A. The domains and ranges of both functions are not restricted.
For f(x) = 5/8x + 1, any real number can be plugged in for x, so the domain is (-∞, ∞). Similarly, any real number can be obtained by evaluating the function, so the range is also (-∞, ∞).
For g(x) = 2/3x^3, any real number can be plugged in for x, so the domain is (-∞, ∞). As x is cubed, the range can be negative or positive infinity, or any real number in between, so the range is also (-∞, ∞).
Therefore, both functions have unrestricted domains and ranges.
The correct answer is A.
the ratio of ducks to geese on a pond is 3:2. which is true. A. there are 2 fewer geese than duck pond. B. There are 13 ducks and 12 geese on the pond. C. There are a total of 20 birds on the pond, of which 8 are ducks. D. There are a total of 45 birds on the pond, of which 27 are ducks
The statement that is true about the ratios is:
There are 2 fewer geese than ducks on the pond.
Option A is the correct answer.
We have,
The ratio of ducks to geese on a pond is 3:2.
This means,
Number of ducks = 3x
Number of geese = 2x
And,
If the total number of ducks and geese = 10
So,
(3x + 2x) = 10
5x = 10
x = 2
Now,
Number of ducks = 3x = 3 x 2 = 6
Number of geese = 2x = 2 x 2 = 4
This means,
There are 2 fewer geese than ducks on the pond.
Thus,
The statement that is true about the ratios is:
There are 2 fewer geese than ducks on the pond.
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Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
The standard deviation of a sample taken from population A is 17.6 for a sample of 25. The standard deviation of a sample taken from population B is 21.2 for a sample of 30.
The standard deviation of the sample mean differences is ____. (Round your answer to the nearest hundredth.)
The standard deviation of the sample mean differences is, 16.98.
Since, We know that;
Standard deviation is defined to be the square root of the population variance of the vector. The sample standard deviation s is defined to the square root of the sample variance of the vector.
Here, The standard deviation of the sample mean differences should be calculated using the standard deviations of the two populations.
In order to see how they differ, we need to first subtract them from each other,
So, we get:
21.2 - 17.6 = 3.6
We then divide this number with the first standard deviation as follows:
⇒ 3.6/21.2 x 100
⇒ 16.98
Therefore, the standard deviation of the sample mean is, 16.98.
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Find the volume of the composite solid. Round your answer to the nearest hundredth.
6 ft
-12 ft
The volume is about
cubic feet.
Christina Sanders is concerned about the financing of a home. She saw a small Cape Cod–style house that sells for $90,000. If she puts 10% down, what will her monthly payment be at (a) 30 years, 5%; (b) 30 years, 512% ; (c) 30 years, 6%; and (d) 15 years, 378% ? What is the total cost of interest over the cost of the loan for each assumption? (Use Table 15.1.) Note: Round your answers to the nearest cent. Do not round intermediate calculations.
The monthly payments and total cost of interest depend on the interest rate and the length of the loan. Generally, a lower interest rate or a shorter loan term results in lower total interest costs.
To calculate the monthly payments, we can use the formula for the present value of an annuity:
[tex]PV = P * (1 - (1 + r)^{-n}) / r[/tex]
where PV is the present value of the loan, P is the principal (the amount borrowed), r is the monthly interest rate, and n is the number of monthly payments.
(a) 30 years, 5%:
PV = 0.9 * $90,000 = $81,000 (since she puts 10% down)
r = 0.05 / 12 = 0.0125(monthly interest rate)
n = 30 * 12 = 360 (number of monthly payments)
Using the formula, we get:
PV = $81,000
Monthly payment = $436.82
Total cost of interest = $57,255.85
(b) 30 years, 5.12%:
r = 0.0512 / 12 = 0.00427 (monthly interest rate)
Using the formula, we get:
PV = $81,000
Monthly payment = $439.88
Total cost of interest = $59,956.19
(c) 30 years, 6%:
r = 0.06 / 12 = 0.005 (monthly interest rate)
Using the formula, we get:
PV = $81,000
Monthly payment = $485.24
Total cost of interest = $95,687.34
(d) 15 years, 3.78%:
n = 15 * 12 = 180 (number of monthly payments)
r = 0.0378 / 12 = 0.00315 (monthly interest rate)
Using the formula, we get:
PV = $81,000
Monthly payment = $591.93
Total cost of interest = $34,147.07
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Please find the surface area of this figure. Ps pls show your work on how you got your answer or explain.
