Answer:
A) ± 54 cm^3 ( maximum possible error in volume )
B) i) 58.625 cm^3 ii) 49.625 cm^3
Step-by-step explanation:
A) using differential
edge of cube = 6 cm , maximum possible error = 0.5 cm
∴ side of cube ( x )= ± 0.5 cm
V = volume of cube
dv /dx = d(x)^3 / dx
∴ dv = 3x^2 dx ---- ( 1 )
input values into 1
dv = 3(6)^2 * ( ± 0.5 )
= ± 54 cm^3 ( maximum possible error in volume )
B) Using calculator
actual error in measuring volume when
i) radius = 6.5 cm instead of 6 cm
V1= ( 6.5)^3 = 274.625 , V = ( 6)^3 = 216
actual error = 274.625 - 216 = 58.625 cm^3
ii) radius = 5.5cm instead of 6cm
actual error = 49.625 cm^3
Suppose you deposit $500 in a savings account where the interest earned is compounded
continuously at a rate of 10%. How many years will it take the balance in the account to reach
$8000 (round your answer to the nearest year)?
The combined mass of 100 nickels is 500,000 milligrams. What is the mass of each nickel?
Answer:
5 grams = 500 centigrams = 5000 milligrams = 5000000 micrograms
Step-by-step explanation:
So the only correct answer in your choices is the third option, 5000 milligrams.
what are all the solutions (in exact values) to tan x = 1/4 [-π,π] ?
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Answer:
arctan(1/4)arctan(1/4) -πStep-by-step explanation:
The inverse tangent of 1/4 is an irrational number, only expressible exactly as ...
arctan(1/4)
This is a first-quadrant angle. There is a matching third-quadrant angle with the same tangent:
arctan(1/4) -π
Locust Software sells computer training packages to its business customers at a price of $102. The cost of production (in present value terms) is $96. Locust sells its packages on terms of net 30 and estimates that about 5% of all orders will be uncollectible. An order comes in for 20 units. The interest rate is 1.5% per month.
Required:
a-1. Calculate the profit or loss if this is a one-time order and sale will not be made unless credit is extended
a-2. Should the firm extend credit if this is a one-time order?
b. What is the break-even probability of collection?
c-1. Now suppose that if the customer pays this month's bill, they will place an identical order in each month indefinitely and can be safely assumed to pose no risk of default.Calculate the present value of the sale.
c-2. Should credit be extended?
d. What is the break-even probability of collection in the repeat-sales case?
Which function has a range of y < 3?
y - 3(2)
y = 2(3)
O y=-(2)x+ 3
Oy- (2) * - 3
Given:
The range of a function is [tex]y<3[/tex].
To find:
The function for the given range from the given options.
Solution:
In option A, the given function is:
[tex]y=3(2)^x[/tex]
Here, [tex](2)^x[/tex] is always greater than 0. So, [tex]3(2)^x[/tex] is also greater than 0, i.e., [tex]y>0[/tex].
In option B, the given function is:
[tex]y=2(3)^x[/tex]
Here, [tex](3)^x[/tex] is always greater than 0. So, [tex]2(3)^x[/tex] is also greater than 0, i.e., [tex]y>0[/tex].
In option C, the given function is:
[tex]y=-(2)^x+3[/tex]
Here,
[tex](2)^x>0[/tex]
[tex]-(2)^x<0[/tex]
[tex]-(2)^x+3<0+3[/tex]
[tex]y<3[/tex]
The range of this function is [tex]y<3[/tex]. So, option C is correct.
In option D, the given function is:
[tex]y=(2)^x-3[/tex]
Here,
[tex](2)^x>0[/tex]
[tex](2)^x-3<0-3[/tex]
[tex]y<-3[/tex]
The range of this function is [tex]y<-3[/tex]
Therefore, the correct option is only C.
given f(x)=2x-4 and g(x)=x213, determine gf[x]]
Step-by-step explanation:
you have to substitute the function g(x) where there's x in the function f(x)
gf(x)=2(x213)-4
if that's x two thirteen then you can multiply the 2 outside the brackets by it
giving you a final answer of
gf(x)=426x-4
hope it helps and sorry if am wrong
d) A product contains three lasers, and the product fails if any of the lasers fails. Assume the lasers fail independently. What should the mean life equal for 99% of the products to exceed 10000 hours before failure
Solution :
Let the probability laser works = p
The probability that the system works = [tex]$P(\text{all three component works}) = p^3 $[/tex]
= 0.99
Therefore, p = 0.9967
Now for the above probability critical z = -2.72
Hence, the mean life is equal to = [tex]10,000 + 2.72 \times 600[/tex]
= [tex]10,000+1632[/tex]
[tex]=11,632[/tex]
Find the length of BC
A. 6.81
B. 7.64
C. 13.37
D. 29.44
Answer:
13.37 = BC
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
cos theta = opp / hyp
cos 27 = BC / 15
15 cos 27 = BC
13.36509 = BC
Rounding to the nearest hundredth
13.37 = BC
PLEASE ANSWER. I WILL GIVE BRAINLIEST FAST
Answer:
It is a right triangle
Step-by-step explanation:
Answer:
a
Step-by-step explanation:
The number of bacteria in a colony increases by 10% every 2 hours. What is the overall percent increase after 4 hours?
The number of bacteria in a culture is increasing according to the law of exponential growth. There are 125 bacteria in the culture after 2 hours and 350 bacteria after 4 hours.
The overall percent increase after 4 hours is 21% if the number of bacteria in a colony increases by 10% every 2 hours option (G) is correct.
What is the percentage?It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
We have:
The number of bacteria in a colony increases by 10% every 2 hours.
Let there be 100 bacteria in the starting
In the first 2 hours :
= (100×10%) + 100
= 10 + 100
= 110
Again after 2 hours:
= (110×10%) + 110
= 11 + 110
= 121
= (121 - 100)
= 21
Thus, the overall percent increase after 4 hours is 21% if the number of bacteria in a colony increases by 10% every 2 hours option (G) is correct.
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Find the area of a rectangle that measures 12ft by 3 1/3 ft
Answer:
40 ft^2
Step-by-step explanation:
The area of a rectangle is given by
A = l*w
=12 * 3 1/3
Change to an improper fraction
= 12 ( 3*3+1)/3
= 12 (10/3)
40
Answer:
[tex]40 {ft}^{2} [/tex]
Step-by-step explanation:
[tex]area = l \times b \\ = 12 \times 3 \frac{1}{3} \\ = 12 \times \frac{10}{3} \\ = \frac{120}{3} \\ = 40 {ft}^{2} [/tex]
Simplify 9 + (-2)³
answer asap
Answer:
[tex]9+(-2)^{3} =9+[(-2)(-2)(-2)]=9+[4(-2)]=9+(-8)=9-8=1[/tex]
[tex]Hello[/tex] [tex]There![/tex]
[tex]AnimeVines[/tex] [tex]is[/tex] [tex]here![/tex]
This is quite simple, actually.
Here's a explanation.
[tex]9 + (-2)^{3}[/tex]
[tex]= 9 + - 8[/tex]
[tex]= 1[/tex]
[tex]HopeThisHelps!![/tex]
[tex]AnimeVines[/tex]
Jeannine needs to decide what size to make a rectangular
garden in her yard. The dimensions must be natural numbers.
Jeannine wants the perimeter of her Chapter Reference
garden to be 50 dm. She wants the
width to be an even number of decimeters. How many
different combinations are possible? (Length is always longer than or equal to width.)
Answer:
Total number of possible combinations are 6
Length width
23 dm 2m
21 dm 4 dm
19 dm 6 dm
17 dm 8 dm
15 dm 10 dm
13 dm 12 dm
Step-by-step explanation:
We are given that
Perimeter of rectangular garden=50 dm
Width is even number.
Length is always longer than or equal to width.
Let length of rectangular garden=x
Width of rectangular garden=y
We have to find the possible number of combinations .
Perimeter of rectangular garden=[tex]2(x+y)[/tex]
[tex]2(x+y)=50[/tex]
[tex]x+y=50/2[/tex]
[tex]x+y=25[/tex]
If y=2 dm
x=25-2=23 dm
If y=4 dm
x=25-4=21 dm
If y=6 dm
x=25-6=19 dm
If y=8 dm
x=25-8=17 dm
If y=10 dm
x=25-10=15 dm
If y=12 dm
x=25-12=13 dm
If y=14 dm
x=25-14=11 dm
x<y
It is not possible
Then, possible combinations are 6
Length width
23 dm 2m
21 dm 4 dm
19 dm 6 dm
17 dm 8 dm
15 dm 10 dm
13 dm 12 dm
Ann, Bob, Carol, and Denis own a candy store. After a large argument, they decide to dissolve their partnership using the sealed bid method. Ann bids $320,000 for the store, Bob bids $440,000 for it, Carol bids $240,000 for it, and Denis bids $400,000 for it.
Required:
a. What is Bob's fair share?
b. What is Carol's fair share?
c. What is Denis's fair share?
Answer:
Following are the solution to the given points:
Step-by-step explanation:
[tex]Ann=\$3,20,000\\\\Bob=\$4,40,000\\\\Carol=\$240,000\\\\Denis= \$4,00,000\\\\[/tex]
Each player's offer divided by the total number of players calculates the fair share
Ann's fair share [tex]= \frac{\$320,000}{4} = \$80,000\\\\[/tex]
Bob's fair share[tex]= \frac{\$440,000}{4} = \$110,000\\\\[/tex]
Carol's fair share [tex]= \frac{\$240,000}{4} = \$60,000\\\\[/tex]
Denis's fair share [tex]= \frac{\$400,000}{4} = \$100,000\\\\[/tex]
Because Bob has the highest bid, that receives in the business.
Payments:
Ann [tex]\$80,000[/tex] paid by estate
Bob [tex]= \$440,000 - \$110,000 = \$330,000[/tex] owes estate
Carol [tex]= \$60,000[/tex] paid by estate
Denis [tex]= \$100,000[/tex] paid by estate
Surplus [tex]= \$330,000 - (\$80,000+\$60,000+ \$100,000) = \$90,000[/tex]
Splitting the equally among the four players. therefore one of the each receives:
[tex]\frac{\$90,000}{4}= \$22,500[/tex]
The final settlement of the Ann receives:
[tex]= \$80,000+ \$22,500 = \$102,500[/tex]
Find the measure of the missing angles in the regular polygon below.
Step-by-step explanation:
First, we can see that the angles inside the polygon form a full circle, as it goes fully around. Therefore, the sum of the angles around the center of the circle (such as m < 7) is 360 degrees. Since it is a regular polygon, and the lines are going from the center to its corners, the 6 angles directly surrounding the center are equal.
Each angle is therefore 360/6 = 60 degrees, so m<7 is 60 degrees.
For m<8, we can see that a line bisects one of the 6 angles surrounding the center. Therefore, m<8 is 1/2 of the angle it bisects, which is equal to 360/6 = 60 degrees, and m<8 = 60/2 = 30 degrees
Finally, we can see that there are 6 sides of the polygon. For a polygon with n number of sides, the sum of its interior angles is equal to (n-2) * 180. Here, there are 6 sides, so the sum of this polygon's interior angles is (6-2) * 180 = 4 * 180 = 720. Because this is a regular polygon, each interior angle is the same, and because there are 6 of them, each one is 720/6 = 120 degrees. As shown in the picture, m < 9 is seemingly one-half of an interior angle, as it is bisected by a line from the center to a corner.
Therefore, m <9 = 120 /2 = 60 degrees
Question 4 please provide explanation for question
Answer:
A
Step-by-step explanation:
We need to find a equation that is where the domain is all real numbers and the range is all real numbers greater than -3
A square root function cannot equal to all real numbers because we cant take the square root of a negative number. so B and C are already wrong.A cubic function range is all real numbers. so y can be greater than -3 but it would also include. values lesser than -3. so D is Wrong.A is right, the domain of a absolute value function is all real numbers. The range of a absolute value is all numbers greater than or equal to zero but if we subtract 3, it changes into all real numbers greater than or equal to -3
Need help giving 10 Points. Answer—and explanation
Salma invested $8000 in a fund for 6 years and was paid simple interest. The total interest that she received on the investment was $1400. As a percentage, what was the annual interest rate of her investment?
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Answer:
about 2.917%
Step-by-step explanation:
The simple interest formula can be used. Fill in the known values and solve for the unknown.
I = Prt . . . . principal P invested at rate r for t years
1400 = 8000(r)(6)
r = 1400/48000 = 7/240 = 0.0291666...
Salma's interest rate was about 2.917% per year.
Determine the area of the given parallelogram with length 11 and altitude five
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Answer:
55 square units
Step-by-step explanation:
The area of a parallelogram is the product of base length and height:
A = bh
A = (11)(5) = 55 . . . area of the given parallelogram in square units
Find x please explanation need it
An employee makes a career change, her original salary was 65,000 and now it’s58,000 at her new job . What percent decrease was the salary change?
Show work
Answer:
about 21 percent
Step-by-step explanation:
three cards are drawn from an ordinary desk and not replaced
find probability a.getting 3 jackets
Answer:
Assuming you meant three jacks:
1 in 5525 or else 1/5525.
Step-by-step explanation:
You start with a full deck of 52 and 4 jacks. After each draw, you reduce both the jacks and total deck by one. Your first draw would be 4/52. The next would be 3/51. The final draw would be 2/50. You multiply each fraction together as you need all of them to happen, and that is your odds of drawing 3 jacks in a row without replacement.
In a sample of 500 adults, 345 had children. Construct a 99% confidence interval for the true population proportion of adults with children.
Answer:
The 99% confidence interval for the true population proportion of adults with children is (0.6367, 0.7433).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
In a sample of 500 adults, 345 had children.
This means that [tex]n = 500, \pi = \frac{345}{500} = 0.69[/tex]
99% confidence level
So [tex]\alpha = 0.01[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.01}{2} = 0.995[/tex], so [tex]Z = 2.575[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.69 - 2.575\sqrt{\frac{0.69*0.31}{500}} = 0.6367[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.69 + 2.575\sqrt{\frac{0.69*0.31}{500}} = 0.7433[/tex]
The 99% confidence interval for the true population proportion of adults with children is (0.6367, 0.7433).
Rewrite the function f(x)=16^x in four different ways, using a different base in each case.
Answer:
X=1
f(x)=16^1
=16
X=2
f(x)=16^2
256
X=3
f(x)=16^3
=4096
X=4
f(x)=16^4
=65536
Here are four different ways to rewrite the function f(x) = 16^x, using a different base for each case:
Using base 2:
f(x) = (2^4)^x = 2^(4x)
Using base 3:
f(x) = (3^2)^x = 3^(2x)
Using base 10:
f(x) = (10^(log10(16)))^x = 10^(log10(16) * x)
Using base e (natural logarithm):
f(x) = (e^(ln(16)))^x = e^(ln(16) * x)
How to explain the functionIn these rewritten forms, the exponentiation of the base is expressed as a simpler expression.
This involves the new base, which helps to illustrate the relationship between the original function and the different bases used.
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AVX Home Entertainment Inc recently began a "no-hassles" return policy. A sample of 505 customers who recently returned items showed 320 thought the policy was fair, 150 thought it took too long to complete the transaction, and the rest had no opinion. On the basis of this information, make an inference about customer reaction to the new policy. (Round your answers to 1 decimal place.)
Customer reaction Percent
Fair %
Too long %
No opinion %
Answer:
[tex]Fair = 63.4\%[/tex]
[tex]Too\ Long = 29.7\%[/tex]
[tex]No\ Opinion =6.9\%[/tex]
Step-by-step explanation:
Given
[tex]Total=505[/tex] --- customers
[tex]Fair = 320[/tex]
[tex]Too\ Long = 150[/tex]
Required
Complete the table
To complete the table, we simply divide each value by the total number of customers.
So, we have:
[tex]Fair = 320[/tex]
[tex]Fair = \frac{320}{505}[/tex]
[tex]Fair = 0.634[/tex]
Express as percentage
[tex]Fair = 0.634*100\%[/tex]
[tex]Fair = 63.4\%[/tex]
[tex]Too\ Long = 150[/tex]
[tex]Too\ Long = \frac{150}{505}[/tex]
[tex]Too\ Long = 0.297[/tex]
Express as percentage
[tex]Too\ Long = 0.297*100\%[/tex]
[tex]Too\ Long = 29.7\%[/tex]
For the last set, the percentage is calculated using:
[tex]No\ Opinion + Fair + Too\ Long = 100\%[/tex]
So, we have:
[tex]No\ Opinion + 63.4\% + 29.7\% = 100\%[/tex]
[tex]No\ Opinion + 93.1\% = 100\%[/tex]
Collect like terms
[tex]No\ Opinion =- 93.1\% + 100\%[/tex]
[tex]No\ Opinion =6.9\%[/tex]
Listed below are the 35 members of the Metro Toledo Automobile Dealers Association. We would like to estimate the mean revenue from dealer service departments. The members are identified by numbering them 00 through 34. We want to select a random sample of five dealers. The random numbers are: 34, 32, 39, 94, 25, 71, 71, 13, 52, 39, 19, and 67. Which dealers would be included in the sample
Answer:
Following are the solution to the given question:
Step-by-step explanation:
There will be 35 members of the Toledo Automotive Metro from such reports
The Organization of Distributors. The membership is sequentially numbered between 00 and 34.
The five traders selected a random sample as follows:
[tex]34, 32, 39, 94, 25, 71, 71, 13, 52, 39, 19, 67[/tex]
The decision should be made in 00 and 34.
In this the remaining numbers 39, 94,. . . . .67 were not chosen because it is beyond the ranges that are 00-34.
The samples contain 34, 32, 25, 13, and 19 distributors.
On September 12, Vander Company sold merchandise in the amount of $7,200 to Jepson Company, with credit terms of 2/10, n/30. The cost of the items sold is $4,700. Jepson uses the periodic inventory system and the gross method of accounting for purchases. The journal entry that Jepson will make on September 12 is:
Answer: See explanation
Step-by-step explanation:
Following the information that is given in the question, the journal entry that Jepson will make on September 18 will be analysed below:
Debit Accounts payable $7,200
Credit Purchases discounts = 2% × $7200 = $144
Credit Cash = $7200 - $144 = $7056
when solving inequalities,name 2 steps that are the same as solving equations and one difference
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Explanation:
same:
the addition property of equalitythe multiplication property of equality (for positive multipliers)different:
the multiplication property of equality for negative multipliers_____
Additional comment
Multiplication by a negative number has the effect of re-ordering numbers:
-1 < 2 . . . 1 > -2 (both sides multiplied by -1)
Other functions can have the same effect, so care must be taken when applying functions to both sides of an inequality.
1/2 > 1/3 . . . 2 < 3 (reciprocal function applied to both sides)
30° < 60° . . . cos(30°) > cos(60°) (cosine function applied to both sides)
An elevator is on the twelfth floor it goes down 11 floors and than up 5 floors what floor is the elevator on now
Answer:
The sixth floor
Step-by-step explanation:
Simplify the attached equation:
4[tex]4\sqrt{6x^{3} }y^{5} . -3\sqrt{24x^{7} } y[/tex]
