Answer:
Step-by-step explanation:
The balance of an account after a year, when the interest rate is 3% per year and there are no additional withdrawals or deposits, can be represented by the formula:
Balance = Principal + Interest
where Principal is the initial amount of money invested (m) and Interest is the interest earned on that amount for the year.
Interest is calculated as the product of the principal, the interest rate, and the time period. In this case, the interest rate is 3% (or 0.03), and the time period is one year. Therefore the Interest can be represented by the following expression:
Interest = Principal * Interest Rate * Time
Substituting the given values:
Interest = m * 0.03 * 1
So the expression that represents Arianys balance after a year is:
Balance = m + (m*0.03)
= m + 0.03m
= 1.03m
This expression represents her balance after a year, assuming she makes no additional withdrawals or deposits.
Using Squeeze/Sandwich Theorem,
Calculate the limit of : lim [(x,y) -> (0,0)] (3 . x^2 . y / (x^2 + y^2))
Using Squeeze theorem, the limit of the function is 0
What is the LimitThe Squeeze Theorem states that if f(x,y) <= g(x,y) <= h(x,y) for all x,y in a region around (x0,y0) and lim (x,y)->(x0,y0) g(x,y) = L, then lim (x,y)->(x0,y0) f(x,y) = lim (x,y)->(x0,y0) h(x,y) = L.
We can use the Squeeze Theorem to find the limit of the given function by finding two other functions that bound it and have known limits as (x,y) approaches (0,0).
We can see that
(x^2+y^2)/(x^2+y^2) <= 3x^2y/(x^2+y^2) <= (3xy)/(x^2+y^2)
As x,y approaches 0, the first inequality approaches 1 and the second one approaches 0, so the limit of the given function is also 0.
Therefore, lim [(x,y) -> (0,0)] (3 . x^2 . y / (x^2 + y^2)) = 0.
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16 People fit comfortably in a 8 feet by 9 feet area. Use this value to estimate the size of a crowd that is
5 feet deep on both sides of the street along a 2-mile section of a parade route.
Answer:
Step-by-step explanation:
It is impossible to accurately estimate the size of the crowd without knowing how many people are standing in each foot of space. However, if we assume that 16 people fit in a 9 ft x 8 ft area, then we can estimate the size of the crowd in a 2-mile section of the parade route that is 5 feet deep on both sides of the street.
Assuming a 5-foot deep crowd on both sides of the parade route, we can estimate that there would be 40 feet of crowd on one side of the parade route and 40 feet of crowd on the other side of the parade route. This means that there would be a total of 80 feet of crowd across the 2-mile parade route.
Using the assumption that 16 people fit in a 9 ft x 8 ft area, we can estimate that there would be 1280 people across the 2-mile parade route (80 feet x 16 people). This is a rough estimate, as it does not account for the gaps between people, which would likely reduce the total number of people in the parade route.
the average of the first two multiples is 28 and the average of the last two is 44 what is the greater multiples on abby's list
Answer:
108
Step-by-step explanation:
average of first two multiples = 28
sum of first two multiples = 28 * 2 = 56
average of last two multiples = 44
sum of last two multiples = 44 * 2 = 88
average of all four multiples = ( 56 + 88 ) / 4 = 36
value of greater multiple = (88 + 56) - 36 = 108
What is the answer of this triangle congruence question.
The value of x in the triangles are 9.
What is a quadratic equation?For variable x : ax² + bx + c = 0, where a≠0 is a standard quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution since it is a second-order polynomial equation, which is guaranteed by the algebraic basic theorem.
Given:
The triangles are congruent.
That means, their corresponding angles are also congruent.
In ΔJKL,
the sum of all the angles of the triangle is 180°.
So,
x²-2x + x + 29 + 3x + 52 = 180
x² + 2x - 99 = 0
Solving the quadratic equation,
x² +11x - 9x - 99 = 0.
x (x + 11) -9 (x + 11) = 0
x = 9 and x = -11
Here, we take x = 9.
Therefore, the value of x is 9.
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Find the average rate of change of g(x) =5x^3+4/x^2 on the interval [-1,2]
The average rate of change of g(x) =5x^3+4/x^2 on the interval [-1,2] is -2
What is a function?A function can be defined as a law, rule or expression explaining the relationship between two variables.
These variables are called;
The independent variableThe dependent variableFrom the information given, we have the function;
g(x) =5x^3+4/x^2
For the interval, {1, -2}
Let's substitute the value of x as 1
g(1) = 5(1)³ + 4/(1)²
find the values
g(1) = 5 + 4/1
g(1) = 9/1 = 9
For x = -2
g(-2) = 5(-2)³ + 4/(-2)²
find the values and substitute
g(-2) =5(-8) + 4/ -8
g(-2) = -40 + 4/-8
add the numerators
g(-2) = -36/8
divide the values
g(-2) = -9/2
The average change = 9 ÷ -9/2 = 9 × 2/-9 = -2
Hence, the value is -2
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how to solve this long division
Answer:
Step-by-step explanation:
Answer:
0.5 is the answer
Step-by-step explanation:
2 clearly cannot be divided by 4
So what we have to do is put a 0 over the 2 and a decimal in the place after the 2 and bring down a 0 making it 20÷4=5
Don't forget the decimal point that was necessary to create the 20
That makes the answer 0.5
Mean, Median and Mode of the following set of numbers.
13, 11, 17, 14, 20, 6, 15, 15, 12, 6, 13, 24, 22, 19
Answer:
Mean: [tex]14 \frac{11}{207}[/tex]
Median: 14.5
Mode: 6, 13, and 15
Step-by-step explanation:
We will start by arranging these numbers from smallest to greatest to get the median and mode:
6, 6, 11, 12, 13, 13, 14, 15, 15, 17, 19, 20, 22, 24
To get the mode, we will look. There are two 6, 13, and 15. So those three are our modes. Then, since there are 14 numbers, we will split the list in half and find the average of the two most inward numbers. We get:
6, 6, 11, 12, 13, 13, 14 15, 15, 17, 19, 20, 22, 24
Our two most inward numbers are 14 and 15, so we add the two together and then divide by 2, giving us:
14 + 15 = 29/2 = 14.5
So our median is 14.5.
Finally, we will add up all the numbers together, then divide by 14 to get our mean. We get:
6 + 6 + 11 + 12 + 13 + 13 + 14 + 15 + 15 + 17 + 19 + 20 + 22 + 24 = 207
Then we divide by 14:
[tex]\frac{207}{14} = 14 \frac{11}{207}[/tex]
So, our median is [tex]14 \frac{11}{207}[/tex].
Hope this helped!
PLEASE HELPP!!!!!!!!!
The number of tickets that Sam can buy, given the amount he has to spend and the price of admission, is 36 tickets.
The rate of change is $ 0.75 per attraction.
The table on the number of tickets and total cost is:
Number of tickets 1 5 10 15
Total cost $ 10. 75 $ 13.75 $17.50 $ 21. 25
How to find the cost of tickets ?The number of tickets that Sam can buy when he has $ 37 is:
= (Amount to spend - Cost of admission ) / Cost per ticket
= ( 37 - 10 ) / 0.75
= 36 tickets
The rate of change is therefore the $ 0.75 charged per ticket per event.
The number of tickets for $ 10. 75 is:
= ( Total cost - Cost of admission ) / cost per ticket
= ( 10. 75 - 10 ) / 0.75
= 1 ticket
The cost of 5 tickets :
= ( Number of tickets x cost per ticket) + cost of admission
= (5 x 0. 75 ) + 10
= $ 13. 75
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A fair coin is tossed 12 times. How many different sequences of tosses could there have been, if the number of tosses was even.
The number of different sequences of tosses could there have been, if the number of tosses was even 1/2
How to determine the number of tosses?You should understand that the tosses involves a sequence which is an array of numbers in a particular order
The question reads thus How many different sequences of tosses could there have been, if the number of tosses was even.
Number of tosses = 12
The tosses are 1,2,3,4,5,6,7,8,9,10,11,12 = 12 Times
The even numbers are
2,4,6,8,10,12 = 6 times
The Probability of the toss is 6/12
Therefore the number of tosses equals 1/2
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need help asap help help help help help help!!!!!!!!!!!
Answer:
Step-by-step explanation:
A coefficient is a number that is blank by a blank or an expression
A coefficient is a number that is multiplied by a function or an expression.
What is a coefficient?A coefficient is a multiplier to a function or an expression.
For example, in a polynomial function, the coefficients are the terms that multiply the powers of x.
Taking the standard quadratic function as follows:
y = ax² + bx + c.
The coefficients are a, b and c.
Considering this concept, the blanks are completed on the answer at the beginning.
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Triangle HIJ is similar to triangle KLM find the measure of side KL around your answer to the nearest tenth if necessary
The measure of side KL from triangle KLM is 22 units.
What are similar triangles?Two triangles are similar if the angles are the same size or the corresponding sides are in the same ratio. Either of these conditions will prove two triangles are similar.
Given that, triangle HIJ is similar to triangle KLM.
From the similar triangles,
JH/MK =HI/KL
31/13.9 =49/KL
31KL=49×13.9
31KL=681.1
KL=681.1/31
KL=21.97
KL≈22
Therefore, the measure of side KL is 22 units.
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Help me find the answer for this question
The graphs of the functions f(x) and g(x) are attached with the answer.
What is a 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.Functions whose domain are the non - negative integers, known as sequences, are often defined by recurrence relations.Given a function as [tex]${\displaystyle f\colon X\to Y}[/tex] its graph is, formally, the set -[tex]${\displaystyle G=\{(x,f(x))\mid x\in X\}.}[/tex]
Given are the functions f(x) and g(x).
The given functions are -
f(x) = [tex]$100(\frac{3}{5})^{x}[/tex]
g(x) = [tex]$100(\frac{2}{5})^{x}[/tex]
Refer to the graphs of the function f(x) and g(x).
Therefore, the graphs of the functions f(x) and g(x) are attached with the answer.
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Keisha reads a label on a measuring cup that shows 16 fluid ounces is the same as 2 cups. Using this information, how many fluid ounces are in 4.5 cups?
There are 36 fluid ounces in 4.5 cups
How to calculate the number of fluid ounces in 4.5 cups?
Keisha reads a label on a measuring cup
The reading shows that 16 fluid ounces is the same as two cups
Therefore the number of fluid ounces in 4.5 cups can be calculated as follows
16/2
= 8
8 × 4.5
= 36
Hence there are 36 fluid ounces in 4.5 cups
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What is the probability of getting the sum ‘10’, when you role 2 dices?
Answer:
total probability (1,1),(1,2),(1,3)(1,4) (1,5)(1,6)
(2,1) (2,2) (2,3) (2,4) (2,5)(2,6)
(3,1)(3,2)3,3 3,4) (3,5) (3,6)
(4,1) (4,2)(4,3)(4,4)(4,5)(4,6)
(5,1)(5,2)(5,3)(5,4)(5,5)(5,6)
(6,1)(6,2)(6,3)(6,4)(6,5)(6,6)
3/36=1/12
Step-by-step explanation:
A population of pea aphids doubles every week. The population begins with 300 individual pea aphids. In how many weeks will the population reach 9,600 individuals?
Answer:
To find out how many weeks it will take for the pea aphid population to reach 9,600 individuals, we need to determine how many times the population needs to double to reach that number.
We can use logarithms to find this out. Using the rule log(A) / log(B) = log(A) to base B, we can calculate the number of times the population needs to double.
log(9600) / log(2) = log(9600) to base 2 = 9.98
So the population needs to double 9.98 times.
Since the population doubles every week, it will take 9.98 weeks for the population to reach 9,600 individuals.
Vote Branliest!
Answer: 5 weeks
Step-by-step explanation: Based on the information given, let's conduct an equation. It'd look something like this:
300 * [tex]2^{x}[/tex] = 9600
Now, we need to "reduce" the greatest common factors on both sides of the equation. This is so we can find the value of "x" It should look like this:
[tex]2^{x}[/tex] = 32
Now, we need to covert both sides to have the same base, which should look like this:
[tex]2^{x} = 2^{5}[/tex]
Based on the information given, we now know that x = 5, making it have a constant rate of 5 weeks to reach 9,600 individuals. I hope this helped!
Select the correct answer.
Which type of investment offers both capital gains and interest income?
Α. property
B. CDs
C. stocks
D. bonds
Answer:
D
Step-by-step explanation:
A manufacturer has an order from flower shop to make gift boxes. A gift box is to be constructed from a piece of cardboard 60x60 cm by cutting out squares from the corners and folding up the sides. What is the size of cut out that will provide a gift box of maximum volume?
To maximize the volume we need to cut squares with a side length of 20cm.
How to maximize the volume?
Suppose that the length of the sides of the squares that we cut is X, that will be the height of the box, then its volume will be:
V = (60 - X)*(60 - X)*X
Now we just need to maximize that cubic equation.
V = X*( X^2 - 120*X + 3600)
V = X^3 - 120X^2 + 3600X
To maximize this we need to differentiate it and find the value of X that makes it equal to zero, we will get:
V' = 3*X^2 - 2*120*X + 3600
V' = 3*X^2 - 240*X + 3600
Now we make this equal to zero:
3*X^2 - 240*X + 3600 = 0
The solutions are given by the quadratic formula:
[tex]X = \frac{240 \pm \sqrt{240^2 - 4*3600*3} }{2*3} \\\\\\X = \frac{240 \pm 120 }{6}[/tex]
We will take the smaller solution:
X = (240 - 120)/6 = 20
Because the other solution makes the volume equal to zero.
This means that we need to cut squares with a side length of 20 cm.
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The brain volumes (cm³) of 20 brains have a mean of 1085.2 cm³ and a standard deviation of 125.6 cm³. Use the
given standard deviation and the range rule of thumb to identify the limits separating values that are significantly low or
significantly high. For such data, would a brain volume of 1386.4 cm³ be significantly high?
If the brain volumes (cm³) of 20 brains have a mean of 1085.2 cm³ and a standard deviation of 125.6 cm³. For such data: it is significantly low for a brain because 1386.4 cm³ is less than the upper limit.
How to find the lower and upper limits?Mean = 1085.2 cm³
Standard deviation = 125.6 cm³
Hence,
Lower limit = Mean - 2 x Standard deviation
Lower limit =1085.2 - 2 x 125.6
Lower limit =1161.2 - 251.2
Lower limit =910
Upper Limit = Mean + 2 x Standard deviation
Upper Limit = 1161.2 + 2 x 125.6
Upper Limit =1161.2 +251.2
Upper Limit =1412.4
The limit of values is from 910 to 1412.4.
A value below 910 will be is considered low and a value above 1412.4 will be considered high
Therefore 1386.4 cm³ is less than the upper limit. Thus it is significantly low for a brain.
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Could you please verify this answer ?
Answer:
The equation that this graph corresponds to is y -3/4x + 8
Step-by-step explanation:
The answer choice you chose is correct.
The nutrition fact sheet at a fast food restaurant says a small portion of chicken nuggets has 180 calories, and 108 calories are from fat. What percent of the total calories is from fat?
Answer:
60% of the total calories is from fat
Step-by-step explanation:
We already have our first value 180 and the second value 108. Let's assume the unknown value is Y which answer we will find out.
As we have all the required values we need, Now we can put them in a simple mathematical formula as below:
STEP 1Y =
108
180
By multiplying both numerator and denominator by 100 we will get:
STEP 2Y =
108
180
×
100
100
=
60
100
STEP 3Y = 60
Is 17/4 an mixed number an improper fraction
Answer:
improper fraction
Step-by-step explanation:
A mixed number has a whole number and a fraction.
An improper fraction is a fraction with a numerator bigger than the denominator.
Since 17 > 4 and there is no whole number, this is an improper fraction.
