Calculate the area of the composite figure please help me with the total area and shape part especially the solve for area please

The solution is,  the domain is: x ∈ (-∞, ∞).

Here, we have,

When we have two functions, f(x) and g(x), the composite function:

(f°g)(x)

is just the first function evaluated in the second one, or:

f( g(x))

And the domain of a function is the set of inputs that we can use as the variable x, we usually start by thinking that the domain is the set of all real numbers, unless there is a given value of x that causes problems, like a zero in the denominator, for example:

f(x) = 1/(x + 1)

where for x = -1 we have a zero in the denominator, then the domain is the set of all real numbers except x = -1.

Now, we have:

f(x) = x^2

g(x) = x + 9

then:

(f ∘ g)(x) = (x + 9)^2

And there is no value of x that causes problems here, so the domain is the set of all real numbers, that, in interval notation, is written as:

x ∈ (-∞, ∞)

(g ∘ f)(x)

this is g(f(x)) = (x^2) + 9 = x^2 + 9

And again, here we do not have any problem with a given value of x, so the domain is again the set of all real numbers:

x ∈ (-∞, ∞)

(f ∘ f)(x) = f(f(x)) = (f(x))^2 = (x^2)^2 = x^4

And for the domain, again, there is no value of x that causes a given problem, then the domain is the same as in the previous cases:

x ∈ (-∞, ∞)

(g ∘ g)(x) = g( g(x) ) = (g(x) + 9) = (x + 9) +9 = x + 18

And again, there are no values of x that cause a problem here,

so the domain is:

x ∈ (-∞, ∞)

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complete question:

Consider the following functions. f(x) = x2, g(x) = x + 9 Find (f ∘ g)(x). Find the domain of (f ∘ g)(x). (Enter your answer using interval notation.) Find (g ∘ f)(x). Find the domain of (g ∘ f)(x). (Enter your answer using interval notation.) Find (f ∘ f)(x). Find the domain of (f ∘ f)(x). (Enter your answer using interval notation.) Find (g ∘ g)(x). Find the domain of (g ∘ g)(x). (Enter your answer using interval notat

The amount that would be in the account when Alana is 21  is $2890

We have to know the formula for simple interest.

This is expressed as;

S.I = PRT/100

Given that the parameters of the formula are enumerated as;

From the information given, substitute the values, we have;

SI = 1000 × 9 × 21/100

Multiply the values,

Then, divide by the denominator, we have;

SI = $1890

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Answer:

one solution, no solution, infinitely many solutions

Step-by-step explanation:

I rearranged the first equation into x=6-2y

plug that into the second equation

2(6-2y)-3y=26

12-4y-3y=26

12-7y=26

-7y=14

y=-2

Then you plug that into one of the equations

x+2(-2)=6

x-4=6

x=10

The solution to the first system is (10,-2)

the second system already has one equation as something equal to a single variable so you just plug that into the other one

4x-2(2x-4)=-6

4x -4x +8 =-6

8=-6

this is a false statement so the system of equation has no solution

Lastly I rearranged the first equation into y=2x-4 and then plug that in

6x-3(2x-4)=12

6x-6x+12=12

12=12

this statement is true so the system of equations has infinite solutions

implifying

4z + -15 = 4z + 11

Reorder the terms:

-15 + 4z = 4z + 11

Reorder the terms:

-15 + 4z = 11 + 4z

Add '-4z' to each side of the equation.

-15 + 4z + -4z = 11 + 4z + -4z

Combine like terms: 4z + -4z = 0

-15 + 0 = 11 + 4z + -4z

-15 = 11 + 4z + -4z

Combine like terms: 4z + -4z = 0

-15 = 11 + 0

-15 = 11

Solving

-15 = 11

Answer:

12 rabbits

Step-by-step explanation:

Take long word problems like these step-by-step:

The pet store has 96 pets. Since half are fish, there are 48 fish. If one eighth of the pets are hamsters, there are 12 hamsters

If an eighth of the pets are dogs then there are 12 dogs and if an eighth of the pets are cats then there are also 12 cats. Since the rest are rabbits, we can subtract the amount of non-rabbits from the total (96 pets). There are 48+12+12+12=84 non-rabbits, and therefore 96-84=12 rabbits.

 By the definition of perpendicular lines, EA and FG is the pair of lines perpendicular to RS.

  This question is incomplete without a figure. Find the figure attached with the answer.

From the figure attached,

Measure of angles between the lines EA, FG and RS are 90°.

And the definition of the perpendicular lines states that if the angle between two lines is 90°, lines are said to be perpendicular.

  Therefore, EA and FG are the lines perpendicular to RS.

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Answer:

RM = 12 cm

Step-by-step explanation:

\(a^{2} + b^{2} = c^{2}\)

Assuming 20 is the hypotenuse cus there is no picture:

\(a^{2} + 16^{2} = 20^{2}\)

\(a^{2} +256 = 400\)

\(a^{2} = 144\)

\(a=144\)

If It's not the hypotenuse:

\(16^{2}+ 20^{2} =c^{2}\)

\(256+400 =c^{2}\)

\(656=c^{2}\)

\(c = 25.61249695\)

But I find it unlikely that 20 wasn't the hypotenuse so ignore that unless it applies.

Hope this helped. :0)

Answer:

H = 14

Step-by-step explanation:

Plug in the numbers.

77 = 1/2h (10+1)

77 = 1/2h (11)

7 = 1/2h

multiply by 2 to get rid of fraction

14 = h

Answer:

I think the total is 628.20$

Step-by-step explanation:

15*12=180

180*2.99=538.2

180*.5=90

90+538.2=628.2

Hope this helped :)

The coordinates to which the portable irrigation system should be sent to water the area are:

(495.75, 672).

The portable irrigation system should be sent right to the middle of the dry area given by the rectangle at the end of the answer.

Hence the coordinates are given as follows:

Hence the x-coordinate of the point to which the system should be sent is:

x = (56 + 144 + 888 + 895)/4 = 495.75.

(the mean is given by the sum of the observations divided by the number of observations).

The y-coordinate of the point to which the system should be sent is:

y = (289 + 332 + 1012 + 1055)/4 = 672.

The area is given by the image at the end of the answer.

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Answer:

Add your x values and divide by 2. Then add your y values and divide by 2. This is the midpoint.

Step-by-step explanation:

-1 + -5 = -6

-6 / 2 = -3 = x

-2 + 9 = 7

7 / 2 = 3.5 = y

Midpoint is (-3, 3.5)

Therefore, the solution to the inequality 3(y + 1/4) > 3/4 is y > 0.

An inequality is a mathematical statement that shows a relationship between two values, which are not necessarily equal. Inequalities are represented using symbols such as > (greater than), < (less than), ≥ (greater than or equal to), and ≤ (less than or equal to). Inequalities are commonly used in algebra and other areas of mathematics, as well as in real-world applications such as finance, economics, and science. They can be used to represent constraints or limits on a variable, such as the maximum or minimum value that it can take.

Here,

We can solve the inequality 3(y + 1/4) > 3/4 by first distributing the 3 to the expression inside the parentheses:

3y + 3/4 > 3/4

Next, we can simplify by subtracting 3/4 from both sides:

3y > 0

Finally, we can solve for y by dividing both sides by 3:

y > 0/3

y > 0

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Answer:

Calculated z= 3.515

The Z∝/2 = ±1.96  for ∝= 0.05

The Z∝/2 = ± 2.58  for ∝= 0.01

Yes the company claims valid at a level of significance of 0.05 and 0.01

Step-by-step explanation:

Here p1= 70% = 0.7

p2= 20/45= 0.444   q= 1-p= 1-.444= 0.56

The level of significance is 0.05 and 0.01

The null and alternative hypotheses are

H0; p1= p2                Ha: p1≠p2

The test statistic used here is

Z= p1-p2/ √pq/n

Z= 0.7-0.44/ √ 0.44*0.56/45

z= 0.26/ √0.2464/45

z= 3.515

The Z∝/2 = ±1.96  for ∝= 0.05

The Z∝/2 = ± 2.58  for ∝= 0.01

For the significance level 0.05 reject null hypothesis

For the significance level 0.01 reject null hypothesis

Yes the company claims valid at a level of significance of 0.05 and 0.01

Answer:

a) The first term of the progression is 4.5.

b) The common difference of the progression is 4.

c) The sum of the first 10 terms of the progression is 225.

Step-by-step explanation:

To solve this problem, you can use the formula for the sum of an arithmetic series. An arithmetic series is a sequence of numbers in which each term is obtained by adding a fixed number, called the common difference, to the preceding term.

The sum of an arithmetic series with n terms and a common difference d is given by:

Sum = n/2 * (2a + (n-1)d)

Where a is the first term of the series and d is the common difference.

In this problem, you are given that the sum of the 4th and 6th terms is 42 and the sum of the 3rd and 9th terms is 52. You can use these two equations to solve for a and d.

First, let's find the sum of the 4th and 6th terms:

Sum = 4/2 * (2a + 3d) = 42

This simplifies to:

2a + 3d = 21

Next, let's find the sum of the 3rd and 9th terms:

Sum = 6/2 * (2a + 5d) = 52

This simplifies to:

2a + 5d = 26

Now that we have two equations, we can solve for a and d by using substitution or elimination.

To use substitution, we can solve the second equation for d:

d = (26 - 2a)/5

Then, we can substitute this expression for d into the first equation:

2a + 3((26 - 2a)/5) = 21

This simplifies to:

2a + 3(26 - 2a)/5 = 21

Which simplifies to:

2a + 3(26)/5 - 3(2a)/5 = 21

This simplifies to:

2a + 3(26)/5 - 6a/5 = 21

This simplifies to:

-4a + 3(26)/5 = 21

This simplifies to:

-4a + 39 = 21

This simplifies to:

-4a = -18

This simplifies to:

a = 4.5

Now that we know the value of a, we can substitute it back into one of the original equations to find the value of d:

2(4.5) + 3d = 21

This simplifies to:

9 + 3d = 21

This simplifies to:

3d = 12

This simplifies to:

d = 4

Now that we have found the values of a and d, we can use the formula for the sum of an arithmetic series to find the sum of the first 10 terms of the progression:

Sum = 10/2 * (2(4.5) + (10-1)(4))

= 10/2 * (9 + 36)

= 10/2 * 45

= 225

Therefore, the sum of the first 10 terms of the progression is 225.

Answer:

Hence,

Common difference is

First term is

Sum of first 10 terms is 47

Step-by-step explanation:

a4 + a6 =42 eq1

a3 + a9 =52 eq

a1=?

d=?

S10=?

From eq 1,

a4 + a6=42

a1+3d + a1+5d =42

2a1 + 8d= 42 eq 3

From eq 2,

a3 + a9 =52

a1+2d + a1+8d = 52

2a1 + 10d = 52 eq 4

Subtract eq 3 from eq

2a1 + 10d =52

-2a1 -8d = -42

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

2d = 10

d=5....

≈=======================

Putting value of d in eq

2a1 +10 d=52

2a1+ 50 =52

a1 =1

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

Now we find sum of first 10 terms,

S10 = 2a1 + 9d

S10 = 2+45

S10 = 47

===========

Answer:

c. domain: {-2, 0, 2}, range: {-1, 1, 3}

Step-by-step explanation:

From the given points (negative 2, negative 1), (0, 1), (2, 3), we can determine the domain and range.

The domain represents the set of all possible x-values of the points, and the range represents the set of all possible y-values of the points.

In this case, we can see that the x-values are -2, 0, and 2, and the corresponding y-values are -1, 1, and 3.

Therefore, the correct answer is:

c. domain: {-2, 0, 2}, range: {-1, 1, 3}

Answer:

88 dollars

Step-by-step explanation:

To make it easier, divide 160 by half (80) and find 5 percent of 160 which is 8. Math go brrr

Answer:

The effective rate of interest per quarter is 40%.

Step-by-step explanation:

This can be calculated using the formula for calculating the Present Value of a Perpetuity as follows:

PV = A / r ........................................ (1)

Where;

PV = Present value of the series of payments = $5,000

A = Quarterly payment = $2,000

r = Quarterly effective rate of interest = ?

Substituting the values into equation (1) and solve for r, we have:

5,000 = 2000 / r

5,000 * r = 2,000

r = 2,000 / 5,000

r = 0.40, or 40%

Therefore, the effective rate of interest per quarter is 40%.

Answer:

Weight of decaf coffee = 5 pounds.

Weight of regular coffee = 8 pounds.

Step-by-step explanation:

(a) Let x be the weight of decaf coffee and y the weight of regular coffee. Then:

x + y = 13

2x + 3y = 34

(b) From the first equation x = 13 - y, so substituting for x in second equation:

2(13 - y) + 3y = 34

26 - 2y + 3y = 34

y = 34 - 26 = 8.

Substituting for y in the first equation:

x + 8 = 13

x = 5.

Based on the location of 0 in the bottom distribution (meaning no difference in the means), the best conclusion is:

A- The distribution of differences between the sample means of each group has a mean at or near zero making it likely the two groups are not statistically different.

In mathematics, distribution describes the probability that a system or a data set will take on a specific value or set of values.

Probability distribution shows how data values are distributed.  It is also known as statistical distribution because it demarcates values into common and uncommon (left and right), making a bell-shaped normal distribution.

Thus, when there is no difference in the means, the best conclusion of the statistical distribution is Option A.

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A- The distribution of differences between the sample means of each group has a mean at or near zero making it likely the two groups are not statistically different.

B- The distribution of differences between the sample means of each group has a mean at or near 325 making it likely the two groups are not statistically different.

C- The distribution of differences between the sample means of each group has a mean at or near zero making it likely the two groups are statistically different.

D- The distribution of differences between the sample means of each group has a mean at or near 325 making it likely the two groups are statistically different.

Answer:

D ...

Step-by-step explanation:

Use the Pythagorean Theorem to figure out which triangle is NOT a right triangle. Square each leg and add them together. Then, square the hypotenuse (longest side). If the sums are equal, then the triangle IS a right triangle.

Pythagorean Theorem:

a(a) + b(b) = c(c) ; a squared plus b squared equals c squared

6(6) + 24(24) =? 26(26) ; leg a =6, leg b=24, hypotenuse=26

36 + 576 =? 676 ; simplify

612 =? 676 ; is 612 equal to 676?

Factor 2 is 4x greater, Factor 3 is 9x greater and Factor 5 is 25x greater and  the pattern in part A is Factor square.

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

A cylinder is formed by 2 circles and a rectangle in the middle. That's why surface area is given by circumference of a circle, which is the length of the rectangle times height of the rectangle, i.e.:

A = 2.π.r.h

A cylinder of radius r and height h has area:

A₁= 2πrh

If multiply both dimensions by a factor of 2:

A₂= 8πrh

Comparing A₁ to A₂ :

A₁/A₂=4

Doubling radius and height creates a surface area of a cylinder 4 times greater.

By factor 3:

A₃=18πrh

Comparing areas:

A₃/A₁=9

Multiplying by 3, gives an area 9 times bigger.

By factor 5:

A₅=50πrh

Comparing A₅ to A₁

A₅/A₁=25

The new area is 25 times greater.

We can notice the increase in area is factor².

For example, when multiplied by a factor of 3, the new area is 9 times greater.

Hence, Factor 2 is 4x greater, Factor 3 is 9x greater and Factor 5 is 25x greater and  the pattern in part A is Factor square.

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Answer:

x = 3 x = ‐1/4

Step-by-step explanation:

Was right on the quiz

Answer:

x = 3 x = ‐1/4

Step-by-step explanation:

the first one is also right!!

The appropriate hypotheses for this test are: H0: There is no difference in the distribution of responses. Ha: There is a difference in the distribution of responses.

The chosen hypotheses are based on the objective of the investigation, which is to determine if there is convincing evidence that the distribution of responses about eating the potato salad differs between employees who are sick and those who are not sick.

The null hypothesis (H0) assumes that there is no difference in the distribution of responses about eating the potato salad between the sick and non-sick employees. This means that the proportion of employees who ate the potato salad would be the same in both groups, and any observed difference in the distribution of responses is due to random chance or factors unrelated to being sick or not sick.

On the other hand, the alternative hypothesis (Ha) proposes that there is a difference in the distribution of responses about eating the potato salad between the sick and non-sick employees. This suggests that the proportion of employees who ate the potato salad would be significantly different in the two groups, indicating a possible association between consuming the potato salad and getting sick.

By formulating these hypotheses, the investigation aims to evaluate whether the data provides convincing evidence to reject the null hypothesis in favor of the alternative hypothesis, indicating a meaningful relationship between eating the potato salad and falling sick.

Therefore, the correct answer is:

H0: There is no difference in the distribution of responses about eating the potato salad among those who are and are not sick.

Ha: There is a difference in the distribution of responses about eating the potato salad among those who are and are not sick.

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Answer:

5*8=40, 40 miles

Answer:

40 miles

Step-by-step explanation:

8 x 5 = 40

sheesh

Answer:

12.25

Step-by-step explanation:

3.5*3.5=12.25

Answer:

12.25m^2

Step-by-step explanation:

3 1/2 × 3 1/2

3 1/2 is equivalent to 7/2

7/2 × 7/2= 49/4

this simplifies to 12.25

answer: 12.25 m^2

Answer:

-2.3333333333333333333333

Answer:

number ÷ 7 < -3

Step-by-step explanation:

A number divided by 7 is less than -3.​

let the unknown number be x

\(\frac{x}{7}\) < -3

Answer:

57

Step-by-step explanation:

take both angles of the triangle add them together and subtract from 180

Answer:

The difference in temperature = 27-(-4)=31 degree

Step-by-step explanation: