Rosa and Albert receive the same amount of allowance each week. The table shows what part of their allowance they each spent on video games and pizza.
C. Who spent the greater part of their total allowance? How do you know?
Which is a better investment 8.3% compounded annually or 8% compounded quarterly.
Using compound interest, the better investment is of 8.3% compounded annually.
What is compound interest?The amount of money earned, in compound interest, after t years of the investment, is given by the following formula:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
In which the parameters are given as follows:
P is the principal, which is the value of deposit/loan/....r is the interest rate, as a decimal value.n is the number of times that interest is compounded per year, annually n = 1, semi-annually n = 2, quarterly n = 4, monthly n = 12.For the first option, of 8.3% compounded annually, the multiplier after each year is given as follows:
[tex](1 + \frac{0.083}{1}\right)^{1} = 1.083[/tex]
As the parameters are r = 0.083, n = 1.
For the second option, the parameters are given as follows:
r = 0.08, n = 4.
Hence the multiplier after each year of the investment is given by:
[tex](1 + \frac{0.08}{12}\right)^{12} = 1.0829[/tex]
Due to the higher multiplier, the first option is better, that is, 8.3% compounded annually.
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The 8% compounded quarterly has a higher effective annual rate than 8.3% compounded annually, thereby making it the better investment choice.
To determine which investment is better, we need to compare the effective annual rates (EAR) of the two options: 8.3% compounded annually vs. 8% compounded quarterly. The formula for EAR is (1 + i/n)n - 1, where i represents the interest rate and n is the number of compounding periods per year.
For the 8.3% compounded annually, the EAR is straightforward: (1 + 0.083/1)1 - 1 = 0.083 or 8.3%.
For the 8% compounded quarterly, we calculate the EAR as follows: (1 + 0.08/4)4 - 1 = (1 + 0.02)4 - 1 = (1.02)4 - 1 = 1.082432 - 1 = 0.082432 or 8.2432%.
Comparing the two EARs, the 8% compounded quarterly has a higher effective annual rate than the 8.3% compounded annually, making it the better investment.
Please please help. The table list the heights of four trees, Sycamore 15 and 2/3, Oak 14 and 3/4, Maple 15 and 3/4, Birch 15.72. Study the table above select all true statements. A. The oak tree is the shortest. B. The birch tree is the tallest. C. Two of the trees are the same height. D. The sycamore tree is taller than the maple tree.
Each car on the Steel Force train has 3 rows with 2 seats in each row. How many seats are on the train?
A car is traveling at a speed of 48 miles per hour. What is the car's speed in miles per minute? How many miles will the car travel in 2 minutes? Do not round your answers.
The car speed in miles per minute is 0.8 miles per minute and the car will travel 1.6 miles in 2 minutes.
What is distance?Distance is a numerical representation of the distance between two items or locations. Distance refers to a physical length or an approximation based on other physics or common usage considerations.
The speed of the car = 48 miles per hour
Speed in miles per minute = 48/60 = 0.8 miles per minute
Time = 2 minutes
Speed = 0.8 miles per minute
Distance = 0.8×2 = 1.6 miles
Thus, the car speed in miles per minute is 0.8 miles per minute and the car will travel 1.6 miles in 2 minutes.
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What is an estimate of the solution. If the equation 6n + 3 = 2? Use a table.
Evaluate 5x^3 + 2 for x = -1.
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{5x^3 + 2}\\\mathsf{= 5(-1)^3+2}\\\\\mathsf{(-1)^3}\\\mathsf{= -1\times-1\times-1}\\\mathsf{=1\times-1}\\\mathsf{= \bf -1}\\\\\mathsf{= 5(-1) + 2}\\\\\mathsf{5(-1)}\\\mathsf{= \bf -5}\\\\\mathsf{= -5 + 2}\\\mathsf{=\bf -3}\\\\\\\\\boxed{\boxed{\huge\text{Therefore, your answer is: \bf -3}}}\huge\checkmark\\\\\\\\\huge\text{Good luck on your assignment \& enjoy your day!}\\\\\\\frak{Amphitrite1040:)}[/tex]
My friend sets out walking at a speed of 3 miles per hour. I set out behind her 5 minutes later at 4 miles per hour. For how many minutes will my friend have been walking when I catch up to her?
Determine the prime fractorization of 364
An investment firm recommends that a client invest in bonds rated AAA, A, and B. The average yield on AAA bonds is 4 %, on A bonds 6 %, and on B bonds 11 %. The client wants to invest twice as much in AAA bonds as in B bonds. How much should be invested in each type of bond under the following conditions?
A. The total investment is $26,000 , and the investor wants an annual return of $1,620 on the three investments.
B. The values in part A are changed to $38,000 and $2,360 , respectively
A. The client should invest $(?) in AAA bonds, $(?)in A bonds, and $(?)in B bonds.
Final answer:
To meet the client's investment goals with an investment return of $1,620 on a total of $26,000, the client should invest $8,000 in AAA bonds, $14,000 in A bonds, and $4,000 in B bonds. This is derived from setting up and solving a system of linear equations based on the conditions provided.
Explanation:
Part A: Investment Calculations
To solve for the amount to invest in each type of bond, we can set up a system of equations based on the given conditions. Let x be the amount invested in AAA bonds, y be the amount invested in A bonds, and z be the amount invested in B bonds. We are told that the client wants to invest twice as much in AAA bonds as in B bonds, which gives us the equation x = 2z. The total investment is $26,000, so we have x + y + z = $26,000. The desired annual return is $1,620, and this gives us another equation based on the yields: 0.04x + 0.06y + 0.11z = $1,620.
By solving this system of equations, we can find the amounts to invest in each bond.
From x = 2z, we can substitute for x in the other equations.
The total investment equation becomes 2z + y + z = $26,000, simplifying to 3z + y = $26,000.
The return equation becomes 0.08z + 0.06y + 0.11z = $1,620, simplifying to 0.19z + 0.06y = $1,620.
We can now solve these two new equations for y and z, and then find x using x = 2z.
After solving, we get:
z (B bonds) = $4,000
x (AAA bonds) = 2z = $8,000
y (A bonds) = $26,000 - x - z = $14,000
Part B: Investment Calculations with Updated Values
The process for part B is similar, but with the updated total investment of $38,000 and a desired return of $2,360. The equations are adjusted accordingly, and after solving, we would get the new investment amounts for AAA, A, and B bonds.
The client should invest $8,000 in AAA bonds, $14,000 in A bonds, and $4,000 in B bonds for the conditions in part A.
A system of equations has infinitely many solutions. If 2y-4x=6 is one of the equations, which could be the other equation?
Answer:
Equation is [tex]-8x+4y-12=0[/tex]
Step-by-step explanation:
An equation is a mathematical statement that two things are equal .
A system of equations is a set of two or more equations consisting of same unknowns.
Two equations [tex]a_1x+b_1y+c_1=0\,,\,a_2x+b_2y+c_2=0[/tex] have unique solution if [tex]\frac{a_1}{a_2}\neq \frac{b_1}{b_2}[/tex]
infinite solution if [tex]\frac{a_1}{a_2}= \frac{b_1}{b_2}=\frac{c_1}{c_2}[/tex]
no solution if [tex]\frac{a_1}{a_2}= \frac{b_1}{b_2}\neq \frac{c_1}{c_2}[/tex]
Here, given: [tex]-4x+2y=6[/tex]
We can write this equation as [tex]-4x+2y-6=0[/tex]
Take another equation as [tex]-8x+4y-12=0[/tex]
Here, [tex]a_1=-4\,,\,a_2=-8\,,\,b_1=2\,,\,b_2=4\,,\,c_1=-6\,,\,c_2=-12[/tex]
[tex]\frac{a_1}{a_2}=\frac{-4}{-8}=\frac{1}{2}\\\frac{b_1}{b_2}=\frac{2}{4}=\frac{1}{2}\\\frac{c_1}{c_2}=\frac{-6}{-12}=\frac{1}{2}[/tex]
such that [tex]\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}[/tex]
One number is 2 more than another. The difference between their squares is 32. What are the numbers
The two numbers are 7 and 9, which are determined by setting up an algebraic equation based on the information that one number is 2 more than the other and the difference between their squares is 32.
Explanation:The question involves finding two numbers where one number is 2 more than another and the difference between their squares is 32. To solve this problem, we denote the first number as ‘x’. Therefore, the second number will be '‘x+2’, as it is given to be 2 more than the first number. Next, we set up an equation based on the provided information that the difference between their squares is 32: ‘(x+2)² - x² = 32’.
Expanding the squared terms, we get ‘x² + 4x + 4 - x² = 32’. After simplifying the equation by canceling out ‘x²’ from both sides and subtracting 4 from both sides, we get ‘4x = 28’. Dividing both sides by 4 gives us ‘x = 7’. Thus, the first number is 7, and the second number is 7 + 2, which is 9.
The two numbers in question are 7 and 9, and they meet the criteria given in the problem statement.
Raj is writing 3/2000 as a percent. find his mistake and correct it
The length of the shadow on flat ground of a man who is 6 feet tall and is standing up straight is 8 feet. The distance between the top of his head and the top of his head in the shadow is ___ feet.
20 POINTS
The science fair judges will be teachers and volunteers. Each judge will view 5 projects. There are 133 science teachers. What is the fewest number of volunteers needed to have enough judges
If there are 2115 projects in total, then 665 projects will be covered by 133 science teachers. Therefore, an additional 290 volunteers are needed to judge the remaining projects, making the correct answer option A.
Step 1: Calculate projects judged by science teachers
The number of projects each teacher can judge is 5, so:
133 teachers * 5 projects per teacher = 665 projects
Step 2: Calculate additional projects
The total number of projects should be known to determine the additional requirement. Let's denote the total number of projects as P.
If P projects must be judged and 665 projects are already covered, then:
Remaining projects = P - 665
Each volunteer can also judge 5 projects. Let V be the number of volunteers needed:
Step 3: Solve for the fewest number of volunteers
We need enough volunteers to cover the remaining projects:
5 * V ≥ P - 665
To solve this, we need the total number of projects mentioned in options:
If P = 2115, then:
Remaining projects = 2115 - 665 = 1450
1450 / 5 = 290 volunteers
The correct answer is A (290).
The complete question is
The science fair judges will be science teachers and volunteers. Each judge will only have time to view 5 science fair projects. There are 133 science teachers. What is the fewest number of volunteers needed to have enough judges for all of the projects?
A 290
B 396
C 422
D 423
Reggie Jackson hit five home runs in the 1977 World Series, which lasted six games. By contrast, Lou Gehrig hot four homeruns in the 1982 World Series, a four-game series. On the average, which baseball player hit fewer home runs per game?
Reggie Jackson hit 5 home runs in 6 games sos he hit 5/6 = 0.833 home runs per game
lou gehrig hit 4 home runs in 4 games so he hit 4/4 = 1 home run per game
0.833 is less than 1 so Reggie Jackson hit fewer home runs per game
The sum of three consecutive numbers is 57. What is the largest of these numbers?
57 / 3 =19
18 + 19 +20 = 57
largest number is 20
Answer:
20
Step-by-step explanation:
LaToya had a large collection of basketball cards. She decided to give half of them to her friends, Aaron, and a fourth of them to her brother. She still has 75 cards left. How many cards did she start out with?
LaToya originally had 300 basketball cards. She gave away 3/4 of her collection, keeping 1/4 which is 75 cards. By solving the equation 1/4 x = 75, we find that x equals 300.
Explanation:LaToya originally had a certain number of basketball cards. She gave half of them to Aaron and a fourth of them to her brother, leaving her with 75 cards. To find out how many cards she started with, let's define the total number of cards as x. Given that half and a fourth were given away, this means that 3/4 of x has been given to others, leaving her with 1/4 of her original number of cards.
Now, we can set up the equation: 1/4 x = 75. To solve for x, multiply both sides of the equation by 4, giving us x = 75 * 4, which equals 300. Therefore, LaToya originally had 300 basketball cards.
To find the number of cards LaToya started with, we can set up an equation based on the information given and solve for the unknown value.
Explanation:To find the number of cards LaToya started with, we need to work backwards from the information given. We know that she has 75 cards left after giving half to her friends and a fourth to her brother. Let's assume that the number of cards she started with is 'x'.
If she gave half to her friends, that means she gave x/2 cards to her friends. Then, if she gave a fourth to her brother, she gave x/4 cards to her brother. So the total number of cards given away is x/2 + x/4 = 3x/4.
Since she has 75 cards left, we can set up the equation: x - 3x/4 = 75. Solving this equation will give us the value of x, which represents the number of cards LaToya started with.
In a gambling game, a woman is paid $3 if she draws a jack or a queen and $5 if she draws a king or an ace from an ordinary deck of 52 playing cards. if she draws any other card, she loses. how much should she pay to play if the game is fair?
The amount that the woman should pay to play the game is $1.23. Computed using the expected return and the probability of an event.
What is the probability of an event?The probability of an event is the ratio of the number of favorable outcomes to the event, to the total number of possible outcomes in the experiment.
How to solve the question?In the question, we are given that in a gambling game, a woman is paid $3 if she draws a jack or a queen and $5 if she draws a king or an ace from an ordinary deck of 52 playing cards. If she draws any other card, she loses.
We are asked the amount the woman should pay to play the game if it is fair.
The amount that the woman should pay to play the game is her expected return from the game.
Her expected return can be shown as E(X), where X represents all possible returns, which is calculated as:
E(X) = ∑ x.P(x), where P(x) is the probability of x.
The values of x can be:
3 when she draws a jack or a queen,
5 when she draws a king or an ace, and
0 when she draws any other card.
The probabilities of drawing a:-
The total number of possible outcomes remains constant throughout as 52.
Jack or a queen:
Number of favorable outcomes = 8 {4 jacks + 4 queens}.
Thus, the probability = 8/52 = 2/13.
King or an ace:
Number of favorable outcomes = 8 {4 kings + 4 ace}.
Thus, the probability = 8/52 = 2/13.
Any other card:
Number of favorable outcomes = 36 {All remaining cards, that is, 52 - 8 - 8 = 36}.
Thus, the probability = 36/52 = 9/13.
Thus, the expected return:
E(X) = ∑ x.P(x),
or, E(X) = 0.(9/13) + 3.(2/13) + 5(2/13),
or, E(X) = 0 + 6/13 + 10/13,
or, E(X) = 16/13 = 1.23.
Thus, the amount that the woman should pay to play the game is $1.23. Computed using the expected return and the probability of an event.
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The measure of the largest angle of a triangle is 80º more than the measure of the smallest angle, and the measure of the remaining angle is 10º more than the measure of the smallest angle. Find the measure of each angle.
Solve for x
2+8-x=-24
The perimeter of a rectangular garden is 322 feet. If the width of the garden is 72 feet, what is its length?
divide 322 by 2 and then subtract the width
322 /2 = 161
161-72 = 89
length is 89 feet
A florist has 54 red roses and 36 white roses. If the florist creates the greatest number of identical bouquets possible with a combination of red and white roses without any roses leftover, how many red roses are in each bouquet?
PLEASE ANSWER THIS ASAP!!!!!!!!!!
54-36 =18
they can make 18 bouquets
54/18 =3
36/18 =2
18 bouquets with 3 red and 2 white roses each
Answer:
3
GCF of 54 and 36 = 18
so, 18 bouquets
then,
54 red roses ÷ 18 = 3 red roses in each bouquet
How can you use rates to compare the cost of two boxes of cereal that are different sizes
The volume(capacity) in cubic inches of a reach-in refrigerator that measures 24 inches by 26 inches by 70 inches is_____cubic inches.
Please show work
Find the limit. lim θ→0 cos(4θ) − 1 / sin(7θ)
Can't figure this out. Any help is appreciated!
The limit of the given expression is undefined.
Explanation:To find the limit of lim θ→0 cos(4θ) - 1 / sin(7θ), we can simplify the expression first. Using the identity cos(2θ) = 2cos²θ - 1, we can rewrite the numerator as 2(cos²(2θ) - 1). The denominator, sin(7θ), can be rewritten as sin(2θ + 5θ). By applying the sum-to-product identities, we get sin(2θ)cos(5θ) + cos(2θ)sin(5θ), or cos(5θ)sin(2θ) + cos(2θ)sin(5θ).
Now, if we multiply both numerator and denominator by 1/sin(2θ)cos(5θ), we can simplify the expression further:
lim θ→0 (2cos²(2θ) - 1) / (cos(5θ)sin(2θ) + cos(2θ)sin(5θ)) = lim θ→0 (2cos(2θ) - 1/sin(2θ)) / (cos(5θ) + cos(2θ)tan(5θ)).
Now, we can substitute θ = 0 into the expression. Since cos(0) = 1 and sin(0) = 0, the denominator becomes cos(5(0)) + cos(2(0))tan(5(0)) = cos(0) + cos(0)tan(0) = 1 + 1(0) = 1. Thus, the limit is:
lim θ→0 (2cos(2θ) - 1/sin(2θ)) / (cos(5θ) + cos(2θ)tan(5θ)) = (2cos(2(0)) - 1/sin(2(0))) / 1 = (2cos(0) - 1/0) / 1 = (2(1) - 1/0) / 1 = (2 - 1/0) / 1 = 1/0 = undefined.Learn more about Limits here:https://brainly.com/question/8533149
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The manager at a movie theater keeps track of the number of evening tickets and matinee tickets sold each day and the total money received. On Friday, a total of 63 tickets were sold, and the money collected was $742. If evening tickets are sold for $14 and matinee tickets are sold for $10, how many evening tickets and matinee tickets were sold?
Ellen drove 220 miles in 3.5hours. To the nearest tenth, find Ellen's average speed in miles per hours
divide total miles by time:
220 / 3.5 = 62.857
rounded to nearest tenth = 62.9 miles per hour
The number that appears more frequently than any other in a set of numbers is the ________.
what is the final amount of $70.00 that is put into a savings account with 16% interest rate for 25 years, if the interest is comounded 4 times per year?