7. Two functions are defined below.
F(x) = 5x + 1
g(x) = x/5 - 1/5
Which presentation best establishes that the functions are inverse functions?

If the observed t-value exceeds the critical t-value, then the difference between the sample means is most likely statistically significant.

In other words, the difference between the sample means is unlikely to have occurred by chance and is likely due to a real difference in the population means. The direction and magnitude of the difference must be further examined using effect size measures and confidence intervals.

Therefore, the most suitable value to be fit in the blank space of the given incomplete statement is, statistically significant.

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The indefinite integral of x²(x³+7)⁷dx is (1/57)(x⁵⁷) + (7/36)(x³⁶) + C, where C is the constant of integration and indefinite integral of (3x-3)¹⁸dx is (1/19)(3x-3)¹⁹ + C, where C is the constant of integration.

To evaluate the indefinite integral ∫x²(x³+7)⁷dx, we can apply the power rule for integration and distribute the x² term:

∫x²(x³+7)⁷dx

= ∫x^(2+3)(x³+7)⁷dx

= ∫x^(5)(x³+7)⁷dx

Now, we can simplify the integral and apply the power rule again:

\(∫x^{(5)}(x³+7)⁷dx\\= ∫(x^8+7x^5)⁷dx\\= ∫(x^56 + 7^7x^35)dx\)

Using the power rule for integration, the integral becomes:

\((1/57)(x^{57}) + (7/36)(x^{36}) + C\)

Therefore, the indefinite integral of x²(x³+7)⁷dx is (1/57)(x⁵⁷) + (7/36)(x³⁶) + C, where C is the constant of integration.

For the indefinite integral ∫(3x-3)¹⁸dx, we can again apply the power rule for integration:

∫(3x-3)¹⁸dx

= (1/19)(3x-3)¹⁹ + C

Therefore, the indefinite integral of (3x-3)¹⁸dx is (1/19)(3x-3)¹⁹ + C, where C is the constant of integration.

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Correct question is "Evaluate the indefinite integral. (Use C for the constant of integration.)

∫x²(x³+7)⁷dx

Evaluate the indefinite integral. (Use C for the constant of integration.)

∫(3x−3)¹⁸dx"

The least positive integer that will be divisible by both 15 and 35 will be 105.

The given integers are 15 and 35.
As we know that the least positive integer will be divisible by both 15 and 35 will be LCM ( least common factor) of 15 and 35.
The least common multiple of LCM of two integers is the common multiple of two numbers such that it is the least among all common multiples.
For example, LCM of 3 and 5 will be 15 because among all common multiples of 3 and 5, 15 will be least common multiple.
For LCM of 15 and 35, let's write multiples of both the numbers.
Multiples of 15 = 15,30,45,60,75,90,105,120,135,150,165,180,195,210,....
Multiples of 35= 35,70,105,140,175,210,...
We can see that 105 and 210 are two common multiples out of which 105 is the least multiple.
Therefore, the least positive integer that will be divisible by both 15 and 35 will be 105.

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The volume of the container is 576 cubic inches.

To calculate the volume of the container, we need to multiply its length, width, and height. From the given information, we have the dimensions of the container: 2 inches, 6 inches, and 8 inches. Multiplying these values together, we get:

Volume = 2 inches * 6 inches * 8 inches = 96 cubic inches.

However, this calculation does not match the given volume of 576 cubic inches. Therefore, there might be an error or misunderstanding in the information provided. If the volume of the container is indeed 576 cubic inches, it is necessary to reevaluate the dimensions or measurements to ensure accuracy.

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Answer:

1. 3

2. 1

Step-by-step explanation:

Answer:

1.3. now mark brainlieet plsssssssssss like you said you would

Answer:

2.31 is not 2,200 times greater than 1.05.

(2,200)(1.05) = 2310

Did you mean 2.200 times greater?

I don't understand what to do with x and y.  It seems the correct values are listed, absent any additional information.

Step-by-step explanation:

Answer: u just need to do 335.0/0.67

Step-by-step explanation:

Answer:

y = 1/2x + 1.

Step-by-step explanation:

Use the point-slope form of a straight line:

y - y1 = m(x - x1)     (where m=slope and(x1,y1) is a point on line).

y - 3 = 1/2(x - 4)

y = 1/2x - 2 + 3

y = 1/2x + 1.

Answer:

-16r^2 - 10r

Step-by-step explanation:

all you got to do is distribute

Given :

1.) Mr. Castro had 7/8 gallons of paint. He used 2/5 of it to paint his bicycle.

2.) Mother bought 14/15 kilograms of pepper. She 1/3 used of it in cooking adobo for the visitors.

To Find :

1.) What part of the paint he had used?

2.) What part of the pepper did she use?

Solution :

Part of paint used by Mr. Castro, p = 7/8 × 2/5 = 7/20 .

Part of pepper used by mother = 14/15 × 1/3 = 14/45 .

Hence, this is the required solution.

Answer:

602 .6

Step-by-step explanation:

∴14,400=160b

⇒b=90m

902m=45m

2πr=2π×45≈282.6m

320m+282.6m=602.6m

A graph of the system of equations is shown in the image attached below.

A solution to the given system of equations y = -x and y = 2/5(x) - 7 is 5 and -5.

In Mathematics, a system of equations can be defined an algebraic equation that only has two (2) variables and can be solved simultaneously or graphically.

In this scenario, we would use an online graphing calculator to plot the given system of equations and then take note of the point of intersection;

y = -x                 .....equation 1.

y = 2/5(x) - 7     .....equation 2.

Based on the graph (see attachment), we can reasonably infer and logically deduce that the required solution for the given system of equations is the point of intersection of the two (2) lines on the graph, which is given by the ordered pair (5, -5);

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Answer:

223

Step-by-step explanation:

(a)We have to use a continuous exponential growth model to write a formula relating to t and N(t), where t is the time (in years) since the initial population is introduced, and N(t) is the number of fish at time t. Continuous exponential growth models can be expressed as;
N(t) = N₀ * e^(kt)
where N₀ is the initial population, t is the time elapsed, k is the continuous growth rate, and e is Euler's number.

(b)Given that the initial population is introduced into a lake and it grows according to a continuous exponential growth model. The number of fish in the lake is 300 after 4 years. Using N(t) = N₀ * e^(kt);300 = N₀ * e^(4k)So, the formula relating to t and N(t) is;
N(t) = N₀ * e^(kt)
Putting the values into the formula;
N(t) = 300/ e^(4k)We know the number of fish in the lake after 4 years is 300.
Therefore;300 = N₀ * e^(4k)
Dividing by N₀; 300/N₀ = e^(4k)
We have; N(t) = N₀ * e^(kt)
Putting the values into the formula;
N(t) = N₀ * e^(kt)N₀ = N(t) / e^(kt)
At t = 0; N₀ = N(0) / e^(k*0)N₀ = N(0) / e^0
N₀ = N(0)
Now we can substitute the value of N₀ into the formula;
N(t) = N(0) * e^(kt)
Substituting the values in N(t) = N₀ * e^(kt);
N(t) = 1000 * e^(0.23t)

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The statement "There is a 60 percent chance of rain and a 40 percent chance of pure sunshine" illustrates the definition of a probability distribution.

A probability distribution is a function that describes the likelihood of different outcomes in a random event or experiment. It assigns probabilities to each possible outcome, where the probabilities add up to 1 (or 100%).

In the given options, the statement "There is a 60 percent chance of rain and a 40 percent chance of pure sunshine" is a clear example of a probability distribution because it assigns probabilities to two possible outcomes - rain and sunshine - with a total probability of 1. Specifically, the statement is saying that there is a 60% chance of rain and a 40% chance of sunshine. This statement describes the likelihood of different outcomes for the weather, making it an example of a probability distribution.

The other two statements do not illustrate a probability distribution because they only provide information about specific events that have already occurred (i.e., "it rained three-quarters of the day yesterday" and "the sun is shining today and is supposed to shine tomorrow") or possible events that may occur in the future without any mention of their likelihood (i.e., "it may snow either today or tomorrow").

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S is not continuous at c, and since this is true for any irrational number in (0,1), S is not continuous at any point in (0,1).

To show that S is continuous at 0 and at 1, we need to show that the limit of S(x) as x approaches 0 and 1 exists and is equal to S(0) and S(1), respectively.

First, let's consider the limit as x approaches 0. We have:

lim x→0 S(x) = lim x→0 x² = 0² = 0

Since S(0) = 0, we have lim x→0 S(x) = S(0), and thus S is continuous at 0.

Now let's consider the limit as x approaches 1. We have:

lim x→1 S(x) = lim x→1 x² = 1² = 1

Since S(1) = 1, we have lim x→1 S(x) = S(1), and thus S is continuous at 1.

To show that S is not continuous at any point in (0,1), we need to find a point c in (0,1) such that S is not continuous at c. One way to do this is to show that the limit of S(x) as x approaches c does not exist.

Let c be any irrational number in (0,1), and let {r_n} be a sequence of rational numbers in (0,1) that converges to c. Then we have:

lim n→∞ S(r_n) = lim n→∞ r_n = c

On the other hand, since c is irrational, S(c) = c². Therefore, we have:

lim x→c S(x) = c²

Since lim n→∞ S(r_n) ≠ lim x→c S(x), the limit of S(x) as x approaches c does not exist. Therefore, S is not continuous at c, and since this is true for any irrational number in (0,1), S is not continuous at any point in (0,1).

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The equation of the plane is -5x + 5y - 3x = 25.

What is the equation of the plane?

A plane in mathematics is a flat, two-dimensional surface that extends infinitely in all directions. The equation of a plane is a mathematical representation that defines the position of the plane in space. It can be used to describe the relationship between the coordinates of the points that lie on the plane.

The equation of a plane can be found using the point-normal form, which is given by:

ax + by + cz = d

where (a,b,c) is the normal vector and (x,y,z) are the coordinates of a point on the plane.

In this case, we have the normal vector n = ⟨−5,5,−3⟩ and a point on the plane (5,−5,−1). To find the equation of the plane, we first need to find d, which can be found by substituting the coordinates of the point into the equation:

d = −5 * 5 + 5 * (−5) + −3 * (−1) = 25

So the equation of the plane can be expressed as:

-5x + 5y - 3z = 25.

Hence, the equation of the plane is -5x + 5y - 3x = 25.

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The series of transformations correctly maps △ABC to △XYZ the correct series of transformations that maps △ABC to △XYZ is to dilate △ABC by a scale factor of 3 centered at the origin, then translate the result down 5 units.

To determine the correct series of transformations that maps △ABC to △XYZ, we need to compare the corresponding sides and angles of the two triangles. If we can show that the two triangles are similar, then we can use a dilation to map one triangle onto the other.

Let's assume that △ABC is mapped to △XYZ by a dilation centered at the origin with scale factor k, followed by a translation down 5 units. This can be written as:

△ABC → Dilate(k) → △A'B'C' → Translate down 5 units → △XYZ

To show that △ABC and △XYZ are similar, we need to show that their corresponding angles are congruent, and their corresponding sides are proportional.

Let's first consider the angles. We are not given any information about the angles of the two triangles, so we assume that they are the same. Therefore, we only need to show that their corresponding sides are proportional.

The dilation centered at the origin scales all distances by a factor of k. Therefore, the length of each side of △A'B'C' is k times the length of the corresponding side of △ABC. Then, the translation down 5 units shifts all points 5 units downwards. Therefore, the length of each side of △XYZ is equal to the length of the corresponding side of △A'B'C' minus 5 units.

From this analysis, we can conclude that the sides of △ABC and △XYZ are proportional, with a scale factor of k, and therefore, △ABC and △XYZ are similar triangles.

Now, let's look at the answer choices and see which one fits the description of a dilation centered at the origin with a scale factor of k, followed by a translation down 5 units:

Dilate △ABC by a scale factor of 3 centered at the origin, then translate the result down 5 units.

Dilate △ABC by a scale factor of 13 centered at the origin, then translate the result down 5 units.

Dilate △ABC by a scale factor of 1/3 centered at the origin, then translate the result down 5 units.

Dilate △ABC by a scale factor of 13 centered at the origin, then reflect the result across the x-axis.

Dilate △ABC by a scale factor of 1/3 centered at the origin, then reflect the result across the x-axis.

Dilate △ABC by a scale factor of 13 centered at the origin, then rotate the result 90 degrees clockwise about the origin.

Dilate △ABC by a scale factor of 1/3 centered at the origin, then rotate the result 90 degrees clockwise about the origin.

The only answer choice that fits the description of a dilation centered at the origin with a scale factor of k, followed by a translation down 5 units, is the first one:

Dilate △ABC by a scale factor of 3 centered at the origin, then translate the result down 5 units.

Therefore, the correct series of transformations that maps △ABC to △XYZ is to dilate △ABC by a scale factor of 3 centered at the origin, then translate the result down 5 units.

Answer:

\(y - 3 = - 4(x + 2)\)

Answer:

D

Step-by-step explanation:

Instead of 2x + 11 = 5x + 16, you should have put 2x+11 = 5x - 16. There is a sign change right before the 16, and you may have accidentally written down +16 instead of -16. I think that's where the problem is.

2x + 11 = 5x - 16

subtract 5x from both sides to make all variables on one side

-3x + 11 = -16

subtract 11 from both sides to isolate the x and its coefficient

-3x = -27

divide both sides by -3 to isolate x

x = 9

Answer:

a. 48 salads were bought on Wednesday

b. 42 chickens were bought on Thursday

c. 39 cheese were bought on Friday

Step-by-step explanation:

Given

\(------- M -- T - W -- T -- F\)

Cheese ----- 50 -- 45 - 52 - 47 --39

Salad -------- 61 -- 44 - - 48 - 38 -- 51

Chicken ---- 53 -- 46 - - 39 - 42 -- 52

First, it should be noted that the horizontal data represent the row while the vertical data represent the column.

Having said that, the solution is as follows:

Solving (a): Second Row, Third column

The data at the second row are:

\(------- M -- T - W -- T -- F\)

Salad -------- 61 -- 44 - - 48 - 38 -- 51

The data at the third column is then limited to:

------------------W

Salad -------- 48

So the number at this position implies that: 48 salads were bought on Wednesday

Solving (b): Third Row, Fourth column

The data at the second row are:

\(------- M -- T - W -- T -- F\)

Chicken ---- 53 -- 46 - - 39 - 42 -- 52

The data at the fourth column is then limited to:

------------------- T

Chicken ---- 42

So the number at this position implies that: 42 chickens were bought on Thursday

Solving (c): First Row, Fifth column

The data at the first row are:

\(------- M -- T - W -- T -- F\)

Cheese ----- 50 -- 45 - 52 - 47 --39

The data at the fifth column is then limited to:

------------------F

Cheese ----- 39

So the number at this position implies that: 39 cheese were bought on Friday

In this context, the dependent variable is t (amount of tax due) and the independent variable is c (cost of the order).In this scenario, the variables are t (the amount of tax due) and c (the cost of the order).

To determine which variable is independent and which is dependent, we need to understand their relationship.In this case, the amount of tax due, t, is calculated based on the cost of the customer's order, c. The tax amount is dependent on the cost of the order because it is directly influenced by the value of c. As the cost of the order changes, the amount of tax due will also change accordingly.

On the other hand, the cost of the order, c, is independent. It is not influenced or determined by the amount of tax due. The customer can choose the cost of their order, and the tax will be calculated based on that chosen amount.

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a) Since the triangles are congruent, and ΔABC is congruent to ΔDEF, segments AB and DE have the same value. Therefore, you can use algebra to solve for x when using the knowledge that (12 - 4x) is equal to (15 - 3x).

To solve:

12 - 4x = 15 - 3x

12 = 15 + x

-3 = x

Therefore, x is equal to -3.

b) To find the value of AB, plug in the value of x found in part a).

12 - 4x

12 - 4(-3)

12 - (-12)

12 + 12 = 24

Thus, segment AB is equal to 24.

c) As shown in part b), plug in the value of x found in part a) to find the value of segment DE.

15 - 3x

15 - 3(-3)

15 - (-9)

15 + 9 = 24

Thus, segment DE is also equal to 24.

We can confirm the knowledge of the equal side lengths because the triangle are congruent. This means that all the side lengths in the triangle are the same, which is confirmed when algebraically plugging in the value of x to solve for the values of the segments AB and DE.

I hope this helps!

Answer:

below

Step-by-step explanation:

9 2/5 = [(9*5)+2]/5=(45+2)/5=47/5

Answer:

check image for answers

Step-by-step explanation:

Hope this is not to late. Have a good day!

Answer:

4x - 8

Step-by-step explanation:

Let x be the number

I hope this helps!

The area of the region enclosed by one loop of the polar curve r = 4cos(3θ) can be found by evaluating the definite integral of (1/2)r^2dθ over the appropriate range of θ values. By identifying the bounds of θ where the curve completes one loop, the area can be calculated.

To find the area enclosed by one loop of the polar curve r = 4cos(3θ), we need to determine the bounds of θ that correspond to one complete loop of the curve. The curve completes one loop when 3θ goes from 0 to 2π. Solving for θ, we have θ = 0 to θ = (2π)/3.

The area of the region enclosed by the curve is given by the integral of (1/2)r^2dθ over the range of θ values. Substituting r = 4cos(3θ), we have:

A = (1/2)∫[0 to (2π)/3] (4cos(3θ))^2 dθ

Simplifying and evaluating this integral gives the desired area. The result is approximately 4.207 square units.

Therefore, the area of the region enclosed by one loop of the curve r = 4cos(3θ) is approximately 4.207 square units.

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Answer:

Give the full question, then I might be able to solve it.

The $10 scale is a good scale to use for the y-axis. 12 months is sufficient to plot the graph and display the changes.

What is a coordinate system?

coordinate system, Setup of reference lines or curves that are used to pinpoint the locations of points in space The most popular two-dimensional system is called Cartesian (after René Descartes). Points are identified by their separation from a reference point, known as the origin, along a horizontal (x) and vertical (y) axis (0, 0).

Let the y-axis represent the money for groceries and the x-axis the number of months.

Given is that, the grocery bills range from $110 to $170.

We can thus view the changes in the grocery bills over 7 intervals by placing a scale of $10 on the y-axis.

Consequently, a $10 scale is a good scale.

Additionally, the y-axis shows the number of months. It will be sufficient to plot the graph and display the changes in grocery bills over the course of 12 months.

Therefore, 12 points are enough to represent a month.

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Answer:

The positive difference in the 'y' coordinates of where they agreed to meet and where they should actually meet is 4

Step-by-step explanation:

The segement they form is, using the distance formula,

\(d=\sqrt{((x1-x2)^2+(y1-y2)^2)}\)

but since we only need to find the y coordinates,

we do not need it in this case

now ,

in our case, x1 = 5, y1 = -11

x2=-7, y2=13

so,

y1-y2 is the total y difference for the first points,

so d1=-11-13

d1 = -24

but since distance is positive,so,

d1 = 24

and the midpoint of that would be m= d/2,

m1 = 12

if Barbara is at (-5,5), then the distance will be,

since then, x2=-5,y2=5,

d2 = -11-5

d2=-16

or,

d2 = 16

and

m2 = 16/2

m2 = 8

so the positive difference in the 'y' coordinates of where they agreed to meet and where they should actually meet is,

diff = 12-8

diff = 4

so the difference in y coordinates is 4