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2 years ago

If the recipe calls for 3 cups of sugar for every 4 cups of flour, how many cups of sugar would be used for one cup of flour?

1 answer:

5 0

Answer: Amount of sugar 2 cups, amount of flour 3 cups, this means that for every cup of flour you will need 2/3 of cup of sugar

Step-by-step explanation:

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Here are some values of sequence Q. Write a recursive definition for the sequence.

Rashid [163]

Answer: Q(n) = Q(n - 1) + 2.5

Step-by-step explanation:

We have 3 values of the sequence Q(n)

These values are:

Q(1) = 3

Q(3) = 8

Q(7) = 18

I would think that this is a geometric sequence.

Remember that the equation for the n-th term of a geometric sequence is:

A(n) = A(1)*r^(n-1)

where r is a constant, and A(1) is the first term of the sequence.

If we rewrite the terms that we know of Q(n) in this way we get:

Q(3) = Q(1)*r^(3 - 1) = 3*r^2 = 8

Q(7) = Q(1)*r^(7 - 1) = 3*r^6 = 18

Then we have two equations:

3*r^2 = 8

3*r^6 = 18

We should see if r is the same for both equations:

in the first one we get:

r^2 = 8/3

r = (8/3)^(1/2) = 1.63

and in the other equation we get:

r^6 = 18/3

r = (18/3)^(1/6) = 1.34

Then this is not a geometric sequence.

Now let's see if this is an arithmetic sequence.

The n-th term of an arithmetic sequence is written as:

A(n) = A(1) + (n - 1)*d

where d is a constant.

If we write the terms of Q(n) that we know in this way we get:

Q(3) = Q(1) + (3 - 1)*d = 3 + 2*d = 8

Q(7) = Q(1) + (7 - 1)*d = 3 + 6*d = 18

We need to see if d is the same value for both equations.

in the first one we get:

3 + 2*d = 8

2*d = 8 - 3 = 5

d = 5/2 = 2.5

In the second equation we get:

3 + 6*d = 18

6*d = 18 - 3 = 15

d = 15/6 = 2.5

d is the same for both terms, then this is an arithmetic sequence.

An arithmetic sequence is a sequence where the difference between any two consecutive terms is always the same value (d)

Then the recursive relation is written as:

A(n) = A(n - 1) + d

Then the recursive relation for Q is:

Q(n) = Q(n - 1) + 2.5

4 0

3 years ago

What is 6 times 340 = ?

Debora [2.8K]

Answer:

6 x 340 = 2,040

Step-by-step explanation:

3 0

2 years ago

Read 2 more answers

Select ALL the correct answers.

DaniilM [7]

Be:
Number of hours: n

The cost of renting a bike for the first hour is $7:
n=1→f(n)=f(1)=$7

He is charged $2.50 for every additional hour of renting the bike:
f(n)=f(n-1)+2.50, for n ≥ 2

f(1)=7; f(n)=f(n-1)+2.50, for n ≥ 2 (sixth option)

f(n)=f(1)+2.50(n-1)
f(n)=7+2.50(n-1)
f(n)=7+2.50n-2.50
f(n)=2.50n+4.50 (fifth option)

Answers:
Fifth option: f(n)=2.50n+4.50, and
Sixth option: f(1)=7; f(n)=f(n-1)+2.50, for n ≥ 2

7 0

3 years ago

If P->q is true and q->r is true them the conclusión of p->r is also true this is called?

tino4ka555 [31]

Answer:

This is called transitivity property

4 0

3 years ago

A new television set was recently purchased for the common room in a residence hall for $436.80 including tax the tax rate is 4%

garri49 [273]

Answer:

The price of the television before taxes is $420

Step-by-step explanation:

* Lets explain how to solve the problem

- The purchased price = cost price + taxes

- A new television set was recently purchased for the common room

in a residence hall for $436.80

- This price including tax

- The tax rate is 4%

- We need to find the price of the television before taxes

* Lets solve the problem

- Assume that the price of the television before tax is 100%

∵ The tax rate is 4%

∵ The price after tax = price before tax + tax

∵ The price before tax = 100%

∴ The price after tax = 100% + 4% = 104%

∵ 104% equivalent to $436.80

∴ 100 ⇒ ?

104 ⇒ 436.80

- By using cross multiplication

∴ ? = $\frac{(436.80)(100)}{104}=420$

∴ The price of the television before taxes is $420

6 0

3 years ago

If the recipe calls for 3 cups of sugar for every 4 cups of flour, how many cups of sugar would be used for one cup of flour? ​

If the recipe calls for 3 cups of sugar for every 4 cups of flour, how many cups of sugar would be used for one cup of flour?