The (equivalent) compound annual rate at which Anders' salary has grown during the 12 years is 4.9%.
What does the compound annual rate signify?The compound annual rate is the equivalent rate of interest at which the present value of money grows to attain a future value.
At a 4.9% compound annual rate, Anders' salary has been growing by adding the growth amount to the initial salary and compounding both the principal and subsequent interest amounts until 12 years.
N (# of periods) = 12 years
PV (Present Value) = $2,800
PMT (Periodic Payment) = $0
FV = $-4,971.23
Results:
I/Y (Interest per year) = 4.9%
Total Interest = $2,171.23
Thus, using the online finance calculator, we can determine that Anders' salary has been compounded at 4.9% annually.
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A university has 10,000 students of which 45% are male and 55% are female. If a class
of 30 students is chosen at random from the university population, find the variance of
the number of male students.
The variance of the number of male students is 7.42 if the university has 10,000 students of which 45% are male and 55% are female.
What are the population and sample?It is described as a collection of data with the same entity that is linked to a problem. The sample is a subset of the population, yet it is still a part of it.
P(male) = 45% = 0.45
P(female) = 55% = 0.55
Variance = SD²
Variance = nP(male)xP(male)
Variance = 30x0.45x0.55
Variance = 7.42
Thus, the variance of the number of male students is 7.42 if the university has 10,000 students of which 45% are male and 55% are female.
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7/5 15/4 3/2 11/4 13/3 what is the least to greatest
We can conclude that the ascending to descending order of the given fractions are, 7/5, 3/2, 11/4, 15/4, and 13/3.
What are fractions?Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many parts of a particular size there are when spoken in everyday English. There are three main categories of fractions in mathematics. Proper fractions, incorrect fractions, and mixed fractions are these three types. The terms with a numerator and a denominator are called fractions.So, first, we need to find the LCM of all the denominators:
LCM of 5, 4, 2, 4, 3: 60(Refer to the attached image for calculation)Now, the fractions will be:
12(7)/60, 15(15)/60, 30(3)/60, 15(11)/60, 20(13)/6084/60, 225/60, 90/60, 165/60, 260/60So, ascending to descending order will be:
84/60, 90/60,165/60, 225/60, 260/60That is 7/5, 3/2, 11/4, 15/4, 13/3
Therefore, we can conclude that the ascending to descending order of the given fractions are, 7/5, 3/2, 11/4, 15/4, and 13/3.
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|x-4|=7x+12 solve for x
Step-by-step explanation:
................ N.....
1) Multiply. Write your answer in scientific notation.
60. (5 x 102)
There are 8 students in the class in art club. If 40%of the class is in art club, how many students are in class in all?
Answer: 20 is the answer
Step-by-step explanation:
Answer: 20 students
Step-by-step explanation
40% of 20 can be written as 40% × 20.
= 40/100 × 20
= 8
Cecil Green sells high quality golf hats. But, he knows that very few people will pay morethan $25 for a golf hat Cecil's standard mark up on apparel is 40%. What is the maximumCecil should pay for his golf hats?
$17.85
Explanation
you can easily solve this by using a rule of three.
Let
x represents the maximum vale
then
if
[tex]\begin{gathered} 25usd\rightarrow140\text{ percent} \\ \text{then} \\ x\rightarrow100 \end{gathered}[/tex]Step 2
the proportion is the same, so
[tex]\begin{gathered} \frac{25}{140}=\frac{x}{100} \\ 25\cdot100=140\cdot x \\ x=\frac{2500}{140} \\ x=17.85 \end{gathered}[/tex]What is the value of p?
when a number is power to a number a, and it is also power to another number b we can apply the property
[tex](x^a)^b=x^{a\cdot b}[/tex]apply this to the expression above
[tex]\begin{gathered} x^{22}\cdot(x^{7\cdot3)} \\ x^{22}\cdot x^{21} \end{gathered}[/tex]continue by applying the property of a product between the same number as a base but with a different exponent
[tex]x^a\cdot x^b=x^{a+b}[/tex]apply this to the expression above
[tex]\begin{gathered} x^{22}\cdot x^{21^{}} \\ x^{43} \end{gathered}[/tex]the value of p is equal to 43.
