Work Shown:
4.5% of 125 = 0.045*125 = 5.625
That rounds to 5.63
Answer:
5.625
Step-by-step explanation:
what is e and in
calculus for business
Question 10 of 20
What is the domain of the exponential function f(x)=3*-5?
O A. (-∞0, +00)
O B. (3,+00)
O C. (-∞0,-5)
O D. (-5,+00)
Answer: The answer is A. (-∞0, +00)
Finance. A person wishes to have $22,500 cash for a new car 3 years from now. How much should be placed in an
account now, if the account pays 4.8% annual interest rate, compounded weekly?
(Round to the nearest dollar.)
Answer:
$20,907
Step-by-step explanation:
To calculate the amount that needs to be placed in an account now to have $22,500 in 3 years, you can use the formula for compound interest:
A = P * (1 + r/n)^(nt)
Where:
A = final amount
P = principal (the initial amount placed in the account)
r = annual interest rate as a decimal
n = number of times the interest is compounded in a year
t = number of years
In this case, r = 0.048, n = 52 (since the interest is compounded weekly), and t = 3.
So, we have:
A = 22,500
P = ?
r = 0.048
n = 52
t = 3
Plugging these values into the formula:
22,500 = P * (1 + 0.048/52)^(52 * 3)
Solving for P, we get:
P = 22,500 / (1 + 0.048/52)^(52 * 3)
P = 22,500 / (1 + 0.048/52)^(156)
Rounding to the nearest dollar, we get:
P = $20,907
So, a person should place $20,907 in the account now, if the account pays 4.8% annual interest rate, compounded weekly, to have $22,500 in 3 years.
find the sum of the series. make sure you use the formula and show your work for credit.
please help me I didn't get this at all!
Answer:
The sum of the series is 260.
------------------------
Each term of given series is expressed as:
tₙ = 3n - 1This is an arithmetic progression with 13 terms and the first and last terms are:
t₁ = 3*1 - 1 = 2t₁₃ = 3*13 - 1 = 38Use the sum of the first terms of AP formula:
Sₙ = (t₁ + tₙ)*n/2S₁₃ = (2 + 38)*13/2 = 40*13/2 = 20*13 = 260Answer:
The sum of the series is 260.
Step-by-step explanation:
[tex]\displaystyle \sum^{13}_{n=1}(3n-1)[/tex]
The given sigma notation means:
Sum of the series with nth term (3n - 1), starting with n = 1 and ending with n = 13.As (3n - 1) is linear, the series is arithmetic.
The first term (n = 1) is:
a₁ = 3(1) - 1 = 2The second term (n = 2) is:
a₂ = 3(2) - 1 = 5The third term (n = 3) is:
a₃ = 3(3) - 1 = 8… and the last term (n = 13) is:
a₁₃ = 3(13) - 1 = 38Therefore, we need to find 2 + 5 + 8 + ... + 38.
Since we know that the first term, a, is 2, the last term, l, is 38, and the common difference, d, is 3, we can use the sum of the first n terms formula to calculate the sum of the series of the first 13 terms.
[tex]\begin{aligned}\text{Using:} \quad S_{n}&=\dfrac{1}{2}n(a+l)\\\\\implies S_{13}&=\dfrac{1}{2}(13)(2+38)\\\\&=\dfrac{1}{2}(13)(40)\\\\ &=\dfrac{520}{2}\\\\&=260\end{aligned}[/tex]
Therefore, the sum of the series is 260.
The number of a country's unemployed workers increased from 3.4 million to 5.5 million last year. If the country's population remained constant at 76 million, how did its unemployment rate change last year? A. It increased by about 27%. B. It decreased by about 27%. C. It increased by about 3%. D. It decreased by about 3%.
The rate at which its unemployment changes is, 54.6 %
What is the rate?Rate is a ratio of change in one quantity w.r.t. change in another quantity. The net change in one quantity is written as, Δy and the net change in another quantity is written as, Δx.
So formula for the rate is,
m = change in one quantity/change in another quantity = Δy/Δx
Given that,
The initial number of unemployed workers was 3.4 million and the final number was 5.5 million.
The change in the number of unemployed workers is:
5.5 million - 3.4 million = 2.1 million
To find the initial number of employed workers, we need to subtract the initial number of unemployed workers from the total population:
76 million - 3.4 million = 72.6 million
Now, we can calculate the initial unemployment rate as:
3.4 million / 72.6 million = 0.0469 or 4.69%
Similarly, the final unemployment rate is:
5.5 million / 76 million = 0.0724 or 7.24%
The change in the unemployment rate is:
(0.0724 - 0.0469) / 0.0469 ≈ 0.546 or 54.6%
Therefore, the unemployment rate increased by about 54.6%, which is closest to answer choice A. It increased by about 27%.
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A student is trying to prove that the triangle XAB is similar to triangle XYZ.
Answer:
Below
Step-by-step explanation:
See image
L side goes from 3 units to 6 units so scale factor is 2
You purchase 5 action figures per week. You have 30 action figures, which is 40% of the total number of action figures you need to complete your collection. How many weeks until your collection is complete?
Answer: Let's call the total number of action figures you need to complete your collection "x". Based on the information given, we know that 30 action figures is 40% of x, so we can write the equation:
30 = 0.40x
To solve for x, we'll divide both sides of the equation by 0.40:
x = 30 / 0.40
x = 75
So, the total number of action figures you need to complete your collection is 75. Since you purchase 5 action figures per week, it will take you 75 / 5 = 15 weeks to complete your collection.
Step-by-step explanation:
What benefits came from the collapse of communism in eastern europe? select three answers.
Greater freedom of movement, growing entrepreneurship, more contact with Western Europe.
three benefits came from the collapse of communism in eastern europe
Entrepreneurship is the creation or receipt of financial rewards. Under this definition, entrepreneurship is generally viewed as a change that involves more risk than is normally incurred when starting a business, and that may also involve value beyond its actual economic value.
An entrepreneur is a person who creates and/or invests in one or more groups while taking maximum risk and enjoying maximum return. [citation needed] The way to start a business is known as entrepreneurship. Entrepreneurs are usually seen as innovators, sources of new ideas, objects, offerings and ventures/technologies.
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Ten thousand marbles were produced on a production line. The first 100 marbles off the line were taken and tested for roundness. Does this sampling result in a simple random sample? Yes, because each group of n items has an equal chance of being selected. No, because each group of n items does not have an equal chance of being selected. Yes, because each item has an equal chance of being selected. No, because each item does not have an equal chance of being selected.
No, because each item does not have an equal chance of being selected. That is option D.
What is a simple random sample?A simple random sample is defined as the type of random sampling where by a particular amount of data (subset) is being selected from the total population of data that is under study.
The simple random sampling method which is used by researchers has the following disadvantages such as:
It relies on the quality of the researchers performing the work.It can require a sample size that is too large.It must have a significant population or demographic at the beginning of the process.It does not provide a guarantee that the data conclusions will be accurate because not all the data have equal chance to be selected.Learn more about random sampling here:
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A number, k, truncated to 2 d.p. is 47.00
Write an inequality to show the lower and
upper bounds of k. help quickly please!!!!!
MARK ME BRAINLIEST TOO!! :)
The lower and upper bounds of h - k are 42.31 and 42.49 respectively.
Upper and lower bounds are the maximum and minimum values that a number could have been before it was rounded. They can also be called limits of accuracy.
The upper and lower bounds can be written using error intervals
The lowest value of h is 47.15
The greatest value of h is 47.24
The greatest value of k is 4.84
The lowest value of k is 4.75
Thus upper bound of h -k = 47.24 - 4.75 = 42.49
Thus lower bound of h -k = 47.15 - 4.84 = 42.31
Thus the lower and upper bounds of h - k are 42.31 and 42.49 respectively. dont forget mark me brainliest
The confidence interval for a population proportion is (0.61, 0.81). What the the sample proportion and the margin of error.
The margin of error for the confidence interval for a population is 0.71 ± 0.1.
What is margin of error?The degree of error in survey findings from random sampling is known as the margin of error in statistics. A wider margin of error in statistics denotes a reduced likelihood of relying on a survey's or poll's findings, meaning that there will be less confidence in the results' ability to accurately reflect a community. It is a very important tool for market research since it shows the degree of assurance that should be placed in survey data by the researchers.
