Answer:
a)
the total surface area of the 3 cylinders is11.4296 m²
b)the number of tins paints that Tim will need to buy is 7 tins of paints.
Step-by-step explanation:
Given:
Height = 1.9m
Diameter = 1.4m
The radius = diameter/2 = 1.4/2 = 0.7
From the question, each of the tank is cylindrical in shape we can make use of surface area of the cylinder formula in calculating this.
Total surface area = (2πr² + 2πrh)
Where
r = the height of the cylinder.
h = the height of the cylinder.
π = 3.14 or 22/7
Total surface area = (2 × 3.14 × 0.7²) + (2 × 3.14 × 0.7 × 1.9 )
= (3.0772 + 8.3524)
= 11.4296 m²
Then to calculate the total surface area of the 3 cylinders we multiply by 3.
= 11.4296 × 3
= 34.29 m²
But the question says a tin of paint covers 5 m², then the number of tins paints that Tim will need to buy can be calculated as
=34.29/5
= 6.858
If we round it up to whole number we have 7 tins of paints.
Therefore, the number of tins paints that Tim will need to buy is 7 tins of paints.
Tim should buy 7 tins of paint.
Since Tim has to cover 3 tanks completely with paint, and each tank is in the shape of a cylinder with a top and a bottom, and the tank has a diameter of 1.4 meters and a height of 1.9 m, while a tin of paint covers 5 m, to find the total surface area of the 3 tanks and state how many tins of paint Tim will need to buy, the following calculation must be performed:
Surface area of a cylinder = 2π x r x h + 2π x r² r = diameter / 2 = 1.4 / 2 = 0.7 2 x 3.14159 x 0.7 x 1.9 + 2 x 3.14159 x (0.7 x 0.7) = X 6.283 x 0.7 x 1.9 + 6.283 x 0.49 = X 8,356 + 3,078 = X 11.43 = X (11.43 x 3) / 5 = X 34.3 / 5 = X 6.86 = X
Therefore, Tim should buy 7 tins of paint.
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The shape of the distribution of the time required to get an oil change at a 15-minute oil-change facility is unknown. However, records indicate that the mean time is 16.2 minutes, and the standard deviation is 3.4 minutes.
Requried:
a. What is the probabilty that a random sample of n = 40 oil changes results in a sample mean time less than 15 minutes?
b. Suppose the manager agrees to pay each employee a $50 bonus if they meet a certain goal. On a typical Saturday, the oil-change facility will perform 40 oil changes between 10 A.M. and 12 P.M. Treating this as a random sample, there
would be a 10% chance of the mean oil-change time being at or below what value? This will be the goal established by the manager.
Answer:
(a) Probability that a random sample of n = 45 oil changes results in a sample mean time < 10 minutes i=0.0001.
(b) The mean oil-change time is 15.55 minutes.
Step-by-step explanation:
Let us denote the sample mean time as x
From the Then x = mean time = 16.2 minutes
The given standard deviation = 3.4 minutes
The value of n sample size = 45
CHECK THE ATTACHMENT FOR DETAILED EXPLANATION
Tommy has "n" friends and he wants to give each friend 5 pencils. Write an expression to show how many pencils pencils Tommy will share.
Answer:
5n
Step-by-step explanation:
Think about it:
If Tommy has 4 friends (n = 4), then he will have to give 5 pencils to each person. The total number of pencils is 5 * n or 5 * 4 = 20.
Similarly, if Tommy has 0 friends (I can relate), then he will have to give 5 pencils to each of his imaginary friends. The total number of pencils he has to give out to his real friends is 5 * n or 5 * 0 = 0.
acccording to this diagram what is cos 28
Answer:
[tex] \frac{15}{17} [/tex]Option B is the correct option.
Here,
Adjacent=15
Hypotenuse=17
Now,
[tex]cos \: theta = \frac{adjacent}{hypotenuse} \\ cos \: 28 = \frac{15}{17} [/tex]
Hope this helps..
Good luck on your assignment..
Answer:
B. 15/17
Step-by-step explanation:
(see attached graphic for reference)
Because we have a right triangle (i.e one of the internal angles is 90 degrees), we can use trigonometry to solve
from the diagram, we can see that
cos 28° = adjacent length / hypotenuse
we can also see that the length adjacent to 28° = 15 units and the hypotenuse is 17 units,
hence, substituting these values into the equation:
cos 28° = 15 / 17 (answer)
edit: typo
You obtain a simple interest loan from National city for $2500 at 7.6% for 5 years. Find the amount of interest on the loan
Answer:
950
Step-by-step explanation:
2500(0.076)(5) = 950
Please tell the answer o the attached photo
Answer:
A. The perimeter is more, but the area is less.
Step-by-step explanation:
You want to know the effect on perimeter and area if the rectangle is cut and rearranged so the pieces overlap.
AreaThe overlap means the area of the figure is reduced (by the area of the overlap, inside the dashed lines on the right). This eliminates choices B and D.
PerimeterThe dashed line on the left becomes two solid lines of the same length in the figure on the right, thus the perimeter is increased by twice that dashed line length.
However, the perimeter of the figure on the right is reduced by the perimeter of the part of the figure that no longer sees the outside world: the length of the dashed line on the right.
Since twice the length of the left dashed line is substantially greater than the length of the right dashed line, we must conclude the perimeter has increased in Figure 2 compared to Figure 1. This eliminates choice C.
The perimeter is more, but the area is less.
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What is the median for the set of data shown below?
16, 23, 24, 39, 45, 78, 95
Answer:
39
Step-by-step explanation:
The median is the middle number
16, 23, 24, 39, 45, 78, 95
There are 7 numbers so the middle number is the 4th number
6, 23, 24, 39 , 45, 78, 95
The median is 39
Answer:
39
Step-by-step explanation:
The median is the number in the middle of a data set.
First, arrange the numbers from least to greatest.
16, 23, 24, 39, 45, 78, 95
Then, cross one number off both sides of the data set until the middle is reached.
16, 23, 24, 39, 45, 78, 95
23, 24, 39, 45, 78
24, 39, 45,
39
The median is 39
if my medical expenses are $30,000 per year for 35 years with inflation at 5.13% how much money would I have to put in an interest bearing account with a 5% return to cover all medical expenses and the account be $0 at the end of 35 years
Answer:
$1,021,337.13
Step-by-step explanation:
The sum of present values of medical expenses is ...
30,000/1.05 +30,000(1.0513)/1.05^2 +30,000(1.0513^2)/1.05^3 +...
So, the series has an initial value of 30,000/1.05 and a common ratio of 1.0513/1.05. Its sum is given by ...
S = a(r^n -1)/(r -1)
where a = 30,000/1.05, n = 35, r = 1.0513/1.05.
Filling in these values and doing the arithmetic, we get ...
S = $1,021,337.13
You need an initial deposit of $1,021,337.13 to cover rising expenses for 35 years.
consider a politician discussion group consisting of eight Democrats three Republicans and seven Independents suppose that two group members are randomly selected in succession to attend political convention find the probability of selecting an independent and then a Democrat
Answer:
(38.8%...7/10), than (47%...8/17) I didnt know if u needrd it in fraction or percent.
Step-by-step explanation:
You want to first add up everyone. So in total there are 18 people.
There is than a 38.8% chance that a independent will be picked first. 7/18.
But since one person was picked already you have to subtract 1 person from the total, so now its out of 17.
There is now a 47% chance that a democrat will be picked next. 8/17.
Who'd be better at speed answering? Datguy323 or some Helping Hand? (Not a serious question) Solve for the variables: [tex]x^3+y^7=28\\x^3=27[/tex]
Answer:
x = 3
y = 1
Step-by-step explanation:
The equations are:
[tex]x^3+y^7 = 28[/tex]
and
[tex]x^3 = 27[/tex]
Putting second equation in the first one:
=> [tex]27+y^7 = 28[/tex]
Subtracting 27 to both sides
=> [tex]y^7 = 28-27[/tex]
=> [tex]y^7 = 1[/tex]
Taking power 7 to both sides
=> y = 1
Now,
[tex]x^3 = 27[/tex]
Taking cube root on the both sides
x = 3
Answer: (3,1)
Step-by-step explanation:
First, to find x, simply take the cube root of 27, or 3. Thus, x = 3.
Then, simply plug it in:
[tex]27+y^7=28\\Subtract(27)\\y^7=1\\y=1[/tex]
Thus, y = 1
Hope it helps <3
p.s. for some reason, in a graphing calculator, it shows no solutions
Hope it helps <3
2 in a row!
The number of degrees of freedom for the appropriate chi-square distribution in a test of independence is a. k – 1. b. A chi-square distribution is not used. c. number of rows minus 1 times number of columns minus 1. d. n – 1.
Answer:
Option C
Step-by-step explanation:
The chi square test of independence is used to determine if there is a significant association between two categorical variables from a population.
It tests the claim that the row and column variables are independent of each other.
The degrees of freedom for the chi-square are calculated using the following formula: df = (r-1) (c-1) where r is the number of rows and c is the number of columns.
A box of Jell-O costs $0.50, and makes 2 cups. How much would it cost to fill a swimming pool 4 feet deep, 8 feet wide, and 12 feet long with Jell-O? (1 cubic foot is about 7.5 gallons)
Answer:
$11,520
Step-by-step explanation:
4 * 8 * 12 = 384 cu ft.
384 * 7.5 = 2880 gallons
There are 16 cups in a gallon
2880 * 16 = 46,080 cups
46,080/2 * .50 = $11,520
Pls help me help me
Answer:
C. -4/3
Step-by-step explanation:
Perpendicular lines have negative reciprocal slopes.
We know that line m is perpendicular to line l.
Line l has a slope of 3/4. To find the slope of line m, find the negative reciprocal of 3/4. Negate the fraction and find the reciprocal.
Negative: switch the sign
3/4 --> -3/4
Reciprocal: switch the numerator (top number) and denominator (bottom number)
-3/4 --> -4/3
Line m has a slope of -4/3 and C is correct.
Let X be the damage incurred (in $) in a certain type of accident during a given year. Possible X values are 0, 1000, 5000, and 10000, with probabilities 0.80, 0.08, 0.10, and 0.02, respectively. A particular company offers three different policies: a $200 deductible with a $780 premium, a $500 deductible with a $700 premium, and a $1000 deductible with a $590 premium. (A $Y deductible means the insurance company pays X - Y for X Y and 0 for X Y.) Compute the expected profit for each policy.
Answer:
Expected profit policy 1 = $40
Expected profit policy 2 = $20
Expected profit policy 3 = $10
Step-by-step explanation:
X values | Probability P(x)
0 | 0.80
1,000 | 0.08
5,000 | 0.10
10,000 | 0.02
A particular company offers three different policies:
Policy 1: $200 deductible with a $780 premium
Policy 2: $500 deductible with a $700 premium
Policy 3: $1000 deductible with a $590 premium
The company pays X - Y in damages if X > Y and 0 otherwise.
So the expected profit is given by
Expected profit = Premium amount - Expected payout
Expected profit = Premium amount - [ (X - deductible) × P(x) ]
Expected profit Policy 1:
E(x) = $780 - [ 0×0.80 + (1,000 - 200)×0.08 + (5,000 - 200)×0.10 + (10,000 - 200)×0.02 ]
E(x) = $780 - [ 0 + 64 + 480 + 196 ]
E(x) = $780 - $740
E(x) = $40
Expected profit Policy 2:
E(x) = $700 - [ 0×0.80 + (1,000 - 500)×0.08 + (5,000 - 500)×0.10 + (10,000 - 500)×0.02 ]
E(x) = $700 - [ 0 + 40 + 450 + 190 ]
E(x) = $700 - $680
E(x) = $20
Expected profit Policy 3:
E(x) = $590 - [ 0×0.80 + (1,000 - 1,000)×0.08 + (5,000 - 1,000)×0.10 + (10,000 - 1,000)×0.02 ]
E(x) = $590 - [ 0 + 0 + 400 + 180 ]
E(x) = $590 - $580
E(x) = $10
Therefore, the expected profits for the three policies are:
Expected profit policy 1 = $40
Expected profit policy 2 = $20
Expected profit policy 3 = $10
Determine the area (in units2) of the region between the two curves by integrating over the x-axis. y = x2 − 24 and y = 1
The area bounded by region between the curve [tex]y = x^2- 24[/tex] and [tex]y = 1[/tex] is
[tex]0[/tex] square units.
