Kinetic energy is defined as the work required to accelerate a body of a given mass from rest to its stated speed. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes.
Mass - (Measured in Kilogram) - Mass is the amount of matter in a body, regardless of its volume or the forces acting on it.
Velocity - (Measured in Meters per Second) - Velocity is a vector quantity (has both magnitude and direction) and is the rate of change of an object's position with respect to time.
What is the kinetic energy of a 158 kg Green Sea Turtle swimming at 0.42 m/s? With work shownWe have that the data is:
m = 150 kgv = 0.42 m/sThe formula to calculate kinetic energy is:
Ec = m * v²/2
Since it only asks us to calculate the kinetic energy, it is not necessary to clear the formula.
[tex]\boldsymbol{\sf{Ec=\dfrac{158 \ kg*\left(0.42 \ \frac{m}{s}\right)^2 }{2} }}[/tex]
[tex]\boldsymbol{\sf{Ec=\dfrac{158 \ kg*0.1764 \ \frac{m^2}{s^2} }{2} }}[/tex]
[tex]\boldsymbol{\sf{Ec=13.9356 \ kg*\dfrac{m^2}{s^2} }}[/tex]
We work with the units, in this case with m^2 = m*m.
[tex]\boldsymbol{\sf{Ec=13.9356 \boxed{\boldsymbol{\sf{Kg*\frac{m}{s^2} }}}*m }}[/tex]
Newton's units are: Kg*m/s^2.
[tex]\boldsymbol{\sf{Ec=13.9356 \ N*m \longmapsto Joule \ units=N*m}}[/tex]
[tex]\boldsymbol{\sf{Ec=13.9356 \ J}}[/tex]
The kinetic energy (E) of a body with mass m = 158 kilograms and speed v = 0.42 m/s is equal to 13.9356 JBut if you need the rounded answer, then 13.94 Joules.
Write an ordered pair for the point in Quadrant III that is 3 units away from point Q (1.5, -1.5) on the coordinate plane.
The point Q'(x, y) = (- 1.5, - 1.5) is located in quadrant III and 3 units away from point Q(x, y) = (1.5, - 1.5).
What is the possible ordered pair related to another one on the coordinate plane?
In this question we find the location of an ordered pair on the coordinate plane and we are asked to find a possible solution that is in quadrant III and three units away from the original point.
A point (x, y) is in the quadrant III if x < 0 and y < 0 and we can determine a resulting point by using the following translation formula:
(x, y) → (x - 3, y)
If we know that (x, y) = (1.5, - 1.5), then the resulting point is:
Q'(x, y) = (1.5, - 1.5) + (- 3, 0)
Q'(x, y) = (- 1.5, - 1.5)
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The probability that aperson living in a certaincity owns a dog is estimated to be 0.3. Find the probabilitythat the tenth person randomly interviewed inthat city is the fifth one to own a dog.
The probability that the tenth person randomly interviewed in that city is the fifth one to own a dog = 0.051
Given,
Consider the interview of a person is a trial.
Lets consider it success if a person owns a dog and consequently , a person without a dog will be a failure.'
Let the random variable X represent the number of persons to be interviewed to get 5 dog owner: in other words, to get 5 successors.
Probability of a success in each trial is p = 0.3. Therefore probability of a failure in each trial is q = 1 - p = 0.7 .
Because trials are independent. X has a negative binomial distribution with parameters k = 5, p = 0.3
P(X =x ) = b(x: k, p) = [tex][(x-1)(k-1)] p^kq^r^-^k[/tex]
where, x = k , k + 1 , k + 2......(1)
Now, Lets find the probability that the tenth person randomly interviewed in that city is the fifth one to own a dog
Using equation (1), we get:
P(X = 10) = b(10: 5, 0.3)
= [(10-1) (5 - 1)][tex](0.3)^5(0.7)^1^0^-^5[/tex]
= [(9)(4)] [tex](0.3)^5(0.7)^1^0^-^5[/tex]
= 0.05146
Hence, The probability that the tenth person randomly interviewed in that city is the fifth one to own a dog = 0.051
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1.45 + -1/5 + -5/8
faststtttt and please explain how you get it
Answer: 5/8
Step-by-step explanation:
remove the +'s because -'s are more valued. -1/5 is 0.2 and because we're subtracting 1.45-0.2 its 1.25. -5/8 = 0.625 and if you subtract 1.25-0.625 its 0.625 so its just 5/8
[tex]\frac{5}{8} .[/tex]
Step-by-step explanation:1. Write the expression.[tex]1.45 + (-\frac{1}{5} )+ (-\frac{5}{8} )[/tex]
2. Rewrite the signs.[tex]1.45 -\frac{1}{5} -\frac{5}{8}[/tex]
3. Convert all numbers into fractions.[tex]\frac{145}{100} -\frac{1}{5} -\frac{5}{8}[/tex]
4. Simplify the first fraction.[tex]\frac{145/5}{100/5} -\frac{1}{5} -\frac{5}{8}\\ \\\frac{29}{20} -\frac{1}{5} -\frac{5}{8}[/tex]
5. Find a common denominator between the 3 fractions by multiplying their terms.Note. You always need to multiply each fraction by the same number on both numerator and denominator.
[tex]\frac{29*2}{20*2} -\frac{1*8}{5*8} -\frac{5*5}{8*5}\\ \\\frac{58}{40} -\frac{8}{40} -\frac{25}{40}[/tex]
6. Rewrite and solve.[tex]\frac{58-8-25}{40} \\ \\\frac{25}{40}[/tex]
7. Simplify the fraction.[tex]\frac{25/5}{40/5}\\ \\\frac{5}{8}[/tex]
8. Express your result.[tex]1.45 + (-\frac{1}{5} )+ (-\frac{5}{8} )= \frac{5}{8} .[/tex]
Suppose that the functions and are defined for all real numbers as follows.
Write the expressions for and and evaluate .
The expression we get from the given functions f and g defined for all real numbers x.
(f+g)(x)=4x+1
(f-g)(x)=2x+11
(f.g)(3)=-30
Given that,
All real numbers x are defined by the functions f and g.
f(x)=3x+6
g(x)=x-5
We have to find the expression
(f+g)(x), (f-g)(x) and (f.g)(3)
Take the functions,
f(x)=3x+6
g(x)=x-5
Now, First
(f+g)(x)
f(x)+g(x) (Substitute in the place of f and g functions)
Which is
3x+6+x-5
4x+1
(f+g)(x)=4x+1
Now, second
(f-g)(x)
f(x)-g(x)
Which is
3x+6-(x-5)
3x+6-x+5
2x+11
(f-g)(x)=2x+11
Now, third
(f.g)(3)
f(3)×g(3)
Which is
(3(3)+6)×((3)-5)
(9+6)×(3-5)
15×-2
-30
(f.g)(3)=-30
Therefore, The expression we get from the given functions f and g defined for all real numbers x.
(f+g)(x)=4x+1
(f-g)(x)=2x+11
(f.g)(3)=-30
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Make the subject of
9x = u
Making the subject as x, the expression is x = u/9
The given equation is
9x = u
It can be written as
u = 9x
We need to make x as the subject in the given expression
9x = u
u = 9x
here u is the subject
9x = u
x = u/9
Therefore, making the subject as x, the expression is x = u/9
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An appliance manufacturer wants to contract with a repair shop to handle authorized repairs in Indianapolis. The company has set an
acceptable range of repair time of 50 minutes to 90 minutes. Two firms have submitted bids for the work. In test trials, one firm had a
mean repair time of 74 minutes with a standard deviation of 4.0 minutes and the other firm had a mean repair time of 72 minutes with a
standard deviation of 5.1 minutes. (Do not round intermediate calculations. Round your answers to 2 decimal places.)
Firm Cpk
1 ___
2 ___
Which firm would you choose?
Firm 1
Firm 2
None
The best firm for the Appliance manufacturer for the repair work is Firm 2 .
In the question ,
it is given that ,
An appliance manufacturer wants to contract with a repair shop to handle authorized repairs in Indianapolis .
The acceptable range of the repair time is 50 minutes to 90 minutes.
the mean repair time for firm 1 = 74 minutes and standard deviation of 4 minutes .
the mean repair time for firm 2 = 72 minutes and standard deviation of 5.1 minutes .
the range is calculated using the formula
Range = Mean ± Standard Deviation
So , for firm 1 ,
the Range = 74 ± 4
= 74 [tex]+[/tex] 4 and 74 - 4
= 78 and 70
the range for firm 2 is
= 72 ± 5.1
= 72 [tex]+[/tex] 5.1 and 72 - 5.1
= 7.1 and 66.9
The second company has a lower range and it should be preferred .
Therefore , The best firm for the Appliance manufacturer for the repair work is Firm 2 .
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Pls can someone give me the answer
Answer:
[tex]-\frac{1}{2}(x-1)[/tex]
Step-by-step explanation:
The slope of the line is [tex]\frac{3-1}{1-5}=-\frac{1}{2}[/tex].
Using the point (1,3), the equation is [tex]y-3=\boxed{-\frac{1}{2}(x-1)}[/tex].
Determine an nth degree polynomial that satisfies the aforementioned conditions.
A polynomial that satisfies given conditions is:
P(x) = x³ - x² + 81x - 81
In this question, we need to find a polynomial that satisfies given conditions.
We have been given that -9i is a root of polynomial.
This means, the conjugate of -9i that is, 9i must be a root of polynomial p.
From given information we can say that the zeros of polynomial p(x) must be (x - 1), (x + 9i), and (x - 9i)
So, we get a polynomial p(x) = 0
(x - 1)(x + 9i)(x - 9i) = 0
(x - 1)(x² - (9i)²) = 0
(x - 1)(x² - (-81)) = 0
(x - 1)(x² + 81) = 0
x³ - x² + 81x - 81 = 0
Therefore, a polynomial that satisfies given conditions is:
P(x) = x³ - x² + 81x - 81
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What is the answer to: 5/23 ÷ 23/24:
Willl mark brainliest
Answer:
It is 120/529
Step-by-step explanation:
The steps are:
Step 1: When we divided, we change the dividing fraction into mutiplying fraction at the last fraction: 5/23 x 24/23
Step 2: We mutiply it on each row like 5 x 24 & 23 x 23
Step 3: When we finished with the answer, we put it like the order of the fraction: 120 & 529 so we get 120/529
Thats all the step by step explaination!
Please mark me brainliestttttttttttttttttttttttttttttttttttttttttttttttt !!!!!!!!!!!!!!!!!!!!!!!!11
PLEASE HELP
The access code for a car's security system consists of four digits. The first digit cannot be zero and the last digit must be odd. How many different codes are available? (Note that 0 is considered an even number.)
The number of different codes available is ___
(Type a whole number.)
The number of different codes available is 4500 unique codes
What is digit?
A positional numeral system uses a single symbol, such as "2," or a combination of symbols, such as "25," to represent numbers. This single symbol is known as a numerical digit. The word "digit" derives from the fact that ten fingers (Latin: digiti) on each hand correspond to the ten numeral symbols used in the base-10 system, or decimal digits (Old Latin: decem, meaning "ten"). The absolute value of the base determines how many different digits are necessary for a given numeral system with just an integer base. For instance, the binary system (base 2) only needs two digits, whereas the decimal system (base 10) necessitates ten digits (0 through 9). (0 and 1).
The digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
There are nine options because the first digit cannot be 0. (assuming 1 can be the first digit as well as all others)
There are 10 options for the second digit, third digit, fourth digit, and fifth digit.
4 digits must be odd, giving you 5 options (1,3,5,7,9)
9*10*10*5=4500 unique codes
Hence, there are 4500 unique codes available
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the sum of two numbers is 46. the larger number is two less than three times the lesser number.
Answer:
y=12
x=34
Step-by-step explanation:
x+y=46
3y-2=x
(3y-2)+y=46
4y-2=46
+2. +2
4y=48
/4. /4
y=12
x+12=46
-12. -12
X=34
Hopes this helps please mark brainliest
Last year, Melissa opened an investment account with $5200. At the end of the year, the amount in the account had decreased by 27%.
(a) Fill in the blank to write the year-end amount in terms of the original amount. Write your answer as a decimal.
(b) Use your answer in part (a) to determine the year-end amount in Melissa's account.
The amount in terms of the original amount is $1,404 and the year end amount is $6,604.
How to find the original amount?a. Original amount
Original amount = 5200 - (5200× .27)
Original amount = $5200 - $1,404
Original amount = $3,796
b. Year-end amount
Year-end amount = 5200+ $3,796
Year-end amount =$8996
Therefore the original amount is $3,796 and the year end is $8996.
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increase 24in the ratio 2:3
Answer: 16
Step-by-step explanation:
To *increase* 24 in the ratio 2:3
To *increase* a quantity in given ratio consider new quantity and old quantity.
Formula: New quantity:old quantity=given ratio solution: let us take the new quantity as x, old quantity as 24(given) and given ratio=2:3(given)
-> x:24=2:3
-> x/24=2/3
-> Multiply with 24 on both sides to get x
-> 24*x/24=2/3*24
-> x=16
So, the *increase* of 24 in the ratio 2:3 is 16
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Calculate the area of this triangle.
5 cml
13 cm
12 cm•
Answer: Area of triangle=30 cm²
Step-by-step explanation:
Let's name the triangle ABC.
Assuming these are the 3 sides of the triangle, and naming them a,b,c.
a=5 cm
b=13 cm
c=12 cm
Semi perimeter of the triangle ABC= s = (a+b+c)/2
s=(5+13+12)/2 =30/2=15.
Area of triangle ABC= √(s * (s-a)*(s-b)*(s-c)
= √(15*(15-5)*(15-13)*(15-12)
= √15*10*2*3
= √150*6
=√900
=30 cm²
Area of triangle ABC = 30 cm².
Blanche has recently inherited $7900, which she wants to deposit into a savings account. She has determined that her two best bets are an account that compounds semi-annually at an annual rate of 3.7% (Account 1) and an account that compounds daily at an annual rate of 3.9% (Account 2).
Step 2 of 2 : How much would Blanche's balance be from Account 2 over 5.5 years? Round to two decimal places.
9664.9 is the Blanche's balance be from Account 2 over 5.5 years
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given,
Blanche has recently inherited $7900, which she wants to deposit into a savings account. She has determined that her two best bets are an account that compounds semi-annually at an annual rate of 3.7%
an account that compounds daily at an annual rate of 3.9% (Account 2).
We need to find how much Blanche's balance be from Account 2 over 5.5 years
A = p(1 + r/n)nt
A = 7900(1 + 0.037/2)²ˣ⁵⁵
A ≈7900(1 + 0.0185)^11
A ≈ 7900(1.0185)¹¹
A ≈ 7900(1.223)
A=9664.92
9664.9 is the Blanche's balance be from Account 2 over 5.5 years
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The last time it placed an order for ingredients, Sweet Treats Bakery ordered 1,090 kilograms of sugar. This time, the bakery is ordering 654 kilograms. What is the percent of the decrease in the size of the sugar order?
Please help
Answer: The size of the sugar order decreased by 40%.
Step-by-step explanation:
1,090 is 100%
654 is 60% of 1,090 (1,090 ÷ 0.6 = 654)
1,090 - 654 = 436, and 436 is 40% (0.4) of 1,090
1,090 (100%) - 436 (40%) = 654 (60%)
The percent of the decrease in the size of the sugar order is 40%.
markus makes $65,500 annually. assuming markus is paid on the 1st and the 15th of every month, calculate his earnings
Markus' biweekly earnings (gross pay every two weeks) are $2,727.16.
How is the biweekly earnings determined?The annual gross pay can be divided by 26 to get the biweekly earnings.
Another way to compute the biweekly earnings is by adding up the withholding taxes, deductions, and net earnings.
In practice, the net earnings are equal to the gross pay less withholding taxes and deductions.
Annual gross pay = $65,500
Payment period = biweekly (1st and 15th every month)
Withholding taxes:Social Security = $156.19
Medicare = 36.53
Federal tax = 445.96
Total withholding = $636.68
Deductions:Retirement = $45
Health Insurance = $200
Total deductions = $245
Net Earnings = $1,845.48
Biweekly ross pay (earnings) = $2,727.16 ($636.68 + $245 + $1,845.48)
Thus, Markus earns $2,727.16 every two weeks.
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calculate the area (ignore the scribble)
The image of the point (-3, -6)(−3,−6) under a translation is (-1, -8)(−1,−8). Find the coordinates of the image of the point (-9, -3)(−9,−3) under the same translation.
The coordinates of the image of the point (−9,−3) under the same translation will be (-7,-5).
What is geometric transformation?It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.
It is given that the image of the point (-3, -6) under a translation is (-1, -8).
The coordinate by which the first given condition is translated as,
(-3, -6) - (x,y) = (-1, -8)
(x,y) = (-3, -6) - (-1, -8)
(x,y) =(-3-(-1), -6-(-8)
(x,y) =(-3+1),(-6+8)
(x,y) =(-2,+2)
The coordinates of the image of the point (-9, -3) are under the same translation obtained as,
=(−9,−3)- (-2,+2)
=(-9-(-2) , (-3-(+2))
=(-9+2),(-3-2)
= -7,-5
Thus, the coordinates of the image of the point (−9,−3) under the same translation will be (-7,-5).
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Triangle ABC is similar to Triangle MPN. Find x and y. AB=15. BC=18. AC=9. I need this answer ASAP
The value of x and y in the similar triangles are 10 and 12 respectively.
What are similar triangles?Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles.
In other words, similar triangles are the triangles that have corresponding sides in proportion to each other and corresponding angles equal to each other
The triangles ABC and MPN are similar triangles.
Therefore,
∠A = ∠M
∠B = ∠P
∠C = ∠N
Hence, let's find x and y using the proportion as follows:
[tex]\frac{AB}{MP}=\frac{BC}{PN}=\frac{AC}{MN}[/tex]
Hence,
PN = y
MP = x
Therefore, let's find x
[tex]\frac{9}{6}=\frac{15}{x}[/tex]
cross multiply
9x = 90
x = 90 / 9
x = 10
Let's find y
[tex]\frac{9}{6}=\frac{18}{y}[/tex]
cross multiply
9y = 108
y = 108 / 9
y = 12
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Write an equation that expresses the following relationship.
p varies directly. with the square of d and inversely with u
In your equation, use k as the constant of proportionality.
[tex]p = \frac{kd^{2}}{u}[/tex] is an equation that expresses the relation.
Directly proportion means if variable x and y varies equally.
Increment of one variable result to another one.
The ratio of these variable remains same throughout.
Inversely proportion means if one variable increases the second one will decreases. It is opposite of directly proportion.
According to the question,
p varies directly. with the square of d and inversely with u
p ∝ d²
p ∝ 1/u
Combining both the equation,
p ∝ d²/u
Putting k as the constant
p = kd²/u is our required equation
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A store purchased a digital camera and marked it up 100% from the original cost of $863.57. A week later the store placed the digital camera in sale for 40% off. What was the discount price?
Answer:
$1036.28
Step-by-step explanation:
Marking something up by 100% means doubling the price. Let's do this step first:
863.57 * 2 = 1727.14
Next, the discount is 40%
I would find this by taking the 10% value, multiplying that by 4 and subtracting that from our new value
10% = 172.714
40% = 690.856
Now our newest value:
1727.14 - 690.856
1036.284
Round to 2 decimal places (as is proper when dealing with cents):
1036.28
Thus, our newest (discounted) price is:
$1036.28
A classroom ceiling measures 6.8m by 4.7m. It is covered by boards measuring 1m by 1m
a) how many boards are needed altogether
b) How many of them will be cut
c)find the total cost of each board costs #700
There will be 319 boards be required
and the total cost be $223,720.
Given, a classroom ceiling measures 6.8m by 4.7m. It is covered by boards measuring 1m by 1m.
Now, we have to find the number of boards needed altogether
So, the area of the ceiling is
Area = 6.8×4.7
Area = 319.6 m²
Now, the area of the board is
Area = 1 m²
So, 319 boards will be required to cover the ceiling.
Now, if one board costs $700 then,
the total cost be
= 700×319.6
= $223,720
Hence, There will be 319 boards be required
and the total cost be $223,720.
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Trevor is planning a 30-day trip to Africa, where he will visit three countries: first Benin,
then Ghana and then Togo. He wants to spend at least 2 and at most 12 days in Benin, at most 13 days
in Ghana, and at most 9 days in Togo. How many such itineraries are possible? (Assume that each day is
spent in just one country, and that she travels from one country to another at night.
The value of 12 - x can at most be 4 for the given inequality and it is true therefore, all itineraries are possible.
What is inequality?A difference between two values indicates whether one is smaller, larger, or basically not similar to the other.
Inequality is just the opposite of equality for example 2 =2 then it is equal but if I say 3 =6 then it is wrong the correct expression is 3 < 6.
Let's say the day spend in Benin, Ghana and Togo are B, G, and T respectively.
As per the given,
B + G + T = 30
Here, 2 ≤ B ≤ 12, G ≤ 13, and T ≤ 9.
