If one is subtracted from six times a certain number, the result is 47. Find the number.

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.

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.

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

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.

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

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.

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]

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

Answer:

WERES THE GRAPH

Step-by-step explanation:

Answer:

similar and same shape

Step-by-step explanation:

Answer:

Step-by-step explanation:

(3b)^(4/3) is equivalent to  ∛(3b)^4.

∛[81b^4] is also equivalent.

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

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.

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.

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

Answer:

hi

Explanation:

hi

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 :)

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

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]

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

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%

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

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.

Answer:

false

Step-by-step explanation:

parallel lines are lines that never meet or cross and go side by side.

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

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).

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!

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

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↑

Answer:

hope this is correct