Answers
Answer:
The cylinder is cheaper to make because it has less surface area.
Step-by-step explanation:
In order to find the surface area of a cylinder, you do 2πrh+2πr²
We need the radius, which is half of the diameter, so then we have 2π(3·12)+2π·3² which gets us 282.72
We also need the surface area of the rectangular prism which we can get by 7x4 + 7x4 + 12x7 + 12x7 + 12x4 + 12x4 which gets us 320
282.72 < 320
Related Questions
Last year during the hurricane season, the amount of rain that fell on the Texas Gulf Coast in October was 14 inches, which was 3 1/2 times more than the rainfall during September of the same year. How much rain fell during the month of September? helppppp
Answers
Answer:
49
Simple Explanation:
14 x 3 1/2
= 14 x 7/2
= 98/2
= 98/2 ÷ 2/2
= 49
Let R denote the ring Z[i]/(1+3i).(i) Show that i-3 € (1+36) and that [i] = [3] in R. Use this to prove that [10][0] in R and that [a+bi] = [a+3b], where a, b Z.(ii) Show that the unique ring homomorphism6: Z→ Ris surjective.(iii) Show that 1+3i is not a unit and that 1+3i does not divide 2 and 5 in Z[]. Conclude that Ker() = 102.(iv) Show that RZ/10Z
Answers
(i) As we have proved that [10][0] in R and that [a+bi] = [a+3b], where a, b Z.
(ii) As we have proved that the unique ring homomorphism 6: Z→ Ris surjective
(iii) As we have proved that 1+3i is not a unit and that 1+3i does not divide 2 and 5 in Z[].
(iv) We can then show that Ker(ψ) = 10Z in R, which is the ideal generated by 10 in R.
(i) The first part of the problem asks us to show that i-3 € (1+36) and that [i] = [3] in R. To do this, we need to understand what R represents. R is the ring obtained by taking the quotient of the ring of Gaussian integers Z[i] by the ideal generated by 1+3i. In other words, we consider all the possible integers in Z[i], but we identify any two integers that differ by a multiple of 1+3i. So, [i] represents the equivalence class of all the integers in Z[i] that are equivalent to i modulo 1+3i.
Finally, we can use the fact that [a+bi] = [a+3b] in R for any integers a and b. To see this, note that [a+bi] = [(a-3b) + (b+3a)i], which is equivalent to [a+3b] modulo 1+3i. Therefore, we have [a+bi] = [a+3b] in R.
(ii) The second part of the problem asks us to show that the unique ring homomorphism Φ: Z → R is surjective. In other words, every element of R is the image of some integer in Z under Φ.
Now, let [a+bi] be an arbitrary element of R. We need to show that there exists an integer n such that Φ(n) = [a+bi]. To do this, note that [a+bi] = [(a-3b) + (b+3a)i], which is equivalent to (a-3b) modulo 1+3i. Therefore, we can choose n = a-3b, and we have Φ(n) = [n] = [a+bi]. This shows that Φ is surjective.
(iii) The third part of the problem asks us to show that 1+3i is not a unit in R and that 1+3i does not divide 2 and 5 in Z[i]. We then need to use these facts to conclude that Ker(Φ) = 102, which is the kernel of the homomorphism Φ.
To show that 1+3i is not a unit in R, we need to show that there is no element in R that, when multiplied by 1+3i, gives the multiplicative identity in R. Suppose, for the sake of contradiction, that there exists such an element [a+bi] in R. This means that (1+3i)(a+bi) is equivalent to 1 modulo 1+3i, which implies that 3a+b is a multiple of 1+3i. But this is not possible, since 1+3i is not a divisor of any integer of the form 3a+b in Z[i]. Therefore, 1+3i is not a unit in R.
(iv) The final part of the problem asks us to show that RZ/10Z, which is the quotient of R by the ideal generated by 10 in Z[i], is isomorphic to the ring Z/10Z. To do this, we can define a ring homomorphism ψ: R → Z/10Z by ψ([a+bi]) = a mod 10, which maps each equivalence class in R to its residue modulo 10 in Z/10Z.
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uppose that a particular nba player makes of his free throws. assume that late in a basketball game, this player is fouled and is awarded two free throws. a. what is the probability that he will make both free throws? (to 4 decimals) b. what is the probability that he will make at least one free throw? (to 4 decimals)
Answers
Answer:
a. 0.81
b. 0.81
Step-by-step explanation:
Let's assume that the player makes x% of his free throws. Then, the probability that he will make both free throws is (x/100)^2, and he will make at least one free throw is 1 - (1 - x/100)^2.
