A glider files 8 miles south from the airport and then 15 miles east. Then it files in a straight line back to the airport. What was the distance of the glider's last leg back to the airport ?

We can rewrite the question as the probability of getting the event E is 23:77. Find the probability of getting the event not E.

The number 23:77 is a ratio and is it equivalent to:

To get the probability of the event not-E, we can proceed as follows:

So the probability for the event not-E is about 53/77 or 0.7013 (or a little more than 70%).

By elimination, it means that we should apply algebraic operations so we find the value of one variable. So first, lets multiply the first equation by 5. We get

Now, lets multiply by 2 the second equation

With this two equations, lets subtract the second equation from the first equation

We get

If we divide y by 19 we get

Now, using this value in the second equation we get

If we subtract 6 on both sides, we get

Finally, we divide by 5 on both sides and we get

The aspect ratio 16:9 indicates the next relation between x and y:

Applying the Pythagorean theorem to the right triangle formed:

Isolating y from the first equation:

Substituting in the second equation:

Replacing in the equation of y:

The approximate dimensions are:

length = 25 in

height = 44.44 in

we know that

f(4) is the value of the function f(x) when the value of x is equal to 4

so

For x=4

Look at the graph

The value of the function f(x) is equal to 3

therefore

Let u make the first box x and the second box y.

If there is a proportional relationship between the number of bananas and their weights, it means that:

We can take the first pair and solve for x as follows:

We can solve for y in the same manner:

Therefore, the boxes are filled as shown below:

Volume of a rectangular prism = base length x width x heigth

Where;

Volume = 600 cm3

base length = 15

width = x

height = 8

Replacing:

600 = (15) (x) (8)

Isolate x

600/ (15)(8) = x

x = 600/ (8)(15)

option C

two lines are perpendicular when the multiplication of their slopes is equal to -1. The slope of y = 3x - 4 is 3. Then the slope of a perpendicular line ​is:

Slope-intercept form:

y = mx + b

where m is the slope and b is the y-intercept. Replacing with point (-3, 5) and m = -1/3, we get:

5 = -1/3(-3) + b

5 = 1+ b

5 - 1 = b

4 = b

Then, the equation is:

y = -1/3x + 4

solution

For this case the tangent line to the circle and the point should be:

The reason is because the tangent line and the point needs to touch the circle just one time

We must divide the 5 pound bag in 6 different containers, therefore:

Each container will hold 0.83 pet food

As given by the question

There are given that the series

Now,

For step 1:

Put n=1

Then LHS =1

And

So,

P(n) is true for n=1.

Now,

Step 2:

Assume that P(n) istrue for n=k

Then,

Adding 2k+1 on both sides

So, we get:

P(n) is true for n=k+1

By the principle of mathematical induction P(n) is true for all natural numbers n.

Hence,

For all n.

Hence proved.

We will investigate how to solve an equation consisting of one variable

We have the following equation at hand:

The basic rule applied in solving equation like above is mathematical operations. We apply basic operations like:

on both sides of the equation accompained by a variable or a number in an attempt to isolate the variable ( k ).

To isolate the variable ( k ) we need all the terms involving the variable ( k ) on one side of the equation.

We will add ( 4k ) on both sides of the equation as follows:

Now to remove the negative sign accompained by ( k ) on the right hand side of the equation. We wil multiply both sides with ( -1 ) as follows:

Hence, the value of ( k ) is:

ANSWER

P(x) = 2700(1.052)^t

P(4) = 3307. (Rounded to nearest student)

EXPLANATION

Given:

1. The current student population to be 2700

2. The growth rate = 5.2% = 0.052

Desired Outcome

1. The exponential growth model

2. Population of the students in 4 years

The Exponential Growth Model

Population in 4 years

Hence, the Exponential Growth Model P(x) = 2700(1.052)^t and the Population of the students in 4 years P(4) = 3307. (Rounded to nearest student)

traveledGiven:

The total number of students is N = 142.

The number of students riding in a car is n(C) = 50.

The total number of buses is b = 4.

The objective is to find the number of students traveling on each bus.

Explanation:

Consider the number of students travelled in each bus as s.

Then, the total number of students traveling in 4 buses will be 4s.

The algebraic expression for the total number of students N can be represented as,

On plugging the given values in equation (1),

On further solving the above equation,

Hence, the number of students traveling on each bus is 23.

The graph of the function is defined for x greater than or equal to -2 and less than 3. So domain of the function is,

The value of the function lies between -2 and 3. The function value is greater than or equal to -2 and less than 3. So range of function is,

Okay, in this case the statement talks about the sum, according with this we need to find the sum of the number blue bikes (b) and 9 red bikes.

So, in this case the correct option is A. b+9 because it says sum

To find the average rate of change over an interval we need to calculate how much the function has changed over that interval by subtracting the final value by the initial one and dividing by the lenght of the interval. With this in mind we have:

The average rate of change for this interval is 1.5

To graph the solution set, first, we know that the border of the shaded area will be delimited by the dashed line:

Now, to know if the shaded area will be on top or below the line, we evaluate the point (0,0):

therefore, the origin is not a point of the solution set.

And x is divisible by 6 . The natural number of x will be

Recall that:

Therefore:

Answer:

Step 1

List all parameters

Step 2

Write the volume of a sphere

Given the equation:

Apply the properties of logarithms:

Simplify:

Answer: D. x = 1.22

Solution

Given

We want to determine if it's a Polynomial

A polynomial is an expression consisting of indeterminates (also called variables) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.

Hence 4 - 8x + x^2 is a Polynomial

First of all, simplify the given fractions

  The functions is Set A and Set B.

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

A relation in a set is said to be a function, if every first element of an ordered pair in a set is  related with a unique element of a second element.

No, two distinct second elements of an ordered pair, has the same first element.

For, example, {(1,2), (1,3), (4,5)}, is not a function, but it is a relation.

In Ordered pair, (x, y)

x=First Element

y= Second Element

→In Set A

First Element              Second Element

1                                           3

-1                                           5

6                                          4

Every First  element of set A has a unique second element. So, it is a function.

→In Set B

First Element              Second Element

2                                          0

4                                          6

-4                                          5

0                                          0

Every First  element of set B has unique second element and no two distinct Second element of set B, has same first element. So, it is a function.

→In Set C

First Element              Second Element

1                                           1

0                                          2

0                                          3

-3                                          5

As, two same first elements of set C has distinct second element. So, it is not a function.

Therefore, Set A and Set B, are functions .

To learn more about function refer to:

https://brainly.com/question/25638609

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The function is a decreasin line so the more time goes the side will decrease so the correct answer is:

The candle started at 9mm and shrinks 5mm every 4 minutes

11 n+ 12

In this expression, to simplify means to reduce it to the simpler expression. Hence:

1) Grouping similar terms

4n + 12 + 7n =

2) Adding them up:

4n+7n+12=

11n +12

Let

x -----> average temperature

y ----> Electricity Bill

we take the points

(99,150) and (69,80)

step 1

Find out the slope

m=(80-150)/(69-99)

m=-70/-30

m=7/3

step 2

Find out the equation of the line in slope-intercept form

y=mx+b

we have

m=7/3

point (69,80)

substitute and solve for b

80=(7/3)(69)+b

b=80-161

b=-81

the equation is

y=(7/3)x-81

using a graphing tool

Remember that the value of y cannot be a negative number

The given fractions are,

The LCD of fractions is the least common multiple of the denominators.

So, the LCD of the above fractions is,

Multiplying the numerator and the denominator of the fraction by a common term does not change the fraction.

So, the first fraction can be expressed in terms of the LCD as,

The second fraction can be expressed in terms of the LCD as,

For a shape to be considered a parallelogram it has to meet the following conditions:

0. The opposite sides must be equal

1. The opposite sides are equal

2. Adjacent sides are supplementary

3. The diagonals bisect each other

4. The opposite sides are parallel

For the quadrilateral to be considered a parallelogram then, the conditions that should be met are:

MN=QP and MQ=NP

MN || QP and MQ || NP

The diagonals MP and NQ bisect each other.

∠M=∠P and ∠N=∠Q

From the given options, the second one and the third one are not enough to determine MNPQ as a parallelogram

The distance on the map is 14 cm

Parameters:

Map scale: 5 cm = 2 km

Given actual distance = 5.6km

Let x be the distance on map, then

x = 5.6 km

2x = 5 * 5.6

2x = 28

x = 28/2

= 14 cm