Answers
The output of g(x) when x is -2 is 1/3.
How to find output?
To find the output of g(x) when x is -2, we simply substitute -2 into the formula for g(x):
g(-2) = 3⁻²/²
Simplifying the exponent, we get:
g(-2) = 3⁻¹
Now, we need to evaluate 3⁻¹. Recall that any number raised to a negative exponent can be written as its reciprocal raised to the corresponding positive exponent. That is:
a⁻ⁿ = 1/(aⁿ)
In our case, a is 3 and n is 1, so we have:
3⁻¹= 1/(3¹) = 1/3
Therefore, the output of g(x) when x is -2 is 1/3.
Note that 1/3 is already in its simplest form, so we do not need to simplify it any further. We also do not need to round it to two decimal places since it is a fraction.
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Related Questions
the amount of distilled water dispensed by a machine is normally distributed with mean 64 oz and standard deviation 0.78 oz. what container size c will ensure that overflow occurs only 0.5% of the time?
Answers
A container size of at least 66.03 ounces will ensure that overflow occurs only 0.5% of the time.
To make sure overflow occurs only 0.5% of the time, we would have to find the container of size "c" such that the amount of distilled water dispensed by the machine does not exceed c with a probability of 0.995 (or 1-0.005).
Let X be the amount of distilled water dispensed by the machine. Then X ~ N(64, 0.78^2).
We want to find c such that P(X ≤ c) = 0.995.
We can standardize X to a standard normal distribution:
Z = (X - μ) / σ
Z = (c - 64) / 0.78
Then we can find the value of Z such that P(Z ≤ z) = 0.995, where z is the z-score associated with the 0.995 percentile of the standard normal distribution.
Using a standard normal distribution table or a calculator, we can find that z ≈ 2.576.
Therefore, 2.576 = (c - 64) / 0.78. Solving for c, we get:
c = 64 + 2.576 * 0.78 ≈ 66.03
So a container size of at least 66.03 ounces will ensure that overflow occurs only 0.5% of the time.
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Dorothy bought an energy drink for $2.34 and a bag of chips for $1.82
She paid with a $50 bill. How much change should Dorothy have
received?
Answers
Dorothy should have received $45.84 in change.
What is the equivalent expression?
Equivalent expressions are expressions that perform the same function despite their appearance. If two algebraic expressions are equivalent, they have the same value when we use the same variable value.
To find out how much change Dorothy should have received, we need to first calculate the total cost of the energy drink and the bag of chips:
Total cost = Cost of energy drink + Cost of the bag of chips
Total cost = $2.34 + $1.82
Total cost = $4.16
Next, we need to subtract the total cost from the amount paid by Dorothy to get the change:
Change = Amount paid - Total cost
Change = $50 - $4.16
Change = $45.84
Therefore, Dorothy should have received $45.84 in change.
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Puppy fencing comes in sizes thatal 12 feet, 24 feet, and 30 feet in length. Which length would be the best fort pen? How much, if any, will have to B cut off to fit the pen?
Answers
If you want a square pen with each side measuring 6 feet:
- Perimeter = 6 feet x 4 = 24 feet
- The best length would be 24 feet, as it exactly matches the perimeter.
- No fencing needs to be cut off in this case, as the chosen fencing length fits the pen perfectly.
To determine the best length for the puppy pen, you will first need to know the dimensions of the desired pen. Assuming the pen is a square, follow these steps:
1. Measure the length and width of the area you want to fence.
2. Calculate the perimeter of the pen by adding the lengths of all four sides (since it's a square, the length and width are equal, so just multiply one side by 4).
3. Compare the perimeter to the available fencing lengths (12 feet, 24 feet, and 30 feet).
4. Choose the fencing length that is closest to, but not less than, the calculated perimeter.
5. Calculate the excess length by subtracting the perimeter from the chosen fencing length. This is the amount that needs to be cut off.
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A school has 800 students. The staff plans to order a bag for each student. They ask 120 randomly selected students which color bag they prefer. Based on this sample, how many bags of each color should the staff order? Show your work.
Blue 48
Black 54
Gray 18
Answers
The staff should order 48 blue bags, 54 black bags, and 18 gray bags for a total of (48 + 54 + 18) = 120 bags
To determine the number of bags of each color that the staff should order, we need to use the information from the sample of 120 students and make an inference about the entire population of 800 students.
If we assume that the sample of 120 students is representative of the entire population, we can use the proportions from the sample to estimate the number of bags of each color that the staff should order.
Let's use the following proportions from the sample:
40% of the students prefer blue bags (0.40 x 120 = 48)
45% of the students prefer black bags (0.45 x 120 = 54)
15% of the students prefer gray bags (0.15 x 120 = 18)
Therefore, based on this sample, the staff should order 48 blue bags, 54 black bags, and 18 gray bags for a total of (48 + 54 + 18) = 120 bags.
However, it's important to note that this is just an estimate based on a sample, and there may be some variability or uncertainty in the actual preferences of the entire population.
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living at home: according to a 2011 report from the u.s. census, 59% of young men (age 18-24) are living at home with their parents. suppose that we plan to select a random sample of 100 young men from your community. if we use the national figure of 59%, we estimate that the standard error is about 0.05 for results from random samples of 100 young men from your community. when we select a random sample of 100 young men from your community, we find that 50% are living at home. which gives the best interpretation of the 95% confidence interval to estimate the percentage of young men in your community who are living at home?
Answers
The best interpretation of the 95% confidence interval to estimate the percentage of young men in your community who are living at home is 0.40 and 0.60.What is confidence interval?
A confidence interval is a range of values in which an estimated population parameter lies. The value of this parameter is inferred from sample data with a certain level of confidence. To calculate the confidence interval, the margin of error and the sample mean are combined.
A confidence interval expresses the uncertainty around the estimated parameter of a population. Confidence intervals are useful for determining the reliability of an estimate. In statistical inference, confidence intervals can be used to quantify the level of certainty regarding an estimated population parameter.
What is a 95% confidence interval?A 95% confidence interval implies that if we run the same survey many times, calculating the 95% confidence interval for each survey, 95% of those intervals will contain the true value of the population parameter. It is the most common confidence level used in surveys and statistical studies.
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2x10x10x10x10x+4x10x10x10x+8x10x10
Answers
2x10x10x10x10 + 4x10x10x10x + 8x10x10
We can simplify this expression by performing the multiplications and additions in the correct order. Using the order of operations (PEMDAS), we first perform the multiplications from left to right, and then add the resulting terms.
Multiplying the terms in the first expression, we get:
2 x 10 x 10 x 10 x 10 = 200,000
Multiplying the terms in the second expression, we get:
4 x 10 x 10 x 10 = 40,000
Multiplying the terms in the third expression, we get:
8 x 10 x 10 = 800
Adding the three resulting terms, we get:
200,000 + 40,000 + 800 = 240,800
Therefore, the simplified value of the expression 2x10x10x10x10x+4x10x10x10x+8x10x10 is 240,800.
Please help me with this i cant figur out how to do it and it is due in 30 minutes CAN ONE OF YALL HELP ME WITH THIS IT IS EASY
What is the surface area of the triangular prism?
144 mm2
100 mm2
38 mm2
152 mm2
Answer___________
Answers
The calculated surface area of the figure is 152 square feet
Calculating the surface area of the figureFrom the question, we have the following parameters that can be used in our computation:
The triangular prism
The surface area is calculated as
SA = hp + 2B
Where
h = height
p = perimeter of base
B = base area
From the figure, we have
B = 1/2 * 6 * 4 = 12
p = 5 + 5 + 6 = 16
h = 8
So, we have
SA = 8 * 16 + 2 * 12
Evaluate
SA = 152
Hence, the surface area is 152 square feet
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Please Help me I don't get it. (DON'T ANSWER IT IF YOU DON'T KNOW, I'M TIRED OF PEOPLE ANSWERING IT FOR NO REASON TO GET POINTS)
Answers
Answer: 1/8 or 0.125 in decimal form
Step-by-step explanation: Reduce the expression by cancelling the common factors.
$8.40 is what percent of $28?
Percent Proportion-
Percent Equation-
Answers
Answer:
10%
Step-by-step explanation:
Percent proportion:
$28 - 100%
$8,40 - x%
Cross-multiply to find x:
[tex]x = \frac{8.40 \times 100\%}{28} = \frac{840}{84} = 10 \: \%[/tex]
Answer 30%
Step-by-step explanation:
To find what percentage $8.40 is of $28, we can use the following proportion:
part/whole = percent/100
Let x be the percentage we are trying to find, then we can write:
8.40/28 = x/100
To solve for x, we can cross-multiply:
28x = 8.40 * 100
Dividing both sides by 28, we get:
x = (8.40 * 100) / 28 = 30
Therefore, $8.40 is 30% of $28.
The radii of two cylinders are in the ratio of 4:5and their height are in the ratio 7:6 find the ratio of their lateral surface area
Answers
Answer:
Let the radii of two cylinders be 4x and 5x and their heights be 7y and 6y respectively. The lateral surface area of a cylinder is given by the formula 2πrh where r is the radius and h is the height. The lateral surface area of the first cylinder is 2π(4x)(7y) = 56πxy. The lateral surface area of the second cylinder is 2π(5x)(6y) = 60πxy. Therefore, the ratio of their lateral surface area is 56πxy : 60πxy which can be simplified to 14:15. Hence, the ratio of their lateral surface area is 14:15.
on a roadway with eight 11 ft lanes (four in each direction), a horizontal curve is designed with a radius of 1176 ft, and a concrete wall is built at 70 ft from the center line, what is the sight distance for the driver?
Answers
The sight distance for the driver on the given road with the mentioned conditions is calculated to be approximately 860.8 ft.
To calculate the sight distance for the driver, we need to use the horizontal curve sight distance formula. The formula is:
SD = 2/3 × ((h + R)² / (2 × R - f))
Where:
SD = sight distance
h = height of driver's eye above the roadway surface (in feet)
R = radius of the curve (in feet)
f = distance from the driver's eye to the object or obstacle (in feet)
First, we need to determine the height of the driver's eye. A typical height for a driver's eye above the roadway surface is 3.5 feet. Therefore, we will assume that h = 3.5 ft.
Next, we need to determine f, which is the distance from the driver's eye to the concrete wall. Since the wall is located 70 feet from the center line of the roadway, we can determine f as follows:
f = (W / 2) + S
Where:
W = width of the roadway (in feet)
S = distance from the center line to the wall (in feet)
Substituting the given values, we get:
f = (8 × 11 / 2) + 70 = 114 ft
Now, we can plug in the values for h, R, and f into the sight distance formula:
SD = 2/3 × ((3.5 + 1176)² / (2 × 1176 - 114))
Simplifying the formula, we get:
SD ≈ 860.8 ft
Therefore, the sight distance for the driver on this roadway with a horizontal curve of radius 1176 ft and a concrete wall built at 70 ft from the center line is approximately 860.8 ft.
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The math club is planning a meeting. They are planning to serve cookies and brownie bites and want to have one dessert per person. They expect an attendance of a total of 75 people. Cookies (c), come in packs of 12 each, and the brownie bites (b) come in packages of 15. What is the equation for the total number of packages of each dessert that the club treasurer needs to purchase in order to have a dessert for each person who attends? b+ 12 15 75 C= If the treasurer buys 1 package of brownie bites, how many packages of cookies are needed according to this equation? packages of cookies Is this value a reasonable value in this
Answers
Equation for the total number of dessert packages needed for a math club meeting with cookies and brownie bites; 5 packages of brownie bites and 15 packages of cookies needed to serve one dessert per person for a total of 75 attendees.
What is the equation for the total number of dessert packages needed for a math club meeting with cookies and brownie bites?We can use the following equation to calculate the total number of packages of each dessert that the club treasurer must purchase:
Total packages of brownie bites (b) + Total packages of cookies (c) = Total number of attendees (75)
We know that brownie bites come in packages of 15, so the total number of packages of brownie bites the treasurer needs to purchase would be:
b = ceil(75/15) = 5
where "ceil" refers to the ceiling function, which rounds to the nearest integer. In this case, we need at least 5 packages of brownie bites to have one dessert per person.
To find the number of packages of cookies needed, we can substitute the value of b into the equation:
c + 12b = 75
c + 12(5) = 75
c + 60 = 75
c = 15
However, this value is not reasonable since 15 packages of cookies would provide 180 cookies, which is more than 2 cookies per person. Therefore, the treasurer would need to adjust the number of packages of cookies based on the actual number of cookies in each package to ensure that they have exactly one dessert per person.
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Ellie uses 27 yards of fabric for 48 doll dresses she uses that same amount for one dress how many yards of fabric does use for one
Answers
Ellie uses approximately 0.5625 yards or 9/16 of a yard of fabric for one doll dress, which can be useful in calculating the total cost of fabric required for a certain number of doll dresses.
Given that Ellie uses 27 lengths of fabric for 48 doll dresses, we can calculate the amount of fabric she uses for one dress by dividing the total yards of fabric by the number of dresses.
Dividing 27 by 48, we get 0.5625 yards, or approximately 9/16 of a yard, for one doll dress. This means that each dress requires a little more than half a yard of fabric.
This information can be useful in calculating the cost of fabric required to make a certain number of doll dresses. If we know the cost of fabric per yard, we can multiply it by the number of yards required to determine the total cost of fabric. In this case, if the cost of fabric is $5 per yard, the cost of fabric for one doll dress would be approximately $2.81.
In conclusion, Ellie uses approximately 0.5625 yards or 9/16 of a yard of fabric for one doll dress.
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Fourth-grade students recorded the distance it takes to get from home to the nearest grocery store. The distance in miles is recorded on the line plot. Which is the most common distance from home to the grocery store?
Answers
Using the line plot graph, we can conclude that the 5th distance that is 5/4 is the most common distance from home to the grocery store.
Define line plot?A line plot is a type of graph that shows the frequency of each value together with the data using symbols above a frequency number-line. It is used to organise the information simply and is very easy to comprehend.
In the given graph we can see that the distance values are given.
So, in the first instance the number of times the distance is used = 2.
The 2nd distance has been used = 3.
The 3rd distance has been used = 2.
The 4th distance has been used = 4.
The 5th distance has been used = 5.
The 6th distance has been used = 2.
The 7th distance has been used = 2.
The 8th distance has been used = 2.
Hence, we can conclude that the 5th distance that is 5/4 is the most common distance from home to the grocery store.
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the city of raleigh has 10600 registered voters. there are two candidates for city council in an upcoming election: brown and feliz. the day before the election, a telephone poll of 350 randomly selected registered voters was conducted. 135 said they'd vote for brown, 191 said they'd vote for feliz, and 24 were undecided. the target population for this survey is:
Answers
The target population for this survey is the registered voters in the city of Raleigh who are eligible to vote in the upcoming city council election.
The target population for a survey refers to the specific group of people that the survey is intended to represent or provide information about. In this case, the survey was conducted to gather information about the voting preferences of registered voters in the city of Raleigh for the upcoming city council election. Therefore, the target population for this survey would be the registered voters in the city of Raleigh who are eligible to vote in this election.
It's important to note that the target population is not the same as the sample population. The sample population refers to the group of people who actually participated in the survey, while the target population refers to the larger group of people that the sample population is intended to represent. In this case, the sample population was the 350 randomly selected registered voters who participated in the telephone poll.
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Can a non-complex equation have 2 horizontal asymptotes? Excluding piecewise equations, o course. Also, what about 2 vertical asymptotes? And using a complex number as x could an equation pass the vertical asymptote? What about the horizontal one?
Answers
No, a non-complex equation cannot have two horizontal asymptotes. A horizontal asymptote is a line that a function approaches as the input variable increases or decreases without bounds.
Since a non-complex equation represents a single function, it cannot have more than one horizontal asymptote. A non-complex equation cannot have two vertical asymptotes. A vertical asymptote is a vertical line that a function approaches as the input variable approaches a certain value. Again, since a non-complex equation represents a single function, it cannot have more than one vertical asymptote. If a complex number is used as the input variable in an equation, the equation can pass through a vertical asymptote since the notion of "approaching" a point does not apply to complex numbers. However, the concept of a horizontal asymptote does not apply to complex numbers since there is no notion of "increasing" or "decreasing" in the complex plane.
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davis & theo hang pictures using their nails. Davis has a 3/4-inch nail. Theo has a 3/8-inch nail. How much longer is Davis's nail than Theo
Answers
The denominators of fractions that are the same are known as common denominators. Think about the following instances: 1/2 + 1/2 = 1 and 3/4 + 1/4 = 1 Since the fractions' denominators are the same in both instances, it is simple to calculate the solution.
According to the given information :Davi's nail is 3/4 inch long, and Theo's nail is 3/8 inch long. To find how much longer Davis's nail is than Theo's, we need to subtract the length of Theo's nail from the length of Davis's nail:
3/4 inch - 3/8 inch
To subtract these fractions, we need to find a common denominator. The smallest common denominator for 4 and 8 is 8, so we need to convert the fractions:
3/4 inch = 6/8 inch
3/8 inch = 3/8 inch
Now we can subtract:
6/8 inch - 3/8 inch = 3/8 inch
Therefore, Davis's nail is 3/8 inch longer than Theo's nail.
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For problems 8 and 9, find the length of the missing side of each right triangle. Round your
answers to the nearest tenth, if necessary. (2 points each)
Answers
Answer:
8. c ≈ 7,2 cm
9. b ≈ 6,7 in
Step-by-step explanation:
Use the Pythagorean theorem for each of these problems:
8.
[tex] {c}^{2} = {6}^{2} + {4}^{2} = 36 + 16 = 52[/tex]
[tex]c > 0[/tex]
[tex]c = \sqrt{52} ≈7.2[/tex]
.
9.
[tex] {b}^{2} = {7}^{2} - {2}^{2} = 49 - 4 = 45[/tex]
[tex]b > 0[/tex]
[tex]b = \sqrt{45} ≈6.7[/tex]
Help on this question
Answers
The missing entries are (a) $686, (b) $635, (c) $1035, (d) $1010, (e) $938.88 and (f) $447.37.
What is Debit Card?A debit card is one that a person owns, and when they use it to make a purchase, the money is instantly withdrawn from or added to their account.
A table listing Gino's debit card purchases is provided.
He has made a $778.19 starting deposit.
The disparity between the old balance and the payment will be the new balance in the account.
He spent $92.19 on the bat.
a = $778.19 - 92.19 = $686
He bought gas for $51.00.
b = $686 - $51 = $635
He deposited $400.
c = $635 + $400 = $1035
He paid $25 for gas.
d = $1035 - $25 = $1010
Dinner at Spooner's on the shore cost him $71.12.
e = $1010 - $71.12 = $938.88
He spent $491.51 on books for the entire term.
f = $938.88 - $491.51 = $447.37
The missing records are thus discovered.
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std study: a 2008 cdc study estimated that 26% of young women between the ages of 14 and 19 in the u.s. were infected with at least one of the most common sexually transmitted diseases (human papillomavirus [hpv]), chlamydia, herpes simplex virus, and trichomoniasis). is the percentage higher in your community? suppose that we plan to select a random sample of 100 young women in your community. if we use the national figure of 26%, we estimate that the standard error is about 0.04 for results from random samples of 100 young women. when we select a random sample of 100 young women in your community, we find that 20% are infected with at least one of the most common stds. which gives the best interpretation of the 95% confidence interval to estimate the percentage of young women in your community who are infected with at least one of the most common stds?
Answers
Be 95% confident that the true percentage of young women infected with at least one STDs in your community is between 12% and 28% based on the random sample of 100 young women in your community.
The national estimate for the proportion of young women in the United States who are infected with at least one of the most prevalent sexually transmitted diseases is 26% based on the information provided. The study also predicts that the standard error for findings from 100 young women's random sample will be 0.04 percent.
It is discovered that 20% of 100 young women in your community who were chosen at random are infected with at least one of the most prevalent STDs. A 95% confidence interval can be used to calculate the proportion of young women in your community who have at least one of the most frequent STDs.
If the same sample is obtained multiple times, the true value will, in 95% of cases, fall within the computed interval, according to a 95% confidence interval. The range of 12% to 28% is the predicted 95% confidence interval for the proportion of young women in your town who have at least one of the most prevalent STDs.
We therefore have a 95% confidence level that the true percentage of young women infected with at least one of the most prevalent STDs in your community is between 12% and 28% based on the sample of 100 young women in your community. This indicates that there is a chance that the proportion could be either higher or lower than the 26% national estimate.
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Given â–³rst ~ â–³rqp. triangle p q r. side p q is 8 centimeters and side p r is 12 centimeters. triangle s r t. side s t is x centimeters and side r t is 18 centimeters. what is the value of x?
Answers
The required simplified value of x in the △RQP (triangle RQP) is given as x = 12 centimeters.
Similar triangles:
Two triangles are similar if their corresponding sides have the same ratio and if the corresponding pairs of angles are equal. Two or more figures having the same shape but different sizes are called similar figures. Consider a hula hoop and a bicycle wheel, both objects are similar in shape because they have the same shape. Similar triangles are those triangles that have similar properties, i.e. angles and proportionality of sides.
Here,
△RST ~ △RQP
So, the Property of similar triangle states that the ratio of the corresponding side of the triangle is equal.
PQ/ST = PR/RT
From the given data n the question,
8/x = 12 / 18
⇒ x = 8 × 18 / 12
⇒ x = 12
Thus, the required simplified value of x in the △RQP is given as x = 12.
Complete Question:
Given △RST ~ △QRP. Triangle P Q R. Side P Q is 8 centimeters and side P R is 12 centimeters. Triangle S R T. Side S T is x centimeters and side R T is 18 centimeters. What is the value of x?
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which statements are reasons why survey results might not help accurately predict actual results from the population?
Answers
Even if the sample is representative and the survey questions are well-crafted, there is a possibility that the findings will differ from those of the actual population due to sampling error.
Which are the statement why survey results might not help accurately predict actual results?Sampling bias: The survey sample may not be representative of the community, resulting in an imbalance between the representation of some groups in the sample. As a result, there may be inaccuracies in the findings because the sample may not fairly represent the population's diversity. There are a number of factors why survey results might not be a reliable indicator of what the population will actually do. The following claims may help to clarify this:
Non-response bias: A biassed sample may result if some members of the sample decide not to take part in the poll. If the non-response rate is high among specific groups, such as minority groups or low-income households, this may be a particular issue.
Social preference bias: Respondents may be influenced to provide answers that make them appear more desirable.Instead of being fully honest, I'll be polite. As a result, socially acceptable behaviour may be overreported while socially unacceptable behaviour may be underreported.
topic wording: How a topic is worded can have an impact on the responses it receives. It's possible that ambiguous or deceptive questions don't accurately represent the respondent's true viewpoint.
Response options: How respondents react to a survey can also be influenced by the response options that are offered. Respondents might feel under pressure to select a response that doesn't accurately represent their opinions, for instance, if the choices are few or don't include a "neutral" option.
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A principal wants to know if students at a particular high school are in favor of a new dress code at their school. The principal is not able to ask the opinion of every student at the school, so she needs to select an appropriate sample of the students to represent the high school.
Select which sample of students the principal should choose.
Answers
The principal should then survey the selected students to gather their opinions on the new dress code.
To answer your question, the principal should choose a sample of students that is both representative and random. This will ensure that the opinions gathered are an accurate reflection of the entire high school population.
How the principal can achieve this:
Determine the sample size:
The principal should decide on a suitable sample size based on the total number of students in the high school.
A larger sample size will yield more accurate results, but it may not be feasible to survey too many students.
To ensure representativeness, the principal should divide the high school population into different strata, such as grade levels or other relevant demographic categories.
This will help ensure that the sample includes a balanced mix of students from different backgrounds and groups.
Select a random sample:
Within each stratum, the principal should choose a random sample of students.
The principal should then survey the selected students to gather their opinions on the new dress code.
By following these steps, the principal can select an appropriate sample of students that will provide an accurate representation of the high school's overall opinion on the new dress code.
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DeAndre’s older sister saved the same amount of money each month for `4` months.
If she has saved `\$536` altogether, how much money did she save each month?
Answers
Answer:
$134 per month
Step-by- step explanation:
Simply divide 536 by 4, and you get 134.
csc u cot u divided by sec u
Answers
cos² u / sin² u = cos² u / (1 - cos² u) is the simplified expression for (csc u cot u) / sec u in terms of cos u. We can calculate it in the following manner.
We can simplify the expression (csc u cot u) / sec u using trigonometric identities.
Recall that:
csc u = 1 / sin u
cot u = cos u / sin u
sec u = 1 / cos u
Therefore, we have:
(csc u cot u) / sec u
= (1/sin u * cos u / sin u) / (1 / cos u) (substituting the identities)
= (cos u / (sin u)²) * cos u (simplifying the fractions)
= cos² u / sin² u (simplifying further)
Recall that:
sin² u + cos² u = 1
Therefore, we can substitute sin² u by 1 - cos² u:
cos² u / sin² u = cos² u / (1 - cos² u)
This is the simplified expression for (csc u cot u) / sec u in terms of cos u.
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which of the following statements are true? the resample can contain serial numbers that are not in the original sample. the original sample can contain serial numbers that are not in the resample. because the sample size is small, the histogram of the resample might look very different from the histogram of the original sample. the resample has either zero, one, or more than one copy of each serial number. the original sample has exactly one copy of each serial number for every german plane. the resample has exactly the same sample size as the original sample.
Answers
The true statements about the sample are a, c, d and e.
Serial codes in the resample may differ from those in the initial sample. The histogram of the resample may vary significantly from the histogram of the initial sample due to the small sample size. The number of copies of each serial number in the resample can be zero, one, or more. Furthermore, each serial number for every German aircraft is present in the initial sample precisely once.
Using resampling methods like bootstrapping or permutation tests, a new resample is created by arbitrarily selecting some of the initial sample. Therefore, depending on the precise resampling technique employed, the sample amount of the resample may be the same as the initial sample or it may be smaller or bigger.
Complete Question:
which of the following statements are true?
a. the resample can contain serial numbers that are not in the original sample.
b. the original sample can contain serial numbers that are not in the resample.
c. because the sample size is small, the histogram of the resample might look very different from the histogram of the original sample.
d. the resample has either zero, one, or more than one copy of each serial number.
e. the original sample has exactly one copy of each serial number for every German plane.
f. the resample has exactly the same sample size as the original sample.
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Janice would like to have $40,000 to help pay for college in 8 years. Currently, she has $1000. What interest rate, when compounded yearly, would help her reach her goal?
c. Janice's friend Sarah starts with $7800 and wants to have $18, 400 twenty years from now. What interest rate does she need (compounded yearly)?
b. If y represents the amount of money and x represents the number of years after today, find an equation that models Janice's financial situation. What interest rate does she need to earn?
a. What type of function would best model this situation? Explain how you know and write the general form of this function.
d. Is Janice's goal or Sarah's goal more realistic? Justify your response.
Answers
b. Using the given information, we can write the equation as:
40,000 = 1,000(1 + r)^8
Dividing both sides by 1,000, we get:
40 = (1 + r)^8
Taking the eighth root of both sides, we get:
1.047 ≈ 1 + r
r ≈ 0.047 or 4.7%
Therefore, Janice needs an interest rate of approximately 4.7% compounded yearly to reach her goal.
c. Using the same formula as above, we can write:
18,400 = 7,800(1 + r)^20
Dividing both sides by 7,800, we get:
2.359 ≈ (1 + r)^20
Taking the twentieth root of both sides, we get:
1.044 ≈ 1 + r
r ≈ 0.044 or 4.4%
Therefore, Sarah needs an interest rate of approximately 4.4% compounded yearly to reach her goal.
d. Janice's goal is less realistic since she would need to earn a higher interest rate in order to reach her goal. Additionally, starting with only $1,000 and expecting to have $40,000 in 8 years is a very ambitious goal, whereas Sarah's goal seems more achievable as she has a longer time horizon and a larger initial investment.
Using the substitution method, find the solution to this system of equations.
-2x+y=4
-2x+2y=7
Answers
Answer:
The solution to the system of equations is (-1/2, 3).
Step-by-step explanation:
To solve this system of equations using substitution method, we first need to solve one of the equations for one of the variables in terms of the other variable. Let's solve the first equation for y:
-2x + y = 4
y = 2x + 4
Now we can substitute 2x + 4 for y in the second equation:
-2x + 2y = 7
-2x + 2(2x + 4) = 7
Simplifying the equation:
-2x + 4x + 8 = 7
2x = -1
x = -1/2
Now we can use this value of x to find the value of y:
y = 2x + 4
y = 2(-1/2) + 4
y = 3
The points P(1. -2) and Q(7, 1) lie on the circumference of a circle. Show that the centre of the circle lies on the line 4x + 2y = 15
Answers
Answer:
Sure, I can help you with that geometry problem! To find the center of a circle given two points on its circumference, we need to find the perpendicular bisector of the line segment connecting those two points. Let's first find the midpoint of line segment PQ. Midpoint M = ( (1+7)/2 , (-2+1)/2 ) M = (4, -1/2) The slope of the line PQ is: Slope of PQ = (1-(-2)) / (7-1) Slope of PQ = 3/2 The slope of the perpendicular bisector of PQ is the negative reciprocal of the slope of PQ. Slope of perpendicular bisector = -2/3 Now we can find the equation of the perpendicular bisector of PQ in point-slope form using the midpoint M:
i need help pleaseeeeeeeeee
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According the given question the slοpe is 3/4.
What is slοpe?Calculated using the slοpe οf a line fοrmula, the ratiο οf "vertical change" tο "hοrizοntal change" between twο different lοcatiοns οn a line is determined. The difference between the line's y and x cοοrdinate changes is knοwn as the slοpe οf the line.Any twο distinct places alοng the line can be used tο determine the slοpe οf any line.
Here the accοrding to the table , let us take any twο coordinates are,
[tex](x_1,y_1)=(4,6) , (x_2,y_2)=(8,3)[/tex]
Nοw using slope formula then,
=> Slοpe m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
=> Slοpe m = [tex]\frac{6-3}{8-4}=\frac{3}{4}[/tex]
Hence the slοpe οf the linear function is 3/4.
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