Answer:
The answer to your question is [tex]f(x) = \sqrt{x+ 4}[/tex]
Step-by-step explanation:
f(x) = x² - 4
Process
1.- Change f(x) for y
y = x² - 4
2.- Change "x" for "y" and "y" for "x".
x = y² - 4
3.- Make "y" the object of the equation
y² = x + 4
[tex]y = \sqrt{x+ 4}[/tex]
4.- Change "y" for f(x)
[tex]f(x) = \sqrt{x+ 4}[/tex]
In 2000, the population of a country was approximately 6.13 million and by 2015 it is projected to grow to 7 million. Use the exponential growth model Upper A equals Upper A 0 e Superscript kt, in which t is the number of years after 2000 and Upper A 0 is in millions, to find an exponential growth function that models the data.
Answer:
A = 6.13e^(0.00884769t)
Step-by-step explanation:
The exponential growth model can be written two ways. Comparing them, we can find the value of k.
A = 6.13×(7.00/6.13)^(t/(2015-2000)) = 6.13×e^(kt)
Dividing by 6.13 and taking natural logs, we get ...
t/15×ln(7.00/6.13) = kt
k = ln(7.00/6.13)/15 . . . . . divide by t
k ≈ 0.00884769
Then the exponential growth function can be written as ...
A = 6.13e^(0.00884769t)
The top and bottom margins of a poster are each 6 cm and the side margins are each 4 cm. If the area of printed material on the poster is fixed at 384 cm , find the dimensions of the poster with the smallest area.
Answer:
24 cm wide by 36 cm high
Step-by-step explanation:
The poster with the smallest area will have an aspect ratio that makes the margin dimensions the same percentage of overall dimension in each direction.
Since the ratio of margin widths is 6:4 = 3:2, the poster and printed area will have an aspect ratio of 3:2. That is, the width is ...
width of printed area = √(2/3·384 cm²) = 16 cm
Then the width of the poster is ...
width = left margin + printed width + right margin = 4cm + 16 cm + 4 cm
width = 24 cm
The height is 3/2 times that, or 36 cm.
The smallest poster with the required dimensions is 24 cm wide by 36 cm tall.
_____
If you need to see the calculus problem, consider the printed area width to be x. Then the printed height is 384/x and the overall dimensions are ...
(x + 8) by (384/x + 12)
We want to minimize the area, which is the product of these dimensions:
a = (x +8)(384/x +12) = 384 +12x +3072/x +96
a = 12x + 3072/x +480
This is a minimum where its derivative is zero.
a' = 12 -3072/x^2 = 0
a' = 1 -256/x^2 = 0 . . . . . . divide by 12; true when x^2 = 256
This has solutions x=±16, of which the only useful solution is x=16.
If A is the initial amount put into an account, P is the annual percentage rate of interest, which remains fixed, and the account compounds quarterly, which of the following is an expression, in terms of A and P, for the amount in the Account after 5 years?
A 4A(p100)5
B A(p100)20
C 4A(1+p100)5
D A(1+p25)20
E A(1+p400)20
Answer: The amount in the account is A = A(1 + P/400)^20
Step-by-step explanation:
Initial amount deposited into the account is A. This means that the principal is A, so
P = A
It was compounded quarterly. This means that it was compounded once in four months. So
n = 4
The rate at which the principal was compounded is P%. So
r = P/100
It was compounded for a total of 5 years. So
n = 5
The formula for compound interest is
A = P(1+r/n)^nt
A = total amount in the account at the end of n years.
Let A = B
B = A(1 + (P/100)/4)^4×5
A = A(1 + P/400)^20
Final answer:
The correct expression for the amount in an account after 5 years, where interest is compounded quarterly, is D. [tex]A(1 + \frac{P}{25})^{20}[/tex].
