Find the composite function


Please help me! I'm so confused and awful at math

An example of a function that is discontinuous at one and only one point in its domain but is continuous at every other point is the function f(x) = x^2.

This function is continuous at every point in its domain, which is the set of all real numbers (-infinity < x < infinity). However, at the point x = 0, the function is discontinuous. At x = 0, the function f(x) = x^2 is equal to 0, but if we approach the point x = 0 from the left (x = -0.1, -0.01, etc.), the function is equal to a negative value (-0.01, -0.0001, etc.), and if we approach the point x = 0 from the right (x = 0.1, 0.01, etc.), the function is equal to a positive value (0.01, 0.0001, etc.). This means that the function is not continuous at the point x = 0, and is therefore discontinuous at this point.

The point of discontinuity in this example is an essential discontinuity, which means that it cannot be removed by redefining the function at that point. This is because the function f(x) = x^2 is defined differently for x < 0 and x > 0, and there is no way to redefine the function at x = 0 to make it continuous.

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Answer:

The inequality form is 0≤x≤9 0 ≤ x ≤ 9 .

 2 sin A sin B with two angles A and B, 2 sin A sin B = cos (A-B) - cos (A + B). The 2sinasinb formula is equivalent to the difference between the angle sum and the angle difference of the cosine functions. The formula for two sins is two sins A and two sins B: cos (A-B) - cos (A + B).

What is 2SinASinB Identity?

2SinASinB identity is a trigonometric formula and it is used for the simplification of trigonometric expressions. It is also used for evaluating integrals involving trigonometric functions for easy calculation. We can derive the formula for 2SinASinB using the angle sum and angle difference formulas of the cosine function. Using the 2SinASinB formula, we can derive another trigonometric formula for SinA SinB given by, sinA sinB = (1/2)[cos(A - B) - cos(A + B)].

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The tank needs 5 more liters of water to be filled.

Subtraction is one of the basic operations of mathematics where we remove numbers or expressions or objects away from a given value.

Amount of water needed to fill the tank = 8 liters

Amount of water Alejandro filled = 2 liters

Amount of water Anthony filled = 1 less than Alejandro = 2 - 1 = 1 liter.

Total amount of water filled = 2 liters + 1 liter = 3 liters

Remaining space can be filled with 8 liter - 3 liter = 5 liters.

Hence tank still need 5 liters of water to be filled.

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Answer: D is  the right answer .The slope of KM is 1 and the slope of NL is –1.

A rhombus is a parallelogram whose all sides are equal. Its diagonals perpendicularly bisect each other.

i.e. product of its slope should be -1.

[∵if one line is perpendicular to the other lines then product of its slope should be -1.]

Slope of  KM= 1

Slope of NL= -1

Product of slope of diagonals=1×-1=-1

∴diagonals of given parallelogram perpendicularly bisect each other.

Therefore, it is a rhombus.

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Two correct options are option (C) The speed of the canoe in still water is 4 miles per hour and option (D) The speed of the water current is 3 miles per hour.

A canoe travels 7 miles per hour downstream and 1 mile per hour upstream.

x is the Canoe's speed with no water current in miles per hour

y is the speed of the water current, in miles per hour

The equations are

x + y = 7

x - y = 1

Here we have to use the elimination method

Add both the equation

2x = 7 + 1

2x = 8

x = 8/2

x = 4

Then substitute the value of x in the first equation

4 + y = 7

y = 7 -4

y = 3

Therefore, the correct options are option (C) and option (D)

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Based on the table, the equation that can be used to determine the number of pages (p) Lenny can read in t minutes is B. p = 1.8t.

An equation is a mathematical statement showing that two or more mathematical expressions are equal or equivalent.

For this equation, the slope, unit rate, or pages per minute is the quotient of the total number of pages read and the total time (in minutes) used.

Equations are depicted using the equation symbol (=) to show that two or more mathematical expressions are equal to one another.

Lenny's Reading Rate    

Time (minutes)    Pages Read     Pages per Minute

 60                            108                  1.8 (108/60)

 90                            162                  1.8 (162/90)

135                            243                  1.8 (243/135)

Thus, we can conclude that we can find the number of pages Lenny can read in t minutes using the equation provided by Option B.

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Answer:

p=1.8

Step-by-step explanation:

unit rate 108/60=1.8

If m∠ 1=(3 x) degrees and m ∠2=(x+48) degrees

The equation to solve the value of x is

3x = x+48

The value of x = 33

The angle 1 = 99 degrees

The angle 2 = 81 degrees

The measure of angle 1 = 3x degrees

The measure of angle 2 = x + 48 degrees

The sum of the angles on a straight line is add up to 180 degrees. Therefore angle 1 and angle 2 are supplementary angles.

∠1 + ∠2 = 180 degrees

Substitute the values in the equation

3x + x + 48 = 180

4x + 48 = 180

4x = 180 - 48

4x = 132

x = 132/4

x = 33

Part b

Then the measure of angle 1 = 3x

= 3 × 33

= 99 degrees

The measure of angle 2 = x + 48

= 33 + 48

= 81 degrees

Therefore, the equation to solve x is 3x = x + 48 and the measure of angles 1 and 2 is 99 degrees and 81 degrees respectively

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3 is the value of (fog⁻¹)(5) for functions f(x)=7-2x and g(x)=x+3.

A relation is a function if it has only One y-value for each x-value.

Given that the functions are f(x)=7-2x and g(x)=x+3.

We need to find the value of  (fog⁻¹)(5)

g⁻¹(x)=x-3.

By composite functions

f(g⁻¹)(x)=7-2(x-3)

f(g⁻¹)(x)=7-2x+6

Now plug in the value of x as 5

f(g⁻¹)(5)=7-2(5)+6

=7-10+6

=-3+6

=3

Hence, the value of  (fog⁻¹)(5) is 3.

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Cap rate (going in) = 5.6%

The estimated value of this property = 17,85,714.2 $

The needed rate of return is the rate of return that investors are looking for on assets that are similar. The value of the property and the needed rate of return are inversely related. Property value will fall as the needed rate of return rises, and the opposite is also true.

given cash flow is $100,000 and it increases by 5400$ every year hence growth rate would be 5.4 %.

Cash flows = $1,000,00

Growth rate = 5.4%

Required rate of return = 11%

the required rate of the property = cash flow / ( Required rate of return - growth)

the required rate of the property = 100,000 / (11 -5.4 ) = 17,85,714.2 $

Cap rate (going in) = Required rate of return - a growth rate of the property

Cap rate (going in) = (11 - 5.4) %

Cap rate (going in) = 5.6%

Thus, it can be concluded that the decrease in the required rate of return is the cause of the increase in the value of the property.

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The composite solid has a volume equal to 2268π cubic feet.

In this problem we have the case of a solid as a result of the combination of a cylinder and a hemisphere. The volume formulas for the cylinder and the hemisphere are, respectively:

Volume of cylinder

V = π · r² · h

Volume of hemisphere

V = (2π / 3) · r³

Where:

Volume of the composite solid:

V' = π · r² · h + (2π / 3) · r³

If we know that r = 9 ft and h = 22 ft, then the volume of the composite solid is:

V' = π · (9 ft)² · (22 ft) + (2π / 3) · (9 ft)³

V' = 2268π ft³

The volume of the composite solid is equal to 1053π cubic feet.

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Answer:

Step-by-step explanation:

the sum of the interior angles in a triangle is 180°

take off from 180° the know angles and you will find "x".

180 - 68 - 66 =

46°

Answer:

20

Step-by-step explanation:

20.

[tex]\frac{8}{\frac{2}{5} }[/tex]

Check the attached image below.

[tex]\frac{8}{1}* \frac{5}{2}[/tex]

[tex]\frac{8}{1}*\frac{5}{2}=\\\\ \frac{8*5}{1*2} =\\\\ \frac{40}{2}=\\ \\20[/tex]

[tex]\frac{8}{\frac{2}{5} }=20[/tex].

Answer:

26

Step-by-step explanation:

One leg measures 7.

One leg measures 8.

a² + b² = c²

7² + 8² = c²

c² = √113 = 10.630 = 11

perimeter = 7 + 8 + 11

perimeter = 26

T = {(x, y) : 0 ≤ x ≤ 1 and 0 ≤ y ≤ 4x} so that the line integral over C alone is 60/3 - (-44) = 64.

M(x, c) M(x, d) dx is equivalent to = b M(x, c) dx + M(x, d) dx. So, by demonstrating that the two sides of a rectangle are equal, we have established Green's Theorem. The sum of rectangles theorem. Since each region can be as nearly approximated by a sum of rectangles as desired, Green's Theorem must apply to all regions.

It looks like the integral is

[tex]\int\limits^0_c {xy} + x^{2} y^{3} \, dy[/tex]

Let's close the loop by adding a line integral over the line segment joining (1, 4) to (0, 0). Then the closed loop is the triangular region

T = {(x, y) : 0 ≤ x ≤ 1 and 0 ≤ y ≤ 4x}

Since the integrand has no singularities over or on the boundary of T, we have by Green's theorem

Compute the double integral:

From this result, we subtract the line integral over the extra line segment we added. Parameterize this path by

C' : {(1 - t, 4 - 4t) : 0 ≤ t ≤ 1}

The line integral over C' is

[tex]\int\limits^1_0 {(256t^{5} }+1280t^{4}+ 2560t^{3} - 2564t^{2} + 1288t - 260) \, dt[/tex]

T = {(x, y) : 0 ≤ x ≤ 1 and 0 ≤ y ≤ 4x} so that the line integral over C alone is 60/3 - (-44) = 64.

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there are about millions of multinational and national companies which are working for the better Gross National Product(GNP).

The United States is super power and has multiple resources to maintain itself  and the over all economic system. As, there are about millions of multinational and national companies which are working for the better Gross National Product(GNP). As, there is agriculture, car manufacturer, and the military industry for improving and adding the value to the over all GNP of the United States.

The Oil and gas sector is the one major factor for the development of the United State's GNP(Gross National Product). As, the exports of the region is well known to be very high and generates more revenue for the over all system as well.    

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Answer:

Step-by-step explanation:

2. Unit Rate: 1:2

3. A class has 26 kids. Johnny is trying to figure out the number of ears everyone has in total. You can use the ration 1:2. For every kid there are 2 ears. Therefore there are 52 ears total. [tex]\frac{1}{2}=\frac{26}{52}[/tex]

4. Multiplication

5. No, you can't have half an ear

Answer:

x = 1, y = -5.

Step-by-step explanation:

X-3y = 16         Equation (1)

4x- y = 9          Equation (2)

We can solve this by the Method of Elimination.

One way is to multiply the second equation by -3, as follows:

-3(4x - y = 9)

= -12x + 3y = -27     Call this equation (3)

Now if we add equation (3) to equation (1) we eliminate the y terms:

    x - 3y  =  16  

-12x + 3y = -27       Adding:

-11x  + 0    = -11

-11x = -11

x = -11/-11 = 1

Finally, we find the value of y by substituting x = 1 into equation (2):

4(1) - y = 9

-y = 9 - 4

-y = 5

y = -5.

So, the answer is x = 1, y = -5.

or we can write it as an ordered pair (1, -5).

Hope this helps.

Answer:

x=1 and

y= -5

The desired equation is then y -4 = 12/15 (x -9)

Equations of degree 1 are linear equations. It is the straight line's equation. A linear equation with parameters a and b equal to zero has the conventional form ax+by+c = 0.where a ≠ 0 and b ≠ 0.

We need this line's equation in the point-slope form, y - k = m. (x - h).

The point (h, k) in the point-slope form shown above can be chosen at random from the two points (9, 4) and (-6, -8). In the above point slope form, the other point is thus denoted by (x, y):

Let (x, y) be and (h, k) be (9,4). (-6,-8). Consequently, y - k = m(x - h) becomes

-8-4 = m (-6-9), so that -12 = m(-15), and the slope is thus m = 12/15

The desired equation is then y -4 = 12/15 (x -9) (which is in point-slope form).  

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Answer:

4

Step-by-step explanation:

Solve for x over the real numbers:

x^3 = 64

Take cube roots of both sides:

Answer: x = 4

4^2 = 16

4^3 = 64

Multiplication of matrices is not commutative by determining the product matrices ST and TS .

Given :

Consider the matrices

S = [tex]\left[\begin{array}{ccc}4&1\\-3&-2\end{array}\right][/tex]     and  T = [tex]\left[\begin{array}{ccc}0&4\\-4&3\end{array}\right][/tex]

Show that multiplication of matrices is not commutative by determining the product matrices ST and TS.

ST = [tex]\left[\begin{array}{ccc}4&1\\-3&-2\end{array}\right][/tex]  [tex]\left[\begin{array}{ccc}0&4\\-4&3\end{array}\right][/tex]

[tex]ST_{11[/tex] = 4 * 0 + 1 * -4 = -4

[tex]ST_{12[/tex] = 4 * 4 + 1 * 3 = 19

[tex]ST_{21[/tex] = -3 * 0 + -2 * -4 = 8

[tex]ST_{22[/tex] = -3 * 4 + -2 * 3 = -18

ST = [tex]\left[\begin{array}{ccc}-4&19\\8&-18\end{array}\right][/tex]

TS = [tex]\left[\begin{array}{ccc}0&4\\-4&3\end{array}\right][/tex]  [tex]\left[\begin{array}{ccc}4&1\\-3&-2\end{array}\right][/tex]

[tex]TS_{11[/tex] = 0 * 4 + 4 * -3 = -12

[tex]TS_{12[/tex] = 0 * 1 + 4 * -2 = -8

[tex]TS_{21[/tex] = -4 * 4 + 3 * -3 = -25

[tex]TS_{22[/tex] = -4 * 1 + 3 * -2 = -10

TS  = [tex]\left[\begin{array}{ccc}-12&-8\\-25&-10\end{array}\right][/tex]

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The fitted regression model is  y = 0.96+0.38x1 + 1.27 x2, and  Fitted regression model is y = 1.87+0.29x1 + 1.11 x2 -0.61 x3.

a) simple linear regression equation is y=a+bx1+cx2

last maintenance service (x1), repair time (y) given the type of repair (x2).

If x2 = 0 if the type of repair is mechanical and 1 if the type of repair is electrical. The Fitted regression model is y = 0.96+0.38x1 + 1.27 x2

b) Since R2 is 0.84.hence we say that x1 and x2 are 84% variation on. Hence we conclude that the above equation is best fit for the data.

c) simple linear regression equation is y=a+bx1+cx2+dx3

last maintenance service (x1), repair time (y) given the type of repair (x2).

If x2 = 0 if the type of repair is mechanical and 1 if the type of repair is electrical. and x3 = 0 if Bob Jones performed the service and x3 = 1 if Dave Newton performed the service.

The Fitted regression model is y = 1.87+0.29x1 + 1.11 x2 -0.61 x3

d) Since R2 is 0.89.hence we say that x1 and x2 are 89% variation on y. Hence we conclude that the above equation is best fit for the data. compare to part (b).

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In triangle ABC, where AD = DB , BC = 18 units then length of DE is equal to 9 units.

As given in the question,

In the given triangle ABC,

BC = 18 units

AD = DB

⇒ 'D' is the mid-point of AB.

From the given figure of triangle ABC,

DE is parallel to BC.

⇒E is the midpoint of AC.

Using mid-point theorem,

'D' and 'E' are midpoint of AB and AC and parallel to the opposite side BC then DE is half the measure of BC.

DE = ( 1/2) BC.

⇒ DE = ( 1/2) (18)

⇒ DE = 9 units

Therefore, in the given triangle ABC, the length of DE is equal to 9 units.

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Answer: B, Percent

Step-by-step explanation: The formula to find a whole after a percent is:

Worth = Part percent * Wole number / 100

This is the same as the definition says, "the amount or part that results from the base multiplied by the rate."

The ratio of p:r is 6/5

A ratio can be described as the comparison of two or more numbers which indicates their sizes in relation to one another.

From the information given, we have that;

t: w = 7:2

We have that;

Now, substitute the values into the formula

p = 4t + w

p = 4(7) + 2

expand the bracket

p = 28 + 2

Add the values

p = 30

r = t + 9w

r = 7 + 9(2)

expand the bracket

r = 25

The ratio, p:r

p:r = 30/25

p: r = 6/5

Hence, the value is 6/5

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Applying a coat of paint 0.07 cm thick to a hemispherical dome with a diameter of 40 meters will require an estimated 1759291.886 cubic centimeters of paint, using a linear approximation.

Given that,

We have to find applying a coat of paint 0.07cm thick to a hemispherical dome with a diameter of 40 meters will require an estimated volume of paint in cubic centimeters, which may be calculated using a linear approximation.

We know that,

Volume of a sphere = 4/3 πr³

Volume of a hemisphere is

V= 2/3 πr³

dV = 2πr² dr

Here,

dr=0.07cm

r=(1/2)×40m=2000cm

Let plug in the formula

dV = 2×π×(2000²)×(0.07)

dV=1759291.886 cubic centimeters

Therefore, Applying a coat of paint 0.07 cm thick to a hemispherical dome with a diameter of 40 meters will require an estimated 1759291.886 cubic centimeters of paint, using a linear approximation.

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To find a least squares solution using the normal equations, compute AT A and AT b, then solve the new system AT Ax = AT b. Each solution will be a least squares solution x to Ax = b.

What is least square method with example?

By reducing the total of the offsets or residuals of points from the plotted curve, the least squares method is a statistical technique for determining the best fit for a set of data points. In order to forecast the behavior of dependent variables, least squares regression is performed.

The least squares approach, sometimes referred to as the linear or simple least squares method, typically fits a straight line across the provided points. The sum of squares of the distances from the points is reduced along this line, which is known as the line of best fit.

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The time it takes for the stone to fall in the air is 7 seconds, and it takes 5 seconds for the stone to fall in the water in the seabed.

The average speed of the stone in air is shown here as 16 m/s.

The average speed of the stone in water is 3 meters per second.

The total distance from the top of the cliff to the seabed is 127 meters.

Total fall time = 12 seconds

Therefore

Let t1 represent the time spent by the stone in the air and

t2 = time spent by the stone in water

Now using the equations of motion we get :

Therefore, t₁ + t₂ = 12 s........(1)

16·t₁ + 3·t₂ = 127............(2)

From (1) t₁ = 12 - t₂

16×(12 - t₂) + 3×t₂ = 127

13t2 = 65 is the result.

and t2 equals 5 seconds

t1 = 12 - t2 = 12 - 5 = 7 sec

The time it takes for the stone to fall in the air is t1 = 7 seconds.

The time it takes for the stone to fall into the water is t2 = 5 seconds.

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There is actually enough evidence for the manufacturer to believe that the mean number of hours and mobs will last has actually changed.

We are supposed to use Israel and

significance level  α=.05  to perform hypothesis test on the statement of the manufacturer.

So Let's move into our worksheet, our population is 700, our sample size is 48.

The sample mean is 675

Sample standard deviation is 77.

So the first step is to state the null and alternative hypothesis and we have that our hate notes is based on the fact that μ is a cost of 700.

This is what the manufacturer wants, but she thinks that it might have changed probably lesser than or greater than Saddam is our alternative hypotheses, his meal is not equals to 700. So she is not sure whether it does, it's either decrease or increase but it has actually changed.

So after stating our null and alternative protesters, the next needs to state the decision rule that we will be using to either reject or accept the no like protesters.

So will be making a use of the PVA limited to make the decision. It is your roost is that if our evil is better than alpha we are supposed to accept, protesters and if our pivot is lesser than alpha, We are supposed to reject the null hypothesis is that our alpha is equals deserve .05.

So that being said it's time for us to move to draw our test statistics. Now for our test statistic is going to be AT. Test. Yes, our sample size is greater than 30. There's no issue with that. But we actually don't know the value of the population standard deviation. We are making use of the samples and activation which is 27. So that means it would be better if we use our T. Test as our test statistics. So our test statistic is a teacher has given towards us. T is a cost to extra minus meal divided by S divided by the square root of n. Our expert in this case is 6 75 minus. We have 700 divided by our s is 77 divided by the square root of 48. So let's do the math. 6 75 minus 700. We have a -25 divided by so we have 77 divided by the spirit of 48. We have this to be 11.11399. So uh -25 divided by 11.11399. We have our answer to be -2.249. So they simply implies that our test statistics is manners two points 249. So the next step is for us to get the p value attached to this test statistic scenes, we are using the p value method uh to make our decision. So we need a P value. We already have the level of significance. So to get the P value, we can decide to make itself. It it it's a distribution table but that will only give us a range of values in which the p value is located. It won't give us the actual P value. So most times we decide to use calculator to get the p value the exact p value. So our test is actually a two tailed tests were testing for a T score.

Our degree of freedom is the sample size minus one.

48-1=47

And our T score uh is minus two points 249.

So that we have a miners 2.249. And as you can see our p value here is 0.02 0.0294. T. Value is 0.029 so far. Alright, so there's our p value. So the next thing is to make our decision. So we have that as you can see their .0-9 Too far is actually lesser than 0.05 hands.

We make a decision by saying, we are going to reject the null hypothesis. So the decision is that we're going to be rejected the null hypothesis.

As a result, the manufacturer has sufficient reason to think that the average number of hours and mob duration have altered.

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