It can be changed to a mixed number by dividing the numerator by the denominator
17 ÷4 = 4 and there is a remainder of 1. The remainder goes over the denominator
4 1/4
Answer: It's an improper fraction
Step-by-step explanation: It's an improper fraction because an improper fraction is a fraction where the numerator is greater than the denominator, whereas a proper fraction is the opposite. A mixed number is when there is a whole number and then a regular (proper) fraction beside it. Here's an example:
[tex]5\frac{1}{7}[/tex]
Since 17 is greater than 4, 17/4 is an improper fraction. Now, if you wanted to find 17/4 as a fraction, you would divide the 17 by the 4, so the whole number (4 in this case) would be the whole number, and the faction would be 1/4
So, [tex]\frac{17}{4}[/tex]= [tex]4\frac{1}{4}[/tex]
To check, you can multiply the 4 by the 4, which is 16, and add the numerator (1) to it, which would be 17/4. I hope this helps.
The chart below describes the speed of four painters. Which painter is the fastest?
20/04 cash deposit balance 29 385 48 how was it calculated
Solve for x 2/5=6/21-x
The value of x is 6
How to calculate the value of x ?2/5 = 6/21-x
Cross multiply both sides
2(21-x)= 30
42-2x= 30
collect the like terms
-2x= 30-42
-2x= -12
Divide both sides by the coefficient of x which is 2
2x/2 = 12/2
x= 6
Hence the value of x is 6
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Assuming a Perfectly Competitive firm has the following cost function: TC = 1000 + 600Q – 10Q2 + 0.05Q3 . Minimum AVC is
Therefore , to calculate the average AVC, use the formula: TC at 0 output is 5, which equals fixed cost (FC) of 5.
How are AVC, AFC, and TC calculated?The fixed cost per unit of output is known as the AFC, and the variable cost per unit of output is known as the AVC. We previously stated that Bob's Bakery can produce 100 loaves with FC = 40, VC = 500, and TC = 540. ATC = TC/Q = 540/100 = 5.4 as a result. Additionally, AVC = 500/100 = 5 and AFC = 40/100 = 0.4.
Here,
Total cost is equal to total fixed cost plus total variable cost, or TC.
In order to obtain the VC at each output, we must first subtract 5 from the TCs for all subsequent output levels.
AVC is now equal to VC divided by Q.
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Find an ordered pair (x, y) that is a solution to the equation.
-x+2y=7
(x, y) = (_, _)
To answer this, you get to pick any x-value and then solve for y OR you can pick any y-value and solve for x.
For this one, let's pick x = 3. We'll then substitute 3 in for x in the equation:
- (3) + 2y = 7
and then solve for x:
-3 + 2y = 7
Add 3 to both sides:
2y = 10
Divide by 2 on both sides:
y = 5
This shows that (3,5) is a solution for the equation.
Again, you could pick any x-value and solve for y OR pick any y-value and solve for x. There are an infinite number of solutions.
Abe’s apple orchard plants both green apple trees and red apple trees. This years planting will include 21 red apple trees and 18 green apple trees. What is the ratio of green apple trees to red apple trees.
Winston leaned a 32-foot ladder against the side of a building. The
base of the ladder is 3 feet from the base of the building. The top of
the ladder is 15 feet from the top of the building. How tall is the
building? Provide an answer accurate to the nearest tenth of a foot.
Answer:
the building is approximately 28.3 feet tall, accurate to the nearest tenth of a foot.
Step-by-step explanation:
The height of the building can be found using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In this case, the building is the hypotenuse, and the base of the ladder and the top of the ladder form the other two sides.
The height of the building can be found using the following formula:
h = √(32^2 - 15^2)
h = √(1024 - 225)
h = √(799)
h ≈ 28.3 ft
In an elastic collision, momentum and kinetic energy are conserved.T or F?
Answer: True. In an elastic collision, both momentum and kinetic energy are conserved. This means that the total momentum and total kinetic energy of the system before the collision is equal to the total momentum and total kinetic energy of the system after the collision.
Step-by-step explanation:
