Answer:
80 meters (8*10=80)
Answer:
80
Step-by-step explanation:
10 times 8= 80
to find the area is always lenght × height × weight
to find the perimeter is always lenght × lenght × heigth × heigth
example...
a house with the height of 5 and the lenght of 1 .find the perimeter
5+5+1+1= 12
From previous polls, it is believed that 66% of likely voters prefer the incumbent. A new poll of 500 likely voters will be conducted. In the new poll, if the proportion favoring the incumbent has not changed, what is the mean and standard deviation of the number preferring the incumbent?(a)mean = 330, standard deviation = 10.59(b)mean = 0.66, standard deviation = 10.59(c)mean = 330, standard deviation = 18.17
Answer:
The mean and standard deviation of the number preferring the incumbent is mean = 330, standard deviation = 10.59.
Step-by-step explanation:
We are given that From previous polls, it is believed that 66% of likely voters prefer the incumbent.
A new poll of 500 likely voters will be conducted. In the new poll the proportion favoring the incumbent has not changed.
Let p = probability of voters preferring the incumbent = 66%
n = number of voters polled = 500
So, the mean of the number preferring the incumbent is given by;
Mean = [tex]n \times p[/tex] = [tex]500 \times 0.66[/tex]
= 330 voters
And, standard deviation of the number preferring the incumbent is given by;
Variance = [tex]n \times p\times (1-p)[/tex]
= [tex]500 \times 0.66 \times (1-0.66)[/tex]
= 112.2
So, Standard deviation = [tex]\sqrt{Variance}[/tex]
= [tex]\sqrt{112.2}[/tex] = 10.59
Based on the binomial distribution and the probability of 66%, the mean number of likely voters favoring the incumbent is 330, and the standard deviation is approximately 18.17.
Explanation:In this scenario, we are working with a binomial distribution where we have a fixed number of trials, each trial has two possible outcomes (in this case, favoring the incumbent or not), the probability of success is constant, and the trials are independent. Here, a success is a likely voter favoring the incumbent.
To find the mean of the number preferring the incumbent, we use the formula μ = np, where n is the number of trials (or voters), and p is the probability of a success. Thus, the mean is 500 voters times 66%, which gives us:
μ = 500 * 0.66 = 330.
The formula for the standard deviation (σ) of a binomial distribution is σ = √npq, where q is the probability of failure (1 - p). Therefore, standard deviation is:
σ = √(500 * 0.66 * (1 - 0.66)) = 18.17.
The correct answer is: mean = 330, standard deviation = 18.17
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Las tres quintas partes de los animales de un parque natural son mamíferos y, de ellos, cinco sextos son carnívoros ¿Qué fracción del total de animales representan los mamíferos carnívoros? Explicá cómo lo pensaste
The carnivores mammals are (1/2) of the total animals in the natural park.
Step-by-step explanation:
Let the total no. of animals be 'a'
The amount of mammals = (3/5)a
The amount of carnivores= (5/6) (3/5) a
= (1/2) a
So, the carnivores mammals are (1/2) of the total animals in the natural park.
A rectangle has a height of t^2+7t+6t
2
+7t+6t, squared, plus, 7, t, plus, 6 and a width of 2t+12t+12, t, plus, 1.
Answer:
[tex]2t^3+15t^2+19t+6[/tex]
Step-by-step explanation:
Height of the Rectangle[tex]=t^2+7t+6[/tex]
Width of the Rectangle[tex]=2t+1[/tex]
Area of the Rectangle = Height X Width
[tex]=(2t+1)(t^2+7t+6)\\=2t(t^2+7t+6)+1(t^2+7t+6)\\=2t^3+14t^2+12t+t^2+7t+6\\$Collect like terms\\=2t^3+14t^2+t^2+12t+7t+6\\Area=2t^3+15t^2+19t+6\\[/tex]
The area of the rectangle is [tex]2t^3+15t^2+19t+6[/tex]
The height of the rectangle is[tex]t^4 + 26t^3 + 169t^2 + 7t + 6,[/tex] and the width is 26t + 1.
It seems there might be some confusion in the way the dimensions of the rectangle are presented. To clarify, let's break down the height and width of the rectangle:
Height:
The height of the rectangle is given as [tex](t^2 + 7t + 6t)^2[/tex] + 7t + 6.
To simplify the expression inside the parentheses:
[tex](t^2 + 7t + 6t)^2[/tex] = [tex](t^2 + 13t)^2[/tex]= [tex]t^4 + 26t^3 + 169t^2[/tex]
So, the height of the rectangle is[tex]t^4 + 26t^3 + 169t^2 + 7t + 6.[/tex]
Width:
The width of the rectangle is given as 2t + 12t + 12t + 1.
Combine like terms in the width expression:
2t + 12t + 12t + 1 = 26t + 1
So, the width of the rectangle is 26t + 1.
Now you have the height and width of the rectangle expressed as functions of "t":
Height = [tex]t^4 + 26t^3 + 169t^2 + 7t + 6.[/tex]
Width = 26t + 1
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When engaging in weight control (fitness/fat burning) types of exercise, a person is expected to attain about 60% of their maximum heart rate. For 20-year-olds, this rates is approximately 120 bpm. A simple random sample of 100 20-year-olds was taken, and the sample mean was found to be 107 bpm with a standard deviation of 45 bpm. Researchers wonder if this is evidence to conclude that the expected level is actually lower than 120 bpm. To determine this, we test the following hypothesis:
H0 : ? = 120, Ha : ? < 120
Reference: Ref 17-2
A 95% confidence interval for the population mean weight control heart rate, ?, of 20-year-olds is
Answer:
- There is enough evidence to support the claim that the heart rate level lower than 120 bpm (P-value=0.002).
- The 95% confidence interval for the population mean weight control heart rate of 20-year-olds is (98.07, 115.93).
Step-by-step explanation:
This is a hypothesis test for the population mean.
The claim is that the heart rate level lower than 120 bpm
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=120\\\\H_a:\mu< 120[/tex]
The significance level is 0.05.
The sample has a size n=100.
The sample mean is M=107.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=45.
The estimated standard error of the mean is computed using the formula:
[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{45}{\sqrt{100}}=4.5[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{107-120}{4.5}=\dfrac{-13}{4.5}=-2.889[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=100-1=99[/tex]
This test is a left-tailed test, with 99 degrees of freedom and t=-2.889, so the P-value for this test is calculated as (using a t-table):
[tex]P-value=P(t<-2.889)=0.002[/tex]
As the P-value (0.002) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that the heart rate level lower than 120 bpm .
Confidence interval:
We have to calculate a 95% confidence interval for the mean.
The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.
The sample mean is M=107.
The sample size is N=100.
When σ is not known, s divided by the square root of N is used as an estimate of σM:
[tex]s_M=\dfrac{s}{\sqrt{N}}=\dfrac{45}{\sqrt{100}}=\dfrac{45}{10}=4.5[/tex]
The t-value for a 95% confidence interval is t=1.984.
The margin of error (MOE) can be calculated as:
[tex]MOE=t\cdot s_M=1.984 \cdot 4.5=8.929[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=M-t \cdot s_M = 107-8.929=98.07\\\\UL=M+t \cdot s_M = 107+8.929=115.93[/tex]
The 95% confidence interval for the population mean weight control heart rate of 20-year-olds is (98.07, 115.93).
Using the t-distribution, it is found that the 95% confidence interval for the population mean weight control heart rate is (98.07, 115.93). Since the entire interval is lower than 120 bpm, it is evidence to conclude that the expected level is actually lower than 120 bpm.
We are given the standard deviation for the sample, which is why the t-distribution is used to solve this question.
The information given is:
Sample mean of [tex]\overline{x} = 107[/tex].Sample standard deviation of [tex]s = 45[/tex].Sample size of [tex]n = 100[/tex].The confidence interval is:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 100 - 1 = 99 df, is t = 1.984.
Hence:
[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 107 - 1.984\frac{45}{\sqrt{100}} = 98.07[/tex]
[tex]\overline{x} + t\frac{s}{\sqrt{n}} = 107 + 1.984\frac{45}{\sqrt{100}} = 115.93[/tex]
The 95% confidence interval for the population mean weight control heart rate is (98.07, 115.93). Since the entire interval is lower than 120 bpm, it is evidence to conclude that the expected level is actually lower than 120 bpm.
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Consider a finite population with five elements labeled A, B, C, D, and E. Ten possible simple random samples of size 2 can be selected. Using simple random sampling, what is the probability that each sample of size 2 is selected
Answer: 4/25
Step-by-step explanation:
What is bigger 4.17 or 4.085
Answer:
4.17
Step-by-step explanation:
Answer:
4.17 is greater than 4.085
Step-by-step explanation:
HELP ME WITH CALCULUS 1! I am stuck
answer
graph a
speeds up from (0,1) U (2,3) and slows down from (1,2)
if it marks (2,3) incorrectly, it may be from (2,∞) instead
graph b
speeds up from (1,2) U (3,4) and slows down from (0,1) U (2,3)
if it marks (3,4) incorrectly, it may be from (3,∞) instead
step-by-step explanation
looking at the velocity graphs, when the absolute value of velocity is increasing (moving away from the x axis), the particle must be speeding up. we say absolute value because while velocity has direction, speed only has magnitude, so we need to take the absolute value of velocity to get speed.
for graph a, we can see the velocity moving away from the x axis during the interval (0,1), moving towards the x axis during the interval (1,2) and then moving away again during the interval (2,3)
so it speeds up from (0,1) U (2,3) and slows down from (1,2)
if it marks (2,3) incorrectly, it may be from (2,∞) instead since this is at an endpoint
repeat for graph b where it moves toward the x axis from (0,1), moves away from (1,2), moves towards from (2,3), and moves away again from (3,4)
so it speeds up from (1,2) U (3,4) and slows down from (0,1) U (2,3)
if it marks (3,4) incorrectly, it may be from (2,∞) instead since this is at an endpoint
For the following problems, identify the type of investigation used (i.e., non-experimental, experimental, or quasi- experimental) and all independent, dependent, and, if any, extraneous variables
A researcher examines the effects of controlled breaks on reaction times of Air Traffic Controllers. The controllers are randomly assigned to two groups. Group 1 has 20 controllers who spend 45 minutes on a break in a quiet room, with no talking, TV, or other electronics. Group 2 has 20 controllers who spend their 45 minutes on a break in a common area break room where people are allowed to talk, watch TV, or use electronic devices. Following the breaks, each group of controllers returned to their shift where their reaction times were assessed.
What type of investigation is this?
What are the variables?
Answer:
Type of investigation = Experimental
Dependent variable = The reaction time of the controllers
Independent variable = Controlled breaks
Step-by-step explanation:
A researcher is examining the effects of controlled breaks on reaction times of Air Traffic Controllers.
The controllers are randomly assigned to two groups.
Group 1 and Group 2
Group 1 has 20 controllers who spend 45 minutes on a break in a quiet room, with no talking, TV, or other electronics.
Group 2 has 20 controllers who spend their 45 minutes on a break in a common area break room where people are allowed to talk, watch TV, or use electronic devices.
After the breaks, the reaction times of controllers in the two groups were measured.
Type of investigation?
This is clearly an experimental type of investigation where the researcher performs an experiment and after that measures the results.
Type of variables involved?
In this experimental investigation, we have both dependent as well as independent variable.
The controlled break is the independent variable since it can be manipulated by the researcher.
The reaction time of the controllers is the dependent variable since it is being measured and is expected to get affected when the independent variable is manipulated that is controlled breaks.
Final answer:
This is an experimental investigation where the effects of controlled breaks on reaction times of Air Traffic Controllers are examined. The independent variable is the type of break, and the dependent variable is the reaction times of the controllers.
Explanation:
The type of investigation used in this study is an experimental investigation. The independent variable in this study is the type of break given to the Air Traffic Controllers, with two levels: controlled breaks in a quiet room and breaks in a common area with allowed talking, TV, and electronic devices. The dependent variable is the reaction times of the controllers after their breaks. There are no extraneous variables mentioned in the given information.
Suppose the investigator believes that virtually all values of breakdown voltage are between 40 and 70. What sample size would be appropriate for the 95% CI to have a width of 2 kV? (so that m is estimated to within 1 kV with 95% confidence)
Approximately 215 samples are needed for a 95% confidence interval estimating the mean breakdown voltage with a 2 kV width and a 1 kV margin of error, assuming the range is 40 to 70 kV.
To determine the required sample size for estimating the mean breakdown voltage with a 95% confidence interval (CI) width of 2 kV and an estimated margin of error (m) of 1 kV, you can use the formula:
[tex]\[ n = \left(\frac{{Z^2 \cdot \sigma^2}}{{m^2}}\right) \][/tex]
Where:
- n is the required sample size,
- Z is the Z-score corresponding to the desired confidence level (for 95%, it's approximately 1.96),
- [tex]\( \sigma \)[/tex] is the estimated standard deviation of the population.
Since you mentioned the investigator believes breakdown voltage is between 40 and 70, assuming a uniform distribution, you might consider using [tex]\( \sigma = \frac{{\text{{range}}}}{4} \)[/tex] as an approximation. Therefore,
[tex]\[ \sigma = \frac{{70 - 40}}{4} = 7.5 \][/tex]
Now plug these values into the formula:
[tex]\[ n = \left(\frac{{1.96^2 \cdot 7.5^2}}{{1^2}}\right) \][/tex]
Let's calculate the required sample size n:
[tex]\[ n = \frac{{(1.96)^2 \cdot (7.5)^2}}{{1^2}} \]\[ n = \frac{{3.841 \cdot 56.25}}{{1}} \]\[ n \approx \frac{{214.6}}{{1}} \]\[ n \approx 214.6 \][/tex]
So, the required sample size for the 95% confidence interval to have a width of 2 kV (with a margin of error of 1 kV) is approximately 215.
Therefore, the investigator would need a sample size of about 215 to estimate the mean breakdown voltage with the desired level of confidence and precision.
What is the radius and diameter of the following circle?
13 cm
Radius =
cm
Diameter =
Answer:
Radius = 6.5cm
Diameter = 13cm (given)
Step-by-step explanation:
The diameter is the length of one side of a circle to the other. It's already given in the diagram as 13cm.
The radius is half of the diameter. 13 divided by 2 is 6.5cm.
The correct answer are as follows
Radius = 6.5 cm
Diameter = 13 cm
What is Diameter and radius?The Diameter is any straight line segment passing through the center of the circle. The Radius is the half of the diameter.
So , The diameter is 13cm
and The radius is 1/2 x diameter = 1/2 x13 = 6.5cm
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if you have 1,000,000,000 dollars and you want to split between 10 friends how much will they get each
Answer:
Each friend would get 100000000
Step-by-step explanation:
1000000000 ÷ 10 = 100000000
Answer:
$100,000,000
Step-by-step explanation:
divide 1,000,000,000 by 10, be sure to count your zeros.
What is the surface area of the prism?
A rectangular prism with a length of 3 meters, width of 4 meters, and height of 2 meters.
[Not drawn to scale]
(same figure unfolded as net)
a
18 square meters
b
24 square meters
c
52 square meters
d
64 square meters
To find the surface area of ANY prism you need to find the area of individual shape first.
To find 2 faces of the prism, you will need to do bxh. As there is 2 of the same rectangle , you need to multiply it by 2. Therefore, the first number you need is 16m squared.
To find the next part of the prism, you will need to do 2m x 3m which is 6m. You need the area so 6m squared (The units are important). There are also 2 of these, so multiply it by 2 to get 12m squared.
For the final part of the prism, you will need to do 4m x 3m which is 12m squared. There are 2 of these so the it is 24m squared.
Finally, you will need to add all these figures up.
16m squared + 12m squared + 24m squared = 52m squared
Answer:
52 m
Step-by-step explanation:
Consider the equation and its solution.
8(x-2)=64
8x-16 = 64
8x = 80
x= 10
Which property is used in the last step to find that X= 10?
O
A distributive property
B Addition property of equality
C subtraction property of equality
D Division property of equality
PLEASE HELP. I’ll mark you as brainliest if correct
Which of the following could be a value that represents x as a solution?
X>9
A. 0
B. 8
C. 9
D. 18
Which of the following represents K as a solution?
K > 55. There’s a greater or equal sign
A. Any number greater than 55
B. Any number less than or equal to 55
C. Any number less than 55
D. Any number greater than or equal to 55
Answer:
Both of them are D
Step-by-step explanation:
1ST QUESTION
D. 18
2ND QUESTION
D. Any number greater than or equal to 55
brainliest?
Which type of financial institution is a non banking institution
Answer:
A Non-Bank Financial Institution (NBFI)
Step-by-step explanation:
A Non-Bank Financial Institution (NBFI) can be described as any institution without full banking license but offers loans and other financial services.
They are able to provide low cost loans due to the fact that they are privately owned and operated by individuals, as a result of this, they're mostly used by small and medium-sized enterprise.
A Non-Bank Financial Institution (NBFI) includes;
- Insurance companies.
- Pension funds.
- Pawn shops.
- Thrift or mutual credit societies.
- Credit unions.
A certain type of thread is manufactured with a mean tensile strength of 78.3 kilograms and a standard deviation of 5.6 kilograms. How is the variance of the sample mean changed when the sample size is (a) increased from 64 to 196? (b) decreased from 784 to 49?
Answer:
(a) The variance decreases.
(b) The variance increases.
Step-by-step explanation:
According to the Central Limit Theorem if we have a population with mean μ and standard deviation σ and we take appropriately huge random samples (n ≥ 30) from the population with replacement, then the distribution of the sample mean will be approximately normally distributed.
Then, the mean of the sample mean is given by,
[tex]\mu_{\bar x}=\mu[/tex]
And the standard deviation of the sample mean is given by,
[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}[/tex]
The standard deviation of sample mean is inversely proportional to the sample size, n.
So, if n increases then the standard deviation will decrease and vice-versa.
(a)
The sample size is increased from 64 to 196.
As mentioned above, if the sample size is increased then the standard deviation will decrease.
So, on increasing the value of n from 64 to 196, the standard deviation of the sample mean will decrease.
The standard deviation of the sample mean for n = 64 is:
[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}=\frac{5.6}{\sqrt{64}}=0.7[/tex]
The standard deviation of the sample mean for n = 196 is:
[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}=\frac{5.6}{\sqrt{196}}=0.4[/tex]
The standard deviation of the sample mean decreased from 0.7 to 0.4 when n is increased from 64 to 196.
Hence, the variance also decreases.
(b)
If the sample size is decreased then the standard deviation will increase.
So, on decreasing the value of n from 784 to 49, the standard deviation of the sample mean will increase.
The standard deviation of the sample mean for n = 784 is:
[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}=\frac{5.6}{\sqrt{784}}=0.2[/tex]
The standard deviation of the sample mean for n = 49 is:
[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}=\frac{5.6}{\sqrt{49}}=0.8[/tex]
The standard deviation of the sample mean increased from 0.2 to 0.8 when n is decreased from 784 to 49.
Hence, the variance also increases.
Variance has decreased in first case and Variance has increased in second case.
Variation based problem:What information do we have?
Mean tensile stength = 78.3 kilograms
Standard variance = 5.6 kilogram
Variance = sigma² / n
A.
Variance of sample mean with sample size 64 = 5.6² / 64
Variance of sample mean with sample size 64 = 0.49
Variance of sample mean with sample size 196 = 5.6² / 196
Variance of sample mean with sample size 196 = 0.16
Variance has decreased.
B.
Variance of sample mean with sample size 784 = 5.6² / 784
Variance of sample mean with sample size 784 = 0.04
Variance of sample mean with sample size 49 = 5.6² / 49
Variance of sample mean with sample size 49 = 0.64
Variance has increased.
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melanie spent half of her allowance going to the movies. she washed the family car and earned 6 dollars.what is her weekly allowance if she ended with 16 dollars
Her weekly allowance is $20
Step-by-step explanation:
Let her weekly allowance be 'a'
Given that,
She spent half of the allowance (a/2)
So,
Money left with her = (a/2)
She earned $6 by washing the car
She has $16 at the end.
So,
(a/2) + 6 = 16
(a/2) = 16 - 6
(a/2) = 10
a = 10 x 2
a = 20
So, her weekly allowance is $20
Based upon market research, the Hawthorne Company has determined that consumers are willing to purchase 109 units of their portable media player each week when the price is set at $63.00 per unit. At a unit price of $12.80, consumers are willing to buy 360 units per week. (a) Determine the weekly demand equation for this product, assuming price, p, and quantity, x, are linearly related. p
Answer: The weekly demand equation would be
[tex]p=-0.2m+84.8[/tex]
Step-by-step explanation:
Since we have given that
Number of units of their portable media player = 109 units per week
Cost per unit = $63.00
At unit price of $12.80, consumer are buying 360 units per week.
So, here, p = $63.00 and x = 109 units
Here, price and quantity are linearly related by
[tex]p=mx+b\\\\63=109m+b\\\\63-109m=b-----------------(1)[/tex]
If p = $12.80, x= 360
So, the equation of price would be
[tex]12.80=360m+b\\\\12.80-360m=b-------------(2)[/tex]
From eq(1) and (2), we get that
[tex]63-109m=12.80-360m\\\\63-12.80=-360m+109m\\\\50.20=-251m\\\\\dfrac{50.2}{251}=-m\\\\-0.2=m[/tex]
So, the value of b would be
[tex]63=109m+b\\\\63-109(-0.2)=b\\\\63+21.8=b\\\\84.8=b[/tex]
So, the weekly demand equation would be
[tex]p=-0.2m+84.8[/tex]
What is the measure of SRT? 69 79 99 or 101 degrees
Answer:
it would have to be a 99
The solution is, the measure of angle A is 79°.
What is an angle?In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle. The two rays are called the sides of an angle, and the common endpoint is called the vertex.
here, we have,
we know that
the law of cosines establish
c²=a²+b²-2*a*b*cos C------> cos C=[a²+b²-c²]/[2*a*b]
in this problem
a=11 units
b=11 units
c=14 units
C=angle A
so, we get,
cos C=[11²+11²-14²]/[2*11*11]
-----> cos C=0.19008
C=arc cos (0.19008)
------> C=79.04°
the answer is
the measure of angle A is 79°.
