two students are trying to finish labeling the number line with the base 10 logarithmic expression that equal 2. Dylan say the missing logarithm should be log 505 because 505 is halfway between 10 and 1000, just like 2 is halfway between 1 and 3 . Jakob disagree. he says the miss logarithm should be log 100 . Which student is correct

Answers

Answer 1

Answer:

Jakob is correct.

The base 10 logarithmic function is a continuous function, which means that the distance between any two consecutive values on the number line is the same. Therefore, if 2 is halfway between 1 and 3, the value of the logarithm that is halfway between log 1 and log 3 should be the average of log 1 and log 3, which is:

(log 1 + log 3) / 2 = (0 + 0.477) / 2 = 0.2385

To find the value of x such that 10^x = 505, we can take the logarithm of both sides using base 10:

log 10^x = log 505

x = log 505

Using a calculator, we can find that log 505 is approximately 2.702.

To find the value of x such that 10^x = 100, we can take the logarithm of both sides using base 10:

log 10^x = log 100

x = log 100

Using a calculator, we can find that log 100 is exactly 2.

Therefore, the logarithm that is equal to 2 is log 100, not log 505.


Related Questions

Does the function model exponential growth or decay? g ( t ) = 1.7 ⋅ 0. 8 t

Answers

The answer of the given question based on function is  g(t) = 1.7 * 0.8^t models exponential decay.

What is Exponential decay?

Exponential decay is a type of mathematical function that represents a process in which the value of a quantity decreases over time or through a series of events at a constant proportional rate. In exponential decay, the rate of decrease is proportional to the current value of the quantity.

Exponential decay is often modeled by the following equation:

y = a * e^(-kt)

The function g(t) = 1.7 * 0.8^t models exponential decay.

In this function, the base of the exponent is 0.8, which is a number between 0 and 1. When a base of an exponential function is between 0 and 1, it represents exponential decay. This means that as the value of t increases, the value of g(t) decreases at an increasingly rapid rate.

Additionally, the coefficient of the exponent (1.7 in this case) represents the initial value of the function. Since the coefficient is positive, the initial value is also positive. Therefore, the function represents exponential decay from a positive initial value.

To know more about Exponential function visit:

https://brainly.com/question/30240572

#SPJ1

Every day Jin reads for 0.75
hours in the morning and 1.25
hours in the evening. He uses the expression 0.75d+1.25d
to keep track of the number of hours he has read for any number of days, d
. If Jin reads for 20
days, how many hours has he read?

Answers

Answer:

Step-by-step explanation:The number of hours Jin reads in 20 days is 39.8 hours.

The expression for the given situation is 0.75d + 1.24d.

What is an expression?

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.

In the given expression 0.75d + 1.24d, d is number of days.

Substitute d=20 in 0.75d + 1.24d, we get

0.75(20) + 1.24(20)

15+24.8

=39.8 hours

Hence, the number of hours Jin reads in 20 days is 39.8 hours

Solve the equation for the specified variable.

Answers

24.08

Multiply both sides by 4

Simplify −1.48×4 to −5.92

Add 30 to both sides.

Simplify −5.92+30 to 24.08

help I don't understand please show work

Answers

11 is the value of x in this polygon.

What exactly is a polygon in mathematics?

A closed, two-dimensional, flat, closed polygon is a shape that is constrained by geometry and has straight sides. Its sides don't curve inward at all.

                               Another term for a polygon's sides is its polygonal edges. The points where two sides converge are known as a polygon's vertices (or corners).

2x - 4/6  = 9/3

(2x - 4)3  = 6 * 9

 2x - 4 = 54/3

   2x - 4 = 18

     2x = 18 + 4

       2x = 22

          x = 11

Learn more about polygon

brainly.com/question/24464711

#SPJ1

Anna borrowed N$20 000 at 5% for three and half years. She wants to pay N$8000 on maturity. To achieve
this, she is planning to pay 2000 in 10 months, 5000 in 16 months from now. How much should she pay in two
and half years from now to meet her obligation?

Answers

Anna should pay N$289,711.85 in two and a half years from now to meet her obligation.

What is interest rate?

An interest rate is the rate at which a borrower pays to a lender for the use of borrowed money. It is expressed as a percentage of the principal amount borrowed and is typically calculated on an annual basis.

According to question:

To solve this problem, we can use the formula for the future value of an annuity:

FV = [tex]P * [(1 + r)^n - 1]/r[/tex]

Where FV is the future value of the annuity, P is the periodic payment, r is the interest rate per period, and n is the total number of periods.

We know that Anna borrowed N$20,000 at 5% for three and a half years, which is equivalent to 42 months. The periodic payment, P, is the sum of N$2,000 and N$5,000, which is N$7,000.

