Base your answer to the question on the diagrams shown below.
What is the probability of drawing a red card and then spinning a 1?
Answers
P(Red)×P(Spinning 1)
P(Red)=2/5
P(Spinning 1)=4/8=1/2
Thus:
P(Red)×P(Spinning 1)=1/2×2/5=1/5
Answer: [tex]\frac{1}{5}[/tex]
Step-by-step explanation:
From the given picture, the total number of cards = 5
The number of red card = 2
Thus, the probability of drawing a red card P(red)=[tex]\frac{2}{5}[/tex]
Also, total number of digits on spinner = 8
Number of 1's=4
Thus, the probability of spinning a 1 P( spinning 1)=[tex]\frac{4}{8}=\frac{1}{2}[/tex]
Since both the events of drawing a red card and spinning a 1 are independent events, therefore, the probability of drawing a red card and then spinning a 1=[tex]\text{ P(red)}\times\text{P( spinning 1)}=\frac{2}{5}\times\frac{1}{2}=\frac{1}{5}[/tex]
Related Questions
One of the mutually exclusive results of an activity conditional probability 2. a combination of one or more outcomes independent events 3. a measure of likelihood of a given result event 4. compound events whose outcomes do not affect each other outcome 5. events involving two or more activities compound events 6. probability of one event given that another has occurred probability
Answers
probability - a measure of likelihood of a given result
compound events - events involving two or more activities
event - a combination of one or more outcomes
independent events - compound events whose outcomes do not affect each other
conditional probability - probability of one event given that another has occurred
From the information given about the probability, the appropriate terms that denotes them will be:
outcome - one of the mutually exclusive results of an activity.probability - a measure of the likelihood of a given result.compound events - events involving two or more activities.event - a combination of one or more outcomes.independent events - compound events whose outcomes do not affect each other.conditional probability - the probability of one event given that another has occurred,ProbabilityIt should be noted that probability is the branch of mathematics that deals with numerical descriptions of how likely an event is to occur.
The probability of an event occuring is a number between 0 and 1. 0 indicates the impossibility of the event while 1 indicates certainty.
The outcome is one of the mutually exclusive results of an activity.
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A family drove 2,275 miles from Los Angeles to Atlanta in a time span of 35 hours . Calculate their average speed in miles per hour .
Answers
The family drove at an average speed of 65 mph from Los Angeles to Atlanta with a span length of 2275 miles
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
The equation for average speed is given as:
Average speed = Total distance / total time
Hence:
Average speed = 2275 miles / 35 hour = 65 mph
The family drove at an average speed of 65 mph from Los Angeles to Atlanta
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Question 19 Unsaved
Ann office building has the same number and size of office units per floor. If there are 21 units on the first 3 floors, then what is the total number of offices in the 10 story building?
Question 19 options:
7
24
63
70
Answers
10 divided by 3=3.33
3.33 times 21= 70
There are a couple ways to find this. You could...
A. Since the question states "21 units on the first 3 floors" you could multiply 21 and 10 to get 210 (number of units if there were 21 on each floor), then divide it by 3 to find the total number in the building. Dividing by 3 compensates for the 21 units on the first 3 floors. Or...
B. Divide 21 by 3 to find how many units are on each floor (7), then multiply by the number of floors in the building (10). Either way, both ways will give you 70.
I hope this helps!
What is the equation of a circle with center (8, 4) and radius 7?
Answers
The standard form of the equation of a circle is given by (x-h)² + (y-k)² = r², where (h, k) are the center and r is the radius. For a circle with center at (8, 4) and radius 7, the equation of the circle becomes (x - 8)² + (y - 4)² = 49.
Explanation:The equation of a circle in standard form is given by (x-h)² + (y-k)² = r², where (h, k) are the coordinates of the center of the circle and r is the radius. This formula comes from Pythagorean theorem and how a circle is defined as the locus of points equidistant from a given point (the center).
By substituting the given center and radius into this formula, we can write the equation of the specific circle you're asking about. The center of this circle is (h, k) = (8, 4), and its radius is r = 7. Therefore, the equation of the circle is (x - 8)² + (y - 4)² = 7² or (x - 8)² + (y - 4)² = 49.
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The equation of the circle is (x-8)^2 + (y-4)^2 = 49.
Explanation:The equation of a circle with center (h, k) and radius r is given by the formula:
(x-h)2 + (y-k)2 = r2
In this case, the center is (8, 4) and the radius is 7. So, the equation of the circle is:
(x-8)2 + (y-4)2 = 72
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A notebook has a perimeter of 36 inches. It’s area is 80 square inches. What are the dimensions of the notebook
__inches by___ inches
Answers
w*l=80
2(w+l)=36
w+l=18
w=18-l
(18-l)*l=80
-l^2+18*l-80=0
l=8 or 10
Therefore, the notebook is 8 by 10 inches
Final answer:
To solve for the dimensions of the notebook, we set up equations based on the perimeter and area, then solved the quadratic equation to find that the dimensions are 10 inches by 8 inches.
Explanation:
To find the dimensions of a notebook with a perimeter of 36 inches and an area of 80 square inches, we will use the formulas for the perimeter and area of a rectangle. The perimeter (P) of a rectangle is 2 times the length (l) plus 2 times the width (w), or P = 2l + 2w. The area (A) of a rectangle is length times width, or A = lw.
Given P = 36 and A = 80, we can set up two equations:
2l + 2w = 36l × w = 80First, we simplify the perimeter equation to l + w = 18 by dividing everything by 2. We can then express w in terms of l: w = 18 - l. Now, we substitute w into the area equation: l(18-l) = 80. Expanding this gives us a quadratic equation: l2 - 18l + 80 = 0.
To solve the quadratic equation, we look for factors of 80 that add up to 18. The factors are 10 and 8, meaning the length is 10 inches and the width is 8 inches, since l = 10 and w = 8 satisfy both the area and perimeter equations.
Therefore, the dimensions of the notebook are 10 inches by 8 inches.
Ronald and Tim both did their laundry today. Ronald does laundry every 666 days and Tim does laundry every 999 days.
How many days will it be until Ronald and Tim both do laundry on the same day again?
Answers
We want the least common multiple (LCM) of 6 and 9. First we find the prime factorization:
6 = 2*3
9 = 3*3
They have a 3 in common; we use this first in the LCM. Then we take the "leftover" factors, 2 and 3:
LCM = 3*2*3 = 18
Answer:
18
Step-by-step explanation:
Write an equation that you can use to solve for x.
Enter your answer in the box.
Answers
So x would equal 180 degrees minus 47 degrees
This can be written as x = 180-47
x = 133 degrees
133 degrees is your answer
The volume of a cylinder is given by the formula v=pi r^2h, where r is the radius of the cylinder and h is the height. Which expression represents the volume of this cylinder? h=2x+7, r=x-3.
Answers
volume = pi (x - 3)^2 * (2x + 7)
= pi* (2x + 7)(x^2 - 6x + 9)
= pi * (2x^3 - 12x^2 + 18x + 7x^2 - 42x + 63)
= (2x^3 - 5x^2 - 24x + 63) pi answer
Gio is studying the rectangular pyramid below.
He believes the surface area, in square millimeters, can be found by simplifying this expression.
(4.2)(9.6)+1/2(4.2)(6.5)+1/2(9.6)(4.8)
What error is Gio making?
He used the wrong values as the bases of the lateral faces.
He used the wrong expression to represent the area of the base of the pyramid.
He used two different values as the heights of the lateral faces. NOT C
He used an expression for surface area that did not include all the faces.
PLZZ HELP
Answers
the answer is A. hope this helps!!!!
The error that Gio is making in finding the surface area of the rectangular pyramid is that He used an expression for surface area that did not include all the faces.
What is Surface Area?The area of a three dimensional object on it's outer surface is called the surface area of the object.
Given a rectangular pyramid.
Pyramid consists of one rectangular side and 4 triangular faces of which each pair of triangular faces is identical.
Total surface area of the pyramid is the total surface area of each faces.
Area of rectangular face = (4.2) (9.6)
Area of the triangular faces = [2 × 1/2 × 4.2 × 6.5] + [2 × 1/2 × 9.6 × 4.8]
= (4.2) (6.5) + (9.6) (4.8)
Total area = (4.2) (9.6) + (4.2) (6.5) + (9.6) (4.8)
So his mistake is that he only find the areas of two triangular faces.
Hence the correct option is that He used an expression for surface area that did not include all the faces.
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Find the coordinate of the point (x,y) shown on the unit circle
Answers
Here the angle is
[tex]\frac{4 \pi}{3}[/tex]
And radius is 1 units .
And
[tex]x = r cos \theta, y = r sin \theta[/tex]
Substituting the values of theta and r, we will get
[tex]x = 1 cos(\frac{4 \pi}{3} ) = -1/2 \\ y=1 sin( \frac{4 \pi}{3} ) =\sqrt3 /2[/tex]
So we will get
[tex]x = \frac{-1}{2} , y = -\frac{ \sqrt 3}{2}[/tex]
The coordinate of the point (x,y) shown on the unit circle is therefore: (-1/2, -√3/2)
The circle given is a unit circle.
In essence, the radius as indicated by the blue line is 1.
The angle subtended by the line is; 4π/3.
Therefore, from trigonometry of right-angled triangles; we have;
x = r Cos(4π/3)y = r Sin(4π/3)where, r = 1
Therefore,
x = -1/2y = -√3/2Read more:
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Use the mid-point rule with n = 4 to approximate the area of the region bounded by y = x3 and y = x. (10 points)
Answers
The midpoint rule states that you can calculate the area under a curve by using the formula:
[tex]M_{n} = \frac{b - a}{2} [ f(\frac{x_{0} + x_{1} }{2}) + f(\frac{x_{1} + x_{2} }{2}) + ... + f(\frac{x_{n-1} + x_{n} }{2})][/tex]
In your case:
a = 0
b = 1
n = 4
x₀ = 0
x₁ = 1/4
x₂ = 1/2
x₃ = 3/4
x₄ = 1
Therefore, you'll have:
[tex]M_{4} = \frac{1 - 0}{4} [ f(\frac{0 + \frac{1}{4} }{2}) + f(\frac{ \frac{1}{4} + \frac{1}{2} }{2}) + f(\frac{\frac{1}{2} + \frac{3}{4} }{2}) + f(\frac{\frac{3}{4} + 1} {2})][/tex]
[tex]M_{4} = \frac{1}{4} [ f(\frac{1}{8}) + f(\frac{3}{8}) + f(\frac{5}{8}) + f(\frac{7}{8})][/tex]
Now, to evaluate your f(x), you need to look at the graph and notice that:
f(x) = x - x³
Therefore:
[tex]M_{4} = \frac{1}{4} [(\frac{1}{8} - (\frac{1}{8})^{3}) + (\frac{3}{8} - (\frac{3}{8})^{3}) + (\frac{5}{8} - (\frac{5}{8})^{3}) + (\frac{7}{8} - (\frac{7}{8})^{3})][/tex]
[tex]M_{4} = \frac{1}{4} [(\frac{1}{8} - \frac{1}{512}) + (\frac{3}{8} - \frac{27}{512}) + (\frac{5}{8} - \frac{125}{512}) + (\frac{7}{8} - \frac{343}{512})][/tex]
M₄ = 1/4 · (2 - 478/512)
= 0.2666
Hence, the area of the region bounded by y = x³ and y = x is approximately 0.267 square units.
Using the mid-point rule with n = 4, we approximate the area bounded by y = x³ and y = x b as 0.2578125.
To approximate the area of the region bounded by y = x³ and y = x using the mid-point rule with n = 4, we follow these steps:
Determine the points of intersection between y = x³ and y = x. Solving x³ = x, we get the points of intersection at x = 0 and x = 1.
Divide the interval [0, 1] into 4 subintervals, each of width Δx = (1 - 0)/4 = 0.25.
Calculate the midpoint of each subinterval: 0.125, 0.375, 0.625, and 0.875.
Evaluate the functions y = x³ and y = x at these midpoints:
At x = 0.125: y = x³ = 0.125³ = 0.001953125 and y = x = 0.125At x = 0.375: y = x³ = 0.375³ = 0.052734375 and y = x = 0.375At x = 0.625: y = x³ = 0.625³ = 0.244140625 and y = x = 0.625At x = 0.875: y = x³ = 0.875³ = 0.669921875 and y = x = 0.875Determine the heights of the rectangles by finding the difference between the values of y:
At x = 0.125: Δy = 0.125 - 0.001953125 = 0.123046875At x = 0.375: Δy = 0.375 - 0.052734375 = 0.322265625At x = 0.625: Δy = 0.625 - 0.244140625 = 0.380859375At x = 0.875: Δy = 0.875 - 0.669921875 = 0.205078125Compute the area of each rectangle (height × width) and then sum them up:
Area at x = 0.125: 0.123046875 × 0.25 = 0.03076171875Area at x = 0.375: 0.322265625 × 0.25 = 0.08056640625Area at x = 0.625: 0.380859375 × 0.25 = 0.09521484375Area at x = 0.875: 0.205078125 × 0.25 = 0.05126953125Add the areas to get the total approximate area:
0.03076171875 + 0.08056640625 + 0.09521484375 + 0.05126953125 ≈ 0.2578125
Therefore, the approximate area of the region bounded by y = x³ and y = x using the mid-point rule with n = 4 is 0.2578125.
A. 3
B. 5
C. 6
D. 10
Answers
_________________
Which of the following choices is the value of cscΘ?
a) 12/15
b) 9/15
c) 15/12
D) 15/9
Answers
r² = 144 + 81
r² = 225
r = √225
r = 15
For Θ,
Base = 9
Perpendicular = 12
Hypotenous = 15
cscΘ = Hypotenous/Perpendicular
= 15/12
Ans:- Option c)15/12
Hope this helps!
3 4 (2)t/3 = 9 Round your answer to the nearest hundredth. A) 1.62 B) 3.24 C) 8.26 D) 10.75
Answers
If a map shows the straight line distance between two cities as 3 1/2 centimeters and the map scale shows that 1 centimeteer equals 100 kilometers what would the actual distance be
Answers
Answer:
The actual distance between the two cities is 350 kilometers
Step-by-step explanation:
Information given to us to answer the question correctly:
Distance between two cities in the map = 3 1/2 centimeters
Scale of the map: 1 centimeter = 100 kilometers
2. What would the actual distance be?
Let's calculate the actual distance between the two cities, this way:
Actual distance = Distance between two cities in the map * Scale of the map
Replacing with the real values:
Actual distance = 3.5 * 100
Actual distance = 350 kilometers
Which of the following rates is proportional to $2.50 for 5 cans?
A. $2.00 for 3 cans
B. $4.00 for 7 cans
C. $4.50 for 9 cans
D. $1.50 for 1 can
Answers
Answer:
C. $4.50 for 9 cans
Step-by-step explanation:
Which values in this data set are outliers?
119, 65, 68, 78, 74, 85, 120, 86, 78, 65, 35
Select outlier or not outlier to whether the following numbers are outliers.
35
65
119
120
Answers
M+M/2=119.04...
M-M/2=39.68...
So I think outliers are 120 and 35
I'm Naarah!!
I'm glad I can be an assistance on helping answer your question!
______________________________________________________________
1. 35 - Not A Outlier
--------------------------
2. 65 - Outlier
-----------------------
3. 119 - Outlier
----------------------------
4. 120 - Outlier
------------------------------
I Really Hope That I Was A Helpful Assistance To You!!
_____________________________________________
I'm Sorry If The Answers I Put Were Wrong.
-------------------------------------------------------------
Have A Great Day Friend :)
Expand and simplify: (x + 5y) (x − 3y)
Answers
(x + 5y) (x - 3y)
Rewriting we have:
x ^ 2 - 3xy + 5xy - 15y ^ 2
Grouping similar terms we have:
x ^ 2 - 15y ^ 2 + 2xy
Answer:
The complete and simplified expression is given by:
x ^ 2 - 15y ^ 2 + 2xy
To find this, you must first distribute one set of parenthesis into the other. This will give you "x^2 - 3xy + 5xy - 15y^2. You then combine like terms (-3xy and +5xy), to get "x^2 + 2xy - 15y^2". Finally, you organize the numbers based on their power (highest to lowest). Your final answer would be x^2 - 15y^2 + 2xy.
I hope this helps!
Christopher is analyzing a circle, y^2 + x^2 = 121, and a linear function g(x). Will they intersect?
A. Yes, at the positive x coordinates.
B. Yes, at negative x coordinates.
C. Yes, at the negative and positive x coordinates.
D. No, they will not intersect
Answers
g(x)=-2x+12 (from given table, find slope and y-intercept)
We can see from the graphics that g(x) will be almost tangent to the circle at (0,11), and that both intersection points will be at x>=11.
To show that this is the case,
substitute g(x) into the circle
x^2+(-2x+12)^2=121
x^2+4x^2-2*2*12x+144-121=0
5x^2-48x+23=0
Solve using the quadratic formula,
x=(48 ± √ (48^2-4*5*23) )/10
=0.5058 or 9.0942
So both solutions are real and both have positive x-values.
Yes, they will intersect at the positive x coordinates.
What is the equation of the circle?The standard equation of a circle is: (x-h)^ 2 + (y-k) ^2 =r ^2 Where (h, k) is the coordinates of the center, and r is the radius of the circle.
Christopher is analyzing a circle, y^2 + x^2 = 121, and a linear function g(x). Will they intersect?
The given equation of the circle is;
[tex]\rm x^2+y^2=121\\\\x^2+y^2=11^2[/tex]
The circle with center at (0,0) and radius r = 11 units and g(x) points (-1,14) (0,12) (1,10).
The linear function is;
[tex]\rm y=mx+b[/tex]
From the graph on drawing all the co-ordinates lies in positive x and y axis.
Hence, they will intersect at the positive x coordinates.
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Rovide an appropriate response.4) assume that adults have iq scores that are normally distributed with a mean of 100 and a standard deviation of 15 (as on the wechsler test). find the iq score separating the top 14% from the others. 4)
Answers
Every day for two full weeks (14 days) jimmy records the number of coins in his pocket. he finds that the mean is 27. he decides to remove one sunday's total because it was an outlier. his new mean is 18 coins. how many coins did he have in his pocket on the sunday he removed?
a.18
b.27
c.126
d.144
Answers
18+x=54
x=36
What have I done wrong?
Answer:
It is D.)144
Step-by-step explanation:
Give the dimensions of a cuboid with a volume of 18cm to the power 3.
Answers
volume of a cuboid=length*width*height
in this problem
we have
volume=(18 cm)³
so
volume=18*18*18 cm³
the dimensions of the cuboid are
length 18 cm
width 18 cm
height 18 cm
18 cm x 18 cm x 18 cm
Suppose f(x) = x. Find the graph of f(x+1)
Answers
f(x) = x
Therefore, if f(x) = x, than f(x + 1) = x + 1, for with an equal sign, what you do to one side, you do to the other.
Answer:
f(x + 1) = x + 1
hope this helps
Sue Baker is given a prescription of MECLIZINE 25MG to be taken three times daily. She was given enough for ten days. She has been given her pills following the six "rights" (right resident, right drug, right dosage, right time, right route, right record/documentation). On the start of day four, how many pills should be in the bottle?
Answers
Assuming she started taking the pills the morning of the first day, 3 pills per day x 3 days = 9 pills.
She had enough for 10 days; 10 days * 3 pills per day = 30 pills
30 pills to begin with - 9 pills taken = 21 pills left
In 2010, 100 japanese yen purchased .88 u.s. dollars and in 2013, it purchased .93 u.s. dollars. how much was 1 u.s. dollar worth in japanese yen, in 2010 and 2013?
Answers
2010:
100 yen x yen (use cross products to solve for x yen)
$0.88 = $1
100 = 0.88x
0.88 0.88
x = 113.6 yen
In 2010, $1 was worth approximately 114 yen.
2013:
100 yen x yen
$0.93 = $1
100 = 0.93x
0.93 0.93
x = 107.5
In 2013, $1 was worth approximately 108 yen.
Write x2 − 2x − 3 = 0 in the form (x − a)2 = b, where a and b are integers.
A.(x − 4)2 = 3
B.(x − 3)2 = 2
C.(x − 2)2 = 1
D.(x − 1)2 = 4
Answers
Answer: D. (x - 1)² = 4.
Used:
(a - b)² = a² - 2ab + b²
Simplify the questions that aren't crossed on the attachment, thank you
Answers
(5) (3(x +1) +4x)/(x(x +1)) = (7x+3)/(x² +x)
(7) same as (5)
(8) (a(a +4))/((a -1)(a +4)) = a/(a -1) . . . . . a ≠ -4
(11) (2a -3b)/(4a(2a -3b)) = 1/(4a)
Chiara pays $21 for 3 DVDs that she finds in a one-price bin. Gunther wants to know how much he would spend for 1 DVD in this bin. Chiara wants to know how many dollars she will need to purchase 9 DVDs the next time she goes.
Answers
If Chiara wants to purchase 9 DVD's next time and needs to know the money, we take our previous information (1 DVD = $7) and input it into this equation.
x (unknown dollars) = 9 (DVD) * 7 ($).
Meaning that 9 * 7 = 63.
It will cost $63 for 9 DVD's, when 1 DVD is $7.
brianna deposit $680.00 into savings account that pays a simple interest rate of 1.29% how much will she earn after 3 years
Answers
0.0129(680) + 680
But because it is 3 years:
3(0.0129(680)) + 680
0.0387(680) + 680
We can make it simpler:
1.0387(680)
Multiply:
706.316
We can round up:
She will have $706.32, and earn $26.32
The total number of points scored by each player throughout a season are listed on a roster by the player's jersey number. is this a function? explain your reasoning.
Answers
Using ordered pairs to represent this, we would have (jersey #, points). A relation is a function if no element of the domain matches more than one element of the range; in our case, the domain is the jersey number and the range is the number of points.
The jersey number will not match two numbers of points throughout the season; a player will only have one total number of points throughout the season. Therefore no element of the domain matches more than one element of the range, and this is a function.
A)Yes, it is a function because each player's jersey number will have only one number for the points scored during the season.
Each jersey number has exactly one number for the total points scored by the player.
In a function, every input has exactly one output. In this situation, each jersey number is an input, and the total points scored for the season by the player is the output.