If I deposit $400 each month into an account earning 8% interest compounded monthly, I will have $6,517 in my account in 35 years. The total money that I will put into the account is $168,000. I will earn a total compound interest of $6,117.
Calculating the Sum of Money in 35 yearsGiven information is as follows,
Principal, P = $400
Rate = 8%
Time, T = 35 years
n = 12 (Compounded monthly)
The amount for compound interest is given as,
A = [tex]P\frac{(1+\frac{R}{n} )^{nT} -1}{R/n}[/tex]
A = [tex]400\frac{(1+\frac{0.08}{12} )^{12.35} -1}{0.08/12}[/tex]
A = 6,517.02
A = $6,517 (to the nearest cents)
Calculating the Amount Put in AccountSince, $400 is deposited every month for 35 years,
Amount Put in 35 years for this compound interest =$400 × 12 × 35
= $168,000
Calculating the Compound InterestA = P + CI
Thus, the compound interest is given by,
CI = A - P
CI = 6517 - 400
CI = $6,117
I will earn a total interest of $6,117
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Convert each rate using dimensional analysis 44yds/s=?mi/h
Using dimensional analysis we have converted 44 yards/sec = 90 miles/hour.
What is dimensional analysis?Dimensional analysis is the study of how dimensions and units of measurement affect the relationship between physical quantities.
Dimensional analysis is crucial because it maintains the consistency of the units, which facilitates accurate mathematical computation.
As we use conversion factors to obtain the same units, dimensional analysis is also known as the Factor Label Method or Unit Factor Method.
We know that 1 yards/sec = 2.04545 miles/hour
Here given that 44yds/s = ? miles/hour
Lets solve
1 yards/sec = 2.04545 miles/hour
44 yards/sec = 44 × 2.04545 miles/hour
44 yards/sec = 89.9998 miles/hour
44 yards/sec = 90 miles/hour
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Examine the straight line depreciation O I/so 1 A value 189 art mintiw graph for a car. 9m 10 Doled 1 35,000 a. At what price was the car purchased? b. After how many years does the car totally depreciate? c. Write the equation of the straight line depreciation graph shown.
a. The y-intercept of the graph is 35,000, which represents the original purchase price of the car. Therefore, the car was purchased for $35,000.
b. We can see from the graph that the car's value becomes 0 after 9 years. Therefore, the car totally depreciates after 9 years.
c. The equation of a straight line can be written as y = mx + b, where m is the slope and b is the y-intercept. The slope of the graph is the rate of depreciation, which is -4000. The y-intercept is the original price of the car, 35000.
So the equation of the straight line depreciation graph is: y = -4000x + 35000
This equation represents the value of the car, where y is the value of the car (in dollars) x is the number of years since the car was purchased and -4000 is the rate of depreciation and 35000 is the original price of the car.
IXL Question‼️
Write the answer in the form mx + b
The equation in slope intercept form is y=-9x-8
What is slope?Slope is defined the rate of change of y with respect to x. the slope is also denoted by increase in y over increase in x.
The slope intercept form of a straight line is one of the most common forms used to represent the equation of a line. The slope intercept formula can be used to find the equation of a line when given the slope of the straight line and the y-intercept( the y-coordinate of the point where the line intersects the y-axis).
The equation of the slope intercept form is in the form y= mx +c
The given equation y= -9x +9
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A cube has sides that measure 12 inches each.
(a) Write an expression using an exponent that
represents the volume, V, of the cube.
12=V
12.
12
12
b) Evaluate the expression from (a) to fund the
cube's volume. Use the correct units.
12 in
12 in
w many cubes that measure 2 inches by 2 inches by 2 inches would fit inside a cube
asures 10 inches by 10 inches by 10 inches? Justify
This calculation yields a volume of a cube equal to 1728 cube inches. In order to calculate the volume, the length must be multiplied by itself three times.
How do you write the volume of a cube?Volume =[tex]a^{3}[/tex], where an is the length of the cube's sides or edges, is how you can calculate the volume of a cube.
