Answer:
The proportion of jugs which receive more than 65 ounces of detergent is 0.0062 or 0.62%
Step-by-step explanation:
Mean amount of detergent = u = 64
Standard deviation = [tex]\sigma[/tex] = 0.4
We need to find the proportion of jugs with over 65 ounces of detergent. Since the population is Normally Distributed and we have the value of population standard deviation, we will use the concept of z-score to solve this problem.
First we will convert 65 to its equivalent z-score, then using the z-table we will desired proportion. The formula to calculate the z-score is:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
x = 65 converted to z score will be:
[tex]z=\frac{65-64}{0.4}=2.5[/tex]
Therefore, the probability of detergent being more than 65 ounces is equivalent to probability of z-score being over 2.5
i.e.
P(X > 65) = P(z > 2.5)
From the z-table and using the property of symmetry:
P(z > 2.5) = 1 - P(z < 2.5)
= 1 - 0.9938
= 0.0062
Therefore,
P(X > 65) = P(z > 2.5) = 0.0062
So, the proportion of jugs which receive more than 65 ounces of detergent is 0.0062 or 0.62%
To find the proportion of jugs that receive more than 65 ounces of detergent when the machine is running on target, we can use the properties of the normal distribution. The proportion is about 0.62%.
Explanation:To find the proportion of jugs that receive more than 65 ounces of detergent when the machine is running on target, we can use the properties of the normal distribution. Since the mean amount is 64 ounces and the standard deviation is 0.4 ounces, we can calculate the Z-score for 65 ounces using the formula Z = (X - μ) / σ, where X is the value of interest, μ is the mean, and σ is the standard deviation.
Plugging in the values, we get Z = (65 - 64) / 0.4 = 2.5. Now, we can look up the cumulative probability for a Z-score of 2.5, which represents the proportion of jugs that receive less than or equal to 65 ounces. Subtracting this proportion from 1 gives us the proportion of jugs that receive more than 65 ounces of detergent when the machine is running on target.
Using a Z-table or a calculator, we find that the cumulative probability for a Z-score of 2.5 is approximately 0.9938. Subtracting this from 1, we find that the proportion of jugs that receive more than 65 ounces of detergent when the machine is running on target is about 0.0062 or about 0.62%.
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A rock is thrown upward from a bridge into a river below. The function f(t) = −16???? 2 + 41t + 130 determines the height of the rock above the surface of the water (in feet) in terms of the number of seconds t since the rock was thrown.
Answer:
The bridge's height above the water is 130 feets.
Step-by-step explanation:
A rock is thrown upward from a bridge into a river below :
[tex]h(t)=-16t^2+41t+130[/tex]
Here t is time in seconds
It is required to find the bridge's height above the water. When it reaches the height of the rock above the surface of the water, then :
h(t) = 0
[tex]f(0)=-16t^2+41t+130\\\\f(0)=-16(0)^2+41(0))+130\\\\f(0)=130\ ft[/tex]
So, the bridge's height above the water is 130 feets.
What is the volume of the right rectangular prism with a length of 2 millimeters, a width of 4 millimeters, and a height of 8 millimeters? 14 Millimeters cubed 16 Millimeters cubed 28 Millimeters cubed 64 Millimeters cubed
Answer:
The volume of this prism is 64 mililmeters cubed.
Step-by-step explanation:
What is the volume of the right rectangular prism with a length of 2 millimeters, a width of 4 millimeters, and a height of 8 millimeters?
The volume of this prism can be calculated as:
[tex]V=l\cdot w \cdot h\\\\V=2\cdot 4\cdot 8=64[/tex]
The volume of this prism is 64 mililmeters cubed.
Answer:
D
Step-by-step explanation:
Sorry if it's wrong.
Suppose that a coin is tossed three times and the side showing face up on each toss is noted. Suppose also that on each toss heads and tails are equally likely. Let HHT indicate the outcome heads on the first two tosses and tails on the third, THT the outcome tails on the first and third tosses and heads on the second, and so forth.
(a) Using set-roster notation, list the eight elements in the sample space whose outcomes are all the possible head-tail sequences obtained in the three tosses.
(b) Write each of the following events as a set, in set-roster notation, and find its probability.
(i) The event that exactly one toss results in a head
(ii) The event that at least two tosses result in a head
Answer:
1a
Step-by-step explanation:
In an electronic system, a sensor measures a crucial parameter and outputs a number, but there is random error in its measurement. The measurement error in a sensor output is known to be RV X with uniform distribution in (-0.05,0.05) and independent from one output to the next, that is, the errors are iid! During a run of the system, n = 1000 samples of the sensor output are recorded. (a) Find the numerical value of the mean ux and the variance oź for the uniform distribution described. (You can use results in the text by listing the theorem or formula.) Further processing of these n= 1000 samples adds them together, and we are concerned about the overall error in the sum resulting from adding 1000 iid errors. Let X, denote the error in the įth sample for 1 1." Show all the steps in how you compute this. (f) Are the answers in (d) and (e) in agreement? If they are different, explain how both can be correct.
Answer:
Step-by-step explanation:
Find attach the solution
Mr. Thompson wants to tile his living room which measures 15.7 feet in length and 12.2 feet in width. What is the area of Mr. Thompson’s living room?
b) If tile costs $10.50 per square foot, how much will it cost Mr.Thompson to tile his living room.
Answer:
A. 191.54 ft²
B. $2011.17
Step-by-step explanation:
Part A involves multiplying to find the area of the living room using the formula to find the area of a rectangle.
A = b*h (original formula)
A = 15.7*12.2 (substitute values)
A = 191.54 (multiply)
The area of his living room is 191.54 ft²
Next, you need to multiply the number of ft² by the cost per ft² to find the cost to tile the living room
Cost = $10.50*191.54 (equation)
Cost = $2011.17 (multiply)
The total cost of tiling the living room would be $2011.17
Answer:
Step-by-step explanation:
What the value 0 in degrees
Answer:
45 degrees
Step-by-step explanation:
Which of theses measurements could describe the volume of a prism? Select all that apply.
Answer:
I did the question and the answer is b and e
Step-by-step explanation:
Or 4 in and 12 cubic yards
in a 45-45-90- triangle what is the length of the hypotenuse when the leg is 22 cm
Answer:
[tex] 22\sqrt 2 [/tex] cm
Step-by-step explanation:
[tex] in \: a \: 45 \degree - 45 \degree - 45 \degree \: \triangle \\ leg = \frac{1}{ \sqrt{2} } \times hypotenuse \\ \\ \therefore \: 22 = \frac{1}{ \sqrt{2} } \times hypotenuse \\ \\ \purple{ \bold{ \therefore \: hypotenuse = 22 \sqrt{2} cm}}[/tex]
What is the mode of the data set?
a. 90
b. no mode
c. 85.5
d. 49
Answer:
90
Step-by-step explanation:
Solve the equation for x.
x2 = 576
/\
||
is supposed to be 2 over x
Answer:
288
Step-by-step explanation:
2/x = 576
you have to make the x by itself so you would have to multiply 1/2 to 2/x for the first part
then you would carry the 1/2 over to 576 and multiply that by 1/2
the answer would become x = 288
Answer:
1/288
Step-by-step explanation:
[tex]\frac{2}{x} = 576[/tex]
Multiply both sides by x to get rid of the fraction.
2 = 576x
Divide to get x by itself.
2 / 576 = .00347222222
Also = 1/288
que valor tiene los numeros que van ala izquierda del punto decimal
Answer:
A decimal number can be divided in a decimal part, a whole part and the decimal point which separates the first two.
So, all numbers that are placed leftside of the decimal point can be classified in units, tens, hundreds, thousands, and so on. Basically, each value depends on a base of 10. This means that thousands are ten times more than hundreds, hundreds are ten times more than tens, tens are ten times more than units.
If we want to a specific value of the whole part in a decimal number, we just need to look units, tens, hundreds, thousands or millions.
For example, if we have the number 1235.8456, the whole part would be 1235, and the value of the numbers that are leftside of the decimal point is 1235 units.
Answer:
The name of the numbers that go to the left of the decimal point is INTEGERS. This is the whole number part of the decimal number.
Step-by-step explanation:
The english translation is
What is the name of the numbers that go to the left of the decimal point?
A number with decimal numbers has 3 parts.
- The whole number part that are to the left of the decimal point. This whole number part is called the INTEGER part.
- The decimal point. The decimal point separates the whole numbers part of the number on the left and the mantissa part that has numbers to the right of the decimal point.
- The numbers to the right of the decimal point constitute a value less than 1. This part of a decimal is called the MANTISSA.
Hope this Helps!!!
What bearing and airspeed are required for a plane to fly 700 miles due north in 3.5 hours if the wind is blowing from a direction of 338 degrees at 10 mph? The plane should fly at nothing mph at a bearing of nothing degrees. Calculator
Answer:
1. Airspeed = 201.17 mph
2. Bearing = 358.93⁰
Step-by-step explanation:
Given Data:
d = 700 mi
t = 3.5 hrs
speed of wind Vx = 10 mph
velocity of plane Vy = d/t
= 700/3.5
= 200 mph
1. Air speed (V) is calculated using the formula;
V² = V²x + V²y -2*Vx *Vy*cos∝
But ∝ = 338 - 180 = 158°
Substituting into the equation, we have
V² = 10² + 200² - 2*10*200*Cos 158
= 40100 - 400 *(-0.92718)
= 40100 + 370.872
V² = 40470.872
V = √40470.872
V = 201.17 mph
2. calculating the bearing using cosine rule, we have;
sin∅/Vx = sin∝/V
sin∅/10 = sin158/201.17
sin∅ = 10*sin 158/201.17
= 3.746/201.17
= 0.0186
∅ = sin⁻¹ 0.0186
= 1.07
Therefore,
Bearing = 360 - 1.07
= 358.93⁰
The airspeed is 201.17 mph and bearing is [tex]358.93^\circ[/tex] and this can be determined by using the vector form of velocity.
Given :
Plane to fly 700 miles due north in 3.5 hours if the wind is blowing from a direction of 338 degrees at 10 mph.
To determine the airspeed the following formula can be used.
[tex]\rm V^2 = V^2_x +V^2_y-2V_xV_y cos \theta[/tex] ---- (1)
where, [tex]\theta = 338-180 = 158^\circ[/tex], [tex]\rm V_y[/tex] is the velocity of the plane and [tex]\rm V_x[/tex] is the velocity of the wind.
Now, put the value of [tex]\rm V_y[/tex], [tex]\rm V_x[/tex] and [tex]\theta[/tex] in the equation (1).
[tex]\rm V^2 = 10^2+200^2+2\times 10\times 200\times cos158[/tex]
[tex]\rm V^2= 100 + 40000+4000(-0.9271)[/tex]
V = 201.17 mph
Now, using cosine rule:
[tex]\rm \dfrac{sin \alpha}{V_x}=\dfrac{sin \theta }{V}[/tex]
[tex]\rm \dfrac{sin\alpha }{10}=\dfrac{sin158}{201.17}[/tex]
[tex]\rm sin\alpha =10\times \dfrac{sin158}{201.17}[/tex]
[tex]\rm sin \alpha = \dfrac{3.746}{201.17}[/tex]
[tex]\rm sin\alpha =0.0186[/tex]
[tex]\alpha = 1.07^\circ[/tex]
Therefore, the bearing is given by 360 - 13.07 = [tex]358.93^\circ[/tex]
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What is the peremeter of this tile 3in 3in 3in 3in I ready
Answer:
12
Step-by-step explanation:
3x4=12
Find the exact length of the curve.
x = 1 + 9t2
y = 2 + 6t3
0 ≤ t ≤ 2
The length of the curve defined by the parametric equations x = 1 + 9t^2 and y = 2 + 6t^3 for t ranging from 0 to 2 can be found using the formula for the length of a curve defined by parametric equations. First, compute the derivatives of x and y with respect to t and then integrate the square root of the sum of their squares from t = 0 to t = 2.
Explanation:Given the parametric equations x = 1 + 9t2 and y = 2 + 6t3, with t ranging from 0 to 2, we can find the length of the curve using the formula for the length of a curve defined by parametric equations.
The formula is: Length = ∫ab sqrt[(dx/dt)2 + (dy/dt)2] dt where dx/dt and dy/dt are the derivatives of x and y with respect to t.
We first find the derivatives dx/dt = 18t and dy/dt = 18t2. Then, we square these, add them together and take the square root to get √[324t2 + 324t4].
Finally, we integrate this from t = 0 to t = 2 to find the length of the curve. As a hint for the integration part, you can use the formula for the integral of tn, which is (tn+1)/(n+1).
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A tank with a capacity of 1000 L is full of a mixture of water and chlorine with a concentration of 0.02 g of chlorine per liter. In order to reduce the concentration of chlorine, fresh water is pumped into the tank at a rate of 10 L/s. The mixture is kept stirred and is pumped out at a rate of 25 L/s. Find the amount of chlorine in the tank as a function of time. (Let y be the amount of chlorine in grams and t be the time in seconds.)
The function for the amount of chlorine in the tank as a function of time is [tex]y(t) = \left(\frac{20}{1000^{\frac{5}{3}}} \right) (1000 - 15t)^{\frac{5}{3}}[/tex].
Let y(t) be the amount of chlorine in grams in the tank at time t seconds. The initial amount of chlorine is given by the concentration of chlorine times the volume of the tank: y(0) = 0.02 g/L * 1000 L = 20 grams.
The tank has a mixture being pumped out at a rate of 25 L/s, and fresh water is being pumped in at a rate of 10 L/s. The change in the volume of the tank per second is -15 L/s (since more is being pumped out than in).
The rate of change of the amount of chlorine in the tank, dy/dt, can be described as the rate of chlorine leaving the tank minus the rate of chlorine entering the tank. Fresh water has 0 g/L concentration, so the rate of chlorine entering the tank is 0. Chlorine is leaving the tank with the water at a rate proportional to the concentration of chlorine in the tank.
The volume of water in the tank at any time t can be written as V(t) = 1000 - 15t. The concentration of chlorine in the tank at any time is y(t) / V(t). Therefore, the rate of chlorine leaving the tank is:
[tex]\frac{dy}{dt} = - \left(\frac{25y}{V(t)}\right)[/tex]
Substitute V(t) into the equation:
[tex]\frac{dy}{dt} = - \left(\frac{25y}{1000 - 15t}\right)[/tex]
This is a separable differential equation. We can solve it by separating variables and integrating both sides.
[tex]\frac{dy}{y} = - \frac{25}{1000 - 15t} dt[/tex]
Integrate both sides:
[tex]\int \frac{1}{y} dy = -25 \int \frac{1}{1000 - 15t} dt[/tex]
The integral of [tex]\frac{1}{y}[/tex] is[tex]\ln|y|,[/tex] and the integral of [tex]\frac{1}{1000 - 15t}[/tex] can be found using a substitution method. Let u = 1000 - 15t, then du = -15 dt, or [tex]dt = -\frac{1}{15}[/tex] du.
[tex]\int \frac{1}{1000 - 15t} dt = - \frac{1}{15} \int \frac{1}{u} du = - \frac{1}{15} \ln|u| = - \frac{1}{15} \ln|1000 - 15t|[/tex]
Putting it all together:
[tex]\ln|y| = \frac{25}{15} \ln|1000 - 15t| + C[/tex]
Simplify further:
[tex]\ln|y| = \frac{5}{3} \ln|1000 - 15t| + C[/tex]
Exponentiate both sides to solve for y:
[tex]y = e^{\frac{5}{3} \ln|1000 - 15t| + C} = e^C (1000 - 15t)^{\frac{5}{3}}[/tex]
Let K = [tex]e^C[/tex]. Then:
[tex]y(t) = K(1000 - 15t)^{\frac{5}{3}}[/tex]
Using the initial condition y(0) = 20:
[tex]20 = K 1000^{\frac{5}{3}}[/tex]
Solve for K:
[tex]K = 20 / 1000^{\frac{5}{3}}[/tex]
This equation describes the amount of chlorine in the tank over time, taking into account the rates at which water is pumped in and out.
The number of accidents per week at a hazardous intersection varies with mean 2.2 and standard deviation 1.4. This distribution takes only whole-number values, so it is certainly not a normal distribution. Let "x-bar" be the mean number of accidents per week at the intersection during a year (52 weeks). What is the approximate probability that there are fewer than 100 accidents in a year? (Hint: Restate this event in terms of "x-bar")
Answer:
The approximate probability that there are fewer than 100 accidents in a year = .9251
Step-by-step explanation:
Given -
Mean [tex](\nu )[/tex] =2.2
Standard deviation [tex]\sigma[/tex] = 1.4
Let [tex]\overline{X}[/tex] be the mean number of accidents per week at the intersection during a year (52 weeks)
Then [tex]\overline{X}[/tex] = [tex]\frac{100}{52}[/tex] = 1.92
the approximate probability that there are fewer than 1.92 accidents per week in a year
[Z = [tex]\frac{\overline{X} - \nu }{\frac{\sigma}{\sqrt{n}}}[/tex] ]
= [tex]P(\overline{X} < 1.92 )[/tex] = ([tex]P(\frac{\overline{X} - \nu }{\frac{\sigma}{\sqrt{n}}}< \frac{1.92 - 2.2 }{\frac{1.4}{\sqrt{52}}})[/tex]
= P( [tex]Z < -1.442[/tex] ) ( Using Z table)
= .9251
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Lily’s car used 5 gallons of gas to drive 230 miles. At what rate does her car use gas in gallons per mile? Answer in simplest form.
____ Gallons per mile
Answer:
0.0217391304
Step-by-step explanation:
Answer:
1/46 gallons per mile
Step-by-step explanation:
Take the gallons used and divide by the number of miles driven
5 gallons /230 miles
1/46 gallons per mile
A peice is paper is 8 1/2 inches by 11 inches. what is the area of the piece of paper?
Answer:
93.5 inches
Step-by-step explanation:
Length times width
which is equal to 5 exponent of -4
Answer:
[tex]\frac{1}{5^{4}}[/tex] = [tex]\frac{1}{625}[/tex] = 0.0016
Step-by-step explanation:
I'm assuming you mean [tex]5^{-4}[/tex] (which could also be written as 5^-4, for future reference).
Negative exponents actually mean you'd use the term in the denominator, taking away the negative portion. It's difficult to explain in words, and is easier to see.
[tex]5^{-4}[/tex] = [tex]\frac{1}{5^{4}}[/tex]
Notice how the -4 changes to 4, and it becomes the denominator.
[tex]5^{4}[/tex] is also 625, so [tex]5^{-4}[/tex] is also 1/625, or the decimal version (0.0016).
I hope this helps!
A shop has the following offers crisps (175g packet) Normal price £1.43. Three for the price of two. Work out the price of 6packets of crisps
in how many distinct ways can the letters of the word READERS be arranged?
Answer:
The letters of the word readers can be arranged in 1260 distinct ways.
Step-by-step explanation:
A word has n letters.
The are m repeating letters, each of them repeating [tex]r_{0}, r_{1}, ..., r_{m}[/tex] times
So the number of distincts ways the letters can be arranged is:
[tex]N_{A} = \frac{n!}{r_{1}! \times r_{2}! \times ... \times r_{m}}[/tex]
In this question:
Readers.
Has 7 letters.
E repeats twice.
R repeats twice.
So
[tex]N = \frac{7!}{2! \times 2!} = 1260[/tex]
The letters of the word readers can be arranged in 1260 distinct ways.
The word 'READERS' can be arranged in 1260 distinct ways, considering the repetition of letters.
Explanation:The problem involves finding the number of distinct ways the letters in the word 'READERS' can be arranged. This is a topic in combinatorics, or counting, in mathematics.
The formula for the number of ways of arranging n objects where some objects are identical is n!/r1!r2!... where r1, r2, ... are the numbers of each type of similar object.
In the word 'READERS', there are 7 letters in total (n=7). Three of these letters are 'E', 'R' and 'R' (r1=2) and two of these letters are 'E' (r2=2).
The remaining letters 'A', 'D' and 'S' are all distinct (r3=1, r4=1 and r5=1). So, applying the formula, we get the number of distinct arrangements as 7!/(2!2!1!1!1!) = 1260.
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HELP ASAP PLEASE!!!
What is the median for the following set of data?
5, 7, 9, 11, 13, 13
A. 10
B. 8
C.9
D.11
Answer:
9
Step-by-step explanation:
Answer:
Step-by-step explanation:
(9+11)/2 = 10
You are interested in estimating the the mean age of the citizens living in your community. In order to do this, you plan on constructing a confidence interval; however, you are not sure how many citizens should be included in the sample. If you want your sample estimate to be within 3 years of the actual mean with a confidence level of 98%, how many citizens should be included in your sample
Answer:
list all the statistics
Step-by-step explanation:
What is the linear equation x×3y=6
Answer:
Find the degree of the equation to determine if linear.
"Not Linear"
Step-by-step explanation:
Answer:
not linear, degree 2
Step-by-step explanation:
The degree of this equation is the highest sum of the exponents of the variables in any given term.
Here, there is one variable term. The variables are x and y. They each have an exponent of 1, so the degree of the variable term is 1+1 = 2.
Since the degree of the equation is not 1, it is not a linear equation.
one side 2^4 ft
another side is 2^3ft
What is the area of the flower bed?
48 square feet
128 square feet
4,096 square feet
16, 384 square feet
Answer:
128
Step-by-step explanation:
2x2x2x2x2x2x2 is 128
Answer:
B
Step-by-step explanation:
Menţionează rolul virgulei în secvența: — Ei, ce ziceți?.
Answer:
The given question is:
"Mention the role of the comma in the sequence: - Well, what do you say?"
The role of the comma is to indicate a separation between words to make a specific sense of the statement.
Actually, the official function of commas is to separate words, ideas, phrases to prevent a misreading, and to give a specific signification so readers won't capture the intended sense.
What is the answer for Two step equations 5n+3=18
Answer: n=3
Step-by-step explanation: 5n+3=18
18-3=15
15/5=3
Answer:
Step-by-step explanation:
5n +3 =18
5n = 18- 3
5n = 15
Dividing through with 5
n =15/5
n = 3
5. Suppose that a particular candidate for public office is in fact favored by p = 48% of all registered voters. A polling organization is about to take a simple random sample of voters and will use the sample proportion to estimate p. Suppose that the polling organization takes a simple random sample of 500 voters. What is the probability that the sample proportion will be greater than 0.5?
Answer:
Probability that the sample proportion will be greater than 0.5 is 0.8133.
Step-by-step explanation:
We are given that the a particular candidate for public office is in fact favored by p = 48% of all registered voters. A polling organization is about to take a simple random sample of voters and will use the sample proportion to estimate p.
Suppose that the polling organization takes a simple random sample of 500 voters.
Let [tex]\hat p[/tex] = sample proportion
The z-score probability distribution for sample proportion is given by;
Z = [tex]\frac{ \hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ~ N(0,1)
where, [tex]\hat p[/tex] = sample proportion
p = population proportion = 48%
n = sample of voters = 500
The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.
So, probability that the sample proportion will be greater than 0.5 is given by = P( [tex]\hat p[/tex] > 0.50)
P( [tex]\hat p[/tex] > 0.50) = P( [tex]\frac{ \hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < [tex]\frac{0.50-0.48}{\sqrt{\frac{0.50(1-0.50)}{500} } }[/tex] ) = P(Z < 0.89) = 0.8133
Now, in the z table the P(Z [tex]\leq[/tex] x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 0.89 in the z table which has an area of 0.8133.
Therefore, probability that the sample proportion will be greater than 0.50 is 0.8133.
Complete the sentence below. The standard deviation of the sampling distribution of x overbar, denoted sigma Subscript x overbar, is called the _____ _____ of the _____. The standard deviation of the sampling distribution of x overbar, denoted sigma Subscript x overbar, is called the ▼ standard population sample ▼ mean error deviation distribution variance of the ▼ mean. sample. error. distribution.
Answer:
The standard deviation of the sampling distribution of x overbar, denoted sigma subscript x overbar, is called the Standard Error of the Mean.
Step-by-step explanation:
Standard deviation of the sampling distribution, or sigma Subscript x overbar, is also known as the standard error of the mean. It represents how much the sample means deviate from the population mean. The standard error can be calculated by dividing the population standard deviation by the square root of the sample size.
Explanation:The standard deviation of the sampling distribution, represented by the symbol sigma Subscript x overbar is also known as the standard error of the mean. This term refers to the standard deviation of the population of all possible sample means from samples of a specific size.
The basic formula to calculate the standard deviation is Σ(x – μ)2 / N for the population and Σ(x – x)² / (n-1) for the sample. Greek symbol µ represents the population mean while 'x' is the sample mean.
The standard error can be calculated by dividing the population standard deviation (σ) by the square root of the sample size (n). Thus, lesser the standard error, closer are the sample means to the population mean and vice versa. This is a very important concept in statistics as it allows one to estimate an unknown population parameter using sample data.
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Which of the following rational functions is graphed below a. F(x)=(x-1)/x(x-2)
The equation of the graphed rational function is f(x) = (x + 1)/(x + 2)(x - 2)
How to determine the graphed rational function
From the question, we have the following parameters that can be used in our computation:
The graph
From the graph, we have vertical asymptotes at
x = 2 and x = -2
This means that the denominator of the function is
(x + 2)(x - 2)
Looking through the list of options, we have the function with a denominator of (x + 2)(x - 2) to be f(x) = (x + 1)/(x + 2)(x - 2)
Hence, the graphed rational function is f(x) = (x + 1)/(x + 2)(x - 2)
The rational functions is graphed below is [tex]F(x) = \frac{(x - 1)}{x(x - 3)},[/tex] (after dividing both the numerator and denominator by (x)). The correct answer is C.
1. Analyze the graph's behavior:
The graph has vertical asymptotes at x = -3 and x = 2. This means the denominator of rational function must have factors (x + 3) and (x - 2).
The graph intersects y-axis at (0, -1). when x = 0, function value is -1.
As x approaches positive / negative infinity, graph approaches line y = 0. The numerator's degree must be smaller than denominator degree.
2. Consider the answer choices:
Only option C, [tex]F(x) = \frac{(x - 1)}{x(x - 3)},[/tex] has correct vertical asymptotes and a numerator degree of 1.
3. Verify the answer choice:
Let's substitute x = 0 into option C:
[tex]F(0) = \frac{(0 - 1)}{(0)(0 - 3)} = \frac{-1}{0} = -\infty[/tex]
This doesn't match the graph's behavior at x = 0. However, this is a common issue with rational functions when the numerator and denominator have a common factor. In this case, both the numerator and denominator have a factor of (x). Dividing both the numerator and denominator by (x) gives:
[tex]F(x) = \frac{\cancel{(x - 1)}}{\cancel{x}(x - 3)} = \frac{1}{(x - 3)}[/tex]
Now, let's substitute x = 0:
[tex]F(0) = \frac{1}{(0 - 3)} = -\frac{1}{3}[/tex]
This matches the graph's behavior at x = 0.
Complete and correct question:
Which of the following rational functions is graphed below?
[tex]A. F(x)=\frac{(x+1)}{(x+3)(x-2)}\\\\B. F(x)=\frac{(x-1)}{(x+2)^{2}}\\\\C. F(x)=\frac{(x-1)}{x(x-3)}\\[/tex]