The probability of observing that the difference between the average height of the 6 waves in California and the average height of the 6 waves in Florida (California minus Florida) is greater than 0.5 feet is 0.55.
A beach in California has an almost normal distribution of wave heights, averaging 7.2 feet. The wave height distribution on a Florida beach is about normal, average 6.6 feet. Six waves are randomly selected from each beach and the heights are recorded.
Probability distributions generate the possible outcomes of any random event. It also defines the set of possible outcomes for any random experiment based on the underlying sample space. These parameters can be a set of real numbers or a set of vectors or a set of any entity. This is part of probability statistics.
A randomized experiment is defined as the result of an experiment whose outcome cannot be predicted.
Suppose if we toss a coin, we cannot predict whether the outcome will be heads or tails. The possible outcomes of a random experiment are called outcomes. The resulting set is called a sample point. With these experiments or events, we can always create tables of probability models based on variables and probabilities.
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Find the area of the kite below:
What is the area?
According to given information, the area of kite is 480 m².
What is area of kite?
The area of a kite can be calculated by multiplying the lengths of its two diagonals and dividing the result by 2:
Area of kite = (diagonal 1 x diagonal 2) / 2
The hypotenuse is usually the slanted line in a triangle.
Area of a kite = pq/2 (p and q = diagonal)
Finding the missing side length of triangle₁
37² = 12² + x² (x = unknown side length)
=> 1369 = 144 + x² (x = unknown side length)
=> 1369 - 144 = x² (x = unknown side length)
=> 1225 = x² (x = unknown side length)
=> x = 35 m
Finding the area:
Area of a kite = pq/2 (p and q = diagonal)
=> Area of a kite = (35 + 5)(12 + 12)/2
=> Area of a kite = (40)(24)/2
=> Area of a kite = 40 x 12 = 480 m².
Therefore, the area of kite is 480 m².
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Help me out I don’t messed this one up, also tell me how to give brainliest and I’ll give it to the first real answer
The value of the given integral function is 10 and option d is the correct answer.
What is continuous function?Any function that may be drawn without removing the pen from the page is said to be continuous. Formally, a function f(x) is continuous at a point c if all three of the following criteria are true:
Definition of f(c) (i.e., c is in the domain of f).
When x gets closer to c, f(x) reaches its maximum.
The limit of f(x) as x gets closer to c equals f. (c).
A function is said to be continuous if it is continuous over its whole domain. In mathematics and the sciences, continuous functions have a wide range of useful features and applications.
For the given function the integral can be written as follows:
[tex]\int\limits^2_{-4} {f(x)} \, dx = \int\limits^0_{-4} {\frac{x^2}{|x|} } \, dx + \int\limits^2_0 {\frac{x^2}{|x|} \, dx[/tex]
[tex]= [\frac{x^2}{2} ]_{-4}^0 + [\frac{x^2}{2} ]_{0}^2\\= 8 + 2\\= 10[/tex]
Hence, the value of the given integral function is 10 and option d is the correct answer.
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a nurse is preparing to administer furosemide 4 mg/kg/day po divided into 2 equal doses daily to a toddler who weighs 22 lb. how many mg should the nurse administer per dose? (fill in the blank with the numeric value only, round the answer to the nearest whole number, and use a leading zero if applicable. do not use a trailing zero.)
The nurse should administer 19.958 mg of furosemide per dose to the toddler.
To use the unitary method, we need to convert the toddler's weight from pounds to kilograms, as the dose is given in mg/kg/day.
1 lb = 0.45359237 kg (conversion factor)
Therefore, the toddler's weight in kilograms is
22 lb x 0.45359237 kg/lb = 9.979 kg (rounded to three decimal places)
Now we can calculate the total daily dose of furosemide for the toddler
4 mg/kg/day x 9.979 kg = 39.916 mg/day (rounded to three decimal places)
Since the dose is divided into 2 equal doses daily, each dose would be half of the total daily dose
39.916 mg/day ÷ 2 = 19.958 mg/dose (rounded to three decimal places)
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explain how, in the fewest possible number of moves, you would measure out exactly 1 gallon of water. note that, if you dump out a jug, you have to dump it out completely, that means it is illegal to, for example, fill up the 12-gallon jug and then dump it into both the 3-gallon jug and the 8-gallon to leave behind 1 gallon in the 12-gallon jug.
To measure out exactly 1 gallon of water we need exactly six possible number of moves.
