Final answer:
Peter invested $3,700 at a 3% loss and $7,800 at a 4% gain. By setting up a system of equations and solving them, we determined the amount invested in each.
Explanation:
To solve the problem of how much was invested by Peter in each investment, we need to set up a system of equations. Let's call the amount invested at 3% loss x, and the amount invested at 4% gain y. The total amount invested is $11,500, so we have x + y = $11,500.
Peter's net annual receipts were $201, which comes from a loss of 3% on investment x and a gain of 4% on investment y. The equation for this would be -0.03x + 0.04y = $201.
Now we have a system of two equations:
-0.03x + 0.04y = $201
Adding (1) and (2) gives us:
0.03y + 0.04y = $546
Combining like terms, we get:
0.07y = $546
Dividing both sides by 0.07, we find that:
y = $7,800
Substituting y back into the first equation, we get:
x = $11,500 - $7,800 = $3,700
So, Peter invested $3,700 in the investment with a 3% loss and $7,800 in the investment with a 4% gain.
Simplifying expressions with exponents
What is the largest possible value of y, if y = - | 3 - x | + 5
What are the orders of 3,7,9,11,13,17 and 19(mod20)?does 20 have primitive roots?
The price of a calculator dropped from $32.88 to $25.95. What was the percent decrease in price
what's 6 3/4 divided by 1 7/8
The value of 6 (3/4) divided by 1 (7/8) is 3 (3/5).
What is a fraction?A fraction is a part of the whole represented by a/b, where a and b are any integers
The given numbers are 6 (3/4) and 1 (7/8).
Simplify the mixed fractions:
6(3/4) = 27/4 and 1 (7/8) = 15/8
Now, divide 27/4 by 15/8:
27/4 ÷ 15/8
= 27/4 × 8/15
= 18/5
= 3 (3/5)
Hence, The value of 6 (3/4) divided by 1 (7/8) is 3 (3/5).
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Can anyone please solve the attached file?
Jane noticed as she was doing her morning run that a 12 m flagpole cast a 18 m shadow. A tree was casting a 36 m shadow. The tree was __? ___ m tall.
Factor completely 2x3 + 14x2 + 4x + 28.
Aurora earns a salary of $25,000 per year. Her benefits are equal in value to 30 percent of her salary. What is the value of Aurora's benefits?
Value of Aurora's benefits as 30percent of her salary is equals to $7500.
What is percentage?" Percentage is defined as the hundredth part of the given whole number."
According to the question,
Salary amount of Aurora = $25,000
Benefit value = 30 percent of ( $25,000)
Therefore,
30 percent of ( $25,000) = 30% of 25,000
= [tex]\frac{(30) * (25,000)}{100}[/tex]
= $7,500
Hence, value of Aurora's benefits as 30percent of her salary is equals to $7500.
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Solve l=14j+3k for j.
To solve the equation l = 14j + 3k for j, subtract 3k from both sides and then divide by 14, giving j = (l - 3k) / 14.
Explanation:To solve the equation l=14j+3k for j, you need to isolate j on one side of the equation. Here's how it is done step by step:
Start with the original equation: l = 14j + 3k Subtract 3k from both sides of the equation to isolate the term with j in it: l - 3k = 14j Divide both sides of the equation by 14 to solve for j: j = (l - 3k) / 14Therefore, the solution to the equation for j is: j = (l - 3k) / 14.
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Ava wants to wash one load of laundry at a local laundromat. At laundromat A, it costs $6.35 to wash and $1.25 to dry one load of laundry. At laundromat B, it costs $5.95 to wash and $0.85 to dry one load of laundry. Which laundromat has the better price for doing one load of laundry, and by how much?
Laundromat A = 6.35 +1.25 = 7.60 for one load
Laundromat B = 5.95 +0.85 = 6.80 for one load
7.60-6.80 = 0.80
Laundromat B is has the better price by 0.80 cents
Using the formula in model 1, choose the correct answers for the new balance and amount of interest earned in the following compound interest problem. $1,050 at 6%, for 25 years, compounded annually. Total Amount = $ Interest Amount =$
The Panthers, a high school basketball team, charges $6 for adult tickets and $3 for children’s tickets. If 120 people went to the most recent game, and the total earnings for ticket sales was $612, how many children went to the game?
There were 36 children at the game.
There were 50 children at the game.
There were 84 children at the game.
There were 108 children at the game.