So if he makes 90% of his free throws, then:
a. The probability that he will make both free throws is (90/100)^2 = 0.81.
b. The probability that he will make at least one free throw is 1 - (1 - 90/100)^2 = 1 - (1 - 0.9)^2 = 1 - 0.19 = 0.81.
The answers to the questions rounded to 4 decimal places are:
a. 0.81
b. 0.81
After giving 1/3 of his money to his wife and 1/4 of it to his mother, Jake still had $600 left. How much money did he give to his mother?
Answers
Let's start by setting up an equation to represent the problem.
Let's say Jake started with x amount of money.
After giving 1/3 to his wife, he has 2/3 left: (2/3)x
After giving 1/4 of that amount to his mother, he has $600 left: (1/4)(2/3)x = $600
We can solve for x by isolating it:
(1/4)(2/3)x = $600
Multiplying both sides by 12/2 gives:
(2/3)x = $3600
Dividing both sides by 2/3 gives:
x = $5400
So Jake started with $5400.
To find out how much he gave to his mother, we can take 1/4 of 2/3 of $5400:
(1/4)(2/3)($5400) = $900
So he gave his mother $900.
Step-by-step explanation:
x = original amount of money
the problem description tells us he gives 1/3 of his money to his wife and 1/4 of his money to his mother. and then he had still $600 left.
x - (1/3)x - (1/4)x = 600
so let's bring every fractional term to .../12.
12x/12 - (4/4)×(1/3)x - (3/3)×(1/4)x = 600
12x/12 - 4x/12 - 3x/12 = 600
5x/12 = 600
5x = 600×12
x = 600×12/5 = 120×12 = $1440
he gave to his mother
(1/4) × 1440 = $360
Find the volume of the composite solid. 12 m I 8 m 4 m 4 m
Answers
Answer:
1536
Step-by-step explanation:
12 x 8 x 4 x 4
(might be wrong)
Find the probability of rolling a 6 -sided dice and getting a number that is a divisor of 20.
Answers
Explanation:
On the die, the divisors or factors of 20 are: 1, 2, 4, 5
We have 4 faces we want out of 6 faces total
So 4/6 = 2/3 is the probability of getting a divisor of 20.
Which two binomials in part A didn't have an equivalent factored form? What made these expressions different from the
three that you could factor?
The two that didn’t have equivalent factored forms were x^2+16 and 16x^2+9
Answers
Answer:
The binomials 16x2 + 9 and x2 + 16 didn’t have an equivalent factored form. Both are sums of perfect squares instead of differences.
Step-by-step explanation:
Official answer
Problem #2
Only seven of the 12 months of the year have 31 days. Which decimal is equivalent
to the fraction of months that have 31 days?
O 0.31
O 0.416
O 0.583
O 0.712
Answers
Fractions can be converted to decimals and vice versa.
The decimal equivalent of the fraction of months with 31 days is 0.583
Given:
\(Total = 12\) --- months in a year
\(Months = 7\) --- months with 31 days
The fraction (n) of months with 31 days is:
\(n = \frac{Months}{Total}\)
So, we have:
\(n = \frac{7}{12}\)
The decimal equivalent is:
\(n = 0.583\)
Hence, (c) is correct.
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The length of a bacterial cell is about 5 x 10−6 m, and the length of an amoeba cell is about 3.5 x 10−4 m. how many times smaller is the bacterial cell than the amoeba cell? write the final answer in scientific notation with the correct number of significant digits. 1.4 x 101 7 x 101 143 x 101 7 x 103
Answers
The bacterial cell is about 7 × 10^(1) times smaller than the amoeba cell in scientific notations.
What are scientific notations?
Scientific notations are a way of representing either a very small or a very large number in the powers of 10. Scientific notations comprise digits from 1 to 9 with powers of 10.
Calculation of the amount by which a bacterial cell is smaller than the amoeba cell
Given the length of amoeba cell in scientific notations is 3.5 × 10^(- 4)
The length of a bacterial cell in scientific notations is 5 × 10^(- 6)
To obtain how small the bacterial cell is from the amoeba cell, we need to divide both the lengths i.e.
= 3.5 × 10^(- 4) / 5 × 10^(- 6)
= 0.7 × 10^(2)
= 7 × 10^(1)
Hence, the bacterial cell is about 7 × 10^(1) times smaller than the amoeba cell in scientific notations.
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$600 is invested for a year. If the yearly interest rate
is 7.5%, how much interest is earned in one year?
Answers
Answer:
45
Step-by-step explanation:
Answer:
45
Step-by-step explanation:
15x+7y=5 find the y-intercept
Answers
So 15(0) + 7y = 5
7y = 5 (divide by 7)
Y = 5/7
Answer:
slope: -15/7
intercept: ( 0, 5/7)
Step-by-step explanation:
Can someone help me with several questions?
1.) [-1] -[0]
2.) [2.8]+ [2.8]
3. [-3/4] - [1/4]
4.[6] - [-6]
that's it if u can give the explanation that would be great
Answers
Answer:
1.) -1
2.) 5.6
3.) -1
4.) 12
a random sample of 25 was drawn from a normal distribution with a standard deviation of 5. the sample mean is 80. determine the 95% confidence interval estimate of the population mean.
Answers
Answer:
For A, the confidence interval formula above cannot be applied because n is less than 30, so we use the t-score confidence interval value
C.I = Mean ± t score × Standard deviation/√n
Mean = 80
Standard deviation = 5
n = 25
Degree of freedom = 25 - 1 = 24
Hence, 95% confidence interval degree of freedom t score = 2.064
Hence, Confidence Interval =
80 ± 2.064 × 5/√25
80 ± 2.064 × 1
80 ± 2.064
Confidence Interval =
80 - 2.064
= 77.936
80 + 2.064
= 82.064
Confidence Interval: (77.936, 82.064)
If you know the diameter of a circle,
how do you find the following. Explain
the steps clearly
a. the area of that circle?
b. the circumference of the circle?
Answers
Step-by-step explanation:
a. Area of a circle = πr², where r means radius.
Step 1: converted diameter to radius.
diameter = 2 radius
In other way of writing, radius = \(\frac{1}{2}\) diameter.
Step 2: substitute radius into the formula.
Area of a circle = π(\(\frac{1}{2}\)d)²
Step 3: substitute π into the formula.
some question is given the value of π), if not substitute 3.14 for π.
Area of a circle = 3.14(\(\frac{1}{2}\)d)²
Step 4: substitute d into the formula, then we can solve its area.
b. a. Circumference of a circle = 2πr, where r means radius.
Step 1: converted diameter to radius.
diameter = 2 radius
In other way of writing, radius = \(\frac{1}{2}\) diameter.
Step 2: substitute radius into the formula.
C = 2π(\(\frac{1}{2}\)d)
Step 3: substitute π into the formula.
some question is given the value of π), if not substitute 3.14 for π.
C = 2(3.14)(\(\frac{1}{2}\)d)
Step 4: substitute d into the formula, then we can solve its circumference.
4. Bob spent $30 playing paintball which
included a $16 entry fee and $3.50 per hour of
play. How many hours did Bob play?
Answers
Answer: 4 hours
Step-by-step explanation:
First, set up an equation. We know that Bob spent $30 on playing paintball so we use that as our 'answer.' We need to find how many hours Bob played so we need to use x, a variable to find it. We also add 16 because we need to account for the entry fee.
3.50x + 16 = 30
Secondly, solve for x. Move 16 across the equal sign(=). Every time you move across the =, you're going to want to change the sign (if it's addition or subtraction). Since it was +16 and we're moving it, it's now -16.
3.50x = 30 - 16
Calculate 30 - 16 = 14.
Now we have
3.50 x = 14.
To calculate x, we're going to need to divide 3.50 from x. Since we multiplied by x we need to do the opposite across the =.
x = 14 / 3.50
x = 4
Bob spent 4 hours playing paintball.
You can plug it in to check answers as well
3.50 (4) +16 = 30
please help me with this!
Answers
10+10+6+6+15+15= 62 units^2
what the answer to 1024/32
Answers
Answer:
32
Step-by-step explanation:
a newsletter publisher believes that more than 51% of their readers own a personal computer. is there sufficient evidence at the 0.05 level to substantiate the publisher's claim? state the null and alternative hypotheses for the above scenario.
Answers
Answer: The null hypothesis for this scenario is that the proportion of readers who own a personal computer is 0.51 or less:
H0: p <= 0.51
The alternative hypothesis is that the proportion of readers who own a personal computer is greater than 0.51:
Ha: p > 0.51
To test this hypothesis, we would need to collect a random sample of readers and determine the proportion of readers who own a personal computer in the sample. We could then use a one-sample proportion test to determine whether the proportion in the sample is significantly different from the null hypothesis value of 0.51. If the p-value is less than 0.05, we would reject the null hypothesis and conclude that there is sufficient evidence to substantiate the publisher's claim that more than 51% of their readers own a personal computer. If the p-value is greater than or equal to 0.05, we would fail to reject the null hypothesis and conclude that there is not sufficient evidence to substantiate the publisher's claim.
