Since the first equation of system B is created by multiplying system A's second equation by four, both equations will have the same answer. option c is correct
What is equations?Equations are mathematical expressions that have two algebraic expressions on either side of an equals (=) sign. . For an unknown quantity represented by an unknown variable, equations can be solved to determine its value. A statement is not an equation if it contains no references to "equal to" symbols.
Here,
you have a two-equation system.
System A: 6x + y = 2, and -x - y = 3.
System B: -10 = 2x - 3y, -3 = x - y
Choose the statement about each of the two systems of equations that is true from the list provided.
System A is an example.
6x + y = 2 ......(1) (1)
-x -y = -3 ....(2) (2)
Equation (2) becomes when we double it by 4.
-4x -4y = -12 ......(3) (3)
We now have, after adding (1) and (3),
6x + y +(-4x - 4y) = 2 - 12
solving, we arrive at,
6x + y -4x - 4y = 2 - 12
Equation (1) of system B is 2x – 3y = – 10.
The answer to system A is now discovered.
Equation (2) is created by adding equation (1).
6x + y - x -y = 2 -3
5x = -1
Value of x in (2) yields,
The answer to system B is now discovered.
System B: 2x - 3y = -10... (4)
-x -y = -3 .....(5) (5)
By dividing equation (5) by 3, we get y=16/5
-3x -3y = -9 .......(6) (6)
Equation (6) is obtained by deducting equation (4).
2x - 3y-(-3x - 3y) = -10 +9
5x = -1
Using (5) as the value of x, we obtain x=-1/5
Therefore, the values of systems A and B are equal.
Thus, choice (C) is the right one.
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Answer:
They will have the same solution because the first equation of System B is obtained by adding the first equation of System A to 4 times the second equation of System A
what is 4.24 divided by 4
Answer:
the answer is 1.06
Step-by-step explanation:
1.06 x 4 = 4.24
A family of 4 goes out to eat at a restaurant. They buy a family dinner platter that costs $29. Each of the 4 family members also gets a dessert for $3 apiece.
Let the variable x represent the total cost of the meal. Which of the following equations is correct?
Select ALL that apply.
A. x = 3 * 4 + 29
B. x = 3 + 4 + 29
C. x = 41
D. x = 36
The equations that model the total cost of the meal are:
A. x = 3 * 4 + 29
C. x = 41
Which of the following equations is correct?
We know that the family has 4 members and they buy:
A family dinner platter, which costs $29Each member also gets a dessert, which costs $3 per piece.Then the total cost is the $29 for the dinner plate plus four times the $3 for the dessert, this is:
x = $29 + $4*3
x = $29 + $12
x = $41
Then the correct options are A and C.
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Miles is renting a meeting room at a college. There is a reservation fee of $21 and an additional fee of $4 per hour. He needs to spend no more than $85. What is the possible number of hours for which Miles could rent the meeting room? Use t for the number of hours.
t ≤26.5
t<4
t ≤ 16
t<21.25
The equation represents that, Miles could rent the meeting room for t ≤ 16 hours.
What is inequality?
The word inequality means a mathematical expression in which the sides are not equal to each other. Basically, an inequality compares any two values and shows that one value is less than, greater than, or equal to the value on the other side of the equation.
The total cost for Miles to rent the meeting room for t hours is given by the equation C = 21 + 4t. We are trying to find the number of hours t for which C is equal to or less than $85.
We can solve this problem by setting up the inequality 21 + 4t ≤ 85 and solving for t.
Subtracting 21 from both sides gives us 4t ≤ 64.
Dividing both sides by 4 gives us t ≤ 16.
Thus, Miles can rent the meeting room for t hours, where t is less than or equal to 16. This means that he can rent the room for 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, or 16 hours.
Hence, the equation represents that, Miles could rent the meeting room for t ≤ 16 hours.
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Determine whether the statement is always, sometimes, or never true.
When the measure of ∠4 is 120° , the measure of ∠1 is 60°
always true
sometimes true
never true
Answer:
always true , because 120+60=180
Given the following exponential function,
identify whether the change represents
growth or decay, and determine the
percentage rate of increase or decrease.
y = 970(1.042)*
The change represents growth and rate of increase is 4.2%
What is an exponential function?Exponential functions model a relationship in which a constant change in the independent variable gives the same proportional change.
Given that, an exponential function y = 970(1.042)ˣ
When the growth rate is greater than 1, then the function represents a growth.
The general form equation is:
y(x)= a(1+r)ˣ such that r is the growth percent.
So,
1+r = 1.042
r = 0.042
r = 4.2%
Hence, the growth rate is 4.2%
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Find the dimensions of the box with volume 4096 cm3 that has minimal surface area. (Let x, y, and z be the dimensions of the box.)
The dimensions of the box with a volume of 4096 cm³ that has a minimal surface area are 16cm×16cm×16 cm.
A solid object's surface area is a measurement of the overall space that the object's surface takes up. It is also known as the overall area of a three-dimensional shape's surface. The formula to calculate surface area is S = 2(xy+yz+zx) where x is length, y is width and z is the height of the object.
Given the volume is 4096 cm³.
Then, V = xyz = 4096. Deriving the value of z from this, we get z = 4096/xy. Substitute value of z in S = 2(xy+yz+zx), we get,
[tex]\begin{aligned}S&=2\left(xy+y\times\frac{4096}{xy}+x\times\frac{4096}{xy}\right)\\&=2\left(xy+\frac{4096}{x}+\frac{4096}{y}\right)\\&=2xy+\frac{8192}{x}+\frac{8192}{y}\\&=2xy+8192\left(\frac{1}{x}+\frac{1}{y}\right)\end{aligned}[/tex]
Differentiating S with respect to x, we get,
[tex]\frac{dS}{dx}=2y-\frac{8192}{x^2}[/tex]
Equating this to zero and multiplying with x² we get,
[tex]\begin{aligned}2y-\frac{8192}{x^2}&=0\\2x^2y-8192&=0\\x^2y&=\frac{8192}{2}\\x^2y&=4096\end{aligned}[/tex]
Differentiating S with respect to y, we get,
[tex]\frac{dS}{dy}=2x-\frac{8192}{y^2}[/tex]
Equating this to zero and multiplying with y² we get,
[tex]\begin{aligned}2x-\frac{8192}{y^2}&=0\\2xy^2-8192&=0\\xy^2&=\frac{8192}{2}\\xy^2&=4096\end{aligned}[/tex]
Dividing x²y by xy², we get,
[tex]\begin{aligned}\frac{x^2y}{xy^2}&=\frac{4096}{4096}\\\frac{x}{y}&=1\\x&=y\end{aligned}[/tex]
Substitute x = y in x²y = 4096, we get,
[tex]\begin{aligned}y^3&=4096\\y&=16=x\end{aligned}[/tex]
Then, the z value is
[tex]\begin{aligned}z &= \frac{4096}{16\times 16}\\&=16\end{aligned}[/tex]
The required answer is 16cm×16cm×16 cm.
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The manager of a water park collects data on daily high temperature and the number of customers entering the park for 15 summer week days. Based on these data he produces a least regression equation y= -3110+51.2x. One day the high temperature was 93F and 1700 customers entered the park. Which of the following is the residual for this observation?
Answer: A residual is the difference between the observed value of a dependent variable and the predicted value based on a given model. In this case, the manager of the water park has produced a least squares regression equation of the form y = -3110 + 51.2x, where y is the number of customers entering the park and x is the daily high temperature. This equation can be used to predict the number of customers based on a given temperature.
On the day in question, the high temperature was 93F and 1700 customers entered the park. Using the given equation, we can predict the number of customers that would be expected based on this temperature:
y = -3110 + 51.2x
= -3110 + 51.2 * 93
= -3110 + 4768.6
= 1658.6
The residual for this observation is the difference between the observed value of 1700 and the predicted value of 1658.6, which is 1700 - 1658.6 = 41.4. This is the residual for this observation.
Write a polynomial function with
zeros: 4, 5i
PLEASE HELP ASAP ITS DUE TMR
Answer:
[tex]85 \sqrt{5} [/tex]
3. provide an equation for converting gain g in db to a linear scale. for example, a 6db gain translates to a factor of 2, so y[n]
The equation for converting gain in decibels to a linear scale is dB → gain-multiplier: [tex]g=2^{\frac{d}6} }[/tex]
gain-multiplier → dB: [tex]6*log_{2} g[/tex]
The decibel is used in a wide range of applications. Decibels are especially used when referring to power or a derived measure, which values can vary in a wide range. The most prominent usage of decibels is in sound volume. So, for example, a sound of 0dB is barely hearable, whereas a vacuum cleaner on average has 75dB and a rock concert reaches about 110 dB.
Practical version-
dB → gain-multiplier: [tex]g=2^{\frac{d}6} }[/tex]
gain-multiplier → dB: [tex]6*log_{2} g[/tex]
So if we set that 0 dB gain as 1.0 factor, and -∞ dB gain is 0.0 factor, it means that (if we are considering voltage gain as in a mixing desk fader) :
gain = 20.0*log10(factor)
therefore :
factor = 10^(gain/20.0)
If, as described in a comment, the 0 dB gain is at 0.65 factor, it means the ref is 0.65.
gain in dB = 20*log10(factor/0.65)
factor = 0.65*10^(gain/20.0)
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The function f(x) is a cubic function and a limited table of values is provided below. Write the equation of the cubic polynomial in standard form.
The equation of the cubic polynomial is f(x) = x³ - x² -9x + 9.
What is a polynomial function?
Polynomial functions are defined for all values of x and have a finite number of roots (x-values at which the function is equal to 0). The roots of a polynomial function can be found by solving the equation f(x) = 0.
By using the given table, we can plot the points on the graph and we can draw a graph
• Fitted coefficients:
a = 9
b = -9
c = -1
d = 1
Then we can prepare the polynomial as
y = 9 - 9x - x² + x³
Now write down in the standard form, we get
f(x) = x³ - x² -9x + 9
Hence, the equation of the cubic polynomial is f(x) = x³ - x² -9x + 9.
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Solve for x. Would appreciate the help thanks
The value of x in the triangles is 24.5
How to determine the value of x?From the question, we have the following parameters that can be used in our computation:
The triangle
On the triangle, we have the following ratio
7 + x : x = 27 : 27 - 6
Evaluate the difference
7 + x : x = 27 : 21
Express as fraction
This gives
x/(x + 7) =21/27
So, we have
27x = 21(x + 7)
Expand
27x - 21x = 147
So, we have
6x = 147
Evaluate
x = 24.5
Hence, the value of x is 24.5
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a least-squares fitting of a simple regression model minimizes the sum of the squares of the perpendicular distances from the data points to the regression line.
The "method is least square" is a least-squares fitting of a simple regression model minimizes the sum of the squares of the perpendicular distances from the data points to the regression line.
The term linear regression refers the predictive method to predict or estimate the values of a dependent quantitative variable denoted by y with the help of other independent variables denoted by x1,x2,x3 by using one of many methods like that of ordinary least squares.
Here we need to find what is the method for a least-squares fitting of a simple regression model minimizes the sum of the squares of the perpendicular distances from the data points to the regression line.
As per the definition of the linear regression, we have know that a least-squares fitting of a simple regression model which minimizes the sum of the squares of the perpendicular distances from the data points to the regression line.
Here we have to take the square for the number to fit into the given interval.
So, this is known as method for least square and it does not use the sum of perpendicular distances between the points and the ‘estimated regression equation’ does not used to minimize.
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Let $ABC$ be a triangle. Points $A_1, B_1, C_1$ are, respectively, on sides $BC, AC, AB$ and:
$\frac{AC_1}{C_1B} = \frac{BA_1}{A_1C} = \frac{CB_1}{B_1A} \neq 1$
If $\frac{AB}{A_1B_1} = \frac{BC}{B_1C_1} = \frac{CA}{C_1A_1}$ prove that triangle $ABC$ is equilateral.Let ABC be a triangle. Points A1, B1, C1 are, respectively, on sides BC, AC, AB and:
AC1/C1B} = BA1/A1C = CB1/B1A which is not equal to 1
If AB/A1B1 = BC/B1C1} = CA/C1A1 prove that triangle ABC is equilateral.
Triangle ABC is equilateral and hence proved.
According to the question,
Let ABC be a triangle
And the given points A1, B1, and C1 are on its sides BC, AC, and AB respectively
Since according to the first equality says that A1, B1, and C1 are not the midpoints and just normal points on the lines.
According to what equality says that ΔABC = ΔA1B1C1 because the sides are in proportion.
Let us consider 3 more triangles = ΔAB1C1, ΔBC1A1, and ΔCA1B1
Now, these above-mentioned triangles will also be similar due to the proportionality insides.
Which results in ⇒ ∠A = ∠B = ∠C due to the phenomenon of corresponding angles of triangles.
Therefore, Triangle ABC is equilateral and hence proved.
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The table shows the depths (relative to sea level) of several scuba divers.
What is the difference between Oscar's depth and Annabelle's depth? Write your answer as a mixed number in simplest form
Answer:(-6 5/6)
Step-by-step explanation:
-12.5=-12-1/2
-5 2/3= -5-2/3
=(-12 3/6)-(-5 4/6)
=(-6 5/6)
gimme brainlliest
Use the figures to answer the questions.
1. What is the diameter of circle A ?
2. What is the diameter of circle B ?
3. What is the radius of circle A ?
4. What is the radius of circle B?
5. Are the radius and diameter of the two circles proportional? Explain.
6. The circumference of circle Q is 21 centimeters.
a. Write a proportion to find the circumference of circle P
b. What is the circumference of circle P?
Answer:
1) 12ft
2) 8ft
3) 6 ft
4) 3ft
5)
Answer:
1. 12ft
2. 8ft
3. 6ft
4. 4ft
5. The diameter and radius of the circles are proportional by a factor of 1.5 because 12/8 = 1.5 and if I multiply circle B's radius by a factor of 1.5 I will get the radius of Circle A as is with the diameter.
6.
A- (3/7)(21) = x
B- x approximately equals 9
Step-by-step explanation:
Circumference formula
C= 2(pi)r
z equals circumference of circle q
Q = 7
P = 3
Z = 21
(P/Q)(Z) = x
Therefore (3/7)(21) = 9
We can prove this by using the Circumference formula
C= 2(pi)r
C=2(pi)1.5
C= 3(pi)
C= 9.4247...
Rounded = 9
hope this helps!!
Solve for x.
− x/2<−1
Answer: x>2
Step-by-step explanation:
To solve for x, we want to use inverse operations to isolate x.
[tex]-\frac{x}{2} < -1[/tex] [multiply both sides by -2]
[tex]x > 2[/tex]
PLEASE HELP!!!!
A group of friends were hanging out discussing the movies. They discovered that altogether, they went to the movies 30 times last year. Clio went 5 times as often as Alex. Bernice went 2 more times than Alex. How many times did Clio go to the movies last year?
A. 5
B. 10
C. 20
D. 4
Step-by-step explanation:
30/4=7.4
30/5=6
6/3=2
Alex went to the moves 4 times that year.
All i need is part C thank you so much brainiest to first person to answer!
Answer:
No, because with Y- represents the reading time & X-Representing the TV time. The two variables are being effected by the age of te viewer/reader
Step-by-step explanation:
There are 1,000 grams in 1 kilogram. Nate is mailing a package that has a mass of 12 kilograms. He wants to know the mass of the package in grams? Complete the statement to describe how to convert kilograms to grams.
12,000g
Step-by-step explanation:Here are the steps to figuring out your problem:Since there are 1,000 grams per kilogram, that means:
1 kg = 1,000 g
2kg = 2,000g
3kg = 3,000g
And so on until we get to 12 kilograms:
12kg = 12,000g
Solution:
12,000g
I hope my answer helped you! If you need more information or help, comment down below and I will be sure to respond if I am online. Have a wonderful rest of your day!
Answer:
12000 gram
Step-by-step explanation:
step 1:
[tex]1 kg=1000g\\12kg = x[/tex]
step 2:
do a criscross multiplication to find x.
[tex]x*1kg=1000g*12 kg[/tex]
step 3:
devide both sides by 1kg
[tex]x=(1000g*12kg)/1kg[/tex]
step 4:
cancel units tha exist on both the numerator and the denominator.(in our case cancel kg)
[tex]x=(1000kg*12)/1[/tex]
Step 5: simplify
[tex]x=12000g[/tex]
Mary wishes to estimate the mean height of women aged 18-24. She picks a sample of 100
women aged between 18 and 24 and constructs a 99% confidence interval for the
population mean. If she were to repeat this procedure 200 times in total, she would obtain
200 different confidence intervals. How many of these intervals would you expect to
contain the population mean, u? Explain your thinking.
We would expect 198 of the intervals to contain the mean.
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data
Given that Mary wishes to estimate the mean height of women aged 18-24.
picks a sample of 100
Women aged between 18 and 24 and constructs a 99% confidence interval for the population mean.
If Mary were to repeat this procedure 200 times in total, she would obtain
200 different confidence intervals.
A confidence interval of a parameter gives an interval in which the parameter is expected to be found. Because the interval either contains or doesn't contain the parameter, the probability is either 0 or 100%, which is not helpful. A 95% CI says that if we construct 100 intervals, 95% will contain the parameter. That is a true percentage, not a confidence. We don't know which 95, however, since the parameter is still unknown or unknowable.
I would expect 99%×200 or 198 of the intervals to contain the mean.
Hence, would expect 198 of the intervals to contain the mean.
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A librarian measured the number of young adult books in a library. The number of books in the library as a function of time (in years since 2008) is shown in the scatterplot.
scatterplot with points at 0 comma 10, 4 comma 42, 8 comma 74 and 12 comma 106
Choose the linear function that best describes the scatterplot relating the number of books in the library, y, to time, x. (1 point)
Group of answer choices
y = 8 − 10x
y = 8 + 10x
y = 10 − 8x
y = 10 + 8x
Therefore ,the linear function that best describes the scatterplot relating the number of books in the library is y = 10 + 8x
What is linear function?Two separate but related concepts are referred to as linear functions in mathematics: A polynomial function of degree 0 or 1 is referred to as a linear function in calculus and related fields if its graph is a straight line.
Here,
The points given on the scatterplot are (0,10),(4,42),(8,74) & (12,106)
By putting in the points in the given linear functions
y = 8 − 10x
y = 8 + 10x
y = 10 − 8x
y = 10 + 8x
Thus ,the linear function which best satisfy the points given on the scatterplot is y = 10 + 8x
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Answer:
y = 10 + 8x
Step-by-step explanation:
we can find the y-intercept first, by observing the point at which x=0, (0,y)
when x = 0, y = 10. The y-intercept is 10.
Let's find the slope. Given the 2 points (0, 10) and (4, 42), we can use the slope calculating formula:
[tex]m(slope)=\frac{y_{2}-y_{1} }{x_{2} -x_{1} }[/tex]
we have:
m = (42-10)/(4-0)
m = 32/4
m=8.
we have y = 8x + 10 (slope-intercept form), which is equal to y = 10 + 8x (unofficial confusing form.)
Hope this helped!
Which statement is correct?
A)The Interquartile Range (IQR) for the Chess Club is equal to the IQR for the Checkers Club.
B)The 3rd Quartile ages for the Chess Club is equal to the 3rd Quartile ages for the Checkers Club.
C)The Median age for the Chess Club members is twice that of the Median age for the Checkers Club members.
D)The Range of the Chess Club members is equal to the Range for the Checkers Club members.
Answer:
B
Step-by-step explanation:
5 The graph shows the relationship between the number of hours Teresa spends
knitting and the number of squares she completes for a blanket. Based on the
equivalent ratios shown in the graph, how many hours does it take Teresa to
knit 265 squares? Show your work.
Teresa's Knitting
Completed Squares
60
50
40
30
20
10
0
0
•
●
6
●
8 10 12
Hours Knitting
It will take 220.8 hour, Teresa to knit 265 squares
What is the ratio?It is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.
Given that the relationship between the number of hours Teresa spends
knitting and the number of squares she completes for a blanket.
We need to find the hours does it take Teresa to knit 265 squares.
Now Based on the equivalent ratios we have;
Teresa's Knitting /Completed Squares
10/12 = x / 265
Thus, Now cross multiplication we get;
x = 265(10/12)
x = 220.8
The answer is 220.8
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Ruby decides to research the relationship between the length in inches and the weight of a certain species of catfish. She measures the length and weight of a number of specimens she catches then throws back into the water. After plotting all her data, she draws a line of best fit. What is the meaning of the x-value on the line when y=25 ?
The required value of x for y = 25 is 32.4
What is a linear function?
A polynomial function of degree 0 or 1 that has a straight line as its graph is said to be linear.
A linear function is given by:
y = mx + b
where:
The slope, or m, indicates how much y changes when x changes by one, or the rate of change.
b is the y-intercept, which is also known as the function's starting point and is the value of y at x = 0.
From the given graph, the line passes through points (32,25) and (48,50), then the slope of the line is given by:
m = (50-25)/(48-32) = 25/16 = 1.6
Then, y = 1.6x + b
For points (48,50) then,
or, 50 = 1.6*48 + b
or, 50 = 76.8 + b
or, b = 50 - 76.8 = -26.8
Then, the equation will be
y = 1.6x - 26.8
So, for y = 25 then x becomes
25 = 1.6x - 26.8
or, 1.6x = 25 + 26.8
or, 1.6x = 51.8
or, x = 32.4
Hence, the required value of x is 32.4.
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Given that 58% of all gold dealers believe next year will be a good one to speculate
in South African gold coins, in a simple random sample of 150 dealers, what is the
probability that between 55% and 60% believe that it will be a good year to
speculate?
The length of a vegetable garden is 6 feet longer than it’s width if the area of the garden is 55 square feet , find its dimensions.
Answer:
Width is 5.
Length is 11.
Step-by-step explanation:
Let the width be x.
x = width
The length is 6 feet longer.
x + 6 = length
Area is
length × width
Area is 55 (given)
55 = x(x+6)
Use distributive property.
55 = x^2 + 6x
Set equal to 0 and factor to solve. See image.
We have to toss out a solution that doesn't make sense. A measure of a side of a rectangle cannot be negative.
see image.
¿Consideras usted que las empresas de servicios pueden incluir todas las cuentas de las empresas comerciales?
Answer:
Step-by-step explanation:
es posible que desee cambiar a la sección de negocios del sitio web porque es posible que puedan responderle mejor
The weight of 10-week-old male children is distributed given a normal with a standard deviation of 87 grams.
How much data is enough to estimate, with a 95% confidence, the average weight of this population with an error not superior to 15 grams?
To determine how much data is enough to estimate the average weight of this population with a 95% confidence and an error not superior to 15 grams, we would need to use a statistical sample size calculator or consult a statistical table. Factors that would need to be considered include the desired confidence level, the desired margin of error, and the standard deviation of the population.
Using a sample size calculator, we can input these values and determine the required sample size. For example, with a 95% confidence level, a margin of error of 15 grams, and a standard deviation of 87 grams, the required sample size would be approximately 38 children. This means that we would need to measure the weight of at least 38 male children who are 10 weeks old in order to estimate the average weight of the population with a 95% confidence and an error not superior to 15 grams.
It is important to note that this is just an estimate and the actual sample size may vary depending on the specific characteristics of the population being studied. Additionally, it is always a good idea to consult with a statistician or other expert to ensure that the appropriate sample size is used in any statistical analysis.
3.4.5* At the end of the section, we let r=1/x-1 in x/x-1+2/3=2/x-1 to get x r+2/3=2 r
While at first we may seem stuck because we have two variables instead of one, we can still use this substitution to solve the problem!
(a) Solve the equation r=1/x-1 for x in terms of r. In other words, manipulate the equation until you have x equal to an expression with r' s in it, but no x's.
(b) Substitute this expression for x in the equation x r+2/3=2 r. Do you have a linear equation now? Solve that equation for r. Use your value of r to find x.
a) Making x the subject of the formula in terms of r is; x = (r + 1)/r
b) Solving for r and x gives; r = 5/3 and x = 8/5
How to change the subject of the formula?a) We are given that;
r = 1/(x - 1)
We are asked to make x the subject of the formula in terms of r. Thus;
Multiply both sides by (x - 1) to get;
rx - r = 1
r + 1 = xr
x = (r + 1)/r
b) We are given that;
xr + ²/₃ = 2r
Put (r + 1)/r for x to get;
r(r + 1)/r + ²/₃ = 2r
r + 1 + ²/₃ = 2r
1 + ²/₃ = r
r = 5/3
Put 5/3 for r into the x equation to get;
x = ((5/3) + 1)/(5/3)
x = (8/3)/(5/3)
x = 8/5
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To obtain information on the corrosion-resistance properties of a certain type of steel conduit, 45 specimens are buried in soil for a 2-year period. The maximum penetration (in mils) for each specimen is then measured, yielding a sample average penetration of x = 52.9 and a sample standard deviation of s = 4.2. The conduits were manufactured with the specification that true average penetration be at most 50 mils. They will be used unless it can be demonstrated conclusively that the specification has not been met. What would you conclude? (Use alpha = 0.05.) State the appropriate null and alternative hypotheses. H_0: mu = 50 H_a: mu notequalto 50 H_0: mu = 50 H_a: mu > 50 H_0: mu notequalto 50 H_a: mu > 50 H_0: mu > 50 H_a: mu = 50 Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) z = P-value = State the conclusion in the problem context. Reject the null hypothesis. There is sufficient evidence to conclude that the true average penetration is more than 50 mils. Do not reject the null hypothesis. There is not sufficient evidence to conclude that the true average penetration is more than 50 mils. Reject the null hypothesis. There is not sufficient evidence to conclude that the true average penetration is more than 50 mils. Do not reject the null hypothesis. There is sufficient evidence to conclude that the true average penetration is more than 50 mils.
Statistic value t=2.27
p-value: < 0.00001
To obtain information on the corrosion-resistance properties of a certain type of steel conduit a random sample of 45 specimens was taken and buried for two years.
The study variable is:
X: Max. penetration of a steel conduit.
The data of the sample
n= 45
sample mean X[bar]= 52.9
sample standard deviation S= 4.2
The conduits are manufactured to have a true average penetration of at most 50 mills, symbolically: μ ≤ 50
The hypothesis is:
H₀: μ ≤ 50
H₁: μ > 50
α: 0.05
To choose the corresponding statistic to use to study the population mean, the variable must have a normal distribution. There is no available information to check this, so I'll just assume that the variable has a normal distribution and, since the population variance is unknown and the sample is small, the statistic to use is a Student t.
Under the null hypothesis, the critical region and the p-value are one-tailed.
Critical value: [tex]t_{n- 1;1-\alpha} =t_{44;0.95} =1.68[/tex]
Rejection rule:
Reject the null hypothesis when t ≥ 1.68
t= [tex]\frac{52.9-50}{\frac{4.2}{\sqrt{45} } }[/tex]
t= 2.9-0.626 = 2.27
If the calculated value is greater than the critical value, the decision is to reject the null hypothesis.
p-value:
P(t ≥ 2.27) = 1 - P(t < 2.27) = < 0.00001.
The p-value is less than α so the decision is to reject the null hypothesis.
Since the null hypothesis was rejected, then the population average of the penetration of the conduits specimens is greater than 50 mils. It is not recommendable to use these conduits.
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