Without using a calculator, convert the fraction to a decimal.
2/4=?

Answer:

Step-by-step explanation:

To find the median, we need to arrange the data in ascending order:

70, 71, 72, 74

Since the data set has an even number of values, the median is the average of the two middle values. In this case, the two middle values are 71 and 72. Therefore, the median is:

(71 + 72) / 2 = 143 / 2 = 71.5

So, the median for the given set of data is 71.5.

=============================================

Reason:

This is a geometric series with

The template is [tex]a(r)^{n-1}[/tex]

If -1 < r < 1, then the infinite geometric series converges to a finite number. This is because we add on smaller and smaller pieces, which prevents the sum going off to infinity.

In the case of r = -1/3, it fits the interval  -1 < r < 1. In other words -1 < -1/3 < 1 is true.

We'll plug those values into the formula below to wrap things up.

[tex]S = \frac{a}{1-r}\\\\S = \frac{-4}{1-(-1/3)}\\\\S = \frac{-4}{1+1/3}\\\\S = \frac{-4}{3/3+1/3}\\\\[/tex]

[tex]S = \frac{-4}{4/3}\\\\S = -4 \div \frac{4}{3}\\\\S = \frac{-4}{1} \times \frac{3}{4}\\\\S = \frac{-4*3}{1*4}\\\\S = -3\\\\[/tex]

Therefore,

[tex]\displaystyle \sum_{n=1}^{\infty} -4\left(-\frac{1}{3}\right)^{n-1} = -3[/tex]

The final answer is -3.

You can verify the answer by generating partial sums with a spreadsheet. The partial sums should steadily get closer to -3.

Here's a few partial sums.

[tex]\begin{array}{|c|c|c|} \cline{1-3}\text{n} & \text{a}_{\text{n}} & \text{S}_{\text{n}}\\\cline{1-3}1 & -4 & -4\\\cline{1-3}2 & 1.333333 & -2.666667\\\cline{1-3}3 & -0.444444 & -3.111111\\\cline{1-3}4 & 0.148148 & -2.962963\\\cline{1-3}5 & -0.049383 & -3.012346\\\cline{1-3}6 & 0.016461 & -2.995885\\\cline{1-3}7 & -0.005487 & -3.001372\\\cline{1-3}8 & 0.001829 & -2.999543\\\cline{1-3}9 & -0.00061 & -3.000153\\\cline{1-3}10 & 0.000203 & -2.99995\\\cline{1-3}\end{array}[/tex]

The interesting thing is that the partial sums [tex]S_n[/tex]  bounce around -3 while also getting closer to it.

Answer:

A and B

Step-by-step explanation:

I took some paper and cut it to the shapes and folded them to see which ones are the answer and got those 2. :3

The chemist needs to use 5 liters of the 30% solution and 5 liters of water.

Answer:

30% solution x liters

30%(water) 10-x liters

15% 10 liters

Step-by-step explanation:

The difference of the given fraction is Negative three-fourths.

Given the following fraction difference as shown:

[tex]\sf -2 \dfrac{1}{2} - \huge \text(-1 \dfrac{3}{4} \huge \text)[/tex]

Convert to improper fraction

[tex]\sf -\dfrac{5}{2} + \dfrac{7}{4}[/tex]

Find the LCM

[tex]\sf 2(-5)+\dfrac{7}{4}[/tex]

[tex]\sf -10+\dfrac{7}{4}[/tex]

[tex]\sf -\dfrac{3}{4}[/tex]

Hence, the difference of the given fraction is Negative three-fourths.

Learn more on fraction difference at: https://brainly.com/question/30489902

Answer:

2x^2-8

Step-by-step explanation:

(2x+4)(x-2)

2x(x-2)+4(x-2

2x^2-4x+4(x-2)

2x^2-4x+4x-8

2x^2-8

2x^2-8

Answer:

2x^2 - 8

Step-by-step explanation:

You have to take one of the equations and distribute it to the other equation. I'll distribute the 1st equation.

(2x+4)(x-2)

2x times x = 2x^2

2x times -2 = -4x

4 times x = 4x

4 times -2 = -8

So you get 2x^2 - 4x + 4x - 8.

- 4x + 4x cancel out each other

So your final answer is 2x^2 - 8

Answer:

77.5

Step-by-step explanation:

Given:

Scores: 65, 70, 75, 80, 85, 90, 95

Number of Students: 8, 5, 3, 6, 6, 4, 2

Step 1: Calculate the sum

Sum = (65 * 8) + (70 * 5) + (75 * 3) + (80 * 6) + (85 * 6) + (90 * 4) + (95 * 2)

= 520 + 350 + 225 + 480 + 510 + 360 + 190

= 2635

Step 2: Calculate the mean

Mean = Sum / Total Number of Students

= 2635 / (8 + 5 + 3 + 6 + 6 + 4 + 2)

= 2635 / 34

≈ 77.5

Answer:77.5

Step-by-step explanation: