If you were to buy one of each bond today, you would have to spend b. ABC $1104.75 and XYZ $1100.50.
Calculate Price of Bonds Based on Yield and Coupon Payment?The following algorithm must be used to determine a bond's price:
[tex]Bond\ price=(\frac{coupon\ payment}{(1+yield)^{time}} )+(\frac{coupon\ payment}{(1+yield)^{time+1}} )+...+(\frac{coupon\ payment+face\ value}{(1+yield)^{Time+n}} )[/tex]
Where:
dividend Payment: The bond's yearly dividend payment (in dollars)
Yield: The bond's yield to expiration (as a decimal)
Time: the interval between the issuance of each coupon and the receipt of its monetary value. (in years)
Face worth: The bond's face worth (in dollars)
The price of each bond can be determined as follows using the data in the table:
a. For bond ABC:
Coupon Payment = $7.50 (7.5% of $1000 face value)
Yield = 3.04% (convert 3.04 to a decimal)
Time = 0.5 years (since the bond's maturity date is July 15 and today marks the midway point between those dates)
Face Value = $1000
[tex]Bond\ price=(\frac{7.5}{(1+0.0304)^{0.5}} )+(\frac{7.5}{(1+0.0304)^{1.5}} )+(\frac{1000}{(1+0.0304)^{2}} )[/tex]
= 7.356 + 7.235 + 925.984
= $940.575
Since we are purchasing one bond and the face value is $1,000, we split this amount by 10 to get the price for one bond:
Price for one bond ABC = $940.575 / 10 = $94.058
b. For bond XYZ:
Coupon Payment = $84 (8.4% of $1000 face value)
Yield = 1.7% (convert 1.7 to a decimal)
Time = 0.5 years
Face Value = $1000
[tex]Bond\ Price = (84 / (1 + 0.017)^{0.5}) + (84 / (1 + 0.017)^{1.5}) + (1000 / (1 + 0.017)^2)[/tex]
= 83.379 + 81.838 + 968.661
= $1133.878
Since the face value of a bond is $1,000 and we are only purchasing one, we split this amount by 10 to get the price for one bond:
Price for one bond XYZ = $1133.878 / 10 = $113.388
Therefore, the correct answer is:b. ABC: $1104.75 XYZ: $1100.50
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how do you solve 11P3 and 11C3? i dont have right calculator and im typing this on my laptop
Answer:
Step-by-step explanation:
11P3=11×10×9=990
[tex]11C_{3}=\frac{11 \times 10 \times 9}{3 \times 2 \times 1} =165[/tex]
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Ximena decides to estimate the volume of an apple by modeling it as a sphere. She measures its diameter as 11.9 cm. Find the apple's volume in cubic centimeters. Round your answer to the nearest tenth if necessary
The volume of the apple is approximately 832.2 cubic centimeters.
What is volume of sphere?The following equation determines a sphere's volume:
V = (4/3)πr³
When V denotes the sphere's volume, r denotes its radius, and denotes the mathematical constant pi (approximately 3.14). By seeing the sphere as an unlimited number of little cylinders piled on top of one another, the formula may be created. Each cylinder has a height equal to the sphere's shell thickness and a radius equal to the sphere's radius.
The volume of a sphere:
V = (4/3)πr³
Here, r = d/2 = 11.9 cm / 2 = 5.95 cm
Substituting the values we have:
V = (4/3)π(5.95 cm)³ ≈ 832.2 cm³
Therefore, the volume of the apple is approximately 832.2 cubic centimeters.
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Can someone please help me with this problem involving Proofs involving similarity in right triangles.
The statement and reason to complete the proof that TU² = TV · TW include the following:
Statement Reason_____
TU² = TV · TW cross product.
What is the Tangent Secant Theorem?In Mathematics and Geometry, the Tangent Secant Theorem states that if a secant segment and a tangent segment are drawn to an external point outside a circle, then, the product of the length of the external segment and the secant segment's length would be equal to the square of the tangent segment's length.
By applying the Tangent Secant Theorem to the given triangles after the definition of similarity step, we would cross-multiply as follows:
TU/TW = TV/TU definition of similarity
TU(TU) = TV(TW) cross product.
TU² = TV · TW cross product.
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The standard form of an absolute value function is f(x) = a|x -h| + k.Which of the following represents the vertex?
A. (-k,h)
B. (-h,k)
C. (k,h)
D.(h,k)
Please help ASAP
Answer:
The correct answer:
D. (h, k)
In a village, 80% of people are Hindus and 2% are Muslims. If 36 people do not follow these two religions, by drawing a Venn diagram find the number of the Hindu.
Explanation:
Assuming the two religions are mutually exclusive, this would mean 80%+2% = 82% of people are either Hindu or Muslim (but not both).
The remaining 100% - 82% = 18% of people are neither religion mentioned.
x = number of people in the village
18% of x = 36
0.18x = 36
x = 36/0.18
x = 3600/18
x = 200
Then,
80% of x = 0.80*x = 0.80*200 = 160 people are Hindu
The Venn diagram is shown below.
Amadou and Olivia are making fruit salads for a picnic. Amadou mixes 9 cups of melon and 10 cups of apple and Olivia mixes 2 cups of melon and 3 cups of apple. Use Amadou and Olivia’s percent of apple to determine whose fruit salad will taste more appley.
Given that 60% of Olivia's fruit salad is made up of apples as opposed to Amadou's fruit salad's 52.63%, Olivia's fruit salad will have a more apple-forward flavor based on percent.
The amount of apples in each fruit salad needs to be compared in order to determine which salad will taste more apple-like.
There are 19 cups of fruit in Amadou's fruit salad, of which 10 cups are apples. By dividing the total number of cups of fruit by the number of cups of apples, and multiplying the result by 100, we can get the proportion of apples in Amadou's salad:
Apple's percent of Amadou's fruit salad is equal to (10/19) x 100, or 52.63%.
There are 5 cups of fruit in Olivia's fruit salad, of which 3 cups are apples. We can use the same formula to determine how much apple is in Olivia's salad:
Olivia's fruit salad contains 60% apples, or (3/5) x 100.
As a result, Olivia's fruit salad will taste more apple-like because apples make up 60% of it as opposed to only 52.63% of Amadou's fruit salad.
It is important to keep in mind that the maturity, sweetness, and freshness of the fruits used, as well as other elements like the dressing and presentation, may all affect how the fruit salad tastes.
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Write the standard form of each equation. Then graph the equation.
x^2+y^2+6x-8y+18=0
The standard form of the equation is (x + 3)² + (y - 4)² = 2.
What is standard form of equation?A linear equation with two variables has the conventional form Ax + By = C, where A, B, and C are constants and where A and B are not equal to zero. The general form of a linear equation is another name for this format. When the line is plotted on the Cartesian plane, the constant term C and coefficient A in this form indicate the line's y-intercept and slope, respectively. When solving systems of linear equations and graphing linear equations, the standard form is helpful.
Complete the squares for the given equation: x² + y²+ 6x - 8y + 18=0.
Starting with the x terms, we add (b/2)² to both sides of the equation:
x² + 6x + 9 + y² - 8y + 18 = 9
For y terms by adding (c/2)² to both sides of the equation:
x² + 6x + 9 + y² - 8y + 16 = -2
The standard form is:
(x + 3)² + (y - 4)² = 2
Hence, the standard form of the equation is (x + 3)² + (y - 4)² = 2.
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A rectangular piece of paper with length 30ft and width 24ft has two semicircles cut out of it. Find the area of the paper that remains. Use the value 3.14 for PIE , and do not round your answer.
Remark
I take it the semicircles cover the full width of the paper.
So the radius is [tex]24\div2 = 12 \ \text{cm}[/tex]
Since there are two of them, the area = a full circle.
Step One
Find the area of the rectangle before the cuts were made.
[tex]\text{Area = L} \times \text{W}[/tex]
[tex]\text{L = 30}[/tex]
[tex]\text{W = 24}[/tex]
[tex]\text{Area} = 30 \times 24 = 720 \ \text{cm}^2[/tex]
Step Two
Find the area of the circle cut outs.
[tex]\text{r} = 12[/tex]
[tex]\text{Area} = \pi \times \text{r}^2[/tex]
[tex]\text{Area} = 3.14 \times 12^2[/tex]
[tex]\text{Area} = 3.14 \times 144[/tex]
[tex]\text{Area} = 452.16 \ \text{cm}^2[/tex]
Step Three
Find the total area left
[tex]\text{Total Area Left = rectangle - circle}[/tex]
[tex]\text{Total Area Left} = 720 - 452.16[/tex]
[tex]\text{Total Area left} = 267.84 \ \text{cm}^2[/tex] Answer
If y = x² - 2x + 3, find the value(s) of x when y = 3.
Answer:
x = 0 , x = 2
Step-by-step explanation:
y = x² - 2x + 3 ← substitute y = 3
3 = x² - 2x + 3 ( subtract 3 from both sides )
0 = x² - 2x ← factor out x from each term on the right side
0 = x(x - 2)
equate each factor to zero and solve for x
x = 0
x - 2 = 0 ⇒ x = 2
The total price of a shirt and a cap is $12. If the price of the shirt was doubled and the price of the cap was three times its original price, the total price of a shirt and a cap would be $26. The following system of equations models this scenario:
x + y = 12
2x + 3y = 26
What is the price of each shirt and cap?
1 The price of a shirt is $7, and the price of a cap is $5.
2 The price of a shirt is $8, and the price of a cap is $4.
3 The price of a shirt is $9, and the price of a cap is $3.
4 The price of a shirt is $10, and the price of a cap is $2.
Answer: Number 4 is the answer.
Hope this helps!
It costs $3.00 per meter for the water pipes to go along the rural roads and $4.50 per meter for the water pipes to go through the field. Which option is less expensive? Explain how you found your answer.
we can say that if the cost per meter of laying pipes along the rural roads is less than the cost per meter of laying pipes through the field, then it would be less expensive to lay the pipes along the rural roads.
What is meter?
A meter is a unit of length in the International System of Units (SI). It is defined as the length of the path travelled by light in a vacuum during a time interval of 1/299,792,458 of a second. The symbol for meter is "m".
To determine which option is less expensive, we need to compare the cost of laying pipes along the rural roads to the cost of laying pipes through the field.
Let's assume that we need to lay a water pipe that is 100 meters long. If we choose to lay the pipe along the rural roads, the cost would be:
Cost = length of pipe x cost per meter = 100 x $3.00 = $300.00
If we choose to lay the pipe through the field, the cost would be:
Cost = length of pipe x cost per meter = 100 x $4.50 = $450.00
Therefore, laying the pipe along the rural roads would be less expensive in this case, with a cost of $300.00 compared to $450.00 for laying the pipe through the field.
In general, we can say that if the cost per meter of laying pipes along the rural roads is less than the cost per meter of laying pipes through the field, then it would be less expensive to lay the pipes along the rural roads. Conversely, if the cost per meter of laying pipes through the field is less than the cost per meter of laying pipes along the rural roads, then it would be less expensive to lay the pipes through the field.
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Full question:
It costs $3.00 per meter for the water pipes to go along the rural roads and $4.50 per meter for the water pipes to go through the field. Which option is less expensive? Explain how you found your answer.
Find the least possible degree shown on the graph
Answer:
The least possible degree is 5.
Calculate the area of the shaded region below
Answer:
Step-by-step explanation:
According to the given situation,
the area of figure A= l*b
=4m * 5m
=20m²
As the measures of the figure A and B is same,
the area of figure B = the area of figure A=20m²
the length of the side C and D are = 16m-8m-4m=4m
the area of figure C = l * b
=4m*5m
=20m²
As the measures of the figure C and D is same,
the area of figure D = the area of figure C=20m²
Area of the figure E=l * b
=8m * 13m
=104m²
∴ the area of the shaded region is =184m²
There was a sample of 600 milligrams of a radioactive substance to start a study. Since then, the sample has decayed by 8.4% each year.
Let t be the number of years since the start of the study. Let y be the mass of the sample in milligrams.
Write an exponential function showing the relationship between Y and t.
Answer: The decay rate is 8.4%, which means that the sample will have 91.6% of its original mass after one year, 91.6% of that amount after two years, and so on.
Therefore, we can write the relationship between y and t as:
y = 600 * (0.916)^t
This is an exponential decay function, where the initial value is 600 milligrams and the decay factor is 0.916 (1 minus the decay rate of 8.4%). As time t increases, the mass of the sample y decreases exponentially.
Step-by-step explanation:
In how many ways cam 2 students be chosen from a group of 15?
Answer:
you could do 2 students in each group with one group of 3
Step-by-step explanation:
sorry if i didn't answer correctly
ala Manufacturing purchases land for $445,000 as part of its plans to build a new plant. The
Ompany pays $37,600 to tear down an old building on the lot and $55,583 to fill and level
me lot. It also pays construction costs of $1,402,600 for the new building and $88,536 for
ghting and paving a parking area.
repare a single journal entry to record these costs incurred by Cala, all of which are paid in
ash.
View transaction list
No
A
View journal entry worksheet
Transaction
1
No Transaction Recorded
General Journal
D
Note that the journal for the above transaction is attached accordingly.
What is the explanation for the above journal?The journal entry records the purchase of land for $445,000, demolition expense of $37,600, land improvement cost of $55,583, building construction cost of $1,402,600 and lighting and paving cost of $88,536, all paid in cash.
Therefore, the amounts are debited to their respective accounts and credited to cash.
The total credit amount is equal to the total debit amount, ensuring the accounting equation remains in balance.
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please help me with this math question i’ll give you brainlist
a- y=-1.2x+30
b- y=2x+20
c- y=0.48x+11
d- y=0.71+22
Option c y=0.48x+11 is the line of best fit to approximate the data in the scatterplot.
What is correlation coefficient?A statistical metric called a correlation coefficient shows the degree and direction of the association between two variables. Its value falls between -1 and 1, with -1 being a perfect negative correlation, 0 denoting no connection, and 1 denoting a perfect positive correlation. If there is a positive correlation, it implies that as one variable rises, the other variable likewise tends to rise, and if there is a negative correlation, it means that as one variable rises, the other variable tends to fall. The letter r is frequently used to represent the correlation coefficient.
Comparing the scatter plot with the given equations we observe that the slope of option b and d are very large as compared to the given distribution.
Observing from the given graph, the y-intercept of the best fit line will be nearly less than 20.
Thus, option c y=0.48x+11 is the line of best fit to approximate the data in the scatterplot.
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Yolanda hiked each day for a week. The first day she hiked mile, the second day she hiked mile, and the third day she hiked 1 mile. By how much did she increase the distance she hiked each day?
the distance she hiked each day, we need to calculate the difference between the distance she hiked on consecutive days. Yolanda increased the distance she hiked by 1 mile each day.
What is the total distance?To find the increase in the distance Yolanda hiked each day, we need to calculate the difference between the distance she hiked on each consecutive day.
The distance Yolanda hiked each day for the first three days can be represented as:
Day 1: d miles
Day 2: [tex]d + 1[/tex] miles
Day 3: [tex]d + 2[/tex] miles
The increase in distance from day 1 to day 2 is [tex](d + 1) - d = 1[/tex] mile.
The increase in distance from day 2 to day 3 is [tex](d + 2) - (d + 1) = 1[/tex] mile.
Therefore, Yolanda increased the distance she hiked by 1 mile each day.
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A normal distribution has a mean of 16 and a standard deviation of 5. Use the 68-95-99.7 rule to find the percentage of values in the distribution between 16 and 21.
What is the percentage of values in a normal distribution between 16 and 21 with a mean of 16 and a standard deviation of 5, according to the 68-95-99.7 rule is approximately 68%.
How to calculate the percentage of values in a normal distribution?
According to the 68-95-99.7 rule, approximately 68% of the values in a normal distribution are within one standard deviation of the mean, approximately 95% are within two standard deviations of the mean, and approximately 99.7% are within three standard deviations of the mean.
In this case, we want to find the percentage of values in the distribution between 16 and 21.
The range from 16 to 21 is one standard deviation above the mean, since the mean is 16 and the standard deviation is 5. Therefore, approximately 68% of the values in the distribution will fall between 16 and 21.
So, the answer is approximately 68%.
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El 15% de una cantidad es 216 cuál es esa cantidad ?
la cantidad buscada es 1440.
Calculating the value of the quantityPara encontrar la cantidad dada el 15% de la misma, podemos usar una ecuación:
15% de x = 216
Podemos convertir el porcentaje a decimal dividiendo por 100:
0.15x = 216
Luego, para despejar x, podemos dividir ambos lados de la ecuación por 0.15:
x = 216 / 0.15
x = 1440
Por lo tanto, la cantidad buscada es 1440.
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A large mixing tank currently contains 300 gallons of water, into which 8 pounds of sugar have been mixed. A tap will open,
pouring 20 gallons of water per minute into the tank at the same time sugar is poured into the tank at a rate of 2 pounds
per minute. Find the concentration (pounds per gallon) of sugar in the tank after 10 minutes.
Answer:
the concentration of sugar in the tank after 10 minutes is approximately 0.056 pounds per gallon.
Step-by-step explanation:
Let's first calculate the amount of sugar that will be added to the tank during the 10 minutes:Amount of sugar added = rate of sugar * time = 2 pounds/minute * 10 minutes = 20 poundsThe initial amount of water in the tank is 300 gallons, and 20 gallons per minute are being added, so after 10 minutes, the amount of water in the tank will be:Amount of water in the tank = initial amount of water + rate of water * time = 300 gallons + 20 gallons/minute * 10 minutes = 500 gallonsTherefore, after 10 minutes, the total volume of the mixture in the tank will be 500 gallons, and the total amount of sugar in the tank will be 8 + 20 = 28 pounds.To find the concentration of sugar in the tank, we divide the total amount of sugar by the total volume of the mixture:Concentration of sugar = total amount of sugar / total volume of mixture = 28 pounds / 500 gallons ≈ 0.056 pounds per gallon
We can use the formula:
concentration = (total sugar added in pounds) / (total water in gallons)
First, we need to find out how much sugar is added in 10 minutes. Since sugar is being added at a rate of 2 pounds per minute , in 10 minutes, we will have:
total sugar added = 2 pounds/minute * 10 minutes = 20 pounds
Next, we need to find out how much water is in the tank after 10 minutes. Since water is being added at a rate of 20 gallons per minute , in 10 minutes, we will have:
total water added = 20 gallons/minute * 10 minutes = 200 gallons
Therefore, the total amount of water in the tank after 10 minutes is:
total water = 300 gallons (initial water) + 200 gallons (water added) = 500 gallons
Finally, we can calculate the concentration of sugar in the tank by plugging in the values:
concentration = total sugar added / total water
concentration = 20 pounds / 500 gallons
concentration = 0.04 pounds/gallon
Therefore, after 10 minutes, the concentration of sugar in the tank is 0.04 pounds per gallon.
A Ferris Wheel is 60 meters in diameter and rotates once every four minutes. The center axle of the Ferris Wheel is 40 meters. from the ground. Write at least 2 mathematical models that represent the motion of the passenger on this Ferris wheel.
y = acos bx +c
y=-25 cos
C. where X = 2.3 min
Another mathematical representation of how a rider on this Ferris wheel might move is :y = cos(0.25x) + 40
What more uses does trigonometry have?Trigonometry is widely used in many fields, including physics, engineering, architecture, surveying, oceanography, and more. Here are several examples:
In astronomy and physics, trigonometry is used to compute the motions of moving objects, gauge the separations between planets and stars, and examine waves. Trigonometry is used in architecture and engineering to determine angles and distances for building structures like bridges and buildings.
In surveying, trigonometry is a tool used to determine angles and separations between points on the surface of the ground.
.
The function y = a cos(bx) + c, where an is the function's amplitude, b is its frequency, and c is its vertical shift, can be used to mimic the height of a rider on a Ferris wheel.
Given that the Ferris wheel's diameter in this instance is 60 meters, its radius is 30 metres. The Ferris wheel's center axle is 40 metres off the ground. This indicates that a rider is 70 metres above the earth when they are at the top of the Ferris wheel (30 + 40). A rider is 10 metres above the ground when they reach the bottom of the Ferris wheel. (40 - 30).
We can determine that the Ferris wheel's period is four minutes because it rotates once every four minutes. The following formula can be used to get our function's frequency:
f = 1/T, 1/4, and 0.25 Hz
Therefore, our function has a frequency of 0.25 Hz.
The vertical shift of our function is equivalent to 50% of the difference between a Ferris wheel passenger's maximum and minimum heights:
, c = (a_max + a_min) /2
c = (70 + 10) /2
c = 40
Therefore, 40 is the vertical shift of our function.
Finally, we must ascertain the function's amplitude. The difference between a Ferris wheel passenger's maximum and minimum heights is equal to half of the amplitude:
For example, c = (a_max + a_min) / 2 c = (70 + 10) / 2 c = 40
Therefore, 40 is the vertical shift of our function.
Finally, we must ascertain the function's amplitude. The difference between a Ferris wheel passenger's maximum and minimum heights is equal to half of the amplitude:
A=(a_max - a_min) / 2 A=(70 - 10) / 2 A=30
Therefore, our function has an amplitude of 30.
When you combine everything, you get:
Y equals a cos(0.25x) + 40
y = -25 cos(C), where C is the time in minutes since the motion started at position, is another potential mathematical model that could describe this motion. (0,-25).
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Find the value of x in the matrix equation.
[-8-14 -2x]-([-19 17 -1]+[14 13 -2])-[-3 -44 -9]
a. x = -5.7
C.
b. x=-17.7
X=7
d. x = 6
Answer:
the answer is x=6
Step-by-step explanation:
I can’t find the answer pls help me!
Answer:
what is it
Step-by-step explanation:
One side of the triangle is 1 inch less than three times the length of the altitude to that side. Write a polynomial that represents the area of this triangle.
By answering the presented question, we may conclude that the answer of the triangle [tex]A = (3/2)h^2 - (1/2)h\\[/tex] => [tex]A(h) = (3/2)h^2 - (1/2)h[/tex]
What precisely is a triangle?A triangle is a closed, double-symmetrical shape composed of three line segments known as sides that intersect at three places known as vertices. Triangles are distinguished by their sides and angles. Triangles can be equilateral (all factions equal), isosceles, or scalene based on their sides. Triangles are classified as acute (all angles are fewer than 90 degrees), good (one angle is equal to 90 degrees), or orbicular (all angles are higher than 90 degrees) (all angles greater than 90 degrees). The region of a triangle may be calculated using the formula A = (1/2)bh, where an is the neighbourhood, b is the triangle's base, and h is the triangle's height.
x = 3h - 1
A = (1/2)bh
A = (1/2)xh
A = (1/2)(3h - 1)h
[tex]A = (3/2)h^2 - (1/2)h\\[/tex]
[tex]A(h) = (3/2)h^2 - (1/2)h[/tex]
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The selling price of an article is N8,000.00. If it is sold at a loss of 20%. What was the cost price?
Answer:
sp= 8000.00.
loss percent= 20%
loss amount = 20% of sp
= 20÷100 × 8000
= 1600
now,
costprice = sp + loss amount
= 8000 + 1600
= 9600
5.2, 5.2, 4.7, 5.4, 3.9, 3.5, 4.1, 4.2, 5.4, 4.7, 4.8, 4.2, 4.6, 5.1, 3.8, 3.9, 4.6, 5.1, 3.6,
4.6, 4.3, 3.4, 4.9, 4.2, 4.0
A manufacturer of pencils randomly selects 25 pencils and measures their length (in
inches). Their data is shown. Create a frequency distribution with 6 classes and a
class width of 0.4 inches. What is the shape of the frequency histogram?
A The histogram is bimodal.
B The histogram is roughly symmetrical.
C histogram is skewed right.
D The histogram is uniform.
E The histogram is skewed left.
Since the sample size is relatively small (n=25), the shape οf the histοgram may nοt perfectly reflect the underlying distributiοn οf the pοpulatiοn.
What is frequency distributiοn?The gathered data is arranged in tables based οn frequency distributiοn. The infοrmatiοn cοuld cοnsist οf test results, lοcal weather infοrmatiοn, vοlleyball match results, student grades, etc. Data must be presented meaningfully fοr understanding after data gathering. A frequency distributiοn graph is a different apprοach tο displaying data that has been represented graphically.
The range οf the data is the difference between the maximum and minimum values:
Maximum value: 5.4
Minimum value: 3.4
Range: 5.4 - 3.4 = 2.0
Next, we divide the range by the desired number οf classes tο find the class width:
Class width = 2.0 / 6 = 0.3333 (rοunded tο 0.4)
Based οn the given data, we can expect the histοgram tο be apprοximately bell-shaped, with a peak arοund the middle classes (4.0-4.8) and fewer pencils in the extreme classes (3.4-3.8 and 5.4-5.8).
Hοwever, since the sample size is relatively small (n=25), the shape οf the histοgram may nοt perfectly reflect the underlying distributiοn οf the pοpulatiοn.
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The probability that Gerald makes a three-point shot in basketball is
20
%
20%20, percent. For practice, Gerald will regularly shoot a series of these shots until he succeeds at one. He's curious how many shots it will typically take him to get his first successful shot.
He simulated
40
4040 trials of three-point shots where each shot had a
0.2
0.20, point, 2 probability of being successful, and in each trial, he counted how many shots it took to get the first successful shot. Here are his results:
A dot plot for number of shots taken has a scale from 0 to 16. The number of dots for each is as follows. 0, 0. 1, 9. 2, 6. 3, 5. 4, 4. 5, 4. 6, 2. 7, 2. 8, 0. 9, 1. 10, 1. 11, 1. 12, 2. 13, 1. 14, 0. 15, 1. 16, 1.
Use his results to estimate the probability that it takes
10
1010 or fewer shots to get his first successful shot.
Give your answer as either a fraction or a decimal.
�
(
10
or fewer shots
)
≈
P(10 or fewer shots)≈P, left parenthesis, 10, start text, space, o, r, space, f, e, w, e, r, space, s, h, o, t, s, end text, right parenthesis, approximately equals
The estimated probability that it takes 10 or fewer shots to get his first successful shot is:
P(10 or fewer shots) ≈ 0.825
What is probability?
Probability is the study of the chances of occurrence of a result, which are obtained by the ratio between favorable cases and possible cases.
To estimate the probability that it takes 10 or fewer shots to get his first successful shot, we need to add up the number of dots for the first 10 bars on the dot plot.
From the given dot plot, we can see that the number of dots for each value up to 10 shots are:
0 + 9 + 6 + 5 + 4 + 4 + 2 + 2 + 0 + 1 = 33
Therefore, the estimated probability that it takes 10 or fewer shots to get his first successful shot is:
P(10 or fewer shots) ≈ 33/40
This can also be written as a decimal:
P(10 or fewer shots) ≈ 0.825
Hence, the estimated probability that it takes 10 or fewer shots to get his first successful shot is:
P(10 or fewer shots) ≈ 0.825
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