Many hotel chains that offer free wi-fi service to their customers have experienced increasing demand for internet bandwidth and increasing costs. marriott international would like to test the hypothesis that the proportion of customers that are carrying two wi-fi devices exceeds 0.60. a random sample of 120 marriott customers found that 78 have two wi-fi devices. marriott international would like to set î± = 0.01. the p-value for this hypothesis test would be ________.
Answers
The p-value for this hypothesis test is approximately 0.1317.
To calculate the p-value for the hypothesis test, we need to perform a one-sample proportion test using the sample data provided.
Let's define the null and alternative hypotheses:
Null hypothesis (H₀): The proportion of Marriott customers carrying two Wi-Fi devices is equal to or less than 0.60.
Alternative hypothesis (H₁): The proportion of Marriott customers carrying two Wi-Fi devices exceeds 0.60.
Sample size (n) = 120
Number of customers with two Wi-Fi devices (x) = 78
To test the hypothesis, we can use the normal approximation to the binomial distribution since the sample size is reasonably large.
First, calculate the sample proportion:
\(\hat{p}\) = x / n = 78 / 120 = 0.65
Next, calculate the test statistic (z-score):
z = \(\frac{\hat{p}-p_0}{\sqrt{\frac{p_0(1-p_0)}{n} } }\)
= (0.65 - 0.60) / √((0.60 * (1 - 0.60)) / 120)
= 0.05 / √(0.24 / 120)
= 1.1180
Now, we can find the p-value corresponding to the calculated test statistic using a standard normal distribution table or a statistical calculator.
In this case, the p-value for a one-sided test (since we are testing if the proportion exceeds 0.60) is approximately 0.1317.
Therefore, the p-value for this hypothesis test is approximately 0.1317.
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Related Questions
The equation $y = -16t^2 + 28t + 144$ describes the height $y$ (in feet) at time $t$ (in seconds) of a ball tossed up in the air at $28$ feet per second from a height of $144$ feet from the ground. In how many seconds will the ball hit the ground?
Answers
Answer:
4 seconds
Step-by-step explanation:
Given the equation y = -16t² +28t +144 describes a ball's height as a function of time in seconds, you want to know when the ball will hit the ground.
ZeroThe ball will hit the ground when the value of y is zero.
0 = -16t² +28t +144
t² -7/4t -9 = 0 . . . . . divide by 16
t² -7/4t +(7/8)² = 9 +(7/8)² . . . . . complete the square
t = 7/8 +√(9 49/64) = 7/8 +3 1/8 = 4 . . . . take the square root, add 7/8
The ball will hit the ground after 4 seconds.
PLEASE HELP MATH 25 POINTS
Answers
Answer: y = x * 0.02
Step-by-step explanation:
When you multiply the number in x by 0.02 you end up with the product of y.
Answer:
y = x * 0.02
Step-by-step explanation:
Write each expression in terms of sines and/or cosines, and then simplify: 37. sec x / tan x. 38. cot x / csc x 39. sin x / csc x + cos x / sec x 40. 1/sin²x – 1/tan^2 x 41. (1 - sin a)(1 + sin a) 42. (sec a – 1) ( sec a + 1)
43. cos B tan B +1 ) (sin B -1)
44. (1 + cos B) (1 – cot B sin B)
45. 1 + cos a tan a csc a / csc a
46. (cos a tan a + 1 ) ( sin a – 1) / cos^2 a
Answers
37. sec x / tan x = (1/cos x) / (sin x/cos x) = cos x / sin x = cot x
38. cot x / csc x = (cos x/sin x) / (1/sin x) = cos x / sin^2 x = cos x * (1/sin^2 x) = cos x * (csc^2 x)
39. sin x / csc x + cos x / sec x = (sin x / 1/sin x) + (cos x / 1/cos x) = sin^2 x + cos^2 x = 1
40. 1/sin²x - 1/tan^2 x = (1/sin^2 x) - (1/(sin^2 x/cos^2 x)) = (1/sin^2 x) - (cos^2 x/sin^2 x) = (1 - cos^2 x)/sin^2 x = sin^2 x/sin^2 x = 1
41. (1 - sin a)(1 + sin a) = 1 - sin^2 a = cos^2 a
42. (sec a - 1)(sec a + 1) = sec^2 a - 1 = tan^2 a
43. (cos B tan B + 1)(sin B - 1) = (cos B * sin B/cos B + 1)(sin B - 1) = (sin B + 1)(sin B - 1) = sin^2 B - 1 = -cos^2 B
44. (1 + cos B)(1 - cot B sin B) = (1 + cos B)(1 - cos B/sin B * sin B) = (1 + cos B)(1 - cos^2 B/sin^2 B) = (1 + cos B)(sin^2 B/sin^2 B - cos^2 B/sin^2 B) = (1 + cos B)(1 - cos^2 B/sin^2 B) = (1 + cos B)(sin^2 B/sin^2 B) = (1 + cos B) * 1 = 1 + cos B
45. 1 + cos a tan a csc a / csc a = 1 + (cos a * sin a/cos a * 1/sin a) / (1/sin a) = 1 + (sin a / sin a) / (1/sin a) = 1 + 1/(1/sin a) = 1 + sin a = sin a + 1
46. (cos a tan a + 1)(sin a - 1) / cos^2 a = (cos a * sin a/cos a + 1)(sin a - 1) / cos^2 a = (sin a + 1)(sin a - 1) / cos^2 a = (sin^2 a - 1) / cos^2 a = -cos^2 a / cos^2 a = -1
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Need help asap!!!!!!!!
Answers
Answer:
The answer is D
Step-by-step explanation:
The number line shows approximately the point 8.5
The \(\sqrt{72}\) equals 7.485 which is the closest to 8.5
show work/zscore please
Between what two z-scores lie the central \( 50 \% \) of scores in the standard normal distribution?
Answers
In the standard normal distribution, the z-scores that correspond to the central 50% of scores lie between approximately -0.674 and 0.674.
The standard normal distribution, also known as the z-distribution, has a mean of 0 and a standard deviation of 1. The z-score represents the number of standard deviations a particular value is from the mean. To find the z-scores that correspond to the central 50% of scores, we need to determine the values that enclose the middle half of the distribution.
Since the normal distribution is symmetrical, the central 50% corresponds to half of the area under the curve. Using a z-table or a statistical calculator, we can find that approximately 34% of scores lie between the mean and 0.674 standard deviations above the mean, and another 34% lie between the mean and 0.674 standard deviations below the mean. Adding these two percentages gives us the desired central 50%.
Therefore, the z-scores that enclose the central 50% of scores in the standard normal distribution are approximately -0.674 and 0.674. Any z-score between these values represents a value within the central 50% of the distribution.
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Which graph represents the equation y equals one half times x minus 1?
graph of a line passing through the points negative 2 comma negative 2 and 0 comma negative 1
graph of a line passing through the points negative 2 comma 0 and 0 comma 1
graph of a line passing through the points negative 2 comma negative 3 and 0 comma negative 2
graph of a line passing through the points negative 4 comma 0 and 0 comma 2
Answers
The correct graph which represents the equation y = 1/2x - 1 is,
⇒ Graph of a line passing through the points negative 2 comma negative 2 and 0 comma negative 1.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The equation is,
⇒ y = 1/2x - 1
Now, After draw the equation we get;
Graph of a line passing through the points (-2, - 2) and (0, - 1).
Thus, The correct statement is,
⇒ Graph of a line passing through the points negative 2 comma negative 2 and 0 comma negative 1.
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How many Pieces of ribbon .6m long can be cut from 13.2m ribbon?
Answers
I think is is 22
because it is asking how many times can .6m go into 13.2m of ribbon? If you start with 20x.6 you will get 12. Then you add on another one and get 12.6. Finally add one more to get 13.2m ribbon which would make the answer 22. You can also divide 13.2m divided by .6m and get 22.
Hopefully this helped you guys. If you guys want more answers please give me those 5 Stars and Give me a thanks to show you appreciation.
Over all the Answer is 22
Have a great day (:
The price of bananas can be determined by the equation p=0.45n where p is the price and n is the number of bananas. What is the constant of proportionality (unit rate)
Answers
Answer:
The constant of proportionality is 0.45.
Step-by-step explanation:
The constant of proportionality is the ration of two different quantities or is the unit value of a quantity.
The expression representing the price of bananas is:
\(p=0.45n\)
To determine the unit rate of bananas divide the price by the number of bananas.
\(\text{Unit Rate}=\frac{p}{n}\)
\(=\frac{0.45n}{n}\\\\=0.45\)
Thus, the constant of proportionality is 0.45.
how to do well on byu calculus bc explorations
Answers
In order to do well on BYU Calculus BC Explorations, you should have a solid understanding of the basic principles of calculus.
This includes understanding derivatives and integrals, as well as the fundamental theorem of calculus. Additionally, it is important to have a strong background in basic algebra and trigonometry, as these skills will be necessary for working with functions and equations. When solving problems, it is important to read the problem carefully and identify what type of calculus concept is being asked for. Once the concept is identified, you can use formulas and calculations to solve the problem. By working through problems in a systematic and logical way, you can make sure that you arrive at the correct answer.
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Complete question:What is the best way to do well on BYU Calculus BC Explorations?
a ramp runs from ground level to a building entrance that is 4 feet high and 20 feet from the base of the ramp. if we think of the base of the ramp as the origin and the building is located on the positive horizontal axis (see figure), find the slope of the line representing the ramp.
Answers
To find the slope of the line representing the ramp, we can use the formula for slope:
slope = (change in vertical distance) / (change in horizontal distance)
In this case, the change in vertical distance is 4 feet (the height of the building entrance), and the change in horizontal distance is 20 feet (the distance from the base of the ramp to the building).
Therefore, the slope of the line representing the ramp is:
slope = 4 feet / 20 feet = 1/5
The slope of the ramp line is 1/5.
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Which equation represents a line which is parallel to the line y-2x =7
Answers
The line which is parallel to the given line is 2x- y= 0 or y= 2x.
The given line y= 7+ 2x
this is written in the form y= mx +c where if we compare these two equations we get m= 2
Now consider a point which passes through the origin (0,0)
Thus y-y₁= m(x-x₁)
y- 0 = 2 ( x- 0)
y= 2x or 2x- y= 0
Thus, the line which is parallel to the given line is 2x- y= 0.
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Enter the correct answer in the box
A triangle has side lengths of 200 units and 300 units. Write a compound inequality for the range of the possible lengths for the third side, X
Answers
Answer:
100-500
Step-by-step explanation:
Both sides of a triangle cannot be shorter than the remaining side. Thus, the side must be less than 500 units. With the same rule, the side must be greater or equal to 100 units, as if it was less, then 200 + 99 < 300.
The compound inequality for the range of the possible lengths for the third side will be 100- 500.
What is inequality?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
The meaning of inequality is to say that two things are NOT equal. One of the things may be less than, greater than, less than or equal to, or greater than or equal to the other things.
p ≠ q means that p is not equal to qp < q means that p is less than qp > q means that p is greater than qp ≤ q means that p is less than or equal to qp ≥ q means that p is greater than or equal to qGiven:
side lengths of 200 units and 300 units.
The largest value of the third side will be
200+300=500
and, the smallest value will be
300-200=100
Hence, 100<X<500
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Clark Property Management is responsible for the maintenance, rental, and day-to-day operation of a large apartment complex on the east side of New Orleans. George Clark is especially concerned about the cost projections for replacing air conditioner compressors. He would like to simulate the number of compressor failures each year over the next 20 years. Using data from a similar apartment building he manages in a New Orleans suburb, Clark establishes a table of relative frequency of failures during a year as shown in the following table:
NUMBER OF A.C. COMPRESSOR FAILURES PROBABILITY (RELATIVE FREQUENCY)
0 0.06
1 0.13
2 0.25
3 0.28
4 0.20
5 0.07
6 0.01
He decides to simulate the 20-year period by selecting two-digit random numbers from the random number table.
