Answers
Answer:
n = -7
Step-by-step explanation:
n - 7/4 = 35/12 + 5/3n
subtract n from both sides of the equation:
-7/4 = 35/12 + 2/3n
convert -7/4 to -21/12:
-21/12 = 35/12 + 2/3n
add 21/12 to both sides:
0 = 56/12 + 2/3n
convert 2/3n to 8/12n:
0 = 56/12 + 8/12n
subtract 56/12 from each side:
8/12n = -56/12
multiply both side by 12:
8n = -56
divide both sides by 8:
n = -7
Related Questions
a sample of 20 cupcakes found the interval for average calories to be (150, 350). which is the correct interpretation of the 95% confidence interval?
Answers
95% is the correct interpretation of the 95% confidence interval.
What is a confidence interval?
Using confidence intervals, one can gauge how "good" an estimate is; the wider the 90% confidence interval is for a given estimate, the more care must be taken when using that estimate. Confidence intervals serve as a crucial reminder of the estimates' limits.The confidence level informs us of the probability that the procedure we are employing will result in an interval of data or a range of data that will capture the population parameter.
A confidence interval's capture of a population parameter is never indicated by the confidence level.
We are therefore 95% certain that it captures the true mean, which seems to be correct.
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For a Scalar function , Prove that X. ( =0)
(b) When X1 ,X2 ,X3 are
linearly independent solutions of X'=AX, prrove that
2X1-X2+3X3 is also a solution of
X'=AX
Answers
To prove that X(=0), we need to show that when X is a scalar function, its derivative with respect to time is zero.
Let's consider a scalar function X(t). The derivative of X(t) with respect to time is denoted as dX/dt. To prove that X(=0), we need to show that dX/dt = 0.
The derivative of a scalar function X(t) is computed as dX/dt = AX(t), where A is a constant matrix and X(t) is a vector function.
Since X(=0), the derivative becomes dX/dt = A(0) = 0. Thus, the derivative of X(t) is zero, which proves that X(=0).
Now, let's consider the second part of the question. We are given that X1, X2, and X3 are linearly independent solutions of the differential equation X'=AX. We need to prove that 2X1-X2+3X3 is also a solution of the same differential equation.
We can verify this by substituting 2X1-X2+3X3 into the differential equation and checking if it satisfies the equation.
Taking the derivative of 2X1-X2+3X3 with respect to time, we get:
d/dt (2X1-X2+3X3) = 2(dX1/dt) - (dX2/dt) + 3(dX3/dt)
Since X1, X2, and X3 are linearly independent solutions, we know that dX1/dt = AX1, dX2/dt = AX2, and dX3/dt = AX3.
Substituting these expressions, we get:
2(dX1/dt) - (dX2/dt) + 3(dX3/dt) = 2(AX1) - (AX2) + 3(AX3)
Using the properties of matrix multiplication, this simplifies to:
A(2X1-X2+3X3)
Thus, we can conclude that 2X1-X2+3X3 is also a solution of the differential equation X'=AX.
The proof shows that for a scalar function X(=0), the derivative is zero. Additionally, for the given linearly independent solutions X1, X2, and X3, the expression 2X1-X2+3X3 is also a solution of the differential equation X'=AX.
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If x= - 2 is a solution to the equation f(x) = g(x), which one of these statements must be true?
• The graphs of f and g intersect each other at x = -2
• The graphs of f and g intersect each other at x = 2
• The graphs of f and g intersect the x-axis at -2
• The graphs of f and g intersect at the y-axis at -2
Answers
Answer:
C
Step-by-step explanation:
Lara plants some sunflowers and notices that they grow 1/9 foot per day. How many days will it take Lara's sunflowers to grow to a height of 7/12 feet?
Enter your answer as a fraction or mixed number, like this: 42/53
Answers
Answer:
68 1/4
Step-by-step explanation:
I used the desmos scientific calculator to divide the plant height by the height they grow per day
Identify the elements of the range of the function shown in the graph.
Responses
6
3
1
5
2
-6
Answers
The range of the relation on the graph is:
R: {1, 2, 6}
How to identify the range on the graph?For a relation y = f(x), the range is defined as the set of the possible outputs of the function (the possible values of y).
Here we can see a graph of 3 points, such that the coordinates of these points (on the form (x, y)) is:
(3, 6), (5, 2) and (6, 1)
The range is the set of the second values of each of these pairs, so the range in this case is:
R: {1, 2, 6}
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Calculators cost $40 each at Tech Central. How many calculators can Mrs.Robinson buy for her class with $1,000 if the tax on each calculator is 0.30? Write an equation.
Answers
1,000/40.30=24.8
she can only buy 24 calculators all together
Answer:
24
Step-by-step explanation:
TRUST
Can anyone help with this?
Answers
Step-by-step explanation:
(a): √8 = √4√2 = 2√2. => k = 2
(b): √50 = √25√2 = 5√2. => k = 5
(c): √98 = √49√2 = 7√2. => k = 7
(d): √12 = √4√3 = 2√3. => k = 2
(e): √300 = √100√3 = 10√3. => k = 10
(f): √45 = √9√5 = 3√5. => k = 3
(g): √125 = √25√5 = 5√5. => k = 5
(h): √28 = √4√7 = 2√7. => k = 2
Lillian built a staircase out of blocks. She used 3 blocks to make the first step, 6 blocks to make the second step and 9 blocks to make the third step. If she continues using the same pattern, how many total blocks will she have used after making the fourth step?
Answers
Answer:
30
Step-by-step explanation:
if you take 3+6+9+12 you get 30
Answer:
C
Step-by-step explanation:
will give brainliest Each exterior angle of a certain regular polygon is 20°, so each interior angle of that polygon must be ______
Answers
Answer:
i think it would be 10 degrees
Answer:
160
Step-by-step explanation:
In ΔOPQ, the measure of ∠Q=90°, the measure of ∠P=79°, and QO = 8.5 feet. Find the length of OP to the nearest tenth of a foot.
Answers
Answer:8.7
Step-by-step explanation:
identify the type of proportion and solve the problem. rose bought 8 bags at 880. if rit buys 12 of such kind of bags, how much will she pay?
Answers
Answer:
1320
Step-by-step explanation:
880/8 = 110
12x110 = 1320
Answer:
1,320
Step-by-step explanation:
880/8= $110
$110×12= 1,320
Mrs. Buchanan gave her two daughters $5 to share equally at the carnival. How much money will each daughter have to spend?
Answers
Answer: $2 and 5 cents each
Step-by-step explanation:
Each daughter will equally split up the 5 dollars, so 5 divided by 2, you will get 2.5
a professor at a local university noted that the exam grades of her students were normally distributed with a mean of 68 and a standard deviation of 17. according to the professor's grading scheme only the top 12.3 percent of her students receive grades of a. what is the minimum score needed to receive a grade of a? write your answer to two decimal points.
Answers
A minimum score of 88.95 is required to receive an "A" grade on the exam.
To determine the minimum score required to receive an "A" grade on an exam, we must first understand the meaning of standard deviation and mean. The mean is the average of a set of values, whereas the standard deviation is a measure of how far apart the values are from the mean. The minimum score required to receive an "A" grade is determined by calculating the z-score that corresponds to the top 12.3 percent of exam scores.
The formula for calculating the z-score is given as: z = (x - μ)/σ, where x is the raw score, μ is the population mean, and σ is the population standard deviation. Solving for z, we have: z = invNorm(1 - 0.123) = invNorm(0.877) ≈ 1.15. The inverse normal distribution function is used to determine the value of z that corresponds to the area to the right of the z-score. We can then use the formula for the z-score to solve for the raw score (x):
x = zσ + μ
Substituting the values we have, we get:
x = 1.15(17) + 68 ≈ 88.95
Therefore, a minimum score of 88.95 is required to receive an "A" grade in the exam.
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For each transformation in the table below, indicate which properties are true and false by selecting true or false from the drop down menus in each box
Answers
Translation, rotation, and reflection are three of the fundamental transformations.
What properties do transformations have?Translation, rotation, and reflection are three of the fundamental transformations.The four main categories of transformations are as follows :Rotation.Translation.Dilation.ReflectionA metamorphosis is a significant alteration in appearance or form. The only change that might provide similarity is dilation.Non-rigid transformations are those that dilate when length and angle measurements are not preserved.Since they maintain length, translation, reflection, and rotation are isometries. Congruency transformations are hence translation, reflection, and rotation.An image that is congruent to the preimage is produced through stiff or isometric transformation.To learn more about transformation refer to:
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Help me please please
Answers
Answer:
a)
\(EH = \sqrt{HG^2+EG^2} = \sqrt{4^2+6^2} = \sqrt{16+36} = \sqrt{52} = 2\sqrt{13}\)b)
EG² = GH*GFEG² = 4*12EG² = 48EG = √48 = 4√3Roller Coaster Engineering. The
height, y m, of a rider above the
ground in a section of roller coaster
ride is given by y=1/3x²- 2x + 8,
where x m is the rider's horizontal
distance from the start of the ride.
(i) Express the function in the form
y = a(x - h)² + k.
(ii) Find the rider's minimum height
above the ground.
(iii) If the rider is 8 m above the dw
ground after the ride starts, find
the rider's horizontal distance from
the start of the ride.
Answers
a) The vertex-form definition of the quadratic function is given as follows: y = 1/3(x - 3)² + 5.
b) The rider's minimum height above the ground is of: 5 meters,
c) The horizontal distance is given as follows: x = 0 m and x = 6 m.
How to obtain the features?The quadratic function in the context of this problem is defined as follows:
y = x²/3- 2x + 8.
In which:
x is the horizontal distance.y is the vertical distance.The coefficients are given as follows:
a = 1/3, b = -2, c = 8.
The x-coordinate of the vertex is given as follows:
x = -b/2a = -(-2)/(2/3) = 3.
Hence the y-coordinate of the vertex is given as follows:
y = (3)²/3 - 2(3) + 8 = 5 meters.
Hence the vertex-form definition of the equation is given as follows:
y = 1/3(x - 3)² + 5.
As the function is concave up, the minimum height is of 5 meters.
For the horizontal distance at a height of 8m, we have that:
x²/3 - 2x + 8 = 8
x²/3 - 2x = 0
x(x/3 - 2) = 0.
Hence:
x = 0 m and x = 6 m.
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A cardboard box is formed by cutting squares from the corners of a 12 in. by 8 in. rectangular piece of cardboard, folding up the sides (along the dotted lines), and taping the corners as shown.
Part A
Formulate a model function for the problem situation, where V(w) is the volume in cubic inches of the box and w is the width in inches of the squares cut out of the rectangular piece of cardboard.
Part B
Create a graph of the function over the appropriate mathematical domain and range, and create a graph of the model function over an appropriate domain and range for the problem situation.
Part C
What are the roots of the graph of V(x) over the domain of all real numbers? What is significant about the roots in terms of this problem situation?
Part D
What is the maximum volume possible for this box and what would be the side width of the cut out square? Round the volume to the nearest tenth of a cubic inch and the width of the cut out square to the nearest hundredth of an inch.
Answers
The maximum volume of the box is the highest volume the box can have.
The model of the function is: \(\mathbf{V(w) = (4 + w) \times w \times \frac{8 - w}{2}}\)The roots of V(x) are: \(\mathbf{x = 0,4,6}\).The maximum volume is: 67.60 cubic inches, and the width of the cut-out is 1.569 inch(a) A model function V(w)
The dimension of the cardboard is given as:
\(\mathbf{l =12}\)
\(\mathbf{w =8}\)
Assume the cut-out is x.
So, we have:
\(\mathbf{l =12 - 2x}\)
\(\mathbf{w =8 - 2x}\)
\(\mathbf{h = x}\)
Make x the subject in \(\mathbf{w =8 - 2x}\)
\(\mathbf{x = \frac{8 - w}{2}}\)
The volume of the box is calculated as:
\(\mathbf{V = lwh}\)
Substitute expressions for l and h
\(\mathbf{V = (12 - 2x) \times w \times x}\)
Substitute \(\mathbf{x = \frac{8 - w}{2}}\)
\(\mathbf{V = (12 - 2\times (\frac{8 - w}{2})) \times w \times \frac{8 - w}{2}}\)
\(\mathbf{V = (12 - (8 - w)) \times w \times \frac{8 - w}{2}}\)
\(\mathbf{V = (12 - 8 + w) \times w \times \frac{8 - w}{2}}\)
\(\mathbf{V = (4 + w) \times w \times \frac{8 - w}{2}}\)
So, we have:
\(\mathbf{V(w) = (4 + w) \times w \times \frac{8 - w}{2}}\)
Hence, the model of the function is: \(\mathbf{V(w) = (4 + w) \times w \times \frac{8 - w}{2}}\)
(b) The graph of the function and the model function
In (a), we have:
\(\mathbf{V = (12 - 2x) \times w \times x}\)
Substitute \(\mathbf{w =8 - 2x}\)
\(\mathbf{V = (12 - 2x) \times (8 -2x) \times x}\)
So, we have:
\(\mathbf{V(x) = (12 - 2x) \times (8 -2x) \times x}\)
See attachment for the graphs of V(x) and V(w)
(c) The roots of V(x)
From the graph of V(x), the roots are:
\(\mathbf{x = 0,4,6}\)
These values represent the possible cut-outs from the cardboard
(d) The maximum volume
From the graphs of V(x) and V(w), the maximum volume is:
\(\mathbf{Maximum = 67.60}\)
And the width of the cut-out is:
\(\mathbf{Width= 1.569}\)
Hence, the maximum volume is: 67.60 cubic inches, and the width of the cut-out is 1.569 inch
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may someone help me please.
Answers
Answer:
c
Step-by-step explanation:
i think
the fluid ounces in syrup bottles is normally distributed with a mean of 18 oz. and a standard deviation of 1 oz. what is the minimum number of ounces a bottle could have and remain in the top 10.56% of all syrup bottles? group of answer choices the answer cannot be determined with the information given. 16.75 ounces 19.25 ounces 18.80 ounces
Answers
The minimum number of ounces a bottle could have and remain in the top 10.56% of all syrup bottles is approximately 19.23 ounces.
To find the minimum number of ounces a bottle could have and remain in the top 10.56% of all syrup bottles, we need to determine the corresponding z-score for that percentile and then calculate the corresponding value using the mean and standard deviation.
The z-score can be calculated using the percentile and the standard normal distribution (Z-distribution).
Step 1: Convert the given percentile to a z-score.
Since we are interested in the top 10.56% of the distribution, the corresponding percentile is 100% - 10.56% = 89.44%.
Using a standard normal distribution table or a calculator, we can find the z-score corresponding to the 89.44th percentile, which is approximately 1.23.
Step 2: Calculate the value using the z-score formula.
The formula for calculating the value from a z-score is:
Value = Mean + (Z-score * Standard Deviation)
Given:
Mean (μ) = 18 oz.
Standard Deviation (σ) = 1 oz.
Z-score (Z) = 1.23
Value = 18 + (1.23 * 1)
Value = 18 + 1.23
Value ≈ 19.23
Therefore, the minimum number of ounces a bottle could have and remain in the top 10.56% of all syrup bottles is approximately 19.23 ounces.
Among the answer choices provided, the closest option is 19.25 ounces.
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Which table has a constant of proportionality between
�
yy and
�
xx of
12
1212?
Choose 1 answer:
Choose 1 answer:
(Choice A)
�
xx
�
yy
1
2
2
1
start fraction, 1, divided by, 2, end fraction
6
66
2
22
24
2424
10
1010
120
120120
A
�
xx
�
yy
1
2
2
1
start fraction, 1, divided by, 2, end fraction
6
66
2
22
24
2424
10
1010
120
120120
(Choice B)
�
xx
�
yy
1
4
4
1
start fraction, 1, divided by, 4, end fraction
3
33
3
33
60
6060
12
1212
144
144144
B
�
xx
�
yy
1
4
4
1
start fraction, 1, divided by, 4, end fraction
3
33
3
33
60
6060
12
1212
144
144144
(Choice C)
�
xx
�
yy
1
3
3
1
start fraction, 1, divided by, 3, end fraction
4
44
6
66
78
7878
9
99
117
117117
C
�
xx
�
yy
1
3
3
1
start fraction, 1, divided by, 3, end fraction
4
44
6
66
78
7878
9
99
117
117117
Answers
The table that have a constant of proportionality between y and x of 12 is the first table
What is the table that have a constant of proportionality between y and x of 12?From the question, we have the following parameters that can be used in our computation:
The table of values
From the first table of values, we have the following readings
(x, y) = (1/2, 6), (2, 24) and (10, 120)
Using the above as a guide, we have the following:
The constant of proportionality between y and x in the graph is
k = y/x
Substitute the known values in the above equation, so, we have the following representation
k = 6/(1/2) = 24/2 = 120/10
Evaluate
k = 12 = 12 = 12
Hence, the constant of proportionality between y and x in the first table is 12
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Complete question
Which table has a constant of proportionality between y and x of 12?
x 1/2 2 10
y 6 24 120
x 1/4 3 12
y 3 60 144
x 1/3 6 9
y 4 78 117
Adult tickets to a concert sold at $8, while student tickets cost $5.
If 70 tickets were sold for a total of $440, how many adult tickets were sold?
40 tickets
30 tickets
55 tickets
15 tickets
Answers
Step by step:
When you multiply 30x8 you get 240. You multiply by 8 because that is how much one adult ticket costs. And they tell you that they sold a total of 70 tickets, which means to find the number of children tickets that were sold would be 70-30=40. Then to prove that for sure, multiply...
40x5=200. You multiply by 5 because that is how much one children ticket costs.
Then when you add the totals of the adult tickets sold and the children tickets sold, you get $440, which means that 30 adult tickets were sold!!
You can use this same process for problems like these or to verify the answer!
Please give me brainliest!
Hope this helped!
The number of adult tickets sold was 30 tickets
The first step is to write out the parameters given in the question;
Adult ticket sold at the concert is at the price of $8
Student tickets sold cost $5
A total of 70 tickets were sold at $440
Therefore the number of adult tickets sold can be calculated as follows;
= 8(5)
= 40
70-40
= 30
Hence the number of adult tickets sold is 30 tickets
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This sample is selected by dividing the population into subgroups and then taking a fixed number of units from each group using the simple random sample. simple random sample stratified random sample cluster random sample Voluntary random sample
Answers
The correct sampling method described in the question is a stratified random sample among the simple random sample, stratified random sample, cluster random sample and Voluntary random sample
The sampling method described in the question is a stratified random sample.
In a stratified random sample, the population is divided into subgroups or strata based on certain characteristics or criteria. Then, a random sample is selected from each stratum. The key idea behind this method is to ensure that each subgroup is represented in the sample proportionally to its size or importance in the population. This helps to provide a more accurate representation of the entire population.
In the given sampling method, the population is divided into subgroups, and a fixed number of units is taken from each group. This aligns with the process of a stratified random sample. The sample selection is random within each subgroup, but the number of units taken from each group is fixed.
Other sampling methods mentioned in the question are:
Simple random sample: In a simple random sample, each unit in the population has an equal chance of being selected. This method does not involve dividing the population into subgroups.
Cluster random sample: In a cluster random sample, the population is divided into clusters or groups, and a random selection of clusters is included in the sample. Within the selected clusters, all units are included in the sample.
Voluntary random sample: In a voluntary random sample, individuals self-select to participate in the sample. This method can introduce bias as those who choose to participate may have different characteristics than those who do not.
Therefore, the correct sampling method described in the question is a stratified random sample.
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Consider the following. f(x) = ex if x < 0 x2 if x ≥ 0 , a = 0
Find the left-hand and right-hand limits at the given value of a. lim x→0− f(x) =_______
lim x→0+ f(x) =_________
Explain why the function is discontinuous at the given number a.
Since these limits are_________ , lim x→0 f(x)________ and f is therefore discontinuous at 0.
Answers
Since these limits are not equal, lim x→0 f(x) does not exist, and f is therefore discontinuous at 0.
The left-hand limit at a = 0 is lim x→0− f(x) = e0 = 1. The right-hand limit at a = 0 is lim x→0+ f(x) = 02 = 0.
The function is discontinuous at a = 0 because the left-hand and right-hand limits do not match. The left-hand limit approaches 1, while the right-hand limit approaches 0. This means that as x approaches 0 from the left and from the right, the function approaches different values, and therefore there is a "jump" in the graph of the function at x = 0.
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Which function has real zeros at x = 3 and x = 7?
f(x) = x2 + 4x - 21
Cf(x) = x2 - 4x - 21
Cf(x) = x2 - 10x + 21
f(x) = x2 - 10x - 21
Answers
Answer:
f(x) = x2 – 10x + 21
Step-by-step explanation:
I got it because you substract and add the last part
A particular mobile phone produced must be less than 8 ounces in weight with a tolerance of 0.3 ounces. The mobiles that are not within the tolerated weight must be recycled. Show which mobiles are tolerable? ( W is the weight of the mobiles).
Answers
The inequality that gat can be used to show the mobiles that are tolerable is w - 8 <= 0.3.
How to illustrate the information?It should be noted that from the information, the
mobile phone produced must be less than 8 ounces in weight with a tolerance of 0.3 ounces.
Therefore, the mobiles are tolerable with an inequality will be:
w - 8 <= 0.3.
where w = weight of the mobiles.
In conclusion, the mobiles are tolerable with an inequality will be w - 8 <= 0.3.
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A particular mobile phone produced must be less than 8 ounces in weight with a tolerance of 0.3 ounces. The mobiles that are not within the tolerated weight must be recycled. Show which mobiles are tolerable with an inequality. ( W is the weight of the mobiles).
Translate the sentence into an equation.
Two times the sum of a number and 5 is 6.
Answers
I hope this helps!! Lmk if you have questions
the logarithm of a product of two numbers is the same as the sum of the logarithms of these numbers. so log4(16 · 64) = log4(16) .
Answers
The missing value is 64. The equation can be written as:
log₄(16 · 64) = log₄(16) + log₄(64)
To find the missing value in the equation log₄(16 · 64) = log₄(16) + ?, we can use the logarithmic property you mentioned.
According to the property, the logarithm of a product is equal to the sum of the logarithms of the individual numbers.
Let's solve the equation step by step:
We know that log₄(16 · 64) is equal to the logarithm of the product of 16 and 64.
log₄(16 · 64) = log₄(1024)
We can simplify the right side of the equation by calculating the logarithms individually.
log₄(16) + ? = log₄(16) + log₄(64)
Now, we can substitute the base 4 logarithms of 16 and 64, which are known values:
log₄(1024) = log₄(16) + log₄(64)
The sum of the logarithms of 16 and 64 is the logarithm of their product:
log₄(1024) = log₄(16 · 64)
Therefore, the missing value is 64. The equation can be written as:
log₄(16 · 64) = log₄(16) + log₄(64)
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The following curve passes through (3,1). Use the local linearization of the curve to find the approximate value of y at x
Answers
m = the slope of the curve at x=3 and b = the y-intercept at x=3. Therefore, the approximate value of y at x=2
We can use the local linearization of the curve to approximate the value of y at x=2.
The local linearization of the curve is given by the equation y = mx + b, where m is the slope of the curve at x=3 and b is the y-intercept at x=3.
Let m be the slope of the curve at x=3 and b be the y-intercept at x=3.
The slope of the curve at x=3 can be found by calculating the derivative of the curve at x=3.
The y-intercept at x=3 can be calculated by substituting x=3 into the equation of the curve and solving for y.
Therefore, m = the slope of the curve at x=3 and b = the y-intercept at x=3.
Substituting the values of m and b into the equation of the local linearization, we get the equation y = mx + b.
Substituting x=2 into the equation, we get y ≈ 0.5 + 1 = 1.5.
Therefore, the approximate value of y at x=2
The local linearization of the curve can be used to approximate the value of y at x=2. Substituting x=2 into the equation, we get y ≈ 1.5, which is the approximate value of y at x=2.
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A simple hypothesis contains one predictor and one outcome variable, e.g. positive family history of schizophrenia increases the risk of developing the condition in first-degree relatives. Here the single predictor variable is positive family history of schizophrenia and the outcome variable is schizophrenia. A complex hypothesis contains more than one predictor variable or more than one outcome variable, e.g., a positive family history and stressful life events are associated with an increased incidence of Alzheimer’s disease. Here there are 2 predictor variables, i.e., positive family history and stressful life events, while one outcome variable, i.e., Alzheimer’s disease. Complex hypothesis like this cannot be easily tested with a single statistical test and should always be separated into 2 or more simple hypotheses
A car company decided to introduce a new car whose mean petrol consumption is claimed to be lower than that of the existing car. A sample of 50 new cars were taken and tested for petrol consumption. It was found that mean petrol consumption for the 50 cars was 30 km per litre with a standard deviation of 3.5 km per litre. Test at 5% level of significance whether the company‟s claim
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Based on the given information and performing a one-sample t-test, the conclusion is that if the population mean (μ) is greater than 30.8294 km per litre, we reject the null hypothesis.
Given:
Sample mean (x') = 30 km per litre
Sample standard deviation (s) = 3.5 km per litre
Sample size (n) = 50
Significance level (α) = 0.05 (5%)
Null hypothesis \((H_0)\): The mean petrol consumption of the new car is equal to or higher than that of the existing car.
Alternative hypothesis \((H_1)\): The mean petrol consumption of the new car is lower than that of the existing car.
We'll calculate the test statistic (t-value) and compare it with the critical t-value.
The formula for the t-value is:
t = (x' - μ) / (s / √n)
where μ is the population mean (mean petrol consumption of the existing car).
First, we need to calculate the critical t-value from the t-distribution table. Since we have a significance level of 0.05 and (50 - 1) degrees of freedom, the critical t-value for a one-tailed test is approximately -1.677.
Now, let's calculate the t-value:
t = (30 - μ) / (3.5 / √50)
To reject the null hypothesis, the t-value should be less than the critical t-value.
Simplifying the equation:
t = (30 - μ) / (0.495)
To find the critical value, we compare it with the calculated t-value:
-1.677 > (30 - μ) / (0.495)
Multiplying both sides of the inequality by 0.495:
-0.8294 > 30 - μ
Rearranging the inequality:
μ > 30 + 0.8294
μ > 30.8294
Therefore, if the population mean (μ) is greater than 30.8294 km per litre, we reject the null hypothesis in favor of the alternative hypothesis, concluding that the mean petrol consumption of the new car is lower than that of the existing car.
To know more about one-sample t-test, refer here:
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Triangle ABC, where Angle C is the Right Angle in the lower left. Side CB is a leg of the triangle and is horizontal--going left and right. Side CA is another leg of the triangle and is vertical--going up and down. Angle A is up on top and is 41 degrees. Angle B (the other acute angle) is unknown. The hypotenuse AB is 30 feet in length. What is the height of the triangle (Side CA)? Round your answer to the nearest tenth of a foot.
help
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Answer:
CA = 22.6 ft
Step-by-step explanation:
For the known angle A, leg CA is the adjacent leg.
Side AB is the hypotenuse.
The trigonometric ratio that relates the adjacent leg tot eh hypotenuse is the cosine.
cos A = adj/hyp
cos 41° = CA/(30 ft)
CA = 30 ft * cos 41°
CA = 22.6 ft