The probability that in any given hour fewer than three new visitors will arrive at the website is 0.5948.
a) The probability that in any given hour zero new visitors will arrive at the website is given by;P(X = 0) = (e^-λ λ^0)/0!Where λ = 2.3Thus;P(X = 0) = (e^-2.3 2.3^0)/0!P(X = 0) = (0.1003)/1P(X = 0) = 0.1003b) The probability that in any given hour exactly one new visitor will arrive at the website is given by;P(X = 1) = (e^-λ λ^1)/1!Where λ = 2.3Thus;P(X = 1) = (e^-2.3 2.3^1)/1!P(X = 1) = (0.2303)/1P(X = 1) = 0.2303c) The probability that in any given hour two or more new visitors will arrive at the website is given by;P(X ≥ 2) = 1 - P(X = 0) - P(X = 1)Thus;P(X ≥ 2) = 1 - 0.1003 - 0.2303P(X ≥ 2) = 0.6694d) The probability that in any given hour fewer than three new visitors will arrive at the website is given by;P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)Thus;P(X < 3) = 0.1003 + 0.2303 + 0.2642P(X < 3) = 0.5948Therefore,The probability that in any given hour zero new visitors will arrive at the website is 0.1003.The probability that in any given hour exactly one new visitor will arrive at the website is 0.2303.The probability that in any given hour two or more new visitors will arrive at the website is 0.6694.The probability that in any given hour fewer than three new visitors will arrive at the website is 0.5948.
Learn more about Probability
brainly.com/question/30034780
#SPJ4
PLEASE HELPPP MEEEEEEEE
The equation that models the relationship between the models to show Ethan's employee benefits is y = 14 + 3(x - 1).
The number of paid vacation days Ethan earned was 35 paid vacation days .
Ethan will reach the maximum number of paid vacation days in 7 years.
How to find the paid vacation days ?Let x represent the number of years he has worked for this employer and y represent the number of paid vacation days he has earned.
The equation that models the relationship between x (years worked) and y (paid vacation days earned) is:
y = 14 + 3(x - 1)
Using the equation from part a, we can find out how many paid vacation days Ethan has earned after eight years:
y = 14 + 3(8 - 1)
y = 14 + 3(7)
y = 14 + 21
y = 35
To determine when Ethan will reach the maximum number of paid vacation days, we can set y equal to 30 and solve for x:
30 = 14 + 3(x - 1)
16 = 3(x - 1)
16/3 = x - 1
x = 16/3 + 1
x = 16/3 + 3/3
x = 19/3
x = 7
Find out more on equations at https://brainly.com/question/19260584
#SPJ1
Mrs Patel and Mrs rose both get paid 25,800 a year. Mrs Patel receives a 2. 5 % rise. Mrs rose gets a pay rise of £55 per month. Who receives the greater pay rise ?
Mrs. Rose receives the greater pay rise of £660 per year compared to Mrs. Patel's pay rise of £645.
To compare the pay rise for Mrs Patel and Mrs Rose, we need to calculate the actual amount of the pay rise for each of them.
For Mrs Patel, her pay rise is 2.5% of her current salary of £25,800:
Pay rise for Mrs Patel = 2.5% of £25,800 = £645
For Mrs. Rose, her pay rise is £55 per month, which is:
Pay rise for Mrs. Rose = £55 x 12 = £660 per year
Comparing the two pay rises, we see that Mrs. Rose receives a greater pay rise of £660 per year, compared to Mrs. Patel's pay rise of £645. Therefore, Mrs. Rose receives the greater pay rise.
Learn more about pay rise here
brainly.com/question/28734222
#SPJ4
Janelle weighed an unknown substance. It had a mass of 20. 609 grams. She exposed the substance to a flame and carefully weighed the substance again. The substance then had a mass of 17. 39 grams. Write and solve an equation to determine the amount of mass x the substance lost.
Janelle calculated that the unknown weighed lost 3.219 grams of mass when exposed to a flame.
Janelle weighed an unknown substance to determine its mass. The initial mass was 20. 609 grams. She then exposed the substance to a flame, and carefully weighed it again. This time, the mass was 17. 39 grams. To determine the amount of mass x the substance lost, Janelle can write and solve an equation. The equation would be: 20.609 - 17.39 = x, where x is the amount of mass lost. To solve for x, Janelle can subtract 17.39 from 20.609. This calculation would result in x = 3.219, meaning the substance lost 3.219 grams of mass. Therefore, the amount of mass x the substance lost is 3.219 grams.
Learn more about weight here
https://brainly.com/question/28355526
#SPJ4
whats 18 divided by 800 solved
Answer:
Step-by-step explanation:44,4444444
Answer:
0.0225
Step-by-step explanation:
18÷800=0.0225
PLEASE HELP THANK YOU A restaurant makes smoothies in batches of 6.4 litres. The smoothies are made from ice cream and a mixed fruit juice in the ratio 5 : 3. 35% of the juice is lime juice. Work out the maximum number of batches of smoothie that can be made from 42 litres of lime juice.
The maximum number of batches of smoothie that can be made from 42 litres of lime juice is 50.
What is the amount of mixed fruit juice required?To determine the amount of mixed fruit juice required to make a batch of smoothie, we need to find the total volume of ice cream and mixed fruit juice in a batch.
The ratio of ice cream to mixed fruit juice is 5 : 3, which means that the total ratio of ingredients in a batch of smoothie is 5 + 3 = 8.
Since the batch size is 6.4 litres, the volume of mixed fruit juice required per batch is:
3/8 x 6.4 litres = 2.4 litres
Next, we need to determine the amount of lime juice in each batch. If 35% of the mixed fruit juice is lime juice, then the amount of lime juice in each batch is:
35/100 x 2.4 litres = 0.84 litres
Now we can determine the number of batches of smoothie that can be made from 42 litres of lime juice.
The amount of lime juice required per batch is 0.84 litres, so the maximum number of batches that can be made from 42 litres of lime juice is:
42 litres ÷ 0.84 litres per batch = 50 batches
Learn more about batch mixing here: https://brainly.com/question/28390600
#SPJ1
Simon and his track team ran on the Heron Peak running trail yesterday after school. The team ran 2 miles due west from the parking lot to a bench. They turned at the bench to run 1.5 miles due north toward an outhouse. To finish the run, the team ran a straight line from the outhouse back to the parking lot. If Simon ran at a constant rate of 8 miles per hour, how long did it take Simon to finish the run?
If necessary, round your answer to the nearest tenth.
how many minutes?
It took Simon 45 minutes to finish the run.
What is distance?
Distance is the measure of how far apart two objects or locations are from each other. It is usually measured in units such as meters, kilometers, miles, or feet.
To solve this problem, we need to use the distance formula:
Distance = Rate x Time
We can break down the run into three parts: the 2 miles due west, the 1.5 miles due north, and the straight line back to the parking lot.
For the first part, Simon ran 2 miles at a rate of 8 miles per hour. Therefore, the time it took him to run this part of the trail was:
Time = Distance / Rate
Time = 2 miles / 8 miles per hour
Time = 0.25 hours
For the second part, Simon ran 1.5 miles at a rate of 8 miles per hour. Therefore, the time it took him to run this part of the trail was:
Time = Distance / Rate
Time = 1.5 miles / 8 miles per hour
Time = 0.1875 hours
To find the distance of the last part, we need to use the Pythagorean theorem to find the hypotenuse of the right triangle formed by the 2-mile and 1.5-mile legs:
c² = a² + b²
c² = 2² + 1.5²
c² = 4 + 2.25
c² = 6.25
c = sqrt(6.25)
c = 2.5 miles
So, Simon ran 2.5 miles at a rate of 8 miles per hour. Therefore, the time it took him to run this part of the trail was:
Time = Distance / Rate
Time = 2.5 miles / 8 miles per hour
Time = 0.3125 hours
Finally, we can add up the times for each part of the trail to find the total time it took Simon to finish the run:
Total Time = 0.25 hours + 0.1875 hours + 0.3125 hours
Total Time = 0.75 hours
To convert this to minutes, we can multiply by 60:
Total Time = 0.75 hours x 60 minutes/hour
Total Time = 45 minutes
Therefore, it took Simon 45 minutes to finish the run.
To learn more about distance from the given link:
https://brainly.com/question/30923151
#SPJ1
Renting a roller rink for your birthday costs $150 plus $6 per person. The total charge for your party was $ 282. Translate this information into an equation using
x to represent the number of guests at your party
The equation that translates the information is $282 = $150 + $6x where x to represent the number of guests at your party
The total charge for renting a roller rink for a birthday party is composed of two parts: a fixed cost of $150 and a variable cost of $6 per person. The variable cost depends on the number of guests, which we can represent with the variable x.
Therefore, the total cost equation can be written as:
Total cost = Fixed cost + Variable cost
Total cost = $150 + $6x
Here, Total cost = $282
So, equation is $282 = $150 + $6x
To find the total charge for a specific number of guests, we can substitute the value of x into the equation and simplify it. For example, if there were 22 guests at the party, the total cost would be:
Total cost = $150 + $6(22)
Total cost = $150 + $132
Total cost = $282
This means that the total charge for a party with 22 guests would be $282.
