
log 3y
Answer:
Step-by-step explanation:
log 3y = log(y)^3 (exponent)
or
= log(y)*log(y)*log(y) (multiples)
The logarithmic expression y = log(3y) can be written as sum or difference of common logarithms as log(3y) = log(3) + log(y).
What is logarithm? What is a mathematical function, equation and expression?logarithmic : It is a quantity representing the power to which a fixed number (the base) must be raised to produce a given number. Mathematically -[tex]$\log_{b}({b^x})=x[/tex] {where [b] is logarithmic base}
function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.Given is the following logarithmic expression as -
y = log(3y)
We have the following logarithmic expression -
y = log(3y)
Using the identity of logarithm -
log(AB) = log(A) + log(B)
log(3y) = log(3) + log(y)
Therefore, the logarithmic expression y = log(3y) can be written as sum or difference of common logarithms as log(3y) = log(3) + log(y).
To solve more questions on functions, expressions and polynomials, visit the link below -
brainly.com/question/17421223
#SPJ2
PLSS HELP ASAP I NEED RN
Answer PLSSS..................
rectangle = 3 x 2 = 6 cm2
cirrel = pier2 = 3.14 x 7 x 7 = 3.14 x 49 = 153.86 cm2
153.86 - 6 = 147.86cm2
need help on this please
Answer:
5.7
Step-by-step explanation:
7^2- 4^2= 33
[tex]\sqrt{33}[/tex]= 5.7
The Science Club went on a two-day field trip. The first day the members paid $50 for transportation plus
$18 per ticket to the planetarium. The second day they paid $95 for transportation plus $15 per ticket to
the geology museum. Write an expression to represent the total cost for two days for the n members of
the club.
An expression that represents the total cost in dollars for two days for the n members of the club is given
by
HARD! [Ma
Answer:
145 + 33n
Step-by-step explanation:
Let
n = number of members in the club
Day 1:
Cost = 50 + 18n
Day 2:
Cost = 95 + 15n
Total cost two-day field trip = day 1 + day 2
= (50 + 18n) + (95 + 15n)
= 50 + 18n + 95 + 15n
= 145 + 33n
Total cost two-day field trip = 145 + 33n
An expression that represents the total cost in dollars for two days for the n members of the club is given by 145 + 33n
Please help me with at least one problem i’m sort of confused on them but I was able to get one. And I will mark brainiest
Answer:
1. 5.75 * 33 = $189.75
The bakers income is $189.75
2. 2 * y - 8 / 4 when y = 7
2 * 7 - 8 / 4 = 12
3. 76 + 4 * y^2 + 1 when y = 3
76 + 4 * 3^2 + 1 = 113
The young mathematician is presented with this problem: (13 + 7) x (5 - 3) / 4 x (1 + 1) = Which operation would the young mathematician do first?
The division
The subtraction
Those inside parentheses
The multiplication
Those inside the parentheses. Rember pemdas or Parentheses Exponets Multiple Divide Add Subtract in that order from left to right
please help!!!!!! i will mark brainliest!
Answer:
d
Step-by-step explanation:
I need the answer immediately!!!!!!!!
Answer:y=-5x-2
Step-by-step explanation:
This will have a negative slope since the line goes from left to right. Use rise over run to find the slope of -5 and look at the y axis where it intersects to get -2
Have a great day!
Evaluate: 4x(5+3)=8-2
A 2
B 8
C 12
D 15
Answer:
The answer to the problem is 15.
HELPPPPPPPPPPPPPPPPPPPPPPPPP
Answer:
720
Step-by-step explanation:
This is a permutation of 10 choose 3
10 ! 10!
----- = ------------ = 10*9*8 = 720
(10-3)! 7!
In right triangle ABC, a = 7, b = 9 and
Answer: the answer is 63,ABC
Step-by-step explanation:
ITEMS
The calculator shown costs $160.00 after a discount of $40.00 was given
Calculate the cost of the calculator before the discount
Answer:
mp=160
dis=40
now,
sp=mp-dis
=Rs. 160-Rs.40
=Rs. 120
Element X is a radioactive isotope such that every 13 years, its mass decreases by half. Given that the initial mass of a sample of Element X is 90 grams, how long would it be until the mass of the sample reached 62 grams, to the nearest tenth of a year?
Answer:
The mass of Element X will reach 62 grams in 7.0 years.
Step-by-step explanation:
We can find the time of decay of Element X by using the exponential decay equation:
[tex] \frac{dm}{dt} = -\lambda t [/tex]
The solution of the above equation is:
[tex]m_{(t)} = m_{0}e^{-\lambda t}[/tex] (1)
Where:
t: is the time =?
λ: is the decay constant
[tex]m_{(t)}[/tex]: is the mass at time t = 62 grams
[tex]m_{0}[/tex]: is the initial mass = 90 grams
First, we need to calculate λ
[tex] \lambda = \frac{ln(2)}{t_{1/2}} [/tex] (2)
Where [tex]t_{1/2}[/tex] is the half-life = 13 years
By entering equation (2) into (1) and solving for "t" we have:
[tex]\frac{m_{(t)}}{m_{0}} = e^{-\frac{ln(2)}{t_{1/2}}*t}[/tex]
[tex]ln(\frac{m_{(t)}}{m_{0}}) = -\frac{ln(2)}{t_{1/2}}*t[/tex]
[tex]t = -ln(\frac{m_{(t)}}{m_{0}})(\frac{t_{1/2}}{ln(2)}) = -ln(\frac{62}{90})(\frac{13}{ln(2)}) = 7.0 y[/tex]
Therefore, the mass of Element X will reach 62 grams in 7.0 years.
I hope it helps you!