The margin of error is given as:
MOE = U - L / 2
MOE = 0.81 - 0.61 / 2
MOE = 0.2 / 2
MOE = 0.1
The interval is:
Interval = P ± 0.1
Interval = (0.61 + 0.1) ± 0.1
Interval = 0.71 ± 0.1
Hence, the margin of error for the confidence interval for a population is 0.71 ± 0.1.
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RECAP NEED HELP PLEASE HELP!!!!!!!!!!!!!!!!!!!!!!!!!!
The required measure of angle x in the triangle is 35°.
What are trigonometric equations?
These are the equation that contains trigonometric operators such as sin, cos.. etc.. In algebraic operations.
From triangle,
Sin x = perpendicular/hypotenuse
Sin x = 4/7
Sin x = 0.57
X =sin⁻¹(0.57)
X = 34.9
x = 35°
Thus, the required measure of angle x in the triangle is 35°.
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A statistics professor gives a survey to each of the 10 students in an introductory statistics course. The survey asks the students how many text messages they think they sent yesterday. The data are included below. Use a TI-83, TI-83 Plus, or TI-84 to calculate the population standard deviation and the population variance. Round your answers to one decimal place . Texts sent yesterday 29 211 130 21 21 19 67 60 O Help Copy to Clipboard Open Provide your answer below: Standard Deviation Variance- FEEDBACK Content attribution
Using a TI-83, TI-83 Plus, or TI-84 Population standard deviation is 56.4 and Population variance is 3178.5 .
To calculate the population standard deviation and variance using a TI-83, TI-83 Plus, or TI-84 calculator, we can use the following steps:
Enter the data into a list on the calculator. To do this, press the STAT key, then select Edit. Enter the data into L1.
Calculate the sample mean by pressing STAT, then CALC, then 1-Var Stats. Make sure L1 is selected as the list, then press ENTER.
Find the population variance by pressing STAT, then CALC, then 2-Var Stats. Make sure L1 is selected as the list, then press ENTER. The variance will be displayed as sX².
Take the square root of the population variance to find the population standard deviation. To do this, press the MATH key, then select PRB, then select 5:√(. Enter the population variance, then press ENTER.
Using this method, we find that the population standard deviation is approximately 56.4 and the population variance is approximately 3178.5.
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Complete question is:
A statistics professor gives a survey to each of the 10 students in an introductory statistics course. The survey asks the students how many text messages they think they sent yesterday. The data are included below. Use a TI-83, TI-83 Plus, or TI-84 to calculate the population standard deviation and the population variance. Round your answers to one decimal place .
Texts sent yesterday: 29 211 130 21 5 21 19 67 60 95
Expand and simplify (x + 2)(x + 1)
Answer:
x^2 + 3x + 2
Step-by-step explanation:
(x + 2) * (x + 1) =
= x * x + x * 1 + 2 * x + 2 * 1 =
= x^2 + x + 2x + 2 =
= x^2 + 3x + 2
Mark bought 4 pounds of bananas for $2.36 this week. Last week he paid $1.83 for 3 pounds of bananas. Which was the lower unit price?
Answer:
4 pounds
Step-by-step explanation:
2.36/4 = 0.59 cents a banana
1.83/3 = 0.61 cents a banana
Help with question 12 (a & b):
A beginning employee will produce 3 items per day
An experienced employee will produce 17 items per day
The number of items per dayBeginning employee
From the question, we have the following parameters that can be used in our computation:
[tex]P\left(d\right)=3\ +\ 15\left(1-e^{-0.2d}\right)[/tex]
Next, we plot the graph (see attachment)
A beginner employee is represented as d = 0
From the graph, we have
P(0) = 3
An experienced employee
Using the graph as a guide, we have
The maximum number of production approximates to 17
This represents the number of items per day for an experienced employee
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NEED HELPP!!!!!!!!!!!!
Answer:
the last one
Step-by-step explanation:
first you have to distribute the 5 to all the variables.
when you do that you get
x---9x5=45
y---1x5=5
z---4x5=20
hope it helped
please mark brainliest
6-90. Evaluate the expression 10-2x for the x-values given below.
(show work)
a. x=2
b. x = 1/2
c. x = -2
Answer:
Step-by-step explanation:
Evaluate the expression 10 - 2x for the x-values given below.
a. x = 2 \quad b. x = \frac {1}{2}\quad c. x = -2
a.x=2b.x=
2
1
a.x=-2
A roll of gasket material is 9 in wide. What length is needed to obtain 19 sq ft of the material? (Careful: The numbers are not expressed in compatible units.)
f
A length of ft is needed to obtain 19 sq ft of gasket material.
(Type an integer, proper fraction, or mixed number.)
The length of gasket material needed to obtain 19 sq ft of the material is approximately 25.33 ft.
What is length?
The length of something measured from end to end or along its longest side, or the length of a specific section of something.
Convert the width from inches to feet:
Since there are 12 inches in a foot, the width in feet is:
9 / 12 = 0.75 ft
Calculate the length needed:
We know that the area of the gasket material is 19 sq ft, and the width is 0.75 ft. Let L be the length needed in feet. Then we have:
Area = Width x Length
19 sq ft = 0.75 ft x L
Solving for L, we get:
L = 19 sq ft / 0.75 ft
L = 25.33 ft (rounded to two decimal places)
Therefore, the length of gasket material needed to obtain 19 sq ft of the material is approximately 25.33 ft.
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Write down all of the options which are true of
similar shapes.
They must be the same shape
They can be different shapes
They must be the same size
They can be different sizes
All of the options which are true of similar shapes include the following:
A. They must be the same shape.
D. They can be different sizes.
What are the properties of similar geometric shapes?In Mathematics, two (2) geometric shapes are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.
What is scale factor?In Geometry, the scale factor of a geometric figure can be calculated by dividing the dimension of the image (new figure) by the dimension of the pre-image (original figure):
This ultimately implies that, two (2) similar geometric shapes can have different sizes depending on the scale factor that is applied.
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A young channel catfish weighs about 0. 1 pound. During the next 8 weeks, its weight increases by about 23% each week.
Weight is 0.229 pounds after 4 weeks.
As a young channel catfish only weights 0.1 pounds,
It gains weight over the following 8 weeks at a rate of roughly 23% every week.
In this case, the exponential growth function is as follows:
Exponential formulas are provided by.
[tex]y=a(1+r)^{x}[/tex]
where an is the starting amount, r is the growth rate, x is the duration, and y is the weight at the end of "x" weeks.
Our values are a = 0.1, r = 0.23 (or 23%), and t = 4.
As a result,
[tex]y=0.1(1+0.23)^{4} \\[/tex]
y = 0.1(2.289)
y = 0.229
Consequently, the weight at 4 weeks is 0.229 pound.
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Complete question:
A young channel catfish weighs about 0.1 pound. During the next 8 weeks, its weight increases by about 23% each week. About how much will the catfish weigh after 4 weeks? Round your answer to the nearest thousandth of a pound.
Suppose a biologist tagged 53 penguins in antarctica during mating season. The next year, they caught 82 and found that 11 of them had tags. Estimate the total number penguins in the area.
It can be estimated that there are 395 penguins in the area.
What is Proportion ?Proportion is a mathematical comparison between two numbers. According to proportion, two sets of specified numbers are said to be directly proportional to each other if they increase or decrease in the same ratio. Symbols of proportions include "::" and "=".
We approach this problem by doing a simple proportion.We can presume that the same proportion of penguins were tagged during mating season if the biologists discovered 11 tagged individuals out of 82 penguins.
The proportion should therefore be [tex]x:53=82:11[/tex] where x represents the total number of penguins. By solving this proportion, we may determine what x is worth:
[tex]11x=53*82\\\\11x=4346\\\\x=395.0909[/tex]
Since there is no such thing as half a penguin, we can round off the answer to the nearest unit.
395 penguins are in the area according to our estimation.
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The lengths of the three sides of a triangle are x + 15 , 2x + 15 and x + 12 (where x cannot equal zero). What is the perimeter of the triangle?.
The perimeter of the triangle is 3x + 42.This can bean represented mathematically as (xd + 15) + (2x + 15) + (x + 12) = 3x + 42.
The perimeter of a triangle is the sum of the lengths of its three sides. In this problem, the lengths of the three sides of the triangle are given as x + 15, 2x + 15, and x + 12, where x cannot equal zero. To calculate the perimeter of the triangle, we need to add these three lengths together. This can bean represented mathematically as (xd + 15) + (2x + 15) + (x + 12) = 3x + 42. Therefore, the perimeter of the triangle is 3x + 42.
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What is the vertex for the graph below?
Answer:B
Step-by-step explanation: the graph moves x vertically -1 while y is moved vertically to 4
The lunch special at Rachel's Restaurant is a sandwich, a drink and a dessert. There are 2 sandwiches, 3 drinks, and 2 desserts to choose from. How many lunch specials are possible?
Answer:
3 lunch specials are possible.
Help me with this question…..
The volume of the cone shown can be described to be A. 513 π cubic units
How to find the volume of a cone ?The volume of a cone can be found by the formula :
= π x radius ² x height / 3
The radius of this cone is 9 units and the height is 19 units.
The volume of this cone then is :
= π x radius ² x height / 3
= π x 9 ² x 19/ 3
= π x 81 x 19/ 3
= π x 513
= 513 π cubic units
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Find the magnitude of the sum
of these two vectors:
The magnitude of the sum of these two vectors is 2.9486m
What is cosine rule?In trigonometry, the law of cosines (also known as the cosine formula, cosine rule, or al-Kashi's theorem) relates the lengths of the sides of a triangle to the cosine of one of its angles.
The parameters that will help us to find the magnitude are
/OB/ = 3.14m
/OA/ = 2.71 m
Let /AB/= x
Sum of the angles is (-60+30)⁰ = 30⁰
Using cosine rule
x²= 3.14² +2.71² - 2*3.14*2.71 *cos30⁰
x² = 9.8596+7.3441 -8.5094
x²= 17.2037 -8.5094
x²= 8.6943
x = √8.6943
x = 2.9486
Therefore, the magnitude of the sum
of these two vectors is 2.9486m or 2.9m approximately
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In complete sentences, explain how to determine the angle measurement for this angle.
WRITER
28
90
50
40 50 60 70
140 130 120 110
£10
umumla
150
30 20 10
160 170 180
UPLOAT
(2
The procedure for angle measurement by the protractor is mentioned below:
What is an angle ?An angle is a mathematical term, which we can define, when two straight lines or rays meet at a common endpoint. The common point is called the vertex of an angle. The word angle comes from a Latin word named ‘angulus,’.
Interior angles:- The inner angle made by the intersection of two polygonal sides.
Exterior angles:- The outer angle made by the intersection of two polygonal sides.
To measure an angle using a protractor, follow these steps:
1. Place the protractor on the angle you want to measure, with the base of the protractor aligned with one side of the angle.
2. Make sure the protractor is centered and level, with the zero-degree mark on the protractor aligned with the vertex (corner) of the angle.
3. Read the measurement of the angle from the protractor, where the second side of the angle intersects with the protractor scale. The measurement is usually given in degrees.
If the angle is larger than 180 degrees, you may need to use a full-circle protractor or measure the angle in two parts and add the measurements together.
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This net will be folded to form a prism.
A net of a rectangular prism. From top to bottom, the rectangles are labeled B, D, E, F. The left side is labeled A and the right side is labeled C.
Which pairs of faces will be opposite one another when the prism is created? Check all that apply.
D and F
A and C
A and B
B and F
B and E
B and C
E and F
A and F
Answer:
i think the answer is A and C, B and E
Answer:
D and F
A and C
B and E
Step-by-step explanation:
Phythagorean inequality
The Pythagorean inequality is given below.
Statement of Pythagoras theorem:
“In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“. The sides of this triangle have been named Perpendicular, Base and Hypotenuse.
[tex]AC^{2}=AB^{2} +BC^{2}[/tex]
Let ABC be a triangle with the longest side opposite B
If the square of the longest side is greater than the sum of the squares of the two shorter sides, then the triangle is obtuse at BIf the square of the longest side is less than the sum of the squares of the two shorter sides, then the triangle is acute.If the square of the longest side is equal to the sum of the squares of the two shorter sides, then the triangle is right angled at B.We can also write as follows:
If [tex]AC^{2} > AB^{2} +BC^{2} \\[/tex], then B is an obtuse angle.
If [tex]AC^{2} < AB^{2} +BC^{2} \\[/tex], then B is an acute angle.
If [tex]AC^{2}=AB^{2} +BC^{2}[/tex], then B is a right angle.
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