NO LINKS!!!!
15. Determine whether the statement is true or false. NOT MULTIPLE CHOICE!!
a. The graph of f^-1(x) is a reflection of the graph of f(x) over the line y = x.
b. if f^-1(x) is the inverse of f(x), then f(x) must be always be increasing.
c. The function y = x^2 has an inverse.
d. If a function has a y-intercept, then its inverse must also have a y-intercept.
e. If a function has a y-intercept, then its inverse must have an x-intercept.

Answer:

49. a)  A - C - 1

49. b)  1 - 2R

49. c)  2Q - P

50.  x = 103

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{5cm}\underline{Log laws}\\\\$\log_axy=\log_ax + \log_ay$\\\\$\log_a \left(\dfrac{x}{y}\right)=\log_ax - \log_ay$\\\\$\log_ax^n=n\log_ax$\\\\$\log_ab=c \iff b=a^c$\\\\&\log_aa=1$\\ \end{minipage}}[/tex]

Part a

Given:

[tex]\log_5 9=A[/tex]

[tex]\log_5 6=B[/tex]

[tex]\log_5 11=C[/tex]

[tex]\begin{aligned}\log_5 \dfrac{9}{55}&=\log_5 9 - \log_5 55\\&=\log_5 9 - \log_5 (11 \cdot 5)\\&=\log_5 9 - (\log_5 11 + \log_5 5)\\&=\log_5 9 - \log_5 11 - \log_5 5\\&=A-C-1\\\end{aligned}[/tex]

Part b

Given:

[tex]\log_3 10=R[/tex]

[tex]\log_3 4=S[/tex]

[tex]\log_3 11=T[/tex]

[tex]\begin{aligned}\log_3 \dfrac{3}{100}&=\log_3 3 - \log_3 100\\&=\log_3 3 - \log_3 (10 \cdot 10)\\&=\log_3 3 - \log_3 10^2\\&=\log_3 3 - 2\log_3 10\\&=1-2R\\\end{aligned}[/tex]

Part c

Given:

[tex]\log_3 4=P[/tex]

[tex]\log_3 10=Q[/tex]

[tex]\log_3 7=R[/tex]

[tex]\begin{aligned}\log_3 25&=\log_3 \dfrac{100}{4}\\&=\log_3 100 - \log_3 4\\&=\log_3 (10 \cdot 10) - \log_3 4\\&=\log_3 10^2 - \log_3 4\\&=2 \log_3 10 - \log_3 4\\&=2Q-P\end{aligned}[/tex]

The error was in line 4 of the calculation.  The log law

was not applied correctly.

The correct solution is:

[tex]\begin{aligned}3 \log (x-3) + 1 & = 7\\3 \log (x-3) & = 6\\\log (x-3) & = 2\\x-3&=10^2\\x&=3+10^2\\x&=103\end{aligned}[/tex]

The average of cost computers was $1,915.79​ 35 years ago. The correct answer would be an option (D).

The percentage is defined as a ratio expressed as a fraction of 100.

Let the average computer cost was x 35 years ago.

As per the question, we have

76% of x = $1,456

76% is expressed as 0.76 in decimal form

0.76x = 1,456

x = 1,456/0.76

x = 1,915.7947

Rounded to the nearest cent, and we get

x = 1,915.79

Thus, the average of cost computers was $1,915.79.

Learn more about the percentages here:

brainly.com/question/24159063

#SPJ1

Answer: This is known as Gay-Lussac's Law.

The relationship states that the pressure and volume of a gas are directly proportional at constant temperature. Therefore, if the pressure is increased by 25%, the volume must be decreased by 25% to maintain the constant product of pressure and volume.

The binomial variable with mean 17 transformers and standard deviation √2.55 transformers.

In math standard deviation is defined as a measure of how dispersed the data is in relation to the mean.

Here we have know that the good electrical transformers operate at approximate 85% of the total time and 20 electrical transformers are chosen at random.

Here let us assuming the variable is a binomial variable.

Then we have written it as in the following form,

=> Mean = number of samples * probability

And the value of standard deviation is calculated as

=> Standard Deviation = √mean (1 − probability)

Here we know that the value of mean is calculated as,

=> 85% * 20 = 0.85*20 = 17 transformers

Then the value of Standard deviation is calculated as,

=> √mean * (1 − 0.85)

Apply the values on the formula, then we get,

=> √17 * 0.15 =√2.55 transformers.

Hence the random variable is a binomial variable.

To know more about Standard deviation here.

https://brainly.com/question/16555520

#SPJ4

The value of x that solves the equation is x = 28.10, and there are 4 eggs per batch.

Particularly x is not in that equation, but we can write:

5x = 140.50

To solve for x, we need to divide both sides by 5, then we will get:

5x/5 = 140.50/5

x = 140.50/5

x = 28.10

To find this, we need to take the quotient between the number of eggs and the number of batches, so we will get:

12 eggs.

3 batches.

12/3 = 4

This means that you need 4 eggs per batch.

Laern more about quotients at:

https://brainly.com/question/629998

#SPJ1

The required probability for the given delta airlines is given by :

a. Probability of flight late no more than 5 minutes is 0.25.

b. Probability of flight late more than 10 minutes is 0.5

c. Expected flight time is equal to 130 minutes.

Flight time from Cincinnati to Tampa = 2 hours 5 minutes

Actual time distributed between 2 hours and 2 hours 20 minutes

2 hours = 120 minutes

2 hours 20 minutes = 140 minutes

f(x) =  [tex]\left \{ {{\frac{1}{( 140 - 120)} , 120 \leq x\leq 140\atop {0 , x = 0 }} \right.[/tex]

a. Probability of flight no more than 5 minutes late

[tex]\int_{130}^{125} \frac{1}{20} dx[/tex]

= 1 / 4

= 0.25

b. Probability of flight  more than 10 minutes late

[tex]\int_{135}^{125} \frac{1}{20} dx[/tex]

= 1/2

= 0.5

c. Expected flight time in minutes

= [tex]\int_{140}^{120} \frac{x}{20} dx[/tex]

= 130 minutes

Therefore, the required probability are given by :

a. Probability of flight late no more than 5 minutes is 0.25.

b. Probability of flight late more than 10 minutes is 0.5

c. Expected flight time is equal to 130 minutes.

The above question is incomplete , the complete question is :

Delta Airlines quotes a flight time of 2 hours, 5 minutes for its flights from Cincinnati to Tampa. Suppose we believe that actual flight times are uniformly distributed between 2 hours and 2 hours, 20 minutes.  What is the probability that the flight will be no more than 5 minutes late (to 2 decimals)? What is the probability that the flight will be more than 10 minutes late (to 2 decimals)? What is the expected flight time, in minutes?

Learn more about probability here

brainly.com/question/30034780

#SPJ4

Answer:

Step-by-step explanation:

0.462

Answer:

0.462 :) hope this helps and please put me as brainiest thankyou !!

Step-by-step explanation:

Answer:

Plane B

Step-by-step explanation:

Plane A: 2800/5 = 560 m/h

Plane B: 3885/7 = 555 m/h

Using slope of the graph, The average rate of change in dollars per year for this time period is -220.

You may determine the slope of the line by determining the rise and the run using two of the line's points. The rise and the run are terms used to describe changes in height between two points. Rise divided by Run gives you the slope. Rise/run on a slope Rise or run is a slope.

We have coordinates that represent the given information,

Let x = number of year,

Y = Change in income,

So, Our coordinates become = (0, 31560) and (13, 28700)

The average rate of change is defined as slope of the graph

Slope of graph = y2 - y1 / x2 - x1

⇒ 28700 - 31560 / 13 - 0

⇒ -2860 / 13

⇒ - 220

The value of slope is negative, which indicates depreciation.

To learn more about slope of graph from given link

https://brainly.com/question/28135850

#SPJ1

Answer:

D. 4x² - x / x² - x - 2

Step-by-step explanation:
First cross multiply then sum the results:

cross:

x(x + 2) = x² + 2x

3x(x - 1) = 3x² - 3x

sum the results of the cross:

x² + 2x + 3x² - 3x

4x² - x (this goes at the top)

Then multiply the bottom:

(x - 1 )(x + 2)

x² + 2x - x - 2

x² - x - 2 (this stays at the bottom)

Fraction ends up like:

4x² - x / x² - x - 2

The variation in the values is due to random error. Hence, it can be reduced by taking more observations to estimate the measure of the mass of the ring.

One way to minimize experimental error in this situation is to take multiple measurements and use the average of those measurements as the final value. This helps to account for any small fluctuations or inaccuracies in the individual measurements.

Also, it is important to ensure that the balance is properly calibrated and that the ring is placed on the balance in the same way each time.

Other ways to minimize experimental error include using a more precise measuring instrument, such as a digital scale, and ensuring that the lab environment is controlled and stable (i.e. no drafts or vibrations that could affect the measurements).

Read more about Errors:

brainly.com/question/28008941

#SPJ4

The complete question is -

You measure the mass of a ring to be used in your experiment three times using the same balance and get slightly different values: 17.46 g, 17.42 g, and 17.44 g. How can you minimize experimental error?

The amount that he pays for the cooler alone without the tax will be $7.37.

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

His total bill, with tax, was $7.95. He paid 6 percent sales tax.

Let 'x' be the total bill without the sales tax. Then the equation is given as,

107.95% of x = $7.95

1.0795x = $7.95

x = $7.37

The amount that he pays for the cooler alone without the tax will be $7.37.

More about the percentage link is given below.

https://brainly.com/question/8011401

#SPJ1

Answer:

11

Step-by-step explanation:

Now:

Shawn: 23

Yu Yan: 15

x years ago:

Shawn: 23 - x

Yu Yan: 15 - x

x years ago, Shawn was 3 times as old as Yu Yan.

23 - x = 3(15 - x)

23 - x = 45 - 3x

2x = 22

x = 11

Check:

11 years ago Shaw was 23 - 11 = 12, and Yu Yan was 15 - 11 = 4.

12 is indded 3 times 4.

Answer: 11

The scale factor for the dilation in this problem is given as follows:

2.

A dilation happens when the coordinates of the vertices of an image are multiplied by the scale factor, changing the side lengths of a figure.

The equivalent side lengths in this problem are given as follows:

The dilated triangle is triangle DAB, hence the scale factor is obtained as follows:

k = 8/4 = 2.

(that is, the side lengths of triangle DEF were multiplied by 2 to generate triangle DAB).

More can be learned about dilation at brainly.com/question/3457976

#SPJ1

Answer: Midpoints (-3/2)

Step-by-step explanation:

Midpoint formula is (x1+x2)/2 , (y1+y2)/2

Plugin x values and solve
(-1 +-5)/2 = -3

Plugin y values and solve
(-5+9)/2 = 2

The midpoint is -3/2

I hope this helped you :D

Totally correct about the mentioned before is 2.5%. This is because the z-score for this situation is (494 - 686) / 96 = -2. According to the Empirical Rule, approximately 95% of observations will fall within 2 standard deviations of the mean. In this case, the question is asking for the percent of students who scored less than 494, which is below 2 standard deviations, so the answer is 2.5%.

The Empirical Rule states that for a normal distribution, approximately 68% of the data will fall within one standard deviation of the mean, approximately 95% of the data will fall within two standard deviations of the mean, and approximately 99.7% of the data would get fall within 3 standard deviations of the mean. So if we know the mean and standard deviation of a normal distribution, we can use this rule to estimate the percentage of data that falls within a certain range.

In this specific question, the mean of Math Level 2 SAT subject test score was 686 with a standard deviation of 96. We were asked to find the percent of students who scored less than 494. To find this we first calculated the z-score which is (494 - 686) / 96 = -2.

Since the z-score is -2 it means that it's 2 standard deviation below the mean, and according to the Empirical rule 95% of observations will fall within 2 standard deviations of mean. This means that 2.5% of observations will fall above 2 standard deviations and 2.5% of observations will fall below 2 standard deviations. So the answer is 2.5%.

Learn more about SAT Math Level 2 Score here:

https://brainly.com/question/14274404

#SPJ4

The solution to an equation is 10.Solving an equation refers to the process of determining its solution.

Make the available

14to obtain the desired amount:

x – 6 + x = 14

Put similar phrases together to get:

2x – 6 = 14

Adding 6 to both sides yields:

2x = 20

x = 10.

The complete question is,

1 4 (4x 24) + x = 14 must be solved.

By dividing the 1 by 4, you can obtain:

Put similar phrases together to get:

Adding 6 to both sides yields:

x =

Consequently, is the necessary response.

To learn more about "equation" can be found here:

https://brainly.com/question/2972832

#SPJ1

Options

Answer: Samantha bought 7 tickets for a concert

Step-by-step explanation:

$11.00 + $9.00 + $8.00 = 28

$196 / 28 = 7

All the equations are matched with the line graph are given below.

And the letter code is AEBG.

In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way.

The relationships between two or more items are frequently represented by the points on a graph.

Given:

All the equations are matched with the line graph:

A: y = 3x + 1 → Line 1

B: y = -2x + 2 → Line 3

G: y = -1/2x + 2 → Line 4

E : y = x+ 4 → Line 2

The letter code is AEBG.

Therefore, the letter code is AEBG.

To learn more about the line graph;

https://brainly.com/question/23680294

#SPJ1

The following systems are :

a) Non-linear

b) Linear

c) Linear

d) Non-linear

e) Linear

a) Non-linear: The equation is non-linear because it contains a product of two variables (x1 - 1) and (x2 + 1). A linear equation only contains variables and their coefficients, not products of variables.

b) Linear: The equation is linear because it only contains variables and their coefficients.

c) Linear: The equation is linear because it only contains variables and their coefficients and the sum of variables.

d) Non-linear: The equation is non-linear because it contains the sine and cosine functions, which are non-linear.

e) Linear: The equation is linear because it only contains variables raised to a constant power (e raised to a constant power) and their coefficients.

To learn more about Linear here:

https://brainly.com/question/20286983

#SPJ4

The measure of diagonal in a rectangular pool is 13.9 meters. Therefore, option A is the correct answer.

Given that, a rectangular pool is 7 meters wide and 12 meters long.

What is the Pythagoras theorem?

The Pythagoras theorem which is also referred to as the Pythagorean theorem explains the relationship between the three sides of a right-angled triangle. According to the Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides of a triangle.

We know that, measure of each angle in a rectangle is 90°.

Let the length of diagonal of rectangular pool be x

So using Pythagoras theorem, we get

x²=12²+7²

⇒ x²=144+49

⇒ x²=193

⇒ x=√193

⇒ x=13.89

≈13.9 meters

The measure of diagonal in a rectangular pool is 13.9 meters. Therefore, option A is the correct answer.

The coordinates of the fourth vertex of the parallelogram are (11, -7).

What is a parallelogram?

A parallelogram is a quadrilateral with opposite sides that are parallel to each other. The opposite sides of a parallelogram are also equal in length.

The fourth vertex of a parallelogram can be determined by finding the vector that connects one vertex of the parallelogram to the opposite vertex, and then adding that vector to the third vertex given in the problem.

The vector that connects the first vertex (-3, 1) to the third vertex (5, -5) is (8, -6). To find the fourth vertex, we add this vector to the second vertex (3, -1) :

(3,-1) + (8, -6) = (11, -7)

Hence, the coordinates of the fourth vertex of the parallelogram are (11, -7).

To learn more about the parallelogram, visit:

https://brainly.com/question/970600

#SPJ1

Answer:

w=7/9

Step-by-step explanation:

6=7/w-3

Move the terms

6=7/w-3, w [tex]\neq[/tex] 0

Calculate

-7/w=-3-6

Multiply both sides

-7/w=-9

Swap the sides

7=9w

Divide both sides

9w=7

w=7/9, w [tex]\neq[/tex] 0

w=7/9

The results of operations between functions:

Case A: (f + g) (x) = x / (x + 9) + x³

Case B: (f - g) (x) = x / (x + 9) - x³

Case C: (f · g) (x) = x⁴ / (x + 9)

Case D: (f / g) (x) = 1 / [x² · (x + 9)]

Function (f / g) (x) has the following domain: x ∈ R - {- 9, 0}.

