need help urgently, don’t think the answers i have are right and i don’t know how to do it!!!
Answers
Answer:
See attached graphy-intercepts = [tex]\dfrac{3}{2}[/tex]Roots: x = - 3Vertical asymptote: x = -2
Horizontal asymptote y = 1End behavior
[tex]\mathrm{as}\:x\to \:+\infty \:,\:y\to \:1,\:\:\mathrm{and\:as}\:x\to \:-\infty \:,\:y\to \:1[/tex]
Table:
x y-4 1/2 - 3 0-1 20 3/21 4/32 5/43 6/5Note that the function is undefined at x = -2
Step-by-step explanation:
Given function is
[tex]f(x) = \dfrac{\left(x^2-9\right)}{\left(x^2-x-6\right)}[/tex]
Part 1
Graph attached
y-intercepts can be found by finding f(0) ie the value of f(x) at x = 0
[tex]f(0) = \dfrac{\left(0^2-9\right)}{\left(0^2-0-6\right)} = \dfrac{-9}{-6} = \dfrac{3}{2}[/tex]
Roots of a function can be found by setting f(x) = 0 and solving for x
Setting f(x) = 0
==> [tex]\dfrac{x^2-9}{x^2-x-6} = 0\\\\[/tex]
We can factor the numerator as follows:
x² - 9 = (x + 3) (x -3) since (a + b)(a-b) = a² - b²
Denominator can be factored as follows
x² - x - 6 = (x-3)(x+2)
So
[tex]f(x) = \dfrac{(x + 3)(x-3)}{(x-3)(x+2)}\\\\[/tex]
The (x-3) term cancels leaving
[tex]f(x) = \dfrac{x+3}{x+2}[/tex]
Setting this equal to 0 gives
[tex]\dfrac{x+3}{x+2} = 0[/tex]
This is 0 when x + 3 = 0 or x = -3
So there is only one root and that is x = -3
Asymptotes
The vertical asymptote occurs when at a value of x when the denominator becomes 0
The given function has been factored as
[tex]f(x) = \dfrac{x + 3}{x + 2}[/tex]
The denominator becomes 0 at x = -2
Vertical asymptote is x = - 2
To find the horizontal asymptote use the fact that when the degrees of the numerator and denominator are equal, the horizontal asymptote is given by
[tex]y=\dfrac{\mathrm{numerator's\:leading\:coefficient}}{\mathrm{denominator's\:leading\:coefficient}}[/tex]
The degree of the numerator x + 3 is 1 and the degree of the denominator x + 2 is also 1
So the horizontal asymptote is y = 1/1 = 1
y = 1 is the horizontal asymptote
End behavior is the behavior of the function as x → ±∞
This is determined by examining the leading term of the function and determining what its behavior is as x → ±∞
In the function
[tex]f(x) = \dfrac{x + 3}{x + 2}[/tex]
which is the factored form of the originally given function
the domain of x = all real numbers with the exception of -2 since at x = -2, the function is undefined
The end behavior can be determined by finding the limit of f(x) as x tends to infinity
[tex]\lim _{x\to \infty \:}\left(\dfrac{x+3}{x+2}\right)\\\\\dfrac{x+3}{x+2} \text{ can be transformed by dividing by x both numerator and denomiator :}\\\\\\=\dfrac{\dfrac{x}{x}+\dfrac{3}{x}}{\dfrac{x}{x}+\dfrac{2}{x}}\\\\\\=\dfrac{1+\frac{3}{x}}{1+\dfrac{2}{x}}[/tex]
[tex]\lim _{x\to \infty \:}\left(\dfrac{x+3}{x+2}\right) \\\\\\\\=\lim _{x\to \infty \:}\left(\dfrac{1+\dfrac{3}{x}}{1+\dfrac{2}{x}}\right)\\\\\\\\=\dfrac{\lim _{x\to \infty \:}\left(1+\dfrac{3}{x}\right)}{\lim _{x\to \infty \:}\left(1+\dfrac{2}{x}\right)}[/tex]
[tex]\lim _{x\to \infty \:}\left(1+\dfrac{3}{x}\right) = 1\\\\\lim _{x\to \infty \:}\left(1+\dfrac{2}{x}\right) = 1[/tex]
[tex]\lim _{x\to \:-\infty \:}\left(\dfrac{x+3}{x+2}\right) = 1[/tex]
End behavior
[tex]\mathrm{as}\:x\to \:+\infty \:,\:y\to \:1,\:\:\mathrm{and\:as}\:x\to \:-\infty \:,\:y\to \:1[/tex]
