What fraction is equivalent to a repeating decimal

Suppose you're making a soup that uses 5 cups of chicken broth and 3⁄4 teaspoons of corn starch for 8 servings. You need to make

yanalaym [24]

Answer:

Option A = 7.5 cups

Step-by-step explanation:

Given : Suppose you're making a soup that uses 5 cups of chicken broth and $\frac{3}{4}$ teaspoons of corn starch for 8 servings. You need to make 12 servings of the soup, so you'll need $1\frac{1}{8}$ teaspoons of corn starch.

To find : How much broth do you need?

Solution :

A soup that uses 5 cups of chicken broth and $\frac{3}{4}$ teaspoons of corn starch for 8 servings.

i.e. 5 cups + $\frac{3}{4}$ teaspoon = 8 servings ......(1)

You need to make 12 servings of the soup, so you'll need $1\frac{1}{8}=\frac{9}{8}$

i.e. x cups + $\frac{9}{8}$ teaspoon = 12 servings ........(2)

So, First we find the ratio

Ratio is $\frac{12}{8}=\frac{3}{2}$

So to equal the ratio multiply (1) by $\frac{3}{2}$

$5\times \frac{3}{2}$ cups + $\frac{3}{4}\times \frac{3}{2}$ teaspoon = $8\times \frac{3}{2}$ servings

$\frac{15}{2}$ cups + $\frac{9}{8}$ teaspoon = 12 servings

On comparing with (2),

The value of x is $\frac{15}{2}$ .

Therefore, The broth do we need is $\frac{15}{2}=7.5$ cups.

So, Option A is correct.

5 0

3 years ago

The scale on a map is 1: 75 000. (a) Calculate the ACTUAL distance, in km, between two places which are 16 cm apart on the map.

finlep [7]

Answer:

a. 1 200 000 km

b. 0.000 773 cm

c. 67 500 000 000 km²

d. 0.000 000 016 cm²

Step-by-step explanation:

a. Calculate the ACTUAL distance, in km, between two places which are 16 cm apart on the map.

Since the scale is 1 : 75000 that is 1 cm : 75000 km, we want to find the actual distance of 16 cm on the map. Let x be the actual distance in km.

So, 1 cm : 75000 km = 16 cm : x km

So, 1 cm/75000 km = 16 cm/x km

Thus x km = 16 cm × 75000 km/1 cm = 1 200 000 km

(b) Calculate length of a road on the map which is 0.58 km.

Let y be the length of road on the map. So, using our scale

1 cm : 75000 km = y cm : 0.58 km

So, 1 cm/75000 km = y cm/0.58 km

Thus y cm = 0.58 km × 1 cm/75000 km = 0.000 773 cm

(c) Calculate, in km², the ACTUAL area of a lake which is 12 cm2 on the map.

Since the scale is 1 : 75000 , the scale for the area would be the square of this. So, 1² : 75000² = 1 : 5 625 000 000 which is 1 cm² : 5 625 000 000 km²

Let z be the actual area of the lake.

So, 1 cm² : 5 625 000 000 km² = 12 cm² : z km²

So, 1 cm²/5 625 000 000 km² = 12 cm²/z km²

Thus z km² = 12 cm² × 5 625 000 000 km²/1 cm² = 67 500 000 000 km²

(d) Calculate the area of a play field on the map which has has an actual area of 90 km².

Let a represent the area of the play field on the map. Using our scale for the area,

1 cm² : 5 625 000 000 km² = a cm² : 90 km²

So, a cm² = 90 km² × 1/5 625 000 000 km² = 0.000 000 016 cm²

4 0

2 years ago

How do you write <br>78/50<br> as a percentage?

Phoenix [80]

That would be 156%. have a great day

8 0

3 years ago

Read 2 more answers

"at the end of the year Juan has $52.71 more than 4 times his balance at the beginning of the year if his ending balance was $17

Salsk061 [2.6K]

At the end of the year, Juan has 52.71 more than 4 times his balance at the beginning. Okay, let's set this up.

4x + 52.71
(4 times) (52.71 more)
His ending was 172.90, so
4x + 52.71=172.90
4x= 120.19
x= 30.05
He had $30.05 at the beginning of the year.

8 0

3 years ago

A triangle has 2 sides that equal 6 inches. The other side equals 4 inches. What kind of triangle is this

Tom [10]

Ισοσκελες τρίγωνο
....

7 0

2 years ago

Read 2 more answers