Answers
Answer:
There are 8 sections and 5 of them are less than 7 so the answer is 5/8 = 62.50%.
Answer:
62.5 percent
Step-by-step explanation:
there are a total of 8 options (2,3,4,5,6,7,8,9) the spinner could land on. 5 of these options are less than 7 (6,5,4,3,2)
5/8 is also 62.5 percent
Related Questions
we nendndhdhebdbdbdd
Answers
Step-by-step explanation:
Joe mama
The displacement (in centimeters) of a particle moving back and forth along a straight line is given by the equation of motion s = 2 sin(πt) + 5 cos(πt), where t is measured in seconds.
A) Find the average velocity during each time period.
1) [1, 2]
2) [1, 1.1]
3) [1, 1.01]
4) [1, 1.001]
B) Estimate the instantaneous velocity of the particle when t = 1. cm/s
Answers
Answer:
A) 10, -3.73, -6.035, -6.259 . . . cm/s
B) -6.2832 cm/s
Step-by-step explanation:
A) For problems like this, where repeated evaluation of a function is required, I find a graphing calculator or spreadsheet to be an appropriate tool. The attached shows that we defined the position function ...
p(t) = 2sin(πt) +5cos(πt)
and a function for computing the average velocity from t=1. For some time interval ending at t2, the average velocity is ...
Va(t2) = Δp/Δt = (p(t2) -p(1))/(t2 -1)
Then, for example, for t2 = 2, the average velocity on the interval [1, 2] is ...
Va(2) = (p(2) -p(1))/(2 -1) = ((2sin(2π) +5cos(2π)) -(2sin(π) +5cos(π)))/(1)
= (2·0+5·1 -(2·0 +5·(-1)) = 10 . . . . matches the table value for x1 = 2.
Then the average velocity values for the intervals of interest are ...
1) [1, 2] Va = 10
2) [1, 1.1] Va = -3.73
3) [1, 1.01] Va = -6.035
4) [1, 1.001] Va = -6.259
__
B) Sometimes a better estimate is obtained when the interval is centered on the point of interest. Here, we can compute the average velocity on the interval [0.999, 1.001] as a better approximation of the instantaneous velocity at t=1. That value is ...
[0.999, 1.001] Va = -6.283175*
Our estimate of V(1) is -6.2832 cm/s.
The exact value is -2π ≈ -6.2831853... cm/s
__
* This is the average of the Va(0.999) and Va(1.001) values in the table.
How did the temperature change if: at first it increased by 25 % and then decreased by 40% ?
Please help!!
Answers
Answer:
At first it increases by 25%, then you have 1.25x the original temp. A drop of 40% gives you .6 x 1.25, or 75% of the original temperature
Step-by-step explanation:
found that on the web for yuh. I really hope it helped.
Answer:
decreased by 25%
Step-by-step explanation:
1. The Wall Street Journal reported that bachelor’s degree recipients with majors in business average starting salaries of $53,900 in 2012 (The Wall Street Journal, March 17, 2014). The results for a sample of 100 business majors receiving a bachelor’s degree in 2013 showed a mean starting salary of $55,144 with a sample standard deviation of $5,200. Conduct a hypothesis test to determine whether the mean starting salary for business majors in 2013 is greater than the mean starting salary in 2012. Use a = .01 as the level of significance
Answers
Answer:
The calculated value t = 4.976 > 2.6264 at 0.01 level of significance
Null hypothesis is rejected
Alternative hypothesis is accepted
The mean starting salary for business majors in 2013 is greater than the mean starting salary in 2012
Step-by-step explanation:
Given Mean of the population μ = $53,900
Given sample size 'n' = 100
Mean of the sample size x⁻ = 55,144
Sample standard deviation 'S' = 5200
Null hypothesis:H₀: There is no difference between the means
Alternative Hypothesis :H₁: The mean starting salary for business majors in 2013 is greater than the mean starting salary in 2012
Test statistic
[tex]t = \frac{x^{-} -mean}{\frac{S}{\sqrt{n} } }[/tex]
[tex]t = \frac{55144-53900}{\frac{5200}{\sqrt{100} } }[/tex]
t = 4.976
Degrees of freedom
ν = n-1 = 100-1 =99
t₀.₀₁ = 2.6264
The calculated value t = 4.976 > 2.6264 at 0.01 level of significance
Null hypothesis is rejected
Alternative hypothesis is accepted
Final answer:-
The mean starting salary for business majors in 2013 is greater than the mean starting salary in 2012
Answer:
We conclude that the mean starting salary for business majors in 2013 is greater than the mean starting salary in 2012.
Step-by-step explanation:
We are given that the Wall Street Journal reported that bachelor’s degree recipients with majors in business average starting salaries of $53,900 in 2012.
A sample of 100 business majors receiving a bachelor’s degree in 2013 showed a mean starting salary of $55,144 with a sample standard deviation of $5,200.
Let [tex]\mu[/tex] = mean starting salary for business majors in 2013.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] [tex]\leq[/tex] $53,900 {means that the mean starting salary for business majors in 2013 is smaller than or equal to the mean starting salary in 2012}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > $53,900 {means that the mean starting salary for business majors in 2013 is greater than the mean starting salary in 2012}
The test statistics that would be used here One-sample t-test statistics because we don't know about population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample mean starting salary = $55,144
s = sample standard deviation = $5,200
n = sample of business majors = 100
So, the test statistics = [tex]\frac{55,144-53,900}{\frac{5,200}{\sqrt{100} } }[/tex] ~ [tex]t_9_9[/tex]
= 2.392
The value of t-test statistic is 2.392.
Now, at 0.01 significance level the t table gives a critical value of 2.369 at 99 degree of freedom for right-tailed test.
Since our test statistic is more than the critical value of t as 2.392 > 2.369, 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 mean starting salary for business majors in 2013 is greater than the mean starting salary in 2012.
Carpetland salespersons average $8000 per week in sales. Steve Contois, the firm's vice president, proposes a compensation plan with new selling incentives. Steve hopes that the results of a trial selling period will enable him to conclude that the compensation plan increases the average sales per salesperson.a. Develop the appropriate null and alternative hypotheses.: - Select your answer -: - Select your answer -b. In this situation, a Type I error would occur if it was concluded that the new compensation plan provides a population mean weekly sales - Select your answer - when in fact it does not.What are the consequences of making this error
Answers
Answer:
The null and alternative hypothesis are:
[tex]H_0: \mu_1-\mu_2=0\\\\H_a:\mu_1-\mu_2> 0[/tex]
where μ1 is the population mean sales with compensation plan, and μ2 is the populatiojn mean sales without compensation plan.
A Type I error is made when a true null hypothesis is rejected. In this case, it would be concluded that the compensation plan increases sales, when in fact it does not (at least, not significantly).
The consequences of this error would be that the compensation plan would have evidence to be implemented in the company when in fact it will not bring the results it is expected to have.
Step-by-step explanation:
This hypothesis test will test the claim that the compensation plan increases the average sales per salesperson. This claim will be stated in the alternative hypothesis, and will state that, with the compensation plan, the sales are significantly higher than without the compensation plan.
The null hypothesis, that Steve wants to falsify, will state that the sales will not differ with or withour compensation plan.
We can write this hypothesis as:
[tex]H_0: \mu_1-\mu_2=0\\\\H_a:\mu_1-\mu_2> 0[/tex]
where μ1 is the population mean sales with compensation plan, and μ2 is the populatiojn mean sales without compensation plan.
A Type I error is made when a true null hypothesis is rejected. In this case, it would be concluded that the compensation plan increases sales, when in fact it does not (at least, not significantly).
The consequences of this error would be that the compensation plan would have evidence to be implemented in the company when in fact it will not bring the results it is expected to have. The sales would be expected to increase due to this implementation, and they will not increase, at least, not for the compensation plan.
Please answer this correctly
Answers
Answer:
0| 2
1| 2
2| 0 0 3 9
3| 2 4 4 4 8 8
4| 2 2 4 5 5 6 7
Step-by-step explanation:
Same as the other similar questions
hope this helps!
Jaden had 2 7/16 yards of ribbon. He used 1 3/8 yards of ribbon to make a prize ribbon. How much does he have now?
Answers
EASY!
Answer: 17/16 or 1 1/16
Step-by-step explanation:
BRO IT'S ELEMANTARY FRACTIONS!!!!
The 2003 Zagat Restaurant Survey provides food, decor, and service ratings for some of the top restaurants across the United States. For 15 top-ranking restaurants located in Boston, the average price of a dinner, including one drink and tip, was $48.60. You are leaving on a business trip to Boston and will eat dinner at three of these restaurants. Your company will reimburse you for a maximum of $50 per dinner. Business associates familiar with the restaurants have told you that the meal cost at 5 of the restaurants will exceed $50. Suppose that you randomly select three of these restaurants for dinner.
Required:
a. What is the probability that none of the meals will exceed the cost covered by your company?
b. What is the probability that one of the meals will exceed the cost covered by your company?
c. What is the probability that two of the meals will exceed the cost covered by your company?
d. What is the probability that all three of the meals will exceed the cost covered by your company?
Answers
Answer:
a. P(x=0)=0.2967
b. P(x=1)=0.4444
c. P(x=2)=0.2219
d. P(x=3)=0.0369
Step-by-step explanation:
The variable X: "number of meals that exceed $50" can be modeled as a binomial random variable, with n=3 (the total number of meals) and p=0.333 (the probability that the chosen restaurant charges mor thena $50).
The probabilty p can be calculated dividing the amount of restaurants that are expected to charge more than $50 (5 restaurants) by the total amount of restaurants from where we can pick (15 restaurants):
[tex]p=\dfrac{5}{15}=0.333[/tex]
Then, we can model the probability that k meals cost more than $50 as:
[tex]P(x=k) = \dbinom{n}{k} p^{k}(1-p)^{n-k}\\\\\\P(x=k) = \dbinom{3}{k} 0.333^{k} 0.667^{3-k}\\\\\\[/tex]
a. We have to calculate P(x=0)
[tex]P(x=0) = \dbinom{3}{0} p^{0}(1-p)^{3}=1*1*0.2967=0.2967\\\\\\[/tex]
b. We have to calculate P(x=1)
[tex]P(x=1) = \dbinom{3}{1} p^{1}(1-p)^{2}=3*0.333*0.4449=0.4444\\\\\\[/tex]
c. We have to calcualte P(x=2)
[tex]P(x=2) = \dbinom{3}{2} p^{2}(1-p)^{1}=3*0.1109*0.667=0.2219\\\\\\[/tex]
d. We have to calculate P(x=3)
[tex]P(x=3) = \dbinom{3}{3} p^{3}(1-p)^{0}=1*0.0369*1=0.0369\\\\\\[/tex]
Use the given probability value to determine whether the sample results could easily occur by chance, then form a conclusion. A study of the effect of seatbelt use in head-on passenger car collisions found that drivers using a seatbelt had a 64.1% survival rate, while drivers not using a seatbelt had a 41.5% survival rate. If seatbelts have no effect on survival rate, there is less than a 0.0001 chance of getting these results. What do you conclude?
Answers
Answer:
As the P-value is very low, we can conclude that there is enough evidence to support the claim that the survival rate is significantly higher when the seatbelt is used.
Step-by-step explanation:
We have a hypothesis test that compares the survival rate using the seatbelt versus the survival rate not using it.
The claim is that the survival rate (proportion) is significantly higher when the seatbelt is used.
Then, the null hypothesis is that the seatbelts have no effect (both survival rates are not significantly different).
The P-value is the probabilty of the sample we have, given that the null hypothesis is true. In this case, this value is 0.0001.
This is very low, what gives enough evidence to claim that the survival rate is significantly higher when the seatbelt is used.
Blake is going to invest in an account paying an interest rate of 1.5% compounded quarterly. How much would Blake need to invest to the nearest dollar, for the value of the account to reach $910 in 10 years
Answers
Answer:
$783.46
Step-by-step explanation:
Compounded interest rate (quarterly) formula: A = P(1 + r/4)^4t
Simply plug in our known variables and solve:
910 = P(1 + 0.015/4)^4(10)
910 = P(1.00375)^40
910 = 1.16151P
P = 783.464
Answer: 783
Step-by-step explanation:
Halfway through the season, a soccer player has made 15 penalty kicks in 19 attempts. Based on her performance to date, what is the relative frequency probability that she will make her next penalty kick?
Answers
Answer:
[tex]\dfrac{15}{19}[/tex]
Step-by-step explanation:
The soccer player so far has made 15 penalty kicks in 19 attempts.
Therefore:
Total Number of trials =19
Number of Successes =15
Therefore, the relative frequency probability that she will make her next penalty kick is:
[tex]=\dfrac{\text{Number of Successes}}{\text{Total Number of Trials}} \\=\dfrac{15}{19}[/tex]
Solve the equation.
5x + 8 - 3x = -10
x = -1
x=1
x=9
Answers
Answer:
x=-9solution,
[tex]5x + 8 - 3x = - 10 \\ or \: 5x - 3x + 8 = -10 \\ or \: 2x + 8 = -10 \\ or \: 2x = -10 - 8 \\ or \: 2x = -18\\ or \: x = \frac{-18}{2 } \\ x = -9[/tex]
hope this helps..
Good luck on your assignment
Answer:
x = -9
Step-by-step explanation:
5x + 8 - 3x = -10
Rearrange.
5x - 3x + 8 = -10
Subtract like terms.
2x + 8 = -10
Subtract 8 on both sides.
2x = -10 - 8
2x = -18
Divide 2 into both sides.
x = -18/2
x = -9
Use reduction of order (NOT the integral formula we developed) to find the general solution of the nonhomogeneous linear DE, showing all work. Also clearly state the particular solution yp that you obtain using the reduction of order process and show a clear check that your particular solution yp satisfies the original nonhomogeneous DE. [Do NOT use the Method of Undetermined Coefficients here!]
''y + 6y' + 9y + 4e^x
Note: Use the characteristic polynomial to find a first solution yi of the associated homogencous DE.)
Answers
Answer:
[tex]y = (e^{4x}{4} + kx+d) \cdot c_1e^{-3x} = \frac{e^{x}}{4} + Ae^{-3x}+Bxe^{-3x}[/tex] where A,B are constants.
Step-by-step explanation:
Consider the differential equation [tex]y''+6y'+9y = 4e^{x}[/tex]. To find the homogeneus solution, we assume that [tex]y = Ae^{rt}[/tex] and replace it in the equation [tex]y''+6y'+9y = 0[/tex]. If we do so, after using some properties of derivatives and the properties of the exponential function we end up with the equation
[tex]r^2+6r+9 = 0 = (r+3)^2[/tex]
which leads to r = -3. So, one solution of the homogeneus equation is [tex]y_h = c_1e^{-3x}[/tex], where c_1 is a constant.
To use the order reduction method, assume
[tex] y = v(x)y_h(x)[/tex]
where v(x) is an appropiate function. Using this, we get
[tex]y'= v'y+y'v[/tex]
[tex]y''=v''y+y'v'+y''v+v'y'=v''y+2v'y'+y''v[/tex]
Plugging this in the original equation we get
[tex]v''y+2v'y'+y''v + 6(v'y+y'v) +9vy=4e^{x}[/tex]
re arranging the left side we get
[tex]v''y+2v'y'+6v'y+v(y''+6y'+9y)=4e^{x}[/tex]
Since y is a solution of the homogeneus equation, we get that [tex]y''+6y'+9y=0[/tex]. Then we get the equation
[tex]yv''+(2y'+6y)v' = 4e^{x}[/tex]
We can change the variable as w = v' and w' = v'', and replacing y with y_h, we get that the final equation to be solved is
[tex] e^{-3x}w'+(6e^{-3x}-6e^{-3x})w =4e^{x}[/tex]
Or equivalently
[tex]w' = 4e^{4x}[/tex]
By integration on both sides, we get that w = e^{4x}+ k[/tex] where k is a constant.
So by integration we get that v = [tex]e^{4x}{4} + kx+d[/tex] where d is another constant.
Then, the final solution is
[tex]y = (e^{4x}{4} + kx+d) \cdot c_1e^{-3x} = \frac{e^{x}}{4} + Ae^{-3x}+Bxe^{-3x}[/tex] where A,B are constants
Seven new employees, two of whom are married to each other, are to be assigned seven desks that are lined up in a row. If the assignment of employees to desks is made randomly, what is the probability that the married couple will have adjacent desks
Answers
Answer:
2/7
Step-by-step explanation:
Seven employees can be arranged in 7! ways. n(S) = 7!
Two adjacent desks for married couple can be selected in 6 ways viz.,(1, 2), (2, 3), (3,4), (4, 5), (5,6),(6,7).
This couple can be arranged in the two desks in 2! ways. Other five persons can be arranged in 5! ways.
So, number of ways in which married couple occupy adjacent desks
= 6×2! x 5! =2×6!
so, the probability that the married couple will have adjacent desks
[tex]\frac{n(A)}{n(s)} =\frac{2\times6!}{7!} \\=\frac{2}{7}[/tex]
Please answer this correctly
Answers
Answer:
9 people
Step-by-step explanation:
37, 39, 41, 46, 61, 63, 69, 77, 80
9 people waited more than 36 minutes.
Nolan is using substitution to determine if 23 is a solution to the equation. Complete the statements.
j – 16 = 7 for j = 23
First, Nolan must substitute
for
.
To simplify, Nolan must subtract
from
.
23
a solution of the equation.
Answers
Answer:
Step-by-step explanation:
Given the equation j – 16 = 7, If Nolan is using substitution to determine if 23 is a solution to the equation, then Nolan need to make j the subject of the formula from the equation. The following statements must therefore be made by Nolan.
First, Nolan must substitute for the value of j in the equation.
To simplify, Nolan must subtract the value of 7 from both sides to have;
j – 16 - 7= 7 - 7
j – 23 = 0
Then Nolan must add 23 to both sides of the equation to get the value of j as shown;
j – 23 + 23 = 0+23
j = 23
23 is therefore a solution to the equation
Answer:First, Nolan must substitute 23 for j.To simplify, Nolan must subtract 16 from 23. 23 is a solution of the equation.
Step-by-step explanation:
I got it right on Edge
Change 3.2t into kilograms please help me
Answers
Let's think:
1 ton ------------ 1000 kilograms
3.2 tons ----------- x kilograms
Multiply in cross
1 . x = 1000 . 3.2
x = 3200
So 3.2t = 3200 kilograms
Answer:
It is 2902.99 to be exact
Step-by-step explanation:
Clarance has a 25% off coupon for a tune-up at Quick Service Auto Repair. If a tune-up is regularly $50, what is the sale price?
Answers
Answer:
$37.50
Step-by-step explanation:
50*.25=12.50
Take $50 - 12.50 = 37.50
Graph g(x)=-2|x-5|-4
Answers
Answer:
Step-by-step explanation:
What is the solution y=-2x+4 and y=x-2
Answers
Answer:
Look below
Step-by-step explanation:
Which statement implies that A and B are independent events?
O A. P(B|A)= P(B and A)
OB.P(B|A)= P(B)
P(A)
OC. P(B|A)= P(A)
OD. P(B|A)= P(B)
Answers
Answer:
Option B
Step-by-step explanation:
When A and B are independent events:
P(A and B) = P(A) * P(B)
OR
P(A|B) = P(A) * P(B)
Please answer this correctly
Answers
Answer:
Pillows:
Blankets:
Pet Beds:
Step-by-step explanation:
18 + 45 + 27 = 90 (there are 90 students)
18 out of 90 = 20%
45 out of 90 = 50%
27 out of 90 = 30%
Hope this helps!
Christian Iris and Morgan each get an equal share of 1/2 of pizza which model represent the fraction of the pizza each person gets
Answers
Answer:
CICI
Step-by-step explanation: NO cici
Christian, Iris and Morgan each get an equal share of 1/2 of the pizza and the model 1/6 represent the fraction of the pizza each person gets.
What is division?The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.
Given:
Christian, Iris and Morgan each get an equal share of 1/2 of the pizza.
To find the fraction of the pizza each person gets:
Divide the amount of pizza by the number of people.
There are 3 people and 1/2 pizza.
The fraction of the pizza each person gets
= The amount of pizza / number of people
The fraction of the pizza each person gets
= (1/2) / 3
Simplifying into multiplication,
The fraction of the pizza each person gets = 1/2 x 1/3
The fraction of the pizza each person gets
= 1/(2x3)
= 1/6
Therefore, the model that represents the requirement is 1/6.
To learn more about the division;
https://brainly.com/question/13263114
#SPJ5
Choose the ratio that you would use to convert 1.5 feet to miles. Remember
that there are 5,280 feet in one mile.
Answers
Answer: B, 1 mile / 5280 ft.
Step-by-step explanation: If you need to convert feet to miles the unit multiplier (ratio) that you use should have miles on top and feet on the bottom so that the feet cancel when you multiply, leaving miles as the unit. B is the only answer that has miles on top and feet on the bottom as well as the correct amounts (1 mile and 5280 ft).
What is the area of the trapezoid below? Select one: a. 88 cm2 b. 44√3 cm2 c. 65 cm2 d. 36√3 cm2
Answers
Answer: D
Step-by-step explanation:
Since we are not given the height of the trapezoid, we can split this into a triangle and a rectangle. We find the area of each and then add them together. In order to do so, we must use Pythagorean Theorem to find the missing length so that we can find the area.
a²+b²=c²
a²+4²=8²
a²+16=64
a²=48
a=√48
a=4√3
Now that we know the missing length of the triangle, we can find the area of the triangle and the rectangle.
Triangle
A=1/2bh
A=1/2(4)(4√3)
A=8√3
-----------------------------------------------------------------------------------------
Rectangle
A=lw
A=7(4√3)
A=28√3
With our areas, we can add them together.
4√3+28√3=36√3 cm²
Heidi looks at the donkeys and
tourists. She counts 50 heads
and 114 legs.
How many donkeys are there?
o
ANSWER:
O The retired question
Answers
Answer:
7 donkeys
Step-by-step explanation:
Given
A system consisting of donkeys and tourists
Heads = 50
Legs = 114
Required
Calculate number of donkeys.
Represent donkeys with D and tourists with T.
By means of identification; donkeys and tourists (human) both have 1 head.
This implies that
Number of Heads = D + T
50 = D + T ----- Equation 1
While each donkey have 4 legs, each tourists have 2 legs.
This implies that
Number of legs = 4D + 2T
114 = 4D + 2T ---- Multiply both sides by ½
114 * ½ = (4D + 2T) * ½
57 = 4D * ½ + 2T * ½
57 = 2D + T ----- Equation 2
Subtract equation 1 from 2
57 = 2D + T
- (50 = D + T)
---------------------
57 - 50 = 2D - D + T - T
7 = D
Recall that D represents the number of donkeys.
So, D = 7 implies that
The total number of donkeys are 7
Which equation represents the line that passes through and left-parenthesis 4, StartFraction 7 Over 2 right-parenthesis.?
Answers
Answer:
We want a line that passes through the point (4, 7/2)
and we have no other information of this line, so we can not fully find it, but we can find a general line.
We know that a line can be written as:
y = a*x + b.
Now we want that, when x = 4, we must have y = 7/2.
7/2 = a*4 + b
b = -a*4 + 7/2
Then we can write this line as:
y = a*x - a*4 + 7/2.
Where a can take any value, and it is the slope of our line.
Answer:
A
Step-by-step explanation:
Please answer this correctly
Answers
Answer:
There are 10 teams.
Step-by-step explanation:
Given that the question wants at least 48 swimmers so any numbers above 47 are counted.
In this diagram, there are 10 teams consisting 48 swimmers and above, 48, 52, 53, 63, 76, 79, 82, 84, 85 and 86.
Answer:
10 teams have 48 or more swimmers.
Step-by-step explanation:
If we look at stem 4 there is one team with 48 members.
So counting from there we have:
1 + 2 + 1 + 2 + 4
= 10 teams.
The measurement of the circumference of a circle is found to be 64 centimeters, with a possible error of 0.9 centimeter. (a) Approximate the percent error in computing the area of the circle. (Round your answer to two decimal places.) 2.81 Correct: Your answer is correct. % (b) Estimate the maximum allowable percent error in measuring the circumference if the error in computing the area cannot exceed 1%. (Round your answer to one decimal place.)
Answers
Answer:
(a) 2.81%
(b) 0.5%
Step-by-step explanation:
We have the following information from the statement:
P = 64 + - 0.9
(a) We know that the perimeter is:
P = 2 * pi * r
if we solve for r, we have to:
r = P / 2 * pi
We have that the formula of the area is:
A = pi * r ^ 2
we replace r and we are left with:
A = pi * (P / 2 * pi) ^ 2
A = (P ^ 2) / (4 * pi)
We derive with respect to P, and we are left with:
dA = 2 * P / 4 * pi * dP
We know that P = 64 and dP = 0.9, we replace:
dA = 2 * 64/4 * 3.14 * 0.9
dA = 9.17
The error would come being:
dA / A = 9.17 / (64 ^ 2/4 * 3.14) = 0.02811
In other words, the error would be 2.81%
(b) tell us that dA / A <= 0.01
we replace:
[P * dP / 2 * pi] / [P ^ 2/4 * pi] <= 0.01
solving we have:
2 * dP / P <= 0.01
dP / P <= 0.01 / 2
dP / P <= 0.005
Which means that the answer is 0.5%
If you spin the spinner 11 times, what is the best prediction possible for the number of times it will land on pink?
Answers
If we spin the spinner 11 times, 4 is the best prediction possible for the number of times it will land on pink.
To calculate the expected value of a random variable, simply multiply it with the respective probability and sum the respective products.
Given, total number of outcomes=11.
Total number of pink colored spin= 4
Probability of a spin resulting pink color=4/11
Expected number of spins of pink color= [tex]\sum xp(x)[/tex]
=(1×4/11)+(2×4/11)+(3×4/11)+(4×4/11)
=4/11(1+2+3+4)
=40/11
=3.63 ≈ 4
Thus, the best prediction possible for the number of times it will land on pink is 4.
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Incomplete:
Image of spinner is missing in the question, Therefore attaching it below: