Answer:
5.5
Step-by-step explanation:
You are to construct a€cylindrical can out of tin that encloses a volume of exactly 100 cubic inches. to three significant figures, which dimensions (r and h) will give you the tin can that requires the least amount of metal?
The formula for volume of cylinder is:
V = π r^2 h
since volume is 100 cubic inches, so:
100 = π r^2 h
Rewriting in terms of h:
h = 100 / π r^2
The least amount of metal means least amount of surface area needed. The surface area of cylinder is:
A = 2 π r h + 2 π r^2
insert the value of h in terms of r:
A = 2 π r (100 / π r^2) + 2 π r^2
A = 200 r-1 + 2 π r^2
Take the 1st derivate and set to 0, dA/dr = 0:
dA/dr = - 200 r-2 + 4 π r
0 = - 200 r-2 + 4 π r
200 / r^2 = 4 π r
r^3 = 50 / π
r = 2.52 inches
So height h is:
h = 100 / π r^2
h = 100 / π (2.52)^2
h = 5.01 inches
Answers:
r = 2.52 inches
h = 5.01 inches
A bag contains 3 yellow, 1 red, and 2 green beads. Charlene draws a bead, keeps it out, then draws another bead. What’s the probability that Charlene drew the red bead, then a green bead? Write your answer in simplified form.
I NEED HELP ASAP WILL GIVE 50 POINTS!!!
This diagram shows a pre-image
△ABC, and its image, A′′B′′C′′, after a series of transformations.
Select from the drop-down menus to correctly complete the statements.
△ABC is rotated 180 degrees about the origin to become △A'B'C'. Then △A'B'C' is translated 3 units down to become △A"B"C". Because the transformations are both rigid, the pre-image and image are congruent.
In Euclidean Geometry, the mapping rule for the rotation of a geometric figure about the origin by 180° in a clockwise or counterclockwise direction can be modeled by the following mathematical expression:
(x, y) → (-x, -y)
Point A (1, -1) → Point A' (-1, 1)
Point B (4, -2) → Point B' (-4, 2)
Point C (7, 2) → Point C' (-7, -2)
Next, we would apply a translation 3 units down to the new figure (△A'B'C'), in order to determine the coordinates of its image as follows;
(x, y) → (x, y - 3)
A' (-1, 1) → (-1, 1 - 3) = A" (-1, -2).
B' (-4, 2) → (-4, 2 - 3) = B" (-4, -1).
C' (-7, -2) → (-7, -2 - 3) = C" (-7, -5).
Therefore, the resulting figure must be located in the third quadrant as illustrated in the diagram shown above.
The length of a rectangle is 4 inches greater than the width. The perimeter of the rectangle is 24 inches. What are the dimensions of the rectangle?
length = 12 in.; width = 8 in.
length = 8 in.; width = 6 in.
length = 8 in.; width = 4 in
length = 6 in.; width = 2 in.
By using the formula for the perimeter of a rectangle and substitution, it is determined that the dimensions of the rectangle are 6 inches for the length and 2 inches for the width.
Explanation:This is a traditional problem in algebra that we can solve using known formulas and principles.
The perimeter of a rectangle is calculated using the formula 2(l+w), where 'l' stands for length and 'w' stands for width. In this problem, we know the perimeter (P) is 24 inches, and we know the length (l) is the width (w) + 4 inches.
We can set up and solve an equation using these facts. Replace 'l' in the equation with '(w + 4)' and solve for 'w': 2[(w + 4) + w] = 24, which simplifies to 2w + 8 = 12, and finally, w = 2.
Having found 'w', we can find 'l' by substituting 'w' in our equation of 'l', l = w + 4 = 2 + 4 = 6.
Therefore, the length is 6 inches and the width is 2 inches.
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How many ways are there to choose a dozen donuts from 21 varieties?
The drama club at smith valley middle school is selling cookie dough in order to raise money for costumes. if each tub cookie dough costs $4.75, how many tubs must members sell to make $570.00?
Jack's mother gave him 505050 chocolates to give to his friends at his birthday party. He gave 333 chocolates to each of his friends and still had 222 chocolates left.
Write an equation to determine the number of friends (x)(x)left parenthesis, x, right parenthesis at Jack's party.
Find the number of friends at Jack's party.
16
This seems to have been miswritten. So I went ahead and just put it as 50, 3 and 2Okay, so Jack started with 50 chocolates and ended with 2.
The simple way to calculate it would be by realizing that Jack only distributed 48 chocolates. We can find how many times 3 fits into 48 by dividing 48÷3=16.
Using algebra, we substitute the value we want to find with x. Here what we want to find is the number of friends that were at Jack's party.
We know that he started with 50 chocolates, then distributed 3× the number of friends present (which is x).
We write that down as 50−3x
(It's minus because when chocolates are distributed, Jack is taking away from what he has.)
We know that after this, there were only 2 chocolates left, so it's
50−3x=2
Then we proceed by moving all the numbers to the right until only x is left:
−3x=2−50
−3x=−48
x=−48−3
x=16
Conclusion: The number of people that attended the party was 16.
Answer:
The equation is 3x+2=50
There were 16 friends at Jack's party.
Step-by-step explanation:
I JUST TOOK THE TEST
Find the next two numbers in the sequence 1, 5, 17, 53, 161, _____, _____
The required missing term of the given sequence is given as 485 and 1457.
What is a sequence?The sequence is a pattern of placing the values in a specified manner.
here,
5 = 1 + 4
Since, [tex]b_0 = 4[/tex] and [tex]a_0 = 1[/tex]
17 = 5 + 12
So, the general term is given as
[tex]a_n = a_{n-1} + b_{n}[/tex]
Where, [tex]b_n = 3b_{n-1}[/tex]
For 6 th term
6 the term = 161 + 3(108)
6 the term = 485
For the 7th term
7th term = 485 + 3(324)
7th term = 1457
Thus, the required missing term of the given sequence is given as 485 and 1457.
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The following are two sets of class scores (you may consider these scores to be normally distributed). Julia received the two scores marked with an asterisk. Did she do better or worse on the second test? Why? (16 points) First Test 48 *56 61 60 39 49 5 57 52 51 Second Test 75 81 63 *74 59 88 77 79 76 69 67
First let’s find the mean and standard deviation for both test and then we can calculate the probability of getting that score in his respective test and compare.
First test
P(x < 56)
P(z < 56-47.80/16.38)
P(z<0.50) = 1 – 0.3085 = 0.6915 or 69 percentile
Second test
P(x < 74)
P(z < 74 – 73.45 / 8.37)
P(z<0.07) = 1 – 0.4721= 0.5279 or 53 percentile
The probability for this normal distribution also means the percentile, so we can say that in the first test she was in the 69 percentile while in the second test she was in the 53 percentile. Therefore, she did worse in the second test
Julia did better on the first test compared to the second test.
Explanation:To determine whether Julia did better or worse on the second test, we need to compare her score on the first test with her score on the second test. For the first test, Julia received a score of 56 and for the second test, she received a score of 74. To determine which score is better, we can compare their positions in the distribution of scores.
First, we can calculate the mean and standard deviation of the scores for each test. For the first test, the mean is 49.9 and the standard deviation is 12.8. For the second test, the mean is 73.6 and the standard deviation is 7.3.
Next, we can calculate the z-scores of Julia's scores on each test. A z-score represents the number of standard deviations a data point is from the mean. For the first test, Julia's z-score is 0.16, and for the second test, her z-score is -0.2538.
Since a higher z-score indicates a better performance relative to the mean, Julia did better on the first test than the second test.
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Ethan buys a video game on sale. If the video game usually costs $39.99, and it was on sale for 20% off, how much did Ethan pay?
Ethan paid $31.99 for the video game on sale.
How to calculate the discount?To calculate the discount that Ethan obtained in the price of his video game, we do the following operations:
We divide the total price by one hundred and multiply the result by the discount, in this case 20.
$39,99 ÷ 100 = $0,3999$0,3999 × 20 = $7,998Subsequently, we subtract the result of the previous operation (value of the discount) from the total value of the video game.
$39,99 - $7,998 = $31,992
According to the above, the value that Ethan paid for the video game was $31,992
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Answer: $31.99
Step-by-step explanation:
$39,99 ÷ 100 = $0,3999
$0,3999 × 20 = $7,998
$39,99 - $7,998 = $31,992
Please help me!!
Solve for B:
C = sqrt(A^2 + B^2)
c^2 = a^2+b^2 now subtract a^2 from both sides
c^2 - a^2 = b^2 Now take the square root of both sides
b = +- sqrt(c^2-a^2)
Final answer:
To solve for B in the equation C = sqrt(A^2 + B^2), you square both sides of the equation, subtract A^2 from both sides, and then take the square root of the result to find B = sqrt(C^2 - A^2).
Explanation:
The equation C = sqrt(A^2 + B^2) is representative of the Pythagorean theorem, which is used in mathematics to relate the sides of a right triangle. To solve for B, we must isolate B on one side of the equation. Here's how you can do it:
Begin with the equation C = sqrt(A^2 + B^2).Square both sides of the equation to eliminate the square root, getting C^2 = A^2 + B^2.Subtract A^2 from both sides to get B^2 = C^2 - A^2.Finally, take the square root of both sides to solve for B, which gives B = sqrt(C^2 - A^2).This gives us the magnitude of B in terms of A and C.
you place a 3 3/8 pound weight on the left side of a balance scale and a 1 1/5 pound weight on the right side of a balance. How much weight do you need to add right side to balance the scale?
Answer:
[tex]2\frac{7}{40}[/tex] pounds
Step-by-step explanation:
Given information:
Weight on the left side = [tex]3\frac{3}{8}[/tex] pounds
Weight on the right side = [tex]1\frac{1}{5}[/tex] pounds
We need to balance both sides.
Let x be the weight which is added to the right side to balance the scale.
[tex]3\frac{3}{8}=1\frac{1}{5}+x[/tex]
[tex]\frac{24+3}{8}=\frac{5+1}{5}+x[/tex]
[tex]\frac{27}{8}=\frac{6}{5}+x[/tex]
Subtract 6/5 from both sides.
[tex]\frac{27}{8}-\frac{6}{5}=x[/tex]
[tex]\frac{135-48}{40}=x[/tex]
[tex]\frac{87}{40}=x[/tex]
[tex]2\frac{7}{40}=x[/tex]
Therefore, [tex]2\frac{7}{40}[/tex] pounds weight is added to the right side to balance the scale.
If two standard six-sided dice are tossed, what is the probability that a 5 is rolled on at least one of the two dice? express your answer as a common fraction.
1/12 is the probability that a 5 is rolled on at least one of the two dice
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
Given that two standard six-sided dice are tossed,
We need to find the probability that a 5 is rolled on at least one of the two dice.
When we roll two dice there is a possibiltiy of 36 outcomes.
In these 36 outcomes atleast one of the dice should show 5.
There are 36 possible rolls
(5, x), (x, 5) and (5, 5) are the possible outcomes with 5 on any of the dice.
x represents any number from one to five.
So the probability that a 5 is rolled on at least one of the two dice is 3/36
which is equal to 1/12.
Hence, 1/12 is the probability that a 5 is rolled on at least one of the two dice
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Please answer as soon as possible.
Eric downloads a coupon for 10% off. He bought a camera for 95 dollars and an extra battery for 15.99 dollars.
a: what is the total cost if the coupon is applied to the digital camera
b: What is the total cost if the coupon is applied to the extra battery
c: To witch item should Eric apply the discount? explain
d: Eric has to pay 8% sales tax after the coupon is applied. How much is his total bill?