Answer:
The answer is 36 children
Step-by-step explanation:
There were 36 children at the game
The number of children who went to the game was 36
What is Linear Equation in 2 variables?
An equation is said to be linear equation in two variables if it is written in the form of ax + by + c = 0, where a, b & c are real numbers and the coefficients of x and y, i.e a and b respectively, are not equal to zero.
Given data ,
Let the number of children be = x
Let the number of adults be = y
Cost of ticket for 1 child = $ 3
Cost of ticket for 1 adult = $ 6
Total number of people who went to the game = 120
So , x + y = 120
Total earnings for the ticket sales = $ 612
Total earnings =
( Cost of one child x Number of children ) + ( Cost of one adult x Number of adult)
Total earnings = 3x + 6y
Now , we have 2 equations to solve
x + y = 120 be equation (1)
3x + 6y = 612 be equation (2)
Multiply equation (1) by 3 , we get
3x + 3y = 360 be equation (3)
Subtract equation (3) from equation (2)
3x + 6y - ( 3x + 3y ) = 612 - 360
3y = 252
Divide by 3 on both sides , we get
y = 84
So , the number of children who went to the game will be
x + y = 120
x + 84 = 120
Subtract 84 on both sides , we get
x = 36
Hence , the number of children who were at the game was 36
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Simplify the expression by using a double-angle formula. 2 cos^2 4 theta -1
A square with an area of 169 cm^2 is rotated to form a cylinder. What is the height of the cylinder?
Answer:
13 cm
Step-by-step explanation:
Area of the square is [tex]169 \:\:cm^{2}[/tex]
The square is rotated to form a cylinder. Now, we first need to find the side of the square, the cylinder is formed by rotating along its side.
Now area of square [tex]169 \:\:cm^{2}[/tex]
We know that area of square is [tex]\text{side}\times\text{side}[/tex]
So, [tex]\text{side}\times\text{side}=169[/tex]
[tex]\text{side}\times \text{side}=13\times13[/tex]
[tex]\text{side}=13 \:\text{cm}[/tex]
Now, as the cylinder is formed by rotating along its length, and we know that all the sides of a square is equal.
So, one side becomes the height of the cylinder and the other becomes the circumference.
Hence, the height of the cylinder is 13 cm.
Rita attends school 180 days out of the 365 days in a year. For what fraction of the year is Rita in school? Write your answer in simplest form.
the fraction is 180/365
this can get reduced to 36/73
EASY 5 POINTS!!!!! You have a 1-gallon paint can in the shape of a cylinder. One gallon is 231 cubic inches. The radius of the can is 3 inches. What is the approximate height of the paint can? Use 3.14 for pi.
A.) 5 inches
B.) 25 inches
C.) 8 inches
D.) 26 inches
Answer:
The height of the cylinder shaped can = 8.17 inches
Step-by-step explanation:
Volume of the cylinder shaped can = 1 gallon
1 gallon = 231 cubic inches
So, Volume of the cylinder shaped can = 231 cubic inches
Radius of the can = 3 inches
[tex]\text{Now, Volume of the cylinder = }\pi\times radius^2\times height\\\\\implies 231=3.14\times 3^2\times height\\\\\implies height=\frac{231}{3.14\times 9}\\\\\implies height\approx 8.17\text{ inchjes}[/tex]
Hence, The height of the cylinder shaped can = 8.17 inches
The distribution of the number of occurrences of the letter t on the pages of a book is found to be a normal distribution with a mean of 44 and a standard deviation of 18. If there are 500 pages in the book, which sentence most closely summarizes the data?
The data represents a normal distribution where approximately 68 percent of the pages will have a number of occurrences of the letter t within one standard deviation of the mean, 95 percent within two standard deviations, and more than 99 percent within three standard deviations.
Explanation:The sentence that most closely summarizes the data is: For data having a distribution that is bell-shaped and symmetric, the following are true:
Approximately 68 percent of the data is within one standard deviation of the mean.Approximately 95 percent of the data is within two standard deviations of the mean.More than 99 percent of the data is within three standard deviations of the mean. This is known as the Empirical Rule.Using this information, we can conclude that approximately 68 percent of the pages in the book will have a number of occurrences of the letter t within one standard deviation of the mean, which is 44. Approximately 95 percent of the pages will have a number of occurrences within two standard deviations, and more than 99 percent will have a number of occurrences within three standard deviations.
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jack is mowing a lawn that has a shed. needs to know area of lawn to mow. dimensions of yard are 5x by 13 x-4 . she'd are 2x by 2x+4. " find polynomial that describes area of lawn needed to mow. Polynomial in answer should have two terms.
please help.
The table below shows the number of marbles of different colors in a bag: Color of Marbles Number of Marbles Pink 5 Blue 2 Green 3 Ursula draws a marble from the bag randomly without looking. She then draws another marble from the bag without replacing the first one. Which expression shows the probability of drawing green marbles in both the trials? plz help!!!!
can someone explain to me multi step algebra equations? 15 points Thaaaanks~
Final answer:
Multi-step algebra equations involve operations like addition, subtraction, multiplication, or division to solve for an unknown. These equations require simplifying terms, solving for unknowns, and checking the answers. Money examples and practice statements are useful for understanding these concepts.
Explanation:
Multi-step algebra equations are problems that require more than one operation, such as addition, subtraction, multiplication, or division, to solve for the unknown variable. The following steps are typically involved in solving these equations:
Eliminate terms wherever possible to simplify the algebra. This might involve combining like terms or canceling out terms on both sides of the equation.Solve the simultaneous equations for the unknowns. This can be done through methods such as substitution or elimination when dealing with more than one equation.Check the answer to ensure it fits the original equation. Substituting the solution back into the original equation can verify its correctness.An example of this process could be the following scenario: You are given two equations in a word problem involving motion, one equation for velocity and another for time. To find the distance traveled, you would identify the known variables and the unknown variable (in this case, distance), simplify both equations as much as possible, and then combine them to solve for distance.
Money examples are often used for educational purposes because they provide a familiar context for understanding mathematical principles, making them easier to grasp. Additionally, practicing with state-ments, such as covering up a number to solve for it with the remaining information, can help build problem-solving skills.
Divide the decimal numbers 12.012÷6
Name the properties that were used to derive the properties of logarithms.
The properties that were used to derive the properties of logarithms are the properties of exponent because logarithms are exponents. The properties of exponents are: product of powers, power to a power, quotient of powers, power f a product and power of a quotient.
As an example, the log property log(a^k) = k log (a) can be derived from the exponential property (b^a)^k = b^(ak).
Likewise,
log (ab) = log (a) + log (b) comes from c^(a+b) = c^a*c^b
Proof:
Let x = c^a and y=c^b
Then,
log (x) = a and log (y) =
b (base c)
log (xy) = log (c^a * c^b) = log (c^(a+b)) = a+b = log(x) + log (y)
14. Simplify (4x^– 4)^– 3.
The sum of two consecutive even integers is 138. Write an equation and solve
The two consecutive even integers that sum to 138 are 68 and 70. The equation n + (n + 2) = 138 was used to determine these integers.
Explanation:The problem is asking for two consecutive even integers whose sum is 138. Let's denote the first integer as n (where n is an even number). As the problem says the numbers are consecutive even integers, we know the next number must be n + 2.
We can form an equation based on the information given. The sum of these two integers is equal to 138, so:
n + (n + 2) = 138If we simplify the equation, it becomes:
2n + 2 = 138By subtracting 2 from both sides, 2n = 136We then divide both sides by 2 to get n = 68Therefore, the two consecutive numbers are 68 and 70 as they add up to 138.
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Under what circumstance are two non right triangles congruent
How do you change a ratio into a fraction baseballs to basketballs
is 70 thousand written in standard form or word form
Which expression is equivalent to the given expression? 100pts giveaway 3x(1.05) 3x + 3x + 3x 1.05x + 1.05x + 1.05x x + 3.15 1.05x + 3
Find all values of c such that f is continuous on (-∞, ∞). $ f(x) = \left\{ \begin{array}{lcl} {\color{red}5} - x^{2}, & & x \le c \\ x, & & x > c \end{array}\right. $
The values of c such that the function f is continuous are: c = -2.79 and c = 1.79
The function is given as:
[tex]f(x) = \left\{ \begin{array}{lcl} {5} - x^{2}, & & x \le c \\ x, & & x > c \end{array}\right.[/tex]
For the function to be continuous, then the following must be true
[tex]5 - x^2 = x[/tex]
Substitute c for x
[tex]5 - c^2 = c[/tex]
Express as a quadratic function
[tex]c^2 + c - 5 = 0[/tex]
Using a graphing calculator, the values of c are:
c = -2.79 and c = 1.79
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