1. What do you think it means when the change is positive? Negative?

2. What do you think it means when the inventory is positive? Negative?

Answer:

B. -6 < y < ∞

General Formulas and Concepts:

Algebra I

Step-by-step explanation:

According to the graph, we have an asymptote at y = -6 and infinite positive y-values. Our range is therefore restricted to -6 to infinity. Both y = -6 and ∞ are excluded:

-6 < y < ∞

Answer:

63

Step-by-step explanation:

Use Pythagorean theorem,

base² + altitude² = hypotenuse²

a² + 9² = 12²

       a² = 12² - 9²

      a² = 144 - 81

     a² = 63

      a = √63

To remove radicals in the denominator, one can use the process of rationalizing. This involves changing the fraction to an equivalent expression with a rational denominator by multiplying the numerator and denominator by a conjugate of the denominator. The conjugate is a binomial radical expression that differs from the given expression only in the arithmetic sign between the terms.

Identify the denominator of the fraction and determine if it contains any radicals.

Find the conjugate of the denominator by changing the sign between the terms of the radical expression. For example, if the denominator is √a + b, the conjugate would be √a - b.

Multiply both the numerator and denominator of the fraction by the conjugate of the denominator. This is equivalent to multiplying the fraction by 1, since the conjugate of the denominator divided by itself equals 1.

Simplify the resulting expression by distributing the multiplication and combining like terms.

If necessary, simplify any remaining radicals in the expression.

For example, to rationalize the denominator of the fraction 2/√3, we would follow these steps:

Identify the denominator √3, which contains a radical.

Find the conjugate of the denominator, which is √3.

Multiply the numerator and denominator by the conjugate of the denominator, which gives us (2 * √3)/(√3 * √3) = (2√3)/3.

Simplify the expression by dividing 2√3 by 3 to get (2/3)√3.

By rationalizing the denominator, we have changed the fraction to an equivalent expression with a rational denominator, which is often preferred in mathematical calculations.

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Answer:

x = 22

Step-by-step explanation:

Solve for x:

6 (2 x - 4) = 10 (x + 2)

Expand out terms of the left hand side:

(12 x - 24) = 10 (x + 2)

Expand out terms of the right hand side:

12 x - 24 = (10 x + 20)

Subtract 10 x from both sides:

(12 x - 10 x) - 24 = (10 x - 10 x) + 20

12 x - 10 x = 2 x:

2 x - 24 = (10 x - 10 x) + 20

10 x - 10 x = 0:

2 x - 24 = 20

Add 24 to both sides:

2 x + (24 - 24) = 24 + 20

24 - 24 = 0:

2 x = 20 + 24

20 + 24 = 44:

2 x = 44

Divide both sides of 2 x = 44 by 2:

(2 x)/2 = 44/2

2/2 = 1:

x = 44/2

The gcd of 44 and 2 is 2, so 44/2 = (2×22)/(2×1) = 2/2×22 = 22:

Answer:  x = 22

Answer:

22

Step-by-step explanation:

To solve for x in the equation 6(2x - 4) = 10(x + 2), we can start by distributing the 6 and 10 on the left and right side of the equation respectively:

12x - 24 = 10x + 20

Next, we can combine like terms by adding x to both sides and subtracting 24 from both sides:

12x - 24 + 24 = 10x + 20 + 24

12x = 10x + 44

subtracting both side by 10x

12x-10x=10x-10x+44

2x=44

x=44/2

x=22

Answer:

Opposite of 7= -7

Step-by-step explanation:

Answer:

x=5

f(x)= -5x-2

f(5)= -5(5)-2

f(5)= -25-2

f(5) = -27

Answer:

See below:

Step-by-step explanation:

So we know that \(f(x)=-5x-2\) therefore to find out what \(f(5)\) is we can insert/replace \(x\) with 5 due to it being a function, after we do that, we get this:

\(f(5)=-5(5)-2\)

Using algebra, we an find out that \(f(5)=-27\)

Cheers!

The statement is True.

The theorem of linear algebra that states that if a and b are invertible matrices, then the product ab is invertible is indeed true.

Proof:

Let A and B be invertible matrices.

Then there exist matrices A^-1 and B^-1 such that AA^-1 = I and BB^-1 = I, where I is the identity matrix.

We want to show that AB is invertible, that is, we want to find a matrix (AB)^-1 such that (AB)(AB)^-1 = (AB)^-1(AB) = I.

Using the associative property of matrix multiplication, we have:

(AB)(A^-1B^-1) = A(BB^-1)B^-1 = AIB^-1 = AB^-1

So (AB)(A^-1B^-1) = AB^-1.

Multiplying both sides on the left by (AB)^-1 and on the right by (A^-1B^-1)^-1 = BA, we get:

(AB)^-1 = (A^-1B^-1)^-1BA = BA^-1B^-1A^-1.

Therefore, (AB)^-1 exists, and it is equal to BA^-1B^-1A^-1.

Hence, we have shown that if A and B are invertible matrices, then AB is invertible.

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Answer:

535.96 (rounded up)

Step-by-step explanation:

Y= a ( 1 + r )^t

The series to 10 term is

1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 + 256 + 512

An equation that represents a sequence based on a rule is called a recurrence relation.

Finding the following term, which is dependent upon the prior phrase, is made easier (previous term). We can readily predict the following term in a series if we know the preceding term.

The term is predicted by multiplying the preceding term by 2

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Answer:

Dont you hate when you have to look through the notes and the teachers get impatient but its not your fault the teacher gives you all the notes to take.

Step-by-step explanation:

Is it just me?

Answer:

$9.98

Step-by-step explanation:

The first step is to calculate the total fabric that Calista has

= 2 1/2 + 1 3/4

= 5/2 + 7/4

= 17/4

The next step is to calculate the fabric that she needs

= 17/4-3

= 5/4

If each yard of fabric costs $7.98 then the amount needed can be calculated as follows

= 7.98 × 5/4

= 7.98 × 1.25

= 9.975

= $9.98

Hence Kalista needs $9.98

ANSWER

Area of the shaded figure is 77.7 square unit (rounded to 1 decimal place).

EXPLANATION

Given:

Rectangle with length = 12 and breadth = 7.

Semi-Circle with diameter = 4

Desired Outcome:

The area of the shaded region.

Looking at the figure carefully, you will notice that it was only half of the circle that was fixed with the rectangle.

Determine the Area of a semi-circle

Area of a semi-circle is half of the area of a circle

Area of the Rectangle

Determine the area of the shaded figure

Hence, the Area of the shaded figure is 77.7 square unit (rounded to 1 decimal place).

Answer:

m*m*m*m*m*m*m*m*n*n*n*n*m*m*m*m*m*m*m

m to the fifteenth power + n to the fourth power

Answer:

B. x

Step-by-step explanation:

The answer would be graph x. A function must be that one x value should only have one y value. graph w doesn't work since when you plug in 0, you get two y's. same thing with z. Y doesn't work since at x value of 3, it curves back so x value 2 has 2 y's. X is the only one that each x value has only one y.

Answer:

X

Step-by-step explanation:

For a relationship to be a function, every input has exactly one output, so for every x value there is only one value.

If you look at answer's w and z for x=1 there is two y values, therefore they are not functions, letter Y is tricky. Even though every x value has only one y value, If you were to extend the graph x=0 would have more than one y values.

That leaves X.  If you extend the graph of X every x value will only have one y value so it is a function

The value of the expression below when x=5x=5?

8x+9 is equal to \(7^{2}\) (or) 49.

Substitute \(\left \{ {{x=5x} \atop {5x=5}} \right. into (8x+9)\)

The expression,

y = 8x + 9

If the domain of the function is x = 5, hence the range of the function is gotten by substituting x = 5 into the given function as shown:

So, we can substitute x = 5,

Then, y = 8 * 5 + 9

Calculate the product or quotient,

y = 40 + 9

Calculate the sum or difference,

y = 49

We can write alternative form,

y = \(7^{2}\)

Therefore,

Hence the value of the expressions if x = 5 is \(7^{2}\) (or) 49.

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Answer:

Step-by-step explanation:

20% of 207.77 = 41.554

1% of 207.77 = 2.0777

21% of 207.77 = 41.554+2.007=43.6317

207.77+43.6317 = 251.4017

Round to 2 decimal places because its money = 251.40

Answer:

Where its the graph??????

I think you meant to write

(2 × 10⁶) × 0.00009

First, convert 0.00009 to scientific notation:

0.00009 = 9 × 10 ⁻⁵

Then

(2 × 10⁶) × 0.00009 = (2 × 10⁶) × (9 × 10 ⁻⁵)

… = (2 × 9) × (10⁶ × 10 ⁻⁵)

… = 18 × 10¹

… = 1.8 × 10²

The equivalent expression for 1.5 cubed over 1.3 raised to the fourth power all raised to the power of negative six is 1.5 to the eighteenth power over 1.3 to the twenty-fourth power.

Here are the steps to simplify the expression:

Apply the negative power rule: (1.5 cubed over 1.3 raised to the fourth power) raised to the power of negative six is equal to (1.3 raised to the fourth power over 1.5 cubed) raised to the power of six.

Apply the power of a quotient rule: (1.3 raised to the fourth power over 1.5 cubed) raised to the power of six is equal to (1.3 raised to the fourth power)⁶ / (1.5 cubed)⁶.

Apply the power of a power rule: (1.3 raised to the fourth power)⁶ is equal to 1.3(⁴*⁶) = 1.3²⁴.

Apply the power of a power rule: (1.5 cubed)⁶ is equal to 1.5(³*⁶) = 1.5¹⁸.

Therefore, the equivalent expression is 1.5¹⁸ / 1.3²⁴.

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A linear inequality to represent how many hours, h, Regina will have to babysit before she has enough money to buy the Oculus is,

10h + 250 ≥ 400.

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

Given, The Oculus costs $400.

Regina has already saved $250, and she earns $10 an hour babysitting on the weekends.

Assuming no. of hours to be h.

∴  A linear inequality to represent how many hours, h, Regina will have to babysit before she has enough money to buy the Oculus is,

10h + 250 ≥ 400.

10h ≥ 150.

h ≥ 15

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a) The six questions of statistical validity of a bivariate correlation are,

b) For correlations shown as bar graphs, questions regarding outliers and curved connections may be irrelevant.

Exactly two variables are needed to establish a relationship in a bivariate correlational investigation.

Scatterplot is a quantitative term (user to describe relationship)

Bar graphs are categorical (use the difference in groups to des. rel.)

For correlations shown as bar graphs, questions regarding outliers and curved connections may be irrelevant.

For correlations shown as bar graphs, questions regarding outliers and curved connections may be irrelevant.

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(a) The probability of having at least one girl is 1 - 0.0625 = 0.9375 or 93.75%.

(b) The probability that all the children will be of the same gender is 0.0625 + 0.0625 = 0.125 or 12.5%.

The probability of having at least one girl can be calculated by finding the probability of having no girls and subtracting it from 1.

Assuming that the probability of having a boy or a girl is equal (0.5), the probability of having no girls is (0.5)^4 = 0.0625.

Therefore, the probability of having at least one girl is 1 - 0.0625 = 0.9375 or 93.75%.

(b) The probability that all the children will be of the same gender is 0.0625 + 0.0625 = 0.125 or 12.5%.

The probability that all the children will be of the same gender can be calculated by finding the probability of having all boys and adding it to the probability of having all girls.

The probability of having all boys is (0.5)^4 = 0.0625, and the probability of having all girls is also 0.0625.

Therefore, the probability that all the children will be of the same gender is 0.0625 + 0.0625 = 0.125 or 12.5%.

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The volume of the cone is (100)π cubic centimeters.

Given that the slant height (l) of the cone is 13 cm, and the height from the vertex to the center of the base (h) is 12 cm, we need to find the volume (V) of the cone.

To do this, we'll first need to find the radius (r) of the cone's base.
We can use the Pythagorean theorem to find the radius, since the slant height, height, and radius form a right triangle:
l² = h² + r²
Plugging in the given values:
13² = 12² + r²
169 = 144 + r²
r² = 25
r = 5 cm
Now that we have the radius, we can find the volume of the cone using the following formula:
V = (1/3)πr²h
Substitute the known values:
V = (1/3)π(5²)(12)
V = (1/3)π(25)(12)
V = (1/3)π(300).

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The formula to derive is 2 tan A tan(2A) = 1 - tan² A from the formulas sin(2A) = 2sinAcosA and cos(2A) = cos² A - sin² A.

We know that: cos(2A) = cos² A - sin² A1 + tan² A = sec² A and also that tan(2A) = 2 tan A/1 - tan² A

Since cos(2A) = cos² A - sin² A, then cos(2A) + sin² A = cos² A1 = cos² A - sin² A + sin² Acos² A = cos² A - sin² A2cos² A = 1 + cos(2A)cos² A = 1 - sin² A and tan² A = sin² A/cos² A

We are required to prove that 2 tan A tan(2A) = 1 - tan² A.

Let's consider the left-hand side of the equation: 2 tan A tan(2A) = 2 tan A (2 tan A)/(1 - tan² A) = 4 tan² A/(1 - tan² A)

Also, the right-hand side of the equation is:1 - tan² A = (cos² A - sin² A)/cos² A = cos² A/cos² A - sin² A/cos² A = 1 - sin² A/cos² A. Therefore:4 tan² A/(1 - tan² A) = 1 - sin² A/cos² A = 1 - tan² A and hence,2 tan A tan(2A) = 1 - tan² A.

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Answer:

Sorry I had to go to dinner here you go hope this helps! :D

Step-by-step explanation:

So, before we start, there are two things we have to go over.

First off, we have "or"

When using or between two probabilitess, you are basically adding them together.

For instance, you first question asks what the probability is of rolling a 5 or a number greater than 3(assuming this is a 6 sided dice).

So, rolling a 5 is a change of 1/6. Since 1 of the 6 dice iwll be 5. The other probability is a 1/2, since 3 of the 6 dice are over 3.

Now lets add these two together because of the "or":

1/2+1/6=3/6+1/6=4/6

So the probabily of rolling a 5 OR rolling a number greater than 3 is 4/6.

This is inclusive, since rolling a 5 is possible and greater than 3.

Now "and" is a bit different and more complex than or is.

Here is an example:

What is the change of rolling a even number or rolling a number above 4?

Well, rolling a even number has a probability of 1/2. Rolling a number above 4 is 1/3.

To find the "and", we multiply the two probabilities.

So 1/3*1/2=1/6

So the probability of rolling a even number and a number above 4 is 1/6.

Now, lets get back to the answers.

So what is the probability of rolling a 2 or a 6?

There is a 1/6 probability to get a 2, and a 1/6 probability to get a 6.

Add it together since they use or:

1/6+1/6=2/6

So the probability of rolling a 2 or a 6 is 2/6, or 1/3.

This is exlusive since you cant roll both a 6 and a 2 at the same time.

Next we have what the probability is of drawing a 6 or a king.

There are 13 different cards in a deck.

There is a 4/52 chance of drawing a 6(spade/heart/etc), and a 4/52 chance of drawing a king. This simplyfies to 1/13 for each.

This is:

1/13+1/13=2/13

So the probability of drawing a 6 or a king is 2/13

This is a exclusive event since a king and 6 cant be drawn at the same time.

Finally, we have:

What is the probability of drawing a queen or a spade?

Again, there is a 4/52 chance of drawing a queen. A spade, however, is different.

13 of the 52 cards can be spades, which simplies to 1/4.

So we have 1/13+1/4=4/52+13/52=17/52

So there is a 17/52 probability of drawing a queen or spade.

This is a inclusive event since it is possible to draw both a spade and queen at the same time.

Hope this answers all your questions and helps you understand what "and" "or" are in probability.

The set of integers is closed under the operation of addition because the sum of any two integers is always another integer and is therefore in the set of integers.

What are integers ?

An integer is a whole number (not a fractional number) that can be positive, negative, or zero. Examples of integers are: -5, 1, 5, 8, 97, and 3,043. Examples of numbers that are not integers are: -1.43, 1 3/4, 3.14, .

According to the Property of Closure, A set has the closure property under a particular operation if the result of the operation is always an element in the set.  If a set has the closure property under a particular operation, then we say that the set is “closed under the operation.”

Hence ,  the set of integers is closed under the operation of addition because the sum of any two integers is always another integer and is therefore in the set of integers.

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The relationship between x and y is given by Y=14*X;

Relationship between the number of tokens Erin uses, x, and the number of pitches thrown by the pitching machine, y. x (tokens) y (pitches) 1 14 2 28 3 42 7 98

by, observing the given data we say that;

x is proportional to y so, the general equation is given by

x ∝ y so, by removing the proportionality sign we get y=k*x;

now using given x and y we put in this equation to get the value of k; then by substituting the value of k in this equation we get our required equation.

so, putting x=1 and y=14 we get k=14;

and, putting x=2 and y=28 we get k=14;

and putting x=3 and y =42 we get k=14;

similarly, the last data satisfy the equation.

By putting k =14 in the equation we get, Y=14*X

thus, Y=14*X is our required answer.

also, we solve this problem by using the equation of line concept;

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Answer:

-3 (x - 4) (x - 1)

Step-by-step explanation:

If the price of the good falls by $4, the quantity demanded will increase by 20 units. A theoretical restriction on the short-run cubic cost equation, \(TVC = aQ + bQ + cQ^2, is a > 0, b > 0, c < 0.\)

1. Quantity Demanded:

According to the estimated demand equation, \(Q = 25 - 5P + 0.32M + 12PR,\) where Q represents the quantity demanded, P is the price of the good, M is income, and PR is the price of a related good R.

If the price of the good falls by $4, we can substitute P - $4 into the equation to calculate the new quantity demanded:

\(Q' = 25 - 5(P - $4) + 0.32M + 12PR\)

Simplifying the equation, we have:

\(Q' = 25 + 20 - 5P + 0.32M + 12PRQ' = 45 - 5P + 0.32M + 12PR\)

Comparing this with the original equation, we see that the coefficient of P is -5. Therefore, a $4 decrease in price would increase the quantity demanded by 20 units.

2. Short-Run Cubic Cost Equation:

The theoretical restriction on the short-run cubic cost equation, \(TVC = aQ + bQ + cQ^2, is a > 0, b > 0, c < 0.\)

This restriction ensures that the total variable cost (TVC) increases as the quantity (Q) increases, as indicated by the positive coefficients of aQ and bQ. Additionally, the negative coefficient of cQ^2 ensures that the cost curve is concave, representing diminishing marginal returns in the short run.

Therefore, the answer is:

If the price of the good falls by $4, the quantity demanded will increase by 20 units. The theoretical restriction on the short-run cubic cost equation, \(TVC = aQ + bQ + cQ^2, is a > 0, b > 0, c < 0.\)

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