HELP!!
Write the slope-intercept form of the equation for each line.
The equation of the line in slope intercept form is y = -5 / 9x + 2 / 9
How to find the equation of a line in slope intercept form?The slope intercept form of the equation of a line can be represented as follows:
y = mx + b
where
m = slope of the lineb = y-interceptLet's find the slope using the points (4, -2)(-5, 3)
Hence,
m = y₂ - y₁ / x₂ - x₁
x₁ = 4
x₂ = -5
y₁ = - 2
y₂ = 3
m = 3 + 2 / -5 - 4
m = 5 / -9
m = - 5 / 9
Therefore, let's find the y-intercept using (4, -2).
-2 = - 5 / 9 (4) + b
-2 = - 20 / 9 + b
b = -2 + 20 / 9
b = -18 + 20/ 9
b = 2 / 9
Therefore, the equation is y = -5 / 9x + 2 / 9
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Which shows the integers in order from least to greatest?
a.20, 6, -2, -13
b. -2, 6, -13, 20
c..-13, -2, 6, 20
d.20, -13, 6, - 2
The integers that are in order from least to greatest will be C. -13, -2, 6, 20.
What is an integer?It should be noted that an integer simply means a natural number or a whole number that given. It should be noted that they can either be positive or negative.
In this case, the numbers will be illustrated as thus:
The smallest number is -13.
The biggest number is 20.
Therefore, the arrangement is -13, -2, 6, 20.
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Find the missing side. Round answer to the nearest tenth.46°X145.910.10 0 0 013.219.5
Given the rigth triangle, you have to determine the length of the missing side marked with an x.
To do so you have to apply the trigonometric functions, these are calculated as:
[tex]\begin{gathered} \sin \theta=\frac{opposite}{\text{hypotenuse}} \\ \cos \theta=\frac{adjacent}{hypotenuse} \\ \tan \theta=\frac{opposite}{adjacent} \end{gathered}[/tex]Where
θ is one of the inner angles of the triangle.
"opposite" indicates the opposite side to than angle
"adjacent" is the side in contact or next to the angle
and "hypotenuse" is the longest side of the triangle.
In this exercise we know the measure of the angle and the hypotenuse, the trigonometric function you have to use to determine the length of "x" is the Sine:
[tex]\begin{gathered} \sin \theta=\frac{opposite}{hypotenuse} \\ \text{opposite}=\sin \theta\cdot hypotenuse \end{gathered}[/tex]Replace with:=46º
hypotenuse=14
opposite=x
[tex]\begin{gathered} x=\sin 46\cdot14 \\ x=10.07\cong10.1 \end{gathered}[/tex]Correct option is b. 10.1
Charles meets with customers on a daily basis. He uses the function f(x) = 5| x - 8| + 20 to calculate how many dollars he charges, per hour, for his time. How much does Charles charge per hour if a customer hires him for 3 hours
Answer:
$45
Step-by-step explanation:
Charles meets with customers on a daily basis. He uses the function f(x) = 5| x - 8| + 20 to calculate how many dollars he charges, per hour, for his time. How much does Charles charge per hour if a customer hires him for 3 hours?
f(x) = 5| x - 8| + 20
solve for when x = 3
f(3) = 5| 3 - 8| + 20
f(3) = 5| -5| + 20
f(3) = 25 + 20
f(3) = 45
what are the account titles needed for statement of cash flows
A cash flow statement is divided into three sections: operating activities, investments, and financial activities.
What is cash flow?The net balance of money coming into and going out of a business at a particular period is referred to as cash flow. A firm constantly receives and expends cash. For instance, when a retailer buys merchandise, money leaves the company and goes to its suppliers.
According to question:
A cash flow statement is divided into three sections: operating activities, investments, and financial activities.
Operating activities: Cash flow activities that either produce income or keep track of the funds used to produce a good or service are referred to as operating activities. Inventory transactions, interest and tax payments, employee paychecks, and rent payments are all examples of operational business activity. This section does not cover any additional sources of cash flow, such as investments, debts, or dividends.
Investment activities: The cash flow statement's second column lists profits and losses resulting from investments in assets like property, plant, or equipment (PPE), demonstrating how the company's overall cash position has changed. Analysts look for changes on a cash flow statement when they want to determine the company's investment in PPE.
Financial activities: The cash flow between the company's owners and creditors is tracked in the third section of the cash flow statement. Transactions involving debt, stock, and dividends are all considered financial operations. In these transactions, the receipt of capital (from lenders or investors, for example) triggers the recording of incoming cash, and the payment of dividends triggers the recording of outgoing cash.
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The net of a right triangular prism is shown below.
What is the surface area of the triangular prism?
The surface area of the triangular prism is 224 square units.
What is surface area?The quantity of space enclosing a three-dimensional shape's exterior is its surface area. The measurement that expresses the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.
Given Data
Surface area = ( S₁ + S₂ + S₃) × Length
S₁ = 6
S₂= 8
S₃ = 2
L = 14
Surface area = ( 6+8+2)14
Surface area = 16(14)
Surface area = 224
The surface area of the triangular prism is 224 square units.
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Need help with number 1
Okay, here we have this:
Considering the provided information, we are going to analize whether it is better to use a sample or the population in the proposed situation, so we obtain the following:
To know the most popular song in an entire country, it is necessary to use the entire population, since the result of the favorite song if only one sample is used will not give results with certainty, considering that the population that is not covered could generate changes in the result.
=
The area of Desert A is five times the area of Desert B. If the sum of their areas is 600,000 square miles, find the area of each desert.
The area of Desert A is 500,000 square miles and the area of Desert B is 100,000 square miles.
What is area?
Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.
Area of a square is side × side.
Let the area of Desert A = x square miles
and the area of Desert B = y square miles
Given that, the area of Desert A is five times the area of Desert B,
i.e. x = 5y ...(1)
and the sum of their areas is 600,000 square miles,
i.e. x + y = 600,000 square miles ...(2)
Putting equation (1) in (2), we get
5y + y = 600,000
or 6y = 600,000 or y = 100,000 square miles
Using equation (1),
x = 5 × 100,000 = 500,000 square miles
Hence, the area of Desert A is 500,000 square miles and the area of Desert B is 100,000 square miles.
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find the measure of LH, EL, JG, EK, KG. LG = 34EH = 22LG = 34
Please, give me some minutes to take over your question
I am working on it
______________________________-
LG = 34
EH= 22
JL= 16
_______________________________
Pythagoras theorem
Hypotenuse = H
Side 1 = S1
Side 2 = S2
H^2 = S1^2 + s^2
__________________________
This is a triangle with multiple right triangles inside
JG
34^2 = 16^2 + JG ^2
[tex]JG=\text{ }\sqrt[]{34^2-16^2}=\text{ 30}[/tex]JG = 30
_________________________________
LH
_________________________________
Answer
LH
EL
JG = 30
EK
KG
1) Analia thought of two different ways to define this quantity. Identify these two definitions among the
following options.
Choose 2 answers:
Graduation rate divided by number of teachers
Graduation rate divided by teachers per student
SAT average divided by number of teachers
SAT average divided by teachers per student
Analia proposed the following two measures to determine which school had a better academic record:
B. Graduation rate and student budget
D. Average SAT score / Per-student budget
How to determine the various amounts Which school has the best academic performance, according to Analia?To specify a number that represents academic accomplishment;
We compare the budget per pupil for each school to a corresponding metric or parameter that measures the academic performance of the students in each school.
The following variables could be used to gauge academic achievement:
the success rate of every school.
The SAT score of each institution.
Consequently, the amount to assess academic success in relation to each student's budget may be represented as;
Graduation rate and student budget
Average SAT score / Per-student budget
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Solve the equation.
²x+3-2x = 1+²x+5
42
If necessary:
Combine Terms
Apply properties:
Add Subtract
Multiply
Divide
To start over:
The answer to the equation is -3/2.
How to solve equations?
1.Remove parentheses from each side of the equation and combine similar phrases to make it simpler.
2.Identify the variable term on one side of the equation by adding or subtracting.
3.You can find the variable's value by multiplying or dividing.
Given equation is x²+ 3-2x= 1+ x² +5
Thus x² from both sides gets cancelled because x²-x²= 0
Now we get 3-2x = 6
-3 = 2x
On dividing by 2 we get,
-3/2 = x
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How can I solve this question
Answer:
x = 10
The interior angles measure 93°, 126°, 60°, and 81°.
Step-by-step explanation:
[tex]9x + 3 + 12x + 6 + 6x + 8x + 1 = 360[/tex]
[tex]35x + 10 = 360[/tex]
[tex]35x = 350[/tex]
[tex]x = 10[/tex]
9(10) + 3 = 90 + 3 = 93°
12(10) + 6 = 120 + 6 = 126°
6(10) = 60°
8(10) + 1 = 80 + 1 = 81°
The incorrect work of a student to solve an equation 2(y + 6) = 4y is shown below:Step 1: 2(y + 6) = 4yStep 2: 2y + 8 = 4yStep 3: 2y = 8Step 4: y = 4Which of the following explains how to correct Step 2 and shows the correct value of y? 2 should be distributed as 2y + 12; y = 62 should be distributed as 2y + 12; y = 3The equation should be y + 6 = 4y after division by 2; y = 2The equation should be y + 6 = 4y after division by 2; y = 1
Solution:
Given the equation;
[tex]2(y+6)=4y[/tex]Now, distribute 2;
[tex]\begin{gathered} 2(y)+2(6)=4y \\ \\ 2y+12=4y \end{gathered}[/tex]Then, step 3;
[tex]\begin{gathered} 12=4y-2y \\ \\ 2y=12 \end{gathered}[/tex]Divide both sides by 2;
[tex]\begin{gathered} \frac{2y}{2}=\frac{12}{2} \\ \\ y=6 \end{gathered}[/tex]CORRECT OPTION: 2 should be distributed as 2y + 12; y = 6
The point E is plotted on the coordinate grid below. Plot the point E’, the reflection of E over the x-axis.
Answer:
E' will be at (2, -6)
Step-by-step explanation:
Here we are given point E at (2, 6).
A reflection over the x-axis will keep the x coordinate the same while changing the y value to become the additive inverse (the number in which adding to the current value will get you zero). In this case, it is -6.
E (2,6) --> E' (2, -6)
Another way of thinking of it is reflecting on the x-axis while change the value from (x, y) to (x, -y).
Increase 270 by 20%
please help asap
Answer:
324
Step-by-step explanation:
20%-> 0.2
0.2(270)= 54
270+54=324
Answer:The answer is 324
Step-by-step explanation:20% of 270 is 54 so add 54 and 270 because you increase by 20 to get the answer
Estimate quotients. Convert decimal division expressions to fractional division expressions to create whole number
divisors. Compute the quotient using the division algorithm. Check your work with a calculator and your estimate.
1. Lisa purchased almonds for $3.50 per pound. She spent a total of $24.50. How many pounds of almonds did she
purchase?
After conducting some mathematical operations, we conclude that Lisa purchased 7 pounds of almonds.
What are mathematical operations?A mathematical function known as an operation is one that converts zero or more discrete input values into discrete output values.Depending on how many operands there are, the operation's complexity changes.The four mathematical operations are transformational functions that change numerical inputs into numerical outputs (i.e., another number).These are addition, subtraction, division, and multiplication.So, pounds of Almonds Lisa purchased:
Almonds per pound costs: $3.50Lisa spends the total amount: $24.50Now, calculate the pounds of almonds Lisa purchased as follows:
24.50/3.50 = 7(Refer to the image attached below for calculation)
Therefore, after conducting some mathematical operations, we conclude that Lisa purchased 7 pounds of almonds.
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The correct question is given below:
Lisa purchased almonds for $3.50 per pound. She spent a total of $24.50. How many pounds of almonds did she purchase?
Please help I’ll mark you as brainliest if correct!
Find the value of x And y. State the Theron’s you used.
Answer:
x = 5, y = 13
Step-by-step explanation:
Solve for x:
42 = 8x + 2
40 = 8x
x = 5
This is solved using the alternate interior angles theorem, which states that alternate interior angles (in this case, the 42-degrees and 8x + 2 degree angles) are the same.
Solve for y:
180 = 42 + 6(2y - 3)
180 = 42 + 12y - 18
180 = 24 + 12y
156 = 12y
y = 13
This is solved using the same-side interior angles theorem, which states that same-side interior angles (in this case, the 42-degrees and 6(2y-3)-degree angles) add up to 180 degrees.
The fraction n/12 is between 1/4 and 2/3. Write down all the possible values of n.
When the fraction n/12 is between 1/4 and 2/3, the possible values of n will be 4, 5, 6, and 7.
How to calculate the fraction?It should be noted that a fraction simply means a number that isn't whole. It can be illustrated as a/b where a is the numerator and b is the denominator.
It should be noted that 1/4 is equivalent to 3/12.
It should be noted that 2/3 is equivalent to 8/12.
Therefore, the values of n will be numbers between 3 and 8. They are 4, 5, 6, and 7.
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Find the indicated Z score the graph depicts the standard normal distribution with a mean of 0 and a standard deviation of one the shaded area iso.80501
By using the method subtraction, the indicated Z score the graph depicts IS 0.30501
What is subtraction?To subtract in mathematics is to take something away from a group or a number of objects. The group's total number of items decreases or becomes lower when we subtract from it. The components of a subtraction issue are the minuend, subtrahend, and difference. An arithmetic operation called subtraction simulates the process of deleting items from a collection. The action of subtracting a matrix, vector, or other quantity from another according to predetermined rules in order to find the difference.
Given that,
The standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1 and it is given by the probability density function and distribution function
Areas of the normal distribution are often represented by tables of the standard normal distribution.
Shaded area is 0.80501 according to the attachment. Then the lookup area is
Find the indicated z score.
z=x-μ/ σ
where Z is the value on the standard normal distribution, X is the value on the original distribution, μ is the mean of the original distribution, and σ is the standard deviation of the original distribution.
According to the picture below z is
z=0.80501- 0.5/1 = 0.30501
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The quadrilateral ABCD is a parallelogram if pairs of consecutive angles are supplementary. Given the angles measures, prove that quadrilateral ABCD is a parallelogram by finding the value of x
REmember that
in a parallelogram, consecutive angles are supplementary
that means
.mmmm
therefore
substitute
120-2x+70+x=180
solve for x
2x-x=190-180
x=10answer is option CTo determine the town pigeon population, researchers tagged and released 27 pigeons. Later,
the researchers counted 380 pigeons. Out of the pigeons they counted, 19 had tags. To the
nearest whole number, what is the best estimate for the pigeon population
The best estimate for the pigeon population is 540.
What is meant by estimation?Finding an estimate or approximation—a value that may be used for a purpose despite the possibility of incomplete, ambiguous, or unstable input data—is the process of estimation. Despite this, the value is still useful because it was created using the most up-to-date data.
Counting a small sample of something and extrapolating that number to a wider population is how estimation is frequently done. Calculating how many sweets of a certain size are contained in a glass jar is an example of estimation.
380 x 27/19
= 540
So the answer is
540
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what is 30/cos40° rounded to 1 d.p.
The value of 30/cos40° rounded to 1 d.p. (decimal point) is 39.2.
How to round off any decimal number to one decimal place?
When you round to the first decimal place, or to the nearest tenth, the number in the hundredth point place will determine whether you round up or down. If the hundredths digit is a number between 5 and 9, round up to the nearest whole number. If it's a number between 0 and 4, you would "round down" by keeping the tenths place the same.
We have 30/cos40°
Value of 30/cos40° = 30/0.766044 = 39.162241 (cos40° = 0.766044)
Since the number in the hundredths place is 6, which is between 5 and 9, we would round the tenth decimal point up to 2.
Therefore, the value of 30/cos40° rounded to 1 d.p. (decimal point) is 39.2.
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