It's important to note that the fixed cost of $150 is the cost that remains the same no matter how many guests attend the party. On the other hand, the variable cost of $6 per person changes based on the number of guests.
To learn more about cost click on,
https://brainly.com/question/30990143
#SPJ4
solve for x in the following:
2x^3+3x^2+12x+1 =0
The value of x in the equation 2x³ + 3x² + 12x + 1 = 0 when solved is x = -0.085
Given the following equation
2x³ + 3x² + 12x + 1 = 0
The equation cannot be factorized
So, we solved graphically
See attachment for the graph of the equation 2x³ + 3x² + 12x + 1 = 0
On the graph, we observe that the curve of the equation crosses the x-axis at
x = -0.085
This means that the solution for x in the equation is x = -0.085
Read more about polynomial equation at
https://brainly.com/question/30536925
#SPJ1
A magazine used the summated rating of 10 restaurants to predict the cost of a restaurant meal. For that data, SSR 131,742.28 and SST 143,920.65. Complete parts (a) through (c) a. Determine the coefficient of determination, r2 , and interpret its meaning.
r2 = ____ (Round to two decimal places as needed.))
Interpret the meaning of r2.
It means that _____ % of the variation in the cost of a meal ______ be explained by the variation in summated ratings. (Round to two decimal places as needed.)
The Coefficient of determination i.e. r²≈ 0.9155.
What is Coefficient of determination?
The coefficient of determination, denoted as r², is a statistical measure that represents the proportion of the variance in the dependent variable that is predictable from the independent variable(s) in a regression model.
To determine the coefficient of determination, we first need to calculate the regression sum of squares (SSR) and the total sum of squares (SST) using the following formulae:
SSR = Σ(y_pred - y_mean)²
SST = Σ(y - y_mean)²
where y_pred is the predicted value of y based on the regression equation, y_mean is the mean of y, and y is the actual value of y.
Once we have calculated SSR and SST, we can use the formula for the coefficient of determination:
r² = SSR / SST
Using the given values, we have:
SSR = 131,742.28
SST = 143,920.65
r² = SSR / SST = 131,742.28 / 143,920.65 ≈ 0.9155
Interpreting the meaning of r², we can say that approximately 91.55% of the variation in the cost of a meal can be explained by the variation in summated ratings. In other words, the model based on summated ratings is able to explain a large proportion of the variability in the cost of a meal.
To learn more about Coefficient of determination, visit the link:
https://brainly.com/question/30100228
#SPJ1
5/14 x4 in simplest form as a fraction
Answer:
the answer is 5 simplify
Answer:
20/14
10/7
0r 5/56
Step-by-step explanation:
i hope you find it helpful
Work out 2/5 x 1 4/7 Give your answer and a fraction in its simplest form.
Answer:
0.62
Step-by-step explanation:
given :
[tex]\frac{2}{5} * 1\frac{4}{7}[/tex]
[tex]=\frac{2}{5} *\frac{11}{7}[/tex]
[tex]= \frac{22}{35}[/tex]
[tex]=0.62[/tex] as a decimal
Hope it helps
What is the answer to 5/8 ÷ 3/4 in fraction form
Answer:
5/6
Step-by-step explanation:
Algebra 1 T.16 Compare linear functions: tables, graphs, and equations GD7 Function A and Function B are linear functions. -10 -8 -6 Function A 104X Which statement is true? 6 2 02 -4 6 -8 -10 2 4 6 8 10 Function B X -1 6 9 The slope of Function A is greater than the slope of Function B. The slope of Function A is less than the slope of Function B. -3 11 17 Video O Qu an 00 Sma out c
Answer:
To compare the slopes of Function A and Function B, we need to find the slope of each function.
Function A: y = 104x
The slope of a linear function in the form y = mx + b is equal to the coefficient of x, which is 104 in this case. Therefore, the slope of Function A is 104.
Function B: y = -x + 7
The slope of a linear function in the form y = mx + b is equal to the coefficient of x, which is -1 in this case. Therefore, the slope of Function B is -1.
Since 104 is greater than -1, the statement "The slope of Function A is greater than the slope of Function B" is true.
Therefore, the answer is: The slope of Function A is greater than the slope of Function B.
0.053053053053053 irrational or rational
Answer: It is rational
Step-by-step explanation:
solve for x and y be sure to show your work
Answer:
x = 3√7.
y = 12.
Step-by-step explanation:
The 2 triangles are similar so:
x/9 = 7/x
x^2 = 63
x = √63
= 3√7.
By Pythagoras' theorem
y^2 = 9^2 + (3√7)^2
= 81 + 63
= 144
y = 12.
David bought 200 shares of Oracle stock yesterday and sold it today. His profit was $22. 0. At what price did he buy the stock yesterday?
Assuming that David sold the stock at $10 per stock today, then, we will agree that he bought the Oracle stock yesterday at a price of approximately $9.89 per share.
How do we calculate the price he bought the stock yesterday?A share, also known as a stock or equity, is a unit of ownership in a corporation. Stock investments provide investors with returns in the form of dividends and capital gains. The higher the expected returns, the more shares an investor owns.
Let the price at which David bought each share of Oracle stock yesterday be x. Then, his total cost for buying 200 shares would be: 200x
Similarly, his total revenue for selling 200 shares at $10 per share today would be:
= 200*($10)
= $2000
His profit was $22, so we can set up the equation which is $2000 - 200x = $22.
Simplifying and solving for x, we get:
$1978 = 200x
x = $1971/200
x = $9.89.
Read more about stock price
brainly.com/question/28143339
#SPJ1
Find the value of x.
Answer:
[tex]\large\boxed{\textsf{x=3}}[/tex]
Step-by-step explanation:
[tex]\textsf{We are asked to find the value of x.}[/tex]
[tex]\textsf{Notice that we have Intersecting Chords inside of the circle.}[/tex]
[tex]\large\underline{\textsf{What are Chords?}}[/tex]
[tex]\textsf{Chords are line segments that have endpoints on the circumference of a circle.}[/tex]
[tex]\textsf{Note that some Chords can be Diameters, but not for this problem. There's no Center.}[/tex]
[tex]\textsf{These Chords don't create Perpendicular Lines, which means the angles aren't equal.}[/tex]
[tex]\textsf{We can identify the unknown angles with a postulate.}[/tex]
[tex]\large\underline{\textsf{What is a Postulate?}}[/tex]
[tex]\textsf{A Postulate is a statement that can never be false. No matter what, it's always}[/tex]
[tex]\textsf{true.}[/tex]
[tex]\textsf{We can use the Linear Pair Postulate to find the needed angle.}[/tex]
[tex]\large\underline{\textsf{What is the Linear Pair Postulate?}}[/tex]
[tex]\textsf{Linear Pair Postulate is a Postulate that proves 2 angles add up to 180}^{\circ}.[/tex]
[tex]\textsf{A Linear Pair is 2 Adjacent Angles that form a Straight Angle.}[/tex]
[tex]\large\underline{\textsf{For our Problem;}}[/tex]
[tex]\tt \angle HLJ \ and \ \angle ILJ \ are \ Linear \ Pairs.[/tex]
[tex]\large\underline{\textsf{Find} \ \angle \textsf{HLJ;}}[/tex]
[tex]\tt \angle HLJ + \angle ILJ = 180^{\circ}.[/tex]
[tex]\tt \angle HLJ + 85.5^{\circ} = 180^{\circ}.[/tex]
[tex]\underline{\textsf{Subtract 85.5 from both sides of the equation;}}[/tex]
[tex]\tt \angle HLJ = 94.5^{\circ}[/tex]
[tex]\textsf{Now that we have} \tt \ \angle HLJ, \textsf{we can find x.}[/tex]
[tex]\textsf{We are given 2 arc measures and we have 2 Intersecting Chords.}[/tex]
[tex]\textsf{We should use} \tt \ \angle HLJ \ \textsf{to find x.}[/tex]
[tex]\large\underline{\textsf{How?}}[/tex]
[tex]\textsf{The Angle is equal to half the sum of the 2 arcs.}[/tex]
[tex]\underline{\textsf{For our Problem;}}[/tex]
[tex]\tt \angle HJL = \frac{1}{2} (42x-6 + 15x+24)[/tex]
[tex]\tt 94.5^{\circ} = \frac{1}{2} (42x-6 + 15x+24)[/tex]
[tex]\large\underline{\textsf{Solve;}}[/tex]
[tex]\textsf{Multiply each side by 2 first.}[/tex]
[tex]\tt 189^{\circ} = 42x-6 + 15x+24[/tex]
[tex]\underline{\textsf{Combine Like Terms;}}[/tex]
[tex]\tt 189^{\circ} = 57x+18[/tex]
[tex]\underline{\textsf{Subtract 18 from both sides;}}[/tex]
[tex]\tt 171^{\circ} = 57x[/tex]
[tex]\underline{\textsf{Divide each side by 57;}}[/tex]
[tex]\large\boxed{\textsf{x=3}}[/tex]
Suppose that X is normally distributed with mean 110 and
standard deviation 17.
A. What is the probability that X is greater than 138.05?
Probability =
B. What value of X does only the top 15% exceed?
Mean = 110
Standard Deviation = 17
The solution is given below:A. What is the probability that X is greater than 138.05?We have, Mean (μ) = 110Standard Deviation (σ) = 17Let's first standardize X = 138.05: Z = (X - μ)/σZ = (138.05 - 110)/17 = 1.650Therefore, P(X > 138.05) = P(Z > 1.650)Using a standard normal table, the probability of Z being greater than 1.650 is:0.0495Probability = 0.0495B. What value of X does only the top 15% exceed?We have, Mean (μ) = 110Standard Deviation (σ) = 17We need to find the value of X such that only the top 15% exceed. In other words, we want to find X such that P(X > x) = 0.15.Using a standard normal table, we can find that the Z-value for the top 15% is 1.0364. We can write this as:P(Z > 1.0364) = 0.15We now standardize the equation:P(Z > 1.0364) = 0.15Z = invNorm(0.15) + 1.0364Z = -1.0364 + 1.0364Z = 0Therefore, we have:Z = (X - μ)/σ0 = (X - 110)/17X = 110Therefore, the value of X such that only the top 15% exceed is 110.
Learn more about standard deviation
brainly.com/question/29088233
#SPJ4
A. The probability that X is greater than 138.05 is 0.0492.
B. The value of X does only the top 15% exceed is 127.57.
Given that X is normally distributed with mean 110 and standard deviation 17.
A. Probability= P(X > 138.05)
First, we need to calculate the z-score of 138.05 by using the formula;
z = (X - μ)/σ
Where
X = 138.05, μ = 110, and σ = 17z = (138.05 - 110)/17 = 1.649
Therefore, P(X > 138.05) = P(Z > 1.649)
Using a standard normal table, the probability P(Z > 1.649) = 0.0492
Thus, the probability that X is greater than 138.05 is 0.0492.
B. We know that the mean of the normal distribution is 110 and the standard deviation is 17, and we need to find the value of X such that only the top 15% exceed.
Therefore, we need to find the value of X such that P(X > x) = 0.15
Using a standard normal table, we find that the Z-value of 0.15 is 1.0364
Therefore, z = (x - μ)/σ = 1.0364
Solving for x, we get,
x = σz + μ = 17 × 1.0364 + 110 = 127.57
Thus, the value of X that only the top 15% exceed is 127.57.
Learn more about probability at https://brainly.com/question/17007499
#SPJ11
The standard form of a quadratic function is f(x)=a(x-h)^+k true or false
Hence, in response to the provided question, we can say that the constant k denotes the graph's vertical shift. The coefficient "a" specifies the function's opening direction and amount.
what is function?Mathematicians research numbers and their variants, equation and related structures, objects and their locations, and prospective locations for these things. The term "module" is used to describe the connection that exists in between set of inputs, each of which has a corresponding output. A function is an input-output connection in which each inputs results in something like a single, distinct return. A domain, codomain, or scope is assigned to each function. Functions are usually denoted by the letter f. (x). An x is used for entry. On capabilities, one-to-one capabilities, multiple prowess, in capabilities, and on capabilities are the four major types of accessible functions.
False.
A quadratic function has the usual form [tex]f(x) = a(x - h)^2 + k[/tex], where "a," "h," and "k" are constants that determine the shape, position, and orientation of the quadratic function's graph. The phrase (x - h)2 denotes the squared distance between the input value x and the horizontal shift h, while the constant k denotes the graph's vertical shift. The coefficient "a" specifies the function's opening direction and amount.
To know more about function visit:
https://brainly.com/question/28193995
#SPJ1
Solve for X Round to the nearest 10th if necessary
The length of the value x in the right triangle is 20.7 units.
How to find the side of a right triangle?A right triangle is a triangle that has one of its angles as 90 degrees. The sum angles in a triangle is 180 degrees.
Therefore, the side of a right triangle can be found using trigonometric ratios as follows:
Hence,
cos 34° = adjacent / hypotenuse
Therefore,
adjacent side = x
hypotenuse side = 25
Hence,
cos 34 = x /25
cross multiply
x = 25 cos 34
x = 25 × 0.82903757255
x = 20.7259393139
Therefore,
x = 20.7 units
learn more on right triangle here: https://brainly.com/question/29157263
#SPJ1
Sandra uses the formula, P = DB, to find her approximate six-month premium when her driver risk factor, D, is 1.0 and the basic six-month premium is $567.
What will her monthly premium be?
A.$170.00
B.$177.50
C.$94.50
D. $201.15
Therefore , the solution of the given problem of unitary comes out to be C is the correct response. $94.50.
