A pizza is divided into 12 equal slice.4 slices have mushrooms only.
2 slices have mushrooms and pepperoni.
6 slices have pepperoni only.
write two equivalent fractions to describe the parts of the pizza with
mushrooms only : ________ and _
pepperoni only : ___ and _
mushrooms and pepperoni : and ______ .

Answers

Answer 1

Answer:

The equivalent fractions for only mushroom, only pepperoni and mushrooms and pepperoni are given as 1/3, 2/6, 1/2, 2/4, 1/6, 2/12 respectively.

What is a fraction?

A fraction is a number written in the form a / b, where a and b are integers and b ≠ 0.

The number a is called as the numerator and b is the denominator.

The given problem can be solved as follows,

(a) The fraction to represent only mushrooms is given as below,

The number of mushroom slices ÷ Total number of slice

⇒ 4 ÷ 12

⇒ 1/3

Multiply numerator and denominator by 2 to get equivalent fraction as2/6

(b) The fraction to represent only pepperoni is given as below,

The number of pepperoni slices ÷ Total number of slice

6 ÷ 12

⇒ 1/2

Multiply numerator and denominator by 2 to get equivalent fraction as 2/4.

The number of mushrooms and pepperoni slices ÷ Total number of slice

⇒ 2 ÷ 12

⇒ 1/6

Multiply numerator and denominator by 2 to get equivalent fraction as 2/12.

Hence, the required fractions for the given case are 1/3, 2/6, 1/2, 2/4, 1/6, 2/12 respectively.

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Answer 2

Answer: Mushroom only: 4/12 and 1/3
Pepperoni only:6/12 and 2/4
Both mushroom and pepperoni: 2/12 and 1/6

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Solve using substitution. 4a=3b+3a=b-1

Divide £300 in a ration of 3:7 help please !

Answers

Divide it by 10 (3+7)
Multiply both sides of the ratio (3:7) by the result (300:10=30)
Left side of ration 3*30=90
Right 7*30=210

Thats gives us £90 and £210

What is the answer..........

Answers

Come on, Kat ! The question tells you everything you could
possibly want to know, except what's for dinner tomorrow.

It gives you the formula at the bottom.
The formula is:
Interest = (Principle) x (Rate) x (Time) .

Above that, in the story, it gives you 3 of the 4 quantities in the formula:

Interest = $656
Principle = $1,000
Rate = 4.1% (that's 0.041)

Do you think you could write those numbers into the formula,
and find out what the (Time) is ?

656 = (1,000) x (0.041) x (T)

Divide each side by 41 .

You're welcome.

in a certain 9th grade class the no. of girls is 83 less than no.of boys the total no. of student is 259. write an expression to represent the relationship between this information.

Answers

259-83=b b is the number of boys b=176

2. Which is larger?The common ratio, r , in a geometric sequence whose second term is
24 and whose fifth term is 1536
or
The common difference, d , in an arithmetic sequence whose fourth
term is 16 and whose seventh term is 31.

Answers

Answer:

The common difference d is larger than the common ratio r

Step-by-step explanation:

The common difference in the arithmetic sequence $d=u_(n)-u_(n-1)$

The nth term in the arithmetic sequence is $a_(n)=a+(n-1)d$ , where a is the first term

The common ratio in the geometric sequence $r=(u_(n))/(u_(n-1))$

The nth term in the geometric sequence is $a_(n)=a(r)^(n-1)$ , where a is the first term

Geometric sequence

∵ The second term is 24

∴ $u_(2)$ = 24

∵ $u_(2)=a(r)^(2-1)=ar$

- Equate it by its value

∴ ar = 24 ⇒ (1)

∵ The fifth term is 1536

∴ $u_(5)$ = 1536

∵ $u_(5)=a(r)^(5-1)=ar^(4)$

- Equate it by its value

∴ $ar^(4)$ = 1536 ⇒ (2)

Divide (2) by (1)

∴ $(ar^(4))/(ar)=(1536)/(24)$

- Divide up and down by ar

∴ r³ = 64

- Take ∛ for both sides

∴ r = 4

Arithmetic sequence

∵ The fourth term is 16

∴ $u_(4)$ = 16

∵ $u_(4)$ = a + (4 - 1)d

∴ $u_(4)$ = a + 3 d

- Equate it by its value

∴ a + 3d = 16 ⇒ (1)

∵ The seventh term is 31

∴ $u_(7)$ = 31

∵ $u_(7)$ = a + (7 - 1)d

∴ $u_(7)$ = a + 6 d

- Equate it by its value

∴ a + 6 d = 31 ⇒ (2)

Subtract equation (1) from equation (2) to eliminate a and find d

∵ (a - a) + (6 d - 3 d) = (31 - 16)

∴ 3 d = 15

- Divide both sides by 3

∴ d = 5

∵ r = 4 and d = 5

∴ d > r

∴ The common difference d is larger than the common ratio r

Find the measure of the central angle.the circle has a circumference of 9 and the arc length is 1. Use 3.14 for pie.

Answers

To start with we have to write down what we know. pi=3.14, r=9, arc length is 1. x is the angle we are trying to find. Saying that the radius is 9

There is an equation that states that the arc length is equal to x/360 (the fraction of the circle) multiplied by the circumference or 2 times pi times the radius.
$L= (x)/(360) * 2 \pi r$
where * means multiply.
$1= (x)/(360) * 3.14 * 9$
Simplify
$1= (x)/(360) *28.26$
Take the 28.26 over to the other side of the equation, where it then it divides the 1.
$(1)/(28.26) = (x)/(360)$
This becomes: $0.035= (x)/(360)$
Then the 360 is brought over to the other side and multiplies the 0.035:
$360*0.035=x$
And finally simplify the whole equation and we get our answer.
$x=12.739 degrees x=12.7 degrees$

Dosha is creating a new dessert that has two layers shaped like cones. The inner cone is frozen ice cream and has a diameter of 12 cm and a height of 6 cm. The outer layer is a thin wafer shell, like an upside-down ice cream cone, with a height of 15 cm and the same diameter as the inner layer. Dosha will inject a cream filling into the space.What is the volume of the cream filling?
Use 3.14 to approximate pi and express your final answer in hundredths.

cm3

nvm.. it was 339.12 !

Answers

Given:
Inner cone: diameter = 12 cm ; height = 6 cm
Outer layer: diameter = 12 cm ; height = 15 cm

Volume of a cone = π r² h/3

Inner cone: V = 3.14 * (6cm)² * 6cm/3 = 3.14 * 36cm² * 2cm = 226.08 cm³
Outer layer: V = 3.14 * (6cm)² * 15cm/3 = 3.14 * 36cm² * 5cm = 565.20 cm³

Volume of Outer layer : 565.20 cm³
less: Volume of inner layer: 226.08 cm³
Volume of cream filling: 339.12 cm³

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