The account's balance after 5 years is given as follows:
[tex]A(5) = P\left(1 + \frac{r}{4}\right)^{20}[/tex]
In which:
P is the principal.r is the interest rate.What is compound interest?The amount of money earned, in compound interest, after t years, is given by:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
In which:
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.
Quarterly compounding means that the value of n is given as follows:
n = 4.
Then the balance of the account after 5 years, when t = 5, is given as follow:
[tex]A(5) = P\left(1 + \frac{r}{4}\right)^{20}[/tex]
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What is the y-intercept (b) of the line that passes through (1,1)(2,5) You must solve for slope (m) first.
b=
Answer:
slope (m) is 4, y-intercept (m) is -3
Step-by-step explanation:
y=4x-3
use y¹-y² over x¹-x² to find slope, then use one of the points to fill in for x and y to find y-intercept
Solve for x questions in picture
Answer:
x = 1
Step-by-step explanation:
2(4x + 5) - 3 = 5x(2+1)
Distribute.
8x + 10 - 3 = 10x + 5x
Subtract 8x from both sides.
10 - 3 = 10x + 5x -8x
Solve
7 = 15x - 8x
7 = 7x
1 = x
5. Ella checks out a book from the library. She does not read any pages that day. Starting the next day, she reads the same number of pages each day. The graph shows the number of pages Ella has left to read to finish the book. Determine the number of pages in the book. Assume that the relationship between the two quantities is linear. Library Book Number of Pages Unread 60 54 48 42 36 30 24 18 12 6 0 1 2 3 4 5 6 7 8 9 10 x Number of Days a. b. C. d. 5 5 8 48 58
The number of pages in the book is given as follows:
58 pages.
How to obtain a linear function?
The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
The slope m represents the rate of change.The intercept b represents the value of y when x = 0.From the graph, two points are given as follows:
(2,48) and (8, 18).
When x increases by 6, y decays by 30, hence the slope m is given as follows:
m = -30/6
m = -5.
Hence:
y = -5x + b.
When x = 2, y = 48, hence the intercept b, representing the number of pages in the book, is given as follows:
48 = -10 + b
b = 58.
Missing InformationThe graph is given by the image presented at the end of the answer.
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In a class of 30 students x +10 study algebra, 10+3 study statistics, 4 study both algebra and statistics. 2x study only Algebra and 3 study neither algebra nor statistics
1. Illustrate the information one a Venn diagram.
2. How many students study;
A. Algebra
B. Only statistics
1. The Venn diagrams are attached
2. When the statistics students number = 10·x + 3, we have;
The number of students that study
Algebra = 128/11Statistic = 213/11When the statistics students number = 2·x + 3, we have;
The number of students that study
Algebra = 16Statistic = 15What is the rationale for the above response?The parameters given are;
Total number of students = 30
Number of students that study algebra n(A) = x + 10
Number of students that study statistics n(B) = 10·x + 3
Number of student that study both algebra and statistics n(A∩B) = 4
Number of student that study only algebra n(A\B) = 2·x
Number of students that study neither algebra or statistics n(A∪B)' = 3
Therefore;
The number of students that study either algebra or statistics = n(A∪B)
From set theory we have;
n(A∪B) = n(A) + n(B) - n(A∩B)
n(A∪B) = 30 - 3 = 27
Therefore, we have;
n(A∪B) = x + 10 + 10·x + 3 - 4 = 27
11·x+13 = 27 + 4 = 31
11·x = 18
x = 18/11
The number of students that study
a. Algebra
n(A) = 18/11 + 10 = 128/11
b. Statistic
n(B) = 213/11
Hence, we have;
n(A - B) = n(A) - n(A∩B) = 128/11 - 4 = 84/11
Similarly, we have;
n(B - A) = n(B) - n(A∩B) = 213/11 - 4 = 169/11
However, assuming n(B) = (2·x + 3), we have;
n(A∪B) = n(A) + n(B) - n(A∩B)
n(A∪B) = 30 - 3 = 27
Therefore, we have;
n(A∪B) = x + 10 + 2·x + 3 - 4 = 27
2·x+3 + x + 10= 27 + 4 = 31
3·x = 18
x = 6
Therefore, the number of students that study
a. Algebra
n(A) = 16
b. Statistics
n(B) = 15
Hence, we have;
n(A - B) = n(A) - n(A∩B) = 16 - 4 = 12
Similarly, we have;
n(B - A) = n(B) - n(A∩B) = 15 - 4 = 11
See the attached Venn Diagrams.
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The number of bacteria in a lab experiment can be modeled by the function y(t)=270(1.129)^4t. Write an equivalent function of the form y(t)=ab^t. Round your final values to 4 decimal places.
Daniel is working two summer jobs, making $8 per hour babysitting and making $15 per hour lifeguarding. In a given week, he can work a maximum of 18 total hours and must earn no less than $200. If Daniel worked 3 hours babysitting, determine the minimum number of whole hours lifeguarding that he must work to meet his requirements
The minimum number of hours life guarding that Daniel must work to meet his requirements = 12 hours
To the nearest whole number approximately:
If the digit following the decimal is less than 5, only the number preceding the decimal should remain unchanged.
Add one to the number before the decimal and eliminate the decimal part if the digit following the decimal is five or greater.
Given the information,
Babysitting pays Daniel $8 per hour, and life guarding pays him $15 per hour.
Daniel can only work a total of 18 hours per week and must make at least $200.
Daniel has been babysitting for three hours.
Daniel thus makes 3 x 8 = 24 dollars.
He has earned $200 - 24 = 176 dollars from the original $200.
Let's say Daniel was a lifeguard for m hours.
He therefore made m x 15 = 176.
15 × m = 176
m = 11.73
m ≈ 12 hours
So, the minimum number of whole hours = 12
This means, Daniel must work 12 hours lifeguarding to meet his requirements.
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convert 1hour 38 min 14 second to seconds
Answer:
5894 seconds
Step-by-step explanation:
Convert 1 hour 38 min 14 seconds to seconds
1 hour = 3600 seconds
1 min = 60 seconds
38 mins = 60 x 38 = 2280 seconds
Now add all numbers together
3600 + 2280 + 14 = 5894 seconds
So, 1 hour 38 minutes 14 seconds is 5894 seconds.
put numbers in order smallest to largest: 0.5, 0.03, 0.42, 0.3, 0.243
Answer: 0.03, 0.243, 0.3, 0.42, 0.5
Step-by-step explanation:
Hope this helps you!
Answer:
Step-by-step explanation:
0.243, 0.03, 0.3, 0.42, 0.5
Sarah earned a 4% commission on all of her sales in December. Her total sales for December were $80,000. How much money did she cam in commission?
On solving the provided question, we can say that Amount of commission = Total sales value x Rate of commission = 3,200
what is amount ?aggregate attempting to calculate the time required, total number or quantity. The quantity at hand or under consideration is incredibly energetic. the overall result, importance, or import. Principal, interest, and a third accounting. amounts, amounting, and amounted are word forms. flexible noun The quantity of something is how much there is, how much you have, how much you require, or how much you obtain. He requires that sum of money to get by.
[tex]Amount of commission = 3,200\\Total sales value = 80,000//[/tex]
Rate of commission = 4% on sales
Amount of commission = Total sales value x Rate of commission
Amount of commission = 80,000 x 4%
Amount of commission = 3,200
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Sarah Meeham blends coffee for Tasti-Delight. She needs to prepare 120 pounds of blended coffee beans selling for $4. 17 per pound. She plans to do this by blending together a high-quality bean costing $5. 25 per pound and a cheaper bean at $2. 00 per pound. To the nearest pound, find how much high-quality coffee bean and how much cheaper coffee bean she should blend
Sarah should blend 80.5 pounds of the high-quality beans and 39.5 pounds of the cheaper beans to make 120 pounds of blended coffee.
In this problem, we are given that Sarah Meeham needs to prepare 120 pounds of blended coffee beans to sell at a rate of $4.17 per pound. She plans to blend two types of coffee beans: a high-quality bean costing $5.25 per pound and a cheaper bean costing $2.00 per pound.
Let x be the number of pounds of the high-quality coffee beans needed and y be the number of pounds of the cheaper coffee beans needed. Since we need 120 pounds of the blended coffee, we have:
x + y = 120
The cost of the blended coffee is $4.17 per pound. This means that the total cost of the blended coffee is:
4.17(120) = 501.6
We can also find the cost of the high-quality and cheaper beans in terms of x and y:
5.25x is the cost of the high-quality beans
2.00y is the cost of the cheaper beans
The total cost of the two types of beans is the sum of their individual costs:
5.25x + 2.00y
Since we need 120 pounds of the blended coffee, we can set up the following equation using the above expressions for total cost:
5.25x + 2.00y = 501.6
Now, we can use the system of equations consisting of x + y = 120 and 5.25x + 2.00y = 501.6 to solve for x and y. One way to do this is by substitution:
x = 120 - y (from the first equation)
5.25(120 - y) + 2.00y = 501.6 (substituting x in the second equation)
Simplifying and solving for y, we get:
630 - 5.25y + 2.00y = 501.6
3.25y = 128.4
y ≈ 39.5
Now we can use this value of y to find x:
x = 120 - y
x = 120 - 39.5
x ≈ 80.5
Therefore, Sarah needs to blend approximately 80.5 pounds of the high-quality coffee beans and 39.5 pounds of the cheaper coffee beans to make 120 pounds of blended coffee that she can sell for $4.17 per pound.
