The equation of slope intercept form is y = 3/2x + 12 if a line passes through the point (-6,3) and has a slope of 3/2.
Define slope intercept form.The line with m as the slope, m and c as the y-intercept is the graph of the linear equation y = mx + c. The values of m and c are real integers in the slope-intercept form of the linear equation. The slope, m, is a measure of how steep a line is. The equation of a straight line that passes through a particular point and is inclined at a specific angle to the x-axis can be found using the point slope form. Every point on a line must satisfy the equation for the line in order for it to exist. This implies that a line is represented by a linear equation in two variables.
Given
A line passes through the point (-6,3)
and has a slope of 3/2
Slope intercept form
y = mx + b
Equation,
y - 3 = 3/2(x - (-6))
y - 3 = 3/2(x+6)
2y - 6 = 3x + 18
2y = 3x + 24
y = 3/2x + 12
The equation of slope intercept form is y = 3/2x + 12 if a line passes through the point (-6,3) and has a slope of 3/2.
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Which expressions are equivalent to 20 divided by 1 plus 4
The expression equivalent to "20 divided by 1 plus 4" is 20 ÷ 1 + 4.
What are the rules of PEDMAS?The rules of PEDMAS can be understood by the full form of the name. B stands for bracket, O for of, D for division, M for multiplication, A for addition and S stands for subtraction. For a mathematical expression involving the combination of any of these operators the priority will be given to the letter that comes first.
The given statement for the problem is, " 20 divided by 1 plus 4".
It can be written in the form of expression as follows,
The sign of plus is given as '+'.
And, for divide it is '÷'.
Now, 20 divided by 1 plus 4 can be written as,
20 ÷ 1 + 4
Which is evaluated by BODMAS to give,
20 + 4 = 24.
Hence, the expression for the given case is 20 ÷ 1 + 4 which is equal to 24.
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A wooden box is in the shape of a regular pentagonal prism. The sides, top, and bottom of the box are 1 centimeter thick. Approximate the volume of wood used to construct the box. Round your answer to the nearest tenth.
The volume of the pentagonal prism as per the given values is obtained as 2.5 cm³.
What is a pentagonal prism?A pentagonal prism has two pentagonal surfaces on the top and the bottom. It has ten vertices, 15 edges and 7 faces. The number of rectangular surfaces are five.
The expression for the volume of a regular pentagon is given as V = 5/2 × abh
Where h is the height and a and b are the length of the sides.
Now, the value of a, b and h as per the question is given as,
a = b = h = 1.
Then, the volume can be calculated as,
V = 5/2 × 1 ×1 × 1
= 2.5
Hence, the volume of the regular pentagonal prism is given as 2.5 cm³.
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consider the value of t such that 0.05 of the area under the curve is to the right of t. step 2 of 2: assuming the degrees of freedom equals 18, select the t value from the t table.
Thus after assuming the degrees of freedom equals 18 so the t-critical value will be =2.306
Degree of freedom {df}=18
We have to calculate the t-value such that 0.05 of the area under the curve is to the right of t
It means that, [tex]$\mathrm{P}(\mathrm{T} > \mathrm{t})=0.05$[/tex]
As we know, t distribution provides the cumulative probability
As the value of the total area under the t distribution will 1
So, we can write it as:
[tex]$$\mathrm{P}(\mathrm{T} \leq \mathrm{t})=1-\mathrm{P}(\mathrm{T} > \mathrm{t})$$$\mathrm{P}(\mathrm{T} \leq \mathrm{t})=1-0.05$$=0.95$[/tex]
Now, using excel, we can easily calculate the t-critical value as follows
=T. INV ( Probability, DF)
Where Probability is the area and DF is the degree of freedom,
Now we will enter these values in excel:
=T. INV (0.95,18)
t-critical value can also be found using t table
Look up for df = 18, in very first column
Now look up for 0.05 in one tail row
Now intersect both of them to get the t-critical value
We will get it as: 2.306
So t-critical value will be =2.306
[tex]$\mathrm{P}(\mathrm{T} > 2.306)=0.05$[/tex]
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two different two-digit whole numbers are selected at random. what is the probability that their product is less than 200. express your answer as a common fraction. (hints: (l) there are 90 different two-digit numbers, (2) the pair {10, 11} produces the smallest product and the pair {11, 18} produces the largest product less than 200).
The probability that the product of the two two-digit numbers is less than 200 is given as follows:
43/8010.
How to calculate the probability?A probability is calculated as the division of the number of desired outcomes in the context of the experiment by the number of total outcomes.
There are 90 different two-digit numbers, hence the number of total outcomes for the product is of:
90 x 89 = 8010.
(the numbers have to be different)
The desired outcomes which result in a product of less than 200 are of given as follows:
10 multiplied by 9 numbers, from 11 to 19.11 multiplied by 10, 12, 13, 14, 15, 16, 17, 18. (8 numbers).12 multiplied by 10, 11, 13, 14, 15, 16. (6 numbers).13 multiplied by 10, 11, 12, 14, 15 (5 numbers).14 multiplied by 10, 11, 12, 13. (4 numbers).15 multiplied by 10, 11, 12, 13. (4 numbers).16 multiplied by 10, 11, 12. (3 numbers).17 multiplied by 10, 11. (2 numbers).18 multiplied by 10, 11. (2 numbers).Hence the number of desired outcomes is given as follows:
9 + 8 + 6 + 5 + 4 + 4 + 3 + 2 + 2 = 43.
Meaning that the probability is of:
43/8010.
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emily surveyed all the students at her school to find out if they plan to attend college. the results are shown in the two-way frequency table. emily knows that the student body at her high school is distributed as follows: freshmen: 28% sophomores: 26% juniors: 24% seniors: 22% according to the information emily has gathered, which of the following statements are true? choose all that are correct. responses more than 40% of the students at the school are freshmen or sophomores who plan to attend college. more than 40% of the students at the school are freshmen or sophomores who plan to attend college. more than 10% of the students at the school are juniors or seniors who do not plan to attend college. more than 10% of the students at the school are juniors or seniors who do not plan to attend college. if a student who plans to attend college is selected at random, the probability that he or she is a senior is 0.1804. if a student who plans to attend college is selected at random, the probability that he or she is a senior is 0.1804. if a student at the high school is selected at random, the probability that he or she is a freshman who does not plan to attend college is 0.15. if a student at the high school is selected at random, the probability that he or she is a freshman who does not plan to attend college is 0.15.
The following statements are true are more than 40% of the students at the school are freshmen or sophomores who plan to attend college.
Given :
emily surveyed all the students at her school to find out if they plan to attend college. the results are shown in the two-way frequency table. emily knows that the student body at her high school is distributed as follows: freshmen: 28 % sophomores: 26 % juniors: 24 % seniors: 22 % .
Freshmen = 0.85
sophomores = 0.80
it is clearly visible that the freshmen or sophomores is greater than the 40 % .
Hence , more than 40% of the students at the school are freshmen or sophomores who plan to attend college.
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If a fair coin is tossed 9 times, what is the probability, rounded to the nearest thousandth, of getting at most 2 tails?
Answer:
Below
Step-by-step explanation:
2^9 possibilities =512
9 possibles with only ONE tails (9 C 1)
36 possibles with TWO tails ( 9 C 2)
45 out of 512 45/512 = .088
1. Which equation describes the line with
slope -4 and y-intercept 2?
A y=-4x+2
B y=-4x-2
C y=4x-2
D y = 4x + 2
Answer:
Step-by-step explanation:
The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.
Therefore, the equation of the line with slope -4 and y-intercept 2 is y = (-4)x + 2.
Check the binomial distribution to see whether it can be approximated by the normal distribution. Round p and q to 1 decimal place, as needed. n = 95 P = 0.96 9 -0.04 np - and ng Is a normal approximation appropriate ? Yes No
As per the binomial distribution, the value of the normal approximation is 0.6573
The term binomial distribution refers the discrete probability distribution that gives only two possible results in an experiment, either success or failure.
Here we have given that n = 95 P = 0.96 and q = 0.04
Now, here we have to check the binomial distribution to see whether it can be approximated by the normal distribution.
While we looking into the given question we know that the value of n = 95 P = 0.96.
Then as per the binomial distribution formula, the normal distribution is calculated as,
=> P(X=1) = 95C4 * (0.96)⁴ * (1-0.96)⁹⁵⁻⁴
When we simplify this one then we get the value as 0.6573
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A train travels at 80 miles per hour. An equation can be written that compares the time (t) with the distance (d). What is the domain and range?
1. The domain is distance (d) and the range is time (t).
2. The domain is time (t) and the range is distance (d).
3. The domain is time (t) and the range is 80.
4. The domain is 80 and the range is time (t).
The required answer is the domain is time (t) and the range is a distance (d) i.e. Option 2.
What are domain and range?
The value range that can be plugged into a function is known as its domain. In a function like f, this set represents the x values f(x). The collection of values that a function can take on is known as its range. The values that the function outputs when we enter an x value are in this set.
From the given question, and the above definition of domain and range,
the time (t) acts as an x-values or input value and the distance (d) acts as a y-value or output value
Hence, the domain is time (t) and the range is a distance (d) i.e. Option 2.
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Which statement correctly demonstrates using limits to determine a vertical asymptote of g (x) = StartFraction 2 (x + 4) squared Over x squared minus 16 EndFraction
There is a vertical asymptote at x = 4 because Limit of g (x) as x approaches 4 minus = infinity and limit of g (x) as x approaches 4 plus = negative infinity
There is a vertical asymptote at x = 4 because Limit of g (x) as x approaches 4 minus = infinity and limit of g (x) as x approaches 4 plus = infinity
There is a vertical asymptote at x = –4 because Limit of g (x) as x approaches 4 minus = infinity and limit of g (x) as x approaches 4 plus = negative infinity
There is a vertical asymptote at x = –4 because Limit of g (x) as x approaches 4 minus = negative infinity and limit of g (x) as x approaches 4 plus = infinity
The correct option that describes the vertical asymptote is; B: There is a vertical asymptote at x = 4 because Limit of g (x) as x approaches 4 minus = infinity and limit of g (x) as x approaches 4 plus = infinity
How to find the vertical asymptote of a function?A vertical asymptote of a graph is defined as a vertical line x = a where the graph tends toward positive or negative infinity as the inputs approach a.
A vertical asymptote is a value of x for which the function is not defined, that is, it is a point which is outside the domain of a function;
In a graph, these vertical asymptotes are given by dashed vertical lines.
An example is a value of x for which the denominator of the function is 0, and the function approaches infinity for these values of x.
We are given the function;
g(x) = 2(x + 4)²/(x² - 16)
Simplifying the denominator gives;
(x² - 16) = (x + 4)(x - 4)
Thus, our function is;
g(x) = 2(x + 4)²/[(x + 4)(x - 4)]
(x + 4 ) will cancel out to give;
g(x) = 2(x + 4)/(x - 4)
Vertical asymptote:
Point in which the denominator is 0, so:
(x - 4) = 0
x = 4
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Type your answers into the boxes.
What are the next two numbers in this sequence?
45.7
46.2
46.7
47.2
Answer:
Step-by-step explanation:
Well, it seems like you're adding 5 each time so
45.7
46.2
46.7
47.7
48.2
48.7
A professor wanted to know what proportion of college students believe in ghosts. She polled 200 students and found that 58% said they believe in ghosts. Create a 99% confidence interval for the true proportion of college students believing in ghosts. a. (0.5116, 0.64840 b. (0.2074, 0.3727) c. (0.4901, 0.6699) d. (0.2271,0.3529)
A 99% confidence interval for the true proportion of college students believing in ghosts is Option(c) (0.4901, 0.6699)
According to the question,
A professor wanted to know what proportion of college students believe in ghosts.
For that he drawn a sample from the college.
Sample size : n = 200
Proportion of students that believed in ghosts in sample = 58%
=> p = 0.58
Proportion of students who does not believe in ghost : q = 1 - p
=> q = 0.42
We have to create a 99% confidence interval for a true proportion of college students believing in the ghosts
Formula of C.I = [tex]p \pm ( z_{\alpha} \sqrt{\frac{pq}{n}})[/tex]
Where p and q is sample proportion , z is value of CI at given α level of significance and n is sample size
C.I at 99% = 0.58 ± 2.576 √0.58×0.42/200
=> 0.58 ± 2.576 √0.001218
=> 0.58 ± 2.576 × 0.035
=> 0.58 ± 0.08958
C.I = ( 0.58 - 0.08958 , 0.58 + 0.08958)
=> C.I = (0.4901, 0.6699)
Hence, Option (c) is correct
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Answer:
41%
Step-by-step explanation:
You install 538 feet of fencing along the perimeter of a rectangular yard. The width of the yard is 127 feet. What is the length of the yard?
There are currently 25 frogs in a (large) pond. The frog population grows exponentially, tripling every 10 days.
How long will it take (in days) for there to be 150 frogs in the pond?
Time to 150 frogs: days
The pond's ecosystem can support 1400 frogs. How long until the situation becomes critical?
Time to 1400 frogs: days
There are 21 days for there to be 150 frogs in the pond.
There are 37 days for there to be 1400 frogs in the pond.
What is exponential growth?
Quantity increases over time through a process called exponential growth. When a quantity's instantaneous rate of change with respect to time is proportional to the quantity itself, it happens.
Given:
There are currently 25 frogs in a (large) pond. The frog population grows exponentially, tripling every 10 days.
The exponential equation for the given problem is,
[tex]A(t) = Ar^t^/^1^0[/tex]
To find the number of days for there to be 150 frogs in the pond.
Here,
A(t) = 250, A = 25, r = 3
⇒
[tex]250 = 25(3)^t^/^1^0\\10 = 3^t^/^1^0\\t = 20.97[/tex]
t ≈ 21
Hence, there are 21 days for there to be 150 frogs in the pond.
Now to find how long for there to be 1400 frogs in the pond, we solve:
[tex]1400 = 25(3)^t^/^1^0\\56 = (3)^t^/^1^0\\t = 36.64[/tex]
t ≈ 37
Hence, there are 37 days for there to be 1400 frogs in the pond.
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A line is graphed on the coordinate grid to the right.
Which equation describes the line?
A.y=x/2+1/3
B.y = x/3+1/2
C.y=x/2+15 1/2
D.y=x/3+15 1/2
The equation of the line would be y = x/3 + 1/2.
Option (B) is correct.
What is the slope-intercept form of the line?
The slope-intercept equation is used to find the general equation of a straight line using its slope and the point where it intersects the y-axis. The slope intercept form equation is given as, y = mx + b.
As we can see in the graph the line cuts the y-axis at y = 1/2
so the y-intercept of the line would be c = 1/2.
And when x=4, y = 2
So we can prepare the equation as y = x/3 + 1/2.
Hence, the equation of the line would be y = x/3 + 1/2.
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The equation of the line would be y = x/3 + 1/2.
Option (B) is correct.
What is the slope-intercept form of the line?
The slope-intercept equation is used to find the general equation of a straight line using its slope and the point where it intersects the y-axis. The slope intercept form equation is given as, y = mx + b.
As we can see in the graph the line cuts the y-axis at y = 1/2
so the y-intercept of the line would be c = 1/2.
And when x=4, y = 2
So we can prepare the equation as y = x/3 + 1/2.
Hence, the equation of the line would be y = x/3 + 1/2.
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I need. Help with this question
Derivative of function is 5(2x + 4) * (x² + 4x + 6)⁴.
What is differentiation?
In arithmetic, the derivative of a function of a true variable measures the sensitivity modification of the perform price with relation to a change in its argument. Derivatives are a elementary tool of calculus.
Main body:
by using product rule;
Let = u = x² + 4x + 6
⇒ du/dx = 2x + 4 .
Now y = u⁵
⇒ dy/dx = 5u⁴ .
dy/dx = dy/dx * du/dx = 5u⁴ * (2x + 4)
= 5 * (x² + 4x + 6)⁴ * (2x + 4)
= 5(2x + 4) * (x² + 4x + 6)⁴
hence , derivative of function is 5(2x + 4) * (x² + 4x + 6)⁴.
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Select all the points that are on the graph of the line Y=2x+5
Answer:
Some points that are on this line are:
(-7,-9) (-6,-7) (-5,-5) (-4,-3) (-3,-1) (-2,1) (-1,3) (0,5) (1,7) (2,9)
The function f(x)=9.25x + 3 represents the amount radda earns dog walking for X hours
Since the function f(x) = 9.25x + 3 represents the amount of money that Radda earns dog walking for x hours, Radda's earnings would increase by $12.25 each hour.
How to write a linear function for the total amount of money Radda earns?In Mathematics, a linear function is sometimes referred to as an expression or the slope-intercept form of a straight line and it can be used to model (represent) the total amount of money that is being earned by Radda for dog walking;
T = mx + b
Where:
T represents the total amount of money earned.m represents the rate of change (slope) per hour.x represents the number of hours or time.b represents the y-intercept or initial amount.Therefore, the required linear function that represents the total amount of money that is being earned by Radda for dog walking per hour is given by this mathematical expression;
f(x) = T = 9.25x + 3
When the number of hours Radda spend dog walking is equal to 1 (x = 1), the rate of change(slope) can be calculated as follows;
f(1) = T = 9.25(1) + 3
f(1) = T = 9.25 + 3
f(1) = T = $12.25.
In this context, we can reasonably infer and logically conclude that Radda's earnings increases each hour by $12.25.
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Complete Question:
The function f(x) = 9.25x + 3 represents the amount Radda earns dog walking for x hours. How much does Radda's earnings increase each hour?
What is the freezing point, in C, of a 2.75 m solution of C8H18 in benzene?
The freezing point of the 2.75 m solution of octane in benzene is -8.56 °C.
The freezing point of a solution is the temperature at which the solution becomes a solid. The freezing point of a solution is lower than the freezing point of the pure solvent because the solute particles interfere with the movement of the solvent molecules, which slows down the freezing process.
To determine the freezing point of a solution, we can use the freezing point depression equation:
ΔTf = Kf x molality
where ΔTf is the change in freezing point, Kf is the freezing point depression constant for the solvent, and molality is the concentration of the solute in the solution expressed in moles of solute per kilogram of solvent.
To find the freezing point of a 2.75 m solution of C8H18 (octane) in benzene, we need to know the freezing point depression constant for benzene, which is 5.12 °C/m. We can then use the equation above to calculate the change in freezing point:
ΔTf = 5.12 °C/m x 2.75 m = 14.06 °C
To find the freezing point of the solution, we need to subtract the change in freezing point from the freezing point of the pure solvent. The freezing point of pure benzene is 5.5 °C, so the freezing point of the 2.75 m solution of octane in benzene is:
5.5 °C - 14.06 °C = -8.56 °C
This means that the freezing point of the 2.75 m solution of octane in benzene is -8.56 °C. At this temperature, the solution will become a solid.
Let f:R→S be a surjective homomorphism of rings with identity.
(a) If R is a PID, prove that every ideal in S is principal.
(b) Show by example that S need not be an integral domain.
Every ideal of S is principal when f:R⇒S be a surjective homomorphism of rings with identity.
In a homomorphism, corresponding elements of two systems behave very similarly in combination with other corresponding elements. For example, let G and H be groups. The elements of G are denoted g, g′,…, and they are subject to some operation ⊕.
In algebra, a homomorphism is a structure-preserving map between two algebraic structures of the same type (such as two groups, two rings, or two vector spaces). The word homomorphism comes from the Ancient
Let f:R⇒S be a surjective homomorphism of rings with identity.
We have to find if R is a PID, prove that every ideal in S is principal.
We know that,
Let I be the ideal of S
Since f is sufficient homomorphism.
So, f⁻¹(I) is an ideal of R.
Since R is PID so ∈ r ∈ R such that
f⁻¹(I) = <r>
I = <f(r)>
Therefore,
Every ideal of S is principal when f:R⇒S be a surjective homomorphism of rings with identity.
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which graph represents the equation y =1/3 x + 2
The graph of the equation y = (1/3)x + 2 is passing through points
(3, 3) and ( -3, 1).
What is a graph?The set of ordered pairings (x, y) where f(x) = y makes up the graph of a function.
These pairs are Cartesian coordinates of points in two-dimensional space and so constitute a subset of this plane in the general case when f(x) are real values.
Given, A linear equation y = (1/3)x + 2.
Now to graph the equation we'll simply put some arbitrary values of x which will correspond to some values of y and plot them then we'll join them with a straightedge.
When x = 3, y = 3 ⇒ (3, 3).
When x = - 3, y = 1 ⇒( -3, 1).
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according to wine-searcher, wine critics generally use a wine-scoring scale to communicate their opinions on the relative quality of wines. wine scores range from to , with a score of indicating a great wine, indicating an outstanding wine, indicating a very good wine, indicating a good wine, indicating a mediocre wine, and below indicating that the wine is not recommended. random ratings of a pinot noir recently produced by a newly established vineyard in follow: excel file: data07-11.xlsx 87 91 86 82 72 91 60 77 80 79 83 96 a. develop a point estimate of mean wine score for this pinot noir (to decimals). 82.00 b. develop a point estimate of the standard deviation for wine scores received by this pinot noir (to decimals). 9.6389
(a) The point estimate of mean wine score for this pinot noir is 82.
(b) The point estimate of standard deviation wine score for this pinot noir is 9.6389.
Below table showing calculation of Point Estimate of Mean and Standard Deviation:
Score X-X’ (X-X’)^2
87 5 25
91 9 81
86 4 16
82 0 0
72 -10 100
91 9 81
60 -22 484
77 -5 25
80 -2 4
79 -3 9
83 1 1
96 14 196
984 1022
Mean(X’) = Total Score/n
n = Total number = 12
X’ = 984/12 = 82
Standard Deviation (σ) = √∑(X-X’)^2/(n-1)
σ = √1022/(12-1)
σ = √1022/ 11
σ = 9.6389
(a) The point estimate of mean wine score for this pinot noir is 82.
(b) The point estimate of standard deviation wine score for this pinot noir is 9.6389
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URGENT!!!!
Find z such that 7% of the area under the standard normal curve lies to the right of z.
The value of z such that 7% of the area under the standard normal curve lies to the right of z is approximately -0.4
How to find z such that 7% of the area under the standard normal curve lies to the right of z?
To find the value of z such that 7% of the area under the curve lies to the right of z, we need to find the value of z such that 43% of the area lies to the left of z.
This value of z is known as the 43rd percentile of the standard normal curve.
We can use a table of the standard normal distribution, also known as the z-table, to find the value of z corresponding to the 43rd percentile.
According to the z-table, the value of z corresponding to the 43rd percentile is approximately -0.4
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What is BC?
BC= units?
The value of BC = 25 using properties of triangle.
What are properties of triangle ?
Let us discuss here some of the properties of triangles.
1. A triangle has three sides and three angles.
2. The sum of the angles of a triangle is always 180 degrees.
3. The exterior angles of a triangle always add up to 360 degrees.
4. The sum of consecutive interior and exterior angle is supplementary.
Properties for isosceles:
Isosceles triangles are those triangles that have at least two sides of equal measure.
1. Two equal sides and two equal angles.
2. The two equal sides of an isosceles triangle are called the legs and the angle between them is called the vertex angle or apex angle.
3. The side opposite the vertex angle is called the base and base angles are equal.
Using 1st property,
in given triangle two angles are equal then opposite side will also be equal.
So, AB = AC
i.e. 4x+4 = 6x-14
4+14 = 6x-4x
18 = 2x
x = 9
Putting value of x in BC
BC = 2*9 +7
= 18+7
= 25.
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The table represents a linear relationship. x −2 0 2 4 y −1 0 1 2 Which of the following graphs shows this relationship?
The graph that shows the linear relationship of the table is attached below.
How to Find the Graph that Represent a Linear Relationship?To determine the graph of a linear relationship, do the following:
Find the slope or rate of change = change in y / change in x.Determine the y-intercept which is the value of y when x = 0, and it represents the value on the y-axis where the line intercepts.Given the table which represents a linear relationship above, use two pairs of values, (0, 0) and (2, 1) to find the slope:
Slope = change in y / change in x = (1 - 0) / (2 - 0)
Slope = 1/2.
The y-intercept (b) = 0.
Thus, this means that the graph of the linear relationship will have a slope of 1/2 and crosses the y-axis at 0.
Thus, the graph is shown below.
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A manufacturer of banana chips would like to know whether its bag filling machine works correctly at the 414 gram setting. Based on a 8 bag sample where the mean is 407 grams and the standard deviation is 18, is there sufficient evidence at the 0.025 level that the bags are underfilled? Assume the population distribution is approximately normal.
Step 1 of 5:
State the null and alternative hypotheses.
Step 2 of 5:
Find the value of the test statistic. Round your answer to three decimal places.
Step 3 of 5:
Specify if the test is one-tailed or two-tailed.
Step 4 of 5:
Determine the decision rule for rejecting the null hypothesis. Round your answer to three decimal places.
Step 5 of 5:
Make the decision to reject or fail to reject the null hypothesis.
Question #2:
Our environment is very sensitive to the amount of ozone in the upper atmosphere. The level of ozone normally found is 4.8 parts/million (ppm). A researcher believes that the current ozone level is at an insufficient level. The mean of 26 samples is 4.6 ppm with a standard deviation of 1.2. Does the data support the claim at the 0.025 level? Assume the population distribution is approximately normal.
Step 1 of 5:
State the null and alternative hypotheses.
Step 2 of 5:
Find the value of the test statistic. Round your answer to three decimal places.
Step 3 of 5:
Specify if the test is one-tailed or two-tailed.
Step 4 of 5:
Determine the decision rule for rejecting the null hypothesis. Round your answer to three decimal places.
Step 5 of 5:
Make the decision to reject or fail to reject the null hypothesis.
A)
A manufacturer of banana chips would like to know whether its bag-filling machine works correctly at the 414-gram setting.
So, Null hypothesis: [tex]H_{0}[/tex] : μ < 414
It is believed that the machine is underfilling the bags.
So, Alternate hypothesis: [tex]H_{1}[/tex] : μ < 414
Given,
n= 8
Population standard deviation (б) = 18
x= 407
We will use the t-test since n > 8 and we are given the population standard deviation.
t=x-μ / (б/[tex]\sqrt{n-1}[/tex])
t= [tex]\frac{407-414}{\frac{18}{\sqrt{7} } }[/tex]
t= -1.028
Use the t table to find p value
p-value = 12.706
Level of significance α = 0.025
p-value>α
It is a two-tailed test.
So, we fail to reject the null hypothesis.
So, its bag-filling machine works correctly at the 414-gram setting.
B)
Let μ be the population mean amount of ozone in the upper atmosphere.
As per the given, we have
[tex]H_{0}[/tex] : μ = 4.8
[tex]H_{1}[/tex] : μ ≠ 4.8
Sample size: n= 26
Sample mean = 4.6
Standard deviation = 1.2
Since population standard deviation is now given, so we use a t-test.
t= [tex]\frac{4.6-4.8}{\frac{1.2}{\sqrt{25} } }[/tex]
t= -0.2/0.24
t= -0.833
It is a two-tailed test.
We are accepting the null hypothesis.
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in the morning there were t people at the beach. later at noon, 2/7 of the people left the beach and there were 30 people left on the beach. find t
Answer:
42
Step-by-step explanation:
If 2/7 left that means that 5/7 are still there.
5/7x = 30 Multiple both sides by 7/5
x = [tex]\frac{30}{1}[/tex] x [tex]\frac{7}{5}[/tex]
x = 42
Is there anyone that can help me with a finance question?
Answer:
Yes, there are many people who can help you with a finance question. Some of the people who can help you include: financial advisors, accountants, financial planners, and financial analysts. Additionally, there are many online resources available such as personal finance forums, websites, and blogs.
Step-by-step explanation:
exercise 28 a sample of 20 joint specimens of a particular type gave a sample mean proportional limit stress of 8.52 mpa and a sample standard deviation of 0.78 mpa.
A 95% % lower confidence bound for the true average proportional limit stress of all such joints is 8.01.
In the given question, a sample of 20 joint specimens of a particular type gave a sample mean proportional limit stress of 8.52 mpa and a sample standard deviation of 0.78 mpa.
We have to calculate and interpret a 95% lower confidence bound for the true average proportional limit stress of all such joints.
Sample size: n = 13
Sample mean: x’ = 8.52 mps
Sample standard deviation: s = 0.78 mps
95% lower confidence bound for the true average proportional limit stress of all such joints
Level of Significance (α) = 1-95% = 5% = 0.05
α/2 = 0.025
So the value of t(α/2) = 1.8
The confidence interval = x’± t(α/2)*s/√n
Now putting the value:
The confidence interval = 8.41± (1.8)*(0.78)/√12
The confidence interval = 8.41± (1.8)*(0.226)
The confidence interval = 8.41± 0.4068
The confidence interval = (8.41- 0.4068, 8.41+ 0.4068)
The confidence interval = (8.01, 8.82)
A 95% % lower confidence bound for the true average proportional limit stress of all such joints is 8.01.
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The right question is:
A sample of 12 joint specimens of a particular type gave a sample mean proportional limit stress of 8.41 mpa and a sample standard deviation of 0.78 mpa.
Calculate and interpret a 95% lower confidence bound for the true average proportional limit stress of all such joints. (Round your answer to two decimal places.)
your ultra modern store is one story round. your square footage is 31,415. what is your he diameter of your store? area of a circle =
The solution is D = 200 feet
The diameter of the circular store is = 200 feet
What is a Circle?
A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle
The perimeter of circle = 2πr
The area of the circle = πr²
where r is the radius of the circle
The standard form of a circle is
( x - h )² + ( y - k )² = r²,
where r is the radius of the circle and (h,k) is the center of the circle
Given data ,
Let the diameter of the circle be represented as = D
Let the radius of the circular store be = r
D = 2r
Now , the area of the circular store be = A
The value of A = 31,415 feet²
The area of the circular store is given by the formula
Area of the circle = πr²
Substituting the values in the equation , we get
31415 = 3.1415 x r²
Divide by 3.1415 on both sides of the equation , we get
r² = 10000
Taking square roots on both sides of the equation , we get
r = 100 feet
Now , the diameter of the store = 2 x radius of the store
Diameter of the store D = 2 x 100 feet
Therefore , diameter of the store D = 200 feet
Hence , The diameter of the circular store is = 200 feet
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