A.) 12 × 3 cubic inches
B.) Volume of a cube equals length × breadth × height, which is 12× 12 × 12 = 123 = 144 × 12 = 1728 cube inches. V=[tex]a^{3}[/tex]=123=1728 [tex]cm^{3}[/tex]is the result, giving the cube's volume.
1,728 times twelve cubed. The term "x cubed," or cubing a number, is identical to: x cubed equals x 3. A real number with a cube equal to 12 is the cube root of 12. It is about equal to 2.289 to take the cube root of 12. Volume per volume, or % v/v, is the way volume concentrations in solutions are stated. This is employed when a solution contains liquid versions of both compounds.
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Jason makes 8 gallons of punch he serves 1 pint containers now he has 12 pints of punch how many pints of punch did jason serve
The pints of punch that Jason served were 52 pints.
How many pints are in a gallon?The number of pints that make up a gallon is 8 pints. So, in 8 gallons, we can expect that there will be 64 pints. Now, we are told that Jason served 1 pint container and now he has 12 points remaining, what we are to do is to subtract the remaining pints from the original pints that he had.
Since the original was 64 pints, removing 12 pints will amount to 52 pints. This means that 52 pints of punch were served in the 1-pint containers.
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Paula downloaded 16 songs at a total cost of $32.00. What is the unit rate, in dollars, for the songs?
Answer: Paula spent $2 for each song.
Step-by-step explanation: For this question, we have to find the unit rate that Paula paid per song. As we're already given the amount of songs downloaded and the total cost, all that we really have to do is divide!
Because we want to know the amount of money spent on one song, we divide the amount of money spent by the amount of songs purchased. This gives us 32/16 = 2.
Paula spent $2 (don't forget the units!) for each song. This is out unit rate. Hope this helps!
The cross-section of the reflector in a flashlight is a parabola. Suppose the light bulb is located at the focus of the cross-section, 2.5 cm in front of the vertex.
Assume the vertex is at the origin and that the parabola is concave left (it opens left as depicted in the picture). What is the equation for the cross-section of the reflector?
The equation of the cross-section of the reflector which is in the form of a parabola is y² = -10x
What is a parabola?A parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped. It fits several superficially different mathematical descriptions, which can all be proved to define exactly the same curves.
Given that, The cross-section of the reflector in a flashlight is a parabola, the light bulb is located at the focus of the cross-section, 2.5 cm in front of the vertex.
We know that, the equation of the parabola turned to the left i.e. to the negative side of the coordinate system is:
y² = -2px
where p is the parameter of the parabola
The relationship between the parameter and the focus is.
p = 2 f
p = 2×2.5 = 5 cm
Since, the equation of the parabola is:
y² = -2p
Therefore, put p = 5
y² = - 2×5x = -10x
y² = -10x
Hence, the equation is y² = -10x
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-5(2x+14)=-2(x+63) x=6
The value of the variable, x is 7
What are algebraic expressions?Algebraic expressions are defined as expressions that are composed of terms, coefficients, variables, constants and factors.
These mathematical operations are also made up of arithmetic operations. These operations includes;
AdditionSubtractionMultiplicationFloor divisionBracketParenthesesDivisionFrom the information given, we have;
-5(2x+14)=-2(x+63)
expand the bracket
-10x -70 = -2x - 126
Now, collect like terms
-10x + 2x = -126 + 70
Add or subtract the terms
-8x = -56
Make 'x'' the subject
x = 7
Hence, the value is 7
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HELP ME OUT PLEASE I NEED HELP
The equation x / y = 4 is an example of direct variation formula. (Correct choice: A)
How to find a case of direct variation formula
Herein we find four types of equations, of which we must determine what choice represents a direct variation formula, whose definition is shown below:
y ∝ x
y = k · x
Where k is the constant of proportionality.
This form is equivalent to the following expressions:
y / x = k, x / y = 1 / k
Then, by direct inspection, we see that equation x / y = 4 represents a direct variation formula.
