Solve V=1/3πr² for h

We want to divide 1/4 / 2/7

If we take the reciprocal of the 2/7, it means that the division sign will change to multiplication. Reciprocal of 2/7 = 7/2

Thus, the expression will be

1/4 x 7/2

= 7/8

Answer:

.5 is less than 6/10 (which is equal to .6)

Step-by-step explanation:

<-l---------l-l-------l->

0 .5 6/10

The equation is x - 2.5 = 5.25.

The elevation of the plane before its descent is 7.75 miles.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

An airplane descends 2.5 miles to an elevation of 5.25 miles.

This means,

The plane was at x miles before it descents.

x - 2.5 = 5.25

Solve for x.

x = 5.25 + 2.5

x = 7.75

Thus,

The elevation of the plane before its descent is 7.75 miles.

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Answer:

Fruit mass = 63.2 g

Biscuit mass = 94.8 g

Step-by-step explanation:

Since the ratio of fruit mass to biscuit mass is 2:3, the fraction of fruit mass to the total of fruit and biscuit mass is 2/5 and the fraction of biscuit mass to the total of fruit and biscuit mass is 3/5.

For Monkey A, the total of fruit and biscuit mass is 73 g, which means that the fraction of fruit mass is 2/5 × 73 g = 29.2 g and the fraction of biscuit mass is 3/5 × 73 g = 43.8 g. Therefore, the values for fruit mass and biscuit mass are:

Fruit mass = 29.2 g

Biscuit mass = 43.8 g

For Monkey B, the total of fruit and biscuit mass is 73 + 85 = 158 g, which means that the fraction of fruit mass is 2/5 × 158 g = 63.2 g and the fraction of biscuit mass is 3/5 × 158 g = 94.8 g. Therefore, the values for fruit mass and biscuit mass are:

Fruit mass = 63.2 g

Biscuit mass = 94.8 g

The number of each type of tickets sold are;

180 adults tickets

260 students tickets

60 children tickets

Let us solve to get the solution using 3 variables.

Let c be the number of children's tickets

Let s be the number of student tickets

Let a be the number of adult tickets

We are told that the total number of tickets was 500

Thus;

a + s + c = 500   ------(1)

The number of adult tickets was 3 times the number of children's tickets. Thus;

a = 3c   ------(2)

The total cost of the tickets was $8070. Thus;

18a + 15s + 12c = 7860  ----(3)

We conclude that solving these three equations simultaneously gives us;

a = 180 adults

s = 260 students

c = 60 children

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The time Jack left Santa Clara is 1 : 55 pm

A word problem in math is a math question written as one sentence or more. These statements are interpreted into mathematical equation or expression.

The time for Jack to walk to lose Altos is 25 min and he uses another 25mins to work to Palo alto.

Therefore, the total time he spent is

25mins + 25 mins = 50 mins

He arrived Palo at 2 :45 pm, therefore the time he left Santa Clare will be ;

2:45 pm = 14 :45

= 14:45 - 50mins

= 13:55

= 1 : 55pm

Therefore he left at 1:55 pm

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Answer:

  745

Step-by-step explanation:

You want the original number of books in the library if adding 298 children's books increased the fraction of children's books from 2/5 to 4/7.

We often like to work problems like this in terms of "ratio units." Here, we'll let x represent the number of books in a ratio unit. This means the number of children's books is originally 2x, and the total number of books is originally 5x. Then we have ...

  (2x +298)/(5x +298) = 4//7

Cross multiplying gives ...

  7(2x +298) = 4(5x +298)

  3(298) = 6x . . . . . . . . . . . . . subtract (14x+4(298))

  149 = x

  745 = 5x . . . . . . the original number of books in the library

There were 745 books in the library at first.

__

Additional comment

If we let x represent the original number of library books, then the arithmetic involves more fractions. You would have an equation like ...

  2/5x +298 = 4/7(x +298)

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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

To find the distance between Basti and Cian, we can use the law of sines in triangle ABC. The law of sines states that the ratio of the length of a side to the sine of the opposite angle is constant for all sides and their corresponding angles in a triangle.

Let's label the distance between Basti and Cian as "x". We know that the measure of angle ABC is 50 degrees and the measure of angle BAC is 60 degrees. We also know that Ali is exactly 150 ft away from Basti.

Using the law of sines, we can set up the following equation:

sin(50°) / 150 = sin(60°) / x

To solve for "x", we can rearrange the equation:

x = (150 * sin(60°)) / sin(50°)

Using a calculator, we can evaluate the expression:

x ≈ (150 * 0.866) / 0.766

x ≈ 168.4 ft

Therefore, the distance between Basti and Cian is approximately 168.4 ft.

Answer:

24xy+6

Step-by-step explanation:

Remove parentheses:

=4x times 6y+6

multiply the numbers:

which gives you: 24xy+6

If the economy is producing 12 units of guns and 4 units of butter, the opportunity cost of increasing the production of butter from 4 units to 11 units is 4 units of guns.

In Economics, an opportunity cost is sometimes referred to as alternative forgone and it can be defined as the value, profit or benefits that are given up and forfeited by an individual or business organization, in order to choose or acquire something that is deemed most significant at a particular point in time.

This ultimately implies that, the opportunity cost of owning or earning a thing is the alternative that is foregone in the attainment or earning of another value, profit or benefits.

Cost increase = 11 units - 4 units = 7 units of butter.

In this context, we can reasonably infer and logically deduce that the opportunity cost of 7 more units of butter would be 4 units of guns.

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The smallest angle of the equilateral triangle is 60 degrees

If the sides of a triangle are in the ratio 4:4:3, it implies that the lengths of the sides are proportional.

To determine the type of triangle, we examine the side lengths. Since all three sides are equal in length, we have an equilateral triangle.

For an equilateral triangle, all angles are equal. To calculate the smallest angle, we divide the total sum of angles in a triangle (180 degrees) by the number of angles, which is 3:

Smallest angle \(= \frac{180}{3} = 60\)\) degrees.

Therefore, the smallest angle of the equilateral triangle is 60 degrees (to the nearest degree).

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Answer: it's b.

Step-by-step explanation:

Answer:

9x - 6

Hope this helps! <3

(If you need a step by step lmk)

Answer:

6x+3(x-2)

6x+3x-6

9x-6

Answer:

Step-by-step explanation:

The first principles method for differentiation involves finding the limit of the difference quotient as h approaches 0. The difference quotient for a function f(x) is given by:

[f(x + h) - f(x)]/h

a) f(x) = 4x

[f(x + h) - f(x)]/h = [4(x + h) - 4x]/h = (4x + 4h - 4x)/h = 4

Therefore, the derivative of f(x) = 4x is 4.

b) f(x) = -3x

[f(x + h) - f(x)]/h = [-3(x + h) - (-3x)]/h = (-3x - 3h + 3x)/h = -3

Therefore, the derivative of f(x) = -3x is -3.

c) g(x) = x^2 - 4

[f(x + h) - f(x)]/h = [(x + h)^2 - 4 - (x^2 - 4)]/h

= [(x^2 + 2hx + h^2) - x^2]/h = 2x + h

Therefore, the derivative of g(x) = x^2 - 4 is 2x.

d) f(x) = 2x + 5

[f(x + h) - f(x)]/h = [2(x + h) + 5 - (2x + 5)]/h

= (2x + 2h + 5 - 2x - 5)/h = 2

Therefore, the derivative of f(x) = 2x + 5 is 2.

There are 15 cats in the animal shelter.

An equation in which is  the highest power of to the  variables 1 is knowns as the  linear equation. Mathematically: it is an  algebraic equations that can be also  written in the form of  ax + b = 0 or ax + by + c = 0, where a, b and c are definitely real numbers and x and y are variables with the highest power one.
In order to solve this problem, we must set up a proportion. Proportions are an equation that states that two ratios are equal. In this case, we are looking for the number of cats (c) in the animal shelter.

Let's set up the proportion.

5/3 = 25/c

We can then solve for c by multiplying both sides by c.

5c/3 = 25

c = 15

Therefore, there are 15 cats in the animal shelter.

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Given statement solution is :- The present value of R13,000 per year invested for 8 years at 10% compound interest is approximately R69,776.60.

To calculate the present value of an investment with compound interest, we can use the formula for the present value of an annuity:

PV = A *\((1 - (1 + r)^(-n)) / r\)

Where:

PV = Present value

A = Annual payment or cash flow

r = Interest rate per period

n = Number of periods

In this case, the annual payment (A) is R13,000, the interest rate (r) is 10% per year, and the investment is made for 8 years (n).

Using the formula and substituting the given values, we can calculate the present value:

PV = \(13000 * (1 - (1 + 0.10)^(-8)) / 0.10\)

Calculating this expression:

PV = \(13000 * (1 - 1.10^(-8)) / 0.10\)

= 13000 * (1 - 0.46318) / 0.10

= 13000 * 0.53682 / 0.10

= 6977.66 / 0.10

= 69776.6

Therefore, the present value of R13,000 per year invested for 8 years at 10% compound interest is approximately R69,776.60.

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The measure of the length EF of the triangle is; 21

We are given the the triangle BCD and we are told that;

E is the midpoint of BD.

F is the midpoint of CD

Now, since we have those midpoints, it means that by the concept of similar triangles, that;

DF/DC = EF/BC

Since F is the midpoint of DC, then it means that;

2DF = DC

We are given;

EF = 43 - 4x, and BC = 32 - 2x

Thus, we now have;

DF/(2DF) = (43 - 4x)/(32 - 2x)

1/2 = (43 - 4x)/(32 - 2x)

Cross multiply to get;

32 - 2x = 43 - 4x

4x - 2x = 43 - 32

2x = 11

x = 11/2

x = 5.5

Thus;

EF = 43 - 4(5.5)

EF = 43 - 22

EF = 21

Thus, we conclude that the side length EF is 21.

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Therefore, the expression (7-3i) + (x - 2i)² - (4i + 2x²) in the simplest a + bi form is: -2x² - 1 - (4x + 7i)

Linear Equation                   General Form                    Example

Slope intercept form             y = mx + b                            y + 2x = 3

Point–slope form                   y – y1 = m(x – x1 )              y – 3 = 6(x – 2)

General Form                            Ax + By + C = 0               2x + 3y – 6 = 0

Intercept form                        x/a + y/b = 1                 x/2 + y/3 = 1

As a Function f(x) instead of y      f(x) = x + C                         f(x) = x + 3

The Identity Function                      f(x) = x                     f(x) = 3x

Constant Functions                      f(x) = C                       f(x) = 6

Let's start by expanding the square term (x - 2i)² using the formula for (a + b)²:

(x - 2i)² = x² - 4xi + 4i²

Note that i² = -1, so we can simplify this expression to:

(x - 2i)² = x² - 4xi - 4

Substituting this expression and the given values into the original expression, we get:

(7 - 3i) + (x² - 4xi - 4) - (4i + 2x²)

Grouping the real and imaginary terms, we get:

(7 - 4 - 2x²) + (-3i - 4i - 4x) + (x²)

Simplifying the real part, we get:

-2x² - 1

Simplifying the imaginary part, we get:

-7i - 4x

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Answer: 40

Step-by-step explanation:

Because 36 / 0.9 = 40

4,8,12,16,20,24,28,32,36,40 that equals 100 percent

Answer:  

40  i hope this helps all of you guys!                                                        

If there were 50 workers, they would set 2,500 stones each day.

Total number is a term used to describe the sum of all the values or items within a set. It is usually used to calculate an aggregate or grand total, such as the sum of all the numbers in a list or the total number of people in a population. Total number can also be used to describe the absolute value or quantity of something, such as the total number of days in a year.

Assuming each worker set the same number of stones each day, the total number of stones set each day would be 50 times the number of workers. For example, if there were 20 workers, they would set 1,000 stones each day.
The number of stones set each day could also vary depending on the number of workers and the number of days they worked in a week. For example, if the workers worked a six day week and worked 50 out of the 52 weeks each year, the total number of stones set each day would be 50 times the number of workers multiplied by six. For example, if there were 20 workers, they would set 12,000 stones each day. If there were 50 workers, they would set 30,000 stones each day.

The number of stones set each day can also be affected by the production rate of the workers, the quality of the stones, and the amount of time required to set each stone. If the production rate was low, the number of stones set each day would also be lower. Similarly, if the quality of the stones was poor, the workers would likely take longer to set each stone, thus reducing the number of stones set each day.

Overall, the exact number of stones set each day depends on the number of workers, the number of days they work each week, their production rate, and the quality of the stones.

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Answer:

Recall that a function f(x) translated n units down, looks as follows:

Therefore, the graph of the function translated is:

Aircraft A has 312 seats.

Let's assume that Aircraft B has x seats.

According to the given information, Aircraft A has 105 more seats than Aircraft B. So, the number of seats in Aircraft A can be expressed as x + 105.

The total number of seats in both aircraft is 519, which can be represented by the equation:

x + (x + 105) = 519

Simplifying this equation, we have:

2x + 105 = 519

Subtracting 105 from both sides, we get:

2x = 414

Dividing both sides by 2, we find:

x = 207

Therefore, Aircraft B has 207 seats.

To find the number of seats in Aircraft A, we substitute the value of x back into the expression x + 105:

Aircraft A = 207 + 105 = 312

Hence, Aircraft A has 312 seats.

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Answer:

parabola opens up

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

• If a > 0 then parabola opens up

• If a < 0 then parabola opens down

y = (x + 3)² - 4 ← is in vertex form

with a = 1

Since a > 0 then parabola opens up

Answer:

if I had that money I would probably buy some Candy

Answer:

Step-by-step explanation:

The smaller polygon is half the size of the original polygon

Answer:

x(7y)x(7y)

Step-by-step explanation:

The given expression: 7(xy)7(xy)

i.e. a product of 7 and xy.

The operation used here: Multiplication.

Commutative property of multiplication :-

a\times b=b\times aa×b=b×a for any numbers a and b.

Associative property of multiplication :-

a\times(b\times c)=(a\times b\times c)a×(b×c)=(a×b×c) for any numbers a , band c.

Now, 7(xy)=(7x)y7(xy)=(7x)y [Associative property of multiplication]

=(x7)y=(x7)y [Commutative property of multiplication]

=x(7y)=x(7y) [Associative property of multiplication]

Answer:

In bold below.

Step-by-step explanation:

p^2 - 4 = (p - 2)(p + 2)

Note that 8 = 2^3 so

p^3 + 8 = ( p + 2)(p^2 + 4 - 2p)

So The HCF is p + 2.

The LCM =  (p + 2)(p - 2)(p^2 + 4 - 2p)