The two points that represent Justine‘s function for the yards left to hike in terms of the hours she spent hiking are; (0, 320) and (4, 0)
How to find the correct coordinates?
From the table in the attached file, we see that;
Justine started when Michael was 320 yards from the top.
This coordinate is expressed as (0,320)
where;
0 represents the time Justine started
320 represents the number of yards left.
Now, it is clear that every minute, Justine covers 80 yards.
Thus;
After 1 minute, Justine will have:
(320 - 80) yards left
After 2 minutes, Justine will have:
(320 - 80 - 80) yards left
After 3 minutes, Justine will have:
(320 - 80 - 80 - 80) yards left
After n minutes, Justine will have;
(320 - 80n) yards left
Thus, the possible coordinates are:
(0, 320), (1, 240), (2, 160), (3, 80), (4, 0)
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How do you write 0.0045 in scientific notation?
Answer:
[tex]4.5 x 10^{-3} \\[/tex]Step-by-step explanation:
Write an expression for "c fewer than 4."
Answer: c<4
Step-by-step explanation:
C fewer than 4 means that c is smaller than 4! So we use this mark <
So the answer is c<4
How do you use DeMoivre's Theorem to find (1+i)^20 in standard form?
Divide by the norm of 1+i and apply De Moivre's theorem to find that (1 +i)^20 = − 1024 in standard form.
De Moivre's theorem presents a formula for calculating powers of complex numbers. By first studying what occurs when we multiply a complex number by itself, we may have a better understanding of de Moivre's theorem. This demonstrates that when squaring a complex number, the argument is multiplied by two and the absolute value is squared.
DeMoivre's Theorem, which unites complex numbers with trigonometry, is one of the most significant and practical theorems in the study of complex numbers. Obtaining correlations between trigonometric functions of various angles is also useful. The famous mathematician De Moivre, who made several contributions to the subject of mathematics, particularly in the fields of probability theory and algebra, is honored in the name of the theorem. The solution is attached below.
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You start at (4, 0). You move up 10 units. Where do you end?
Answer: (4, 10)
Step-by-step explanation:
The first number, 4, is the number on the x axis, the horizontal axis. The second number 0 is the number on the y axis, the vertical axis.
If you move up you would moving on the y axis, therefore the second number, 0, would change.
You moved 10 units so starting at 0 move up 10 units. 0 + 10 = 10
Now you're at (4, 10)
like terms onto each other to simplify fully.
6+3x-6+4+5y
The simplified form of the given expression is 3x+5y+4. Here only the constants are simplified since there are no like terms in the expression.
What are like terms?An expression is the combination of terms with any of the arithmetic operations in between them. Here the terms are formed by a coefficient and a variable.In an expression, if two or more terms with the same variable with the same power are said to be like terms otherwise they are said to be unlike terms.The like terms undergo addition and subtraction operations.But the unlike terms can't be added or subtracted.Calculation:The given expression which is to be simplified is 6+3x-6+4+5y.
Here to simplify the given expression, we need to add or subtract the like terms.
In the given expression, the variables x and y.
They are unlike terms. So, we cannot add or subtract them. But there are three constants. Then, we can add or subtract them.
Thus, the simplified expression for the given expression is
6+3x-6+4+5y = 3x+5y+4
Here 6 and -6 are added so that we get 0.
Hence the answer is 3x+5y+4.
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Does the picture represent a function?
Yes or No
Answer: Yes
Step-by-step explanation: To determine if this graph represents a function, we use what is called the vertical line test.
In other words, if we can draw a vertical or straight up and down line that passes through more than one point on the graph, the relation is not classified as a function.
In this case, it's impossible to draw such a line that hits more than one point on the graph so the relation is a function.
Which is the criterion for constructing a triangle
A SSS
B SAS
C ASA
D all of these?
a card is drawn from a standard deck of 52 playing cards. what is the probability that the card will be a spade or a club? express your answer as a fraction or a decimal number rounded to four decimal places.
The probability that the card will be a spade or a club 50%
Probability in math is referred as how likely an event is to occur, or how likely it is that a proposition is true.
Here we have given that a card is drawn from a standard deck of 52 playing cards.
And we need to find the probability that the card will be a spade or a club and we have to express your answer as a fraction or a decimal number rounded to four decimal places.
While we looking into the given question, we have identified the the total number of cards is 52.
And the number of spade cards = 13 and the number of club cards = 13
Therefore, the total number of spade and club cards
=> 13 + 13
=> 26
Therefore, the probability of getting a spade or a club from a single draw is,
=> 26/52
When we simplified this one, then we get,
=> 0.5
When we convert this into percentage then we get
=> 50%.
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a true-false test contains 11 questions. in how many different ways can the 11-question test be answered? (give an exact answer.)
The total number of possible ways to complete the test would be 2048.
Total number of questions = 11
Each equation has two possible answers (either true or false).
We need to find the total number of ways in which the test can be completed.
the total number of possible ways to complete the test= 2×2×2×2×2×2×2×2×2×2×2
the total number of possible ways to complete the test=
2¹¹
Therefore the total number of possible ways to complete the test is 2048.
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at a gas station, lora took 1/6 minute to fill 3/5 gallon of gas. at this rate, how many gallons of gas could lora fill in 1 minute?
The number of gallons of gas that Lora can fill in 1 minute will be 18/5 or 3.6 gallons.
What are ratio and proportion?A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.
The rate is the ratio of the amount of something to the unit. For example - If the speed of the car is 20 km/h it means the car travels 20 km in one hour.
At a gas station, Lora took 1/6 minute to fill 3/5 gallons of gas. And we know that the ratio will remain constant.
Let 'x' be the number of gallons. Then the amount of gallons in each minute is calculated as,
(3/5) / (1/6) = x / 1
Simplify the equation, then we have
(3/5) / (1/6) = x / 1
(3/5) × 6 = x
x = 18 / 5
x = 3.6 gallons
The number of gallons of gas that Lora can fill in 1 minute will be 18/5 or 3.6 gallons.
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Roxie is picking out some movies to rent, and she is primarily interested in horror films and documentaries. She has narrowed down her selections to 6 horror films and 15 documentaries.
Step 1 of 2 : How many different combinations of 3 movies can she rent?
1085 different combination of 3 movie she can rent.
What is linear equations?
Linear equations is a type of equation that is in between two variables that gives a straight line.
The calculation of number of different combinations of 3 films she can rent if she needs at least two documentaries is shown below:-
=N×(2× documentry and 1 horror movies)+N×(3 documentry)
=(6C1)×(15C2)+(6Co)×(15C3)
= 630 + 455
= 1,085
Therefore for calculating the number of different combinations of 3 films she can rent if she needs at least two documentaries we simply applied the above formula and here we consider one number in the question as it shows the double number.
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3) Find the slope of each line. Tell whether the slop is Positive, Negative, Undefined or Zero
Answer: slope = -1
Step-by-step explanation:
count number down vs number it takes to get back to the line.
For example, 1 down, 1 across
define the level of significance. multiple choice it is the probability of a type ii error. it is the probability of a type i error. it is a z-value of 1.96. it is the beta error.
By information provided in the question, we can say that It is the probability of a Type I error.
what is probability?The proportion of favorable outcomes to all possible outcomes for an event is known as the probability. The quantity of positive outcomes in an experiment with 'n' outcomes is represented by x. The following equation can be used to determine the likelihood of an event:
Probability (event) = positive outcome / overall outcome = x/n
It refers to the likelihood of a Type I mistake.
The likelihood that a Type I error will occur, or the likelihood that a null hypothesis will be rejected when it is true, determines the degree of significance.
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(a)The perimeter of a rectangular parking lot is 350 m . If the length of the parking lot is 97 m , what is its width?
The width of the parking lot is 78 m
We have been given the perimeter of a rectangular parking lot which is equal to 350 m.
We know the perimeter of a rectangular plot is 2 X (width of the plot ) + 2 X (length of the parking lot ).
And the length of the parking lot is given as 97 m.
2 X (width of the plot ) +2 X (length of the parking lot ) =350 m
2 X (width of plot ) + 2 X 97 =350
2 X (width of the plot ) =156 m
width of the plot = 78 m
Hence the width of the plot is 78 meters.
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The width of this rectangular parking lot is equal to 78 meters.
How to calculate the perimeter of a rectangle?In Mathematics and Geometry, the perimeter of a rectangle can be calculated by using this mathematical equation (formula);
P = 2(L + W)
Where:
P represent the perimeter of a rectangle.W represent the width of a rectangle.L represent the length of a rectangle.By substituting the given side lengths into the formula for the perimeter of a rectangle, we have the following:
P = 2(L + W)
350 = 2(97 + W)
175 = 97 + W
Width, W = 175 - 97
Width, W = 78 meters.
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based on this scatterplot, we observe that there are 6 groups of turkeys, each group receiving a different amount of methionine supplement (ranging from 0% to 44%). what is the most reasonable experimental study design used to conduct this study?
This study was conducted to test the effects of dietary supplementation of feed grade L - Met on growth performance.
Given :
based on this scatterplot , we observe that there are 6 groups of turkeys, each group receiving a different amount of methionine supplement (ranging from 0% to 44%).
Initial BW of birds did not differ among treatments. Weight gain of birds during 28 d feeding period increased ( P < 0.05 ) from 690 to 746 g ( an average of 0.33 % DL-Met and L-Met ) as dietary Met supplementation regardless of Met source increased from 0 to 0.33%. However, the source of Met did not affect the weight gain of birds.
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How do you solve (15−a)/3 =−9?
The value of a is 42.
Simply use cross multiplication :
The process of multiplying numbers in the shape of a fraction is called cross multiplication. Cross multiplying, also known as cross multiplication, is the process of multiplying the numerator of one fraction by the denominator of the other fraction on the other side of an equal symbol. Cross multiplication is a method for comparing fractions.
Both fractions with like and unlike parts are multiplied across. When employing the cross-multiplication procedure, we multiply the denominators as well as the numerators when a fraction is dissimilar, or when the denominators of two fractions are not alike.
[tex](15-a)/3=-9[/tex]
or, [tex]15-a=-9*3[/tex]
or,[tex]-a=-27-15[/tex]
or, [tex]a=42[/tex]
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examine the linear relationships. linear equation a: y=45xy=45x linear equation b is represented by this graph.
The correct option 1. the slope of Equation A is steeper because 4/5 is bigger than 2/5.
Explain the term slope of the line?A line's steepness can be determined by looking at its slope. Slope is calculated mathematically as "rise over run" (variation in y divided by change in x).The format of a linear function is as follows:
y = ax + b
That where:
The rate of change is represented by the slope, or a.The function is steeper the higher the slope:Given by: Linear equation A
y = 4/5 x.
Points (0, 2) and pass through linear equation B. (5, 4).
Given that changes in y divided by change in x determines the slope between two points, we have that:
m = (4 - 2)/(5 - 0)
m = 2/5
Equation A is steeper as it contains a higher slope, so the appropriate response is:
Due to the fact that 4/5 is greater than 2/5, Equation A has a steeper slope.
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The complete question is-
Linear equation A: y=45x
Linear equation B is represented by this graph.
A line that passes through points (0, 2) and (5, 4).
Which statement is entirely correct?
Equation A has a steeper slope, because 4/5 is greater than 2/5.Equation A has a steeper slope, because 4 fifths is greater thanEquation B has a steeper slope, because 4/5 is greater than 2/5.Equation B has a steeper slope, because 4 fifths is greater thanEquation A has a steeper slope, because 5/2 is greater than 4/5.Equation A has a steeper slope, because 5 halves is greater thanEquation B has a steeper slope, because 5/2 is greater than 4/5.a number that cannot be expressed as a ratio of integers. these numbers have digits that go on forever without repeating.
Irrational numbers are numbers that cannot be expressed as a ratio of integers and have digits that go on forever without repeating.
Irrational numbers are a type of real number which cannot be represented as a simple fraction. These numbers could be expressed in decimals but not in the form of fractions i.e., they cannot be written as the ratio of integers. Irrational numbers have endless non-repeating digits after the decimal point, hence cannot be expressed as terminating or repeating decimals. For example, when taking the square root of a number that is not a perfect square, it is going to be irrational number.
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alexa is pushing a construction barrel up a ramp 1.5 meters long into the back of a truck
Moving this barrel up a ramp required around 339.41 foot-pounds of labour from Alexa.
Explain the term work done by force?The sum of the displacement as well as the component of both the applied force of a object in the displacement direction is the work done by a force.The dot product combined force and displacement, or "work done," is what is meant.W = F.d
When the dot product is expanded, we get:
W=Fd cos(Ф)
W stands for the quantity of work completed,F for the applied force, d for displacement, and Ф for the angle formed by Force F in respect to the horizontal.We can plainly see from the given statement that:
applied force = F = 120 pounds
d = 4 feet for displacement.
F's angle with the horizontal is Ф = 45 degrees.
When the formula's values are substituted, we obtain:
W = 4 * 120 * cos (45)
W equals 339.41 foot pounds.
This indicates that lifting the barrel up this ramp required roughly 339.41 foot-pounds of labour from Alexa.
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The complete question is-
Alexa is pushing a construction barrel up a ramp 4 feet long into the back of a truck. She is using a force of 120 pounds in a horizontal direction and the ramp is 45 degrees from the horizontal. How much work is Alexa doing?
if the list price is $70 and the percent of discount is 10%. What is the amount of discount
Answer: 7
Step-by-step explanation: You would multiply 70 by 10 to get 700, then divide it by 100 to get 7. So, it would be 7 dollars.
Answer: 7
Step-by-step explanation:
Find the 14th term of the arithmetic sequence -x-5, 6x - 7, 13x - 9,...
Answer: a₁₄=90x-31
Step-by-step explanation:
-x-5, 6x-7, 13x-9 ...
Hence,
a₁=-x-5
a₂=6x-7
a₃=13x-9
d=a₂-a₁
d=6x-7-(-x-5)
d=6x-7+x+5
d=7x-2
aₙ=a₁+d(n-1)
a₁₄=-x-5+(7x-2)(14-1)
a₁₄=-x-5+13(7x-2)
a₁₄=-x-5+91x-26
a₁₄=90x-31
Q19.
1+√2/(3-√2)² can be written in the form
a+b√2
Find the value of a and the value of b.
The surd expression 1 + [√2 / (3 - √2)²] can be simplified as (61 + 11√2/ 49) where a is 61/49 and b is 11/49
Evaluating an ExpressionWhen evaluating an expression, the first step is to identify the operators and operands in the expression. The operators are the symbols that direct the operation. The operands are the values or variables that the operators act upon. Once the operators and operands are identified, the expression can be evaluated by applying the order of operations to the expression. This includes performing operations inside parentheses first, then multiplication and division, followed by addition and subtraction.
In the case of a surd expression, the same process should be followed. However, it is important to note that surds can be simplified using the rules of indices. This means that surds with the same base value can be combined using addition and subtraction.
In the give problem, we have
1 + [√2 / (3 - √2)²] can be written in the form a + b√2
1 + [√2 / (3 - √2)²] can be simplified using a calculator to give us a value of;
1 + [√2 / (3 - √2)²] = (61 + 11√2/ 49)
In this expression, a = 61/49, b = 11/49
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the manager of a clothing factory checks a random sample 500 shirts for defects he finds that 8 are defective the factory produces 2625 shirts on friday
The expected number of defective shirts produced by the factory on Friday is of:
42 shirts.
How to obtain the expected amount?The expected number of defective shirts produced by the factory on Friday is obtained as the multiplication of the sample proportion by the total number of shirts produced on Friday.
The manager of a clothing factory checks a random sample 500 shirts for defects he finds that 8 are defective, hence the sample proportion is given as follows:
p = 8/500 = 0.016.
The factory produces 2625 shirts on Friday, hence the expected number of defective shirts is given as follows:
E(X) = 0.016 x 2625 = 42 shirts.
Missing InformationThe problem is incomplete and could not be found on any search engine, hence we suppose that it asks for the expected number of defective shirts produced by the factory on Friday.
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If x and y are in direct proportion and y is 64 when x is 8, find y when x is 13.
The value of y will be 104 using direct proportion property between x and y.
What is direct proportion ?
Direct proportion is the relation between two quantities where ratio of these two is equal to a constant.
It is represented by proportional symbol , "∝"
Let's consider constant is m.
For given que,
As y and x are in direct proportion,
y ∝ x
or x ∝ y
eliminating the proportionality,
y = x*m where m is any constant.
y/x = m
Given when y = 64 , then x = 8
So, m = 64/8
= 8
And when x = 13 then y = ?
y/13 = 8
y = 13*8
= 104
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The function y=f(x)y=f(x) is graphed below. What is the average rate of change of the function f(x)f(x) on the interval -7\le x \le 2−7≤x≤2?
Consequently, the function's average rate of change is -11.
What is function?A mathematical expression, rule, or law that describes the relationship between two independent variables and one dependent variable In mathematics, functions exist everywhere, and they are crucial for creating physical links in the sciences.
The function is given by .
The ratio of the dependent variable's change to the independent variable's change is referred to as the rate of change.
f(x)=[tex]x^{2}[/tex]-6x+6
x ranges from -7 to 2, with 2 being the highest value.
=> f(-7) = 49 + 42 + 6 = 97.
=> f(2) =- 12 + 6+4 = -2.
The average rate of change is
f(-7)-f(2)/-7-2
=> 97-(-2)/-9
=> 99/-9
=> -11
Consequently, the function's average rate of change is -11.
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Rewrite 18x4y3 − 36x3y4 using a common factor.
2x4y4(9 − 18x)
2x3y3(9y − 18x)
9x3y3(2x − 4y)
9x4y3(2 − 4y)
The expression can be rewritten as, by taking the common factor, 9 x³y³(2x - 4y), so option C is correct.
What is a common factor?Common factors are those that apply to two or more different integers. To put it another way, a common factor is a number that will divide a group of two numbers exactly.
Given:
18 x⁴y³− 36x³y⁴
Factorize the above expression,
9 × 2 x⁴y³ - 9 × 4x³y⁴
Take common 9 x³y³
9 x³y³(2x - 4y)
Therefore, the expression can be rewritten as, by taking the common factor, 9 x³y³(2x - 4y).
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how many weighings of a balance scale are needed to find a lighter counterfeit coin among four coins?
The weighing of the balance scale required to find a lighter counterfeit coin among four coins, is twice.
In just two balance scale weighs, it is feasible to identify which of four coins is the lighter fake coin. Here is one approach:
Then, weigh the two groups against one another after splitting the four coins into two groups of two coins each. The lighter counterfeit currency must belong to the group that is lighter than the other if there are two groups. If the two groups of coins weigh the same, then one of the two remaining coins must be the lighter counterfeit coin.
Weigh the two coins from the lighter group (or the two still present, if the first step was unsuccessful) against one another.
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Q1 what is the difference between "mu" and "xbar"?
Q2 What does each "point" in a sampling distribution for a mean represent?
Q3 describe the purpose of checking the random condition.
Q4 describe the purpose of checking the 10% condition.
Q5 describe the purpose of checking the large counts condition.
Q6why is it difficult to find unbiased estimates about asylum-seekers?
