There are 11 animals on a farm, some of which are goats, while others are ducks. The total number of legs on the ducks and goats is 34.
Explain about the Expression?An expression, often known as an algebraic expression, is any mathematical statement that contains variables, numbers, and an arithmetic operation between them. For instance, the word m in the given equation is separated from the terms 4m and 5 by the arithmetic symbol +, as is the variable m in the expression 4m + 5.
In mathematics, an expression is referred to as an algebraic expression if it contains variables, constants, and algebraic operations (addition, subtraction, etc.). Expressions are made up of multiple terms.
Functions, variables, and numbers make up an expression (such as addition, subtraction, multiplication or division etc.) It is possible to contrast phrases and expressions.
There are 11 animals, and they have a combined total of 34 legs.
Set G and D to the number of goats and ducks, respectively.
Consequently, G = 11 - D when G + D = 11, and vice versa.
therefore 4G + 2D = 34
Using the value as a stand-in for G, we obtain 4(11 - D) + 2D = 34.
By expanding, we have 34 - 44 - 4 + 2D.
The answer is D = 5. Thus, G equals 6.
Proof (5 x 2) plus (6 x 4) equals 34.
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Write the equation of a line that is perpendicular to y=14x - 4 and passes through the point (28, 16)
Write a linear function for the values given in the table below
A function whose equation is of the form y = ax + b, where a and b are constants, a does not equal zero, and x is any real number, and whose graph is a straight line.
Given an equation y = 14x -4 there is an equation that is perpendicular to this given equation.
from the slope-intercept of a linear equation:
The linear function equation is the slope-intercept form. Thus, it is expressed as f(x) = mx + b where m is the slope and b is the y-intercept of the line.
thus the slope of the given equation is 14
The slope of the required equation = 1/14
Since both equations are perpendicular
From the slope intercept of the required line equation of a line:
y = 1/14x + c...(2)
Since, it passes through the point (28, 16)
Thus, 16 = 1/14 *28 + c
c = 16
from equation 2
y = 1/14 x + 14
from the table, two given coordinates of a linear function are (4, 36) and (6, 56)
thus slope of the line = (y₂ - y₁) / (x₂ - x₁)
Slope of the line = 20/2 = 10
Equation of a line:
y = 10x +c
Since, it passes through the point (4, 36)
Thus, 36 = 40 + c
c = -4
Therefore, the required equation from the table is y = 10x - 4
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In the triangle below, the measure of angle G is 45 degrees, and the length of
HI = b cm. What is an expression for the length of HG?
Der b
G
I
H
45
The length of HG can be expressed as HG = b√2.
What is triangle?Triangle is a three-sided polygon with three straight sides that intersect at three vertices. It is one of the most basic shapes in geometry and is found in nature in the form of mountains, icebergs and even the human face. It has a variety of applications in mathematics, engineering, and other fields. Triangles are also used to define angles and even the area of a plane.
This is because the triangle is a right triangle, and the Pythagorean Theorem states that the sum of the squares of the two shorter sides is equal to the square of the hypotenuse. Therefore,
HG2 = b2 + b2 = 2b2,
which reduces to HG = b√2.
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A bag contains 2 snicker bars, 8 trix bars , and 5 crunch bars. A candy is chosen, replaced, then another is chosen, what is the probability of choosing a trix bar then a crunch bar?
The probability of choosing a trix bar then a crunch bar exists 8/45.
What is Probability?Mathematics' field of probability deals with numerical assessments of how likely an event is to occur.
Mathematical explanations of the likelihood that an event will occur or that a statement is true are referred to as probabilities. A number between 0 and 1 represents the likelihood of an event, with 0 generally denoting impossibility and 1 denoting certainty.
The likelihood or chance that a specific event will occur is represented by a probability. Both proportions between 0 and 1 and percentages between 0% and 100% can be used to describe probabilities.
Probability = Number of favorable outcome / Number of total outcome
Given,
Number of snicker bars = 2
Number of trix bars = 8
Number of crunch bars = 5
Total number of candy bars = 2 + 8 + 5 = 15
8 trix, so picking a trix would be 8/15
5 crunch bars, picking a crunch would be 5/15, which reduces to 1/3
Probability of both: 8/15 x 1/3 = 8/45
Therefore, the probability of choosing a trix bar then a crunch bar exists 8/45.
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The probability of choosing a trix bar then a crunch bar exists 8/45.
What is Probability?Probability theory deals with numerical evaluations of the likelihood that an event will occur.
Probabilities are mathematical explanations of the likelihood that an event will occur or that a proposition is true. The likelihood of an event is represented by a number between 0 and 1, with 0 typically signifying impossibility and 1 typically signifying certainty.
A probability represents the likelihood or chance that a particular occurrence will take place. Probabilities can be expressed as ratios between 0 and 1, or as percentages between 0% and 100%.
Probability = Number of favorable outcome / Number of total outcome
Given,
Number of snicker bars = 2
Number of trix bars = 8
Number of crunch bars = 5
Total number of candy bars = 2 + 8 + 5 = 15
8 trix, so picking a trix would be 8/15
5 crunch bars, picking a crunch would be 5/15, which reduces to 1/3
Probability of both: 8/15 x 1/3 = 8/45
Therefore, the probability of choosing a trix bar then a crunch bar exists 8/45.
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Some people advise that in very cold weather, you should keep the gas tank in your car more than half full. Irene’s car had 6.7 gallons in the 15-gallon tank on the coldest day of the year. Irene filled the tank with gas that cost $3.90 per gallon. How much did Irene spend on gas?
The domain and scope of the identity function are the same. Equation for the identity function is f(x) = x, or y = x.
What is function?An statement, rule, or law in mathematics that specifies the connection between an independent variable and a dependent variable (the dependent variable). A relationship between a group of inputs and one output each is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. Y=X2 is an illustration of this. You only receive one output for y if you enter anything for x. The fact that x is the input value leads us to argue that y is a function of x.
identity function are the same.
Equation for the identity function is
f(x) = x, or y = x.
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On solving the provided question, we can say that by unitary method Irene spend on gas = $ 33.82
What is unitary method ?The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.
by unitary method
Irene must pay back the money she used for gas.
Irene filled up her tank with gas for $33.82.
One gallon of gasoline costs $3.80.
There are 6.1 gallons of the petrol Irene purchased in the tank.
amount required = 15 -6.1 = 8.9 gallons
1 gallon = 3.8 dollars
8.9 gallons = $ 33.82
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What are the domain and range of the logarithmic function?
The domain of a logarithm function is (0, ∞). The range of the logarithm function is all real numbers.
What is a function?
A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
The given function is f(x) = log x.
When the value of x is less than or equal to 0, then the value of log x is undefined.
The possible value of x where f(x) exists is the domain of a function.
In the given function the value of x must be greater than zero.
The domain of the function is (0,∞).
log (0.1) = -1
log (0.023) = -1.638
The value of log x can be any real number.
The possible value of the logarithm function is any real number. Thus the range of the function is (-∞, ∞).
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How do you graph 3 4 on a number line?
By drawing a number line and then marking it as 0 and 1, and by dividing the distance in 8 equal parts we can graph 3/4 on the number line, where 3/4 = 6/8, which will be equal to the sixth part from the left end.
A number line is a diagram of a graded straight line used to represent real numbers in introductory mathematics. It is assumed that every point on a number line corresponds to a real number, and that every real number corresponds to a point.
A horizontal line with evenly spaced numerical increments is referred to as a number line. How the number on the line can be answered depends on the numbers present.
For drawing 3/4 on a number line, we will follow the following steps:
We will first draw a line and mark 0 and 1 on it.
In between 0 and 1, we will divide the total distance into 8 equal parts, where one part will represent (1/8)th portion.
As 3/4 can be written as 6/8 which will be equal to 6 parts out of those 8 parts.
Hence. by marking there we can locate 3/4 on the number line.
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The correct question should be like:
How do you plot 3/4 on number line
A spinner is divided into 7 equal regions, numbered 9 through 15. An arrow is spun and lands on one of the numbers. Which of the following best describes the probability of the arrow landing on a number that is greater than 13?
A.
0.143
B.
0.286
C.
0.429
D.
0.571
Therefore , the solution of the given problem of probability comes out to be P =0.286(approx).
Define probability.Probability is the likelihood or potential for something to event. For instance, there is only one way to get a head and a total of two possible outcomes, hence the probability of flipping a coin and getting heads is 1 in 2. (a head or tail). P(heads) must equal 12. Classical: (equally likely results) (equally probable outcomes) S, the sample location (the collection of all distinct outcomes that could occur), Definition of Relative Frequency and Subjective Probability.
Here,
Given : S = {9,10,11,12,13,14,15}
If A is a subset of S, A could be {14,15}.
If a subset A represents the complement of spinning a number greater than 13, its sample space is A = {14,15}.
Thus,
To find the probability that it will land on number greater than 13
P = likelihood of event / total no of events
=> P = 2/7
=> P = 0.2857
=> P =0.286(approx)
Therefore , the solution of the given problem of probability comes out to be P =0.286(approx).
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A statistics content developer at Aplia wanted to know whether study skills are related to memory quality. She invited student volunteers to perform an online memory task. The students saw a list of 60 words and were then asked to recognize a list of five brand new words that are related to words that were on the original list. Students were also asked to provide their GPAs. Consider the following data set, which was collected from student volunteers in 2009. The table gives the frequency for the number of incorrectly identified related words. Use the dropdown menus to complete the table by filling in the missing values for the proportions and percentages
The proportion and percentage is as follows;
[tex]$\begin{array}{cccc}\text { Score Interval } & f & \text { Proportion } & \text { Percentage } \\ 9-10 & 29 & 0.19 & 19 \% \\ 7-8 & 53 & 0.34 & 34 \% \\ 5-6 & 50 & 0.32 & 32 \% \\ 3-4 & 22 & 0.14 & 14 \% \\ 1-2 & 1 & 0.01 & 1 \%\end{array}$[/tex]
What is the difference between proportions and percentages?A percentage represents a ratio or fraction with a denominator that is always 100 as opposed to a proportion, which asserts the equivalent of two ratios or fractions.
Given
[tex]$\begin{array}{cccc}\text { Score Interval } & f & \text { Proportion } & \text { Percentage } \\ 9-10 & 29 & 0.19 & 19 \% \\ 7-8 & 53 & & \\ 5-6 & 50 & & \\ 3-4 & 22 & 0.14 & 14 \% \\ 1-2 & 1 & 0.01 & 1 \%\end{array}$[/tex]
To estimate the total frequency:
Total = sum f
Total = 29 + 53 + 50 + 22 + 1
Total = 155
The proportion (p) exists calculated by:
[tex]$p = \frac{f}{\text { Total }}[/tex]
The percentage (P) exists calculated by:
P = p × 100 %
For interval 7 - 8, we have:
p = 53 / 155 = 0.34
P = 0.34 × 100 % = 34 %
For interval 5 - 6, we have:
p = 50 / 155 = 0.32
P = 0.32 × 100 % = 32 %
So, the complete table is:
[tex]$\begin{array}{cccc}\text { Score Interval } & f & \text { Proportion } & \text { Percentage } \\ 9-10 & 29 & 0.19 & 19 \% \\ 7-8 & 53 & 0.34 & 34 \% \\ 5-6 & 50 & 0.32 & 32 \% \\ 3-4 & 22 & 0.14 & 14 \% \\ 1-2 & 1 & 0.01 & 1 \%\end{array}$[/tex]
The complete question is:
A statistics content developer at Aplia wanted to know whether study skills are related to memory quality. She invited student volunteers to perform an online memory task. The students saw a list of 60 words and were then asked to recognize a list of five brand new words that are related to words that were on the original list. Students were also asked to provide their GPAs.
Consider the following data set, which was collected from student volunteers in 2009. The table gives the frequency for the number of incorrectly identified related words. Use the dropdown menus to complete the table by filling in the missing values for the proportions and percentages.
Score Interval f Proportion Percentage
9â10 29 0.19 19%
7â8 53
5â6 50
3â4 22 0.14 14%
1â2 1 0.01 1%
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Question 6 of 10
Which is the best estimate of the circumference of this circle?
3
OA. 18 units
OB. 42 units
OC. 3 units
O D. 6 units
The best estimate for the circumference of a circle with 3 units radius is equal to 18 units. The correct option is A.
Given the radius of the circle is equal to 3 units.
The formula for the circumference of the circle is equal to
[tex]C=2*\pi *r[/tex].
By substituting the value of the radius and pi we will get:
[tex]C=2*3.14*3\\C=18.86[/tex].
