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Feliz [49]
2 years ago
15

suppose you have $55 in your bank account. You start saving $10 each week. Your friend has $20 in her account and is saving $15

each week. When will you and your friend have the same amount of money in your accounts?
Mathematics
1 answer:
zhenek [66]2 years ago
7 0
The equation is:
55 + 10 x = 20 + 15 x, where x is number of the weeks.
55 - 20 = 15 x - 5 x
35 = 5 x
x = 35 : 5
x = 7
Answer:
The same amount of money in both accounts will be after 7 weeks.
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A chess player moves a knight from the location (3, 2) to (5, 1) on a chessboard. If the bottom-left square is labeled (1, 1), t
KATRIN_1 [288]

Answer:

T(2, -1)

T(1, 2)

Step-by-step explanation:

From (3, 2) to (5, 1), the translation is T(2, -1). x goes up by 2. y goes down by 1.

From (5, 1) to (6, 3), the translation is T(1, 2). x goes up by 1. y goes up by 2.

6 0
2 years ago
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The per capita electric power consumption level in a recent year in Ecuador is normally distributed, with a mean of 471.5 kilo-w
Olin [163]

Answer:

a) 471.5 kilo-watt hours.

b) 31.76 kilo-watt hours

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For the population:

Mean 471.5 kilo-watt hours.

Standard deviation of 187.9 kilowatt-hours.

For the sample:

Sample size of 35, by the Central Limit Theorem:

a) Mean

471.5 kilo-watt hours.

b) Standard deviation

s = \frac{187.9}{\sqrt{35}} = 31.76

31.76 kilo-watt hours

7 0
3 years ago
Use decimals and fractions in the same equation showing the Commutative Property. Repeat for the Associative Property.
Anna71 [15]

For Commutative Property of Addition

Let us take a decimal number 2.14 and a fraction \frac{5}{20}

Now, according to the Commutative property of Addition:

For any two numbers a and b :

a+b = b+a

So, for 2.14 and \frac{5}{20}

Let us add

2.14+\frac{5}{20}  = \frac{214}{100}  +\frac{5}{20}

                                   =\frac{214}{100}  + \frac{5 \times 5}{20 \times 5} \\ \\=\frac{214}{100}  + \frac{25}{100} \\ \\= 2.14 + 0.25 \\ \\ = 2.39

Also,

\frac{5}{20} + 2.14  = \frac{5}{20} + \frac{214}{100}

                                     = \frac{5 \times 5}{20 \times 5} +\frac{214}{100} \\ \\= \frac{25}{100}  + \frac{214}{100} \\ \\=  0.25 + 2.14 \\ \\ = 2.39

Therefore, 2.14+\frac{5}{20} = \frac{5}{20} + 2.14

Hence,  Commutative Property of Addition is satisfied.


For Associated Property of Addition

Let us take two same decimal numbers 2.14 , 7.25 and a fraction \frac{5}{20}

Now, according to the Associated property of Addition:

For any three numbers a, b  and  c

a + (b+c) =(a+b) + c

So, for 2.14 , 7.25 and \frac{5}{20}

The Left hand side:

a + (b+c)

2.14 + (7.25 + \frac{5}{20}) = 2.14 + (\frac{725}{100} + \frac{5 \times 5}{20\times 5})

                                                         = 2.14 + (\frac{725}{100} + \frac{25 }{100})

                                                         = 2.14 + (\frac{750}{100} )

                                                        = \frac{214}{100} + \frac{750}{100}

                                                         = \frac{964}{100}

                                                        =9.64


The Right hand side:

(a + b )+c

(2.14 + 7.25 )+ \frac{5}{20}= ( 9.39 ) + \frac{5 }{20}

                                                = 9.39  + \frac{5 \times 5 }{20 \times 5}

                                                = 9.39  + \frac{25}{100}

                                                = 9.39  + 0.25

                                                = 9.64


Thus,

(2.14 + (7.25 + \frac{5}{20} )= (2.14 + 7.25 )+ \frac{5}{20}

Therefore, 2.14+\frac{5}{20} = \frac{5}{20} + 2.14

Hence,  Associative Property of Addition is satisfied.




8 0
3 years ago
Assume the annual interest rate is 6%. Calculate the value of an investment that pays $100 every two years, starting two
olganol [36]

Answer:

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Step-by-step explanation:

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What is<br> (1/2)^2- 1/2 -6<br><br><br><br><br><br><br><br><br> .
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