which expression can be used to calculate the rate per minute at which the air freshener dispenses sprays? fraction 30 over 6

Answer:

True

Step-by-step explanation:

-6X = 42

Divide each side by -6

-6x/-6 = 42/-6

x = -7

b=24

Main concepts

Concept 1. Congruent Triangles

Concept 2. Hypotenuse-Leg Congruence

Concept 3. Congruent Triangles implies congruent parts

Concept 4. Solving a one-variable equation

Concept 1. Congruent Triangles

For two triangles to be congruent, the three angles of one triangle must be congruent to the three angles of the other triangle, AND the three side lengths of one triangle must be congruent to the three side lengths of the other triangle.

Fortunately, through various proofs about different types of triangles, it isn't necessary to prove all six of those things.

The 5 cases of triangle Congruence are

Concept 2. Hypotenuse-Leg Congruence

Proving they are both right triangles, and that HL congruence can be used

In this situation, we are given that Angle UVT is a right angle.  Under the assumption that US is a line that contains V, then Angle UVT and Angle SVT form a linear pair and are supplementary (their measures add to 180 degrees).

So, Angle SVT is also a right angle.  This means that both Triangle UVT and Triangle SVT are Right Triangles, since they are each a triangle with a right angle.

To prove HL congruence, we need to prove that one leg of each triangle is congruent to the other, and that the hypotenuse of each triangle is congruent to the other.

Proving Hypotenuse congruence

Note that the Hypotenuse (side across from the right angle) of Triangle UVT is side UT with measure 67 units.

The Hypotenuse of Triangle SVT is side ST, also with measure 67 units.

So the Hypotenuses are congruent.

Proving Leg congruence

Note that one leg of the triangles is shared as a common side:  line segment VT is common to both triangles.  Even though we don't know the actual length of VT, the length of VT for the first triangle is the same as the length of VT for the second triangle.

The official reason that VT is congruent to VT is because of the "Reflexive property".  

Since the Hypotenuses and one leg from each triangle are congruent, the two triangle are congruent.  Specifically, Triangle UVT is congruent to Triangle SVT.

Concept 3. Congruent Triangles implies congruent parts

Even though we didn't prove all 6 congruences, we did prove that the triangles ARE congruent.  Therefore, all 6 congruences are true.  This means that any other pair of corresponding parts is also congruent.

Specifically, we're interested in the last pair of sides, because they have measurements that contain "b" the value we're trying to solve for.

Side UV is congruent to Side SV because Corresponding parts of Congruent triangles are Congruent.

This means that their lengths are equal:

\(Length_{UV}=Length_{SV}\)

\(b+24=2b\)

Concept 4. Solving a one-variable equation

For any equation in math where there is only one item that is unknown, (even if it shows up multiple times in the equation), there are two main steps:

Step 1.  Get the variable to show up exactly once

Step 2.  Isolate the variable

Step 1.  Get the variable to show up exactly once

Since we know that in the very end, we want b=__, we know that the b will appear only once (and thus only on one side of the equation, not both), and will be by itself.

In practice, sometimes there are special tricks that have to be employed to make this step happen.  Generally, this means simplify each side of the equation, and try to group like terms together.

For this equation, observe that b appears twice: once on the left side of the equation, and once on the right side of the equation.  

At some point, we'll need to get the "b"s on the same side of the equation, and hopefully combine like terms into a single term with b.

To get the "b"s on one side, we'll subtract b from both sides:

\((b+24)-b=(2b)-b\)

On the left, the positive b and negative b cancel completely, leaving just 24.  On the right, the 2b subtracted by 1b leaves just 1b, or more simply, b.

\(24=b\)

Step 2.  Isolate the variable

While trying to get the variable to show up exactly once, we also incidentally isolated the variable, as the like terms combined.

So, b=24.

Answer:

here it is

Step-by-step explanation:

Simply divide 5 INTO 60.20 to get $ per hour.

Another way of saying this is divide $60.20 BY 5.

A. 50 dollars

B. 100 dollars

C. 50+100x

Answer:

a) 50 b) 75 c) 75x+50

Step-by-step explanation:

those are correct

Checking our answer choices:

Therefore, only options A and C are correct.

The function f(x) = tan(2x) will have vertical asymptotes where the function is undefined.

The general form where the tangent function is undefined is at x = (2n+1)π/2, where n is an integer (because tan(x) is undefined at ±π/2, ±3π/2, ±5π/2, ... and so on).

Since our function is tan(2x), it's undefined when 2x = (2n+1)π/2, which simplifies to x = (2n+1)π/4.

So, the function f(x) = tan(2x) has vertical asymptotes at x = (2n+1)π/4, where n is an integer.

Checking our answer choices:

Therefore, only options A and C are correct.

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The complete question

Which of the following values of x does the function f(x) = tan(2x) have a vertical asymptote? Select all that apply.

A) -π/4

B) 0

C) π/4

D) π/2

E) π

Answer:

\(\frac{1}{a} =\frac{1}{b} +\frac{1}{c} \\ \\\frac{1}{a} = \frac{1}{3} + \frac{1}{2/3} \\\\\frac{1}{a} = \frac{1}{3} + \frac{3}{2}\\\\\frac{1}{a} = \frac{11}{6}\\\\a = \frac{6}{11}\)

Answer: A monomial representation is a way to express a polynomial as a product of powers of its variables, where each power is a non-negative integer. For example, the polynomial 2x^3 + 4x^2 - 6x + 8 can be represented as a monomial representation of (2x^3)(x^2)(-6x)(8).

Symmetric polynomials are polynomials that are invariant under permutation of their variables. A symmetric presentation is a way of expressing a symmetric polynomial as a sum of elementary symmetric polynomials, which are defined as the sum of all possible products of variables taken i at a time, where i ranges from 1 to the number of variables. For example, the symmetric polynomial x^3 + y^3 + z^3 can be expressed as a symmetric presentation of x + y + z.

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

The "radius" is half of the diameter. So basically the diameter ÷ 2. So if the radius is 3, two times three is six.

Hope this helps and have a nice day!

Answer:

d=6

r 3 the answer is 6. please mark brainlyest.

Step-by-step explanation:

I hope this helps!

Reason:

There are 5 different digits given.

We have 5 choices for the first slot, then 4 for the next, and 3 for the last. Count down by 1 each time because we don't reuse any digit.

We have 5*4*3 = 20*3 = 60 different permutations to represent the possible three-digit numbers we can form without repeats.

The cone should have its maximum volume. V=1/*3r2h is the formula for calculating the volume V of a cone with height h and radius r.

The cone has a volume of

V=πr2h/3

Therefore, we must calculate the values of r and h in terms of R. R is the diameter of the cone's top-circular circle, and h is the cone's height.

R is the cone's slant height, and it serves as the hypotenuse of a right triangle.

R2 = h2 + r2, or r2 = R2-h2.

So V = (1/3)π

[R2-h2]

h = (π/3)[R2h-h3]

You must take the derivative of the cone's volume, set it to zero, then solve for h to determine the cone's maximum volume.

dV/dh=(π/3)[R2-3h2]

R2-3h2=0 --> h2=R2/3 -> h = R/√3

Now we can determine r:

r2=R2-R2/3 = (2/3)R2

The volume formula with r and h substituted:

V = (π/3)

r2h = (π/3)(2R2/3)

(R/√3)

V(R)=2πR3/(9√3)

The complete question is:

A cone-shaped drinking cup is made from a circular piece of paper of radius R by cutting out a sector and joining the edges CA and CB. Find the maximum capacity of such a cup (Your answer may depend on R).

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Answer:

well if jenny put 6 MORE marshmellows in her cup thenjulie and they added up  to 6 then julie must of not had any

Step-by-step explanation:

Answer:

the rate of change is 4.

Step-by-step explanation:

It is 4 because to find the rate of change you need to see how many pieces of corn (y) there are for every serving (x). If you see if you plug in the number three in between 2 and 4 for the servings and you follow the pattern of the table you will get 12. Then you subtract 8 from 12 and you get 4.

so basically the rate of change is the difference in corn for every serving.

The measures of the angle is 56 degree and 34 degree. The sum of their measurement is 90 degree.

Let the measure of the angle be x degrees. According to the given information, the measure of its complement will be (90 - x) degrees. The difference between the angle and its complement is 22 degrees.

Let's assume the measure of the angle is x degrees. The complement of the angle is defined as (90 - x) degrees since the sum of an angle and its complement is always 90 degrees for a right angle. According to the given information, the difference between the angle and its complement is 22 degrees. Mathematically, we can express this as:

x - (90 - x) = 22

Simplifying the equation, we get:

x - 90 + x = 22

Combining like terms, we have:

2x - 90 = 22

Adding 90 to both sides:

2x = 112

Dividing both sides by 2:

x = 56

Therefore, the measure of the angle is 56 degrees. By substituting this value into (90 - x), we can find the measure of its complement, which is 90 - 56 = 34 degrees.In conclusion, the angle measures 56 degrees, and its complement measures 34 degrees

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to sketch the graph of the linear inequality:

Step 1. Graph the line.

Since the inequality we have is:

The line we need to graph is:

Here, the number that accompanies the x is called the slope of the line "m"

and the independent number is called the y-intercept "b", which is the point where the line crosses the y-axis.

The graph of just the line is:

And since the symbol of the inequality is ">", we will have the part that is up from the line.

And since the simply is not "≥" we will have the line pointed, the result will be as follows:

Answer:

Step-by-step explanation:

To show that X and Y are independent, we need to check that their joint PMF factorizes into the product of their marginal PMFs, i.e., PXY(k,l) = PX(k)PY(l) for all k,l.

To do this, we need to find the marginal PMFs of X and Y. We can do this by summing over all possible values of the other variable, as follows:

PX(k) = ∑l=1,2,3,... PXY(k,l) = ∑l=1,2,3,... 1/(2^(k+l))

The numbers of passengers that need to be booked to ensure the cruise line makes a profit, using a compound inequality is x ≥ 2,052 and x ≤ 2,462.

From the information given, we are told that the cruise ship needs to book at least 2,052 passengers to be profitable, but the most passengers the ship can accommodate is 2,462.

Learn x be the number of people that can be accommodated. Therefore, the model is x ≥ 2,052 and x ≤ 2,462.

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Answer:

C. x= 4

Step-by-step explanation:

|x + 3| = 7

x + 3 = 7

x = 7 - 3

x = 4

Answer:

x = 4

Step-by-step explanation:

|x + 3| = 7

=> x + 3 = 7

=> x = 7 - 3

=> x = 4

The t-shirts she sell is 24.

What is profit and selling price?

Profit is considered as the gain amount from any business activity. Whenever a shopkeeper sells a product, his motive is to gain some benefit from the buyer in the name of profit.

The selling price is the price that the buyer pays to buy a product or goods. This is a price above cost and includes a profit ratio.

According to Question, Christine sold the t- shirts at $4 each and she earned a profit of $71 and his total expenses were $25

Let the total number of t- shirts sold by Christine be "x"

Profit = Selling price – Expenses

Selling price is given as:

selling price = total number to t-shirt sold ×price of each t shirt

selling price = n ×4

71 = (n×4) -24

71 + 25  = n×4

96/4 = n

n = 24

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Each prerequisite for a binomial variable is met in this circumstance, hence SSS has a binomial distribution.

In probability theory and statistics, the binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a series of n independent experiments, each asking a yes-or-no question and having its own Boolean-valued outcome: success (with probability p) or failure (with probability q=1-p). For a single trial, or n = 1, the binomial distribution is a Bernoulli distribution. A single success/failure experiment is also known as a Bernoulli trial or experiment, while a succession of results is known as a Bernoulli process. The widely used binomial statistical significance test is based on the binomial distribution.

True. Each trial has two possible results (it either lands on one side or it doesn't), each trial's findings are independent, there are a fixed number of trials (202020), and each trial has the same chance of success.

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Answer:

50.27 cm

Step-by-step explanation:

We Know

The area of the circle = r² · π

Area of circle = 64π cm²

r² · π = 64π

r² = 64

r = 8 cm

Circumference of circle = 2 · r · π

We Take

2 · 8 · (3.1415926) ≈ 50.27 cm

So, the circumference of the circle is 50.27 cm.

Answer: C=16π cm or 50.24 cm

Step-by-step explanation:

The formula for area and circumference are similar with slight differences.

\(C=2\pi r\)

\(A=\pi r^2\)

Notice that circumference and area both have \(\pi\) and radius.

\(64\pi=\pi r^2\)        [divide both sides by \(\pi\)]

\(64=r^2\)             [square root both sides]

\(r=8\)

Now that we have radius, we can plug that into the circumference formula to find the circumference.

\(C=2\pi r\)          [plug in radius]

\(C=2\pi 8\)          [combine like terms]

\(C=16\pi\)

The circumference Is C=16π cm. We can round π to 3.14.

The other way to write the answer is 50.24 cm.

Answer:

Formula for gradient is given as (y2-y1)÷(x2-x1) or (y1-y2)÷(x1-x2), where x and y are the coordinates of the points.

(k-4)÷(0-1) = 9

k-4 = 9(0-1)

k-4 = -9

k = -5

The answer is ,  the Taylor series (centered at c=0) for the function f(x) = e^(4x) is given by:

\($$\large f(x) = \sum_{n=0}^{\infty} \frac{4^n}{n!}x^n$$\)

The Taylor series expansion is a way to represent a function as an infinite sum of terms that depend on the function's derivatives.

The Taylor series of a function f(x) centered at c is given by the formula:

\(\large f(x) = \sum_{n=0}^{\infty} \frac{f^{(n)}(c)}{n!}(x-c)^n\)

Using the definition of Taylor series to find the Taylor series (centered at c=0) for the function f(x) = e^(4x), we have:

\(\large e^{4x} = \sum_{n=0}^{\infty} \frac{e^{4(0)}}{n!}(x-0)^n\)

\(\large e^{4x} = \sum_{n=0}^{\infty} \frac{4^n}{n!}x^n\)

Therefore, the Taylor series (centered at c=0) for the function f(x) = e^(4x) is given by:

\($$\large f(x) = \sum_{n=0}^{\infty} \frac{4^n}{n!}x^n$$\)

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The Taylor series for f(x) = e^(4x) centered at c = 0 is:

f(x) = 1 + 4x + 8x^2 + 32x^3/3 + ...

To find the Taylor series for the function f(x) = e^(4x) centered at c = 0, we can use the definition of the Taylor series. The general formula for the Taylor series expansion of a function f(x) centered at c is given by:

f(x) = f(c) + f'(c)(x - c) + f''(c)(x - c)^2/2! + f'''(c)(x - c)^3/3! + ...

First, let's find the derivatives of f(x) = e^(4x):

f'(x) = d/dx(e^(4x)) = 4e^(4x)

f''(x) = d^2/dx^2(e^(4x)) = 16e^(4x)

f'''(x) = d^3/dx^3(e^(4x)) = 64e^(4x)

Now, let's evaluate these derivatives at x = c = 0:

f(0) = e^(4*0) = e^0 = 1

f'(0) = 4e^(4*0) = 4e^0 = 4

f''(0) = 16e^(4*0) = 16e^0 = 16

f'''(0) = 64e^(4*0) = 64e^0 = 64

Now we can write the Taylor series expansion:

f(x) = f(0) + f'(0)(x - 0) + f''(0)(x - 0)^2/2! + f'''(0)(x - 0)^3/3! + ...

Substituting the values we found:

f(x) = 1 + 4x + 16x^2/2! + 64x^3/3! + ...

Simplifying the terms:

f(x) = 1 + 4x + 8x^2 + 32x^3/3 + ...

Therefore, the Taylor series for f(x) = e^(4x) centered at c = 0 is:

f(x) = 1 + 4x + 8x^2 + 32x^3/3 + ...

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for this case we have the folloeing information: In a class we have 17 flute players and 15 Clarinet Players for the Amy's Music Class.

The total of students are:

And then if we need to select one player (student) the probability would be given by:

And the best answer would be A) 1/32

Steps to solve:

4x + 1/3y^2 when x = 2 and y = 3

~Substitute

4(2) + 1/3(3)^2

~Simplify

8 + 1/3(9)

~Simplify

8 + 3

~Add

11

Best of Luck!