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Find an Angle Measure T ✓ The optimal tilt for Keenan's solar panelis between 58° and 60° to the horizontal. Has Keenan placed his solar panel at an optimal angle? SOLUTION COMMON ERROR 18 ft
Keenan has placed his solar panel at an optimal angle.
How determine if Keenan has placed his solar panel at an optimal angle?The cosine law is a mathematical relationship between the sides and angles of a triangle. The cosine law states that:
cos(C) = (a² + b² - c²) / 2ab
where a, b, and c are the lengths of the sides of the triangle and C is the measure of one of the angles. This law can be used to find unknown side lengths or angle measures in a triangle when given the other values.
Check the attached image for labelling.
The angle we are trying to calculate is labelled C.
cos (C) = (20² + 18² - 19²) / (2*20*18)
cos (C) = 363/720
C = cos⁻¹(363/720)
C = 59.72°
Since the angle obtained is between 58° and 60°. Thus, Keenan has placed his solar panel at an optimal angle.
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Use factoring to find the x-intercept(s)
of the function below.
Enter the smaller value first.
0 = 2x² + 5x - 3
Answer: x = -3, 1/2
Step-by-step explanation:
Please help me:
Find the measure of a in parallelogram ABCD 
Answer:
angle a = 122°
Step-by-step explanation:
since the opposite angles in a parallelogram are equal, therefore,
Angle a = angle c
therefore,
14x -4 = 15x - 13
-4 +13 = 15x - 14x
x = 9
therefore angle a = 14 x 9 - 4 = 122°
Jake will run at a constant rate of 8 minutes per mile. Ethan will longboard at rate of 5 minutes per mile for the first two miles then will slow down and longboard at a rate of 10 minutes per mile. Make two tables finding the times for each boys results for 1,2,3,4,5 and 6 miles
The time and distance of both the boys Jake and Ethan when they meet with each other is equal to 40 minutes after covering 5 miles.
Constant rate by which Jake run is equal to 8 minutes per mile.
Rate of Ethan longboard for first two miles = 5 minutes per mile
Rate of Ethan longboard for rest of the miles = 10 minutes per mile
Time taken by each of them is :
Miles Time taken by Jake (minutes) Time taken by Ethan(minutes)
1 8 min 5 min
2 16 min 10 min
3 24 min 20 min
4 32 min 30 min
5 40 min 40 min
6 48 min 50 min
Therefore , time and distance at which Jake and Ethan meet is equal to 40 minutes that is at 5 miles.
The above question is incomplete , the complete question is:
Jake will run at a constant rate of 8 minutes per mile. Ethan will longboard at rate of 5 minutes per mile for the first two miles then will slow down and longboard at a rate of 10 minutes per mile. Make two tables finding the times for each boys results for 1,2,3,4,5 and 6 miles.
Find out the time and distance at which both meet.
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help
(5th-grade math)
Answer: equation: 3/5 * 5/8 = 38 = 0.375
Spelled result in numbers/words is three eighths/ 3/8.
Step-by-step explanation:
the basketball field takes up 3/8 of the playground
3/5 * 5/8 = 38 = 0.375 = 3/8
then (simplify) 0.375 into a fraction.
3/5 * 5/8 = 38 = 3/8
Answer:
Equation: 3/8 * 5/8
Answer:3/8
Step-by-step explanation:
Equation: 3/5 * 5/8. Since it is 5/8 of 3/5, you can do 3/5 * 5/8.
Answer: 3/8. Since 3/5 * 5/8 = 3/8, the answer will be 3/8
each of two persons tosses three gair coincs. what is the probability that they obtain the same numbre of heads
The probability of getting three heads when tossing three coins is 1/2 x 1/2 x 1/2 = 1/8.
1/8
The probability of getting a head or a tail when flipping a coin is 1/2.
