Answer:
a) The volume of the water is approximately 678.6 cm³.
b) The volume of the sphere is approximately 113.1 cm³.
c) The new height of the water is approximately 7 cm, one cm higher than before.
Step-by-step explanation:
To solve this problem we first need to calculate the volume of the water, which is given by the cylinder volume, since it's stored in a cylindrical container.
[tex]\text{water volume} = \pi*r^2*h\\\text{water volume} = \pi*(6)^2*6\\\text{water volume} = \pi*36*6\\\text{water volume} = 678.584 \text{ }cm^3\\[/tex]
We now need to calculate the volume of the sphere, by using the appropriate formula:
[tex]\text{volume sphere} = \frac{4}{3}\pi*r^3\\\text{volume sphere} = \frac{4}{3}\pi*(3^3)\\\text{volume sphere} = \frac{4}{3}\pi*27\\\text{volume sphere} = 113.09 \text{ } cm^3[/tex]
When the sphere is inserted into the cylinder the volume of the things that are inside of the container are added up, so the volume would be the volume of the water plus the volume of the sphere, we can use this information to calculate the height of the water as shown below:
[tex]\text{total volume} = \text{water volume} + \text{sphere volume}\\\text{total volume} = 678.6 + 113.1 = 791.7\\\text{total volume} = \pi*r^2*h_{new}\\791.7 = \pi*(6)^2*h_{new}\\h_{new} = \frac{791.7}{\pi*36} = 7.00016\text{ } cm[/tex]
a) The volume of the water is approximately 678.6 cm³.
b) The volume of the sphere is approximately 113.1 cm³.
c) The new height of the water is approximately 7 cm, one cm higher than before.
!!!WILL MARK THE BRAINIEST!!!
Find the product. Write your answer in exponential form 4^-8 x 4^0
Answer:
[tex]1/65536[/tex]
Step-by-step explanation:
[tex]4^-8 \times 4^0[/tex]
[tex]1/4^8 \times 1[/tex]
[tex]1/4^8[/tex]
[tex]=0.00001525878[/tex]
Answer:
[tex]\frac{1}{4^{8} }[/tex] or [tex]4^{-8}[/tex] but the correct way would be [tex]\frac{1}{4^{8} }[/tex]
Step-by-step explanation:
Last time I did this I was like in 8th grade so I had to watch a video lol, but basically... If you want the answer to stay in exponential form and if the base number is the same than all you gotta do is add or subtract the exponents.
-8+0=-8
But when it's a negative exponent you gotta make it positive by flipping it, so instead of [tex]4^{-8}[/tex] it will be [tex]\frac{1}{4^{8} }[/tex]
Solve this inequality; 4.2x+5.6<7.2 - 8.3x isolate the constant term on the left side odf the inequality by.................... Both sides of the inequaity
Answer:
x < 0.128
Step-by-step explanation:
The inequality given is:
4.2x + 5.6 < 7.2 - 8.3x
Let us collect like terms:
4.2x + 8.3x < 7.2 - 5.6
12.5x < 1.6
=> x < 1.6/12.5
x < 0.128
What is the solution to the system of equations 2x + 3y = 40 and y = x +
10?
oy - y - 12
Answer:
hope this is correct
Which describes the difference between the two sequences?
First Sequence: 1/4,1/2,1,2
Second Sequence1/2,2,8,32
Answer:
The first sequence has a common ratio of 2 while the second sequence has a common ratio of 4.
Step-by-step explanation:
Given the two sequences
[tex]\text{First Sequence:} \dfrac14, \dfrac12,$1, 2\\Second Sequence:\dfrac12$ , 2, 8, 32[/tex]
By observation:
In the first sequence:
[tex]\dfrac14 \times 2 = \dfrac12\\\dfrac12 \times 2 =1\\1 \times 2=2\\[/tex]
In the second sequence
[tex]\dfrac12 \times 4 =2\\ 2 \times 4=8\\8 \times 4=32[/tex]
We can see that both sequences are geometric sequences.
However, the first sequence has a common ratio of 2 while the second sequence has a common ratio of 4.
Solve each problem by forming a pair of simultaneous equations:
Find two numbers with a sum of 15 and a difference of 4.
