Answer:
In summary, the correct statements are:
The domain is the set of all integers from 0 to 43.
The range is the set of all multiples of 3 from 0 to 129.
this is the best i could do, make what you want of it, good luck
Step-by-step explanation:
he domain of this function is the set of all possible inputs, which in this case is the number of watermelons the farmer can sell. Since the farmer has 43 watermelons and cannot sell a fraction of a watermelon, the domain is the set of all integers from 0 to 43. So, the first statement is correct.
The second statement is incorrect because the farmer cannot sell a fraction of a watermelon, so the domain cannot include all real numbers from 0 to 43.
The range of this function is the set of all possible outputs, which in this case is the total sales in dollars. Since the farmer sells each watermelon for $3, her total sales will be a multiple of 3. The minimum sales value is $0 (if she sells no watermelons) and the maximum sales value is $129 (if she sells all 43 watermelons). So, the range is the set of all multiples of 3 from 0 to 129. Therefore, the fourth statement is correct.
The third statement is incorrect because not all integers between 0 and 129 are possible values for the farmer’s total sales. For example, she cannot make $2 in sales because her sales will always be a multiple of 3.
The fifth statement is incorrect because it implies that the farmer can only make sales in multiples of 43, which is not true since she sells each watermelon for $3.
In summary, the correct statements are:
The domain is the set of all integers from 0 to 43.
The range is the set of all multiples of 3 from 0 to 129.
The volume of a rectangular prism is 161. 2 m3. The prism has a base that is 5. 2 m by 3. 1 m. Find the height of the prism. (Example 2)
The height of the rectangular prism is 10 meters, calculated using the formula V = l × w × h with the given values of V, l, and w.
We know that the volume of a rectangular prism is given by:
V = l × w × h
where V is the volume, l is the length, w is the width, and h is the height.
Given that the volume of the rectangular prism is 161.2 m³ and the base of the prism is 5.2 m by 3.1 m, we can write:
161.2 = 5.2 × 3.1 × h
Simplifying the equation, we get:
h = 161.2 / (5.2 × 3.1)
h = 10
Therefore, the height of the rectangular prism is 10 meters.
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State the coordinates of the point.
Answer:
Step-by-step explanation:
look get 8 then 7 then you get 5 and luh tyler.
Which of the following are solutions to the equation
options A and D are solutions to the trigonometric equation sinx cosx = 1/4.
What are trigonometric signs ?
Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. Right triangles are particularly important in trigonometry because they have one angle that measures 90 degrees, which allows us to define the six trigonometric functions: sine, cosine, tangent, cosecant, secant, and cotangent.
In a right triangle, the side opposite the 90-degree angle is called the hypotenuse, and the other two sides are called the legs. We can use the ratios of the lengths of the sides to define the six trigonometric functions.
According to the question:
To solve the equation sinx cosx = 1/4, we can use the identity 2sinx cosx = sin(2x). Then, we have:
sinx cosx = 1/4
2sinx cosx = 1/2
sin(2x) = 1/2
The solutions for sin(2x) = 1/2 are:
2x = π/6 + 2nπ or 2x = 5π/6 + 2nπ, where n is an integer.
x = π/12 + nπ or x = 5π/12 + nπ, where n is an integer.
Then, the solutions for sinx cosx = 1/4 are:
x = π/24 + nπ/2 or x = 5π/24 + nπ/2, where n is an integer.
Therefore, options A and D are solutions to the equation sinx cosx = 1/4.
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etting up squares of known dimension over the entire pattern describes what method of documentation?
The method of documentation described is called gridding. Gridding involves setting up squares of known dimensions (e.g. 1 meter) over the entire pattern, usually starting at the center.
Gridding is setting up squares of known dimension over the entire pattern. The squares are then numbered in a clockwise fashion, allowing each individual artifact found within them to be documented and identified. Gridding ensures that all artifacts found within a pattern can be located and identified. Additionally, it helps to compare patterns with one another and to compare them to other patterns.
Gridding requires the excavation of a larger area than would otherwise be necessary, but the information that is obtained is worth the effort. The data obtained from gridding can be used to compare the relative amounts and types of artifacts present in various locations, which can be used to infer the type of activity that was conducted in the area. Furthermore, it allows for the accurate identification and documentation of individual artifacts, which can be extremely useful for studying a specific culture.
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work out the circumference of this circle, and give your answer in terms of pi.
the radius is 6mm
Answer: 37.7mm
Step-by-step explanation:
c = 2πr
c = 2π(6)
c ≈ 37.7
there are 17 students in a kindergarten class. if each kindergartner can have only one task, in how many ways can the teacher assign out the following tasks: line leader, wipe down the tables, pass out papers?
As per the combination method, there are 4,080 ways for the teacher to assign the tasks of line leader, table wiper, and paper passer to three different students in the class of 17 kindergartners.
To start, let's count the number of ways to choose one student to be the line leader. There are 17 students to choose from, so there are 17 possible choices.
Next, let's count the number of ways to choose one student to wipe down the tables.
Finally, let's count the number of ways to choose one student to pass out papers. We've already chosen two students for the other tasks, so there are only 15 students left to choose from. Thus, there are 15 possible choices for the paper passer.
To find the total number of ways to assign the tasks, we need to multiply the number of choices for each task. So the total number of ways to assign the tasks is:
17 x 16 x 15 = 4,080
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As per the combination method, there are 4,080 ways for the teacher to assign the tasks of line leader, table wiper, and paper passer to three different students in the class of 17 kindergartners.
To start, let's count the number of ways to choose one student to be the line leader. There are 17 students to choose from, so there are 17 possible choices.
Next, let's count the number of ways to choose one student to wipe down the tables.
Finally, let's count the number of ways to choose one student to pass out papers. We've already chosen two students for the other tasks, so there are only 15 students left to choose from. Thus, there are 15 possible choices for the paper passer.
To find the total number of ways to assign the tasks, we need to multiply the number of choices for each task. So the total number of ways to assign the tasks is:
17 x 16 x 15 = 4,080
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20 POINTS NEED HELP DUE TODAY HELP!!!!!!
2. Is the point (-0.5, sin(4π/3)) on the unit circle? Explain your reasoning.
3. Is the point (-0.5, sin(5π/6)) on the unit circle? Explain your reasoning.
4. Suppose that sin(Θ) = -0.5 and that Θ is in quadrant 4. What is the exact value of cos(Θ)? Explain your reasoning.
1) The point is on the unit circle.
2) The point is not on the unit circle
3) cos(Θ) = 0.866
Is the point on the unit circle?We know that all the points on the unit circle have a magnitude of 1, then we can write:
√[ (-0.5)² + (sin(4π/3)²) = 1
This means that the point is on the unit circle.
b) Now the point is (-0.5, sin(5π/6))
We need to do the same thing, this time we will get:
√[ (-0.5)² + (sin(5π/6)²) = 0.71
So this point is not on the number line.
c) Here we know that sin(Θ) = -0.5 and the angle is in the quadrant 4.
Then Θ = Asin(-0.5) = -30°
Remember that -30° is on the fourth quadrant, so this is correct, now the cosine of that is:
cos(-30°) = 0.866
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The expression the quantity cosecant squared of theta minus 1 end quantity over cotangent of theta simplifies to which of the following?
The quantity cosecant squared of theta minus 1 can be simplified as 1/(cosecθ)² - 1. So, the correct answer is -1/tanθ.
What is cosecant?Cosecant, denoted as csc, is a trigonometric function that is the reciprocal of the sine function. It is the ratio of the side opposite the angle over the hypotenuse in a right triangle.
This can be further simplified by multiplying the numerator and denominator of the fraction by the cosecant of theta to get the expression 1 - cosec²θ/cosecθ.
Rearranging this expression gives -cosec²θ/cosecθ.
The cosecant of theta can be further simplified by using the identity cosecθ = 1/sinθ.
Substituting this into the expression gives -1/sin2θ.
The sine of theta can then be further simplified by using the identity
sinθ = 1/tanθ.
Substituting this into the expression gives -1/tan²θ.
Finally, using the identity tan²θ = tanθ/1 simplifies the expression to -1/tanθ.
Therefore, the correct answer is -1/tanθ.
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Question:
The expression the quantity cosecant squared of theta minus 1 end quantity over cotangent of theta simplifies to which of the following?
A. 1
B. 0
C. -cotθ
D. -1/tanθ
Can anyone help me with this?
The quadrilateral given is a square and the measure of the angles as required are as follows;
m<EFG = 90°.m<GDH = 45°.m<FEG = 45°.m<DHG = 90°.What are the measures of the missing angles as required?It follows from the task content that the given quadrilateral is a square.
Recall, that the four interior angles of a square sum up to 360° in which case, each vertices is a right angle.
Additionally, the diagonals of a square intersect at a point to form right angle at the point.
Also, each diagonals is a bisector of the angles at the vertices.
Therefore, we have that;
m<EFG = right angle = 90°.m<GDH = right angle = 90°.m<FEG = right angle = 90°.m<DHG = right angle = 90°.Read more on interior angles of a square;
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suppose we decided to calculate a 95% confidence interval for this same data instead of a 99% confidence interval. how would this change the width of the interval?
If a 95% confidence interval is used instead of a 99% confidence interval, the width of the interval would decrease.
The reason behind this is that a 95% confidence interval is narrower than a 99% confidence interval, as it does not cover as much area as a 99% confidence interval. What is a confidence interval? The concept of a confidence interval (CI) is used in statistics to provide a range of values that may contain an unknown population parameter.
The term "confidence" implies that if the same population parameter were estimated from numerous samples and the confidence intervals calculated for each, the proportion of such intervals that contain the parameter would match the specified confidence level.
The width of the interval is based on the confidence level, sample size, and the data variability. When the confidence level increases, the width of the interval increases because the amount of uncertainty increases. In comparison, when the confidence level decreases, the interval width decreases because there is less uncertainty.
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How is the quotient of 625 and 15 determined using an area model?
Enter your answers in the boxes to complete the equations. Your final answer should be a mixed number in simplest form.
The product of 556 and 16 is therefore 33 1/4 as we express the quotient of 556 and 16 as a mixed number in the simplest form.
what is equations ?A mathematical assertion that two expressions are equal is known as an equation. A typical equation has one or more variables, which are often denoted by letters and have a range of possible values. Equations are frequently used in a variety of fields to describe relationships between distinct numbers or to address issues. For instance, the equation x + 2 = 5 only has one variable, x. It denotes that the product of x and 2 equals 5.
given
We can represent 556 as a rectangle with length 556 and width 1, and 16 as a rectangle with length 16 and width 1 to calculate the quotient of 556 and 16 using an area model.
This is how it goes:
To start, we deduct 16 from 556 to obtain:
556 - 16 = 540
540 = 16 x 33 + 4
Finally, by multiplying the numerator and denominator of the fraction 33 4/16 by 4, we may express the quotient of 556 and 16 as a mixed number in the simplest form, which results in:
556 ÷ 16 = 33 4/16 = 33 1/4
The product of 556 and 16 is therefore 33 1/4 as we express the quotient of 556 and 16 as a mixed number in the simplest form.
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philp made tables of values to solve a system of equations first he found that the x-value of the solution was between 0 and 1 then he found that it was between 0.5 and 11 next time he made this table apex btw
The ordered pair is the best approximation of the exact solution is (0.6, 1.9). The correct option is c.
What is a system of equations?A group of equations comprising one or more variables is known as a system of equations. The variable mappings that satisfy each component equation, or the points where all of these equations cross, are the solutions of systems of equations.
y = -2x + 3
y = 5x - 1
Equate the right sides of both equations:
-2x + 3 = 5x - 1,
-2x - 5x = -1 -3,
x = 4/7
then
y = -2 x 4/7 + 3 = 8/7 + 3 = 3x7-8 /7 = 13/7 = 1 x 5/7
4/7 = 0.6 and 1 x 5/7 is equal to the ordered pair (0.6, 1.9).
Therefore, the correct option is c, (0.6, 1.9).
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The question is incomplete. The full question is given below:
Which ordered pair is the best approximation of the exact solution?
f(x)=x^2
shifted 5 units left
reflect over x-axis
shift 3 down
vertically stretch by a factor of 2
The transformed function is f(x)=(-2*((x+5)²)-3) and green is graph.
The vertical shift depends on the value of k. The vertical shift is described as follows:
g(x) = f (x) + k - The graph is shifted up k units.
g(x) = f (x) − k - The graph shifts down units.
we have,
f(x)=x²
reflected in the x-axis
f(x)=-(x)²
vertically stretched by a factor of 2
f(x)=2*x²
shifted five units to the left
f(x)=(x+5)²
shifted three units to dawn
f(x)=x²-3
we can write all together
f(x)=(-2*((x+5)²)-3)
graphing red original function green is transformed function.
the complete question is-
The graph of f(x) = x^2 is reflected in the x-axis, vertically stretched by a factor of 2, shifted five units to the left, and shifted three units down.
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in the picture .............................................................................................................................................
The graph showing one cycle of the trigonometric function y = 8 cos 8x is plotted and attached
What is trigonometric graph?Trigonometric graphs are graphical representations of trigonometric functions, which are functions that relate the angles of a right triangle to the ratios of its sides. The three most commonly used trigonometric functions are
sine, cosine, and tangent.The graphs of these functions are periodic, meaning they repeat themselves over a regular interval.
In the problem, the graph plotted is that of cosine function and the amplitude of is 8
The 5 points marked are
(-π/16, 0) - the first point
(0, 8) - showing the amplitude and 1/4 cycle
(π/16, 0) - 1/2 cycle
(-π/16, -8) - 3/4 cycle
(3π/16, 0) - one complete cycle
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What is an equation of the line that passes through the point (6,6)(6,6) and is parallel to the line 3x-2y=43x−2y=4?
The equation of the line that passes through (6,6) and is parallel to 3x - 2y = 4 is y = (3/2)x - 3.
What is an equation of the line parallel to the given line?The formula for equation of line is expressed as;
y = mx + b
Where m is slope and b is y-intercept.
To find the equation of the line passing through (6,6) that is parallel to 3x - 2y = 4.
We need to find the slope of the given line first.
3x - 2y = 4
-2y = -3x + 4
y = (3/2)x - 2
The slope of the given line is 3/2.
Since the line we want to find is parallel to this line, it will have the same slope.
Therefore, we can use the point-slope form of the equation of a line to write the equation:
y - y1 = m( x - x1 )
Plug in m = 3/2 and (x1,y1) : (6,6)
y - 6 = (3/2)(x - 6)
Simplifying:
y - 6 = (3/2)x - 9
y = (3/2)x - 3
Therefore, the equation of the parallel line is y = (3/2)x - 3.
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The bases of the prism below are right triangles. If the prism's height measures 11 units and its volume is 130.9 units 3 3 , solve for x x.
The value of x is equal to 4.8 units.
How to calculate the volume of a triangular prism?In Mathematics and Geometry, the volume of a triangular prism can be determined or calculated by using the following formula:
Volume = base area × height of the prism.
Assuming the variable x represent the length of one side of its base. Since the height of this triangular prism measures 11 units and its volume measures 130.9 cubic units, the value of x can be determined as follows;
Base area of triangle = 1/2 × x × 5
Base area of triangle = 5x/2 square units.
Volume of triangular prism = base area × height of the prism.
130.9 = 5x/2 × 11
130.9/11 = 5x/2
11.9 = 5x/2
5x = 23.8
x = 4.8 units.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
In a chemistry lab there are 9. 52 g of powdered substance in a container max needs to place an equal amount of the powdered substance into each of three glass plates the amount of powdered substance he places into each glass glass plate is 1. 98 g
No, the given statement about the lab experiment is not reasonable.
If Max places 1.98 grams of powdered substance into each glass plate and he needs to place the substance into 3 glass plates, then the total amount of the powdered substance he needs is 1.98 x 3 = 5.94 grams. This is greater than the amount Max estimates to be in the container (4.5 grams).
Therefore, it is not reasonable to assume that there are only 4.5 grams of the powdered substance in the container when Max needs to use more than that amount for his experiment.
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Complete Question:
In chemistry lab, there are 9.52 grams of powdered substance in a container. Max needs to place substance into each of 3 glass plates. The amount of powdered substance he places into each glass plate is 1.98 grams. Max estimates that there are 4.5 grams of the powdered substance in the container. Is the statement reasonable?
Thank you for the help!
Answer:
13 bags
Step-by-step explanation:
V = π(2^2)(1/2) = 2π = 6.28 cubic feet
6.28 ÷ .5 = 12.56
So Martin needs to buy at least 13 bags of sand.
I'm not sure what to do on this assignment. Please give the full answer
1) x=7.7942 2) figure not clear 3) 0.866 4) 0.7071 ,we got these answer with the help of tringnometric identities
what is tringnometric identities?
Trigonometric identities are mathematical equations that involve trigonometric functions, such as sine, cosine, tangent, cotangent, secant, and cosecant. These identities relate the values of these functions to one another and can be used to simplify trigonometric
In the given question,
in figure 1 we can take sin(60)=y/9
y=7.7942
then cos(60)=x/7.7942
x=3.8971
3) sin(60)=0.866
4) cos(45)= 0.7071
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a new york city psychologist specializes in treating patients who are phobic and afraid to leave their homes. the following table indicates how many patients the psychologist has seen each year for the past ten years. it also indicates the robbery rate in new york city during the same year. using crime rate to predict patient load, if the crime rate increases to 131.2 in year 11, how many phobic patients will be treated?
Based on a linear regression model, if the crime rate increases to 131.2 in year 11, the predicted patient load would be approximately 72.733, so the psychologist is likely to treat 72 phobic patients.
Based on the given information, the psychologist has used a linear regression model to predict the number of phobic patients based on the crime rate in New York City. The regression equation is:
Predicted patients = 1.229 + 0.545 * Crime rate
Here, 0.545 is the coefficient for the Crime Rate variable.
Using this equation, we can predict the number of phobic patients in year 11 when the crime rate is 131.2
Predicted patients = 1.229 + 0.545 * 131.2
Predicted patients = 72.733
Therefore, by using the linear regression model, we find that the psychologist is expected to treat approximately 72 phobic patients in year 11 if the crime rate in New York City increases to 131.2.
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--The given question is incomplete, the complete question is
"a new york city psychologist specializes in treating patients who are phobic and afraid to leave their homes. the following table indicates how many patients the psychologist has seen each year for the past ten years. it also indicates the robbery rate in new york city during the same year. using crime rate to predict patient load, if the crime rate increases to 131.2 in year 11, how many phobic patients will be treated?
Regression Statistics Multiple R 0.950511723 R Sqar 0.903472536 Adjusted R 0.891406603 Square Standard 3.5485219 Error Observations ANOVA 10 df MS F Significance 1 942.8639386 942.8639386 74.87797 2.4715E-05 Regression Residual Total 8 100.7360614 12.59200768 1043.6 Coefficients Standard tStat P-value Lower 95% Upper 95% Error Intercept 1.229061531 5.497668676 0.223560495 0.828702 -11.44858516 13.90670822 Crime Rate 0.545008057 0.0629833718.653205606 2.47E-05 0.399768144 0.69024797 RESIDUAL OUTPUT Observation Predicted Patients Standard Residuals 33.00303125 34.80155784 41.23265291 42.48617144 45.42921495 49.7347786 56.32937609 52.89582533 57.52839382 64.55899775 0.89579985 0.53848918 0.368442379 -0.444219566 1.622803022 1.573785026 1.097156702 0.330039979 0.140964015 1.063791424 10"
(g+5)(g-4) expand and simplify
PLEASE HELP FAST (giving brainliest)
Answer:
Answer is B The data is asymetrical.
Step-by-step explanation:
a normal population with unknown variance has a mean of 20. is one likely to obtain a random sample of size 9 from this population with a mean of 24 and a standard deviation of 4.1? if not, what conclusion would you draw?
We can conclude that it is unlikely to obtain a random sample of size 9 from this population with a mean of 24 and a standard deviation of 4.1 because the sample mean of 24 is different from the population mean of 20.
To answer this question, we can use a t-test to determine if the sample mean of 24 is significantly different from the population mean of 20.
The t-test formula is:
t = (x' - μ) / (s / √(n))
Where x' is the sample mean, μ is the population mean, s is the sample standard deviation, and n is the sample size.
Plugging in the values given in the question, we get:
t = (24 - 20) / (4.1 / √(9)) = 2.93
To determine if this t-value is significant, we need to compare it to the critical t-value for a two-tailed test with 8 degrees of freedom (n-1). Using a t-table or calculator, we find the critical t-value to be approximately 2.31 at a 5% significance level.
Since our calculated t-value of 2.93 is greater than the critical t-value of 2.31, we can reject the null hypothesis that the sample mean is equal to the population mean.
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a client who weighs 207 lb (94.1 kg) is to receive 1.5 mg/kg of gentamicin sulfate iv three times each day. how many milligrams of medication should the nurse administer for each dose? round to the nearest whole number.
If a client who weighs 207 lb (94.1 kg) is to receive 1.5 mg/kg of gentamicin sulfate iv three times each day, the nurse should administer 141 mg of gentamicin sulfate for each dose.
To calculate the dose of gentamicin sulfate that the nurse should administer to the client, we need to know the client's weight and the desired dosage, which in this case is 1.5 mg/kg.
First, we need to convert the client's weight from pounds to kilograms. To do this, we divide the client's weight in pounds by 2.205 to get the weight in kilograms:
207 lb ÷ 2.205 = 94.1 kg
Now that we have the client's weight in kilograms, we can calculate the dose of gentamicin sulfate for each administration:
1.5 mg/kg × 94.1 kg = 141.15 mg
We round 141.15 mg to the nearest whole number, which is 141 mg.
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help me please I'm not smart
The required value of the ∠DPE = 40°.
What is vertically opposite angle?Angles that are vertically opposite to one another at a particular vertex are formed by two straight lines meeting. Angles that are vertically opposed to one another are identical. These are referred to as perpendicular angles at times.
According to question:Using vertically opposite angle, ∠GPE = 35° and ∠KPF are equal
Then,
∠GPE = ∠KPF = 35°
Then Sum of all angles on straight line is 180°
∠KPF + ∠FP + ∠DPE = 180°
35° + 105° + ∠DPE = 180°
∠DPE = 180° - 140°
∠DPE = 40°
Thus, required value of the ∠DPE = 40°.
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what is the number of cans that can be packed in a certain carton? the interior volume of this carton is 2,304 cubic inches. the exterior of each can is 6 inches high and has a diameter of 4 inches.
Answer:
Step-by-step explanation:
volume of each can
=[tex]\pi[/tex][tex]r^{2}[/tex]h
22/7×[tex]4/2^{2}[/tex]×6
[tex]\frac{88×6}{7}[/tex]
528/7
sara draws the 8 8 of hearts from a standard deck of 52 cards. without replacing the first card, she then proceeds to draw a second card. a. determine the probability that the second card is another 8 8 .
The probability that the second card is another 8 is approximately 0.045
There are 52 cards in a standard deck, and after drawing the first card, there are only 51 cards remaining.
The probability of drawing an 8 as the first card is 4/52, since there are four 8s in the deck.
Since the first card is not replaced, there are only three 8s remaining in the deck.
Therefore, the probability of drawing another 8 as the second card, given that the first card is an 8 and was not replaced, is 3/51.
Thus, the probability that Sara draws the 8 of hearts as the first card and another 8 as the second card is
(4/52) x (3/51) = 0.0045
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The given question is incomplete, the complete question is:
Sara draws the 8 of hearts from a standard deck of 52 cards. Without replacing the first card, she then proceeds to draw a second card. a. Determine the probability that the second card is another 8
Kathy is adding a new slide to her swing set. The slide is 5 feet long, and the ladder is 4 feet high. How
many feet away is the base of the ladder from the end of the slide, g, as shown below?
5 ft
g
4ft
The number of feet away is the base of the ladder from the end of the slide, g, as shown is 3 ft.
How many feet away is the base of the ladder from the end of the slide?The base of the ladder from the end of the slide forms a right triangle.
Hypotenuse² = opposite² + adjacent²
Hypotenuse = 5 ft
Opposite = 4 ft
Adjacent = g
So,
Hypotenuse² = opposite² + adjacent²
5² = 4² + g²
25 = 16 + g²
subtract 16 from both sides
25 - 16 = g²
9 = g²
find the square root of both sides
√9 = g
g = 3 ft
In conclusion, the base of the ladder is 3 ft away from the end of the slide.
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based on the interval, is there convincing evidence that the average number of pepperonis is less than 40? explain your answer.
a) Check the graph for normality as small sample sizes can affect normality tests. b) The hypothesis is inconclusive; the mean may not be less than 40.
c) To reduce margin of error, increase sample size or decrease confidence level. One-tailed hypothesis with t-score = -1.073, df = 9, sig level = 0.5.
a) It is necessary to inspect the graph of the sample data because the normality tests like K-S Test or Anderson Darling test or any test aren't very powerful when it comes to the small sample data. That is why we always need to examine the plot and use our own judgement to whether it is normal or not rather than relying solely on the hypothesis tests. Smallest deviations in the dataset can generate the statistically significant p-value which is not good for the small sample data and these tests are robust against the making of decision like normality due to the certain effects of central limit theorem.
b) The hypothesis would be as followed:
H o: μ=40
H₁: μ<40
t = (X-μ)/(s/√n)
t = (X-μ)/(s/√n) = (37.4 - 40)/(7.662/√10)
t = -2.6/2.423
t = -1.073
p-value= 0.1556
Based on the above calculation, p-value> alpha value which shows that we have insignificant results and we fail to reject the hypothesis. There is no sufficient evidence that the average number of pepperonis is less than 40.
c) Current margin of error would be:
M.E = (t₀.₉₅,₉)(s/√n)
M.E = (2.262)(7.662/√10)
M.E = 5.481
Two ways to reduce the margin error would be:
1) Increase the sample size, margin of error will be reduced as the sample size is inversely proportional.
2) Reduce the confidence level like instead of 95% use 90% or less.
T-Score: -1.073
DF: 9
Significance Level: 0.5
One-tailed or two-tailed hypothesis: One-tailed
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Complete question is below
Tigran drove 2/5 of a 150-mile trip in the first hour of driving. in the second hour of driving, he traveled 5/6 of the remaining miles. what part of the whole trip did Tigran travel during these two hours?
The part (percentage) of the whole trip Tigran travels during the (first) two hours of driving is 90%
What is a percentage?A percentage is a representation of a part of a quantity as a fraction with a denominator of a 100.
The fraction of the whole trip Tigran travels in the first hour = 2/5
The distance Tigran drove in the first hour of driving = (2/5) × 150-mile = 60-miles
The distance Tigran travels in the second hour = (5/6) × (150 - 60) = 75
The distance he drove in the second hour = 75 miles
The distance, d, Tigran travels during these two hours is therefore;
d = 60 miles + 75 miles = 135 miles
The part of the whole trip traveled in the two hours is therefore;
Part of trip = 135/150 = 9/10 = 90%
The part of the whole trip Tigran travels in these two hours is therefore, 90% of the trip
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