Mathematics High School

What is larger: The height of a standard can of tennis balls, or the circumference of its lid?
(Assume the can fits three tennis balls perfectly). Explain your reasoning. ...?

Answers

Answer 1
Circumference of the lid, I think.
Consider the radius as r. Then circumference is 2*pi*r and the height is 6r. 2*pi*r-6r is greater than zero and hence circumference is larger.
Answer 2

Final answer:

The height of a can holding three tennis balls is 20.1 cm, while the circumference of the lid is approximately 21.02 cm. Hence, the circumference of the can's lid is slightly larger than its height.

Explanation:

The question is comparing two different measurements of a can that holds tennis balls. One measurement is the height of the can, and the other is the circumference of the can's lid. In a standard can of tennis balls, three tennis balls are stacked on top of each other perfectly. Knowing that the diameter of a standard tennis ball is approximately 6.7 cm, we can calculate the height of the can by multiplying the diameter of one tennis ball by three (since the diameter is the same as the height for a ball stacked in such a can).

Height of can = Diameter of tennis ball × number of balls
= 6.7 cm × 3
= 20.1 cm.

To determine the circumference of the can's lid, we first need to find the radius of the lid which would be half the diameter of a tennis ball:

Radius of lid = Diameter of tennis ball / 2
= 6.7 cm / 2
= 3.35 cm.

Then, we use the formula for the circumference of a circle, which is C = 2πr:

Circumference of lid = 2π × Radius of lid
= 2π × 3.35 cm
≈ 21.02 cm.

The circumference of the lid is slightly larger than the height of the can. Therefore, the circumference of the can's lid is larger than the height of the can of tennis balls.

Related Questions

What 3 times itself equals 1331?

Answers

So [tex] x^{3} =1331[/tex].
Then, [tex]x= \sqrt[3]{1331} [/tex].
[tex]x=11[/tex]

The answer's 11.

Answer:

11

Step-by-step explanation:

A boy throws a baseball across a field. The ball reaches its maximum height, 18 meters, after 1 second. After approximately 2.3 seconds, the ball lands on the ground. The ball’s motion can be modeled using the function f(x) = –10x2 + 20x + 8. What is the height of the ball 1.5 seconds after it is thrown?

Answers

Answer:

15.5 NOT 17

Step-by-step explanation:

A sneaker store salesman had $4,125 in total monthly sales last month. he made $165 in commission from those sales. what is the salesman's commission as a percent of his total monthly sales?

Answers

He made [tex]\frac{165}{4125}[/tex] as a commission. To turn that into a percentage, you need to make the bottom become 100. Multiply the top and bottom by [tex]\frac{100}{4125}[/tex] to get the proper fraction. The fraction now is [tex]\frac{\frac{16500}{4125}}{100}[/tex] This simplifies to [tex]\frac{4}{100}[/tex]. Now all you need to do is take the top of that fraction to get the percentage, which is 4%.

4%

Tess has 2 1/2 cups of fruit. how many 3/4 cup servings can she make?

Answers

only 3 full servings.

Solve -9-8(1+4h)=-17

Answers

-9-8(1+4h) = -17. We need to solve for h.
First, use the distributive property for 8(1+4h):
8(1+4h) = 8*1 + 8*4h = 8 + 32h

So -9-8(1+4h) = -17
-9 - (8+32h) = -17
-9 - 8 - 32h = -17
-17 - 32h = - 17
Add 17 on both sides to have the variables on a side and the numbers on the other:
-17 - 32h + 17 = -17 + 17
-32h = 0
divide both sides by -32 to get the variable h alone and its value on the other side:
(-32h)/-32 = 0/-32
h = 0.

So -9-8(1+4h) = -17 for h = 0.

You can recheck your answer (very important):
-9 - 8(1+4h) = -9 -8(1+4*0) = -9 - 8(1+0) = -9-8*1 = -9-8 = -17
The answer has been approved.

Hope this Helps! :)
Hi Jeannie

-9-8(1+4h) = -17
First, we need to distribute
-9 +(-8)(1) +(-8)(4h) = -17
-9 -8 - 32h = -17
-17 - 32h = -17
-32h = -17 + 17
-32h = 0
h = 0/-32
h = 0


I hope that's help ! 

If 4(x-2/3)=-18, what is the value of 2x?

Answers

4(x-2/3) = -18
4x - 8/3 = -18
4x = -54/3 + 8/3
4x = -46/3
x = -46/3 * 1/4
x = -46/12
x = -23/2

2x = -23/2 * 2
2x = -46/2
2x = -23

Molly's basic cell phone plan charges $35.99 for service plus $0.21 per minute beyond the included 250 minutes in the plan. How much will it cost if she used her cell phone for 480 minutes in one month? ...?

Answers

The answer is $84.29

Let the number of minutes be x.
$35.99 is fixed price and does not depend on the number of minutes x. Each minute costs $0.21 so it depends on x and we have 0.21x in the function. However, 250 minutes are already included and should not be included in x. Therefore, the function that represents the monthly cost looks like this:
f(x) = 35.99 + 0.21 * (x - 250)

Now, let's calculate for x = 480 minutes:
f(480) = 35.99 + 0.21 * (480 - 250)
f(480) = 35.99 + 0.21 * 230
f(480) = 35.99 + 48.30
f(480) = 84.29

What does the line -5+8y=8 look like?

Answers

Answer:

Is a horizontal line

Step-by-step explanation:

we have

[tex]-5+8y=8[/tex]

Solve for y

Adds [tex]5[/tex] both sides

[tex]-5+8y+5=8+5[/tex]

[tex]8y=13[/tex]

Divide by [tex]8[/tex] both sides

[tex]y=13/8[/tex]

[tex]y=1.625[/tex]

This is a horizontal line parallel to the x-axis

The slope is equal to zero

see the attached figure to better understand the problem


What conditions give 2 roots, one root and no root?

Answers

The discriminant D is found by this formula

D = b^2 - 4ac

there are 3 possible outcomes

1) If D is smaller than 0, ie D < 0, then there are no roots

2) If D is equal to zero (D = 0), then there is exactly one root. This root is rational assuming the coefficients are integers. This is called a double root

3) If D > 0, then there are 2 different roots. If D is a perfect square, then these two roots are rational numbers (aka fractions of whole numbers) assuming the coefficients are integers. If D is not a perfect square, then the two roots are irrational numbers. 

Mr. jones has agreed to borrow $3500 for one year st 10% interest. what is the total amount he will pay back to the bank?

Answers

$ 3500 × 10 /100 × 1 = $ 3850

The total amount Mr. Jones will pay back after borrowing $3500 for a year at 10% interest rate is $3850, simply add the interest to the principal amount borrowed.

Mr. Jones borrowed $3500 for one year at 10% interest rate. The total amount he will pay back to the bank can be calculated as follows:

Interest = Principal x Rate = $3500 x 0.10 = $350

Total amount to be paid back = Principal + Interest = $3500 + $350 = $3850

The area of a trapezoid is given by the formula A =1/2 (b 1 + b 2)h, where base b 1 is parallel to base b 2 and h is the height. Solve the formula for b 2. Show your work.

Answers

The answer is b2 = 2A/h - b1

A = 1/2(b1 + b2)h

Multiply both sides by 2:
2 * A = 2 * 1/2(b1 + b2)h
2A = (b1 + b2)h

Divide both sides by h:
2A/h = (b1 + b2)h/h
2A/h = b1 + b2

Subtract b1 from both sides:
2A/h - b1 = b1 + b2 - b1
2A/h - b1 = b2


The discriminant of a quadratic equation is negative. One solution is 3+4i . What is the other solution?
A.4-3i
B.3-4i
C.4+3i
D.-3+4i

Answers

I hope this helps you



3-4i
The way you stated the problem, there is an infinity of possibilities for the other solution. 

► For instance, the quadratic equation: 
   x² – (6 + 4i)x + (9 + 12i) = 0 
has for discriminant: 
   Δ = (6 + 4i)² – 4(9 + 12i) = 36 – 16 + 48i – 36 – 48i = -16 
which is indeed negative. 
Its solutions will then be: 
   x₁ = [(6 + 4i) + 4i]/2 = 3 + 4i 
   x₂ = [(6 + 4i) – 4i]/2 = 3 
And the other solution here is 3. 

► If you are not convinced, the quadratic equation: 
   x² – (6 + 5i)x + (5 + 15i) = 0 
has for discriminant: 
   Δ = (6 + 5i)² – 4(5 + 15i) = 36 – 25 + 60i – 20 – 60i = -9 
which is indeed negative. 
Its solutions will then be: 
   x₁ = [(6 + 5i) + 3i]/2 = 3 + 4i 
   x₂ = [(6 + 5i) – 3i]/2 = 3 + i 
And the other solution here is 3+i. 

► In fact, every quadratic equation of the form: 
   x² – [6 + (4 + α)i]x + (3 + 4i)(3 + αi) = 0 
where α is any real, has for discriminant: 
   Δ = [6 + (4 + α)i]² – 4(3 + 4i)(3 + αi) 
      = 36 – (4 + α)² + 12(4 + α)i – 36 + 16α – 12(4 + α)i 
      = 16α – (4 + α)² 
      = 16α – 16 – 8α – α² 
      = -16 + 8α – α² 
      = -(α – 4)² 
WILL be negative. 
Their solutions will then be: 
   x₁ = [ [6 + (4 + α)i] – (α – 4)i ]/2 = 3 + 4i 
   x₂ = [ [6 + (4 + α)i] + (α – 4)i ]/2 = 3 + αi 
And the other solution will then be is 3+αi. 

Since α can take any real value, you'll obtain an infinity of solutions of the form 3+αi. 

► So conclusively: 
If the discriminant of a quadratic is negative AND one of the solutions is 3+4i, the only thing we can say about the other solution is that its real part must be 3. 

23 + 45 - 48 + 34 * x = 292


What does x equal

Answers

Solve for x by simplifying both sides of the equation, then isolating the variable.
x = 8
Simplifying
23 + 45 + -48 + 34x = 292

Combine like terms: 23 + 45 = 68
68 + -48 + 34x = 292

Combine like terms: 68 + -48 = 20
20 + 34x = 292

Solving
20 + 34x = 292

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right

Add '-20' to each side of the equation.
20 + -20 + 34x = 292 + -20

Combine like terms: 20 + -20 = 0
0 + 34x = 292 + -20
34x = 292 + -20

Combine like terms:
292 + -20 = 272 34x = 272

Divide each side by '34'.
x = 8

Simplifying x = 8

Hope it helped : )

How many times does 6 go into 87?

Answers

87 ÷ 6
8 ÷ 6 = 1 (remainder 2)
27 ÷ 6 = 4 (remainder 3)
30 ÷ 6 = 5
So it goes in 14 times, but exactly 14.5 times if you want a decimal.

Jill Barkely obtained a 25-year, $460,000 mortgage loan from University Savings and Loan Association with 6% interest. The monthly payment is $2,962.40. For the first payment, find the interest to the nearest cent.

Answers

Have you considered calculating it directly? $2,962.40*(0.06/12)
If you do that then your answer would be 14.81...
Hope this helps...  :)

What is 1 and 3\11 as an improper fraction?

Answers

14/11
11×1 +3 and you will get your answer
What you have to do to find the improper fraction is you ...

•multiply the denominator with the whole number

•add what you got to the numerator

•still use the same denominator


1•11=11
11+3=14

14/11
14/11=1.3/11

Simplify 7x 7 6x - 9.

Answers

7x + 7 + 6x - 9 =13x - 2

Answer:

[tex]13x -2[/tex]

Step-by-step explanation:

7x +7+6x - 9

simplify the given expression

To simplify the given expression we add like terms

the terms that as same variables with same exponent are like terms

7x and 6x are like terms

7x + 6x = 13x

+7 -9 = -2

So expression becomes [tex]13x -2[/tex]

Translate this word phrase into an equation. one increased by two equals the quotient of nine and three

Answers

Here is the equation for this word phrase:
1 + 2 = 9 / 3
Quotient is the result of division. 

Final answer:

The translation of the word phrase into an equation is 1 + 2 = 9 ÷ 3. Solving the equation by performing division before addition verifies its correctness, resulting in 3 = 3.

Explanation:

The word phrase "one increased by two equals the quotient of nine and three" can be translated into an algebraic equation as follows:

1 + 2 = 9 ÷ 3

To solve the equation, perform the division on the right side of the equals sign first, as per the order of operations (PEMDAS/BODMAS), which states that division should be completed before addition:

1 + 2 = 3

Then adding the numbers on the left side:

3 = 3

This confirms that the given translation of the word phrase into an equation is correct, as both sides of the equation are equal.

during a special sale all video games cost $26 & all movied cost $14. Jack plans to spend some or all of his $220 in bday money on these movies & video games.
WRITE AN INEQUALITY

Answers

$26g + $14m ≤ $220

g represents the number of video games bought
m represents the number of movies bought
Final answer:

The inequality that represents Jack's budget constraints for purchasing video games and movies is 26x + 14y ≤ 220, where x is the number of video games and y is the number of movies.

Explanation:

To write an inequality representing Jack's spending on movies and video games with the given budget, we first assign a variable to the quantity of each item Jack could purchase. Let x represent the number of video games and y represent the number of movies. Since video games cost $26 each and movies cost $14 each, and Jack has $220 to spend, the inequality representing this scenario is:

26x + 14y ≤ 220

Here, x and y must be non-negative integers because you cannot purchase a negative amount or a fraction of a game or movie. This inequality ensures that the total amount spent on video games and movies does not exceed Jack's budget of $220.

Louann and Carla received equal scores on a test made up of multiple choice questions and an essay. Louann got 14 multiple choice questions correct and received 24 points for her essay. Carla got 16 multiple choice questions correct and received 14 points for her essay.

How many points was each multiple choice question worth?

Answers

Let the number of points of each multiple choice question be x, then
14x + 24 = 16x + 14
16x - 14x = 24 - 14
2x = 10
x = 10/2 = 5.

Therefore, each multiple choice question is 5 marks.

How many faces does a rectangle have?

Answers

4 because it has four sides
Would you many rectangular prism?
If so it would be 6 just like a cube

During a period of deflation, the graph of the consumer price index (CPI) will rise.

A. True
B. False ...?

Answers

The correct answer for this statement would be option B. FALSE. It is not true not during a period of deflation, the graph of the consumer price index or CPI will rise, but rather, it would show a downward pattern. The consumer price index measures changes in the price level of a market basket of consumer goods and services. Hope this answer helps. 

Final answer:

The statement is false; during a period of deflation, the Consumer Price Index (CPI) would decrease, not rise, reflecting a decrease in the average level of prices.

Explanation:

The answer to the student's question is B. False. During a period of deflation, the Consumer Price Index (CPI) would not rise; it would actually decrease. This is because deflation is characterized by a decrease in the average level of prices. For instance, during the Great Depression, a notable period of deflation, the CPI in the United States fell from 17.2 in 1929 to 12.9 in 1933, illustrating a decline in the general price level. Conversely, inflation will cause the CPI to rise because it reflects an increase in prices over time.

The Consumer Price Index is an economic indicator often used to measure inflation or deflation in an economy. A rise in CPI indicates inflation, whereas a drop indicates deflation. As inflation and deflation affect the real value of money, observing the changes in the CPI helps to understand the purchasing power of currency over time.

525.4 is 74% of what number

Answers

Let, that number = x
It would be: x * 0.74 = 525.4
x = 525.4 / 0.74
x = 710

So, the number would be 710

Hope this helps!

An angle measures 41 degrees. What is the measure of its complement?

Answers

This angle is called and acute angle.
Hope This Helps!!
:)
49 is the answerfawertgsdrgeatat4w3

An isosceles trapezoid has shorter base of measure a, longer base of measure c, and congruent legs of measure b. The perimeter of the trapezoid is 58 inches. The average of the bases is 19 inches and the longer base is twice the leg plus 7. Find the lengths of the sides.

Answers

Perimeter of the trapezoid = a + c + 2b
58 = a + c + 2b

Average of bases = (a + c)/2
19 = (a + c)/2
a + c = 38
Substituting (a + c) into the first equation:

58 = 38 + 2b
b = 10 in

We also know that:
c = 2b + 7
c = 2(10) + 7
c = 27 in

a + 27 = 38
a = 11 in

a = 11 in; b = 10 in; c = 27 in

What are the coordinates of the focus of the conic section shown below?

y^2-4x+4y-4=0



...?

Answers

the answer is 
y^2-4x+4y-4=y^2+4y-4x-4=(y+2)²-4x - 8= 0
it is the same of    x + 2 = (1/4 ) (y+2)²
   
the main formula is  x-h= a (y-k)² so h=-2, k= - 2 and a=1/4

Answer:

(-1,-2) is the correct answer

Step-by-step explanation:

The elevation of park city Utah is 6900 feet above sea level.What integer represents the elevation

Answers

6900 is an integer. This might be a trick question.
Final answer:

The elevation of Park City, Utah is presented as 6900 feet above sea level. Therefore, the integer that symbolizes this elevation is +6900, considering that elevation position above sea level is depicted by a positive integer.

Explanation:

The elevation of Park City, Utah is indicated as 6900 feet above sea level. As an integer, such elevation is simply represented by the number 6900. An integer is a whole number that can be either greater than 0, termed positive, 0, or less than 0, termed negative. In this scenario, the elevation above sea level is higher than 0. It means the integer representing the elevation is a positive integer. So, the elevation, as an integer, of Park City, Utah is +6900.

Learn more about Positive Integer here:

https://brainly.com/question/18380011

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A student studying for a vocabulary test knows the meanings of 16 words from a list of 26 words. If the test contains 10 words from the study list, what is the probability that at least 8 of the words on the test are words that the student knows? (Round your answer to three decimal places.)

Answers

To get the probability that at least 8 of the words on the test are words that students know we need to do the following calculations.

=[C(16,8)*C(10,2) + C(16,9)*C(10,1) + C(16,10)*C(10,0)] / C(26,10)

=0.132 
Final answer:

To find the probability that at least 8 of the words on a 10-word test are known by a student, calculate the probabilities for exactly 8, 9, and 10 known words and sum them. Use combinations to determine the probabilities and round the final answer to three decimal places.

Explanation:

The student knows 16 words out of 26, and the test contains 10 words. To find the probability that at least 8 out of 10 words on the test are known to the student, we need to calculate the probability for exactly 8, 9, and 10 known words, using combinations, and then sum these probabilities.

Let's denote K as knowing the word and N as not knowing the word. The total number of ways to choose 10 words out of 26 is given by 26 choose 10, denoted as C(26,10).

The probability of getting exactly 8 known words is given by (C(16,8) * C(10,2)) / C(26,10).

The probability of getting exactly 9 known words is (C(16,9) * C(10,1)) / C(26,10).

The probability of getting all 10 known words is (C(16,10) * C(10,0)) / C(26,10).

We add these probabilities together to get the total probability that the student knows at least 8 out of 10 words:


 P(8 known words) = (C(16,8) * C(10,2)) / C(26,10)
 P(9 known words) = (C(16,9) * C(10,1)) / C(26,10)
 P(10 known words) = (C(16,10) * C(10,0)) / C(26,10)

We sum these individual probabilities to obtain the final answer. The result should be rounded to three decimal places as per the instructions given in the question.

Learn more about Probability here:

https://brainly.com/question/32117953

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Find the slope the line that contains (2,4) and (4,4)

Answers

4+4/4+2    =4/3 ...The answer is this 
Slope between points (x,y) and (a,b) is given by( b-y) over (a-x).. Thus4-4 over 4-2 equals 0 is your answer... The line joining these two above points is parallel to X axis or perpendicular to y axis .on y axis this line intersects at (0,4)...

2x -3 =6

Value of x

Help_

Answers

2x - 3 = 6
2x = 6 + 3
2x = 9
x = 9/2
x = 4.5

The value of x is 4.5
Add 3 to both sides 

[tex]2x=6+3 [/tex] 

Simplify 6+3 to 9 

[tex]2x=9[/tex] 

Divide both sides by 2

[tex]x=9/2[/tex]
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