October 8, 1982 267.38 Yen = 1 US dollar

June 30, 1995 84.90 Yen = 1 US dollar

a. Determine the cost, in US dollars, for a souvenir that cost 3,500 Yen

on October 8, 1982. Show your work in the provided space.

Using** proportions**, the value of 3500 Yen on October 8, 1982 is 13.1 USD

**Proportion** is a mathematical comparison between two numbers. According to **proportion**, if two sets of given numbers are increasing or decreasing in the same **ratio**, then the ratios are said to be directly proportional to each other.

On October 8, 1982;

267.38 Yen = 1US

The cost of 3500 Yen = ?

267.38 Yen = 1 USD

35000 Yen = x USD

Cross multiply both sides and solve for x

x * 267.38 = 3500 * 1

267.38x = 3500

Divide both sides by coefficient of x

267.38x / 267.38 = 3500 / 267.38

x = 13.1

The value of 3500 Yen is 13.1 USD

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There were 616 tickets purchased for a major league baseball game. The lower box tickets cost $12.50 and the upper reserved tickets cost $8.00. The total amount of money spent was $6543.50. How many of each kind of ticket were purchased?

The **number **of the tickets **purchased **for upper reserve is 146 and lower is 470.

The **mathematical **expression combines **numerical **variables and operations **denoted **by addition, **subtraction**, multiplication, and division signs.

Mathematical **symbols **can be used to **represent **numbers (constants), variables, operations, **functions**, brackets, punctuation, and grouping. They can also **denote **the logical syntax's **operation **order and other properties.

Given that there were 616 tickets **purchased **for a major league baseball game. The **lower **box tickets cost $12.50 and the **upper **reserved tickets cost $8.00. The total **amount **of money spent was $6543.50.

The **equations **will be formed as,

L + U = 616

12.5L + 8U = 6543.5

**Solve **the above **equations**,

12.50L + 8 (616-L) = 6543.5

12.5L + 4928 - 8L = 6543.5

12.50L - 8L = 6543.5 - 4428

4.50L = 2118.5

L = 470

U = 616 - 470

U = 146

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What is the sum of the interior angles of a regular polygon with 9 sides?

1,260°

1,620°

1,800°

1,980°

The **sum **of the interior **angles **of a regular **polygon **with 9 sides will be 1260°. The correct option is A.

An **angle **is defined in mathematics as the figure **formed** by joining two rays at their common **endpoint**. An interior angle is an angle that exists within a shape. Polygons are closed shapes with **sides **and vertices. All of the **interior **angles of a regular polygon are equal.

Given that the **number **of the sides of the **polygon **is 9. The sum of the interior **angles **of the polygons will be calculated as,

Sum = ( n - 2 ) 180°

Sum = ( 9 - 2 ) 180

Sum = 7 x 180

Sum = 1260°

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Question 1 of 9

Use the scale to help you solve the equation and find the value of x. Enter the

value of x below. x+8=10

Answer: x + 8 - 8 = 10 - 8

Simplifying the left side of the equation gives us:

x = 2

Therefore, the value of x in this equation is 2.

NO LINKS!!

Rewrite the logarithm as a ratio of common logarithms and natural logarithms.

log_1/3(4)

a. common logarithms

b. natural logarithms

**Common logarithm** is the logarithm with the base 10, it is written as:

**Natural logarithm** is the logarithm with the base of e and is written as ln a.

How to **rewrite a logarithm** [tex]log_a\ b[/tex] as a ratio of logarithms with a different base c:

**Apply **this to the given logarithm:

a. Common logarithms:

[tex]log_{1/3}\ 4=log\ 4\ /\ log\ (1/3)[/tex]b. Natural logarithms:

[tex]log_{1/3}\ 4=ln\ 4\ /\ ln\ (1/3)[/tex]**Answer:**

[tex]\textsf{a)} \quad \dfrac{\log_{10}4}{\log_{10}\dfrac{1}{3}}=-\dfrac{\log_{10}4}{\log_{10}3}[/tex]

[tex]\textsf{b)} \quad \dfrac{\ln 4}{\ln \dfrac{1}{3}}=-\dfrac{\ln 4}{\ln 3}[/tex]

**Step-by-step explanation:**

Given logarithm:

[tex]\log_{\frac{1}{3}}(4)[/tex]

Part (a)The **common logarithm** is the logarithm with **base 10**.

[tex]\boxed{\textsf{Change of base}: \quad \log_ba=\dfrac{\log_xa}{\log_xb}}[/tex]

Use the **change of base formula **to rewrite the given logarithm as a **ratio **of **common logarithms**:

[tex]\implies \log_{\frac{1}{3}}(4)=\dfrac{\log_{10}4}{\log_{10}\dfrac{1}{3}}[/tex]

[tex]\boxed{\begin{minipage}{5cm} \underline{Log quotient law}\\\\$\log_a \left(\dfrac{x}{y}\right)=\log_ax - \log_ay$\\\end{minipage}}[/tex]

This can be simplified using the** log quotient rule**:

[tex]\implies \log_{\frac{1}{3}}(4)=\dfrac{\log_{10}4}{\log_{10}\dfrac{1}{3}}[/tex]

[tex]\implies \log_{\frac{1}{3}}(4)=\dfrac{\log_{10}4}{\log_{10}1-\log_{10}3}[/tex]

[tex]\implies \log_{\frac{1}{3}}(4)=\dfrac{\log_{10}4}{0-\log_{10}3}[/tex]

[tex]\implies \log_{\frac{1}{3}}(4)=-\dfrac{\log_{10}4}{\log_{10}3}[/tex]

Part (b)The **natural logarithm** is the logarithm with **base e**.

[tex]\textsf{Also} \; \log_ex=\ln x[/tex]

Use the **change of base formula **to rewrite the given logarithm as a **ratio **of **natural logarithms**:

[tex]\implies \log_{\frac{1}{3}}(4)=\dfrac{\log_{e}4}{\log_{e}\dfrac{1}{3}}[/tex]

[tex]\implies \log_{\frac{1}{3}}(4)=\dfrac{\ln 4}{\ln \dfrac{1}{3}}[/tex]

[tex]\boxed{\begin{minipage}{5cm} \underline{Log quotient law}\\\\$\ln \left(\dfrac{x}{y}\right)=\ln x - \ln y$\\\end{minipage}}[/tex]

This can be simplified using the** log quotient rule**:

[tex]\implies \log_{\frac{1}{3}}(4)=\dfrac{\ln 4}{\ln \dfrac{1}{3}}[/tex]

[tex]\implies \log_{\frac{1}{3}}(4)=\dfrac{\ln 4}{\ln1 - \ln 3}[/tex]

[tex]\implies \log_{\frac{1}{3}}(4)=\dfrac{\ln 4}{0 - \ln 3}[/tex]

[tex]\implies \log_{\frac{1}{3}}(4)=-\dfrac{\ln 4}{\ln 3}[/tex]

Q30: Work out the surface of the following prism

**Surface area **of the given prism is **6 square cm .**

**How to Calculate the Surface Area of Prism?**

The steps to determine the surface area of the prism are:

Step 1: Note down the given **dimensions** of the prism.

Step 2: Substitute the dimensions in the surface area of prism formula (2 × **Base** Area) + (Base perimeter × height).

Step 3: The value of the surface area of the prism is obtained and the unit of the surface area of the prism is placed in the end (in terms of square units).

The lateral area is the area of the **vertical** faces, in case a prism has its bases facing up and down. Thus, the lateral surface area of prism = base **perimeter** × height

The total surface area of a Prism = Lateral surface area of prism + area of the two bases = **(2 × Base Area) + Lateral surface area or (2 × Base Area) + (Base perimeter × height)**.

Area of triangular cross-section:

Area = 1/2 . b . h

Area = 1/2 . 4. 3

Area = 6 square cm

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Create a multiplication equation with a solution of 2/7

**Answer:**

1 / 7 · 2 = 2 / 7

What is the equation in standard form of the line that passes through the

point (4, −8) and 1 has a slope of 1/4?

The **equation **in **standard form **of the line that has a slope of 1/4 and passes through the point (4, −8) is written as: -x + 4y = -36.

The **equation** of a line can be written in **standard form** as Ax + By = C.

Given the following:

A point (4, -8) = (a, b).

Slope (m) = 1/4.

Substitute m = 1/4 and (a, b) = (4, -8) into y - b = m(x - a):

y - (-8) = 1/4(x - 4)

y + 8 = 1/4(x - 4)

Rewrite the **equation **in **standard form**:

4(y + 8) = x - 4

4y + 32 = x - 4

4y = x - 4 - 32

4y = x - 36

-x + 4y = -36

The **equation** is: -x + 4y = -36.

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Which of the following expressions has the leftmost value on the number line?

A.-7-10 O

B. 7-10

C.10-(-7)

D.10-7

**Answer:**

A.-7-100. *[**Since** **it **is** **-**1**0**7**]*

Determine which of the lines, if any, are parallel or perpendicular. Explain.

6. Line a passes through (0, 4) and (4, 3).

Line b passes through (0, 1) and (4, 0).

Line c passes through (2, 0) and (4, 4).

**Answer:**

**Step-by-step explanation:**

c 0,4 .01

Suppose the COMBINED area is known to be 0.10416, assume there is equal area on each side. Determine the corresponding Z-scores.A) z=±1.62 B) z=±1.58 C) z=±1.72 D) z=±1.66 E) z=±1.69 F) z=±1.49 G) None of These

An **combined** area of 0.10416 to the right means that it must have an area of 0.90 to the left, so the answer is again 1.28.

Every normally distributed random variable has a slightly different distribution shape, the only way to find areas using a table is to standardize the variable - transform our variable so it has a mean of 0 and a** **standard deviation of 1. How do we do that? Use the **z-score**!

Z = ( x - μ)/σ

if the **random** variable X has a mean μ and standard deviation σ,

then transforming X using the z-score creates a random variable with mean 0 and standard deviation 1!

With that in mind, we just need to learn how to find areas under the standard normal curve, which can then be applied to any normally distributed random variable.

An **area** of 0.10416 to the right means that it must have an area of 0.90 to the left, so the answer is again 1.28.

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Every normally distributed random variable has a slightly different distribution shape, the only way to find areas using a table is to standardize the variable - transform our variable so it has a mean of 0 and a standard deviation of 1. How do we do that? Use the z-score!

Z = ( x - μ)/σ

if the random variable X has a mean μ and standard deviation σ,

An area of 0.10416 to the right means that it must have an area of 0.90 to the left, so the answer is again 1.28.

A newsletter publisher believes that 43% of their readers own a Rolls Royce. A testing firm believes this is inaccurate and performs a test to dispute the publisher's claim. After performing a test at the 0.02 level of significance, the testing firm fails to reject the null hypothesis.

The **conclusion **regarding the **test of the hypothesis** is given as follows:

At the **null **hypothesis, it is tested if there is not enough evidence to conclude that the percentage is not of 43% = proportion of 0.43, hence:

[tex]H_0: p = 0.43[/tex]

At the **alternative **hypothesis, it is tested if there is enough evidence to conclude that the percentage is not of 43%, hence:

[tex]H_1: p \neq 0.43[/tex]

The decision was to **not reject** the null hypothesis, meaning that there is not sufficient evidence at the 0.02 level of significance that the percentage is not of 43%.

The problem asks to identify the correct conclusion from these two options:

There is not sufficient evidence at the 0.02 level of significance that the percentage is not of 43%.There is sufficient evidence at the 0.02 level of significance that the percentage is not of 43%.More can be learned about the **test of an hypothesis **at https://brainly.com/question/13873630

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What does MW equal or mean

The value of MW in the given **figure** is 5.

In **Euclidean geometry**, an angle is a figure made up of two rays that have a shared vertex, also known as a common terminus, and are referred to as the angle's sides. The angles of two rays are situated in the plane containing the rays. An angle is also created when two planes intersect at an angle. These are referred to as** dihedral angles**. Another technique to define two curves is to specify the angle generated by rays that are tangent to the intersection of two curves. Angle is another word for how long a rotation or angle is.

Given,

In the figure,

PM=MW

It means PM is similar to MW

As given in the figure,

PM=5

Since PM is similar to MW

Then,

MW=5

Therefore, the value of MW in the given figure is 5.

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Find the point of intersection between a line that is tangent to the function

() = x^2 + 4 at = −1 ,

and the function

() = x^2 − 4

There is no point of **intersection **between a line that is tangent to the function () = x² + 4 at = −1 , and the **function **() = x² − 4

To find the point of intersection between the line that is **tangent **to the function y = x² + 4 at x = −1 and the function y = x² − 4 , we can set the two equations equal to each other and solve for x. This will give us the x-coordinate of the point of intersection.

Setting the two **equations **equal to each other, we have:

x^2 + 4 = x² - 4

This simplifies to:

2 = -8

This equation has no solutions, so the two functions do not intersect. This means that the point of intersection does not exist.

Alternatively, we could see that the two functions have different slopes at the point x = −1 .

The function y = x² + 4 has a slope of 2x at this point, which is equal to -2 . The function y = x² − 4 has a slope of 2x , which is equal to -2 at this point as well. However, since the two **functions** have different y-intercepts, they cannot be tangent to each other at this point. Therefore, the point of intersection does not exist.

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Function A and Function B are linear functions.

Function A

Function B

y=x-1

Which statement is true?

The y-intercept of Function A is greater than the y-intercept of Function B.

The y-intercept of Function A is less than the y-intercept of Function B.

The **y-intercept** of Function A is **greater** than the y-intercept of Function B.

**What is y-intercept ?**

The y intercept of a **graph** is the point where the graph **intersects** the y-axis. We know that the x-coordinate of any point on the y-axis is 0. So the **x-coordinate** of a y-intercept is 0.

Here are the steps to find the y intercept of a function y = f(x),

we just substitute x = 0 in it.solve for y.represent the y-intercept as the point (0, y).Given:

Function A : y=x-1

y-intercept of Function A (x=0) is y = -1

y-intercept of Function B are -6 , -4 and -3.

Since , -1 > -6 , -1 > -4 and -1 > -3

Hence , the **y-intercept **of Function A is **greater** than the y-intercept of Function B.

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Harry and Tim both made New Year’s Resolution. Harry made 5 more resolutions than Tim. Together they made 13 resolutions. How many resolutions did Harry make?

Answer:

Harry made 9 resolutions.

Step-by-step explanation:

Tim made x resolutions.

Harry made five more, x + 5.

Harry and Tim's together was 13.

x + x + 5 = 13

combine like terms.

2x + 5 = 13

subtract 5

2x = 8

divide by 2

x = 4

Tim made 4 resolutions.

Harry made 4 + 5, that is, 9 resolutions.

Check:

Harry and Tim together is 13.

4 + 9 = 13

Harry made 9 resolutions.

Keyshawn is asked to compare and contrast the domain and range of two functions F(x)=5x g(x)=5^x which statements could he include in his explanation

**Domain **is the input and **range **is the output of a function. By considering the options The domain of both function is all real number and The range of g(x) >0 are the correct answers.

**Domain **is the input of a **function**.

Range is the output of a function.

The domain of both functions is the set of all real numbers, since both functions are defined for all values of x.

The range of the function g(x)=5^x is the set of all positive real numbers, since any positive real number can be obtained by raising 5 to the power of a real number

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karla is offered a job as parking lot attendant. the job will pay 2400 per month, paid biweekly. along with the base salary, the company offers to pay half the cost of medical insurance and will match karlas contribution to a retirment plan up to a total of 1500. if the full cost of the medical insurance is 450 a month and karla plans to contribute the full 1500 every year tpa retirement plan, what is the actual annual value of this job to karla?

The **actual annual **value of this job to Karla is **33000**.

**What are arithmetic operations?**

**Arithmetic operations **is a branch of mathematics that studies **numbers** and the **operations** on numbers that are useful in all other branches of mathematics. It consists primarily of **operations** like addition, subtraction, multiplication, and division.

We have,

the job will pay 2400 per month,

if the full cost of the medical insurance is 450 a month and Karla plans to contribute the full 1500 every year tpa retirement plan,

the actual annual value of this job to Karla is:

2400 per month

annual value = 2400 * 12 = 28,800

the medical insurance is 450 a month

half the cost of medical insurance is 225 a month

annual value = 225 * 12 = 2700

the full 1500 every year tpa retirement plan,

So, the total value is:

= 28,800 + 2700 + 1500

= 33000

Hence, the **actual annual **value of this job to Karla is **33000**.

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Compare these numbers.

>

<

=

none of the above

8.2 x 10^4 < 4.6 x 10^5

82000 < 460000

82000 < 460000

Can someone please answer this problem for me.

**Answer:**

$1 per movie

$5.50 per video game

**Step-by-step explanation:**

We know 5 movies and 2 video games cost $16 and 3 movies and 8 video games cost $47.

Let x be the cost of 1 movie and y be the cost of a video game.

5x + 2y = 16

3x + 8y = 47

In the first equation, lets solve for y

2y = 16 - 5x

y = 8 - 2.5x

Now, we can substitute this into the other equation.

3x + 8(8 - 2.5x) = 47

3x + 64 - 20x = 47

-17 x = - 17

x = 1

So a movie costs $1 to rent.

2y = 16 - 5(1)

2y = 11

y = 5.5

A video game costs $5.50 to rent.

What is the y/x ratio

The angles whose measure are **greater** than the measure of ∠1 are** ∠2**,** ∠3**,** ∠7**,** ∠5** .

The general equation of a straight line is -

where -

[m] : slope[c] : y - interceptGiven is a **graph** as shown in the image.

The ratio of **{y/x} **is called the **slope** of a line. So, we can write -

m = 3/2

m = 1.5

Therefore, the** ratio** of [y] by [x] is equivalent to **1.5**.

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determine the z transform for each of the following sequences. sketch the pole-zero plot and indicate the region of convergence. indicate whether or not the (discrete time) fourier transform of the sequence exists.

The **Fourier** **transform** of this **sequence** does **not** **exist**

**What is Fourier Transform?**

The output of a **Fourier** **transform** is a **function** of **frequency** and is a **mathematical** **transformation** that breaks down functions into **frequency** **components**.

To determine the** z-transform** of a given **sequence**, we need to find the **sum** of the **sequence's** terms **multiplied** by z raised to the negative of the term's **position**. For example, given a sequence x[n], the **z-transform** X(z) is given by:

[tex]X(z) = sum_{n=-infinity}^{infinity} x[n] * z^{-n}[/tex]

To sketch the **pole**-**zero** plot of a **z-transform**, we need to plot the poles (values of **z** where the **z-transform** is **infinite**) and **zeros** (values of z where the **z-transform** is zero) in the complex plane. The **region** of **convergence** (ROC) is the set of values of z for which the **sum** defining the **z-transform** **converges**.

[tex]x[n] = a^n u[n][/tex], where a is a **constant** and u[n] is the **unit** **step** **function**[tex](u[n] = 1 for n > = 0[/tex] and [tex]u[n] = 0 for n < 0)[/tex]

The **z-transform** of this sequence is given by:

[tex]X(z) = sum_{n=0}^{infinity} a^n * z^{-n}= 1 / (1 - a*z^{-1})[/tex]

This **z-transform** has a **pole** at z = 1/a and a **zero** at z = 0. The **pole**-**zero** **plot** consists of a **single** pole at 1/a in the **complex** plane. The ROC is the set of values of z such that [tex]|a*z^{-1}| < 1[/tex], which is the **region** inside the **unit** **circle** **centered** at the **origin**. The **Fourier** **transform** of this sequence exists.

[tex]x[n] = (-1)^n u[n].[/tex]

The **z-transform** of this sequence is given by:

[tex]X(z) = sum_{n=0}^{infinity} (-1)^n * z^{-n}= 1 / (1 + z^{-1})[/tex]

This **z-transform** has a pole at z = -1 and a zero at z = 0. The pole-zero plot **consists** of a single pole at -1 in the **complex** **plane**. The ROC is the set of **values** of z such that [tex]|z^{-1}| < 1[/tex], which is the region inside the **unit** circle **centered** at the **origin**. The **Fourier** **transform** of this **sequence** exists.

[tex]x[n] = n^2 u[n].[/tex]

The z-transform of this sequence is given by:

[tex]X(z) = sum_{n=0}^{infinity} n^2 * z^{-n}= z^{-2} / (1 - z^{-1})^3[/tex]

This **z-transform** has **poles** at z = 1, z = 1, and z = 1. The **pole**-**zero** plot consists of **three** **poles** at the **origin** in the **complex** plane. The ROC is the **set** of **values** of z such that [tex]|z^{-1}| > 1[/tex], which is the **region **outside the **unit** circle **centered** at the **origin**.

Hence, The **Fourier** **transform** of this **sequence** does **not exist**.

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What type of number is -560,114?

Choose all answers that apply:

A Whole number

B

C

D

Integer

Rational

Irrational

Answer:

It is an integer.

It is rational.

Step-by-step explanation:

A whole number is in the set

0, 1, 2, 3...

This set starts at zero and only includes zero and the positive numbers. So the given number is NOT a whole number.

It IS an integer. Integers include positive and negative numbers. That is, whole numbers and their opposites.

The number IS rational. That is, it can be written as a ratio:

-560114/1

Since it is rational, it is not irrational.

5k^2+20k-25=0

please i need help

The **value **of k is 1 and -5.

**What is factorization?**

A **number **or other mathematical object is **factorized **or **factored **when it is written as the **product **of numerous factors, typically smaller or simpler things of the same kind.

Here, we have

Given **function**: 5k²+20k-25 = 0

Now, we **factorize **the given **function **and we get

5k²+20k-25 = 0

5(k²+4k-5) = 0

k² + 4k - 5 = 0

k² + 5k - k -5 = 0

k(k+5) -1(k+5) = 0

(k+5)(k-1) = 0

k+5 = 0, k-1 = 0

k = -5, k = 1

Hence, The **value **of k is 1 and -5.

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A train travelling along a straight line with constant acceleration is observed to travel consecutive distances of 1km in times of 30s and 60s respectively. Find the initial velocity of the train.

**Answer:**

116.7m/s

**Step-by-step explanation:**

distance(s) = 1km = 1 × 1000m = 1000m

Time(t) = 60– 30 = 30s

initial velocity = u

acceleration (a) = 10m/s

using the formula

S = ut + ½at²

1000 = 30u + ½ × 10 × 30²

1000 = 30u + 5 × 900

1000 = 30u + 4500

30u = 4500 – 1000

30u = 3500

divide both sides by 30

u = 116.7m/s

i hope i helped

The table shows the colour of the bicycles in

a bike shed.

Bookwork code: S79 EX

<

< Back

Colour Frequency

Silver

3

Green

1

a) What fraction of the bicycles are silver?

Give your answer in its simplest form.

b) How many sections on this pie chart

would you shade to show the bicycles that

are silver?

✓ Scroll down

Watch video

Answer >

A **fraction** of the bicycles which are** silver** is 3/4.

You should shade three (3) sections on the pie chart to show the number of bicycles that are **silver**.

In Mathematics, a **pie chart** can be defined as a type of graph that is used for the graphical representation of the proportion relationship between each part or unit to a whole, especially by dividing a circle into various sectors.

Based on the information provided, we can logically deduce the following parameters;

Number of silver bicycles = 3 silver **bicycles**.

Number of green **bicycles** = 1 green bicycles.

Therefore, the total number of **bicycles** is equal to 4 bicycles.

For the fraction of silver bicycles, we have;

Fraction = 3/4 **bicycles**.

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Miguel earns extra money working two weekends with his dad. He is saving to buy a new bike that costs $140. Heather says that Miguel needs to earn more than $6 for each hour that he works to have enough money to buy the bike. Her work is shown below. Write an inequality to explain why she is incorrect

An inequality to explain the reason **Heather** is **incorrect** is t > $8.75.

In Mathematics, an **inequality** can be defined as a mathematical relation that is typically used for comparing two (2) or more numerical data and variables in an algebraic equation based on any of the following **inequality** symbols:

From the histogram, we can logically deduce the following information;

Miguel’s work record during Weekend 1 = 9 **hours**.

Miguel’s work record during Weekend 2 = 7 hours.

Therefore, the total number of **hours** which Miguel worked in two Weekends is given by;

Total hours = 9 hours + 7 **hours**

Total **hours** = 16 hours.

Next, we would calculate the amount of money that Miguel would earn per hour;

Amount = $140/16

Amount = $8.75 per hour.

Note: Let the variable t represent the total earnings.

In conclusion, the correct **inequality **is t > $8.75.

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The terminal side of an angle θ in standard position intersects the unit circle at (√30/7,-√19/7). What is cot(θ)?

The** cotangent **of the **angle **is -√570/30

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

(√30/7,-√19/7)

This means that

(x, y) = (√30/7,-√19/7)

The **cot(θ)** is calculated as

cot(θ) = y/x

Substitute the known values in the above **equation**, so, we have the following representation

cot(θ) = (-√19/7)/(√30/7)

Evaluate

cot(θ) = -√19/√30

Rationalize

cot(θ) = -√570/30

Hence, the **value **of cot(θ) is -√570/30

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please help with this

The** equation** variation for the **electric circuit** is V = 25R.

In each **electric circuit**, the voltage in a battery is measured in volt and the resistance in the circuit is measured in ohms.

The voltage, V is **directly proportional** to the resistance, R. In a given circuit the voltage is 200 volts, when the resistance is 8 ohms.

The **equation** variation for the circuit can be represented as follows:

V α R

V = kR

where

k = constant of proportionalityTherefore,

voltage = 200 volts

resistance = 8 ohms

200 = 8k

k = 200 / 8

k = 25

Therefore, the equation is V = 25R

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Leila works mowing lawns and babysitting.She earns $8.80 an hour for mowing and $7.30 and hour and babysitting.How much will she earn for 1 hour of mowing and 5 hours of babysitting?

**Answer: $45.3**

**Step-by-step explanation:**

**1 hour of mowing: $8.80**

**5 hours of babysitting: $7.30 x 5 = $36.5**

**$36.5 + 8.80 = $45.3**

**$45.3 is your answer.**

**Answer:**

45.30

**Step-by-step explanation:**

its simple math bro lol

Colette bought 1/4 of a pound of green grapes and 1/8 of a pound of red grapes. How much more did the green grapes weigh than the red grapes?

**The green grapes weigh 0.125 pounds more than the red grapes.**

1/4 of a pound = 0.25 pounds

1/8 of a pound = 0.125 pounds

0.25 - 0.125 = 0.125 pounds

Hope this helps :)

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