MATHEMATICS COLLEGE

This graph shows a proportional relationship.What is the constant of proportionality?
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Answers

Answer 1

Answer:

Hey, this is worked out the same way as the last problem you posted!

Remember that constant of proportionality is slope...

(y2-y1) ÷ (x2 -x1)

↓

(225 - 135) ÷ (5 - 3)

↓

90 ÷ 2

↓

The constant of proportionality is 45

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You have 14 gallons of lemonade to sell. You use cone-shaped cups that are 9 centimeters in diameter and 11 centimeters tall. Eachcustomer uses one paper cup. How many paper cups will you need if you sell all of the lemonade? (1 gal = 3785 cm)

Answers

Answer:

You need to sell approximately 119 paper cups to sell all of the lemonade.

Step-by-step explanation:

If the typos are randomly distributed over the 10 pages, find the probability of having a single typo on each page

Answers

1/10 assuming there is are 10 typos in total

Write a formula for the general term or nth term for the sequence. Then find the indicated term. three fourths comma three sixteenths comma StartFraction 3 Over 64 EndFraction comma StartFraction 3 Over 256 EndFraction ...; a 8

Answers

Sequence: 3/4, 3/16, 3/64, 3/256
a8=?
a1=3/4
a2=3/16
a3=3/64
a4=3/256

a2/a1=(3/16)/(3/4)=(3/16)*(4/3)=4/16=1/4
a3/a2=(3/64)/(3/16)=(3/64)*(16/3)=16/64=1/4
a4/a3=(3/256)/(3/64)=(3/256)*(64/3)=64/256=1/4
a2/a1=a3/a2=a4/a3=r=1/4

an=a1*r^(n-1)
an=(3/4)*(1/4)^(n-1)
an=(3/4)*(1)^(n-1)/(4)^(n-1)
an=(3/4)*(1/4^(n-1))
an=(3*1)/[4*4^(n-1)]
an=3/4^(1+n-1)
an=3/4^n

n=8→a8=3/4^8
a8=3/65,536

Answers:
The general term or nth term for the sequence is: an=3/4^n
a8=3/65,536

Insert <, >, or = between the given pair of numbers to make a true statement.- |-11| - (-11)

Answers

Answer:

- |-11| < - (-11)

Step-by-step explanation:

Given the pair of numbers - |-11| and - (-11), we want to determine which is greater or whether they are equal

First lets rewrite both numbers.

- |-11| = -11 (note that the modulus sign will change any negative value into a positive value and that's why |-11| is equivalent to 11)

- (-11) = 11 (note that the negative sign here was retained since it is not an absolute value like the former)

It can be seen that both numbers are therefore not equal i.e - |-11| is less than - (-11). Hence the expression - |-11| < - (-11) is a true statement

use the exact value of cos 11pi/6 and the half-angle identity for sine to find the exact value of sin 11pi/12

Answers

Recall that

$\sin^2x=\frac{1-\cos2x}2$

So you have

$\sin^2(11\pi)/(12)=\frac{1-\cos\frac{11\pi}6}2=\frac{1-(\sqrt3)/(2)}2=\frac{2-\sqrt3}4$

This means

$\sin(11\pi)/(12)=\frac{√(2-\sqrt3)}2$

where you take the positive square root because $\sin x$ must be positive for angles $x$ in the interval $0<x<\pi$ .