Therefore the best estimate will be 18 units.
Complete question:
Which is the best estimate of the circumference of this circle?
radius = 3 units.
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Determine the intercepts of the line. Do not round your answers. y-4=7(x-6)y−4=7(x−6)y, minus, 4, equals, 7, left parenthesis, x, minus, 6, right parenthesis xxx-intercept: \Big((left parenthesis ,,comma \Big))right parenthesis yyy-intercept: \Big((left parenthesis ,,comma \Big))
The y-intercept of the line y = 7x -38 is -38. And the x-intercept is 0
What is a slope?In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.
Given:
The equation of the line,
y-4=7(x-6)
Simplify,
y -4 = 7x - 42
y = 7x -38
And slope-intercept form:
y = mx + b,
where m is the slope and y is the intercept.
Comparing with the slope intercept form,
we get,
m = 7 and b = -38
And the x-intercept is 0
Therefore3, y-intercept is -38.
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Why is it called logarithmic function?
A logarithm is the inverse operation of exponentiation, that is to say, log(a^b) = b, where log is logarithm, a is the base and b is the exponent.
A logarithmic function is called such because it relates the logarithm of a number to the number itself.
In other words, it is a function that expresses the value of the logarithm for a given number. This function is represented by the notation y = logb(x) where y is the logarithm, b is the base, and x is the number.
The logarithmic function is used to solve exponential equations, it is also useful in many fields such as mathematics, physics, engineering, and finance.
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please help me out will give brainliest
Answer:
Step-by-step explanation:
At a recent graduation at a naval flight school, 18 Marines, 10 members of the Navy, and 3 members of the Coast Guard got their wings. Choose three pilots at random to feature on a training brochure. Find the probability that there will be
Probability measures how probable something is to occur.
What the probability?Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, if we are unclear of how an event will turn out. Statistics is the study of occurrences subject to probability.
Probability is a measure of how likely something is to happen.
18 Marines, 10 Navy personnel, and 3 Coast Guard troops received their wings at a recent naval aviation school graduation.
Total: 18 + 10 + 3 = 31
a. 1 of each. P = C 18 * C 10 * C 3 / C 3 31
= (18 * 10 * 3) / 4495 = 0.120
b: 0 members of the navy = (C_{21} ^ 3)/(C_{21} ^ 3) = 1330/4495 = 0.296
c: 3 Marines.
p = (G ^ 3)/(C_{31} ^ 3) = (8 + 6)/4495 = 0.182
The complete question is
At a recent graduation at a naval flight school, 18 Marines, 10 members of the Navy, and 3 members of the Coast Guard got their wings. Choose three pilots at random to feature on a training brochure. Find the probability that there will be
a.1 of each 0.120 b. members of the Navy 0.296 c. Marines 0.182.
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divide using long division
When 392,196 is divided by 87, the answer obtained using long division is 4,508.
What does math's long division mean?The mathematical procedure for splitting big numbers into several smaller groups or sections is known as long division. The dividend is the number we divide into smaller groups, while the divisor is the number through which we divide. Difficulty difficulty can be solved by breaking it down into manageable parts.
According to the given information:Dividend : 392,196
Divisor: 87 (number that divides)
39 / 87 = 0
392 / 87 = 4 (87x 4 = 348) - 4 is the first digit of the result
392 - 348 = 44 (remainder)
441 (next digit is one) / 87 = 5 (87x 5= 435) - 5 is the second digit
441-435 = 6 (remainder)
69 / 87 = not possible so add a 0, which is the third digit
696 / 87 = 8 (87x 8 = 696)
696- 696 = 0 (not remainder)
When 392,196 is divided by 87, the answer obtained using long division is 4,508.
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I understand that the question you are looking for is:
392,196 divided by 87 (Using long division)
Find the distance between point k and point L.
The distance between points L and K is 4 units.
What is the distance formula between two points?The distance formula between two points (x₁, y₁) and (x₂, y₂) is gien by,
[tex]D = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2[/tex].
Given, Are two points L and K.
The coordinate points of L(- 2, 6) and K(- 2, 2).
Therefore, The distance between points L and K is,
[tex]|LK| = \sqrt{(- 2 + 2)^2 + (2 - 6)^2}[/tex].
[tex]|LK| = \sqrt{16}[/tex].
[tex]|LK| = 4[/tex].
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In the figure below, side AC of ABC lies on line l.
A. 25
B. 30
C. 22
D. 24
Can u please help.........................
The triangle ABC, along with it's image after the reflection x = -3, is given on the graph presented at the end of the answer.
How to obtain the image of the triangle?The coordinates for the original vertices of the triangle are given as follows:
A(-5, -6), B(-4, -3) and C(-3,-7).
The reflection line is given as follows:
x = -3.
The reflection lines is a vertical line, meaning that for the reflected triangle, the y-coordinate remains constant, while the x-coordinate means that the triangles will be on the same distance relative to the reflected line, however on the opposite direction.
Vertex A has a x-coordinate two units left of x = -3, hence the coordinates of the image will be two units right, hence:
A'(-3 + 2, -6) = (-1, -6).
Vertex B has a x-coordinate one unit left of x = -3, hence the coordinates of the image will be one unit right, hence:
B'(-3 + 1, -3) = B'(-2,-3).
Vertex C remains at the same position, as it has a x-coordinate of -3.
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What does the slope of a log-log graph represent?
The Slope of log - log graph represents the power of the relationship, and a straight line which indicates that there exists a definite power relationship .
What is Logarithm ?
The Logarithm is defined as power to which a number must be raised to get some other number .
A log-log plot is the plot in which both the x-axis and y-axis use a log scale.
The plot of logarithms of variables helps in extracting the information about the power relationship. The case of freely falling object is used to illustrate a log - log plot.
A plot of the logarithm of freefall distance as a function of logarithm of time gives a straight line of slope 2.
Therefore , The slope of log-log plot gives the power of relationship, and a straight line indicating that a definite power relationship exists.
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What multiplication expression can I use to find 3/8 divided 3/4
Answer: [tex]\frac{3}{8}[/tex]➗[tex]\frac{3}{4}[/tex]
Step-by-step explanation: Are you looking to work out and calculate how to multiply 3/8 by 3/4? In this really simple guide, we'll teach you exactly what 3/8 times 3/4 is and walk you through the step-by-process of how to multiply two fractions together.
Describe how the graph might be misleading. Then explain how someone might misinterpret the graph…
Answer For Both Graphs And 25 Points!!!
Answer: 1. The first graph has the x and y axis values as minutes and frequency, but the title is bicycling.
2. it's a dotted graph, which doesn't give enough information since that graph does not have to be linear, but when you have a graph like that you want a line graph.
Answer:
the other dude answered it better than i did
Step-by-step explanation:
Don’t know need help
Answer:
37?
I am SO sorry if this is wrong
Ana has bought 12 3/6 kg of flour. Mary has brought 14 2/8 kg of flour and Kristina has bought 11 8/12 kg of flour. Who bought the most flour?
Answer:
Mary bought the most flour
Step-by-step explanation:
Ana bought 12 3/6 kg of flour
12 3/6 = 75/6 = 12.5 kg of flour
Mary has brought 14 2/8 kg of flour
14 2/8 = 114/8 = 14.25 kg of flour
Kristina bought 11 8/12 kg of flour.
11 8/12 = 140/12 = 11.66 kg of flour
So, Mary bought the most flour.
Sara had 222 dollars to spend on 9 books after buying then she had 15 dollars how much did each book cost
Answer:
each book cost=222-15=207/9=22.88 dollar
If f(x)= x² (x≠2), then lim f(x) =4? Can I think of this as ignoring the x≠2 rule?
x→2
Answer: No, the statement "if f(x)= x² (x≠2), then lim f(x) =4" is not correct. The limit of a function is a value that the function approaches as the input (in this case, x) gets closer and closer to some specific number. In this case, the limit of f(x) as x approaches 2 would be 4, since f(x)=x² for all values of x other than 2. However, if you ignore the x≠2 restriction and consider all values of x, then the limit of f(x) as x approaches 2 would be undefined, since f(x)=4 for x=2.
Step-by-step explanation:
You decide to make 10 lb of a peanut-and-raisin mixture to sell at the class snack sale. You can buy peanuts for $2.50 per pound and raisins for $1.75 per pound. If you want to sell the mixture for $2 per pound, how many pounds of peanuts and how many pounds of raisins should you use
On solving the provided question, we can say that by linear equation 10/3 pounds of peanuts and how many pounds of raisins should you use.
What is a linear equation?A linear equation is one that has the form y=mx+b in algebra. B is the slope, and m is the y-intercept. It's usual to refer to the previous clause as a "linear equation with two variables" because y and x are variables. The two-variable linear equations known as bivariate linear equations. There are several instances of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. It is referred to as being linear when an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept.When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.
here,
the linear equation that is formed is
10p +7 (10 - p) = 80
10p + 70 - 7p = 80
3p = 70
p = 10/3
10/3 pounds of peanuts and how many pounds of raisins should you use
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which of the following inequalities orders the numbers 0.1, 0.04, and 1/6 from least to greatest?
Answer:
0.04 < 0.1 < 1/6
Step-by-step explanation:
Yesterday the temperature at noon was 11.4 f . By midnight the temperature had decreased by 15.7 degrees. What was the temperature at midnight ?
Answer:
-4.3
Step-by-step explanation:
It is asking for the temperature at midnight so to find out what it is. We simply subtract the starting temperature of 11.4f from 15.7 degrees
( 11.4 - 15.7 ). That would leave us with -4.3f at night.
50 POINTS! Calculate the expression in the most efficient way possible. Show steps.
5^1125 * 0.2^1123
Answer:
25
Step-by-step explanation:
Given expression:
[tex]5^{1125} \times 0.2^{1123}[/tex]
Rewrite 0.2 as a fraction:
[tex]\implies 5^{1125} \times \left(\dfrac{1}{5}\right)^{1123}[/tex]
[tex]\textsf{Apply exponent rule} \quad \left(\dfrac{a}{b}\right)^c=\dfrac{a^c}{b^c}:[/tex]
[tex]\implies 5^{1125} \times \dfrac{1^{1123}}{5^{1123}}[/tex]
Simplify the numerator by applying the exponent rule a¹ = a:
[tex]\implies 5^{1125} \times \dfrac{1}{5^{1123}}[/tex]
[tex]\textsf{Apply the fraction rule} \quad a \times \dfrac{b}{c}=\dfrac{ab}{c}:[/tex]
[tex]\implies \dfrac{5^{1125} \times1}{5^{1123}}[/tex]
[tex]\implies \dfrac{5^{1125}}{5^{1123}}[/tex]
[tex]\textsf{Apply exponent rule} \quad \dfrac{a^b}{a^c}=a^{b-c}:[/tex]
[tex]\implies 5^{1125-1123}[/tex]
Simplify the exponent:
[tex]\implies 5^{2}[/tex]
Simplify:
[tex]\implies 5 \cdot 5[/tex]
[tex]\implies 25[/tex]
Input the correct values into the point-slope
formula.
y - [?] = [](x - [ ])
A. 3
A line is parallel to y = 3x - 2 and
intersects the point (3, 5).
C. -2
B. 5
D. 1/3
Answer:
B
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 )
y = 3x - 2 ← is in slope- intercept form
with slope m = 3
• Parallel lines have equal slopes
then slope of parallel line is 3
the equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b ) a point on the line
here m = 3 and (a, b ) = (3, 5 ) , then
y - 5 = 3(x - 3) ← equation of parallel line in point- slope form
On average, what value is expected for the F-ratio if the null hypothesis is true? a. 1 b. k-1 c. N-k on average, what value is expected for the F-ratio if the null hypothesis is false? a.1 b. 0
c. Between 0 and 1.00 d. Much greater than 1.00
The F-ratio is a measure used in statistical tests, specifically in ANOVA (Analysis of Variance) to test for differences between means of multiple groups.
a) On average, what value is expected for the F-ratio if the null hypothesis is true?
The answer is a. 1. If the null hypothesis is true, it means that there is no significant difference between the means of the groups being compared. Under this assumption, the F-ratio is expected to have a value close to 1, as the variance between the groups is not significantly different from the variance within the groups.
b) On average, what value is expected for the F-ratio if the null hypothesis is false?
The answer is d. Much greater than 1.00. If the null hypothesis is false, it means that there is a significant difference between the means of the groups being compared. Under this assumption, the F-ratio is expected to have a value much greater than 1, as the variance between the groups is significantly larger than the variance within the groups.
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