First, we can calculate the future value of the annuity after 42 months:

FV = 7,000 * [(1 + 0.05/12)[tex]^42[/tex] - 1]/(0.05/12)

FV = 7,000 * 56.3743

FV = N$394,120.10

Since Anna wants to pay N$8,000 on maturity, she will need to pay N$386,120.10 at the end of the 42 months to meet her obligation.

Now we can calculate how much Anna should pay in two and a half years from now, which is equivalent to 30 months:

[tex]PV = FV / (1 + r)^n[/tex]

PV = 386,120.10 / (1 + 0.05/12)[tex]^30[/tex]

PV = N$289,711.85

Therefore, Anna should pay N$289,711.85 in two and a half years from now to meet her obligation.

Learn more about interest rate visit:

https://brainly.com/question/30470960

#SPJ1

James Kamau stocks and sells cabbages, oranges and mangoes in his grocery at Kitengela market. On Monday last week, he sold 55 cabbages, 100 oranges and 95 mangoes making a total sale of sh. 1,625. On Tuesday, he sold 60 cabbages, 120 oranges and 80 mangoes making a total sale of sh. 1,580. On Wednesday, he sold 75 cabbages, 150 oranges and 120 mangoes making a total sale of sh. 2,175. He buys these items from a distributor at sh.3, sh.2 and sh.6 for a cabbage, an orange and a mango respectively. Required: a) Three simultaneous equations connecting the number of units sold and total sales. (3 Marks) b) The selling price for each. (9 Marks) c) The profit that James Kamau made on each of the three days and his total profits.​

Answers

a) Let x, y, and z be the selling price of one cabbage, one orange, and one mango, respectively.

From the given data, we can write three simultaneous equations:

Monday: 55x + 100y + 95z = 1625

Tuesday: 60x + 120y + 80z = 1580

Wednesday: 75x + 150y + 120z = 2175

b) To find the selling price of each item, we need to solve the system of equations. We can use any method of solving systems of equations, such as substitution or elimination. Here, we will use the elimination method.

Multiplying the first equation by 6, the second equation by -5, and the third equation by 3, we get:

Monday: 330x + 600y + 570z = 9750

Tuesday: -300x - 600y - 400z = -7900

Wednesday: 225x + 450y + 360z = 6525

Adding all three equations, we get:

255x + 450y + 530z = 8385

Dividing both sides by 5, we get:

51x + 90y + 106z = 1677

Now we can use this equation and any of the original equations to solve for one of the variables. Let's use the first equation:

55x + 100y + 95z = 1625

Multiplying both sides by 106 and subtracting 530 times the first equation from it, we get:

76x + 45z = 43

Solving for x, we get:

x = (43 - 45z)/76

Now we can substitute this value of x into any of the previous equations to solve for y and z. Let's use the third equation:

75x + 150y + 120z = 2175

Substituting x, we get:

75[(43-45z)/76] + 150y + 120z = 2175

Simplifying, we get:

43z/2 - 375/2 + 150y = 825

Solving for y, we get:

y = (825 - 43z/2 + 375/2)/150

Now we can substitute the values of x and y into any of the previous equations to solve for z. Let's use the second equation:

60x + 120y + 80z = 1580

Substituting x and y, we get:

60[(43-45z)/76] + 120[(825-43z/2+375/2)/150] + 80z = 1580

Simplifying, we get:

z = 4.6

Substituting z into the equation for y, we get:

y = 3.45

Substituting z and y into the equation for x, we get:

x = 1.5

Therefore, the selling price for one cabbage is sh. 1.5, for one orange is sh. 3.45, and for one mango is sh. 4.6.

c) The profit that James Kamau made on each of the three days and his total profits:

To calculate the profit, we need to subtract the cost of the items from the revenue generated by selling them.

On Monday:

Cost of cabbages = 55 x 3 = 165 shillings

Cost of oranges = 100 x 2 = 200 shillings

Cost of mangoes = 95 x 6 = 570 shillings

Total cost = 935 shillings

Revenue = 1625 shillings

Profit = Revenue - Cost = 1625 - 935 = 690 shillings

On Tuesday:

Cost of cabbages = 60 x 3 = 180 shillings

Cost of oranges = 120 x 2 = 240 shillings

Cost of mangoes = 80 x 6 = 480 shillings

Total cost = 900 shillings

Revenue = 1580 shillings

Profit = Revenue - Cost = 1580 - 900 = 680 shillings

On Wednesday:

Cost of cabbages = 75 x 3 = 225 shillings

Cost of oranges = 150 x 2 = 300 shillings

Cost of mangoes = 120 x 6 = 720 shillings

Total cost = 1245 shillings

Revenue = 2175 shillings

Profit = Revenue - Cost = 2175 - 1245 = 930 shillings

Total profit over three days:

Profit on Monday + Profit on Tuesday + Profit on Wednesday = 690 + 680 + 930 = 2300 shillings

Therefore, James Kamau made a profit of 690 shillings on Monday, 680 shillings on Tuesday and 930 shillings on Wednesday, with a total profit of 2300 shillings over the three days.

Can someone explain 1+8×6091+689+8×879+68×9+7​

Answers

Answer:

Step-by-step explanation:

1+8×6091+689+8×879+68×9+7​

We need to do the multiplications first

1+(8×6091)+689+(8×879)+(68×9)+7​=

1+(48728)+689+(7032)+(612)+7​

Now we add all of them up

48729 + 7721 + 619 =

57069

Answer is 57069

the breaking strength of a rivet has a mean value of 9,950 psi and a standard deviation of 502 psi. (a) what is the probability that the sample mean breaking strength for a random sample of 40 rivets is between 9,850 and 10,150? (round your answer to four decimal places.) (b) if the sample size had been 15 rather than 40, could the probability requested in part (a) be calculated from the given information? explain your reasoning. - yes, the probability in part (a) can still be calculated from the given information.
- no, n should be greater than 30 in order to apply the central limit theorem. - no, n should be greater than 20 in order to apply the central limit theorem. - no, n should be greater than 50 in order to apply the central limit theorem.

Answers

a) The probability that the sample mean breaking strength for a random sample of 40 rivets is between 9,850 and 10,150 is equal to 0.8903.

b) No, because n should be greater than 30 in order to apply the central limit theorem. So, right choice for answer is option (b).

The normal distribution forms a bell shaped curve. The parameter of normal distribution is [tex]\mu[/tex] and [tex]\sigma ^2 [/tex]. It is a continuous distribution. Now, Mean value of breaking strength of a rivet = 9,950

Standard deviations = 502

Let's X be variable denotes breaking strength of a rivet.

a) Now, a random sample is choosen from X such that, Sample size, n = 40. By using central limit theorem, sample mean follows approximately normal distribution with mean 9950 and standard deviations = 502/√40 = 79.3732 that is [tex]\bar X \: \tilde \: \: N( 9950, ( 79.3732)²)[/tex]

[tex]P( 9,850 < \bar X < 10,150 ) = P( \bar X < 10,150) -

P( \bar X < 9,850) \\ [/tex]

= [tex] P(\frac{\bar X - \mu }{\sigma} < \frac{10,150 - 9950}{79.3732} )- P(\frac{\bar X - \mu }{\sigma} < \frac{10,150 - 9850}{79.3732}) \\ [/tex]

= P( Z < 2.52 ) - P( Z < -1.26)

= 0.9941 - 0.1038

= 0.8903

b) If sample size,n is 15 instead of 40, then the probability requested in part (a) will not be calculated from the provide information. Because, for applying central limit theorem we have sample size must be grater than 30. So, option(b) is correct.

For more information about central limit theorem, visit :

https://brainly.com/question/18403552

#SPJ4

23 cats and 27 dogs were entered into a cat and dog show. What percentage of the entries were dogs?​

Answers

27+23= 50
50 x 2 = 100
27 x2 = 54
54/100 = 54%

Find the inverse and original steps of the inverse equation

Answers

Step-by-step explanation:

To find the inverse of an equation, we need to switch the roles of the dependent variable and the independent variable. In other words, if we have an equation of the form y = f(x), we need to rewrite it as x = f^{-1}(y), where f^{-1}(y) is the inverse function of f.

Once we have found the inverse equation, we can perform the original steps of the inverse equation by plugging in the output of the inverse function into the original equation.

For example, let's say we have the equation y = 2x + 3. To find the inverse equation, we first switch the roles of x and y to get:

x = 2y + 3

Next, we solve for y in terms of x:

x - 3 = 2y

(y = x - 3)/2

So the inverse equation is y = (x - 3)/2.

To perform the original steps of the inverse equation, we can plug the output of the inverse function, (x - 3)/2, into the original equation, y = 2x + 3:

y = 2((x - 3)/2) + 3

y = x - 3 + 3

y = x

We have arrived back at the independent variable, x, so the inverse and original steps have canceled each other out, as expected.

X =
Solve for x,
using the secant lines.
[?
8 cm
20 cm
X
13 cm
Round to the
nearest tenth.
cm_ Remember: a·b= c.d
Enter

Answers

Using the formula for lines intersecting in a circle, we get the value of x to be = 32.5cm.

What are lines inside circle?

A diameter is a line segment that traverses a circle by going through its centre.

The radius is twice as long as the diameter.  A chord is a segment that does not have to pass through the centre and has endpoints on the circle.

We know that in a circle when lines are intersecting each other than the lines divided are in the formula:

a × b = c × d

Here,

13 × 20 = 8 × x

⇒ x = 260/8

⇒ x = 32.5cm.

To know more about lines inside circle, visit:

https://brainly.com/question/23265136

#SPJ1

Abbey is getting new carpet in her living room and hallway. The following diagram shows the two together. Note: Figure not drawn to scale If a = 34 ft, b = 13 ft, c = 17 ft, and d = 17 ft, what is the area of the living room and hallway together?

Answers

Therefore, the combined area of the living room and hallway is 731 square feet.

What is area?

In geometry, the term "area" refers to the measurement of the size of a two-dimensional surface. It is typically measured in square units, such as square meters or square feet. The area of a shape can be found by multiplying its length by its width or by using other specific formulas that depend on the shape itself. Some common examples of shapes for which we might want to calculate the area include squares, rectangles, triangles, circles, and irregular polygons.

by the question.

The area of the living room can be calculated as:

[tex]Area of living room = length x width\\Area of living room = a x b\\Area of living room = 34 ft x 13 ft\\Area of living room = 442 sq ft[/tex]

The area of the hallway can also be calculated using the same formula:

[tex]Area of hallway = length x width\\Area of hallway = c x d\\Area of hallway = 17 ft x 17 ft\\Area of hallway = 289 sq ft[/tex]

To find the total area of the living room and hallway together, we simply add the two areas:

[tex]Total area = Area of living room + Area of hallway\\Total area = 442 sq ft + 289 sq ft\\Total area = 731 sq ft[/tex]

To learn more about area:

https://brainly.com/question/11952845

#SPJ1

PLEASE HURRY WILL GIVE BRAINLIEST AND 5 STARS!!!!!!

To add (or subtract) in Scientific Notation, you must have the same Response area. Then you can Response area the co-efficients and Response area the power of 10.

To multiply in Scientific Notation, you must multiply the Response area and Response area the powers of 10.

To divide in Scientific Notation, you must Response area the co-efficients and Response area the powers of 10.

Answers

According to the given information, divide in Scientific Notation, you must divide the co-efficients and subtract the powers of 10.

What is Scientific Notation?

Scientific notation, also known as standard form or exponential notation, is a way of expressing numbers that are either very large or very small, using powers of 10. In scientific notation, a number is expressed in the form:

a x 10ⁿ

where "a" is a number between 1 and 10 (usually a decimal), and "n" is an integer (positive or negative) that represents the power of 10 by which the number is multiplied.

To add (or subtract) in Scientific Notation, you must have the same power of 10. Then you can add (or subtract) the co-efficients and keep the power of 10.

To multiply in Scientific Notation, you must multiply the co-efficients and add the powers of 10.

To divide in Scientific Notation, you must divide the co-efficients and subtract the powers of 10.

To know more about Scientific Notation visit:

brainly.com/question/18073768

#SPJ1

Which of the following relations is a function? A. (7, 1), (-2, 4), (4, 1), (7, 2) B. (4, 0), (-2, 3), (7, 1), (-2, 5) C. (4, 4), (-2, 2), (7, 1), (-7, 2) D. (4, 4), (-2, 6), (4, 3), (-7, 2)

Answers

C. (4, 4), (-2, 2), (7, 1), (-7, 2)

In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y.[1] The set X is called the domain of the function[2] and the set Y is called the codomain of the function

Drop down 1 drop 2 = AOB or BOD
Drop3 = angles addition postulate, d definition of complementary angles, addition, property of equality, definition of perpendicular line segments

Answers

There is a missing step between step 8 and 9 because the student did not state that m∠BOC + m∠COD = m∠BOD. This statement is true because of the angles addition postulate.

What is angles addition postulate?

The Angle Addition Postulate states that if point P lies in the interior of angle ∠RST, then the measure of ∠RST is equal to the sum of the measures of ∠RSP and ∠PST. In other words, for any angle ∠RST with point P in its interior, says that m∠RST = m∠RSP + m∠PST.

The Angle Addition Postulate is used in geometry to find the measures of angles that are formed by two intersecting lines or when a point is located in the interior of an angle.

Learn more on angles addition postulate here: https://brainly.com/question/24746945

#SPJ1

Image transcribed:

Select the correct answer from each drop-down menu.

Given: ∠BOC and ∠COD are complementary angles

lines BO intersects lines AD at point O

Prove: ∠AOB ≅∠BOD

Statements--|--Reasons

1. ∠BOC and ∠COD are complementary angles; BO intersects AD at point O--|--1. given

2. m∠BOC+ m∠COD = 90°--|--2. definition of complementary angles

3. substitution property of equality--|--3. m∠BOD 90°

4. ∠AOB and ∠BOD are supplementary angles--|--4. linear pair theorem

5. m∠AOB + m∠BOD = 180°--|--5. definition of supplementary angles

6. m∠AOB+90° = 180°--|--6. substitution property of equality

7. m∠AOB = 90°--|--7. subtraction property of equality

8. m∠AOB = m/BOD--|--8. substitution property of equality

9. ∠AOB∠ BOD--|--9. definition of congruent angles

There is a step missing in the proof. Identify where in the proof there is a missing step and what this step should be.

