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Ratios are simply used to compare two or more related quantities

(a) Comparing quantities

To compare quantities, we make use of ratios.

Hence, a way to compare two or more quantities is by using ratio

(b) Statement of equality between ratios

When two or more ratios are equal, the ratios are said to be equivalent ratios

Hence, the statement of equality between ratios is equivalent ratios

(c) Express (3) and (4) as ratios

There are 10 stars and 8 crosses.

So, the ratio is 10 : 8

There are 3 toys and 9 books.

So, the ratio is 3 : 9

(d) Compare balloons and party hats

There are 12 balloons and 18 party hats.

So, the ratio is 12 : 18

Reduce the ratio as follows:

12 : 18 = 2 : 3 ---- this is done by dividing 12 and 18 by 6

So, the comparison is:

There are 2 balloons for every 3 party hats

(e) Simplify (4)

In (4), we have:

Ratio = 3 : 9

Divide by 3

Ratio = 1 : 3

Hence, the simplified ratio is 1  3

(f) Express the currency ratio in its simplest form

The ratio is given as:

Ratio = 4 * 1 peso coin : Php80.00 coin

Evaluate the product

Ratio = 4 peso coin : Php80.00 coin

Divide both sides by 4

Ratio = 1 peso coin : Php20.00 coin

Hence, the simplest form of the ratio is 1 : 20

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We want to find the two numbers you picked, we will find that the two numbers you picked are 3 and 7.

First, you pick a number between 0 and 10, let's say that the number is N.

Then multiply it by 5 and add 7, so we get:

(5*N + 7)

Now we multiply this by 2

2*(5*N + 7)

Now we add another number between 0 and 10, let's call it M.

We need to add that to the product, and then subtract 6, and that will be equal to 45.

2*(5*N + 7) + M - 6 = 45

Now let's simplify the expression:

2*(5*N + 7) + M = 45 + 6 = 51

10*N + 14 + M = 51

10*N + M = 51 - 14 = 37

10*N + M = 37

With this, we want to find the values of N and M, but remember that these two values belong to the interval [0, 10]

So the only two solutions are:

N = 3 and M = 7

such that:

10*3 + 7 = 30 + 7 = 37

So the two numbers you picked are 3 and 7.

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Probability that it rains and you go over in data tomorrow = 0.0539

Percentage of time it takes to go over your data limit = 49%

Probability that you go over your data limit, P(data) = 49/100

P(data) = 0.49

The chance that it rains tomorrow = 11%

Probability that it rains tomorrow, P(rain) = 11/100

Probability that it rains tomorrow, P(rain) = 0.11

Probability that it rains and you go over your data tomorrow = P(rain) x P(data)

Probability that it rains and you go over in data tomorrow = 0.11 x 0.49

Probability that it rains and you go over in data tomorrow = 0.0539

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Answer:

D) t = 5

Step-by-step explanation:

when t =5 both functions have the same x and y value

Answer:

7.5 cm

Step-by-step explanation:

Since it's a right triangle, apply pythegorean theorem

Let the missing side be x

[tex] {7.8}^{2} = 2.1 { }^{2} + x {}^{2} [/tex]

[tex]60.84 = 4.41 + {x}^{2} [/tex]

[tex] {x}^{2} = 60.84 - 4.41[/tex]

[tex] {x}^{2} = 56.43[/tex]

[tex] \sqrt{ {x}^{2} } = \sqrt{56.43} [/tex]

[tex]x = 7.5[/tex]

Therefore, the length of the missing side is 7.5 cm

Answer:

y = — 9/2x + 6

Step-by-step explanation:

m= —9/2

y — y1 = m (x — x1)

y + 3 = —9/2 (x — 2)

y = — 9/2x + 6

Answer:

79.04 liters

Step-by-step explanation:

20.8 x 3.8 = 79.04

Answer:

It is the third one

Step-by-step explanation:

Answer:

3 x 26 = 78

Step-by-step explanation:

It's quite simple, when you look at the problem, it states Juan at 26 carrots. Carmen on the other hand ate 3 times as much. For the answer choices, they put Carmen's 3 first and Juan's 26 second.

Answer:

a) 50

b) 86

c) x = 130      y = 50

Step-by-step explanation:

Opposite angles that share the same lines are always the same.

Answer:

B.   21.  A    22.  c

Step-by-step explanation:

8.75 ÷1000   move decimal point three places to the left.

21.  A    a whole number  0.80

22.   C   nonterminating decimal.   0.6666...

Answer:

Step-by-step explanation:

An acute triangle is a triangle in which all three angles measure less than 90 degrees. If any angle measures 90 or more degrees, we no longer have an acute triangle.

Step-by-step explanation:

a) We are going g to use the definition of tangent to find x:

[tex]\tan{18°} = \dfrac{opp}{adj} = \dfrac{15}{x}[/tex]

[tex]\Rightarrow x = \dfrac{15}{\tan{18°}} = 46.2[/tex]

b) To solve this problem, we are going to use the definition of cosine:

[tex]\cos{70°} = \dfrac{adj}{hyp} = \dfrac{x}{46}[/tex]

[tex]\Rightarrow x = 46\cos{70°} = 15.7[/tex]

Answer:

D

Step-by-step explanation:

it's 100% I'm super sure

Answer:

Inverse:  (3, 2)

Step-by-step explanation:

Given the point, (2, 3), as an ordered pair of the function, f(x):

Since we know that for any functions, there is a one-to-one correspondence between each domain and range values.  Conversely, each range value also corresponds to one domain value.  

The inverse of a function, [tex]f^{-1}(x)[/tex], also has a one-to-one correspondence. Simply put, we are essentially switching the x and y values to determine the inverse of a function.

Therefore, given the ordered pair from f(x) = (2, 3), then the corresponding coordinates in the inverse function, [tex]f^{-1}(x)[/tex], must be (3, 2).

Answer:

E

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

<STR = <SRT                      Given the markings of the triangle

<STR + <STU = 180            Supplementary angles

(2x - 9) + 7x = 180               Remove the brackets

2x - 9 + 7x = 180                 Combine

9x - 9 = 180                         Add 9 to both sides

9x = 180 + 9                        Combine

9x = 189                              Divide by 9

9x/9 = 189/9

x = 21

Answer:

Step-by-step explanation:

(5, 0) (6, 8)

(8 - 0)/(6 - 5) = 8/1 = 8

Answer:

3 1/4

Step-by-step explanation:

Linear.

[tex] \rm {6x}^{2} = 12[/tex]

[tex] \rm {x}^{2} = 12 \div 6[/tex]

[tex] \rm {x}^{2} = 2[/tex]

[tex] \rm x = \sqrt{2} [/tex]

Answer:

distance, speed, time, temperature , work, energy, charge, voltage are all scalar quantities. Displacement, velocity, acceleration, force, electromagnetic field are all vector quantities.

Step-by-step explanation:

Displacement and velocity.

9514 1404 393

Answer:

Step-by-step explanation:

All of these exponential function problems use the same equation, but with different plug-in values. These can be easily accommodated by a spreadsheet or graphing calculator.

The general form of the value after t years is ...

  (initial value)×(1 +annual growth rate)^(years)

The growth rate is positive for an increase, negative for a decrease.

a) Initial value: 22385; growth rate: -0.14; years: 10

  value after 10 years: $22385×(1-0.14)^10 = $4953.84

__

b) initial value: 290; growth rate: 0.09; years: 5

  population after 5 years: 290(1+.09)^5 = 446

__

c) initial value: $4000; growth rate: -0.10; years: 8

  value after 8 years: $4000(1 -0.10)^8 = $1721.86

Selling the car for $1500 is selling it for less than its estimated value. That may not be a good decision.

_____

Additional comment

The property value of the car is not the only consideration when evaluating the sale. Other costs related to the car may come into play, and there may be tax implications.

Perfect squares are the squares of integers

There are 990 integers between 50000 and 60000 that are squares of integers

There are 1000 perfect squares, and 100 perfect cubes between 1 and 1000000

This is because:

[tex]\mathbf{100000 = 1000^2 = 100^3}[/tex]

Rewrite as:

[tex]\mathbf{100000 = x^2 = y^3}[/tex]

Where x lies between 1 and 1000, and y lies between 1 and 100.

If y^3 is a perfect square, then y is a perfect square

List out the perfect squares from 1 to 1000

[tex]\mathbf{y = 1, 4, 9, 16, 25, 36, 49, 64, 81, 100}[/tex]

Take the cube of these numbers

[tex]\mathbf{y^3 = 1^3, 4^3, 9^3, 16^3, 25^3, 36^3, 49^3, 64^3, 81^3, 100^3}[/tex]

[tex]\mathbf{y^3 = 1, 64, 729, 4096, 15625, 46656, 117649, 262144, 531441, 1000000}[/tex]

So, the count of numbers that are perfect squares and perfect cubes between 1 and 1000000 is 10.

The count of integers between 50000 and 60000 that are squares of integers is:

[tex]\mathbf{n = x -10}[/tex]

Substitute 1000 for x

[tex]\mathbf{n = 1000 -10}[/tex]

[tex]\mathbf{n = 990}[/tex]

Hence, there are 990 integers between 50000 and 60000 that are squares of integers

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Answer:

29

Step-by-step explanation:

12000/425

Answer:

6sqrt5

Step-by-step explanation:

Step-by-step explanation:

1hr = 60

½ hr = 30

60 + 30 = 90

The completed ratio chart is provided below:

Feet of Ribbon    1             5   10    15

Cost                     $0.60   $3  $6   $9

The amount Serena would get if she has $12 is 20 yards.

The amount Serena would pay if she wants 17 feet of the ribbon is $10.20.

The first step is to determine the unit cost of a ribbon.

Unit cost of a ribbon = $3 / 5 = $0.60

The cost of 10 feet of the ribbon = $0.60 x 10 = $6

The cost of 15 feet of the ribbon = $0.60 x 15 = $9

The feet of ribbon Serena can buy if she has $12 = $12 / $0.60 = 20 yards.

The cost of 17 feet of the ribbon = $0.60 x 17 = $10.20

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Answer:

Step-by-step explanation:

We know from the property of 30°x60°x90° right triangle:

We see AC = 2*BC, therefore:

Correct choice is B

The ratio of angles is directly proportional to the ratio of sides

The ratio of sides here is 1:1/2:1

Now

[tex]\\ \sf\longmapsto 2x+x=90°[/tex]

[tex]\\ \sf\longmapsto 3x=90[/tex]

[tex]\\ \sf\longmapsto x=30[/tex]

Answer:

8/5 cups

Step-by-step explanation:

equal 5/4 to 2/x x representing the amount of flour

cross multiply: 5x=8

divide: x=8/5

Answer:

7

8

1

10

Step-by-step explanation:

the coefficient of x you look at x the number associated with x is the coefficient.same applies to z y and constant number independent of any letter