According to function theory, we can obtain a function with more complexity by operations between two functions, the most common operations are listed below:

Now we proceed to determine the resulting function:

Case A:

(f + g) (x) = f(x) + g(x)

(f + g) (x) = x / (x + 9) + x³

Case B:

(f - g) (x) = f(x) - g(x)

(f - g) (x) = x / (x + 9) - x³

Case C:

(f · g) (x) = f (x) · g (x)

(f · g) (x) = [x / (x + 9)] · x³

(f · g) (x) = x⁴ / (x + 9)

Case D:

(f / g) (x) = f(x) / g(x)

(f / g) (x) = [x / (x + 9)] / x³

(f / g) (x) = 1 / [x² · (x + 9)]

The domain of (f / g) (x) is the set of all values of x-values such that the function exists. In this case, we must determine the values of the denominator of (f / g) (x) such that it is not equal to zero.

x² · (x + 9) = 0

x = 0 or x = - 9

The domain of (f / g) (x) is: x ∈ R - {- 9, 0}.

To learn more on operations between functions: https://brainly.com/question/27915566

#SPJ1

The correct alternative is -

Given is the graph of the function.

The correct alternatives are -

Therefore, the correct alternative is -

To solve more questions on graphs, visit the link below-

brainly.com/question/1041084

#SPJ1

If the ratio of dolphins to penguins is 2:5, then for every 2 dolphins, there are 5 penguins. If there are 30 penguins, you can use this ratio to find out how many dolphins there are. To find out how many dolphins there are, you can set up a proportion:

(number of dolphins) / (number of penguins) = (2) / (5)

You know that the number of penguins is 30, so you can substitute that in and solve for the number of dolphins:

(number of dolphins) / 30 = 2 / 5

Multiply both sides by 30 to solve for the number of dolphins:

number of dolphins = (2/5) * 30 = 6

So, if there are 30 penguins, there would be 6 dolphins.

The exponential equation that represents the relationship between the air pressure and the elevation above the Earth's surface is

y = 14.7 x 0.827^x

The air pressure at the top of Mount Everest, elevation 29,000 feet is approximately 1.931 psi

To write an exponential equation for the relationship between the air pressure and the elevation above the Earth's surface, we can use the form y = a x b^x,

where y is the air pressure,

x is the elevation,

and a and b are constants.

We can use the data given in the problem to find the values of a and b.

Let y = air pressure (psi)

x = elevation (feet)

We know that at sea level (x = 0), y = 14.7 psi

At Denver, Colorado, elevation 5280 feet, y = 12.15 psi

We can use these two points to find the values of a and b in the equation y = a x b^x

12.15 = 14.7 x b^5280

b = (12.15/14.7)^(1/5280)

b = 0.827

a = 14.7

The exponential equation that represents the relationship between the air pressure and the elevation above the Earth's surface is

y = 14.7 x 0.827^x

b.) To find the air pressure at the top of Mount Everest, elevation 29,000 feet, we can substitute that value for x into the exponential equation.

y = 14.7 x  0.827^29000

y = 1.931 psi

The air pressure at the top of Mount Everest, elevation 29,000 feet is approximately 1.931 psi. It's worth noting that this is a very low air pressure and the human body is not able to survive with such low pressure without proper equipment.

Learn more about Finding exponential equation:https://brainly.com/question/29264976

#SPJ1

The glide reflection that maps triangle ABC into triangle A'B'C' is given as follows:

Shift right of 7 units and reflection over the x-axis.

The glide reflection is a combination of a reflection with a translation.

The vertices of the original triangle are given as follows:

A(-3,-2), B(-6,-5) and C(-1,-4).

The vertices of the reflected triangle are given as follows:

A'(4,2), B'(1,5) and C'(6,4).

Hence the composite rule is given as follows:

(x,y) -> (x + 7, -y).

Meaning that the glide reflection is defined as follows:

More can be learned about glide reflections at brainly.com/question/5612016

#SPJ1