A poll used a sample of randomly selected car owners. Within the sample, the mean time of ownership for a single car was years with a standard deviation of years. Test the claim by the owner of a large dealership that the mean time of ownership for all cars is less than years. Use a 0. 05 significance level
Answers
If t is less than -1.699, we reject the null hypothesis.
To test the claim by the owner of the large dealership, we will use a one-sample t-test with the following hypotheses:
Null Hypothesis: H0: µ >= µ0 (The population mean time of ownership is greater than or equal to µ0)
Alternative Hypothesis: Ha: µ < µ0 (The population mean time of ownership is less than µ0)
where µ is the population mean time of ownership, µ0 is the claimed mean time of ownership by the owner of the dealership.
The significance level is α = 0.05.
We can calculate the t-value as:
t = (\(\bar{x}\) - µ0) / (s / √n)
where \(\bar{x}\) is the sample mean time of ownership, s is the sample standard deviation, n is the sample size.
Plugging in the values given in the problem, we get:
t = (\(\bar{x}\) - µ0) / (s / √n) = (5.7 - µ0) / (1.8 / √n)
Since the alternative hypothesis is one-tailed (less than), we need to find the critical t-value from the t-distribution table with n-1 degrees of freedom and a significance level of 0.05. For a sample size of n = 30 (assuming it is large enough), the critical t-value is -1.699.
If the calculated t-value is less than the critical t-value, we reject the null hypothesis and conclude that there is evidence to support the claim that the mean time of ownership for all cars is less than the claimed mean time of ownership by the owner of the dealership.
If the calculated t-value is greater than the critical t-value, we fail to reject the null hypothesis and conclude that there is not enough evidence to support the claim that the mean time of ownership for all cars is less than the claimed mean time of ownership by the owner of the dealership.
So, if we assume that the sample is representative of the population and meets the assumptions of the t-test, we can calculate the t-value as:
t = (5.7 - µ0) / (1.8 / √30)
If t is less than -1.699, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.
Note that we don't have any information about the claimed mean time of ownership by the owner of the dealership, so we cannot calculate the t-value or make any conclusions.
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Related Questions
Anyone smart enough to do this
Answers
Answer: B and F I believe
Step-by-step explanation:
which of the following is true about the approximate number system?group of answer choicesit is easier to discriminate smaller numbers (8 vs. 16) than larger ones (16 vs. 32).
Answers
The statement that is NOT true about infants' approximate number system is option (b) Infants can only discriminate approximate numbers when there is a large difference between the numbers.
Infants possess an innate sense of quantity that enables them to discriminate between different numerical magnitudes. This sense of quantity, also known as the approximate number system, is present in infants as young as 6 months old. Infants are able to discriminate between numerical quantities even when the difference between them is small, and their ability to do so improves with age.
However, their ability to discriminate between numerical quantities can be affected by various factors, including the numerical ratio between the stimuli, the duration of the presentation, and the task demands. Overall, the approximate number system is an important precursor to the development of more advanced mathematical skills.
Therefore, the correct option is (b) Infants can only discriminate approximate numbers when there is a large difference between the numbers.
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The given question is incomplete, the complete question is:
Which of the following is NOT true about infants' approximate number system?
Select one: a. Infants are able to discriminate approximate numbers by 6 months of age.
b. Infants can only discriminate approximate numbers when there is a large difference between the numbers.
c. Infants are unable to discriminate approximate numbers when dots change in both size and position simultaneously.
d. Infants' ability to discriminate approximate numbers is not dependent on non-numeric perceptual properties.
NEED HELP FAST PLEASEEE!!!! When Talia performs in a cheerleading competition she makes 2 mistakes
in every 3 minutes of performance. If she performs for a total of 18
minutes in the competition tonight, how many mistakes will she
make?
A. 12
B. 15
C. 16
D. 27
E. 30
Answers
Answer:
(A) 12
Step-by-step explanation:
This is actually very simple!
If Talia makes 2 mistakes every 3 minutes then the ratio is 2:3
Going along with that if you know how ratios work then that should be easy. But this is also the long way. You dont really need to know ratios you just need to know the steps but knowing ratios would be helpful.
You first divide
18 / 3 = 6
Then multiply
6 x 2 = 12
That's it!
Hope this helped! :)
A survey was conducted to investigate whether alcohol consumption and smoking are related. In a random
sample of 300 smokers, 196 said they had consumed alcohol at least once in the past week. In an
independent random sample of 300 non-smokers, 159 said they had consumed alcohol in the past week. If
P, is the proportion of smokers in the population who have had a drink in the past week and P is the
corresponding proportion of non-smokers, then a test of the hypotheses H, P, -P-0 against the two-sided alternative produces a test statistic of z=3.07 and a P-value of 0.002. If we had instead analyzed these results with a chi-square test of homogeneity, which of the following would be the test statistic and P-value?
a-942, P-value = 0.002
b. -942, P-value-0.004
-3.07, P-value - 0.004
d. -1.75, P-value = 0.002
e-1.75, P-value=0.004
Answers
e) The test statistic and P-value for the chi-square test of homogeneity would be -1.75 and 0.004, respectively.
A chi-square test of homogeneity is a useful tool for comparing two or more categorical variables. In this case, the two variables are smoking (smokers and non-smokers) and alcohol consumption (those who had consumed alcohol in the past week and those who hadn't).
The chi-square statistic is calculated by finding the difference between the observed and expected frequencies of the two groups and squaring it. The expected frequencies are found by multiplying the sample size by the overall probability of success (in this case, drinking alcohol).
The P-value is then calculated based on the chi-square statistic and the degrees of freedom (in this case, one). In this case, the chi-square statistic is -1.75 and the P-value is 0.004.
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Find side AB and round your answer to the nearest hundredth, help please.
Answers
Answer:
? = 5.12
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
sin B = opp/ hyp
sin 65= 5/ ?
? = 5/ sin 65
? =5.516889595
To the nearest hundredth
? = 5.12
Select the correct answer. If the graph of f(x) = 4x is shifted 7 units to the left, then what would be the equation of the new graph? A. g(x) = 4x + 7 B. g(x) = 4(x + 7) C. g(x) = 4x − 7 D. g(x) = 4(x − 7)
Answers
The equation of the new graph would be \(g(x) = 4(x + 7)\).
The correct answer is B.
When a graph is shifted 7 units to the left, we write \((x + 7)\) inside the parentheses.
Therefore, the equation of the new graph would be
\(f(x + 7) = 4(x + 7)\)
which can be simplified to \(f(x + 7) = 4x + 28\)
But, the question is asking for the equation of the new graph.
So, we replace f(x) with g(x), since we are creating a new function and not modifying the existing one.
Therefore, the equation of the new graph would be \(g(x) = 4(x + 7)\).
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Please help
Write an equation of the line in point-slope form that passes through the given points in the table. Then write the equation in slope-intercept form.
An equation of the line in point-slope form is
(Simplify your answer. Type an equation. Type your answer in point-slope form. Use integers or fractions for any numbers in the equation)
Answers
The equation of the line in slope-intercept form is y = 6x + 55.
Describe Equation?Equations can involve variables, which are placeholders for unknown values that we wish to find. For example, the equation x + 3 = 7 asserts that the value of x plus 3 is equal to 7. We can solve for x by subtracting 3 from both sides of the equation, obtaining x = 4.
Equations can be linear or nonlinear, and they can involve one or more variables. They can be represented in various forms, such as standard form, slope-intercept form, or quadratic form.
To find the equation of the line in point-slope form, we need to first find the slope of the line. We can use any two points from the table to find the slope using the formula:
slope = (change in y)/(change in x)
Let's use the first and last points in the table:
slope = (295 - 175)/(40 - 20) = 120/20 = 6
Now we can use the point-slope form of the equation of a line:
y - y1 = m(x - x1)
where m is the slope and (x1, y1) is any point on the line. Let's use the first point (20, 175):
y - 175 = 6(x - 20)
To write this equation in slope-intercept form, we need to isolate y:
y - 175 = 6x - 120
y = 6x + 55
So the equation of the line in slope-intercept form is y = 6x + 55.
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Which transformation produces shapes that are not congruent?
Answers
Dilation and rotation transformation produces shapes that are not congruent.
Rotations, reflections and translations are known as rigid transformations; this means they do not change the size or shape of a figure, they simply move it. These rigid transformations preserve congruence.
Dilation, however, are not rigid transformations, since they change the size of a shape. Dilation would not change the shape, just the size; the angle measures would be the same, and the ratio of corresponding sides would be equal to the scale factor used in the dilation. This would give us a similar, but not congruent, figure.
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The median of a boulevard i 8 feet wide and 300 feet long. What i the area of the median?
Answers
By using the formula for area of rectangle, it can be calculated that Area of the median is 2400 sq. feet
What is area of rectangle?
The area of a rectangle is calculated by multiplying the length by the width. For example, if a rectangle has a length of 10 feet and a width of 6 feet, the area would be 10 x 6 = 60 square feet. The area of a rectangle is a two-dimensional measurement and is typically expressed in units squared, such as square feet or meters squared. Other shapes, such as a triangle or a circle, also have areas and are calculated differently.
If l is the length of the rectangle and b is the breadth of the rectangle, then area of rectangle is calculated by the formula
Area = \(l \times b\)
Length of the median = 300 feet
Width of the median = 8 feet
Area of the median = 300 \(\times\) 8 = 2400 sq. feet
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Linda practiced her free throw shots and missed 26% of her shots. If she
shot the ball 50 times, how many times did she miss? *
Answers
Answer:
13
Step-by-step explanation:
Find 26% of 50 by doing
.26 * 50
resulting in 13
let r(x) = f(g(x)) and s(x) = g(f(x)), where f and g are shown in the figure. find r'(1) and s'(4).
Answers
The value of r'(1) and s'(4) is 0 that can be interpreted with the help of the graph that is given in the question.
Derivative in mathematics, the rate of change of a characteristic with recognize to a variable. Derivatives are essential to the answer of troubles in calculus and differential equations. The essence of calculus is the by-product. The by-product is the immediately price of extrade of a characteristic with recognize to certainly considered one among its variables. This is equal to locating the slope of the tangent line to the characteristic at a point
\(r(x) = f(g(x))\)therefore the derivative of r is given by \(r'(x) = f'g(x)\times g'(x)\)
\(r'(1) = f'(g(1))\times g'(1)\) from the graphs
r'(1) = f'4 \times g'1 = (5/4) \times(0) = 0
Similarly s'(1) = g'(f(1))\times f'(1) from the graphs
f(1)=1.5, f'(1)
=\dfrac{ (3-0)}{(0-2)}
= -3/2 , g'(3/2) = 0
s'(4) = g'(3/2) \times f'(4) = 0(-1.5) = 0
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Complete question:
let r(x) = f(g(x)) and s(x) = g(f(x)), where f and g are shown in the figure. find r'(1) and s'(4).
I don’t understand this someone pls help me! (Question 10)
Answers
Answer:
a. f(n) = n(n+1)/2
b. 351
c. 19
d. no; n would not be an integer for f(n) = 17.
Step-by-step explanation:
a. The terms are 1, 3, 6, 10, ...
Each term has the term number added to the previous term. That is, first differences are 3-1 = 2, 6-3 = 3, 10-6 = 4. These differences have a constant difference of 1.
When the 2nd differences are constant, a 2nd degree polynomial can describe the sequence. It is a little bit of trouble to find that polynomial.
For the polynomial ...
\(f(n)=an^2+bn+c\)
We can substitute values for n and f(n) to get 3 equations in 3 unknowns:
\(1=a\cdot1^2+b\cdot1+c\\\\3=a\cdot2^2+b\cdot2+c\\\\6=a\cdot3^2+b\cdot3+c\)
Solving these equations by your favorite method gives ...
(a, b, c) = (1/2, 1/2, 0)
That is, the function representing the relationship is ...
f(n) = n(n+1)/2 . . . . the function describing the relationship
__
b. f(26) = 26(27) = 13(27) = 351 . . . . the number of squares in term 26
__
c. The number of the term having 190 squares can be found by solving ...
n(n +1)/2 = 190
n(n +1) = 380 = 19(20)
The 19th term will have 190 squares.
__
d. Terms 5 and 6 are 15 and 21.
17 is not the value of one of the terms in this sequence.
For each of the following examples, imagine that some researcher has found the reported pattern of covariation between X and Y. Can you think of a variable Z that might make the relationship between X and Y spurious?
(a) The more firefighters (X) that go to a house fire, the greater property dam- age that occurs (Y).
(b) The more money spent by an incumbent member of Congress’s campaign (X), the lower their percentage of vote (Y).
(c) Increased consumption of coffee (X) reduces the risk of depression among women (Y).
(d) The higher the salaries of Presbyterian ministers (X), the higher the price of rum in Havana, Cuba (Y).
Answers
(a) The presence of a confounding variable Z, such as the severity of the fire, could make the relationship between the number of firefighters (X) and property damage (Y) spurious.
(b) The presence of a confounding variable Z, such as the popularity of the incumbent member or the characteristics of the constituency, could make the relationship between campaign spending (X) and percentage of vote (Y) spurious.
(c) The presence of a confounding variable Z, such as the overall lifestyle or socioeconomic status of the women, could make the relationship between coffee consumption (X) and the risk of depression (Y) spurious.
(d) The presence of a confounding variable Z, such as the overall economic conditions or demand for rum in Havana, could make the relationship between Presbyterian ministers' salaries (X) and the price of rum (Y) spurious.
In each of the given examples, the reported pattern of covariation between X and Y may be influenced by a confounding variable Z. A confounding variable is a variable that is related to both the independent variable (X) and the dependent variable (Y), which can lead to a spurious relationship between X and Y.
The presence of a confounding variable can create the illusion of a direct relationship between X and Y when, in reality, the observed relationship is due to the influence of Z.
For example, in the case of firefighters and property damage, the severity of the fire (Z) could be the underlying factor driving both the number of firefighters and the extent of property damage.
Similarly, in the case of campaign spending and percentage of vote, factors such as the popularity of the incumbent member or the characteristics of the constituency (Z) could be influencing both variables.
In the case of coffee consumption and the risk of depression, other lifestyle or socioeconomic factors (Z) may be responsible for the observed relationship rather than coffee itself. And in the case of Presbyterian ministers' salaries and the price of rum, economic conditions or demand for rum (Z) in Havana could be driving both variables.
Identifying and controlling for confounding variables is crucial in research to ensure accurate interpretations of the relationship between X and Y. It allows researchers to isolate the true causal relationship between the variables of interest.
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Write the equation of the line that has a gradient of -6 and passes through the point (4, -2)
y-2=-6(x + 4)
y+4= -6(x - 2)
y-2=-6(x-4)
y + 2 = -6(x-4)
y -4 = -6(x + 2)
Answers
The equation of the line that has a gradient of -6 and passing through the point (4,-2) is y+2 = -6(x-4)
The gradient of the the line = -6
The line passing through the point = (4,-2)
The equation of the line y = mx+c
Here the gradient of the line is -6, which is the value of m in the equation of the line
Next we have to find the value of c
The line is passing through the point (4,-2)
y = mx+c
-2 = -6(4)+c
-2 = -24+c
c = -2+24
c= 22
The equation will be
y = -6x+22
Add both sides by 2
y+2 = -6x+22+2
y+2 = -6x+24
y+2 = -6(x-4)
Hence, the equation of the line that has a gradient of -6 and passing through the point (4,-2) is y+2 = -6(x-4)
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Carla has a rectangular garden in her backyard. The width of the garden is 9 meters. The area of the garden is 360 square meters. What is the length of the garden? Show your work.
Answers
Answer:
l = 40 m
Step-by-step explanation:
The formula for area of a rectangle is
A = lw, where
A is the area in square units,l is the length,and w is the widthStep 1: Since we're given the area and width, we plug in these two values for A and w and to solve for l (length):
360 = 9l
Step 2: Divide both sides by 9 to solve for l
(360 = 9l) / 9
40 m = l
Optional Step 3: We can check our answers by checking that the product of 40 and 9 is 360
40 * 9 = 360
360 = 360
Problem 4. [20 points] Cost minimization Assume a continuum of consumers are uniformly distributed along the interval [0,1]. A social planner chooses the placements of three "shops". Consumers have linear transportation costs and visit the shop that is closest to their location. Each consumer incurs a cost of l if she or he travels a distance l. Please note that to obtain full marks, you need to provide detailed solutions and show your work. (a) [10 points] Derive the locations a
∗
,b
∗
and c
∗
of the three shops that minimize aggregate transportation cost T(a,b,c). What is the corresponding minimum cost? (b) [10 points] Suppose now that two shops already exist: one at location 0 and the other at location 5/6. The social planner is choosing where to place another (the third) shop but can also relocate the existing two shops. The cost of relocating a shop depends on the distance required: if a shop needs to be "moved" distance d, then the relocation cost is
2
1
d
2
. What are the optimal locations x
∗
,y
∗
and z
∗
of the three shops that minimize aggregate transportation and relocation cost
T
^
(x,y,z). What is the corresponding minimum cost?
Answers
A continuum of consumers are uniformly distributed along the interval [0, 1]. Consumers have linear transportation costs and visit the shop that is closest to their location. Derive the locations a*, b*, and c* of the three shops that minimize aggregate transportation cost .
Let A, B, and C be the three shops’ locations on the line.[0, 1] Be ai and bi, Ci be the area of the line segments between Ai and Bi, Bi and Ci, and Ai and Ci, respectively.Observe that any consumer with a location in [ai, bi] will visit shop A, and similarly for shops B and C. For any pair of locations ai and bi, the aggregate transportation cost is the same as the sum of the lengths of the regions visited by the consumers.
Suppose, without loss of generality, that 0 ≤ a1 ≤ b1 ≤ a2 ≤ b2 ≤ a3 ≤ b3 ≤ 1, and let t = T(a, b, c) be the aggregate transportation cost. Then, t is a function of the five variables a1, b1, a2, b2, and a3, b3. Note that b1 ≤ a2 and b2 ≤ a3 and the bounds 0 ≤ a1 ≤ b1 ≤ a2 ≤ b2 ≤ a3 ≤ b3 ≤ 1.In particular, we can reduce the problem to the two-variable problem of minimizing the term b1−a1 + a2−b1 + b2−a2 + a3−b2 + b3−a3 with the additional constraints (i) and 0 ≤ b1 ≤ a2, b2 ≤ a3, and b3 ≤ 1.
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Please help answer correctly !!!!!!!!!!!!!!!!! Will mark Brianliest !!!!!!!!!!!!!!!!!!!!
Answers
Answer:
DH is perpendicular to HG
[Easy Points] Kanna Kamui sees 3 snowmen. Then he sees 2 more. How many snowmen did Kanna see in all?
![[Easy Points] Kanna Kamui sees 3 snowmen. Then he sees 2 more. How many snowmen did Kanna see in all?](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/UmsaM9GtWcWOBQ2TsaIaFiSiYugyWNdd.png)
Answers
Answer:
the correct answer is 5 snowmen
Destiny just received two separate gifts from her great-great-grandmother.
The first gift is a box of
18
1818 chocolate candy bars, and the second gift is a pack of
12
1212 cookies.
Destiny wants to use all of the chocolate candy bars and cookies to make identical snack bags for her cousins.
Answers
Answer:
6 bags
Step-by-step explanation:
The first gift is a box of 18 chocolate candy bars, and the second gift is a pack of 12 cookies. Destiny wants to use all of the chocolate candy bars and cookies to make identical snack bags for her cousins. What is the greatest number of snack bags that Destiny can make? Answer: 6 bags
Answer: 6 snack bags
Step-by-step explanation:
In rder to know mnay bags destiny ca make, we need a number is a factor of 18 and 12, so that the 18 chocolate candy bars and the 12 cookies can be divided up evenly.
So, if there were 2 bags, thre would be 18÷2=9 chocolate candy bars and 12÷2=6 cookies in a bag. This creates identical snack bags, but isn't the greatest number of bags!
To find the greatest snack bag, we want to find the greatest common factor of 18 and 12
To do so, let's find factors of 18 ans 12
18: 1, 2, 3, 6, 9, 18
12: 1, 2, 3, 4, 6, 12
The greatest common factor of 18 and 12 is 6. in math notation this looks like:
gcf (18, 12) = 6
The greatest number of identical bags can make is 6
y = x + 2
5x - 4y = -3
Solving systems by equations
Answers
Answer: x = 5, y = 7
Step-by-step explanation:
1. First, put the variables together/rearrange:
y - x = 2 & 5x - 4y = -3
2. Cancel out variable x by multiply the first equation by 5:
5y - 5x = 10 & 5x - 4y = -3
3. Add equations:
y = 7
4. Then determine x by plugging y back into the first equation y = x + 2:
x = 5
Solve the following quadratic equation for all values of x in simplest form. 2 ( x+ 8 ) ^2 + 9 =29
Answers
Answer:
x = -8 + sqrt(10) and x = -8 - sqrt(10)
Step-by-step explanation:
The quadratic equation to be solved is:
2(x + 8)² + 9 = 29
First, we need to simplify the left-hand side of the equation by expanding the squared term:
2(x + 8)(x + 8) + 9 = 29
Simplifying further, we get:
2(x² + 16x + 64) + 9 = 29
Distributing the 2, we get:
2x² + 32x + 128 + 9 = 29
Combining like terms, we get:
2x² + 32x + 137 = 29
Subtracting 29 from both sides, we get:
2x² + 32x + 108 = 0
Dividing both sides by 2, we get:
x² + 16x + 54 = 0
We can solve this quadratic equation by factoring or by using the quadratic formula :
The equation presented is a quadratic equation in standard form, ax² + bx + c = 0, where a = 1, b = 16, and c = 54. To solve this equation, we can use the quadratic formula, x = (-b ± sqrt(b² - 4ac)) / 2a. Plugging in the values, we get x = (-16 ± sqrt(16² - 4(1)(54))) / 2(1) = (-16 ± sqrt(16)) / 2 or (-16 ± 2sqrt(10)) / 2. Simplifying, we get x = -8 ± sqrt(10). Therefore, the two solutions to this equation are x = -8 + sqrt(10) and x = -8 - sqrt(10).
(1/4)^2 / (-5/9)
PLASE SHOW WORK!!! :)
Answers
Which set of numbers does NOT describe the side lengths of a right
triangle?
F 7, 24, 25
G 9, 40, 41
H 12, 35, 37
J 15, 18, 23
Answers
Answer: J
Step-by-step explanation:
Just substitute each of the sets into the Pythagorean Theorem - only J doesn't work.
PLEASE HELP Tony received a $45.25 gift card for a photo center. He used it to buy prints that cost 5 cents each. The remaining balance, B in dollars), on the card after buying x prints is given by the following function. B (x)=45.25 -0.05x What is the remaining balance on the card if Tony bought 50 prints?
Answers
Answer:You have too add $45.25 by 5 and divided the answer you got from adding the $45.25
Step-by-step explanation:
Hope this helps!
Teena and Adil have a total of 560 counters. Adil has 2/5 of the number of counters that Teena has. How many more counters does Teena have then Adil?
A) 240
B) 336
C) 400
D) 224
Answers
ANSWER:
:2/5 * 560 = D) 224
I need some help please
Answers
Answer:
Step-by-step explanation:
I think is x-1
It is because you need to find f(1) and the formula of x-1 when x is greater and equal to 1.
The discount allowed in a store for a cash payment is 6%. Find what a buyer pays for an article whose marked prices $567.50
Answers
Answer:
A buyer would have to pay $533.45 for an article whose marked prices $567.50.
Step-by-step explanation:
Marked price = $567.50
Discount=6%
Price after discount = 567.50 - 6% of 567.50
\(=\:567.50\:-\frac{6}{100}\:\times \:567.50\)
\(=567.5-34.05\)
\(=533.45\) $
Therefore, a buyer would have to pay $533.45 for an article whose marked prices $567.50.
the least common multiple of and is , and the least common multiple of and is . what is the least possible value of the least common multiple of and ?
Answers
The LCM of a and c is 20.
Here we need to find the minimum possible LCM of a and c. For this a and c must have the minimum possible values.
Now,
LCM of a and b is 12
LCM of b and c is 15
Now for this to be true, b must be a number that is a common factor of 12 and 15, which is 3
Hence, b is 3.
Hence a will obviously be 4 and c will be 5.
Hence the LCM of a and c is 20.
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Complete Question
The least common multiple of a and b is 12, and the least common multiple of b and c is 15. What is the least possible value of the least common multiple of a and c?
IS
Find the circumference.
11 in
C = [?] in
C = πD = 2πr Use π = 3.14
T
![ISFind the circumference.11 inC = [?] inC = D = 2r Use = 3.14T](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/l2rwvhlh0nplaRGSVkmntQoKLqHepXOn.png)
Answers
The circumference of the circle is 69.08 inches.
Circumference is the distance around the outside of a circle.
We can use the formula C = πD or C = 2πr to find the circumference.
- Given radius = 11 inches, we can find the circumference of a circle as follows:
C = πD or C = 2πr
We are given that 11 inches is the radius (r) of a circle.
So, we could use C = 2πr where r is the radius of the circle.
Now we can use C = 2πr to find the circumference of the circle
(using π = 3.14):
C = 2πr = 2π × 11 inches
= 69.08 inches
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A car is rolling south at 8 miles per hour, and a man pushes the car north at 10 miles per hour. What is the resultant vector on the car
Answers
The resultant vector on the car would be a vector pointing north with a magnitude of 2 miles per hour.
The resultant vector is the net effect of two or more individual vectors on an object. It is the overall force or movement that is produced when all the individual vectors are combined. To find the resultant vector, you would add together all of the individual vectors using vector addition. The resultant vector would be represented by a single vector with a certain magnitude and direction.
If a car is rolling south at 8 miles per hour, and a man pushes the car north at 10 miles per hour, subtract the southward velocity from the northward velocity.
10 mph northward - 8 mph southward= 2 mph northward
Therefore, the resultant vector on the car is 2 mph northward.
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