Help me please and thank you!

The following are some examples of irrational numbers from the list:

B. the square root of the number 7.

E. 8.070070007..

Numbers that cannot be represented by fractions are referred to as irrational numbers. Some examples of irrational numbers are non-exact roots, non-terminating decimals, and non-repeating decimals.

In relation to this issue, the following are examples of irrational numbers from the list:

B. the root squared of 7, even if it is not an exact root.

E. 8.070070007, since it is a decimal that does not repeat itself and does not terminate.

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Answer: x= -2/9

Step-by-step explanation:

-12x-2(x+9)=5(x+4)

= -12x-2x+18=5x+20

= -14x+18=5x+20

= -9x+18=20

= -9x=2

/-9    /-9

x= -2/9

Given:

The given function is

\(y=\sec x\)

To find:

The period of given function.

Solution:

General sec function is defined as

\(y=A\sec (Bx+C)+D\)

Where, A is amplitude, \(\dfrac{2\pi}{B}\) is period, \(-\dfrac{C}{B}\) is phase shift and D is vertical shift.

We have,

\(y=\sec x\)

Here, B=1. So,

\(Period=\dfrac{2\pi}{1}\)

\(Period=2\pi\)

Therefore, the period of given function is 2π.

The value of period of function y = sec x is, 2π.

The given function is,

y = sec x

Since, We know that,

General form of equation for sec x is,

y = A sec (Bx + C) + D

Where, A is amplitude, 2π/B is period and D is vertical shift.

Here, function is,

y = sec x

Hence, B = 1,

So, Period = 2π/B

                = 2π/1

                = 2π

Thus, The value of period of function y = sec x is, 2π.

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The statements supported by the data in the table are:

The mean number of cars sold in a month is the same at both dealerships.

The total number of cars sold is the same at both dealerships.

The data for Admiral Autos shows greater variability.

To determine which statements are supported by the data in the table, let's analyze the given information:

The mean number of cars sold in a month is the same at both dealerships.

To calculate the mean, we need to find the average number of cars sold each month at each dealership.

For Admiral Autos:

(4 + 19 + 15 + 10 + 17) / 5 = 65 / 5 = 13

For Countywide Cars:

(9 + 17 + 14 + 10 + 15) / 5 = 65 / 5 = 13

Since both dealerships have an average of 13 cars sold per month, the statement is supported.

The median number of cars sold in a month is the same at both dealerships.

To find the median, we arrange the numbers in ascending order and select the middle value.

For Admiral Autos: 4, 10, 15, 17, 19

Median = 15

For Countywide Cars: 9, 10, 14, 15, 17

Median = 14

Since the medians are different (15 for Admiral Autos and 14 for Countywide Cars), the statement is not supported.

The total number of cars sold is the same at both dealerships.

To find the total number of cars sold, we sum up the values for each dealership.

For Admiral Autos: 4 + 19 + 15 + 10 + 17 = 65

For Countywide Cars: 9 + 17 + 14 + 10 + 15 = 65

Since both dealerships sold a total of 65 cars, the statement is supported.

The range of the number of cars sold is the same for both dealerships.

The range is determined by subtracting the lowest value from the highest value.

For Admiral Autos: 19 - 4 = 15

For Countywide Cars: 17 - 9 = 8

Since the ranges are different (15 for Admiral Autos and 8 for Countywide Cars), the statement is not supported.

The data for Admiral Autos shows greater variability.

To determine the variability, we can look at the range or consider the differences between each data point and the mean.

As we saw earlier, the range for Admiral Autos is 15, while for Countywide Cars, it is 8. Additionally, the data points for Admiral Autos are more spread out, with larger differences from the mean compared to Countywide Cars. Therefore, the statement is supported.

Based on the analysis, the statements supported by the data are:

The mean number of cars sold in a month is the same at both dealerships.

The total number of cars sold is the same at both dealerships.

The data for Admiral Autos shows greater variability.

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Answer:

Step-by-step explanation:

The question is incomplete. Find the complete question in the attached file.

a) Given the expression 9x^2 - y^2 = 1

Differentiating implicitly will give;

\(18x-2y\frac{dy}{dx} = 0\\\)

We can then make dy/dx the subject of the formula as shown;

\(18x = 2y\frac{dy}{dx}\\\frac{dy}{dx} = \frac{18x}{2y} \\\frac{dy}{dx} = \frac{9x}{y} \\y' = \frac{9x}{y}\)

b) In order to solve the question explicitly, we will first have to make x the subject of the formula before differentiating.

\(9x^{2} -y^{2} = 1\\9x^{2} = 1+ y^{2}\\y^{2} =9x^{2}- 1\\y^{2} = 9x^{2} - 1\\y = \sqrt{9x^{2}- 1 } \\\)

Using chain rule to solve the equation;

let;

\(u = 9x^{2} -1\\ y = u^{1/2}\)  

du/dx = 18x

dy/du = \(1/2u^{-1/2}\)

dy/dx = dy/du * du/dx

dy/dx = \(1/2u^{-1/2} * 18x\)

\(\frac{dy}{dx} = \frac{1}{2}({9x^{2}-1 } )^{-1/2} * 18x\\\frac{dy}{dx} = 9x({9x^{2} -1 } )^{-1/2} \\\frac{dy}{dx} = 9 x(\sqrt{{\frac{1}{9x^{2} -1} } }) \\\frac{dy}{dx} = \frac{9x}{\sqrt{9x^{2}-1 } }\)

c) In order to confrim that solutions to part (a) and (b) are consistent, we will substitute \(y = \sqrt{9x^{2} - 1 } \\\) into the answer in (a) as shown;

From (a) \(\frac{dy}{dx} = \frac{9x}{y} \\\)

\(y' = \frac{9x}{ \sqrt{9x^{2} - 1 } \\} } \\}\)

This shows that they are consistent

Answer:

$129.44

Step-by-step explanation:

15% of $212.50 + 15% of $235.00 + 15% of $215.75 + 15% of $199.67 =

= 0.15 * $212.50 + 0.15 * $235.00 + 0.15 * $215.75 + 0.15 * $199.67

= $31.88 + $35.25 + $32.36 + $29.95

= $129.44

Answer: $129.44

Given

we are given an angle of 285 degrees.

Required

we need find sin, cos and tan of 285 degrees

Explanation

Here we know that

so

Again

so

and finally

so

The value of the radical √48 is 4√3.

Radical is a symbol (√) that denotes square roots and nth roots. The number inside the symbol is called Radicand and the expression containing the radical or a square root is called a Radical expression.

Here, we are given the radical √48

To find the value of the radical, we will factorize 48

i.e., 48 = 2×2×2×2×3

           = 16×3

Now, the square root of 48, that is, √48

                                                       = \(\sqrt{16\cdot3}\) =\(\sqrt{16} \cdot \sqrt{3}\)

We know 16 is a perfect square of 4, that is, the square root of 16= 4

⇒√16=4

Using this, we have √48= 4√3

The correct answer is 4√3.

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The length of each side of the wood is 5 centimetres.

Doug has 8 square pieces of wood. Each piece of wood have a side length of s cm. The total area of all 8 pieces of wood is 200 cm².

Hence, using quadratic equation let's find the length of each side of the wood.

Therefore,

8s² = 200

Hence,

8s² = 200

divide both sides of the equation by 8

s² = 200 / 8

s² = 25

s = √25

s = 5 centimetres

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Answer:

The y intercept is (0,-22)

Step-by-step explanation:

The y intercept is the value when x =0

Y=5x-22

y = 5*0 -22

y = -22

The y intercept is (0,-22)

Step-by-step explanation:

2-×^2

t(×)=3×

(s o t )(x)=st(×)=s(t(x))=2-(3×)^2=2-9x^2

(s o t)(-7) =2-9(-7)^2=2-9(49)= 2-441= -439

\(\dfrac{2}{3}\)

Step-by-step explanation:

Let \(P_1 = (-5, 0)\) and \(P_2 = (7, 8).\) The slope of the line passing through these points is given by

\(m = \dfrac{y_2 - y_1}{x_2 - x_1} = \dfrac{8 - 0}{7 - (-5)}\)

\(\:\:\:\:\:= \dfrac{8}{12} = \dfrac{2}{3}\)

The result of the sum in this problem is given as follows:

675

An arithmetic sequence is a sequence of values in which the difference between consecutive terms is constant and is called common difference d.

The sum of the first n terms is given by the equation presented as follows:

\(S_n = \frac{n(a_1 + a_n)}{2}\)

The parameters for this problem are given as follows:

Hence the sum is given as follows:

S = 10/2 x (27 + 108)

S = 675.

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Hello !

Answer :

Explanation :

\( \to \boxed{ ({x}^{a}) {}^{b} = {x}^{ab} } \)

\( \to \boxed{ {x}^{ \frac{1}{n} } {}^{} = \sqrt[n]{x} } \)

\( ({x}^{4} ) {}^{ - \frac{2}{3} } = {x}^{- \frac{2}{3} \times 4} \\ \boxed{= {x}^{ - \frac{8}{3} } } \\ \boxed{= \sqrt[3]{ {x}^{ - 8} }} \\ \boxed{ = \sqrt[3]{ ({x}^{ 4}) {}^{ - 2} }}\)

Have a nice day ;)

Answer:

D. all real numbers where x ≤ –1 or x ≥ 1.

Step-by-step explanation:

The graph of the function  f(x) = (1/x)cos √(x² - 1) is continuous for all real numbers, where - 1 ≤ x ≤ 1. The correct is option C.

A relation between a collection of inputs and outputs is known as a function. A function is a connection between inputs in which each input is connected to precisely one output. Each function has a range, co-domain, and domain.

Given:

f(x) = (1/x)cos √(x² - 1)

To prove continuous function:

At that value, the limit must exist.

At that value, the function must be defined, and.

And at that point, both the limit and the function must have equal values.

In mathematics, a continuous function is one where a continuous variation of the argument results in a continuous variation of the function's value (i.e., a change without a leap).

As you can see in the attached image.

Function is not defined in between (-1, 1)

And function have a leap in between (-1, 1).

Therefore, the function is continuous for all real numbers, where - 1 ≤ x ≤ 1.

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Answer:

Step-by-step explanation:

Happy paws: y = 3.50h + 19

Woof Watchers: y = 4.75h + 13

set them equal to eachother (this is the equation you need)

3.50h + 19 = 4.75h + 13

to find when they will be equal solve for h

6 = 1.25h

4.8 = h

so they will be equal at 4.8 hours

Answer:

Correct answer is B, 69.3 feet

Step-by-step explanation:

Since we have a 30°-60°-90° right triangle, the length of the longer leg is √3 times the length of the shorter leg, so the length of the shorter leg is 1/√3, or √3/3 times the length of the longer leg.

\(120( \frac{ \sqrt{3} }{3}) = 40 \sqrt{3} = 69.3\)

The expected value of the number of upgrades selected is 1.04.

The given probability mass function provides the probabilities for the number of upgrades purchased per customer. We are asked to find the expected value, which is a measure of central tendency in probability theory. To do this, we need to multiply each possible value of upgrades by its probability and then sum them up.

First, we need to figure out the value of f(3). We know that the sum of all probabilities in a probability mass function is 1. Therefore, we can use the given probabilities to calculate f(3) as follows:

1 = f(0) + f(1) + f(2) + f(3)

1 = 0.50 + 0.20 + 0.06 + f(3)

f(3) = 1 - (0.50 + 0.20 + 0.06)

f(3) = 0.24

Now that we know the value of f(3), we can calculate the expected value as follows:

E(X) = (0 x 0.50) + (1 x 0.20) + (2 x 0.06) + (3 x 0.24)

E(X) = 0 + 0.20 + 0.12 + 0.72

E(X) = 1.04

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The cost of each ticket bought by each of the group is $15.

The linear equation that represents the total cost spent by group 1 on the tickets is:

Amount spent = total amount spent on the tickets - discount

9x - 120

The linear equation that represents the total cost spent by group 2 on the tickets is:

3x - 30

Where:

x = is the cost of the tickets

If both groups spend the same amount, the above two linear equations would be equal to each other

3x - 30 = 9x - 120

In order to determine the value of x, take the following steps:

Combine similar terms together: 120 - 30 = 9x - 3x

Add similar terms: 90 = 6x

Divide both sides by 6

x = 90 / 6

x = 15

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After 24 years, the amount will be $40,000

What is annual interest rate?

An annual percentage rate is expressed as an interest rate. It calculates what percentage of the principal you'll pay each year by taking things such as monthly payments into account.

It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.

Formula:

a(t) = p*2^(t/8)

given, t=24 , p =5000

a(24) = 5000*2^(24/8)

a(24) = 5000*2^3

a(24) = 5000*8

a(24) = $40,000

Thus, after 24 years, the amount will be $40,000

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When a recipient not-for-profit entity receives a gift for transfer to another charitable entity, it records it as revenue upon receipt.

If the donor retains the right to revoke or redirect the gift, it's recognized as a "Contribution Receivable" liability until the restrictions lapse or are fulfilled. Consult accountants for proper accounting.

When a recipient not-for-profit entity receives a gift that will be transferred without restriction to another charitable entity,

The accounting treatment typically involves two steps:

Recognition on Receipt:

The recipient not-for-profit entity should recognize the gift as revenue or contribution in its financial records upon receipt.

This is because the organization has legal control and possession of the gift, even if it intends to transfer it to another charitable entity.

The accounting entry will depend on the nature of the gift received ( cash, securities, in-kind donation).

Classification as a "Contribution to be Transferred":

The second step involves classifying the received gift as a "Contribution to be Transferred" on the recipient's balance sheet.

This classification reflects that the entity intends to pass the gift along to another charitable entity

and that the funds are not restricted for use within the recipient organization.

If the donor retains the right to revoke or redirect the gift,

The recipient not-for-profit entity should follow the guidelines for recognizing contributions subject to donor restrictions.

Until the restrictions lapse or are fulfilled, the contribution should be recorded as a liability ( "Contribution Receivable").

Accounting for contributions with donor-imposed restrictions can be complex,

and the specific treatment will depend on the terms of the gift and applicable accounting standards.

It's essential for the not-for-profit organization to consult with its accountants

or financial advisors to ensure compliance with relevant accounting principles and reporting requirements.

Also, it's important to note that accounting standards and regulations may vary across different countries or regions,

so organizations should adhere to the accounting principles applicable in their specific jurisdiction.

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Answer:

p = 3 dollars    d = 4 dollars

Step-by-step explanation:

2 p + 1 d  = 10     given

4 p + 1 d  = 16     given       Subtract second equation from first to get:

-2p = - 6

p = 3 dollars        then use this value in either of the equations to find  'd'

2(3)   + d = 10

d = 4

Answer:

square root of 25 is 5

Step-by-step explanation:

when you take the numbers that multiply together to make 25 which in this case is 5 5*5=25

The function modelled for the given condition is \(y = -16x^{2} + 6x +22\) and the time after which the skier is 5 feet above the water is 1.23 seconds.

A competitive water skier's heights y, x seconds after soaring off a ramp.

For x = 0, y = 22

for x = 0.25, y = 22.5

For x = 0.75, y = 17.5

For x = 1, y = 12

For x = 1.1, y = 9.24

The general equation of a quadratic equation is y = \(ax^{2} + bx +c\)

Putting x = 0 and y = 22 in the equation, we get :

\(y = ax^{2} +bx +c\)

c = 22

Now, putting x = 1 and y =12, we get,

12 = a*1 + b*1 + 22

a +b = 12 - 22 = -10 equation (1)

Putting x = 0.25, y = 22.5,

22.5 = a* \(22.5^{2}\) +b*22.5 +22

506.25 a +22.5b = 0.5 equation(2)

Solving equation (1) and equation(2), we get :

a = -16 and b = 6 and c = 22

So, the quadratic equation becomes,

\(y = -16x^{2} + 6x +22\)

Now, Time when the skier is 5 feet above the water,

\(x = \frac{3 +\sqrt{281} }{16} = 1.23 seconds\)

Hence, the function modelled for the given condition is \(y = -16x^{2} + 6x +22\) and the time after which the skier is 5 feet above the water is 1.23 seconds.

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Answer:

100

Step-by-step explanation:

3/4 is a quarter

1/4 of 400 is 100 seeing as 100x4 is 400.

The graph of the function y = 5|x - 4| is added as an attachment

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

y = 5|x - 4|

The above function is an absolute value function that has been transformed as follows

Next, we plot the graph using a graphing tool by taking not of the above transformations rules

The graph of the function is added as an attachment

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The solutions to the system of equations are x = 2 and 4

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

f(x) = x - 3

g(x) = 1/(x - 3)

The solution to the system of equations implies that

f(x) = g(x)

So, we have

x - 3 = 1/(x - 3)

Cross multiply the equation

This gives

(x - 3)² = 1

So, we have

x - 3 = ±1

Add 3 to both sides

x = 3 ± 1

So, we have

x = 2 and 4

Hence, the solutions to the system of equations are x = 2 and 4

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a) The value in four years is 2,207,626

b) The growth rate percent is 102.5 %

c) It would attain the value in 11 years.

We know that a function has to do with a mathematical rule that is used for the establishment of a fact. We have from the question that the function that models the car is; V = 2000000(1.025)^n

Let us recall that n has to do with the number of years.

a) In four years, the value of the car would be;

V = 2000000(1.025)^4

V = 2,207,626

b) The growth rate percent of the function can  be obtained as;

1.025 * 100 = 102.5 %

c) To obtain the year in which the value of the car would reach 2624173.32, we have;

2624173.32 = 2000000(1.025)^n

2624173.32/2000000 = (1.025)^n

1.312 = (1.025)^n

ln1.312 = n ln (1.025)

n = ln1.312 /ln (1.025)

n = 0.272/0.025

n = 11

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