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2 years ago

Select all of the following that are equivalent to 1/8

Mathematics

1 answer:

kykrilka [37]2 years ago

6 0

Answer:

4/8: 1/2 or/and 50%

2/8: 1/4 or/and 25%

6/8: 3/4 or/and 75%

Hope this helps!

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Andrew is planning to save allowance money for 20 years. In year one he saves $100, in year

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Answer:

$500

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3 years ago

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shepuryov [24]

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i think y=3/4x-4.2

Step-by-step explanation:

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2 years ago

Mr. Sánchez owns a square field. The side lengths are 0.9 kilometers. There are 1,980 prairie dog burrows in the fields. What is

Simora [160]

The first thing we are going to do is find the area of the field. To do this we are going to use the area of a square formula: $A=s^2$
Were
$A$ is the area in square kilometers
$s$ is one of the sides of the square
We know for our problem that the side lengths of the field are 0.9 kilometers, so $s=0.9$ . Lets replace that value in our formula to find $A$ :
$A=(0.9)^2$
$A=0.81$

Now, to find the population density of the filed, we are going to use the population density formula: $P_{d}= \frac{I}{A}$
where
$P_{d}$ is the population density in <span>in burrows per square kilometer
</span> $I$ is the number of burrows
$A$ is the are of the field
We know that $I=1980$ and $A=0.81$ , so lets replace those values in our formula:
$P_{d}= \frac{1980}{0.81}$
$P_{d}=2444.4$

We can conclude that the <span>density of prairie dog burrows is approximately 2444 burrws per square kilometer.</span>

5 0

2 years ago

Dont really understand how to do this

bija089 [108]

Answers:

$t_{10} = -22 \ \text{ and } S_{10} = -85$

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

Explanation:

$t_1 = \text{first term} = 5\\t_2 = \text{first term}-3 = t_1 - 3 = 5-3 = 2$

Note we subtract 3 off the previous term (t1) to get the next term (t2). Each new successive term is found this way

$t_3 = t_2 - 3 = 2-3 = -1\\t_4 = t_3 - 3 = -1-3 = -4$

and so on. This process may take a while to reach $t_{10}$

There's a shortcut. The nth term of any arithmetic sequence is

$t_n = t_1+d(n-1)$

We plug in $t_1 = 5 \text{ and } d = -3$ and simplify

$t_n = t_1+d(n-1)\\t_n = 5+(-3)(n-1)\\t_n = 5-3n+3\\t_n = -3n+8$

Then we can plug in various positive whole numbers for n to find the corresponding $t_n$ value. For example, plug in n = 2

$t_n = -3n+8\\t_2 = -3*2+8\\t_2 = -6+8\\t_2 = 2$

which matches with the second term we found earlier. And,

$tn = -3n+8\\t_{10} = -3*10+8\\t_{10} = -30+8\\t_{10} = \boldsymbol{-22} \ \textbf{ is the tenth term}$

---------------------

The notation $S_{10}$ refers to the sum of the first ten terms $t_1, t_2, \ldots, t_9, t_{10}$

We could use either the long way or the shortcut above to find all $t_1$ through $t_{10}$ . Then add those values up. Or we can take this shortcut below.

$Sn = \text{sum of the first n terms of an arithmetic sequence}\\S_n = (n/2)*(t_1+t_n)\\S_{10} = (10/2)*(t_1+t_{10})\\S_{10} = (10/2)*(5-22)\\S_{10} = 5*(-17)\\\boldsymbol{S_{10} = -85}$

The sum of the first ten terms is -85

-----------------------

As a check for $S_{10}$ , here are the first ten terms:

t1 = 5
t2 = 2
t3 = -1
t4 = -4
t5 = -7
t6 = -10
t7 = -13
t8 = -16
t9 = -19
t10 = -22

Then adding said terms gets us...

5 + 2 + (-1) + (-4) + (-7) + (-10) + (-13) + (-16) + (-19) + (-22) = -85

This confirms that $S_{10} = -85$ is correct.

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1 year ago

Teague is participating in a 50K run to raise money for a charity. He has already raised $102 and will receive $1.40 for each ki

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He has to run 45 kilometers

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2 years ago