Based on your understanding of the ideas of external consistency and fruitfulness, which of the following statements best describes the relevance of these ideas to the acceptance of hypotheses?a. A fruitful hypothesis is considered stronger because fruitful hypotheses are always externally consistent with previously held theories. b. A fruitful hypothesis is considered stronger because fruitful hypotheses promote scientific progress by revealing new avenues of research and analysis.c. An adequate theory is always a fruitful theory. d. All internally coherent theories are fruitful.
Answers
Answer:
b
Step-by-step explanation:
externally consistent ideas are the ideas that are consistent with other well-confirmed hypothesis.
Fruitfulness of a hypothesis can be measured from the fact it it suggests something other than what it was originally suppose to explain.
Related Questions
PLSSS HELP!!
Given that sin(a)=3/6 and cos(b) = -4/5 find the exact values of sin(a+b) and cos(a-b)
Answers
On expanding the given trigonometric expressions, we can write -
sin {(3/6) + (-4/5)} = -0.2cos ((3/6) - (-4/5)) = 0.26Expand -1. Sin (a + b) 2. Cos (a - b)We can write -
Sin (A + B) = sinA cosB + cosA sinB
Cos (A - B) = cosA cosB - sinA sinB.
Given is that -
sin(A) = 3/6
cos (A) = - 4/5
sin {(3/6) + (-4/5)} = sin(3/6) cos(-4/5) + cos(3/6) sin(-4/5) = - 0.2
sin {(3/6) + (-4/5)} = -0.2
cos ((3/6) - (-4/5)) = cos(3/6)cos(-4/5) - sin(3/6)sin(-4/5) = 0.26
cos ((3/6) - (-4/5)) = 0.26
Therefore, on expanding the given trigonometric expressions, we can write -
sin {(3/6) + (-4/5)} = -0.2cos ((3/6) - (-4/5)) = 0.26To solve more questions on trigonometric expressions, visit the link below -
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Maximus is playing a game. When he rolls the dice he wins if he gets an even number and loses if he gets an odd number. Which of the following statements is FALSE?
a. The count of rolling an odd number from a sample proportion size of 100 can be approximated with a normal distribution
b. Rolling an even number is considered a success
c. The count of rolling an even number can be approximated with a normal distribution
d. The count of rolling an odd number can be approximated with a normal distribution
Answers
Answer:
a. The count of rolling an odd number from a sample proportion size of 100 can be approximated with a normal distribution.
Step-by-step explanation:
Whenever we roll a fair dice, the possible outcomes are { 1, 2, 3, 4, 5, 6}. In this three numbers are even numbers, i.e. {2, 4, 6}.
The probability of getting an even number is \($p (\text{even}) =\frac{3}{6} = \frac{1}{2}$\)
Since each of the rolls is independent and each probability of getting even remains the same.
Using the central limit theorem, the sampling distribution of a large sample, usually more than 30 can be approximated by the normal distribution. A single roll of an even or odd number cannot be approximated by a normal distribution, it follows the Binomial distribution.
If number of rolls are large, then a normal approximation can be used.
Answer:
The count of rolling an odd number from a sample proportion size of 100 can be approximated with a normal distribution.
Step-by-step explanation:
A machine shop has 100 drill presses and other machines in constant use. The probability
that a machine will become inoperative during a given day is 0.002. During some days, no
machines are inoperative, but on other days, one, two, three, or more are broken down.
What is the probability that fewer than two machines will be inoperative during a
particular day?
Answers
Answer:
Math mode activated
Step-by-step explanation:
The number of machines that become inoperative during a given day follows a binomial distribution with parameters n = 100 (the number of machines) and p = 0.002 (the probability that a machine will become inoperative).
The probability that fewer than two machines will be inoperative during a particular day is the sum of the probabilities that zero or one machine will be inoperative. This can be calculated using the binomial probability mass function as follows:
P(X < 2) = P(X = 0) + P(X = 1)
= (100 choose 0) * (0.002)^0 * (1 - 0.002)^100 + (100 choose 1) * (0.002)^1 * (1 - 0.002)^99
= 1 * 1 * 0.817 + 100 * 0.002 * 0.818
= 0.817 + 0.164
= 0.981
Therefore, the probability that fewer than two machines will be inoperative during a particular day is approximately 0.981.
Which set of ordered pairs represents a function?
{(2, –2), (1, 5), (-2, 2), (1, –3), (8, –1)}
{(-3, –1), (-7, 1), (–6, –1), (-8, 1), (2, –1)}
{(1, 8), (5, 2), (2, –5), (1, –3), (–2, 9)}
{(–3, 1), (6, 3), (4, 2), (6, –3), (1, –1)}
Answers
Answer:
A
Step-by-step explanation:
A function is a relation for which each value from the set the first components of the ordered pairs is associated with exactly one value from the set of second components of the ordered pair.
Given l ∥ m ∥ n, find the value of x.
Answers
Check the picture below.
James is following this recipe to make flapjacks.
James uses 330 g of sugar
How many flapjacks is James making?
Recipe: Makes 15 flapjacks
110 g margarine
150 ml syrup
220 g oats
110 g sugar
60 g sultanas
Answers
Answer:
A student studies the graph shown below and determines that the reflection of point A over the x-axis will result in a point at (6, 3). State whether or not the student is correct, and explain how the correct answer can be found or confirmed.
Step-by-step explanation:
Mr. Nelson is checking some of the school's sport balls to make sure they are in good shape and properly inflated. Use the table of recommended air pressures to define the ranges for properly inflated balls. Ball Average recommended psi (pounds per square inch) Tolerance Soccer ball 12.05 ±3.55 Basketball 8.00 ±0.5 Volleyball 4.44 ±0.18 Part I: Write an absolute value inequality for the recommended air pressure range for each type of ball. Use the variable x for the ball's actual air pressure. (3 points)
Answers
Answer:
Step-by-step explanation:
Hello!
Be X: air pressures of properly inflated sports balls.
Average recommended psi Tolerance(pounds per square inch)
Soccer ball 12.05 ±3.55
Basketball 8.00 ±0.5
Volleyball 4.44 ±0.18
Each recommendation is expressed like the "average air pressure" ± "standard deviation of the recommended air pressure" so if you express it in inequality it will be:
X[bar]-S ≤ X ≤ X[bar]+S
So for each ball type, you can write it as:
Soccer ball
12.05-3.55 ≤ X ≤ 12.05+3.55
8.5 ≤ X ≤ 15.6
Basketball
8.00-0.5 ≤ X ≤ 8.00+0.5
7.5 ≤ X ≤ 8.5
Volleyball
4.44-0.18 ≤ X ≤ 4.44+0.18
4.26 ≤ X ≤ 4.62
I hope this helps!
Answer:
Soccer ball: 8.5 <= lxl <= 15.6
Basketball: 7.5 <= lxl <= 8.5
Volleyball: 4.26 <= lxl <= 4.62
Step-by-step explanation:
hope this helps
Z^4= -625 find the solution
Answers
Answer:
z = 5i
Step-by-step explanation:
√-1 = i
Step 1: Write equation
z⁴ = -625
Step 2: 4th root both sides
z = \(\sqrt[4]{-625}\)
Step 3: Factor out negative
z = \(\sqrt[4]{625}(\sqrt[4]{-1} )\)
Step 4: Simplify
z = 5i
Past experience indicates that the standard deviation of the time it takes for a dentist to perform dental scaling for patients is 4 minutes. A researcher wishes to estimate the mean time to perform dental scaling with 95 percent confidence and a margin of error of ± 0.75 minutes. Given this, what must the sample size be? Round up your answer to the next whole number.
Answers
Answer:
n = 110
Step-by-step explanation:
Margin of Error :
Zcritical * s/ sqrt(n)
s = standard deviation = 4
Margin of Error = ±0.75
Zcritical at 95% level of confidence = 1.96
Margin of Error = Zcritical * s/ sqrt(n)
0.75 = 1.96 * 4 / sqrt(n)
0.75 = 7.84 / sqrt(n)
Take the square of both sides
0.5625 = 61.4656 / n
0.5625 * n = 61.4656
0.5625 = 61.4656
n = 61.4656 / 0.5625
n = 109.27217
About 110 samples
what are the similarities and differences in linear and exponential in intercepts?
what are the similarities and differences in linear and exponential in domain and range?
what are the similarities and differences in linear and exponential in asymptotes?
what are the similarities and differences in linear and exponential in misc.?
Answers
Answer:
What is a linear function? A linear function is a function whose graph is a straight line. The rate of change of a linear function is constant. The function shown in the graph below, y = x + 2, is an example of a linear function.
Graph of linear function
Graph of linear function
A linear function has a constant rate of change. The rate of change is the slope of the linear function. In the linear function shown above, the rate of change is 1. For every increase of one in the independent variable, x, there is a corresponding increase of one in the dependent variable, y. This gives a slope of 1/1 = 1.
A linear function is typically given in the form y = mx + b, where m is equal to the slope, or constant rate of change.
Examples of linear functions include:
If a person drives at a constant speed, the relationship between the time spent driving (independent variable) and the distance traveled (dependent variable) will remain constant.
Assuming no change in price, the relationship between the number of pounds of bananas a person buys (independent variable) and the total cost of the bananas (dependent variable) will remain constant.
If a person earns an hourly wage at their job, the relationship between the time spent working (independent variable) and the amount earned (dependent variable) will remain constant.
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Exponential Functions
What is an exponential function? An exponential function is a function that involves exponents and whose graph is a smooth curve. The rate of change in an exponential function is not constant. The functions shown in the graph below, y = 0.5x and y = 2x, are examples of exponential functions.
Graphs of exponential functions
Graphs of exponential functions
An exponential function does not have a constant rate of change. The rate of change in an exponential function is the value of the independent variable, x. As the value of x increases or decreases, the rate of change increases or decreases as well. Rather than a constant change, as in the linear function, there is a percent change.
An exponential function is typically given in the form y = (1 + r)x, where r represents the percent change.
Examples of exponential functions include:
Step-by-step explanation:
Please help I’m going to fail
Answers
Answer:
d
Step-by-step explanation:
how to find the area
Answers
Step-by-step explanation:
multiple height by width
Answer:
Area of a square: side × side
Area of a circle: π\(r^{2}\)
Area of a triangle: \(\frac{1}{2}bh\) (1/2 × base × height)
read and answer the following:
Answers
Answer:
here ,
origin means (0,0)
so ,
h and k are 0 and 0
and diameter ( d) is 4
r = d/2
using formula
(x-h)^2 +( y-k)^2 = r^2
(x-0)^2 +( y-0)^2= 2^2
x^2+y^2= 4 is the equation.
What is the x- coordinate of the ordered pair that satisfies this system of linear equations?
Answers
PLZ HELP ME I NEED HELP PLZZZ
There are 6 red marbles, 9 blue marbles, and 10 green marbles in a bag.
What is the theoretical probability of randomly drawing either a blue marble or a green marble?
36%
76%
19%
40%
Answers
Answer:
76%
Step-by-step explanation:
Total Outcomes (9 blue + 10 green)/Total options (9+10+6)
19/25
=76%
If you have a quadratic equation in standard form and it has values of a=4, b = -8 and c = -60, what would the equation look like if you factored it out completely
Answers
The quadratic equation so formed will be \(x^{2}\) - 2x - 15 = 0.
What is a quadratic equation?
Any algebraic equation that can be expressed in standard form as where x represents an unknown value and where a, b, and c represent known values, where a 0 is a quadratic equation.
We know that the standard form of a quadratic equation is represented as: a\(x^{2}\) + bx + c = 0.
Here, we are given a = 4, b = -8 and c = -60.
On substituting these values, we get
⇒ a\(x^{2}\) + bx + c = 0
⇒ 4\(x^{2}\) - 8x - 60 = 0
On dividing both sides by 4, we get
⇒ \(x^{2}\) - 2x - 15 = 0
Hence, the quadratic equation so formed will be \(x^{2}\) - 2x - 15 = 0.
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find the missing angle
Answers
Answer:
? = 77°
Step-by-step explanation:
the 3 angles in a triangle sum to 180° , that is
? + 35° + 68° = 180°
? + 103° = 180° ( subtract 103° from both sides )
? = 77°
Answer:77
Step-by-step explanation:
180-103=77
Hexagon DEFGHI is translated on the coordinate plane below to create hexagon D′E′F′G′H′I′: Hexagon DEFGHI and Hexagon D prime E prime F prime G prime H prime I prime on the coordinate plane with ordered pairs at D 2, 5, at E 5, 5, at F 6, 3, at G 5, 1, at H 2, 1, at I 1, 3, at D prime negative 6, negative 2, at E prime negative 3, negative 2, at F prime negative 2, negative 4, at G prime negative 3, negative 6, at H prime negative 6, negative 6, at I prime negative 7, negative 4
Answers
Answer: To find the image of a figure under a translation, you need to apply the same translation to every point in the figure.
In this case, the image of hexagon DEFGHI is hexagon D′E′F′G′H′I′. To find the image of each point, you can apply the translation that maps point D to point D′.
For example, to find the image of point E under the translation, you can apply the same translation that maps point D to point D′:
Point D is located at (2, 5).
Point D′ is located at (-6, -2).
The translation that maps point D to point D′ is a translation 6 units to the left and 2 units down.
To find the image of point E under this translation, you can apply the same translation to point E:
Point E is located at (5, 5).
The image of point E is located at (5 - 6, 5 - 2) = (-1, 3).
You can follow the same process to find the images of the other points under the translation.
Alternatively, you can use the coordinates of point D and point D′ to find the translation vector that describes the translation. The translation vector is a displacement that describes the change in position of a point under the translation.
In this case, the translation vector is given by the displacement from point D to point D′:
Point D is located at (2, 5).
Point D′ is located at (-6, -2).
The translation vector is given by the displacement (-6 - 2, -2 - 5) = (-8, -7).
To find the image of any point under the translation, you can add the translation vector to the coordinates of the point. For example, to find the image of point E under the translation, you can add the translation vector to the coordinates of point E:
Point E is located at (5, 5).
The translation vector is (-8, -7).
The image of point E is located at (5 - 8, 5 - 7) = (-3, -2).
You can follow the same process to find the images of the other points under the translation.
Step-by-step explanation:
Is 13/ 4 the same as 3 1/4 ? Explain your answer in complete sentences.
Answers
Answer:
no it is not the same.
Step-by-step explanation:
it is not the same because 13/4 is smaller than 3/14. 3 1/4 includes a whole number, and 13/4 doesn't.
Which of the following pairs show(s) two congruent triangles?
O B only
OB and C only
O A, B, and C
O A and C only
Answers
Answer:
B only
Step-by-step explanation:
Triangles A and C are similar, but not congruent to each other. Similar triangles have proportional sides and congruent angles, while congruent triangles have congruent sides and congruent angles.
Therefore, only B is correct
The question is asking for pairs of congruent triangles but lacks key information needed to accurately answer this, such as lengths or angles. Congruent triangles are identified in geometry based on either side-lengths or angles.
Explanation:The question is about congruent triangles, which in mathematics means triangles that have the same size and shape. But to accurately answer which pairs show two congruent triangles, we need more information. The options provided include 'A', 'B', and 'C' but without knowing more about these elements (for example their lengths or angles), it is impossible to determine which are congruent. Congruent triangles are identified in geometry based on either side lengths (SSS: Side-Side-Side, SAS: Side-Angle-Side, ASA: Angle-Side-Angle) or angles (AAS: Angle-Angle-Side, HL: Hypotenuse-Leg for right triangles). Without this vital information, we cannot definitively answer the question. Be sure to verify all the properties required to prove two triangles congruent.
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(a) The equation of a straight line, 4, is given as y=-²x = ³
(i) State the gradient of the line, l₁.
(ii)The point A (b, 4) lies on the line l₁. Determine the value of b.
(iii) A line, 12, passing through the point (0,-5), is perpendicular to l₁. Find the equation of the straight line l2.
Answers
(ii) Substituting the coordinates of point A (b, 4) into the equation of the line l₁, 4 = -2b + 3. Solving for b, we have b = -1/2.
(iii) Since the line 12 is perpendicular to l₁, its gradient is the negative reciprocal of the gradient of l₁. Thus, the gradient of the line 12 is 1/2. Using the point-slope form of the equation of a straight line, the equation of the line 12 is y + 5 = 1/2(x - 0) or y = 1/2x - 5.
Jacob's lock combination is a 3 digit number. If the digits cannot repeat, the product of the digits is 84, and the digits are increasing from left to right, how many combinations can Jacob have?
Answers
There are a total of 5 + 4 + 2 + 2 + 1 = 14 possible combinations for Jacob's lock.
The first digit of Jacob's lock combination can be any of the factors of 84: 1, 2, 3, 4, 6, 7, or 12.
If the first digit is 1, then the second digit can be any of the factors of 84/1 that are greater than 1 and less than 10 (to avoid repeating digits): 2, 3, 4, 6, or 7. There are 5 choices for the second digit.
If the first digit is 2, then the second digit can be any of the factors of 84/2 that are greater than 2 and less than 10: 3, 4, 6, or 7. There are 4 choices for the second digit.
If the first digit is 3, then the second digit can be any of the factors of 84/3 that are greater than 3 and less than 10: 4 or 6. There are 2 choices for the second digit.
If the first digit is 4, then the second digit can be any of the factors of 84/4 that are greater than 4 and less than 10: 6 or 7. There are 2 choices for the second digit.
If the first digit is 6, then the second digit can only be 7. There is 1 choice for the second digit.
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Which number line represents the solution to 2.5 – 1.2x < 6.5 – 3.2x? A number line from negative 5 to 5 in increments of 1. An open circle is at 4 and a bold line starts at 4 and is pointing to the left. A number line from negative 5 to 5 in increments of 1. An open circle is at 4 and a bold line starts at 4 and is pointing to the right. A number line from negative 5 to 5 in increments of 1. An open circle is at 2 and a bold line starts at 4 and is pointing to the left. A number line from negative 5 to 5 in increments of 1. An open circle is at 2 and a bold line starts at 4 and is pointing to the right.
Answers
Answer:
Graph C
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
I did the asignment and got it right
What is the area of this figure? Please help
Answers
Answer:
369.5 ft²
Step-by-step explanation:
Area of figure :
Area (rectangle 1) + Area (rectangle 2) + Area (triangle 1) + Area (triangle 2)
5 x 4 + 13 x 8 + 1/2 x 23 x 13 + 1/2 x 24 x 820 + 104 + 149.5 + 96124 + 96 + 149.5220 + 149.5369.5 ft²
Answer:
369.5 ft²
Step-by-step explanation:
Separate the figure into 2 rectangles and 2 triangles.
(see attached image)
Area 1
Area of a rectangle = width × length
= 4 × 5
= 20 ft²
Area 2
Area of a rectangle = width × length
= 8 × (4 + 4 + 5)
= 8 × 13
= 104 ft²
Area 3
Area of a triangle = 1/2 × base × height
= 1/2 × (6 + 4 + 5 + 4 - 6) × 23
= 1/2 × 13 × 23
= 149.5 ft²
Area 4
Area of a triangle = 1/2 × base × height
= 1/2 × 8 × (21 + 8 - 5)
= 1/2 × 8 × 24
= 96 ft²
Total Area
Area 1 + Area 2 + Area 3 + Area 2 = 20 + 104 + 149.5 + 96
= 369.5 ft²
Circle a has area 500 in the diameter of circle b is three times the diameter of circle a estimate the area of circle b
Answers
Answer: D=2r
Step-by-step explanation:
sorry if im wrong!
Answer:
D=2r i hope i aint wrong
Step-by-step explanation:
Hi there!
Question: Find area of shaded area (chapter: class 9 heron's formula)
Answers
in the given diagram, by using the Heron's formula, the area of the shaded area is 1074.18 m²
Calculating the area of a triangle by using the Heron's formulaFrom the question, we are to find the area of the shaded area in the given diagram
Area of the shaded area = Area of triangle ABC - Area of triangle OBC
From Heron's formula, we know that
Area of triangle = √[s(s - a)(s - b)(s - c)]
Where s is half the perimeter of the triangle
That is,
s = (a + b + c)/2.
Using Heron's formula,
Area of triangle ABC = 1320.11 m²
Area of triangle OBC = 245.93 m²
Thus,
Area of the shaded area = 1320.11 m² - 245.93 m²
Area of the shaded area = 1074.18 m²
Hence, the area of the shaded area is 1074.18 m²
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what is 5(-2x-3) written in distributive property
Answers
Expand the bracket
5 (2x - 3) = 10x - 15
The midpoint of AB is M(-4,2). If the coordinates of A are (-7,3), what are the
coordinates of B?
Answers
The midpoint of AB is M(-4,2). If the coordinates of A are (-7,3), and the coordinates of B is (-1, 1).
To find the coordinates of point B, we can use the midpoint formula, which states that the coordinates of the midpoint between two points (A and B) can be found by averaging the corresponding coordinates.
Let's denote the coordinates of point A as (x1, y1) and the coordinates of point B as (x2, y2). The midpoint M is given as (-4, 2).
Using the midpoint formula, we can set up the following equations:
(x1 + x2) / 2 = -4
(y1 + y2) / 2 = 2
Substituting the coordinates of point A (-7, 3), we have:
(-7 + x2) / 2 = -4
(3 + y2) / 2 = 2
Simplifying the equations:
-7 + x2 = -8
3 + y2 = 4
Solving for x2 and y2:
x2 = -8 + 7 = -1
y2 = 4 - 3 = 1
Therefore, the coordinates of point B are (-1, 1).
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of 30 students, 1/3 play sports. of those who play sports,2/5 play soccer. How many students play soccer?
Answers
Answer: 4
Step-by-step explanation:
1 third of 30 is 10 and 2/5s of 10 is 4
How many solutions does this system have? no solutions one unique solution O O two solutions O or an infinite number of solutions
Answers
Answer:
no solutions
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 )
equation of blue line is y = x + 2 , in slope- intercept form
with slope m = 1
equation of red line is y = x - 3 , in slope- intercept form
with slope m = 1
• Parallel lines have equal slopes
then the blue and red lines are parallel.
the solution to the system is at the point of intersection of the 2 lines
since the lines are parallel then they do not intersect each other.
thus the system shown has no solution.