An unitary method is what?The task can be finished by combining the data expression obtained to use this nanosection methodology with in all supplemental data from two people who employed a particular variable tactic. In plain English, this indicates that, if the desired result occurs, either the stated individual will be known or, in fact, the colour by both enormous processes would be skipped. A refundable fee of Rupees ($1.01) may be necessary for forty pens.
Here,
By dividing both sides by D, we can determine B if P = DB:
=> B = P/D
Sandra's premium P will be equal to the $567 base premium because her risk factor D is 1.0.
So,
=> B = P/D = $567/1.0 = $567
Her monthly payment will be as follows because this is her six-month premium:
=> Monthly premium = six-month premium / six,
which equals $567 / six, or $94.50.
Thus, C is the correct response. $94.50
To know more about unitary method visit:
https://brainly.com/question/28276953
#SPJ1
How to rewrite the problem so it only had positive exponents
To rewrite a problem with negative exponents into a problem with positive exponents, you can use the following rules.
Move any negative exponent to the denominator (or numerator, depending on where it is located) by changing the sign of the exponent to positive.
If there are any fractions with negative exponents, flip the fraction so that the exponent becomes positive.
For example, if you have the expression:
[tex]X^-2 / y^-3[/tex]
To rewrite this with positive exponents, you can move the negative exponents to the denominator and change the signs:
[tex]y^3 / x^2[/tex]
learn more about numerator here:
https://brainly.com/question/11156074
#SPJ4
Cindy has read 13 chapters of a 22 chapter book. What percent of the chapter has she read?
59.1%
Step-by-step explanation:
100% / 22 x 13 =59.1%
A geometric solid has 12 faces and 25 vertices. How many vertices does the solid have?
Answer: 35
Step-by-step explanation:
Let's use Euler's formula to solve this problem. According to Euler's formula, for any convex polyhedron (geometric solid with flat faces), the number of faces (F), vertices (V), and edges (E) satisfy the equation F + V - E = 2.
We are given that the geometric solid has 12 faces and 25 vertices. Let's call the number of edges "E" and substitute these values into Euler's formula:
12 + 25 - E = 2
Simplifying this equation, we get:
E = 35
Therefore, the geometric solid has 35 edges.
A cell tower is 3km from the highway. It has a circular range with a radius of 7km. What length of the highway is in the range.
Answer:
Below
Step-by-step explanation:
With questions like this it is helpful to draw the scenario as in the image below. Using Pyhtagorean theorem , you can calculate 'x'..... then the highway distance in range is two times this = 12.6 km
A tennis court is 78 feet long with the net located at the center. The distance from the net to the back of the service box is 21 feet, and the net is 3 feet tall. Assuming Carina can hit the ball so hard that its path is linear, from what height must she hit the ball to have the serve just clear the net and land in the service box? Decide whether or not it is reasonable for Carina to reach this height if she is 5′7" tall. Also, at what angle does the ball hit the ground? Your solution should include: A labeled diagram that shows a bird's-eye view of the path of the ball. A labeled diagram that shows the side view of Carina, the ideal height of the tennis racket, the ideal path of the tennis ball, and the measurements that are needed from the bird's-eye view diagram.
Carina needs to hit the ball at a height of about 3.04 feet to clear the net and land in the service box.
What is the trigonometric ratio?
There are six trigonometric ratios- sine(sin), cosine(cos), tangent(tan), cotangent(cot), secant(sec), cosecant(cosec). Let θ be the angle of the right-angled triangle then, sin θ = opposite side/hypotenuse or 1/cosθ.
To determine the height Carina needs to hit the ball to clear the net and land in the service box, we can use the following steps:
Draw a bird's-eye view diagram of the tennis court, including the net, the service box, and the path of the ball.
Draw a side view diagram of Carina and the ideal path of the tennis ball, including the measurements that are needed from the bird's-eye view diagram.
Use trigonometry to calculate the height Carina needs to hit the ball.
Determine whether it is reasonable for Carina to reach this height, given her height of 5'7".
Calculate the angle at which the ball hits the ground.
Here are the steps in more detail:
Bird's-eye view diagram:
We can draw a bird's-eye view diagram of the tennis court, with the net located at the center and the service box 21 feet away from the net. The distance from the net to the service box is (78-21)/2 = 28.5 feet. We can label the diagram with these distances and the height of the net (3 feet).
Side view diagram:
Next, we can draw a side view diagram that shows Carina, the ideal path of the tennis ball, and the measurements that are needed from the bird's-eye view diagram. We can label the diagram with the height of the tennis racket (h) and the distance from the racket to the net (x). We also need to label the height Carina needs to hit the ball to clear the net (y) and the height of the net (3 feet).
Calculate the height Carina needs to hit the ball:
To calculate the height Carina needs to hit the ball, we can use the following trigonometric formula:
tan(θ) = y / x
where theta is the angle between the ideal path of the ball and the ground, y is the height Carina needs to hit the ball, and x is the distance from the racket to the net.
Solving for y, we get:
y = x * tan(θ)
We know that x = 21 feet, and we can estimate that the angle theta is about 8 degrees (since the ball needs to clear the net by at least 3 feet). Plugging in these values, we get:
y = 21 * tan(8) = 3.04 feet
So Carina needs to hit the ball at a height of about 3.04 feet to clear the net and land in the service box.
Determine whether it is reasonable for Carina to reach this height:
Carina's height is 5'7", which is equivalent to 67 inches.
If we assume that Carina's arm reaches to about shoulder height, which is roughly halfway between her height and the height she needs to hit the ball (3.04 feet), then she would need to hit the ball about 1.5 feet above her shoulder.
This seems like a reasonable height for a skilled tennis player.
Calculate the angle at which the ball hits the ground:
To calculate the angle at which the ball hits the ground, we can use the following trigonometric formula:
tan(θ) = y / (x + d)
where d is the distance from the net to where the ball lands. We know that y = 3.04 feet, x = 21 feet, and d = 21 + 21 = 42 feet (since the ball travels the same distance on the other side of the court). Plugging in these values, we get:
tan(θ) = 3.04 / 42
θ = arctan(3.04 / 42)
θ = 0.07225
Hence, Carina needs to hit the ball at a height of about 3.04 feet to clear the net and land in the service box.
To learn more about the trigonometric ratio visit:
https://brainly.com/question/30339634
#SPJ1
Find x give brief reason
Q1 . By pytagorean therom ,
CA ^ 2 + AB ^2 = BC^2
2^2 +4^2 = BC^2
4 + 16 = BC ^2
20 = BC^2
BC = [tex]\sqrt{20}[/tex]
BC = 4.4
1/2 BC = x = 2.2 ( Midpoint)
Q2 .
OQP = 90
(5+X)^2 = X^2 + 7^2
25 + 10X + X^2 = X^2 + 49
25 + 10X = 49
10X = 49 - 25 = 24
X = 2.4
Answer:
see explanation
Step-by-step explanation:
(a)
the angle in a semicircle is a right angle , then Δ ABC is right with ∠ BAC = 90°
the radius of the circle OB = x , then BC = 2x
using Pythagoras' identity in the right angle
BC² = AB² + AC²
(2x)² = 4² + 2²
4x² = 16 + 4 = 20 ( divide both sides by 4 )
x² = 5 ( take square root of both sides )
x = [tex]\sqrt{5}[/tex]
-----------------------------------------------------------------
the angle between a tangent and the radius of the circle at the point of contact is 90° , that is
∠ OQP = 90° and Δ OPQ is right
note that OP = 5 + radius = 5 + x
using Pythagoras' identity in the right triangle
OP² = OQ² + PQ²
(5 + x)² = x² + 7² ← expand left side using FOIL
25 + 10x + x² = x² + 49 ( subtract x² from both sides )
25 + 10x = 49 ( subtract 25 from both sides )
10x = 24 ( divide both sides by 10 )
x = 2.4
Find a logarithmic equation that relatesyandx. (Round all numerical values to three decimal places.). ln(y)=
X: 1 2 3 4 5 6
Y: 1 0.630 0.481 0.397 0.342 0.303
ln(y) = -0.544x + 1.099
The logarithmic equation that relates x and y is given by ln(y) = -0.544x + 1.099. To get this equation, the given table of values is considered.Let's first find the value of "a" in the general logarithmic equation, which is y = a ln(x). We use the given table of values to get this value. When x = 1, y = 1, and so a ln(1) = 1, which implies that a = 1. Hence, the equation becomes y = ln(x).Now, we need to convert this to an equation in terms of y and x. That is, we need to find ln(y) in terms of x. To do this, we substitute y for x in the equation y = ln(x). That is, we get ln(y) = ln(x).Now, we substitute the given values of x and y in this equation to get the required logarithmic equation. That is, we have:ln(y) = -0.544x + 1.099 (rounded to three decimal places). Therefore, the logarithmic equation that relates x and y is ln(y) = -0.544x + 1.099.
Learn more about Logarithmic
brainly.com/question/30085872
#SPJ4
The length of time, in minutes, for an airplane to obtain clearance for takeoff at a certain airport is a random variable Y=3X−2, where X has the density function f(x) = ¼ e^−x/4, for x > 0, f(x) = 0, elsewhere. Find the mean and variance of the random variable Y.
The mean of Y is -5/4 and the variance of Y is 144.
What is mean?In statistics, the mean is a measure οf central tendency that represents the average οf a set οf data. It is alsο knοwn as the arithmetic mean. The mean is calculated by adding up all the values in the dataset and dividing the sum by the tοtal number οf values. It is οften used tο describe the typical οr average value in a set οf data.
What is variance?Variance is a statistical measure that describes hοw much the values in a set οf data vary frοm the average value οr mean. It measures the spread οr dispersiοn οf the data pοints arοund the mean.
In the given questiοn,
Tο find the mean and variance οf the randοm variable Y, we need tο use the fοrmulas fοr the expected value and variance οf a functiοn οf a randοm variable:
The expected value (mean) of Y is given by:
E(Y) = E(3X - 2) = 3E(X) - 2
The variance of Y is given by:
Var(Y) = Var(3X - 2) = 9Var(X)
To find E(X), we need to integrate the density function f(x) over all possible values of X:
E(X) = ∫0∞ x f(x) dx
= ∫0∞ x (1/4)[tex]\rm e^{(-x/4)[/tex]dx
This integral can be solved using integration by parts, with u = x and dv/dx = (1/4)[tex]\rm e^{(-x/4)[/tex] dx.
Integrating by parts, we get:
E(X) = [-x/4 [tex]\rm e^{(-x/4)[/tex]]_0∞ + ∫0∞ (1/4)[tex]\rm e^{(-x/4)[/tex] dx
= [0 + (1/4)]/1 + [0]
= 1/4.
Therefore, the expected value of Y is:
E(Y) = 3E(X) - 2 = 3(1/4) - 2 = -5/4.
To find Var(X), we can use the formula for the variance of an exponential distribution, which is:
Var(X) = (1/λ²) = (4²) = 16.
Therefore, the variance of Y is:
Var(Y) = 9Var(X) = 9(16)
= 144.
Therefore, the mean of Y is -5/4 and the variance of Y is 144.
To know more about Variance , visit:
https://brainly.com/question/29727198
#SPJ1
The mean of Y is 10 minutes, and the variance of Y is 144 minutes squared.
What is integration?
Integration is a mathematical operation that is the reverse of differentiation. Integration involves finding an antiderivative or indefinite integral of a function.
To find the mean and variance of Y, we will first need to find the mean and variance of X.
Mean of X:
The mean of X is given by:
E(X) = integral from 0 to infinity of xf(x) dx
E(X) = integral from 0 to infinity of x * 1/4 e^(-x/4) dx
Using integration by parts with u = x and dv = e^(-x/4) dx, we can evaluate this integral to get:
E(X) = 4
Variance of X:
The variance of X is given by:
Var(X) = E(X^2) - [E(X)]^2
We will first need to find E(X^2). Using integration by parts again, we can evaluate this integral as:
E(X^2) = integral from 0 to infinity of x^2 * 1/4 e^(-x/4) dx
E(X^2) = 32
Therefore, the variance of X is:
Var(X) = E(X^2) - [E(X)]^2
Var(X) = 32 - 16
Var(X) = 16
Now, we can use the formula for the mean and variance of a linear transformation of a random variable to find the mean and variance of Y.
Mean of Y:
The mean of Y is given by:
E(Y) = E(3X - 2)
E(Y) = 3E(X) - 2
E(Y) = 10
Variance of Y:
The variance of Y is given by:
Var(Y) = Var(3X - 2)
Var(Y) = 9Var(X)
Var(Y) = 144
Therefore, the mean of Y is 10 minutes, and the variance of Y is 144 minutes squared.
To learn more about integration from the given link:
https://brainly.com/question/18125359
#SPJ1
you and your family went to riverside cafe for dinner and the total bill was $54.95. since you have a hawk card, you can get a 20% discount. how much would you save using your hawk card? what would be the final amount you pay?
To find the amount of the discount, we can multiply the total bill by the discount rate of 20% (or 0.2):
Discount = 0.2 x $54.95
Discount = $10.99
What is percentage ?
Percentage is a way of expressing a fraction or proportion as a portion of 100. It is often used to represent rates, discounts, or increases/decreases in values.
So you would save $10.99 using your Hawk card.
To find the final amount you would pay after the discount, we can subtract the discount from the total bill:
Final amount = Total bill - Discount
Final amount = $54.95 - $10.99
Final amount = $43.96
So the final amount you would pay with the Hawk card discount is $43.96.
Learn more about percentage
https://brainly.com/question/24877689
#SPJ1