Answer:
2(1/2)(11)(13) + 2(1/2)(10)(13.2) + 10(11)
= 143 + 132 + 110 = 385 square feet
B is the correct answer.
12 Kittens to 15 puppies ratio in
Answer:
4:5 or 4/5 or .8 or 80%
Step-by-step explanation:
divide both by 3. then convert to percent or decimal
determine the value of x (asap)
The values of the missing terms are 1) 24 and 2) 1.6.
Given are two similar figures, we need to find the value of x,
According to the definition of similar figures, the ratios of the corresponding sides are equal,
So,
1) GE / EF = RS / TR
5/6 = 20/x
5x = 120
x = 24
2) JH / LK = WX / ZY
3.84 / 2.04 = 3.2 / x
3.84x = 2.04 × 3.2
3.84x = 6.528
x = 1.7
Hence, the values of the missing terms are 1) 24 and 2) 1.6.
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In 2012, the population of a city was 6.53 million. The exponential growth rate was 2.79% per year. a) Find the exponential growth function. b) Estimate the population of the city in 2018. c) When will the population of the city be 10 million? d) Find the doubling time.
a) The exponential growth function for a city's population that was 6.53 million in 2012 with an exponential growth rate of 2.79% per year is y = 6.53(1.0279)^t.
b) Based on the exponential growth function y = 6.53(1.0279)^t the population of the city in 2018 is 7.7 million.
c) The population of the city will be 10 million in 2028.
d) The doubling time for the population is 25 years.
What is an exponential growth function?An exponential growth function is one of the two exponential functions, including an exponential decay function.
An exponential growth function shows the relationship between two variables with an exponent and exhibits a constant rate of growth per period.
Population of the city in 2012 = 6.53million
Exponential growth rate = 2.79% per year
Let the number of growth years = t
Exponential growth function:a) y = 6.53(1.0279)^t
b) From 2012 to 2018, the number of years = 6 years
Population in 2018, y = 6.53(1.0279)^6
= 7.7 million
c) When the population will be 10 million = 15.5 years
10 = 6.53(1.0279)t
t = 15.5 years
= 16 years
= 2028
d) 13.06 = 6.53(1.0279)t
t = 25.189 years
= 25 years
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Given the figure below, find the values of x and z.
120°
(8x
+ 96).
Answer:
x = 3; z = 60°
Step-by-step explanation:
x:
The angles measuring 120° and (8x + 96)° are vertical angles, which means they're congruent and equal.
Thus, we can solve for x by setting the two angles equal to each other and isolate x:
[tex]120=8x+96\\24=8x\\3=x[/tex]
We can check our answer by plugging in 3 for x and ensure that we get 120:
[tex]120=8(3)+96\\120=24+96\\120=120[/tex]
z:
We see that a horizontal straight line separates the angle measuring 120° and z°. Straight lines create straight angles, which equal 180°.
Thus, we can find the measure of z by adding the 120° angle and the z° and set them equal to 180. Then, we must isolate z:
[tex]120+z=180\\z=60[/tex]
An object is dropped from a height of 400 feet. The amount of time, in seconds, the object takes to hit the ground can be found by solving the equation - 16r2 + 400 = 0. How many seconds will it take to hit the ground?
05
O 5 or-5
O 12
O 25
It will take 5 seconds for the object to hit the ground
How many seconds will it take to hit the ground?From the question, we have the following equation that can be used in our computation:
-16r^2 + 400 = 0
So, we have
- 16r^2 = -400
Divide by -16
This gives
r^2 = 25
Take the square root of both sides
r = 5
Hence, the number of seconds is 5
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A bushel of apples costs $15.00 in the U.S. The same apples cost 1,600 yen in Japan. If the exchange rate is 80 yen per dollar, what is the real exchange rate? Is there a possibility for arbitrage? Explain and defend your answer.
The real exchange rate is 0.75.
It is not possible to make a profit by buying apples in one country and selling them in another.
We have,
To find the real exchange rate, we need to compare the price of apples in the two countries in terms of their respective currencies.
In the U.S., a bushel of apples costs $15.00.
In Japan, the same apples cost 1,600 yen.
Using the exchange rate of 80 yen per dollar, we can convert the cost in yen to dollars:
1,600 yen / 80 yen per dollar
= $20.00
So, the price of a bushel of apples in Japan is equivalent to $20.00 in the U.S.
The real exchange rate is the ratio of the prices of the same goods in two different countries, taking into account the exchange rate.
In this case, the real exchange rate is:
Real exchange rate = Price in U.S. / Price in Japan
= $15.00 / $20.00
= 0.75
This means that it takes 0.75 U.S. dollars to buy the same goods in Japan which would cost 1 Japanese yen.
To determine if there is an arbitrage opportunity, we need to compare the real exchange rate with the actual exchange rate.
If the real exchange rate is greater than the actual exchange rate, there is an arbitrage opportunity for someone to buy the good in one country and sell it in another country for a profit.
However, if the real exchange rate is less than the actual exchange rate, there is no arbitrage opportunity.
In this case,
The real exchange rate is 0.75, while the actual exchange rate is 80 yen per dollar, or 0.0125.
Since the real exchange rate is less than the actual exchange rate, there is no arbitrage opportunity.
Therefore,
The real exchange rate is 0.75.
It is not possible to make a profit by buying apples in one country and selling them in another.
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Probability Skill Check
DOOR Numbers
1
2
3
4
5
Coloured Blue, Red, Yellow and Green
What is the probability you will sit in a yellow seat? Give your answer as a fraction.
1/4
But what is the probability you will enter using an odd numbered door and sit in a green seat? Give your answer as a fraction.
Exponential model (10,160) (11,250)
The Exponential model is y = 0.74 (1.79)ˣ
We have,
(10, 160) and (11, 250)
Using the Exponential model
y = abˣ
where a is the initial amount and be is the constant.
Now, the value of b is
= 250/ 140
= 1.79
Now, y = abˣ
140 = a (1.79)⁹
a = 0.74
So, the Exponential model is y = 0.74 (1.79)ˣ
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I need help on the things in the image
The match of the given words as per the definition of the terms related to data set is as follow.
1 → g
2 →c
3 → b
4 → d
5 → f
6 → a
7 → e
The description of the each word as per the definition is ,
Mean represents the average of the data.
1→g
Spread represents the similarity or variability of the set of observed values of the data.
2→c
Center represents the middle value of the data set.
3→ b
Shape represents the values of the data set when plotted on the graph.
4 → d.
Median represents the middle value of the data set after arranging in ascending or descending order.
5 →f
Distribution represents measure of all the values of the data set spread.
6→a
variability represents the set of such values which satisfies the statistical question or relation.
7 → e.
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PLEASEEEE HELP MEMEMEMEM PLESSEEE I WILL GIVE U BRAINLIST QUICK
The numeric value of the function graphed is given as follows:
f(-8) = 6.
How to obtain the numeric value of the function?The expression for the numeric value of the function in this problem is given as follows:
f(-8).
This means that the input is given as follows:
x = -8.
Passing a vertical line through x = -8, the value of y in which the vertical line crosses the graph is given as follows:
y = 6.
Hence the numeric value is given as follows:
f(-8) = 6.
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Help please (time limit)
Answer:
It is a function
Step-by-step explanation:
It's a function because it does not over lapp
Need help solving this problem please help
The height of tree is given as follows:
40 ft.
How to obtain the height of the tree?The height of the tree is obtained applying the proportions in the context of this problem.
The proportions are applied as a rule of three can be formed between the heights and the shadows for both the tree and the person, as follows:
h/30 = 6/4.5
Applying cross multiplication, the value of h is obtained as follows:
4.5h = 30 x 6
4.5h = 180
h = 180/4.5
h = 40 ft.
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How do I do my calculations?
The area of the shaded region for the normal distribution is approximately 0.6985.
We have,
To find the area of the shaded region under the standard normal distribution curve between z = -0.87 and z = 1.24, we can use a standard normal distribution table or a calculator with a standard normal distribution function.
Using a standard normal distribution table, we look up the area to the left of z = -0.87 and the area to the left of z = 1.24 and then subtract the smaller area from the larger area to find the area between z = -0.87 and z = 1.24.
The table value for z = -0.87 is 0.1949, and the table value for z = 1.24 is 0.8934.
The area between z = -0.87 and z = 1.24 is:
= 0.8934 - 0.1949
= 0.6985
So the area of the shaded region is approximately 0.6985.
Thus,
The area of the shaded region for the normal distribution is approximately 0.6985.
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Calculus help please, thank you
The limit as a definite integral is given as lim (n → ∞) Σ(8i²)/n³ = 8/3n³
What is a definite integra l?The area under the curve f(x) from x= a to x = b is represented by the definite integral of f(x )
There are 2 kinds of integrals
definite integrals (also known as Riemann integrals ) and indefinite integrals (also known as antiderivatives) .To express the limit as a definite integral, we can use the following formul
lim(n → ∞ ) Σf(i)/n = ∫ a^bf(x)dx
where....
a and b are the lower and upper limts of the definite integral
f (x) is the function being integrated
In this case, we have
lim(n → ∞) Σ(8i²)/n³
Let f (x) = x ²
So, f(i/n) = (i/n) ²
And, the sum can be written as
Σ(8i^2)/n³ = 8/n³ Σi²
= 8/n³ Σ(i/n)²
= 8/n³ Σ[f(i/n)]
= 8/n³ ∫0¹ f(x) dx (using the formula above)
Therefore, the limit can be expressed as
lim(n → ∞) Σ(8i²)/n³ = 8/n³ ∫0¹ x² dx
Simplifying the integral, we get....
8/n³ ∫0¹ x₂ dx = 8/n^3 [x³/3] from 0 to 1
= 8/3n ³
Se we can say here that the limit as a definite integral is lim(n → ∞) Σ(8i ₂)/n^3 = 8/3n ₃
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Graph with x axis labeled Quantity Demanded and numbered in hundreds, 100 to 500. Y axis is Price, with prices 0 to 6. A line representing the Demand Curve starts at 100, 5 and drops at an angle down to 500, 1. Solid lines extend upward from the x axis to the green line at points 100, 5, 200, 4, 300, 3, 400, 2, and 500, 1. Public Domain Based on the graph, how is quantity demanded related to price? (5 points) Quantity demanded decreases as price decreases. Quantity demanded is equal to the product's price. Quantity demanded decreases as price increases. Quantity demanded increases as price increases.
Based on the information, the correct information regarding the graph is that C. Quantity demanded decreases as price increase.
How to explain the graphThe graph shows that for every increase of 100 units of the goods demanded, price reduces by 1 unit.
When 500 units was demanded, the price was at 1. Therefore, if 550 units are demanded, the price will reduce by half, which means the price would drop to 0.5.
The price would drop to 0.5. In this case, the the correct information regarding the graph is that Quantity demanded decreases as price increase.
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You want to purchase a new car in 4 years and expect the car to cost $76,000. Your bank offers a plan with a guaranteed APR of 4.5 %if you make regular monthly deposits. How much should you deposit each month to end up with $76,000 in 4years?
Monthly you should deposit approximately $43 to accumulate $76,000 in 4 years.
Given that,
f = $76,000
r = 4% = 0.04/12 = 0.0033
n = 4×12 = 48
We know that, a = (f×r)/((1+r)ⁿ⁻¹)
a is the annuity.
f is the future amount.
r is the interest rate per time period.
n is the number of time periods.
Here,
a = (76,000 ×0.0033)/((1.0033)⁴⁸⁻¹)
a = 76,000 ×0.0033×0.17132
a = 42.96
a ≈ $43
Therefore, monthly you should deposit approximately $43 to accumulate $76,000 in 4 years.
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The die shown below is a perfect cube with sides of length s.
What is the distance from point A to point B?
Responses
s√2
s √ 2
s√3
s √ 3
2s
2 s
s√5
The distance from the point A to point B is s√3
What is the distance from point A to point B?From the question, we have the following parameters that can be used in our computation:
Perfect cube with sides of length s.
The distance from point A to point B is calculated as
Distance^2 = s^2 + s^2 + s^2
When evaluated, we have
Distance^2 = 3s^2
Take the square roots of both sides
Distance = s√3
Hence, the distance = s√3
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A painter needs 3/8 gallon of green paint to finish a job. He has 5/8 gallon of red paint. He has 1/2 gallon more red paint than green paint. Can he finish the job?
Answer: 17/24 for both jobs
Step-by-step explanation:
19. A restaurant wants to study how well its salads sell. The circle
graph shows the sales of salads during the past few days. If 5 of
the salads sold were Caesar salads, how many total salads did
the restaurant sell?