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(7g+3)(−g−3)
polynomial in standard form
Step-by-step explanation:
[tex](7g + 3)( - g - 3) \\ = 7g( - g - 3) + 3( - g - 3) \\ = - 7 {g}^{2} - 21g - 3g - 9 \\ \red{ \bold{ = - 7 {g}^{2} - 24g - 9 }} \\ is \: in \: the \: standard \: form.[/tex]
-7g² - 24g - 9 is the polynomial in standard form.
What is a polynomial?In equations like the quadratic equation, cubic equation, etc., a polynomial function is a function that only uses non-negative integer powers or only positive integer exponents of a variable.
Given an equation (7g+3)(−g−3) to convert it into the polynomial form we need to simplify it. Hence,
(7g+3)(−g−3) => -7g² - 21g- 3g -9
=> -7g² - 24g - 9
Therefore, for the given problem -7g² - 24g - 9 is the polynomial in standard form.
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When choosing an item from a group, researchers have shown that an important factor influencing choice is the item's location. This occurs in varied situations such as shelf positions when shopping, filling out a questionnaire, and even choosing a preferred candidate during a presidential debateIn this experiment, five identical pairs of white socks were displayed by attaching them vertically to a blue background that was then mounted on an easel for viewingOne hundred participants from the University of Chester were used as subjects and asked to choose their preferred pairs of socksIn situations of this type, subjects often exhibit the "center stage effect," which is a tendency to choose the item in the center. this experiment, 34 subjects chose the pair of socks in the center. Are these data evidence of the "center stage effect"? STATE: Are the students choosing pairs of socks randomly? If the students were choosing socks at random, what would be the chance, of a pair being selected? (Enter your answer rounded to one decimal place.) p 0
Answer:
a) We have evidence of the " center stage effect" pair number 3 was selected 34 times almost double the probability of random process
b) probability of ocurrency in random case is 20 %
Step-by-step explanation:
To answer this question we first look at the probability of chossing a pair in case of random selection
P = successful event / total outcomes
P₁ = 1/5
P₁ = 0,2 or P₁ = 20 %
Then if the central pair was selected 34 times from 100 participants ( almost the double ) we have evidence of the center stage effect
P₂ = 34/100 or P₂ = 0,34
In this experiment, the data showing 34 subjects choosing the center pair of socks out of 100 participants does indicate evidence of the "center stage effect" as the observed frequency surpasses the expected frequency under randomness.
To determine if the data provided is evidence of the "center stage effect," we need to analyze whether the subjects' choices align with randomness or if there is a noticeable bias towards the center socks.
1. Calculate the expected frequency of selecting the center pair of socks under the assumption of randomness:
- Since there are 5 pairs of socks, the chance of randomly selecting the center pair would be 1 out of 5.
- This gives us a probability of 1/5 or 0.2.
2. Determine the expected number of subjects choosing the center pair out of 100 participants:
- Expected frequency = Probability of selection x Total number of participants
- Expected frequency = 0.2 x 100 = 20
3. Compare the expected frequency (20) with the actual frequency observed in the data (34):
- If the observed frequency significantly exceeds the expected frequency, it suggests a bias towards selecting the center pair of socks, supporting the "center stage effect" hypothesis.
Therefore, in this experiment, the data showing 34 subjects choosing the center pair of socks out of 100 participants does indicate evidence of the "center stage effect" as the observed frequency surpasses the expected frequency under randomness.
Bob flips a fair coin. If Bob’s outcome is heads, Chuck draws a card randomly from a Poker deck where the four kings have been removed beforehand; If Bob’s outcome is tails, Chuck draws a card randomly from another Poker deck where the four aces have been removed beforehand. (There are 52 cards in a standard deck, among which there are 4 kings and 4 aces). Finally, if Chuck gets a king David raises a red flag; otherwise David raises a green flag. What is the probability that David raises a green flag?
Answer:
The probability is 0.9583
Step-by-step explanation:
First, we have 2 possibilities, Bob's outcome is heads or Bob's outcome is tails.
If Bob's outcome is heads, the probability that Chuck doesn't get a king is equal 1, because there aren't kings in the poker deck. it means that if Bob's outcome is heads, the probability that David raises a green flag is 1.
On the other hand, if Bob's outcome is tails, the probability that Chuck doesn't get a king is equal to:
[tex]\frac{44}{48}=0.9166[/tex]
Because there are 48 cards in the poker deck (without the 4 aces) and 44 of them aren't kings. So, if Bob's outcome is Tails, the probability that David raises a green flag is 0.9166.
Now, the probability that David raises a green flag is calculated as:
[tex]P=0.5(1)+0.5(0.9166)=0.9583[/tex]
Because there is a probability of 0.5 that Bob's outcome is heads and there is a probability of 0.5 that Bob's outcome is Tails.
Suppose you own a restaurant and have a cook whose ability and attitude you are suspicious of. One of the dishes on the menu is duck cassoulet, which uses duck legs that have been slow fried over a couple of hours in oil that does not exceed a temperature of 175 degrees. This is a time consuming and monotonous process, but one that results in excellent meat that you sell for a large mark-up. You suspect your cook is lazy and doesn't properly monitor and maintain the oil temperature. You take a random sample of 15 duck legs and take them to a forensics lab where you are able to discover the maximum temperature the meat has reached. Within your sample the mean maximum temperature of the duck legs is 180 degrees with a standard deviation of 4 degrees. Meat cooked precisely to 175 degrees is what your cook is supposed to do.
A) Which of the following is true about a hypothesis test for the claim that your employee is capable (meaning he doesn't over-fry the meat) at the 90% confidence level?
Group of answer choices:
O Reject the null with a test statistic value of 1.83
O Reject the null with a test statistic value of 2.17
O Fail to reject the null with a test statistic value of 1.59
O Fail to the null with a test statistic value of 1.47
O None of the above are true
Answer:
[tex]t=\frac{180-175}{\frac{4}{\sqrt{15}}}=4.84[/tex]
[tex]df=n-1=15-1=14[/tex]
[tex]p_v =P(t_{(14)}>4.84)=0.000131[/tex]
We got a very low value for the p value so then we have enough evidence to reject the null hypothesis at any significance level commonly used. And the best conclusion based on the possible options are:
None of the above are true
Step-by-step explanation:
Data given
[tex]\bar X=180[/tex] represent the sample mean
[tex]s=4[/tex] represent the sample standard deviation
[tex]n=15[/tex] sample size
[tex]\mu_o =175[/tex] represent the value that we want to test
[tex]\alpha=0.1[/tex] represent the significance level for the hypothesis test.
t would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p value for the test (variable of interest)
System of hypothesis
We need to conduct a hypothesis in order to check if the true mean is above the limit of 175 degrees, the system of hypothesis would be:
Null hypothesis:[tex]\mu \leq 175[/tex]
Alternative hypothesis:[tex]\mu > 175[/tex]
The statistic is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
And replacing we got:
We can replace in formula (1) the info given like this:
[tex]t=\frac{180-175}{\frac{4}{\sqrt{15}}}=4.84[/tex]
P-value
The degrees of freedom are given by:
[tex]df=n-1=15-1=14[/tex]
Since is a one sided test the p value would be:
[tex]p_v =P(t_{(14)}>4.84)=0.000131[/tex]
We got a very low value for the p value so then we have enough evidence to reject the null hypothesis at any significance level commonly used. And the best conclusion based on the possible options are:
None of the above are true
2•2•2•n•n what is the product using exponents
Answer:
2³n²
Step-by-step explanation:
An exponent signifies the number of times the base is a factor in the product. Here, 2 is a factor 3 times; n is a factor 2 times. Their exponents will be 3 and 2, respectively:
2•2•2•n•n = 2³n²
A manager is deciding whether or not to build a small facility. Demand is uncertain and can be either at a high or low level. If the manager chooses a small facility and demand is low, the payoff is $300. If the manager chooses a small facility and demand is high, the payoff is $100. On the other hand, if the manager chooses a large facility and demand is low, the payoff is -$200, but if demand is high, the payoff is $800.
(a) What would be the best decision based on the maximax criterion?
(b) What would be the best decision based on the maximin criterion?
(c) What would be the best decision based on the minimax regret?
Answer:
Check the explanation
Step-by-step explanation:
(a) Best decision based on maximax criterion= large facility
maximum in the two facilities is $300 and $800 of which $800 is the maximum, So larger facility satisfies maximax.
(b) Best decision based on maximin criterion= small facility
minimum in the two facilities is $100 and -$200 of which $100 is the maximum, So smaller facility satisfies maximin.
(c) Best decision based on minimax regret= large facility
maximum in the two facilities is $300 and $800 of which $300 is the minimum, So larger facility satisfies minimax regret.
Final answer:
Explanation of maximax, maximin, and minimax regret criteria for decision-making in uncertain scenarios.
Explanation:
Maximax criterion: This criterion involves selecting the decision with the maximum possible payoff under each possible outcome. In this case, the manager would choose the large facility due to the potential high payoff of $800 in case of high demand.
Maximin criterion: This criterion involves selecting the decision with the maximum possible payoff under the worst-case scenario. Here, the manager would choose the small facility to minimize the loss to -$200 in case of low demand.
Minimax regret: This criterion involves minimizing the maximum regret that could be incurred based on the wrong decision. The manager would need to calculate regrets for each decision and choose the one with the least possible regret
Roll the number cube 20 times to represent 20 purchases. What is the experimental probability of receiving a 50% coupon? Write the probability as a decimal.
Answer:
0.10
Step-by-step explanation:
The experimental likelihood of getting a 50% coupon is thus 2/20, or 0.1 to the decimal place.
What is the probability?The likelihood of rolling any one of the number cube's 6 equally likely results is 1/6. We must roll the number cube 20 times and tally how many times we receive a 50% discount in order to determine the experimental chance of doing so.
Assume that rolling a 1, 2, or 3 means you won't receive a coupon, a 4 means you'll receive a 25% coupon, a 5 means you'll receive a 50% coupon, and a 6 means you'll receive a 75% coupon.
The following outcomes are possible after 20 rolls of the number cube:
10 rolls were not given a coupon (50%)Getting a discount of 25%: 4 rolls (20%)2 rolls (10%) when using a 50% discount.4 rolls (20%) when using a 75% discount.More about the probability link is given below.
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Find the Lowest Common Multiple of 3, 5 and 6.
Answer:
30
Step-by-step explanation:
6*5= 30
3*10= 30
5*6= 30
The Lowest Common Multiple of 3, 5, and 6. is 30
The lowest common multiple of a group of numbers is the smallest number that is a multiple of all the numbers.
Given the integers 3, 5 and 6, to get the Lowest common multiple, we will need to take the product of all the integers as shown:Lowest common multiple = 3 * 5 * 6 = 60But note that 60 is not the lowest value that can go easily in the integers, hence the LCM of the numbers will be 5*6 = 30Learn more here: https://brainly.com/question/4913940
Natalie consumes only apples and tomatoes. Her utility function is U(x, y) = x 2y 8 , where x is the number of apples consumed and y is the number of tomatoes con-sumed. Natalie’s income is $320, and the prices of apples and tomatoes are $4 and $3, respectively. How many apples will she consume?
Answer:
16 apples.
Step-by-step explanation:
[tex]U(x, y) = x^2y^8[/tex]
[tex]MU_x =\frac{\partial U}{\partial x} = 2xy^8\\MU_y = \frac{\partial U}{\partial x} = 8x^2y^7\\[/tex]
Price of apples, Px=$4
Price of tomatoes, Py=$3
Ratio of their Marginal Utilities
[tex]\frac{MU_x}{MU_y} = \frac{Px}{Py}[/tex]
[tex]\frac{y}{4x} = \frac{4}{3}[/tex]
[tex]y=\frac{16x}{3}[/tex]
Since Natalie’s income is $320
320 = xPx+yPy
[tex]320=4x + 3*\frac{16x}{3} \\320= 4x+16x = 20x\\x=\frac{320}{20} = 16\\Also\\y=\frac{16x}{3}=\frac{16X16}{3}=\$85.33[/tex]
Since x=16, Natalie will consume 16 apples.
Given Natalie's budget and the prices of apples and tomatoes, plus the fact that her utility function indicates she consumes two as many tomatoes as apples, we determined that Natalie will consume up to 32 apples under these conditions.
Explanation:To determine how many apples Natalie will consume, we first need to solve the utility maximization problem where she chooses 'x' and 'y' to maximize her utility subject to her budget constraint. This problem is typically solved using calculus, but here is a simplified way of solving it:
Firstly, let's consider Natalie's budget constraint. With $320, the prices of apples and tomatoes being $4 and $3 respectively, her budget constraint is $4x + $3y ≤ $320.
Due to the nature of Natalie's utility function U(x, y) = x 2y 8, it's clear that for every apple she buys, she consumes twice as many tomatoes (since y=2x). Replacing 'y' in the budget constraint yields to $4x + $3(2x) ≤ $320, or $10x ≤ $320.
Finally, solving x gives usx ≤ 32, that is, Natalie will consume up to 32 apples.
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3(n+8)=13
Gizmos Solving Algebraic Equations 2
Answer:
n= - 11/3
Step-by-step explanation:
3(n+8)=13
3n+24=13
3n=13-24
3n-11
n= - 11/3
in the past year Rita watch 14 movies that he thought were very good he wants 20 movies over the whole year of the movie she watched what percentage did she think we're very good
Answer:
70%
Step-by-step explanation: