What is the circumference of a circle with a radius of 14 feet? Use 22 over 7 for π.

Answer:

Step-by-step explanation:

fly

The derivative of the function at P0 in the direction of A is,

([tex]\frac{df}{dx}[/tex])[tex]p_{0}[/tex] = -3 , ([tex]\frac{df}{dy}[/tex])[tex]p_{0}[/tex] = -1 , ([tex]\frac{df}{dz}[/tex])[tex]p_{0}[/tex] = 0

Geometrically, the derivative of a function can be interpreted as the slope of the graph of the function or, more precisely, as the slope of the tangent line at a point. Its calculation, in fact, derives from the slope formula for a straight line, except that a limiting process must be used for curves.

Given that,

The derivative of the function at P0 in the direction of A.

f(x, y, z) =

f(x, y, z) = (1,-1,-2)

x = 1

y = -1

z = -2

Derivative of f(x, y, z) = xy + yz + zx

[tex]\frac{df}{dx}[/tex] = y + z

[tex]\frac{df}{dy}[/tex] = x + z

[tex]\frac{df}{dz}[/tex] = x + y

We can substitute f(x, y, z) = (1,-1,-2) values,

([tex]\frac{df}{dx}[/tex])[tex]p_{0}[/tex] = y + z

([tex]\frac{df}{dx}[/tex])[tex]p_{0}[/tex] = -1 + (-2)

([tex]\frac{df}{dx}[/tex])[tex]p_{0}[/tex] = -3

([tex]\frac{df}{dy}[/tex])[tex]p_{0}[/tex] = x + z

([tex]\frac{df}{dy}[/tex])[tex]p_{0}[/tex] = 1 + (-2)

([tex]\frac{df}{dy}[/tex])[tex]p_{0}[/tex] = 1-2

([tex]\frac{df}{dy}[/tex])[tex]p_{0}[/tex] = -1

([tex]\frac{df}{dz}[/tex])[tex]p_{0}[/tex] = x + y

([tex]\frac{df}{dz}[/tex])[tex]p_{0}[/tex] = 1 + (-1)

([tex]\frac{df}{dz}[/tex])[tex]p_{0}[/tex] = 1-1

([tex]\frac{df}{dz}[/tex])[tex]p_{0}[/tex] = 0

Therefore,

The derivative of the function at P0 in the direction of A is,

([tex]\frac{df}{dx}[/tex])[tex]p_{0}[/tex] = -3 , ([tex]\frac{df}{dy}[/tex])[tex]p_{0}[/tex] = -1 , ([tex]\frac{df}{dz}[/tex])[tex]p_{0}[/tex] = 0

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The probability that hugo will solve rubik's cube in less than 8 minutes is 0.4375.

We have given that,

the amount of time it takes hugo to solve a rubik's cube is continuous and uniformly distributed between 4.5 minutes and 12.5 minutes.

i.e. a = 4.5 and b = 12.5

The probability that we find a value of X lower than x is given by the f

P(X < x) = [tex]\frac{x-a}{b-a}[/tex]

We have to find probability that it takes hugo less than 8 minutes to solve rubik's cube.

Therefore

P(X < 8) =  [tex]\frac{8-4.5}{12.5-4.5}[/tex]

             = [tex]\frac{3.5}{8}[/tex]

P(X < 8) = 0.4375

Hence the probability that it takes hugo less than 8 minutes to solve a rubik's cube is 0.4375%.

The uniform continuous distribution is one of the simplest probability distributions in statistics. Is is a continuous distribution, this means that it takes values within a specified range. A continuous uniform distribution takes values in a range [a,b].

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We can find the equation of any line passing through a given point and parallel or perpendicular to a given line by finding the slope of the given line and using slope-intercept form.

Given, the line passing through a given point and parallel and perpendicular to a given line

we have to find the equation of the lines

Let l1 be a line passing through a point (p , q) and parallel to a line l2.

suppose the equation of the line l2 be,

y = mx + c

the line l2 has slope m

Now to find the equation of the line l1,

(y - q)/(x - p) = m

On cross-multiplying, we get

y - q = m(x - p)

y = mx - pm + q

So, the equation of the line l1 be,

y = mx + (q - pm)

Similarly, we can find the equation of any line passing through a point and parallel to a given line.

Hence, we can find the equation of any line with the slope.

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Answer:

$15400

Step-by-step explanation:

1 year = 12 month

10 years = 120 months

12% = month

1440% = 120 months

1440% = 14.4

Take 1000 times 14.4 = $14400

So, we add the two numbers

1000 + 14400 = $15400

So, $15400 will be in the account at the end of 10 years.

Answer:

Step-by-step explanation:

The ratio of basketballs to soccer balls is 2 : 1

The quantity which would be written first if basketballs to soccer balls is 2 : 1 is basketball

This refers to a number representing a comparison between two or more named things.

If the ratio of basketballs to soccer balls = 2 : 1

This means,

Basketball : soccer ball = 2 : 1

Therefore, Basketball is the quantity which would be written first because it comes first in the given expression.

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Answer:

5

Step-by-step explanation:

1.24 × 4 = 5

or it can be 1.24 ÷2 =0.265

Answer:

b

Step-by-step explanation:

By using multiplication, it can be calculated that

There are 391 houses in 23 blocks

What is multiplication?

Repeated addition is called multiplication. Multiplication is used to find the product of two or more numbers.

This is a word problem on multiplication

Number of houses in one block = 17

Assuming there are equal number of houses in each block,

Number of houses in 23 blocks = 23 [tex]\times[/tex] 17 = 391

There are 391 houses in 23 blocks

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The value of composite function g(f(-2) is when f(x) = x^2+9 and g(x) = x-9 is 4

What is a function?

A function in mathematics from a set X to a set Y assigns exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

We are given two functions  f(x) = x^2+9 and g(x) = x-9

and we are asked to find g(f(-2))

this term means we first substitute f(x) in the place of x in function g

We get

g(f(x))= f(x) - 9

Now substitute the value of f(x) in the above function

g(f(x))= x^2+9 -9

g(f(x))= x^2

g(f(-2))= (-2)^2

g(f(-2))= 4

Hence the value of the function if 4

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a) The amount of ounces in 8 liters is of: 270.5 ounces.

b) The number of containers needed is of: 90 containers.

A proportion is a fraction of a total amount, which serves as an unit rate in the context of a problem, used along basic arithmetic operations such as multiplication or division, to find the desired measures in the context of a problem.

The number of ounces per liter is given as follows:

33.814 ounces.

Hence the number of ounces in eight liters is given as follows:

8 x 33.814 = 270.5 ounces.

Each container has three ounces, hence the number of containers is obtained as follows:

270.5/3 = 90 containers.

(as the total amount is of 270.5 ounces, and each container is composed by three ounces, hence the proportion was applied).

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Answer:

x = 135

Step-by-step explanation:

the 2 situations are similar with ratios of corresponding sides in proportion , that is

[tex]\frac{x}{54}[/tex] = [tex]\frac{90}{36}[/tex] ( cross- multiply )

36x = 54 × 90 = 4860 ( divide both sides by 36 )

x = 135

True, Mandy claims that there are no fixes for the system.

What do you mean by the system of linear equation?

A system of linear equations is usually a set of two linear equations in two variables. A linear equation in two variables has an infinite number of solutions. The goal of solving a system of equations is to transform two bivariate equations into a single univariate equation.

Given system of linear equation:

9x + 15y = 6 ....(1)

5y = -3x + 4 ....(2)

Using elimination method,

Substitute the value of x from eq (1) to eq(2)

9x + 15y = 6

9x = 6 - 15y

x = [tex]\frac{6-15y}{9}[/tex]

Now, substitute this in eq(2)

5y = - 3x + 4

5y = -3( [tex]\frac{6-15y}{9}[/tex]) + 4

5y = -1([tex]\frac{6-15y}{3}[/tex]) + 4

5y = -2 + 5y + 4

5y - 5y = 2

0 = 2

Which is not possible, hence given system of linear equation has no solution.

Hence, Mandy's statement is true.

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Common data sources like social media comments are categorized as unstructured data. (Option 2)

Unstructured data refers to information that does not have a pre-defined data model or is not organized in a pre-defined manner. Unstructured data is a dataset that is not stored in a specific structured format and is generally text-heavy, but may contain data such as dates, numbers, and facts. Unstructured data does have an internal structure, but it is not predefined through data models. It might be human generated, or machine generated in a textual or a non-textual format. Examples of unstructured data are social media comments, blog posts, videos, and documents.

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Answer: slope = -1

Step-by-step explanation:

count number down vs number it takes to get back to the line.

For example, 1 down, 1 across

The number 11% of 40 can solve by  .11 times 40. Option A is the correct option.

What is percentage of a number?

A value or ratio that may be stated as a fraction of 100 is referred to in mathematics as a percentage. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means.

The value of a% is equal to a/100.

Thus the value of 11% is 11/100 = 0.11.

Given that 11% of 40.

Now putting 11% = 0.11 in above expression:

= 0.11 of 40.

Of means times:

= 0.11 times 40.

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The amount of money with Adam and Braulio as per given system of equations is equal to $84 and $69.

As given in the question,

Let 'a' be the amount of money with Adam

And 'b' be the amount of money with Braulio

System of equations as per given given data:

b = a - 15___(1)

a + b = 153 ___(2)

Substitute the value of 'b' in (2) we get,

a + a -15 = 153

⇒2a = 153 + 15

⇒2a = 168

⇒ a = $84

Amount of money with Adam is $84

Amount of money with Braulio is b = 84 - 15

                                                          = $69

Therefore, the amount of money with Adam and Braulio is equal to $84 and $69.

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Answer: f(x) = -x^2 - 9x - 90

Correct answer is the last one (D)

Step-by-step explanation:

Graph every single one of them using Desmos Graphing Calculator

The derivative of the given function sin(xy)=3x−2y is obtained as;

dy/dx =  3sec(xy)/x - y/x

The given equation is-

sin(xy) = 3x − 2y

Be sure to account for both sides of this argument.

d/dx(sin(xy)) = d/dx(3x − 2y)

Differentiate the equation's left side.

Set the left side equal to a right side to reform the equation.

x.cos(xy).y' + y.cos(xy) = 3

Solve for y'.

y' = 3sec(xy)/x - y/x

Thus, replace y' with dy/dx

dy/dx =  3sec(xy)/x - y/x

Thus, the derivative of the given function sin(x y)=3x−2y is obtained as;

dy/dx =  3sec(xy)/x - y/x

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The graph crosses the x-axis at x = 0 and touches the x-axis at x = –5.

Option (C) is correct.

What is a function in mathematics?

In mathematics, a function is a relation between a set of inputs and a set of possible outputs with the property that each input is related to exactly one output. The set of inputs is called the domain of the function, and the set of possible outputs is called the range of the function.

First, factorize the function f(x):

[tex]f(x)=4x^7+40x^6+100x^5\\\\f(x)=4x^5(x^2+10x + 25)\\\\f(x)=4x^5(x+5)^2[/tex]

When f(x)=0, you get that

[tex]4x^5(x+5)^2 = 0\\\\x=0 $ or $ x = -5[/tex]

This means that the graph intersects the x-axis at points (0,0) and (-5,0). But:

1. since the degree at term [tex]x^5[/tex] is odd, point (0,0) is x-intercept;

2. since the degree at term [tex](x+5)^2[/tex] is even, point (-5,0) is the tangent point (see the attached graph of the function).

Hence, The graph crosses the x-axis at x = 0 and touches the x-axis at x = –5.

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If the original quantity is 8 and the new quantity is 2, then the correct answer is 75%.

For this question we need to subtract and multiply the numbers. We know that 2 = 25% of 8 so:

[tex]\boxed{8-2=6}\\\boxed{6/2=3}[/tex]

We are going to take that 25% and multiply it with 3 to get are final answer.

[tex]\boxed{25*3=75}\\\boxed{So,2=75}[/tex]

Therefore, If the original quantity is 8 and the new quantity is 2, then the correct answer is 75%.

Answer:

3 years

Step-by-step explanation:

we can use the equation 14+3x=8+5x to determine when they will be they same height. X I'd

The values of the x of the given equation [tex]x^{2} + 6x + 1 = 0[/tex]  using quadratic formula is -10 and -2.

The quadratic formula helps us solve any quadratic equation. First, we bring the equation to the form ax²+bx+c=0, where a, b, and c are coefficients. Then, we plug these coefficients in the formula:

(-b±√(b²-4ac))/(2a)

Given equation;

[tex]x^{2} + 6x + 1 = 0[/tex]

Using  quadratic formula

x = [tex]-b[/tex] ± [tex]\frac{\sqrt{(b^{2} - 4 (ac) } }{4a}[/tex]

Substitute the values a = 1, b = 6, c = 1, we get;

x = [tex]-6[/tex] ± [tex]\frac{\sqrt{( (6) ^{2} - 4. 1.1)} }{2*1}[/tex]

x = -6 ± 4

x = -6 - 4      &    x = -6 + 4

  = -10                = -2

x = -10,  -2

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The mean number of pages is 13.8.

What is the mean?

There are various mean types in mathematics, particularly in statistics. Each mean helps to summarize a certain set of data, frequently to help determine the overall significance of a specific data set.

We have,

Kamari is reading a novel for his English class.

For the first 10 days, he records the number of pages he reads each day.

14,10,8,20,15,15,12,10,14,20

We have to calculate the mean of the number of pages he has red.

The mean is calculated by dividing the sum of all values in a data set by the number of values.

so,

14  + 10 + 8 + 20 + 15 + 15 + 12 + 10 + 14 + 20

= 138

Mean = 138 ÷ 10

= 13.8

Hence, the mean number of pages is 13.8.

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Answer:rise over rub

Step-by-step explanation:

The number of students is 30 while the number of adults will be 37.

Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.

In other words, an equation is a set of variables that are constrained through a situation or case.

Suppose the number of students ticker is x and the number of adults is y.

7x + 9y = total revenute

7x + 9y = 543

Total tickets = x + y

x + y = 67

Multiply the above equation by 9

9x + 9y = 603

Subtract equations as

7x + 9y - 9x - 9y = 543 - 603

-2x = -60

x = 30

And, y = 67 - 30 = 37

Hence "The number of students is 30 while the number of adults will be 37".

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Answer:

A.  The graph that Larry created is a correct representation of his company's charges.

Step-by-step explanation:

The equation for the services charges, y, is made up of the $10 initial service call fee plus $5 times the number of hours, x.

y = 5x + 10

Try any 2 values for x to see if they fits the graph.

x(hr)   y($)

0        10

1         15

4        30

This is the line already drawn on the graph.  Larry did everything correctly, so options B, C, and D are all false/incorrect.

The probability the property has oil, given that both tests report positive.

P(O|A∩B) = 0.6 * 0.5 / 0.8 = 0.375

P(O|A∩B) = P(A∩B|O)P(O) / P(A∩B)

P(A∩B|O) = 0.8 * 0.75 = 0.6

P(O) = 0.5

P(A∩B) = P(A|O)P(O) + P(A|¬O)P(¬O)

P(A|O) = 0.8, P(¬O) = 0.5

P(A∩B) = 0.8 * 0.5 + 0.8 * 0.5 = 0.8

P(O|A∩B) = 0.6 * 0.5 / 0.8 = 0.375

The study of random events is the focus of probability theory, a subfield of mathematics. It is impossible to predict the outcome of a random event before it happens, although it could take any of numerous different forms. It is believed that chance played a role in how things turned out.

Information on possibility of occurrence is provided by probability. For instance, meteorologists can forecast the likelihood of rain by looking at weather patterns. Probability theory is utilized in epidemiology to comprehend how exposures and the risk of health impacts are related.

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