Since each birth is independent and the probability of giving birth to a boy or a girl is equal, the probability of giving birth to a boy is 0.5, and the probability of giving birth to a girl is also 0.5.
The probability of the first baby being a boy is 0.5. The probability of the second baby also being a boy is also 0.5, since the gender of one baby does not affect the gender of the other.
The probability of both events occurring together (i.e., the probability of having two boys in a row) is equal to the product of their probabilities. Thus, the probability of having two boys in a row is 0.5 x 0.5 = 0.25 or 25%.
Since simultaneous births do not happen (i.e., babies are born one after another), the probability of the first two babies that are born being boys is the same as the probability of any two specific babies being boys. Therefore, the probability of the first two babies being boys is 0.25 or 25%.
Note that the fact that 8 out of the 17 mothers will give birth to girls is irrelevant to this particular probability problem, since we are only interested in the probability of two specific babies being boys.
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I NEED THIS ANSWER TO THIS QUESTION!!
In order to have $140,000 in 20 years, you should deposit $371 each month.
$89,040 of the $140,000 comes from deposits and $50,960 comes from interest.
How to calculate the periodic deposit (payment)?In Mathematics and Financial accounting, the periodic deposit (payment) for an investment can be calculated by using the following mathematical equation (formula):
[tex]FV=PMT(\frac{(1+\frac{r}{n})^{nt} -1}{\frac{r}{n} })[/tex]
Where:
P represents the periodic deposit (payment).r represents the interest rate.FV represents the future value.t represents the time or number of years.n represents the number of periodic deposits.By substituting the given parameters into the formula for the periodic deposit (payment), we have:
[tex]140,000=PMT(\frac{(1+\frac{0.0425}{12})^{12 \times 20} -1}{\frac{0.0425}{12} })[/tex]
140,000(0.0425/12) = PMT(1.33613612561)
495.8333333333 = PMT(1.33613612561)
PMT = 495.8333333333/1.33613612561
PMT = $371.0949 ≈ $371.
For the amount that comes from deposits, we have:
Total deposit = $371 × 12 × 20
Total deposit = $89,040
For the amount that comes from interest, we have:
Interest = $140,000 - $89,040
Interest = $50,960.
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whats the total amount
Answer: The answer is 4.64$
Step-by-step explanation:
9 pencils is 2.25$. and we have 2.39$ for the notebook. 2.25 + 2.39 = 4.64
leah peeled 175 oranges in 7 hours at that rate how many ornages would she peel in 12 min
Answer:
The answer is 5
Step-by-step explanation:
You divide 175 divided by 7 to find the hourly rate of how many oranges Leah peels. 60 minutes are in a hour. So 12 times 5 is 60. If 175 divided by 7 is 25. And that's hour much she peels in an hour. You divide it by five to find the 12 minute rate, because 12 times 5 is 60 that is equivalent to your hourly rate.
Answer:
Step-by-step explanation:
--> If 7 hrs= 175 oranges
1 hr= 175/7=25
1hr= 60 minutes
So, leah can peal 25 oranges in 60 mins.
Let the number of oranges peeled in 12 mins be x.
60x=25*12
x= 25*12/60
x=300/60
x=5
Leah can peel 5 oranges in 12 minutes,
In 2012, the population of a city was 5.94 million. The exponential growth rate was 3.77% per year.
a) Find the exponential growth function.
b) Estimate the population of the city in 2018.
c) When will the population of the city be 9 million?
d) Find the doubling time.
The exponential growth function can be written as P0 * [tex]e^(rt)[/tex] where P0 is the initial population, r is the annual growth rate expressed as a decimal, t is the time in years, and e is the mathematical constant e. To estimate the population in 2018, we need to find the value of P(t) when t = 6 (since 2018 is six years after 2012).
What is an exponential growth function?An exponential growth function is a mathematical function that models the growth of a quantity at an exponential rate over time.
a) The exponential growth function can be written as:
P(t) = P0 * [tex]e^(rt)[/tex]
where P0 is the initial population, r is the annual growth rate expressed as a decimal, t is the time in years, and e is the mathematical constant e (approximately equal to 2.71828).
In this case, P0 = 5.94 million, r = 0.0377 (3.77% expressed as a decimal), and t is the time in years. Therefore, the exponential growth function for this city is:
P(t) = 5.94 * [tex]e^(0.0377t)[/tex]
b) To estimate the population in 2018, we need to find the value of P(t) when t = 6 (since 2018 is six years after 2012). So, we plug in t = 6 into the exponential growth function:
P(6) = 5.94 * [tex]e^(0.0377 * 6)[/tex] ≈ 7.58 million
Therefore, the estimated population of the city in 2018 was 7.58 million.
c) To find when the population of the city will be 9 million, we need to solve the exponential growth function for t when P(t) = 9. So, we plug in P(t) = 9 into the exponential growth function:
9 = 5.94 * [tex]e^(0.0377t)[/tex]
Divide both sides by 5.94:
1.516835016835017 = [tex]e^(0.0377t)[/tex]
Take the natural logarithm of both sides:
ln(1.516835016835017) = 0.0377t
Solve for t:
t ≈ 8.39
Therefore, the population of the city will reach 9 million approximately 8.39 years after 2012, which is around 2020.
d) The doubling time is the amount of time it takes for the population to double. We can use the exponential growth function to find this time by solving for t when P(t) = 2P0 (twice the initial population):
2P0 = P0 * [tex]e^(rt)[/tex]
Divide both sides by P0:
2 = [tex]e^(rt)[/tex]
Take the natural logarithm of both sides:
ln(2) = rt
Solve for t:
t = ln(2) / r
Substituting r = 0.0377, we get:
t = ln(2) / 0.0377 ≈ 18.38
Therefore, the doubling time for the population of this city is approximately 18.38 years.
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Calculate the area of the shape below
The shape given below consists of a rectangle and a triangle, and its area is 91 m²
Based on the image, we can see that the shape is composed of a rectangle and a triangle.
In order to find the width of rectangle we have to subtract the height of the triangle from the total length:
9m - 4m = 5 m .
Area of Rectangle:
Length = 13 m
Width = 5 m
Area of Rectangle = Length x Width
= 13 m x 5 m
= 65 m²
Triangle:
Base = 13 m
Height = 4 m
Area of Triangle = (1/2) x Base x Height
= (1/2) x 13 m x 4 m
= 26 m²
Total area of the shape = Area of Rectangle + Area of Triangle
= 65 m² + 26 m²
= 91 m²
Therefore, the area of the shape is 91 square meters (m²)
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find exact value by using half angle
sin 75 degrees
Answer: [tex]\frac{\sqrt{6}+\sqrt{2} }{4}[/tex]
Step-by-step explanation:
Half angle formula for sine is
sin([tex]\frac{x}{2}[/tex])=[tex]\sqrt{1-cosx}/2[/tex]
If x is 150, then sin 75=[tex]\sqrt{1-cos150}/2[/tex] =[tex]\sqrt{1-\frac{cos(180-30)}{2} }[/tex]=[tex]\sqrt{1+cos30}/2[/tex]
=[tex]\sqrt{(1/2)+(\sqrt{3}/4)}[/tex] =[tex]\frac{\sqrt{6}+\sqrt{2} }{4}[/tex]
A healthcare provider prescribes a continuous infusion of 0.9% sodium chloride with pancuronium (Pavulon) 25 mg/250 ml at a rate of 0.1 mg/kg/hr for a client with coronary artery bypass grafting. The client weighs 78 kg. The practical nurse should program the infusion pump to deliver how many ml/hour? (Enter numeric value only. If rounding is required, round to the nearest tenth.)
Answer:
To calculate the infusion rate, we need to use the formula:
Infusion rate (ml/hour) = (dose ordered * patient weight * 60) / (drug concentration * 1000)
where:
Dose ordered is the prescribed dose of the drug per unit of time (0.1 mg/kg/hr in this case).
Patient weight is the weight of the client (78 kg in this case).
Drug concentration is the concentration of the drug in the solution (25 mg/250 ml or 0.1 mg/ml in this case).
Substituting the values we have:
Infusion rate = (0.1 mg/kg/hr) * (78 kg) * 60 / (0.1 mg/ml * 1000)
Simplifying:
Infusion rate = 4.68 ml/hour
Therefore, the practical nurse should program the infusion pump to deliver 4.68 ml/hour (rounded to the nearest tenth).
Answer:
To calculate the infusion rate, we need to use the following formula:
Infusion rate (mL/hour) = Total volume (mL) x Infusion rate (mL/hour) / Time (hour)
First, let's calculate the client's infusion rate in mg/hour:
Infusion rate (mg/hour) = 0.1 mg/kg/hour x 78 kg = 7.8 mg/hour
Now, let's convert the pancuronium dose to mg/mL:
25 mg/250 mL = 0.1 mg/mL
To calculate the total volume of the infusion, we need to assume a time frame. Let's assume that the client needs the infusion for 1 hour. Then:
Total volume (mL) = Infusion rate (mg/hour) / Dose (mg/mL) = 7.8 mg/hour / 0.1 mg/mL = 78 mL/hour
Therefore, the practical nurse should program the infusion pump to deliver 78 ml/hour.
Below is how many wild unicorns live in each of the six enchanted forests on Mystical Island.
12
,
3
,
7
,
9
,
18
,
14
12,3,7,
9,18,14
Using the data, create a histogram.
The histogram below shows the distribution of wild unicorns across the six enchanted forests on Mystical Island. To create a histogram, we first need to determine the range and interval for our bins. We can set the range from 0 to 20 and choose an interval of 5.
The x-axis represents the range of unicorn counts, and the y-axis shows the number of forests that fall into each range of 0 5 10 15 20
As we can see from the histogram, the majority of the enchanted forests have between 10 and 15 wild unicorns. Only one forest has fewer than 5 wild unicorns, while another has more than 15. This visualization allows us to easily compare the unicorn populations across the different forests and identify any outliers.
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Does anyone know what they mean by this?
Step-by-step explanation:
The vertical line exactly between them x = -1 is the axis of rotation
Mrs. Williams wants to determine which year-end celebration to choose for the students. She wants student input, so she needs to choose a sample of 20 students from the school. Which of the samples shown is a random sample? Select two answers.
Answer: make sure to add options.
fifteen thousand raffle tickets are sold. One first prize of $3000, two second prizes of $750, and three third prizes of $300 each will be awarded, with all winners selected randomly. If you purchased one ticket, what are your expected gross winnings?
if you purchased one ticket, your expected gross winnings are $0.36.
what is gross winnings ?
Gross winnings refer to the total amount of money won before any taxes or fees are deducted. In other words, it is the total amount of money won by an individual in a lottery or other type of game of chance, without taking into account any deductions that may be made
In the given question,
To calculate the expected gross winnings, we need to multiply the probability of winning each prize by the value of the prize and then add up these values.
First, let's find the probability of winning each prize:
First prize: There is only one first prize, and there are 15,000 tickets sold, so the probability of winning the first prize is 1/15,000.
Second prize: There are two second prizes, so the probability of winning a second prize is 2/15,000.
Third prize: There are three third prizes, so the probability of winning a third prize is 3/15,000.
Now we can calculate the expected gross winnings:
First prize: The probability of winning the first prize is 1/15,000, and the value of the prize is $3,000, so the expected value of the first prize is (1/15,000) x $3,000 = $0.20.
Second prize: The probability of winning a second prize is 2/15,000, and the value of each prize is $750, so the expected value of a second prize is (2/15,000) x $750 = $0.10.
Third prize: The probability of winning a third prize is 3/15,000, and the value of each prize is $300, so the expected value of a third prize is (3/15,000) x $300 = $0.06.
Now we can add up these value to find the total expected gross winnings:
$0.20 + $0.10 + $0.06 = $0.36
Therefore, if you purchased one ticket, your expected gross winnings are $0.36.
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write an equation of the line that passes through the given point and has the given slope. (1, -5); slope -3/2
Answer: 4 ft 2 in i believe <3
Step-by-step explanation:
Your current CD matures in a few days. You would like to find an investment with a higher rate of return than the CD. Stocks historically have a rate of return between 10% and 12%, but you do not like the risk involved. You have been looking at bond listings in the newspaper. A friend wants you to look at the following corporate bonds as a possible investment. A 5-column table with 2 rows. Column 1 is labeled Bond with entries A B C 7 and one-half 15, X Y Z 7 and three-fourths 15. Column 2 is labeled current yield with entries 7.5, 8.4. Column 3 is labeled volume with entries 128, 17. Column 4 is labeled Close with entries 104 and three-fourths, 100 and one-half. Column 5 is labeled Net change with entries blank, + one-fourth. If you buy three of the ABC bonds with $10 commission for each, how much will it cost? a. $3142.50 b. $1047.50 c. $3172.50 d. $1077.50
The total cost of buying three of the ABC bonds would be $334.25 + $321.50 + $55 = $710.75.
What is probability?
Probability is a measure of the likelihood of an event occurring.
To calculate the cost of buying three of the ABC bonds, we first need to determine which bond is being referred to as the "ABC bond." The table lists three bonds: A, B, and C.
Next, we need to calculate the cost of each bond, taking into account the current yield and the price at which the bond is being sold. The current yield is the annual return on the bond expressed as a percentage of the bond's current market price.
For bond A, the current yield is 7.5%, and the bond is being sold at a price of 104 and three-fourths (104.75). For bond B, the current yield is 8.4%, and the bond is being sold at a price of 100 and one-half (100.5). For bond C, the current yield is also 7.5%, and the bond is being sold at a price of 15.
To calculate the cost of buying three of the ABC bonds, we need to multiply the price of the bond by the number of bonds purchased, and then add the commission. For bond A, the cost would be (104.75 x 3) + (10 x 3) = $334.25. For bond B, the cost would be (100.5 x 3) + (10 x 3) = $321.50. For bond C, the cost would be (15 x 3) + (10 x 3) = $55.
Therefore, the total cost of buying three of the ABC bonds would be $334.25 + $321.50 + $55 = $710.75.
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Indiana Company began a construction project in 2024 with a contract price of $161 million to be received when the project is completed in 2026. During 2024, Indiana incurred $36 million of costs and estimates an additional $86 million of costs to complete the project. Indiana recognizes revenue over time and for this project recognizes revenue over time according to the percentage of the project that has been completed.
The percentage of the project that has been completed 29.5%.
What is percenatge?
Percentage is a way of expressing a fraction or a portion of a whole as a number out of 100. The word "percent" comes from the Latin phrase "per centum", which means "by the hundred".
Based on the information given, Indiana Company began a construction project in 2024 with a contract price of $161 million to be received when the project is completed in 2026. During 2024, Indiana incurred $36 million of costs and estimates an additional $86 million of costs to complete the project.
Indiana Company recognizes revenue over time and for this project recognizes revenue over time according to the percentage of the project that has been completed. This means that Indiana Company will recognize a portion of the revenue each year based on the percentage of the project that has been completed.
To calculate the percentage of the project that has been completed, we need to divide the total costs incurred by Indiana Company by the estimated total costs of the project.
Total costs incurred in 2024 = $36 million
Estimated total costs of the project = $36 million + $86 million = $122 million
Therefore, the percentage of the project that has been completed in 2024 is:
Percentage of project completed = Total costs incurred / Estimated total costs
Percentage of project completed = $36 million / $122 million
Percentage of project completed = 0.295 or 29.5%
Based on this calculation, Indiana Company can recognize 29.5% of the total contract price as revenue for 2024.
Revenue recognized in 2024 = 29.5% x $161 million
Revenue recognized in 2024 = $47.5 million
So, Indiana Company can recognize $47.5 million in revenue for 2024. However, it is important to note that this is only an estimate and the actual revenue recognized may differ based on the progress of the project.
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Solve the triangle: a=100, b=90, a 29 degrees If it is not possible, say so.
It is not possible to solve the triangle with the given information.
What is Triangle ?
A triangle is a polygon with three sides and three angles. It is one of the basic shapes in geometry and is widely used in mathematics, science, and engineering. Triangles can be classified in different ways based on their side lengths, angle measures, and other properties.
To solve a triangle, we need at least three pieces of information, including at least one side length. In this case, we have the side lengths a=100 and b=90, and the angle opposite side a is 29 degrees. However, we don't have enough information to find the remaining angles and side lengths of the triangle.
We can use the Law of Cosines and the Law of Sines to solve a triangle, but we need at least one more piece of information. For example, if we had the length of side c or another angle, we could solve the triangle.
Therefore, It is not possible to solve the triangle with the given information.
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Graph the following inequality on the sketchpad below. Be sure to shade in the correct
area on the graph.
y>1/4x+2
The graph of the inequality y > 1/4x + 2 is a straight line with a slope of 1/4 passing through the point (0, 2), and the shaded area is above the line. The graph looks like a half-plane that is unbounded in the upward direction.
How to graph the inequality?To graph the inequality y > 1/4x + 2, we can follow these steps:
Start by drawing the line y = 1/4x + 2. To do this, we can use the slope-intercept form of a line, which is y = mx + b, where m is the slope and b is the y-intercept. In this case, the slope is 1/4 and the y-intercept is 2. So we can plot the point (0, 2) and then use the slope to find another point on the line. The slope tells us that for every increase of 4 in x, y will increase by 1. So we can plot the point (4, 3) and draw a straight line passing through both points.
Next, we need to determine which side of the line to shade. To do this, we can pick a point not on the line and test whether it satisfies the inequality. For example, we can pick the point (0, 0) and substitute its x and y values into the inequality y > 1/4x + 2. We get 0 > 1/4(0) + 2, which simplifies to 0 > 2. Since this is false, the point (0, 0) is not a solution to the inequality, so we shade the other side of the line.
Finally, we can label the shaded area to indicate the solution set of the inequality. We can write y > 1/4x + 2 above the shaded area to show the inequality that represents the shaded region.
Therefore, the graph of the inequality y > 1/4x + 2 is a straight line with a slope of 1/4 passing through the point (0, 2), and the shaded area is above the line. The graph looks like a half-plane that is unbounded in the upward direction.
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URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
What point do these two lines Have in common? The answer choices are (3,3) (2,4) (2,5) (0,3)
Answer:
3,3,0,3
Step-by-step explanation:
because it's right
What is the solution to the expression a² +26÷c when a = 6, b = 8, and
c=2?
Ayuda Porfa
Answer: 49
Step-by-step explanation:
6^2=36
26/2=13
36+13=49
HOPEFULLY I HELPED :)
Mr. and Mrs. Burnet's gross earnings total $5,825. How much of the amount earned is spent on
taxes and insurance?
Taxes, 15%
Entertainment,3%
Car/Gas, 9%
Insurance, 7%
College Fund,
10%
Utilities, 8%
Rent, 21%
Savings, 14%
Food, 8%
Clothing, 5%
Answer:
The Burnets spent .22 × $5,825 = $1,281.50 on taxes and insurance.
a⁴b⁴x⁴-2a²b²c²d²xy+c⁴d⁴y²
Step-by-step explanation:
This expression cannot be factored using simple techniques like factoring out common terms or using the difference of squares formula. It is a polynomial of degree 4 in four variables and has no obvious patterns or factors. Therefore, it is a fully factored expression.
Anyone know what this might be?
Answer:
y ≈ 13,9
Step-by-step explanation:
Use trigonometry:
[tex] \tan(60°) = \frac{y}{8} [/tex]
Cross-multiply to find y:
[tex]y = 8 \times \tan(60°) = 8 \times \sqrt{3} = 8 \sqrt{3} ≈13.9[/tex]
Answer:
y ≈ 13.9
Step-by-step explanation:
using the tangent ratio in the right triangle
tan60° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{y}{8}[/tex] ( multiply both sides by 8 )
8 × tan60° = y , then
y ≈ 13.9 ( to the nearest tenth )
Show that the following number is rational by writing it as a ratio of two integers.
52.4744174417441…
52.4744174417441… is a rational number because it can be expressed as the ratio of two integers: 524691.7 and 9999.
What is a rational number?A rational number is one that can be represented as the product of two numbers with a non-zero denominator. Integers, fractions, terminating decimals, and repeating decimals are all examples of rational numbers. A rational number can either have its decimal representation end, as in the instance of 1/2 = 0.5, or it can repeat a pattern of digits, as in the case of 1/3 = 0.3333. Irrational numbers, on the other hand, have decimal representations that do not end or recur and cannot be stated as the ratio of two integers. The square root of 2, pi, and e are a few examples of irrational numbers.
The given rational number is x = 52.4744174417441….
Now, x as a ratio of two integers is shown as:
10000x = 524744.1744174417…
Subtract x from both sides:
9999x = 524691.7
x = 524691.7/9999
Hence, 52.4744174417441… is a rational number because it can be expressed as the ratio of two integers: 524691.7 and 9999.
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Which is not true please help me I also have a picture on here !
Answer:
A is not true
Step-by-step explanation:
If the line was diagonal it wouldn't make a pair of parallel lines when reflected
Pedro's car completes 2.2 laps for every 2 laps Noor's car completes. a. How many laps does Pedro's car complete when Noor's car completes 100 laps?
B) Pedro's car completes what percent of the number of laps that Noor's car completes?
a) Pedro's car completes 110 laps while Noor's car completes 100 laps.
b) Pedro's car completes 110% of the number of laps that Noor's car completes.
What do laps mean?A lap refers to a complete circuit or rotation around a racetrack or other designated course. It is a standard unit of distance used in racing and other related sports. The length of a lap can vary depending on the specific track or course being used. In general, completing more laps than your competitors in a race is an indication of better performance and can help you win the race.
According to the given informationa)We can start by setting up a proportion to represent the relationship between the number of laps Pedro's car completes and the number of laps Noor's car completes:
2.2 laps / 2 laps = x laps / 100 laps
We can solve for x by cross-multiplying:
2.2 laps * 100 laps = 2 laps * x laps
220 laps = 2x
Dividing both sides by 2, we get:
x = 110 laps
b)If Pedro's car completes 2.2 laps for every 2 laps Noor's car completes, then we can find the ratio of the number of laps Pedro's car completes to the number of laps Noor's car completes as follows:
2.2 laps / 2 laps = 1.1
This means that Pedro's car completes 1.1 laps for every 1 lap Noor's car completes.
To find the percentage that Pedro's car completes compared to Noor's car, we can multiply this ratio by 100:
1.1 * 100 = 110%
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What is the area of the region of points
satisfying the inequalities x ≤ 0, y ≤ 0, and
y ≥ |x + 4| − 5?
the area of the region of points satisfying the inequalities x ≤ 0, y ≤ 0, and y ≥ |x + 4| − 5 is 12.5 square units.
Which box plot represents the data above? O A. OB. Y O C. N OD. X 27, 25, 28, 26, 22, 26, 27, 25, 23, 24, 24, 22, 24, 23, 26 W 21 22 23 24 25 26 27 28 29 30 W. 21 22 23 24 25 26 27 28 29 30 Y. +++ ++ 21 22 23 24 25 26 27 28 29 30 X. 21 22 23 24 25 26 27 28 29 30 Z.
Based on the data given, the box plot that represents the data is B.
What is minimum value?The minimum value is the smallest value in a given set of data. In other words, it is the lowest number in the set. The minimum value is an important measure of central tendency in statistics and is often used in data analysis to understand the range and distribution of the data.
According to question:Based on the data given, the box plot that represents the data is B.
This is because the minimum value of the data set is 22, which is shown by the bottom whisker of the box plot. The first quartile is 23, the median is 25, and the third quartile is 27, which are shown by the box. The maximum value is 28, which is shown by the top whisker. The outlier is not shown in this box plot, but it would be indicated by a small circle or asterisk outside of the whiskers.
Box plot A does not include the maximum value of 28, while box plot C does not include the minimum value of 22. Box plot D shows the minimum and maximum values correctly, but the quartile values and whiskers are incorrect. Box plot Y does not have any boxes or whiskers, and box plot X and Z do not show all of the values correctly.
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In a roll of 50 pennies, there are 12 dated 1977. If a penny is drawn at random, what is the probability that it is dated 1977?
The probability of drawing a penny dated 1977 is 0.24 or 24%.
What is Probability:Probability is a branch of mathematics that deals with the study of random events. It is used to measure the likelihood or chance of a particular event occurring.
Probability is expressed as a fraction or a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain.
The probability of drawing a penny dated 1977 can be found by dividing the number of pennies dated 1977 by the total number of pennies.
Here we have
Total number of pennies = 50
Number of pennies dated 1977 = 12
Probability of drawing a penny dated 1977
= Number of pennies dated 1977 / Total number of pennies
= 12 / 50
= 0.24
Therefore,
The probability of drawing a penny dated 1977 is 0.24 or 24%.
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An ordinary (fair) die is a cube with the numbers 1 through 6 on the sides (represented by painted spots), Imagine that such a die is roiled twice in
succession and that the face values of the two rolls are added together, This sum is recorded as the outcome of a single trial of a random experiment
Compute the probability of each of the following events.
Event A: The sum is greater than 9.
Event B: The sur is not divisible by
Write your answers as fractions.
A sum is divisible by 3 if and only if both of the dice rolls are either 1 and 2 or 2 and 1, or both of the dice rolls are either 1
How to solve the problem?
To solve this problem, we first need to determine the total number of possible outcomes when rolling the die twice. Each roll has six possible outcomes, so the total number of outcomes when rolling the die twice is 6 x 6 = 36.
Next, we can create a table to list all possible outcomes and their corresponding sums:
Die 1 Die 2 Sum
1 1 2
1 2 3
1 3 4
1 4 5
1 5 6
1 6 7
2 1 3
2 2 4
2 3 5
2 4 6
2 5 7
2 6 8
3 1 4
3 2 5
3 3 6
3 4 7
3 5 8
3 6 9
4 1 5
4 2 6
4 3 7
4 4 8
4 5 9
4 6 10
5 1 6
5 2 7
5 3 8
5 4 9
5 5 10
5 6 11
6 1 7
6 2 8
6 3 9
6 4 10
6 5 11
6 6 12
Using this table, we can calculate the probability of each event:
Event A: The sum is greater than 9.
There are four possible outcomes where the sum is greater than 9: 10, 11, and 12. The probability of getting each of these outcomes is:
P(sum = 10) = 3/36
P(sum = 11) = 2/36
P(sum = 12) = 1/36
Therefore, the probability of Event A is:
P(Event A) = P(sum = 10) + P(sum = 11) + P(sum = 12)
= (3/36) + (2/36) + (1/36)
= 6/36
= 1/6
Event B: The sum is not divisible by 3.
A sum is divisible by 3 if and only if both of the dice rolls are either 1 and 2 or 2 and 1, or both of the dice rolls are either 1
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PLEASE HELP
Which statement is true?
Responses
Interior angles should all be congruent, so neither of these pictures show parallel lines.
Same side interior angles are supplementary so picture i shows parallel lines.
Same side interior angles are supplementary so picture ii shows parallel lines.
It doesn't look like any lines will intersect, so both pictures i and ii are parallel lines.
Find the missing side lengths. Leave your answers and radicals in the simplest form.
Answer:
u = 12;
v = 6
Step-by-step explanation:
Use trigonometry:
[tex] \tan(60°) = \frac{6 \sqrt{3} }{v} [/tex]
Use the property of proportion to find v:
[tex]v = \frac{6 \sqrt{3} }{ \tan(60°) } = \frac{6 \sqrt{3} }{ \sqrt{3} } = 6[/tex]
Use the Pythagorean theorem to find u:
[tex] {u}^{2} = {v}^{2} + ( {6 \sqrt{3}) }^{2} [/tex]
[tex] {u}^{2} = {6}^{2} + ( {6 \sqrt{3}) }^{2} = 36 + 36 \times 3 = 36 + 108 = 144[/tex]
[tex]u > 0[/tex]
[tex]u = \sqrt{144} = 12[/tex]