There is a missing step between _______ (options 8. and 9.,1. and 2., 2 and 3., 4. and 6.)because the student did not state m∠BOC+m∠COD - m∠______  (options AOB or BOD). This statement is true because of the _____ (options angles addition postulate, d definition of complementary angles, addition, property of equality, definition of perpendicular line segments)

A university is trying to determine what price to charge for tickets to footbal games. At a price of $20 per ticket, attendance averages 40,000 people per game. Every decrease of $5 adds 10,000 people to the average number.
Every person at the game spends an average of $5.00 on concessions. What price per ticket should be charged in order to maximize revenue? How many people will attend at that price?

Answers

The price that maximizes revenue is $10 per ticket, which will bring in $1,500,000 in revenue. 60,000 people will attend at that price.

What is price?

Price is the amount of money that is required to purchase or obtain a good or service. It is a numerical value that is assigned to a particular product or service and is used to indicate its value in the market. The price of a product or service is determined by a variety of factors, including the cost of production, supply and demand, competition, and market conditions.

In the given question,

To maximize revenue, we need to find the price per ticket that will bring in the greatest total revenue. Let's start by figuring out how many people will attend at various price points:

At $20 per ticket, 40,000 people attend.

At $15 per ticket, 50,000 people attend.

At $10 per ticket, 60,000 people attend.

At $5 per ticket, 70,000 people attend.

Now we can calculate the total revenue at each price point:

At $20 per ticket, revenue is 40,000 × $20 + 40,000 × $5 = $1,000,000.

At $15 per ticket, revenue is 50,000 × $15 + 50,000 × $5 = $1,250,000.

At $10 per ticket, revenue is 60,000 × $10 + 60,000 × $5 = $1,500,000.

At $5 per ticket, revenue is 70,000 × $5 + 70,000 × $5 = $700,000.

From these calculations, we can see that the price that maximizes revenue is $10 per ticket, which will bring in $1,500,000 in revenue. 60,000 people will attend at that price.

To know more about price and revenue, visit:

https://brainly.com/question/30990889

#SPJ1

You randomly survey students about whether they play a sport or a musical instrument. Of 110 students who play a sport, 46 play an instrument. Of 140 students who do not play a sport, 61 play an instrument. Organize the results in a two-way table. Include the marginal frequencies.

Answers

Answer:

Step-by-step explanation:

20% OF a IS 15. WHAT IS a

Answers

Answer:

The answer is 3

Step-by-step explanation:

20% of 15 can be written as 20% × 15

= 20/100 × 15

= 3

Thus, 20% of 15 is 3.

hope this helps

3, I asked Alexa hope this helps

Assume that the Poisson distribution applies and that the mean number of hurricanes in a certain area is 7.7 per year. a. Find the probability​ that, in a​ year, there will be 5 hurricanes. b. In a 45​-year ​period, how many years are expected to have 5 ​hurricanes? c. How does the result from part​ (b) compare to a recent period of 45 years in which 4 years had 5 ​hurricanes? Does the Poisson distribution work well​ here?

Answers

if the probability of observing 4 or fewer years with 5 hurricanes is much lower (e.g., less than 5%), then we might conclude that the Poisson distribution does not work well for this particular scenario.

What is the role of Poisson distribution?

a. The probability of observing 5 hurricanes in a year can be calculated using the Poisson distribution formula:

[tex]P(X=5) = (e^(-λ) * λ^5) / 5![/tex]

where λ is the mean number of hurricanes per year. In this case [tex], λ = 7.7[/tex] . Thus,

[tex]P(X=5) = (e^(-7.7) * 7.7^5) / 5! = 0.0834[/tex]   (rounded to four decimal places)

Therefore, the probability of observing 5 hurricanes in a year is approximately  [tex]0.0834[/tex] or   [tex]8.34[/tex] %.

b. The number of hurricanes in a 45-year period follows a Poisson distribution with mean [tex]λ = 7.7 \times 45 = 346.5[/tex] . The expected number of years with 5 hurricanes in a 45-year period is then:

[tex]E(X) = λ = 346.5[/tex]

Therefore, we expect about [tex]346.5/45 ≈ 7.7[/tex] % or 8 years out of 45 to have 5 hurricanes.

c. If in a recent period of 45 years, only 4 years had 5 hurricanes, we can compare this to the expected number of years with 5 hurricanes based on the Poisson distribution. Using the same mean λ = 346.5, we can calculate the probability of observing 4 or fewer years with 5 hurricanes in a 45-year period:

[tex]P(X ≤ 4) = Σ(i=0 to 4) [(e^(-λ) * λ^i) / i!] ≈ 0.2088[/tex]

This means that there is about a 20.88% chance of observing 4 or fewer years with 5 hurricanes in a 45-year period, based on the Poisson distribution with [tex]λ = 346.5[/tex]  .

Therefore,  This is not a very low probability, so the observed 4 years with 5 hurricanes in the recent [tex]45[/tex]  -year period is not necessarily inconsistent with the Poisson distribution.

Learn more about Poisson here:

https://brainly.com/question/17280826

#SPJ9

If a coordinate system is set up such that the positive x axis points in a direction 60° above the horizontal, what should be the angle between the x axis and the y axis?


What should be the direction of the positive y axis?
(measured from the horizontal)

Answers

The two axes should be perpendicular, so the angle betwen them is 90°, and the y-axis is 150° above the horizontal.

What should be the angle between the x axis and the y axis?

If we have a coordinate axis, the two axis should be perpendicular between them, this means that the angle between the positive x-axis and the positive y-axis should always be 90°.

Now, what should be the direction of the positive y axis?

We know that the positive x-axis is 60° above the horizontal, and the angle between the two axes is 90°, then the positive y axis is at:

60° + 90° = 150°

The positive y-axis is at 150° above the horizontal line.

Learn more about coordinate axis at:

https://brainly.com/question/11337174

#SPJ1

HELP ASAP PLEASE URGENT

Answers

By answering the presented question, we may conclude that Option D is false because function addition is not commutative in general.

what is function?

In mathematics, a function seems to be a link between two sets of numbers in which each member of the first set (known as the domain) corresponds to a specific member of the second set (called the range). In other words, a function takes input from one collection and creates output from another. The variable x has frequently been used to represent inputs, whereas the variable y has been used to represent outputs. A formula or a graph can be used to represent a function. For example, the formula y = 2x + 1 depicts a functional form in which each value of x generates a unique value of y.

The correct statement about functions is:

C. If f is a function, then f(2 + h) = f(2) + f(2 + h) (h)

This is known as the additivity property or the additivity rule. It indicates that evaluating a function at a total of two values is equivalent to evaluating the function at each value individually and then adding the results. This is true for a wide range of functions, including linear and polynomial functions.

Option A is false since the order of function composition matters in general.

Option B is false because matrix multiplication is not always defined unless the matrices' dimensions are compatible.

Option D is false because function addition is not commutative in general.

To know more about function visit:

https://brainly.com/question/28193995

#SPJ1

a. Find the present value of 350 000 which is due after 10 years if the interest rate is 8% per year
i. compounded annually, or (4 marks) ii. compounded continuously.

Answers

The present value of 350,000 due after 10 years, compounded annually at an interest rate of 8% per year, is approximately 157,456.41, while the present value of 350,000 due after 10 years, compounded continuously at an interest rate of 8% per year, is approximately 147,252.13.

i. To find the present value of 350,000 due after 10 years, compounded annually at an interest rate of 8% per year, we can use the formula:

[tex]PV = FV / (1 + r)^n[/tex]

where PV is the present value, FV is the future value, r is the interest rate, and n is the number of periods.

Substituting the given values, we get:

PV = 350,000 / (1 + 0.08)^10

PV ≈ 157,456.41

Therefore, the present value of 350,000 due after 10 years, compounded annually at an interest rate of 8% per year, is approximately 157,456.41.

ii. To find the present value of 350,000 due after 10 years, compounded continuously at an interest rate of 8% per year, we can use the formula:

[tex]PV = FV / e^(r * n)[/tex]

where e is the mathematical constant approximately equal to 2.71828.

Substituting the given values, we get:

[tex]PV = 350,000 / e^(0.08 * 10)[/tex]

PV ≈ 147,252.13

Therefore, the present value of 350,000 due after 10 years, compounded continuously at an interest rate of 8% per year, is approximately 147,252.13.

To learn more about present value please click on below link.

https://brainly.com/question/17322936

#SPJ1

Choose the three true statements about the angles in the figure

Answers

Answer-

answer marked on the picture

Step-by-step explanation:

angle 1 and 55 is not vertical angles thus is the wrong answer

angle 2 can be determined with the given info by subtracting the other two angles to 180

Angle 2 not equal to 125 as the angles are not supplementary from each other

Find the length of the segment indicated. Round your answer to the nearest tenth if necessary. (Please show step by step on how to figure this out! I want to understand!)

Answers

By pythagorean theorem, 21.095 is the length of the segment indicated..

What is the Pythagorean theorem in plain English?

The Pythagorean Theorem states that the squares on the hypotenuse of a right triangle, which is the side that faces the right angle, are equal when added together. This is written as a2 + b2 = c2 in the usual algebraic notation.

  In triangle we apply pythagorean theorem

    x² = 11.8² + 17.5²

         = 139.24 +  306.25

     x   = √445.49

      x = 21.095

     

Learn more about Pythagorean theorem

brainly.com/question/14930619

#SPJ1

Show that f(x) can be written as Px2+Qx+R+Vx+3+Wx-5and find the values of P, Q, R, Vand W.

Answers

f(x) = (3/2)*x² + (13/2)*x - 5/2 - 6/(x + 3) + 15/(x - 5)

and the values of P = 3/2, Q = 13/2, R = -5/2, V = -6, W = 15

What is the fraction?

A fraction is a number that represents a part of a whole or a ratio between two quantities. It is written with a numerator (the top number) and a denominator (the bottom number) separated by a horizontal line. The numerator represents the number of parts being considered, while the denominator represents the total number of parts that make up a whole unit.

First, let's factor in the denominator of the given function:

x² - 2x - 15 = (x - 5)(x + 3)

Now we can use partial fraction decomposition to express the given function as the sum of simpler fractions:

f(x) = (x⁴ + 2x³ - 29x² - 47x + 77) / (x² - 2x - 15)

= (x⁴ + 2x³ - 29x² - 47x + 77) / ((x - 5)(x + 3))

= (Px² + Qx + R) + V/(x + 3) + W/(x - 5)

where P, Q, and R are constants to be determined, and V and W are constants to be determined as well.

To find the values of P, Q, and R, we can use polynomial long division to divide the numerator by the denominator:

        x² + 5x - 2

x² - 2x - 15 | x⁴ + 2x³ - 29x² - 47x + 77

- (x⁴ - 2x³ - 15x²)

----------------------

4x³ - 14x² - 47x

- (4x³ - 8x² - 60x)

------------------

-6x² + 47x

- (-6x² + 12x + 90)

--------------

35x - 90

Therefore,

f(x) = (x⁴ + 2x³ - 29x² - 47x + 77) / (x² - 2x - 15)

= x² + 5x - 2 - (6x² - 35x + 90) / ((x - 5)(x + 3))

= -5/2 + (13/2)x + (3/2)x² + V/(x + 3) + W/(x - 5)

Comparing this to the given form, we can see that:

P = 3/2

Q = 13/2

R = -5/2

V = -6

W = 15

Therefore, we have:

f(x) = (3/2)*x² + (13/2)*x - 5/2 - 6/(x + 3) + 15/(x - 5)

and the values of P = 3/2, Q = 13/2, R = -5/2, V = -6, W = 15

To learn more about the fraction visit:

https://brainly.com/question/20712359

#SPJ1

15 points will mark as brainlist !! please help

Answers

Angle 1 and the angle of 38° lie on the transversal, and thus they are supplementary because the angle of a straight line is always 180.° Angle 1 and the 38° angle form the 180° angle for the line.

This, we can form the following equation to find the measure of angle 1:

38°+∠1=180°

Subtract 38 from both sides:

∠1=180-38

∠1=142°

Now, we know the measure of angle 1. Angle 1 and angle 5 are alternating interior angles. By the Alternate Interior Angles Theorem, alternate interior angles are always congruent.

Therefore, ∠1=∠5; 142°=∠5

Answer: m∠5=142°

I need help with this

Answers

Answer:

g(0)= -1/3

g(-1)=0

g(1)=-1

g(2)=-3

g(3)=∞

Step-by-step explanation:

g(0)= -1/3

g(-1)=0

g(1)=-1

g(2)=-3

g(3)=∞

Antiderivative of
(tan^-x× e^tan^-1x)/(1+x^2) ​

Answers

Let u = tan⁻¹x, then du/dx = 1/(1+x²).

Using the formula for the derivative of inverse tangent, we have:

tan(u) = x

sec²(u) du/dx = 1

du/dx = cos²(u)

Substituting into the original expression, we get:

∫(tan⁻¹x × e^tan⁻¹x)/(1+x²) dx = ∫(tan⁻¹x × e^u × cos²(u)) du

Using integration by parts with u = tan⁻¹x and dv = e^u × cos²(u) du, we get:

v = (1/2) e^u (sin(u) + u cos(u))

∫(tan⁻¹x × e^u × cos²(u)) du = (1/2) e^u (sin(u) + u cos(u)) tan⁻¹x - ∫[(sin(u) + u cos(u)) / (1+x²)] dx

Substituting back u = tan⁻¹x, we get:

∫(tan⁻¹x × e^tan⁻¹x × cos²(tan⁻¹x)) dx = (1/2) e^tan⁻¹x (x sin(tan⁻¹x) + cos(tan⁻¹x)) tan⁻¹x - ∫[(x cos(tan⁻¹x) + sin(tan⁻¹x)) / (1+x²)] dx

Using the identity sin(tan⁻¹x) = x / √(1+x²) and cos(tan⁻¹x) = 1 / √(1+x²), we simplify the expression to:

∫(tan⁻¹x × e^tan⁻¹x × cos²(tan⁻¹x)) dx = (1/2) x e^tan⁻¹x + (1/2) ∫[e^tan⁻¹x / (1+x²)] dx

The remaining integral can be solved using another substitution with v = tan⁻¹x, which results in:

∫(tan⁻¹x × e^tan⁻¹x × cos²(tan⁻¹x)) dx = (1/2) x e^tan⁻¹x + (1/2) ln(1+x²) + C, where C is the constant of integration

The width of a rectangle is 4 units less than the length. The area of the rectangle is 12 square units. What is the width, in units, of the rectangle

Answers

The width and length of the rectangle will be -1 units and 3 units, respectively.

What is the area of the rectangle?

Let W be the rectangle's width and L its length.

The area of the rectangle is the multiplication of the two different sides of the rectangle. Then the rectangle's area will be

[tex]\text{Area of the rectangle = L x W square units}[/tex]

The width of a square shape is 4 units less than the length. The region of the square shape is 12 square units. Then the equations are given below.

[tex]W = L - 4[/tex]              ...1

[tex]L \times W = 12[/tex]           ...2

From equations 1 and 2, then we have

[tex]L \times (L - 4) = 12[/tex]

[tex]L^2 - 4L = 12[/tex]

[tex]L^2 - 4L - 12 = 0[/tex]

[tex]L^2 - 3L + 4L - 12 = 0[/tex]

[tex]L(L - 3) + 4(L - 3) = 0[/tex]

[tex](L - 3)(L + 4) = 0[/tex]

[tex]L = 3, -4[/tex]

Then the width of the rectangle is given as,

[tex]W = 3 - 4[/tex]

[tex]W = -1 \ \text{units}[/tex]

The width and length of the rectangular shape will be -1 units and 3 units, separately.

More about the area of the rectangle link is given below.

https://brainly.com/question/20693059

Which statement describes the relationships between x and y in these two equations? y = 10x y = x + 10

Answers

Answer is

In y = 10x, the value of y is 10 times the value of x.
In y= x + 10, the value of y is 10 more than the value of x.
Other Questions
write the balanced equation for the reaction in which aluminum is added to aqueous manganese(ii) sulfate. you do not need to include states of matter in your answer. I need help with this math problem. Its from the course Apply Math. now suppose that the machine already has gone 15 full days without a breakdown since the last repair was completed. how does the expected number of full days here- after that the machine will remain operational before the next breakdown compare with the corresponding result from part (b) when the repair had just been completed? explain A) 142B) 146C) 138D) 132E) 144 Roger and Rohan are partners of R&R Biscuit Company. Given below is details of items that appeared in their current account for the year ended December 31, 2019: Can someone PLEASE help me ASAP its due today!! I will give brainliest if its all done correctly. Answer part A, B, and C for brainliest!! . the contract states that the purchase is conditional upon him securing an acceptable mortgage by a certain date. this is an example of What is the role of the primary standard in an acid-base titration? It serves as an unknown concentration that is determined using the secondary standard. It is used to find the stoichiometry of the titration reaction. O It is used to determine the unknown concentration of an acid or base that is more difficult to measure. It changes color to determine the equivalence point of a titration. The mineral sample in this graduated cylinder has a mass of30.4 g. When placed in the cylinder, the water level changed from 60 mL to 64 mL. Calculatethe density 9. What's a possible symptom of overnutrition?O A. Clear skinB. Healthy heartC. Weight lossO D. Dizziness A bike rental company rents out scooters for $8.50 per day and bikes for $15.20 per day. On Tuesday, they rent out a combined total of 8 scooters and bikes. They make $101.50 from the rentals. how many scooters and bikes does the bike rental company rent on Tuesday? A cart travels with a constant nonzero acceleration along a straight line. Which graph best represents the relationship between the acceleration the cart travels and time of travel? the general process in which solid particles form from a gas is called ____________.a.Acceretionb.Solifluctionc.Sublimationd.condensation malware that records any keys pressed on the keyboard; often used to steal usernames, passwords, and/or financial information is called? 1+1 I dont know Im in 7 th grade What important inference can we draw from the coupling of slow neural waves and haemodynamic and CSF flow during sleep? In general what did farmers and factory owners in the South use to transport their goods? Which of the following statements about perfect competition is correct?. Which of the following bulk properties of substances are affected by intermolecular forces? Select all that apply.A. ductilityB. boiling pointC. volatilityD. malleabilityE. melting point jake, who was leasing a house, retained possession even after his right to possess had terminated. jake has a(n) .