Answer:
5.5, 9.5
Step-by-step explanation:
Let x and y be the numbers
x+y = 15
x-y = 4
Add the two equations together to eliminate y
x+y = 15
x-y = 4
------------------
2x = 19
Divide by 2
2x/2 =19/2
x = 9.5
Now find y
x+y = 15
9.5+y = 15
Subtract 9.5
x = 15-9.5
x =5.5
Answer:
11/2 and 19/2
Step-by-step explanation:
We have to make a system of equations:
1) X + Y = 15
2) X - Y = 4
Working on the first one:
X = 15 - Y
And now let's plug it in the second one:
(15 - Y) - Y = 4
15 - 2Y = 4
2Y = 11
Y = 11/2
Let's substitute this in one of the two equations:
X + 11/2 = 15
X = 19/2
Luca decides to play Wheel of Letters. To play the game, contestants spin a wheel with 26 equal sections, lettered A through Z. If the pointer lands on any letter in the phrase "County Fair," the contestant wins a prize. What is the probability that Luca will win Wheel of Letters? Your answer must be simplified
Answer:
10/26, simpified to 5/18
Step-by-step explanation:
10 letters in "County Fair" None repeat.
26 letters in the alphabet
10/26
5/18
WILL MARK BRAINLIEST!! Lorri took a 240 km trip to Waterloo. On her way there, her average speed was 120 km/h. She was stopped for speeding, so on her way home, her average speed was 80 km/h. What was her average speed, in km/h, for the entire round-trip?
Answer: Her average speed was 480 km/ 5h which is 96.
Step-by-step explanation: When she went there her speed 120 km/ h and if the distance was 240 km, then it took her 2 hours to get there. 240 divided by 120 is 2. When she returned her average speed was 80 km/h and since the distance was 240, 240 divided by 8 is 3 which means it took her 3 hours to get back home. She drove a total of 480 km , because the distance to the trip was 240 and the distance from the trip to the back was 240. 240 + 240 is 480. She drove a total of 480 km in 5 hours because it took her 2 hours to go there and 3 hours to come back . 480 km / 5h
The ratio of lions to tigers at the Metropolitan Zoo is 12 to 8. Which ratio is equivalent to 12 to 8? A.6 to 3 b.8 to 12 c.15 to 10 d.24 to 18
Answer:
c.15 to 10
Step-by-step explanation:
The ration 12 to 8 means that for every 12 lions there are 8 tigers in the zoo.
Ratios have the quality of conservate their meaning when both values in the ratio are multiplied or divided by the same number.
For example:
a ratio of 2 to 4 is the same as a ratio of 3 to 6 (both values are multiplied by 1.5 (or in fraction by 3/2) ).
in the same way that the ratio 9 to 3 is the same as 3 to 1 (divide both values by 3).
In this case we are looking for an equivalent ratio to the 12 to 8 ratio, the answer is
c.15 to 10
because this results from multiplying the two original values by 1.25 or, in fraction, by 5/4. You can see this becase
12*1.25 = 15
and
8*1.25 = 10
we get that when we multiply the ratio 12 to 8 by 1.5 the equivalent ratio is option C.
Find the slope of the following graph and write your result in the empty box.
Answer:
WERES THE GRAPH
Step-by-step explanation:
HELP! ASAP: The graph relates the number of gallons of white paint to the number of gallons of red paint Jess used to make the perfect pink. Write an equation that describes the relationship.
Answer:
y = (2/3)*a
Step-by-step explanation:
We can write the equation using the linear equation model:
y = ax + b
Then, to find the values of 'a' (slope) and 'b' (y-intercept), we can use two points of the graph.
Using the point (0,0), we have:
0 = a*0 + b
b = 0
Using the point (3,2), we have:
2 = a*3 + b
a = 2/3
So our equation is:
y = (2/3)*a
Answer:
The correct answer is Y= 3/4x
Step-by-step explanation:
I did savvas realize, the is the the correct answer↑
4) Use the discriminant to determine how many real roots the following function has. Reminder: Discriminant = b^2 - 4ac
2x2 – 8x + 25
a. 2 real solutions
b. 1 real solution
c. No real solutions
Answer:
c
Step-by-step explanation:
We have a = 2, b = -8 and c = 25
D = b² - 4ac = (-8)² - 4 * 2 * 25 = 64 - 200 = -136
Since D < 0, the answer is no real solutions.
What is 2.18 as a fraction
Answer:2 9/50
Step-by-step explanation:
2 18/100
Simplifies to 2 9/50
Answer:
109/50
Step-by-step explanation:
First, let's split this number up.
2.18 = 2.00 + 0.18
Remember that 0.18 means 18 hundredths, which can be represented as 18/100. Simplified, this equals 9/50.
Now, we have the mixed number 2 9/50.
