Answer:
The balance after 1 year is;
$1,014.05
Step-by-step explanation:
To do this, we use the compound interest formula
That will be ;
A =P (1 + r/n)^nt
A is the amount generated which we want to calculate
r is the rate = 1.4% = 0.014
P is the amount deposited = $1,000
n is the number of times it is compounded annually which is 2 (semi-annually means 2 times in a year)
this the number of years which is 1
we have this as:
A = 1,000( 1 + 0.014/2)^(2*1)
A = 1,000(1 + 0.007)^2
A = 1,000(1.007)^2
A = $1,014.05
Joey likes beer and whisky and spends £75 in total on drink. His utility function for whisky (w) and beer (b) is = 5 + .
He can buy beer at £2 a can but the liquor store tries to discourage overconsumption of spirits by charging higher prices for larger quantities: the cost in dollars of bottles of whisky works out at !.
a. How many cans of beer and how many bottles of whisky does Joey consume?
b. Illustrate your answer with a clearly labelled diagram showing Joey's budget constraint and his indifference curve passing through the optimal consumption bundle.
c. Joey's friend Ross shops at the same liquor store and spends the same amount on drink. Jim, however, insists on drinking beer and whisky together. His utility function is = min{5, } How much beer and whisky does Jim buy?
To answer the questions, we need to understand the utility functions and budget constraints for both Joey and Jim. Let's break it down step by step:
Joey's Utility Function and Budget Constraint:
Joey's utility function for whisky (w) and beer (b) is given by: U(w, b) = 5 + (w^0.3 * b^0.7)
w: The quantity of whisky (in bottles) consumed by Joey
b: The quantity of beer (in cans) consumed by Joey
Joey spends £75 in total on drink. The cost of beer is £2 per can, and the cost of whisky is £6 per bottle.
To find how many cans of beer and bottles of whisky Joey consumes, we need to maximize his utility function while staying within his budget constraint.
Joey's Budget Constraint:
Joey's total expenditure on drink (E) is given by: E = 2b + 6w
And we know that E = £75.
So, the budget constraint is: 2b + 6w = 75
Now, we can solve this problem using optimization techniques. However, without specific numerical values for the utility function and budget constraint, it's not possible to determine the exact quantities of beer and whisky consumed by Joey. We can only find the optimal consumption bundle if the specific values are given.
Joey's Indifference Curve and Budget Constraint Diagram:
To illustrate Joey's optimal consumption bundle, we would need to plot his indifference curve (representing his preferences) and his budget constraint (showing all possible affordable combinations of beer and whisky). However, without the exact values, we cannot draw the diagram.
Jim's Utility Function and Consumption:
Jim's utility function for beer (b) and whisky (w) is given by: U(b, w) = min{5, (w^0.3 * b^0.7)}
Jim's utility function shows that he insists on drinking beer and whisky together, and his utility is the minimum of 5 and the product of whisky and beer raised to certain powers.
Again, without specific numerical values for the utility function, we cannot determine the exact quantities of beer and whisky consumed by Jim.
In summary, to fully answer the questions, we would need the specific numerical values for the utility function and the budget constraint. With those values, we could then calculate the optimal consumption bundles for both Joey and Jim.
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which one would it be?
find x and y this is geometry
The difference of three times Faye's age and four times Joshua's age is 31. If Faye's age is five more than twice Joshua's age, how old is Faye?
You have 5 choices of shirts: red, blue, green, yellow, brown; 3 choices of pants: green, brown, black; 4 choices of
socks: black, brown, tan, white; and 3 choices of shoes: white, brown, black. What is the probability that you will
dress all in brown-shirt, pants, socks, and shoes?
Answer:
15% chance
Step-by-step explanation:
The required probability is 0.0166 that you will dress all in a brown shirt, pants, socks, and shoes.
How to find probability?The probability that you will dress all in brown is the product of the probability of selecting each brown item.
There is only one choice of brown shirt out of a total of 5 shirt choices, so the probability of selecting a brown shirt is 1/5.
Similarly, there is only one choice of brown pants out of a total of 3 pant choices, so the probability of selecting brown pants is 1/3.
There is also only one choice of brown socks out of a total of 4 sock choices, so the probability of selecting brown socks is 1/4.
Finally, there is also only one choice of brown shoes out of a total of 3 shoe choices, so the probability of selecting brown shoes is 1/3.
To find the overall probability of dressing all in brown, you need to multiply these probabilities together: (1/5) × (1/3) × (1/4) × (1/3) = 1/60.
This means the probability of dressing all in brown is approximately 0.0166, or about 1.7%.
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Find the equation of the line that passes through each pair of points in y = mx + b form.
(-6, -19) and (2,5)
Answer:
y = 3x - 1
Step-by-step explanation:
A carpenter sands 1/2 of a dresser in 3/4 hour ,how long does it take the carpenter to sand 1 dresser
Answer:
1.5 hours = 1 hour 30 mins
Step-by-step explanation:
3/4 = 0.75
0.75 x 2 = 1.5
daily wages of a factory workers are recorded as:
C.I 12-126. 127-137. 133-138. 139-144
Freq. 5. 27. 20. 18
the lower limit of model class is. :-
a)127
b)126
c)126.5
d)133
Answer:
seee I won the waaaarrrrrr.... [:
Answer:
126
Step-by-step explanation:
cause it's the smallest
i need help finding the missing angle measurement
The population of a small town was 3500 in 2005. The population increases by 4% annually. A. Write an exponential growth function to represent this situation. B. What will the population be in 2025?
Answer: The population in 2025 will be 7669
Step-by-step explanation:
a) When we have an initial quantity A, and we have an increase of the X%, the new quantity is written as:
new quantity = A + A*(X%/100%) = A*(1 + X%/100%)
In this case, our initial quantity is 3500, the town's population in 2005.
And X% = 4%.
We know that each year, the population increases by 4%.
Then if P(1) is the population one year after 2005, this is:
P(1) = 3500*(1 + 4%/100%) = 3500*(1.04)
After another year, the population increases again:
P(2) = (3500*(1.04))*(1 + 4%/100%)) = 3500*(1.04)*(1.04) = 3500*(1.04)^2
Well, we already can see the pattern here, the population N years after 2005 will be:
P(N) = 3500*(1.04)^N
b) Now we want to know the population in 2025.
N represents the number of years after 2005, then we will have:
N = 2025 - 2005 = 20
2025 is 20 years after 2005.
Then the population in 2025 will be:
P(20) = 3500*(1.04)^20 = 7,668.9
And we can not have a 0.9 of a person, so we should round it up to the next whole number, then the population in 2025 will be 7669
PLS HELP NOOOOOOOOOWWWWWWWW
simplify 6a+5w-2a+w .....,,.,,.,..,..,,
At a concert 30% of the audience were tennnagers. If there was a total of 1600 audience members, how many of the audience were not teenagers
Answer:
Not teenagers = 1120
Step-by-step explanation:
Total number of audience members = 1600
30% of the audience were teenagers.
It means 70% of the audience were not teenagers. It can be given by :
x = 70% of 1600
[tex]x=\dfrac{70}{100}\times 1600\\\\x=1120[/tex]
Hence, 1120 audiences were not teenagers.
5x - 19 = 2(x - 5)
Show all work
Answer:
x=3
Step-by-step explanation:
I did a 2-column proof for the explanation :)
Answer:
Step-by-step explanation:
Here you go mate
∴Use PEMDAS
Parenthesis,Exponent,Multiplication,Division,Addition,Subtraction
Step 1
5x-19=2(x-5) Equation/Question
Step 2
5x-19=2(x-5) Remove parenthesis
5x=2x+9
Step 3
5x=2x+9 Subtract 2x from sides
3x=9
Step 4
3x=9 Divide sides by 3
Answer
x=3
Hope this helps
Martin purchased a book. The receipt says that the total cost of the book is $11.65, including a 6% sales tax. What was the original price of the book without the tax?
Answer:
11.65$ : 100% = x : 94
94 because 100 - 6
Step-by-step explanation:
Do this:
11.65 x 94 = ?
divide the answer by 100
and that is your answer
A steel ball is dropped from a height and hits the ground 6.7 seconds after its release. From what height (in feet) was the ball released?
Step-by-step explanation:
Acceleration = g = 32.17ft/s²
Initial velocity = 0ft/s
Time taken = 6.7s
Using Kinematics,
we have s = ut + 0.5at².
=> s = (0)(6.7) + 0.5(32.17)(6.7)²
=> s = 722.06ft.
Henry can write 5 pages of his novel in 3 hours.
At this rate, how many pages can Henry write in 8 hours?
Answer:
imma say 12 pages
Step-by-step explanation: sorry if wrong
Please help! The expressions 3x - 9 and 23 - 5x represent the lengths (in feet) of two sides of an equilateral triangle. Find the length of a side. Show your work.
We are dealing with an equilateral triangle which has 3 equal sides.
length of a side = 3 ft
Since the three sides of an equilateral triangle are equal and we are given two sides to have lengths of 3x - 9 and 23 - 5x , it means that;
3x - 9 = 23 - 5x
Rearranging this gives;
3x + 5x = 23 + 9
8x = 32
x = 32/8
x = 4
putting 4 for x in 3x - 9, we have;
3(4) - 9 = 3 ft
Thus,
length of a side = 3 ft
read more at; brainly.com/question/1626548
Part B.
Describe two different ways you could find measure of CFD. What is the measure of
this angle?
Answer:
∠CFD = 60°
Step-by-step explanation:
Along line CE:
∠AFE + ∠AFB + ∠BFC = 180° (sum of angles on a straight line)
(7x + 4) + (8x + 6) + (6x + 2) = 180
collecting alike terms:
7x + 8x + 6x + 4 + 6 + 2 = 180
21x + 12 = 180
21x = 168
x = 8°
We could find the measure of CFD using:
a) Along line AD:
∠AFB + ∠BFC + ∠CFD = 180° (sum of angles on a straight line).
(8x + 6) + (6x + 2) + ∠CFD = 180
14x + 8 + ∠CFD = 180
∠CFD = `180 - (14x + 8)
∠CFD = 172 - 14x
b) ∠CFD = ∠AFE (vertical opposite angles are equal)
∠CFD = 7x + 4
To find value of ∠CFD, substitute x = 8
∠CFD = 7(8) + 4
∠CFD = 60°
I need help please help me with this question because I don’t know it
Find the surface area of the rectangular prism:
5 cm
4 cm
3 cm
4 cm
5 cm
3 cm
Answer:
94 cm²
Step-by-step explanation:
= 2 × (5×3 + 5×4 + 3×4)
= 2 × (15 + 20 + 12)
= 2 × 47
= 94 cm²
what was his hourly rate of pay ?
Answer:
the answer is A
Step-by-step explanation:
5 * 8 = 40
300/40 = 7.5
At the movies, a couple bought 2 medium drinks and a large popcorn for $13.85. At the same theater, a family bought 3 medium drinks and 2 large popcorns for a total of $23.90. What is the cost of a large popcorn?
Find the slope of the line that passes through the points (1,-4) and (3,-1).
Answer:
(2,3)
Step-by-step explanation:
you go up 3 and forward 2 so it would be positive positive.
Plzzzzzzzz help ......
Answer:
its purple
Step-by-step explanation:
The area of square ABCD is 7cm
Answer:
We know that the area of a square of sidelength L, is:
Area = L^2
In this case, we have:
L = 2cm + x cm
And we know that the area of the square is 7cm, then:
Area = 7cm^2 = (2cm + x cm)^2
7cm^2 = 4cm^2 + 4cm*xcm + (x cm)^2
7cm^2 = 4cm^2 + (4*x)cm^2 + x^2 cm^2
Now we can remove all the "cm^2" and just get the numbers:
7 = 4 + 4*x + x^2
We can subtract 4 in both sides to get
7 - 4 = 4 + 4*x + x^2 - 4
3 = 4*x + x^2
This is what whe wanted to prove.
Determine whether the triangles are similar.
similar it is just 3 times bigger but similar
Increase 386.3 by 4%
Given:
Increase 386.3 by 4%.
To find:
The value for given statement.
Solution:
We have,
Initial value = 386.3
Increasing rate = 4%
The increased value is
[tex]\text{New value}=\text{Initial value + Increasing rate }\times \text{Initial value}[/tex]
[tex]\text{New value}=386.3+\dfrac{4}{100}\times 386.3[/tex]
[tex]\text{New value}=386.3+15.452 [/tex]
[tex]\text{New value}=401.752[/tex]
Therefore, the required value is 401.752.
Adriel answered 54 questions correctly on his multiple choice history final and earned a grade of 45%. How many total questions were on the final exam?
Answer:
There were 120 questions on the test.
Step-by-step explanation:
It is given that:
Number of questions answered = 54
Grade percent = 45%
Let,
x be the total number of questions
45% of x = 54
[tex]\frac{45}{100}x=54\\0.45x = 54[/tex]
Dividing both sides by 0.45
[tex]\frac{0.45x}{0.45}=\frac{54}{0.45}\\x=120[/tex]
Therefore,
There were 120 questions on the test.
I NEED HELP PLEASE!!!!!!
Answer:
y-intercept: 11
which means the baby weighs 11 lb when it is born (t=0).
Step-by-step explanation: