Answer:
I think the answer is 9 3/4, 9.5, 9 3/8, 9.125
In a business class, 15% of the students have never taken a statistics class, 40% have taken only one semester of statistics, and the rest have taken two or more semesters of statistics. The professor randomly assigns students to groups of three to work on a project for the course. Assume everyone in the group is independent. What is the probability that neither of your two group mates has studied statistics
Answer:
Pr(neither of two groups) = 0.0225
Step-by-step explanation:
Given:
15% of the students have never taken a statistics class = Pr(none)
Pr(none) = 0.15
40% have taken only one semester of statistics =Pr(one semester)
Pr(one semester) = 0.40
the rest have taken two or more semesters of statistics = Pr(two or more semester)
Pr(two or more semester) = 1 - [Pr(one semester) + Pr(none) ]
Pr(two or more semester) = 1-(0.40+0.15) = 1 - 0.55
Pr(two or more semester) = 0.45
Where Pr = probability
Let probability that neither of your two group mates has studied statistics = Pr(neither of two groups)
=Pr(none in group 1) ×Pr(none in group 2)
= 0.15 × 0.15
Pr(neither of two groups) = 0.0225
Twelve synchronized swimmers are forming a circle. The locations of three of those swimmers are (13,-2),(-1,-2),and (6,-9). A 4th swimmer will appear in the middle of the circle. Where would the center swimmer need to be located?
Answer:(6,-2)
Step-by-step explanation:
The center swimmer need to be located at the point (6, -2).
What is the Standard form of a Circle?Standard form of a circle is given by the equation,
(x - h)² + (y - k)² = r²
where, (h, k) is the center of the circle and r is the radius of the circle.
Given are three points on a circle.
(13, -2), (-1, -2) and (6, -9).
Substituting each of the point in the standard form,
(13 - h)² + (-2 - k)² = r²
(-1 - h)² + (-2 - k)² = r²
(6 - h)² + (-9 - k)² = r²
Since the radius are equal,
(13 - h)² + (-2 - k)² = (-1 - h)² + (-2 - k)² = (6 - h)² + (-9 - k)²
Solving the first two equations, we get,
(13 - h)² = (-1 - h)²
28h = 168
h = 6
From the last two equations,
(-1 - h)² + (-2 - k)² = (6 - h)² + (-9 - k)²
49 + (-2 - k)² = (-9 - k)²
k = -2
Hence the center of the circle is (h, k) = (6, -2).
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simplify: 2{10-5+x[1+3(6-2)]}
Answer:
10+26x
Step-by-step explanation:
To solve this, work your way from the inner most parentheses to the outer most:
The inner most parentheses is around 6-2, meaning you solve this first. When you solve this, you get 4.The second most inner parentheses is around (1+3 times 4) using PEMDAS, you first solve the multiplication, and then add. Once you solve this, you get 13.Next, the outer most parentheses is around (10-5+13x). When you simplify this, you get 5+13xFinally, you multiply 2(5+13x). Using distributive property, you get 10+26x as your final simplified answer.Question 3
State the value of the discriminant of 5x2 + 9x = 3.
a) 21
b) 12
c) 141
d) 5
Answer:
D = 141
Step-by-step explanation:
The given quadratic equation is
[tex]5x^2+9x=3\\\\5x^2+9x-3=0[/tex].
It is required to find the value of the discriminant. The value of discriminant of any quadratic equation is given by :
[tex]D=b^2-4ac[/tex]
Here, a = 5, b = 9 and c = -3
On plugging all the values, we get :
[tex]D=(9)^2-4\times 5\times (-3)\\\\D=141[/tex]
So, the value of discriminant for y is 141.
Charlie is driving to Boston. Suppose that the distance to his destination (in miles) is a linear function of his total driving time (in minutes). Charlie has 49 miles to his destination after 15 minutes of driving, and he has 32.2 miles to his destination after 39 minutes of driving. How many miles will he have to his destination after 47 minutes of driving
Answer:26.6 miles
Step-by-step explanation:
Given
Charlie distance to his destination is a linear function of total driving time
suppose distance d is related to time t as
[tex]d=mt+c\quad \ldots(i)[/tex]
at [tex]d=49\ miles[/tex] after [tex]t=15\ min[/tex]
Substitute in (i)
[tex]49=m(15)+c\quad \ldots(ii)[/tex]
at [tex]d=32.2\ miles[/tex] after [tex]t=39\ min[/tex]
[tex]32.2=m(39)+c\quad \ldots(iii)[/tex]
Solving (ii) and (iii) we get
[tex]m=-0.7[/tex]
substitute in eq (ii) we get
[tex]c=59.5[/tex]
so after [tex]t=47\ min[/tex]
[tex]d=(-0.7)47+59.5[/tex]
[tex]d=59.5-32.9=26.6\ miles[/tex]
So 26.6 miles is left to travel after 47 minutes
A 4-story office building has cubicles for 348plus313plus306plus308 workers. While one floor is closed for repairs, the office has cubicles for 348plus306plus308 workers. How many cubicles are there on the floor that is closed? Explain.
Answer:
313
Step-by-step explanation:
We observe that the numbers of cubicles on the open floors have not changed, so we can match the numbers to find the missing one.
The closed floor has 313 cubicles.
To find the number of cubicles on the closed floor, one must subtract the total number of cubicles available when one floor is closed from the original total of all floors. The closed floor has 313 cubicles.
The question asked is about determining the number of cubicles on a floor that is closed for repairs in a 4-story office building. Initially, the building has cubicles for 348 + 313 + 306 + 308 workers. When one floor is closed, it has cubicles for 348 + 306 + 308 workers. To find the number of cubicles on the closed floor, we subtract the total number of cubicles available while the floor is closed from the original total when all floors were open.
The calculation would be as follows:
Total number of cubicles when all floors are open = 348 + 313 + 306 + 308Total number of cubicles with one floor closed = 348 + 306 + 308Cubicles on the closed floor = (Total number of cubicles when all floors are open) - (Total number of cubicles with one floor closed)Step-by-step calculation:
First, calculate the total when all floors are open: 348 + 313 + 306 + 308 = 1275 cubicles.Then, calculate the total with one floor closed: 348 + 306 + 308 = 962 cubicles.Finally, subtract to find the number on the closed floor: 1275 - 962 = 313 cubicles.Therefore, there are 313 cubicles on the floor that is closed.
The graph of y=h(x) is shown below. The function f(x) is defined by f(x) =-1/2h(x)+3. (a) What three transformations have occurred to the graph of h to produce the graph of f? Specify the transformations and the order they occurred in.
Answer:
Reflection over x, Stretch by 1/2, translate up 3 units
Step-by-step explanation:
:)
The graph of the function h(x) has undergone three transformations to produce the function f(x) = -1/2h(x) + 3: a reflection in the x-axis, a vertical scaling by 1/2, and a vertical shift upward by 3 units.
Explanation:The function f(x) = -1/2h(x) + 3 has gone through three transformations to become the graph of h(x), which are determined by applying different values of x and the corresponding values of y. Firstly, the graph h(x) is reflected in the x-axis due to the negative sign in front of the h(x), which reverses the direction of the graph. Secondly, the graph is scaled vertically by a factor of 1/2 due to the multiplication of h(x) by 1/2, which compresses the graph towards the x-axis. Lastly, the graph is translated vertically upwards by 3 units as a result of the +3 in the equation, shifting the entire graph upwards.
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Determine the graph that represents a function
The circle graph and parabola graph do not represent the function because they both fail the vertical line test option (A) and (C) are correct.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
Since a circle fails the vertical line test, it cannot be a function. In other words, we can create a vertical line that crosses a circle's graph more than once.
Not every parabola is a function. Only parabolas with upward or downward openings are regarded as functions.
Thus, the circle graph and parabola graph do not represent the function because they both fail the vertical line test option (A) and (C) are correct.
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The only graph that represents a function is the: Third Graph
What graph depicts a function?
To check whether the graph represents a function or not, we perform vertical line test.
Vertical Line test:
The Vertical Line Test is a method used to determine whether a given graph represents a function or not. To apply the test, draw a vertical line through the graph and observe the points of intersection. If the vertical line intersects the graph at exactly one point for each value of x, then the graph represents a function. If the vertical line intersects the graph more than once for any value of x, then the graph does not represent a function
Looking into the graphs, the vertical line intersects the graph C at only one point.
Hence, graph C represents a function.
if h is positive how does the parabola's move?
Answer:
it would move upwards.
Step-by-step explanation:
there is no such thing as a negative exponent because, if you were suppose to graph that you have the parabola go up and down, and that is not how it works.
Rafaela is a physical education teacher and has 252525 girls and 353535 boys in her class.
She wants to divide the class into teams of the same size, where each team has the same number of girls and the same number of boys.
If Rafaela creates the greatest number of teams possible, how many boys will be on each team?
Answer:
7 boys
Step-by-step explanation:
252525=3*5²*7*13*37
353535=3*5*7²*13*37
(252525; 353535)= 3 * 5 * 7 * 13 * 37 = 50505
The greatest number of teams possible=50505
252525=5*50505
353535=7*50505
So, are 50505 teams, each containing 5 girls and 7 boys.
7 boys
find the solution set x^2+2x-8=0 separate the two answers with a comma
Answer:
-4, 2
Step-by-step explanation:
The equation can be factored as ...
(x +4)(x -2) = 0
This has solutions that make the factors zero:
x = -4, x = 2
The solution set is {-4, 2}.
The effect of drugs and alcohol on the nervous system has been the subject of considerable research recently. Suppose a research neurologist is testing the effect of a drug on response time by injecting 150 rats with a unit of dose of the drug, subjecting each to neurological stimulus, and recording its response time. The neurologist knows that the mean response time for rats not injected with the drug (the "control" mean) is 1.2 seconds. S/he wishes to test whether the mean response time for the drug-injected rats is greater than 1.2 seconds. If the sampling experiment is conducted with the sample mean equal to 1.05 second, set up the test of hypothesis for this experiment and determine if the results are significant. Suppose drug-injected rats have a mean response time of 1.1 .seconds, that is mu = 1.1 seconds.
Calculate the value of beta corresponding to the two rejection regions.
The student's question involves a statistical hypothesis test to compare the mean response times between drug-injected and control rats. The calculation of beta, representing the risk of Type II error, requires more information not provided in the question.
Explanation:The given scenario involves setting up a hypothesis test to determine if the mean response time for drug-injected rats is significantly different from the control group (rats not injected with the drug) with a known mean response time of 1.2 seconds. The null hypothesis would state that the mean response time for drug-injected rats (μ) is equal to 1.2 seconds (H0: μ = 1.2), while the alternative hypothesis would state that the mean response time is greater than 1.2 seconds (Ha: μ > 1.2).
Given that the sample mean response time for drug-injected rats is 1.05 seconds, which is actually lower than the control mean, this initially suggests that the drug does not increase the response time but rather decreases it or has no effect. However, as the question indicates a confusion with the typo in sample mean, we will proceed with testing the hypothesis based on the provided assumption that the drug-injected rats have a mean response time of 1.1 seconds.
To calculate the value of beta (the probability of a Type II error, which occurs when the null hypothesis is not rejected even though it is false), we would need to define the rejection regions for our test. The rejection region is typically defined based on the significance level (alpha) and the distribution of the test statistic under the null hypothesis. Without specifics such as the sample size, standard deviation, and significance level for defining the rejection regions, we cannot calculate beta directly.
Several years ago, 38% of parents who had children in grades K-12 were satisfied with the quality of education the students receive. A recent poll asked 1 comma 165 parents who have children in grades K-12 if they were satisfied with the quality of education the students receive. Of the 1 comma 165 surveyed, 499 indicated that they were satisfied. Construct a 95% confidence interval to assess whether this represents evidence that parents' attitudes toward the quality of education have changed.
Answer:
[tex]0.428 - 1.96\sqrt{\frac{0.428(1-0.428)}{1165}}=0.3995[/tex]
[tex]0.428 + 1.96\sqrt{\frac{0.428(1-0.428)}{1165}}=0.4564[/tex]
We are confident that the true proportion of people satisfied with the quality of education the students receive is between (0.3995, 0.4564), since the lower value for this confidence level is higher than 0.38 we have enough evidence to conclude that the parents' attitudes toward the quality of education have changed.
Step-by-step explanation:
For this case we are interesting in the parameter of the true proportion of people satisfied with the quality of education the students receive
The confidence level is given 95%, the significance level would be given by [tex]\alpha=1-0.95=0.05[/tex] and [tex]\alpha/2 =0.025[/tex]. And the critical values are:
[tex]z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96[/tex]
The estimated proportion of people satisfied with the quality of education the students receive is given by:
[tex]\hat p =\frac{499}{1165}= 0.428[/tex]
The confidence interval for the proportion if interest is given by the following formula:
[tex]\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex]
And replacing the info given we got:
[tex]0.428 - 1.96\sqrt{\frac{0.428(1-0.428)}{1165}}=0.3995[/tex]
[tex]0.428 + 1.96\sqrt{\frac{0.428(1-0.428)}{1165}}=0.4564[/tex]
We are confident that the true proportion of people satisfied with the quality of education the students receive is between (0.3995, 0.4564), since the lower value for this confidence level is higher than 0.38 we have enough evidence to conclude that the parents' attitudes toward the quality of education have changed.
The function f(x)=-(x-3)^2+9 can be used to represent the area of a rectangle with a perimeter of 12 units, as a function of the length of the rectangle, x. What is the maximum area of the rectangle?
Answer:
9.
Step-by-step explanation:
[tex]f(x) = -(x - 3)^2 + 9[/tex] is a parabola in its vertex form. For clarity, let [tex]f(x) = a (x - h)^2 + k[/tex] represent this function.
[tex]a = -1[/tex].[tex]h = 3[/tex].[tex]k = 9[/tex].Note that [tex]a[/tex], the leading coefficient, is negative. Therefore, this parabola opens downwards. The vertex of the parabola would be [tex](h,\, k)[/tex], which in this question is the point [tex](3,\, 9)[/tex]. Since the parabola opens downwards, that vertex would be a local maximum (a crest) on its graph.
Before concluding that the maximum area of this rectangle is [tex]9[/tex], make sure that [tex](3,\, 9)[/tex] is indeed on the graph of [tex]y = f(x)[/tex].
The length of a rectangle should be positive. Since [tex]x[/tex] represents the length of this rectangle, [tex]x > 0[/tex]. Also, since the perimeter should be less than [tex]12[/tex], the length of one side should be less than [tex]12 / 2 = 6[/tex]. Therefore, the domain of [tex]f[/tex] should be the open interval [tex](0,\, 6)[/tex]. (Endpoints not included.)
Indeed, [tex]x = 3[/tex] is in that interval. [tex](3,\, 9)[/tex] would be on the graph [tex]y = f(x)[/tex]. Therefore, [tex]9[/tex] is indeed the maximum area of this rectangle.
Side note: if the domain is a closed interval (i.e., endpoints included,) then consider checking the endpoints, as well.
Answer:
Step-by-step explanation:
9
Can anyone help me, thanks
Answer:
When x=0 y=6
When x=3 y=0
Step-by-step explanation:
-6x-3y ≤-18
Let x = 0
-6x-3y =-18
-3y =-18
Divide each side by -3
-3y/-3 = -18/-3
y = 6
Let y = 0
-6x-3y =-18
-6x =-18
Divide each side by -6
-6x/-6 = -18/-6
x = 3
In a right triangle, which ratio represents the sine of an angle?
a.
StartFraction opposite Over hypotenuse EndFraction
c.
StartFraction opposite Over opposite Endfraction
b.
StartFraction adjacent Over hypotenuse EndFraction
d.
StartFraction opposite Over adjacent EndFraction
Please sele
Answer:
A
Step-by-step explanation:
A spherical boulder is 18 ft in diameter and weighs almost 8 tons. Find the volume. Use 3.14 for piπ.
The volume of a spherical boulder with a diameter of 18 ft can be calculated using the formula V = 4/3πr³, with 'r' being the radius of the sphere. By substituting the radius of 9 ft (half of 18 ft), we find that the volume is approximately 3053.62 cubic feet.
Explanation:To find the volume of a sphere, we use the formula: V = 4/3πr³, where 'r' is the radius of the sphere. The radius can be found from the diameter by dividing it by 2; therefore, for this boulder, the radius will be 18 ft/2 = 9 ft. Substituting 'r' into the volume equation: V = 4/3 * 3.14 * (9ft)³ = 3053.62 cubic feet. Therefore, the spherical boulder has a volume of approximately 3053.62 cubic feet.
To find the volume of a spherical boulder, we can use the formula for the volume of a sphere, which is V = (4/3)πr³. Given that the diameter of the boulder is 18 ft, we can find the radius by dividing the diameter by 2, which gives us a radius of 9 ft. Plugging this value into the formula, we get V = (4/3)π(9 ft)³. Using the value of π as 3.14, we can calculate the volume:
V = (4/3)(3.14)(9 ft)³ = (4/3)(3.14)(729 ft³) = 3053.96 ft³
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For each 11 mm of coloured fabric Nick uses to make his curtains, he also uses 2 cm of white fabric. Express the amount of white fabric to coloured fabric as a ratio in its simplest form.
Answer:
The amount of white fabric to coloured fabric as a ratio is 20:11
Step-by-step explanation:
We are given that For each 11 mm of colored fabric Nick uses to make his curtains, he also uses 2 cm of white fabric.
Length of colored fabric = 11 mm
Length of White fabric = 2 cm
1 cm = 10 mm
2 cm = 20 mm
So, length of white fabric = 20 mm
So, Ratio of the amount of white fabric to coloured fabric = [tex]\frac{20}{11}[/tex]
Hence the amount of white fabric to coloured fabric as a ratio is 20:11
how many gallons of paint are needed to paint one coat, if a gallon of paint covers 400ft squared?
Answer:
6.28 gallons
Step-by-step explanation:
first we need to find the area of a half sphere, and then find how much paint will be needed for that area.
The area of a sphere:
[tex]a=4 \pi r^2[/tex]
thus, the area of half a sphere is:
[tex]a=2 \pi r^2[/tex]
we know that the radius is:
[tex]r=20ft[/tex]
we substitute this to find the area of the half sphere (the area they need to paint):
[tex]a=2\pi (20ft)^2\\a=2(3.1416) (400ft^2)\\a=2,513.27ft^2[/tex]
now the question is how many gallons of paint are needed to paint 2,513.27 square feet.
We are told that 1 gallon covers 400 square feet
thus, we must divide 2,513.27 by 400:
[tex]\frac{2,513.27ft^2}{400ft^2} =6.28[/tex]
6.28 gallons of paint are needed.
The weekly earnings of students in one age group are normally distributed with a standard deviation of 10 dollars. A researcher wishes to estimate the mean weekly earnings of students in this age group. Find the sample size needed to assure with 95 percent confidence that the sample mean will not differ from the population mean by more than 2 dollars.
Answer:
We need a sample size of at least 97.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1-0.95}{2} = 0.025[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].
So it is z with a pvalue of [tex]1-0.025 = 0.975[/tex], so [tex]z = 1.96[/tex]
Now, find the margin of error M as such
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
Find the sample size needed to assure with 95 percent confidence that the sample mean will not differ from the population mean by more than 2 dollars.
We need a sample size of at least n.
n is found when [tex]M = 2, \sigma = 10[/tex].
So
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
[tex]2 = 1.96*\frac{10}{\sqrt{n}}[/tex]
[tex]2\sqrt{n} = 1.96*10[/tex]
[tex]\sqrt{n} = \frac{1.96*10}{2}[/tex]
[tex](\sqrt{n})^{2} = (\frac{1.96*10}{2})^{2}[/tex]
[tex]n = 96.04[/tex]
Rouding up
We need a sample size of at least 97.
With Claudia’s loan does loan length or interest rate have a greater effect on the cost of the interest for the loan explain
Loan length affects total interest by spreading payments; interest rate directly impacts borrowing cost. Relative effect depends on borrower's goals.
The cost of interest for a loan is influenced by both the loan length (term) and the interest rate, but the degree of impact each has depends on several factors, including the specific terms of the loan and the borrower's financial situation. Let's break down their effects:
1. Loan Length (Term):
- Longer loan terms typically result in lower monthly payments since they spread the principal amount over more payments.
- However, longer terms also mean more time for interest to accrue, resulting in higher overall interest costs over the life of the loan.
- For example, if Claudia takes out a loan with a longer term, she may pay less each month but end up paying more in total interest over the entire term compared to a shorter-term loan with the same interest rate.
2. Interest Rate:
- The interest rate directly impacts the cost of borrowing. Higher interest rates mean higher monthly payments and more interest paid over the life of the loan.
- Lower interest rates, on the other hand, result in lower monthly payments and less interest paid overall.
- Even a small difference in interest rates can significantly affect the total interest paid over the life of the loan, especially for large loan amounts or longer terms.
Now, to determine which factor has a greater effect on the cost of interest for Claudia's loan, we need to consider her specific situation:
- If Claudia prioritizes minimizing her monthly payments, she might opt for a longer loan term despite potentially paying more interest in the long run.
- If Claudia is focused on minimizing the total interest paid over the life of the loan, she might prioritize securing a lower interest rate, even if it means higher monthly payments.
Ultimately, the relative importance of loan length and interest rate in determining the cost of interest depends on Claudia's financial goals, her ability to make monthly payments, and her overall financial situation. It's essential for her to carefully consider both factors and choose the loan terms that best align with her needs and financial objectives.
ASAP! GIVING BRAINLIEST! Please read the question THEN answer correctly! No guessing. Show your work or give an explaination.
Answer:
D
Step-by-step explanation:
Look at the graph. You want to see how much distance he is at 9 minutes. Go all the way to 9 minutes, then go up. What coordinate does it fall in? (9,80). He travelled 80 meters in 9 minutes. (D)
Which inequality is equivalent to this one?
Y-8≤-2
Answer:
y-8+8
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
Write the equation of the line that is parallel to y = -2x - 9 and passes through the point (-2,-4).
Answer: y=-2x-8
Step-by-step explanation:
Parallel lines need to have the same slopes but different y-intercept.
y=-2x -9 is parallel to y=-2x - 8
Vignesh owns a cottage in the shape of a cube with each edge of length 26 feet. The roof is in the shape of a square pyramid and it extends two feet over the edge of the cottage on each side. The lateral sides of the roof are 17 feet long. What is the total surface area of the roof?
Answer:
Step-by-step explanation:
The shape of the cottage is cube
The edge of the cube is of length is 26ft
L_1 = 26ft.
The roof is in form of a square with with length 17ft.
L_2 = 17ft.
The roof is made up of 4 congruent isosceles triangles. Since the roof extends 2 ft over the edge of the cottage on each side, then the base of each triangle is 26 + 2 = 28 ft.
L_2 = 28 ft
Then, area of the roof is
A = 28²
A = 784 ft²
The triangular pyramid.
The triangular has four sides
Then,
Each of the area can be calculated using
A = ½ × b × h
Then, the four area of the triangular pyramid
A_total = 4 × ½ × b × h
A_total = 2 × b × h
The base of the triangle is 28ft.
The calculate the height of the triangle
Let's calculate the area of one of the triangles and then just multiply by 4. See attachment. Drop a perpendicular from the vertex of a triangle to its base. We now have the triangle broken up into two right triangles. The hypotenuse is 17 ft and one of the legs of the right triangle is 28 / 2 = 14 ft. Then the height is using Pythagoras theorem
a² = b² + c²
17² = 14² + h²
17² - 14² = h²
h² = 93
h = √93
Then, the area of the triangular pyramid is
A = 2 × b × h
A = 2 × 28 × √93
A = 540.04 ft²
Then, the area of the pyramid is approximately 540 ft², since the base of the pyramid cannot be seen.
But if we include the base, then, the total surface area is
A_t = A_triangular + A_base
A_t = 540 + 784
A_t = 1324 ft²
How do you solve this?
A cone with height 12 centimeters and volume 16 pi centimeters cubed. What is the radius of the cone? 1 cm 2 cm 4 cm 8 cm
Answer:
2
Step-by-step explanation:
Answer:
2
Step-by-step explanation:
Took the assignment
In 1943, an organization surveyed 1100 adults and asked, "Are you a total abstainer from, or do you on occasion consume, alcoholic beverages?" Of the 1100 adults surveyed, 429 indicated that they were total abstainers. In a recent survey, the same question was asked of 1100 adults and 352 indicated that they were total abstainers. Has the proportion of adults who totally abstain from alcohol changed? Use the alphaequals0.10 level of significance.
Answer:
We conclude that the proportion of adults who totally abstain from alcohol has changed.
Step-by-step explanation:
We are given that in 1943, an organization surveyed 1100 adults and asked, "Are you a total abstainer from, or do you on occasion consume, alcoholic beverages?"
Of the 1100 adults surveyed, 429 indicated that they were total abstainers. In a recent survey, the same question was asked of 1100 adults and 352 in
Let p = proportion of adults who totally abstain from alcohol.
where, p = [tex]\frac{429}{1100}[/tex] = 0.39
So, Null Hypothesis, [tex]H_0[/tex] : p = 39% {means that the proportion of adults who totally abstain from alcohol has not changed}
Alternate Hypothesis, [tex]H_A[/tex] : p [tex]\neq[/tex] 39% {means that the proportion of adults who totally abstain from alcohol has changed}
The test statistics that would be used here One-sample z proportion statistics;
T.S. = [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ~ N(0,1)
where, [tex]\hat p[/tex] = sample proportion of adults who totally abstain from alcohol = [tex]\frac{352}{1100}[/tex] = 0.32
n = sample of adults surveyed = 1100
So, test statistics = [tex]\frac{0.32-0.39}{\sqrt{\frac{0.32(1-0.32)}{1100} } }[/tex]
= -4.976
The value of z test statistics is -4.976.
Now, at 0.10 significance level the z table gives critical values of -1.645 and 1.645 for two-tailed test.
Since our test statistics doesn't lie within the range of critical values of z, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.
Therefore, we conclude that the proportion of adults who totally abstain from alcohol has changed.
The table shows the results for spinning the spinner 75 times. What is the relative frequency for the event "spin a 3"?
Answer: 0.267
Step-by-step explanation:
The relative frequency is the number of times that we obtained a given outcome divided by the total numer of trials.
In this case we have 75 trials.
in 20 trials the outcome was a 3.
Then the relative frequency of the event "spin a 3" is:
p = 20/75 = 0.266... = 0.267
Answer:
look under the 3 and you get
20
Kelsey's car can go 120 miles on 4.8 gallons of gas.If her tank holds 18 gallons,how far can she travel on a full tank of fuel.
Answer: She can travel 450 miles with 18 gallons.
Step-by-step explanation:
[tex]\frac{4.8}{120}[/tex] = [tex]\frac{18}{x}[/tex] solve by cross product
4.8x = 2160
x= 450
Kelsey's car gets 25 miles per gallon, and with an 18-gallon tank, she can travel a total of 450 miles on a full tank.
Explanation:To calculate how far Kelsey can travel on a full tank of fuel, first we need to determine her car's fuel efficiency and then apply it to the full tank capacity. We are given that her car can travel 120 miles on 4.8 gallons of gas. This gives us a fuel efficiency rate we can use to find out the total distance she can travel on 18 gallons.
Step-by-step CalculationCalculate the miles per gallon (mpg) her car gets by dividing the total miles traveled by the gallons of gas used: 120 miles ÷ 4.8 gallons = 25 mpg.Calculate the total distance that can be traveled on a full 18-gallon tank by multiplying the fuel efficiency rate by the tank size: 25 mpg × 18 gallons = 450 miles.Therefore, Kelsey can travel 450 miles on a full tank of fuel.
Learn more about Fuel Efficiency Calculation here:https://brainly.com/question/28314501
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