To find the Area,
Integrate the difference between the two curves over the interval of intersection.
Find the points of intersection between the curves [tex]y = x^2- 24[/tex] and [tex]y = 1[/tex] .
The point of Intersection is the common point between the two curve.
Value of [tex]x[/tex] and [tex]y[/tex] coordinate will be equal for both curve at point of intersection
In the equation [tex]y = x^2- 24[/tex], Put the value of [tex]y = 1[/tex].
[tex]1 = x^2-24[/tex]
Rearrange, like and unlike terms:
[tex]25 = x^2[/tex]
[tex]x =[/tex] ±5
The point of intersection for two curves are:
[tex]x = +5[/tex] and [tex]x = -5[/tex]
Integrate the difference between the two curve over the interval [-5,5] to calculate the area.
Area = [tex]\int\limits^5_{-5} {x^2-24-1} \, dx[/tex]
Simplify,
[tex]= \int\limits^5_{-5} {x^2-25} \, dx[/tex]
Integrate,
[tex]= [\dfrac{1}{3}x^3 - 25x]^{5} _{-5}[/tex]
Put value of limits in [tex]x[/tex] and subtract upper limit from lower limit.
[tex]= [\dfrac{1}{3}(5)^3 - 25(5)] - [\dfrac{1}{3}(-5)^3 - 25(-5)][/tex]
= [tex]= [\dfrac{125}{3} - 125] - [\dfrac{-125}{3} + 125][/tex]
[tex]= [\dfrac{-250}{3}] - [\dfrac{-250}{3}]\\\\\\= \dfrac{-250}{3} + \dfrac{250}{3}\\\\\\[/tex]
[tex]= 0[/tex]
The Area between the two curves is [tex]0[/tex] square units.
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[10 points] A manufacturer wants to design an open box having a square base and a surface area of 108 square inches. What dimensions will produce a box with maximum volume?
Answer:
6 inches square by 3 inches high
Step-by-step explanation:
For a given surface area, the volume of an open-top box is maximized when it has the shape of half a cube. If the area were than of the whole cube, it would be 216 in² = 6×36 in².
That is, the bottom is 6 inches square, and the sides are 3 inches high.
_____
Let x and h represent the base edge length and box height, respectively. Then we have ...
x² +4xh = 108 . . . . box surface area
Solving for height, we get ...
h = (108 -x²)/(4x) = 27/x -x/4
The volume is the product of base area and height, so is ...
V = x²h = x²(27/x -x/4) = 27x -x³/4
We want to maximize the volume, so we want to set its derivative to zero.
dV/dx = 0 = 27 -(3/4)x²
x² = (4/3)(27) = 36
x = 6
h = 108/x² = 3
The box is 6 inches square and 3 inches high.
_____
Comment on maximum volume, minimum area
In the general case of an open-top box, the volume is maximized when the cost of the bottom and the cost of each pair of opposite sides is the same. Here, the "cost" is simply the area, so the area of the bottom is 1/3 the total area, 36 in².
If the box has a closed top, then each pair of opposite sides will have the same cost for a maximum-volume box. If costs are uniform, the box is a cube.
Professor Sanchez has been teaching Principles of Economics for over 25 years. He uses the following scale for grading. Grade Numerical Score Probability A 4 0.090 B 3 0.240 C 2 0.360 D 1 0.165 F 0 0.145 a. Convert the above probability distribution to a cumulative probability distribution. (Round your answers to 3 decimal places.)
The question is incomplete! Complete question along with answer and step by step explanation is provided below.
Question:
Professor Sanchez has been teaching Principles of Economics for over 25 years. He uses the following scale for grading. Grade Numerical Score Probability A 4 0.090 B 3 0.240 C 2 0.360 D 1 0.165 F 0 0.145
a. Convert the above probability distribution to a cumulative probability distribution. (Round your answers to 3 decimal places.)
b. What is the probability of earning at least a B in Professor Sanchez’s course? (Round your answer to 3 decimal places.)
c. What is the probability of passing Professor Sanchez’s course? (Round your answer to 3 decimal places.)
Answer:
a. Cumulative Probability Distribution
Grade P(X ≤ x)
F 0.145
D 0.310
C 0.670
B 0.910
A 1
b. P(at least B) = 0.330
c. P(pass) = 0.855
Step-by-step explanation:
Professor Sanchez has been teaching Principles of Economics for over 25 years.
He uses the following scale for grading.
Grade Numerical Score Probability
A 4 0.090
B 3 0.240
C 2 0.360
D 1 0.165
F 0 0.145
a. Convert the above probability distribution to a cumulative probability distribution. (Round your answers to 3 decimal places.)
The cumulative probability distribution is given by
Grade = F
P(X ≤ x) = 0.145
Grade = D
P(X ≤ x) = 0.145 + 0.165 = 0.310
Grade = C
P(X ≤ x) = 0.145 + 0.165 + 0.360 = 0.670
Grade = B
P(X ≤ x) = 0.145 + 0.165 + 0.360 + 0.240 = 0.910
Grade = A
P(X ≤ x) = 0.145 + 0.165 + 0.360 + 0.240 + 0.090 = 1
Cumulative Probability Distribution
Grade P(X ≤ x)
F 0.145
D 0.310
C 0.670
B 0.910
A 1
b. What is the probability of earning at least a B in Professor Sanchez’s course? (Round your answer to 3 decimal places.)
At least B means equal to B or greater than B grade.
P(at least B) = P(B) + P(A)
P(at least B) = 0.240 + 0.090
P(at least B) = 0.330
c. What is the probability of passing Professor Sanchez’s course? (Round your answer to 3 decimal places.)
Passing the course means getting a grade of A, B, C or D
P(pass) = P(A) + P(B) + P(C) + P(D)
P(pass) = 0.090 + 0.240 + 0.360 + 0.165
P(pass) = 0.855
Alternatively,
P(pass) = 1 - P(F)
P(pass) = 1 - 0.145
P(pass) = 0.855
Find the work (in ft-lb) required to pump all the water out of a cylinder that has a circular base of radius 7 ft and height 200 ft. Use the fact that the weight-density of water is 62.4 lb/ft3
Answer:
work done is equal to 384279168 lb-ft
Step-by-step explanation:
The cylinder has a circular base of 7 ft.
The height of the cylinder is 200 ft
The weight density of water in the cylinder is 62.4 lb/ft^3
First, we find the volume of the water in the cylinder by finding the volume of this cylinder occupied by the water.
The volume of a cylinder is given as [tex]\pi r^{2} h[/tex]
where, r is the radius,
and h is the height of the cylinder.
the volume of the cylinder = [tex]3.142* 7^{2}*200[/tex] = 30791.6 ft^3
Since the weight density of water is 62.4 lb/ft^3, then, the weight of the water within the cylinder will be...
weight of water = 62.4 x 30791.6 = 1921395.84 lb
We know that the whole weight of the water will have to be pumped out over the height of cylindrical container. Also, we know that the work that will be done in moving this weight of water over this height will be the product of the weight of water, and the height over which it is pumped. Therefore...
The work done in pumping the water out of the container will be
==> (weight of water) x (height of cylinder) = 1921395.84 x 200
==> work done is equal to 384279168 lb-ft
The required work done will be "384279168 lb-ft".
Work done:Whenever a force pushes anything across distances, work is performed. This same energy transmitted, as well as work done, maybe determined by calculating the force through the kilometers moved throughout the direction of the applied force.
According to the question,
Circular base of cylinder = 7 ft
Height of cylinder = 200 ft
Weight density of water = 62.4 lb/ft³
The Volume of cylinder be:
= πr²h
By substituting the values,
= [tex]3.142\times (7)^2\times 200[/tex]
= [tex]3.142\times 49\times 200[/tex]
= [tex]30791.6[/tex] ft³
Now,
The weight of water be:
= [tex]62.4\times 30791.6[/tex]
= [tex]1921395.84[/tex] lb
hence,
The work done be:
= Water's weight × Cylinder's height
= [tex]1921395.84\times 200[/tex]
= [tex]384279168[/tex] lb-ft
Thus the above answer is right.
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For the following data at the near-ground level, which location will residents likely see dew on their lawns in the morning? Group of answer choices City C: Dew Point Temperature = 25°F, expected low Temperature = 20°F City A: Dew Point Temperature = 65°F, expected low Temperature = 60°F City B: Dew Point Temperature = 45°F, expected low Temperature = 50°F
Answer: CITY B: Dew Point Temperature = 45°F, expected low Temperature = 50°F
Step-by-step explanation:
CITY C: Dew Point Temperature = 25°F, expected low Temperature = 20°F
CITY A: Dew Point Temperature = 65°F, expected low Temperature = 60°F
CITY B: Dew Point Temperature = 45°F, expected low Temperature = 50°F
city B is going to have dew on their lawn in the morning as the dew point temperature is less than the lowest temperature.
When surface temperature drops, eventually reaching the dew point, atmospheric water vapor condenses to form small droplets on the surface. Thus dew will be formed as the conditions are suitable only for city B.
Find the slope of the line passing through (6,8) and (-10,3)
Answer:
5/16
Step-by-step explanation:
Use the formula to find slope when 2 points are given.
m = rise/run
m = y2 - y1 / x2 - x1
m = 3 - 8 / -10 - 6
m = -5 / -16
m = 5/16
The slope of the line is 5/16.
Answer: m=5/16
Step-by-step explanation:
Would this be correct even though I didn’t use the chain rule to solve?
Answer:
Dy/Dx=1/√ (2x+3)
Yeah it's correct
Step-by-step explanation:
Applying differential by chain differentiation method.
The differential of y = √(2x+3) with respect to x
y = √(2x+3)
Let y = √u
Y = u^½
U = 2x +3
The formula for chain differentiation is
Dy/Dx = Dy/Du *Du/Dx
So
Dy/Dx = Dy/Du *Du/Dx
Dy/Du= 1/2u^-½
Du/Dx = 2
Dy/Dx =( 1/2u^-½)2
Dy/Dx= u^-½
Dy/Dx=1/√ u
But u = 2x+3
Dy/Dx=1/√ (2x+3)
Hartman Motors has $15 million in assets, which were financed with $6 million of debt and $9 million in equity. Hartman's beta is currently 1.4, and its tax rate is 30%. Use the Hamada equation to find Hartman's unlevered beta, bU. Do not round intermediate calculations. Round your answer to two decimal places.
Answer:
Unlevered beta ≈ 1.09
Step-by-step explanation:
Unlevered beta is basically the unlevered weighted average cost as it shows the volatility of returns without financial leverage. Unlevered beta is also known as asset beta, while the levered beta is commonly known as equity beta. Unlevered beta is calculated from the hamada equation as:
Unlevered beta = Levered beta/[1 + ((1 - Tax rate) × (Debt / Equity))]
We are given;
Levered beta = 1.4
Tax rate = 30% = 0.3
Debt = $6 million
Equity = $15 million
Thus, plugging these into the hamada equation, we have;
Unlevered beta = 1.4/[1 + ((1 - 0.3) × (6/15))]
Unlevered beta = 1.4/(1 + (0.7 × 0.4)
Unlevered beta = 1.4/(1 + 0.28)
Unlevered beta = 1.4/1.28
Unlevered beta = 1.09375
To 2 decimal places;
Unlevered beta ≈ 1.09
HELP I KEEP GETTING WRONG ANSWERS!!!!!
Answer:
B) 65
Step-by-step explanation:
Plug in the corresponding numbers to the corresponding variables:
w = -4 ; v = 5 ; u = 2
4w² - v + 3u
4(-4²) - (5) + 3(2)
Remember to follow PEMDAS.
PEMDAS =
Parenthesis
Exponents
Multiplications
Division
Addition
Subtraction
& is the order of operation.
First, solve the power:
4(-4²) - (5) + 3(2)
(-4²) = (-4)(-4) = 16
Next, multiply:
4(16) - 5 + 3(2)
64 - 5 + 6
Finally, combine the terms:
(64 + 6) - 5
70 - 5
65
B) 65 is your answer.
~
Among 20 golden hamster litters recorded, there was a sample mean of =7.72 baby hamsters, with a sample standard deviation of s=2.5 hamsters per liter. Create a 98% confidence interval for the mean number of baby hamsters per liter.
