Suppose that a category of world class runners are known to run a marathon (26 miles) in an average of 145 minutes with a standard deviation of 12 minutes. Consider 49 of the races.
Let
X = the average of the 49 races.

Please see attachment for questions

Answer:36

Step-by-step explanation:

Assume the total number of students to be x

According to the question

25% of x =9

⇒x=900/25=36

Given:

Sample space = 10

Rate = 1/3 per second

hello

to solve this problem, we need to identify the shape of the soup can first since soup is a liquid and carries the shape of whatever container its in.

volume of a cylinder is given as

from the calculations above, the volume of the soup is equal to 673.9cm^3 which corresponds with option D

Answer:

9207/10 is equivalent to 920.7

Answer: Width =14, Length = 18

Step-by-step explanation:

L = W + 4

2W + 2L = 64

W+ L = 32

2W+ 4 = 32

2W = 28

W = 14

Given

x = 5

5x + 2 = 27

Procedure

d. Yes, because when x is replaced by 5 the equation is true. ​

Given,

The expression is:

Required:

The value of y at x = -2, -1, 0, 1, 2.

The value of y at x = -2.

The value of y at x = -1.

The value of y at x = 0.

The value of y at x = 1.

The value of y at x = 2.

The table for the different value of the function:

x y

-2

In a relationship between two variables x and y, the data set is a function, if every element of the domain corresponds to exactly one element of the range

that means

one element of x corresponds to exactly one element of y

In any function, there is an input value (independent variable or x variable) and there is an output value (dependent variable or y variable)

What makes a function a function? ------> one element of the input (variable x) corresponds to exactly one element of the output (variable y)

The coordinates of point A are (7/5, 0), and the perpendicular line that also passes through that point is:

y = 0.

Here we want to get a line perpendicular to:

5x - 7 = 0

Solving this for x, we get:

5x = 7

x = 7/5.

This is a vertical line, so the perpendicular line will be a horizontal line, which is of the form:

y = a.

We know that the line:

x = 7/5.

Cuts the x-axis at point A.

Remember that the x-axis as coordinates (x, 0).

So the coordinates of point A are (7/5, 0).

Now, the perpendicular line:

y = a

Needs to pass through the point (7/5, 0), so the value of a must be zero, then the line is:

y = 0.

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Solution

The functions that define the region in consideration are given below:

The Washer Method:

- Plotting these functions would help us visualize the question better. This is done below:

- The question would like us to revolve around the region about line x = 2. The region is bounded by the Blue, Red, and Green line. This requires that we use the formula given below:

-

We can represent the region bounded by the function by rearranging the functions as follows:

1 mile= 1.609 km

Then,

2*1.609=3.218 km

He walked 3.218 kilometers

In this case, we'll have to carry out several steps to find the solution.

Step 01:

x - 7y = 20

slope-intercept form = ?

Step 02:

Slope-intercept form of the line

y = mx + b

x - 7y = 20

x = 20 + 7y

x - 20 = 7y

7y = x - 20

The answer is:

y = x/7 - 20/7

The function 2x + 3x^2 represents the result of adding the two provided functions, f(x) and g(x).

An operation known as "function composition" takes two functions, f and g, and produces a new function, h, that is equal to both g and f and has the property that h(x) = g.

Given the f(x) = 2x and g(x) = 3x^2 functions

The sum of the two functions must be calculated as illustrated;

f(x) + g = (f+g)(x)

Put the provided functions in place of (f+g)(x) to have:

(f+g)(x) = 2x + 3x^2

Standard version of the expression is (f+g)(x) = 2x + 3x^2

Consequently, the sum of the functions f(x) and g(x) is2x + 3x^2

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Explanation

Given the expression

The remainder when it is divided by x+9 can be seen below;

Answer: -3490

The price of gas = $2.85 per gallon

It was $1.36 cheaper than a year before.

So, the price before = 2.85 + 1.36 = $4.21

So, the percent of decrease = 1.36/4.21 = 0.323 = 32.3%

The value of the expression 7+[9÷(9x1 to the second power)] is 64/9

A fraction can be described as the part of a whole set or element.

There are several types of fractions, which includes;

Some examples of these fractions are given as;

Simple fractions: 1/5, 1/6

Mixed fractions: 2 1/8, 3 1/4

Proper fractions: 2/3, 4/5

Improper fractions; 4/1, 6/3

Given the expression;

7+[9÷(9x1 to the second power)]

This is expressed as;

7 + ( 9 ÷ (9)^2

Find the square

7 + ( 9 ÷ 81)

find the ratio

7 + 1/9

Find the common multiple

63 + 1 /9

64/9

Hence, the value is 64/9

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The original picture Katie and Jacob want to enlarge is 3 by 4 photographs

This means that the initial length of the photograph is 3 and the intial width of the photographs is 4

If both of them want to enlarge the photograph, then the scaling factor must be the same for both the width and length

Katie enlarge the photo to a 9 x 12

The ratio of the original photograph is 3 to 4

That is, 3 : 4

Katie enlarge the photo to a 9 x 12

Ratio of the enlarged photo by katie is 9 to 12

That is, 9 : 12

Equate the two ratio together

3/4 = 9/12

Introduce cross multiplication

We have,

3 x 12 = 4 x 9

36 = 36

Therefore, the ratio which katie enlarged the photo results to a proportion

For Jacob

Jacob enlarged the photo to 11 x 12

Equating the two ratios

3/4 = 11/12

3 x 12 = 4 x 11

36 = 44

This does not give us a proportion

Therefore, Katie is correct while Jacob is wrong

The trigonometric identity cos(α + β)cos(α - β) = cos²(α) - sin²(β) is verified in this answer.

The identity is defined as follows:

cos(α + β)cos(α - β) = cos²(α) - sin²(β)

The cosine of the sum and the cosine of the subtraction identities are given as follows:

Hence, the multiplication of these measures is given as follows:

cos(α + β)cos(α - β) = (cos(α)cos(β) - sin(α)sin(β))(cos(α)cos(β) + sin(α)sin(β))

Applying the subtraction of perfect squares, it is found that:

(cos(α)cos(β) - sin(α)sin(β))(cos(α)cos(β) + sin(α)sin(β)) = cos²(α)cos²(β) - sin²(α)sin²(β)

Then another identity is applied, as follows:

Then the expression is:

cos²(α)cos²(β) - sin²(α)sin²(β) = cos²(α)(1 - sin²(β)) - (1 - cos²(a))sin²(β)

Applying the distributive property, the simplified expression is:

cos²(α) - sin²(β)

Which proves the identity.

The complete identity is:

cos(α + β)cos(α - β) = cos²(α) - sin²(β)

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Solution:

Given:

Kiran multiplied the left-hand side of the equation by (x-1) and multiplied the right-hand side of the equation by x(x-1).

That was where he made the mistake. He ought to have multiplied both sides with the same quantity (Lowest Common Denominator) so as not to change the actual value of the question.

Multiplying both sides by the same quantity does not change the real magnitude of the question.

The actual solution goes thus,

Solving the quadratic equation;

Therefore, the actual solutions to the expression are;

The quadartic equation is 3x^2+10x+8=3.

Simplify the quadratic equation to obtain the equation in standard form ax^2+bx+c=0.

The coefficent of x^2 is a=3, coefficient of x is b=10 and constant term is c=5.

The quadartic formula for the values of x is,

Substitute the values in the formula to obtain the value of x.

The value of x is,

SOLUTION:

Step 1:

In this question, we have that:

Step 2:

Part A:

We are meant to show that the equation:

can be written in the form

Proof:

Re-arranging, we have that:

Part B:

b) Hence, solve for x in the interval:

Given:

x+2y = 8

x=2, y=0

Substitute x=2 then find value of x as,

2+2y=8

2y=6

y=3

(x,y) = (0,3)

Now, substitute y=0 then find value of y as,

x+2(0)=8

x=8

(x,y) = (8,0)

It is given that P = x+3y

(x,y) = (0,3) then P= 0+3x3

P=9

The maximum valu P=9 and vertiex (0,3)

(x,y) = (8,0) then P=8+0= 8

The mininmum val

⇒It is way more appropriate if I use the product rule. That states that:

⇒f(x)g(x)=f'(x)g(x)+f(x)g'(x)

[tex]t^{4} In(8cos(t))\\=4t^{3}In(8cos(t))+t^{4} \frac{1}{8cos(t)} *(0cos(t)+8*(-sin(t))*1)\\=4t^{3}In(8cos(t))+\frac{t^{4}-8sin(t)}{8cos(t)}[/tex]

Note:

Given F(x)=In(x)

⇒[tex]F'(x)=\frac{1}{x}[/tex]

Goodluck

Answer:

t^3 (4 ln(cos8t) - t tant)

Step-by-step explanation:

Using the Product Rule:

dy/dt = t^4 * d(ln(8cost) / dt + ln(8cost) * d(t^4)/dt

         = t^4 * 1/ (8cost) * (-8sint) + 4t^3 ln(8cost)

         = -8t^4 sint / 8 cost + 4t^3 ln(8cost)    

         = -t^4 tan t + 4t^3 ln(8cost)  

          = t^3 (4 ln(cos8t) - t tant)

we have the second degree polynomial

we must find two numbers a,b such that

We can see that, a=-2 and b=-9 fulfill the above conditions. Therefore, we have

EXPLANATION

Savings account balance = $2,764

Desired amount = $5,000

Let's call x to the amount of money the family needs.

The inequality that could be used to determine the amount of money the family needs is the following:

2,764 + x ≥ 5,000

If triangle ABC can be taken to triangle A'B'C', it means that they are similar triangles. If tow triangles are similar, it means that the ratio of their corresponding sides are equal. Thus, we have

A'B'/AB = B'C'/BC = A'C'/AC

Thus, looking at the options, the true equations are

A) A'C'/B'A' = AC/BA

D) CA/C'A' = CB/C'B'

E) A'B'/AB = C'B'/CB

If we look at these options the ratios are always the same

Part a: The standard equation of circle: (x - r)² + (y - s)² = t².

Part b: Domain = {17, -3} and Range = {-14, 6}.

Part c: Point (9, 1) lies inside the circle.

For the given question,

The right triangle are given with two of ts vertices as (r, s) and (x, y).

The distance between these two points is 't'.

Part a: The standard equation of the circle.

Centre of circle = (r,s) and

Point on the circle = (x, y)

Using Pythagorean Theorem,

(x - r)² + (y - s)² = t²

Thus, the standard equation of the circle is (x - r)² + (y - s)² = t²

Where, t is the radius of the circle.

Part b: Domain and range.

(r, s) = (7, –4) and t = 10,

For x values in the domain  r ± t and y values in the range s ± t, the circle would be defined.

Domain = 7 ± 10 = {17, -3}

Range = -4 ± 10 = {-14, 6}

Part c: Point (9, 1) lies inside or not.

(r, s) = (7, –4) and t = 10

Point (9, 1) = (x, y)

Put the values;

(x - r)² + (y - s)² ≤ t²

(9 - 7)² + (1 + 4)² ≤ 10²

2² + 5² ≤ 10²

4 + 25 ≤ 100

29 ≤ 100

Thus, the points (9, 1) lies inside the circle.

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Let's remember what the variables mean:

F= temperature (in Fahrenheit),

v= wind speed.

A) The formula "works" when the wind speed is between 4 and 45 miles per hour. The question asks for a wind speed of 20 miles per hour. Then, we can apply the formula. Here,

Then,

Approximating, the answer is

B) This question is just about to find F in the provided equation after replacing the given v and WCI. Let's do that:

Then, the actual temperature is