Step-by-step explanation:
A restaurant surveys customers with the following results: 8 pizzas, 12 hamburgers, 14 pastas, and 6 steaks. What is the experimental probability of pizza or steak?P(pizza or steak)
Answers
Answer:
To find the experimental probability you have to find the number of times the event occurred and the number of times the activity is preformed then divide the two numbers
Step-by-step explanation:
I’m not quite sure on the answer I believe it’s 1.3
have a great day!
brainliestif correct I need 4 more to rank up thanks!
Sue has a crate, open at the top, in the shape of a cuboid. The internal dimensions of the crate are 36cm long by 36cm wide by 60cm high. Sue has a stick of length 90cm. She places the stick in the crate so that the shortest possible length extends out above the top of the crate. A) Calculate the length of the stick that extends out of the crate. B) Calculate the angle the stick makes with the base of the crate.
Answers
Answer:
Step-by-step explanation:
When the stick is placed along the diagonal of the cuboid , shortest possible length will extend out above top of the crate .
Length of the diagonal
= \(\sqrt{36^2+36^2+60^2}\)
= 78.69 cm
the length of the stick that extends out of the crate
= 90 - 78.69
= 11.31 cm
If θ be the angle made by stick with the base
cosθ = hypotenuse of base / diagonal of cuboid
=\(\frac{\sqrt{2}\times36 }{78.69}\)
= \(\frac{50.90 }{78.69}\)
θ = 50°
Answer: This is the answer to B) 47.9 degrees
Step-by-step explanation:
Pythagoras: a^2+b^2=c^2
36²+36²=C²
√2592=C
C=50.9cm
Used Trigonometry: SOH CAH TOA
Tan=Opposite/Adjacent
Tan=60/50.9
The angle stick makes when it meets the base:
Tan^-1(60/50.9)
=49.7˚
A firm issues three-month commercial paper with a $1000000
face value and pays an EAR of 7.4%. What is the amount the firm
receives?
Answers
If firm issues commercial paper with $1000000 face-value and pays EAR of 7.4%, then amount the firm will receive is $981500.
To calculate the amount the firm receives from issuing the three-month commercial paper, we need to determine the total interest earned over the three-month period.
The Effective Annual Rate (EAR) of 7.4% indicates the annualized interest rate. Since the commercial paper has 3-month term, we adjust the EAR to account for the shorter period.
To find the quarterly interest rate, we divide the EAR by the number of compounding periods in a year. In this case, since it is a 3-month period, there are 4-compounding periods in a year (quarterly compounding).
Quarterly interest rate = (EAR)/(number of compounding periods)
= 7.4%/4
= 1.85%,
Now, we calculate interest earned on "face-value" of $1,000,000 over 3-months,
Interest earned = (face value) × (quarterly interest rate)
= $1,000,000 × 1.85% = $18,500,
So, amount firm receives from issuing 3-month commercial paper is the face value minus the interest earned:
Amount received = (face value) - (interest earned)
= $1,000,000 - $18,500
= $981,500.
Therefore, the amount that firms receives is $981500.
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NEED HELP ASAP - Algebra 2
Answers
The solution to the equation in this problem is given as follows:
y = -4.
How to solve the equation?The equation for this problem is defined as follows:
\(\frac{y - 6}{y^2 + 3y - 4} = \frac{2}{y + 4} + \frac{7}{y - 1}\)
The right side of the equality can be simplified applying the least common factor as follows:
[2(y - 1) + 7(y + 4)]/[(y + 4)(y - 1)] = (9y + 26)/(y² + 3y - 4)
The denominators of the two sides of the equality are equal, hence the solution to the equation can be obtained equaling the numerators as follows:
9y + 26 = y - 6
8y = -32
y = -32/8
y = -4.
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Simplify the following Boolean function using Boolean Algebra rule. F = xy'z' + xy'z + w'xy + w'x'y' + w'xy
Answers
When the above is simplified using Boolean Algebra, we have F = x' + y' + w'xy.
What is the explanation for the above ?
We can simplify the Boolean function F = xy'z' + xy'z+ w'xy + w'x'y' + w'xy using the following Boolean Algebra rules.
Absorption - x + xy = x
Commutativity - xy = yx
Associativity - x(yz) = (xy)z
Distributivity - x(y + z) = xy + xz
Using the above , we have
F = xy'z' + xy'z+ w'xy + w'x'y' + w'xy
= xy'(z + z') + w'xy(x + x')
= xy' + w'xy
= (x' + y)(x' + y') + w'xy
= x' + y' + w'xy
This means that the simplified expression is F = x' + y' + w'xy.
