work out the area of this circle give your answers in terms of pi and state its units

The equation are y = 0.59x + 29.95 for company A and y = 0.79x + 19.95 for company B.

Linear equation is in the form:

y = mx + b

where y,x are variables, m is the rate of change and b is the initial value of y.

Let y represent the total cost of rental for each truck in x hours.

From the table, for company A:

For company B:

The equation are y = 0.59x + 29.95 for company A and y = 0.79x + 19.95 for company B.

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Answer:

The correct response is "0.0129".

Step-by-step explanation:

Given:

\(n=1500\)

\(p=0.47\)

\(np=1500\times 0.47\)

    \(=705\)

\(nq=1500\times (1-0.47)\)

    \(=795\)

Mean of sampling distribution will be:

\(\mu_\hat{p}\) = \(0.47\)

hence,

The standard deviation will be:

⇒  \(\sigma_\hat{p}\) = \(\sqrt{\frac{p(1-p)}{n} }\)

By putting the values, we get

         = \(\sqrt{\frac{0.47(1-0.47)}{1500} }\)

         = \(0.012886686\)

         = \(0.0129\)

Answer:

Step-by-step explanation:

7 quarter mile laps totals 7/4 miles, or 1 3/4 miles.

1 3/4 miles is between 1 and 2, a subset of real numbers.

Answer:

− x + 16y

Step-by-step explanation:

2x + 5y − 3x + 11y

= 2x + 5y + − 3x + 11y

Combine Like Terms:

= 2x + 5y + − 3x + 11y

= (2x + − 3x) + (5y + 11y)

= − x + 16y

Answer:

n=3

Step-by-step explanation:

9625 = 5^n x 7 x 11

9625= 5^n x 77

/77                /77

125= 5^n

5³= 125

n=3

Answer:

n=3

Step-by-step explanation:

9625 = 5^n x 7 x 11

9625= 5^n x 77

/77                /77

125= 5^n

5³= 125

n=3

The cosine of angle J is given as follows:

\(\cos{J} = \frac{14\sqrt{2}}{49}\)

The three trigonometric ratios are the sine, the cosine and the tangent of an angle, and they are obtained according to the rules presented as follows:

For the angle J in this problem, we have that:

Hence the cosine of angle J is given as follows:

\(\cos{J} = \frac{4}{\sqrt{98}} \times \frac{\sqrt{98}}{\sqrt{98}}\)

\(\cos{J} = \frac{4\sqrt{98}}{98}\)

\(\cos{J} = \frac{2\sqrt{98}}{49}\)

As 98 = 2 x 49, we have that \(\sqrt{98} = \sqrt{49 \times 2} = 7\sqrt{2}\), hence:

\(\cos{J} = \frac{14\sqrt{2}}{49}\)

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The mass number of the deuterium isotope is 2.

Let us recall that it is possible for atoms of an element to have the same atomic number but have different mass numbers. This goes to show us that the mass numbers show the number of neutrons that are present in the nucleus since they have the same number of protons.

There are three isotopes of hydrogen and they are;

1) protium ( Mass number 1

2) Deuterium ( Mass number 2)

3) Tritium ( Mass number 3)

This shows us the mass numbers of each of the isotopes of hydrogen known.

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A graph of the given mathematical expression (x = -6) is shown in the image attached below.

In Mathematics, a number line can be defined as a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.

This ultimately implies that, a number line primarily increases in numerical value towards the right and decreases in numerical value towards the left.

In this scenario, a number line would be used to graph the given mathematical expression because it only contains one (1) variable.

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As angle OAB =40-degree, angle AOB is 100 degrees according to the properties of circle and triangle.

Some Properties of circle are distance from center of the circle to each point on the circumstances are equal. hence, OA=OB

Diameter is twice of radius.

The triangle having two equal side length is called isosceles triangle. In the figure, triangle OAB is an isosceles as OA=OB=radius

According to the criteria of isosceles triangle angle OAB =OBA =40°

hence, angle AOB= 180 degrees - (40°+40°) [angle sum of triangle =180°]

                  angle AOB= 100 degrees.

We get, AOB = 100 degrees

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The model can then be used to determine the relationship between the two variables and make predictions about future values of the dependent variable based on the independent variable.

I can suggest a general process for selecting a topic and relevant data for a simple linear regression model. First, choose a topic or question of interest, for example, "Does the amount of exercise affect the quality of sleep?" or "Is there a relationship between the number of hours spent studying and exam scores?" Next, identify relevant datasets that contain at least two numerical variables, one for the dependent variable (e.g., quality of sleep or exam score) and one for the independent variable (e.g., amount of exercise or number of hours spent studying). Datasets can be found on websites such as Kaggle or through academic research databases.

Once the dataset is selected, the data must be cleaned and prepared for analysis. This includes checking for missing values, outliers, and ensuring that the variables are in the correct format for analysis.

Finally, a simple linear regression model can be constructed using statistical software such as R or Python.

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The base length should be twice the width, and the volume of the box is given as 1152 cm³. The dimensions that minimize the cost are approximately 6 cm by 12 cm by 16 cm.

Let’s denote the width of the base of the box as x, and the height of the box as h. Since the length of the base is twice its width, it can be denoted as 2x. The volume of the box is given as 1152 cm³, so we can write an equation for the volume: V = lwh = (2x)(x)(h) = 2x²h = 1152. Solving for h, we get h = 576/x².

The cost of the material for the base and top is 0.80$/cm², and the area of each is 2x², so their total cost is (0.80)(2)(2x²) = 3.2x². The cost of the material for the sides is 0.20$/cm². The area of each side is 2xh, so their total cost is (0.20)(4)(2xh) = 1.6xh. Substituting our expression for h in terms of x, we get a total cost function:

C(x) = 3.2x² + 1.6x(576/x²) = 3.2x² + 921.6/x.

To minimize this cost function, we take its derivative and set it equal to zero: C'(x) = 6.4x - 921.6/x² = 0. Solving for x, we find that x ≈ 6. Substituting this value into our expression for h, we find that h ≈ 16. Thus, the dimensions of the box that can be constructed at minimum cost are approximately 6 cm by 12 cm by 16 cm.

To justify that this is indeed a minimum, we can take the second derivative of the cost function: C''(x) = 6.4 + 1843.2/x³ > 0 for all positive values of x. Since the second derivative is always positive, this means that our critical point at x ≈ 6 corresponds to a local minimum of the cost function.

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Answer:

line 2 has a mistake, you are supposed to add 6x to both sides and instead they subtracted

OK! SO, I'm not accurately sure, But I typed your problems into any online (Problem Solver) and got (3,2) for the first one and (4,4) for the second equation.

I'm sorry if this answer isn't right.

Step-by-step explanation:

Just type them into any online problem solver.

This is a fundamental counting principle problem and can be solved by multiplying the number of choices you have for each digit of the license plate.

For the first five digits you can choose from the numbers 0,1,2...,9 or 10 choices.

A we cannot repeat the digits, so, first five digits will be:

10 × 9 × 8 × 7 × 6

Now the next 1 digit will all be letter all being different

There are 26 letters in the alphabet.. for our second digit we have 26 choices,

Here is the whole calculation:

= 10 × 9 × 8 × 7 × 6 × 26

= 786240

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Answer:

i think B but I’m not 100% sure lol

Step-by-step explanation:

Here’s what I found on this app

3w + 8 - w = 4w - 2(w - 4)

2w + 8 = 4w - 2w + 8

2w + 8 = 2w + 8

0 = 0

Answer:  C. 3w + 8 – w = 4w – 2(w – 4)

Identity equations are equations that are true no matter what value is plugged in for the variable. If you simplify an identity equation, you'll ALWAYS get a true statement. Learn about identity equations in this tutorial, and then create your own identity equation.

Step-by-step explanation:  Algebra.com

a. 11 - (2v + 3) = -2v - 8

Simplify

    11 - 2v - 6 = -2v - 8

         5 - 2v = -2v - 8

Add 3v to both sides

              5 = -8

That's false, so it is not an identity.

b. 5w + 8 - w = 6w - 2(w - 4)  

Simplify

      4w + 8 = 6w - 2w + 8

      4w + 8 = 4w + 8

That's exactly the same on both sides, so it's

an identity.

c. 7m - 2 = 8m + 4 - m

  7m - 2 = 7m + 4

Subtract 7m from both sides:

      -2 = 4

That's false, so it is not an identity.

d. 8y + 9 = 8y - 3

Subtract 8y from both sides:

       9 = -3

That's false, so it is not an identity.

Using monthly payment formula, the Smith Family's total monthly payment is approximately $2,360.99.

To calculate the total monthly payment for the Smith Family, we need to consider the mortgage payment, insurance, property tax, and HOA fees.

1. Mortgage Payment:

The loan amount is the house price minus the down payment:

$350,000 - $70,000 = $280,000.

To calculate the monthly mortgage payment, we need to determine the interest rate and loan term. Since you mentioned it's a 15-year loan, we'll assume an interest rate of 4% (which can vary depending on market conditions and the borrower's credit).

We can use a mortgage calculator formula to calculate the monthly payment:

M = P [i(1 + i)ⁿ] / [(1 + i)ⁿ⁻¹]

Where:

M = Monthly mortgage payment

P = Loan amount

i = Monthly interest rate

n = Number of months

The monthly interest rate is the annual interest rate divided by 12, and the loan term is 15 years, which is 180 months.

i = 4% / 12 = 0.00333 (monthly interest rate)

n = 180 (loan term in months)

Plugging in the values into the formula:

M = $280,000 [0.00333(1 + 0.00333)¹⁸⁰] / [(1 + 0.00333)¹⁸⁰⁻¹]

Using a calculator, the monthly mortgage payment comes out to be approximately $2,014.99.

2. Insurance:

The monthly insurance payment is given as $66.

3. Property Tax:

The monthly property tax payment is given as $230.

4. HOA Fees:

The HOA fees are stated as $600 per year. To convert this to a monthly payment, we divide by 12 (months in a year): $600 / 12 = $50 per month.

Now, let's add up all these expenses:

Mortgage payment: $2,014.99

Insurance: $66

Property tax: $230

HOA fees: $50

Total monthly payment = Mortgage payment + Insurance + Property tax + HOA fees

Total monthly payment = $2,014.99 + $66 + $230 + $50

Total monthly payment = $2,360.99

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Therefore, the double integral that computes the given function is ∫∫(x+y)dA, where the region D is bounded by the curves y = x^2 and x = y-6.

Sketch the region D to visualize the limits of integration.

Determine the limits of integration for x and y. Since x goes from y-6 to y, and y goes from 0 to 36, the limits of integration are:

0 ≤ y ≤ 36

y-6 ≤ x ≤ y

Set up the double integral with the limits of integration:

∫0^36 ∫y-6^y (x+y) dxdy

Integrate with respect to x first, then with respect to y:

∫0^36 [1/2(x^2+2xy)]y-6^y dy

= ∫0^36 [(1/2)y^3 - (3/2)y^2 + 9y - 27] dy

= 3960

Therefore, the double integral that computes the given function is ∫∫(x+y)dA, where the region D is bounded by the curves y = x^2 and x = y-6, and its value is 3960.

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Answer:

(3,2)

Step-by-step explanation:

I hope this helps : )

Answer:

true

Step-by-step explanation:

because there's less humidity

An open box is to be made out of a 6-inch by 14-inch piece of cardboard by cutting out squares of equal size from the four corners and bending up the sides. Find the dimensions of the resulting box that has the largest volume.

Dimensions of the bottom of the box: L x W

Height of the box:

SOLUTION

Diagram

Cardboard with x2 area cutouts...

··················14 - 2x

···x··¦¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¦···x··

¦——¦·······························¦——¦

¦·············································¦

¦·············································¦ 6 - 2x

¦·············································¦

¦——¦·······························¦——¦

···x··¦___________________¦··x···

Volume = l·w·h

After cutouts:

l = 14 - 2x

w = 6 - 2x

h = x

V = (14 - 2x)(6 - 2x)(x) in3

V = 4x3 - 40x2 + 84x in3

To maximize the volume, take the derivative of V with respect to x, set it equal to zero, and solve for x:

dV/dx = 0 = 12x2 - 80x + 24

x2 - (20/3)x + 7 = 0

x = (10 ± √37)/3 in

Since (6 - 2x) yields a negative number for x = (10 + √37)/3 we use only x = (10 - √37)/3

Thus, the dimensions are:

l = 14 - 2x = 11.39 in

w = 6 - 2x = 3.39 in

h = x = 1.31 in

Base = l·w = 38.59 in2

Volume = 50.39 in3

Answer:

It's 38.1

Step-by-step explanation:

I'm not the best at explaining these type of things but I hope this helps you out

The roots of the equation x³ + 4x² + x - 6 = 0 are x = 1, x = -2, and x = -3.

To find the roots of the equation x³ + 4x² + x - 6 = 0 without using a calculator, we can use factoring or synthetic division. By trying out different values for x, we can find that x = 1 is a root of the equation. Dividing the equation by (x - 1) using synthetic division, we obtain:

1 |   1    4    1   -6

   |        1    5    6

   |........................

      1    5    6    0

The result after dividing is the quadratic expression x² + 5x + 6. To find the remaining roots, we can factor this quadratic expression:

x² + 5x + 6

= (x + 2)(x + 3)

Setting each factor equal to zero, we have:

x + 2 = 0 or x + 3 = 0

Solving these equations, we find that x = -2 and x = -3.

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The original amount borrowed was $517.

Simple Interest is the method to calculate the interest charged for a given number of years and given rate , in simple interest the principle remains same for each year.

Simple interest =\(\frac{P*R*T}{100}\)

where P= principle, R=rate in % , T= time

We know that Amount= Principle+ Simple Interest........(1)

According to the question

Amount=$610.06

Rate=18%

time = 1yr

Substituting the value in equation (1) we get

\(610.06=P+\frac{P*18*1}{100}\)

\(610.06=\frac{100P+18P}{100}\)

\(610.06=\frac{118P}{100}\)

\(61006=118P\)

\(P=\frac{61006}{118}\)

\(P=517\)

Therefore  , The original amount borrowed was $517.

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Multiplying values by 2 in a normally distributed random sample and population increases the effect size as measured by Cohen's d.

The impact of multiplying all values in a normally distributed random sample and population by 2 on Cohen's d is an increase in effect size. Cohen's d measures the degree of difference between two sets of scores, calculated by dividing the difference between the two means by the pooled standard deviation. Therefore, when values are multiplied by 2, the means increase, leading to an increase in effect size as measured by Cohen's d.

In addition, multiplying values by 2 also increases the magnitude of the standard deviation, which is a measure of spread. When the standard deviation is larger, it requires a larger mean difference for Cohen's d to register a significant effect. Therefore, by increasing the standard deviation, the effect size measure will increase.

To summarize, multiplying values by 2 in a normally distributed random sample and population increases the effect size as measured by Cohen's d. This is because multiplying values by 2 increases both the mean and the standard deviation, which results in a larger mean difference and a larger standard deviation, respectively. Consequently, the effect size measure increases.

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Given:

\(f(1)=7\)

\(f(n)=3f(n-1)+3\)

To find:

The value of f(3).

Solution:

We have,

\(f(n)=3f(n-1)+3\)               ...(i)

Substituting \(n=2\) in (i), we get

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

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

Substituting \(f(1)=7\) in the above equation, we get

\(f(2)=3(7)+3\)

\(f(2)=21+3\)

\(f(2)=24\)

Now, substituting \(n=3\) in (i), we get

\(f(3)=3f(3-1)+3\)

\(f(3)=3f(2)+3\)

Substituting \(f(2)=24\) in the above equation, we get

\(f(3)=3(24)+3\)

\(f(3)=72+3\)

\(f(3)=75\)

Therefore, the value of f(3) is 75.

To calculate the mean of a data set, we need to sum up all the values and then divide by the total number of values.

Sum of the data set = 33 + 42 + 49 + 49 + 53 + 55 + 55 + 61 + 63 + 67 + 68 + 68 + 69 + 69 + 72 + 73 + 74 + 78 + 80 + 83 + 88 + 88 + 88 + 90 + 92 + 94 + 94 + 94 + 94 + 96 + 100

Count of values = 31

Mean = (Sum of the data set) / (Count of values)

Now we can substitute the values and calculate:

Mean = (33 + 42 + 49 + 49 + 53 + 55 + 55 + 61 + 63 + 67 + 68 + 68 + 69 + 69 + 72 + 73 + 74 + 78 + 80 + 83 + 88 + 88 + 88 + 90 + 92 + 94 + 94 + 94 + 94 + 96 + 100) / 31

After evaluating this expression, we find that the mean of the given data set is approximately 71.29 (rounded to two decimal places).

Therefore, the mean of the data set is 71.29.

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The number of ways of 3 volumes chosen at random is 455.

The number of ways that will include volume 1 and volume 2 is 13 and

The number of ways that will include volume 1 but not volume 2 is 156

Permutation and combination

In Mathematics, Permutation and combination are the ways of representing a group of objects by selecting from a set and forming subsets. These define the different types of ways to arrange a certain group of data.

When we select objects from a group, it is said to be permutations, whereas the combination is a way of selecting items, here the order of selection does not matter.

The formula for the combination of x things from a set of n things without replacement is given by

Here we have,

Number of volumes of  an encyclopedia = 15

Number volumes were chosen at a time = 3

From above formula

The number of ways of 3 volumes is chosen at random is

¹⁵C₃ = 15!/3!(15 - 3)!  

= 15!/3!(12)!  

= 15 × 14 × 13 × 12! / 6 (12!)

= 455  

(b) Including volume 1 and volume 2

To Include volume 1 and volume 2 in the set, first, we choose volume 1 and volume 2, and then we must choose the 3rd volume from the remaining volumes from 3 to 15 volumes [total 13 volumes].

Therefore the number of ways that will include volume 1 and volume 2

= 1 × 1 × 13 = 13  

(c) Including volume 1 but not volume 2

Here we are including volume 1 but not volume 2, for that in the first place we chose volume 1, for the second and third place we must choose from the remaining volumes 3 to 15 [total 13 volumes except 2 ]

The number of ways that will include volume 1 but not volume 2

= 1 × 13 × 12

= 156

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The solution to the given differential equation is \(y = a_0x^{[0]} + a_1x^{[1]} + a_2x^{[2]}\), where a_0, a_1, and a_2 are constants.

To fathom the given differential equation, xy'' + y' = 0, we will begin by expecting a control arrangement of the frame y = ∑(n=0 to ∞) a_nx^n, where a_n speaks to the coefficients to be decided.

Separating y with regard to x, we get:

\(y' = ∑(n=0 to ∞) a_n(nx^[(n-1))] = ∑(n=0 to ∞) na_nx^[(n-1)]\)

Separating y' with regard to x, we get:

\(y'' = ∑(n=0 to ∞) n(n-1)a_nx^[(n-2)]\)

Presently, we substitute these expressions for y and its subsidiaries into the differential condition:

\(x(∑(n=0 to ∞) n(n-1)a_nx^[(n-2))] + (∑(n=0 to ∞) na_nx^[(n-1))] =\)

After improving terms, we have:

\(∑(n=0 to ∞) n(n-1)a_nx^[(n-1)] + ∑(n=0 to ∞) na_nx^[n] =\)

Another, we compare the coefficients of like powers of x to zero, coming about in a boundless arrangement of conditions:

For n = 0: + a_0 = (condition 1)

For n = 1: + a_1 = (condition 2)

For n ≥ 2: n(n-1)a_n + na_n = (condition 3)

Disentangling condition 3, we have:

\(n^[2a]_n - n(a_n) =\)

n(n-1)a_n - na_n =

n(n-1 - 1)a_n =

(n(n-2)a_n) =

From equation 1, a_0 = 0, and from equation 2, a_1 = 0.

For n ≥ 2, we have two conceivable outcomes:

n(n-2) = 0, which gives n = or n = 2.

a_n = (minor arrangement)

So, the solution to the given differential equation is \(y = a_0x^{[0]} + a_1x^{[1]} + a_2x^{[2]}\), where a_0, a_1, and a_2 are constants.

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