Salads Sold
56%
20%
24%
Caesar
Garden
Cobb
Answer:
56% Caesar
Step-by-step explanation:
The only salads sold were Caesar and it is majority
I need help fast I’ll rate
The polynomial equation of the smallest degree is f(u) = (u + 2)³(u - 1)²(u - 3)
The minimal degree of the graphGiven that we have the graph of a polynomial
The degree of the graph is the number of times the graph intersect and/or crosses the x-axis
In this case, we have the following points at which the graph intersect and/or crosses the x-axis
Lies on the x-axis at u = -2; so the multiplicity is 3Intersects with the x-axis at u = 1; so the multiplicity is 1Touches the x-axis at u = 3; so the multiplicity is 2When the multiplicities are added, we have
Degree = 3 + 1 + 2
Degree = 6
So, the degree is 6
The zero at u = 1In (a), we have
Intersects with the u-axis at x = 1; so the multiplicity is 1This means that
The zero at u = 1 has a multiplicity of 1
The equation of the smallest degreeThe equation is represented as
f(u) = (u - zero)^multiplicity
So, we have
f(u) = (u + 2)³(u - 1)²(u - 3)
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Linear or exponential interest
The function that represents the fox population is P(t) = 6100 x [tex]1.06^{t}[/tex]
The fox population in 2008 is 9722.
What is the fox population in 2008?The equation that would represent the population of the foxes is an exponential equation.
The form of the exponential equation would be
Future population = present population x [tex](1 + r)^{t}[/tex]
Where:
r = interest rate = 6%t = number of years after 2000P(t) = 6100 x [tex](1 + 0.06)^{t}[/tex]
P(t) = 6100 x [tex]1.06^{t}[/tex]
Fox population in 2008 = 6100 x [tex]1.06^{8}[/tex] = 9722
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the graph of y=g(x) is shown. draw the graph of y=g(-x)
To draw the graph of y = g(-x), we need to replace x with -x in the original function.
If y = g(x) is given by the following graph:
(see attachment labeled "Attachment1")
Then y = g(-x) can be obtained by reflecting the graph of y = g(x) about the y-axis:
(see attachment labeled "Attachment 2")
Therefore, the graph of y = g(-x) is the reflection of the graph of y = g(x) about the y-axis.
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In circle V, VW = 8 and the area of shaded sector = 167. Find the length of
WY X. Express your answer as a fraction times .
W
The length of m∠WYX is equal to 12π units.
How to calculate the area of a sector?In Mathematics and Geometry, the area of a sector can be calculated by using the following formula:
Area of sector = θπr²/360
Where:
r represents the radius of a circle.θ represents the central angle.By substituting the given parameters into the area of a sector formula, we have the following;
Area of sector = θπr²/360
16π = θ(π/360) × 8²
Central angle, θ = 0.5π
m∠WYX = 2π - m∠WX
m∠WYX = 2π - 0.5π
m∠WYX = 1.5π
Length of m∠WYX = (1.5π)/2π × 2πr
Length of m∠WYX = (1.5π)/2π × 2π(8)
Length of m∠WYX = 12π units.
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Classify the following into finite and infinite set
(i) The set of months in a year
(ii)The set of stars in the galaxy
(iii)The set of even integers
(iv)The set of odd integers
(v)The set of alphabets
i) finite set, ii) infinite set, iii) infinite set, iv) infinite set, and v) finite set are the required solutions.
A Set is a collection of objects with similar properties. There are different types of set two of them are finite and infinite set.
Finite set- A set is called a finite set when the elements inside the set are countable or where we can know the starting and the ending of the elements. For example- A set of players in a cricket team.
Infinite set- A set is called an infinite set when the elements inside the set are uncountable or where the ending of the elements is not known. For Example- A set of positive numbers.
Here in the question the option (i) and (v) are finite sets because the no.of months in the year and no.of alphabets are countable or finite. Option (ii), (iii), and (iv) are infinite sets as no.of stars in the galaxy, even integers, and odd integers are uncountable.
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Answer:
the set of months in a year is finite
the set of star in the Galaxy is finite
the set of even integers is infinite
the set of odd integers is infinite
the set of alphabet is finite
Step-by-step explanation:
1) the set of month in a year is finite because they are limit and we can count them easily
2) the set of star in the galaxy is finite cause there are zillions of stars
3) the set of even integer is infinite because numbers are unlimit or infinite
4) the set of odd integers is infinite cause numbers are infinite ir they have not limit
5) the set of alphabet is finite because we can count them limitedly
Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)
F(x) = (x^4/5)((x − 5)^2)
The critical values of the function are x = 0 and x = 4.
The critical values of a function f(x) are the values of x for which f'(x) = 0.
In this problem, the function is:
f(x) = [tex]\frac{x^4}{5(x-2)^2}[/tex]
The derivative is found as follows, applying the quotient rule:
f'(x) = [tex]\frac{2x^3(x-4)}{5(x-2)^3}[/tex]
The zeros of the function are the zeros of the numerator, thus:
2x³(x-4) = 0
∴ x = 0, 4
Hence, the critical values of the function are x = 0 and x = 4.
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