The basal energy rate is the daily amount of energy (measured in calories) needed by the body at rest to maintain body temperature and the basic life processes of respiration, cell metabolism, circulation, and glandular activity. As you may suspect, the basal energy rate differs for individuals, depending on their gender, age, height, and weight. The formula for the basal energy rate for men is 4072-01-02-03-00_files/i0270000.jpg, where B is the basal energy rate (in calories), W is the weight (in kilograms), H is the height (in centimeters), and A is the age (in years). A male patient is 70 years old, weighs 55 kilograms, and is 172 centimeters tall. A total daily caloric intake of 1000 calories is prescribed for him. Determine if his caloric intake is sufficient for his needs and explain why or why not.
Belinda keeps a record of her expenses for the week as shown: Bus fare $8.70 Lunch out $7.35 Hair cut $16 Movie rental $5.95 What is the total of Belinda’s expenses for the week? a. $22.16 b. $23.60 c. $37.90 d. $38.00 Please select the best answer from the choices provided A B C D
Final answer:
Belinda's total expenses for the week are the sum of her bus fare, lunch out, hair cut, and movie rental, which adds up to d. $38.00.
Explanation:
To calculate the total of Belinda's expenses for the week, we should add up each of the expenses mentioned. This includes the bus fare, lunch out, hair cut, and movie rental. Here's how we do it step-by-step:
Bus fare: $8.70Lunch out: $7.35Hair cut: $16.00Movie rental: $5.95Now, let's add them up:
$8.70 (Bus fare) + $7.35 (Lunch out) + $16.00 (Hair cut) + $5.95 (Movie rental)
When we sum these amounts, we get $8.70 + $7.35 + $16.00 + $5.95 = $38.00.
Therefore, the total of Belinda's expenses for the week is $38.00, which corresponds to option D.
Greatest common factor
Take a look at the figure. What is the value of y?
A. y = 32 B. y = 64 C. y = 14 D. y = 16
Determine the graph
An isosceles right triangle has leg lengths of 4 centimeters. What is the length of the altitude drawn from the right angle to the hypotenuse?
How do you convert 0.45 (45 being repeated) to a fraction?
Sam deposited $350 into a savings account that paid 5% in simple interest. When he withdrew his money 8 months later, how much interest did he receive?
What is 435 000 in standardform?
A car was moving 110 km/h how long did it take to go 25.5 miles?
A bracelet was marked up $50 from cost, which amounts to a 20% increase. Find the original cost of the bracelet.
What is the quotient?
158÷(−135)
Enter your answer as a mixed number, in simplified form, in the box.
Answer:
the answer is -1 1/64
Step-by-step explanation:
i have k12
Answer:
got 80 percent cuz i missed this :l
Step-by-step explanation:
15 3/4 is the right hope it help
Look at ΔABC. Which triangle is congruent to ΔABC by the ASA criterion? triangle 1 triangle 2 triangle 3 triangle 4
Answer:
Triangle 4
Step-by-step explanation:
Congruent triangles are identical in all aspects. They have identical sides and angles.
The ASA the Angle Side Angle criterion.
Congruent triangles should be able to "close up" on each other if one triangle is placed on top of the other. Let's look at the triangle in question.
The triangle ABC is made distinct by the lines on it.
The lines mark the different angles on the triangle.
By looking at the triangle and comparing, Triangle satisfies the ASA criterion
Every square is a rectangle.
always
never
sometimes
Winnie Pooh Boo Boo
Needs help
:P XD
YEEET im so hyper right know
Answer:
Always! I mean that is easy...
Step-by-step explanation:
john and brian work for a toy manufacturers putting stuffing in teddy bears. On average, john can stuff x teddy bears in one day and brian can stuff y in one day. They both the same number of days,t. What does the expression (x +y)t represent? A. the number of teddy bears John can stuff in t days B.the number of teddy bears Brian can stuff in t days C. the number of teddy bears John and Brian can stuff in t days D.the number of teddy bears John and Brian can stuff in one day
Answer:
C
Step-by-step explanation:
Because The Equation Represents how many of those thingy's were stuffed
How many sides does a polygon have if the sum of its interior angles is 2340?