The maximum error of the given confidence interval is 0.815, meaning that the true mean is likely to be within 0.815 of the known mean of 9.375.
Maximum Error = (Upper Limit - Lower Limit) / 2
In this case, we have a confidence interval from 8.56 to 10.19 and the mean is known to be 9.375. To calculate the maximum error, we first need to subtract the lower limit (8.56) from the upper limit (10.19), which gives us a difference of 1.63. We then divide this number by 2, which gives us a maximum error of 0.815. This means that the maximum error of the given confidence interval is 0.815. This means that the true mean is likely to be within 0.815 of the known mean of 9.375.
The maximum error of the given confidence interval is 0.815, meaning that the true mean is likely to be within 0.815 of the known mean of 9.375.
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6 is subtracted from the square of a number.
Answer:
x^2 - 6
Step-by-step explanation:
square of a number: x^2
6 is subtracted: -6
what is the slope of the line that passes through the points (-4,-10) and (-7,-19)?
Answer:
y-(-10)=3(x-(-4)
Step-by-step explanation:
Using slope point formula (y-y1=m(x-x1)) we can use the given coordinates to fill in the equation.
y1=-10 & x1= -4
Put those into the equation: y-(-10)= m(x-(-4))
Now we need to find the slope using slope formula y2-y1/x2-x1: -19-(-10)/-7-(-4)= -9/-3
Simplify the slope: -9/-3= 3
End up with your final equation: y-(-10)=3(x-(-4))
-Hope this helped
Please!please help! I don’t have good internet so I go to my aunts house (I’m here right now to do homework) and I’m having so much trouble I’m trying to hurry up so my mom and I can go to sleep. Here are the problems (8th grade)
Image 1: A.
Image 2: B
About function in mathThe definition of a function in mathematics is the confluence of each member of a set (named a domain), to members of another set (named a codomain). The function in question is different from the definition of function in a general sense.
In functions, there are several important terms, including:
Domain, namely the origin of the function f is denoted by D f. The codomain is the co-domain of the function f denoted by K f. Range is the result area which is a subset of the codomain. The function range f is denoted by R f.Learn more about function in math at
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the first box has two white balls. the second box has two black balls. the third box has a white and a black ball. all boxes are labeled but all labels are wrong! you are allowed to open one box, pick one ball at random, see its color and put it back into the box without seeing the color of the other ball. how many such operations are necessary to correctly label the boxes?
To correctly label the boxes, you need to perform two operations. In the first operation, you can choose to open any of the three boxes. Regardless of which box you open, you will be able to determine the color of one ball.
Then, you can use that information to deduce which of the other two boxes must contain two balls of the same color and which must contain one ball of each color. In the second operation, you can choose to open the box which contains two balls of the same color. The color of the ball you take out will tell you the correct label of the box. By performing these two operations, you can correctly label the boxes with only two ball selections.
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which variable is the dependent variable--the variable that responded to or depended on the treatment, and was measured by the researchers?
The dependent variable is the variable that responds to or depends on the treatment and is measured by the researchers.
The dependent variable is also known as the outcome variable, response variable, or dependent measure. The dependent variable is the result that the researchers are interested in observing and understanding the relationship with the independent variable, which is the variable that the researchers manipulate or control in the study. The dependent variable is what the researchers are trying to explain or predict based on the independent variable.
In other words, the value of the dependent variable is dependent on the independent variable.
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zelma is 18 years older than her son. she was three times older as old as he was last year. how old are they now?
Zelma is 28 years old and her son is 10 years old. We brought this conclusion with the help of algebra.
Let x = son's age now
Then, x+18 = Zelma's age now
x-1 = son's age one year ago
x+17 = Zelma's age one year ago
x+17 = 3(x-1)
x+17 = 3x-3
2x = 20
x = 10
Algebra is the study of variables and the rules for manipulating these variables in formulas; it is a unifying thread of almost all of mathematics. Elementary algebra deals with the manipulation of variables as if they were numbers and is therefore essential in all applications of mathematics.
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AC = 3x + 3, AB= -1 + 2x, and BC = 11.
The value of x is 7.
What are Collinear Points?Collinear points are the points which are formed on a straight line, whether they are close or far away.
Figure representing the question is given below.
From the figure, we have,
AB + BC = AC
(-1 + 2x) + (11) = 3x + 3
2x + 10 = 3x + 3
Like terms adding together,
2x - 3x = 3 - 10
-x = -7
x = 7
Hence the value of x is 7.
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following a dramatic drop of 500 points in the dow jones industrial average in september 1998, a poll conducted for the associated press found that 92% of those polled said that a year from now their family financial situation will be as good as it is today or better. the number 92% is a a. statistic b. sample c. parameter d. population e. none of the above.
A statistic is a numerical summary of a sample of data used to make inferences about a population. So, option A is the answer.
A statistic is a numerical value calculated from a sample of data. In the case of the poll, 92% represents the percentage of people in the sample who reported that their family's financial situation would be as good or better in a year's time. The statistic summarizes the data collected from the sample, and is used to make inferences about the population from which the sample was drawn.
Statistics play a crucial role in many fields, including economics, business, medicine, and social sciences. By analyzing a sample of data, rather than the entire population, statisticians can draw inferences and make predictions about the population.
For example, in the case of the poll mentioned in the question, the 92% statistic provides an estimate of the proportion of the population who believe their financial situation will be as good or better in a year's time. While the sample is not the entire population, the statistic provides valuable information about the population and can be used to make decisions and plan for the future.
It's important to note that statistics are only as good as the sample from which they are derived. The sample should be representative of the population, and the method of sampling should be carefully chosen to ensure that the sample is representative. Otherwise, the statistic may not accurately reflect the population, and any inferences or predictions made based on the statistic may be incorrect.
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three numbers in an arithmetic progression have a sum of 39 and a product of 2145. find the smallest number of that progression.
Thus, the three terms of an arithmetic progression are (8, 13, and 18) or, (9, 13, and 17).
Let three terms of an arithmetic progression = (a - d), a, ( a + d)
According to the question:
The sum of three terms of an arithmetic progression = 39
∴ (a - d) + a + ( a + d) = 39
⇒ 3a = 39
⇒ a = 13
Also, The product of three terms of an arithmetic progression = 2145
∴ (a - d)a( a + d) = 2145
⇒ a(a^2 - d^2) = 2145
Put a = 13, and we get
d=4
Three terms of an arithmetic progression = (13 - 4), 13 and ( 13 + 4)
= 9,13,17
Put a = 13 and d = 4
Thus, the three terms of an arithmetic progression are (8, 13, and 18) or, (9, 13, and 17).
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Mark is a carpenter. He is trying to decide how much money to charge for his
next job. To do the job, he will need to buy supplies that will cost $275. He
will also need to rent a machine that will cost $125. He wants to charge
enough to have $150 profit (money left over for himself). How much money
should Mark charge for the job?
The money to charge for his next job, Mark should charge $550 to earn a profit from the job.
What are arithmetic operations?A subject of mathematics known as arithmetic operations deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and division are included.
Given that Mark is trying to decide how much money to charge for his next job,
cost of supplies = $275
cost of machine = $125
total expenditure = $275 + $125
total expenditure = $400
profit Mark wants = $150
minimum amount he should charge to get the profit = $400 + $150
minimum amount he should charge to get the profit = $550
Hence he should charge at least $550.
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Can somebody please help me
[tex]4-\cfrac{2}{3}b+\cfrac{1}{4}a~~ + ~~\cfrac{1}{2}a+\cfrac{1}{6}b-7\implies 4-\cfrac{2b}{3}+\cfrac{a}{4}~~ + ~~\cfrac{a}{2}+\cfrac{b}{6}-7 \\\\\\ \left( \cfrac{a}{4}+\cfrac{a}{2} \right)+\left(-\cfrac{2b}{3} + \cfrac{b}{6}\right)+(4-7)\implies \left( \cfrac{a}{4}+\cfrac{a}{2} \right)+\left( \cfrac{b}{6}-\cfrac{2b}{3} \right)+(4-7)[/tex]
[tex]\left( \cfrac{(1)a+(2)a}{\underset{\textit{using this LCD}}{4}} \right)+\left( \cfrac{(1)b-(2)2b}{\underset{\textit{using this LCD}}{6}} \right)+(-3) \\\\\\ \left( \cfrac{a+2a}{4} \right)+\left( \cfrac{b-4b}{6} \right)-3\implies \left( \cfrac{3a}{4} \right)+\left( \cfrac{-3b}{6} \right)-3 \\\\[-0.35em] ~\dotfill\\\\ ~\hfill {\Large \begin{array}{llll} \cfrac{3}{4}a-\cfrac{1}{2}b-3 \end{array}}~\hfill[/tex]
Do the following lengths form a right triangle?
The lengths form a right triangle are Triangle 2,3 and 4.
Side lengths a , b , c form a right triangle if, and only if, they satisfy a² + b² = c² . We say these numbers form a Pythagorean triple.
About Pythagorean theoremThe Pythagorean theorem reads:
"In a right triangle, the square of the hypotenuse equals the sum of the squares of the other sides."
Thus the three sides of a right triangle have an interrelated relationship.
This theorem has two mandatory properties, namely it only applies to right triangles and you must know at least two sides first to be able to determine the other side.
While the purpose of this theory is basically to determine the length of one side of a right triangle. Whereas for a right triangle it is actually very easy because one of the characteristics of a right triangle is that it has one of the 90° angles.
However, this theory can also be used to calculate the length of the diagonal of a square or beam and cube which also looks like a right triangle.
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9 units to the left, 7 units up
The Equation of parabola is .y = a(x + 9)² + 7
What is Equation of Parabola?The general equation of a parabola is: y = a(x – h)² + k where (h,k) denotes the vertex. The standard equation of a regular parabola is y² = 4ax.
Given:
The general equation of a parabola is given by
y = a(x – h)² + k
Here (h, k) denotes the vertex.
We have 9 units to the left which is represented by '+9' and 7 units up which is represented by '+7'
So, the Equation of parabola is
y = a(x – h)²
y = a(x + 9)² + 7
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which of the following is most likely a parameter as opposed to a statistic? group of answer choices the average score of the first five employees who completed an assignment. every third person to arrive in a bank. respondents to a newspaper survey. registered voters in a county.
The following is most likely a parameter as opposed to a statistic is registered voters in a county.
A parameter in statistics is any measurable number of a statistical population that summarises or describes some aspect of the population, as opposed to its typical application in mathematics, such as a mean or a standard deviation. A limited collection of factors that perfectly characterise a population and may be used to create a probability distribution for the purposes of taking samples from that population can be assessed if it exactly follows a known and defined distribution, such as the normal distribution.
The family is a parameterized family if the index is also a parameter of its members. The normal distributions, Poisson distributions, binomial distributions, and exponential family of distributions are examples of parameterized families of distributions.
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Help with thisss pleasseeeee
Answer:
y[tex]\geq[/tex]2x-3
Step-by-step explanation:
y intersect is -3
slop is 2, which eliminates option 2 and 4
when plugging in the point 2,2 in the equation- its a true solution for option 3.
y[tex]\geq[/tex]2x-3
2[tex]\geq[/tex]4-3
2[tex]\geq[/tex]1 True.
The graph of F(x), shown below, resembles the graph of G(x) = x^2, but it has been changed somewhat. Which of the following could be the equation of F(x)?
A possible equation for F(x) is given as follows:
A. F(x) = 0.4x² + 1.
What is a translation?A translation happens when either a figure or a function are moved horizontally or vertically.
The four translation rules for functions are given as follows:
Left a units: f(x + a).Right a units: f(x - a).Up a units: f(x) + a.Down a units: f(x) - a.From this graph, function f(x) is moved up one unit, hence:
F(x) = ax² + 1.
The function f(x) was also vertically compressed, meaning that a < 1, hence:
F(x) = 0.4x² + 1.
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A 20-minute TV program consists of two commercials, each 13 over 4 minutes long, and three equal-length entertainment segments. How long is each entertainment segment? Enter your answer as a decimal. ( read the question in the picture instead its easier to understand)
Answer:
6.0 min
Step-by-step explanation:
20/3=6 remain 2 = 2 x 1min commercial
6 mins long
consider the statistical experiment of randomly choosing one of the great lakes from a map. what is the sample space of this statistical experiment?
The sample space of the statistical experiment of randomly choosing one of the great lakes from a map is the set of all possible outcomes, which are the five great lakes: Superior, Huron, Erie, Ontario, and Michigan.
A random experiment's sample space S is defined as the set of all potential experiment results. The outcomes of a random experiment, also known as sample points, are mutually exclusive (i.e., they cannot occur simultaneously).
A random experiment's sample space is the collection of all conceivable results. A random experiment's related event is a subset of the sample space. Any outcome's probability is a number between 0 and 1. All of the outcomes have a probability of one.
The sign "S" is used to indicate the sample space. An experiment's events are the subset of conceivable outcomes. Depending on the experiment, a sample area may contain a variety of outcomes.
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(2x+5)
(4y -1)
(3x-33)
Answer: (38, 25) or x = 38 and y = 25
Step-by-step explanation:
We will use the measurement of a straight line and vertical angles to help us solve.
First, vertical angles are congruent. We will set up an equation and use inverse operations to isolate the x variable.
Given:
(3x - 33) = (2x + 5)
Add 33 and subtract 2x from both sides of the equation:
x = 38
Next, we know a straight line is equal to 180 degrees. We can substitute the value we found above for x. Then we will simplify and use inverse operations to isolate the y variable.
Given:
(2x + 5) + (4y - 1) = 180
Substitute for x:
(2(38) + 5) + (4y - 1) = 180
Simplify:
81 + (4y - 1) = 180
Subtract 80 (81 - 1) from both sides of the equation:
4y = 100
Divide both sides of the equation by 4:
y = 25
solve the problem. the average gas mileage of the top selling mini-vans for each u. s. car manufacturer is an example of what type of variable?
The average gas mileage of the mini-vans for each u. s. car manufacturer is an example of a quantitative variable. A quantitative variable is a type of variable that measures a numerical value.
The average gas mileage of the top-seller mini-vans for each U.S. car manufacturer is a numerical value, as it is measuring the average number of miles a mini-van can travel on one gallon of gas. This numerical value can be used to compare the performance of different mini-vans from different manufacturers.
Quantitative variables are usually expressed as numerical values and are usually measured on an interval or ratio scale. gas mileage for the mini-vans for each U.S. car manufacturer is an example of a quantitative variable because it is a numerical value that can be used to compare the performance of different mini-vans from different manufacturers.
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Please help! so stuck on this! (Find the standard form of the equation and explain)
Answer:
The standard form of a linear equation is Ax+By=C. To change an equation written in slope-intercept form (y=mx+b) to standard form, you must get the x and y on the same side of the equal sign and the constant on the other side.
Step-by-step explanation:
13. the mean score of a college entrance test is 500; the standard deviation is 75. the scores are normally distributed. what percent of the students scored below 320? * a. about 50.82% b. about 34.13% c. about 7.86% d. about 0.82%
The percentage of students who scored below 320 is about 0.82%.
To find the percentage of students who scored below 320, we need to use the Z-score formula to find the Z-score for 320 and then use a Z-table to find the proportion of scores below 320.
Z = (320 - 500) / 75 = -3.73
Using a Z-table, we find that the proportion of scores below -3.73 is 0.0002. So, the proportion of scores above 320 is 1 - 0.0002 = 0.9998 or 99.98%.
Therefore, the percentage of students who scored below 320 is 100% - 99.98% = 1.02%. Rounded to the nearest hundredth, this is about 0.82%.
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What is the solution to this inequality?
4x + 2 ≤ -14 or 3x − 5 > 16
A.
x ≤ -4 or x > 7
B.
x ≤ -4
C.
x ≤ -5 or x > 8
D.
-4 ≤ x < 7
Answer:
A. x ≤ -4 or x > 7
Step-by-step explanation:
4x + 2 ≤ -14
Subtract 2 from both sides:
4x ≤ -16
Divide both sides by 4:
[x ≤ -4]
3x - 5 > 16
Add 5 to both sides:
3x > 21
Divide 3 from both sides:
[x > 7]
find the value of angle x
Answer:
72⁰
Step-by-step explanation:
180-36= 144 (angles in a triangle=180)
144/2=72 (parallel lines are equal)
For what values of a and b is the quadrilateral a parallelogram?
Answer:
a = 3, b = 10
Step-by-step explanation:
Opposite sides of a parallelogram are equal, so:
3a + 1 = b
5a = 2b - 5
Substituting 3a + 1 = b in the second equation,
5a = 2(3a + 1) - 5
= 6a + 2 -5
= 6a -3
6a - 5a = 3
So, a = 3
Now, 3a + 1 = b
So, b = 3(3) + 1
= 9 + 1
= 10
To make his special energy drink Jerome uses 8 cups of water and 3 cups of drink mix. What is the ratio of drink mix to mixed energy drink?
The ratio of drink mix to mixed energy drink is 3:11
8 cups water
3 cups drink mix
We already know the amount of drink mix because the problem gives it to us (3 cups)
As for the amount of mixed energy drink we have to add the two values to get the total.
8 + 3 = 11
Hence the ratio of drink mix to mixed energy drink is 3:11
hope that helps :)
you have invented a drug that you think will relieve anxiety and help students score better on exams. you want to test the drug on a group of statistics students who are about to take their final exam. you will give some students your new drug and others a dummy pill. why?
In order to test the efficacy of the drug, some students are provided with the actual drug whereas others are provided with a dummy version of the drug.
To test the efficacy of the drug, you want to compare the exam scores of the students who took the drug to those who took the placebo. This is known as a double-blind, randomized controlled trial and it is considered the gold standard for evaluating the effectiveness of a treatment. By comparing the scores of the students who took the drug to those who took the placebo, you can determine whether the drug is actually improving exam performance or if the improvement is due to other factors such as placebo effect or chance.
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suppose the 99% confidence interval for the mean sat scores of applicants at a business college is given by [1,692, 1,842]. this confidence interval uses the sample mean and the sample standard deviation based on 25 observations. what are the sample mean and the sample standard deviation used when computing the interval?
The upper bound is 1842 and lower bound is 1692. By using these boundaries and t-table, the sample mean is 1767 and sample standard deviation = 133.98.
Here, the two boundaries are 1692 and 1842.
Mean = (1692+1842) /2 = 1767
Here the degree of freedom, df = (n-1) = 25-1 =24
Margin of error = (1842-1692)/2 = 75
Confidence level = 99%
From the t table, value of T with confidence level 99% and df= 24 is 2.80
The equation for margin of error is M = Ts/√n
M= 75 , T= 2.80, n =25
75 = (2.80 × s) / √25
75 = 2.80s/ 5
s = (75×5)/2.80 = 133.928 = 133.93
So the sample mean is 1767 and the standard deviation is 133.93.
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8/12 = y/30 using proportion how can I solve this?
Answer:
y = 20
Step-by-step explanation:
[tex]\frac{8}{12}[/tex] = [tex]\frac{y}{30}[/tex] ( cross- multiply )
12y = 8 × 30 = 240 ( divide both sides by 12 )
y = 20
becky and amber want to rent bikes to ride while they are vacationing at the beach. beach bikes company charges $10 bike fee and $8 per hour. bikes unlimited charges $5 per hour and a $19 bike fee. after how many hours will the two companies cost the same amount?
The time when the two companies would cost the same amount is after 3 hours.
How to determine the number of hours when the two companies cost the same amount?Based on the information provided above, beach bikes company charges $10 bike fee and $8 per hour. Therefore, the total cost, y, can be represented by this equation:
y = 8x + 10 .......equation 1.
where:
x represents the number of hours.
For the second option, bikes unlimited charges $5 per hour and a $19 bike fee. Therefore, the total cost, y, can be represented by this equation:
y = 5x + 19 ....equation 1.
By equating equation 1 and equation 2, we have the following:
8x + 10 = 5x + 19
8x - 5x = 19 - 10
3x = 9
x = 9/3
x = 3 hours.
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