(12 - B) + (13 - G) + (9 - T) = -30 + 12 + 13 + 9 = 4
Also, B ≥ 2 or B ≤ -2 ⇒ 12 - B ≤ 12 - 2 = 10
Hence "The value of 12 - x can at most be 4 for the given inequality and it is true therefore, all itineraries are possible".
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Which number line represents the solution set for the given inequality? X + 1<_ -3 Or -4x < _
-8
Answer:
B
Step-by-step explanation:
OR means that they don't overlap and based on the answer you have in you know how to solve the innequality.
Please help I was sick and missed out on class.Thank you
Answer:
Slope is the same thing as gradient
The formula is
y2-y1/x2-x1
where y2 is =8
y1 is =5
x2 is=-7
x1 is =-4
when we substitute, your answers will be
= -1
sophie went to the lake with her family first they spent 1 1/4 hours fishing then they spent twice as much time swimming how much time did they spend swimming
Answer:
They spent a total of 1 and 1/2 hours swimming.
Step-by-step explanation:
It is because 1 1/4 plus 1 1/4 equals 1 2/4 which mean 2/4=1/2 so in total they spent 1 1/2 hours swimming
On July 1 2019, crane company purchased new equipment for $75,000. Its estimated useful life was 5 years with a $8000 salvage value. On December 31,2022, the company estimated that the equipment's remaining useful life was 10 years with a revised salvage value of $5000
1. The revised annual depreciation on December 31, 2022, is $3,650.
2. The journal entry to record depreciation on December 31, 2022 is as follows:
Journal Entry:Debit Depreciation Expense $3,650
Credit Accumulated Depreciation $3,650
To record the depreciation expense for the year.
3. The balance in Accumulated Depreciation for Equipment on December 31, 2022, is $37,150.
Cost of equipment = $75,000
Purchase date = July 1, 2019
Estimated useful life = 5 years
Salvage value = $8,000
Depreciable amount = $67,000 ($75,000 - $8,000)
Annual depreciation expense = $13,400 ($67,000/5)
Accumulated Depreciation for two and half years to December 2021 = $33,500 ($13,400 x 2.5)
Book value after 2.5 years = $41,500 ($75,000 - $33,500)
New estimated useful life = 10 years
Revised salvage value = $5,000
Revised depreciable amount = $36,500 ($41,500 - $5,000)
Revised annual depreciation expense = $3,650 ($36,500/10)
Accumulated Depreciation on December 31, 2022 = $37,150 ($33,500 + $3,650)
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Jenni wrote a conditional statement an it’s converse conditional if the angles are right angles then the angles have the same measure
Jenni wrote the converse statement properly, however the statement is false, hence the correct option with a counter example is:
Yes; two angles that each measure 41°.
What are conditional and converse statements?A conditional statement is written as follows:
p -> q.
In which the terms of the conditional statement are listed as follows:
p is the hypothesis.q is the conclusion.In this problem, the statement is:
If angles are right angles, then the angles have the same measure.
Hence the terms is:
p: right angles.q: same measure.For the converse statement, the hypothesis and the conclusion are exchanged, hence:
q -> p.
Thus the converse of Jenni's statement is:
If two angles have the same measure, then they are right angles.
Which means that she wrote the converse statement properly.
However, the angles do not necessarily need to measure 90º, they only need to have the same measure, hence the correct option is:
Yes; two angles that each measure 41°.
Missing InformationThe complete problem is:
Jenni wrote a conditional statement and its converse.Conditional: If angles are right angles, then the angles have the same measure.Converse: If angles have the same measurement, then they are right angles.Did Jenni write the converse statement properly? Give a counterexample to dispute the validity of the converse statement.No; two angles that each measure 45°Yes; two angles that each measure 90°Yes; two angles that each measure 41°No; two angles that each measure 82°.
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A researcher is interested in determining the average number of years employees of a company stay with the company.
If past information shows a standard deviation of 7 months, what size sample should be taken so that at 95% confidence the margin of error will be 2 months or less?
The size sample that should be taken so that at 95% confidence the margin of error will be 2 months or less is:47.0596.
How to find the sample size?Using this formula to find the sample size
n = z² × σ² / e²
Where,
n = sample size =?
z = z-score = 1.96
σ = Standard deviation = 7 months
e = Margin of error = 2 months or less
Let plug in the formula
n = (1.96²× 7²) /2²
n = 3.8416 × 49 / 4
n =47.0596
Therefore the sample size is 47.0596.
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