11. Find the average rate of change of the equation y = x2 + 4x + 1 on the interval -1 < x < 4.

So, the prime factors of 42 are 2 × 3 × 7, where 2,3 and 7 are prime numbers.

Answer:

The third step would be to construct a hypothesis.

Step-by-step explanation:

Answer: 18.5 equals x.

You set the equation to 90 since it's a square.

Answer:

60 inches²

Step-by-step explanation:

Unit test

1275 spaces are in the parking garage.

What is linear addition?
The phrase "the addition" refers to combining two or more numbers. Adding two numbers is indicated by the plus sign (+), therefore adding three is written as three plus three. Two whole numbers added together result in another whole number. Two natural numbers added together will provide the original natural number once again. Two integers added together will result in an integer; two positive integers added together will result in a positive integer; two negative integers added together will result in a negative number; and one positive and one negative integer added together will result in an integer with the same sign as the largest number.

Given, total number of cars parked in garage = 551
Empty spaces available in first floor = 128
Empty spaces available in second floor = 294
Empty spaces available in third floor = 302
Therefore, total spaces in the parking garage = 551 + 128 + 294 + 302
= 1275
Thus, 1275 spaces are in the parking garage.

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The stem-and-leaf display of the data is

Stem | Leaves

1 | 2

2 | 2

3 | 3

4 | 5, 8

To start, let's assume we have a set of data values, such as 12, 22, 33, 45, 48, 53, 61, 62, 72, 83, 91, 96, 99.

The stem-and-leaf display consists of two parts: the "stem" and the "leaf." The stem represents the leading digit(s) of the data values, and the leaf represents the trailing digit(s). For example, the number 12 has a stem of 1 and a leaf of 2.

Now, let's organize the data values into their corresponding stems:

Stem 1: 12

Stem 2: 22

Stem 3: 33

Stem 4: 45, 48

Next, we list the leaves corresponding to each stem. The leaves are listed in ascending order next to their respective stems:

Stem 1: 2

Stem 2: 2

Stem 3: 3

Stem 4: 5, 8

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Statistical hypothesis testing employs the null and alternate hypotheses.

The alternative hypothesis of a test expresses the prediction of an effect or relationship based on your study, while the null hypothesis of the test does not yet predict an effect or an association between the variables.

A statement that there is no relationship between two variables is called a null hypothesis. Another hypothesis is that the two variables are statistically correlated.

Alternative unilateral (directional) or the bilateral (non-directional) hypotheses are also possible. Simple, complex, true, and false are the four main categories of null hypotheses. If the p-value is greater than the statistical significance level, null hypothesis is preferred.

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Answer: 606000 pls mark as brainliest

Step-by-step explanation:

multiply 10x 2020x 30which=606000

Answer:

The numbers are 0 and 1

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Answer:

The truck is on pace.

Step-by-step explanation:

To find which truck will arrive first, you need to find each vehicle's mph. To get the mph of each vehicle you just need to divide the distance by time.

Bus: 110 (miles) ÷ 2 (hours) = 55 (miles per hour)

Truck: 180 (miles) ÷ 3 (hours) = 60 (miles per hour)

When you do this you can see the mph of the bus is < the mph of the truck.

If you have any questions please leave them in the comments.

Answer:

y = 5x - 3, so M = 5 and C = -3.

The optimal point values for x1, x2, λ, and μ (Lagrange multipliers) in the given problem are:

x1 = 1

x2 = 1

λ = -4

μ = 2

To solve the optimization problem using the Lagrange multipliers technique, we first construct the Lagrangian function L(x1, x2, λ) by incorporating the equality constraint:

L(x1, x2, λ) = f(x1, x2) - λ(g(x1, x2))

Where f(x1, x2) is the objective function, g(x1, x2) is the equality constraint, and λ is the Lagrange multiplier.

In this case, the objective function is f(x1, x2) = 2x1^2 - 2x1x2 + 2x2 - 6x1 + 6, and the equality constraint is g(x1, x2) = x1 + x2 - 2.

The Lagrangian function becomes:

L(x1, x2, λ) = 2x1^2 - 2x1x2 + 2x2 - 6x1 + 6 - λ(x1 + x2 - 2)

To find the optimal values, we need to find the critical points by taking partial derivatives of L with respect to x1, x2, and λ and setting them equal to zero. Solving these equations simultaneously, we get:

∂L/∂x1 = 4x1 - 2x2 - 6 - λ = 0

∂L/∂x2 = -2x1 + 2 + λ = 0

∂L/∂λ = -(x1 + x2 - 2) = 0

Solving these equations, we find x1 = 1, x2 = 1, and λ = -4. Substituting these values into the equality constraint, we can solve for μ:

x1 + x2 - 2 = 1 + 1 - 2 = 0

Therefore, μ = 2.

The optimal point values for the variables in the optimization problem are x1 = 1, x2 = 1, λ = -4, and μ = 2. The Lagrange multipliers λ and μ represent the rates of change of the objective function and the equality constraint, respectively, with respect to the variables. They provide insights into the sensitivity of the objective function to changes in the constraints and can indicate the impact of relaxing or tightening the constraints on the optimal solution. In this case, the Lagrange multiplier λ of -4 indicates that a small increase in the equality constraint (x1 + x2 - 2) would result in a decrease in the objective function value. The Lagrange multiplier μ of 2 indicates the shadow price or the marginal cost of satisfying the equality constraint.

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Since a is a subset of b and b is a subset of a, we can conclude that a = b.

To prove that if a ∩ b = a ∪ b then a = b, we can follow these steps:

1. Note that a ∩ b is a subset of both a and b.
2. Since a ∩ b = a ∪ b, this implies that a ∪ b is also a subset of both a and b.
3. Now, a is a subset of a ∪ b. Since a ∪ b is a subset of b, it follows that a is a subset of b.
4. Similarly, b is a subset of a ∪ b. Since a ∪ b is a subset of a, it follows that b is a subset of a.
5. Since a is a subset of b and b is a subset of a, we can conclude that a = b.

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The intervals of concavity for f(x) = 3 cos x, with 0 < x < 21, are (0, π/2) and (3π/2, 2π).

To find the intervals of concavity for f(x) = 3 cos x, we need to analyze the second derivative of the function.

First, let's find the second derivative of f(x):

f'(x) = -3 sin x (derivative of cos x)

f''(x) = -3 cos x (derivative of -3 sin x)

Now, we can analyze the concavity of f(x) by considering the sign of the second derivative:

When x ∈ (0, π/2): In this interval, cos x > 0, so f''(x) < 0. The second derivative is negative, indicating concavity downwards.

When x ∈ (π/2, 3π/2): In this interval, cos x < 0, so f''(x) > 0. The second derivative is positive, indicating concavity upwards.

When x ∈ (3π/2, 2π): In this interval, cos x > 0, so f''(x) < 0. The second derivative is negative, indicating concavity downwards.

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Answer:

I think this would be 182

Step-by-step explanation:

Answer:

9 pi

Step-by-step explanation:

First find the circumference of the circle

C =2 * pi *r

C = 2 * pi *9

C = 18 pi

This is a semicircle which is 1/2 of a circle

Take 1/2 of the circumference

1/2 C = 1/2 ( 18 pi)

1/2 C = 9 pi

Answer:

Check below:

Step-by-step explanation:

To factorize the algebraic expression 3x² + 6x + 4x + 8, you can follow these three steps:

Step 1: Grouping

Group the terms in pairs so that you can factor out a common factor from each pair.

3x² + 6x + 4x + 8

(3x² + 6x) + (4x + 8)

Step 2: Factoring out the common factors

Factor out the common factors from each pair separately.

3x(x + 2) + 4(x + 2)

Step 3: Factoring out the common factor from the resulting expression

Notice that we have a common factor, (x + 2), in both terms.

(x + 2)(3x + 4)

Therefore, the factored form of the expression 3x² + 6x + 4x + 8 is (x + 2)(3x + 4).

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Best describe a parallelogram with diagonals that are perpendicular is rectangle.

A parallelogram with diagonals that are perpendicular is called a rectangle. A rectangle is a special type of parallelogram that has four right angles. This means that the diagonals of a rectangle are perpendicular to each other, and they bisect each other.

In addition to having perpendicular diagonals, a rectangle has other unique properties. Its opposite sides are congruent and parallel, and all angles are right angles. The diagonals of a rectangle have the same length, and they divide the rectangle into four congruent right triangles.

The properties of a rectangle make it a useful shape for many practical applications. For example, rectangular shapes are commonly used in building construction, furniture design, and graphic design. The perpendicular diagonals of a rectangle also make it useful for geometric proofs and calculations.a

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The required composite function is fox = 24y² - 145.

Rewrite x(y) so that the function it represents is equal to z is z = 4y² - 25.

The function f(x) = 6x + 5 in terms of z is f(z) = 6z + 5.

In Mathematics, a function can be defined as a mathematical expression which is typically used for defining and representing the relationship that exists between two or more variables such as an ordered pair.

Based on the information provided, we have the following functions;

f(x) = 6x + 5  

x(y) = 4y² – 25

Next, we would create the required composite function as follows:

fox = 6[4y² - 25] + 5

fox = 24y² - 150 + 5

fox = 24y² - 145

By rewrite x(y) to represent z, we have:

z = 4y² - 25

In terms of z by substituting z for x, we have:

f(x) = 6x + 5

f(z) = 6z + 5

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Complete Question:

The first step in combining the functions is to use a variable to represent one of the functions to make it easier to use. Rewrite x(y) so that the function it represents is equal to z.

a. In this activity, you'll combine two related functions, f(x) = 6x + 5 and x(y) = 4y² – 25, to create a type of function called a composite function. Then you’ll evaluate the composite function.

b. The first step in combining the functions is to use a variable to represent one of the functions to make it easier to use. Rewrite x(y) so that the function it represents is equal to z.

c. Write the function f(x) = 6x + 5 in terms of z by substituting z for x in the function.

Answer: ents is equal to z is z = 4y² - 25.

The function f(x) = 6x + 5 in terms of z is f(z) = 6z + 5.

What is a function?

In Mathematics, a function can be defined as a mathematical expression which is typically used for defining and representing the relationship that exists between two or more variables such as an ordered pair.

Based on the information provided, we have the following functions;

f(x) = 6x + 5  

x(y) = 4y² – 25

Next, we would create the required composite function as follows:

fox = 6[4y² - 25] + 5

fox = 24y² - 150 + 5

fox = 24y² - 145

By rewrite x(y) to represent z, we have:

z = 4y² - 25

In terms of z by substituting z for x, we have:

f(x) = 6x + 5

f(z) = 6z + 5

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Complete Question:

The first step in combining the functions is to use a variable to represent one of the functions to make it easier to use. Rewrite x(y) so that the function it represents is equal to z.

a. In this activity, you'll combine two related functions, f(x) = 6x + 5 and x(y) = 4y² – 25, to create a type of function called a composite function. Then you’ll evaluate the composite function.

b. The first step in combining the functions is to use a variable to represent one of the functions to make it easier to use. Rewrite x(y) so that the function it represents is equal to z.

c. Write the function f(x) = 6x + 5 in terms of z by substituting z for x in the function.

Step-by-step explanation:

Answer:

12 miles

Step-by-step explanation:

Total miles = Length of trail ×

Number of times she rode

Total miles = 3 miles × 4 times

Total miles = 12 miles

Mika traveled a total of 12 miles.

Answer:

D

Step-by-step explanation:

Either try all the numbers and see which ones work or do the following.

Times both sides by 2x-5.

3=x(2x-5)=2x^2-5x

Rearrange and solve the quadratic. I will factorise.

2x^2-5x-3=0

(2x+1)(x-3)=0

so x = -1/2 or 3

The probability of incurring a loss when it rains is:P (loss | raining) = 80%So, there is a 20% chance that the food truck will not have incurred a loss when it rains.

The P (not raining | not loss) = 90% × 30% = 27%.Thus, the probability that it had not rained on that randomly selected day given that the food truck did not incur a loss is 27%.

The chance of not raining on a given day in Seattle can be calculated as follows:When it does not rain, there is a 10% probability that the food truck will incur a loss, as given in the statement. Similarly, when it rains, there is an 80% chance that the food truck will incur a loss on that day.

To calculate the probability that the food truck will not have incurred a loss on that day, we must first calculate the probability that the food truck will have incurred a loss on that day.Suppose the probability of rain is 70%, so the chance that it won't rain will be: P (not raining) = 100% - 70% = 30%When it rains, there is a 80% probability that the food truck will have incurred a loss, as given in the statement.

The probability of not incurring a loss when it does not rain is:P (not loss | not raining) = 100% - 10% = 90%The probability of not raining when the food truck does not incur a loss can be calculated as follows:P (not raining | not loss) = P (not loss | not raining) × P (not raining)P (not loss | not raining) = 90%P (not raining) = 30%

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The boundary lines are y > -3x + 4: dotted line and  y <= 8x + 1: solid line

From the question, we have the following parameters that can be used in our computation:

y > -3x + 4

y <= 8x + 1

The boundary line for the inequality "<" is a dotted line, which means that the endpoint is not included in the solution set.

The boundary line for the inequality ">=" is a solid line, which means that the endpoint is included in the solution set.

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The coordinates of X that partitions XY in the ratio 5 to 4 include the following: X (-1.6, -7).

In this scenario, line ratio would be used to determine the coordinates of the point X on the directed line segment AB that partitions the segment into a ratio of 5 to 4.

In Mathematics and Geometry, line ratio can be used to determine the coordinates of X and this is modeled by this mathematical equation:

M(x, y) = [(mx₂ + nx₁)/(m + n)],  [(my₂ + ny₁)/(m + n)]

By substituting the given parameters into the formula for line ratio, we have;

M(x, y) = [(5(2) + 4(-6))/(5 + 4)],  [(5(-11) + 4(-2))/(5 + 4)]

M(x, y) = [(10 - 24)/(9)],  [(-55 - 8)/9]

M(x, y) = [-14/9],  [(-63)/9]

M(x, y) = (-1.6, -7)

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

8x + 4

Step-by-step explanation:

You just gotta distribute 4(2x+1) and it gives you the expression 8x + 4

For given triangle ABC, the measurement DC will be 90m.

With three sides and three vertices, triangles are a particular type of polygon in geometry. It has three straight sides and is a two-dimensional figure. As a 3-sided polygon, a triangle is included. Three triangle angles added together equal 180 degrees. In one plane, the triangle is contained. The triangle can be categorised into six different types based on its sides and angle measurements.

Triangles can be divided into 3 categories according to their sides, including:

Triangle with scalene dimensions: Each side has a different size.

Triangle with an isosceles shape, in which two of the sides have the same length and the third side is shorter.

All three of a triangle's sides have the same length, or equilateral triangle.

Now for given triangle ABC,

ad² +bd² =ab²  by Pythagoras theorem

ab² =10² +30²

ab² =1000

ab=10√10

and

bc² =cd^2+bd²   by Pythagoras theorem

and also b² =ac² -ab²  by Pythagoras theorem

Therefore,

cd² +bd² =ac² -ab²

cd² +30² =(10+cd)² -1000

cd² +900+1000=100+cd² +20cd

20cd=1800

cd=90m

Hence, For given triangle ABC, DC will be 90m.

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Yes, there are different processes at work in statements about the world and arithmetical statements such as "2 + 2 = 4."

Statements about the world, also known as empirical statements or factual statements, involve making claims or assertions about the way the world is or the way things are in reality. These statements are based on observations, evidence, and empirical data. The process involved in evaluating and verifying the truth or falsity of such statements often relies on empirical evidence, experimentation, logical reasoning, and inference from available information.

On the other hand, arithmetical statements, such as "2 + 2 = 4," belong to the realm of mathematics and are considered analytical or logical statements. These statements are based on mathematical principles, definitions, and axioms. The process of evaluating the truth or falsity of arithmetical statements relies on the rules and properties of mathematics, such as addition, subtraction, multiplication, and division, as well as logical reasoning and deductive arguments.

In summary, statements about the world involve empirical processes that rely on observations and evidence from the real world, while arithmetical statements involve mathematical processes based on logical reasoning and mathematical principles.

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Answer:

A

Step-by-step explanation:

on the left of the equation, (6^4)^-5 = 6^-20

the right side you add the exponents so it would be (-7-3) =-10

so it would be 6^-10, which is greater than 6^-20