Therefore, the probability of getting two heads when tossing two coins is 1/2 x 1/2 = 1/4.
The probability of getting three heads when tossing three coins is 1/2 x 1/2 x 1/2 = 1/8.
Since each person is tossing three coins, the probability that they both obtain the same number of heads is 1/8.
The probability of getting n heads when tossing n coins is 1/2^n. Therefore, the probability of getting the same number of heads when two people toss n coins is 1/2^n. This means that if two people each toss a coin, the probability that they both get heads is 1/4; if they each toss two coins, the probability that they both get two heads is 1/16; if they each toss three coins, the probability that they both get three heads is 1/64; and so on.
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Karen,Sam, and Hector order a pizza.
Karen eats 1/3 of the pizza, Sam eats 1/3 of
what is left after Karen is done, and Hector
eats 1/3 of what is left after Sam is done.
What part of the pie is left after Hector is
done?
Actividades de Apertura
a) Dos ángulos rectos.
b) Dos ángulos agudos.
c) Dos ángulos suplementarios.
d) Dos ángulos complementarios
e) Dos rectas paralelas.
f) Dos rectas perpendiculares
g) Una recta transversal.
Las actividades de apertura son descripciones de diferentes relaciones geométricas. Aquí está la explicación de cada una:
a) Dos ángulos rectos tienen una medida de 90 grados.
b) Dos ángulos agudos tienen una medida menor a 90 grados.
c) Dos ángulos suplementarios suman a 90 grados.
d) Dos ángulos complementarios suman a 90 grados.
e) Dos rectas paralelas no se cruzan.
f) Dos rectas perpendiculares se cruzan en un ángulo recto de 90 grados.
g) Una recta transversal corta a dos o más rectas, creando ángulos en los puntos de intersección.
Qué es Dos ángulos rectos?Dos ángulos rectos son dos ángulos que tienen una medida de 90 grados. En geometría, un ángulo recto es un ángulo que tiene una medida de 90 grados y se representa con una línea diagonal que forma cuatro cuartos iguales.
Los ángulos rectos son importantes en la construcción y el diseño, ya que permiten la creación de formas simples y precisas. Por ejemplo, dos ángulos rectos pueden ser utilizados para formar un cuadrado o un rectángulo, mientras que un ángulo recto y un ángulo agudo pueden ser utilizados para formar un triángulo rectángulo.
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HELLLPPPP PLEASEEEEEEEEEEEEE
Answer: look at the image for the answer and the solution
Step-by-step explanation:
Answer: the home of it is 78 degrees
Step-by-step explanation:
as the angular bisector is shown then we can say that its right
Please help me with this problem fast.
The transformation that maps △UVW onto △U'V'W' is (d) 270 degrees counterclockwise
How to determine the transformationFrom the question, we have the following parameters that can be used in our computation:
The figure
From the figure, we can see that
Triangle △UVW has the same side length as the triangle △U'V'W'
This means that
(x, y) = (x, y)
The orientations are 270 degrees apart in the counterclockwise direction
So, we have
(x, y) = (y, -x)
Hence, the transformation is (d)
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show that the following function are continuos and discontinuos
A.(f×)={×+1 ,for×less than or equai to 2
{ 2×–1 ,for 1<×<2
{×–1 ×<1
The function f(x) = [tex]\left \{ {{x+1} ,for x \leq 2 \atop {2x-1}, for 1 < x < 2} \atop {x-1} , for x < 1 \right.[/tex] is continuous to all the values.
In mathematics, a function is a rule that assigns each element from one set (called the domain) to exactly one element of another set (called the range). The continuity of a function describes how smoothly it behaves as its input values change. In this context, we will analyze the continuity of the given function.
The given function is a piecewise function, which means it has different rules for different intervals of its domain. Let's analyze each interval separately to determine if the function is continuous or discontinuous.
For x less than or equal to 2, the function is f(x) = x + 1. This is a linear function, and we know that all linear functions are continuous everywhere. Therefore, the function is continuous for x less than or equal to 2.
For 1 < x < 2, the function is f(x) = 2x - 1. This is also a linear function, and as we said before, all linear functions are continuous. Therefore, the function is continuous for 1 < x < 2.
For x less than 1, the function is f(x) = x - 1. This is also a linear function and is continuous for all values of x less than 1.
Therefore, we can conclude that the given function is continuous for all values of x.
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For nitrogen to be a liquid, its temperature must be within 12.78 °F of –333.22 °F. Which equation can be used to find the maximum and minimum temperatures at which nitrogen is a liquid, x?
The equation that can be used to find the maximum and minimum temperatures is
|x +
| =
.
Answer:
its b
Step-by-step explanation:
3. In the figure below, what is m/2 if m26 = 120°?
A.
60°
B. 90⁰
32
41
5 6
87
C. 120°
D. 150°
The value of m <2 is C. 120°
What is a Corresponding Angle?In geometry, corresponding sides and corresponding angles of polygons are compared as part of the tests for congruence and resemblance.
In these tests, the order of adjacency is maintained by pairing each side and each angle of one polygon with a side or angle of the other polygon.
Therefore,
m<2 = m<6
This is because they are corresponding angles
With this in mind, m<6 = 120°
Therefore, m<2 = 120°
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Classify the triangle by its sides.
A.acute
B.scalene
C.isosceles
D.equilatera
Answer:
D because all sides are equal
if the mean is 9,8,10,x,14 is 11 then find the value of x
The value of x is 14
In statistics, in addition to the mode and median, the mean is one of the measures of central tendency. Simply put, the mean is the average of the values in the given set. It indicates that values in a particular data set are distributed equally. The three most frequently employed measures of central tendency are the mean, median, and mode. The total values provided in a datasheet must be added, and the sum must be divided by the total number of values in order to determine the mean. When all of the values are organised in ascending order, the Median is the median value of the given data. While the number in the list that is repeated a maximum of times is the mode.
To find the mean, add up all the numbers and then divide by the number of numbers
(9+ 8+10+ x+14)/5 = 11
Multiply each side by 5
9+ 8+10+ x+14 = 55
Combine like terms
41 +x = 55
Subtract 41 from each side
x =14
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two quadrilaterals are described
The statements that MUST be true based on the given information are:
Opposite angles of Quadrilateral C are congruent.Opposite angles of Quadrilateral L are congruent.Why are these statements true?For Quadrilateral C, if all four sides are congruent, then opposite sides are parallel and opposite angles are congruent. This can be proven using the fact that in an isosceles trapezoid (which is a special case of Quadrilateral C), opposite angles are congruent.
For Quadrilateral L, having two pairs of parallel sides and congruent diagonals means that it is a parallelogram with congruent diagonals. This type of parallelogram is known as a rhombus, and its opposite angles are congruent. Additionally, in a rhombus, consecutive angles are not necessarily supplementary or congruent.
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5) There are 7,213 applicants Only one half of the applicants which is about will be accepted in the program for the astroment progogiem
In a case whereby there are 7213 applicants for the astronaut program only one half of the applicants which is about 3607 applicants will be accepted into the program.
How can the number of the applicants be determined?The concept that will be used here is multiplication. One of the four fundamental mathematical operations, along with addition, subtraction, and division, is multiplication. Multiply in mathematics refers to the continual addition of sets of identical size.
The symbols for multiplication are cross (), asterisk (*), and dot (). You seem to utilize the cross a lot when you write in your notebooks. In both algebra and computer languages, the asterisk and dot are symbols (higher mathematics).
Total applicants =7213 applicants
Then one half of the applicants = 1/2 of 7213
=7213/2
= 3607 applicants
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complete question:
There are 7213 applicants for the astronaut program only one half of the applicants which is about ______will be accepted into the program
Find the value of x.
6x
60°
Answer:
Step-by-step explanation:
If you are implying that the equation is "6x = 60"
Divide both sides by 6 to get just x by itself, then you'd have your answer.
X = 10
Robin and 2 friends each were able to jump rope for 4/5 minute. How long did they jump rope for altogether?
Answer:
[tex]p(3and7)andq(1and9)[/tex]
Latanya plans to repaint some classroom bookcases. She has 5 3/5 gallons of paint. All of the bookcases are the same size and each requires 1/2 gallon of paint. What is the maximum number of complete bookcases she can paint?
With her 5 3/5 gallons of paint, Latanya can paint up to 11 full bookcases.
What does the equation's solution consist of?Any value of the variable that makes the Left Hand Side (LHS) and the Right Hand Side (RHS) of the equation equal is a solution to the problem. Solving an equation is locating its solution or solutions.
Let's first translate 5 3/5 gallons of paint into an incorrect fraction:
5 3/5 = (5 x 5 + 3)/5 = 28/5
Next, we can find the number of bookcases she can paint by dividing the total amount of paint by the amount needed for each bookcase:
28/5 ÷ 1/2
= 28/5 x 2/1
= 56/5
=11 1/5.
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