Answer:
To earn $65 in interest in 16 months at a simple interest rate of 3%, you would need to invest $2,166.67. The formula for calculating simple interest is I = P * R * T, where I is the interest earned, P is the principal amount invested, R is the interest rate, and T is the time in years. In this case, we are given that the interest rate is 3%, the time is 16 months, and the interest earned is $65, so we can plug these values into the formula to solve for the principal amount invested:I = P * R * T
$65 = P * 0.03 * (16/12)
$65 = P * 0.03 * (4/3)
$65 = P * 0.01
P = $2,166.67Therefore, to earn $65 in interest in 16 months at a simple interest rate of 3%, you would need to invest $2,166.67.
The fox population in a certain region has a continuous growth rate of 6 percent per year. It is estimated that the population in the year 2000 was 25100.
(a) Find a function that models the population
t
years after 2000 (
t
=
0
for 2000).
Your answer is
P
(
t
)
=
(b) Use the function from part (a) to estimate the fox population in the year 2008.
Your answer is (the answer must be an integer)
The function is f(x) = 25100(1 + 0.06)ˣ and the estimate fox population in the year 2008 is 40,0005.
What is an exponential function?It is defined as a function that rapidly increases and the value of the exponential function is always a positive. It denotes with exponent y = a^x
where a is a constant and a>1
It is given that:
The fox population in a certain region has a continuous growth rate of 6 percent per year
f(x) = a(1 + r)ˣ
f(x) = 25100(1 + 0.06)ˣ
Plug x = 8 years
f(8) = 25100(1 + 0.06)⁸
f(8) = 40,0005
Thus, the function is f(x) = 25100(1 + 0.06)ˣ and the estimate the fox population in the year 2008 is 40,0005.
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IJ is a midsegment of triangle MLN. What is the length of segment IJ?
The length of segment IJ is 6 units.
What is a line segment?
A line segment in geometry has two different points on it that define its boundaries. A line segment is sometimes referred to as a section of a line that links two places. The difference between a line and a line segment is that a line has no endpoints and can go on forever in either direction.
Given that IJ is a midsegment of △LMN.
The line segment IJ is parallel to NL.
Thus the length of IJ is half of NL.
Therefore,
2 × IJ = LN
2 (x + 3) = 3x
2x + 6 = 3x
Subtract 3x from both sides:
-x + 6 = 0
x = 6.
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What does n equal? n^2=100
Answer:
10
Step-by-step explanation:
100 = 10 x 10 = 10^2
n^2 = 10^2
n = 10
Mr. Freeze is a freelance ice artist who creates ice sculptures. He is paid $30 per pound of ice he uses. Last week it took him 73 hours to sculpt 5 sculptures weighing a total of 530 pounds. Based on this, what is his approximate hourly wage?
The required hourly wage of Mr. Freeze is given as $217.8.
What is a wage?Wage is defined as the defined earnings of the worker for their respective work. It can be evaluated in parameters based on degrees of time and difficulty.
Here,
As mentioned in the question,
Mr. Freeze is paid $30 per pound of ice,
it took him 73 hours to sculpt 5 sculptures weighing a total of 530 pounds.
Total ice he used = 530 pounds,
For 530 pounds of ice Mr. Freeze gets paid,
= 530 × 30
= $15900
Now, Divide the whole amount for a pound of ice by the total hours Mr. Freeze works so we get the hourly wage.
hourly wage,
= 15900 / 73
= $217.8
So, Mr. Freeze gets paid of $217.8 hourly.
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A bag contains 7 green marbles, 3 yellow marbles and 10 black marbles. If a green marble is drawn, you win $20. If a yellow marble is drawn, you win $30. If a black marble is drawn, you lose $15. It costs $1 to play. What are you expected winnings over time?
The expected winnings are $3 for each time that you play the game.
What is expected winnings?
The expected value is a generalization of the weighted average in probability theory. Informally, the expected value is the arithmetic mean of a significant number of outcomes of a random variable that were independently chosen.
For an event with the outcomes {x₁, x₂, x₃,...} each one with correspondent probabilities {p₁, p₂, ...}
The expected value (here is equivalent to the expected winnings) is given by:
EV = x₁*p₁ + x₂* p₂ + ...
Here the outcomes are:
Winning $20, this happens if you draw a green marble, and there are:
7 green ones
3 yellow ones
10 black ones.
So 7 out of 20, then the probability is p₁ = 7/20
The second outcome is win $30 if you get a yellow one, there are 3 yellow ones, so the probability is p₂ = 3/10
Finally, you lose $15 if you get a black one, the probability now is
p₃ = 10/20
Then the expected winnings (remember that costs $1 to play, so we need to take that in consideration) is:
W = -$1 + $20*(7/20) + $30*(3/20) - $15*(10/20) = $3
Hence, the expected winnings are $3 for each time that you play the game.
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With enough variables, it is possible to get an R2 value close to 1, even if the variables have no particular meaning in the model
A)True
B)False
With enough variables, it is possible to get an R2 value close to 1, even if the variables have no particular meaning in the model - True
If the model has a significant number of variables, it is still possible to obtain an R-squared value that is near to 1, even if the variables have no particular significance. R-squared is a metric used to evaluate how well a model fits data; it has a range from 0 to 1, with 1 denoting a perfect fit.
A high R-squared value does not, however, guarantee that the model fits the data well or that the variables it uses are significant. To ensure that the model accurately represents the underlying relationships in the data, it is crucial to carefully analyze the meaning and relevance of the variables included in the model, as well as other evaluation metrics like residual plots and cross-validation.
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Binary form can be represented as
a A B C A
b A B
c A B A
d A B A C B A
The binary form can be represented as AB or AABB. So the write option is b.
One of the four different kinds of number systems is the binary number system. When used in computer programmes, binary numbers are solely represented by the digits 0 (zero) and 1. (one). Here, the base-2 numeric format is used to express the binary numbers.
Because the binary system is directly implemented in electronic circuits using logic gates, nearly all modern computers and computer-based gadgets employ it internally. A bit is used to describe each digit.
The binary form is a set of alphabetical character that is used to describe a musical piece using two sections of equal length. It can be represented as AB or AABB. So the write option is b.
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How do you complete the square for this problem ? (if you just explain to me how to complete the square of a trinomial it would be gladly appreciated)
a^2 + 2a - 3
a^2 - 2a - 8
p^2 + 16p - 22
The complete square of the a² + 2a - 3 = 0,a² - 2a - 8 = 0 and p² + 16p - 22 = 0 are (a + 1)² - 4 = 0,(a - 1)² - 9 = 0 and (p + 8)² - 86 = 0 respectively.
What is an expression?A mixture of variables, numbers, addition, subtraction, multiplication, and division are called expressions.
An expression is a mathematical proof of the equality of two mathematical expressions.
As per the given trinomial,
a² + 2a - 3 = 0
a² + 2a = 3
Add 1 on both sides,
a² + 2a + 1 = 3 + 1
(a + 1)² = 4
(a + 1)² - 4 = 0
As per the given trinomial,
a² - 2a - 8 = 0
a² - 2a = 8
Add 1 on both sides,
a² - 2a + 1 = 8 + 1
(a - 1)² = 9
(a - 1)² - 9 = 0
As per the given trinomial,
p² + 16p - 22 = 0
p² + 16p = 22
Add 64 on both sides,
p² + 16p + 64 = 22 + 64
(p + 8)² = 86
(p + 8)² - 86 = 0
Hence "The complete square of the a² + 2a - 3 = 0,a² - 2a - 8 = 0 and p² + 16p - 22 = 0 are (a + 1)² - 4 = 0,(a - 1)² - 9 = 0 and (p + 8)² - 86 = 0 respectively".
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2/125x10,13+2/27x10,13
The value of the expression 2/125x1013 + 2/27x1013 is 91.248.
How to illustrate the expression?It is important to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator.
The expression will be Illustrated as:
2/125x1013 + 2/27x1013
= (0.016 × 1013) + (0.0740741 × 1013)
= 16.208 + 75.04
= 91.248
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Complete question
2/125x1013 + 2/27x1013
The Video “The Math and Magic of Origami”describes several examples in which scientists and engineers use origami to solve problems. Which of the following is NOT one of the applications described?
The option that is not one of the application described is C. Building a bridge.
What role does origami play in engineering?Origami created through mathematical interpretation and computation is known as mathematical origami, and it has resulted in the modeling of numerous novel origami-based structures outside of the realm of the arts. Furthermore, mathematical origami inspires the creation of new structures and mechanisms in engineering.
Origami-inspired engineering has been used in NASA space equipment, the development of better heart stents, and even DNA folding in microbiology.
Origami-based designs are the use of the ancient art of origami to solve various engineering problems. Regardless of the scale at which they are implemented, origami-based designs are always defined by the laws that govern their geometrical properties at any scale.
Furthermore, for large flat structures, origami allows for the reduction of dimensions while ensuring simple deployment this is especially useful for solar arrays in space applications.
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The Video "The Math and Magic of Origami" describes several examples in which scientists and engineers use origami to solve problems. Which of the following is NOT one of the applications described?
A.A heart stent
B. A space telescope
C. Building a bridge
D. Air bags in cars
Suppose you get $1000 from your uncle. you deposited that money in a bank and added $15 per month.
Write an equation to model how much money you have deposited after m months. Let s be the amount you have deposited.
What equation would you solve to figure out how many months it would take to save $10,000 dollars?
How many months would it take to save $10,000?
Answer:
s = 1000 + 15m
Save $10,000 equation: 10,000 + 15 m
Months it takes to save = 600 months
Step-by-step explanation:
You first deposit the $1000 your uncle gave you and then, each month, you add $15. So the first month the account will have,
1000 + 15
After the second month, it will have,
1000 + 15 + 15
And so on. Therefore, the equation that models your savings s after m months is,
s = 1000 + 15m
If we want to find how many months it will take to save $10,000 we have to solve the equation for s = 10,000:
10,000 = 1000 + 15m
To solve it, subtract 1000 from both sides of the equation,
10,000 - 1000 = 1000 - 1000 + 15m
9000 = 15m
And divide both sides by 15,
9000/55 = 55m/55
600 = m
It will take 600 months to save $10,000.
A politician's support increases from 34% to 55% Determine the absolute and relative change in
this sitation.
Answer:The relative change is a fraction that describes the size of the absolute change in comparison to the reference value: relative change = absolute change reference value = new value − reference value reference value . 100 100 = 100%. When a quantity triples in value, its relative change is 2 = 200%.
Step-by-step explanation:
The most common way to represent the absolute value of a number or expression is to surround it with the absolute value symbol: two vertical straight lines. |6| = 6 means “the absolute value of 6 is 6.” |–6| = 6 means “the absolute value of –6 is 6.” |–2 – x| means “the absolute value of the expression –2 minus x.”
Which relation is a function?
The relation is a function in the first graph.
How to check which relation is function in given graph?
By applying the vertical line test to the graph of an equation, we may quickly identify whether or not it represents a function. The graph does not represent a function if any vertical line crosses it more than once. We can use the notation f(x)=y to indicate that an algebraic equation defines a function.Check the graph to check if any vertical lines that were generated would repeatedly cross the curve. If such a line exists, the graph does not depict a function. A function is depicted by the graph if no vertical line may pass across the curve more than once.To know more about function check the below link:
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In a survey conducted by the Gallup organization on September 1017 adults were asked how confident they are in the media accurately reporting news. 81 said that they had a great deal of confidence. 325 said that they had a fair amount of confidence. 397 said they had not a lot of confidence. 214 said they had no confidence at all. Suppose the parameter of interest is the proportion of U.S adults who have no confidence at all. Use the data to estimate this parameter.
To estimate the proportion of U.S adults who have no confidence at all in the media accurately reporting news, you can use the following steps:
Calculate the total number of adults surveyed by the Gallup organization. You can do this by adding the number of adults who said they had a great deal of confidence, a fair amount of confidence, not a lot of confidence, and no confidence at all:
Total number of adults = 81 + 325 + 397 + 214 = 1017
Calculate the proportion of adults who have no confidence at all by dividing the number of adults who said they had no confidence at all by the total number of adults:
Proportion of adults with no confidence = 214 / 1017
= 0.2113
Therefore, the estimated proportion of U.S adults who have no confidence at all in the media accurately reporting news is approximately 0.2113, or 21.13%. This represents the proportion of adults who responded "no confidence at all" to the survey question.
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4x²-17x+ k = 0 has the reciprocal roots.
Answer: k=4
Step-by-step explanation:
4x²-17x+k=0
Divide both parts of the equation by 4:
[tex]\displaystyle\\\frac{4x^2}{4}-\frac{17x}{4}+\frac{k}{4}=0\\\\x^2-\frac{17}{4} x +\frac{k}{4} =0\\[/tex]
Let one of the roots of this equation be α
Then the other root of this equation is 1/α
Hence,
[tex]\displaystyle\\\alpha (\frac{1}{\alpha })=\frac{k}{4} \\\\\frac{\alpha }{\alpha }= \frac{k}{4} \\\\1=\frac{k}{4}[/tex]
Multiply both parts of the equation by 4:
4=k
Thus, k=4
Please help
Algebra 2
How do I solve this?
The required probability is 0.8437 that a dart hitting the board will land in the unshaded area.
The total area of the board = 8 x 8 = 64 square inches
The area of the shaded region = 15 square inches
The probability of landing in the shaded region is the ratio of the unshaded area to the total area.
The unshaded area = 64 - 15 = 54 square inches
So, the required probability is:
P(unshaded) = 54/64 = 0.8437
Thus, the required probability is 0.8437 that a dart hitting the board will land in the unshaded area.
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What is the simplified expression for 2 power 2 multiplied by 2 power 3 over 2 power 4
Answer:
ANS:- 2
Step-by-step explanation:
= (2^2)(2^3/2^4)
= (4)(8/16)
=(4)(1/2)
=4/2
= 2
If the volume of the cylinder is 942 in³, what is the radius of the base of the cylinder? Use 3.14 for pie and enter your answer as a whole number.
The radius of the given cylinder is equal to r = 10 inches.
What is volume?Volume is defined as the space occupied by any object in the three-Dimensions. All three parameters are required for the volume like length, width, and height of the Cuboid.
For the cylinder, the formula for the volume will be,
V = πr²h
Given that the volume of the cylinder is 942 cubic inches. the radius of the cylinder base will be calculated as,
942 = π x ( r² ) x 12
r² = ( 942 x 4 ) / ( 12 x π)
r² = 100
r = 10 inch
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2. Which of the following inequalities would represent the graph shown?
f(x) ≤ √1-x
f(x) < √1-x
f(X) > √1-x
f(x) ≥ √1-x
Answer:
[tex]f(x) > \sqrt{1 -x}[/tex]
which is the third choice
Step-by-step explanation:
We could just plot each and see which plot corresponds to the given graph
However, that is not necessary.
First note that the plot is a dotted line. This means the inequality is either a < inequality or a > inequality. If it were a ≤ or ≥ inequality, the plot of the line would be a solid line
That eliminates first and last choices
To see which of the remaining two options fits the graph, take a point in the shaded region and see which one satisfies which inequality .
Checking second choice....
Point (0, 2) is in the shaded region
Does (0, 2) satisfy the second choice: [tex]f(x) < \sqrt{1-x}\;\; ?[/tex]
Let's check by substituting 0 for the value of x
[tex]1-x = 0\; so \; \sqrt{1-x} = \sqrt{0} = 0[/tex]
But the corresponding value of y should be 2, not 0 so this inequality is not satisfied for a point in the shaded region. Eliminate second choice
Third choice is the correct answer
The following stem and leaf plot shows the average high temperatures during each month in the state of Ohio. Use the data to answer questions 7-8.
7) What is the minimum temperature?
A) 38
B) 31
C) 91
D) 67
Answer:
B) 31
Step-by-step explanation:
Given a stem and leaf plot, you want to identify the minimum value.
OrderingThe values in a stem and leaf plot are ordered with the smallest stems at the top, and the smallest leaves to the left. The smallest value on the plot will be the one at upper left.
Minimum valueThe minimum value on this chart has a "stem" of 3 and a "leaf" value of 1. That is the representation of the data value 31.
The minimum temperature shown on the chart is 31.
write 8/10 in simplest form:
-
write the answer in the form a/b for example, 1/2
Class records at a particular college indicate that a student selected at random has probability 0.67 of passing French 101. For the student who passes French 101, the probability is 0.88 that he or she will pass French 102. What is the probability that a student selected at random will pass both French 101 and French 102?
The required probability that a student selected at random will pass both French 101 and French 102 is 0.58.
Given that,
Class records at a particular college indicate that a student selected at random has a probability 0.67 of passing French 101. For the student who passes French 101, the probability is 0.88 that he or she will pass French 102.
Probability can be defined as the ratio of favorable outcomes to the total number of events.
Here,
P(a) = 0.67 for passing French 101.
p(b) = 0.88 for passing French 102.
The probability that a student selected at random will pass both French 101 and French 102 = 0.67 × 0.88 = 0.58
Thus, the required probability that a student selected at random will pass both French 101 and French 102 is 0.58.
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Identify the expression that can be used to solve 335 ÷ 5 = ___.
(200 ÷ 5) + (35 ÷ 5)
(250 ÷ 5) + (35 ÷ 5)
(300 ÷ 5) + (35 ÷ 5)
(350 ÷ 5) + (35 ÷ 5)
Answer:
(300 ÷ 5) + (35 ÷ 5)
Step-by-step explanation:
You want an expression that has the same value as 335÷5.
EquivalentsThe given division expression can be rewritten as ...
[tex]335\div5=\dfrac{335}{5}\\\\=\dfrac{300+35}{5}=\dfrac{300}{5}+\dfrac{35}{5}\\\\=\boxed{(300\div5)+(35\div5)}[/tex]
University Car Wash built a deluxe car wash across the street from campus. The new machines cost $267,000 including installation. The company estimates that the equipment will have a residual value of $24,000. University Car Wash also estimates it will use the machine for six years or about 12,000 total hours. Actual use per year was as follows: Year Hours Used 1 3,000 2 1,200 3 1,300 4 2,700 5 2,500 6 1,300 Required: 1. Prepare a depreciation schedule for six years using the activity-based method. (Do not round your intermediate calculations.)
The depreciation schedule for the new machines of University Car Wash, using the activity-based method, is as follows:
Year Initial Cost Depreciation Accumulated Net Book Value
Expense Depreciation
1 $267,000 $60,750 $60,750 $206,250
2 $267,000 $24,300 $85,050 $181,950
3 $267,000 $26,325 $111,375 $155,625
4 $267,000 $54,675 $166,050 $100,950
5 $267,000 $50,625 $216,675 $50,325
6 $267,000 $26,325 $243,000 $24,000
What is a depreciation schedule?A depreciation schedule is a table that shows the annual depreciation expense, the accumulated depreciation over the years, and the net book value of each asset, including the initial cost.
An activity-based method of depreciation uses the machine hours or other activity bases used to determine each year's depreciation expenses.
Cost of machines = $267,000
Residual value = $24,000
Depreciable amount = $243,000 ($267,000 - $24,000)
Estimated useful life = 6 years or 12,000 total hours
Hourly depreciation rate = $20.25 ($243,000/12,000)
Year Annual Depreciation Expense
1 $60,750 (3,000 x $20.25)
2 $24,300 (1,200 x $20.25)
3 $26,325 (1,300 x $20.25)
4 $54,675 (2,700 x $20.25)
5 $50,625 (2,500 x $20.25)
6 $26,325 (1,300 x $20.25)
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PLEASE HELP NO PLAYING ON MY QUESTION
The percentage for blue balls will be 56% and the percentage for red balls will be 44%.
What is the percentage for the colors of the gumball?A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100. The percentage, therefore, refers to a component per hundred.
In this situation, there are 4000 balls and 2240 of then are blue while 1760 are red.
The percentage for blue balls will be:
= Number of blue balls / Total balls × 100
= 2240 / 4000 × 100
= 56%
The percentage for red balls will be:
= Number of red balls / Total balls × 100
= 1760 / 4000 × 100
= 44%
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Which estimated solution is closest to the actual solution shown in the graph?
Question 7 options:
(3,3)
(6,1)
(0,2)
(4,5)
(7,7)
(4,3)
(2,4)
Answer:
(7) (2, 4)
Step-by-step explanation:
You want to know which of the offered points is closest to the point of intersection of the two graphed lines.
SolutionThe point of intersection can be read from the graph as approximately (2 1/3, 3 3/4). The nearest grid intersection to that point is (2, 4), which is the last point on the list of choices.
(2, 4) is closest to the actual solution
__
Additional comment
You can see this, too, by graphing the offered choices. There are none closer than (2, 4).
What is the greatest common factor of 30, 21, and 56?
Answer:
Step-by-step explanation:
For 30: 1,2,3,5,6,10,15,30
For 21: 1,3,7,21
For 56: 1,2,4,7,8,14,28,56
Because you always go times it by the number. Example is: 1 is always in the factors (Doesn't matter if it's the least common factor or whatever) because whatever you times by 1, it's that answer. Or you can look at the answer, (I'm doing the 30) First, find the middle which is 5 and 6. You times 5 and 6 and it will give you 30. People call it a rainbow, 5x6=30, 3x10=30, 2x15=30, and 1x30=30.
I hope this helps
-10 - 11x + 24 = 3x
I need help with this and I can’t figure it out can someone break it down for me
Answer:
x=1
Step-by-step explanation:
move 11x on the other side so -11x will be postive -10+24=3x+11x -10+24=14x14=14xsimplify or divide both side by 14x=1Solve for v
12.5 = 5v
Answer:v=2.5
Step-by-step explanation:
isolate the variable by dividing both sides by 5
v=2.5