Answer:
Price of hamburgers = $2
Price of white-dogs = $3
Step-by-step explanation:
Let
The number price of hamburgers be x
The number price of white-dogs be y
Then the first family buys 3 hamburgers and 2 white -dogs for $13
3x + 2y = 13-----------------------------(1)
Another first family buys 2 hamburgers and 5 white -dogs for $16
2x + 5y = 16----------------------------(2)
To solve let us multiply eq(1) by 2 and eq(2) by 3, we get
6x + 4y = 26-----------------------------(3)
6x + 15y = 48----------------------------(4)
subracting (3) from (4)
6x + 15y = 48
6x + 4y = 26
(-)
-------------------------
11y = 22
---------------------------
[tex]y =\frac{22}{11}[/tex]
y =2
Now substituting the value of y in eq(1),
3x + 2(2) = 13
3x + 4 = 13
3x = 13-4
3x = 9
x =[tex]\frac{9}{3}[/tex]
x =3
Sam makes $400 per week plus $20 commission on each new sell phone plan he sells. Write an equation to determine how many new plans she sold to earn $680 last week
Answer:
She sold 14 new plans to earn $680 last week.
Step-by-step explanation:
$400 + 20(x) = $680
Take 400 away from total cost. So, 680 - 400 = 280.
Now, divide 280 by 20, and x = 14.
The equation would be $400 + 20(14) = $680
help me with 17.
(I know the image is upside down, but there's a flip button and u can click It to flip it)
Answer:
look at the photo below for the answer.
:)
A rocket is located on a platform that is 200 feet above a deep canyon. After launching the rocket with an initial velocity of 50 ft/sec, the platform is moved.
a.) What is the max height the rocket will reach?
b.) When will it reach the max height?
c.) When will it be 300 feet off the ground?
d.) How high will it be after 4.2 seconds?
e.) Where will the rocket be after seven seconds?
Answer:
a) Max height it will reach is 327.55 ft above the ground
b) It will reach max height after 5.1 seconds
c) It will be 300 feet off the ground at 12 seconds
d) It will be 305 ft above the ground
e) The rocket will be 247.55 ft above the ground after seven seconds
Step-by-step explanation:
a) Using the equations of kinematics:
v² = v_i² + 2 g Δy
where
v is the final velocityv_i is the initial velocityg is the acceleration due to gravityΔy is the rocket's displacementTherefore,
0² = 50² + 2(- 9.8) Δy
(the negative sign shows that the positive direction is upwards. Gravity acts downwards)
Δy = -(50)² / 2(-9.8)
Δy = 127.55 ft
Thus, the maximum height that the rocket reaches will be
200 ft + 127.55 ft
= 327.55 ft above the ground
b) Using the equations of kinematics:
Δy = [(v + v_i) / 2 ] × t
t = Δy / [(v + v_i) / 2 ]
t = 127.55 / [(0 + 50) / 2]
t = 5.1 seconds
Therefore, the rocket will reach its maximum height after 5.1 seconds.
c) Using the equations of kinematics:
t₃₀₀ = Δy / [(v + v_i) / 2 ]
t₃₀₀ = 300 / [(0 + 50) / 2]
t₃₀₀ = 12 seconds
Therefore, the rocket will reach 300 feet after 12 seconds
d) Using the equations of kinematics:
Δy = [(v + v_i) / 2 ] × t
Δy = [(0 + 50) / 2] × 4.2
Δy = 105 ft
Therefore, the rocket will be
105 ft + 200 ft
= 305 ft above the ground after 4.2 seconds
e) Using the equations of kinematics:
Δy = [(v + v_i) / 2 ] × t
Δy = [(0 + 50) / 2] × 7
Δy = 175 ft
Therefore,
175 - 127.55 = 47.55 ft
Thus, the rocket will be
47.55 ft + 200 ft
= 247.55 ft above the ground after seven seconds
The expression 120-15x represents how many invitations Luanne has to address after x days. The expression 120 + 15(7-x) represents the number of invitations Darius has to address after x days. After how many days do Luanne and Darius have the same sumber of invitations to address?
Answer:
not possible.
Step-by-step explanation:
number of invitations luanne has to address after x days = 120-15x
number of invitations Darius has to address after x days = 120 + 15(7-x)
so, if the number of invitations should be the same for both of them,
we have to equate their number of invitations
120-15x = 120 + 15(7-x)
subtracting 120 from both the sides,
-15x = 15(7-x) = 105 -15x
adding we 15x on both sides, we wont find any solution for x.
so, this isnt possible or the question must be wrong.
The unemployment rate has risen more than a percentage point to 8.8% in February from 6.7% last November. What is the relative change in the unemployment rate expressed as a percentage? The unemployment rate has risen what percent?
Answer:
7.6
Step-by-step explanation:
Final answer:
The relative change in the unemployment rate expressed as a percentage is approximately 31.34%.
Explanation:
The relative change in the unemployment rate expressed as a percentage can be computed by taking the difference between the two unemployment rates and dividing it by the initial unemployment rate. In this case, the initial unemployment rate was 6.7% and the new unemployment rate is 8.8%, so the change is 8.8% - 6.7% = 2.1%. To express this change as a percentage, we divide the change by the initial unemployment rate and multiply by 100: (2.1% / 6.7%) * 100 = 31.34%. Therefore, the unemployment rate has risen by approximately 31.34%.
A painting is covering up some of the tiles on the wall. The tiled wall is shaped like a rectangle . There are 28 square tiles on the whole wall. How many of the tiles are covered by the painting?
Answer:
The number of tiles are covered by the painting are 12.
Step-by-step explanation:
Consider the provided information.
The painting is covering up some of the tiles on the wall as shown below:
Here it is given that there are 28 squares tiles on the wall.
Total tiles = Number of tiles covered by the painting - uncovered tiles
28 = Number of tiles covered by the painting - 16
Number of tiles covered by the painting = 28 - 16
Number of tiles covered by the painting = 12
Hence, the number of tiles are covered by the painting are 12.
Please help with this question on area!
Answer:
Step-by-step explanation:
The area of a triangle is one-half times the base times the height. The height of both triangles is 4 (the height of the triangle on the left is "outside" of the triangle). So the area of the triangle on the left is
[tex]A=\frac{1}{2}(6)(4)[/tex] so the area is 12
The area of the triangle on the right is
[tex]A=\frac{1}{2}(8)(4)[/tex] so the area is 16.
Adding those 2 areas together gives you a total area of 28 in squared.
A T-shirt makes wants to open his first store. If he chooses the store on Main Street, he will pay $640 in rent and will charge $30 per T-shirt. If he chooses the store on Broad Street, he will pay $450 in rent and will charge $25 per T-shirt. How many T-shirts would he have to sell in 1 month to make the same profit at either location?
Answer:38 t-shirts
Step-by-step explanation:
P=30t-640 main street
p=25t-450 broad street
30t-640=25t-450
30t-25t-640=-450
5t-640+640=-450+640
5t/5=190/5
t=38
enjoy
f(m) = 2.5 + 0.12m
If Natalie paid $6.82 for one call, how many minutes long was it?
Select one:
A. 28
B. 36
C. 42
D. 45
Answer:
36 minutes long
Step-by-step explanation:
6.82 = 2.5 + 0.12m
4.32 = 0.12m
36 = m; 36 minutes long.
Answer:
B. 36.
Step-by-step explanation:
Substituting 6.82 for m:
6.82 = 2.5 + 0.12m
0.12 m = 6.82 - 2.5
0.12m = 4.32
m = 4.32 / 0.12
m = 36 minutes.
In the figure, BP is an angle bisector of ∠CBD. Find x if m∠1 = 4x - 8 and m∠2 = 3x + 2.
A) 5
B) 7
C) 9
D) 10
I am spacing out the words of the link for the picture, so just put the symbols/letters into place. https://www. usatestprep.com /modules/questions /files /image/ 451840.j pg
Answer:
Option D) 10
Therefore the value of x is 10.
Step-by-step explanation:
Given:
BP is an angle bisector of ∠CBD.
m∠1 = 4x - 8 and
m∠2 = 3x + 2.
To Find:
x = ?
Solution:
Angle Bisector:
A line that splits an angle into two equal angles.
Bisect means to divide into two equal parts.
Here, BP is an angle bisector of ∠CBD.
∴ m∠ 1 = m∠ 2
Substituting the given values we get
[tex](4x-8)=(3x+2)\\\\4x-3x=8+2\\\\x=10\\\\\therefore x = 10[/tex]
Therefore the value of x is 10.
Geometry Help!!!
I can’t seem to find the missing third side of the isosceles triangle.
Doesn’t have to equal 180?
This is the equation I’m doing but doesn’t give me an answer from the choices: 12.25 + 12.25 + x =180
===============================
Explanation:
Let's say we had a triangle with side lengths a,b,c.
If we know that a = 12.25 and b = 12.25, then the third side c has its length restricted in such a way that
b-a < c < b+a
This is a variation of the triangle inequality theorem.
-------------
So,
b - a < c < b + a
12.25 - 12.25 < c < 12.25 + 12.25
0 < c < 24.5
which means the third side c is between 0 inches and 24.5 inches.
The value of c cannot be 0, and it cannot be 24.5 either.
Among the answer choices given, we see that only 24.0 is the only valid option here. The other two choices are too large.
-------------
Side Note: If your teacher gave you two angles (instead of two sides) to be 12.25 degrees, and wanted the third missing angle of the triangle, then you would be correct in having 12.25+12.25+x = 180 as your first step.
Can the positive integer p be expressed as the product of two integers, each of which is greater than 1?1) 31 < p < 372) p is odd
Answer:
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Step-by-step explanation:
Consider the provided information.
Can the positive integer p be expressed as the product of two integers, each of which is greater than 1.
Statement 1: 31 < p < 37
The value of p is greater than 31 and less than 37.
Thus the possible values of p are: 32, 33, 34, 35, 36
All these numbers can be expressed as the product of two integers. Each of which is greater than 1,
Hence, statement 1 Alone is Sufficient.
Statement 2: p is odd
The statement is not sufficient because All prime numbers are odd numbers and if p is a prime number then p can't be expressed as the product of two integers, each of which is greater than 1.
Although if p is odd it is not necessarily to be prime for example 9 is an odd number but not a prime number. 9 can be expressed as the product of two integers, each of which is greater than 1.
Therefore, statement 2 Alone is not sufficient.
Final answer:
1. Statement 1 alone is sufficient to determine if the integer p can be expressed as the product of two integers greater than 1 or not.
2. Statement 2 alone is not sufficient.
Explanation:
Consider the provided information. Can the positive integer p be expressed as the product of two integers, each of which is greater than 1.
Statement 1: 31 < p < 37
The value of p is greater than 31 and less than 37. The possible values of p are 32, 33, 34, 35, 36. All these numbers can be expressed as the product of two integers each greater than 1. Therefore, statement 1 alone is sufficient.
Statement 2: p is odd
The statement is not sufficient as odd numbers like 9 can be expressed as the product of two integers each greater than 1. Not all odd numbers are prime. Thus, statement 2 alone is not sufficient.
A certain food has a gluten ratio of 13\,\text{mg}13mg13, start text, m, g, end text of gluten per \text{L}Lstart text, L, end text of the food. What is the gluten ratio in micrograms per milliliter \left(\dfrac{\mu\text{g}}{\text{mL}}\right)( mL μg )left parenthesis, start fraction, mu, start text, g, end text, divided by, start text, m, L, end text, end fraction, right parenthesis?
Answer:
The gluten ratio in micrograms per milliliter is 13 µg/mL.
Step-by-step explanation:
Consider the provided information.
It is given that the food has a gluten ratio of [tex]13 \frac{mg}{L}[/tex].
Now we need to convert gluten ratio in micrograms per milliliter
To convert mg to micro grams use the information shown below:
1 mg = 1000 micro-grams.
1 L = 1000 milliliter
Now, substitute 1 mg = 1000 micro-grams and 1 L = 1000 milliliter in the above ratio.
[tex]13( \frac{1000 \ micro-grams}{1000 \ milliliter} )= 13( \frac{micro-grams}{milliliter})[/tex]
Hence, the gluten ratio in micrograms per milliliter is 13 µg/mL.
Answer:
the answer is 4μm to the power of⁻1
Step-by-step explanation:
khan academy said
What is the perimeter of rectangle ABCDABCD? (1) The longer side of the rectangle is 2 meters shorter than its diagonal (2) The ratio of the shorter side of the rectangle to its diagonal is 13
Answer:
(1) P=4a+4
(2) P=2a+4[tex]\sqrt{42}[/tex]a
Step-by-step explanation:
Well, let us call longer side b, shorter side a and diagonal d. The perimeter of a rectangle is 2*(a+b). Let us write this formula as P=2*(a+b)
In (1) it is stated that b=a+2. Hence, the perimeter of the rectangle is P=2*(a+b). In terms of b, let us write (a+2). So P=2*(a+a+2)=4a+4.
In (2) it is stated that d/a=13 or d=13a. From Pythagorean theorem d^2=a^2+b^2. Hence, b^2=168a^2 or b=2[tex]\sqrt{42}[/tex]a. Finally, P=2*(a+b)=2*(a+2[tex]\sqrt{42}[/tex]a)=2a+4[tex]\sqrt{42}[/tex]a
The following is the graph of f(x) = sin (x-180 degrees) -1
True
False
Answer:
True
Step-by-step explanation:
Check the values of [tex]f(x)[/tex] at [tex]x=0,\pm0.5\pi,\pm\pi,\pm1.5\pi,\pm2\pi[/tex]
[tex]x \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ f(x)\\0 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \sin(0-180)-1=-1\\0.5\pi \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \sin(0.5\pi-180)-1=-2\\\pi \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \sin(\pi-180)-1=-1\\1.5\pi \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \sin(1.5\pi-180)-1=0\\2\pi \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \sin(2\pi-180)-1=-1\\-0.5\pi \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \sin(-0.5\pi-180)-1=0\\-\pi \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \sin(-\pi-180)-1=-1\\\\[/tex]
[tex]-1.5\pi \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \sin(-1.5\pi-180)-1=-2\\-2\pi \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \sin(-2\pi-180)-1=-1[/tex]
Each [tex](x,y)[/tex] point is on the graph.
Hence graph represents the given function.
A value one standard deviation from the mean is less likely to occur than a value three standard deviations from the mean.
True or False?
Answer: false is correct
The statement is false; a value one standard deviation from the mean is more likely to occur than a value three standard deviations from the mean due to the Empirical Rule for normal distributions.
The statement is false. A value one standard deviation from the mean is more likely to occur than a value three standard deviations from the mean. According to the Empirical Rule, which applies to bell-shaped and symmetric distributions, about 68 percent of the data lies within one standard deviation of the mean, while more than 99 percent of the data is within three standard deviations. This means that as you move further away from the mean, the likelihood of occurrence decreases.
The ratio of the number of Barbies that Jenny owns to the number of Barbies that Sharon owns is 5 : 2. Sharon owns the 24 Barbies. How many Barbies does Jenny own?
Answer:
60
Step-by-step explanation:
The ratio of Barbies is ...
Jenny : Sharon = 5 : 2 = 60 : 24 . . . . . . multiplying ratio values by 12
Jenny owns 60 Barbies to Sharon's 24.
Answer:
25:2
Step-by-step explanation:
What is the percent of change from 6,000 to 60?
Answer: 99% decrease
Step-by-step explanation: Since the number changes from 6,000 to 60, we know that it's decreasing. Now to find the percent decrease, we divide the amount of change by the original number.
The amount of change is the difference between 6,000 and 60 and the original number is 6,000.
6,000 - 60 is 5,940 so we are left with [tex]\frac{5,940}{6,000}[/tex] and dividing 6,000 into 5,940 gives us 0.99.
Finally, since the problem is asking us for the percent, we write 0.999 as a percent by moving the decimal point 2 places to the right to get 99%.
So when a number changes from 6,000 to 60, it has decreased by 99%.
List each term of the domain
{(-4, 3), (-4, 4), (-3, 1), (1, 1)}
Kind of struggling on this, would really appreciate the help!
Answer:
Domain: {-4, -3, 1 }
Step-by-step explanation:
As we know that domain of a relation basically consists of all the first elements or x-coordinates of order pairs.
As the relation is : {(-4, 3), (-4, 4), (-3, 1), (1, 1)}
So,
Domain: {-4, -3, 1 }
Note: We can not duplicate an element when we determine the domain of any relation. As -4 was present in first and second order pairs i.e. (-4, 3), (-4, 4). But, we have to write it only once when we write the domain of any relation.
So, the domain will be listed as:
Domain: {-4, -3, 1 }
Keywords: domain, relation
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A bank says you can do or your money in 10 years if you put 1000 in in a simple interest account.What annual interest rate does the bank Pay?
Answer:
[tex]r=10\%[/tex]
Step-by-step explanation:
The correct question is
A bank says you can double your money in 10 years if you put $1,000 in a simple interest account. What annual interest rate does the bank pay?
we know that
The simple interest formula is equal to
[tex]A=P(1+rt)[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest
t is Number of Time Periods
in this problem we have
[tex]t=10\ years\\ P=\$1,000\\ A=\$2,000\\r=?[/tex]
substitute in the formula above
[tex]2,000=1,000(1+10r)[/tex]
Solve for r
Divide by 1,000 both sides
[tex]2=1+10r[/tex]
Subtract 1 both sides
[tex]10r=2-1[/tex]
[tex]10r=1[/tex]
Divide by 10 both sides
[tex]r=1/10[/tex]
[tex]r=0.10[/tex]
Convert to percentage (multiply by 100)
[tex]r=0.10*100=10\%[/tex]
Function f(x) is positive, decreasing and concave up on the closed interval[a, b]. The interval [a, b] is partitioned into 4 equal intervals and these are used to compute the left sum, right sum, and trapezoidal rule approximations for the value of integral from a to b f(x)dx. Which one of the following statements is true?
a) Left sum < trapezoidal rule value < Right sumb) Left sum < Right sum < trapezoidal rule valuec) Right sum
Answer:
Right sum < trapezoidal rule value < Left sum
Non of the completed options are valid. Option c is incomplete but it starts correctly. If there are no more options, the answer is (c).
Step-by-step explanation:
Lets call a = x0, x1, x2, x3 and x4 = b the endpoints of the intervals in increasing order. Lets also call L the length of each subinterval. Note that b-a = 4L. Lets denote yi = f(xi) for i in {0,1,2,3,4}.
Lets compute each sum:
Left sum = x0*L + x1*L + x2*L + x3*L = (y0+y1+y2+y3)L
Similarly
Right sum = (y1+y2+y3+y4)L
and trapezoidal rule value = L((y0)/2 + y1+ y2 + y3+ (y4)/2)
Since f is decreasing, we have that y0 > y1 > y2 > y3 > y4. Therefore, y0 > y4 and, as a result, Left sum > Right sum, because the Right sum has y4 instead of y0 multiplying by L.
On the other hand, multiplying L we have (y0)/2 + y1+ y2 + y3+ (y4)/2 on the trapezoidal rule value, thus it has half of y0 and half of y4, and as a consecuence, the trapezoidal sum is between the left sum and the right sum.
The correct answer is
Right sum < trapezoidal rule value < Left sum
Answer:
answer is c, i took the test
Step-by-step explanation:
Yesterday Mike bought 2 gallons of regular gasoline and 3 gallons of premium gasoline at a gas station for $13.60 today he bought 3 gallons of regular gasoline and 4 gallons a premium gasoline for $18.95 if the prices do not change how much does one gallon of premium gasoline cost
Answer:
Cost of 1 gallon of Regular gasoline is $2.45 and Cost of 1 gallon of Premium gasoline is $2.90.
Step-by-step explanation:
Let the Cost of Regular gasoline be 'x'.
Let the Cost of Premium gasoline be 'y'.
Given:
Amount of regular gasoline bought yesterday = 2 gallons
Amount of premium gasoline bought yesterday = 3 gallons
Total Cost of yesterday = $13.60
Now we know that Total Cost of yesterday is equal to sum of Amount of regular gasoline bought yesterday multiplied by Cost of Regular gasoline and Amount of Premium gasoline bought yesterday multiplied by Cost of premium gasoline.
Framing in equation form we get;
[tex]2x+3y=13.60 \ \ \ \ equation\ 1[/tex]
Also Given:
Amount of regular gasoline bought today = 3 gallons
Amount of premium gasoline bought Today = 4 gallons
Total Cost of Today = $18.95
Now we know that Total Cost of Today is equal to sum of Amount of regular gasoline bought Today multiplied by Cost of Regular gasoline and Amount of Premium gasoline bought Today multiplied by Cost of premium gasoline.
