Answer:
Step-by-step explanation:
Quadratic: binomial
Cubic: trinomial
Quartic: four terms
Quintic: five terms
8th degree: six terms
Find the sum. Simplify
2 2/10
Answer:
2 1/5
Step-by-step explanation:
my grandpa has 10 pieces of art, including 3 prints by escher. if he hangs the pieces of art in a row in a random order, what is the probability that all three pieces by escher will be placed consecutively?
The probability that all three Escher prints will be placed consecutively is 3/5 or 0.6
The probability that all three pieces by Escher will be placed consecutively when hanging the 10 pieces of art in a random order is the probability that the 3 Escher prints will be in a row among the other 7 pieces.
There are 10!/(3! × 7!) = 120 ways to order the 10 pieces of art, and 3! = 6 ways to order the 3 Escher prints among themselves.
So the total number of ways to order the art such that the Escher prints are consecutive is 120 × 6 = 720.
Now to find the probability that all three Escher prints will be placed consecutively, we divide the number of ways that this can happen (720) by the total number of ways the art can be arranged (120) to get 720/120 = 6/10 = 3/5.
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if you knew a student's overall act score, would you be more confident predicting that student's score on the algebra test or their satisfaction with first-semester classes?
Algebra test because the correlation is higher.
What does a statistical correlation mean?
A statistical metric known as correlation, which is given as a number, describes the strength and direction of a relationship between two or more variables.
Although there may be a correlation between two variables, this does not necessarily imply that the change in one variable is what led to the change in the values of the other variable.
Why correlation, you ask?
In common conversation, we use the word correlation to describe situations where two or more items seem to be connected.
In the field of analytics, correlations are certain numbers that are computed to express how closely related variables are to one another.
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Does this set of ordered pairs represent a function? why or why not?
(-2,2), (-1, 2), (3, -1), (3, 1), (4, 11))
oa. yes, because there are two xvalues that are the same.
o b. yes, because every xvalue corresponds to exactly one y-value.
o c. no, because two of the y-values are the same.
od. no, because one xvalue corresponds to two different y-values
The ordered set pairs (-2, 2), (-1, 2), (3, -1), (3, 1), (4, 11),
is not a function. Because one x value corresponds to two different y values.
Determine whether or not the function of the set of ordered pairsGiven a set of ordered pairs (-2, 2), (-1, 2), (3, -1), (3, 1), (4, 11),
Function is special relations that pair each member of set A (domain) with exactly one member of set B (codomain).
Discuss the options provided.
a. yes, because there are two x values that are the same that is 3. Then the statement is false, the value of x cannot be the same.
b yes, because every x value corresponds to exactly one y-value. Then the statement is false.
c. no, because two of the y-values are the same. Then the statement is false.
d. no, because one xvalue corresponds to two different y-values. Then the statement is true.
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A trampoline salesman makes $25,000 annually plus 6% commission on his total sales.
If he sold $40,000 worth of trampolines this year, what are his total earnings?
Answer:
$27,400.
Step-by-step explanation:
We know that the salesman makes $25,000 annually plus 6% commission on his total sales.
We also know that he sold $40,000 worth of trampolines this year.
So we can find out his commission by multiplying the value of sales with 6% commission rate.
Commission = 0.06 * $40,000 = $2400
To find out his total earnings we need to add his annual salary with commission earned.
Total earnings = $25,000 + $2400 = $27,400
So the salesman's total earnings for this year is $27,400.
3. Jonny has 12 pairs of shoes, some are Nike and some are Adidas. He has 6 more pairs of Nikes than Adidas shoes. How many pairs of each shoe brand does he have?
Step-by-step explanation:
let addicts be x and Nike be x+6
so ,
x+x+6=12
or,2x=6
or x=-3
now x+6=3+6=9
therefore he had 9 Nike and 3 Adidas
write the ratio in simplest form 1. 30 treadmills to 36 elliptical machines / 2. 180 red marbles to 145 blue marbles / 3. in the word flashlight what is the ratio of vowels to total letters? /
The ratio in simplest form in the three cases is 5 : 6, 36 : 29 and 1 : 5.
30 treadmills to 36 elliptical machines can be simplified to 5 treadmills to 6 elliptical machines. To simplify, you can divide both numbers by their greatest common factor, which in this case is 6.
30/6 = 5 and 36/6 = 6
So 30 : 36 = 5 : 6
180 red marbles to 145 blue marbles can be simplified to 12 red marbles to 11 blue marbles. To simplify, you can divide both numbers by their greatest common factor, which in this case is 5.
180/5 = 36 and 145/5 = 29
180 : 145 = 36 : 29
In the word "flashlight", the ratio of vowels to total letters is 2:8. The word "flashlight" has 2 vowels (a,i) and 10 total letters. To simplify divide by 2.
2 : 10 = 1 : 5
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sam wishes to cross a circular lake with diameter 1 km. he can row across the water at a rate of 4 km/hour, or he can walk along the shore (carrying the rowboat) at a rate of 6 km/hour. what is the minimum amount of time necessary to cross the lake?
25 minutes. The time it would take to row across the lake is 15 minutes (1 km/4 km/hour = 0.25 hour), and the time it would take to walk around the lake is 10 minutes (1 km/6 km/hour = 0.1666 hour). Thus, the minimum amount of time necessary to cross the lake is 25 minutes (15 + 10).
1 km/4 km/hour = 0.25 hour (time to row across the lake)
1 km/6 km/hour = 0.1666 hour (time to walk around the lake)
Minimum amount of time necessary to cross the lake = 0.25 + 0.1666 = 0.4166 hour
0.4166 hour x 60 minutes/hour = 25 minutes
Sam can row across the lake in 15 minutes (1 km/4 km/hour = 0.25 hour) or walk around it in 10 minutes (1 km/6 km/hour = 0.1666 hour). The minimum amount of time necessary to cross the lake is 25 minutes (15 + 10), as this is the lowest total time to get from one side to the other.
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help with this question pls
Step-by-step explanation:
(a)
the line for time = 0 minutes starts at y (pounds of candy) = 40 pounds
(b)
as the line goes up, when the time goes up, it is clear that the function result (the amount of candy in the container) increases, as the time increases.
so, the second answer option is correct.
to find the rate of pound of candy per minute, we need to find the slope.
one unit on the coordinate grid in the time (x) direction is 1 minute.
one unit in the pounds of candy (y) direction is 40 pounds (0, 40, 80, 120, ...).
when we look at what corners of the coordinate grid units the line goes through (to find integer numbers of the function), we see that the line goes through e.g.
(0, 40)
(1, 160)
(2, 280)
...
we see that x anyways changes by +1, and y anyways charges by +120.
the slope is therefore +120/+1 = 120.
the increase rate of the amount of candy in the container is 120 pounds per minute
(a) write the joint density f(x, y). (b) find e(ax by c). (c) find e[x2 ]. (hint: use the variance identity.) (d) find var(ax by c).
i) Joint density distribution function is given as
f(x,y) = 1/2Πσ1σ2 exp[(-1)/2 {((x-µ1)^2)/(σ1^2)+ ((y-µ2))/(σ2^2)}]
ii) E(aX + bY + c) = aµx + bµy + c iii) E(X^2) = σx^2 + µx^2
We have been given that, X ~ N(µx , σx^2) and Y~ N(µy , σy^2)
and X and Y are independent that is
ρ = 0
Note that the joint density function of two normal distribution is known as bivariate normal distribution which is given as
(X , Y) ~ BVN(µ1 , µ2 , σ1^2 , σ2^2 , ρ)
And whose joint density function is
f(x,y) = 1/(2Πσ1σ2√(1-ρ^2)) exp[(-1)/(2(1-ρ^2)) {((x-µ1)^2)/(σ1^2)-2ρ (x-µ1)(y-µ2)/σ1σ2+ ((y-µ2))/(σ2^2)}]
Where ρ = correlation coefficient of (x,y)
i) Joint density function of given X and Y which follows
(X , Y) ~ BVN(µx , µy , σx^2 , σy^2 , 0) is given as
f(x,y) = 1/2Πσ1σ2 exp[(-1)/2 {((x-µ1)^2)/(σ1^2)+ ((y-µ2))/(σ2^2)}]
ii) E(aX + bY + c) = aE(X) + bE(Y) + c
= aµx + bµy + c
iii) E(X^2) = V(X) + [E(X)]^2 {V(X) = E(X^2) - [E(X)]^2}
= σx^2 + µx^2
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Find the area, not sure if that's a 1.5 or 15
Answer:
8.25
Step-by-step explanation:
trapezoid area =
(a+b)/2 times h =
if its 1.5
(4+7)/2 times 1.5 =
11/2 times 1.5 =
5.5 times 1.5 =
8.25
if its 15
5.5 times 15 =
82.5
its probably 1.5
wikipedia
1) Why were the colonists upset with the new taxes that Great Britain passed prior to the American Revolution
This implied that they were unable to rule themselves and establish their own rules. The king demanded that they pay enormous taxes.
