Let the functions f : R → R, g : R → R and h : R → R be defined by
f (x) = 1/(x - 5) , g (x) = 3 x + 6, h (x) = cos (x + 1).

Find
(a) The domain and range of f.
(b) The composite functions (fog)(x), (foh)(x) and (gof)(x).
(c) g^(-1) (x)
(d) The domain of (f + g)(x):

Answer:

362

Step-by-step explanation:

15xy=5430...therefore 5430divided by 15 is 362...so 362x15 their product is 5430

Answer:

x²-9=x²-3²=(x+3)(x-3)

Step-by-step explanation:

use formula

a²-b²=(a+b)(a-b)

If segment BD is congruent to segment BC, and BD = 4x - 18, BC = x + 3, and AC = 34, then AB = 31/x.

Let the equation be AB + BC = AC

substitute the values in the above equation, we get

AB + x + 3 = 34

simplifying the value of x,

Subtract A B from both sides AB + x + 3 - AB = 34 - A B

x + 3 = 34 - AB

Subtract 3 from both sides,

x + 3 - 3 = 34 - AB - 3

x = -AB + 31

Plug in this value of x into the line segments to find BC and AC.

Where, BC = x + 3

substitute the value of x in the above equation, we get

BC = [-AB + 31 ] + 3

BC = -AB + 34

Then, AB + BC = AC

x = -AB + 31

AB = 31/x

Hence, If segment BD is congruent to segment BC, and BD = 4x - 18,

BC = x + 3, and AC = 34, then AB = 31/x.

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Answer: A. 2x+2y

Step-by-step explanation:

Answer:

its d

Step-by-step explanation:

Answer:

2.5

Step-by-step explanation:

I'm sorry I don't know how to explain it but I'm pretty sure the answer is a. 2.5

===================================================

Work Shown:

Let's find out how many smaller cubes are needed to go along the 2 & 2/3 inch side length of the bigger box.

First convert to an improper fraction

2 & 2/3 = 2 + 2/3 = 6/3 + 2/3 = 8/3

Divide this over the side length of the small cube to get

8/3 divided by 1/3 = (8/3)*(3/1) = 24/3 = 8

So we need exactly 8 small cubes along the 2 & 2/3 inch side length.

Let A = 8 so we can use this later.

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

Repeat the same steps for the 3 & 1/3 inch side length

3 & 1/3 = 3 + 1/3 = 9/3 + 1/3 = 10/3

10/3 divided by 1/3 = (10/3)*(3/1) = 30/3 = 10

We need 10 cubes along the 3 & 1/3 inch side length.

Let B = 10.

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

Repeat for the 2 & 1/3 inch side length

2 & 1/3 = 2 + 1/3 = 6 + 1/3 = 7/3

7/3 divided by 1/3 = (7/3)*(3/1) = 21/3 = 7

We need 7 cubes along the 2 & 1/3 inch side length

Let C = 7

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

Multiply out the values of A,B,C to get

A*B*C = 8*10*7 = 560

This means we need 560 cubes that are each 1/3 of an inch along the the side to fill up a box that has dimensions of 2 & 2/3 inches by 3 & 1/3 inches by 2 & 1/3 inches.

Answer:

m= -3

b= 4

Step-by-step explanation:

whatever number has x next to it is always slope, that is how you find slope in a equation. To find y-intercept (b) you can just use the other number that doesn't have x to it.

Hope this helps!!!

Answer:

Step-by-step explanation:

a2 = -2

a + d  =  -2

a + 6d = 7

-5d  =  -9

d  =  9/5

a = -19/5

an  =  a + ( n-1 ) d

an =  -19/5 + ( n-1 ) 9/5

Based on the two-way table, there seems to be a relationship between the type of books Julia's friends like best and the number of books they have read this month, A. Yes, because those who like fiction read one book at a rate four times that of those who read non-fiction books.

A two-way table, also called a contingency table, is a statistical table that shows the observed frequency for two variables.

The rows of a two-way table indicate one category and the columns indicate the other category.

For instance, based on the two-way table, one can observe that 80% of Julia's friends prefer fiction while 20% prefer non-fiction.

Among those who read 1 book this month, 80% read fiction against 20% who read non-fiction.  Similarly, among those who read 2 books this month, the same 80% read fiction against 20% who read non-fiction.

The number of students who prefer fiction = 60

The number of students who prefer non-fiction = 15

The number of fiction-preferring students who read 1 book this month = 40, which is 80% of the total (40/50 x 100).

The number of fiction-preferring students who read 2 books this month = 20, which is 80% of the total (20/25 x 100).

Thus, we can conclude that Option A is correct.

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The Two-way Table:

                                       Read 1 book         Read 2 books     Total

Prefer fiction books               40                            20              60

Prefer non-fiction books        10                              5               15

Total                                       50                            25              75

Equivalent to 5(x+7)+7(x+5) is expression 12x + 70 .

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Given expression

5(x+7)+7(x+5)

Using distributive property

= 5x + 35 + 7x + 35

Adding like terms

= 12x + 70

Hence, expression 12x + 70 is  equivalent  to 5(x+7)+7(x+5).

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The statement about using the line of best fit for the given scatter plot is; False

When we have a scatter plot, it is always best to look for the line of best fit or curve of best fit depending on the nature of the variation of the plotted points.

Now, from the scatter plot image attached, we can see that the points are already looking like a curved plot form and so what we will need her will be a curve of best fit and not a line of best fit plot and as such the statement about using a line of best fit plot is false.

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Answer:

1. a

2. 422

3. 156.06

Step-by-step explanation:

The probability that she succeeds at 10 or more free throws in a sample of 12 free throws is 4/5.

What is probability?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

Here, we have

The probability that Shruti succeeds at any given free throw is 80%. She was curious how many free throws she can expect to succeed in a sample of 12 Free-throws. She simulated 25 samples of 12 free throws where each free throw had a 0.8 probability of being a success.

The probability that she succeds at 10 or more free-throws in a sample of 12 free-throws is estimated from  the simulation with 25 samples of 12 free-throws:

=  number of times she succeded at 10 or more free-thrown /number of trials

The number of times she succeeded at 10 or more free throws is equal to the sum of the number of times she succeeded at 10 + the number of times she succeeded at 11 + the number of times she succeeded and 12 free throws.

9 + 9 + 2 = 20

The number of trials is 25.

Probability (10 or more successes) = 20/25 = 4/5

Hence, the probability that she succeeds at 10 or more free throws in a sample of 12 free throws is 4/5.

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We have sufficient evidence to conclude that the over all percentages of 3 categories are not same.

The percentage refers to a specific percentage out of a hundred. It is a fraction with the denominator 100, and the sign for it is 1%.

The Latin word per centum, which means "hundred" or "by the hundred," is the source of the word "percent." The Italian phrase per cento, which means "for a hundred," gradually shrank to become the symbol for "percent," which is now used globally. It finally vanished totally. The word "per" was frequently shortened to "p." The contemporary "%" symbol was created by condensing the "cento" to two circles divided by a horizontal line.

Category    Observed(\(O_{i}\))          Expected(\(E_{i}\))              (\(O_{i}\)-\(E_{i}\))²/\(E_{i}\)

A or B           100                           120                          3.333

C                   130                           105                          5.9524

D or F             70                            75                            0.056

Total               300                        300                         9.3417

H₀:over percentages are same at UC Davis and at SSC

H₁:They are not same

Test statistic

X²=∑  (\(O_{i}\)-\(E_{i}\))²/\(E_{i}\)

=9.3417

P-value=P(X²(n-1)>9.3417)

=0.0094

Here we can see that the P-value is very low(<0.05 and <0.01)

So, we reject the null hypothesis H₀.

Therefore, we have sufficient evidence to conclude that the over all percentages of 3 categories are not same.

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Answer:

108

Step-by-step explanation:

3(6*3*2)

Answer:

L x W x H is the formula to solving this problem.

It looks like 6 is the length, 3 is the width and 2 is the height!

6 x 3 x 2 = 36

BUT WAIT!

It seems like the 2 is on one of the tissues, if it isn't 36, the other answer is definitely something else...

2 + 2 + 2 = 6

6 x 3 x 6 = 108!

_ _ _ _ _

The answers could either be 36 or 108!

the asymptote is y = 2 and the y - intercept is (0,5)

An asymptote is a line that the graph of a function approaches as either x or y go to positive or negative infinity. There are three types of asymptotes: vertical, horizontal and oblique. That is, as approaches from either the positive or negative side, the function approaches positive or negative infinity.

According to the question

The function reaches the y-axis at the point (0,5).

The asymptote is the line that the function follows but never quite reaches. In this case, the function follows the path of y = 2. However, it never exactly fits the line.

The y-intercept is (0,5) and the asymptote is y = 2. The answer, then, is B.

Hence, the asymptote is y = 2 and the y - intercept is (0,5)

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Using proportions, it is found that you will need to save $54.89 more each month in order to reach your goal.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

The amount you will need is:

75 x 17 = $1,275.

After 10 months you have only saved $524, hence the amount you will have to save is:

1275 - 524 = 751.

In 7 months, hence the monthly amount is:

751/7 = $107.29.

The difference is:

107.29 - (524/10) = $54.89.

You will need to save $54.89 more each month in order to reach your goal.

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To prove that the expression (36^5−6^9)(38^9−38^8) is divisible by 30, we need to show that it is divisible by both 2 and 3.

First, we can factor out a 6^9 from the first term:

(36^5−6^9)(38^9−38^8) = 6^9(6^10-36^5)(38^9-38^8)

Notice that 6^10 can be written as (2*3)^10, which is clearly divisible by both 2 and 3. Also, 36 is divisible by 3, so 36^5 is divisible by 3^5. Thus, we can write:

6^9(6^10-36^5) = 6^9(2^10*3^10 - 3^5*2^10) = 6^9*2^10*(3^10 - 3^5)

Since 2^10 is divisible by 2, and 3^10 - 3^5 is clearly divisible by 3, the whole expression is divisible by both 2 and 3, and therefore divisible by 30.

To prove that the expression is divisible by 37, we can use Fermat's Little Theorem. Fermat's Little Theorem states that if p is a prime number and a is any positive integer not divisible by p, then a^(p-1) is congruent to 1 modulo p, which can be written as a^(p-1) ≡ 1 (mod p).

In this case, p = 37, and 36 is not divisible by 37. Therefore, by Fermat's Little Theorem:

36^(37-1) ≡ 1 (mod 37)

Simplifying the exponent gives:

36^36 ≡ 1 (mod 37)

Similarly, 38 is not divisible by 37, so:

38^(37-1) ≡ 1 (mod 37)

Simplifying the exponent gives:

38^36 ≡ 1 (mod 37)

Now we can use these congruences to simplify our expression:

(36^5−6^9)(38^9−38^8) ≡ (-6^9)(-1) ≡ 6^9 (mod 37)

We know that 6^9 is divisible by 3, so we can write:

6^9 = 2^9*3^9

Since 2 and 37 are relatively prime, we can use Euler's Totient Theorem to simplify 2^9 (mod 37):

2^φ(37) ≡ 2^36 ≡ 1 (mod 37)

Therefore:

2^9 ≡ 2^9*1 ≡ 2^9*2^36 ≡ 2^(9+36) ≡ 2^45 (mod 37)

Now we can simplify our expression further:

6^9 ≡ 2^45*3^9 ≡ (2^5)^9*3^9 ≡ 32^9*3^9 (mod 37)

Notice that 32 is congruent to -5 modulo 37, since 32+5 = 37. Therefore:

32^9 ≡ (-5)^9 ≡ -5^9 ≡ -1953125 ≡ 2 (mod 37)

So:

6^9 ≡ 2*3^9 ≡ 2*19683 ≡ 39366 ≡ 0 (mod 37)

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Answer: A) Juan buys 3 packs of markers. Each pack has 6 markers. How many markers does Juan buy in all?

Answer: A) Juan buys 3 packs of markers. Each pack has 6 markers. How many markers does Juan buy in all?

Answer:

Step-by-step explanation:

he has 1/4 remaining as he has only used 3/4

Designing a roller coaster that lasts 4 minutes, starts at 250 feet in the air, and dives into a tunnel at least once requires polynomial design, which is explained .

The company wants the zeros to have a minimum of one real root of multiplicity one and a maximum of one real root of multiplicity two, as well. Following that, let's begin by drawing a rough sketch of a roller coaster that satisfies the conditions provided:img

Now, as per the amusement park's new guidelines, the zeroes of the polynomial must have at most one real root of multiplicity two and at least one real root of multiplicity one. The polynomial will have all of the original requirements and the new requirements. The new polynomial, P(x), will have the necessary zeroes.

1. P(x) in factored form: Let (x−a) be the real root of multiplicity one, and (x−b)2 be the real root of multiplicity two. Then, P(x)=(x−a)(x−b)2.

2. P(x) in standard form: As the standard form of the quadratic equation is y = ax2 + bx + c, then P(x)= a(x−a)(x−b)2.

3. End behavior of P(x) and provide a real-world explanation: P(x) increases without bound as x increases or decreases without bound. Because the ride is designed to have a steep upward climb and drop, this is expected.

4. Number of turning points in P(x) and mathematical justification: The curve can have at most two turning points. When x=a, the curve shifts direction from increasing to decreasing. When x=b, the curve shifts direction from decreasing to increasing. When x=b, the slope is zero; hence, the curve must flatten out at this point. The slope at the turning points must be zero.

5. Part of P(x) that guarantees criteria (i) is satisfied: The term a guarantees criteria (i) is satisfied. It determines the maximum height of the coaster.

6. Part of P(x) that guarantees criteria (ii) is satisfied: The zero of multiplicity two guarantees criteria (ii) is satisfied. It directs the roller coaster from a steep downward slope and upwards again, with the subsequent upslope being less steep.

7. Part of P(x) that guarantees criteria (iii) is satisfied: The tunnel is made possible by the zero of multiplicity one, which leads the roller coaster through the ground.

8. Real-world explanation for the real root of multiplicity two: The root of multiplicity two occurs when the roller coaster begins its steep downward slope after reaching its maximum height. When the coaster reaches the lowest point of the curve, it starts to climb again, albeit at a less steep slope.

9. Real-world explanation for the real root of multiplicity one: The root of multiplicity one dictates the steepness of the first and last curves of the roller coaster. It also guides the roller coaster down into a tunnel that goes beneath the ground.

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In order for the system of equations to be a consistent system, the value of k must be equal to -4.

To determine the value of k that makes the system of equations consistent, we can use the method of elimination or substitution. Let's use the method of elimination.

First, we can multiply the first equation by 5, the second equation by -1, and the third equation by 2 to make the coefficients of x in the three equations cancel each other out when added together.

The modified system of equations becomes:

5x - 10y + 20z = 20

5x - 9y + 22z = 16

-4x + 6y - 20z = 2k

Now, let's subtract the first equation from the second equation:

(5x - 9y + 22z) - (5x - 10y + 20z) = 16 - 20

y + 2z = -4

Next, let's add this equation to the third equation:

(-4x + 6y - 20z) + (y + 2z) = 2k - 4

-4x + 7y - 18z = 2k - 4

For the system of equations to be consistent, there must be no contradictions or inconsistencies. This means that the equations must be linearly dependent, and the last equation must be a multiple of the second equation.

Comparing the last equation (-4x + 7y - 18z = 2k - 4) with the second equation (y + 2z = -4), we can see that the two equations will be dependent and consistent if 2k - 4 is equal to 0.

2k - 4 = 0

2k = 4

k = 2

Therefore, in order for the system of equations to be a consistent system, the value of k must be equal to -4.

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Answer:

I don't know but I can help you understand it.

Step-by-step explanation:

First find the the answer to the problem and then try to compare all of them to each other and choose the one that makes the most sense.

Answer:

Step-by-step explanation:

Equation: $4 = 0.2x + $1.60

1. Subtract $1.60 from both sides to get $2.4 = 0.2x

2. Divide both sides by 0.2 to get the value of x. 12 = x.

ANSWER: You need to buy 12 chicken wings at restaurant Z for the cost to be the same. Hope this helped

It has been determined that the continuous random variable X has a variance of 0.2500.

We need to utilise the formula Var[X] = E[X2] - (E[X])2 in order to compute the variance of X, where E[X] stands for the expected value of X. In this particular instance, we have already arrived at the conclusion that E[X] equals 1, as was decided in the inquiry that came before this one.

In order to get E[X2], we have to integrate x2 multiplied by the probability density function (pdf) of X throughout its range. This allows us to calculate E[X2]. In this particular scenario, the range is between 0 and 1. The integral of 3x2 from 0 to 1 is x3 evaluated at 1 and 0, which may be rewritten as 1 since it is simpler.

Therefore, the answer is 1 for E[X2].

When we put these numbers into the calculation for the variance, we get the result that Var[X] = 1 - (1)2 = 0.

The continuous random variable X has a variance of 0.2500 as a result of this.

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Answer:

8.5°

Step-by-step explanation:

25 + (-8)

=25 - 8

=17 ÷ 2

= 8.5°