f a container contains 18,000 ounces (oz) of beans, about how many pounds (lb) does it contain? [1 pound = 16 ounces]

James answered 14 items correctly on a 16-item quiz. what percent did he answer correctly?

Troyanec [42]

So,

I like to simplify a fraction first. This is what I do when I'm in a store trying to find the unit price.

$\frac{14}{16}$

Factor.
$\frac{2*7}{2*2*2*2}$

Cross out ones.
$\frac{7}{2*2*2}$

Multiply it out.
$\frac{7}{8}$

In my head, I remember that one-eighth is equal to 0.125.

So seven-eighths is equal to 0.125 times 7.
0.125 * 7 = 0.875

Convert to percent form.
0.875 --> 87.5%

James answered 87.5% of his quiz correctly.

I actually have the decimal equivalents for eighths in my head when I'm shopping. So once I get seven-eighths, I immediately know how much that is. I can also subtract 0.125 from 1.000 to get seven-eighths.

3 0

3 years ago

Read 2 more answers

QUESTION IN THE ATTACHMENT

eimsori [14]

Answer:

A. The sum of the first 10th term is 100.

B. The sum of the nth term is n²

Step-by-step explanation:

Data obtained from the question include:

Sum of 20th term (S20) = 400

Sum of 40th term (S40) = 1600

Sum of 10th term (S10) =..?

Sum of nth term (Sn) =..?

Recall:

Sn = n/2[2a + (n – 1)d]

Sn is the sum of the nth term.

n is the number of term.

a is the first term.

d is the common difference

We'll begin by calculating the first term and the common difference. This is illustrated below:

Sn = n/2 [2a + (n – 1)d]

S20 = 20/2 [2a + (20 – 1)d]

S20= 10 [2a + 19d]

S20 = 20a + 190d

But:

S20 = 400

400 = 20a + 190d .......(1)

S40 = 40/2 [2a + (40 – 1)d]

S40 = 20 [2a + 39d]

S40 = 40a + 780d

But

S40 = 1600

1600 = 40a + 780d....... (2)

400 = 20a + 190d .......(1)

1600 = 40a + 780d....... (2)

Solve by elimination method

Multiply equation 1 by 40 and multiply equation 2 by 20 as shown below:

40 x equation 1:

40 x (400 = 20a + 190d)

16000 = 800a + 7600. ........ (3)

20 x equation 2:

20 x (1600 = 40a + 780d)

32000 = 800a + 15600d......... (4)

Subtract equation 3 from equation 4

Equation 4 – Equation 3

32000 = 800a + 15600d

– 16000 = 800a + 7600d

16000 = 8000d

Divide both side by 8000

d = 16000/8000

d = 2

Substituting the value of d into equation 1

400 = 20a + 190d

d = 2

400 = 20a + (190 x 2)

400 = 20a + 380

Collect like terms

400 – 380 = 20a

20 = 20a

Divide both side by 20

a = 20/20

a = 1

Therefore,

First term (a) = 1.

Common difference (d) = 2.

A. Determination of the sum of the 10th term.

First term (a) = 1.

Common difference (d) = 2

Number of term (n) = 10

Sum of 10th term (S10) =..?

Sn = n/2 [2a + (n – 1)d]

S10 = 10/2 [2x1 + (10 – 1)2]

S10 = 5 [2 + 9x2]

S10 = 5 [2 + 18]

S10 = 5 x 20

S10 = 100

Therefore, the sum of the first 10th term is 100.

B. Determination of the sum of the nth term.

First term (a) = 1.

Common difference (d) = 2

Sum of nth term (Sn) =..?

Sn = n/2 [2a + (n – 1)d]

Sn = n/2 [2x1 + (n – 1)2]

Sn = n/2 [2 + 2n – 2]

Sn = n/2 [2 – 2 + 2n ]

Sn = n/2 [ 2n ]

Sn = n²

Therefore, the sum of the nth term is n²

6 0

2 years ago

What is 5+5 and then divided by 8

JulijaS [17]

Answer: 1.25

Step by step:

= 10/8

= 1.25

5 0

2 years ago

“If it takes 20 minutes to walk each block on the grid, how long will it take to walk from the art supply store to the game stor

Jet001 [13]

Answer:

20 minutes

Step-by-step explanation:

There is only one grid between the art supply store and the game story, so it will only take 20 minutes.

-> See attached

Have a nice day!

I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather

6 0

2 years ago

At what angle does a diffraction grating produce a second-order maximum for light having a first-order maximum at 20.0 degrees?

hichkok12 [17]

Answer:

At 43.2°.

Step-by-step explanation:

To find the angle we need to use the following equation:

$d*sin(\theta) = m\lambda$

Where:

d: is the separation of the grating

m: is the order of the maximum

λ: is the wavelength

θ: is the angle

At the first-order maximum (m=1) at 20.0 degrees we have:

$\frac{\lambda}{d} = \frac{sin(\theta)}{m} = \frac{sin(20.0)}{1} = 0.342$

Now, to produce a second-order maximum (m=2) the angle must be:

$sin(\theta) = \frac{\lambda}{d}*m$

$\theta = arcsin(\frac{\lambda}{d}*m) = arcsin(0.342*2) = 43.2 ^{\circ}$

Therefore, the diffraction grating will produce a second-order maximum for the light at 43.2°.

I hope it helps you!

6 0

3 years ago