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2 years ago

4 pounds of grapes cost 5$ 7 pounds of grapes cost $8.75. What is the cost per pound?

Mathematics

2 answers:

Deffense [45]2 years ago

5 0

The answer is 32.92$ because you add up then decide by 3

Simora [160]2 years ago

4 0

Answer:

$1.25 per pound

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Someeee one?????????????????

Ad libitum [116K]

Answer:

Option B) $a_{n} = 2\cdot 4^{n-1}$

Step-by-step explanation:

The given geometric sequence is

2, 8, 32, 128,....

The general form of a geometric sequence is given by

$a_{n} = a_{1}\cdot r^{n-1}$

Where n is the nth term that we want to find out.

a₁ is the first term in the geometric sequence that is 2

r is the common ratio and can found by simply dividing any two consecutive numbers in the sequence,

$r=\frac{8}{2} = 4$

You can try other consecutive numbers too, you will get the same common ratio

$r=\frac{32}{8} = 4$

$r=\frac{128}{32} = 4$

So the common ratio is 4 in this case.

Substitute the value of a₁ and r into the above general equation

$a_{n} = 2\cdot 4^{n-1}$

This is the general form of the given geometric sequence.

Therefore, the correct option is B

Note: Don't multiply the first term and common ratio otherwise you wont get correct results.

Verification:

$a_{n} = 2\cdot 4^{n-1}$

Lets find out the 2nd term

Substitute n = 2

$a_{2} = 2\cdot 4^{2-1} = 2\cdot 4^{1} = 2\cdot 4 = 8$

Lets find out the 3rd term

Substitute n = 3

$a_{3} = 2\cdot 4^{3-1} = 2\cdot 4^{2} = 2\cdot 16 = 32$

Lets find out the 4th term

Substitute n = 4

$a_{4} = 2\cdot 4^{4-1} = 2\cdot 4^{3} = 2\cdot 64 = 128$

Lets find out the 5th term

Substitute n = 5

$a_{5} = 2\cdot 4^{5-1} = 2\cdot 4^{4} = 2\cdot 256 = 512$

Hence, we are getting correct results!

6 0

3 years ago

A business executive bought 40 stamps for

alekssr [168]

Answer:

32 33-cent stamps, 8 23-cent stamps

Step-by-step explanation:

In order to solve this question, we need to set up a system of equations. Also known as solving for two variables (the number of each stamp).

Let's set x to be the number of 33-cent stamps. Similarly, let's set y to be the number of 23-cent stamps.

To make our first equation, let's think about the number of stamps total we have. We can say:

$x + y =40$

<em>(AKA - The number of 33-cent stamps, plus the number of 23-cent stamps, equals 40 stamps.)</em>

Now, let's make an equation for the cost of these stamps.

$0.33x + 0.23y = 12.40$

<em>(AKA - The cost of the stamps in total, should equal $12.40).</em>

So now, we have our two equations:

$x + y =40\\0.33x+0.23y=12.40$

If you have a TI-84 graphing calculator, you can go to apps -> polysmlt2 -> simultaneous eqn solver, and then input these equations into the menu. This will solve the problem for you.

If you need to do this manually, let's use substitution. Condense our first equation to make it more substitutable.

$x+y=40\\x=40-y$

Now, let's put this into our second equation.

$0.33x+0.23y=12.40\\0.33(40-y)+0.23y=12.40$

Distribute, and solve for y.

$13.2-0.33y +0.23y =12.40\\13.2-0.1y=12.40\\-0.1y=-0.8\\y=8$

Now, we plug this into one of our equations.

$x+y=40\\x+8=40\\x=32$

In the end, we have thirty-two 33-cent stamps, and eight 23-cent stamps.

3 0

1 year ago

-7x-3x+2=-8x-2 can you please show your work how

iVinArrow [24]

Answer:

x = 2

Step-by-step explanation:

Given

- 7x - 3x + 2 = - 8x - 2 ← simplify left side

- 10x + 2 = - 8x - 2 ( add 8x to both sides )

- 2x + 2 = - 2 ( subtract 2 from both sides )

- 2x = - 4 ( divide both sides by - 2 )

x = 2

8 0

3 years ago

A $300 suit is marked down by %20. Find the sale price

avanturin [10]

Answer:

1499

(Decimal: 299.8)

Step-by-step explanation: =

300

−

100

300

−20

100

300

−1

1500

−1

1500+−1

7 0

2 years ago

Read 2 more answers

Which expression is equal to 5^4⋅5^8 ? 512 54 52 5−4

KiRa [710]

Answer is 5^12 which is choice A (assuming you meant to put the ^ symbol)

The bases are the same (both are 5), so you add the exponents: 4+8 = 12. The base stays the same the entire time.

So, 5^4*5^8 = 5^(4+8) = 5^12

3 0

3 years ago