A hypothesis must be testable and falsifiable to be scientifically valid. Being testable and falsifiable means that __________.

Answers

Answer 1

Answer:

Final answer:

A scientifically valid hypothesis must be testable and falsifiable. Testable means that it can be evaluated through observations or experimentation. Falsifiable means that it's possible to design an experiment whose results would prove the hypothesis to be incorrect.

Explanation:

Within the scientific community, a hypothesis is considered to be scientifically valid only if it is testable and falsifiable. When we say a hypothesis is testable, it means that it can be evaluated through observations or experimentation, using the scientific method. An example of this could be the hypothesis 'If I water my plants more, they will grow faster.' This hypothesis is testable because we can carry out an experiment to confirm or refute it.

On the other hand, a hypothesis is said to be falsifiable if it is possible to design an experiment whose outcome could prove the hypothesis to be incorrect. For example, the hypothesis 'All swans are white' is falsifiable because finding just a single swan of a different color would falsify the hypothesis. However, it's important to note that falsifiable doesn't mean the hypothesis is incorrect, rather it means that it's possible to prove it's incorrect through testing.

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Answer 2

Answer:

Final answer:

A hypothesis must be testable and falsifiable in order to be considered scientifically valid. This means that it can be tested through experimentation or observation, and can be proven false if the experimental results contradict it.

Explanation:

A hypothesis must be testable and falsifiable to be scientifically valid. Being testable and falsifiable means that it can be tested through experimentation or observation and can be proven false if the experimental results contradict it. Testability and falsifiability are key requirements in scientific research as they allow for the advancement of knowledge and the development of more accurate explanations of natural phenomena.

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Brian is ordering books online. He has $100 to spend on the books. Each book costs $7. The shipping charge for the entire order is $8. The number of books, b, that Brian can buy is represented by the inequality 7b + 8 < 100. How many books can Brian buy without overspending?13

15

18

20

Answers

You have to plug in the numbers.
So first let's plug in 13. 7*13+8=99
Now 15. 7*15+8=113
Now 18. 7*18+8=134
Lastly 20. 7*20+8=148
The answer is 13.

You have $100 but the shipping is $8 so you subtract that from $100 and get $92, At $7 dollers a book you can get 13 books before going over 7x13=91. So the answer is 13 and you will spend $99 total.

Analyze the function f(x) = - 2 cot 3x. Include: - Domain and range
- Period
- Two Vertical Asymptotes

Answers

Answer and Explanation :

Given : Function $f(x)=-2\cot 3x$

To find :

1) Domain and range

2) Period

3) Two Vertical Asymptotes

Solution :

1) Domain is defined as the set of possible values of x where function is defined.

$f(x)=-2\cot 3x$

$f(x)=-2((\cos 3x)/(\sin 3x))$

For domain, $\sin3x\neq 0$

So, $\sin3x\neq \sin n\pi$

$3x\neq n\pi$

$x\neq (n\pi)/(3)$

The value of x is define as $x\neq n\pi+(-1)^n(\pi)/(3)$

The domain of the function is all real numbers except $x\neq n\pi+(-1)^n(\pi)/(3)$

The range is defined as all the y values for every x.

So, The range of the function is all real numbers.

2) The general form of the cot function is $y=A\cot (Bx-C)+D$

Where, Period is $P=(\pi)/(|B|)$

On comparing, B=3

So, The period of the given function is $P=(\pi)/(|3|)$

3) Vertical asymptote is defined as the line which approaches to infinity but never touches the line.

The vertical asymptote is at $x= n\pi+(-1)^n(\pi)/(3)$ where function is not defined.

The two vertical asymptote is

Put n=0,

$x= (0)\pi+(-1)^(0)(\pi)/(3)$

$x=(\pi)/(3)$

Put n=1,

$x= (1)\pi+(-1)^(1)(\pi)/(3)$

$x=\pi-(\pi)/(3)$

$x=(2\pi)/(3)$

So, The two vertical asymptote are $x=(\pi)/(3),(2\pi)/(3)$

The domain for the function is:
all real numbers except n π/3 where n is an an integer

The range for the function is:
all real numbers

The period is
π/3

Vertical asymptotes
x = n π/3 where n is an integer

What is the inverse of the function f(x) = 2x – 10

Answers

f(x) is y given x
y=2x-10
inverse is switching x and y so
x=2y-10
solve for y
y=(x+10)/2

a 75 inch boars is cut into 2 pieces one piece is 4 times the length of the other find the lengths of the 2 pieces the short piece is _inches long

Answers

Length of the long piece = 4 times the length of the short piece
Length of the short piece = 1 times the length of the short piece.
Total length of both pieces = (4 + 1) = 5 times the length of the short piece.

5 times the length of the short piece = 75 inches

The length of the short piece =75 / 5 = 15 inches

Length of the long piece = 4 times the length of the short piece = 60 inches

Check: 15 + 60 = 75 inches
yay

The shorter piece is 15 inches, and the longer piece is 60 inches.
This would be a system of equations problem. If x is the shorter piece and y is the longer piece, then your two equations would be:
x + y = 75
y = 4x
Since the second equation tells you what y is, you can substitute the y in the first equation with 4x to get the equation x + 4x = 75. x + 4x is 5x, so you'll have 5x = 75. To get x by itself, divide off the 5 on both sides. 75 ÷ 5 = 15, so x = 15. The shorter piece would be 15 inches long.
Now that you know x, go to the second equation and plug it in: y = 4·15. 4·15 is 60, so that makes the longer piece 60 inches long.
Sorry if this was confusing; I'm really bad at giving written directions :/

A group of biologists found a total of 28 loggerhead turtle nests along a beach during a certain season. This was 40% of the total number of turtle nests the group found during that season. What was the total number of turtle nests the group found during that season?70
85
110
143

Answers

First divide 28 by 40 to get the unit rate which is 0.7. Then, since that is 1% mulitiply 0.7 times 100 to get 70 turtles as your answer. hope that helped!

28=.4x
70=x
They found 70

32) Identify the turning point of the function f(x)= x^2-2x+8 by writing its equation in vertex form. Show your work.

Answers

(1,7)

Working;
Start by finding the derivative of the function f(x);
$f^(') (x)$ =2x-2
Turning points occur when the derivative function=0;
Thus
2x-2=0
x=1
when x=1 then
f(1)= $1^(2) -2(1)+8$
=7
Turning point then is (1,7)

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