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3 years ago

Kylie just accepted a job at a new company where she will make an annual salary of

Mathematics

1 answer:

Softa [21]3 years ago

4 0

Answer:

$73,000

$43,000 + $5,000 x t

Step-by-step explanation:

Every year increase $5,000, after 6 years increase $5000 x 6 = $30,000

Her salary will be $43,000 + $30,000 = $73,000

After t years, her salary will be

$43,000 + $5,000 x t

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The 5th term in a geometric sequence is 160. The 7th term is 40. What are possible values of the 6th term of the sequence?

omeli [17]

Answer:

C. The 6th term is positive/negative 80

Step-by-step explanation:

Given

Geometric Progression

$T_5 = 160$

$T_7 = 40$

Required

$T_6$

To get the 6th term of the progression, first we need to solve for the first term and the common ratio of the progression;

To solve the common ratio;

Divide the 7th term by the 5th term; This gives

$\frac{T_7}{T_5} = \frac{40}{160}$

Divide the numerator and the denominator of the fraction by 40

$\frac{T_7}{T_5} = \frac{1}{4}$ ----- equation 1

Recall that the formula of a GP is

$T_n = a r^{n-1}$

Where n is the nth term

So,

$T_7 = a r^{6}$

$T_5 = a r^{4}$

Substitute the above expression in equation 1

$\frac{T_7}{T_5} = \frac{1}{4}$ becomes

$\frac{ar^6}{ar^4} = \frac{1}{4}$

$r^2 = \frac{1}{4}$

Square root both sides

$r = \sqrt{\frac{1}{4}}$

r = ± $\frac{1}{2}$

Next, is to solve for the first term;

Using $T_5 = a r^{4}$

By substituting 160 for T5 and ± $\frac{1}{2}$ for r;

We get

$160 = a \frac{1}{2}^{4}$

$160 = a \frac{1}{16}$

Multiply through by 16

$16 * 160 = a \frac{1}{16} * 16$

$16 * 160 = a$

$2560 = a$

Now, we can easily solve for the 6th term

Recall that the formula of a GP is

$T_n = a r^{n-1}$

Here, n = 6;

$T_6 = a r^{6-1}$

$T_6 = a r^5$

$T_6 = 2560 r^5$

r = ± $\frac{1}{2}$

So,

$T_6 = 2560( \frac{1}{2}^5)$ or $T_6 = 2560( \frac{-1}{2}^5)$

$T_6 = 2560( \frac{1}{32})$ or $T_6 = 2560( \frac{-1}{32})$

$T_6 = 80$ or $T_6 = -80$

$T_6 =$ ±80

Hence, the 6th term is positive/negative 80

8 0

3 years ago

A garden measures 6 feet by 7 feet. A gravel path of constant width is placed around the garden so that the total area is 72 squ

frosja888 [35]

the answer is 114 because first u have to × and then +

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3 years ago

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What is 6 1/2 - 2 2/5 - 2 1/2 =

VikaD [51]

Answer:

1 3/5

Step-by-step explanation:

Change to mixed fractions, that'll give:

13/2 - 12/5 - 5/2

Using lcm:

16/10

Change back to mixed fractions:

1 6/10

Lowest term:

1 3/5

4 0

3 years ago

How do you convert 0.580 (80repeating) as a fraction?

Gnom [1K]

Answer:

58/100

Step-by-step explanation:

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3 years ago

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A set of scores with a normal distribution has a mean of 50 and a

dimaraw [331]

36, 43, 50, 57, 64

36 and 64 are two standard deviations out, so the empirical rule tells us 95% of scores will fall here with a normal distribution

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3 years ago