Conduct the simulation for Clark. Is it common to have three or more consecutive years of operation with two or fewer compressor failures per year?
Answers
The probability of having three or more consecutive years with two or fewer compressor failures per year is about 6.16%.
Clark Property Management should expect to experience some consecutive years with higher compressor failure rates.
Let X represent the number of AC compressor failures. Thus, the probability distribution of X is as follows :
Number of Compressor Failures Probability (Relative Frequency)
0 0.061 0.132 0.253 0.284 0.205 0.076 0.01.
We will select two-digit random numbers from a table of random numbers. We will simulate 20 years of compressor failure.
As a result, there will be a total of 20 values of X, each representing a year's worth of data.
We may now determine whether it is typical to have three or more consecutive years with two or fewer compressor failures per year.
The Monte Carlo simulation is used to complete this task. We may use an online random number generator if a table of random numbers is not available.
Monte Carlo simulation is a statistical modeling method that employs random sampling techniques to simulate the output of a complicated system.
It is a stochastic modeling technique that allows for uncertainty and risk evaluation in complex systems where deterministic methods are insufficient.
Monte Carlo simulation generates random input values for a system with a mathematical model, allowing it to calculate possible outcomes.
These results are then used to generate probability distributions of potential results.
In essence, the Monte Carlo simulation is an experiment conducted on a computer that provides insight into the degree of risk related to decision-making.
1. Set up a model: Determine the system and create a mathematical model that will be utilized in the Monte Carlo simulation.
2. Define input values: Identify the variables that will affect the model's output and define input probability distributions for each.
3. Generate random numbers: Using the input probability distributions, generate random numbers for each variable
4. Run simulations: Run a large number of simulations using the random numbers generated in step 3.
5. Analyze the results: Using the outputs of the Monte Carlo simulation, estimate potential outcomes and the likelihood of different results.
6. Make decisions: Use the data and insights obtained from the Monte Carlo simulation to inform your decision-making.
After conducting the Monte Carlo simulation, it was determined that it is unusual to have three or more consecutive years with two or fewer compressor failures per year.
The probability of having three or more consecutive years with two or fewer compressor failures per year is about 6.16%.
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The two-way table given shows the results from a survey of pet owners.
Owns a Dog Does Not Own a Dog Total
Owns a Cat 126 45 171
Does Not Own a Cat 54 15 69
Total 180 60 240
Does the data show an association between owning a dog and owning a cat?
There is a strong, positive association.
There is a strong, negative association.
There is a weak, negative association.
There is a weak, positive association.
Answers
From the total amounts, the correct option regarding the association between owning a dog and owning a cat is given by:
There is a strong, positive association.
What are positive and negative association between amounts?If there is a positive association, both behave similarly, that is, either both increase and both decrease simultaneously.If there is a negative association, both behave inversely, that is, one amount decreases and the other increases.Whether the association is strong or weak depends on the rate of change, the rate of increase or decrease.
From the amounts in the table, we have that:
126 own both a cat and a dog, 15 own neither.45 own a cat but not a dog, 54 own a dog but not a cat.Having a cat increases the likelihood of having a dog and vice-versa, hence there is a strong, positive association and the first option is correct.
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What is an equation of the line that passes through the point
(−3,−5) and is parallel to the line
2x+3y=15
Answers
Therefore, the equation of the line passing through (-3, -5) and parallel to the line 2x + 3y = 15, in slope-intercept form, is y = (-2/3)x - 7.
What is the Equation of Parallel Lines?To find the equation of a line parallel to the line 2x + 3y = 15 and passing through the point (-3, -5), we need to determine the slope of the given line and use it to construct the equation in slope-intercept form (y = mx + b).
The given line is in the form Ax + By = C, where A = 2, B = 3, and C = 15. To find the slope of this line, we can rearrange the equation to isolate y:
2x + 3y = 15
3y = -2x + 15
y = (-2/3)x + 5
The slope of the given line is -2/3.
Since the line we want to find is parallel to this line, it will have the same slope. Therefore, the slope of the line passing through (-3, -5) will also be -2/3.
Now, we can use the point-slope form of a linear equation to write the equation of the line:
y - y1 = m(x - x1)
Substituting the values of (-3, -5) and -2/3 for (x1, y1) and m, respectively:
y - (-5) = (-2/3)(x - (-3))
y + 5 = (-2/3)(x + 3)
To convert this equation into slope-intercept form, we can simplify and rearrange:
y + 5 = (-2/3)x - 2
y = (-2/3)x - 2 - 5
y = (-2/3)x - 7
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three students (a, b, and c) are asked to determine the volume of a sample of ethanol. each student measures the volume three times with a graduated cylinder. the results in milliliters are: a (87.1 , 88.2, 87.6); b (86.9, 87.1 , 87.2); c (87.6, 87.8, 87.9). the true volume is 87.0 ml. which student has the best precision?
Answers
The values in b are compared with the true volume. And we conclude that b is precise and accurate.
Accuracy determines how closely measured values match the actual value. The degree to which two measured values are inside a certain range, or how closely they agree, is called precision.
First calculate the mean of a, b, and c. We get, the mean of a is 87.63, the mean of b is 87.06, and the mean of c is 87.77.
From the values in "a", we can tell there is no good agreement between the given values, and just one (87.1) value is near to the true value. So a is neither precise nor accurate.
From the values in "b", we can tell these given values are reasonably close to the true value and exhibit good agreement. So b is precise and accurate.
From the values in "c", we can tell there is a considerable agreement between the given values but they are not very close to the true value. So c is precise but not accurate.
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Help needed ASAP please
Answers
Answer:
19. 0•7431
20. 1•2800
21. 0•4850
Compare and contrast natural numbers and rational numbers.
Answers
Natural numbers are strictly only plain numbers like no percents or integers, such as 1, 2, 3, 4, 5, 6 etc. Natural numbers are whole numbers and positive, so 0 would not be considered natural since it is not positive or negative
Rational numbers are numbers like 1, -100, .33, -10000, 2.4, etc it can be ALMOST anything, rational numbers fit every category but one IRRATIONAL
Irrational numbers are numbers like pie (3.145.......) it goes on forever and ever if the number never stops and repeats its called a repeating decimal, (HUGE TIP, IF YOU CAN MAKE IT A FRACTION IS IS ALMOST ALWAYS RATIONAL)
For the function f(x) = 2x-4/x+3
What is the x-intercept, y-intercept, and vertical asymptotes
Answers
Answer:
x-intercept: (2,0)
y-intercept: (0,-4/3)
vertical asymptote: x = -3
Step-by-step explanation:
To find the x-intercepts, we can set f(x) to 0, which is y=0:
2x-4/x+3 = 0
2x-4 = 0
2x = 4
x = 2
To find the y-intercepts, we can set x to 0:
2(0)-4/(0)+3 = y
y = -4/3
To find the vertical asymptote, we can set the denominator equal to 0:
x+3 = 0
x = -3
You plan to retire in 30 years. After that, you need $75,000 per year for 20 years (first withdraw at t=31 ). At the end of these 20 years, you will enter a retirement home where you will stay for the rest of your life. As soon as you enter the retirement home, you will need to make a single payment of 2 million. You want to start saving in an account that pays you 8% interest p.a. Therefore, beginning from the end of the first year (t=1), you will make equal yearly deposits into this account for 30 years. You expect to receive $350,000 inheritance at t=30 from your late uncle and you will deposit this money to your retirement account. What should be the yearly deposits?
6587.25
7198.40
8066.36
8744.81
Answers
The yearly deposit needed to achieve the retirement goal is approximately $17,650.23. None of the given options match this amount, so the correct answer is not provided in the given options.
To calculate the yearly deposits needed, we can use the concept of future value of an annuity. The future value formula for an annuity is given by:
FV = P * [(1 + r)^n - 1] / r
Where:
FV = Future value of the annuity
P = Yearly deposit amount
r = Interest rate per period
n = Number of periods
In this case, the future value needed is $2 million, the interest rate is 8% (0.08), and the number of periods is 30 years. We need to solve for the yearly deposit amount (P).
Using the given formula:
2,000,000 = P * [(1 + 0.08)^30 - 1] / 0.08
Simplifying the equation:
2,000,000 = P * [1\(.08^3^0 -\) 1] / 0.08
2,000,000 = P * [10.063899 - 1] / 0.08
2,000,000 = P * 9.063899 / 0.08
Dividing both sides by 9.063899 / 0.08:
P = 2,000,000 / (9.063899 / 0.08)
P ≈ 2,000,000 / 113.298737
P ≈ 17,650.23
Therefore, the yearly deposit needed to achieve the retirement goal is approximately $17,650.23. None of the given options match this amount, so the correct answer is not provided in the given options.
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Marie is saving $75 each week so she can buy a new laptop which costs $1200. She has already saved $125. Find the minimum number of weeks she will have to save in order to be able to make this purchase.
Answers
Answer:
Step-by-step explanation:
\(125+75w\ge 1200\\ \\ 75w\ge 1075\\ \\ w\ge 14.33\\ \\ \text{So she must save for at least 15 weeks.}\)
Using the unit circle, determine the value of sin(-240°).
A) -1/2
B) √3/2
C) 1/2
D) -√3/2
Answers
Answer:
B. √3/2.
Step-by-step explanation:
If we follow the circle from (1,0) clockwise through 240 degrees we end up at 120 degrees.
sin(120)
= √3/2
A person invests 8000 dollars in a bank. The bank pays 7% interest compounded
annually. To the nearest tenth of a year, how long must the person leave the money
in the bank until it reaches 15600 dollars?
nt
A=P(1+
)
п
Answers
Answer:
The person must leave the money for around 9.9 years.
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to RightAlgebra I
Equality Properties
Multiplication Property of EqualityDivision Property of EqualityAddition Property of EqualitySubtraction Property of EqualityTerms/Coefficients
Compounded Interest Rate Formula: \(\displaystyle A = P \bigg( 1 + \frac{r}{n} \bigg)^{nt}\)
P is principle amount (initial amount)r is interest raten is compounded ratet is time (in years)Algebra II
Logarithms
Logarithmic Property [Exponential]: \(\displaystyle \log (a^b) = b \cdot \log (a)\)Step-by-step explanation:
Step 1: Define
Identify variables.
A = $15600
P = $8000
r = 0.07
n = 1
Step 2: Find Time Elapsed
Substitute in variables [Compounded Interest Rate Formula]: \(\displaystyle 15600 = 8000 \bigg( 1 + \frac{0.07}{1} \bigg)^{1(t)}\)[Exponents] Simplify: \(\displaystyle 15600 = 8000 \bigg( 1 + \frac{0.07}{1} \bigg)^{t}\)(Parenthesis) Simplify: \(\displaystyle 15600 = 8000(1.07)^{t}\)[Division Property of Equality] Divide 8000 on both sides: \(\displaystyle \frac{39}{20} = (1.07)^{t}\)[Equality Property] Log both sides: \(\displaystyle \log \frac{39}{20} = \log (1.07)^{t}\)Simplify [Logarithm Property - Exponential]: \(\displaystyle \log \frac{39}{20} = t \log (1.07)\)[Division Property of Equality] Isolate t: \(\displaystyle t = \frac{\log \frac{39}{20}}{\log 1.07}\)Evaluate: \(\displaystyle t = 9.87057\)Round: \(\displaystyle t \approx 9.9\)∴ it will take the person approximately 9.9 years investing $8,000 with a 7% interest rate compounded annually for them to obtain $15,600.
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Topic: Algebra II
Solve (5x-5)
6x-3 = 5x-5
Answers
Answer:
x=-2 willl be your answer
Answer:
X=-2
please mark brainliest if satisfied
Step-by-step explanation:
Subtract 5x from both sid
The scatter plot shows the amount of sleep Aria got the night before a test and her test scores. Use the y-intercept and the point (6, 80) from the line on the scatter plot. What is the equation of the trend line? Drag numbers to complete the equation. Numbers may be used once, more than once, or not at all.
Answers
Answer:
y= 3x+62
Step-by-step explanation:
You draw one card from a 52-card deck. Then the card is replaced in the deck and the deck is shuffled, and you draw again. Find the probability of drawing a diamond each time.
Answers
Solution:
Given:
A 52-card deck
There are four suits in a standard deck of cards, Clubs, Hearts, Spades, and Diamonds.
There are 13 diamond cards.
Hence,
\(\begin{gathered} \text{Diamond cards = 13} \\ \text{Total cards = 52} \end{gathered}\)Probability is calculated by;
\(\text{Probability}=\frac{n\text{ umber of required outcomes}}{n\text{ umber of total or possible outcomes}}\)Thus, the probability of drawing a diamond on the first draw is;
\(\begin{gathered} \text{Probability of drawing a diamond}=\frac{n\text{ umber of diamond cards}}{\text{total number of cards}} \\ \text{Probability of drawing a diamond}=\frac{13}{52} \\ \text{Probability of drawing a diamond}=\frac{1}{4} \\ P(D_1)=\frac{1}{4} \end{gathered}\)Since two draws are made with replacement, the cards are completed back again before the next draw.
Hence, the probability of drawing a diamond on the second draw is;
\(\begin{gathered} \text{Probability of drawing a diamond}=\frac{n\text{ umber of diamond cards}}{\text{total number of cards}} \\ \text{Probability of drawing a diamond}=\frac{13}{52} \\ \text{Probability of drawing a diamond}=\frac{1}{4} \\ P(D_2)=\frac{1}{4} \end{gathered}\)Therefore, the probability of drawing a diamond each time;
\(\begin{gathered} P(D_1D_2)=\frac{1}{4}\times\frac{1}{4} \\ P(D_1D_2)=\frac{1}{16} \end{gathered}\)
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Answers
Answer:
≈ 94.9 mi²
Step-by-step explanation:
The area (A) of Δ WXY can be calculated as
A = \(\frac{1}{2}\) × WY × WX × sinW
∠ W = 180° - (40 + 21)° = 180° - 61° = 119°
Calculate WX using the Sine rule, that is
\(\frac{11}{sin21}\) = \(\frac{WX}{sin40}\) ( cross- multiply )
WX sin21° = 11 sin40° ( divide both sides by sin21° )
WX = \(\frac{11sin40}{sin21}\) ≈ 19.73 mi , thus
A = 0.5 × 11 × 19.73 × sin119° ≈ 49.9 mi² ( to the nearest tenth )
I need help with this question
Answers
The length of the legs of the right triangle are 2.83 units.
How to find the side of a right triangle?A right tangle triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.
Therefore, the legs of the triangle can be found using trigonometric ratios.
Hence,
sin 45 = opposite / hypotenuse
sin 45 = a / 4
cross multiply
a = 4 × 0.70710678118
a = 2.83 units
Therefore,
cos 45 = b / 4
cross multiply
b = 0.70710678118 × 4
b = 2.82842712475
b = 2.83 units
Therefore, the legs are 2,83 units
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What fraction is equivalent to 150%?
A. 1 2/5
B. 15/1
C. 3/5
D. 1 1/2
Answers
Answer:
D : 1 1/2
Step-by-step explanation:
150% converted into a decimal is 1.5, this is the same as 1 1/2, so the answer is D.
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The 150% as a fraction in simplest form is D. 1 1/2
What is the fundamental principle of multiplication?Multiplication is the mathematical operation that is used to determine the product of two or more numbers. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.
We have to write 150% as a fraction in simplest form.
So we put 150 over 100
That is (150/100)
Now multiply the top and the bottom by 10 to get rid of the decimal as;
15/10
1.5 = 1 1/2
Hence, the fraction in simplest form is 1 1/2
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what would this be!?
Answers
Answer:
Well sum up the angles then do that and subtract it from 180Then you get 148Answer:
you do 124+18 which is 142
and then you do 180 -142 because a triangle adds to 180
this equals 38
After this you then do 180-34 because angles on a straight line equal 180
this gives you the answer of 142