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Awnser???? Pleaseee….
Answers
Answer:
just imagine those as a proportion
\( \frac{x}{7} = \frac{12}{8} \)
\(x = \frac{7 \times 12}{8} = \frac{84}{8} = 10.5\)
Consider the polynomial: StartFraction x Over 4 EndFraction – 2x5 + StartFraction x cubed Over 2 EndFraction + 1 Which polynomial represents the standard form of the original polynomial?
Answers
Answer:
\(- 2x^5+ 0x^4 + \frac{x^3}{2} +0x^2+\frac{x}{4} + 1\)
Step-by-step explanation:
Given
\(\frac{x}{4} - 2x^5 + \frac{x^3}{2} + 1\)
Required
The standard form of the polynomial
The general form of a polynomial is
\(ax^n + bx^{n-1} + cx^{n-2} +........+ k\)
Where k is a constant and the terms are arranged from biggest to smallest exponents
We start by rearranging the given polynomial
\(- 2x^5+ \frac{x^3}{2} +\frac{x}{4} + 1\)
Given that the highest exponent of x is 5;
Let n = 5
Then we fix in the missing terms in terms of n
\(- 2x^5+ 0x^{n-1} + \frac{x^3}{2} +0x^{n-3}+\frac{x}{4} + 1\)
Substitute 5 for n
\(- 2x^5+ 0x^{5-1} + \frac{x^3}{2} +0x^{5-3}+\frac{x}{4} + 1\)
\(- 2x^5+ 0x^{4} + \frac{x^3}{2} +0x^{2}+\frac{x}{4} + 1\)
Hence, the standard form of the given polynomial is \(- 2x^5+ 0x^4 + \frac{x^3}{2} +0x^2+\frac{x}{4} + 1\)
Answer:
Its B
Step-by-step explanation:
Got it right on edu 2022
I will give you 30 points
Answers
1. Three examples of situations where consistency is important:
HealthcareFinancial transactionsSports RulesHow do these portray consistency?Healthcare: when treating patients, healthcare providers must follow consistent procedures and protocols to ensure that every patient receives the same level of care.
Financial transaction: when making financial transactions, it is important to follow regular security rules to prevent fraud.
Support rules: Adherence to consistent rules and regulations in sports is essential to ensure fair play and the safety of all participants.
2. The number 0 is important in mathematical systems because it represents the absence of a number and serves as a placeholder. Without zero, our mathematical system would be affected in many ways. For example, writing the number 100 would be difficult without the zero. Without the invention of zero, progress in mathematics would have been delayed.
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A glass is
1
2
full. Then 65cm3 of orange juice is poured in.
The glass is now
6
7
full. What is the total volume of the glass?
Answers
Answer:
Answer is v=182
Step-by-step explanation:
v=volume of the glass
v/2+65=6v/7
Multiply by 14
7V+910=12V
910=5V
V=182
I hope it's helpful!
find two integers whose sum is -5 and whose product is 4
Answers
Answer:
ooh this hard um...
Step-by-step explanation:
isn't that impossible?
Answer:
-4 and -1
Step-by-step explanation:
a cook starts baking pies at the clock shown below. The first pie is done 25 min later. The 2nd pie is done 30 min later after the first pie which clock shows when the second pie was done
Answers
Answer:
1:45 pm
Step-by-step explanation:
its the hand thats a littke more on the left after 6
a group of ten women and ten men are in a room. if five of the 20 are selected at random and put in a row for a picture, what is the probability that the five are of the same sex?
Answers
The probability that the five selected individuals are of the same sex is 0.252.
To calculate the probability, we need to consider the total number of possible outcomes and the number of favorable outcomes.
Total number of outcomes: The total number of ways to select 5 individuals out of 20 is given by the combination formula, which is denoted as C(20, 5) and is equal to 15504.
Number of favorable outcomes: We need to consider two cases: selecting 5 women or selecting 5 men.
Case 1: Selecting 5 women: The number of ways to select 5 women out of 10 is given by C(10, 5), which is equal to 252.
Case 2: Selecting 5 men: The number of ways to select 5 men out of 10 is also C(10, 5), which is equal to 252.
Therefore, the total number of favorable outcomes is 252 + 252 = 504.
Probability: The probability of selecting 5 individuals of the same sex is the ratio of favorable outcomes to total outcomes. So, the probability is 504/15504 = 0.0325.
The probability that the five individuals selected at random are of the same sex is 0.0325, which is equivalent to approximately 0.252 when expressed as a fraction.
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