1) Solve and graph the inequalitiy x + 8 < - 3
2) Write a statement that repersent the number line below


the pet shelter, for every 7 dogs there are 5 cats. What is the ratio of dogs to cats?

Integration techniques from chapter 6, such as the power rule, substitution rule, and integration by parts, can be used to solve real-world problems involving calculus.

For example, the power rule can be used to calculate the area of an object by integrating its equation. The substitution rule can be used to calculate the volume of a solid by substituting the equation of its surface. Finally, integration by parts can be used to calculate the arc length of a function given its equation. All these techniques provide a way to calculate the area, volume, and arc length of various objects given their equations, allowing us to apply calculus to real-world situations. Integration techniques from chapter 6, such as the power rule, substitution rule, and integration by parts, can be used to solve real-world problems involving calculus.

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1.  Every composite number can be expressed as a product of primes - True

2.  Some quadratic equation has infinite solution - True

3. False (ix-yl = |x-y|, which may not equal ly = |y|)

4. 2(3+√7)-2√7 = 6√7 - False

5. False (25,471,287 is divisible by 3)

6. √6 is not rational number - True

7. Between every two real numbers there is another real number -True

8. For any natural numbers a and b GCF (a, b) * LCM (a, b) = a*b. -True

9. Integer is not closed under division -True

10. False (The product of a non-zero rational number and an irrational number is not necessarily rational)

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The solution of the equation for all real values of x is πk, π/6.

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles, specifically right triangles.

3 tan²x = √3 tan x

Divide both sides by 3tan x:

tan x = (√3)/3

x = tan⁻¹((√3)/3)

x = 30°

x = π/6 radian

Note: multiply 30° by π/180 to convert to radian. 180° = π radian

Since π/6 (i.e. 30°) falls between 0 and 180°.

Thus, the solution of the equation for all real values of x is πk, π/6. We can choose πk, π/6.

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At the significance level of a = 0.05, there is no strong statistical support for the manager's assertion.

Accepting it would be a type II error because the null hypothesis might not be true.

The 'null' and 'alternative' hypotheses should be

p 0.4 for H0 and p > 0.4 for Ha

q= 1-p= 1-0.4= 0.6

The alpha level for significance is 0.05.

For one-tailed tests, the crucial area is Z> ± 1.645

The sample proportion is p^= x/n= 38/90=0.42222

Using the z statistic

z= p^- p/ √pq

z= 0.422-0.4/ √0.4*0.6

z= 0.04536

We are unable to reject the null hypothesis since the calculated value of z=0.04536 does not fall within the crucial zone Z> 1.645.

The manager's assertion is not sufficiently supported by the available data.

When we reject the actual null hypothesis, we commit a type I mistake.

When we accept the incorrect null hypothesis, we make type II errors.

Accepting it would be a type II error because the null hypothesis might not be true.

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Answer:

greetings!!!

Look at the attachment above

and If you have any questions or unclear ideas tag on the comments.

Hope it helps!!!

The activation energy for the given reaction is166 KJ/mol. (Option B)

Activation energy refers to the minimum amount of extra energy that is required by a reacting molecule to be converted into product. It is the minimum amount of energy required to energize or activate atoms or molecules so that they can undergo a chemical reaction or transformation. In order to calculate the activation energy (Ea), the Arrhenius equation is used which is given by:

k=Ae^((-E)/RT)

where k is the rate of chemical reaction, A is a constant depending on the chemicals involved, E is the activation energy, R is the universal gas constant, and T is the temperature.

The equation can be expressed as

ln⁡〖k=ln⁡〖A-(E/RT)lne〗  〗

2.303 log⁡〖k=2.303 log⁡〖A-E/RT〗 〗

log⁡〖k=log⁡〖A-E/2.303RT〗 〗

As there are two temperatures and two rate constants given, the Arrhenius equation is rearranged:

log⁡〖k2/k1=E/2.303(1/T1〗-1/T2)

According to the data,

k1 = 2.7 x 10^-4

T1 = 600 K

k2 = 3.5 x 10^-3

T2 = 650 K

R = 8.314

log⁡〖(3.5 x10^(-3))/(2.7 x 10^(-4) )=E/(2.303*8.314)(1/600〗-1/650)

E = 166208 J/mol or 166 KJ

Note: The question is incomplete. The complete question probably is: Calculate the activation energy (Ea) in kJ/mol for a reaction if the rate constant (k) is 2.7 × 10^-4 (M^−1sec^−1) at 600 K and 3.5 × 10^−3 (M−^1sec^−1) at 650 K. a. −166 kJ/mol b. 166 kJ/mol c. 1.64 kJ/mol d. 1.66 × 10^5 kJ/mol. (R

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The probability of x successes in the n independent trials of the experiment is 0.1640625

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.

Given that, n=9​, p=0.5​, x≤3 we need to find probability of x successes in the n independent trials of the experiment.

We know that,

P(X=x) = ⁿCₓpˣq⁽ⁿ⁻ˣ⁾

q = 1-p = 1-0.5

q = 0.5

P(X=x) = ⁹C₃(0.5)³(0.5)⁹⁻³

P(X=3) = ⁹C₃ (0.5)³(0.5)⁶

⁹C₃ = 9! / 3!(9-3)! = 9!/3! × 6!

⁹C₃ = 84

P(X=3) = 84×0.125×0.015625

= 0.1640625

Hence, the probability of x successes in the n independent trials of the experiment is 0.1640625

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Write each vector in component form and add the components separately. This new vector will represent the sum of the two original vectors. This is the most straightforward way to add two vectors.

1. Write each vector in component form. This means breaking down each vector into its x- and y-components.

2. Add the x-components of each vector together and the y-components of each vector together.

3. The result will be a single vector with both x- and y-components.

To add two vectors, I should write each vector in component form, breaking them down into their x and y components. Then, I should add the components together, resulting in a new vector with components that are the sum of the two original vectors' components. This new vector will represent the sum of the two original vectors. This is the most way to add two vectors.

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Answer:

3

Step-by-step explanation:

12/4=3

Answer:

Car Value Depreciation Graph

The graph that represents the value of the car, y, in dollars, after x years is the graph that starts at $8,000 on the y-axis and decreases at a steady rate of 25% each year on the x-axis. It would be the graph V.

Approximately 95% of housing prices are between a low price of $133,000 and a high price of $161,000.

These approximate percentages are defined by the Empirical Rule, for a normally distributed variable.

Hence the prices within two standard deviations of the mean are given as follows:

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The graph below is an example of graph function is cubic.

We must identify the kind of the graph after receiving it.

A parabola represents the graph of a quadratic function. As a result, the presented graph is not a quadratic function graph.

A straight line is represented by a linear function. The presented graph is not a graph of a linear function as a result.

A square root function's graph resembles a half parabola. Therefore, it can't be the square root function graph.

A cubic function's final behaviour is "opposite at both ends." We can see that the provided graph satisfies this requirement.

As a result, the shown graph illustrates a cubic function.

The right graph is C.

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Answer:

Step-by-step explanation:

Each bracelet need 7 inches of string. Jenna has a total of 16 feet of string.

Divide the total amount of string by the number of inches needed for each bracelet.

Step 1: Convert 16 feet into inches. 12 inches = 1 foot

16 feet x (12 inches/1 foot) = 192 inches

This is the total inches of string.

Note that feet and foot units cancel and you are left with inches.

Step 2: Find the number of bracelets that can be made. Use the answer from step 1. Each bracelet needs 7 inches of string.

Total inches of string / 7 inches of string for each bracelet

192 inches / 7 inches = 27.4

Round the answer to 27.

The value of the equations are

n = 6

x = 20

b = -4

k = 176

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

a)

-15 + n = -9   be equation (1)

On simplifying the equation , we get

Adding 15 on both sides of the equation , we get

n = -9 + 15

n = 6

Therefore , the value of n is 6

b)

x - 7 = 13   be equation (2)

On simplifying the equation , we get

Adding 7 on both sides of the equation , we get

x = 13 + 7

x = 20

Therefore , the value of x is 20

c)

14b = -56   be equation (3)

On simplifying the equation , we get

Dividing 14 on both sides of the equation , we get

b = - ( -56/14 )

b = -4

Therefore , the value of b is -4

d)

16 = k/11   be equation (4)

On simplifying the equation , we get

Multiply by 11 on both sides of the equation , we get

k = 16 x 11

k = 176

Therefore , the value of k is 176

Hence , the equations are solved

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Answer:

5/4

Step-by-step explanation:

divide 20 and 16 by 4

20/4=5

16/4=4

Using the graph,  it's cheaper to use Company B instead of Company A; when the number of miles is less than 5 miles.

For us to solve this question, we need to first create an equation;

If A company initially supplies $30 and then $2 per mile, then the equation here is:

y = 2x + 30

If B company initially supplies $20 and then $4 per mile, then the equation is expressed as:

y = 4x + 20

Due to the fact that the two wages are asked to be equalized, we equate these two equations with each other and find the result.

2x + 30 = 4x + 20

2x = 10

x = 10/2

x = 5

This is the number of miles that both companies will charge a customer the same amount.

Then the time for which it is cheaper to use company B is when number of miles is less than 5.

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The distance covered by the bicycle at a speed of 19 miles per hour is 418 feet

The rate of change in an object's position with regard to a scalar quantity of reference and time is what is meant by speed, according to its definition. Although it may appear difficult, speed is essentially speeding in a particular direction. Due to the fact that it is a scalar quantity, speed must be defined in terms of both magnitude (speed) and direction. It has a meter per second SI unit (ms-1). A body is considered to be accelerating if there is a change in the magnitude or the direction of its speed.

we know that 1 mile is 5280 feets

so, the speed of 19 miles per hour will be 100320 feet in 3600 seconds

we know

distance = speed × time

distance = 100320/ 3600 ×15

distance = 418 feet

hence the distance covered is 418 feet.

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The value of given expression 12*9  is 108

What is Algebraic expression ?

Algebraic expressions are the concept of expressing numbers the usage of letters or alphabets without specifying their real values. The basics of algebra taught us how to express an unknown fee using letters which includes x, y, z, and so forth. these letters are known as here as variables. An algebraic expression can be a aggregate of both variables and constants. Any price that is placed before and accelerated through a variable is a coefficient.

Given expression ,

12*9 = (3*4) * (3*3)

= 9*(3*4)

= 9* 12

= 108

Hence, The value of given expression 12*9 is 108

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The total surface area of the triangular pyramid will be 106.86 yd².

The formula to calculate the total surface area of a triangular pyramid is -

T.S.A. = [tex]\frac{1}{2}[/tex](a × b) + [tex]\frac{3}{2}[/tex](b × s).

Given is a triangular pyramid with dimensions -

The total surface area of the triangular prism will be -

T.S.A. = [tex]\frac{1}{2}[/tex](a × b) + [tex]\frac{3}{2}[/tex](b × s).

T.S.A. = 1/2(5.2 x 6) + 3/2(5.2 x 11.7)

T.S.A. = 31.2/2 + 182.52/2

T.S.A. = 15.6 + 91.26

T.S.A. = 106.86 yd²

Therefore, the total surface area of the triangular pyramid will be 106.86 yd².

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Here is the attached image for the answer. If you write it in in slope-intercept form, y=mx+b. You will get the answer below in the attached image.

The quantitative variable is continuous for any given value of the amount of water in a dog's bowl.

In order to give an answer to this question, we need to recall the definition of continuous and discrete variables. Then according to the definition, we get the answer if the quantitative variable is discrete or continuous for the given amount of water in a dog's bowl.

As we understand that a discrete variable is a variable whose value is fetched by counting. A discrete random variable holds countable possible values. A random variable is one whose value is numerical. On the other hand, a continuous variable is a variable whose value is fetched by measuring.

The amount of water in a dog's bowl has any value. So the amount of water in a dog's bowl is a continuous variable.

Hence, the quantitative variable is continuous for any given amount of water in a dog's bowl.

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Same-sized rectangles are possible. However, because their sides might differ in length, they are not congruent.

Congruent refers to two rectangles having the same dimensions and shape. So, two rectangles are said to be congruent if their length and width are equivalent in size. The length and width of two rectangles must match for them to be congruent.

Also having the same area are congruent shapes, such as rectangles. However, congruent rectangles with the same area are not always the case. There are differences among rectangles. Figures that have the exact same shape but differ in size are referred to as similar figures.

These two polygons are incongruent because while their matching sides are equal, their corresponding angles are not. Despite the sides being the same size, they have different forms.

The complete question is:

Draw two rectangles that have the same area but are not congruent.

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In a basketball game,Benito score 3 points less than twice the number of points that Carnell scored. Benito scored 13 points therefore the number of  points Carnell scored was 16 points.

Benito scored 13 points which means that the number of points Carnell scored was:

8 multiplied by 2 = 16

When we subtract 3 from 16 we get 13 which is Benito score mentioned in the question thereby making it the correct choice.

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Answer: We can set up the following system of inequalities to represent the situation:

8x + 2.5y <= 95 (the total cost of the hamburgers and drinks must be less than or equal to $95)

x >= 18-y (William must buy no less than 18 hamburgers and drinks altogether)

x >= 0, y >= 0 (non-negative values for the number of hamburgers and drinks purchased)

To graph the system of inequalities, we can start by graphing the inequality 8x + 2.5y <= 95, which represents a boundary line in the xy-plane. Since it's a less or equal sign, we will shade the area that is below the line.

The second inequality represents a boundary line which is the line x = 18-y. Since x must be greater than or equal to 18-y, we will shade the area that is on or above the line.

The third inequality is a non-negative constraint for both x and y, so we will graph the x and y axis and shade the area that is above them.

After combining all the shaded areas, we'll get a feasible solution region that represents possible values of x and y that satisfies the system of inequalities.

One possible solution to the system of inequalities is x=24 and y=6, which is a point in the feasible region that satisfies all the inequalities.

It's worth noting that there could be other solutions as well, depending on the number of hamburgers and drinks William wants to buy.

Step-by-step explanation:

The matrix multiplication is possible for option (b) 1 × 3 by 3 × 3, and option (c) 2 × 1 by 1 × 2.

What is a matrix?

A matrix is a rectangular array or table with numbers or other objects arranged in rows and columns. Matrices is the plural version of matrix. The number of columns and rows is unlimited. Matrix operations include addition, scalar multiplication, multiplication, transposition, and many others.

It is known that if the number of columns of a matrix A be equal to the number of rows of another matrix B then the product of matrix A and matrix B i.e. AB is defined.

a)  In this option no of columns in first matrix is 1 and the no of rows in second matrix is 2.

That means no of columns in first matrix is not equal to no of rows in second matrix.

Hence, in this case matrix multiplication is not possible.

Therefore, option (a) is incorrect.

b)  In this option no of columns in first matrix is 3 and the no of rows in second matrix is also 3.

That means no of columns in first matrix is equal to no of rows in second matrix.

Hence, in this case matrix multiplication is possible.

Therefore, option (b) is correct.

c)  In this option no of columns in first matrix is 1 and the no of rows in second matrix is 1.

That means no of columns in first matrix is equal to no of rows in second matrix.

Hence, in this case matrix multiplication is possible.

Therefore, option (c) is correct.

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The value of angle mZB is 28. 8 degrees

It is important to note that supplementary angles are described as pair of angles that sum up to angles on a straight line.

Also, angles on a straight is equal or equivalent to 180 degrees.

From the information given, we have that;

Now, susbtitute the values, we get;

mZB + mZA = 180

5mZB + 7. 2 + mZB = 180

collect like terms, we get;

5mZB + mZB = 180 - 7.2

Add or subtract the like terms

6mZB = 172.8

Now, divide both sides by the coefficient of mZB, we get;

mZB = 172.8/6

Divide the values

mZB = 28. 8 degrees

Hence, the value is 28. 8 degrees

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The mistake of Derek is that 72 divided by 8 is 9, not 8.

An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side

Given is an equation that Derek is trying to solve.

The equation is 8d = 72.

8d = 72

In the first step, Derek divided both sides of the equation by 8, which is a correct way to solve the problem.

We have to divide both sides of the equation by 8.

8d / 8 = 72 / 8

This step is correct.

After dividing, in the left hand side, there will be only 'd' remaining and in the right hand side, 27/8 = 9.

d = 9

But Derek got 8 instead of 9 in the right hand side.

Hence the value of d is 9 and not 8, which is the mistake of Derek.

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Answer:

Exact Form:

21/10

Decimal Form:

2.1

Mixed Number Form:

2 1/10

Step-by-step explanation:

The actual speed of Mr Casey is 39.71 miles per hour and his estimation is greater than the actual speed at which he should travel.

Estimation is a roughly calculated answer of something for which we get an approximate result of it.

Given that, Mr. Casey needs to drive 278 miles in 7 hours. He estimates that he should drive at a speed of 50 miles per hour. We need to find whether his estimation correct or not,

We know that,

Speed = distance / time

Therefore, Mr. Casey's actual speed =

Speed = 278 / 7

= 39.71 miles per hour

As, he estimated his speed being 5o miles per hour, and actual speed is 39.71 miles per hour, therefore, his estimation is greater than the actual speed at which he should travel.

Hence, the actual speed of Mr Casey is 39.71 miles per hour and his estimation is greater than the actual speed at which he should travel.

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Equation for the cost of company A: f(x) = 15 + x

Equation for the cost of company B: g(x) = 45 + x/2

For 80 miles, company B is cheaper than company A.

A linear equation is an algebraic equation where each term has an exponent of 1 and when this equation is graphed, it always results in a straight line.

Given,

Company A charges an initial fee of $15 for the rental plus $1 per mile driven

f(x) = 15 + x

Company B charges an initial fee of $45 for the rental plus $0.50 per mile driven

g(x) = 45 + 0.5x

g(x) = 45 + x/2

x is number of miles

For 80 miles company A charges

f(80) = 15 + 80

        = 95

For 80 miles company B charges

g(80) = 45 + 80/2

         = 85

By the above calculation, Company B is cheaper than Company A for 80 miles drive.

Hence,

f(x) = 15 + x is Equation for the cost of company A

g(x) = 45 + x/2 is Equation for the cost of company B

Company B is cheaper than company A for drive of 80 miles.

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