Eddie and Fran are scuba diving. Eddie is 35 meters
below the surface of the water, and Fran is 8 meters
directly above him.

Answer:

By contradiction it can be proved that:

Average of four real numbers will be greater than or equal to at least one of the four real numbers.

Step-by-step explanation:

Method of contradiction means we assume opposite to the facts to be proved and then we contradict our assumption.

As a result, we prove the fact.

Here, let the four number be:

[tex]p, q, r, s[/tex]

The average will be Sum of all numbers divided by count of numbers.

[tex]\dfrac{p+ q+ r+ s}4[/tex]

Now, let us assume the opposite that the average is less than all the numbers.

i.e.

[tex]\dfrac{p+ q+ r+ s}4 <p[/tex]

[tex]\dfrac{p+ q+ r+ s}4 <q\\\dfrac{p+ q+ r+ s}4 <r\\\dfrac{p+ q+ r+ s}4 <s[/tex]

Now, let us add all of them:

[tex]\dfrac{p+ q+ r+ s}4 +\dfrac{p+ q+ r+ s}4 +\dfrac{p+ q+ r+ s}4 +\dfrac{p+ q+ r+ s}4 < p+q+r+s\\\Rightarrow \dfrac{4(p+q+r+s)}4<p+q+r+s\\\Rightarrow p+q+r+s<p+q+r+s[/tex]

Which can never be possible hence, our assumption is contradicted.

our assumption is wrong.

Therefore, by contradiction it is proved that:

Average of four real numbers will be greater than or equal to at least one of the four real numbers.

An average of four real numbers will be greater than or equal to at least one of the four real numbers.

What is average?

An average is simply defined as the mean of the given set of numbers. The mean is said to be an arithmetic mean. It is the ratio of the sum of the observation to the total number of observations.

Prove the following using proof by contradiction.

The average of four real numbers is greater than or equal to at least one of the numbers.

Method of a contradiction means we assume opposite to the fact to be proved and then we contradict our assumption.

Let the four numbers be a, b, c, and d.

The average will be

[tex]\rm \dfrac{a+b+c+d}{4}[/tex]

Now let us assume the opposite that the average is less than all the numbers.

[tex]\rm \dfrac{a+b+c+d}{4} < a\\\\\rm \dfrac{a+b+c+d}{4} < b\\\\\rm \dfrac{a+b+c+d}{4} < c\\\\\rm \dfrac{a+b+c+d}{4} < d[/tex]

Let us add all of them.

[tex]\rm \rightarrow \dfrac{a+b+c+d}{4} +\dfrac{a+b+c+d}{4} +\dfrac{a+b+c+d}{4}+\dfrac{a+b+c+d}{4} < a+b+c+d\\\\\rightarrow \dfrac{4(a+b+c+d)}{4} < a+b+c+d\\\\\rightarrow a+b+c+d < a+b+c+d[/tex]

That can never be possible hence, our assumption is contradicted.

Our assumption is wrong.

Therefore, by contradiction, it is proved that;

An average of four real numbers will be greater than or equal to at least one of the four real numbers.

More about the average link is given below.

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$915 I’m pretty sure

Answer:

112

Step-by-step explanation:

Answer:

[tex]y=5x-37[/tex]

Step-by-step explanation:

So we want to find the equation of a line with a slope of 5 and passes through (8,3).

To do so, we can use the point-slope form. This point-slope form is:

[tex]y-y_1=m(x-x_1)[/tex]

Let's let (8,3) be x₁ and y₁ and let's let m equal 5. Therefore:

[tex]y-3=5(x-8)[/tex]

Distribute the right:

[tex]y-3=5x-40[/tex]

Add 3 to both sides:

[tex]y=5x-37[/tex]

That would be our equation in slope-intercept form.

And we're done!

Answer:

rational

Step-by-step explanation:

ans

a) Rational

Hope this helps you...

The largest stem is 3, found in the bottom row. This represents 300 thousand or 300,000.

The largest leaf in the bottom row is 7 and that represents

7*(10 thousand) = 70 thousand = 70,000

Adding the stem and leaf values gets us

300,000 + 70,000 = 370,000

Answer:

d.f.(treatment) = 6

d.f.(error) = 35

Step-by-step explanation:

In the question we have

k = 7

r= 6

n= rk= 42

1. The degrees of freedom for the numerator is calculated as under

d.f.(treatment) = k-1= 7-1= 6

Where k gives the number of columns

2. The degrees of freedom for the denominator is calculated as under

d.f.(error) = k (r-1)= n-k= 42-7=35

where k gives the number of columns and r gives the number of rows.

This is for one way ANOVA as asked above.

Answer:

Multiplying a number by -1 means the sign on the number is made opposite. If the number was positive, it becomes negative. If the number was negative, it becomes positive.

edmentum answer!!

Answer:

The answer for both apples and bananas is 21

The answer for only apples or only bananas is 45

Step-by-step explanation:

36 plus 30 minus 45

50-5 is 45

only apples or bananas is 15 + 9

Answer:

She has 28 pennies

Step-by-step explanation:

Janae has 280 dimes in her piggy bank she has 10 times as many pennies .

If she has 280 dimes in piggy bank

And has 10 times as many pennies

Let dimes= x

Let pennies= y

X= 10y

But x= 280

280= 10y

280/10 = y

28 = y

She has 28 pennies

Your question is not complete

Answer:

Step-by-step explanation:

Least to greatest:

2/5, 4/7,  5/8, 2/3, 3/4

Answer:

[tex]i^{54}=-1[/tex]

Step-by-step explanation:

First, recall the 4 basic imaginary exponents:

[tex]i^1=i \text{, }i^2=-1\text{, }i^3=-1\text{ and } i^4=1[/tex]

So, we want to find:

[tex]i^{54}[/tex]

This is the same as:

[tex]=i^{52}\cdot i^2[/tex]

52 is 4 times 13. Thus:

[tex]=(i^4)^{13}\cdot i^2[/tex]

Since we know that i to the fourth is 1:

[tex]=(1)^{13}\cdot i^2[/tex]

Simplify:

[tex]=i^2[/tex]

And this equals:

[tex]=-1[/tex]

So:

[tex]i^{54}=-1[/tex]

Answer: x=4

Step-by-step explanation:

8x-13=19

first, add 13 to both sides.

8x= 32

then, divide both sides by 8 to isolate x.

x= 32/8

x=4

Answer:

rational numbers

Step-by-step explanation:

Answer:

[tex] \boxed{ \bold{ \huge{ \boxed{ \sf k = - 13}}}}[/tex]

Step-by-step explanation:

[tex] \sf{k + ( - \frac{5}{3} ) = - \frac{44}{3} }[/tex]

When there is a ( + ) in front of an expression in Parentheses, there is no need to change the sign.

That means the expression remains the same.

⇒[tex] \sf{k - \frac{5}{3} = - \frac{44}{3} }[/tex]

Move 5/3 to right hand side and change it's sign

⇒[tex] \sf{k = - \frac{44}{3} + \frac{5}{3} }[/tex]

While performing the addition or subtraction of like fractions , you just have to add or subtract the numerator respectively in which the denominator is retained same.

⇒[tex] \sf{k = \frac{ - 44 + 5}{3} }[/tex]

Calculate

⇒[tex] \sf{k = \frac{ - 39}{3} }[/tex]

Divide -39 by 3

⇒[tex] \sf{k = - 13}[/tex]

Hope I helped!

Best regards!!

Answer:

3rd Option: -1

5th Option: 2

7th Option: i√6

8th Option: -i√6

Step-by-step explanation:

Graph the function first to find our real root factors.

When you find your real root factors, factor the equation down with x + 1 and x - 2 and then use Quadratic Formula to find complex roots.

Answer:

-2, 1. i[tex]\sqrt{6}[/tex], and -i[tex]\sqrt{6}[/tex]

Step-by-step explanation:

just took the test

Answer:

53.5 DEGREES

Step-by-step explanation:

90 + 36.5 = 125.6

180 - 126.5 = 53.5 degrees

The measure of the other small angle will be 53.5 degree.

What is mean by Triangle?

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

In a right triangle, One angle measures 36.5 degrees.

Now,

Since, The triangle is a right triangle.

So, One of the angle = 90 degree

And, One angle measures 36.5 degrees.

Let the measure of the other small angle = x degree

Since, The sum of all the interior angles in a triangle = 180 degree

So, We can formulate;

⇒ x + 90 + 36.5 = 180

⇒ x + 126.5 = 180

⇒ x = 180 - 126.5

⇒ x = 53.5 degree.

Thus, The measure of the other small angle will be 53.5 degree.

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Answer:

5

can be done by multiplication multiplicative property

Step-by-step explanation:

2/3 * (3/2 * 5)

1st = 2/3 * 3/2 * 5

2nd = 2 * 3 * 5

             3 * 2

3rd = 3 * 5

            3

therefore

the answer = 5

Answer:

[tex]\Large \boxed{\mathrm{associative \ property \ of \ multiplication}}[/tex]

[tex]\rule[225]{225}{2}[/tex]

Step-by-step explanation:

The associative property of multiplication can be use to make the problem easier to solve.

In associative property of multiplication, when we multiply a bunch of numbers, we can group the numbers in any combination.

[tex]a \times (b \times c) = (a \times b) \times c[/tex]

[tex]\rule[225]{225}{2}[/tex]

Answer:

  >

Step-by-step explanation:

1 - 3 ?? -4

-2 ?? -4

The appropriate symbol for this ?? relation is >.

  1 -3 > -4

Answer:

D.

Step-by-step explanation:

A irrational number can be defined as those numbers which are real but can NOT be expressed in simple fractions. The term 'irrational' means 'a number which can not be expressed in ratio of two integers', 'no ratio.'

When a irrational number is expressed in decimal, the numbers keep on expanding without repeating andd without terminating, which means it keeps on expanding infinitely.

For example, π (pi) is an irrational number. When it is expressed in decimals it keeps on expanding non-repeatedly and unendingly.

Another example of an irrational number is √2.

Thus the correct statement that defines irrational number is option D.

Answer:

D. a number with a nonrepeating and nonterminating decimal expansion​

Step-by-step explanation:

Complete question is;

Multiple-choice questions each have 5 possible answers, one of which is correct. Assume that you guess the answers to 5 such questions.

Use the multiplication rule to find the probability that the first four guesses are wrong and the fifth is correct. That is, find P(WWWWC), where C denotes a correct answer and W denotes a wrong answer.

P(WWWWC) =

Answer:

P(WWWWC) = 0.0819

Step-by-step explanation:

We are told that each question has 5 possible answers and only 1 is correct. Thus, the probability of getting the right answer in any question is =

(number of correct choices)/(total number of choices) = 1/5

Meanwhile,since only 1 of the possible answers is correct, then there will be 4 incorrect answers. Thus, the probability of choosing the wrong answer would be;

(number of incorrect choices)/(total number of choices) = 4/5

Now, we want to find the probability of getting the 1st 4 guesses wrong and the 5th one correct. To do this we will simply multiply the probabilities of each individual event by each other.

Thus;

P(WWWWC) = (4/5) × (4/5) × (4/5) × (4/5) × (1/5) = 256/3125 ≈ 0.0819

P(WWWWC) = 0.0819

learners of Agriculture: 34/58

semplify it

divide by 2

34 > 17

58 > 29

they are prime numbers, so can't be semplify anymore

17/29 will do Agriculture

in percentage we have a proportion:

17 : 29 = x : 100

x = (17 * 100) / 29 = 1700 / 29 ≅ 48,62

Answer:

Rate of depreciation = 27%

Step-by-step explanation:

Given:

Purchase price = $32,650

Rate in 2020 = $23,834.50

Find:

Rate of depreciation

Computation:

Depreciation = Purchase price - Rate in 2020

Depreciation = $32,650 - 23,834.50

Depreciation = $8,815.5

Rate of depreciation = [8,815.5 / 32650] 100

Rate of depreciation = 27%

Answer:

2.69 x [tex]10^{9}[/tex]

Step-by-step explanation:

We are given the heart's speed - 70 bpm

We count the number of minutes in 73 years :

We multiply the heart's bpm with 73 years worth of minutes

38,368,800 x 70 = 2,685,816,000

Write the number in scientific notation = 2.68581 x [tex]10^{9}[/tex] ≈ 2.69 x [tex]10^{9}[/tex]

The number of times a heart will beat in 73 years is required.

The heart will beat [tex]1.6\times 10^{11}\ \text{times}[/tex] in a lifetime.

The number of times heart beats per minute is 70.

Number of years in a lifetime is 73 years

Ignoring leap year a year has 365 days.

So minutes in a leap year is

[tex]365\times 24\times 60\times 60[/tex]

Minutes in a lifetime of 73 years

[tex]73\times 365\times 24\times 60\times 60[/tex]

The product of beats per minute and the minutes in a lifetime will given the required heart beats

[tex]70\times 73\times 365\times 24\times 60\times 60=1.6\times 10^{11}\ \text{beats}[/tex]

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Explanation:

If order mattered, then we'd have 17*16*15 = 4080 different permutations. Notice how I started with 17 and counted down 1 at a a time until I had 3 slots to fill. We count down by 1 because each time we pick someone, we can't pick them again.

So we have 4080 different ways to pick 3 people if order mattered. But again order doesn't matter. All that counts is the group itself rather than the individual or how they rank. There are 3*2*1 = 6 ways to order any group of three people, which means there are 4080/6 = 680 different combinations possible.

An alternative is to use the nCr formula with n = 17 and r = 3. That formula is

[tex]_n C _r = \frac{n!}{r!*(n-r)!}[/tex]

where the exclamation marks indicate factorials

The number of different ways that are there to select 3 players is 680.

Since there is A team of 17 softball players need to choose three players to refill the water cooler.

So here we can say there are [tex]17\times 16\times 15 = 4080[/tex]

And, since we have to select 3 people so the no of ways should be [tex]3\times 2\times 1 = 6\ ways[/tex]

So, here the number of different ways should be

[tex]= 4080\div 6[/tex]

= 680

Therefore, The number of different ways that are there to select 3 players is 680.

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Answer:

.18n+2400-.06n=6000

.12n=3600

n=3600/.12=$30000 at 18%, $10000 at 6%

Step-by-step explanation:

Answer:

Can you show the diagram please?

Answer:

y = - 2x + 2

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 1, 4) and (x₂, y₂ ) = (2, - 2)

m = [tex]\frac{-2-4}{2+1}[/tex] = [tex]\frac{-6}{3}[/tex] = - 2 , thus

y = - 2x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (2, - 2 ), then

- 2 = - 4 + c ⇒ c = - 2 + 4 = 2

y = - 2x + 2 ← equation of line