we can reject the null hypothesis at the 5% significance level since the p-value is less than 0.05.
To calculate the p-value, we need to perform a hypothesis test.
Let's assume the null hypothesis is that the proportion of defective systems produced by x-game is equal to or less than the industry standard of 0.02, while the alternative hypothesis is that the proportion is greater than 0.02.
We can use the normal approximation to the binomial distribution since we have a large sample size (n=120) and np and n(1-p) are both greater than or equal to 10.
The test statistic can be calculated as:
[tex]z = (p_hat - p) / \sqrt{(p*(1-p)/n)}[/tex]
where [tex]p_hat[/tex] is the sample proportion of defective systems, p is the hypothesized proportion under the null hypothesis, and n is the sample size.
Using the values given in the question, we have:
[tex]p_hat = 6/120 = 0.05[/tex]
p = 0.02
n = 120
Plugging these values into the formula, we get:
[tex]z = (0.05 - 0.02) / \sqrt{(0.02*(1-0.02)/120) = 2.041}[/tex]
The p-value can be calculated as the probability of getting a test statistic as extreme or more extreme than 2.041 under the null hypothesis.
Since this is a one-tailed test (the alternative hypothesis is one-sided), we look up the area in the right tail of the standard normal distribution table.
Using a standard normal distribution table, we find that the area to the right of 2.041 is 0.0207.
Therefore, the p-value is 0.0207.
Therefore, we can reject the null hypothesis at the 5% significance level since the p-value is less than 0.05.
This means that there is strong evidence that the proportion of defective systems produced by x-game exceeds the industry standard of 0.02.
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Which expressions are equivalent to 27^4/3?
Select the three correct answers.
A. 4^3
B. (27^1/3)^4
C. 3^1/4
D. 81
D) 81 is equivalent to 27^(4/3).
The expression 27^4/3 can be simplified using the rule that (a^m)^n = a^(m*n). Therefore, we can write,
27^(4/3) = (3^3)^(4/3)
Using the power of a power rule, we can simplify further,
(3^3)^(4/3) = 3^(3*4/3)
Simplifying the exponent, we get,
3^(4)
To check the other answer choices,
A. 4^3 is not equivalent to 27^4/3.
B. (27^1/3)^4 is equivalent to 27^(4/3), which we already simplified to 3^4. Therefore, this expression is also equivalent to 3^4.
C. 3^1/4 is not equivalent to 27^4/3.
D. 81 is equivalent to 3^(4).
Therefore, the expression 27^4/3 is equivalent to 3^4, which is answer choice D) 81.
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The solid below is dilated by a scale factor of 1/2. Find the volume of the
solid created upon dilation.
24
26
10
34
Answer: 4080
Step-by-step explanation:
First you have to find the area of the triangle. 24*10 = 240. 240/2 = 120. Then you multiply the area of the triangle and multiply it by 34. 120 * 34 = 4080. This means the answer is 4080
dora drove east at a constant rate of 75 kph. one hour later, tim started driving on the same road at a constant rate of 90 kph. for how long was tim driving, before he caught up to dora? a. 5 hours b. 4 hours c. 3 hours d. 2 hours
Tim was driving for 5 hours before he caught up to Dora.
The answer is (a) 5 hours.
To solve this problem, we can use the formula:
distance = rate × time
Let's denote the time Tim drove as t hours.
Since Dora started driving one hour earlier, her driving time would be (t + 1) hours.
Dora's distance: 75 kph × (t + 1)
Tim's distance: 90 kph × t
Since Tim catches up to Dora, their distances will be equal:
75(t + 1) = 90t
Now we can solve for t:
75t + 75 = 90t
75 = 15t
t = 5.
The answer is (a) 5 hours.
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the die will be rolled 12 times. let x be the number times the die lands on a green square. x has a binomial distribution. what is a trial? a single roll of the 20-sided die what would be considered a success? a green square how many trials? n
The probability of getting 'p' success when a die rolled 12 times with 'x' success that has binomial distribution is equal to ¹²Cₓ pˣ ( 1 - p )¹²⁻ˣ.
Number of times die to be rolled = 12
In this scenario, a trial refers to a single roll of the 20-sided die.
Here , 'x' represents the the number times the die lands on a green square.
A success would be defined as landing on a green square,
And a failure would be landing on any other color.
Since the die will be rolled 12 times, there are 12 trials in total.
This implies, the number of times the die lands on a green square, x, has a binomial distribution.
With parameters n = 12 the number of trials and p the probability of success which is landing on a green square.
Probability = ⁿCₓ pˣ ( 1 - p )ⁿ⁻ˣ
Therefore, the probability of rolling a die 12 times with 'x' success which has binomial distribution and 'p' probability of success is equal to ¹²Cₓ pˣ ( 1 - p )¹²⁻ˣ.
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What happens to the value of the function as the number of iterations increases? Be specific with the value.
Without knowing which specific function you're referring to, the answer to this question may depend on the type of function and the nature of the iterative process applied to it. In some cases, the function value may converge towards a limiting value as the number of iterations increases, while in other cases it may oscillate or diverge.
For example, in the case of the fixed-point iteration method used to find the root of a function, the value of the function typically converges towards the root as the number of iterations increases. More specifically, if we have a function f(x) and a starting guess x0 for its root, we can use the iterative formula x(+1)=g(x()), where g(x) is some function that we set based on f(x), to generate a sequence of increasingly accurate approximations to the root. As the number of iterations increases, this sequence of approximations typically converges towards the root of the function, unless some conditions are not met (e.g., the method is not well-suited for some functions, or the iteration formula is not properly set.)
In the case of other types of iterative methods or other functions, however, the behavior of the function value as the number of iterations increases may differ. For instance, in some cases, the function value may oscillate between two or more values or diverge to infinity as the number of iterations increases.
Therefore, the specific behavior of the function value as the number of iterations increases may depend on the specific function being evaluated and the iterative method used.
what is 72% written in a deciamal
slove and answer x+y=11 2x-y=19
Answer:
x + y = 11
2x - y = 19
--------------
3x = 30
x = 10, so y = 1
Can someone answer this please and thank you.
The blue base is the face (put in 1).
The black line is the edge (put in 2).
The dot up top is the vertex (put in 3).
126, 128, 107, 113, 120, 126
Mean
Mode
Median
Range
The mean is 120
The mode is 126
The median is 123
The range is 21
How to calculate the mean, mode, median and range?
Mean= 126 + 128 + 107 + 113 + 120 + 126/6
= 720/6
= 120
Mode= 126
Median= 120 + 126/2
= 246/2
= 123
Range= Highest-lowest
= 128-107
= 21
Hence the mean is 120, the mode is 126, the median is 123 and the range is 21
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Questions three and four please
The 'footprint' of CO2 emissions for a person in 1830 would be 818,199 tons of CO2 emissions per person.
What is the 'footprint' of CO2 emissions for a person in 1830??"To find the 'footprint' of CO2 emissions for a person in 1830, we need to substitute the value of x = 1830 - 1800 = 30 into the given function C(x) = 0.0365 (1.758)^x.
Plugging in x = 30 into the function, we get:
C(30) = 0.0365 * (1.758)^30
Substituting this value back into the function, we get:
C(30) = 0.0365 * 22416413.1381
C(30) = 818199.079541
C(30) ≈ 818,199.08
Answered question "Scientists studying the 'footprint' of carbon dioxide (CO2) emissions attributed to the average person for each decade from 1800 to 1910 used the function C(x) = 0.0365 (1.758)*, where x is the number of decades since 1800 and C is the number of tons of CO2 emissions per person. What is the 'footprint' of CO2 emissions for a person in 1830??"
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Find the area of the image below: (4 points)
answer options:
41 square units
44 square units
52 square units
56 square units
Answer:
4(4) + (1/2)(10)(5) = 16 + 25
= 41 square units
Step-by-step explanation:
The area of the square is 4 × 4 = 16 square units.
The area of the triangle is (1/2) × 10 × 5 = 25 square units.
So the area of the image is 16 + 25 = 41 square units.
Lona bought two pairs of shoes from her favorite store. The regular price of each pair was $116. With the purchase of one pair of shoes, the second pair was half price. How much did Lona pay for the two pairs of shoes?
In a Harris Poll survey of smokers, 848 of a sample of 1010 smokers agreed that smoking would probably shorten their lives. Harris announces a margin of error of ±
3 percentage points for all samples of about this size. Opinion polls announce the margin of error for 95% confidence.
Part 1: What is the actual margin of error (in percent) for the large-sample confidence interval from this sample?
a) 3%
b) 1.15%
c) 2.26%
d) 6%
Part 2: The margin of error is largest when ^p
= 0.5. What would the margin of error (in percent) be if the sample had resulted in ^p
= 0.5? Give your answer to 2 decimal places.
Part 3: Why do you think that Harris announces a ±
3% margin of error for all samples of about this size?
a) Because the margin of error for samples of about this size is no less than the announced margin of error.
b) Because the confidence level from the announced margin of error is closer to the actual confidence level than the one computed from a single sample.
c) Because the margin of error for samples of about this size is no more than the announced margin of error.
d) Because the large-sample margin of error from a single sample is not accurate.
Part 1- The actual margin of error (in percent) for the large-sample confidence interval from this sample is c) 2.26%.
Part 2- The margin of error (in percent) would be 3.1% if the sample had resulted in p-hat = 0.5.
Part 3- The reason why Harris announces a ±3% margin of error for all samples of about this size is c) because the
margin of error for samples of about this size is no more than the announced margin of error.
Part 1: The actual margin of error for the large-sample confidence interval from this sample can be calculated using the
formula: Margin of error = (z-score)*(standard error),
where the z-score for 95% confidence level is 1.96 and the standard error is [tex]\sqrt{[(p-hat \times(1-p-hat))/n]}[/tex]
Here, p-hat (proportion of smokers who agreed that smoking would probably shorten their lives) = 848/1010 = 0.84 and
n (sample size) = 1010.
Plugging these values into the formula, we get
Margin of error =[tex]1.96\times(sqrt[(0.84\times(1-0.84))/1010])[/tex] = 0.026 = 2.6%.
Part 2: The margin of error is largest when p-hat = 0.5, which means that the sample is equally split between two
options.
In this case, the standard error becomes [tex]\sqrt{[(0.5\times(1-0.5))/1010] } = 0.0158.[/tex]
Using the same formula as in Part 1, we get
Margin of error = [tex]1.96\times0.0158 = 0.031 = 3.1%.[/tex]
Part 3: The reason why Harris announces a ±3% margin of error for all samples of about this size is c) because the
margin of error for samples of about this size is no more than the announced margin of error.
This means that Harris is being conservative in their estimate of the margin of error and is ensuring that they do not
overstate the precision of their results. Additionally, they may want to account for other sources of error such as non-
response bias or sampling bias, which can also contribute to the overall margin of error.
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Help please? I just need an answer. A clear explanation earns brainliest.
the simplified form of expression is: -(x² + 2x - 2)/((x+2)*(x+4))
what is expression ?
In mathematics, an expression is a combination of numbers, variables, operators, and/or functions that represents a mathematical quantity or relationship. Expressions can be simple or complex
In the given question,
To evaluate the expression 1/(x+2) - (x+1)/(x+4), we need to find a common denominator for the two terms. The least common multiple of (x+2) and (x+4) is (x+2)(x+4).
So, we can rewrite the expression as:
(1*(x+4) - (x+1)(x+2))/((x+2)(x+4))
Expanding the brackets, we get:
(x+4 - x² - 3x - 2)/((x+2)*(x+4))
Simplifying the numerator, we get:
(-x² - 2x + 2)/((x+2)*(x+4))
Therefore, the simplified expression is:
-(x² + 2x - 2)/((x+2)*(x+4))
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please solve correctly my grade depends on it
Just use the pythagorean theorem to solve the hypotenuse!
(3^2)+(2^2)=x^2
9+4=13^2
[tex]\sqrt{13}[/tex] = [tex]\sqrt{x}[/tex]
[tex]13^{2}[/tex] km
Hope this helps <3
Write your answer as an integer or decimal.
please help
The value of angle GFH is 18°
What is circle geometry?A circle is a special kind of ellipse in which the eccentricity is zero and the two foci are coincident.
A theorem in circle geometry starts that angle in the same segment are equal. In triangle EFG, angle F and G are on the same segment, this means that angle F and G are equal.
Represent angle F as x
therefore 144+2x = 180° ( sum of angle in a triangle)
2x = 180-144
2x = 36
x = 36/2 = 18°
Therefore the measure of angle GFH is 18°
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the key difference between the binomial and hypergeometric distribution is that, with the hypergeometric distribution a. the trials are independent of each other. b. the probability of success changes from trial to trial. c. the random variable is continuous. d. the probability of success must be less than 0.5.
Key difference between binomial distribution and hypergeometric distribution is that with hypergeometric distribution is given by
Option b. the probability of success changes from trial to trial.
In the binomial distribution, each trial is independent of the others.
Probability of success remains constant from trial to trial.
Hypergeometric distribution involves sampling without replacement.
Probability of success changes from trial to trial as the size of the population changes.
Example of drawing cards from a deck.
In the binomial distribution,
if we wanted to know the probability of drawing three hearts in a row.
Probability of drawing a heart would remain constant at 13/52 .
In the hypergeometric distribution,
Probability of drawing three hearts without replacement from a deck of 52 cards.
Probability of drawing a heart would change with each trial.
As the size of the population would be different for each trial.
The other options listed are not correct,
The trials in the hypergeometric distribution are not independent of each other.
Because sampling without replacement affects the probability of success in subsequent trials.
Hypergeometric distribution is a discrete distribution not a continuous one.
Probability of success in the hypergeometric distribution does not have to be less than 0.5.
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I WILL MARK BRAINLIEST
When the algebraic expression that was given in words in being evaluated, the outcome would be = 38.
How to evaluate algebraic expressions?The algebraic word given is as follows;
one more than the product of a number and seven. That is;
1 + 7(n)
decreased by five;
1+7(n) -5
where n = 6
The evaluation of the algebraic expression;
= 1+7(6)-5
= 1+42-5
= 43-5
= 38
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Find unknown sides and angle of the triangle
The sides and the angle of the right triangle are a = 10√2, b = 10√2 and B = π / 4.
How to find the missing information of a right triangle
In this problem we need to determine the values of two sides and an angle of the right triangle. This can be done by means of the following properties:
A + B + C = π
sin A = a / c
cos A = b / c
tan A = a / b
Where:
A, B, C - Angles of the right triangle, in radians.a, b, c - Sides of the right triangle.If we know that A = π / 4, C = π / 2 and c = 20, then the missing angle and missing sides are, respectively:
B = π - π / 4 - π / 2
B = π / 4
cos (π / 4) = b / 20
b = 20 · cos (π / 4)
b = 10√2
sin (π / 4) = a / 20
a = 20 · sin (π / 4)
a = 10√2
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a plane travels 600 from salt lake city, utah, to oakland, california, with a prevailing wind of 30. the return trip against the wind takes longer. find the average speed of the plane in still air.
the average speed of the plane in still air is s + 30.
Let's call the average speed of the plane in still air "s" (in miles per hour).
We can use the formula:
time = distance / speed
to find the time it takes the plane to travel from Salt Lake City to Oakland with the wind and against the wind.
With the wind:
time with wind = [tex]600 / (s + 30)[/tex]
Against the wind:
time against wind =[tex]600 / (s - 30)[/tex]
time against wind > time with wind
So we can set up an inequality:
[tex]600 / (s - 30) > 600 / (s + 30)[/tex]
Multiplying both sides by [tex](s - 30)(s + 30)[/tex], we get:
[tex]600(s + 30) > 600(s - 30)[/tex]
Expanding and simplifying, we get:
[tex]600s + 18000 > 600s - 18000[/tex]
Subtracting 600s from both sides, we get:
[tex]18000 > -18000[/tex]
This inequality is true for all values of s. In other words, there are no restrictions on the value of s that would make the return trip take longer than the trip with the wind.
Therefore, we can use the average of the two speeds (with and against the wind) to find the average speed of the plane in still air:
Average speed = [tex]2s(s + 30) / (s + 30 + s - 30)[/tex]
Simplifying, we get:
Average speed = [tex]2s(s + 30) / (2s)[/tex]
Canceling the common factor of 2s, we get:
Average speed = s + 30
We know that the distance from Salt Lake City to Oakland is 600 miles, and we can use the formula:
time = distance / speed
to find the time it takes the plane to travel this distance:
time = [tex]600 / (s + 30)[/tex]
We also know that the return trip (against the wind) takes longer, so we can set up another equation:
time return trip =[tex]600 / (s - 30)[/tex]
We can use these two equations to solve for s:
[tex]600 / (s + 30) = 600 / (s - 30)[/tex]
Cross-multiplying, we get:
[tex]600(s - 30) = 600(s + 30)[/tex]
Expanding and simplifying, we get:
[tex]600s - 18000 = 600s + 18000[/tex]
Subtracting 600s from both sides, we get:
[tex]-18000 = 18000[/tex]
This is not a valid equation, so there must be no solution.
However, we can still find the average speed of the plane in still air by using the equation we derived earlier:
Average speed = s + 30
So the average speed of the plane in still air is s + 30. We don't have a specific value for s, but we can say that the average speed is equal to the speed with the wind plus 30 (which is the speed of the wind).
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Using the graph, determine the coordinates of the x-intercepts of the parabola.
Answer:
x = -5, x = 1
As (x, y) coordinates, the x-intercepts are (-5, 0) and (1, 0).
Step-by-step explanation:
The x-intercepts are the x-values of the points at which the curve crosses the x-axis, so when y = 0.
From inspection of the given graph, we can see that the parabola crosses the x-axis at x = -5 and x = 1.
Therefore, the x-intercepts of the parabola are:
x = -5x = 1As (x, y) coordinates, the x-intercepts are (-5, 0) and (1, 0).
please help me find the answer!! this is due tmmr!!
Answer:
Step-by-step explanation:
I need some help pretty please
Answer:
Step-by-step explanation:
Change in Y/Change in X
5- -1/6- -2
5+1/6+2
6/8
3/4
Area of a triangle with base, b, and height, h:
A = 1/2 bh = 1/(____)(____) =
Area of a rectangle with length, e, and width, w:
A = lw= (______)(______) = .
square feet
Area of base of prism
=
square feet
+
square feet
The area of the triangle is: 15 square feet
The area of a rectangle is: 96 square feet
How to find the area of the composite figure?The formula for the area of a triangle is:
Area = ¹/₂ * base * height
This triangle has the dimensions:
base = 12 ft
height = 2.5 ft
Thus:
Area = ¹/₂ * 12 * 2.5
Area = 15 square feet
The area of a rectangle is:
A = length * width
A = 12 * 8
A = 96 square feet
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Five balls, A, B, C, D, and E, weigh 30g, 50g, 50g, 50g, and 80g each. Which ball weighs 30g?
The ball that weighs 30g is ball A.
What is accuracy and precision?The degree to which a measured value resembles the true or recognised value is known as accuracy. On the other hand, precision describes how closely two measurements of the same quantity agree. In other words, precision is a measure of consistency, whereas accuracy is a measure of correctness. The values obtained are consistent but not always close to the genuine value when a measurement is precise but not exact. On the other hand, a measurement might be accurate without being exact, which means that the result is close to the correct value but produces erratic or dispersed results when repeated.
From the given weights corresponding to different balls, 30 g corresponds to ball A.
Hence, the ball that weighs 30g is ball A.
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a coin is tossed 10,000 times. what is the chance that the number of heads will be in the range 4850 to 5150?
The chance that the number of heads will be in the range 4850 to 5150 is approximately 0.9973, or about 99.73%.
The number of heads in 10,000 coin tosses follows a binomial distribution with parameters n = 10,000 (the number of trials) and p = 0.5 (the probability of heads on a single toss).
We can approximate this binomial distribution using the normal distribution, with mean μ = np = 5000 and variance σ² = np(1-p) = 2500.
To find the probability that the number of heads is in the range 4850 to 5150, we can use the normal distribution and standardize the range using the z-score formula:
z = (x - μ) / σ
where x is the number of heads in the range we're interested in.
For the lower bound of 4850, we have:
[tex]z_lower = (4850 - 5000) / \sqrt{(2500)}[/tex]
= -3
For the upper bound of 5150, we have:
[tex]z_upper = (5150 - 5000) / \sqrt{(2500)} = 3[/tex]
Using a standard normal distribution table or calculator, we can find the probability of being within 3 standard deviations of the mean:
P([tex]z_lower[/tex] < Z < [tex]z_upper[/tex] ) ≈ P(-3 < Z < 3)
= 0.9973.
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40000 is divided by the smallest number so that the result is a perfect cube. find the cube root of the resulting number.
The Cube root of the resulting number is 8.
The smallest number that 40000 can be divided by so that the result is a perfect cube, we need to factorize 40000 into its prime factors:
[tex]40000 = 2^6 \times 5^4[/tex]
To make this a perfect cube, we need to ensure that the powers of each prime factor are multiples of 3.
The smallest number we can divide 40000 by so that the result is a perfect cube is:
[tex]40000 = 2^6 \times 5^4[/tex]
Now we can find the cube root of the resulting number:
[tex]3\sqrt (40000 \div 100) = 3\sqrt400 = 8.[/tex]
Factories 40000 into its prime components in order to determine.
The least number that the result may be divided by while still producing a perfect cube.
The powers of each prime factor must be multiples of three in order for this to be a perfect cube.
The least number that 40000 may be divided by to produce a perfect cube is:
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Kira bought 14 pounds of flour for $7 . How many pounds of flour did she get per dollar?
Answer:
2
Step-by-step explanation:
i know
erin is playing darts at the adventure arcade. she scores a bullseye 15% of the time, and she is about to throw 5 darts. how likely is it that she will get at least one bullseye?
the likelihood of Erin getting at least one bullseye in 5 throws is 0.5563 or 55.63%.
To calculate the likelihood of Erin getting at least one bullseye, we need to first calculate the probability of her not getting a bullseye in a single throw. Since she scores a bullseye 15% of the time, the probability of her not getting a bullseye in a single throw is 85% (100% - 15%).
Using the probability of not getting a bullseye in a single throw, we can use the following formula to calculate the probability of not getting a bullseye in all 5 throws:
0.85 x 0.85 x 0.85 x 0.85 x 0.85 = 0.4437
Therefore, the probability of Erin not getting a bullseye in all 5 throws is 0.4437 or 44.37%.
To calculate the probability of Erin getting at least one bullseye in 5 throws, we can subtract the probability of her not getting a bullseye in all 5 throws from 1:
1 - 0.4437 = 0.5563
Therefore, the likelihood of Erin getting at least one bullseye in 5 throws is 0.5563 or 55.63%.
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The probability that Erin will get at least one bullseye in her 5 throws at the adventure arcade is approximately 55.63%.
To find the probability that she will get at least one bullseye in 5 throws, we can use the complementary probability.
This means we will first find the probability of her not getting a bullseye in all 5 throws, and then subtract that from 1.
Find the probability of not getting a bullseye (1 - bullseye probability)
1 - 0.15 = 0.85
Calculate the probability of not getting a bullseye in all 5 throws
0.85^5 ≈ 0.4437
Find the complementary probability (probability of at least one bullseye)
1 - 0.4437 ≈ 0.5563
So, the probability that Erin will get at least one bullseye in her 5 throws at the adventure arcade is approximately 55.63%.
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Let a, b, c, and d be positive numbers. Which one of the following is an expression for the area of the rectangular region whose boundary is formed by the equations x=−c, x=+d, y=+a, y=−b?
The expression for the area of the rectangular region whose boundary is formed by the equations x=−c, x=+d, y=+a, y=−b is ad + bd + ac + bc.
The rectangular region whose boundary is formed by the equations x=−c, x=+d, y=+a, y=−b can be visualized as a rectangle with width d+c and height a+b.
Area is a measurement of the size of a two-dimensional surface, such as a plane or a flat shape.
Therefore, the area of the rectangular region is given by
Area = Width x Height
Substitute the values in the equation and find the expression of area
= (d + c) x (a+b)
= ad + bd + ac + bc
So the expression for the area of the rectangular region is
ad + bd + ac + bc.
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The given question is incomplete, the complete question is:
Let a, b, c, and d be positive numbers. Find the expression for the area of the rectangular region whose boundary is formed by the equations x=−c, x=+d, y=+a, y=−b?