The population of a city with 400,000 population growing at a rate of 4% per year can be calculated using the following formula:
P(t) = P0 (1 + r)t
Where P0 is the initial population, r is the growth rate, and t is the number of years the growth is applied.
In this example, the initial population is 400,000, the growth rate is 0.04, and t is 17 years. Applying this formula, we get:
P(17) = 400,000 (1 + 0.04)17
P(17) = 615,288
Therefore, the population of this city in 17 years will be 615,288 if the growth rate of 4% per year continues.
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If variance of the data a, b, c, ta, e is 2032 , then variance of 3a+2,3b+2, 3c+2,3d+2,3c+2, is :
The variance of 3a+2,3b+2, 3c+2,3d+2,3c+2, is 3657.6.
What is Variance?
Variance is a statistical measurement of the variation in numbers within a data set. Variance, in more precise terms, indicates how far apart any number in the set is from both the mean (average) and, consequently, from every other number in the set.
First, we can calculate the mean of the original dataset:
Mean = (a + b + c + ta + e) / 5
Then, we can calculate the variance using the formula:
Variance = ((a - Mean)² + (b - Mean)² + (c - Mean)² + (ta - Mean)² + (e - Mean)²) / 5
Given that the variance of the original dataset is 2032, we can substitute this value in the formula and solve for the mean:
2032 = ((a - Mean)² + (b - Mean)² + (c - Mean)² + (ta - Mean)² + (e - Mean)²) / 5
Simplifying this equation, we get:
(a - Mean)² + (b - Mean)² + (c - Mean)² + (ta - Mean)² + (e - Mean)² = 10160
Now, we can apply the transformation to the dataset by adding 2 and multiplying by 3:
New dataset: 3a + 2, 3b + 2, 3c + 2, 3d + 2, 3e + 2
To find the variance of the new dataset, we follow the same steps as before:
Mean = (3a + 2 + 3b + 2 + 3c + 2 + 3d + 2 + 3e + 2) / 5 = 3Mean + 2
Variance = ((3a + 2 - Mean)² + (3b + 2 - Mean)² + (3c + 2 - Mean)² + (3d + 2 - Mean)² + (3e + 2 - Mean)²) / 5
Simplifying this equation, we get:
Variance = ((3a - 3Mean)² + (3b - 3Mean)² + (3c - 3Mean)² + (3d - 3Mean)² + (3e - 3Mean)²) / 5
Variance = 9((a - Mean)² + (b - Mean)² + (c - Mean)² + (d - Mean)² + (e - Mean)²) / 5
Variance = 9(2032) / 5
Variance = 3657.6
Therefore, the variance of the new dataset is 3657.6.
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One angle of a triangle measures 80°. The other two angles are in a ratio of 3:7. What are the measures of those two angles?
Answer:
30 degrees and 70 degrees
Step-by-step explanation:
A triangle has 180 degrees, and if you take away the known 80, you are left with 100 degrees to be split in a 3:7 ratio.
Find the difference of 42 3/4−34 1/8
The difference of the fractions 42¾ - 34⅛ is equal to 8⅝.
How to evaluate the difference of the fractionsThe given fractions are expressed as mixed numbers, so we shall first rewrite them as improper fractions, find the lowest common multiple of their denominators to have a single fraction, before then subtracting the resulting numerators to have their difference.
42¾ = 171/4
34⅛ = 273/8
42¾ - 34⅛ = 171/4 - 273/8
LCM of 4 and 8 is 8, so;
42¾ - 34⅛ = (171 ×2 - 273 × 1)/8 {simplifying to a single fraction}
42¾ - 34⅛ = (342 - 273)/8
42¾ - 34⅛ = 69/8
42¾ - 34⅛ = 8⅝
Therefore, difference of the fractions 42¾ - 34⅛ is equal to 8⅝.
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A pharmaceutical company receives large shipments of aspirin tablets. The acceptance sampling plan is to randomly select and test 17 tablets, then accepts the whole batch if there is only one or none that doesn't meet the required specifications. If a particular shipment of thousands of aspirin tablets actually has a 3% rate of defects, what is the probability that this whole shipment will be accepted?The probability that this whole shipment will be accepted is ____.
The probability that this whole shipment will be accepted is 0.000133. The probability that this whole shipment will be accepted can be found using the binomial probability formula, where n is the number of trials, x is the number of successes, p is the probability of success, and q is the probability of failure.[tex]P(x) = (n! / (x! * (n - x)!)) * (p^x) * (q^(n - x))[/tex]
In this case, n = 17, p = 0.97 (the probability of a tablet meeting the required specifications), and q = 0.03 (the probability of a tablet not meeting the required specifications).
We want to find the probability of either 0 or 1 defects, so we will calculate the probabilities for both and add them together.
[tex]P(0) = (17! / (0! * (17 - 0)!)) * (0.97^0) * (0.03^(17 - 0)) = 0.00000497P(1) = (17! / (1! * (17 - 1)!)) * (0.97^1) * (0.03^(17 - 1)) = 0.000128P(0 or 1) = P(0) + P(1) = 0.00000497 + 0.000128 = 0.000133[/tex]
Therefore, the probability that this whole shipment will be accepted is 0.000133.
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Construct a cumulative frequency distribution table from the frequency table given below. Class Interval 0 − 8 8 − 16 16 − 24 24 − 32 32 − 40 Frequency 9 13 12 7 15
The frequency of all the five intervals is 9 + 13 + 12 + 7 + 15 = 56.
The cumulative frequency distribution table from the given frequency table:Class IntervalFrequencyCumulative Frequency0 − 89 89 + 1312 25 + 12 + 7 32 + 1515 47 + 15 62It is clear that the frequency of the first interval is 9. Therefore, the frequency of the first interval is 9.Next, the frequency of the second interval is 13. Therefore, the frequency of the first and second intervals is 9 + 13 = 22.Next, the frequency of the third interval is 12. Therefore, the frequency of the first, second and third intervals is 9 + 13 + 12 = 34.Then, the frequency of the fourth interval is 7. Therefore, the frequency of the first, second, third, and fourth intervals is 9 + 13 + 12 + 7 = 41.Finally, the frequency of the fifth interval is 15. Therefore, the frequency of all the five intervals is 9 + 13 + 12 + 7 + 15 = 56.
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HELP. Turn the equation into y=mx+b if not already. Figure out whether it has one solution, no solution or infinite solutions. Use graphing, substitution or elimination.
-3x+3y=4
-x+y=3
(same slope or different slop?)
(same y-intercept or different y-intercept?)
Answer:
Starting with the given system of equations:
-3x + 3y = 4
-x + y = 3
To solve for y in terms of x, we can rearrange each equation to the slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.
For the first equation, we can add 3x to both sides and divide by 3 to obtain:
3y = 3x + 4
y = x + 4/3
So the slope of the first equation is 1 and the y-intercept is 4/3.
For the second equation, we can add x to both sides to obtain:
y = x + 3
So the slope of the second equation is also 1, but the y-intercept is different at 3.
To determine the number of solutions, we can use either substitution or elimination.
Using substitution, we can solve for x in the second equation:
x = y - 3
Then substitute this expression for x in the first equation:
-3(y - 3) + 3y = 4
Simplifying, we get:
-3y + 9 + 3y = 4
9 = 4
This is a contradiction, so the system has no solution.
Alternatively, we can use elimination to solve for y:
-3x + 3y = 4
-x + y = 3
Multiplying the second equation by 3, we get:
-3x + 3y = 4
-3x + 3y = 9
Subtracting the second equation from the first, we get:
0x + 0y = -5
This is a contradiction, so the system has no solution.
In summary, the given system of equations has no solution. The two equations have the same slope but different y-intercepts.
Hope this helps you! I'm sorry if it's wrong. If you need more help, ask me! :]
Answer:
Equation 1: y = x + 4/3
Equation 2: y = x +3
No solution, same slope, different y-intercepts.
Step-by-step explanation:
The two equations have been converted to y=mx+b or slope-intercept form. The slope is the same (1), but the intercepts are different. Equation 1 crosses the y-axis at (0, 4/3), Equation 2 crosses the y-axis at (0,3). Both equations represent parallel lines, so there is no solution because they will never intersect each other.
Ava spent 3 hours yesterday practicing the piano. She is going to spend at least 3 hours practicing today which number line shows
this
The number line that models the total amount of time Ava will practice piano in all is shown in the figure and Ava will practice piano for a total of 6 hours.
We can model the total amount of time Ava will practice piano in all using a number line. Since she practiced for 3 hours yesterday and is going to practice for another 3 hours today, we can represent this on a number line as follows:
The number line above represents the total amount of time Ava will practice piano in all. The first mark (0) represents the starting point, which is when she has not started practicing yet. The second mark (3) represents the time she spent practicing yesterday, and the third mark (6) represents the time she will spend practicing today. The distance between the first mark and the third mark (0 to 6) is the total amount of time Ava will practice piano in all, which is 6 hours.
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A freight train left the main station heading east at average speed of 100kph. An hour later an express train left the same station heading west at an average of 170kph. At what time will they be 600kms apart from each other?
Apart from each other 3.33 hours
To determine at what time the freight and express trains will be 600 km apart from each other, we must first determine the distance covered by each train. We can then use these distances to determine the total distance between the two trains at any given time.In this problem, we are given the following information:A freight train leaves the main station heading east at an average speed of 100 km/h.An hour later, an express train leaves the same station heading west at an average speed of 170 km/h.We are asked to determine the time at which they will be 600 km apart from each other.We can use the following formula to determine the distance covered by each train:D = RTwhere:D is the distance coveredR is the average speedT is the time takenTo find the distance covered by the freight train, we can use the following formula:D1 = RT1where:D1 is the distance covered by the freight trainR is the average speed of the freight trainT1 is the time taken by the freight trainTo find the distance covered by the express train, we can use the following formula:D2 = RT2where:D2 is the distance covered by the express trainR is the average speed of the express trainT2 is the time taken by the express trainNow, let's determine the distances covered by each train:D1 = 100(T1+1)D2 = 170T2We know that the total distance between the two trains is 600 km, so we can use the following equation to solve for the time at which they will be 600 km apart:D1 + D2 = 600100(T1+1) + 170T2 = 600100T1 + 170T2 + 100 = 600100T1 + 170T2 = 500(100/170)T1 + T2 = 5.9 hoursThe time taken by the freight train is T1 + 1, so we can substitute T1 + 1 for T1 in the equation above to solve for T1:T1 + T2 = 5.9100(T1+1)/170 + T2 = 5.9T1 + 1 + 1.7T2 = 5.9T1 + 1.7T2 = 4.9T1 = (4.9 - 1.7T2)/1.9Now, we can substitute this value of T1 into the equation we used earlier to solve for T2:100T1 + 170T2 = 500100((4.9 - 1.7T2)/1.9) + 170T2 = 500T2 ≈ 2.33Therefore, the time at which the two trains will be 600 km apart from each other is approximately 2.33 hours after the express train leaves the main station. To find the exact time, we need to add this value to the time at which the express train left the main station:Time = 1 + 2.33 = 3.33 hoursTherefore, the two trains will be 600 km apart from each other 3.33 hours after the express train leaves the main station.
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Please help I do not understand this .
Nuhome movers charges $95 per
hour for loading/unloading
Jay is moving a distance of 200 miles and needs 9 hours of loading/unloading and 7 hours of packing/ unpacking. His total moving cost including tax charges equals to the $2,053.8375.
We have to calculate Jay's moving cost if the service also charges 7.25% tax on the total. Here, Jay is moving a distance of 200 miles and needs 9 hours of loading/unloading and 7 hours of packing/ unpacking. Now, first we determine the NuHome Movers charges,
Rate of NuHome Movers charges for loading/unloading services = $95 per hour and NuHome Movers charges for 9 hours of loading/unloading services = Multiplication of number of hours by rate of service = 9× $95 = $855 --(1)
Rate of NuHome Movers charges for packing/unpacking services = $80 per hour land NuHome Movers charges for 7 hours of packing/unpacking services = Multiplication of number of hours by rate of service = 7× $80 = $560--(2)
Now, determine charge for truck rental,
Rate of NuHome Movers charges for truck rental = $2.50 per mile
and NuHome Movers charges for 200 miles truck rental = number of miles × rate of each mile = $2.50 × 200
= $500--(3)
Thus, total cost of charges which Jay will pay = charges cost for packing/unpacking services + charges cost for loading/unloading services + charges for truck rental
= $855 + $560 + $500 ( from (1), (2),(3))
= $1,915
Tax charges on total = 7.25%
Determine the Jay's total moving cost including taxes = $1,915 + $1915(7.25/100)
= $1,915 + $1915( 0.0725)
= $1,915 + $138.8375
= $2,053.8375
Hence, required cost value is $2,053.8375.
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Complete question :
NuHome Movers charges $95 per hour for loading/unloading services and $80 per hour for packing/unpacking services. Their charge is $2.50 per mile for truck rental. Jay is moving a distance of 200 miles and needs 9 hours of loading/unloading and 7 hours of packing/ unpacking. What will his moving cost be if the service also charges 7.25% tax on the total?
A circle has a radius of 3/2x^5y^-2 centimeters. To find the area of a circle the formula A = π • r^2 can be used. Which expression represents the are of the circle in square centimeters?
Answer:
Step-by-step explanation:
Correct option is B)
Center is the point of intersection of diagonals.
⇒2x−3y=5
⇒3x−4y=7
Solving simultaneous equation, x=1,y=−1
Center =(1,−1)
For radius r ( let )
⇒r=
π
154
⇒
22
154
×7
=7
Equation -
⇒(x−1)
2
+(y+1)
2
=7
2
⇒x
2
+1−2x+y
2
+1+2y=49
⇒x
2
+y
2
−2x+2y=49−2
⇒x
2
+y
2
−2x+2y=47
Hence, the answer is x
2
+y
2
−2x+2y=47.
Select all equations that are equivalent to x2+6x=16.
The equivalent equation of x^2 + 6x = 16 are (x + 3)^2 = 25 and x^2 + 6x + 9 = 25
How to determine the equivalent equationFrom the question, we have the following parameters that can be used in our computation:
x2+6x=16
Express properly
So, we have the following representation
x^2 + 6x = 16
Add 9 to both sides of the equation
x^2 + 6x + 9 = 25 --- this represents option (c)
Expand
x^2 + 3x + 3x + 9 = 25
When the expression is factorized, we have
(x + 3)^2 = 25
Hence, the equivalent equation is (x + 3)^2 = 25
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Complete question
Select all equations that are equivalent to x2+6x=16.
The options are added as an attachment
A lake near Susan's house is predicted to lose water every day because of a drought. The table shows the estimated water depth in feet, y, after x days of drought. 0 100 1 99.5 2 99 3 98.5 4 98 5 97.5 Choose the function that represents the data. O y = -0,5x + 100 O y=-x05 + 100 O y=-0.5x² + 100 Oy= - +100 X 0.5
As the table shows the estimated water depth in feet, y, after x days of drought. The function that represents the data is y = -0,5x + 100. The Option A is correct.
What does a function means?A function is defined as a relationship between a set of inputs that each have one output. A function is a relationship between inputs in which each input is related to exactly one output.
Based on the given table, it appears that the water depth is decreasing by 0.5 feet every day due to the drought. Additionally, the initial depth of the lake was 100 feet.
Therefore, the function that represents the data is y = -0.5x + 100 where y represents the water depth in feet and x represents the number of days of drought.
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I just need q24. a) i dunno how to do it
The product in diagram A is: (3x)*(2x + 3y)
And the product in diagram B is: 5a*(8a + 3)
How to write the given products?
Let's start with the diagram A, we can define the long stripe as x and the short one as y.
On the top side we can see 3x.
On the left side we can se 2x + 3y
Then the product modeled is just:
(3x)*(2x + 3y)
Now let's go to diagram B.
Here we can see that the left side has a length 5a, and then we have two top sides, so this can be written as a sum:
8a + 3
The product between these two quantities is:
p = 5a*(8a + 3)
These are the two products.
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Please help
A passenger train and a freight train traveling in the same direction leave San Jose at 3 pm. The passenger train travels 3 times at fast. At 6 pm, the trains are 240 miles apart. How fast is each traveling?
Therefore , the solution of the given problem of speed comes out to be train is moving at 60 miles per hour while the freight train is moving at 20 miles per hour.
What is speed, exactly?By keeping an eye on something from a distance, we can gauge its speed. An object's speed determines how far it can travel in a given period of time. Utilizing the equation velocity = distance/time, velocity is determined. Kilometers per hour (mileage), kilometres per hour (km/h), and metres per second (m/s) are the three most widely used measures of speed (mph).
Here,
The freight train would cover the following distance in three hours at the speed of "x" miles per hour:
=> Distance = speed x duration = x miles/hour x 3 hours = 3x miles.
The passenger train would cover the following distance in three hours at "3x" kilometres per hour:
Distance is calculated as follows: 3 kilometres per hour times 3 hours equals 9 miles.
We can now determine the 240-mile overall distance between the two trains at 6 o'clock:
Overall distance equals the sum of the routes taken by the passenger and freight trains.
=> 240 miles = 3x miles + 9x miles
=> 240 miles = 12x miles
Therefore,
=> x=20 kilometres per hour
=> 3x = 60 mph
As a result, the passenger train is moving at 60 miles per hour while the freight train is moving at 20 miles per hour.
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Sarah invested £12 000 in a unit trust five years ago.
The value of the unit trust has increased by 7% per annum for each of the last 3 years.
Before this, the price had decreased by 3% per annum.
Calculate the current price of the unit trust.
Give your answer to the nearest whole number of pounds.
Answer:efefef
Step-by-step explanation:
efregtythth
Angie is x years old. Mandy is 22 years older than Angie. In 2 years’ time, Mandy will be twice Angie’s age. Calculate Angie and Mandy’s current age
Answer:
Angie is 20, Mandy is 42.
Step-by-step explanation:
Angie's current age = x
Mandy's current age = y, also x + 22
Mandy's age in 2 years = 2x+2
2x + 2 = x + 22
x + 2 = 22
x = 20
y = x + 22
y = 20 + 22
y = 42
A survey asked a group of adults and youths if they prefer reading books printed on paper or electronic books.
Book Preference
------------Print Electronic
Youths 28 40
Adults 37 38
What percent of the youths surveyed prefer reading electronic books? Round your answer to the nearest whole number percent.
Answer: 59%
Step-by-step explanation:
To find the percentage of youths who prefer reading electronic books, we need to divide the number of youths who prefer electronic books by the total number of youths surveyed and then multiply by 100.
The total number of youths surveyed is:
28 + 40 = 68
The number of youths who prefer electronic books is:
40
Dividing the number of youths who prefer electronic books by the total number of youths surveyed and multiplying by 100, we get:
(40/68) x 100% = 58.82%
Rounding to the nearest whole number percent, we get:
59%
Therefore, approximately 59% of the youths surveyed prefer reading electronic books.
Answer:
59%
Step-by-step explanation:
16) Choose the picture that correctly shows the first image being reflected across *
line s, then across line t.
Answer:
Number C shows to be first image being reflected across.
how many ounces of cornstarch are there in a box containing 300 grams of cornstarch
Answer:
Roughly 10 oz, exact amount is 10.58219
Consider a box with dimensions 3 cm × 5 cm × 11 cm. If all of its dimensions are increased by x cm, what values of x will give a box with a volume between 300 cm3 and 900 cm3?
Explain your solution and solve using the topic of inequalities.
The correct answers are x³ + 19 x² + 103 x - 135 = 0 and x³ + 19 x² + 103 x - 735 = 0.
Given:
A box with dimensions 3 cm × 5 cm × 11 cm
Current volume of given box = 3×5×11 = 165 cm^3
New volume of box = (3+x) × (5+x) × (11+x)
= (15 + 8 x + x²) × (11+x)
= 165 + 103 x + 19 x^2 + x³
For volume to be 300 cm³
=> x³+ 19 x² + 103 x + 165 = 300
=> x³ + 19 x² + 103 x - 135 = 0
For volume to be 900 cm³ -
=> x³ + 19 x² + 103 x + 165 = 900
=> x³ + 19 x²+ 103 x - 735 = 0
Therefore, x^3 + 19 x^2 + 103 x - 135 = 0 and x³ + 19 x² + 103 x - 735 = 0 are the solution.
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EXERCISE
Based on what you've read, decide which of the four basic operations you need to use. Then, solve the problems.
On a trip to Florida, Santina drove 203 miles and Carole drove 189 miles. How many more miles did Santina drive than Carole?
A restaurant uses 80 pounds of potatoes per week. The restaurant owner buys the potatoes in 10-pound bags from a local farmer. How many bags will the owner need to buy this week?
Six-packs of cola were on sale at a grocery store. John bought the limit, which was 8 six-packs. How many individual cans of cola is this?
Lori is reading The Grapes of Wrath for her American literature class. She read 85 pages last weekend, 135 pages during the week, and 98 pages this weekend. What is the total number of pages she has read so far?
A football team scored 34 points in their first game, 21 points in their second game, 9 points in their third game, and 28 points in their fourth game. What is the team’s average score for the season so far?
Reuben chews four pieces of chewing gum a day. The gum is sold in packages containing seven pieces. How many packages of gum will he need to buy this week?
Apply the rules of order of operations to solve the following problems.
52 – 6 × 7 = ?
108 ÷ 9 × 5 = ?
(54 + 42) ÷ 12 =?
183 – [(12 + 7) × 4] = ?
Chan wants to buy a used car that costs $8,500. He took out a loan for the cost of the car, and his payments are $209 per month for four years. At the end of four years, how much more than the car’s original price will he have paid? (Remember, there are twelve months in one year.)
Linda commutes a total of 54 miles to and from work every day. She needs a new car, and good gas mileage is important to her. She’s considering two models. The first model averages 30 miles per gallon, and the second averages 27 miles per gallon. How many gallons of gas will she save in a five-day work week if she buys the first car instead of the second car?
A waitress earned the following tips during one hour: $4.50, $3.00, $5.00, and $3.75. She gave each of the two busboys working with her $2.50. In addition to tips, the restaurant pays her $4.25 per hour. How much did she earn during that one hour of work?
Juan went out to lunch with five friends. They decided to divide the bill evenly among them. Juan estimated that his lunch cost $5.25. The entire bill came to $37.20. Would Juan’s lunch have cost more or less if he paid for it separately? How much more or less?
Santina drive 14 miles more than Carole. The owner needs to buy 8 bags this week. John bought 48 individual can of cola.
What do you means by mile?Mile is measurement unit of land or any surface. We use it to calculate the distance.
Now we have to calculate these questions,
a. Santina drive 203 miles and Carole drive 189 Miles.
Santina drive 14 miles more than Carole.
b. A restaurant uses 80 pounds of potatoes per week and the owner buys the potatoes in 10 pound bags.
So, Number of bags, 80/10 = 8 bags.
The owner needs to buy 8 bags this week.
c. Six-packs of cola were on sale at a grocery store (i.e. 6 cola in pack) and he buy 8 six-packs of cola.
Total number of cola can = 8 X 6 = 48 cola can
John bought 48 individual can of cola.
d. Lori read 85 pages last weekend, 135 pages during the week, and 98 pages this weekend.
So, total number of pages read by Lori = 85 + 135 + 98
= 318
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Select the shapes that have at least 1 apex.
Right circular cone
Right circular cylinder
Right pyramid
Right triangular prism
A and B
A and C
B and C
C and D
Answer:
A and C : cones and pyramids
Step-by-step explanation:
only cones, pyramids and isosceles triangles have apexes
The shapes that have at least 1 apex are:
Right circular cone
Right pyramid
Therefore, the answer is C and D.
Crystal is buying new carpet for her room. Carpeting is on sale for 20% off. Find the sale price of the carpeting if the original price was $480.
Answer: $384
Step-by-step explanation: 480 - 20% = 384
If P(A) = 7/13, P(B) = 5/13, and P(A and B) = 3/13, what will be P(A|B)?
If P(A) = 7/13, P(B) = 5/13, and P(A and B) = 3/13, then the probability of P(AIB) = 3/5.
Probability is a measure of the likelihood of an event occurring. Many events cannot be predicted with absolute certainty. We can only predict the probability of an event by using it, i.e. the probability of it occurring.
The probability can range from 0 to 1, where 0 means the event is unlikely to happen and 1 means it will definitely happen. All events in the sample space have a probability of 1. For example, when we flip a coin, heads or tails, there are only two possible outcomes (H, T). But when you toss two coins, there are four possible outcomes, namely {(H, H), (H, T), (T, H), (T, T)}.
According to the Question:
Given that:
P(A) = 7/13
P(B) = 5/13
P(A∩B) = 3/13
We know that :
P(A|B) = P(A∩B) / P(B).
(By formula for conditional probability)
P(AIB) = (3/13)÷ (5/13)
= 3/5
Hence, the value of P(A|B) = 3/5.
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Miguel is playing a game in which a box contains four chips with numbers written on them. Two of the chips have the number 1, one chip has the number 3, and the other chip has the number 5. Miguel must choose two chips, and if both chips have the same number, he wins $2. If the two chips he chooses have different numbers, he loses $1 (–$1).
Let X = the amount of money Miguel will receive or owe. Fill out the missing values in the table. (Hint: The total possible outcomes are six because there are four chips and you are choosing two of them.)
questions to answer:
What is Miguel’s expected value from playing the game?
Based on the expected value in the previous step, how much money should Miguel expect to win or lose each time he plays?
What value should be assigned to choosing two chips with the number 1 to make the game fair? Explain your answer using a complete sentence and/or an equation.
On average, Miguel loses half a dollar every time he plays.
How to solve
To check all the events (6), we label the chips.
Suppose one chip with 1 is labeled R1 and the other B1 (as if they were red and blue). Now, lets take all combinations; for the first chip, we have 4 choices and for the 2nd chip we have 3 remaining choices.
Thus there are 12 combinations. Since we dont care about the order, there are only 6 combinations since for example R1, 3 is the same as 3, R1 for us.
The combinations are: (R1, B1), (R1, 3), (R1, 5), (B1, 3), (B1, 5), (3,5)
We have that in 1 out of the 6 events, Miguel wins 2$ and in five out of the 6 events, he loses one.
The expected value of this bet is: 1/6*2+5/6*(-1)=-3/6=-0.5$.
In general, the expected value of the bet is the sum of taking the probabilities of the outcome multiplied by the outcome; here, there is a 1/6 probability of getting the same 2 chips and so on.
On average, Miguel loses half a dollar every time he plays.
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Ms. Brown's class has 7 boys and 8 girls. Mrs. Ball's class has 4 boys and 10 girls. If one student is randomly selected from each class, what is the probability they are both girls? Answer as simplified fraction.
Considering the probability of independent events, if one student is randomly selected from each class, the probability they are both girls is 8/21.
Definition of probabilityProbability establishes a relationship between the number of favorable events and the total number of possible events.
Then, the probability of any event A is defined as the ratio between the number of favorable cases (number of cases in which event A may or may not occur) and the total number of possible cases:
Probability= number of favorable cases÷ number of possible cases
Probability of Independent EventsTwo events A and B are said to be independent if and only if the probability of event B is not influenced by the occurrence of event A or vice versa.
For any number of independent events, the probability that all the events will occur is the product of the probabilities that the individual events will occur. That is, if A and B are independent events, P(A and B) = P(A)×P(B).
Probability in this caseYou know:
Ms. Brown's class= 8 girls and 7 boys= 15 studentsMrs. Ball's class= 10 girls and 4 boys= 14 studentsIf one student is randomly selected from each class, the probability that a girl is selected in each class is calculated as:
Probability in Ms. Brown's class= 8÷ 15= 8/15Probability in Mrs. Ball's class= 10÷ 14= 10/14Now, the probability that both students selected for the classes are girls, considering that these are independent events, is calculated as:
Probability of both students selected for the classes are girls = Probability in Ms. Brown's class× Probability in Mrs. Ball's class
Probability of both students selected for the classes are girls = 8/15× 10/14
Probability of both students selected for the classes are girls = 8/21
Finally, the probability they are both girls is 8/21.
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A house painter charges a fee for supplies and an hourly fee for the time spent painting. A paint job
that takes 3 h costs $140. A paint job that takes 5 h costs $200.
Equation for the total cost of paint job 'y' with number of hours spent on paining 'x' is formed as:
y = 50 + 3x
y = 50 + 5x
Explain about linear equation in two variables?To determine the values of the variables, we should solve an equation in 2 variables using several techniques and making sure there are 2 equations in the supplied system of equations. If there is only one solution, the given equations are always of parallel lines, and if there isn't a solution at all, the offered equations are of intersecting lines.Let the total cost of paint job be' 'y'.
Let 'x' be the number of hours spent on paining.
Then,
Total cost = supplies + hourly fee* number of hours.
Let the supplies cost be 'z'
140 = z + 3x
200 = z + 5x
Solving both equation.
2x = 60
x = 30
z = 50
Thus, equation for the total cost of paint job 'y' with number of hours spent on paining 'x' is formed as:
y = 50 + 3x
y = 50 + 5x
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Work out the volume of the cone radius is 3. 5 and length is 12
To work out the volume of the cone, we can use the formula V = (1/3) * π * r² * h, where r is the radius of the base of the cone and h is the height of the cone. The volume of the cone is approximately 171.55 cubic units.
The formula for calculating the volume of a cone is given as V = (1/3) * π * r² * h. In this formula, 'r' represents the radius of the base of the cone, and 'h' represents the height of the cone. By substituting the given values, the volume of the cone is calculated to be approximately 171.55 cubic units. This formula is widely used in various fields, such as architecture, engineering, and manufacturing. Calculating the volume of a cone is useful in determining the amount of material required to construct or fill a cone-shaped object, such as a cone-shaped container or a cone-shaped structure. The formula is also used in solving real-life problems related to cones, such as calculating the volume of ice cream in a cone-shaped ice cream cone or the volume of a cone-shaped tank used for storing liquids.
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what is solved 5x+6=3l