Framing in equation form we get;
[tex]3x+4y=18.95 \ \ \ \ equation\ 2[/tex]
Now Multiplying equation 1 by 3 we get;
[tex]2x+3y=13.60\\\\3(2x+3y)=13.60\times3\\\\6x+9y= 40.80 \ \ \ \ \ equation\ 3[/tex]
Now Multiplying equation 2 by 2 we get;
[tex]3x+4y=18.95\\\\2(3x+4y)=18.95\times2\\\\6x+8y= 37.90 \ \ \ \ \ \ equation\ 4[/tex]
Subtracting equation 4 from equation 3 we get;
[tex](6x+9y)- (6x+8y)= 40.80-37.90\\\\6x+9y-6x-8y= 2.9\\\\y=\$2.90[/tex]
Substituting the value of y in equation 1 we get;
[tex]2x+3y=13.60\\\\2x+3\times2.90 =13.60\\\\2x+8.7=13.6\\\\2x=13.6-8.7\\\\2x=4.9\\\\x=\frac{4.9}{2} =\$2.45[/tex]
Hence Cost of 1 gallon of Regular gasoline is $2.45 and Cost of 1 gallon of Premium gasoline is $2.90.
find the radius pls. help
Good morning,
Answer:
r = 4 cmStep-by-step explanation:
V = h × (base area)
= 12 × (π×r²)
then 192π = 12π×r²
Then 192 = 12×r²
Then r² = 192÷12 = 16
Then r = √16 = 4.
:)
Jade normally leaves work at 5:00 pm, but she is leaving work 10 minutes late today. She decides to make up time by taking the toll road instead of side streets. She can travel two times faster by taking the toll road. Create an equation in terms of x to represent the number of minutes after 5:00 pm she arrives home from work if she leaves late. Let x represent the number of minutes her normal commute takes when she leaves on time.
Answer:
[tex]Required\ number\ of\ minutes= \frac{x}{2}+10[/tex]
Step-by-step explanation:
Usual time(side streets) taken [tex]=x\ minutes[/tex]
Jade can travel two times faster by taking the toll road so the time taken will be half from the toll road.
So travel time[tex]=\frac{x}{2}[/tex]
Jade is [tex]10\ minutes[/tex] late
So total minutes after 5:00 PM to reach home[tex]=\frac{x}{2}+10[/tex]
Answer:
It will be answer choice D.
Step-by-step explanation:
It'll take the half the usual time because she is taking a road that get's her there 2 times faster, but also add 10 because she was 10 minutes late
What is the slope of the line containing the midpoint of the segment with endpoints at (0, 0) and (2, 3) and the midpoint of the segment with endpoints at (5, 0) and (6, 3)? Express your answer in simplest form.
Answer:
The slope = 0.
Step-by-step explanation:
The midpoint of the first line =
(0+2)/2, (0+3)/ 2
= (1, 1.5).
For the second line :
(5+6)/2 , (0+3)/2
= (5.5, 1.5).
The required slope = rise / run
= (1.5-1.5)/(5.5-1))
= 0/4.5
= 0.
Answer:
0
Step-by-step explanation:
Ur welcome
In the past month, Josh rented one video game and six DVDs. The rental price for the video game who is $2.50. The rental price for each DVD is $3.40. What is the total amount paid josh spent on video games in this past month?
Answer:
total amount paid = $ 22.9
Step-by-step explanation:
total price = $ 2.5 + $3.4(6)= $22.9
Answer:
2.50
Step-by-step explanation:
An urn contains 12 balls, of which 4 are white.
Three players successively draw from the urn, A first, then B, then C, then A, and so on. The winner is the fist one to draw a white ball.
Find the probability of winning for each player if:
a) each ball is replaced after being drawn.
b) the balls that are withdrawn are not replaced.
The probability of a player winning depends on whether balls are replaced after each draw. With replacement, the probabilities remain constant and A has a higher chance of winning (9/20) compared to B and C (11/40 each). Without replacement, the probabilities change after each turn and require complex computation.
Explanation:This is a probability problem involving sequence of events. The outcome is dependent on whether the balls are replaced or not after each draw.
For case a), if each ball is replaced after being drawn, the probabilities for A, B, and C stay constant each round. There are 4 white balls out of 12 total, so the probability of drawing a white ball is 4/12 = 1/3. Because the players draw successively and stop once a white ball is drawn, we need to consider the rounds of draws. For A to win, a white ball needs to be drawn on the 1st, 4th, 7th turns, and so on. For B to win, a white ball needs to be drawn on the 2nd, 5th, 8th rounds, and so forth. Similar logic applies to player C. Using geometric distribution to compute these, we have [tex]P(A) = 1/3 * (2/3)^0 + 1/3 * (2/3)^3 + 1/3 * (2/3)^6 +... = 9/20.[/tex] Applying similar logic to players B and C, we get P(B) = P(C) = 11/40. (Note that the sum of P(A), P(B), and P(C) = 1, which verifies our calculation is correct.)
For case b), if the balls are not replaced after each draw, the probability changes after each turn. Initially the probability of drawing a white ball is 4/12 = 1/3, then it becomes 4/11, 4/10, and so forth if a white ball is not drawn, and 3/11, 3/10, and so forth if a white ball is drawn. Therefore a recursive method computing the probability is needed in this case and the calculation could be quite complicated depending on when we stop the game.
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Point C = (4/9,-5/9) lies on the circle with the center at S=(-2/3, 3/4). If CD is a diameter of circle S, find the coordinates for D. Answer must be given as a simplified fraction to receive full credit.
Answer:
Step-by-step explanation:
If CD is a diameter of circle S, then CD goes through circle S at point S. CS is a radius, and so is DS. That means that they are the same length. That also means that S is the midpoint of CD. We can use the midpoint formula and the 2 points we are given to find the other endpoint, D.
[tex](-\frac{2}{3},\frac{3}{4}) =(\frac{\frac{4}{9}+x }{2},\frac{-\frac{5}{9}+y }{2})[/tex]
To solve for x, we will use the x coordinate of the midpoint; likewise for y. x first:
[tex]-\frac{2}{3}=\frac{\frac{4}{9}+x }{2}[/tex]
Multiply both sides by 2 to get rid of the lowermost 2 and get
[tex]-\frac{4}{3}=\frac{4}{9}+x[/tex]
Subtract 4/9 from both sides to get
[tex]x=-\frac{16}{9}[/tex]
Now y:
[tex]\frac{3}{4}=\frac{-\frac{5}{9}+y }{2}[/tex]
Again multiply both sides by that lower 2 to get
[tex]\frac{3}{2}=-\frac{5}{9}+y[/tex]
Add 5/9 to both sides to get
[tex]y=\frac{37}{18}[/tex]
And there you go!
[tex]D(-\frac{16}{9},\frac{37}{18})[/tex]
Mr. Kim's age in years is 6 more than 3 times the age of his daughter. Mr. Kim is 48 years old. How old, in years is Mr. Kim's daughter?
Answer:
14
Step-by-step explanation:
48 - 6 = 42
42 divided by 3 = 14.
Mr. Kim's daughter is 14 years old.
Mr. Kim's daughter is 14 years old. This was determined by setting up the equation 48 = 3x + 6 and solving for x step-by-step, which resulted in x = 14.
To find Mr. Kim's daughter's age, we can set up an equation based on the problem statement.
Let's denote the daughter's age by x.
According to the problem, Mr. Kim's age is 6 more than 3 times his daughter's age. This can be written as:
48 = 3x + 6
We need to solve for x step-by-step:
Subtract 6 from both sides of the equation:
48 - 6 = 3x
Simplify the left side:
42 = 3x
Divide both sides by 3:
[tex]\frac{42}{3}[/tex] = x
Simplify the right side:
x = 14
Therefore, Mr. Kim's daughter is 14 years old.
What conic section degenerates into a line?
Parabola
Hyperbola
Circle
Ellipse
I think it's Ellipse? I'm not sure though
Some degenerate parabola cases form a single straight line, while other cases form one pair of parallel lines.
A degenerate hyperbola forms two lines that intersect at the vertex of the cone. We can rule out choice B.
A degenerate circle is a single point, so we can rule out choice C.
A degenerate ellipse is also a single point. Any circle is an ellipse (but not the other way around). We can rule out choice D.