Find the linear approximation of f(x)=lnx at x=1 and use it to estimate ln1.38.
L(x)= ?
ln1.38 approximately = ? ...?
At sumer camp the ratio of boys to girls is 7:3 if there were 63 boys how many girls were there
If ƒ(x) = 2x2 + 3, then which of the following represent ƒ(x + 1)?
A. 2x^2 + 2
B. x^2 + 3
C. 2x^2 + 4x + 1
D. 2x^2 + 4x + 5
Answer:
option (d) is correct.
[tex]f(x+1) = 2x^2+4x+5[/tex]
Step-by-step explanation:
Given : [tex]f(x) = 2x^2 + 3[/tex]
We have to choose out of given option which represent f(x + 1)
Consider the given function [tex]f(x) = 2x^2 + 3[/tex]
Since we have to find f( x + 1 ) , replace x by x + 1 in the given function f(x) , we have,
[tex]f(x+1) = 2(x+1)^2+3[/tex]
Using algebraic identity, [tex](a+b)^2=a^2+b^2+2ab[/tex] , we have,
[tex]f(x+1) = 2(x^2+1+2x)+3[/tex]
Simplify the expression by multiplying 2 with each term in bracket, we have,
[tex]f(x+1) = 2x^2+2+4x+ 3[/tex]
Simplify , we have,
[tex]f(x+1) = 2x^2+4x+5[/tex]
Thus, option (d) is correct.
What is the average rate of change of the function f(x)=2(3)^x from x = 2 to x = 4?
The average rate of change of the given function will be 72.
What is the average rate of change of the function?It quantifies how much the function changed per unit on average throughout that time interval. The slope of the straight line connecting the interval's ends on the function's graph is used to calculate it.
The given function is f(x)=2(3)ˣ and the interval is x ∈ [2,4].
The formula to calculate the average rate of change is (f(b)-f(a))/(b-a).
Here, a = 2 and b = 4
So,f (2) = 2.3² = 18
Now,f (4) = 2.3⁴ = 162
The average rate of change = (162 - 18)/(4 - 2)
The average rate of change = 144/2
The average rate of change = 72
Therefore, the average rate of change of the given function will be 72.
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The average rate of change of the function f(x) = 2(3)ˣ from x = 2 to x = 4 is 72. This means the secant line that intersects the graph of the function at x = 2 and x = 4 has a slope of 72.
Step 1: Formula for Average Rate of Change
The average rate of change of a function f(x) over the interval [a, b] is calculated using the following formula:
Average rate of change = (f(b) - f(a)) / (b - a)
where:
f(b) is the function's value at the upper bound (x = 4 in this case).f(a) is the function's value at the lower bound (x = 2 in this case).b is the upper bound of the interval (x = 4).a is the lower bound of the interval (x = 2).Step 2: Find f(b) and f(a)
We are given the function f(x) = 2(3)ˣ . Let's find the function's values at x = 4 (upper bound) and x = 2 (lower bound):
f(4) = 2(3)⁴ = 2 × 81 = 162f(2) = 2(3)⁴ = 2 × 9 = 18Step 3: Calculate the Average Rate of Change
Now that we have f(b) and f(a), we can plug them into the formula along with the interval's bounds:
Average rate of change = (f(4) - f(2)) / (4 - 2)Average rate of change = (162 - 18) / (2)Average rate of change = 144 / 2Average rate of change = 72the quotient of a number and four decreased by ten is two
Last year, Gena’s food cart business was $225 in debt. This year, the debt has tripled. Which expressions show how much Gena’s business is currently in debt? Check all that apply.
A. 225(3)
B. (3)(–225)
C. –225 + 3
D. 3 – 225
E. –225(3)
Both B & E; They are both using -225 which represents debt
The expression that shows the given statement will be equal to -225(3). Hence, options B and E are correct.
What are arithmetic operations?The four basic operations of arithmetic can be used to add, subtract, multiply, or divide two or even more quantities.
They cover topics like the study of integers and the order of operations, which are relevant to all other areas of mathematics including algebra, data processing, and geometry.
As per the given information in the question,
Gena's food cart business last year = $225 in debt = -225
The dept has tripled this year.
Then, the equation according to the statement will be,
(-225) × 3
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The surface area of two similar solids are 340yd^2 and 1,158yd^2. The volume of the larger solid is 1,712yd^2. What is the volume of the smaller solid? ...?
In 2007, the FDIC’s insurance limit was $100,000 per person per bank. If Sam had a $150,000 savings account and $80,000 checking account at Bank J, a $95,000 money market account at Bank K, and a $200,000 savings account at Bank L, how much of Sam’s money was FDIC insured? a. $295,000 b. $300,000 c. $375,000 d. $525,000
In 2009, the population of a country passed the 307.5 million marker. The total area of the country is 3.79 million square miles. What is the population density for that country for 2009? Find the number of people per square mile. Round to the nearest hundredth as needed. ...?
The population density for a country with a population of 307.5 million and an area of 3.79 million square miles is approximately 81.14 people per square mile. This figure is calculated by dividing the population by the area and is rounded to the nearest hundredth.
Explanation:To calculate the population density of a country for 2009, when the population was reported to be 307.5 million and the total area was 3.79 million square miles, you must divide the population by the total area. The formula for population density is:
Population Density = Population / Area
In this case, the calculation would be:
Population Density = 307,500,000 people / 3,790,000 square miles
When you do the math, you get:
Population Density ≈ 81.14 people per square mile
This result has been rounded to the nearest hundredth as requested. Comparing this with other countries' population densities, such as those of South Asian countries, can provide a remarkable insight into how population distribution and globalization impact living conditions and resource availability.
The population density of a country with a population of more than 307.5 million and an area of 3.79 million square miles, in 2009, was approximately 81.14 people per square mile after rounding to the nearest hundredth.
Explanation:To calculate the population density of a country for the year 2009 when the population was more than 307.5 million and the total area was 3.79 million square miles, we use the following formula:
Population Density = Population / Area
Now, let's substitute the given values:
Population Density = 307.5 million people / 3.79 million square miles
To proceed with the calculation, we need to convert the population into a number without the word 'million' since 'million' is also part of the area's units. Therefore, 307.5 million people become 307,500,000 people and 3.79 million square miles become 3,790,000 square miles.
Population Density = 307,500,000 people / 3,790,000 square miles
After doing the division, we get:
Population Density ≈ 81.14 people per square mile (rounded to the nearest hundredth)
Therefore, the population density for that country in 2009 was approximately 81.14 people per square mile.
20 % of 2 is equal to
A. 20
B. 4
C. 0.4
D. 0.04
If (x-y)^2=71 and x^2+y^2=59 what is the value of xy?
In the game of roulette, a player can place a $4 bet on the number 22 and have a 1/38 probability of winning. If the metal ball lands on 22, the player gets to keep the $4 paid to play the game and the player is awarded $140. Otherwise, the player is awarded nothing and the casino takes the players $4. What is the expected value of the game to the player? If you played the game 1000 times, how much would you expect to lose? ...?
Final answer:
The expected value of the game to the player is $3.68. If played 1000 times, the player would expect to lose $320.
Explanation:
Expected value for the game:
Probability of winning (landing on 22): 1/38Payout for winning: $140 + $4 initial bet = $144Cost of playing (losing bet): -$4Expected value = (Probability of winning * Payout for winning) + (Probability of losing * Cost of losing)Expected value = (1/38 * $144) + (37/38 * -$4)Expected value = -$0.2105 per gameExpected Loss in 1000 Games:
Expected loss per game = -$0.2105Expected loss in 1000 games = Expected loss per game * Number of gamesExpected loss in 1000 games = -$0.2105 * 1000Expected loss in 1000 games = -$210.50Therefore, you can expect to lose an average of $210.50 if you play this game 1000 times.
Matt had a full jar of marbles. He gave Kayla 3/4 of the marbles. Then Kayla returned 1/3 of a jar's worth of marbles to the jar. How much of the jar is now full of marbles?
Which is a correct first step in solving 5 – 2x < 8x – 3?
choices
5 < 6x – 3
3x < 8x – 3
5 < 10x – 3
2 – 2x < 8x
Kayla has a bowl of beads that contains 42 yellow beads, 28 green beads, 12 white beads, and 18 red beads. She randomly draws a bead from the bowl.
The probability of Kayla not drawing a yellow or a green bead is______ %. The probability of Kayla drawing a red or a green bead is______ %.
Answer:
1. 30%
2.46%
Step-by-step explanation:
The probability of Kayla not drawing a yellow or a green bead is 30 %. The probability of Kayla drawing a red or a green bead is 46 %.
Correct for plato! :)
A wire 24inches long is to be cut into four pieces to form a rectangle whose shortest side has a length of x:
Determine the domain of the function and use a graphing utility to graph the function over that domain
Use the graph of the function to approximate the maximum area of the rectangle. Make a conjecture about the dimensions that yield a maximum area. ...?
Answer:
Area function : [tex]A(x)=12x-x^2[/tex]
Domain: (0,6)
The area of rectangle is maximum at x=6. The area of a rectangle is maximum if it is a square.
Step-by-step explanation:
It is given that the length of wire is 24 inches. It is to be cut into four pieces to form a rectangle.
Let x be the length of shortest side.
Perimeter of a rectangle is
Perimeter = 2( Shortest side + longest side).
[tex]24 = 2( x + \text{longest side})[/tex]
[tex]12 = x + \text{longest side}[/tex]
[tex]12 - x = \text{longest side}[/tex]
So, length of longest side is (12-x) inches.
Area of a rectangle is
[tex]A=length \times width[/tex]
Area function is
[tex]A(x)=x(12-x)[/tex]
The area of rectangle and dimensions of a rectangle can not be a negative.
[tex]A(x)>0[/tex]
[tex]x(12-x)>0[/tex]
It means,
[tex]x>0[/tex]
[tex]12-x>0\Rightarrow 12>x[/tex]
One side is less that the other side.
[tex]x<12-x[/tex]
[tex]2x<12[/tex]
[tex]x<6[/tex]
It means the domain of the function is (0,6).
The simplified form of the area function is
[tex]A(x)=12x-x^2[/tex]
Differentiate with respect to x.
[tex]A'(x)=12-2x[/tex]
[tex]A'(x)=0[/tex]
[tex]12-2x=0[/tex]
[tex]x=6[/tex]
Differentiate A'(x) with respect to x.
[tex]A''(x)=-2<0[/tex]
Therefore the area of rectangle is maximum at x=6.
[tex](12-x)=12-6=6[/tex]
It means the area of a rectangle is maximum if it is a square.
Compute the amount of interest earned in the following simple interest problem. A deposit of $1,295 at 7% for 180 days = _____. (Note: Use 365 days in a year)
The interest earned on a deposit of $1,295 at a 7% annual rate for 180 days is approximately $44.70.
To compute the amount of interest earned we can use the simple interest formula:
Interest = Principal × Rate × Time
Since simple interest does not complicate by itself, and the time is less than a year, we'll adjust the time and rate accordingly.
First, we express the annual interest rate as a decimal by dividing the percentage by 100:
Rate = 7% / 100 = 0.07
Next, we convert the time period of 180 days into years, considering there are 365 days in a year:
Time = 180 days / 365 days/year = 0.49315 years (approximately)
Now, let's plug the values into the simple interest formula:
Interest = $1,295 × 0.07 × 0.49315
Calculating the interest:
Interest = $44.70
Find the sum of the first 50 terms of the sequence below.
An = 3n + 2
Answer:
3925
Step-by-step explanation:
this arithmetic sequence the first term is : A1 = 3(1)+2=5
and common difference is r = 3
the sum of the first 50 terms is : S50 = 50/2(A1 + A50)
A50 = 3(50)+2 = 152
S50 = 50/2(5 + 152)= 3925
WHICH CONSTRUCTION DOES THE IMAGE BELOW DEMONSTRATE??
A square circumscribed about a circle
A square inscribed in a circle
The circumcenter of a square
The incenter of a square
Answer:
This is a square inscribed in a circle.
Step-by-step explanation:
Simplify (4xy^-2)/(12x^(-1/3)y^-5) and Show work ...?
Ben has $3.40 consisting of quarters and dimes. How many coins of each kind does he have if he has 22 coins?
Show a system of equation to represent the word problem.
There are 8 quarters and 14 dimes.
Step-by-step explanation:Let there are x quarters.
and y dimes.
Also as we know,
1 quarter= 0.25 dollar
Hence, x quarter= $ 0.25x
and 1 dime= $ 0.10
Hence, y dimes= $ 0.10y
Ben has $3.40 consisting of quarters and dimes.This means that:
0.25x+0.10y=3.40
Also, in non-decimal form it could be written as:
25x+10y=340
He has 22 coinsThis means that:
x+y=22
Now on solving it graphically we see what is the point of intersection of the two lines or system of linear equations.
We get the point of intersection as: (8,14)
i.e. x=8 and y=14
Hence, there are 8 quarters.
and 14 dimes.
One more and I should be good, i'm pretty familar with this but i'd like to make sure,
Two brothers, Bill and Eric, are 4 years apart, and Bill is the older of the two. If the sum of the boys' ages is 28, how old is bill and how old is eric?
Both boys age is unknown, yet we can mark both with say,
x = Eric's age
y = Bills' age
There are many ways to solve this, but we DO know they're 4 years apart, so it'd have to be
x + y4 = ?,
actually that's off but you understand what i'm saying... Thanks!
What is the value of x+2x when x=4 ? Enter your answer in the box.
What multiplies to 9 and adds to 1
Express answer in exact form.
A regular hexagon with sides of 3" is inscribed in a circle. Find the area of a segment formed by a side of the hexagon and the circle.
(Hint: remember Corollary 1--the area of an equilateral triangle is 1/4 s2 √3.)
Answer:
A = { 3/2 π - 9/4 √ 3 } in^2
Step-by-step explanation:
Hope it helps, sorry for answering late.
Which three statements below are true about an acute isosceles triangle?two side measures are the sameall angle measures are less than 90°one angle is obtusetwo angle measures are the sameall angle measures are different
Answer:
two side measures are the same
all angle measures less than 90°
two angle measures are the same
Step-by-step explanation:
The three true statements about an acute isosceles triangle are:
- Two side measures are the same:
- All angle measures are less than 90°:
- Two angle measures are the same:
What is a triangle?A triangle is a 2-D figure with three sides and three angles.
The sum of the angles is 180 degrees.
We can have an obtuse triangle, an acute triangle, or a right triangle.
We have,
About an acute isosceles triangle are:
- Two side measures are the same:
In an isosceles triangle, two sides have the same length.
In an acute isosceles triangle, all angles are acute, which means they are less than 90°.
Therefore, the two sides that are the same length must be the two sides opposite the acute angles.
- All angle measures are less than 90°:
An acute triangle is a triangle in which all angles are less than 90°.
Since an acute isosceles triangle has two equal acute angles, all three angles in the triangle are less than 90°.
- Two angle measures are the same:
An isosceles triangle is a triangle in which two sides have the same length. In an acute isosceles triangle, the two sides that have the same length are opposite the two equal acute angles.
Therefore, the two angles opposite those sides must also have the same measure.
Thus,
The three true statements about an acute isosceles triangle are:
- Two side measures are the same:
- All angle measures are less than 90°:
- Two angle measures are the same:
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What is the value of the function y = 2x + 3 when x=−1
5
2
1
−5
Answer:
I took the test its 1
Step-by-step explanation:
Using the properties of equality to solve the equation -2b + 7 = -13, you would _____.
add 13 and then divide by -2
add 13 and then add 2
subtract 7 and then add 2
subtract 7 and then divide by -2
To solve the equation, firstly subtract 7 from both sides, converting the equation into -2b = -20. Then divide both sides by -2 to find the value of b, which is 10.
Explanation:To use the properties of equality to solve the given equation, -2b + 7 = -13, follow these steps:
First, isolate the term containing the variable b on one side of the equation. This is done by subtracting 7 from both sides of the equation. The equation becomes -2b = -20.Next, to find the value of the variable b, divide both sides of the equation by -2. So, the final equation becomes b = 10.Learn more about Properties of Equality here:https://brainly.com/question/10617252
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a certain game consists of rolling a single fair die and pays off as follows: $5 for a 6, $2 for a 5, $1 for a 4, and no payoff otherwise. find the expected winnings for this game.
The expected winnings for this game is calculated by multiplying the value of each possible outcome by their probability, providing an overall expected value of $1.33. This indicates that over a long period of repeated games, the average winnings per game would be $1.33.
Explanation:In this question, we're dealing with calculating the expected value in a game of probability. The game involves rolling a dice with outcomes ranging from 1 to 6 and the associated payoffs for roll outcomes of 4, 5, and 6 are $1, $2, and $5 respectively.
We calculate the expected winnings (value) for a single round of the game by multiplying all possible outcomes by their respective probabilities, then summing these products. In this case, symbols represent the payout (in $) and P represents the probability of each outcome.
(6) $5*P(1/6) = $0.83 (5) $2*P(1/6) = $0.33 (4) $1*P(1/6) = $0.17 (1-3) $0*P(1/2) = $0.00Adding up these expected outcomes gives us our overall expected winnings: $0.83 + $0.33 + $0.17 + $0.00 = $1.33 per game
If you play this game repeatedly, over the long term, you'd expect to win around $1.33 on average each game. Note that the exact winnings in a single instance of the game could be $0, $1, $2, or $5, and this value simply provides an average expected outcome over time.
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What is the answer to
3n-5=7n+11