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If you are surveying students about whether or not they own a bicycle, where are you more likely to get a random sample?
A) at a bicycle parking area
B) at a bicycle repair shop
C) inside the school cafeteria
Answer: C. Inside the school cafeteria.
Step-by-step explanation:
The square below represents one whole.
What percent is represented by the shaded area?
Answer:
Step-by-step explanation:
77/100 or 0.77
How many different ways can you rearrange the letters in the word RECEIVER
a. 40320
b. 1120
C. 70
d. 3360
e. 20160
f. 6720
Answer:
don’t care 9
Step-by-step explanation:lol
Evaluate the expression when x=6. X^2-9x-7
The value of the expression x² - 9x - 7 when x = 6 is -25.
What is Quadratic Equation?Quadratic equations are second degree polynomial equations which are of the form ax² + bx + c = 0, where a, b and c are real numbers and x is the variable with the highest degree of 2.
Given the quadratic expression,
x² - 9x - 7
We have to find the value of the expression when x = 6.
Substitute x = 6, we get,
6² - (9 × 6) - 7 = 36 - 54 - 7
= -25
Hence the value of the given expression when the value of x = 6 is -25.
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Every day your heart creates enough energy to drive a truck for 32 kilometers. If you combined the energy created all the students in your math class for a week, how many meters could the truck drive?
For a combined energy of 15 students in a week, a truck will drive for 914.24 meters subjective to the number of students.
How to find the meter?To find the meters a truck will drive when the energy of a class is combined in one week;
1 day per person = 32 kilometers
One week = 7 days
Assuming a math class with 15 students for 7 days = (15 students x 7 days)
= 1/(15 x 7) x 32
= 1/35 x 32 = 0.02857 x 32 = 0.91424 kilometers
Changing 0.91424 kilometers to meter = 0.91424 x 1000 = 914.24 meters. It will take 15 students 914.24 meters truck drive in one week.
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Dave is 4 years older than Colin. Ruth is three times as old as Dave. The total of their three ages is 56 Work out Ruth's age.
Answer:
Ruth is 36 years old
Step-by-step explanation:
let Colin's age be x , then
Dave's age is x + 4
Ruth's age is 3(x + 4) = 3x + 12
sum their ages and equate to 56
x + x + 4 + 3x + 12 = 56
5x + 16 = 56 ( subtract 16 from both sides )
5x = 40 ( divide both sides by 5 )
x = 8
Then
Ruth's age = 3x + 12 = 3(8) + 12 = 24 + 12 = 36
The age of Ruth is 36 years while Dave is 12 years old and Colin is 8 years old.
What is an equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
Using variables to represent the ages of Colin and Dave:
C = Colin's age
D = Dave's age
From the given statement,
D = C + 4 (Dave is 4 years older than Colin)
We know that Ruth's age is three times Dave's age:
R = 3D (Ruth is three times as old as Dave)
Now, the sum of their ages is 56:
C + D + R = 56
Substituting the expressions for D and R in terms of C, we get:
C + (C + 4) + 3(C + 4) = 56
Simplifying and solving for C:
5C + 16 = 56
5C = 40
C = 8
So Colin is 8 years old. Using the expression for Dave's age in terms of C, we get:
D = C + 4 = 8 + 4 = 12
So, Dave is 12 years old.
Ruth's age in terms of D:
R = 3D = 3(12) = 36
Therefore, Ruth is 36 years old.
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What is the domain of the function y=3^√x?
-∞AX<∞
O 0
O 0
0 1
Answer: The domain of a function is the set of all input values (x-values) for which the function produces a valid output value (y-value).
For the function y = 3^√x, the input value x can't be negative because the value under the square root should be non-negative and 3^√x is defined for all x in the domain of real numbers. This means that the domain of the function y = 3^√x is (-∞,∞).
Step-by-step explanation:
The domain of the function is [0, ∞).
What is a function?A function has an input and an output.
A function can be one-to-one or onto-one.
