There are two unmarked buckets by a stream. The buckets hold 19 and 8 gallons of​ water, respectively. How can 14 gallons of water be​ obtained, to take​ home? Complete the sequence below. The numbers represent the number of gallons in each bucket in each successive step.

Answer:

32449.3

Step-by-step explanation:

use the formula A = P(1+r / 100)^t

20000 × (1+ (8.4 / 100))^6

=32449.3

Answer:

Let's start by assigning a variable to Susan's present age. Let's call it "x".

According to the problem, in seven years, Susan will be "x + 7" years old.

Three years ago, Susan was "x - 3" years old.

The problem tells us that Susan will be 2 times as old in seven years as she was 3 years ago. So we can set up the following equation:

x + 7 = 2(x - 3)

Now we can solve for x:

x + 7 = 2x - 6

x = 13

Therefore, Susan's present age is 13 years old.

Let's assume Susan's present age is "x" years. According to the information provided, "Susan will be 2 times old in seven years as she was 3 years ago."

Seven years from now, Susan's age would be x + 7, and three years ago, her age would have been x - 3. According to the given statement, her age in seven years will be two times her age three years ago:

x + 7 = 2(x - 3)

Let's solve this equation to find Susan's present age:

x + 7 = 2x - 6

Subtracting x from both sides:

7 = x - 6

Adding 6 to both sides:

13 = x

Therefore, Susan's present age is 13 years.

Answer:

\( a_2 =\frac{1}{2}\\\\

a_3 =2\\\\

a_2 =\frac{1}{2}\)

Step-by-step explanation:

\(a_1 = 2......(given)\\\\

a_n =\frac{1}{a_{n-1}}\\\\

Plug\: n = 2\\

a_2 =\frac{1}{a_{2-1}}=\frac{1}{a_1}=\frac{1}{2}\\\\

Plug\: n = 3\\

a_3 =\frac{1}{a_{3-1}}=\frac{1}{a_2}=\frac{1}{\frac{1}{2}}=2\\\\

Plug\: n = 4\\

a_4 =\frac{1}{a_{4-1}}=\frac{1}{a_3}=\frac{1}{2}\\\\\)

Answer:

The sum will be close to 1/4

Step-by-step explanation:

1/8+1/6 is 7/24, and 1/4th of that is 6/24, so it is very close.

Answer: The sum will be close to 1/4

Step-by-step explanation:

You can start by making the fractions have the same denominator, (8*6) which gets you 48

You then want to use the butterfly method, so 1/8 becomes 6/48 and 1/6 becomes 8/48. You then add these up to 14/48.

12/48 is 1/4, and 14/48 is close to 12/48, thus making the answer the first option.

Answer:

the mean is 7

Step-by-step explanation:

used a mean calculator

Answer:

\(3\sqrt{85}\) = EC

Step-by-step explanation:

21² + 18² = EC²

441 + 324 = EC²

765 = EC²

\(\sqrt{765}\) = EC

Simplified: \(3\sqrt{85}\) = EC

Hope this helps!

Answer:

57327392393629324

Step-by-step explanation:

Answer:

126

Step-by-step explanation:

(7x6) + (7 x 12)= 126

Answer: Ans is 990. First such a number is 5×0 +2=2, then 5×1 +2=7, like that in all 20 numbers are there from 2 to 97 in A.P.with common difference of 5.

Step-by-step explanation:

Answer:

ΔABC is a right triangle

length of the concession stand = 42.4 ft (nearest tenth)

Step-by-step explanation:

Given:

We can use Pythagoras' Theorem to prove if ΔABC is a right triangle.

Pythagoras' Theorem: a² + b² = c²  (where a and b are the legs, and c is the hypotenuse of a right triangle)

Given:

⇒ a² + b² = c²

⇒ 30² + 40² = 50²

⇒ 900 + 1600 = 2500

⇒ 2500 = 2500

Therefore, ΔABC is a right triangle

To find the diagonal of square A, use Pythagoras' Theorem:

Given:

⇒ a² + b² = c²

⇒ 30² + 30² = c²

⇒ 900 + 900 = c²

⇒ c² = 1800

⇒ c = √(1800)

⇒ c = 42.42640687

Therefore, the length of the concession stand (diagonal of square A) is 42.4 ft (nearest tenth)

Divide the total number of blocks by the total number of storage containers.

5144/8 = 643 blocks in each storage container.

Answer:

no solutions

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

equation of blue line is y = x + 2 , in slope- intercept form

with slope m = 1

equation of red line is y = x - 3 , in slope- intercept form

with slope m = 1

• Parallel lines have equal slopes

then the blue and red lines are parallel.

the solution to the system is at the point of intersection of the 2 lines

since the lines are parallel then they do not intersect each other.

thus the system shown has no solution.

The mean absolute deviation is 0.75

To calculate the mean absolute deviation (M.A.D.), you need to find the average of the absolute differences between each data point and the mean of the data set

From the information given, we have that the data set is;

8 9 9 7 8 6 9 8

Let's calculate the mean, we get;

Mean = (8 + 9 + 9 + 7 + 8 + 6 + 9 + 8) / 8

Mean = 64 / 8

Divide the values

Mean = 8

Let's determine the absolute difference, we get;

Absolute differences=

|8 - 8| = 0

|9 - 8| = 1

|9 - 8| = 1

|7 - 8| = 1

|8 - 8| = 0

|6 - 8| = 2

|9 - 8| = 1

|8 - 8| = 0

Find the mean of the absolute differences:

Average of absolute differences = (0 + 1 + 1 + 1 + 0 + 2 + 1 + 0) / 8

Absolute difference = 6 / 8 = 0.75

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Answer:

$30.00

Step-by-step explanation:

The original price of the sweater is $75.00.  The new sale price is the original price of  100% less  60% of the original price.  That means the sales price is 40% of the original price.

You can do this 2 ways:

1.  $75 x 60% or .60 = $45

  $75-45 = $30

or

2.  $75 x 40% or .40 = $30

Consider the formula,

Here, P is the principal, r is the rate of interest, n is the number of periods, and A is the amount.

According to the problem, the compund interest is to be applied quarterly i.e 3 times per year, so the rate of interest is calculated as,

Substitute the values and solve for 'n',

Consider the formula,

Then the equation becomes,

Thus, the required number of periods in 54.

The corresponding number of years will be 54 by 3 i.e. 18, since the compounding is done 3 time

The cat is not hungry, or doesn't like the can of tuna food, which is why they refused to eat it when it was given to them.

Try to give the cat the food again and see their reaction, if that fails, try to give the cat other foods and note the reaction to determine if the cat just doesn't like the tuna in a can or just wasn't hungry at the moment.

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Further explanation:

The large pizza is clearly not the same size as the small pizza. So we cannot combine these unlike terms so to speak. It would be like saying 1 apple + 1 orange = 2 apples or 2 oranges, which is of course incorrect. Therefore, 1/3 + 1/4 isn't particularly meaningful here.

But what if the pizzas were the same exact size? The next section covers this aspect.

Keep in mind that the next section is optional and not something you'd write on your homework. It's simply meant to show how fractions work.

--------------

Let's call the two pizzas A and B, and we'll assume they are the same size.

Assuming the pizzas are the same size, then 1/3 + 1/4 does represent how much of a whole single pizza you have grabbed when getting both slices.

Think of it like this: 1/3 = 4/12 since we can multiply top and bottom by 4, and the fraction will be equivalent. What's going on is that each of the three original slices from pizza A is divided further into 4 smaller pieces. That gives 3*4 = 12 smaller slices. Grabbing 4 slices out of 12 leads to 4/12 = 1/3 of pizza A.

Through similar logic, 1/4 = 3/12 is the amount you get from pizza B.

Then we add the fractions like so:

1/3 + 1/4 = 4/12 + 3/12 = (4+3)/12 = 7/12

This says you have 7 tiny slices overall. The denominators must be the same when adding fractions.

Check out the diagrams below. Figure 1 uses the pizza/cake/pie model to represent the fractions being added; while figure 2 uses the fraction tape method. Feel free to use whichever is your favorite.  

Once again, this only works when the two pizza sizes are the same. Otherwise, the answer is simply "no 1/3+1/4 doesn't represent the total fractional amount received".

Step-by-step explanation:

It's not 3 triangles and 1 square because you need four triangles to make the siding and the square wont go anywhere because of how it's going to look.

It's not 3 triangles and 1 rectangle because still you need four to make the sides and a rectangle is too long.

4 triangles and 1 rectangle is still not correct because the rectangle on the bottom of the net is going to mess it up fir the whole shape.

So in conclusion, 4 triangles and 1 squares is the correct answer.

The coordinates of point B are (-3, 17).

The given equation is M = I₁ + I₂ = 31 + 32.

Now let's substitute in our given values:

(-2, 2) = ((-5 + x₂) / 2, (-5 + 2 + y₂) / 2)

We will now set up two equations to solve for our two unknowns, x₂ and y₂:

Equation 1: (-5 + x₂) / 2 = -4

Multiply both sides by 2:

-5 + x₂ = -8

Add 5 to both sides:

x₂ = -3

This gives us the x-coordinate of point B.

Equation 2: (-5 + 2 + y₂) / 2 = 7

Simplify:

(-3 + y₂) / 2 = 7

Multiply both sides by 2:

-3 + y₂ = 14

Add 3 to both sides:

y₂ = 17

This gives us the y-coordinate of point B.

Therefore, the coordinates of point B are (-3, 17).

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The output voltage of the op-amp circuit shown is -5v.

It should be noted that voltage is the electric potential difference between two points l.

In this case, the output voltage will be:

= -5 × i

where I = 1.

Voltage = -5 × 1

= -5v

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Answer:

Hi there!

Your answer is two times.

Step-by-step explanation:

The distributive property is multiplying the coefficient in front of parentheses into the parentheses. You have two sets of parentheses both with a coefficient that needs to be distributed.

The first time you use it is on 2(x+5), distributing the 2.

The second time you use it is on the -3(2x+7), distributing the -3

Please let me know if you have questions :)

To find all points on the x-axis that are 16 units away from the point (5, -8), we can use the distance formula. The distance between two points (x₁, y₁) and (x₂, y₂) is given by the formula:

d = √((x₂ - x₁)² + (y₂ - y₁)²)

In this case, the y-coordinate of the point (5, -8) is -8, which lies on the x-axis. So, any point on the x-axis will have a y-coordinate of 0. Let's substitute the given values and solve for the x-coordinate.

d = √((x - 5)² + (0 - (-8))²)

Simplifying:

d = √((x - 5)² + 64)

Now, we want the distance d to be equal to 16 units. So, we set up the equation:

16 = √((x - 5)² + 64)

Squaring both sides of the equation to eliminate the square root:

16² = (x - 5)² + 64

256 = (x - 5)² + 64

Subtracting 64 from both sides:

192 = (x - 5)²

Taking the square root of both sides

√192 = x - 5

±√192 = x - 5

x = 5 ± √192

Therefore, the two points on the x-axis that are 16 units away from the point (5, -8) are:

Point 1: (5 + √192, 0)

Point 2: (5 - √192, 0)

In summary, the points on the x-axis that are 16 units away from the point (5, -8) are (5 + √192, 0) and (5 - √192, 0).

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If the sales tax is 7%, the price of the sunglasses is  $61.6962

She has $70 gift card for a department store.

She buys a new glasses with her gift card.

The gift card had a remaining balance of $3.66.

Therefore,

amount she bought the sunglasses with tax = 70 - 3.66 = $66.34

Hence,

Sales tax = 7 / 100 × 66.34 = $4.6438

Therefore,

The original price before tax = 66.34 - 4.6438 = $61.6962

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Answer: The value of the limit of the function may not be equal to the value of the function evaluated at a particular x-value. In other words, just because a function takes on a certain value at a particular x-value doesn't mean that the limit of the function at that x-value is equal to that value. To determine the limit of the function, you may need to use different methods such as L'Hopital's Rule or other limit laws. Additionally, it's important to keep in mind that the limit of the function may not exist, in which case it wouldn't be equal to any specific value.

Step-by-step explanation:

The equation 7.5s + 1.6t - 4.2s is simplified to give a result of

The given equation 7.5s + 1.6t - 4.2s is simplified by following the mathematical operator that is acting on the values after a consideration of like terms

The variables in the equation are t and s

terms in t: 1.6

terms in s: 7.5, -4.2

collecting like terms

this will lead to rearranging the equation to give

7.5s - 4.2s + 1.6t

using the mathematical operator (addition and subtraction)

= 3.3s + 1.6t

unlike terms cannot be operated on, because of this the answer is 3.3s + 1.6t

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Answer:.

Step-by-step explanation im not sure

Answer:

Step-by-step explanation:

47.)  sin20 = 6/b

b = 6(sin20) = 17.5

c = √6²+17.5² = 18.5

48.)  tan61 = y/18

y = 18(tan61) = 32.5

z = √18²+32.5² = 37.1

49.)  r = √25²+23² = 34

50).  d = √30²+7² = 30.8

51.)  sin71 = j/19

j = 19(sin71) = 18

k = √19²-18² = 6.2

52.)  y = √4²-1² = √7 = 2.6

53.)  sin49 = f/26

f = 26(sin49) = 19.6

h = √26²-19.6² = 17

54.)  t = √7²+4² = 8.1

Answer:

  20 1/85 ≈ 20.01 square units

Step-by-step explanation:

There are several ways we can find the area of the shaded triangle in the attached figure. We can use proportions, and we can use the triangle area formula.

__

We know all of the triangles involved are right triangles, and that AB, AD, and BD are their hypotenuses.

The location of point B is the y-intercept of the boundary line: y = 9.

The location of point D is the x-intercept of the equation of the boundary line, so will be found where y=0:

  y = 9 -6/7x

  0 = 9 -6/7x

  0 = 10.5 -x . . . . . multiply by 7/6

  x = 10.5

That means the scale factor between ΔABC and ΔDAC is ...

  AB/DA = 9/10.5 = 6/7

The ratio of the triangle areas is the square of the scale factor:

  (area ΔABC)/(area ΔDAC) = (6/7)² = 36/49

The ratio of the area of ΔABC to the total of the areas ΔABC+ΔDAC will then be ...

  area ΔABC/(area ΔABD) = 36/(36+49) = 36/85

The formula for the area of a triangle gives the area of ΔABD:

  A = 1/2bh = 1/2(10.5)(9) = 47.25 . . . . square units

Then the area of ΔABC is ...

  area ΔABC = (fraction of whole) × (whole)

  = (36/85)×47.25 = 20 1/85 ≈ 20.01 . . . . square units

__

To use the area formula for ΔABC, we need to know a base and height. We already know the length of side AB = 9, so we only need to find the x-coordinate of point C. That is at the intersection of the boundary lines.

The perpendicular line AC has a slope that is the opposite reciprocal of the slope of line BC: -1/(-6/7) = 7/6. Since line AC goes through the origin, its equation is ...

  y = 7/6x

Substituting for y in the equation y = f(x), we have ...

  7/6x = 9 -6/7x

  (7/6 +6/7)x = 9 . . . . . add 6/7x

  85/42x = 9   ⇒   x = 9(42/85) = 4 38/85

This is the height from AB to C of ΔABC. So, the area of ΔABC is ...

  area = 1/2bh = 1/2(9)(4 38/85) = 20 1/85 . . . . square units

_____

Additional comment

We could finish the solution of the coordinates of C, then find AC and BC using the distance formula. These lengths could then be used in the area formula for a triangle to find area ΔABC. We suspect either of the methods used here involves less work and opportunity for mistakes.

Answer:

150

Step-by-step explanation:

30 + 30 + 45 + 45 = 150

Answer:

exponent

Step-by-step explanation:

Answer:

power or exponent it can be both, but being specific here, choose exponent

Step-by-step explanation:

i studied this concept trust me