They believed they were contributing taxes to an unrepresentative administration. They were also upset that the colonists had to allow the British soldiers to eat and sleep in their residences.
The colonists of America formed a protest in response to the actions of Parliament. A network of covert organizations called the Sons of Liberty was established throughout the colonies with the intention of scaring the tax collectors for Parliament. migrated to America because they wanted political liberty. They desired both economic opportunity and religious freedom. Self-government and individual liberties are valued in the United States.
Because the colonists opposed the British,
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Determine appropriate ____ to model scenarios.
Determine appropriate formula to model scenarios.
How to determine appropriate formulas to model scenarios?Sometimes, different formulas can generate similar results. The key is to choose the formula that is most appropriate for the scenario, and it's also important to consider the complexity of the formula and its interpretability.
Based on the problem or question, the available data, and the literature review, determine the appropriate mathematical model to use. The model should be able to capture the key features of the problem or question and provide an accurate representation of the data.
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Can someone please help me with this math problem, ASAP? I've been trying to figure it out, but still couldn't get the right answer for it, Thanks!
The linear function with a slope of -1/4 and intercept of -5 is given as follows:
f(x) = -0.25x - 5.
How to define a linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
The slope m represents the rate of change of the output variable y relative to the input variable x.The intercept b represents the value assumed by y when x = 0.The parameters for this problem are given as follows:
Slope of -1/4 -> m = -1/4 = -0.25.f(0) = -5 -> b = -5.Comparing to the standard definition, the linear function is defined as follows:
f(x) = -0.25x - 5.
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Given the following point on the unit circle, find the angle, to the nearest tenth of a
degree (if necessary), of the terminal side through that point, 0° 0 < 360°.
P =
3
4
ܠܛܕ
47)
Answer: [tex]303^{\circ}[/tex]
Step-by-step explanation:
The point [tex]P[/tex] lies in the fourth quadrant, so the angle is given by [tex]360^{\circ}-\alpha[/tex], where [tex]\alpha[/tex] is the reference angle.
The reference angle is given by [tex]\arctan \left(\frac{\frac{\sqrt{7}}{4}}{\frac{\sqrt{3}}{4}} \right)=\arctan \left(\sqrt{\frac{7}{3}} \right)[/tex].
This means [tex]\theta=360^{\circ}-\arctan \left(\sqrt{\frac{7}{3}}} \right) \approx 303^{\circ}[/tex].
The table shown represents a linear relationship.
x 0 1 2 3
y -6 -4 -2 0
Based on the table, what is the equation of the linear relationship in slope-intercept form?
Oy=2x + 6
Oy=2x-6
Oy=-2x + 3
Oy=-2x - 3
The slope intercept form of the equation is B) y=2x-6.
What is slope intercept form of the equation?
When the slope of the line being studied is known, and the provided point is also the y intercept, the slope intercept formula, y = mx + b, is utilised (0, b). It provides both a slope and an intercept, which is why the form is known as the slope-intercept form.
Here According to the table using two points [tex](x_1,y_1) =(0,-6)[/tex] and [tex](x_2,y_2)=(3,0)[/tex] .
Now using slope formula m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
=> m = [tex]\frac{0-(-6)}{3-0}[/tex]
=> m = [tex]\frac{6}{3} = 2[/tex]
Now using equation formula then
=> [tex]y-y_1=m(x-x_1)[/tex]
=> y-(-6)=2(x-0)
=> y+6 = 2x
=> y = 2x-6
Hence the slope intercept form of the equation is B) y=2x-6.
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Question 4 a) The following table shows the distribution of voters in an electior. for class prefect. Name Acquaye Borquaye Commey Number of votes 6 12 18 i) Draw a pie chart to illustrate the information. ii) What fraction of the votes was cast for Borquaye?
A circle chart, often known as a pie chart, is a means to summarize a set of nominal data or a visual depiction of the many values of a particular variable (e.g. percentage distribution).
A circle is what?A circle is created in the plane by each point that is a specific distance from another point (center). Thus, it is a curve made up of points that are separated from one another by a defined distance in the plane. Additionally, it is rotationally symmetric about center at every angle. Every pair of vertices in a circle's closed, two-dimensional plane are evenly spaced apart from the "center." A circular symmetry line is made by drawing a line through the circle. Additionally, it is rotationally symmetric the about center at every angle.
Here,
The pie chart is divided into sectors and segments, and each sector and segment corresponds to a specific amount of the overall (percentage).
The data is a representation of 360°. The pie is always valued at 100% overall.
A pie chart is useful for organising and displaying data by percentage of the total.
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Can absolute value equal zero?
Answer:
yes
Step-by-step explanation:
The absolute value is only greater than or equal to zero.
Mary and Ryan each have some sweets.
The ratio of the number of sweets Mary has to the number Ryan has is 3:2
If Mary gave 5 sweets to Ryan they would have the same number of sweets.
Work out how many sweets Mary and Ryan have altogether.
Answer:
Let x be the number of sweets that Ryan has.
Since the ratio of the number of sweets Mary has to the number Ryan has is 3:2, we can say that Mary has 3/2*x sweets.
We know that if Mary gave 5 sweets to Ryan they would have the same number of sweets, so we can write the following equation:
3/2*x -5 = x
By solving this equation, we can find that x = 10. So, Ryan has 10 sweets
Therefore, Mary has 3/2*10 = 15 sweets.
Altogether, Mary and Ryan have 15+10 = 25 sweets.
Answer: 25
Step-by-step explanation:
3x - 5 = 2x, so
x = 5.
And 5x = 5*5 = 25
What is the slope represented in the table?
Answer:
add up variables and divide by 2
Is zero positive proof?
No, The number zero is neither positive nor negative.
Aryabhata, who is known as a great astronomer of the classic age of India was the one who invented the digit “0” for which he became immortal but later on is given to Brahmagupta.
The numbers to the right of zero on the number line are positive and those on the left side are negative.
Positive numbers are greater than 0 and located to the right of 0 on a number line. Negative numbers are less than 0 and are located to the left of 0 on a number line.
Positive and negative numbers are sometimes called signed numbers.
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How many 2 1/7 inch pieces of thread can be
cut from a spool with 8 3/4 inches of thread?
A spool of thread measuring 8 3/4 inches long and 4 inches wide can be cut into 2 1/7 inch pieces.
How many pieces of thread can be cut ?In light of the conditions stated, come up with: [tex]$\frac{8 \frac{3}{4}}{2 \frac{1}{7}}$[/tex] To improper fractions, change the mixed numbers to: [tex]$\frac{\frac{35}{4}}{\frac{15}{7}}$[/tex] Multiply the reciprocal of a fraction to get its division: [tex]$\frac{35}{4} \times \frac{7}{15}$[/tex]
Mark this common element as a no-go: Multiplying [tex]$\frac{7}{4} \times \frac{7}{3}$[/tex] Mark the common element as absent: Multiplying [tex]$\frac{7 \times 7}{4 \times 3}$[/tex] . Put the following in one fraction : [tex]$\frac{49}{12}$[/tex] . The product or quotient should be
calculated.Find the biggest number that is greater than [tex]$\frac{49}{12}$[/tex] and less than or equal to it . A spool of thread measuring 8 3/4 inches long and 4 inches wide can be cut into 2 1/7 inch pieces.Otherwise, you or a device will need to count 127 turns (the irreducible repeat, independent of thread pitch), after which the half nut must be closed.
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Determine whether each of the following sentences is a proposition. If the sentence is a proposition, then write its negation (a) Have a nice day. (b) The soup is cold (c) The patient has diabetes.(d) The light is on (e) It's raining today (f) Do you like my new shoes? (g) The sky is purple (h) 2 + 3 = 6 0 Every prime number is even.(i) There is a number that is larger than 17
The sentence which is Proposition is b,c,d,e,g,h, i. We will find its Negation below.
What is Proposition?
An assertion that can be either true or untrue is referred to as a proposition (but not both). For instance, the statements "Paris is in France" (true), "London is in Denmark" (false), "2 equals 4" (true), and "4 Equals 7 (false)" are examples of propositions. The questions "what is your name?" and "complete your homework" are not propositions, nor are the statements "this sentence is wrong" "x is an even number" or "Socrates" (which is not even a phrase). A proposition's truth value refers to whether it is true or false.
What is Negation of Proposition?
The words " ¬" or " ~" are used to denote a statement's denial. For instance, "Arjun's dog has a black tail" is the given sentence. The statement "Arjun's dog does not have a black tail" is the negation of the one that has been said. As a result, the negation of the provided statement is false if the given statement is true.
Our first sentence is “Have a nice day”.
The phrase "Have a nice day" cannot be true or wrong, hence it cannot be a proposition. Additionally, a proposition is a declarative sentence, whereas this sentence is imperative.
The second sentence is "The soup is cold". Its Negation will be "The soup is not cold".
The third sentence is "The patient has diabetes". Its Negation will be "The patient does not have diabetes".
Fourth is "The light is on". Its Negation will be "The light is not on".
Fifth is "It’s raining today". Negation will be "It’s not raining today".
The Sixth is "you like my new shoes". This Sentence is not a proposition.
Seventh is "The sky is purple". Its Negation will be "The sky is not Purple".
Eight is "Every prime number is even". Its Negation will be "It’s not true that every prime number is even".
The ninth sentence is “There is a number that is larger than 17”. Its Negation will be "There is not a number that is larger than 17".
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1.4 unit conversion. (a) convert a mass of 2.2 kg into ounces and lbm. (b) convert 12 lbf /in2 into kpa and mmhg. (c) convert 160 hp into cal/s and btu/s. (d) convert 82 gallons into quarts and ml. (e) convert 34 in into m and cm.
Converted (a) 2.2 kg = 77.6 oz, 4.83 lbm. (b) 12 lbf/in2 = 82.7 kPa, 620.6 mmHg. (c) 160 hp = 119,360 cal/s, 88,000 Btu/s. (d) 82 gallons = 328 quarts, 313,981.8 mL. (e) 34 in = 0.8636 m, 86.36 cm.
What is conversion factor ?
A conversion factor is a ratio of two equivalent measurements used to convert a quantity from one unit to another.
(a) To convert 2.2 kg to ounces, we can use the conversion factor 1 kg = 35.274 oz. So, 2.2 kg = 2.2 * 35.274 oz = 77.6 oz. To convert 2.2 kg to lbm, we can use the conversion factor 1 kg = 2.205 lbm. So, 2.2 kg = 2.2 * 2.205 lbm = 4.83 lbm.
(b) To convert 12 lbf/in2 to kPa, we can use the conversion factor 1 lbf/in2 = 6.894 kPa. So, 12 lbf/in2 = 12 * 6.894 kPa = 82.7 kPa. To convert 12 lbf/in2 to mmHg, we can use the conversion factor 1 lbf/in2 = 51.715 mmHg. So, 12 lbf/in2 = 12 * 51.715 mmHg = 620.6 mmHg.
(c) To convert 160 hp to cal/s, we can use the conversion factor 1 hp = 746 cal/s. So, 160 hp = 160 * 746 cal/s = 119,360 cal/s. To convert 160 hp to Btu/s, we can use the conversion factor 1 hp = 550 Btu/s. So, 160 hp = 160 * 550 Btu/s = 88,000 Btu/s.
(d) To convert 82 gallons to quarts, we can use the conversion factor 1 gallon = 4 quarts. So, 82 gallons = 82 * 4 quarts = 328 quarts. To convert 82 gallons to mL, we can use the conversion factor 1 gallon = 3785.4 mL. So, 82 gallons = 82 * 3785.4 mL = 313,981.8 mL
(e) To convert 34 in to m, we can use the conversion factor 1 in = 0.0254 m. So, 34 in = 34 * 0.0254 m = 0.8636 m. To convert 34 in to cm, we can use the conversion factor 1 in = 2.54 cm. So, 34 in = 34 * 2.54 cm = 86.36 cm.
Converted (a) 2.2 kg = 77.6 oz, 4.83 lbm. (b) 12 lbf/in2 = 82.7 kPa, 620.6 mmHg. (c) 160 hp = 119,360 cal/s, 88,000 Btu/s. (d) 82 gallons = 328 quarts, 313,981.8 mL. (e) 34 in = 0.8636 m, 86.36 cm.
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[tex]\frac{tan(\frac{-2π}{3}} {sin\frac{7π}{4}} -sec (-π)\\[/tex]What is the exact value of the trigonometric expression? State your answer in simplified radical form
The exact value of the trigonometric expression [tex]\frac{tan-(2\pi/3) }{sin(7\pi /4)} - sec(-\pi )[/tex] in the simplified radical form is √6 + 1.
[tex]\frac{tan-(2\pi/3) }{sin(7\pi /4)} - sec(-\pi )[/tex]
We have the angle,
-2π/3 = -120° = (360 - 120)° = 240° = 60°
Put the value of -2π/3 in tan -2π/3, we get
tan -2π/3 = tan (60) = √3
7π/4 × 180/π = 7 × (180/4) = 7 × 45 = 315° = 45°
Put the value of 7π/4 in sin 7π/4, and we get
sin 7π/4 = sin (45°) = √2/2
sec (-π) = sec (π) = -1
Now, substitute all the values in the given equation,
= {√3/(√2/2)} - (-1)
= (2√3/√2) + 1
= (2√3 × √2/√2 × √2) +1
= (2√6/2) + 1
= √6 + 1
--The given question is incorrect, the correct question is
''What is the exact value of the trigonometric expression? [tex]\frac{tan-(2\pi/3) }{sin(7\pi /4)} - sec(-\pi )[/tex] State your answer in simplified radical form."--
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(7,349) (2,114) slope
Answer:
Slope = 47
Step-by-step explanation:
Slope:Substitute the x and y coordinates in the formula and find the slope.
(7 , 349 ) ; x₁ = 7 ; y₁ = 349
(2 , 114) ; x₂ = 2 ; y₂ = 114
[tex]\sf \boxed{Slope=\dfrac{y_2-y_1}{x_2-x_1}}[/tex]
[tex]\sf = \dfrac{114-349}{2-7}\\\\=\dfrac{-235}{-5}\\\\=47[/tex]
Answer: m=47
Step-by-step explanation:
[tex]\displaystyle\\The \ slope\ m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Given: (7,349) (2,114) Find: m
x₁=7 x₂=2 y₁=349 y₂=114
[tex]\displaystyle\\m=\frac{114-349}{2-7} \\\\\\m=\frac{-235}{-5} \\\\\\m=47[/tex]
what percentage of fruits and vegetables is water? 8 to 10 percent 20 to 25 percent ~50 percent 80 to 95 percent\
Answer:
About 50 percent
Step-by-step explanation:
Rewrite the following equations in the form y = mx + b.
8x + 2y = 10
12x - 3y = -25
Answer:
8x + 2y = 10 ==> y = -4x + 5
12x - 3y = -25 ==> y = 4x + 25/3
Step-by-step explanation:
8x + 2y = 10 ==> solve for y
2y = 10 - 8x ==> subtract 8x on both sides
(2y = 10 - 8x) / 2 ==> divide the equation by 2 to make 2y into y
y = 5 - 4x ==> simplify
y = -4x + 5 ==> put the equation in y=mx+b form
12x - 3y = -25 ==> solve for y
12x = -25 + 3y ==> make y positive by adding 3y on both sides
12x + 25 = 3y ==> add 25 on both sides to isolate y
(3y = 12x + 25) / 3 ==> divide the equation by 3 to make 3y into y
y = 4x + 25/3 ==> simplify
PLS HELP I WILL MARK IT BRAINLIEST
Consider the line -7x - 5y = -1
What is the slope of a line parallel to this line?
What is the slope of a line perpendicular to this line?
Answer:
I find it best to view these equation in the slope-intercept form.
-7x - 5y = -1
Let's rearrange the terms to isolate the y and put the equation in the y=mx+b form
5y = -1 + 7x
y = -1/5 + (7/1)x
or y = +(7/1) x + -1/5
Here m, the slope, = 7/1
A line parallel to this line will have the same slope or 7/1
A line perpendicular to this line will have a slope that is the negative inverse of this slope, in other words -1/7
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your roommate has six pets (fish, cat, turtle, dog, rock, and pony). he will take three of his six pets with him as he skips town and leaves you to pay rent. how many different collections of pets can he take if he cannot take both the dog and the cat (because they will fight like cats and dogs)?
The total number of different collections of pets your roommate can take is 10 + 10 = 20.
In this scenario, your roommate has two options for which pets to take with him: either the dog or the cat. If he takes the dog, he can take any two of the remaining five pets (fish, turtle, rock, pony). There are 5 choose 2 = 10 ways for him to do this. If he takes the cat, he can take any two of the remaining five pets (fish, turtle, rock, pony, dog). There are 5 choose 2 = 10 ways for him to do this.
Therefore, the total number of different collections of pets your roommate can take is 10 + 10 = 20.
To learn more about permutation and combination, refer to the link:brainly.com/question/13387529
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