It simply indicated the relationships between the input and the output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
The function y = 3^√x has a base of 3, which means that the output of the function is always a positive number.
For the function to be defined, the input x must also be a positive number or zero, as the square root of a negative number is not a real number.
Therefore,
The domain of the function is all non-negative real numbers, or [0, ∞).
In interval notation, the domain can be written as [0, ∞).
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Which table shows a proportional relationship between x and y? Responses x 3 9 10 15 y 1 3 4 5x 3 9 10 15 y 1 3 4 5 , x 2 3 5 6 y 3 4 7 9x 2 3 5 6 y 3 4 7 9 , x 1 5 8 10 y 15 75 120 150x 1 5 8 10 y 15 75 120 150 , x 4 6 8 10 y 6 8 10 12 PLEASE I NEED HELP I NEED HELP NOW!!!!!!!!!
The table that shows a proportional relationship between x and y is:
C. x 1 5 8 10 y 15 75 120 150
What is a proportional relationship?Relationships between two variables that are proportional occur when their ratios are equal. Another way to consider them is that in a proportional relationship, one variable is consistently equal to the other's constant value. The "constant of proportionality" is the name of that constant.
If every pair of data values is related in the same way, by multiplying by a factor, then the relationship is proportional. A proportional relationship can be identified by looking at data, an equation, or a graph.
In this case, the constant based on the information will be:
= 15 / 1
= 15
Also when x is 5, y will be:
= 5 × 15.
= 75..
The correct option is C.
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HELP ME PLEASE I WILL GIVE BRAINLIEST AND 10 POINTS!! PLS EXPLAIN
DE and FG have the same slope, so both the sides are parallel. The opposite side of the quadrilateral are equal. Because, the opposite side of the quadrilateral are equal and parallel, DEFG is a parallelogram.
What is a parallelogram?A quadrilateral having two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Additionally, the interior angles that are additional to the transversal on the same side. 360 degrees is the sum of all interior angles.
A parallelepiped is a three-dimensional shape with parallelogram-shaped faces.
DE and FG have the same slope, so both the sides are parallel.
Since, DE = FG, the opposite side of the quadrilateral are equal.
Because, the opposite side of the quadrilateral are equal and parallel, DEFG is a parallelogram.
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hi can someone please help with this i’m confused by the graph. helpppp
Therefore , solving the provided question, we can say that the, probability P( 24 period hour) = 5/24
What is probability?The probability that an event will occur or a claim will be true is measured by probability theory, a branch of mathematics. The probability of an occurrence is a number from 0 and 1, in which about 0 represents how likely the event should be to occur and 1 represents certainty. A probability is a quantitative illustration of the possibility that a specific occurrence will take place. Probabilities can also be expressed as percentages ranging from 0% to 100% or from 0 to 1. the ratio of the number of outcomes to the proportion of occurrence in a whole set all equally likely options that lead to a specific occurrence.
Here,
=> E1 = stops at 5 clock
=> E2 = start at 24 hours
=> P( 24 period hour) = 5/24
=> the, probability P( 24 period hour) = 5/24
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Split 500m in the ratio 1:4
If 500m is split in the ratio of 1:4, then the first part would equal 125m and the second part would equal 375m.
What is the ratio ?The ratio is a comparison of two or more related values or amounts. It is expressed as a fraction or a decimal number, and is used to compare the relative size of two or more values. Ratios can be used to compare numbers, objects, people, or other elements in order to study their relative size or relationships.
If 500m is split in the ratio of 1:4, then the first part would equal 125m and the second part would equal 375m. This is because the ratio of 1:4 can be simplified to 1/5 and 1/5 of 500m is 125m. Therefore, the first part is 125m and the second part is 375m.
