How do you do mathematical inductions?!

Answers

Answer 1

Answer:

THE NATURAL NUMBERS are the counting numbers: 1, 2, 3, 4, etc.Mathematical induction is a technique for proving a statement -- a theorem, or a formula -- that is asserted about every natural number.

By "every", or "all," natural numbers, we mean any one that we might possibly name.

Hope this helps.

Related Questions

There is 12 inches in 1 foot and there is 5,280 feet in one mile. Elena ran 3-1/4 miles. How many feet is that?
What is the approximate value of y − x? (a.) 4.9° (b.) 6.2° (c.) 11.1° (d.)17.2° Its not A
Please help me thank u
Peaches are being sold for $2 per pound. If x represents the number of pounds of peaches bought and y represents the total cost of the peaches, which best describes the values of x and y?
Using standard form, writean equation to represent aline passing through (-6.10)with a slope of -1.

The Museum of Science in Boston has an exhibit in which metal balls drop down a chute, bounce around, and wind up in one of 21 bins. After 1000 balls have dropped, the heights within the bins clearly follow a bell-shaped curve. If the standard deviation is 3 bins, approximately how many balls are in bins 1 through 7?

Answers

This is example of Normal distribution. The central bin is: (21+1)/2=11
If the standard deviation is 3, we have 11-3=8 For bins:1-7 (graph of Normal distribution, or bell-shaped curve) we have 15.87% of all of the balls.
0.1587*1000=158.7.
Answer: We have approximately 159 balls in bins 1 through 7.

Write the equation of the line that passes through the given points. (0,-5) and (8,0)

Answers

Answer:

$y=(5)/(8)x-5$

Step-by-step explanation:

You're given two points, using that you can use the slope-finding formula:

$slope=((y^(2) - y^(1)) )/((x^(2) - x^(1)))$

After that, match up the y-coordinates with each other and the same goes for the x-coordinates. It should look something like this:

$slope = ((0-(-5)))/((8-0)) \n\n=(5)/(8)$

5/8 is your slope. Using the general slope formula y=mx + b, you know that m is the slope and b is the y-intercept. So now you know your slope, plug it into the formula, along with one of the given points. In this case, I will be using (8, 0) because it is easier to solve.

$m = (5)/(8)\n \ny = ((5)/(8) )x+b\n(8, 0)\n(0) = (5)/(8)(8) + b\n 0 = 5 + b\n\n-5 =b\n \ny=(5)/(8)x-5$

You can see I replaced the x and y with the given values accordingly. Then you simplify by subtracting the five on both sides and your y-intercept is -5. Then combine your slope and y-intercept to get your answer!

Hope that helped!

-Bob Ross

In order to maximize the chances that experimental groups represent the population of interest, researchers should conduct ________ and ________. blind sampling; random group assignment blind group assignment; random sampling random sampling; random group assignment blind group assignment; blind sampling

Answers

In order to maximize the chances that experimental groups represent the population of interest, researchers should conduct random sampling and random group assignment

Explanation:

The terms Random sampling and Random group assignment are greatly different in process of the sample selection. The study related to the determination of how sample participants can be drawn from the population refers to the process of Random sampling. The sample participants are subjected to a treatment by the usage of a random procedure comprises the Random group assignment.

When a researcher wants validate externally then random selection can be used. When a researcher wants to determine the effects of treatment within that group which is known as determination of internal validity then he can opt for Random group assignment.

Answer:

In order to maximize the chances that experimental groups represent the population of interest, researchers should conduct random sampling/random group assignment.

Explanation:

Random selection is a representation of the sample of people for your research from a community. Random assignment is the assigning of the sample that describes various groups or operations in the study.

Reasons:

Random sampling enables us to get a sample representative of the community.
Random assignment enables us to make positive that the only distinction among the various treatment combinations is what needs to study.

Random assignment is crucial for sound empirical design. With adequately large representations, random assignment performs it unlikely that there are methodical variations among the groups.

Thus we can say in order to maximize the chances that experimental groups represent the population of interest, researchers should conduct random sampling/random group assignment.

To learn more about random sampling/random group assignment, refer:

brainly.com/question/9423006

What is the first term in the pattern with formula 20 · 5n – 1?A.0

B.20

C.25

D.100

Answers

What is the first term in the pattern with formula 20 · 5n – 1?

The first term in the pattern is B.20.

In a sequence, the format would be:
first term * common difference(number of term - 1)

The hypotenuse AB of a right triangle ABC is 5 ft, and one leg, AC, is decreasing at the rate of 2 ft/sec. The rate, in square feet per second, at which the area is changing when AC = 3 is?

Answers

Answer: $-(7)/(4) \quad \text{ft}^(2)/\sec$

Step-by-step explanation:

Since ABC is a right triangle, at any moment it holds that

$5^2=(AC)^2+(BC)^2$

Moreover, the area A of the triangle is given by

$A= (1)/(2)(AC)(BC)$

and we know that the rate of change of the length (AC) is

constant decreasing 2, which may be written using the Leibniz

notation as

$(d(AC))/(dt)=-2$ .

Using the chain rule and the product rule for derivation, the two

first equations tell us

that

$0 = 2 (d(AC))/(dt)(AC) + 2 (d(BC))/(dt)(BC)$

and

$(dA)/(dt) = (1)/(2) \left( (d(AC))/(dt) \cdot (BC) + (d(BC))/(dt) \cdot (AC)\right)$

Moreover, using the first of the last two equations we get

$(AC)(d(AC))/(dt) = -(BC)(d(BC))/(dt) \Rightarrow\n\n\n(AC)(-2) = -(BC) (d(BC))/(dt) \quad \Rightarrow \quad (d(BC))/(dt)=2 ((AC))/((BC))$

Now, when (AC)=3, we have that

$25=(AC)^2 + (BC)^2 \quad \Rightarrow 25 = 9 + (BC)^2\n \n\Rightarrow \quad 16=(BC)^2 \quad \Rightarrow (BC)=4$

and

$(d(BC))/(dt) = 2 ((AC))/((BC))=2 (3)/(4)=(3)/(2)$ .

Hence, at this moment the rate of change of the area of the triangle is

$(dA)/(dt) = (1)/(2) \left( (d(AC))/(dt) \cdot (BC) + (d(BC))/(dt) \cdot(AC) \right)=(1)/(2)\left( -2 \cdot 4 + (3)/(2)\cdot 3\right ) = -(7)/(4)$

okay
we have the rate of change of AC = d(AC)/dt = -2
the rate of change od BC = d(BC)/dt
area = (1/2) *AC) (BC)
taking differential on both sides we ge
d(A)/dt = 1/2){ (BC) d(AC)/dt + (AC) d(BC)/dt)}....(1)
again
when AC= 3
applying pythagorous thm
we get
(5)^2 =(3)^2 +(BC)^2
hence we get BC = 4
now we need to find d(BC)/dt
we have
(5)^2 = (AC)^2 +(BC)^2
taking differenial
0=2(AC) d(AC/dt) +2BC d(BC)/dt
that is
d(BC)/dt = -(3) *(-2)/4 ..(at AC =3)
hence
d(BC)/dt = 3/2
substituting these values in equation (1)
d(A)/dt = (1/2) {4 * -2 + 3 *3/2}

which gives
d(A)/dt = -7/4

The rate, in square feet per second, at which the area is changing when AC = 3 is -7/4 ft/sec.

I hope my answer has come to your help. Thank you for posting your question here in Brainly.

Help me plzzzzzzzzzzz

Answers

Simple use the cuboid volume formula for each of them

You should use the Cuboid Volume Formula for each of them.

Hope this helps.

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