Step-by-step explanation:
1) We can start by finding the adjacent and opposite sides of the right triangle using the Pythagorean theorem. Let x be the length of the adjacent side, then:
tan θ = (3-√3)/9
tan θ = opposite/adjacent
(3-√3)/9 = opposite/x
opposite = (3-√3)x/9
Using Pythagorean theorem:
(adjacent)^2 + (opposite)^2 = (hypotenuse)^2
x^2 + [(3-√3)x/9]^2 = (hypotenuse)^2
x^2 + (9-6√3+3)x^2/81 = (hypotenuse)^2
(82-54√3)x^2/81 = (hypotenuse)^2
We can simplify this expression to find the hypotenuse:
(hypotenuse)^2 = [(82-54√3)/81]x^2
hypotenuse = sqrt[(82-54√3)/81]x
Now we can find the other trig ratios:
cos θ = adjacent/hypotenuse = x/sqrt[(82-54√3)/81]x
cos θ = 1/sqrt[(82-54√3)/81]
cos θ = sqrt[(82+54√3)/81] / [(82-54√3)/81]
cos θ = sqrt(82+54√3) / (82-54√3)
sin θ = opposite/hypotenuse = (3-√3)x/9 / sqrt[(82-54√3)/81]x
sin θ = (3-√3) / sqrt(82-54√3)
2) To find the other trig ratios, we need to first find the adjacent and hypotenuse sides of the right triangle. Let x be the length of the adjacent side, then:
sin θ = opposite/hypotenuse = 8/10
opposite = (8/10)hypotenuse = 0.8hypotenuse
Using Pythagorean theorem:
(adjacent)^2 + (opposite)^2 = (hypotenuse)^2
x^2 + (0.8hypotenuse)^2 = hypotenuse^2
x^2 + 0.64h^2 = h^2
x^2 = 0.36h^2
x = 0.6h
Now we can find the other trig ratios:
cos θ = adjacent/hypotenuse = 0.6h/h = 0.6
tan θ = opposite/adjacent = (8/10)/0.6 = 4/3
cot θ = 1/tan θ = 3/4
What are the correct characteristics of the following rational function?
Answer: Crosses the x-axis at 3
touches the x-axis at -2
has a vertical asymptote at x=1
has a horizontal asymptote at y=2
Step-by-step explanation:
Needd help please!!!
If you're hoping to land a job, carry out your research and compile a list of potential questions to inquire. Doing this will communicate that you are seriously interested in the position and significantly increase your chances of being chosen.
How to explain the verbIt should be noted that to master something, practise is key. If I had an interview coming up, I'd practice my answers prior to entering the room.
If you long to receive money for your efforts, get active by filing for a job. During the interviewing process, it may be nerve-racking but with the right preparation, nothing should obstruct you from showing the interviewer why you're suited for the role. Here are some helpful tips:
When you are ready to attend an interview, jot down a list of queries to ask the recruiter. This will indicate that you have investigated the company and undeniably demonstrate a passionate interest in the occupation.
If they question if you comprehend anything regarding the corporation, you need to respond with assurance. Doing so implies that you are well informed on the business and have done your research beforehand.
Always don your professional attire when participating in an interview; slipping into casual garments against the recruiter in smart-looking attire could cause discomfort or result in failure at garnering the job.
If during the interview, you happen to feel uneasy, breathe deeply and take some time to chill out. This way, conducting oneself calmly, any queries answered will make more sense.
In respect of disclosing personal weaknesses, truthfully give an account but without overly criticising yourself. Exhibiting self-comprehension as well as striving towards improving these areas will reflect self-awareness and commitment to development.
Finally, thank the interviewer for their time once the interview reaches its conclusion. Doing so displays politeness and appreciation.
Up to this point, solely exhibiting positive impressions, even after affirmative results, extend gratitude with a follow-up note. Doing this illustrates excitement for the job whilst displaying admiration for the opportunity.
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A local carpet store sells carpet at $5. 25 per square foot. If they are carpeting a room that measures 9 feet by 6 feet , what is the cost of the carpet ? math problem
The total cost of the carpeting for the room is [tex]$283.50[/tex].
To calculate the cost of carpeting a room, we need to find the total area of the room and multiply it by the cost per square foot of the carpet. In this case, the room measures 9 feet by 6 feet, so its area is 9 x 6 = 54 square feet.
The carpet is sold at [tex]$5.25[/tex] per square foot, the cost of the carpeting for the room can be calculated by multiplying the total area of the room (54 square feet) by the cost per square foot ([tex]$5.25[/tex]). The cost of the carpet for the room is therefore:[tex]54[/tex] sq ft x[tex]$5.25[/tex] /sq ft = [tex]$283.50[/tex].
This cost only covers the carpeting itself, and does not include any additional expenses such as padding or installation. It's always a good idea to get a detailed estimate from a professional carpet installer to ensure that you have a clear understanding of the total cost of the project.
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Find the sum of the following series. Round to the nearest hundredth if necessary.
Required sum of the given series is 3069.00
What is the sum of a geometric series?
We can use the formula for the sum of a finite geometric progression:
[tex]S_n = \frac{a(1 - r^n)}{(1 - r)}[/tex] where
[tex]S_n[/tex] is the sum of the first n terms of the series.
Here,
The series 3+6+12+... is a geometric progression with the first term a=3 and the common ratio r=2. To find the sum of the series.
We can see that the common ratio r=2 is greater than 1, so the series does not have a finite sum.
We can find the sum of the first few terms to get an approximation of the sum. Let's find the sum of the first 10 terms:
[tex]S_{10} = \frac{3(1 - 2^{10})}{(1 - 2)} \\ = \frac{3(1 - 1024)}{(-1)} \\ = 3(1023 = 3069[/tex]
So the sum of the first 10 terms is 3069. To round this to the nearest hundredth, we can write the answer as 3069.00.
Hence, required sum of the given series is 3069.00
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Answerrrrrrrrr pleaseeeeeee
Answer:
x= 1 and y= 10
Step-by-step explanation:
y= 4x+6 (1)
x= 21-2y (2)
sub (1) into (2):
x= 21-2(4x+6)
x= 21-8x-12
9x= 9
x= 1 (3)
sub (3) into (1):
y= 4(1)+6
= 10
mrs. candy has a large box of lollipops, chocolate bars, and caramels. she wants to give each of the nine children in her neighborhood three pieces of candy. taking into account that each type of candy is available in a quantity greater than 30, in how many ways can mrs. candy distribute the candy?
There are 122,305,536 ways Mrs. Candy can distribute the candy.
How to calculate total number of ways to distribte the candy?There are three types of candy, and each child receives three pieces, so a total of nine children will receive a total of 27 pieces of candy. Let's consider each type of candy separately.
First, let's consider the lollipops. Mrs. Candy can give each child up to three lollipops, and there are more than 30 lollipops available.
Using the stars and bars method, we can represent the distribution of lollipops as a sequence of 3 bars (|) and 30 stars (), where the bars represent the boundaries between each child's lollipops.
For example, the sequence " * | * * * | * * * * | * * *" represents a distribution where the first child receives 2 lollipops, the second child receives 3 lollipops, the third child receives 4 lollipops, and the fourth child receives 2 lollipops.
Using this method, we can count the number of possible distributions of lollipops as:
(30 + 3 - 1) choose (3 - 1) = 32 choose 2 = 496
Next, let's consider the chocolate bars. Mrs. Candy can give each child up to three chocolate bars, and there are more than 30 chocolate bars available.
Using the same method as before, we can represent the distribution of chocolate bars as a sequence of 3 bars and 30 stars. Counting the number of possible distributions of chocolate bars, we get:
(30 + 3 - 1) choose (3 - 1) = 32 choose 2 = 496
Finally, let's consider the caramels. Using the same method as before, we can represent the distribution of caramels as a sequence of 3 bars and 30 stars. Counting the number of possible distributions of caramels, we get:
(30 + 3 - 1) choose (3 - 1) = 32 choose 2 = 496
To find the total number of ways Mrs. Candy can distribute the candy, we need to multiply the number of ways of distributing each type of candy together, since the distributions are independent.
Thus, the total number of possible distributions of candy is:
496 * 496 * 496 = 122,305,536
Therefore, there are 122,305,536 ways Mrs. Candy can distribute the candy.
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It takes 3 egg to make two dozen cookies about what fracion of an aegg are in two cookiies
Answer:1/4
Step-by-step explanation:3*2/(2*12)=1/4 so our answer is 1/4.
what is the probability that the mean lifetime of 25 randomly selected tires of this type will exceed than 42,000 miles?
The probability that the mean lifetime of 25 randomly selected tires of this type will exceed than 42,000 miles is 25.14.
To break this problem, we need to use the standard normal distribution, assuming that the distribution of tire continuances is roughly normal. We can regularize the value of 42,000 using the formula
z = ( x- μ)/ σ
where x is the value of interest( 42,000 long hauls), μ is the mean tire continuance( 40,000 long hauls), and σ is the standard deviation( 3,000 miles). Plugging in the values, we get
z = ( 42,000- 40,000)/ 3,000 = 0.67
Using a standard normal distribution table or calculator, we can find the probability that an aimlessly named tire will last further than 42,000 long miles by looking up the area to the right of z = 0.67 under the standard average wind. This probability is roughly 25.14.
thus, the probability that a tire named arbitrarily from this brand will last more than 42,000 miles is roughly 25.14.
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The correct question is given below-
A particular brand of tires lasts an average of 40,000 miles with a standard deviation of 3,000 miles. What is the probability a tire selected at random lasts more than 42,000 miles?
students estimated the length of one minute without reference to a watch or clock, and the times(seconds) are listed below. assume that a simple random sample has been selected. use a 0.01 significance level to test the claim that these times are from a population with a mean equal to 60 seconds. does it appear that students are reasonably good at estimating one minute? 68 81 39 64 40 22 62 61 67 48 64 69 94 91
The null hypothesis that the population mean is equal to 60 seconds cannot be rejected at a 0.01 significance level based on the available sample data, indicating that the students are reasonably good at estimating one minute.
To test the claim that the population mean is equal to 60 seconds, we can use a one-sample t-test. The null hypothesis is that the population mean is equal to 60 seconds, and the alternative hypothesis is that it is not equal to 60 seconds.
We can first calculate the sample mean and standard deviation:
sample mean (x') = (68 + 81 + 39 + 64 + 40 + 22 + 62 + 61 + 67 + 48 + 64 + 69 + 94 + 91) / 14 = 63.57
sample standard deviation (s) = 20.11
The test statistic can be calculated as:
t = (x' - μ) / (s / √n)
where μ is the hypothesized population mean (60 seconds), n is the sample size (14), and x' and s are the sample mean and standard deviation, respectively.
Substituting the values, we get:
t = (63.57 - 60) / (20.11 / √14) = 1.74
The degrees of freedom for the t-distribution is n - 1 = 13. Using a t-table or calculator, the p-value associated with a two-tailed test with 13 degrees of freedom and t = 1.74 is approximately 0.106.
Since the p-value is greater than the significance level of 0.01, we fail to reject the null hypothesis. Therefore, we do not have enough evidence to suggest that the students are not good at estimating one minute. We can conclude that it is plausible that the population mean is equal to 60 seconds, based on the available sample data.
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In a survey about shopping behaviors, 300 300 randomly selected sophomores are asked about their shopping preferences. It is found that 12.5% 12.5 % of the sophomores shop online at least once per month. The margin of error is ±1% ± 1 % . There are approximately 12,000 12,000 sophomores in the state. Using the data from the sample survey, what is the estimated number of sophomores who shop online, at least once per month? Between 1,380 1,380 and 1,500 1,500 Between 1,500 1,500 and 1,620 1,620 Between 1,380 1,380 and 1,620 1,620 Between 1,350 1,350 and 1,620 1,620
The estimated number of sophomores is between 1,380 and 1,620. Then the correct option is C.
Given that:
The sample proportion is 12.5% or 0.125, and the population size is 12,000.
We can use the following formula to calculate the estimated number of sophomores who shop online at least once per month:
Estimated number = sample proportion x population size
The estimated number using this lower bound (i.e., 12.5% - 1%):
Estimated number = 0.115 x 12,000 = 1,380
Similarly, the estimated number using this upper bound (i.e., 12.5% + 1%):
Estimated number = 0.135 x 12,000 = 1,620
Therefore, the estimated number of sophomores who shop online, at least once per month, is between 1,380 and 1,620, which means that the answer is "Between 1,380 and 1,620".
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Consider the steps to solve the equation.
(y + 20 ) - = (2y − 1)
Distribute: +8-04-20
10
What is the next step after using the distributive
property?
O Use the multiplication property of equality to isolate
the variable term on one side of the equation.
O Use the multiplication property of equality to isolate
the constant on one side of the equation.
O Combine the like terms on the right side of the
equation.
O Combine the like terms on the left side of the
equation.
Isolate the variable term on one side of the equation by using equality's multiplication property. Then the correct option is A.
Given information:
[tex]\dfrac{2}{5} \left ( \dfrac{1}{2} y + 20 \right) - \dfrac{4}{5} = \dfrac{9}{20} \left ( 2y-1 \right)[/tex]
The distributive property is often expressed as:
a(b + c) = ab + ac
a(b - c) = ab - ac
Where "a" is a coefficient (or factor) and "b" and "c" are terms.
The equation is simplified as,
[tex]\dfrac{1}{5} y + 8 - \dfrac{4}{5} = \dfrac{9}{10} y- \dfrac{9}{20}[/tex]
Isolate the variable term on one side of the equation by using equality's multiplication property. Then the correct option is A.
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What value will make the equation true?
Answer: C (-0.6)
Step-by-step explanation:
-2.1--0.6=-1.5
-1.5 as fraction = -1 1/2
an amount of 150€ is divided among four people in such a way that each following person gets half as much as the previous one gets. what are the partial amounts?
Answer:
the first person gets €80, the second person gets €40, the third person gets €20 and the fourth person gets €10.
Step-by-step explanation:
Let’s call the amount of money that the first person gets “x”. Then, the second person gets half of x, which is x/2. The third person gets half of x/2, which is x/4. The fourth person gets half of x/4, which is x/8.
The sum of these amounts should be equal to 150€.
x + x/2 + x/4 + x/8 = 150
Multiplying both sides by 8 gives:
8x + 4x + 2x + x = 1200
15x = 1200
x = 80
Therefore, the first person gets €80, the second person gets €40, the third person gets €20 and the fourth person gets €10.
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I hope this helps! Let me know if you have any other questions.
I NEED HELP ASAP PLEASE
Answer:
Using the Pythagorean Theorem to find the height of this right triangle:
[tex] {h}^{2} + {8}^{2} = {(2 \sqrt{19} )}^{2} [/tex]
[tex] {h}^{2} + 64 = 76[/tex]
[tex] {h}^{2} = 12[/tex]
[tex]h = 2 \sqrt{3} [/tex]
From this, the area of this right triangle is:
[tex] \frac{1}{2} (8)(2 \sqrt{3} ) = 8 \sqrt{3} [/tex]
A is the correct answer.
Answer:
Step-by-step explanation
Use Pythagorean Theorem:
8² + b² = (2√19)²
64 + b² = 4 × 19
64 + b² = 76
64 -64 + b² = 76 -64
b² = 12
√b² = √12
b = √4 · 3
b = 2√3
This is the height - use in the area formula:
1/2(8)(2√3)
4(2√3)
8√3
El denominador de una fracción es 3 unidades menor que su numerador, y la fracción es 2,1 unidades mayor que su recíproco. ¿Cuál es esta fracción si tanto su numerador como su denominador son números enteros?
20 POINTS!
A department store is holding a drawing to give away free shopping sprees. There are 9 customers who have entered the drawing: 2 live in the town of Gaston, 2 live in Pike, and 5 live in Wells. Two winners will be selected at random. What is the probability that the first winner lives in Gaston and the second lives in Pike? Write your answer as a fraction in the simplest form.
Answer:
There are a total of 9 customers who have entered the drawing. The probability that the first winner lives in Gaston is 2/9, since there are 2 customers from Gaston out of 9 total customers.
Once the first winner is selected, there will be 8 customers remaining, out of which 2 live in Pike. Therefore, the probability that the second winner lives in Pike, given that the first winner lives in Gaston, is 2/8 or 1/4.
To find the probability that the first winner lives in Gaston and the second winner lives in Pike, we need to multiply the probabilities of the two events:
P(Gaston first and Pike second) = P(first winner from Gaston) * P(second winner from Pike, given that first winner is from Gaston)
P(Gaston first and Pike second) = (2/9) * (1/4)
P(Gaston first and Pike second) = 2/36
Therefore, the probability that the first winner lives in Gaston and the second winner lives in Pike is 2/36, which simplifies to 1/18.
Brooke is purchasing tile to add a backsplash to her kitchen wall. Each tile covers 25 in sq. If each tile cost $1.75, what is the total amount Brooke will spend on tile?
Answer:
Step-by-step explanation:
ee
Answer: $92.75
Step-by-step explanation:
I think this is the answer, sorry if incorrect. When finding the total area of the wall you split the shape in 2. You would get 175 + 1150 inches squared. You then get the total of 1,325 inches squared as the total area of the wall. You divide that number by the number of inches of each tile, which would get you 53 tiles that will be on the wall. Times 53 by the price of each tile, $1.75, and get the answer of $92.75. Hope this helps!
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According to a recent survey of adults, approximately 62% carry cash on a regular basis. The adults were also asked if they have children. Of the 46% who have children, 85% carry cash on a regular basis. Is carrying cash independent from having children in this sample? No, P(carry cash) = P(carry cash|have children). No, P(carry cash) ≠ P(carry cash|have children). Yes, P(carry cash) = P(carry cash|have children). Yes, P(carry cash) ≠ P(carry cash|have children).
The correct statement regarding whether the events are independent is given as follows:
No, P(carry cash) ≠ P(carry cash|have children).
What is Conditional Probability?Conditional probability is the probability of one event happening, considering the result of a previous event. The formula is:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which:
P(B|A) is the probability of the event B happening, given that the event A happened.[tex]P(A \cap B)[/tex] is the probability of both the events A and B happening.P(A) is the probability of the event A happening.An event B is classified as independent if:
P(B|A) = P(B).
According to a recent survey of adults, approximately 62% carry cash on a regular basis, hence:
P(carry cash) = 0.62.
The adults were also asked if they have children. Of the 46% who have children, 85% carry cash on a regular basis, hence the conditional probability is given as follows:
P(carry cash|children) = 0.85.
As the probabilities are different, the events are not independent.
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What factor is represented by the blue shading in the model? [ Hint: Remember shading represents numerator]
A. 4/5
B. 1 2/3
C. 1 4/5
D. 4/15
Answer:
The answer to your problem is, A. [tex]\frac{4}{5}[/tex]
Step-by-step explanation:
We would need to count the entire shaded area both green and blue for the numerator. Which shown the denominator will be all the colors yellow, blue and green squares.
Total Green and blue 24, numerator
Total Green, blue Yellow 30, denominator
Which then divide 24 ÷ 30.
Simplify: divide numerator and denominator by 6
= [tex]\frac{4}{5}[/tex]
Thus the answer to your problem is, A. [tex]\frac{4}{5}[/tex]
Which statement regarding the equation below is true?
x² + y²-8x+12y+34 = 0
A) It has an area of 34.
B) It has an area of 18.
C) It has a center at (-8, 12).
D) It has a diameter of 18 units.
The correct statement regarding the circle with equation x² + y²-8x+12y+34 = 0 is given as follows:
Neither.
What is the equation of a circle?The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:
[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]
The equation for this problem is given as follows:
x² + y² - 8x + 12y + 34 = 0.
Completing the squares, we obtain the equation as follows:
(x - 4)² + (y + 6)² = -34 + 16 + 36
(x - 4)² + (y + 6)² = 18.
Hence the center and radius are given as follows:
The center is of (4, -6).The radius is of sqrt(18) = 4.2 units.The diameter is of 2r = 2 x 4.2 = 8.4 units.The area of the circle is given as follows:
A = 2πr = 2π x 4.2 = 26 square units.
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Match each type of lever with the correct diagram.
Match each type of lever with the correct diagram.
Thanks
Answer:
Step-by-step explanation:
2,3,1
Please help!!!
What is 3^2, aka 3*3*3?
Answer:
Step-by-step explanation:
First of all 3^2 is equal to 3*3 NOT 3*3*3
3^2 means "3 raised to the power of 2," which is equal to 3 multiplied by itself 2 times:
3^2 = 3 x 3 = 9
Therefore, 3^2 is equal to 9.
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urgent help pls. full working out needed
The number of cubes that can be fitted in the crate is 22
Finding the number of cubes:To solve this problem, first calculated the volume of the crate and the volume of one cube, both of which are measured in cubic units (cubic centimeters, in this case).
We then divided the volume of the crate by the volume of one cube to find the number of cubes that can fit inside the crate.
Here we have
The dimensions of the crate are 2.4m × 1.8 m × 1.1 m
The volume of the crate
= 2.4m × 1.8 m × 1.1 m
= 4.752 m³
Given that side of the cube = 60 cm = 0.6 m
Hence, Volume of the cube = (0.6 m)³ = 0.216 m³
Using the formula,
Number of boxes = Volume of box/ Volume of the cube
= 4.752 m³/0.216 m³ = 22
Therefore,
The number of cubes that can be fitted in the crate is 22
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Cost of 5m of cloth is 320 then cost of 3cm 6cm 9cm prices are
Using the unitary method, the cost of 3 meters, 6 meters, and 9 meters of cloth with a cost of 320 for 5 meters is 192, 384, and 576 respectively
To use the unitary method, we need to find the cost per unit length of the cloth first.
Cost per unit length = Cost of 5m of cloth / Length of cloth = 320 / 5 = 64 per meter
Now, we can use this cost per meter to find the cost of different lengths of cloth
Cost of 3 meters of cloth = 64 x 3 = 192
Cost of 6 meters of cloth = 64 x 6 = 384
Cost of 9 meters of cloth = 64 x 9 = 576
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Un tren en marcha acelera a razón de 12 metros por segundo ¿ Cual seria tu masa si la fuerza aplicada fuera de 10N ?
If the force and acceleration are in the same direction, the mass of the object would be 0.83 kg.
The mass of the object cannot be determined with the given information. Acceleration is related to force and mass through Newton's Second Law: F = ma. However, in this case, we are given the acceleration and force, but not the mass. To find the mass, we would need either the acceleration and the force, or the force and the mass.
However, if we assume that the force and acceleration are both in the same direction, we can use the formula F = ma to find the mass. Rearranging the formula, we get m = F/a.
Substituting the given values, we get:
m = 10 N / 12 m/s²
m = 0.83 kg
So, if the force and acceleration are in the same direction, the mass of the object would be 0.83 kg.
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Complete Question:
A moving train accelerates at a rate of 12 meters per second. What would your mass be if the applied force were 10N?
a poll for a statewide election has a margin of error of percentage points. how many voters should be sampled for a confidence interval? round up to the nearest whole number.
The number of voters that should be sampled for a confidence interval depends on the desired level of confidence and the margin of error.
A larger sample size generally leads to a smaller margin of error and a higher level of confidence in the accuracy of the results. However, the relationship between sample size and margin of error is not linear, meaning that doubling the sample size will not necessarily halve the margin of error.
To calculate the required sample size, a formula can be used that takes into account the margin of error, level of confidence, and population size.
the number of voters that should be sampled for a confidence interval depends on several factors and cannot be determined without more information.
To determine the required sample size, you can use the following formula:
n = (Z^2 * p * (1-p)) / E^2
Where:
- n is the sample size
- Z is the Z-score (usually 1.96 for a 95% confidence interval)
- p is the estimated proportion of the population (usually 0.5 for the worst-case scenario)
- E is the margin of error (in decimal form)
Hence, without the specific margin of error, we cannot provide the exact sample size needed.
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fruits are important sources of dietary fiber and vitamins (especially vitamin c). from a sack of fruit containing three oranges, two apples, and three bananas, a random sample of four pieces of fruit is selected. if x is the number of whole oranges and y is the number of whole apples in the sample, find the joint probability distribution and marginal probability distributions of x and y.
The joint probability distribution, we first need to find the total number of ways to select four fruits from the sack, which is:C(8,4) = 70.
Next, we need to find the number of ways to select x whole oranges and y whole apples. There are C(3,x) ways to select x whole oranges and C(2,y) ways to select y whole apples. Once the oranges and apples have been selected, there are C(3-x+2-y, 4-x-y) ways to select the remaining fruits. Therefore, the number of ways to select x whole oranges and y whole apples is:
C(3,x) * C(2,y) * C(3-x+2-y, 4-x-y)Finally, we can calculate the joint probability distribution by dividing the number of ways to select x whole oranges and y whole apples by the total number of ways to select four fruits:
P(X = x, Y = y) = C(3,x) * C(2,y) * C(3-x+2-y, 4-x-y) / C(8,4)The marginal probability distributions can be found by summing the joint probability distribution over the appropriate variable. For example, to find the marginal probability distribution for x, we sum the joint probability distribution over all values of y:
P(X = x) = Σ P(X = x, Y = y) for all ySimilarly, to find the marginal probability distribution for y, we sum the joint probability distribution over all values of x:
P(Y = y) = Σ P(X = x, Y = y) for all xLearn More about probability
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14. Matthew had $4.10 in his pocket. He bought 3 notebooks. Now he has $0.35 in his pocket.
Which equation below can be used to find how much each notebook, n, costs?
A. 4.10-3n=0.35
B. 3n-0.35-4.10
C. 4.10 +0.35=3n
D. 3n+4.100.35
Answer: A
Step-by-step explanation:
pls help due in an hour if you get it right ill mark you brainiest
Step-by-step explanation:
B to B'
( 7,-2) to (-2,-7)
(x,y) changed to (y,-x) this is a 90 degree clockwise rotation
Answer:
Step-by-step explanation:
It is a 90 degree clockwise rotation.
A = (2, -5)
A' = (-5, -2)
90° clockwise will reverse the x an y points and change the sign of x.
(x, y) becomes (y, -x)
You only need to use one point to figure the rotation.