Remember how to turn a mixed number into a fraction? Multiply 2 by 50, then add 9! That's the numerator. The denominator will be 50, the denominator of the fraction in the mixed number.
2 9/50 in fraction form is 109/50.
This is the simplest form!
Hope this helps! Feel free to reach out to me if you have any more questions :)
What is the y-value when x equals 7?
y = 310 - 25(x)
Answer:
y=135
Step-by-step explanation:
To find the solution, we must put 7 in for x and solve, as shown:
[tex]y=310-(25)(7)\\y=310-175\\y=135[/tex]
Which of the binomials below is a factor of this
trinomial?
x2 - 13x + 30
O A. X-3
O B. X+5
O c. x-5
O D. X+ 3
Answer:
A
Step-by-step explanation:
Given
x² - 13x + 30
Consider the factors of the constant term (+ 30) which sum to give the coefficient of the x- term (- 13)
The factors are - 3 and - 10, since
- 3 × - 10 = + 30 and - 3 - 10 = - 13 , thus
x² - 13x + 30 = (x - 3)(x - 10) ← in factored form
Thus (x - 3) is a factor of the polynomial → A
Answer:
[tex](x - 3)[/tex]
Answer A is correct
Step-by-step explanation:
[tex]{x}^{2} - 13x + 30 \\ {x}^{2} - 10x - 3x + 30 \\ x(x - 10) - 3(x - 10) \\ = (x - 3)(x - 10)
\\ [/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
3/10 is equivalent to how many hundreths
Three times a number is three more than twice the number. Which equation can be used to find the value of x, the unknown
number?
O 3x = 3 + 2x
O x = 3 + 2x
O 3x + 3 = 2x
O 3x = 3 + 2 + x
Answer:
The first option: 3x = 3 + 2x
Step-by-step explanation:
The question answers itself. In short:
x is our unknown number.
If three times a number (3x) is (=) three more (3) than (+) twice the number (2x).
Write each expression in radical form. (3b)^4/3
Answer:
Step-by-step explanation:
(3b)^(4/3) is equivalent to ∛(3b)^4.
∛[81b^4] is also equivalent.
Choose the correct product of (8x − 4)(8x + 4). (1 point) 64x2 − 16 64x2 + 16 64x2 − 64x + 16 64x2 + 64x + 16
Answer:
The correct answer is "[tex]64*x^2 - 16[/tex]".
Step-by-step explanation:
The product [tex](8*x - 4)*(8*x + 4)[/tex] is a notable product, which happens when we have the product of the sum of two values with the subtraction of these same two values. In cases like this the answer will always be the first term squared minus the second term squared, therefore we have:
[tex](8*x - 4)*(8*x + 4) = 64*x^2 - 16[/tex]
The correct answer is "[tex]64*x^2 - 16[/tex]".
Answer:
64x^2 -16
took the test
Two consecutive positive numbers have a sum of 27. What are the two numbers?
The smaller number is The larger number is k _________________ _________________
Answer:
k=14
Step-by-step explanation:
z+1=k
z+k=27
z=k-1
k-1+k=27
2k=28
k=14
Answer:
The smaller number is 13. The larger number is 14. (k?)
Step-by-step explanation:
If you add all the 2 consecutive integers up:
1+2=3
2+3=5
3+4=7
4+5=9
5+6=11
6+7=13
7+8=15
8+9=17
9+10=19
10+11=21
11+12=23
12+13=25
13+14=27
14+15=29
Only 13 & 14 add up to 27. Of course you don't have to do this and just find consecutive integers whose one's place is 3 and 4
5.) In 2012 the cost of a ticket to an arts
festival was $30.This was 20% more
than the ticket cost in 2011.
Calculate the cost of the ticket in 2011.
9514 1404 393
Answer:
$25
Step-by-step explanation:
If c is the 2011 cost, then we are told ...
30 = c + 20%×c
30 = 1.2c . . . . . . simplify
30/1.2 = c = 25 . . . . . divide by the coefficient of c
The 2011 cost was $25.
hihihihihihihihihihi
hi
Answer:
hi
Explanation:
hi
Which descriptions from the list below accurately describe the relationship
between AXYZ and AUVW? Check all that apply.
Answer:
similar and same shape
Step-by-step explanation:
2 people are trying different phones to see which one has the better talk time. ChatLong has an average of 18 hours with a standard deviation of 2 hours and Talk-a-Lot has an average of 20 hours with a standard deviation of 3. The two people who tested their phones both got 20 hours of use on their phones. For the z-scores I got 1 for the ChatLong company and 0 for Talk-a-lot. What is the percentile for each z-score?
Answer:
Step-by-step explanation:
The percentile for the z scores are gotten from the normal distribution table. The z cores are already known.
1) For the ChatLong company, the z score is 0. The area corresponding to the z score from the normal distribution table is 0.5. Therefore, the percentile is
0.5 × 100 = 50%
2) For the Talk-a-lot company, the z score is 1. The area corresponding to the z score from the normal distribution table is 0.84. Therefore, the percentile is
0.84 × 100 = 84%
It costs $10 to make earphones, and the start-up costs for manufacturing are $5,000. How many earphones must be produced to get to a cost per unit of $20 a. 100 b. 30 c. 200 d. 500
With that information we can create the equation
10x + 5000 = 20x
where x is the number of earphones produced
10x is the cost to make each earphone, 5000 being the fixed costs of manufacturing, and 20x being the total revenue of selling each earphone for $20
Now to solve the equation:
subtract both sides by 10x
10x - 10x + 5000 = 20x - 10x
5000 = 10x
Now divide both sides by 10
5000/10 = 10/10 x
500 = x
Answer: D
Hope it helps :)
500 earphones must be produced to get the cost price of one ear phone of $20.
What is linear equation in one variable?The linear equations in one variable is an equation which is expressed in the form of ax + b = 0, where a and b are two integers, and x is a variable and has only one solution.
According to the given question
The start-up costs for manufacturing earphones is $5,000.
Also, the cost to make earphones is $10.
Let x number of earphones will produced to get a cost per unit of $20.
From the given conditions, we will get a linear equation in one variable
10x + 5000 = 20x
⇒ 5000 = 20x -10x
⇒ 5000 = 10x
⇒ x = 500
Hence, 500 earphones must be produced to get the cost of earphone of $20.
Learn more about linear equation in one variable here:
https://brainly.com/question/17139602
#SPJ2
A recipe uses 1/3 cup of brown sugar to make 18 cookies. How many cups of brown sugar are needed to make 45 cookies?
Answer:
5/6 of a cup of brown sugar
Step-by-step explanation:
45 divided by 18 equals 2.5.
So, 2.5 times 1/3 of a cup equals 5/6 of a cup of brown sugar.
The number of cups of brown sugar needed is 5/6 cups.
Ratio expresses the relationship between two or more numbers. It shows the frequency of the number of times that one value is contained within other value(s).
The ratio of brown sugar to cookies is [tex]\frac{1}{3}[/tex] : 18. In order to determine the amount of brown sugar needed for 45 cookies, use this formula:
Number of cookies = (45 x [tex]\frac{1}{3}[/tex] ) / 18 = 15 / 18 = 5/6
To learn more about ratios, please check: https://brainly.com/question/17995727?referrer=searchResults
Parallel lines are defined as lines that have only one point in common True or false
Answer:
false
Step-by-step explanation:
parallel lines are lines that never meet or cross and go side by side.
Angela travels to a friend's house, which is 4 miles east and
8 miles north of her house. Will Angela have cell phone
service at her friend's house?
Answer:
Depends?
Step-by-step explanation:
She lives 8.9 miles away from her friend if she were to go at a diagonal (the fastest way to her house). If her cell service can go farther than that, then she will have service and vice versa
Answer:
A.
Step-by-step explanation:
Just did the quiz
Is the purple triangle a right triangle? Explain.
15.5
20.8 m
14.0 m
Answer:
15.5^2 + 14.0^ = 20.8^2
436.25 = 432.64
it is not a triangle because a+b is not = c
Answer: These given lengths do not make up a right triangle.
Step-by-step explanation:
In order to figure out if this is a right triangle or not, we would need to use the Pythagorean Theorem in order to verify if these lengths satisfy the properties of a right triangle. We would need to use the formula a^2 + b^2 = c^2.
14^2 + 15.5^2 = 20.8^2
196 + 240.25 = 432.64
436.25 ≠ 432.64
Therefore, this is not a right triangle.
if 2^n+2-2^n+1+2^n= C*2^n, find the value of C
Answer:
c= 1
Step-by-step explanation:
To get rid of (c) on the right side, simply divide 2^n both side. But first collect like terms on the left side so you will get 2^n + 1 which you will then simplify the like term(2^n) and you will left with c= 1.
at the farmer’s market, you can buy 3 melons for $13.50. What is the cost of one melon
Answer:
4.50 per melon
Step-by-step explanation:
Take the price and divide by the number of melons
13.50/3
4.50 per melon
