Answer:
Option C) is the correct answer.
Step-by-step explanation:
We are given the following in the question:
Mean = 192
Sample mean, [tex]\bar{x}[/tex] = 212
Sample size, n = 40
Alpha, α = 0.05
Population standard deviation, σ = 56.5
95% Confidence interval:
[tex]\mu \pm z_{critical}\dfrac{\sigma}{\sqrt{n}}[/tex]
Putting the values, we get,
[tex]z_{critical}\text{ at}~\alpha_{0.05} = 1.96[/tex]
[tex]192 \pm 1.96(\dfrac{56.5}{\sqrt{40}} ) = 192 \pm 17.5 = (174.5,209.5)[/tex]
Thus, the correction answer is
Option C)
"The interval that contains 95% of the sample means is 174.5 and 209.5 visits. Because the sample mean is not between these two values, we have support for the results of the May 2011 study."
If the standard deviation of a random variable X is 20 and a random sample of size nequals19 is obtained, what is the standard deviation of the sampling distribution of the sample mean?
The standard deviation of the sampling distribution of the sample mean is 4.587 and this can be determined by using the formula of the standard deviation of the sample mean.
Given :
The standard deviation of a random variable X is 20 and a random sample of size n equals 19.
The formula of the standard deviation of the sample mean can be used to determine the standard deviation of the sampling distribution of the sample mean.
The standard deviation of the sample mean is given by:
[tex]\sigma_m=\dfrac{\sigma}{\sqrt{n} }[/tex] --- (1)
Now put the value of [tex]\sigma[/tex] that is 20 and the value n that is 19 in the equation (1).
[tex]\sigma_m = \dfrac{20}{\sqrt{19} }[/tex]
[tex]\sigma_m = \dfrac{20}{4.36}[/tex]
[tex]\sigma_m = 4.587[/tex]
So, the standard deviation of the sampling distribution of the sample mean is 4.587.
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The standard deviation of the sampling distribution of the sample mean, also referred to as the standard error, for this scenario is approximately 4.58.
Explanation:The standard deviation of a sampling distribution of the sample mean, also known as the standard error, can be calculated using the formula Standard Error = σ/√n, where σ is the population standard deviation and n is the sample size. In your case, the standard deviation (σ) of the random variable X is 20, and your sample size (n) is 19.
Plugging these values into the formula, we get Standard Error = 20/√19, which can be approximated as 4.58.
Therefore, the standard deviation of the sampling distribution of the sample mean for this scenario is approximately 4.58.
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100 POINTS HELP ME PLEASE!!!!!! DONT HAVE ALOT OF TIME HURRY PLEASE!!!!!!!!!!!!!
100 POINTS!!!!!
Luke is designing a scale model of a clock tower. The design of the front of the tower is shown below.
A figure can be broken into a triangle and rectangle. The rectangle has a base of 200 millimeters and height of 50 millimeters. The triangle has a base of 50 millimeters and height of 100 millimeters.
What will be the area of the front face of his model?
2,500 square millimeters
10,000 square millimeters
12,500 square millimeters
15,000 square millimeters
Answer:
12,500 square millimeters
Step-by-step explanation:
Answer:
c(12,500)
Step-by-step explanation:
Please help :(
There are 10^9 bytes in a gigabyte. There are 10^6 bytes in a megabyte. How manny times greater is the storage capacity of a 1-gigabyte flash drive than a 1-megabyte flash drive?
answer choices above^^^
Answer:
In the screenshot you have the right answer, it is indeed 1000 times greater
Step-by-step explanation:
Half of the sum of 32 and 2
Answer:
17
Step-by-step explanation:
32+2=34
34/2= 17
Half of the sum of 32 and twice a number 'x' expressed as '2ans' would be calculated by adding 32 and 2x and then dividing by 2, resulting in the expression 16 + x.
The question asks to find half of the sum of 32 and an unspecified number (mentioned as '2ans'). Assuming '2ans' means twice the number 'ans', which can be represented as 2x, where 'x' is the particular value of 'ans'. First, calculate the sum of 32 and 2x, and then divide that sum by two to find half of it.
The steps to solve this are:
Calculate the sum: 32 + 2x.
To find half of the sum, divide by 2: (32 + 2x) / 2.
Simplify the expression: 16 + x.
Therefore, half of the sum of 32 and twice a number 'x' (2x) is 16 + x.
The fictional rocket ship Adventure is measured to be 65 m long by the ship's captain inside the rocket.When the rocket moves past a space dock at 0.5c. As rocket ship Adventure passes by the space dock, the ship's captain flashes a flashlight at 2.00-s intervals as measured by space-dock personnel. Part A How often does the flashlight flash relative to the captain
Answer:
a) t₀ = 1.73205 s
b) 1.0 C
Step-by-step explanation:
(A)
The time dilation (t) observed by an observer at rest relative to the time (t₀) measured by observer in motion is;
[tex]t = \frac{t_0}{\sqrt{1 - \frac{V^2}{C^2}}}[/tex]
[tex]t_0 = t \sqrt{1 - \frac{V^2}{C^2}}[/tex] time measured by captain
⇒ [tex]t_0 = 2.0 \sqrt{1 - \frac{0.5^2C^2}{C^2}}[/tex] V = 0.5 c
⇒ t₀ = 1.73205 s
(B)
Speed of the light never exceeds by its real value. The speed of the light in any frame of reference is constant.
∵ It will be "1.0C" or just "C"
Exhibit 13-2 Source of Variation Sum of Squares Degrees of Freedom Mean Square F Between treatments 2,073.6 4 Between blocks 6,000.0 5 1,200 Error 20 288 Total 29 The test statistic to test the null hypothesis equals _____. a. 4.17 b. 28.8 c. 1.8 d. .432
Answer:
option C is correct,the null hypothesis equals 1.8
Lucia hit a golf ball 240 feet. How many yards did she hit the ball?
A) 80 yards
B) 60 yards
C) 120 yards
D) 300 yards
Answer:
80 yards
Step-by-step explanation:
There are 3 feet in a yard, therefore you take 240 feet divided by 3 to get how many yards there are, and in your case it is 80 yards.
A teacher used the change of base formula to determine whether the equation below is correct.
(log Subscript 2 Baseline 10) (log Subscript 4 Baseline 8) (log Subscript 10 Baseline 4) = 3
Which statement explains whether the equation is correct?
Answer:
The equation is correct
Step-by-step explanation:
The equation, written as:
[log_2 (10)][log_4 (8)][log_10 (4)] = 3
Consider the change of base formula:
log_a (x) = [log_10 (x)]/ [log_10 (a)]
Applying the change of base formula to change the expressions in base 2 and base 4 to base 10.
(1)
log_2 (10) = [log_10 (10)]/[log_10 (2)]
= 1/[log_10 (2)]
(Because log_10 (10) = 1)
(2)
log_4 (8) = [log_10 (8)]/[log_10 (4)]
Now putting the values of these new logs in base 10 into the left-hand side of original equation to verify if we have 3, we have:
[log_10 (2)][log_8 (4)][log_10 (4)]
= [1/ log_10 (2)][log_10 (8) / log_10 (4)][log_10 (4)]
= [1/log_10 (2)] [log_10 (8)]
= [log_10 (8)]/[log_10 (2)]
= [log_10 (2³)]/[log_10 (2)]
Since log_b (a^x) = xlog_b (a)
= 3[log_10 (2)]/[log_10 (2)]
= 3 as required
Therefore, the left hand side of the equation is equal to the right hand side of the equation.
Answer:
B on E2020.
Step-by-step explanation:
A delivery truck was purchased for $60,000 and is expected to be used for 5 years and 100,000 miles. The truck’s residual value is $10,000. By the end of the first year, the truck has been driven 16,000 miles. What is the depreciation expense in the first year using activity-based depreciation?
Answer:
Step-by-step explanation:
Cost of Truck = $60,000
Expected use = 100,000 miles
Residual value = $10,000
Depreciation per mile = ( Cost of Truck- Residual value)/ Estimated use
= ( 60,000-10,000)/100,000
= 50,000/100,000
= $0.5
Miles driven in first year = 16,000
Depreciation expense for first year = Miles driven in first year x Depreciation per mile
= 16,000 x 0.5
= $8,000
The depreciation expense in the first year using activity-based depreciation is $ 8,000.
What is Depreciation ?An asset loses value over time as a result of use, damage, or obsolescence. Depreciation is the measurement for this decline.
Depreciation, or a decline in asset value, can be brought on by a variety of other variables, such as bad market conditions, etc.
Calculation of Depreciation for first year
Purchase Cost of Truck = $60,000
Estimated lifetime use = 100,000 miles
Salvage value = $10,000
Depreciation per mile = ( Cost of Truck- Residual value)/ Estimated use
= ( 60,000-10,000)/100,000
= 50,000/100,000
= $0.5
Miles driven in first year = 16,000
Depreciation for 1st year = Miles drove in first year x Depreciation per mile
= 16,000 x 0.5
= $8,000
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# SPJ 2
Suppose x is a normally distributed random variable with muμequals=1616 and sigmaσequals=22. Find each of the following probabilities. a. P(xgreater than or equals≥17.517.5) b. P(xless than or equals≤1212) c. P(16.7816.78 less than or equalsxless than or equals≤20.4620.46) d. P(11.4811.48less than or equals≤xless than or equals≤19.0619.06)
Answer:
Step-by-step explanation:
Since x is a normally distributed random variable, we would apply the formula for normal distribution which is expressed as
z = (x - µ)/σ
Where
x = the random variable
µ = mean
σ = standard deviation
From the information given,
µ = 16
σ = 2
a. P(x ≥ 17.5) = 1 - (x < 17.5)
For x < 17.5
z = (17.5 - 16)/2 = 0.75
Looking at the normal distribution table, the probability corresponding to the z score is 0.77
P(x ≥ 17.5) = 1 - 0.77 = 0.23
b. P(x ≤ 12)
z = (12 - 16)/2 = - 2
Looking at the normal distribution table, the probability corresponding to the z score is 0.023
P(x ≤ 12) = 0.023
c) P(16.78 ≤ x ≤ 20.46)
For x = 16.78,
z = (16.78 - 16)/2 = 0.39
Looking at the normal distribution table, the probability corresponding to the z score is 0.65
For x = 20.46,
z = (20.46 - 16)/2 = 2.23
Looking at the normal distribution table, the probability corresponding to the z score is 0.987
Therefore,
P(16.78 ≤ x ≤ 20.46) = 0.987 - 0.65 = 0.337
d) P(11.48 ≤ x ≤ 19.06)
For x = 11.48,
z = (11.48 - 16)/2 = - 2.26
Looking at the normal distribution table, the probability corresponding to the z score is 0.012
For x = 19.06,
z = (19.06 - 16)/2 = 1.53
Looking at the normal distribution table, the probability corresponding to the z score is 0.94
Therefore,
P(11.48 ≤ x ≤ 19.06) = 0.94 - 0.012 = 0.928
Can someone please work this out. With step by step instructions. Thank you
Answer:
12m^3
Step-by-step explanation:
Basically, you are looking for the volume of the Oil. In order to do that you simply need to use the rectangular prism volume formula: lwh
lwh=V
(5)(2)(1.2)=V
10(1.2)=V
12=V
What is the area of the following circle
Answer:
16*pi=50.24
Step-by-step explanation:
Answer:
16* pi = 50.24
Step-by-step explanation:
a survey amony freshman at a certain university revealed that the number of hours spent studying the week before final exams was normally distributed with mean 25 and standard deviation 15. a sample of 36 students was selected. what is the probability that the average time spent studying for the sample was between 29.0 and 30 hours studying?
Answer:
Probability that the average time spent studying for the sample was between 29 and 30 hours studying is 0.0321.
Step-by-step explanation:
We are given that the number of hours spent studying the week before final exams was normally distributed with mean 25 and standard deviation 15.
A sample of 36 students was selected.
Let [tex]\bar X[/tex] = sample average time spent studying
The z-score probability distribution for sample mean is given by;
Z = [tex]\frac{ \bar X-\mu}{\frac{\sigma}{\sqrt{n} } }} }[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = population mean hours spent studying = 25 hours
[tex]\sigma[/tex] = standard deviation = 15 hours
n = sample of students = 36
The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.
Now, Probability that the average time spent studying for the sample was between 29 and 30 hours studying is given by = P(29 hours < [tex]\bar X[/tex] < 30 hours)
P(29 hours < [tex]\bar X[/tex] < 30 hours) = P([tex]\bar X[/tex] < 30 hours) - P([tex]\bar X[/tex] [tex]\leq[/tex] 29 hours)
P([tex]\bar X[/tex] < 30 hours) = P( [tex]\frac{ \bar X-\mu}{\frac{\sigma}{\sqrt{n} } }} }[/tex] < [tex]\frac{ 30-25}{\frac{15}{\sqrt{36} } }} }[/tex] ) = P(Z < 2) = 0.97725
P([tex]\bar X[/tex] [tex]\leq[/tex] 29 hours) = P( [tex]\frac{ \bar X-\mu}{\frac{\sigma}{\sqrt{n} } }} }[/tex] [tex]\leq[/tex] [tex]\frac{ 29-25}{\frac{15}{\sqrt{36} } }} }[/tex] ) = P(Z [tex]\leq[/tex] 1.60) = 0.94520
So, in the z table the P(Z [tex]\leq[/tex] x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 2 and x = 1.60 in the z table which has an area of 0.97725 and 0.94520 respectively.
Therefore, P(29 hours < [tex]\bar X[/tex] < 30 hours) = 0.97725 - 0.94520 = 0.0321
Hence, the probability that the average time spent studying for the sample was between 29 and 30 hours studying is 0.0321.
A garden shop determines the demand function q = D(x) = 5x + 200 / 30x + 11 during early summer for tomato plants where q is the number of plants sold per day when the price is x dollars per plant.
(a) Find the elasticity.
(b) Find the elasticity when x = 2.
(c) At $2 per plant, will a small increase in price cause the total revenue to increase or decrease?
Answer: a) [tex]E(x)=\dfrac{-5945}{(30x+11)(5x+200)}[/tex], b) 0.7975, demand is inelastic, c) increase.
Step-by-step explanation:
Since we have given that
[tex]D(x)=\dfrac{5x+200}{30+11}[/tex]
So, derivative w.r.t x would be
[tex]D'(x)=\dfrac{5(30x+11)-30(5x+200)}{(30x+11)^2}\\\\D'(x)=\dfrac{150x+55-150x-6000}{(30x+11)^2}\\\\D'(x)=\dfrac{5945}{(30x+11)^2}[/tex]
As we know that
[tex]E(x)=\dfrac{-xD'(x)}{D(x)}\\\\\\E(x)=\dfrac{\dfrac{-(-)5945x}{(30x+11)^2}}{\dfrac{5x+200}{30x+11}}\\\\\\E(x)=\dfrac{5945x}{(30x+11)(5x+200)}[/tex]
(b) Find the elasticity when x = 2.
So, we put x = 2, we get that
[tex]E(2)=\dfrac{5945\times 2}{(30(2)+11)((5(2)+200))}\\\\E(2)=\dfrac{11890}{(60+11)(10+200)}\\\\E(2)=\dfrac{11890}{71\times 210}\\\\E(2)=\dfrac{11890}{14910}\\\\E(2)=0.7975[/tex]
Since, 0.7975 < 1, so the demand is inelastic.
(c) At $2 per plant, will a small increase in price cause the total revenue to increase or decrease?
The total revenue will also increase with increase in price.
As total revenue = [tex]price\times quantity[/tex]
Hence, a) [tex]E(x)=\dfrac{-5945}{(30x+11)(5x+200)}[/tex], b) 0.7975, demand is inelastic, c) increase.
This problem involves the calculation of the elasticity of a demand function using the derivative of the function. The elasticity is then used to analyze the effect on the total revenue when the price changes. The elasticity at a specific point is calculated and used for further analysis.
Explanation:For part (a), to find the elasticity of the demand function, we need to use the formula for the price elasticity of demand, which is E = (dQ/dX) * (X/Q). Here, dQ/dX is the derivative of the demand function concerning X. This needs to be calculated first. The value of E provides us with the measure of elasticity.
For part (b), when x = 2 we substitute this value into the formula for E to get the elasticity at x = 2.
For part (c), based on the concept of elasticity, if E > 1, the demand is said to be elastic and a price decrease will result in an increase in total revenue, and vice versa. If E < 1, the demand is said to be inelastic and a price decrease will result in a decrease in total revenue, and vice versa. So, after calculating E at x = 2, we can use it to determine the effect on total revenue.
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Design a regular grammar to generate the set of all integers beginning with the digit 3 such that the digits are consecutive and odd. If a digit is 9, its following digit (if present) will be 1. The set of valid strings is {3, 35, 357, 35791, 357913, ...}
Answer:
The grammar has start symbol S, terminals are 1,3,5,7 an 9 ; and the variables are S, A, B, C and D
Step-by-step explanation:
CHECK THE ATTACHMENT FOR EXPLANATION
A photo of a mosquito in a science book is magnified to 635% of the mosquito's actual size.If the mosquito is 16 millimetres long,what is the length of the mosquito in the picture.
Answer:
The length of the mosquito in the picture is 117.6 mm.
Step-by-step explanation:
This question can be solved using a rule of three.
The real size of the mosquito is 16 mm, which is 100% = 1.
In the picture, the size is magnified 635%, so it is 100+635 = 735% = 7.35. So
16mm - 1
x mm - 7.35
x = 7.35*16 = 117.6
The length of the mosquito in the picture is 117.6 mm.
Final answer:
To find the magnified length of a mosquito in a picture, multiply its actual size (16 mm) by the magnification factor (6.35), resulting in a magnified length of 101.6 millimeters.
Explanation:
The question involves calculating the magnified length of a mosquito in a picture, given that the magnification is 635% of its actual size and the actual size is 16 millimeters. First, understand that 635% magnification means the mosquito's image is 6.35 times its actual size. To find the magnified length, multiply the actual length by the magnification factor.
Magnified length = Actual length × Magnification factor
= 16 mm × 6.35
= 101.6 mm
Therefore, the length of the mosquito in the picture is 101.6 millimeters.
The number 20 is no less the difference of 4 times the number C and 8
The mathematical statement translates to an inequality 20 ≤ 4C - 8, and solving this results in C ≥ 7.
Explanation:The question provides a mathematical statement which can be translated into an equation. The statement 'The number 20 is no less the difference of 4 times the number C and 8' translates into the equation 20 ≤ 4C - 8. In this equation, 4 times a number C minus 8 can result in a value that is at least 20. To find the value for C, you would need to isolate C. This is done by first adding 8 to both sides to get 28 ≤ 4C, then dividing by 4 to get C ≥ 7. C, therefore, could be any value that is 7 or greater.
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(Urgent! please help!) Find the constant of proportionality for the ratio of cost to number of bananas from the table.
______
Answer: 0.25
Step-by-step explanation:
I did the quiz
Answer:
0.25
Step-by-step explanation:
Hope this helps, have a nice day
is 119x10-3 to the power a scientific notation? yes or no? explain
Answer:
Yes, if I'm assuming that it was written as [tex]119*10^-3[/tex], then this is a basis for a scientific notation.
A circle with radius four has a sector with a central angle of 8/5 pi radians. what is area of the sector
Answer:
area of sector = 40.192 unit²
Step-by-step explanation:
Area of a sector = ∅/360 × πr²
where
∅ = angle in degree
r = radius
Area of sector when ∅ = radian
area of a sector = 1/2r²∅
where
∅ = radian
r = radius
area of sector = 1/2 × 4² × 8/5 × π
area of sector = 1/2 × 16 × 8/5 × π
area of sector = 128/10 × π
area of sector = 12.8 × π
area of sector = 12.8 × 3.14
area of sector = 40.192 unit²
HELLPP
A cardboard box has the shape of a rectangular prism. Its height is 10
inches. Its length is three times its width. The volume is 540 cubic inches.
Find the width of the box. *
Answer
Step-by-step explanation:
H*W*L
280=7*W*(6+W)
280=42W+7W^2
40=6w+w^2
W^2+6W-40=0
(W-4)(W+10)=0
W=4
We can only use positive results
L=6+W
L=4+6=10
Given that, the height of the cardboard box=10 inches and volume = 540 cubic inches.
Let the width of the cardboard box be x, then the length will be 3x.
What is the formula to find the volume of a rectangular prism?The formula to find the volume of a rectangular prism is Volume=Length×Width×Height.
Now, 540=10×x×3x
⇒x²=18
⇒x=3√2 inches.
Therefore, the width of a cardboard box is 3√2 inches.
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The weights of 6-week-old poults (juvenile turkeys) are normally distributed with a mean 8.6 pounds and standard deviation 1.9 pounds. A turkey farmer wants to provide a money-back guarantee that her 6-week poults will weigh at least a certain amount. What weight should she guarantee so that she will have to give her customer's money back only 1% of the time?
Answer:
She should guarantee a weight of 4.18 pounds.
Step-by-step explanation:
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
[tex]\mu = 8.6, \sigma = 1.9[/tex]
What weight should she guarantee so that she will have to give her customer's money back only 1% of the time?
She should guarantee the 1st percentile of weights, which is X when Z has a pvalue of 0.01. So it is X when Z = -2.327.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-2.327 = \frac{X - 8.6}{1.9}[/tex]
[tex]X - 8.6 = -2.327*1.9[/tex]
[tex]X = 4.18[/tex]
She should guarantee a weight of 4.18 pounds.
The turkey farmer should guarantee that her 6-week poults will weigh at least 4.2 pounds to ensure that she will have to give money back only 1% of the time.
Given:
- Mean weight [tex](\( \mu \))[/tex] of poults: 8. 6 pounds
- Standard deviation [tex](\( \sigma \))[/tex] of poults: 1.9 pounds
1. Use the z-score corresponding to the 1st percentile of the normal distribution, which is approximately [tex]\( z_{0.01} \approx -2.3263 \)[/tex].
2. Calculate the guaranteed weight X:
[tex]\[ X = \mu + z_{0.01} \cdot \sigma \] \[ X = 8.6 + (-2.3263) \cdot 1.9 \] \[ X \approx 4.2 \text{ pounds} \][/tex]
Therefore, the turkey farmer should guarantee that her 6-week poults will weigh at least 4.2 pounds to ensure that she will have to give her customers' money back only 1% of the time. This ensures that 99% of the poults will weigh at least 4.2 pounds.
A new car can go 490 miles on 10 gallons of gas. How many miles can it go on 55 gallons of gas?
Answer:
2695 miles
Step-by-step explanation:
The car can travel 2,695 miles on 55 gallons of gas.
To determine how many miles a car can go on 55 gallons of gas if it can go 490 miles on 10 gallons, we need to find the car's miles per gallon (mpg) and then use that to calculate the distance for 55 gallons.
First, calculate the miles per gallon (mpg):
mpg = 490 miles / 10 gallons = 49 miles per gallon
Now, use the mpg to find the distance the car can travel on 55 gallons:
Distance = 49 miles per gallon * 55 gallons = 2,695 miles
Therefore, the car can go 2,695 miles on 55 gallons of gas.
Does anyone know this?
Answer:
A. 5 * 1/7
Step-by-step explanation:
When solving division, you can also multiply by the reciprocal of the second number to get the same answer.
Now focus on the boundary of D, and solve for y2. Restricting f(x,y) to this boundary, we can express f(x,y) as a function of a single variable x. What is this function and its closed interval domain?
Answer:
At critical point in D
a
[tex](x,y) = (0,0)[/tex]
b
[tex]f(x,y) = f(x) =11 -x^2[/tex]
where [tex]-1 \le x \le 1[/tex]
c
maximum value 11
minimum value 10
Step-by-step explanation:
Given [tex]f(x,y) =10x^2 + 11x^2[/tex]
At critical point
[tex]f'(x,y) = 0[/tex]
=> [tex][f'(x,y)]_x = 20x =0[/tex]
=> [tex]x =0[/tex]
Also
[tex][f'(x,y)]_y = 22y =0[/tex]
=> [tex]y =0[/tex]
Now considering along the boundary
[tex]D = 1[/tex]
=> [tex]x^2 +y^2 = 1[/tex]
=> [tex]y =\pm \sqrt{1- x^2}[/tex]
Restricting [tex]f(x,y)[/tex] to this boundary
[tex]f(x,y) = f(x) = 10x^2 +11(1-x^2)^{\frac{2}{1} *\frac{1}{2} }[/tex]
[tex]= 11-x^2[/tex]
At boundary point D = 1
Which implies that [tex]x \le 1[/tex] or [tex]x \ge -1[/tex]
So the range of x is
[tex]-1 \le x \le 1[/tex]
Now along this this boundary the critical point is at
[tex]f'(x) = 0[/tex]
=> [tex]f'(x) = -2x =0[/tex]
=> [tex]x=0[/tex]
Now at maximum point [tex](i.e \ x =0)[/tex]
[tex]f(0) =11 -(0)[/tex]
[tex]= 11[/tex]
For the minimum point x = -1 or x =1
[tex]f(1) = 11 - 1^2[/tex]
[tex]=10[/tex]
[tex]f(-1) = 11 -(-1)^2[/tex]
[tex]=10[/tex]
Use the given degree of confidence and sample data to construct a confidence interval for the population mean mu. Assume that the population has a normal distribution. Thirty randomly selected students took the calculus final. If the sample mean was 95 and the standard deviation was 6.6, construct a 99% confidence interval for the mean score of all students.
Answer:
[tex]95-2.76\frac{6.6}{\sqrt{30}}=91.674[/tex]
[tex]95+2.76\frac{6.6}{\sqrt{30}}=98.326[/tex]
We can say at 99% confidence that the true mean is between (91.674;98.326)
Step-by-step explanation:
Data given
[tex]\bar X=95[/tex] represent the sample mean
[tex]\mu[/tex] population mean (variable of interest)
s=6.6 represent the sample standard deviation
n=30 represent the sample size
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
We need to find the critical value [tex]t_{\alpha/2}[/tex] and we need to find first the degrees of freedom, given by:
[tex]df=n-1=30-1=29[/tex]
Since the Confidence is 0.99 or 99%, the value of [tex]\alpha=0.01[/tex] and [tex]\alpha/2 =0.005[/tex], and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.005,29)".And we see that [tex]t_{\alpha/2}=2.76[/tex]
And replacing we got:
[tex]95-2.76\frac{6.6}{\sqrt{30}}=91.674[/tex]
[tex]95+2.76\frac{6.6}{\sqrt{30}}=98.326[/tex]
We can say at 99% confidence that the true mean is between (91.674;98.326)
4 pints, 2 quarts, 8 cups, 1 gallon which one dose not belong and why
Answer:
1 gallon does not belong
Step-by-step explanation:
4 pints = 2 quarts
2 quarts = 8 cups
8 cups does not equal 1 gallon, 16 cups does
What is the selling price if the original cost is $145 and the markup is 150%? PLEASE HELP!! :(
Answer:
$362.50
Profit: $217.50
Step-by-step explanation:
A movie theater has a seating capacity of 317. The theater charges $5.00 for children, $7.00 for students, and $12.00 of adults. There are half as many adults as there are children. If the total ticket sales was $ 2296, How many children, students, and adults attended?
Answer:
There are 154 children, 77 adults and 86 students in attendance
Step-by-step explanation:
Given
Seat capacity = 317
Total tickets = $2296
Charges is as follows;
Children = $5.00
Students = $7.00
Adults = $12.00
Required
Number of children, students and adults
Let A, C and S represent adults, children and students respectively.
So,
From sales of tickets, we have the following:
12A + 5C + 7S = 2296 --- Equation 1
From attendance, we have
A + C + S = 317 --- Equation 2
Given that, there are half as many adults as there are children.
So, A = ½C
Substitute ½C for A in equation 1 and 2
12A + 5C + 7S = 2296 becomes
12 * ½C + 5C + 7S = 2296
6C + 5C + 7S = 2296
11C + 7S = 2296 ---- Equation 3
A + C + S = 317
½C + C + S = 317
Multiply through by 2
2(½C + C + S) = 2 * 317
C +2C + 2S = 634
3C + 2S = 634 ----- Equation 4
We'll solve equations 3 and 4, simultaneously.
First, write out the two equations.
11C + 7S = 2296 ---- (3)
3C + 2S = 634 ------ (4)
Using elimination method to eliminate S.
Multiply (3) by 2 and multiply (4) by 7.
2 (11C + 7S = 2296 )
22C + 14S = 4592 ---- Equation 5
7 (3C + 2S = 634 )
21C + 14S = 4438 ------ Equation 6
Subtract (6) from (5)
22C + 14S = 4592
21C + 14S = 4438
---------------------------
22C - 21C + 14S - 14S = 4592 - 4438
C = 154
Recall that A = ½C
So, A = ½ * 154
A = 77
Recall equation 2
A + C + S = 317
Make S the subject of formula
S = 317 - A - C
Substituton 77 for A and 154 for C
So,
S = 317 - 77 - 154
S = 86
Hence, there are 154 children, 77 adults and 86 students in attendance
Megan finds a bag of 24 craft bows at the store. The bag indicates that 23 of the bows are striped. Megan wants to know the number of bows in the package that are striped. Select ALL the statements that are true. A Megan can divide the number 3 by 24 and then multiply the result by 2 to find the number of striped bows. B Megan can divide the number 24 by 3 and then multiply the result by 2 to find the number of striped bows. C Megan can multiply the number 24 by 2 and then divide the result by 3 to find the number of striped bows. D Megan can multiply the number 24 by 3 and then divide the result by 2 to find the number of striped bows. E The number of striped bows in the package is 36. F The number of striped bows in the package is 16.
Answer:
B
Step-by-step explanation: