Answer:
A change from 55 to 77 represents a positive change (increase) of 40%.
Hope this helps!
Answer:
Increase
Step-by-step explanation:
55 videos to 77 videos is equal to 140% increase
so how we find the result?
multiply 77 with 100 and divide it by 55
77*100/55 = 140
For the equation f(x) = 1.1 * (0.44) ^ x state the initial value C, the growth or decay factor a, and percent change R for each unit increase in x
c = (Type an integer or a decimal)
a = (Type an integer or a decimal)
R = % (Simplify your answer. Type an integer or a decimal)
The parameters of the exponential function in this problem are given as follows:
c = 1.1.a = 0.56.R = -56%.What is an exponential function?The standard format of an exponential function is given as follows:
y = c(1 - a)^t.
This is the case for a decaying exponential function, and the meaning of each parameter is given as follows:
c is the initial value, value assumed by y when t = 0.a is the decay rate.In this problem, the function is given as follows:
f(x) = 1.1(0.44)^x.
Hence the values for the parameters are given as follows:
c = 1.1, which is the initial value.a = 0.56, as 1 - a = 0.44 -> a = 0.56.Then the percent of change is of -56%, as it is a decaying exponential function with a = 0.56.
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Find the value of x.
If necessary, you may learn what the markings on a figure indicate.
Check
71°
X
x =
Tables and figures must all be labelled with numbered captions that clearly identify and describe them.
What do the marks on shapes mean?Little tick marks are used to show that two sides are the same length (congruent). You can use just one tick mark, two or three or more -- just as long as you use the same number on sides that are equal. Notation for congruent angles in a triangle: This works a lot like congruent sides Tick marks (shown in orange) indicate sides of a shape that have equal length (sides of a shape that are congruent or that match). The single lines show that the two vertical lines are the same length while the double lines show that the two diagonal lines are the same length.We mark the congruent sides by a slash mark. The angles in an equilateral triangle are always 60°. When a triangle has two congruent sides it is called an isosceles triangle.While "hash marks" are used to represent segments of equal length on diagrams, "arcs" are used to represent angles of equal measure.Indicator marks for sides and angles in a triangle diagram. Indicator marks are used to show whether two or more sides are congruent (equal in measure).x = 61
Left hand triangle containing 1 angle of 74
Label the other angle opposite the marked side also as 74
Find the third angle. Call it y.
y + 74 + 74 = 180 Combine like terms
y + 148 = 180 Subtract 148 from both sides.
y = 180 - 148
y = 32
Now work with the triangle on the right.
label the angle making up the right angle = z
32 + z = 90 These two angles are complementary = 90
32 - 32 + z = 90 - 32 Subtract 32 from both sides
z = 58 Use 58 wherever you see z
x + x + z = 180 Substitute
2x + 58 = 180 Subtract 58 from both sides
2x = 122 Divide by 2
x = 61
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(15points) Let 21, 22, ..., Ik be linearly independ vectors in a vector space V. If we add a vector Ik+1 to the collection, will we still have a linear independent collection of vectors? Explain. If we delete a vector, say, 2k , from the collection, will we still have a linearly independent collection of vectors? Explain.
If we add a vector I{k+1} to the collection of 21, 22, ... I{k}, the collection will no longer be linearly independent and yes, we will still have a linearly independent collection of vectors if we delete a vector {say 2k}.
What are linearly independent vectors? What is a mathematical function, equation and expression?linearly independent vectors : In the theory of vector spaces, a set of vectors is said to be linearly dependent if there is a nontrivial linear combination of the vectors that equals the zero vector. If no such linear combination exists, then the vectors are said to be linearly independent. These concepts are central to the definition of dimension
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
Expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators
Equation : A mathematical equation is used to equate two expressions.
Given is a linearly independent vectors in a vector space V.
If we add a vector I{k+1} to the collection of 21, 22, ... I{k}, the collection will no longer be linearly independent.
If we delete a vector {say 2k}, from the collection, yes, we will still have a linearly independent collection of vectors
Therefore, if we add a vector I{k+1} to the collection of 21, 22, ... I{k}, the collection will no longer be linearly independent and yes, we will still have a linearly independent collection of vectors if we delete a vector {say 2k}.
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Let me know by Thursday pls
The angle relationships formed in the diagram are as follows;
∠1 and ∠5 are corresponding angles.∠4 and ∠7 are corresponding angles∠3 and ∠5 are alternate interior angles.∠1 and ∠8 are alternate exterior angles.∠2 and ∠7 are alternate exterior angles ∠3 and ∠6 are same interior anglesHow to find angles when parallel line s are cut by transversal ?When parallel lines are cut by a transversal, angle relationships can be formed such as corresponding angles, alternate interior angles, alternate exterior angles, vertically opposite angles, linear angles, etc.
Therefore, let's find the angles relationship formed in the diagram as follows:
∠1 and ∠5 are corresponding angles.
∠4 and ∠7 are corresponding angles
Corresponding angles are the angles which are formed in matching corners or corresponding corners with the transversal when two parallel lines are intersected by any other line.
∠3 and ∠5 are alternate interior angles.
Alternate interior angles are the angles formed when a transversal intersects two coplanar lines.
∠1 and ∠8 are alternate exterior angles.
∠2 and ∠7 are alternate exterior angles.
Alternate exterior angles are the pair of angles that are formed on the outer side of the parallel lines but on the opposite side of the transversal.
∠3 and ∠6 are same interior angles. Same interior angles are supplementary angles.
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Perform the following mathematical operation, and report the answer to the appropriate number of significant figures.
1204.2 + 4.72613 = [?]
The answer is not 1208.92613 / 1200
Answer:
1,208.92613
Step-by-step explanation:
this is the answer
the measure of one angle of a right is 23 degrees. Find the measure of the other angle
Answer: The measure of the three angles is 23, 67, and 90.
Step-by-step explanation:
The sum of three angles is equal to 180. We set the equation as:
x + 23 + 90 = 180
x + 113 = 180
x = 67
The measure of the three angles is 23, 67, and 90.
to test whether or not there is a difference between treatments a, b, and c, a sample of 12 observations has been randomly assigned to the 3 treatments. you are given the results below.
The required null hypothesis of the given observation is μ1 = μ2 = μ3.
What is the null hypothesis?The null hypothesis is a typical mathematical theory that asserts that there is no statistical relationship and significance between two sets of observed data and measured phenomena for each set of specified, single observable variables.
The null hypothesis can be evaluated to determine whether or not there is a relationship between two measured phenomena, which makes it valuable.
It can let the user know if the outcomes are the product of random chance or deliberate manipulation of a phenomenon.
The null hypothesis, often known as "H-nought," "H-null," or "H-zero," is written as H0 to distinguish it from other hypotheses.
The null hypothesis of the given observation:
μ1 = μ2 = μ3
Therefore, the required null hypothesis of the given observation is μ1 = μ2 = μ3.
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Complete question:
To test whether or not there is a difference between treatments A, B, and C, a sample of 12 observations has been randomly assigned to the 3 treatments. You are given the results below.
Treatment
Observations
A
20
30
25
33
B
22
26
20
28
C
40
30
28
22
The null hypothesis for this ANOVA problem is?
A rental car company charges $71.87 per day to rent a car and $0.09 for every mile driven. Aaliyah wants to rent a car, knowing that: She plans to drive 475 miles. She has at most $320 to spend. Which inequality can be used to determine dd, the maximum number of days Aaliyah can afford to rent for while staying within her budget?
Answer:
To rent a car from this company, Aaliyah will be charged a base rate of $71.87 per day, plus $0.09 for every mile she drives. In total, she plans to drive 475 miles, so she will be charged an additional $0.09 * 475 = $42.75 for the miles she drives.
The total cost of renting the car for one day will therefore be $71.87 + $42.75 = $114.62.
Aaliyah has a budget of $320, so she can afford to rent a car for a maximum of $320 / $114.62 = 2.79 days. However, since she can only rent the car for whole number of days, the maximum number of days she can afford is 2 days.
The inequality that can be used to determine the maximum number of days Aaliyah can afford to rent while staying within her budget is:
dd <= 2
Where dd is the number of days she plans to rent the car for. This inequality states that the maximum number of days Aaliyah can afford is 2.
The following standards for variable overhead have been established for a company that makes only one product:
Standard hours per unit of output 3.6 hours
Standard variable overhead rate $16.05 per hour
The following data pertain to operations for the last month:
Actual hours 5,000 hours
Actual total variable overhead cost $80,000
Actual output 1,300 units
Required:
a. What is the variable overhead rate variance for the month?
b. What is the variable overhead efficiency variance for the month?
Answer:
Step-by-step explanation:
the following standards for variable manufacturing overhead havebeen established for a company that makes only one product:standard hours per unit of output.. 5.6 hoursstandard variable overhead rate. $19.15 per hourthe following data pertain to operations concerning the productfor the last month:actual hours .. 5,100
Strontium 90 decays at a constant rate of 2.44% per year. Therefore, the equation for the amount P of strontium 90 after t years is P = Po e^-0.0244t, How long will it take for 15 grams of strontium to decay to 5 grams? Round answer to 2 decimal places.
45 years will take for 15 grams of strontium to decay to 5 grams
What is strontium?
The chemical element strontium has the atomic number 38 and the symbol Sr. Strontium is a soft, silver-white, yellowish metallic element that is an alkaline earth metal and has a strong reactivity to chemicals. When the metal is exposed to air, a thick layer of dark oxide forms.
Equation Given.
[tex]P = Po e^{-0.0244t}[/tex]
given P = 5 gram
[tex]P_o = 15 gram[/tex]
Hence ,time taken
[tex]5 = 15 e^{-0.0244t}[/tex]
[tex]\frac{5}{15} = e^{-0.0244t}[/tex]
Taking log both side,
[tex]ln(\frac{1}{3} )=ln (e^{-0.0244t})\\\\-1.098 = -0.0244t\\\\t=\frac{1.098}{0.0244}\\\\t=45years[/tex]
Hence, 45 years will take for 15 grams of strontium to decay to 5 grams.
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What is the area of a right triangle with a height of seven and three fourths yards and a base of 20 yards?
A: 140 yds2
B: 155 yds2
C: thirty eight and three fourths yds2
D: seventy seven and one half yds2
The following data are available in monetary value: - buildings and structures
36,000; - machinery and equipment - 18,600; - spare parts for repair - 608; - raw materials and materials - 7020. The cost of fixed assets will be:
1) 64 258
2) 56 630
3) 57 238
4) 54 600
1
The answer is 1 because if u use your brain you'd understand
The cost of the fixed assets will be $64258. The correct option is 1.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the data is, 36,000; - machinery and equipment - 18,600; - spare parts for repair - 608; - raw materials and materials - 7020.
The cost of the fixed assets will be calculated by adding all the values,
Cost = 36000 + 608 + 18600 + 7020
Cost = 62228 ≈ 64258
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A jacket is normally priced at $120. At the end of the winter season, the jacket is offered with a
discount of $18 off the normal price. What percentage of the normal price is the discount?
Answer:
15%
Step-by-step explanation:
18/120 = 0.15
0.15*100 = 15%
...
The solution is 15 %
The percentage of discount on the normal price of the jacket is given by the equation A = 15 %
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the percentage of discount be represented as A
Now , the equation will be
The normal price of the jacket = $ 120
The discounted price of the jacket = $ 18
So ,
Discounted price of the jacket = A % of normal price of the jacket
Substituting the values in the equation , we get
18 = A % x 120
On simplifying the equation , we get
( A / 100 ) x 120 = 18
Divide by 120 on both sides of the equation , we get
A / 100 = 18/120
A / 100 = 0.15
Multiply by 100 on both sides of the equation , we get
A = 15 %
Therefore , the value of A is 15 %
Hence , the discounted percentage is 15 %
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7. Sylvia went on a trip. The number of shirts she packed was 2 fewer than twice the number of pants
she packed. The total number of pairs of pants and shirts was 16.
A. Let x the number of pants she packed and let y = the number of shirts she packed. Write a system of
equations to represent the problem.
B. Solve the system of equations using substitution to find the number of shirts and pairs of pants Sylvia
brought.
Answer:
10 shirts, 6 pants
Step-by-step explanation:
Let y = the number of shirts
Let x = the number of pants
y + 2 = 2x
x + y = 16
y = 2x - 2
x + (2x - 2) = 16
3x = 18
x = 6
y + 6 = 16
y = 10
Answer:
[tex]\textsf{A.} \quad \begin{cases}y=2x-2\\x+y=16\end{cases}[/tex]
[tex]\textsf{B. \quad 6 pants and 10 shirts}[/tex]
Step-by-step explanation:
Part AGiven variables:
Let x = the number of pants Sylvia packed.Let y = the number of shirts Sylvia packed.If the number of shirts Sylvia packed was 2 fewer than twice the number of pants she packed:
[tex]\implies y=2x-2[/tex]
If the total number of pairs of pants and shirts was 16:
[tex]\implies x+y=16[/tex]
Therefore, the system of equations that represents the problem is:
[tex]\begin{cases}y=2x-2\\x+y=16\end{cases}[/tex]
Part BSystem of equations:
[tex]\begin{cases}y=2x-2\\x+y=16\end{cases}[/tex]
Substitute the first equation into the second equation and solve for x:
[tex]\implies x+2x-2=16[/tex]
[tex]\implies 3x-2=16[/tex]
[tex]\implies 3x=18[/tex]
[tex]\implies x=6[/tex]
Substitute the found value of x into the first equation and solve for y:
[tex]\implies y=2(6)-2[/tex]
[tex]\implies y=12-2[/tex]
[tex]\implies y=10[/tex]
Therefore, Sylvia packed:
6 pants10 shirtsy=-1/2x-3 how to graph
Given line:
y = - 1/2x - 3Plot two points and connect.
One point is the y-intercept:
x = 0 ⇒ y = - 3, the point is (0, - 3)Another point with an even value of x as its slope is a fraction with denominator of 2:
x = 6 ⇒ y = - 1/2*6 - 3 = - 3 - 3 = - 6, the point is (6, - 6)Plot these two points and connect.
See below graph.
All of the following are equivalent forms of 9/11 except _____.
18
22
1.22
0. 81
What is 555,555 rounded to the nearest hundred thousand?
Answer:
6 hundred thousand
Step-by-step explanation:
there is 6 numbers in total.Each number is 5.The next number should be 6.
The National Center for Education Statistics keeps careful records of the number of degrees awarded in the United states. ⢠Let f(t) model the number of PhDs awarded to men in terms of the number of years after 1980, t. ⢠Let g(t) model the number of PhDs awarded to women in terms of the number of years after 1980, t. f(t) e(t) ⢠Let h(t) model the ratio of the number of PhDs awarded to men compared to women in the U.S. in terms of, t. That is h(t) Given that h(t) = 2.8 for some value of t, which of the following statements is true? O For that value of t, women in the U.S. earned 2.8 more PhDs than men O For that value of t, men in the U.S. earned more PhDs than women. O For that value of t, women in the U.S. earned 2.8 times as many PhDs as men. O For that value of t, men in the U.S. earned 2.8 more PhDs than women. O For that value of t, women in the U.S. earned 2.8 times as many PhDs as men.
When t is that value, American men earned 2.8 more PhDs than women.
The given equation for h(t) is h(t) = f(t)/g(t), where f(t) models the number of PhDs awarded to men and g(t) models the number of PhDs awarded to women.
Since h(t) = 2.8 for some value of t, this means that the number of PhDs awarded to men is 2.8 times the number of PhDs awarded to women. Therefore, for that value of t, men in the U.S. earned 2.8 more PhDs than women.
The equation h(t) = f(t)/g(t) models the ratio of the number of PhDs awarded to men compared to women in the U.S., where f(t) models the number of PhDs awarded to men and g(t) models the number of PhDs awarded to women. Thus, if h(t) = 2.8 for some value of t, it means that the number of PhDs awarded to men is 2.8 times the number of PhDs awarded to women. In other words, for that value of t, men in the U.S. earned 2.8 more PhDs than women. This indicates that more men have received PhDs than women in the U.S. over the past few decades. The National Center for Education Statistics has kept track of this data and it is clear that men are receiving more degrees than women in the U.S.
h(t) = f(t)/g(t)
h(t) = 2.8
f(t) = 2.8g(t)
Therefore, for that value of t, men in the U.S. earned 2.8 more PhDs than women.
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1. The graph of a quadratic function is called a(an)
Copy and complete the table of values for the function.
2.
y=-1/3 x²
The graph of a quadratic function is called a parabola
The complete table is
x = -6, -3, 0, 3 6
y = -12 -3 0 -3 -12
How to complete the table of values?From the question, we have the following equation that can be used in our computation:
y=-1/3 x²
From the table of values , we have the following x values
x = -6, -3, 0, 3 and 6
Substitute x = -6, -3, 0, 3 and 6 in y=-1/3 x²
So, we have the following representation
y = -1/3 (-6)² = -12
y = -1/3 (-3)² = -3
y = -1/3 (0)² = 0
y = -1/3 (3)² = -3
y = -1/3 (6)² = -12
So, the complete table of values is
x = -6, -3, 0, 3 6
y = -12 -3 0 -3 -12
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Find the probability of no more than 2
successes in 5 trials of a binomial
experiment in which the probability of
success in any one trial is 18%.
Answer:
To find the probability of no more than 2 successes in 5 trials of a binomial experiment in which the probability of success in any one trial is 18%, we can use the formula for the probability mass function of the binomial distribution:
P(X = k) = (n choose k) * p^k * (1 - p)^(n-k)
Where:
X is the number of successes in the binomial experiment
n is the number of trials
p is the probability of success in any one trial
k is the number of successes we are interested in
So, in this case, we want to find the probability of X being equal to 0, 1, or 2 successes. We can do this by summing the probabilities of each of these events:
P(X = 0) + P(X = 1) + P(X = 2)
Plugging in the values from the problem, we get:
P(X = 0) = (5 choose 0) * (0.18)^0 * (1 - 0.18)^(5-0) = 0.3199
P(X = 1) = (5 choose 1) * (0.18)^1 * (1 - 0.18)^(5-1) = 0.4199
P(X = 2) = (5 choose 2) * (0.18)^2 * (1 - 0.18)^(5-2) = 0.2082
So the probability of no more than 2 successes in 5 trials of a binomial experiment in which the probability of success in any one trial is 18% is:
0.3199 + 0.4199 + 0.2082 = 0.948
Step-by-step explanation:
Monday through Thursday of this week, Raphael ran a total of 7 3/5 miles. How many miles will he need to run on Friday so that he will have a total of 11 1/2 miles for the week?
Raphael needs to run 3.9 miles on Friday so that he will have a total of 11 1/2 miles for the week.
What is Subtraction ?
An arithmetic operation called subtraction simulates the process of deleting items from a collection. The negative symbol, or, denotes subtraction.
Raphael ran a total of 7 3/5 miles through Monday to Thursday.
We'll convert it from mixed fraction to simple fraction :
7 3/5 miles = [(7×5) + 3] / 5
= 38/5 miles.
He wants to have a total of 11 1/2 miles for the week.
Again, we will convert it into simple fraction :
11 1/2 miles = [(11×2) + 1 ] / 2
= 23/2 miles.
Let's he needs to run x miles to a total of 23/2 miles.
So, x + 38/5 = 23/2
x = 23/2 - 38/5
= [(23×5) - (38×2)] / 10
= (115 - 76)/10
= 39/10 miles = 3.9 miles.
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The costs (in dollars) of 10 college math textbooks are listed below. ( 16 pts)) 70 72 71 70 69 73 69 68 70 71 a) Find the median. b) Find the sample mean. ( 4pts) c) Find the sample variance and standard deviation. Create the table. (
Given the costs of 10 college math textbooks, we can calculate that:
a. The median is 70
b. The mean is 70.3
c. The variance is 2.01 and the standard deviation is 1.42
Median, mean, variance, and standard deviation
Median, mean, variance, and standard deviation are very basic but very important concepts of statistics.
Median is the middle value of the data that has been arranged sequentially from the smallest to the largest.
The median for the number of data (n) is odd:
[tex]M_{e} = x_{(\frac{n+1}{2} )}[/tex]
The median for the number of data (n) is even:
[tex]M_{e} = \frac{1}{2} (x_{(\frac{n}{2})} + x_{(\frac{n}{2} +1)} )[/tex]
Mean is the average of all data in a sample group, which is obtained by adding up all the data values, then dividing by the number of samples.
[tex]Mean = \frac{Sum of all data}{size of data (n)}[/tex]
Variance is a value that describes the variation of data, by measuring how far each piece of data is spread from the average of a data set.
[tex]Variance = \frac{sum (x_{i} - mean)^{2}}{n}[/tex]
Standard Deviation is a measure of the spread of observations in a data set relative to their mean. it measures how many observations in a data set differ from the mean and is the square root of the variance.
σ = [tex]\sqrt{variance}[/tex]
To do the problem, we first create a table for the given data.
Then we calculate the median as follows:
[tex]M_{e} = \frac{1}{2} (x_{(\frac{n}{2})} + x_{(\frac{n}{2} +1)} )\\= \frac{1}{2} (x_{5} + x_{6} )\\[/tex]
= 1/2 (70 + 70)
= 70
After that, we calculate the mean as follows:
[tex]Mean = \frac{Sum of all data}{size of data (n)}[/tex]
= (70 + 72 + 71 + 70 + 69 + 73 + 69 + 68 + 70 + 71) / 10
= 703 / 10
= 70.3
Now we calculate the difference between the data and the mean and put it into the table, and find the sum.
Then we can calculate the variance as follows:
[tex]Variance = \frac{sum (x_{i} - mean)^{2}}{n}[/tex]
= 20.1 / 10
= 2.01
Standard deviation can be calculated from the variance:
σ = [tex]\sqrt{variance}[/tex]
= [tex]\sqrt{2.01}[/tex]
= 1.42
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ShivamG yt where r u
Answer:
Somoeone can talk here boring
Answer:
this a quesy=tion?
Step-by-step explanation:
write an equation of the line below.
Answer:
y = (1/2)x + 2
Step-by-step explanation:
Go from point (-2,1) to (0, 2).
Start at point (-2, 1). First, go up 1 unit. That is a rise of 1.
Now go 2 units right. That is a run of 2.
slope = rise/run = 1/2 = m
The graph intersects the y-axis at 2, so the y-intercept = b= 2.
y = mx + b
y = (1/2)x + 2
Distribute to create an equivalent expression with the fewest symbols possible.
(1−2g+4h)⋅5=
Answer:
5−10g+20h
Step-by-step explanation:
To distribute the 5 to the terms inside the parentheses, we can use the distributive property:
(1−2g+4h)⋅5 = 5⋅1−5⋅2g+5⋅4h
= 5−10g+20h
This is the simplest equivalent expression we can get, as there are no more terms that can be combined.
Oscar bought 4/5 of a kilogram of clay for the students in his pottery class. He then divided the clay evenly into pieces that were 1/5 of a kilogram. Into how many pieces did Oscar divide the clay?
To calculate the number of pieces into which Oscar divided the 4/5 kilogram of clay, we need to divide the total weight of the clay by the weight of each piece. We can do this by first converting the weight of the clay to kilograms and then dividing it by the weight of each piece. The weight of the clay in kilograms is 4/5 * 1 kilogram = 0.8 kilograms. And the weight of each piece is 1/5 * 1 kilogram = 0.2 kilograms. So, to find the number of pieces into which Oscar divided the clay, we divide the total weight of the clay by the weight of each piece, giving us 0.8 kilograms / 0.2 kilograms/piece = <<0.8/0.2=4>>4 pieces. Thus, Oscar divided the 4/5 kilogram of clay into 4 pieces.
R 0, -180(x, y) maps to the same point as R 0, 180(x, y).
O True
O False
Answer:
True.
Step-by-step explanation:
Whether you do a rotation 180 degrees clockwise( [tex]R__(-180,O)[/tex]), or a rotation 180 degrees counterclockwise ([tex]R__(180,O)[/tex]), the image will always end up in the coordinate diagonal from the pre-image.
Perform the following mathematical operation, and report the answer to the appropriate number of significant figures.
1204.2 + 4.72613 = [?]
The answer is not 1208.92613
The result of the addition operation of 1204.2 + 4.72613 is approximately 1208.93.
What is an addition operation?An addition operation involves two addends added together to result in a number called the sum.
The addition operation is one of the four basic mathematical operations, including subtraction, division, and multiplication.
Mathematical operations combine numbers, variables, and values with mathematical operands to solve mathematical questions.
1204.2 + 4.72613
= 1208.92613
= 1208.93
Thus, the addition of 1204 and 4.72613 yields a total of 1208.93 approximately.
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The sum of the lengths of the sides of this triangle is 30cm.
What is the length of the LONGEST side of the triangle in centimeters?
The longest side of the triangle has a length of 11 cm.
How to Find the Length of the Longest Side of a Triangle?Given that the sum of the lengths of the triangle is equal to 30 cm, and the sides are:
(x + 6)
(x + 4)
2x
Create an equation to find the value of x:
(x + 6) + (x + 4) + 2x = 30
x + 6 + x + 4 + 2x = 30
Combine like terms
4x + 10 = 30
4x = 30 - 10
4x = 20
4x/4 = 20/4
x = 5
Find the length of each of the sides of the triangle:
(x + 6) = 5 + 6 = 11 cm
(x + 4) = 5 + 4 = 9 cm
2x = 2(5) = 10 cm
The longest side is 11 cm.
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NO LINKS!! (NOT MULTIPLE CHOICE)
Use the formula A = P( 1 + r/n)^(nt) to calculate the balance A of an investment (in dollars) when P = $4000, r = 4%, and t= 10years, and compunding is done by the day, by the hour, by the minute, and by the second. (Round your answers to the nearest cent).
a. compounding by the day: A= $
b. compounding by the hour: A= $
c. compounding by the minute: A= $
d. compounding by the second: A= $
Does increasing the number of compoundings per year result in unlimited growth of the balance? yes or no (choose one)
Answer:
a. compounding by the day: A = $5967.17
b. compounding by the hour: A = $5967.29
c. compounding by the minute: A = $5967.30
d. compounding by the second: A = $5967.30
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Compound Interest Formula}\\\\$ A=P\left(1+\frac{r}{n}\right)^{nt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $n =$ number of times interest is applied per year \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}[/tex]
Part (a)If the interest is compounding by the day then n = 365.
Given:
P = $4000r = 4% = 0.04n = 365t = 10 yearsSubstitute the values into the compound interest formula and solve for A:
[tex]\implies A=4000\left(1+\dfrac{0.04}{365}\right)^{365 \times 10}[/tex]
[tex]\implies A=4000\left(1.00010958...\right)^{3650}[/tex]
[tex]\implies A=4000(1.49179200...)[/tex]
[tex]\implies A=5967.16801...[/tex]
[tex]\implies A=\$5967.17[/tex]
Part (b)If the interest is compounding by the hour then:
n = 365 × 24 = 8760Given:
P = $4000r = 4% = 0.04n = 8760t = 10 yearsSubstitute the values into the compound interest formula and solve for A:
[tex]\implies A=4000\left(1+\dfrac{0.04}{8760}\right)^{8760 \times 10}[/tex]
[tex]\implies A=4000\left(1.00000456...\right)^{87600}[/tex]
[tex]\implies A=4000\left(1.49182333...\right)[/tex]
[tex]\implies A=5967.29333...[/tex]
[tex]\implies A=\$5967.29[/tex]
Part (c)If the interest is compounding by the minute then:
n = 365 × 24 × 60 = 525600Given:
P = $4000r = 4% = 0.04n = 525600t = 10 yearsSubstitute the values into the compound interest formula and solve for A:
[tex]\implies A=4000\left(1+\dfrac{0.04}{525600}\right)^{525600 \times 10}[/tex]
[tex]\implies A=4000\left(1.00000007...\right)^{5256000}[/tex]
[tex]\implies A=4000(1.49182466...)[/tex]
[tex]\implies A=5967.29867...[/tex]
[tex]\implies A=\$5967.30[/tex]
Part (d)If the interest is compounding by the second then:
n = 365 × 24 × 60 × 60 = 31536000Given:
P = $4000r = 4% = 0.04n = 31536000t = 10 yearsSubstitute the values into the compound interest formula and solve for A:
[tex]\implies A=4000\left(1+\dfrac{0.04}{31536000}\right)^{31536000 \times 10}[/tex]
[tex]\implies A=4000\left(1.00000000...\right)^{315360000}[/tex]
[tex]\implies A=4000\left(1.49182390...\right)[/tex]
[tex]\implies A=5967.29562...[/tex]
[tex]\implies A=\$5967.30[/tex]
The more compounding periods throughout the year, the higher the future value of the investment. However, the difference between compounding by the day and compounding by the second results in a difference of 13 cents over the year, which is negligible comparatively.