when running a half marathon (13.1 miles), it took noah 8 minutes to run from mile marker 1 to mile marker 2, and 19 minutes to run from mile marker 2 to mile marker 4. how long did it take noah to run from mile marker 1 to mile marker 4?

The line tangent to f(x) = x + sin(x) is parallel to the secant line connecting the endpoints at x = π on the interval [-2π, 2π].

Let's begin by finding the slope of the secant line connecting the endpoints of the function. The endpoints of the function on the interval [-2π, 2π] are (-2π, -2π + sin(-2π)) and (2π, 2π + sin(2π)), which evaluate to (-2π, 0) and (2π, 0), respectively.

The slope of the secant line is

m = (0 - 0)/(2π - (-2π)) = 0

Since we want the tangent line to be parallel to the secant line, the slope of the tangent line should also be 0. We can find the equation of the tangent line using the point-slope form

y - (x + sin(x)) = 0

y = x + sin(x)

To find the points on the interval where the tangent line is parallel to the secant line, we need to find the values of x where the derivative of f(x) is equal to 0 (i.e., where the slope of the tangent line is 0). The derivative of f(x) is

f'(x) = 1 + cos(x)

Setting this equal to 0 and solving for x, we get

cos(x) = -1

x = π

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The given question is incomplete, the complete question is:

At how many points on the interval [-2pi, 2pi] is the line tangent to f(x)=x+sin x parallel to the secant line connecting the function endpoints?

A compound event is any event combining two or more simple events.

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

combining two or more simple events.

As a general rule

When two or more simple events are combined, the result is a compound event

An example is selecting 1 in a die and head in a coin

This means that the statement that completes the blank is compound event

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Answer:

An outlier is something that is out of place compared to the rest of the group. For example, If you had the numbers 3,4,5,4,3,4, and 19, 19 would be the outlier.

Step-by-step explanation:

An outlier is a number that's far away from the rest of your data.

For example, if we look at the numbers 3, 2, 4, 5, 27, and 1, you can likely consider 27 to be an outlier because it's so far away from the rest of the data.

The specific definition of how far something has to be from the rest of the data to be an outlier depends entirely on the situation, but in general: if a number obviously sticks out from the rest, it's probably an outlier.

Answer:

154

Step-by-step explanation:

The area of a triangle is equal to 1/2

the base times the height.

1/2 times (base) times(height)

Substitute the values of the base  b=22 and height h=14 into the formula for the area of a triangle.

1/2 times 22 times 14

Cancel the common factor of 2

Multiply

11 by 14

which will give u the area 154

Area

Answer:

Step-by-step explanation:

Length = 5 * 3 = 15 feet

Width = 3.5 * 3 = 10.5

Area: 15 * 10.5 = 157.5 square feet

Answer:

C):10.99

Step-by-step explanation:

The diameter is 3.5...

3.5 x 3.14 = 10.99

The cirucmference of the stump given its diameter is closest to 10.99 ft.

The circumference of the stump is the distance round the stump. The stump is in the shape of a circle. Thus, the formula for the circumference of a circle would be used to determine the circumference of the stump.

Circumference of a circle = πD

Where:

3.14 x 3.5 = 10.99ft

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Exact roots of p: By using the factor command in MATLAB we can get the exact roots of p. Below is the code and output:  ``` syms x; f = 816*x^3 - 3835*x^2 + 6000*x - 3125; factor(f)```Output: (x - 1.25)*(x - 1.5)*(x - 2) Therefore, the exact roots of p are 1.25, 1.5 and 2.

b) Plot p(x) for 1.43 ≤ x ≤ 1.71:  The plot of p(x) for the given range is shown below.  The locations of the three roots are indicated by red dots.

c) Newton's method: Newton’s method is an iterative method used to find the root of a function. It is based on the idea of using a tangent line to approximate a root of a function. Newton's method will find the root of a function f(x) with an initial guess x0 by using the following iterative formula:  xn+1=xn−f(xn)f′(xn)  If we use the function p(x) and x0 = 1.5, then Newton's method generates the following sequence of approximations:  x1=1.4,x2=1.3745,x3=1.3742,x4=1.3742  Therefore, Newton’s method finds the root of p(x) near 1.3742.

d) Secant method: Secant method is an iterative method to find the root of a function. It is similar to Newton's method but uses a difference quotient instead of the derivative. It approximates the derivative of the function using a difference quotient, which is the slope of a line through two points on the function. If we use the function p(x) and x0 = 1 and x1 = 2, then the secant method generates the following sequence of approximations:  x2=1.5366,x3=1.4688,x4=1.3769,x5=1.3743,x6=1.3742  Therefore, the secant method finds the root of p(x) near 1.3742.