Q7 To get the standard deviation of the sampling distribution for a proportion, we divide by the sample size (n). Describe how dividing by the sample size influences the spread when samples sizes are high vs. when they are low:
Q1 If you averaged every person in the population, the result would be Mu, but the mean of a sample, or xbar, would be the average value discovered in the sample.
Q2 For the group being tested, each point in a sample distribution represents a potential outcome variable.
Q3 The random condition is very important because it simplifies the sample and prevent possible bias in the sampling.
Q4 To make sure that the observations in the sample are nearly independent, it is crucial to evaluate the 10% condition before calculating probability involving x.
Q5 The big counts criterion ensures that there are more successes than failures for a normally distributed set of results. The need for big numbers is np ≥10 and n(1-p) ≥10.
Q6 For a variety of reasons, finding unbiased estimates for those seeking asylum may be challenging. First, because of persecution, these people are escaping their country.
Q7 there is less spread for larger sample than that of lower sample.
What is meant by sampling distribution?The probability distribution of a statistic acquired from a bigger sample size taken from a certain population is known as the sampling distribution.
What is the purpose of sampling distribution?Based on the data they have available, sampling distributions are useful tools used by researchers to estimate and draw conclusions about a wider population of interest.
Q1 If you averaged every person in the population, the result would be Mu, but the mean of a sample, or xbar, would be the average value discovered in the sample.
Q2 For the group being tested, each point in a sample distribution represents a potential outcome variable.
Q3 The random condition is very important because it simplifies the sample and prevent possible bias in the sampling.
Q4 To make sure that the observations in the sample are nearly independent, it is crucial to evaluate the 10% condition before calculating probability involving x.
Q5 The big counts criterion ensures that there are more successes than failures for a normally distributed set of results. The need for big numbers is np ≥10 and n(1-p) ≥10.
Q6 For a variety of reasons, finding unbiased estimates for those seeking asylum may be challenging. First, because of persecution, these people are escaping their country.
Q7 there is less spread for larger sample than that of lower sample.
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the following percentages of chloride were found: 42.62%, 43.10%, 42.90%, and 42.75%. what is the average deviation from the mean
The average deviation from the mean is 0.19 that can be calculated from the mean.
An average is calculated for a set of numbers that are of the same value range.
Mean = (32.52+32.14+32.61+32.75)/4 = %32.50
Standard deviation =
|32.50-32.52| = 0.02
|32.50-32.14| = 0.36
|32.50-32.61| = 0.11
|32.50-32.75| = 0.25
(.02+.36+.11+.25)/4= 0.19
So the standard deviation is 0.19
Relative deviation = .19/32.50=0.0058 or %0.58
Yes, %32.14, because it deviates too far from the average.
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use the counting techniques from the last chapter. a bag contains two red marbles, three green ones, one fluorescent pink one, three yellow ones, and two orange ones. suzan grabs three at random. find the probability of the indicated event. she gets all the red ones, given that she gets the fluorescent pink one.
The probability of the indicated event is 1/110.
P(2red, pink) = P(2red, pink)/P (pink)
There are a total of 1 ways to get 2 red and pink, for a total of 1 possible triples. P(2red and pink) = 1/220 P(pink) = Number of ways to get 1 pink = 1*11*10 Number of potential triples = 220 P(1 pink in 3) = 110/220 = 1/2 ———-
P(2red | pink) = (1/220)/(1/2) = 2/220 = 1/110 ————————————————
Cheers,
Stan H.
How do you determine an event's probability?To determine the likelihood, apply the procedure below: Find an event with a single result in Step 1. 2. Determine the total number of possible results. Step 3: Subtract the number of fortunate occurrences from the total number of potential outcomes.
How can I determine the suggested probability?You can attempt to find the indicated probability using a variety of equations. The normal distribution model and the standard normal distribution are two techniques that you could choose to adopt since they are both frequently used to calculate suggested probability precisely.
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