To measure out exactly 1 gallon of water using two jugs, one with a 3-gallon capacity and one with an 5-gallon capacity, you can follow some steps
Fill the 5-gallon jug with water completely. Pour the water from the 5-gallon jug into the 3-gallon jug, leaving 2 gallons of water in the 5-gallon jug.
Empty the 3-gallon jug completely. Pour the 2 gallons of water from the 5-gallon jug into the empty 3-gallon jug.
Fill the 5-gallon jug with water again. Pour water from the 5-gallon jug into the 3-gallon jug until it is full, which will leave exactly 1 gallon of water in the 5-gallon jug.
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Jada works at an orchard. She wants to see if an apple tree or orange tree has more healthy fruit, as opposed to spoiled fruit. She examines the trees and picks the fruit before beginning to create the following relative frequency table, which is incomplete.
Apple
Orange
Total
Healthy 33=0.38 ₽ 38% 39=0.44 s 44% blank A Spoiled =0.11 ~ 11% §=0.07 ~ 7% blank B
Total
87-1.00 = 100%
The marginal relative frequency for healthy fruit is approximately
[ Select I
-, and the marginal relative frequency for spoiled fruit
is approximately
[ Select ]
Answer:
the healthy fruit is 77.07
and the spoiled fruit is 20.19
Step-by-step explanation:
the explanation is a little long but if you want one just ask in the comments and ill edit this
Find the mean, median, and mode(s) of the data. Calculator use is ok.
18, 21, 22, 18, 19
Mean
Median
Mode(s)
Answer:
The mean is 19.6. you have to add up all the numbers given and divide it by the number of numbers which in this case it's 18+18+19+21+22=98
98/5=19.6
The median is the middle number when you arrange the numbers in order therefore it's 19
The mode is that number which appears the multiple time in the numbers given therefore it's 18
Mr. Lawson also makes cupcakes in his bakery . He made 9 dozen cupcakes for the school to sell at its Spring Fling
- The school sold 36 cupcakes by noon
- They sold 24 more cupcakes by 3:30
- The remaining cupcakes were sold equally during each of the 2 hours between 4 and 6 o’ clock.
Write an equation that can be used to find c , the number of cupcakes that were sold in each of the hours between 4 and 6 o’ clock
The number of cupcakes that were sold in each of the hours between 4 and 6 o’ clock is 24 cupcakes.
How to write an equation that can be used to find c?Since the total number of cupcakes that were sold is equal to 9 dozen cupcakes.
Total number of cupcakes = 9 * 12 = 108 cupcakes.
Since c is the number of cupcakes that were sold in each of the hours between 4 and 6 o’ clock.
We can write an equation that represents the total number of cupcakes sold as follows:
36 + 24 + c + c = 108
Solve for c:
36 + 24 + c + c = 108
36 + 24 + 2c = 108
60 + 2c = 108
2c = 108 - 60
2c = 48
c = 48/2
c = 24
Therefore, the number of cupcakes that were sold in each of the hours between 4 and 6 o’ clock is 24 cupcakes.
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What is p( less than 7) in fraction form ?
p is =probability btw.
The probability of rolling a number less than 7 would be written as 1/1 or simply 1.
What is a probability?Probability is a branch of statistics that deals with the study of random events and their likelihood of occurrence.
Without additional information, it's impossible to determine the probability of an event being less than 7. We need to know the context of the situation and the possible outcomes that can occur to calculate the probability.
However, if we assume that the context is related to rolling a fair six-sided die, then the probability of rolling a number less than 7 is 1 because all the possible outcomes (1, 2, 3, 4, 5, and 6) are less than 7.
In fraction form, the probability of rolling a number less than 7 would be written as 1/1 or simply 1.
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The probability of getting a card less than 7 would be 0.75. So, p( less than 7) in fraction form will be 3/4.
What is a probability?Probability is a branch of statistics that deals with the study of random events and their likelihood of occurrence.
The given cards are numbered as:
s = [4,5,6,7]
n(s) = 4
The event here is the probability of picking the cards less than 7
Cards less than 7 i.e. 4,5,6
n(e) = 3
Probability of picking the card lesser than 7 is:
P(e) = n(e)/n(s)
P(e) = 3/4
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The complete question is as follows:
You pick a card at random. 4 5 6 7 What is P(less than 7)? Write your answer as a fraction or whole number.
p = probability.
I need help please 1. Neville Manley, the owner of American Realty Group, called and left a
message with the receptionist. He stated that he wanted the most economical
looring to the patio that covers the area. It's a 3.2 m x 5.0 m. covered patio.