Answer:
[tex] 7.72 -2.539 \frac{2.5}{\sqrt{20}} =6.30[/tex]
[tex] 7.72 +2.539 \frac{2.5}{\sqrt{20}} =9.14[/tex]
Step-by-step explanation:
For this case we have the following info given:
[tex]\bar X= 7.72[/tex] represent the sample mean
[tex]s= 2.5[/tex] represent the sample deviation
[tex] n=20[/tex] represent the sample size
The confidence interval is given by:
[tex] \bar X \pm t_{\alpha/2} \frac{s}{\sqrt{n}}[/tex]
The confidence interval is 98% and the significance level is [tex]\alpha=0.02[/tex] the degrees of freedom are given by:
[tex] df= n-1 = 20-1=19[/tex]
And the critical value would be:
[tex] t_{\alpha/2}= 2.539[/tex]
And replacing we got:
[tex] 7.72 -2.539 \frac{2.5}{\sqrt{20}} =6.30[/tex]
[tex] 7.72 +2.539 \frac{2.5}{\sqrt{20}} =9.14[/tex]
The 98% confidence interval is between 6.42 hamsters per liter to 9.02 hamsters per liter
Mean (μ) = 7.72, standard deviation (σ) = 2.5, sample size (n) = 20, Confidence (C) = 98% = 0.98
α = 1 - C = 0.02
α/2 = 0.01
The z score of α/2 is the same as the z score of 0.49 (0.5 - 0.01) which is equal to 2.326.
The margin of error E is:
[tex]E = Z_\frac{\alpha }{2} *\frac{\sigma}{\sqrt{n} } \\\\E=2.326*\frac{2.5}{\sqrt{20} } =1.3[/tex]
The confidence interval = (μ ± E) = (7.72 ± 1.3) = (6.42, 9.02)
Hence the 98% confidence interval is between 6.42 hamsters per liter to 9.02 hamsters per liter
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An integer is 3 less than 5 times another. If the product of the two integers is 36, then find the integers.
Answer:
3, 12
Step-by-step explanation:
Et x and y be the required integers.
Case 1: x = 5y - 3...(1)
Case 2: xy = 36
Hence, (5y - 3)*y = 36
[tex]5 {y}^{2} - 3y = 36 \\ 5 {y}^{2} - 3y - 36 = 0 \\ 5 {y}^{2} - 15y + 12y - 36 = 0 \\ 5y(y - 3) + 12(y - 3) = 0 \\ (y - 3)(5y + 12) = 0 \\ y - 3 = 0 \: or \: 5y + 12 = 0 \\ y = 3 \: \: or \: \: y = - \frac{12}{5} \\ \because \: y \in \: I \implies \: y \neq - \frac{12}{5} \\ \huge \purple{ \boxed{ \therefore \: y = 3}} \\ \because \: x = 5y - 3..(equation \: 1) \\ \therefore \: x = 5 \times 3 - 3 = 15 - 3 = 12 \\ \huge \red{ \boxed{ x = 12}}[/tex]
Hence, the required integers are 3 and 12.
let
x = one integer
y = another integer
x = 5y - 3
If the product of the two integers is 36, then find the integers.
x * y = 36
(5y - 3) * y = 36
5y² - 3y = 36
5y² - 3y - 36 = 0
Solve the quadratic equation using factorization method
That is, find two numbers whose product will give -180 and sum will give -3
Note: coefficient of y² multiplied by -36 = -180
5y² - 3y - 36 = 0
The numbers are -15 and +12
5y² - 15y + 12y - 36 = 0
5y(y - 3) + 12 (y - 3) = 0
(5y + 12) (y - 3) = 0
5y + 12 = 0 y - 3 = 0
5y = - 12 y = 3
y = -12/5
The value of y can not be negative
Therefore,
y = 3
Substitute y = 3 into x = 5y - 3
x = 5y - 3
x = 5(3) - 3
= 15 - 3
= 12
x = 12
Therefore,
(x, y) = (12, 3)
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The equation of a parabola in the xy-plane is given as
y= n(x + 5)(x - 3) where n is a non-zero constant. What
is the y-coordinate of the vertex of this parabola in
terms of n?
A. -18n
B. -16n
C. -15n
D. -12n
Answer:
B
Step-by-step explanation:
y=n(x+5)(x-3)
or y=n(x²-3x+5x-15)
or y=n(x²+2x-15)
=n(x²+2x+1-1-15)
=n(x+1)²-16n
y -coordinate of vertex=-16n
What ordered pair is closest to a local minimum of the
function, f(x)?
Х
-2
-1
0
f(x)
-8
-3
-2
4(-1, -3)
(0, -2)
(1.4)(2, 1)
Answer:
(-1, -3)
Step-by-step explanation:
Of the ordered pairs given in the table, the one with the smallest y-value is (-2, -8). That is not among the answer choices, so you must select the answer choice that has the smallest y-value that is -8 or greater.
(-1, -3) is the closest to the local minimum
Of the ordered pairs given in the table, the one with the smallest y-value is (-2, -8). The smallest y-value that is -8 or greater. (-1, -3) is the closest to the local minimum.
What is mathematical function?In mathematics, a function is a statement, rule, or law that establishes the relationship between an independent variable and a dependent variable. In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
Y and x are coupled in such a way that there is a distinct value of y for each value of x, and this relationship is frequently represented as y = f(x), or "f of x." In other words, the same x cannot include multiple values for f(x). A function connects an element x with an element f(x) within another set, which utilises the language underlying set theory. Of the ordered pairs given in the table, the one with the smallest y-value is (-2, -8). The smallest y-value that is -8 or greater. (-1, -3) is the closest to the local minimum.
Therefore, (-1, -3) is the closest to the local minimum.
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Use matrix operations to solve the following systems of linear equations. Use comments to explain which value is x1, x2, etc
3x1-10 x2- 5x3+30x4 = -1
4x1+7x2+ 5x3- 3x4=0
x2+ x3-3x4 =1
x1-2x2-10x3+6x4 = -1
Answer:
x⁴ = -0.955939
x³ = 0.206897
x² = -2.07471
x = 2.65517
Step-by-step explanation:
Step 1: Rewrite equations in standard form
30x⁴ - 5x³ - 10x² + 3x = -1
-3x⁴ + 5x³ + 7x² + 4x = 0
-3x⁴ + x³ + x² = 1
6x⁴ - 10x³ - 2x² + x = -1
Step 2: Write in matrix form
Top Row: [30 -5 -10 3 | -1]
2nd Row: [-3 5 7 4 | 0]
3rd Row: [-3 1 1 0 0 | 1]
Bottom Row: [6 -10 -2 1 | -1]
Step 3: Plug in calc with RREF function
Top Row: [1 0 0 0 | -499/522]
2nd Row: [0 1 0 0 | 6/29]
3rd Row: [0 0 1 0 | -361/174]
4th Row: [0 0 0 1 | 77/29]
why do insects undergo moulting
Answer:
Hello!
______________________
It is for shedding their outer skin or exoskeleton. During the process, they grow and develop. This is controlled by hormones. If these hormones are not formed, their body will become deformed and they will die.
Step-by-step explanation: In many insects in the larval stages, about 5 nos, moulting occurs. The science of moulting is an intricate subject. Man also undergoes hormonal stages in life. But in case of insects, they shed outer skin, to enable them grow, leading to pupal stage and adult stage. Hormones are wonderful chemicals and they play a major role in biology.
Hope this helped you!
Answer:
it is to allow their bodies to expand under controlled and protected conditions/environments.
Hope that helps...
Find the general formula for the following sequence.
300000, 480000, 768000, 1228800, 1966080, ....
Answer:
3,145,728
Step-by-step explanation:
x1.6
300000 x 1.6 = 4800000
480000 x 1.6 = 7680000
768000 x 1.6 = 1228800
122800 x 1.6 = 1966080
1966080 x 1.6 = 3145728
I NEED HELP PLEASE, THANKS! :)
Answer:
68
Step-by-step explanation:
The number of chips tested is the integral of the rate over the specified time interval: t = 2 to 6.
[tex]\displaysyle n=\int_2^6{-3t^2+16t+5}\,dt=\left.-3\dfrac{t^3}{3}+16\dfrac{t^2}{2}+5t\right|_2^6\\\\=-(6^3-2^3) +8(6^2-2^2)+5(6-2)=-(216-8)+8(32) +5(4)\\\\=-208+256+20=\boxed{68}[/tex]
The technician can test 68 chips in that time period.