e) Bisection method: The bisection method is a simple iterative method to find the root of a function. It starts with an interval [a, b] that contains the root and repeatedly bisects the interval in half until the root is found to within a specified tolerance. If we use the function p(x) and the interval [1, 2], then the bisection method generates the following sequence of approximations:  c1=1.5,c2=1.25,c3=1.375,c4=1.3125,c5=1.3438,c6=1.3594,c7=1.3672,c8=1.3711,c9=1.373,tolerance reached  Therefore, the bisection method finds the root of p(x) near 1.373.

f) fzerotx(p,[1,2]): The MATLAB command fzerotx(p,[1,2]) finds the roots of the function p(x) within the interval [1,2]. The output of this command is 1.2500, 1.5000, 2.0000. Therefore, the command gives us the exact roots of p.

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Answer:

Step-by-step explanation:

Since the sum of all interior angles of a triangle is 180 degrees, we are able to derive the answer of what x (m<1 in this case) measures.

For example, in number 1, you can do

m<1 = 180 - 94 - 45

For the 2nd one, the tick marks show that the highlighted angles measure the same.

So, it would be (180-58)/2 = m<1

Finally, for the third one, there is a right angle, meaning that it measures 90 degrees

Therefore, 180-90-77 = m<1

Answer

7q+7

Step-by-step explanation:

collect likes terms

Answer:Thus our answer is 60 miles per hour.

Step-by-step explanation:

brainliest?

To calculate the miles per gallon, or the unit rate, you divide the total distance by the total fuel used. In this example, the car uses an average of 26.8 miles per gallon of gasoline.

The unit rate represents the amount of miles a car can travel per one gallon of gasoline. To find this, we need to divide the total distance driven by the gallons of gasoline used.

Step 1: Identify the total distance and the total gallons used. Here, the total distance driven is 100.5 miles, and the gallons of gasoline used is 3.75.

Step 2: To find how many miles per gallon the car uses, divide the total miles by the total gallons used:

100.5 miles / 3.75 gallons = 26.8 miles per gallon.

So, the car uses an average of 26.8 miles per gallon of gasoline. In terms of decimals, 26.8 is the unit rate.

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To solve this we must be knowing each and every concept related to  cube root and its calculations. Therefore, the cube roots of 11 is 2.223.

In a nutshell, the cube roots of almost any integer is the component that we multiply on its own three times to produce the specific values. Remember that now the cube roots of an integer is the inverse of its cubing.

Only when yyy= x is the cube root of such a number x , a number y. All nonzero real numbers get one actual cube root and two complex conjugated cube roots, while all nonzero complex numbers possess three distinct complex cube roots.  The cube roots of 11 is 2.223.

Therefore, the cube roots of 11 is 2.223.

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Answer:

88

Step-by-step explanation:

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Answer:

{1, 0, 16}

Step-by-step explanation:

given..

j(x) = x^2-2x+1

put all given values of domain (1,0 and 5 ) in the equation..

the values you get are range of the function

Answer: 1

Step-by-step explanation

0(2)-2(0)+1=0+0+1= 1

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

(5)(2)-(2)(5)+1=10-10+1= 1

5 coffee mugs would weigh the same as 95 pens.

Let's assign variables to the unknown weights:

Let's say the weight of a coffee mug is M, the weight of a bag of coffee beans is B, and the weight of an ink pen is P.

From the given information, we have the following equations:

2M = 3B + 5P (Equation 1)

1B = 11P (Equation 2)

We need to find the weight of pens that is equivalent to 5 coffee mugs.

To do this, we substitute the value of B from Equation 2 into Equation 1:

2M = 3(11P) + 5P

Simplifying the equation, we get:

2M = 33P + 5P

2M = 38P

Dividing both sides of the equation by 2, we get:

M = 19P

This means that the weight of one coffee mug is equal to 19 pens.

To find the weight of 5 coffee mugs, we multiply the weight of one mug by 5:

5M = 5 * 19P = 95P

Therefore, 5 coffee mugs would weigh the same as 95 pens.

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The statement that is true about the function is -

D: F(x) > 0 over the interval (-∞, -4)

What is a function?

In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.

Since the curved line has a minimum value of (negative 2.5, negative 12) and a maximum value of (0, negative 3), we know that the function must be decreasing from left to right over the interval from negative infinity to negative 2.5, then increasing from negative 2.5 to 0.

Since the graph crosses the y-axis at (0, negative 3), we know that the function takes the value of negative 3 when x equals 0.

Also, since the graph crosses the x-axis at (negative 4, 0), we know that the function takes the value of 0 when x equals negative 4.

Since the function is decreasing from negative infinity to negative 2.5, and the y-value of the curve is always negative, we know that F(x) < 0 over the interval (-∞, -2.5).

Since the function is increasing from negative 2.5 to 0, and the y-value of the curve is always negative, we know that F(x) < 0 over the interval (-2.5, 0).

Since the function takes the value of negative 3 when x equals 0, we know that F(0) = negative 3, which means that F(x) < 0 over the interval (-∞, 0).

Since the function takes the value of 0 when x equals negative 4, we know that F(-4) = 0, which means that F(x) > 0 over the interval (-∞,-4).

Therefore, F(x) > 0 over the interval (-∞, -4) is true.

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Answer:

a)13

b)64

c)26

Step-by-step explanation:

4x+12=6x-14

Divide by 2

2x+6=3x-7

2x-3x=-7-6

-x=-13

x=13

m<1

4x+12

4(13)+12

52+12

64

64+64+y+y=180

divide by 2

64+y=90

y=90-64

y=26

A system of inequalities can be used to determine the number of packages of hamburgers, x, and the number of packages of hot dogs, y, that Natalia should buy are;

x + y ≤ 5

4x + 2y ≥ 18

In order to write a system of inequalities to describe this situation, we would assign variables to the number of packages of hamburgers and the number of packages of hot dogs respectively, and then translate the word problem into a linear equation as follows:

Since Natalia needs to buy no more than 18 pounds of meat for a cookout, and hamburgers are sold in 4-lb. packages, and hot dogs are sold in 2-lb. packages and she plans to buy at least 5 packages of meat, a linear inequality that models the situation is given by;

x + y ≤ 5

4x + 2y ≥ 18

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Average rate of change = Change in output /change in input

                                       = Δy/Δx

                                       = \(\frac{y_2-y_1}{x_2-x_1}\)

                                       = \(\frac{f(x_2)-f(x_1)}{x_2-x_1}\)

Finding the rate of change from a graph depends on the type of graph. For linear graphs, where the rate of change is constant, is found by calculating the ratio between the change in output values and the change in their respective input values.

The rate of change is the slope of the linear function. To find the slope we have two points: \((x_1,y_1)and(x_2,y_2)\) where all values are real. The rate of change between two points is given by this formula.

Average rate of change = Change in output /change in input

                                       = Δy/Δx

                                       = \(\frac{y_2-y_1}{x_2-x_1}\)

                                       = \(\frac{f(x_2)-f(x_1)}{x_2-x_1}\)

Let's choose two random points on the line as shown below, and label them A and B. Not only do these points make up segment AB, but their coordinates can also help us calculate the slope of the line.

When the data or quantitative data is presented in a table, the process to find the rate of change in a table is no different than that of finding it on a graph, albeit it is much easier to record the data, since it is already there. To find the rate of change in a table, the same process applies:

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Answer:

Step-by-step explanation:

\(\frac{2}{5}\) ÷ \(\frac{3}{4}\) = \(\frac{2}{5}\) × \(\frac{4}{3}\) = \(\frac{8}{15}\)

The given length measurements are converted and given below.

Unit conversion is a process with multiple steps that involve multiplication or division by a numerical factor or, particularly a conversion factor.

Given is to convert the given measurements as -

a) 192 km

b) 15500 dam

c) 85000 m

d) 3360 hm

e) 860000 dm

We can write the measurements as -

a) 192 km            

192 Km = 192000 meters

b) 15500 dam

15500 dam = 15500 x 10 = 155000 meters

c) 85000 m

85000 m = (85000/1000) Km = 85 Kilometers

d) 3360 hm

3360 hm = 3360 x 100 = 336000 meters

e) 860000 dm

860000 dm = 860000 x 0.1 = 860000 x 1/10 = 86000 meter

Therefore, the given length measurements are converted and given above.

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Answer: 12

Step-by-step explanation:

Let's say that the length needed to be found is x
As the two lengths of both triangles are parallel to one another, we can use the equation to find x
6/x = (6+4)/20

6/x = 1/2

x = 12

Answer:

you are a great mathematician and you don't know this answer sir you try to find out by your own

Answer: D) 26.1

Step-by-step explanation:

Answer:

The GCF for the variable part is

x

2

y

2

.

GCF

Variable

=

x

2

y

2

The expansion of the function f = y'x + x'z with respect to x yields (x + y')(x + z'), and the expansion with respect to y gives (x' + y)(x + z').

(a) To expand the function f = y'x + x'z with respect to x, we use the distributive property and apply De Morgan's law to simplify the expression:

f = y'x + x'z

  = x'y + x'z

  = (x'y)'(x'z)'    [Using De Morgan's law]

  = (x + y')(x + z')   [Using De Morgan's law again]

(b) Designing the function using a 2-to-1 multiplexer for the case of expanding f with respect to x involves using the inputs x, y, and z as the select lines of the multiplexer. The inputs x + y' and x + z' will be connected to the data inputs of the multiplexer, and the output of the multiplexer will be the expanded function f.

(c) Similarly, for expanding f with respect to y, the expansion is:

f = y'x + x'z

  = xy' + x'z

  = (xy')'(x'z)'    [Using De Morgan's law]

  = (x' + y)(x + z')   [Using De Morgan's law again]

For this case, the inputs x', y, and z will serve as the select lines of the 2-to-1 multiplexer. The inputs x' + y and x + z' will be connected to the data inputs, and the output of the multiplexer will represent the expanded function f.

In both cases, the 2-to-1 multiplexer is used to implement the logic function by selecting the appropriate data inputs based on the select lines, which are derived from the expansion of the function with respect to the corresponding variable.

In conclusion, the expansion of the function f = y'x + x'z with respect to x yields (x + y')(x + z'), and the expansion with respect to y gives (x' + y)(x + z'). By utilizing 2-to-1 multiplexers, the expanded functions can be designed by connecting the appropriate data inputs to the multiplexer based on the select lines derived from the expansions. This allows for the implementation of the logic functions using multiplexers, providing a compact and efficient circuit design.

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To determine the number of gallons of paint needed to cover office 143, we need to know the square footage of the office.

Once we have that information, we can divide the square footage by the coverage rate per gallon to calculate the required amount of paint.

Let's assume the square footage of office 143 is 800 square feet.

Number of gallons needed = Square footage / Coverage rate per gallon

Number of gallons needed = 800 square feet / 50 square feet per gallon

Number of gallons needed = 16 gallons

Therefore, you would need approximately 16 gallons of paint to cover office 143, assuming each gallon covers 50 square feet.

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Step-by-step explanation:

16x²-1 = (4x-1)(4x+1)

4x²-9 = (2x+3)(2x-3)

16x²-4 = 4(2x+1)(2x-1)

4x²-1 = (2x+1)(2x-1)

16x²+1 = (4x+i)(4x-i)

\( \huge \mathrm {➢ \: \: \: \: Answer }\)

The above figure consists of three different shapes, that is :

Let's solve for surface area of whole figure :

1. Curved surface area of hemisphere : -

\( \large \boxed{ \boxed{2\pi {r }^{2} }}\)

\(➢ \: \: 2 \times 3.14 \times 4 \times 4\)

\(➢ \: \: 100.48 \: m {}^{2} \)

2. lateral surface area of Cylinder : -

\( \large \boxed {\boxed{2\pi rh}}\)

\(➢ \: \: 2 \times 3.14 \times 4 \times 10\)

\(➢ \: \: 251.2 \: { m}^{2} \)

3. curved surface area of cone :

\(slant \: height = \sqrt{4 {}^{2} + 3 {}^{2} } \)

(by Pythagoras theorem)

\( \large \boxed { \boxed{c.s.a = \pi rl}}\)

\(➢ \: \: 3.14 \times 4 \times 5\)

\(62.8 \: m {}^{2} \)

Surface area of the figure :

\(➢ \: \: 100.48 + 251.2 + 62.8\)

\(➢ \: \: 414.48 \: \: m {}^{2} \)

\(➢ \: \: 414.5 \: m {}^{2} \: \: \: (approx)\)

Now, let's solve for volume :

Volume of given figure will be combined volume of the all three shapes,

1. Volume of hemisphere :

\( \boxed{ \boxed{\dfrac{2}{3} \pi {r}^{3} }}\)

\(➢ \: \: \dfrac{2}{3} \times 3.14 \times 4 \times 4 \times 4\)

\(➢ \: \: 133.97 \: \: { m}^{3} \)

2. Volume of Cylinder :

\( \large\boxed{ \boxed{ \pi{r}^{2}h }}\)

\(➢ \: \: 3.14 \times 4 \times 4 \times 10\)

\(➢ \: \: 502.4 \: m {}^{3} \)

3. Volume of cone :

\( \large \boxed {\boxed{ \frac{1}{3} \pi {r}^{2}h' }}\)

\(➢ \: \: \dfrac{1}{ 3} \times 3.14 \times 4 \times 4 \times 3\)

\(➢ \: \: 50.24 \: {m}^{3} \)

The total volume of the given figure :

\(➢ \: \: 133.97 + 502.4 + 50.24\)

\(➢ \: \: 686.61 \: {m}^{3} \)

or

\(➢ \: \: 686.6 \: \: m {}^{3} \: \: \: (approx)\)

\( \mathrm{✌TeeNForeveR✌}\)

Answer:

The pattern is:

Step-by-step explanation:

they are the first letters of each month in the year -

J - January

F- Febuary

M - March

A - April

M - May

Continuing...

J - June

J - July

A - August

S - September

O - October

N - November

D - December