A local mechanic charges customers a flat fee of $60 before any work is done and a rate of $85 per hour for labor. Which
equation represents the relationship between the total charge for labor, L, in dollars and the number of hours worked, H?

The given equation is a circle with center = (0, 0) and radius = 4.

We compare the given equation with the standard form of a circle\((x-h)^2+(y-k)^2=r^2\)

So, h = 0 , k = 0, \(r^2=16\) or r = 4.

So the given equation is a circle with center = (0, 0) and radius = 4.

The graph is attached.

Learn more: https://brainly.com/question/8806877

Answer:

Go to the botom of the page

Step-by-step explanation:

Answer:

\(3 \log 2\)

Step-by-step explanation:

Given expression:

\(\log 2 + \log \left(\dfrac{3}{2}\right)+\log \left(\dfrac{4}{3}\right)+\log \left(\dfrac{5}{4}\right)+\log \left(\dfrac{6}{5}\right)+\log \left(\dfrac{7}{6}\right)+\log \left(\dfrac{8}{7}\right)\)

\(\textsf{Apply the \underline{Log Product Law}}: \quad \log_ax + \log_ay=\log_axy\)

\(\implies \log \left(2 \cdot \dfrac{3}{2} \cdot \dfrac{4}{3} \cdot \dfrac{5}{4} \cdot \dfrac{6}{5} \cdot \dfrac{7}{6} \cdot \dfrac{8}{7}\right)\)

Cross out common factors:

\(\implies \log \left(\diagup\!\!\!\!2 \cdot \dfrac{\diagup\!\!\!\!3}{\diagup\!\!\!\!2} \cdot \dfrac{\diagup\!\!\!\!4}{\diagup\!\!\!\!3} \cdot \dfrac{\diagup\!\!\!\!5}{\diagup\!\!\!\!4} \cdot \dfrac{\diagup\!\!\!\!6}{\diagup\!\!\!\!5} \cdot \dfrac{\diagup\!\!\!\!7}{\diagup\!\!\!\!6} \cdot \dfrac{8}{\diagup\!\!\!\!7}\right)\)

Therefore:

\(\implies \log 8\)

Factor the number:  8 = 2³

\(\implies \log 2^3\)

\(\textsf{Apply the \underline{Log Power Law}}: \quad \log_ax^n=n\log_ax\)

\(\implies 3 \log 2\)

If 10p4₅ = 134₁₀, then p is such that

\(10p4_5 = 1\times5^3 + 0\times5^2 + p\times5^1+4\times5^0 \\\\ \implies 134 = 125 + 0 + 5p + 4\)

Solve for p :

134 = 129 + 5p

5 = 5p

p = 1

Larger sample sizes provide more accurate estimates of the population mean, even if the population is not normally distributed.

For a population that is not normally distributed, the distribution of the sample means will approach a normal distribution as the size of the sample increases.

This is known as the Central Limit Theorem, which states that as the sample size increases, the distribution of sample means becomes more normal regardless of the shape of the population distribution.

Therefore, larger sample sizes provide more accurate estimates of the population mean, even if the population is not normally distributed.

to learn more about sample sizes click here:

brainly.com/question/30526686

#SPJ11

Answer:

Step-by-step explanation:

Find the distance to walk along the arc NQ

Find the area inside one of the 4 sectors

⇒ Circle area = π * r² = π * 36 [cm²] ≈ 113.1 [cm²]

π ≈ 3.14159265 ≈ 3.14

d = r * 2 = 6 [cm] * 2 = 12 [cm]

Find the distance to walk along the following path: Start at point P and go to R then to Q and over to N then back to P:

Answer:

2nd one

Step-by-step explanation:

Answer:

12862.83cm³

Step-by-step explanation:

Volume of the Box: [L×W×H] or [30x30x30] or [27000cm³]

Volume of the Sphere: [\(\frac{4}{3}\pi r^{3}\)] (\(\pi\)=pi=3.14) (r=radius=15) or [\(\frac{4}{3}\)×3.14×3375] or [14137.17cm³]

Volume of the empty space: 27000cm³-14137.17cm³=12862.83cm³

Btw there are online tools to help you find the volume of a sphere (just use it after you understand the equation)

Hope I helped!

Answer:

9

Step-by-step explanation:

i can not really tell what letters are on the picture but i think it is 9

The 99.9% confidence interval for the true average trunk girth of four-year-old apple trees at East Malling Research Station is (145.76 mm, 154.24 mm).

To calculate a 99.9% confidence interval for the true average trunk girth of four-year-old apple trees at East Malling Research Station, we can use the following formula:

Confidence Interval = X ± Z * (σ / √n)

Where:

X is the sample mean trunk girth

Z is the critical value corresponding to the desired confidence level (in this case, 99.9%)

σ is the population standard deviation (unknown)

n is the sample size

Since the population standard deviation is unknown, we can use the sample standard deviation (s) as an estimate. The critical value can be obtained from the standard normal distribution table or using a statistical software.

You mentioned that the data is in an Excel spreadsheet, so I will assume you have access to the sample mean (X) and sample standard deviation (s). Let's assume X = 150 mm and s = 10 mm (these values are just for demonstration purposes).

Using the formula, we can calculate the confidence interval as follows:

Confidence Interval = 150 ± Z * (10 / √60)

Now we need to find the critical value Z for a 99.9% confidence level. From the standard normal distribution table, the critical value corresponding to a 99.9% confidence level is approximately 3.29.

Plugging in the values:

Confidence Interval = 150 ± 3.29 * (10 / √60)

Calculating the values:

Confidence Interval = 150 ± 3.29 * (10 / 7.746)

Confidence Interval = 150 ± 3.29 * 1.29

Confidence Interval = 150 ± 4.24

To know more about confidence interval,

https://brainly.com/question/30103396

#SPJ11

Answer:

1=27

2=34

Step-by-step explanation:

1)9y power 2÷3

or, y=9 power 2÷3

or, y=9×9÷3

or, y=81÷3

or, y=27

2) (8x power 2+4x)÷2

=(8x×8+4x)÷2

=(64x+4x)÷2

=68x÷2

or, x=68÷2

or, x=34

Answer:

10.50

Step-by-step explanation:

The price of a ticket without a discount will be $10.50. The correct option is H.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that discounted tickets to the cinema cost $6.00 each. James spent $72.00 on discounted tickets, $54.00 less than he would have spent if he had bought tickets without the discount.

The price of the ticket will be calculated as below:-

Number of the tickets = 72 / 6 = 12

Total price without discount = 72 + 54 =126

Price of each ticket = 126 / 12 = 10.5

Therefore, the price of a ticket without a discount will be $10.50. The correct option is H.

To know more about an expression follow

https://brainly.com/question/4541471

#SPJ2

Answer:

119 is the value of x when y = 7

Step-by-step explanation:

Since y varies inversely with x, we can use the following equation to model this:

y = k/x, where

Step 1:  Find k by plugging in values:

Before we can find the value of x when y = k, we'll first need to find k, the constant of proportionality.  We can find k by plugging in 49 for y and 17 for x:

Plugging in the values in the inverse variation equation gives us:

49 = k/17

Solve for k by multiplying both sides by 17:

(49 = k / 17) * 17

833 = k

Thus, the constant of proportionality (k) is 833.

Step 2:  Find x when y = k by plugging in 7 for y and 833 for k in the inverse variation equation:

Plugging in the values in the inverse variation gives us:

7 = 833/x

Multiplying both sides by x gives us:

(7 = 833/x) * x

7x = 833

Dividing both sides by 7 gives us:

(7x = 833) / 7

x = 119

Thus, 119 is the value of x when y = 7.

Answer:

all work pictured and shown

The estimate for y(0.4) using the Adam Moulton fourth order method with a step length of h = 0.05 is approximately 0.75067.

To estimate y(0.4) using the Adam Moulton fourth order method, we start with the given initial condition y(0) = 0.5 and the ordinary differential equation dy/dx = y - x² + 1.

Using a step length of h = 0.05, we proceed as follows:

- For the first step, x1 = 0, y1 = 0.5.

- For subsequent steps, we use the Adams-Bashforth method to estimate the next y-value.

- Calculate the predicted value of y using the Adams-Bashforth method.

- Use the predicted value in the Adams-Moulton formula to obtain a more accurate estimate of y.

By following these steps, we obtain an estimate for y(0.4) using the Adam Moulton fourth order method with a step length of h = 0.05, which is approximately 0.75067.

Learn more about Fourth order method

brainly.com/question/31987604

#SPJ11

The solution to the given system of linear equations is x = 3, y = -3. That is, (3, -3)

The graph of the system of equations is shown below

From the question, we are to determine the apparent solution to the given system of linear equations

The given system of equations is

y = -2x + 3

y = 1/3x - 4

Set the two equations equal

That is,

-2x + 3 = 1/3x - 4

Multiply through by 3

-6x + 9 = x - 12

Add 6x to both sides of the equation

-6x + 6x + 9 = x + 6x - 12

9 = 7x - 12

Add 12 to both sides of the equation

9 + 12 = 7x - 12 + 12

21 = 7x

x = 21/7

x = 3

Substitute the value of x into the first equation

y = -2x + 3

y = -2(3) + 3

y = - 6 + 3

y = - 3

The solution is (3, -3)

The graph is shown below

Learn more on Solving system of linear equations here:

#SPJ1

Answer: 12.5%

(Don't worry!)

1. plug in the values

3(2) - (-1) = 7; true

2(2) + 3(-1) = 1

4 -3 = 1; true

yes, the point is true for the system. .

2.

the solution is referring to where both the lines intercept on the graph.

3. replace 'y' in the first equation with the second equation

3x + 6x + 1 = 10

9x + 1 = 10

9x = 9

x = 1

plug x = 1

y = 6(1) + 1

y = 7

(1,7)

4. elimiate the common terms which is 'n' which gives;

5m = -5

m = -1

plug in to find 'y' AKA 'n'

3(-1) - n = 2

-3 - n = 2

-n = 5

n = -5

I can futher explain if you'd like, let me know.

Answer:

Number of candy = 8 candy canes.

Step-by-step explanation:

Cost per candy = $1.05

Amount paid = $10

Change received = $1.60

Total cost = amount paid - change received

Substituting into the equation, we have;

Total cost = 10 - 1.6

Total cost = 8.4

To find the number of candy purchased;

Number of candy = total cost/cost per candy

Number of candy = 8.4/1.05

Number of candy = 8 candy canes.

Therefore, Molly purchased 8 candy canes.

Answer:

ok, here is your answer

Step-by-step explanation:

The answer is (d) 258.000 g and 2.58×10^-2g.Both numbers have the same number of significant figures, which is six.The first number, 258.000 g, has three significant figures after the decimal point, and three before the decimal point. The zeros after the decimal point are significant because they are part of a measured quantity.The second number, 2.58×10^-2g, is written in scientific notation. It also has six significant figures because the number 2.58 has three significant figures, and the exponent -2 has two significant figures.-

The answer for the fraction 1/4 of 100 is 25.

Given,

The fraction; 1/4

We have to find the 1/4 of 100.

Fraction;

A fraction is referred to as the portion of a whole in mathematics. For instance, if a pizza is cut into four equal pieces, each one is represented by a quarter. Fractions make calculations quicker and easier by making it easier to distribute and judge numbers.

There are three main categories of fractions in mathematics. Proper fractions, incorrect fractions, and mixed fractions are these three types. The expressions with a numerator and a denominator are called fractions

Here,

1/4 of 100 = 1/4 x 100 = 25.

That is,

The answer for the fraction 1/4 of 100 is 25.

Learn more about fractions here;

https://brainly.com/question/17058737

#SPJ1

Answer:

1/25

Step-by-step explanation:

Convert to a fraction by placing the expression over  100 .

Answer : 4/100 and / or 1/25

Step-by-step explanation:

when converting percentages to fractions its always out of 100

for example, if the percentage is 4% then its 4/100

Answer:

The answer is 7x^3 - 8x^2 - 20x + 3

Step-by-step explanation:

Simplify the expression.

Hoped this helped!

Answer:

\(\displaystyle m=0\)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

Point (-9, 9)

Point (3, 9)

Step 2: Find slope m

Simply plug in the 2 coordinates into the slope formula to find slope m

Answer:

This question has a slope of zero.

Step-by-step explanation:

When trying to solve a problem like this, what I recommend doing is subtracting the y value in the first ordered pair from the y value in the second ordered pair, and doing the same for the x values. To write it as a formula,

y2 - y1

––––– = m          the 2 in the formula means that the y or x value was from the  

x2 - x1                  second ordered pair. The 1 means it was from the first                                      

                            ordered pair. The m means slope.

Answer:        我不知道你好

Step-by-step explanation:

Answer:

1 & 2

1 & 8

2 & 7

Step-by-step explanation:

Any two angles that add up to 180 degrees (aka a straight line) are supplementary angles.