What do you suggest for the Manley's project? Be sure to defend your
answer. Sketch the flooring project, show your calculation, and make your
explanation.
Using concrete pavers for the patio flooring is a cost-effective and durable option for Mr. Manley's project. Approximately 176 pavers will be needed to cover the 3.2 m x 5.0 m area of the patio.
Based on Mr. Manley's request for the most economical option for the patio flooring, I would suggest using concrete pavers. Concrete pavers are a durable and cost-effective option for outdoor flooring. They come in various shapes, sizes, and colors, allowing for a range of design options. To calculate the number of pavers needed, we first need to determine the total area of the patio. The formula for the area of a rectangle is length times width, so the area of the patio is 3.2 m x 5.0 m = 16 square meters. Next, we need to determine the size of the pavers. Let's assume we use 30 cm x 30 cm pavers. To cover 1 square meter with these pavers, we will need 11 pavers (100 cm / 30 cm = 3.33 pavers per meter, and 3.33 x 3.33 = 11.11 pavers per square meter, rounded to 11). Therefore, to cover the 16 square meter patio, we will need approximately 176 pavers (11 pavers per square meter x 16 square meters = 176 pavers).
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HELP GEMOTRY DUE TODAY
Last week, there were 150 student absences at Johnson High. The table below summarizes them by the day of the week on which they occured. This information is also presented as a circle graph.
Find the central angle measure, x°, for the Monday slice in the circie graph. Do not round.
Answer: 43.2
Step-by-step explanation:
Do this by ration method:
[tex]\frac{18+36+15+33+48}{18} = \frac{360}{x}[/tex]
x = 43.2
Help Please And Thank You
Answer:
B
Step-by-step explanation:
Mr. and Mrs. Sanchez want to invest money for their child’s college education. They have decided to invest $2000 initially. If the investment is in an account that earns 8% annual interest, compounded yearly for 10 years, how much will their investment be worth at the end of the 10th year?
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$2000\\ r=rate\to 8\%\to \frac{8}{100}\dotfill &0.08\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{yearly, thus once} \end{array}\dotfill &1\\ t=years\dotfill &10 \end{cases} \\\\\\ A = 2000\left(1+\frac{0.08}{1}\right)^{1\cdot 10}\implies A=2000(1.08)^{10} \implies A \approx 4317.85[/tex]
44
Use simple interest to find the ending balance to the nearest penny
5) $1,730 at 6% for 4 years
Step-by-step explanation:
decimal interest = .06
$ interest = prt
= $ 1730 * .06 * 4 = $ 415.20
Solve the equation in the interval from 270° to 810°
Your answer should be in degrees
cos(x)=1
Choose all answers that apply
A. 0°
B. 90°
C. 360°
D. 540°
E. 720°
F. 1080°
Answer:
Step-by-step explanation:
cos(x)=1
Choose all answers that apply
A. 0°
B.90°
C.360°
D.540°
E. 720°
F.1080°
Answer:
C or E
Step-by-step explanation:
The answer should be choice.C or E
What is the End Behavior of the following Graph?
Answer:
The answer is B
Step-by-step explanation:
The asymptote of this graph is -4. If you look at the bottom of the graph, the line is going flat to -4, that means it's the asymptote. B has the only option where -4 occurs. Therefore, it's B.
Hope this helps.
What is a valid signature do you need to be able to read it or what
Sincerly,
Xavier Martinez
Nope, and there's an stereotype on medical doctors that their signature is just a garbled or gibberish, which very often is true
these days we also have "digital signatures" you can include in an email, which are just encrypted material verifyable by some encryption keys, it varies but the leading ones are PGP and/or GPG types
so valid is one that's consistent, could be your fingerprint if you wish, and due to its consistency also verifyable.
A square is inscribed in a circle as shown below. The radius of the circle is 7 inches, and the distance from the centers of the square and circle to the edge of the square is 5 inches. What is the area, in square inches, of the shaded region? Responses A. 14π – 100 A. 14π – 100 B. 14π – 25 B. 14π – 25 C. 49π – 100 C. 49π – 100 D. 49π – 25 D. 49π – 25 E. (72 – 52)π
the space is A there because A is the one
Suppose another one of your credit cards offers 3% cash back on gas, 2% at grocery stores, and 1% on all other purchases. If you spent a total of $2,738.21 on everything, with $384.23 of that total at the grocery store and $134.92 for gas, how much would your cash back be?
The cash back you would receive on your purchases of $2,738.21 using this credit card is $33.92.
To calculate the cash back you would receive using the given credit card, we need to multiply the total amount spent in each category by the corresponding cash back percentage, and then add up those amounts.
For gas purchases, you spent $134.92, so the cash back earned on that amount would be:
$134.92 x 3% = $4.05
For grocery store purchases, you spent $384.23, so the cash back earned on that amount would be:
$384.23 x 2% = $7.68
For all other purchases, you spent a total of:
$2,738.21 - $134.92 - $384.23 = $2,219.06
So the cash back earned on that amount would be:
$2,219.06 x 1% = $22.19
Adding up the cash back earned in each category, we get:
$4.05 + $7.68 + $22.19 = $33.92
∴ Cashback = $33.92
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9. Higher Order Thinking Suppose you have a graph of speed that shows a lion can run four times as fast as a squirrel. Name an ordered pair that shows this relationship. What does this ordered pair represent?
Answer: : The point (4,5)
Step-by-step explanation:
(09.02) Alex wanted to understand whether grade level had any relationship to their opinion on extending the school day. She surveyed some students and displayed the results in the table below: In favor Opposed Undecided Grade 9 5 3 9 Grade 10 8 12 9 Grade 11 15 16 10 Grade 12 12 6 11 Compare P(Grade 12 | opposed) with P(opposed | Grade 12). (1 point) Group of answer choices P(Grade 12 | opposed) = P(opposed | Grade 12) P(Grade 12 | opposed) > P(opposed | Grade 12) P(Grade 12 | opposed) < P(opposed | Grade 12) There is not enough information.
When P(opposed | Grade 12) exceeds P(Grade 12 | opposed), the correct response is: P(opposed | Grade 12) P(opposed | Grade 12) (Option C)
what is permutation ?An arrangement of things in a particular order is known as a permutation in mathematics. In more detail, an arrangement of a set's members in a certain order is known as a permutation. To give one example, the set 1, 2, 3 contains six permutations: 1, 2, 3, 1, 2, 3, 1, and 3, 2, 1. The formula P(n, r) is frequently used to express permutations, which are the various methods to select r things from a group of n objects and arrange them in a particular order. P(n, r) has the following formula: P(n, r) equals n!/(n-r)! where the factorial of n is represented by n! (i.e., the product of all positive integers from 1 to n).
given
Using Bayes' theorem, we can contrast P(Grade 12 | opposed) with P(grade 12 | opposed):
Grade 12 opposition formula: P(opposed) = P(Grade 12 opposition) * P(opposed) / P (Grade 12)
The table contains the values we require:
P(grade twelve) = (12+6+11)/(5+3+9+8+12+9+15+16+10+12+6+11) = 0.15 P(opposition) = (3+12+16+6)/(5+3+9+8+12+9+15+16+10+12+6+11) = 0.5 P(opposition | grade twelve) = 6/(12+6+11) = 0.24
Although we do not directly know the value of P(Grade 12 | opposed), we can calculate it using the following formula:
P (12th grade | opposed) = P (12th grade | opposed) * P (12th grade | opposed) / P (12th grade | opposed) = 0.24 * 0.15 / 0.5 = 0.072
As a result, we have:
P (12th grade | opposed) = 0.072 P (12th grade | opposed) = 0.24
When P(opposed | Grade 12) exceeds P(Grade 12 | opposed), the correct response is: P(opposed | Grade 12) P(opposed | Grade 12) (Option C) .
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# 2) What will be the probability of getting odd numbers if a dice is
thrown?
A) 1/2
B) 2
C) 4/2
D) 5/2
Pls show ur work
1/2 will be the probability of getting odd numbers if a dice is
thrown.
What does the math term "probability" mean?
The simple definition of probability is the likelihood that something will occur. We can discuss the probabilities of various outcomes—how likely they are—when we aren't sure how a particular event will turn out.
Statistics describes the examination of events subject to probability. Probability is a measure of how likely or likely-possible something is to happen. For instance, the chance of flipping a coin and obtaining heads is 1 in 2, as there is only one way to acquire a head and there are a total of 2 possible outcomes (a head or tail). P(heads) = 12 is the formula.
The total number of possible outcomes n=6.
Sample space = 1,2,3,4,5,6
odd nos. = 1, 3, 5
probability of getting odd nos.= 3/6 = 1/2
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A couple of two-way radios were purchased from different stores. Two-way radio A can reach 8 miles in any direction. Two-way radio B can reach 11.27 kilometers in any direction.
Part A: How many square miles does two-way radio A cover? Use 3.14 for pi and round to the nearest whole number. Show every step of your work.
Part B: How many square kilometers does two-way radio B cover? Use 3.14 for pi and round to the nearest whole number. Show every step of your work.
Part C: If 1 mile = 1.61 kilometers, which two-way radio covers the larger area? Show every step of your work.
Part D: Using the radius of each circle, determine the scale factor relationship between the radio coverages.
Part A: Two-way radio A covers approximately 201 square miles.
Part B: Two-way radio B covers approximately 483 square kilometers.
Part C: Two-way radio A covers the larger area.
Part D: The scale factor relationship between the radio coverages is approximately 0.8746.
What is area of circle?
The area of a circle can be found using the formula A = πr², where A is the area and r is the radius of the circle.
Part A: For two-way radio A, the radius is 8 miles, so the area covered by the radio is:
A = π8²
A = 64π
A ≈ 201 square miles
Therefore, two-way radio A covers approximately 201 square miles.
Part B:For two-way radio B, the radius is 11.27 kilometers. We need to convert this to miles in order to use the formula for the area of a circle.
1 kilometer is equal to 0.621371 miles (to 6 decimal places).
So, 11.27 kilometers is equal to: 11.27 km × 0.621371 mi/km = 7.00142 miles
Now, we can find the area covered by two-way radio B:
A = π(7.00142)²
A = 153.94π
A ≈ 483 square kilometers
Therefore, two-way radio B covers approximately 483 square kilometers.
Part C:
We can compare the areas covered by the two-way radios by using their respective areas calculated in Part A and Part B.
Area covered by two-way radio A = 201 square miles
Area covered by two-way radio B = 483 square kilometers
We need to convert the area covered by two-way radio B to square miles in order to compare the two areas. We know that 1 mile is equal to 1.61 kilometers, so:
1 square mile = (1.61)² square kilometers
1 square kilometer = (1/1.61)² square miles
1 square kilometer = 0.386 square miles (rounded to 3 decimal places)
Therefore, the area covered by two-way radio B in square miles is:
483 km²× 0.386 mi²/km² ≈ 186 square miles
Now we can compare the two areas:
Area covered by two-way radio A = 201 square miles
Area covered by two-way radio B = 186 square miles
Since 201 is greater than 186, two-way radio A covers the larger area.
Part D:
To determine the scale factor relationship between the radio coverages, we can compare their radii.
The radius of two-way radio A is 8 miles.
The radius of two-way radio B is 11.27 kilometers, which is approximately 6.997 miles (as calculated in Part B).
The scale factor is the ratio of the radii of the two circles.
So,scale factor = radius of two-way radio B / radius of two-way radio A
scale factor = 6.997 / 8
scale factor ≈ 0.8746
Therefore, the scale factor relationship between the radio coverages is approximately 0.8746.
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A rectangular playing field is 80m by 100m, if Ali wants to make 3 rounds around this field, how many meters will he cover altogether
Answer:
1080
Step-by-step explanation:
the perimeter of the field is 2(80) + 2(100) or 360
if he goes around the field 3 times then its 3*360 or 1080
~lmk if u got Qs
What is the result of the equation: 2+5+6+7*(5-2)
Answer:
34
Step-by-step explanation:
1)Simplify 5−2 to 3
2+5+6+7×3
2)Simplify 7×3 to 21.
2+5+6+21
3)Simplify 2+5 to 7.
7+6+21
4)Simplify 7+6 to 13.
13+21
5)Simplify.
34
Do you think the ratio of hypotenuse to a leg is the same for all isosceles right triangles? Explain
Yes, the ratio of the hypotenuse to a leg is the same for all isosceles right triangles.
What is hypotenuse ?
In a right triangle, the hypotenuse is the side that is opposite to the right angle. It is also the longest side of the triangle. The hypotenuse is always opposite the right angle and is found using the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides. In a right triangle with legs of length "a" and "b", the length of the hypotenuse "c" can be found using the formula:
[tex]c^2 = a^2 + b^2[/tex]
Taking the square root of both sides gives us:
[tex]c = \sqrt{a^2 + b^2}[/tex]
The hypotenuse plays an important role in trigonometry, as it is used in the calculation of trigonometric ratios such as sine, cosine, and tangent.
According to the question:
Yes, the ratio of the hypotenuse to a leg is the same for all isosceles right triangles.
In an isosceles right triangle, the two legs are congruent, which means they have the same length. Let's call the length of each leg "a". The hypotenuse of the triangle can be found using the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the legs:
[tex]hypotenuse^2 = a^2 + a^2 = 2a^2[/tex]
Taking the square root of both sides, we get:
[tex]hypotenuse = \sqrt{2a^2} = a * \sqrt{2}[/tex]
So, the ratio of the hypotenuse to a leg is:
[tex]hypotenuse / a = (a * \sqrt{2}) / a = \sqrt{2}[/tex]
This shows that the ratio of the hypotenuse to a leg in an isosceles right triangle is always equal to the square root of 2, which is a constant value. Therefore, the ratio is the same for all isosceles right triangles.
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Keiko received a $80 gift card for a coffee store. She used it in buying some coffee that cost $7.37 per pound. After buying the coffee, she
had $43.15 left on her card. How many pounds of coffee did she buy?
Let's start by finding out how much money Keiko spent on coffee. She started with an $80 gift card and ended up with $43.15 left, so she spent:
$80 - $43.15 = $36.85
We also know that the coffee costs $7.37 per pound. Let's use "x" to represent the number of pounds of coffee Keiko bought. Then we can set up an equation:
$7.37x = $36.85
To solve for x, we can divide both sides by $7.37:
x = $36.85 ÷ $7.37
x = 5
So Keiko bought 5 pounds of coffee.
A water sprinkler sends out water in a circular pattern . What is the area formed by the water pattern if it can spray out 22 feet in any direction use 3.14 for pi
The sprinkler will water an area of approximately 1519.76 square feet.
What is Area?Area is the measurement of the size of a surface or region. It is usually measured in square units such as square meters, square feet, or square inches.
The area watered by the sprinkler can be calculated using the formula for the area of a circle:
Area = πr²
where r is the radius of the circle.
In this case, the radius of the sprinkler's spray is given as 22 ft. So, we can substitute this value in the formula:
Area = π(22 ft)²
Area = π(484 ft²)
Area = 1519.76 ft² (rounded to two decimal places)
Therefore, the sprinkler will water an area of approximately 1519.76 square feet.
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If mzA + mzB = 180, then
mA and mzB are
classified as what kind of
angles?
Answer:
Step-by-step explanation:
yes yes no 180 which is an angle of time
Answer:
. yes no.180 is angle of time
i have no idea how to get this and nothing is leading me in the right direction
Answer:
Expanding the function:
[tex](x+6)^4\\[/tex]
You should get this:
[tex]x^4+24x^3+216x^2+864x+1296[/tex]
Step-by-step explanation:
Hope it helps
studysoup the time between arrivals of taxis at a busy intersection is exponentially distributed with a mean of
The required probability of waiting taxi longer than one hour and waiting for one hour is equals to 0.0821 and 0.1725 respectively.
Use the exponential distribution formula,
For an exponentially distributed random variable X with mean μ, the probability density function is given by,
f(x) = (1/μ) × e^(-x/μ)
And the cumulative distribution function is ,
F(x) = P(X ≤x)
= 1 - e^(-x/μ)
Mean time between taxi arrivals is 24 minutes,
Rate parameter
λ = 1/μ
= 1/24.
Probability of waiting longer than one hour for a taxi,
Probability that the time between arrivals is greater than 60 minutes. Using the cumulative distribution function,
P(X > 60)
= 1 - P(X ≤ 60)
= 1 - (1 - e^(-60/24))
= e^(-2.5)
≈ 0.0821
Probability of waiting longer than one hour for a taxi is approximately 0.0821.
Already been waiting for one hour,
the time you have to wait for the next taxi to arrive is 10 minutes.
Using the cumulative distribution function,
P(X ≤70 | X > 60)
= P(60 < X ≤ 70) / P(X > 60)
= (1 - e^(-70/24) - (1 - e^(-60/24))) / e^(-60/24)
≈ 0.1725
Therefore, the probability of waiting longer than one hour for a taxi is and that a taxi arrives within the next 10 minutes waiting for one hour is equals to 0.0821 and 0.1725 respectively.
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The above question is incomplete, the complete question is:
The time between arrivals of taxis at a busy intersection is exponentially distributed with a mean of 24 minutes. (a) What is the probability that you wait longer than one hour for a taxi? (b) Suppose you have already been waiting for one hour for a taxi, what is the probability that one arrives within the next 10 minutes? Round your answers to 4 decimal places.