What is the amplitude of the sinusoidal function?

Answer:

[tex]f \left( g \left( f \left( 1 \right) \right) \right)=45[/tex]

[tex]g \left( f \left( g \left( 0 \right) \right) \right)=3[/tex]

We had to use the equation on the first problem as the graph does not show the value of function f(x) when x = -6.

Step-by-step explanation:

When calculating composite functions, work from the inside out.

Given composite function:

[tex]f \left( g \left( f \left( 1 \right) \right) \right)[/tex]

First use the graph to find f(1):

[tex]\implies f \left( g \left( f \left( 1 \right) \right) \right)= f \left( g \left(-4\right)\right)[/tex]

Now use the graph to find g(-4):

[tex]\implies f \left( g \left(-4\right)\right)=f(-6)[/tex]

As the graph does not show the value for f(x) when x = -6, we need to use the equation:

[tex]\implies f(-6)=(-6)^2-2(-6)-3=45[/tex]

Therefore:

[tex]f \left( g \left( f \left( 1 \right) \right) \right)=45[/tex]

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Given composite function:

[tex]g \left( f \left( g \left( 0 \right) \right) \right)[/tex]

First use the graph to find g(0):

[tex]\implies g \left( f \left( g \left( 0 \right) \right) \right)=g \left( f \left( -2 \right) \right)[/tex]

Now use the graph to find f(-2)

[tex]\implies g \left( f \left( -2 \right) \right)=g \left(5 \right)[/tex]

Finally, use the graph to find g(5):

Therefore:

[tex]g \left( f \left( g \left( 0 \right) \right) \right)=3[/tex]

We had to use the equation on the first problem as the graph does not show the value of function f(x) when x = -6.

Answer:

Just find the LCM of all the days.

LCM of 4,5 and 12 is 60

Therefore, u will have to do all the activities again after 60 days.

Answer:

The domain of a function is the set of all input values (x-values) for which the function produces a valid output (y-value). In the case of the function H(x) = x+2/x^2+4x+4, we need to find the values of x for which the denominator x^2+4x+4 is not equal to zero.

x^2+4x+4 = 0

(x+2)^2 = 0

The denominator is always non-zero as the square of any real number is always positive. Therefore, the function H(x) = x+2/x^2+4x+4 is defined for all real values of x. Therefore, the function H(x) does not have any values that are not in its domain.

Step-by-step explanation:

Answer:

P = 5c + 11 , c = 3

Step-by-step explanation:

(a)

the perimeter P) is the sum of the sides.

Note that the 2 sides with a ' dash' through them are congruent

summing the 4 sides

P = c + 5 + 3c - 2 + 10 - 2c + 3c - 2 ( collect like terms )

  = 5c + 11

(b)

equate the expression for P from (a) to 26

5c + 11 = 26 ( subtract 11 from both sides )

5c = 15 ( divide both sides by 5 )

c = 3

Answer:2200 seats per minute

Step-by-step explanation:

draw a line from 6 minutes upwards till your line and the line on the graph meet then where the line meets draw another line going across(left)

Read across (left side) and the number will be your answer

Answer:

Step-by-step explanation:

Ad and BC because they are 2 lines going in the same place , they are the same

The profit from Lube for Store A would be = $8.31.

Unit profit can be obtained by subtracting the cost of the product from the selling price.

Data and calculations:

Selling price for oil change = $275

Percentage of total oil revenue = 39.1%

Cost of oil per gallon = $21.25

Selling price per gallon = $29.56 ($21.25 x $1,391)

Total income = $8.31 ($29.56 - $21.25)

Therefore, the profit from Lube for Shop A would be= $8.31.

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Complete question:

Shop A charges $275.00 for an oil change and has a gross oil profit percent of 39.1% for its total oil gross profit %. Shop B charges $275.00 for an oil change and has a gross oil profit percent of 28.4% for its total oil gross profit %. Both shops pay $21.25 per gallon of oil. What is the Profit per Lube for Shop A?

The two triangles below show the property of similarity.

The first property is the Side.

The side PN is similar to the side DG.

The second property his angle.

∠PNK = ∠DGK = 90°

The third property would be side as well.

Side NK is similar to the side GK.

Thus, the two triangles are similar.

Similarity is the mathematical property of triangles, wherein two triangles are called similar if they have either two congruent angles and one similar side, or two similar sides in ratio with one another and a congruent angle.

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Team Tackle's score was 28 points. And team Sack's score was 9 points.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

During the 2005 football season, Team Tackle beat Team Sack by 19 points. If their combined scores totaled 37.

Let 'x' be the Tackle's score and 'y' be the Sack's score. Then the equations are given as,

x + y = 37        ...1

x = y + 19        ...2

From equations 1 and 2, then we have

y + 19 + y = 37

2y = 18

y = 9

Then the value of 'x' is given as,

x = 9 + 19

x = 28

Team Tackle's score was 28 points. And team Sack's score was 9 points.

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Answer:

93

Step-by-step explanation:

the mode is the value in the data set that occurs most often.

in this case that is 93 , so

mode = 93

Answer:

93

Step-by-step explanation:

the number which has higher frequency is the mode. here 93 comes 2 times. thus, 93 is the mode.

The expression 8h + (-7.7d) -14 +5d - 3.3h can be simplified as

4.7h - 2.7d - 14

A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power (1). In other words, none of the exponents can be greater than 1.

For example, x² is a variable raised to the second power, but x is a variable raised to the first power.

5 is an example of a constant.

8h + (-7.7d) -14 +5d - 3.3h

Taking like terms

8h - 3.3h + 5d - 7.7d - 14

4.7h - 2.7d - 14

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The table is not linear.

Answer:

Step-by-step explanation:

To convert minutes to hours, we divide by 60, since there are 60 minutes in an hour.

So 4 hours is equal to 4 * 60 = 240 minutes

Charise can pick 1/3 pound of berries in 15 minutes. This is her unit rate. To find out how many pounds of berries she can pick in 4 hours, we need to multiply this unit rate by the number of 15-minute intervals in 4 hours.

240 minutes / 15 minutes = 16 (four-hour intervals)

So the amount of berries Charise can pick in 4 hours is:

1/3 pound/15 minutes * 240 minutes = (1/3) * 16 = 16/3 = 5.333 pounds of berries.

Answer:

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

Charise can pick 1/3 pound of berries in 15 minutes.

There are 4 of 15 minutes in an hour and we need to calculate it for 4 hours.

She picked:

By using the fact that the sum of the interior angles must be 180°, we wil see that:

x = 110°.

First, remember that the sum of the interior angles of a triangle is alway equal to 180°.

We also can see that the interior angle that is adjacent to x can be written as:

a = 180° - x

Then the sum of the interior angles will give:

30° + 80° + (180° - x) = 180°

30° + 80° - x = 0

110° - x = 0

110° = x

That is the value of x.

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Answer:

1 cm - 25 miles

4 cm - 25 x 4 = 100 miles

The required distance is 100 miles.

Answer:

1734

Step-by-step explanation:

We can simply solve the volume of the 2 different cubes. The bigger cube's volume is 15*12*8 = 1440. The volume of the small cube is 6*7*(15-4-4)=294.

So the total volume should be 1734

Answer:

1944 cm³

Step-by-step explanation:

Two rectangular parallelepipeds:

Upper: 12 x 7 x 6 = 504 cm³

Lower: 12 x 15 x 8 = 1440 cm³

Total: 504  + 1440 = 1944 cm³

Answer:

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

From the given information we can see:

Use the equation for the sum of the first n terms:

Answer:

[tex]S_7=6554[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{7 cm}\underline{Sum of the first $n$ terms of a geometric series}\\\\$S_n=\dfrac{a(1-r^n)}{1-r}$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\ \phantom{ww}$\bullet$ $r$ is the common ratio.\\\end{minipage}}[/tex]

Given geometric series:

[tex]2-8+32-...+a_n[/tex]

The first term (a) of the sequence is 2:

[tex]\implies a=2[/tex]

To find the common ratio (r), divide consecutive terms:

[tex]\implies r=\dfrac{a_2}{a_1}=\dfrac{-8}{2}=-4[/tex]

To find the sum of the first 7 terms, substitute the found values of a and r into the formula, along with n = 7:

[tex]\implies S_7=\dfrac{2(1-(-4)^7)}{1-(-4)}[/tex]

[tex]\implies S_7=\dfrac{2(1-(-16384))}{5}[/tex]

[tex]\implies S_7=\dfrac{2(16385)}{5}[/tex]

[tex]\implies S_7=\dfrac{32770}{5}[/tex]

[tex]\implies S_7=6554[/tex]

The required simplified value of the given expression is given as 62.96.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Given expression
= 3.04 × 21.5 - 9.12 / 3.8
= 65.36 - 2.4
= 62.96

Thus, the required simplified value of the given expression is given as 62.96.

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The probability that people aged between 34 to 65 have a certain disease is 0.95.

Probability is the chance of occurrence of a certain event out of the total no. of events that can occur in a given context.

Given, A stem-leaf diagram of people of different ages having a certain disease.

The probability that people have a certain disease between 35 and 64 years of age is,

= P(35 - 44) + P(45 - 54) + P(55 - 64).

= 0.14 = 0.39 + 0.42.

= 0.95.

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Gina sold more than twice as many TVs as Ethan, because 19 > (2 * 8)

An equation is an expression composed of variables and numbers linked together by mathematical operations.

Ethan sold exactly eight TVs this quarter.

Ethan TV = 8

Gabriel sold more TVs than Ethan, hence:

Gabriel TV (G) > 8

Gabriel TV > 8

Gina sold exactly three more TVs than Gabriel and Ethan combined

Gina TV = Gabriel TV + 8 + 3

Gina TV > 8 + 8 + 3

Gina TV > 19

Frank sold exactly twice as many TVs as Gina, hence:

Frank TV = 2 * Gina TV

Frank TV > 2 * 19

Frank TV > 38

Gina sold more than twice as many TVs as Ethan.

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Discontinuities are points where the function is undefined. Holes are points where the graph has a break in it. Vertical asymptotes are lines on a graph where the function approaches infinity and horizontal asymptotes are lines on a graph where the function approaches a limit.

The theory used in this question is the theory of rational functions. This theory is used to identify points of discontinuity, holes, vertical asymptotes, and horizontal asymptotes in rational functions.

In the given question,

2. f(x) = x-2/x-4

Points of discontinuity: x = 4

Holes: None

Vertical Asymptote: x = 4

Horizontal Asymptote: None

3. f(x)= 3x-3/x2-1

Points of discontinuity: x = 1

Holes: None

Vertical Asymptote: x = 1

Horizontal Asymptote: y = 0

4. f(x)  = x²+5x+6/x²+6x+9

Points of discontinuity: None

Holes: None

Vertical Asymptote: None

Horizontal Asymptote: y = 1

5. f(x) = (x+3)(x-2)/(x-2)(x+1)

Points of discontinuity: None

Holes: x = -1, x = 2

Vertical Asymptote: x = -1, x = 2

Horizontal Asymptote: y = 1

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Answer: first one is D 15 1/2

second one is B 11 2/8

Third one is C (already had the correct answer)

fourth answer would be A 3 2/12

Step-by-step explanation:

hope this helps

Answer:

795

Step-by-step explanation:

you mutiply 53 x 15 which gives you 795

Answer:

You have to take the 53 and divide it by 15 which gives you 3.53 repeating so than take 3.53 and multiply by 100 and that gives you 353 minutes as you answer

Step-by-step explanation:

Answer: 157.5

Step-by-step explanation:

Answer:

A is an Irregular Polygon

B is Neither a Polygon

C is an Irregular Polygon

D is a Regular Polygon

E is a Regular Polygon

Step-by-step explanation:

[tex]p(x) = 3 {(x + 1)}^{2} - 3[/tex]

Step-by-step explanation:

annual interest = 1650

10

= 165

[tex] \frac{165}{8000} \times 100 = 2.0625\%[/tex]

The fraction will change by 200%.

Let the fraction is = x/y.

If its numerator is decreased by 10% then the new numerator is:

x - 10% of x

= x - 0.10x

= 0.90x

If its denominator is decreased by 70% then the new denominator is:

y - 70% of y

= y - 0.70y

= 0.30y

So the new fraction is = .

So the change in fraction is in percentage is:

So the fraction will change by 200%.

The measure of m<1 is 108 degrees from the provided figure.

A line is an object in geometry that is indefinitely long and has neither breadth nor depth nor curvature. Lines are therefore one-dimensional objects, even if they can exist in spaces with two, three, or more dimensions.

From the diagram, we have the following parameters

m<2 = 72 degrees

Required parameters

The measure of angle m<1

From the figure, the sum of the interior angle is equivalent to 180 degrees, that is:

m<1 + m<2 = 180

m<1 = 180 - m<2

m<1 = 180 - 72

m<1 = 108 degrees

Hence the measure of m<1 from the given figure is 108 degrees.

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