Answer:
h(x)=2x+7
h(8)=2(8)+7
h(8)=16+7
h(8)=23
Step-by-step explanation:
Put 8 in h(x) and simplify the equation.
In other words, put 8 wherever you see x and simplify the equation.
A study was conducted on the educational level of patients with AIDS, it was asume that
with ten years of education will be in group A, between 10 and 20 group B and between 20
group C. After the analysis it was realized that group A had 100 persons while group B and C had 30 persons
(a) If you decide to select based on proportion of 10% from each group how many patien
selected from each group. Show your calculation.
(b) What name can be given to the classified groups?
(c) What method of sampling was employed in the selection process?
1. State and explain the three major data collection techniques.
What is a variable?
What is a Parameter?
A variable is a characteristic or attribute that can take on different values. It is an observable and measurable property of an object or phenomenon, which can be used to describe and analyze it.
Parameters are used in inferential statistics to make conclusions about a population based on a sample of data.
(a) If you decide to select based on proportion of 10% from each group, the number of patients selected from each group would be: Group A = (10/100) x 100 = 10 patients Group B = (10/100) x 30 = 3 patients Group C = (10/100) x 30 = 3 patients.
(b) The classified groups can be named as follows: Group A = 10 years of education or less Group B = More than 10 years but less than or equal to 20 years of education Group C = More than 20 years of education.
(c) The sampling method employed in the selection process was stratified sampling. Stratified sampling is a type of probability sampling technique where the population is divided into homogeneous subgroups or strata, and the researcher selects a simple random sample from each subgroup or stratum.
The researcher chooses a proportion of participants from each subgroup to represent the population as a whole, which allows for more precise estimates of the population parameters than simple random sampling.
The sample is selected randomly from the stratified sample, which ensures that the sample is representative of the population.
A variable is a characteristic or attribute that can take on different values. It is an observable and measurable property of an object or phenomenon, which can be used to describe and analyze it.
Variables are used in research to test hypotheses, determine relationships between different phenomena, and make predictions about future outcomes.
A parameter is a numerical summary of a population, which describes a characteristic of the population. It is an unknown constant that can only be estimated from a sample of data.
Parameters are used in inferential statistics to make conclusions about a population based on a sample of data.
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Fizzy Waters promotes their alkaline water product for everyone on the basis that alkaline water is good for health as it neutralizes acids produced in the body. They boast having a mean alkalinity level of 50 mg/liter. Alkaline water has a higher pH level than regular drinking water and Fizzy Waters claims that its higher Hydrogen content provides better hydration than regular water. To test their claim, you contact Fizzy Waters and they allow you to collect samples from their manufacturing plant to test for yourself. You collect 100 random samples of their alkaline water and find that the mean and standard deviation are y = 32.2mg/liter and 14.4mg/liter. With 99% confidence, is there enough evidence to support their claim that the population mean exceeds 50 mg/liter?
Answer:
The mean of 50 mg/liter is not inside the 99% interval, so there is not enough evidence to support their claim.
Step-by-step explanation:
First we need to find the z-value for a confidence of 99%
The value of alpha for a 99% confidence is:
\(1-\alpha/2 = 0.99\)
\(\alpha/2 = 0.01\)
\(\alpha = 0.005\)
Looking in the z-table, we have z = 2.575.
Now we can find the standard error of the mean:
\(\sigma_{\bar{x} }= s_x/\sqrt{n}\)
\(\sigma_{\bar{x} }= 14.4/\sqrt{100}\)
\(\sigma_{\bar{x} }=1.44\)
Finding the 99% confidence interval, we have:
\(99\%\ interval = (\bar{x} - z\sigma_{\bar{x}}, \bar{x} + z\sigma_{\bar{x}})\)
\(99\%\ interval = (32.2 - 2.575*1.44, 32.2 + 2.575*1.44)\)
\(99\%\ interval = (28.492, 35.908)\)
The mean of 50 mg/liter is not inside the 99% interval, so there is not enough evidence to support their claim.
Hannah took a taxi from her house to the airport. The taxi company charged a pick-up fee of $1.90 plus $3.75 per mile. The total fare was $80.65, not including the tip. Write and solve an equation which can be used to determine mm, the number of miles in the taxi ride.
Answer: y=3.75x+1.9
Step-by-step explanation: the pick up fee would be the y-intercept and the per mile cost would be the slope.
The equation that can be used to determine the number of miles in the taxi ride is 1.90 + 3.75x = 80.65.
The number of miles traveled is 21 miles.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
We have,
Pick up fee charges = $1.90
Charges per mile = $3.75
Total fare = $80.65
The number of miles traveled = x
We can write an equation as:
1.90 + 3.75x = 80.65
The number of miles traveled:
1.90 + 3.75x = 80.65
Subtract 1.90 on both sides.
1.90 + 3.75x - 1.90 = 80.65 - 1.90
3.75x = 78.75
Divide both sides by 3.75.
x = 21.
Thus,
The equation that can be used to determine the number of miles in the taxi ride is 1.90 + 3.75x = 80.65.
The number of miles traveled is 21 miles.
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X +4> -10
..........
Answer:
X>-14
Step-by-step explanation:
Just had to solve it
Find the standard deviation of the given data rounded to the nearest hundredth, 147,141,120,124,128
Answer:
The correct answer is 10.30
Step-by-step explanation:
First, find the mean of the numbers by averaging them. Then, subtract the observation from the mean. Square them, then average them. Find the square root of this number and round to the nearest hundredth.
Answer:
10.30
Step-by-step explanation:
1. A right triangle LMN is given where: side MN = 8 side NL (the hypotenuse) =
10 What is the length of side LM?*
Step-by-step explanation:
\( \underline{ \underline{ \text{Given}}} : \)
Length of MN ( Base ) = 8 Length of NL ( Hypotenuse ) = 10\( \underline{ \underline{ \text{To \: find}}} : \)
Length of LM ( Perpendicular )\( \underline{ \underline{ \text{Using \: pythagoras \: theorem}}} : \)
\( \boxed{ \sf{ {Hypotenuse}^{2} = {Perpendicular}^{2} + {Base}^{2} }}\)
⤑ \( \sf{ Perpendicular = \sqrt{ {(Hypotenuse)}^{2} - {(Base)}^{2} } }\)
⤑ \( \sf{ \sqrt{ {(10)}^{2} - {(8)}^{2} } }\)
⤑ \( \sf{ \sqrt{100 - 64}} \)
⤑ \( \sf{ \sqrt{36}} \)
⤑ \( \boxed{ \sf{6\: units}}\)
\( \pink{ \boxed{ \boxed{ \tt{Our \: final \: answer : \boxed{ \underline { \tt{6 \: units}}}}}}}\)
Hope I helped ! ツ
Have a wonderful day / night ! ♡
▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁
4. Amy, Betty and Carol have 96 books altogether. Betty has 6 books less than Amy and Carol has half as many as Betty. How many books does each girl have?
The Amy has 42 books, Betty has 36 books, and Carol has 18 books.
Let's set up equations to represent the given information:
Let A represent the number of books Amy has.
Let B represent the number of books Betty has.
Let C represent the number of books Carol has.
Let's say Amy has x books.
Betty has 6 books less than Amy, so Betty has (x - 6) books.
Carol has half as many books as Betty, so Carol has (x - 6)/2 books.
According to the problem, the total number of books they have is 96.
So, we can write the equation:
x + (x - 6) + (x - 6)/2 = 96
To solve the equation, we can simplify it by multiplying through by 2 to remove the fraction:
2x + 2(x - 6) + (x - 6) = 192
2x + 2x - 12 + x - 6 = 192
5x - 18 = 192
5x = 210
x = 42
Amy has 42 books.
Betty has (42 - 6) = 36 books.
Carol has (36)/2 = 18 books.
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in the fruit bowl there are 12 bananas 8 apples and 4 oranges. do for every one orange there are ___ bananas
For every 1 orange in the fruit bowl there are three bananas.
According to the question,
We have the following information:
In the fruit bowl there are 12 bananas, 8 apples and 4 oranges.
Now, in order to find the number of bananas in this fruit bowl for 1 orange can be as written below:
4 oranges = 12 bananas
Now, to find the number of bananas for 1 orange, we will divide the total number of bananas by the number of oranges.
So, we have the following expression:
1 orange = 12/4 bananas
1 orange = 3 bananas
Hence, for every 1 orange in the fruit bowl there are three bananas.
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Determine the Domain and Range for promblems 1 and 2.
Answer:
Nvgjvfknh
Step-by-step explanation:
What is the solution and how do I solve?
20 + 4x+2 = 6x+8 --- By exterior angle
4x+22=6x+8
4x-6x=8-22
-2x=-14
x=7
Hope it helps
-1000 2/3 is not real fraction. True or false
True, While "-1000 2/3" is not a real fraction, it can be represented as the improper fraction -2998/3.
The statement "-1000 2/3 is not a real fraction" is true. A real fraction is a mathematical expression that represents a ratio of two real numbers. In a fraction, the numerator and denominator are both real numbers, and they can be positive, negative, or zero.
In the given statement, "-1000 2/3" is not a valid representation of a fraction. The presence of a space between "-1000" and "2/3" suggests that they are separate entities rather than being part of a single fraction.
To represent a mixed number (a whole number combined with a fraction), a space or a plus sign is typically used between the whole number and the fraction. For example, a valid representation of a mixed number would be "-1000 2/3" or "-1000 + 2/3". However, without the proper formatting, "-1000 2/3" is not considered a real fraction.
It's important to note that "-1000 2/3" can still be expressed as an improper fraction. To convert it into an improper fraction, we multiply the whole number (-1000) by the denominator of the fraction (3) and add the numerator (2). The result would be (-1000 * 3 + 2) / 3 = (-3000 + 2) / 3 = -2998/3.
In conclusion, while "-1000 2/3" is not a real fraction, it can be represented as the improper fraction -2998/3.
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Solve the following system of linear equations. If there is no solution, write DNE.
Answer:
x₁ = 179 , x₂ = 17 , x₃ = - 3
Step-by-step explanation:
x₁ - 9x₂ + 7x₃ = 5 → (1)
x₂ + 7x₃ = - 4 → (2)
x₃ = - 3
substitute x₃ = - 3 into (2) and solve for x₂
x₂ + 7(- 3) = - 4
x₂ - 21 = - 4 ( add 21 to both sides )
x₂ = 17
substitute x₂ = 17 and x₃ = - 3 into (1) and solve for x₁
x₁ - 9(17) + 7(- 3) = 5
x₁ - 153 - 21 = 5
x₁ - 174 = 5 ( add 174 to both sides )
x₁ = 179
solution is x₁ = 179 , x₂ = 17 , x₃ = - 3
The graph of f(x)=√x is reflected across the y-axis to create the graph of function g. How do the domains off and g
compare?
The domains off and g are both x ≥ 0.
The domains off and g are both all real numbers.
The domain of f is x ≥ 0, while the domain of g is x ≤ 0.
The domain of fis x ≤0, while the domain of g is x ≥ 0.
When the graph of f(x) = √x is reflected across the y-axis, the domain of g becomes x ≤ 0, while the domain of f remains x ≥ 0.
The correct statement is: The domain of f is x ≥ 0, while the domain of g is x ≤ 0.
The function f(x) = √x represents the square root function, which is defined for x values greater than or equal to 0 (x ≥ 0). This is because the square root of a negative number is not a real number.
When the graph of f(x) = √x is reflected across the y-axis, it creates the graph of function g. This reflection results in a reversal of the x-values. In other words, the positive x-values of f(x) become negative in g(x) and vice versa.
Since the domain of f is x ≥ 0, the reflection across the y-axis flips the domain, resulting in the domain of g being x ≤ 0. This means that the x-values of g are less than or equal to 0.
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15% of 9 is what number and how to solve using proportions
Answer:
Step-by-step explanation
Okay so lets solve step by step/
15% can be written as a fraction: 15/100
The of in the equation means multiplying.
15/100= 3/20
3/20*9= 270/20
27/2 is answer
The graph show the probability distribution of a random variable.What is the value of P(2≤X≤5)?0.300.350.400.45
The solution is : the value of P(2≤X≤5) is 0.50.
Here, we have,
given that,
The graph show the probability distribution of a random variable.
we know that,
The probability distribution of a random variable X is P(X = xi) = pi for x = xi and P(X = xi) = 0 for x ≠ xi. The range of probability distribution for all possible values of a random variable is from 0 to 1, i.e., 0 ≤ p(x) ≤ 1.
so, we have,
P(2≤X≤5)
=P(x=2)+ P(x=3)+ P(x=4)+ P(x=5)
= 0.2+ 0.1 +0.05+0.15
= 0.50
Hence, The solution is : the value of P(2≤X≤5) is 0.50.
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A group of 6 children and 6 adults are going to the zoo. Child tickets cost $10, and adult tickets cost $14. How much will the zoo tickets cost in all?
Answer:
i believe it'll cost 200 dollars
You are thinking of opening a small copy shop. It costs $5000 to rent a copier for a year, and it costs $0.03 per copy to operate the copier. Other fixed costs of running the store will amount to $400 per month. You plan to charge an average of $0.10 per copy, and the store will be open 365 days per year. Each copier can make up to 100,000 copies per year.
Required:
a. For one to five copiers rented and daily demands of 500, 1000, 1500, and 2000 copies per day, find annual profit. That is, find annual profit for each of these combinations of copiers rented and daily demand.
b. If you rent three copiers, what daily demand for copies will allow you to break even?
c. Graph profit as a function of the number of copiers for a daily demand of 500 copies; for a daily demand of 2000 copies. Interpret your graphs.
Answer and explanation:
A. To calculate annual profit, we find:
Total income - total cost for the 365 days in a year
Total income for different daily demands:
For 500 copies= 500×365×0.10=$18250
For 1000 copies= 1000×365×0.10=$36500
For 1500 copies=1500×365×0.10=$54750
For 2000 copies=2000×365×0.10=$73000
Total cost using five copiers= 400×12+5000×5+500000×0.03= $44800
Total cost using four copiers=
400×12+5000×5+400000×0.03=
$36800
Annual profit with daily demand of 2000 and five copiers available= $73000-$44800= $28200
B.
Pls help I’ll mark brainliest!!
Answer:
Answer is explained in the photo
Please help! Will mark Brainly!!
(Math)
Hello!
Let's solve the following:
Let's first do some conversions:
\(1\dfrac{2}{3} = \dfrac{5}{3}\)
\(-1=\dfrac{-3}{3}\)
Now, let's plug in all the values for a,b, and c: \(\hookrightarrow\dfrac{-|a+b|}{2-c} =\dfrac{-|\dfrac{5}{3}+(-\dfrac{3}{3}) | }{2-(-3)} =\dfrac{-|\dfrac{2}{3} | }{5}=\dfrac{-\dfrac{2}{3} }{5}=-\dfrac{2}{3} *\dfrac{1}{5} =-\dfrac{2}{15}\)
Answer: \(-\dfrac{2}{15}\)
Hope that helps!
What is the total square inches
Square Area = side x side = 3x3 = 9
Rectangle Area = side x side= 7x3= 21
9 + 21 = 30 square inches
Answer:
30 square inches
Step-by-step explanation:
\(\boxed{\text{\bf Area of rectangle = length *width}}\)
Rectangle1:
Area = 6 * 3
= 18 square inches
Rectangle2:
Area = 4 * 3
= 12 square inches
Area of the figure = area of rectangle1 + area of rectangle2
= 18 + 12
= 30 square inches
What should I buy? A study conducted by the Pew Research Center reported that 58% of cell phone owners used their phones inside a store for guidance on purchasing decisions. A sample of 15 cell phone owners is studied. a. What is the probability that six or more of them used their phones for guidance on purchasing decisions?
Answer:
Buy My Shlong
Step-by-step explanation:
Eat my virginia
The question is in le picture below U-U
Answer:
30%
Also I LOVE THE EMMA PIC!!!!!!!!
The following transformations are performed on the right triangle, in the order shown below.• Reflect about the y-axis.• Translate 6 units in a positive y-direction.• Translate 3 units in a positive x-direction.What are the coordinates of vertex W after all three steps?
B) W'''(6,0)
1) Let's locate the points at first:
U (3, -2)
V (7,-2)
W (3, -6)
A Reflection about the y-axis follows this rule:
Pre-image Rule Image
(x, y) (x, -y)
W (3, -6) W' (3,6)
2) Let's apply now the other transformation over point W
To translate 6 units in a positive y-direction (that means to go up) therefore to subtract 6 units to the y-coordinate
W' (3,6) (x, y-6) W'' (3, 0)
And finally, let's translate that Image 3 units in the positive x-direction (to the right)
W''(3,0) (x+3, y) W'''(6,0)
3) Hence, the answer is B
The average score for games played in the NFL is 22 and the standard deviation is 9.3 points. 41 games are randomly selected. Round all answers to 4 decimal places where possible and assume a normal distribution.
a. What is the distribution of ¯x x¯
? ¯xx¯ ~ N( , )
b. What is the distribution of ∑x ? ∑x ~ N ( , )
c. P( ¯x > 19.8214) =
d. Find the 60th percentile for the mean score for this sample size.
e. P(20.6214 < x¯< 23.2262) =
f. Q1 for the x¯distribution =
g. P( ∑x > 829.0774) =
For part c) and e), Is the assumption of normal necessary? NoYes
Using the normal distribution and the central limit theorem, it is found that:
a) The distribution is: x¯ ~ N(22, 1.45).
b) The distribution is: ∑x ~ N(902, 59.55).
c) P( ¯x > 19.8214) = 0.9332 = 93.32%.
d) The 60th percentile for the mean score for this sample size is of 22.37 points a game.
e) P(20.6214 < x¯< 23.2262) = 0.6312 = 63.12%.
f) Q1 for the x¯distribution = 21 points a game.
g) P( ∑x > 829.0774) = 0.8888 = 88.88%.
Assumption of normality is not necessary, as the sample sizes are greater than 30.
Normal Probability DistributionThe z-score of a measure X of a variable that has mean \(\mu\) and standard deviation \(\sigma\) is given by the rule presented as follows:
\(Z = \frac{X - \mu}{\sigma}\)
The z-score measures how many standard deviations the measure X is above or below the mean of the distribution, depending if the z-score is positive or negative.From the z-score table, the p-value associated with the z-score is found, and it represents the percentile of the measure X in the distribution.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).Also by the Central Limit Theorem, for the sum of n instances of a variable, the mean is of \(\n\mu\) and the standard deviation is of \(\sigma\sqrt{n}\).Finally, by the Central Limit Theorem, assumption of normality is only necessary when the sample size is less than 30.For a single game, the mean and the standard deviation of the number of points scored are given as follows:
\(\mu = 22, \sigma = 9.3\)
For the average of 41 games, the standard error is:
\(s = \frac{9.3}{\sqrt{41}} = 1.45\)
Hence the distribution is: x¯ ~ N(22, 1.45).
For the sum of the 41 games, the mean and the standard error are given as follows:
41 x 22 = 902.\(s = 9.3\sqrt{41} = 59.55\).Hence the distribution is: ∑x ~ N(902, 59.55).
In item c, the probability is one subtracted by the p-value of Z when X = 19.8214, hence:
\(Z = \frac{X - \mu}{\sigma}\)
By the Central Limit Theorem:
\(Z = \frac{X - \mu}{s}\)
Z = (19.8214 - 22)/1.45
Z = -1.5
Z = -1.5 has a p-value of 0.0668.
1 - 0.0668 = 0.9332 = 93.32%.
The 60th percentile for the distribution is X when Z = 0.253, hence:
\(Z = \frac{X - \mu}{s}\)
0.253 = (X - 22)/1.45
X - 22 = 0.253 x 1.45
X = 22.37.
For item e, the probability is the p-value of Z when X = 23.2262 subtracted by the p-value of Z when X = 20.6214, hence:
X = 23.2262:
\(Z = \frac{X - \mu}{s}\)
Z = (23.2262 - 22)/1.45
Z = 0.85
Z = 0.85 has a p-value of 0.8023.
X = 20.6214:
\(Z = \frac{X - \mu}{s}\)
Z = (20.6214 - 22)/1.45
Z = -0.95
Z = -0.95 has a p-value of 0.1711.
0.8023 - 0.1711 = 0.6312 = 63.12%.
The first quartile for the distribution is X when Z = -0.675, hence:
\(Z = \frac{X - \mu}{s}\)
-0.675 = (X - 22)/1.45
X - 22 = -0.675 x 1.45
X = 21.
For item g, the probability is one subtracted by the p-value of Z when X = 829.0774, hence:
\(Z = \frac{X - \mu}{s}\)
Z = (829.0774 - 902)/59.55
Z = -1.22
Z = -1.22 has a p-value of 0.1112.
1 - 0.1112 = 0.8888 = 88.88%.
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What is the midpoint of 125 and 12?
A shipment of 8 computers contains 3 with defects. Find the probability that a sample of size 2, drawn from the 8, will not contain a defective computer.
What is the probability that a sample of 2 of the 8 computers will not contain a defective computer?
(Type an integer or a simplified fraction.)
Answer:
5/28
Step-by-step explanation:
First of all, probability is defined as the number of ways a certain event can happen divided by the total ways of an event happening. In this scenario, we are asked to find the number of non-defective computers divided by the total ways that a sample of two can be chosen.
The number of ways to choose 2 computers from 8 can be written as \(8\choose2\), which is equal to \(\frac{8\cdot7}{2}\), which is 28. Now, there are 3 defective computers, for a total of 5 non-defective computers, so the probability is 5/28.
1 hour is equal to how many seconds
Answer: 3600 seconds
Step-by-step explanation:
60 seconds in a minute
60 minutes in an hour
(60)(60) = 3600
Answer:
3600
Step-by-step explanation:
There are 60 seconds in 1 minute
30 minutes equal 1800
So, 1800 + 1800 is 3600.
Hope this helps! :)
write and equation for the nth term of the geometric sequence for 2,8,32,128
then find a6 round to the nearest tenth if necessary.
The sixth term of the geometric sequence is 2048.
The given geometric sequence is 2, 8, 32, 128. We can observe that each term is obtained by multiplying the previous term by 4. Therefore, the common ratio (r) of the sequence is 4.
The formula for the nth term (an) of a geometric sequence is given by:
an = a1 * r^(n-1)
where a1 is the first term and r is the common ratio.
For this sequence, a1 = 2 and r = 4. Plugging in these values into the formula, we get:
an = 2 * 4^(n-1)
To find a6, we substitute n = 6 into the formula:
a6 = 2 * 4^(6-1)
= 2 * 4^5
= 2 * 1024
= 2048
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The Probable question may be:
Write an equation for the nth term of the geometric sequence 2, 8, 32, 128,
Then find a6. Round to the nearest tenth if necessary.
a = 5×4 X
a1 = n-1 X
Solve for y c=7(y-k)
Concept
You are to make y the subject of the formula or subject of the relation.
Next, write the equation and solve for y.
c = 7(y - k)
first, multiply 7 with y and k to remove the bracket.
c = 7y - 7k
Next, move negative 7k to the left of the equation.
c + 7k = 7y
Divide through by 7 to make y subject of the relation.
\(\begin{gathered} We\text{ have} \\ \frac{c\text{ + 7k}}{7}\text{ = y} \\ or \\ y\text{ = }\frac{c}{7}\text{ + }\frac{7k}{7} \\ y\text{ = }\frac{c}{7}\text{ + k} \end{gathered}\)Final answer
y = c/7 + k or y = (c + 7k) /7
What is the value of x in the equation 3/2(4x – 1) – 3x = 5/4 – (x + 2)?
i have attached a file you can see it from there.