I deal myself 5 cards from a standard 52-card deck. Find the probabilities of each of the following events: (a) 2 of a kind: (b) 3 of a kind: (c) 2 pair (e.g., 2 eights and 2 queens): (d) a flush (65 cards all of the same suit): (e) a full house (3 of one kind and 2 of another kind): (f) a straight (5 cards in consecutive order).
the probabilities of each of the following events are a) 9.23×10⁻⁶ and b) 0.00144
Since we have given that
Number of cards = 52
a) Probability that we draw 3 aces and 2 kings.
As we know that
Number of aces = 4
Number of kings = 4
Number of cards drawn = 5
So, the probability becomes,
9.23×10⁻⁶
(b) a "full house" (3 cards of one kind, 2 cards of another kind)
Since there are 13 sets of each type and we have to select and 2 kinds of it, so, it becomes
So, it becomes,
Hence, a) 9.23×10⁻⁶ and b) 0.00144
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Problem No. 8
A rectangular schoolroom floor can be covered by 2400 square tiles. If the tiles are 5cm longer and
5cm wider, 1350 tiles are needed.
If none of the tiles are cut, what is the area of the floor in m²?
The area covered by the tiles is 54 square meters.
How to determine the area of a set of tiles
In this problem we find that 2400 square tiles can cover a rectangular school room and 1350 square tiles if each tile is 5 centimeters longer and 5 centimeters wider. Algebraically speaking, this situation is represented by following formula:
2400 · x² = 1350 · (x + 5)²
Where x is in centimeters.
First, expand and simplify by algebraic properties:
2400 · x² = 1350 · (x² + 10 · x + 25)
2400 · x² = 1350 · x² + 13500 · x + 33750
1050 · x² - 13500 · x - 33750 = 0
Second, find the roots of quadratic equation by quadratic formula:
x₁ = 15 or x₂ = - 15 / 7
Since lengths are positive variables, then only valid solution is x = 15 cm.
Third, calculate the area covered by the tiles:
A = 2400 · (15 cm)²
A = 540000 cm² (54 m²)
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A carnival game charges each contestant $ 10 to spin a wheel with 6 equally likely spaces: 3 spaces result in the contestant winning nothing. 2 spaces result in the contestant winning a prize whose value is $ 5. 11 space results in the contestant winning a prize whose value is $ 20 .
Based on the information above, the probability of winning the $20 prize is 0.16.
How to find the probability that the contestant wins $20?To find the probability that the contestant wins $20 we must carry out the following mathematical procedure:
1 / 6 = 0.160.16 * 1 = 0.16Based on this result, we can infer that the probability that the contestant wins the $20 is 0.16. Additionally, you have a 0.5 chance of winning nothing and a 0.33 chance of winning $5.
0.16 * 3 = 0.50.16 * 2 = 0.33Note: This question is incomplete because there is some information missing. Here is the complete information:
Tasks
Find the probability that the contestant will win the $20 prize.
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help me with this problem pls
Answer:
Heres how to do it
(i know you arent using macbook)
Step-by-step explanation:
The normal price of a cooker is £540
Stan has to work out the sale price of the cooker.
Here is his working.
10% of 540 = 54
6 x 54 = 324
Sale price £324
Sale price
60% off normal price
Stan's answer is wrong.
(b) What mistake has Stan made?
Stan forgot to subtract the discount from the total price to correctly calculate the sale price.
What is the price of a cooker if it has 60% off its normal price?Regular price: £540
Now, let's calculate the 60%:
£540 / 100 = £5.4 x 60= £324
In this case, £324 represents 60% of the total price but not the sale price. To find the sale price, let's subtract the discount from the total price as shown below:
£540 - £324 = 216
Based on this, it can be concluded that Stan forgot the last step or subtracting the discount.
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Answer:
stan did not deduct the calculation with the original price hence stan is wrong
Step-by-step explanation:
the rate of college enrollment immediately after high school completion was 67
The statement " Rate of college enrollment immediately after completing high school was 67% by 1997" is an example of (a) Descriptive Statistics.
The Descriptive statistics involves the use of measures, such as averages, proportions, and frequencies, to summarize and describe the main features of a set of data.
In this statement, the rate of 67% is a summary statistic that describes the proportion of high school graduates who enrolled in college immediately after completing high school in 1997.
Whereas; the inferential statistics involves making inferences or predictions about a population based on a sample of data.
The statement provides a summary statistic for the rate of college enrollment for a specific year, 1997, but it does not provide any inferences or predictions about the rate of college enrollment for other years or other populations , so it denoted a Descriptive Statistics .
The given question is incomplete , the complete question is
What type of Statistics does the statement "the rate of college enrollment immediately after high school completion was 67" represents ?
(a) Descriptive
(b) Inferential
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Dexter thinks of a number, x. He subtracts 4 from his number and multiplies the answer by his original number. His answer is 60 a) Use this information to form a quadratic equation of the form x² + ax + b = 0
Answer:
Let y = x - 4, then xy = 60.
Expanding the product on the right side, we have x(x-4) = 60.
Expanding the left side, we have x² - 4x = 60.
Adding 4x to both sides, we have x² = 60 + 4x.
Re-arranging the equation, we have x² - 4x - 60 = 0.
Thus, the quadratic equation is x² - 4x - 60 = 0.
a researcher chooses 100 random samples for an experiment, and for each sample he obtains a 95% confidence interval for an unknown parameter. approximately how many of those confidence intervals will not contain the value of the unknown parameter?
5 samples will not contain the value of the confidence interval of the unknown parameter. The rest will have the confidence interval.
x% confidence interval implies that the mean of x% is in the interval, also x% in the sample space will have the value of unknown parameter.
Here 95% of confidence interval is present and the sample space is 100. So, 100%- 95% = 5%. Thus only 5% of the sample space will not contain the confidence level of the unknown parameter.
5% of 100 = [tex]\frac{5}{100}[/tex] × [tex]100[/tex] = 0.5 × 100 = 5
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sam estimates that if he leaves his car parked outside his office all day on a weekday, the chance that he will get a parking ticket is 13%. if sam leaves his car parked outside his office all day next tuesday, what is the chance that he will not get a parking ticket?
The chance that Sam will not get a parking ticket is 87%.
No Parking Ticket ChanceTo find the chance of not getting a parking ticket, subtract the chance of getting a ticket from 100%.
Step 1: Take the chance of getting a ticket, which is 13%
Step 2: Subtract it from 100%
100% - 13% = 87%
So, the chance that he will not get a parking ticket is 87% if Sam want to leaves his car parked outside his office all day next tuesday.
This question is about the probability of Sam getting a parking ticket if he leaves his car parked outside his office on a weekday. Sam estimates that the chance of getting a ticket is 13%. To find the chance of not getting a ticket, the probability of getting a ticket (13%) was subtracted from 100%. The result, 87%, represents the chance that Sam will not get a parking ticket.
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PLEASE HELP MEEEEEE!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
34
Step-by-step explanation:
every corner here is 90⁰,because it says so.
QRP would be 90-56 =34⁰ and the opposite corner is the same,so 34⁰
Answer:
34
Step-by-step explanation:
KRL = QRP, so finding QRP can get us our answer. We were given 56 and 90 because 90 is the degree of a right angle.
A straight line is 180 degrees.
If we subtract 90 and 56 from that 180, we'll find out QRP
180-90=90
90-56=34
Since QRP = 34, that means KRL does also
All monkeys are good chess players. All wookies are monkeys. All wookies are good chess players. what is the conclusion?
The average conclusion is that since they are monkeys, all wookies are good chess players.
Two premises form the basis for the conclusion. All monkeys are skilled chess players, according to the first postulate. The idea that all Wookies are monkeys is the second premise. The first assumption indicates that all monkeys are brilliant chess players, and since the second premise states that all wookies are monkeys, it follows that all wookies must likewise be good chess players. The conclusion is that since they are monkeys, all wookies are good chess players. This conclusion comes logically from the two supplied premises. The conclusion is also presumptively true because the premises are believed to be true.
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The slope Ab is 3. The slope of A’B is A’B through the point O
The slope will remain constant, thus it will still be 3.
What is dilation?Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size.
Given AB is dilated by a scale factor of 3 to form A'B',
and Point O, which lies on AB, is the center of dilation,
AB has expanded due to the scaling factor, to form A'B'
The image is thus consistent with the preimage according to the laws of dilation.
This suggests that other than the size, the image won't change in any way.
Therefore, the slope will stay the same, the slope of A'B' is 3.
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The complete question is,
AB is dilated by a scale factor of 3 to form A'B'. Point O, which lies on AB , is the center of dilation. The slope of AB is 3. The slope of A'B' is . through point O.
2x-1=1+x i need help
Answer:
X = 2
2x-1+1=x+1+1
Twenty-four 4 cm cube are ued to make a olid. If 2 cm cube were ued intead, how many cube would be needed?
Twenty-four 4 cm cube are used to make a solid. If 2 cm cube were used instead, 192 cube would be needed.
A cube is a solid object in three dimensions with six square faces that all have the same length sides. It is one of the five platonic solids and is also referred to as a regular hexahedron. Six square faces, eight vertices, and twelve edges make up the form. Since the 3D figure is a square with equal-length sides, the length, breadth, and height of a cube are all the same measurement.
Number of cubes = Volume of the solid / Volume of the cube
= 24 x 4x4x4 / 2x2x2
=24x64/8
=192
Number of cubes will be 192 of 2cm
The area that a cube takes up is known as its volume. Finding the cube of the cube's side length will provide the volume of the cube. There are numerous formulas that use various parameters to calculate a cube's volume.
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Why is a rhombus not a square?
The primary distinction between a square and a rhombus is that whereas the angles in a square are all 90 degrees, the angles in a rhombus are not.
How do you prove a rhombus is not a square?Since a rectangle need not have equal sides, it is not square. Every square is a rectangle and a rhombus. Due to the fact that every square has an equal number of sides, they are all rhombuses. Due of the 90-degree interior angles, all squares are also rectangles.
The main difference between a square and a rhombus is that whereas a square's angles are all 90 degrees, a rhombus's angles are not. However, both shapes have equal sides on every side.
Both a square and a rhombus have equal-length sides. But while a rhombus only has its opposite angles equal, a square only has angles that are all 90 degrees.
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find the coordinates of point p along the directed line segment from j(-4,12) to k(10,-9) that partitions the segment in a ratio of 3:4
Answer:
Step-by-step explanation:
By graphing the line, it is easy to see that the point (4,10) will partition the line in a ratio of 3:4.
By graphing the line, it is easy to see that the point (4,10) will partition the line in a ratio of 3:4.You could also calculate this by finding the difference in x and y coordinates of the given points, and partitioning those differences in a 3:4 ratio on a number line.
By graphing the line, it is easy to see that the point (4,10) will partition the line in a ratio of 3:4.You could also calculate this by finding the difference in x and y coordinates of the given points, and partitioning those differences in a 3:4 ratio on a number line.In this case,
By graphing the line, it is easy to see that the point (4,10) will partition the line in a ratio of 3:4.You could also calculate this by finding the difference in x and y coordinates of the given points, and partitioning those differences in a 3:4 ratio on a number line.In this case,X coord difference: 12 - (-2) = 14
By graphing the line, it is easy to see that the point (4,10) will partition the line in a ratio of 3:4.You could also calculate this by finding the difference in x and y coordinates of the given points, and partitioning those differences in a 3:4 ratio on a number line.In this case,X coord difference: 12 - (-2) = 14Y coord difference: 18 - 4 = 14
By graphing the line, it is easy to see that the point (4,10) will partition the line in a ratio of 3:4.You could also calculate this by finding the difference in x and y coordinates of the given points, and partitioning those differences in a 3:4 ratio on a number line.In this case,X coord difference: 12 - (-2) = 14Y coord difference: 18 - 4 = 14To partition 14 in a 3:4 ratio, we could use a 6:8 ratio.
By graphing the line, it is easy to see that the point (4,10) will partition the line in a ratio of 3:4.You could also calculate this by finding the difference in x and y coordinates of the given points, and partitioning those differences in a 3:4 ratio on a number line.In this case,X coord difference: 12 - (-2) = 14Y coord difference: 18 - 4 = 14To partition 14 in a 3:4 ratio, we could use a 6:8 ratio.One way to think of it, is that you are "adding" 6 and 8 to the x and y coordinates of the lower coordinate, in the case (-2,4).
By graphing the line, it is easy to see that the point (4,10) will partition the line in a ratio of 3:4.You could also calculate this by finding the difference in x and y coordinates of the given points, and partitioning those differences in a 3:4 ratio on a number line.In this case,X coord difference: 12 - (-2) = 14Y coord difference: 18 - 4 = 14To partition 14 in a 3:4 ratio, we could use a 6:8 ratio.One way to think of it, is that you are "adding" 6 and 8 to the x and y coordinates of the lower coordinate, in the case (-2,4).By "adding" 6 to the x coordinate, and 8 to the y coordinate, we get (4,10), as we showed in the graph.
I need help with this question please and thank you .
Step 1: [tex]6.3^2+x^2=15.4^2[/tex]
Step 2: [tex]x^2=15.4^2-6.3^2[/tex]
Step 3: [tex]x=\sqrt{15.4^2-(6.3)^2}[/tex]
Step 4: [tex]x=14.05[/tex]
what is the graters common divisor of 3,4 and 5
The HCF of 3, 4, and 5 is 1. ∴ The most increased numeral that diverges 3, 4, and 5 is 1.
What is divisor?The dividend is the number that is being divided (in this case, 15), and the divisor is the number that is being divided (in this case, 3). The quotient is the end result of division. A number that divides another number is known as a divisor, sometimes known as a factor (written ). Only positive divisors are typically taken into account for integers, despite the fact that any positive divisor's opposite is obviously also a divisor. a list of the (positive) factors that divide a given number. The number you are dividing by is referred to as the divisor in mathematics. The divisor in the equation 24 6 4 is 6.To learn more about divisor, refer to:
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(0,-1)
(2,-5)
find slope
Answer: The slope between the points (0,-1) and (2,-5) is (-5 - (-1)) / (2 - 0) = -4 / 2 = -2.
Step-by-step explanation:
Gerad's DVD club charges a $10 annual fee and then $2 per DVD purchased. Karen's DVD club charges a $15 annual fee and then $1 per DVD purchased. After purchasing how many DVDs will Gerad and Karen pay the same amount?
Answer: 5
Step-by-step explanation:
Gerad's DVD club costs = Karen's DVD costs = y
Gerad - y = 2x + 10
Karen - y = x +15
2x + 10 = x + 15
x = 5
A ballet dancer whose weight is 60 kg performs a move on one foot during which she
applies a pressure of 1,500,000 Pa on the ground. Is she likely to be standing with her foot
flat on the ground, or is she on tiptoe?
It is likely that she is on tiptoe, as a pressure of 1,500,000 Pa is a high pressure for a 60 kg person to be applying with just one foot while standing flat on the ground.
How to know if the dancer is tiptoeingThe unit of pressure Pa is equivalent to Newton per square meter
A mass of 60 kg is converted to force by
= m * g
= 60 * 10
= 600 N
Pressure = Force / Area
Area = Force / Pressure
Area = 600 N / 1,500,000 Pa
Area = 0.0004 square meter
Area = 4 square centimeter
This area is much smaller than the foot hence the dancer is tiptoeing
A pressure of 1,500,000 Pa suggests that the dancer is applying a significant amount of force to a small area, which is typical of being on tiptoe.
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A urvey wa given to people who own a certain type of car. What percent of the people urveyed were completely with the car?
Using the percentage concept, it is found that 60.29% of the people surveyed were completely satisfied with the car.
A percentage is the number of desired outcomes, multiplied by 100%, and divided by the number of total outcomes and also defines a number or ratio that can be expressed as a fraction of 100.
To calculate the percentage, we have to divide the value by the total value and then multiply the resultant by 100.
In this problem, researching the internet, it is found that:
A total of 1260 + 650 + 180 = 2090 people were surveyed.
Of those, 1260 were completely satisfied.
Hence:
[tex]P=\frac{1260}{2090} *100 =60.29[/tex]
60.29% of the people surveyed were completely satisfied with the car.
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two players a and b play a game rolling a fair die. if a rolls a 1, they immediately roll again, and if it is a 2, then a wins. otherwise, b rolls. if b rolls a 6, they win, otherwise a rolls again and so on. what's the probability player a wins?
The probability player a wins is [tex]\frac{1}{36}[/tex] . Probability is a measure of the likelihood of an event to occur.
Sample space for the given event is :
{(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),(3,1),(3,2),(3,3),(3,4),(3,5),(3,6),(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),(5,1),(5,2),(5,3),(5,4),(5,5),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)}
A sample space is the total numbers of outcomes that can happen with respect to a given single event or a combination of different event, like in this case there were two events both of rolling a dice
Player a wins if he gets (1,1) otherwise he looses. As we can see there is only one choice for the given event to happen. So his probability is less likely to happen that is 1 time in every 36 time.
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four $12$-sided dice are rolled. what is the probability that the number of dice showing a two digit number is equal to the number of dice showing a one digit number? express your answer as a common fraction. (assume that the numbers on the $12$ sides are the numbers from $1$ to $12$ expressed in decimal.)
27/128 is the probability that the number of dice showing a two-digit number is equal to the number of dice showing a one-digit number.
Probability means Possibility. It states how likely an event is about to happen.
The probability of an event can exist only between 0 and 1 where 0 indicates that the event is not going to happen i.e. Impossibility and 1 indicates that it is going to happen for sure i.e. Certainty.
I'll take a stab at this one. if the number of dice showing a two-digit number = the number of dice showing a one-digit number, then 2 must show a two-digit number and 2 must show a one-digit number
There are 3 two-digit numbers and 9 one-digit numbers on each die
So....the probability is
C(4,2) (3/12)^2 (9/12)^2
C(4,2) (1/4)^2 (3/4)^2
=27/128.
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Two types of stereos were on sale at a local car stereo dealer.
The J-Series model sold for $II8. The K-Series model sold for $92. During the sale, 32 stereos were sold. The receipts for these stereos totaled $3,230. How many of each type of stereo did the local dealer sell during this sale?
Answer:
11 J- series and 21 K- series
Step-by-step explanation:
create a pair of equations in 2 variables and solve simultaneously.
let x represent J- series and y the K- series , then
x + y = 32 ( subtract x from both sides )
y = 32 - x → (1)
118x + 92y = 3230 → (2)
substitute y = 32 - x into (2)
118x + 92(32 - x) = 3230
118x + 2944 - 92x = 3230
26x + 2944 = 3230 ( subtract 2944 from both sides )
26x = 286 ( divide both sides by 26 )
x = 11
substitute x = 11 into (1)
y = 32 - 11 = 21
11 of J- series and 21 of K- series models were sold
two sides of an isosceles triangle are 20 and 30. what is the difference of the largest and the smallest possible perimeters?
Two sides of an isosceles triangle are 20 and 30. Then the difference of the largest and the smallest possible perimeters is 10.
Determine the difference of the largest and the smallest possible perimetersThese are the specified parameters:
Two sides of an isosceles triangle are 20 and 30.
The perimeter of the largest isosceles triangle
With a side measurement of 30 feet and a base of 20.
Roving = 30 + 30 + 20
= 80
The perimeter of the smallest isosceles triangle
With a side measurement of 20 feet and a base of 30.
Roving = 20 + 20 + 30
= 70
The difference of the largest and the smallest perimeters
= 80 - 70
= 10
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△ABC has vertices at A(5,1), B(−3,1), and C(−2,5).
Point D is located on the intersection of the altitude and AB¯¯¯¯¯¯¯¯, in such a way that D has coordinates at (−2,1).
What is the area of △ABC?
Answers:
16 units squared
28 units squared
18 units squared
14 units squared
The area of △ABC is 22 square units.
How to determine the area of △ABC?From the question, we have the following parameters that can be used in our computation:
△ABC has vertices at A(5,1), B(−3,1), and C(−2,5).
The area of △ABC is then calculated as
Area = |(1/2)(x1)(y2 - y3) + (x2)(y3 - y1) + (x3)(y1 - y2)|
Plugging in the given vertices for △ABC, the area can be calculated as follows:
Area = |(1/2)(5)(1 - 5) + (-3)(5 - 1) + (-2)(1 - 1)|
This gives
Area =|-22|
= 22
The area of △ABC is 22 square units.
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The population of a town is 7,000, and it grows at a rate of 4.6% per year. What will the population be in 10 years?
Answer:
10,975
Step-by-step explanation:
If you multiply 7,000 by 0.046 10 times and added them together, it would be 10,975
Answer:
10975
Step-by-step explanation:
which expression is equivalent to 6x + 2 - 3x
Answer: 3x+2
Step-by-step explanation:
6x+2-3x
3x+2
97
Use the ALEKS calculator to write as a percentage.
32
Round your answer to the nearest tenth of a percent.
The answer is 0.3% when rounded to the nearest tenth of a percent.
Solving using ALEKS calculator we have:Using the ALEKS calculator, let's divide 32 by 100 and write the result up to 2 decimal places:
= 32
100
= 0.32
Rounding to the nearest tenth of a percent., the result of the division is 0.3%.
(The second decimal place is 2, which is smaller than 5, so after rounding, the first decimal place is not changed).
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