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Unit price of 3 scarves totaling 26.25
Answer:
Step-by-step explanation:
26.25 divided by three = 8.75
Solve for y, x+10i=y-yi
The value of y in the equation that we have here is given as , y = x + (10 + y)i
How to solve for yTo solve for y, we can start by isolating y on one side of the equation. We can do this by adding yi to both sides:
x+10i+yi = y-yi+yi
This simplifies to:
x+10i+yi = y
We can then rearrange the equation to get:
y = x+10i+yi
So, y = x + (10 + y)i
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Which situation could be represented by the equation
18x=19+12x
A situation which could be represented by the equation 18x = 19 + 12x include the following: J. Krystal can make $18 per hour by tutoring. Jondo can make $12 per hour by tutoring. Jondo already has $19. How many hours, x, would Krystal and Jondo need to tutor for them to have the same amount of money?
What is an algebraic expression?In Mathematics, an algebraic expression simply refers to a mathematical equation that can be used for showing the relationship which exist between two (2) or more variables, numerical quantities, as well as in conjunction with different mathematical operations.
Assuming the variable x represents the number of hours spent tutoring, an algebraic expression which relates the number of hours which these two tutors must spent during tutorial to earn the same amount of money is given by:
18x = 19 + 12x
18x - 12x = 19
6x = 19
x = 19/6 hours.
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Complete Question:
Which situation can be represented by this equation?
18x = 19 + 12x
F Krystal reads 12 pages per hour. Jondo reads 18 pages per hour.
How many hours, x, would it take for Krystal and Jondo to read
the same number of pages?
G Krystal paid a deposit of $19 plus $18 per hour to rent a dining
room at a restaurant. Jondo paid $12 per hour to rent a dining
room at a restaurant. How many hours, x, would it take for
Krystal and Jondo to pay the same amount of money?
H Krystal installs 12 tiles per hour. Jondo installs 19 tiles per hour
and started with 18 tiles already installed. How many hours, x,
would it take for Krystal and Jondo to install the same number
of tiles?
J. Krystal can make $18 per hour by tutoring. Jondo can make $12 per hour by tutoring. Jondo already has $19. How many hours, x, would Krystal and Jondo need to tutor for them to have the same amount of money?
whats the answer with all the work shown?
The answer to the work shown is x = 8.
The law of indices.The law of indices are laws that has to be applied to expressions involving powers or fractions. These laws have individual application.
Considering the given question, we have;
16^(3x - 6) = 64^(x + 4)
It can be deduced that, the factors of;
16 = 4 x 4
= 4^2
and
64 = 4 x 4 x 4
= 4^3
So that;
4^2(3x - 6) = 4^3(x + 4)
Divide through by 4 to have;
2(3x - 6) = 3(x + 4)
6x - 12 = 3x + 12
collect like terms,
6x - 3x = 12 + 12
6x = 24
x = 24/6
= 8
The answer to the work shown in the question is: x = 8
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1. A boat is 15 ft away from a point perpendicular to the shoreline. A person stands at a point down the shoreline so that a 65° angle is formed between the closest point to the boat, the person, and the boat. How far is the person from the boat? Round your answer to the nearest tenth of a foot. Show your work.
The person is 16. 55ft from the boat
How to determine the distanceFrom the information given, we have that;
The boat is 15ft away from the shoreline65° angle is formed between the closest point to the boatTo determine the distance between the boat and the person, let's use the trigonometric identity, sine
sine θ = opposite side/hypotenuse side
Given that;
Opposite side = 15ftHypotenuse side = dθ = 65 degreeSubstitute the value
sin 65 = 15/d
cross multiply
d = 15/sin 65
Find the value
d = 15/0.9063
divide the values
d = 16. 56 ft
Hence, the value is 16.56ft
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What is the product of 6\sqrt{8}6 8 and 3\sqrt{24}3 24 in simplest radical form?
The product of 6√8 and 3√24 in simplest radical form is 144√3
How to determine the productWe can solve this problem by using the distributive property and simplifying the radicals.
6√8 * 3√24 = (6 * 3) * √(8 * 24)
Evaluate the products
6√8 * 3√24 = 18 * √(8 * 24)
Evaluate the products of radicals
6√8 * 3√24 = 18 * √(192)
Simplify the radical
6√8 * 3√24 = 18 * 4 * √12
So, we have
6√8 * 3√24 = 72√12
Now to simplify the radical, we can divide the radicand by the greatest perfect square that is a factor of it.
So, we have
72√12 = 72 * 2 * √3
= 144√3
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The management team of a company with 10,000 employees is considering installing charging stations for electric cars in the company parking lots. In a random sample of 500 employees, 15 reported owning an electric car. Which of the following is a 99 percent confidence interval for the proportion of all employees at the company who own an electric car?
answer choices
0.03
±
2.326
(
0.03
)
(
0.97
)
500
0.03±2.326 500
(0.03)(0.97)
0.15
±
2.326
(
0.15
)
(
0.85
)
500
0.15±2.326 500
(0.15)(0.85)
0.03
±
2.576
(
0.03
)
(
0.97
)
500
0.03±2.576 500
(0.03)(0.97)
0.15
±
2.576
(
0.15
)
(
0.85
)
500
0.15±2.576 500
(0.15)(0.85)
The confidence interval is (0.0104, 0.0496) (can include those endpoints too)
You can find the standard mean error and then use that to find the confidence interval limits.
The 99% confidence interval for the proportion of all employees at the company who own an electric car is given by
Lower limit = 0.0104
Upper limit = 0.0496
The confidence interval is (0.0104, 0.0496) (can include those endpoints too)
To find the confidence interval for proportions
Let the sample size be n
Let the interested quantities in the sample be present x times
Let the confidence level be of p%.
Then the level of significance is given by
The standard mean error is calculated by:
Then the confidence interval limits can be found by
Using the above formula for finding the confidence interval
We have n = 500, x = 15 and
Finding the standard mean error:
From the z tables, we get z = 2.5758
Thus, the confidence interval is obtained by
Lower limit = 0.0104
Upper limit = 0.0496
Thus,
The 99% confidence interval for the proportion of all employees at the company who own an electric car is given by
Lower limit = 0.0104
Upper limit = 0.0496
Therefore, The confidence interval is (0.0104, 0.0496) (can include those endpoints too)
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**********************EXTRA CREDIT********************
A drink stand is selling small drinks for $2 each and large drinks for $4 each. One day, a total of 150 drinks were sold for $552. How many large drinks were sold?
Answer:
Step-by-step explanation:
is either x = 6 or x = 4 a solution to 33 - x = 27?
A: x = 6 is a solution, but x = 4 is not.
B: x = 4 is a solution, but x = 6 is not.
C: Neither are solutions
D: they are both solutions
Answer: A: x=6
Step-by-step explanation: If we plug in 6 for X in the equation we get
33 - 6. 33 - 6 does equal 27.
Now to make sure X = 4 is not an answer, we plug that in too. 33 - 4.
33 - 4 = 29, so this is not the answer.
Answer:
A: x = 6 is a solution, but x = 4 is not.
Step-by-step explanation:
33-x=27
-33 -33
-x=-6
-x/ -x/
x=6
yvette buys sandwiches for $22from a restaurant using its online ordering system her bill includes the food purchase price as well as 8.5% sales tax she choose to add an 18%tip for delivery driver to the bill when she completes the online order.to the nearest whole percent what percent did she pay over the price of the sandwiches
To the nearest whole percent, the percentage Yvette paid over the price of the sandwiches is 27%.
How is the percentage determined?The percentage represents a proportion of a whole value.
The percentage is determined as the quotient of the difference (increase or decrease) and the initial value, multiplied by 100.
The purchase price of restaurant sandwiches = $22
Sales tax = 8.5%
= $1.87 ($22 x 8.5%)
Additional tip for delivery = 18%
= $3.96 ($22 x 18%)
Total bill = $27.83 ($22 + $1.87 + $3.96)
Difference between the total bill and the purchase price = $5.83 ($27.83 - $22)
Percent difference = 26.5% ($5.83/$22 x 100)
= 27%
Thus, Yvette paid 27% above the price of the sandwiches in form of sales tax and tips.
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