Explanation:
When calculating the future value of an investment with compound interest, it's important to consider the initial amount A, the annual interest rate P, the number of times the interest is compounded per year, and the total number of years the money is invested. In this question, where the account compounds quarterly for 5 years, the formula for compound interest applies, which is:
P(t) = [tex]A(1 + \frac{r}{n})^{nt}[/tex]
Here, r represents the annual nominal interest rate in decimal form [tex](\frac{P}{100})[/tex], n is the number of times interest is compounded per year, and t is the number of years the money is invested. Given that the account compounds quarterly, n equals 4. So after 5 years, the formula would be:
P(5) = [tex]A(1 + \frac{P}{400})^{(4 \times 5)}[/tex]
Based on the options provided in the question, the correct expression for the amount in the account after 5 years, in terms of A and P, when compounded quarterly is:
D. [tex]A(1 + \frac{P}{25})^{20}[/tex]
Craig has £13.40 he sees this offer in a restaurant :main courses £8.90 each.Buy one main course and get the second half price. Can he afford to buy two main courses?Show your working
Answer:
Yes
Step-by-step explanation:
Full price for first course: £8.90
Half price: £4.45
One and one half times
full price is then: £13.35
Since this is less than Craig's £13.40, he can just barely afford to buy two main courses at these prices.
A bank wishes to estimate the mean credit card balance owed by its customers. The population standard deviation is estimated to be $300. If a 98 percent confidence interval is used and an interval of $78 is desired, how many customers should be sampled?A. 725B. 80C. 57D. 320
Answer: B. 80
Step-by-step explanation:
We know that the formula to find the sample size is given by :-
[tex]n=(\dfrac{z^*\cdot\sigma}{E})^2[/tex]
, where [tex]\sigma[/tex] = population standard deviation.
E= margin of error
z*= Two -tailed critical z-value
Given : Confidence level = 98% =0.98
[tex]\alpha=1-0.98=0.02[/tex]
Population standard deviation : [tex]\sigma=300[/tex]
Also, from z-table for [tex]\alpha/2=0.01[/tex] (two tailed ), the critical will be = [tex]z^*=2.326[/tex]
Then, the required sample size must be :
[tex]n=(\dfrac{2.326\cdot300}{78})^2\\\\ n=(8.94615)^2\\\\ n=80.0336686391\approx80[/tex] [To the nearest option]
Hence, the required sample size = 80
Hence, the correct option is option B. 80
Final answer:
To estimate the mean credit card balance owed by the bank's customers using a 98 percent confidence interval and a desired interval of $78, the sample size should be 725 customers.
Explanation:
To estimate the mean credit card balance owed by the bank's customers, we need to determine the sample size. We can use the formula for sample size calculation for a mean with a desired margin of error: n = (Z * σ / E)².
Here, Z is the Z-score for the desired confidence level, σ is the population standard deviation, and E is the desired margin of error. In this case, the Z-score for a 98 percent confidence level is approximately 2.33. Plugging in the values, we get: n = (2.33 * 300 / 78)² = 724.9.
Since we can't have a fractional sample size, we round up to the nearest whole number. Therefore, the bank should sample 725 customers.
Standing on the edge of a cliff 30 m tall, Bob notices a kayak on the lake. If the angle of depression to the kayak is 400, what is the distance, to the nearest meter, from the kayak to the base of the mountain?
Answer:
36 mExplanation:
The vertical height of the cliff, 30 m tall, and the horizontal distance from the kayak to the base of the mountain form a right triangle.
The angle of depression is 40º.
By the alternate interior angles theorem, that depression angle is congruent to the elevation angle from the kayak to the spot where Bob is standing on.
The tangent trigonometric ratio relates the height (30 m) with the distance from the kayak to the base of the mountain:
tan(40º) = height of the cliff / distance from the kayak to the base of the mountaintan(40º) = 30 m / xx = 30m / tan(40º) ≈ 35.75 m ≈ 36 mSuppose your local school district decides to randomly test high school students for attention deficit disorder (ADD). There are there high schools in the district, each with grades 9-12. The school board pools all of the students together and randomly samples 250 students. Is this a simple random sample?
a. Yes, because the students were chosen at random
b. Yes, because each student is equally likely to be chosen
c. Yes, because they could have chosen any 250 students from throughout the district
d. No, because we can't guarantee that there are students from each school in the sample
e. No, because we can't guarantee that there are students from each grade in the sample
f. Yes, because they could have chosen any 250 students from throughout the district
Answer:
Option C is correct. Option f is the same as option C
Step-by-step explanation:
From the question, There are three high schools in the district, each with grades between nine to twelve. The school board decided to pool all of the students together and randomly samples 250 students in the whole district that has schools between the grade of nine to twelve.
In order to test for high school students in the district for Attention Deficit disorder(ADD), they could have chosen any 250 students from any school with grades betweem nine to twelve throughout the district.
Jose spent 2 3/10 hours playing basketball outside, and he played outside for a total of 5 hours. How many hours did he NOT spend playing basketball?
Answer:2 7/10 hours
Step-by-step explanation:
Subtract 2 3/10 out of 5
Answer: 2 7/10
Step-by-step explanation:
Hours spent in basketball= 2 3/10
Total hours spent outside= 5 hours
To get The number of hours he didn't basketball will be (5hours - 2 3/10)
5 - 23/10 = 2 7/10 .
A man is flying in a hot-air balloon in a straight line at a constant rate of 6 feet per second, while keeping it at a constant altitude. As he approaches the parking lot of a market, he notices that the angle of depression from his balloon to a friend's car in the parking lot is 37°. A minute and a half later, after flying directly over this friend's car, he looks back to see his friend getting into the car and observes the angle of depression to be 38°. At that time, what is the distance between him and his friend?
Answer: 336.4447 feet
Step-by-step explanation: from the picture I attached to this answer, you will see how I represented the question in a diagram
Point A being the point of his friends car, point B being the point of the hot air balloon when he noticed the angle of depression to his friends car to be 37 degrees, point C being the point of the hot air balloon after passing his friends car and noticing the angle of depression to be 38 degrees
From my diagram, I labeled y as the distance between B and C and we are told he traveled when a speed of 6 feet per second with a constant altitude, and after 1 and a half minutes he reached point C, which is 90 seconds
To get value of y we multiply the speed and the time, 90 multiplied by 6 which will give 540 feet
From my diagram, I calculated the angle inside the triangle to be 105, we all know the sum of angles in a straight line to be 180, and also knowing alternate angles, we have 37 and 38 degree as the angle outside the triangle at that point, so adding both angle 37+38=75 and subtracting that from 180 we get 105
So the get the distance between him and his friends when the angle of depression is 38 degree, which is the distance between point A and C which I labeled x, we use the sin rule
Sin rule states that the ratio between the length of a side of a triangle and the sin of the angle opposite it is constant for all sides of the triangle,
The steps are also solved in the picture I sent
So we have the ratio of x and sin37 is also equal to the ratio of 540 and sin105
So x divided by sin37 equals 540 divided by sin105
Sin37 equals 0.6018, sin105 equals 0.9659
So making x the subject of formula
We get x will be equal to (540*0.6018)/0.9659 which will give you 336.4447 feet
Using trigonometry and applying the concept of tangent to the angles of depression, we can construct two right triangles to calculate the horizontal distances and then use the Pythagorean theorem to calculate the distance from the balloon to the friend's car.
Explanation:The question involves a man in a hot-air balloon tracking his distance from a car in a parking lot using the angles of depression before and after flying over the car. To solve this question, we will apply trigonometry specifically, the concept of tangent which relates the angle of depression to the sides of a right triangle formed by the observer's altitude and the horizontal distance.
Firstly, let's find the horizontal distance the man travels in a minute and a half at 6 feet per second:
Distance = speed × time = 6 feet/second × 90 seconds = 540 feet
Now, we form two right triangles: one before he flies over the car and one after. Both have the same altitude (since he maintains a constant altitude).
For the first triangle, using the 37° angle of depression, we can denote:
For the second triangle, using the 38° angle of depression, we can denote:
Solving these two equations we find the horizontal distance (x) and then can find the direct line distance using Pythagoras' theorem.
To find the distance, we will use the tangent of 38° (the angle of depression after passing the car) since that relates the perpendicular distance from the balloon to the car (which we are interested in) to the horizontal distance. Let's denote the perpendicular distance as 'h' (altitude of the balloon).
Tan(38°) = h / (x - 540 feet)
After some algebraic manipulation and applying trigonometry, we can solve for 'h' and find the direct line distance from the balloon to the car.
Quiz: The Discriminant and Modeling Data 7:Solving Quadratic Equations
esday
Find the number of real number solutions for the equation. x2 - 10x + 25 = 0
oo
O
1
2
cannot be determined
100%
For this case we must find the solution of the following quadratic equation:
[tex]x ^ 2-10x + 25 = 0[/tex]
Where:
[tex]a = 1\\b = -10\\c = 25[/tex]
Then, the solution is given by:
[tex]x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2a}[/tex]
Substituting the values:
[tex]x = \frac {- (- 10) \pm \sqrt {(- 10) ^ 2-4 (1) (25)}} {2 (1)}\\x = \frac {10 \pm \sqrt {100-100}} {2}\\x = \frac {10 \pm \sqrt {0}} {2}\\x = \frac {10} {2} = 5[/tex]
Thus, we have two equal real roots.
[tex]x_ {1} = 5\\x_ {2} = 5[/tex]
Answer:
We have two equal real roots.
Answer:
cannot be determined
Step-by-step explanation:
i tried 1,0,2 dont work
A conical tank is 8 meters high. The radius of the top is 2 meters. At what rate is the water running out if the depth is 3 meters and is decreasing at the rate of 0.4 meters per minute
Answer:
DV/dt = 0,2355 m³/min
Step-by-step explanation:
Conical tank volume V = 1/3 *π*r²*h
r radius at the top 2 meters
when depth of water is 3 meters the radius of the level of water is:
let α angle of vertex of cone then
tan∠α = 2/8 tan∠α = 1/4 tan∠α = 0,25
At the same time when water is at 3 meters depth radius is
tan∠α = r/3 0,25*3= r r = 0,75 m
Now
DV/dt = (1/3)*π*r²*Dh/dt
Dh/dt = 0,4 meters/min
By substitution
DV/dt = 0,2355 m³/min
Prehistoric cave paintings were discovered in a cave in France. The paint contained 10 %10% of the original carbon-14. Use the exponential decay model for carbon-14, Upper A equals Upper A 0 e Superscript negative 0.000121 t=A0e−0.000121t, to estimate the age of the paintings.
Answer:
t=19188.2 y
Step-by-step explanation:
The exponential decay equation is:
[tex] A=A_{0}e^{-0.00012t}[/tex] (1)
But, A is 10% of A₀, it means that A=0.10A₀.
If we put it into equation (1), we will have:
[tex] 0.10A_{0}=A_{0}e^{-0.00012t}[/tex]
[tex] 0.10=e^{-0.00012t}[/tex] (2)
Now, we just need to solve (2) for t.
[tex] t=\frac{ln(0.10)}{-0.000121} = 19188.2 y [/tex]
I hope it helps you!
Consider the following Polynomial.
S(x)= -3x^2 +x-9
Describe the behavior of the graph of S(x) as x ---> +/- ∞
S(x)--> ? as x--> -∞
S(x)-->? as x-->∞
Answer:
S(x) → -∞ as x → -∞S(x) → -∞ as x → ∞Step-by-step explanation:
The leading term tells you what you want to know. It is of even degree, so the value of S(x) is the same regardless of the sign of x as the magnitude of x gets large.
The sign of S(x) matches the sign of the leading coefficient (-3), so is negative as x gets large.
Hence ...
S(x) → -∞ as x → -∞S(x) → -∞ as x → ∞
What is DC ?
Enter the answer in the box.
Answer:
DC = 30
Step-by-step explanation:
Point D is the circumcenter of triangle ABC, so it is equidistant from A, B, and C.
We are given the measures of DE and AE, so we can figure AD using the Pythagorean theorem:
AD² = AE² + DE² . . . . . . . . . . . . . . . E bisects AB, so AE=AB/2=18
AD = √(18² +24²) = √900 = 30
DC = AD
DC = 30
On a certain multiple-choice test, 9 points are awarded for each correct answer, and 7 points are deducted for each incorrect or unanswered question. Sally received a total score of 0 points on the test. If the test has fewer than 30 questions, how many questions are on the test?
Answer:
21
Step-by-step explanation:
A textbook store sold a combined total of 257 math and psychology textbooks in a week. The number of math textbooks sold was 87 more than the number of psychology textbooks sold. How many textbooks of each type were sold?
Answer:
85 psychology172 mathStep-by-step explanation:
Let p represent the number of psychology textbooks sold. Then the total number sold was ...
p + (p+87) = 257
2p = 170 . . . . . .subtract 87; next divide by 2
p = 85 . . . . . . . psychology books sold
p+87 = 172 . . . math books sold
85 psychology textbooks and 172 math textbooks were sold.
Explanation:Let's denote the number of psychology textbooks sold as x. According to the problem, the number of math textbooks sold, which is 87 more than the psych books, can be represented as x + 87. The total number of textbooks sold is expressed in the problem as 257, which is the sum of the psych books (x) and the math books (x + 87). So:
x (psych books) + x + 87 (math books) = 257
We can simplify this to 2x + 87 = 257. If we subtract 87 from both sides, we'll get 2x = 170. Dividing both sides by 2 results in x = 85. This tells us that 85 psychology books were sold.
Then to find the number of math books, we can use the original relationship given: math books = psychology books + 87, therefore, 85 + 87 = 172 math books.
Learn more about Solving Systems of Equations here:https://brainly.com/question/31653301
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20 POINTS AND BRAINIEST FOR THOSE WHO ANSWER CORRECTLY
~
What is the simplest radical form of the expression?
(x^4y^7)^3/4
~
Thank you!
Answer:
x^2 y ^4 ∛ [x^2 y ^2 ] is the answer that I got
Step-by-step explanation:
Answer:
PLEASE MARK BRAINLIEST!Step-by-step explanation:
[tex](x^{4}y^{7})^{\frac{3}{4}}[/tex]
Answer 1:
[tex]= x^{3}y^{5} \sqrt[4]{y}[/tex]
Answer 2:
[tex]x^{3}y^{\frac{21}{4}}[/tex]
Answer 3:
[tex]\sqrt[4](x^{4}y^{7})^{3}[/tex]
I didn't know which one was correct, so I included all of them. I hope this helps!
Use the list of five irrational below to answer the questions
Square root of 2, Square Root of 6, Square Root of 12, Square Root of 18, and Square Root of 24.
Part A. Choose two numbers whose product is RATIONAL. Explain.
Part B. Choose two numbers whose product is IRRATIONAL. Explain.
Answer:
[tex]\text{A.}\ \sqrt{2}\times\sqrt{18}\\\\\text{B.}\ \sqrt{2}\times\sqrt{6}[/tex]
Step-by-step explanation:
A: The root will be rational if the product of the numbers under the radicals is a perfect square. For this part, there are a couple of choices.
[tex]\text{1.}\ \sqrt{2}\times\sqrt{18}=\sqrt{36}=6\\\\\text{2.}\ \sqrt{6}\times\sqrt{24}=\sqrt{144}=12[/tex]
__
B: The root will be irrational if the product of the numbers under the radicals is not a perfect square. For this part, there are many choices.