Table:
x y
-4 1/2
- 3 0
-1 2
0 3/2
1 4/3
2 5/4
3 6/5
Note that the function is undefined at x = -2
Related Questions
Focus: (-5,3); Directrix: y = 1
Answers
The equation of the parabola is: y = (1/4)(x-3)²+ 2
In Parabola mathematics, it is defined as a set of points that are equidistant from a fixed point called the focus and a fixed line called the directrix. In this case, we are given the focus (3,5) and the directrix y=1, y=1, and we need to find the equation of the parabola.
To find the equation of the parabola, we first need to determine the vertex. The vertex is the midpoint between the focus and the directrix, which in this case is (3,3). Since the parabola is symmetric, we know that the axis of symmetry passes through the vertex and is perpendicular to the directrix. Therefore, the equation of the axis of symmetry is x=3.
Next, we need to find the distance between a point on the parabola and the focus, as well as the distance between that same point and the directrix. Let (x,y) be a point on the parabola. The distance between (x,y) and the focus is given by the distance formula: √((x-3)² + (y-5)²)
The distance between (x,y) and the directrix is simply the absolute value of the difference between y and 1: |y-1|
Since the point (x,y) is equidistant from the focus and the directrix, we have: √((x-3)²+ (y-5)²) = |y-1|
Squaring both sides and simplifying, we get: (x-3)²= 4(y-2)
Therefore, the equation of the parabola is: y = (1/4)(x-3)²+ 2
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NOTE : I HAVE ANSWERED THE QUESTION IN GENERAL AS GIVEN QUESTION IS INCOMPLETE.
Complete Question : Find the Parabola with Focus (3,5) and Directrix y=1 (3,5) , y=1
What is the domain of f(x)? {x | 1 < x < 5} {x | 1 < x < 5} {y | −4 < y < 1} {y | −4 < y < 1}
Answers
The domain of function f(x) is given as follows:
{x | 1 ≤ x < 5}.
How to define the domain and range of a function?The domain of a function is defined as the set containing all possible input values of the function, that is, all the values assumed by the independent variable x in the context of the function.The range of a function is defined as the set containing all possible output values of the function, that is, all the values assumed by the dependent variable y in the context of the function.The values of x of the function given at the end of the answer are as follows:
Starts at x = 1(closed interval).Ends at x = 5 (open interval).Hence the domain is given as follows:
{x | 1 ≤ x < 5}.
Missing InformationThe function is given by the image presented at the end of the answer.
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Answer:
A - {x | 1 < x < 5}
Step-by-step explanation:
took the Quiz
The volume of a tree stump can be modeled by considering it as a right cylinder. Xavier measures its height as 2.1 ft and its circumference as 61 in. Find the volume of the stump in cubic inches. Round your answer to the nearest tenth if necessary.
Answers
The volume of the stump is 7451.9 cubic inches.
How to find the volume of the stump in cubic inches?The volume of a cylinder can be calculated using formula below:
V = πr²h
where r is the radius and h is the height of the cylinder
We have circumference (C) = 61 in.
Let's find the radius (r) using the formula:
C = 2πr
61 = 2 * 22/7 * r
r = 9.70 in
h = 2.1 ft = 2.1 * 12 = 25.2 in
Substituting into V = πr²h:
V = 22/7 * 9.70² * 25.2
V = 7451.9 cubic inches
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879 dived by 8 with remainder ad fraction
Answers
Answer: 109.875
Step-by-step explanation: 879 / 8 = 109.875 because if you divide 8 by 9 you get 1 so after you would divide 79 by 8 = 9.875 so then you put 109 then after but the decimals 109.875.
mathmatically indication example with solution
Answers
A mathematically indication example would be to solve the equation 3x + 2 = 14 for the value of x. The solution would be 4.
How to solve the equation ?Looking for a mathematically indication example, we can consider a simple mathematical equation with one variable and solve it.
The equation would be 3 x + 2 = 14.
So we can solve for the equation to be :
3x + 2 - 2 = 14 - 2
3x = 12
3 x / 3 = 12 / 3
x = 4
In conclusion, the mathematically indication example would be 3x + 2 = 14 and the value of x would be 4.
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Leigh designs and conducts a computer simulation with 30 trials and uses the data from the stimulation to create the relative frequency bar graph shown. The graph shows the relative frequency of the number of spins needed for a spinner divided into 6 equal sections labeled A through F on each letter at least once
Answers
The experimental probability that more than 10 spins are needed to land on each letter at least once is 75%
How to explain the probabilityExperimental probability is a type of probability that is based on actual observations or experiments.
In experimental probability, the probability of an event occurring is calculated by conducting experiments and observing the outcomes. The probability of the event is then calculated by dividing the number of times the event occurred by the total number of trials or experiments.
In this case, experimental probability = number of times the event occurred / total number of trials
Experimental probability = 0.1 + 0.35 + 0.3 / 1
= 0.75 / 1
= 75%
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Help Quickly! Which line in the graph contains the point (4,3) and has a slope of 2/5?
*Giving Brainlyest if correct*
A. line r
B. line p
C. line s
D. line t
Answers
Which of the following is an example of a statistical experiment?
A Twenty people in a neighborhood are asked if they want more streetlights on the street.
OB. More streetlights are installed on one street and people are then asked if they like the change.
OC. The number of accidents on the street is compared to last year's rate.
OD. People are asked to call a number to comment about the need for new streetlights.
Answers
Answer:
B. More streetlights are installed on one street and people are then asked if they like the change.
Step-by-step explanation:
An experiment is a type of research method that involves manipulating one or more variables and measuring their effects on other variables. In this case, the experiment is to change the color of the product packaging and see how many people like the change. This is because the outcome of the experiment (the number of people who like the change) depends on chance and can be measured using numerical data. The other options are not experiments, but surveys or observations. Surveys involve asking people questions and collecting their opinions or preferences. Observations involve watching and recording people's behavior or reactions without interfering with them.
What is the volume of a square based pyramid with based side lengths of 6cm, a slant height of 7 cm, and a height of 5cm
Answers
Answer:
60 cm^3
Step-by-step explanation:
The formula for volume of a pyramid is
V = 1/3Bh, where B is the area of the base and h is the regular height (aka the altitude that connects the top of the pyramid and the base so we can simply ignore the slant height in the problem)
Step 1: The base of a square pyramid is a square and the formula for area (A) of a square is A = s^2, where s is the side.
Since we're told that the length of the base side length is 6 cm, we can find the area of the base:
A = 6^2 = 36
Step 2: Now, we can plug in 36 for B and 5 for h in the volume formula to find the volume:
V = 1/3(36)(5)
V = 12 * 5
V = 60 cm^3
Find the greatest common factor of 56xy and 16y³.
Answers
Answer:
8y
Step-by-step explanation:
Lets put these two parts into addition to make it easier.
(y)56x + 16y^2
(8y)7x + 2y^2
8y is the GCF(grates common factor)
Roughly how much more does auto insurance cost for a 16 year old compared to a middle aged (40-50 year old) driver
Answers
A 16-year-old on their own policy pays on average $4,000 more per year than a 50-year-old would have to pay
The cost of insuranceAuto insurance costs vary significantly depending on factors such as location, vehicle type, and driving history. However, on average, a 16-year-old driver can expect to pay significantly more for auto insurance compared to a middle-aged driver (40-50 years old).
The exact amount varies, but it's not uncommon for a 16-year-old driver to pay two to three times more for auto insurance than a middle-aged driver. This is mainly because younger drivers are considered riskier due to their inexperience and higher likelihood of being involved in accidents.
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The dosage the pharmacy carries in stock (on hand), is different than the prescribers order. Use ratio and proportion to calculate the total quantity of tablets to dispense for each of the prescriptions below: Order: Zocor 40 mg po qd for 60 days On hand: 20 mg tabs How many 20 mg tabs should be given? Give:
Answers
Using ratios and proportions, the number of 20 mg tabs that should be given in place of 40 mg po qd for 60 days is 120 tabs.
How the number is determined:Using ratios and proportions, the number of tabs of 20 mg that should be given in place of 40 mg qd for 60 days is determined as follows:
Order: Zocor 40 mg po qd for 60 days
= 60 tabs since it is once per day (qd)
Total mg = 2,400 mg (40 mg x 60 tabs)
On hand: 20 mg tabs
Proportionately, 20 mg = 120 tabs (2 x 60) since 40 mg is for 60 tabs
Total mg = 2,400 mg (20 mg x 120 tabs)
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Please help me find the perpendicular height
Answers
The perpendicular height of the pyramid is 83.65 cm
How to find the perpendicular height?To find the perpendicular height we can define a right triangle.
The perpendicular height is one leg, and the other leg will be half of the diagonal of the base.
The base is a square whose sidelength is 23cm, then the diagonal is:
D = √( (23cm)² + (23cm)²)
D = 32.527cm
Half of that is
D/2 = 32.527cm/2 = 16.26cm
Now, we know one side of the right triangle and the angle of 79°, for which the known cathetus is adjacent.
The perpendicular height is the opposite cathetus.
Then we can use the relation:
tan(79°) = H/16.26cm
Solving for H, the heigt, we will get.
H = tan(79°)*16.26cm = 83.65 cm
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The figure below is a net for a square pyramid. What is the surface area of the square pyramid, in square inches?
Answers
Answer:
183.89
Step-by-step explanation:
S = square area + area of 4 triangles =
7.1^2 + 4*0.5*9.4*7.1 = 183.89
Answer: your answer is 266.44 square inches
Explanation: Triangles:
6.1x7.6=46.36in
Each triangle is 46.36in
46.36x4=185.44in
Rectangle:
9x9=81in
The rectangle is 81in
All together:
185.44+81=266.44in
So the square is the easiest do 4×4=16
The triangles its just Base×Height/2 in that order so 4×3=12/2=6
Mulitply 6 by 4 because there's 4 triangles and add 16 so 6×4=24+16=40
Hope this helped:)
Finding the angle when given the right angle and two sides. Please show explanation. Thank you.
Answers
The measure of angle A in the right triangle is 75.52°
What is the measure of angle A?The figure in the image is a right triangle.
Measure of angle A = ?
Adjacent to angle A = 2
Hypotenuse = 8
To solve for the measure of angle A, we use the trigonometric ratio.
Note: cosine = adjacent / hypotensue
Hence:
cos( A) = adjacent / hypotensue
cos( A ) = 2/8
cos( A ) = 1/4
Take the cos inverse
A = cos⁻¹( 1/4 )
A = 75.52°
Therefore, the measure of the angle is 75.52 degree.
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here are five number cards
2,5,7,8,9
one of the cards is removed and the mean average of the remaining four number cards is 6
which card was removed
show your working
Answers
Answer:
7
Step-by-step explanation:
Since one card was removed:
6 = x/4
x = 6 X 4
x = 24
Then you sum the numbers on the five cards and subtract 24 from it
(2 + 5 + 7 + 8 + 9) - 24
= 31 - 24
= 7
Therefore card with number 7 was removed.
HELP ASAP PHOTO INCLUDED
Answers
I cannot solve that problem at the moment.
Step-by-step explanation:
But I will help you in the future
Lai Lal Chinese Restaurant has seven items in its breakfast menu. The management of Lai Lai has just acquired some data and they would like to find out both popularity and profitability of its breakfast menu items based on their selling price, food cost percentage, sales volume and contribution margin (CM) from the past period. The financial data for the selling price, sales volume, and individual food cost dollar amounts are presented in the table below:
Breakfast Selling Price Food Cost Menu Item ($) (52 Sales Volume А $10.00 $3.00 250 B $16.00 $6.00 50 с $18.45 $8.00 60 D $14.75 $4.25 300 E $8.75 $2.50 80 F $12.50 $5.75 180 G $9.00 $2.60 280 TOTAL 1.200
Based on the information given in the table above, what are the specific classification of the breakfast menu items based on their profitability and popularity in order?
Answers
Based on the contribution margin and the sales volume, Menu Item D is the most profitable and popular.
What is the contribution margin?The contribution margin is the profitability that is shown in the difference between the selling price and the variable cost per unit of an item.
The contribution margin can be computed per unit or in total. Using the sales volume to multiply the contribution margin per item gives the total contribution margin in dollars.
Breakfast Selling Price Food Cost Sales Contribution Margin
Menu Item ($) ($) Volume Unit Total
А $10.00 $3.00 250 $7.00 $1,750
B $16.00 $6.00 50 $10.00 $500
C $18.45 $8.00 60 $10.45 $627
D $14.75 $4.25 300 $10.50 $3,150
E $8.75 $2.50 80 $6.25 $500
F $12.50 $5.75 180 $6.75 $1,215
G $9.00 $2.60 280 $6.40 $1,792
TOTAL 1,200
Thus, we can conclude that Menu Item D enjoys the highest profitability and popularity.
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What is the amount of discount
Answers
Answer: 26.40
Step-by-step explanation:
i dont know the answer to this
Answers
A small toy rocket is launched from a 48-foot pad. The height (h, in feet) of the rocket t seconds after
taking off is given by the formula h = - 3t2 +0t + 48. How long will it take the rocket to hit the
ground?
t =
Answers
Okay, here are the steps to solve this problem:
1) The height (h) of the rocket t seconds after launch is given as: h = - 3t2 + 0t + 48
2) We want to find the time (t) when the rocket hits the ground (h = 0)
3) Set the formula equal to 0: - 3t2 + 0t + 48 = 0
4) Factor the left side: - 3(t2 - 0t) + 48 = 0
5) Solve for t2 - 0t: t2 - 0t = 16
6) Add 0t to both sides: t2 = 16 + 0t
7) Take the square root of both sides: t = 4
Therefore, the time for the rocket to hit the ground is 4 seconds.
So in this case, t = 4
Let me know if you have any other questions!
Answer:
4 seconds.
Step-by-step explanation:
When the rocket hits the ground, its height will be 0. Therefore, since we are given an expression for the height of the rocket dependent on the time, we can simply set it equal to 0 and solve for the time and find how long the rocket will take to hit the ground. I'm assuming the equation is[tex]h = -3t^{2} + 48[/tex]
Now set this equal to 0
[tex]0 = -3t^2+48[/tex]. Solve for t by isolating it.
[tex]-48 = -3t^2[/tex]
[tex]16 = t^2[/tex]
From here, by taking the square root, we see that t is either equal to 4 or -4 in seconds. Since we can't have negative time, we can clearly see that the answer is 4 seconds.
Hope this helps
Brenda types 15 words per minute. How long will it take her to type 750 words?
Answers
It will take Brenda 50 minutes to type 750 words at a rate of 15 words per minute.
To solve this problem, we can use the formula:
time = amount of work / rate
In this case, the amount of work is typing 750 words, and the rate is 15 words per minute. Substituting these values into the formula, we get:
time = 750 / 15 = 50 minutes
This calculation assumes that Brenda types at a constant rate of 15 words per minute. If her typing speed varies, the time it takes her to type 750 words may be different.
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Diondra wants to know the most popular movie of this year but is unsure of the best way to determine this answer. Which of the following questions would Diondra ask that does NOT allow for variability?
Which movie did her best friend like the most?
How many awards did each movie win?
What is the total dollar amount that each movie made from ticket sales?
How many weeks did each movie play in the theater?
Answers
The question that Diondra would ask that does not allow for variability is A. Which movie did her best friend like the most?
How does this question not show variability ?The other three questions ("How many awards did each movie win?", "What is the total dollar amount that each movie made from ticket sales?", and "How many weeks did each movie play in the theater?") all offer metrics by which a movie's popularity could be measured, and those measurements could vary from movie to movie.
However, the question about her best friend's favorite movie depends solely on the opinion of one individual, not a variable measure, and therefore doesn't allow for variability.
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johnny can build in 3 1/2 lego planes in 60 minutes. how many can he build in 40 minutes?
Answers
The number of lego planes that can be build in 40 minutes is A = 2.33
Given data ,
Johnny can build in 3 1/2 lego planes in 60 minutes
On dividing the number of planes he can build in 60 minutes (3 1/2) by 60:
From the proportion , we get
To find out how many planes he can build in 40 minutes, we can multiply the amount he can build in one minute by 40:
3.5 / 60 = A / 40
Multiply by 40 on both sides , we get
A = 2.33
Hence , Johnny can build approximately 2.33 lego planes in 40 minutes
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How is the graph of y(x-1)²-3 transformed to produce the graph of y(x+4)²
O The graph is translated left 5 units, compressed vertically by a factor of 2, and translated up 3 units.
O The graph is stretched vertically by a factor of 2, translated left 5 units, and translated up 3 units.
The graph is translated left 5 units, compressed horizontally by a factor of 2, and translated down 3 units.
O The graph is stretched horizontally by a factor of 2, translated left 5 units, and translated down 3 units.
Mark this and return
Save and Exit
Next
Submit
Answers
The transformations are:
Shift up 3 units.
Shift left 5 units.
Vertical compression of scale factor 2.
The correct option is the first one.
Here, we have,
Here we start with the original function:
y = (x - 1)^2 - 3
And it will be transformed into the new function:
y = (1/2)*(x + 4)^2
So let's start with the first function, and apply transformations until we reach the new one.
y = (x - 1)^2 - 3
If we shift it up by 3 units, then we get:
y = [ (x - 1)^2 - 3 ] + 3 = (x - 1)^2
If now we shift it to the left 5 units, then we get:
y = ( (x + 5) - 1)^2 = (x + 4)^2
finally, we compress the graph by a factor of 2, so we get:
y = (1/2)*(x + 4)^2
The order may be different, but from that we conclude that the correct option is the first option.
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complete question:
graph of y = (x- 1)2 -3 transformed to produce the graph of y = - 1/2(X+-4)2?
O The graph is translated left 5 units, compressed vertically by a factor a of 2, and translated up 3 units.
The graph is stretched vertically by a factor of 2, translated left 5 units, and translated up 3 units.
• The graph is translated left 5 units, compressed horizontally by a factor of 2, and translated down 3 units.
• The graph is stretched horizontally by a factor of 7, translated left 5 units, and translated down 3 units:
x=1
x=3
z=x-25y
print(z)
Answers
The output of the program for the variable z is -22 or it returns an error if z = x - 25y
Evaluating the output of the programFrom the question, we have the following parameters that can be used in our computation:
x = 1
x = 3
z = x - 25y
print(z)
The value of the variable y is not given
So, the program would return an error
However, if the complete program is as follows (removing the variable y)
x = 1
x = 3
z = x - 25
print(z)
Using the above as a guide, we have the following:
The final value of x is 3
So, we have
z = 3 - 25
Evaluate
z = -22
This means that the output of the program for z is -22
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Answer these 3 questions if not able to answer all try question 10 thank you
Answers
9. A function p(x) with x intercepts of (-1,0) and (3,0) can be written as p(x) = a(x+1)(x-3), where 'a' is the leading coefficient.
10. The vertex form of the parabola is given by f(x) = a(x-h)^2 + k, where (h,k) is the vertex of the parabola. Since the parabola is translated 5 units down and 2 units right from the parent function f(x), its vertex is at (-2+2, 6-5) = (0,1). We can substitute (-2,6) into the equation and solve for 'a' to get the final equation.
f(x) = a(x-0)^2 + 1
6 = a(-2-0)^2 + 1
5 = 4a
a = 5/4
Therefore, the equation of the parabola in vertex form is f(x) = (5/4)(x-0)^2 + 1.
(If this doesn’t seem right to you comment!)
WINGSUIT A wingsuit flyer jumps off a tall cliff. He falls freely for a few seconds before deploying the wingsuit and -4.9x² +420, where y is = slowing his descent. His height during the freefall can be modeled by the function y the height above the ground in meters and x is the time in seconds. After deploying the wingsuit, the flyer's height is given by the function y = −3x + 200. deploy the wingsuit?
Answers
The total height of the flyer at any time after deploying the wingsuit would be;
y = -3x + 200 + (-4.9t² + 420),
Now, Based on the given information, we can use the two functions to determine the height of the wingsuit flyer at a particular time.
During the freefall, the height of the flyer can be calculated using the function
y = -4.9x² + 420.
Let's say the flyer falls freely for t seconds before deploying the wingsuit.
Therefore, the height at the moment of deploying the wingsuit would be,
y = -4.9t² + 420.
After deploying the wingsuit, the height of the flyer is given by the function
y = -3x + 200.
We can combine these two functions to get the total height of the flyer at any given time after deploying the wingsuit.
So, the total height of the flyer at any time after deploying the wingsuit would be;
y = -3x + 200 + (-4.9t² + 420),
where x is the time after deploying the wingsuit and t is the time of freefall before deploying the wingsuit.
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URGENT HELP PLEASE!!!
In a class of students, the following data table summarizes how many students have a
a
cat or a dog. What is the probability that a student chosen randomly from the class
has a cat and a dog?
Answers
Answer: 5/13
Step-by-step explanation:
To solve this problem, we can use the formula for conditional probability:
P(A|B) = P(A and B) / P(B)
where P(A and B) is the probability of both events A and B happening, and P(B) is the probability of event B happening.
Let's first calculate the total number of people in the class:
Total number of people = 5 + 6 + 2 + 11 = 24
Now, let's calculate the probability of having a cat and a dog:
P(cat and dog) = 5 / 24
Next, let's calculate the probability of having a cat:
P(cat) = (5 + 6 + 2) / 24 = 13 / 24
Finally, let's calculate the probability of having no dog:
P(no dog) = (6 + 11) / 24 = 17 / 24
Using the formula for conditional probability, we can calculate the probability of having both a cat and a dog given that a person has a cat:
P(cat and dog | cat) = P(cat and dog) / P(cat) = (5 / 24) / (13 / 24) = 5 / 13
Therefore, the probability that a student chosen randomly from the class has a cat and a dog is 5/13.
One shirt at H&M cost $7. what is the cost of 40 shirts
Answers
Answer:
$280
Step-by-step explanation:
7•40=$280
