Answer:
09165574045I want 2 use dis medium 2 thk y’all 4 being part of my 2022.
As a frnd I say a Big Thk u
As a customer I say a Big Thk u
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God bless u n see y’all in 2023 in Grand Style. Amending of your 7
a group of marketing students at a large university wants to determine the proportion of first year students who use certain types of social media. the students want their estimate to be within 0.03 of the true proportion with a 90% level of confidence. how large of a sample is required if the population proportion is not known?
The required sample size is 8.90400.
Given a student wants to make a guess within 0.03 of the true ratio with a 90% confidence level.
Margin of Error, E = 0.03
significance level α=0.10 {90% confidence}
A given estimate of the percentage of population p is p = 0.79.
The critical value for the significance level α = 0.10 is Zc = 1.645. This can be determined using either Excel or a normal probability table.
Use the following formula to calculate the minimum sample size required to estimate the percentage of population p within the required margin of error.
n≥p(1-p)(Zc÷E)²
n = 0.796×(1-0.796)(1.645÷0.03)²
n = 0.796 x 0.204 x 54.833
n = 8.90400
Therefore, the resample size required to meet the condition is n ≥ 8.90400 and must be an integer. From this, we conclude that the minimum sample size required is n = 8.90400
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find three consecutive integers such that four times the first added to the third is 92
SOLVE QUICKLY
Thanks
Answer: the three consecutive integers are 18, 19, and 20.
Step-by-step explanation:
Answer:
18, 19, and 20
Step-by-step explanation:
let the first integer be 'x'.
Thus, the three consecutive integers are:
x, (x+1), (x+2).
Therefore, if 4 × x added to (x+2) = 92, then:
[tex](x+2)+4x=92\\5x+2=92\\5x=90\\x=18[/tex]
Hence x = 18, and thus, the three consecutive integers are 18, 19, and 20.
Jenny and Hong each opened a savings account today. Jenny opened her account with a starting amount of $160, and she is going to put in $50 per month.
Hong opened his account with no starting amount, and he is going to put in $90 per month.
Let x be the number of months after today.
(a) For each account, write an expression for the amount of money in
the account after x months.
Amount of money in Jenny's account (in dollars) =
Amount of money in Hong's account (in dollars) =
(b) Write an equation to show when the two accounts have the same
the fol
amount of money?
Answer:
a)
jenny - $160 + $50X = total
hong - $90X = total
b)
$160 + $50X = $90X
Step-by-step explanation:
a)
jenny starts with $160 so that is the flat rate, does not depend on X. the $50 does depend on X. add these together and you get the total amount on money in x amount of monthshong starts with $0 dollars, and because it doesnt depend on x, it does not need to be in the equation. $90 does depend on x. so it's just 90X = totalb)
all you need to combine these is put an equal sign between the two equations.Find two algebraic expressions for the area of each figure. First, regard the figure as one large rectangle, and then regard the figure as a sum of four smaller rectangles
According to the algebraic expressions, the sum of four smaller rectangles is 96.
First, let's consider the figure as one large rectangle. To find the area of a rectangle, we multiply its length by its width. In this case, the length of the rectangle is 8 and the width is 6 + 2 + 4 = 12. Therefore, the expression for the area of the rectangle can be written as:
Area = length x width
Area = 8 x 12
Area = 96
So the area of the figure as one large rectangle is 96 square units.
To find the area of each rectangle, we'll use the formula for the area of a rectangle, which is length x width. We can see from the figure that:
Rectangle A has a length of 8 and a width of 6
Rectangle B has a length of 8 and a width of 2
Rectangle C has a length of 4 and a width of 6
Rectangle D has a length of 4 and a width of 2
Therefore, the expressions for the area of each rectangle can be written as:
Area_A = length x width
Area_A = 8 x 6
Area_A = 48
Area_B = length x width
Area_B = 8 x 2
Area_B = 16
Area_C = length x width
Area_C = 4 x 6
Area_C = 24
Area_D = length x width
Area_D = 4 x 2
Area_D = 8
To find the total area of the figure, we simply add up the areas of the four rectangles. Therefore, the expression for the area of the figure as a sum of four smaller rectangles can be written as:
Area = Area_A + Area_B + Area_C + Area_D
Area = 48 + 16 + 24 + 8
Area = 96
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Charles darwin was a naturalist that proposed the idea of
Charles Darwin was a naturalist who proposed the concept of evolution via natural selection.
He discovered that versions exist inside species, and that those variations can be inherited via offspring. Darwin theorized that over the years, sure variations might be more positive for survival in a specific surroundings, and people developments could be more likely to be surpassed directly to the subsequent technology.
This method, which he called "natural selection," would lead to the evolution of latest species over long intervals of time. Darwin's concept of evolution thru herbal choice changed into a groundbreaking idea that challenged conventional ideals about the origins and diversity of lifestyles in the world, and it is still a important concept inside the fields of biology and ecology.
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Point B has coordinates (2,1). The x-coordinate of point A is -2. The distance between point A and point B is 5 units. What are the possible coordinates of point A?
The possible coordinates of point A are (-2, -2) and (-2, 4).
What is distance?Distance is a numerical measurement of the amount of space between two points. It is the length of a path that connects two points in a space, usually measured in units such as meters, kilometers, miles, etc.
In Euclidean space (a type of space
We can use the distance formula to find the possible coordinates of point A. The distance formula between two points (x1, y1) and (x2, y2) is:
d = √((x2 - x1)² + (y2 - y1)²)
Let the coordinates of point A be (x, y), where x = -2 (the x-coordinate of point A is -2, as given in the problem).
Then, we can write the distance formula as:
5 = √((2 - (-2))²+ (1 - y)²)
Simplifying this equation, we get:
25 = (2 - (-2))²+ (1 - y)²
25 = 16 + (1 - y)²
9 = (1 - y)²
Taking the square root of both sides, we get:
3 = 1 - y or 3 = -(1 - y)
Solving for y in each case, we get:
y = -2 or y = 4
Therefore, the possible coordinates of point A are (-2, -2) and (-2, 4).
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Practice & Problen In 8-13, complete each conversion. 2 8. 5 pt = C
The value of 5 pints is equal to 10 cups.
A liquid measurement with a capacity of 1/8 of a gallon. If we recall, 8 ounces equals 1 cup and 2 cups (or 16 ounces) equals 1 pint. One pint is made up of 16 fluid ounces, which is also equivalent to 2 cups, 1/4 quart, and 1/8 gallon. Normally, there are 2 cups in 1 pint, however this might vary depending on the ingredients. A pint has two cups in it.
Two cups equal one pint. You must multiply the volume in pints by a factor of two to convert from pt to c.
Hence, 1 pt = 2c
Substitute the values;
Multiple both the sides by 5
5 * 1pt = 5* 2c
5pt = 10c
Therefore, The value of 5 pints is equal to 10 cups.
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an experimenter flips a coin 100 times and gets 42 heads. find the 90% confidence interval for the probability of flipping a head with this coin. a) [0.239, 0.451] b) [0.339, 0.501] c) [0.259, 0.501] d) [0.339, 0.301]
The 90% confidence interval for the probability of flipping a head with this coin is approximately b. [0.339, 0.501], which corresponds to option b). [0.339, 0.501].
Calculate the sample proportion (p-hat):
p-hat = number of heads / total flips = 42/100 = 0.42
Determine the confidence level, which is 90% in this case.
Find the corresponding z-score for the confidence level.
For a 90% confidence level, the z-score is approximately 1.645.
Calculate the standard error:
[tex]SE = \sqrt{(p-hat \times (1 - p-hat) / n)} = \sqrt{ (0.42 \times 0.58 / 100)} = 0.0496[/tex]
Calculate the margin of error:
ME = z-score × SE = 1.645 × 0.0496 ≈ 0.0816
Determine the confidence interval:
CI = (p-hat - ME, p-hat + ME)
= (0.42 - 0.0816, 0.42 + 0.0816)
= (0.3384, 0.5016)
Therefore, option b.[0.339, 0.501] is correct.
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I need help making a two column proof for this question please
Since angle AOB and angle COD are vertical angles, they are congruent. Since angle AOB is a central angle of the first circle, it intercepts arc AB.
what is congruent ?
Congruent is a term used in geometry to describe figures or objects that have the same shape and size. When two figures are congruent, they are identical in every way, including their angles, sides, and dimensions
In the given question,
Proof:
1) Since angle AOB and angle COD are vertical angles, they are congruent.
2) Since angle AOB is a central angle of the first circle, it intercepts arc AB.
3) Similarly, angle COD is a central angle of the second circle, and it intercepts arc CD.
4) Using the fact that central angles of a circle intercept arcs of the same measure, we have that arc AB and arc CD have the same measure, since they are intercepted by congruent central angles.
Therefore, arc AB = arc CD, as required.
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If a1 =5 and an=-2an-1 then find the value of a4
Answer:
We are given the following recursive formula:
an = -2an-1
We are also given that a1 = 5. Using the recursive formula, we can find the values of a2, a3, and a4 as follows:
a2 = -2a1 = -2(5) = -10
a3 = -2a2 = -2(-10) = 20
a4 = -2a3 = -2(20) = -40
Therefore, the value of a4 is -40.
Write the equation of the line in slope-intercept form.
Answer:
y = 1/2x - 4
Step-by-step explanation:
The y-intercept is at -4 (counting by ones).
The slope would be 1/2, going up one time and to the right twice, plotting the point (2, -3).
you and 9 friends are playing a game of basketball. after the game is overall, everyone shakes hands. how many distinct handshakes took place if every player shook hands with everyone who played?
45 Distinct handshakes took place when every player shook hands with everyone who played.
To find out how many distinct handshakes took place if every player shook hands with everyone who played, we will
use the concept of combinations.
Identify the number of players involved, which is 10 (you plus 9 friends).
Use the formula for combinations: C(n, k) = n! / [k! × (n-k)!],
where n is the total number of players and k is the number of players in each handshake (which is 2).
Plug in the values: C(10, 2) = 10! / [2! × (10-2)!].
Calculate the factorial values: 10! = 3,628,800, 2! = 2, and 8! = 40,320.
Plug in the factorial values and calculate: C(10, 2) = 3,628,800 / (2 × 40,320) = 3,628,800 / 80,640 = 45.
So, 45 distinct handshakes took place when every player shook hands with everyone who played.
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Part B
Describe how you would design the selection of subjects for this study. Assume there are 1,000 total sales representatives in the Midwest and Northeast regions, with 500 in each region. About half of the representatives in each region were assigned the training, and half were not. Be sure to also describe any processes you would include in your study to contribute to the best design possible.
The method regarding to the sampling to pick the 200 sales representatives is to be make 20 groups of 10.
What is sampling?Sampling is the process of selecting a subset of individuals from a population to represent the whole. It is a technique used in research to gather data from a larger population. The goal of sampling is to reduce the cost, time, and effort required to collect data from a large population. Sampling allows researchers to get a better understanding of the population by being able to study a smaller, more representative group of individuals. Sampling also allows researchers to make more accurate generalizations about a population.
In this case, the best way for the sales directors to including 200 sales representatives, with equal Numbers from each region is simply to make 20 groups of 10.
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Complete questions as follows-
Suppose there are 1,000 total sales representatives in the Midwest and Northeast regions, with 500 sales reps in each
region. Describe the best way for the sales director to include 200 sales representatives, with an equal number from each
region and an equal number in each group, while yielding valid conclusions in the study.
Type your response in the box.
The value of the digit five in 24,513 is how many times the value of the five in 357
The value of the digit 5 in 24,513 is 1,000 times the value of the digit 5 in 357.
In the number 357, the digit 5 is in the ones area, which means that its value is just 5. We can write this number as 5 x 10^0, where 10 is the base of our number system, and the exponent 0 represents the ones area.
Now, to find out how many times the value of the digit 5 in 357 is compared to the value of the digit 5 in 24,513, we need to divide the value of the digit 5 in 24,513 by the value of the digit 5 in 357.
We have:
Value of 5 in 24,513 = 5 x 10³
Value of 5 in 357 = 5 x 10⁰
So,
Value of 5 in 24,513 ÷ Value of 5 in 357 = (5 x 10³) ÷ (5 x 10⁰)
We can simplify this expression by dividing 5 by 5, which gives us:
(5 x 10³) ÷ (5 x 10⁰) = 10³ = 1000
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Find the volume of each prism below and show your work
Number 5 and 6
1. The volume of the prism is 950.4m³
2. The volume of the prism is 16110m³
What is volume of a prism?A prism is a solid shape that is bound on all its sides by plane faces. The volume of a prism is expressed as;
V = base area × height.
1. Volume of prism = base area × height
base area = l×w
= 11×16
= 176m²
height = 5.4m
v = 176 × 5.4
= 950.4 m³
2. Volume of the prism = base area × height
base area = 25×36 = 900m²
height = 17.9m
Volume = 900 × 17.9m
= 16110 m³
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a humanities professor assigns letter grades on a test according to the following scheme. a: top 8% of scores b: scores below the top 8% and above the bottom 58% c: scores below the top 42% and above the bottom 22% d: scores below the top 78% and above the bottom 7% f: bottom 7% of scores scores on the test are normally distributed with a mean of 77.1 and a standard deviation of 7.4 . find the minimum score required for an a grade. round your answer to the nearest whole number, if necessary.
The minimum score required for an A grade is approximately 87 when the standard deviation is 7.4 and the mean is 77.1
What is the standard deviation?The standard deviation is a measure of the amount of variation or dispersion in a set of data. It measures how much the individual data points deviate or differ from the mean or average of the data set.
Mathematically, the standard deviation is the square root of the variance, which is calculated by taking the average of the squared differences of each data point from the mean. The formula for the standard deviation is:
σ = sqrt(Σ(x - μ)^2 / n)
where σ is the standard deviation, x is a data point, μ is the mean, and n is the number of data points.
According to the given informationFirst, we need to find the z-score corresponding to a score that is at the 92nd percentile (the top 8%). We can use the inverse normal distribution function (also known as the probit function) to do this:
invNorm(0.92) ≈ 1.41
This means that a score at the 92nd percentile corresponds to a z-score of approximately 1.41.
Next, we need to convert this z-score to a raw score on the test. We can do this using the formula:
z = (x - μ) / σ
where z is the z-score, x is the raw score, μ is the mean, and σ is the standard deviation.
Rearranging this formula to solve for x, we get:
x = z*σ + μ
Substituting the values we have, we get:
x = 1.41*7.4 + 77.1 ≈ 87.4
Therefore, the minimum score required for an A grade is approximately 87, rounded to the nearest whole number.
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Evaluate the expression shown below and write your answer as a fraction in simplest form (11/9) + (5/9)
Answer:
16/9
Step-by-step explanation:
(11/9) + (5/9) = 11/9 + 5/9 = 16/9
16/9 is already in simplest form, so the answer is 16/9
Answer: (11/9) + (5/9) = (11 + 5)/9 = 16/9
Step-by-step explanation:
We have to find a common denominator for the two fractions. Since both fractions have a denominator of 9, we can add the numerators directly.
Add the numerators of the two fractions: 11 + 5 = 16.
Write the sum over the common denominator: 16/9.
Simplify the fraction if possible. In this case, it is already in simplest form.
Therefore, (11/9) + (5/9) = 16/9.
A doctor collected data to determine the association between age of an infant and its weight. She modeled the
equation y - 1. 25x + 7 for the line of best fit The independent variable, x, is time in months and the dependent
variable, y, is weight in pounds. What does the y-intercept mean in this context?
A)
The infant's starting weight is 7 pounds.
B)
The infant's starting weight is 1. 25 pounds.
The infant's weight increases by an additional 7 pounds for each month,
D)
The infant's weight increases by an additional 1. 25 pounds for each month.
The y-intercept in the given equation ( y = -1.25x + 7) predict the infant's weight to be 7 pounds. So, the correct option is option A - The infant's starting weight is 7 pounds.
Y-intercepts are when the line touches the y-axis. To find these, find the y when x = 0. The point for a y-intercept will look like (0,y) x-intercepts are when the line touches the x-axis.
y = mx + b
The y-intercept of the line of best fit is the value of y when x is equal to 0. In this case, the equation of the line of best fit is y = -1.25x + 7. Therefore, when x is equal to 0, we have:
y = -1.25(0) + 7 = 7
So, the y-intercept of the line of best fit is 7. This means that when the infant is born (i.e., at 0 months), the predicted weight is 7 pounds.
Therefore, option 'A', "The infant's starting weight is 7 pounds," is the correct answer.
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PLEASE HELP! WILL GIVE BRAINLYEST ANSWER
Answer: your right its 0,1
Step-by-step explanation:
(Compound interest)
$17,525 deposit, interest at 1/2% for 3 years; find interest earned.
so 0.5% rate
[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$17525\\ r=rate\to 0.5\%\to \frac{0.5}{100}\dotfill &0.005\\ t=years\dotfill &3 \end{cases} \\\\\\ I = (17525)(0.005)(3) \implies I \approx 262.88[/tex]
Pam is a hairdresser. Before her lunch break, she gave 2 haircuts and colored the hair of 1 client in 83 minutes. After lunch, she gave 1 haircut and colored the hair of 3 clients in 164 minutes. How long does it take for Pam to perform each type of service, assuming the amount of time doesn’t vary from client to client?
Pam takes 17 minutes for haircut and 49 minutes for hair coloring. The solution has been obtained by using the arithmetic operations.
What are arithmetic operations?
Using the four basic operations, also referred to as "arithmetic operations," all real numbers may be explained. In mathematics, operations such as division, multiplication, addition, and subtraction come before operations such as quotient, product, sum, and difference.
Let x be the time taken for haircut and y be for hair coloring.
Now, she gave 2 haircuts and colored the hair of 1 client in 83 minutes.
So, using addition operation, we get
2x + y = 83 ...(1)
Similarly, she gave 1 haircut and colored the hair of 3 clients in 164 minutes.
So, we get
x + 3y = 164 ...(2)
From (1), we get
y = 83 - 2x
On substituting this in (2), we get
⇒ x + 3 * (83 - 2x) = 164
⇒ x + 249 - 6x = 164
⇒ 249 - 5x = 164
⇒ 5x = 85
⇒ x = 17
So,
⇒ y = 83 - 2 (17)
⇒ y = 83 - 34
⇒ y = 49
Hence, Pam takes 17 minutes for haircut and 49 minutes for hair coloring.
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What is a horizontal asymptote?
A horizontal line that a function's graph appears to coincide with but does not actually do so is said to be its horizontal asymptote.
What is a function?
A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.
A horizontal line that a function's graph appears to coincide with but does not actually do so is said to be its horizontal asymptote. The end behaviour of the function is determined using the horizontal asymptote.
Hence, this is what is known as horizontal asymptote.
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A random sample of 100 middle schoolers were asked about their favorite sport. The following data was collected from the students.
Sport Basketball Baseball Soccer Tennis
Number of Students 17 12 27 44
Which of the following graphs correctly displays the data?
histogram with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled basketball going to a value of 17, the second bar labeled baseball going to a value of 12, the third bar labeled soccer going to a value of 27, and the fourth bar labeled tennis going to a value of 44
histogram with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled baseball going to a value of 17, the second bar labeled basketball going to a value of 12, the third bar labeled tennis going to a value of 27, and the fourth bar labeled soccer going to a value of 44
bar graph with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled basketball going to a value of 17, the second bar labeled baseball going to a value of 12, the third bar labeled soccer going to a value of 27, and the fourth bar labeled tennis going to a value of 44
bar graph with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled baseball going to a value of 17, the second bar labeled basketball going to a value of 12, the third bar labeled tennis going to a value of 27, and the fourth bar labeled soccer going to a value of 44
Question 8(Multiple Choice Worth 2 points)
Favorite sport bar graph with the words "favorite sport," "sport" on the x-axis, and "y-axis" labelled. The correct graph to display the data is: C.
Why is a Bar Graph appropriate?The data gathered from the middle school kids is best represented by a bar graph since it enables us to compare distinct categories (in this case, sports) and their related frequencies (number of pupils).
The information in this case is as follows:
Basketball: 17 students
Baseball: 12 students
Soccer: 27 students
Tennis: 44 students
To identify the subject of the data being depicted, the label "Favorite Sport" is used in the appropriate bar graph.
Basketball, baseball, soccer, and tennis are listed in separate, unique categories along the "Sport" axis. The frequency or count of students who selected each sport as their favourite is shown on the "Number of Students" y-axis.
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Graph attached below,
Given the following exponential function,identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease. Y=640(0.23)^x
the exponential function [tex]Y=640(0.23)^x[/tex]represents a decay of 77% per unit increase in x.
What is exponential?
The exponential is an example of a mathematical function that is useful in determining if something is increasing or decreasing exponentially is the exponential function. As implied by its name, an exponential function uses exponents. But take note that an exponential function does not have a variable as its exponent and a constant as its base (if a function has a variable as the base and a constant as the exponent then it is a power function but not an exponential function).
To determine the percentage rate of decrease, we can find the difference between the initial value (640) and the final value (when x = 1) and express it as a percentage of the initial value.
When x = 1, we have:
Y = 640(0.23)^1 = 147.2
The difference between the initial value (640) and the final value (147.2) is:
640 - 147.2 = 492.8
To express this as a percentage of the initial value, we can use the formula:
percentage change = (difference / initial value) * 100%
So, the percentage rate of decrease is:
percentage change = (492.8 / 640) * 100% = 77%
Therefore, the exponential function Y=640(0.23)^x represents a decay of 77% per unit increase in x.
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null hypothesis researchers want to investigate the relationship between caffeinated coffee consumption and the risk of depression in women. which statement is not appropriate for our null hypothesis? the distribution of caffeinated coffee consumptions for different levels of depression status are the same. the levels of depression status and caffeinated coffee consumptions are equally likely. the distribution of depression status for different levels of caffeinated coffee consumptions are the same. the depression status and caffeinated coffee consumptions are independent.
The appropriate statement for the null hypothesis is "the depression status and caffeinated coffee consumptions are independent."
How to find which statement is appropriate for null hypothesis?The statement that is not appropriate for the null hypothesis according to hypothesis testing is "the levels of depression status and caffeinated coffee consumptions are equally likely."
This statement implies that there is an equal chance of having different levels of depression status and different levels of caffeinated coffee consumption, which is not a suitable assumption for the null hypothesis.
The null hypothesis should state that there is no significant relationship between the two variables, and the distribution of one variable does not depend on the distribution of the other variable.
Therefore, the appropriate statement for the null hypothesis is "the depression status and caffeinated coffee consumptions are independent."
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Estimate 4 2/5 − 1 7/9 by rounding to the nearest half
Answer:
118/45
Step-by-step explanation:
4 2/5 − 1 7/9
4 2/5 = 22/5
1 7/9 = 16/9
22/5 - 16/9 = 198/45 - 80/45 = 118/45
So, the answer is 118/45
i have a new hobby - a saltwater fish tank that will contain mostly live corals (called a reef tank). i am currently in the planning stage and am gathering knowledge to give me the best chance of success with my tank. as part of the planning stage, i reached out to 700 experienced central florida reefers (people who currently have a reef tank) and asked them to provide the following information: size of the tank (in gallons), type of lighting used (florescent, led, hybrid, or other), and how long (in years) they have been in the hobby. part of the analysis involves trying to estimate the proportion of all central florida reefers who use led lighting. a 95% confidence interval was constructed to be: (.648, .752) which of the following practical interpretations is correct? group of answer choices in repeated sampling, 95% of the intervals created will contain the population mean. we are 95% confident that the proportion of all central florida reefers who use led lighting falls between .648 and .752. we are 95% confident that the proportion of the sampled central florida reefers who use led lighting falls between .648 and .752. all central florida reefers use led lighting 95% of the time.
We are 95% confident that the proportion of all central Florida reefers who use LED lighting falls between .648 and .752.
The correct practical interpretation is: "We are 95% confident that the proportion of all central Florida reefers who use led lighting falls between .648 and .752."
This means that if we were to take multiple random samples of 700 experienced central Florida reefers, 95% of the intervals created would contain the true population proportion of reefers who use LED lighting.
So, based on this sample, we can say with 95% confidence that the true proportion of all central Florida reefers who use LED lighting is somewhere between .648 and .752.
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We are 95% confident that the proportion of all central Florida reefers who use LED lighting falls between .648 and .752 from mean.
The correct practical interpretation is: "We are 95% confident that the proportion of all central Florida reefers who use LED lighting falls between .648 and .752." This means that based on the sample of 700 experienced reefers, we can estimate with 95% confidence that the true proportion of all reefers in central Florida who use LED lighting is likely to be between .648 and .752.
This confidence interval was constructed using sampling techniques, and in repeated sampling, 95% of the intervals created would contain the population mean.
We are 95% confident that the proportion of all central Florida reefers who use LED lighting falls between .648 and .752.
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A tidal wave caused by an earthquake off the Alaskan coast begins running toward Carmel, California. The water first goes down from its normal level, and then rises an equal distance above its normal level; the water then returns to normal. Assume that the depth of the water varies sinusoidally with time as the wave passes. Suppose the wave, with a period of 20 minutes and an amplitude of 12 meters, approaches a dock in Carmel where the normal depth is 8 meters.
y = 6 sin [(π/10)t] + 8; equation gives us the depth of the water at the dock as a function of time elapsed since the wave started passing the dock.
Define the sinusoidal function?A sinusoidal function is a mathematical function that oscillates or fluctuates in a periodic manner, following a sine or cosine curve.
If the wave approaches a dock in Carmel where the normal depth is 8 meters and varies sinusoidal with time, then we can use the equation for a sinusoidal function:
y = A sin (ωt + φ) + C
where: A is the amplitude of the wave, which is given as 12 meters
ω is the angular frequency, which can be calculated as 2π / T, where T is the period of the wave (20 minutes in this case)
t is the time elapsed since the wave started passing the dock
φ is the phase angle, which we can assume to be 0 since we are not given any information about it
C is the vertical displacement of the wave from the normal depth, which is 8 meters in this case
putting the given values into the equation,
y = 12 sin [(2π/20)t] + 8
Simplifying this equation,
y = 6 sin [(π/10)t] + 8
This equation gives us the depth of the water at the dock as a function of time elapsed since the wave started passing the dock.
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A seed company planted a floral mosaic of a national flag the perimeter of the flag is 2220 feet determine the flags width and length if the length is 450 feet greater than the width
A seed company planted a floral mosaic of a national flag the perimeter of the flag is 2220 feet determine the flags width and length if the length is 450 feet greater than the width
The width of the flag is 330 feet and the length is 780 feet.
What is width?.
Width refers to the measurement or extent of something from side to side, typically in reference to its distance between its two opposite edges or boundaries. It is one of the two dimensions of a two-dimensional object or the distance between opposite sides of a three-dimensional object. In other words, width is the measurement of the distance between the left and right edges of an object or shap
Let's assume that the width of the flag is x feet.
As per the given information, the length of the flag is 450 feet greater than the width. Therefore, the length of the flag will be:
length = x + 450 feet
The perimeter of the flag is given as 2220 feet.
Perimeter of the flag = 2(length + width)
Substituting the values of length and width in the above equation, we get:
2220 = 2[(x + 450) + x]
Simplifying the above equation, we get:
2220 = 4x + 900
Subtracting 900 from both sides of the equation, we get:
1320 = 4x
Dividing both sides of the equation by 4, we get:
x = 330
Therefore, the width of the flag is 330 feet.
Using the length equation we derived earlier, we can find the length of the flag:
length = x + 450 = 330 + 450 = 780 feet
So the width of the flag is 330 feet and the length is 780 feet.
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Write and graph an inequality for the situation.
12. A cruise ship can carry at most 3500 passengers.
An inequality for this situation "A cruise ship can carry at most 3500 passengers." is x ≤ 3,500.
A graph of the inequality x ≤ 3,500 is shown in the image attached below.
What is an inequality?
In Mathematics and Geometry, an inequality simply refers to a mathematical relation that is typically used for comparing two (2) or more numerical data and variables in an algebraic equation based on any of the inequality symbols;
Less than (<).Greater than (>).Greater than or equal to (≥).Less than or equal to (≤).Note: At most simply refers to less than or equal to (≤) in Mathematics.
Since the cruise ship can only carry at most 3500 passengers, an inequality that models this situation is given by;
x ≤ 3,500
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