[tex]\text{1.}\ \sqrt{2}\times\sqrt{6}=\sqrt{12}\\\\\text{2.}\ \sqrt{2}\times\sqrt{12}=\sqrt{24}\\\\\text{3.}\ \sqrt{2}\times\sqrt{24}=\sqrt{48}\\\\\text{4.}\ \sqrt{6}\times\sqrt{12}=\sqrt{72}\\\\\text{5.}\ \sqrt{6}\times\sqrt{18}=\sqrt{108}\\\\\text{6.}\ \sqrt{12}\times\sqrt{18}=\sqrt{216}\\\\\text{7.}\ \sqrt{12}\times\sqrt{24}=\sqrt{288}\\\\\text{8.}\ \sqrt{18}\times\sqrt{24}=\sqrt{432}[/tex]
To choose two numbers whose product is rational, we can use the square roots of 2. For two numbers whose product is irrational, we can use the square roots of 2 and 6.
To choose two numbers whose product is rational, we need to find two numbers whose square roots are rational.
Let's consider the numbers Square Root of 2 and Square Root of 2. Their product is 2, which is a rational number.
For two numbers whose product is irrational, we need to find two numbers whose square roots are irrational.
Let's consider the numbers Square Root of 2 and Square Root of 6. Their product is 2 x Square Root of 6, which is an irrational number.
Find the solution u(x, y) of Laplace's equation in the rectangle 0 < x < a, 0 < y < b, that satisfies the boundary conditions u(0, y) = 0, u(a, y) = 0, 0 < y < b, u(x, 0) = 0, u(x, b) = g(x), 0 ≤ x ≤ a.
Answer:
The solution has been given in the attachment.
Step-by-step explanation:
please help me will mark brainly
Answer:
A
Step-by-step explanation:
Ok. All coordinate are multiplied by factor of 1/3.
So,
(0,0) becomes (0,0).
(6,9) becomes (2,3).
(15,0) becomes (5,0).
In order to obtain a sample of voters in Pennsylvania, a simple random sample of 10 counties is selected. From each of the selected counties, 10 precincts are chosen at random. Finally, from each of these 100 precincts , a simple random sample of 20 voters students is selected. Thus, the final sample consists of 2,000 voters.
This is an example of which type of sampling strategy?a) Simple random samplingb) Stratified samplingc) Multistage samplingd) Convenience sampling
Answer:
c) Multistage sampling.In statistics, there are several strategies to select a sample. Remember that a sample is a sub group selected from a population. This sample selection must be random to have more reliability in the research, each answer option represents a type of sampling.
In this case, the researcher is using a multistage sampling, because it consists in taking smaller sample units at each stage, which is being done in this example. First, is selected a number of counties, then the precincts, and at the end the voters. By this way, the sample is being reduced to less subjects at each stage.
The sampling strategy described is an example of c) multistage sampling. This technique helps in reducing complexity and cost.
The sampling strategy described in the question is an example of multistage sampling.
In this process:
A simple random sample of 10 counties in Pennsylvania is selected.From each of these counties, 10 precincts are chosen randomly.Finally, from each of these 100 precincts, a simple random sample of 20 voters is selected.This results in a final sample of 2,000 voters.Multistage sampling is used to reduce the complexity and cost of data collection by breaking the population into smaller groups at each stage.
Slader records show that the average life expectancy of a pair of shoes is 2.2 years with astandard deviation of 1.7 years. A manufacturer gaurantees that shoes lasting less than a year are replaced for free. For every 1000 pairs sold how many pairs should the manufacturer expect to replaces free? Assume a normal distributiom.
Answer:
For every 1000 pairs sold, the manufacturer expect to replace 239 pairs for free.
Step-by-step explanation:
Given:
Mean (μ) = 2.2, Standard deviation(S.D) (σ) = 1.7 years and x = 1 (1 year)
Let's find the Z score.
Z = [tex]\frac{x - mean}{S.D}[/tex]
Now plug in the given values in the above formula, we get
Z = [tex]\frac{1 - 2.2}{1.7} = -0.71[/tex]
Now we have to use the z-score table.
The z-score for 0.71 is 0.2611
Since it z is negative, so we subtract 0.2611 from 0.5000
0.5000 - 0.2611 = 0.2389
Percentage = 0.2389 × 100 = 23.89%
To find replaces for 1000 pairs, we need to multiply 23.89% by 1000
= [tex]\frac{23.89}{100} .1000 = 238.9[/tex]
= 239
The cannot be in decimal, when we round off to the nearest whole, we get
239
Elena is feeding her neighbor's dogs each dog gets two thirds cup of dog food and she uses three and one third cups of food how many dogs does her neighbor have
Answer:
Total number of dogs is 5.
Step-by-step explanation:
Cups of food each dog gets=[tex]\frac{2}{3}[/tex]
Here,each dog eats two-third cups of dog food.
Amount of dog food used=[tex]\frac{10}{3}[/tex]
A total of three and one-third cups of food is used up.
Let the number of dogs be x.
To find the number of dogs,divide total dog food used by the amount of dog food eaten by each dog.
Hence, x =[tex]\frac{\frac{10}{3} }{\frac{2}{3} }[/tex]
x =[tex]\frac{10}{2}[/tex]
x =5
What is the equation of the function?
Answer:
y = x + 1
Step-by-step explanation:
This line passes through (-1, 0) and (0, 1) As we move from the first point to the second, x increases by 1 and y also increases by 1. Therefore, the slope of this line is m = rise / run = 1 / 1, or m = 1.
Start with the general equation of a line y = mx + b. Substitute 1 for m and 1 for b. Then the equation of the line shown is:
y = x + 1
The equation of the graphed function is y = x + 1 .
The equation of the line can be written in the form ;
y = bx + c b = slope; c = interceptThe slope of the line ; is the ratio of the rise to the run of the line ;
b = (3 - 1) / (2 - 0) = 1The intercept which is the value of y when x = 0 from.the graph is 1 .
Hence, the equation is :
y = x + 1Learn more on linear equation : https://brainly.com/question/30884929
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A vendor has 30 umbrellas to sell. He sells them for $20 each. The function m(u) = 20u models the total amount of money the vendor makes from selling u umbrellas. What are the practical domain and range of the function?
Answer:
Step-by-step explanation:
Domain={0,30},Range={0,600
Total number of umbrellas=3
Price for each umbrella is =$20
m(u)=20u
as we know
u = umber of umbrellas
m(u) total amount vendor makes by selling u number of umbrellas
So Practically,The extreme cases are
when the vendor sells 0 umbrellas/ no umbrellas
when he sells all the umbrellas
So Domain is {0,total number of umbrellas}={0,30}
Putting this extreme value of domains as u in function m(u),
we get the range of m(u)={0$20,30$20}
⇒ Range={0,$600}
Answer:
domain 0,30 range 0,600
Step-by-step explanation:
The number of houses that can be served by a water pipe varies directly as the square of the diameter of the pipe. A water pipe that has a 10-centimeter diameter can supply 40 houses. a. How many houses can be served by a water pipe that has a 30-centimeter diameter? b. What size of water pipe is needed for a new subdivision of 1440 houses?
Answer:
Step-by-step explanation:
Given
no of houses that can be served by water is directly Proportional to the square of diameter
[tex]N\propto d^2[/tex]
[tex]N=kd^2[/tex]
where k =constant
10 cm diameter can supply 40 houses
[tex]40=k(10)^2[/tex]-----------1
For d=30 cm Pipe
[tex]N_1=k(30)^2[/tex]-------------2
divide 1 & 2
[tex]\frac{N_1}{40}=(\frac{30}{10})^2[/tex]
[tex]N_1=40\times 9=360 [/tex]
(b)for N=1440 houses
[tex]1440=k(d_2)^2[/tex] ----------------3
[tex]\frac{1440}{40}=(\frac{d_2}{10})^2[/tex]
[tex]d_2=6\times 10[/tex]
[tex]d_2=60 cm[/tex]
A water pipe with a diameter of 30 cm can serve 360 houses. And to serve 1440 houses, a water pipe with a diameter of 60 cm is required.
Explanation:The relationship between the number of houses that could be supplied by the water pipe and the diameter of the pipe can be described as a direct square relationship. This means if you square the diameter of the pipe, you'll get the number of houses that can be served. We know from the given info that a 10 cm diameter pipe can serve 40 houses. Therefore, the constant of variation (k) can be calculated as k=No. of houses/diameter². Hence, k=40/10²=0.4.
a.) A pipe with a 30 cm diameter can serve 0.4*(30)² = 360 houses.
b.) For a new subdivision of 1440 houses, we rearrange the formula to find the required diameter: Diameter= sqrt(No. of houses/k) = sqrt(1440/0.4) = 60 centimeters.
Learn more about Direct Variation here:https://brainly.com/question/9775007
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A bag of sawdust costs $5.00 and can cover 9 feet of ground. By buying part of the bag, how much would it cost to buy enough to cover 1 foot of ground?
What is the area of the figure?
Answer:
90 in²
Step-by-step explanation:
The figure's area is that of four right triangles, each with legs of 6 in and 7.5 in. The area of each triangle is half the product of the leg lengths, so is ...
triangle area = (1/2)(6 in)(7.5 in)
Then the area of 4 of those triangles is ...
figure area = 4 · triangle area = 2(6 in)(7.5 in) = 90 in²
A group of science students spotted 53 birds there were six times as many sparrows as Blue Jays and there were four Falcons how many of each bird were there
Final answer:
We found there were 7 Blue Jays, 42 sparrows, and 4 Falcons.
Explanation:
The question involves solving a simple algebraic problem to determine the number of sparrows and Blue Jays when given the total number of birds and the number of Falcons.
To solve this, let's define the number of Blue Jays as x.
The number of sparrows is six times the number of Blue Jays, so we can express that as 6x.
We are told there are four Falcons.
The total number of birds spotted is 53.
We can set up the equation as:
x + 6x + 4 = 53
Solving this equation:
Combine like terms: 7x + 4 = 53Subtract 4 from both sides: 7x = 49Divide both sides by 7: x = 7Since x represents the number of Blue Jays, there are 7 Blue Jays.
To find the number of sparrows, multiply 7 by 6, which gives us 42 sparrows.
We were also told there are four Falcons.
So the group saw 42 sparrows, 7 Blue Jays, and 4 Falcons.
Larry is using an online calculator to calculate the outputs f(n) for different inputs n. The ordered pairs below show Larry's inputs and the corresponding outputs displayed by the calculator:
(1, 5), (2, 9), (3, 13), (4, 17)
Which of the following functions best represents the rule that the calculator uses to display the outputs?
a
f(n) = 5n − 1
b
f(n) = 5n + 1
c
f(n) = 4n + 1
d
f(n) = 4n − 1
Answer:
Option c:
[tex]f(n)=4n+1[/tex]
Step-by-step explanation:
The functional relationship between two variables can be easily found if it's represented as a line.
Larry's online calculator collects these points
(1, 5), (2, 9), (3, 13), (4, 17)
We can see there is a linear relation because every time the first component increases by 1, the second increases by 4.
The equation of a line is given by
[tex]f(n)=m.n+b[/tex]
Where m is the slope of the line and can be computed as
[tex]\displaystyle m=\frac{d-b}{c-a}[/tex]
Where (a,b), (c,d) are two known points of the line. Let's use the first two points (1, 5), (2, 9)
[tex]\displaystyle m=\frac{9-5}{2-1}=4[/tex]
We now know that
[tex]f(n)=4n+b[/tex]
To compute the value of b, we use one of the points again, for example (1,5):
[tex]5=4(1)+b => b=1[/tex]
The relation is
[tex]f(n)=4n+1[/tex]
We can test our results by using other points like (3,13)
[tex]f(3)=4(3)+1=13[/tex]
And also
[tex]f(4)=4(4)+1=17[/tex]
All points belong to the same function or rule
[tex]f(n)=4n+1[/tex]