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shusha [124]
3 years ago
13

lauren wants to keep her cell phone bull under $60 per month. Her current cell phone plan is $30 per month plus $0.50 per text.

Write an inequality to represent the number of texts t, Lauren can send each month while staying within her budget
Mathematics
1 answer:
stellarik [79]3 years ago
8 0

Answer:

The correct answer is t < 60.

Step-by-step explanation:

Lauren wants to keep her cell phone bill below $60 per month.

Lauren's current cellphone plan charges her a fixed price of $30 and per text price for one text is $0.50.

Let Lauren sends t texts in a complete month.

Total money spent on texts in a month is given by $ (0.50 × t)

Therefore Lauren's total spent in a month is given by $ (30 + (0.50 × t)).

But this amount should be under $60 as per as the given problem.

∴ 30 + (0.50 × t) < 60

⇒ (0.50 × t) < 30

⇒ t < \frac{30}{0.50}

⇒ t < 60.

So in order to keep her phone monthly bill under $60, Lauren should keep her number of texts below 60.

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A radioactive substance decreases in the amount of grams by one-third each year. If the starting amount of the
katovenus [111]

Answer:

The sequence is geometric. The recursive formula is a_{n}=2/3a_{n-1}

Step-by-step explanation:

In order to solve this problem, you have to calculate the amount of the substance left after the end of each year to obtain a sequence and then you have to determine if the sequence is arithmetic or geometric.

The substance decreases by one-third each year, therefore:

After 1 year:

1452-\frac{1}{3}(1452)

Using 1452 as a common factor and solving the fraction:

1452(1-\frac{1}{3})=1452(\frac{2}{3})=968

You can notice that in general, after each year the amount of grams is the initial amount of the year multiplied by 2/3

After 2 years:

968(\frac{2}{3})=\frac{1936}{3}

After 3 years:

\frac{1936}{3}(\frac{2}{3})=\frac{3872}{9}

The sequence is:

1452,968,1936/3,3872/9....

In order to determine if the sequence is geometric, you have to calculate the ratio of two consecutive terms and see if the ratio is the same for all two consecutive terms. The ratio is obtained by dividing a term by the previous term.

The sequence is arithmetic if the difference of two consecutive terms is the same for all two consecutive terms.

-Calculating the ratio:

For the first and second terms:

968/1452=2/3

For the second and third terms:

1936/3 ÷ 968 = 2/3

In conclussion, the sequence is geometric because the ratio is common.

The recursive formula of a geometric sequence is given by:

a_{n}=ra_{n-1}

where an is the nth term, r is the common ratio and an-1 is the previous term.

In this case, r=2/3

7 0
3 years ago
10. Use the formula for the
dimulka [17.4K]

9514 1404 393

Answer:

  48 m³

Step-by-step explanation:

The correct formula for the volume of a pyramid is ...

  V = 1/3Bh

For the given values, the volume is ...

  V = 1/3(36 m²)(4 m) = 48 m³

3 0
3 years ago
HaLp PwEaSe <br>what is the least common denominator(LDC) of 5/6 and 11/4 hurry pwease
AleksAgata [21]

Answer:

2

Step-by-step explanation:

3 0
3 years ago
Angelina wants to buy the same number of pens and pencils. Pens come in 8 packs and pencils come in packs of 9. What is the leas
andrew11 [14]

Answer:

Angelina should buy 9 packs of pens and 8 packs of pencils.

Step-by-step explanation:

Each pack of pens = 8 pens

Each pack of pencils = 9 pencils.

Also we know that, Commutative Property of Multiplication states that

a x b = b x a for any two numbers a and b.

So, 8 x 9 = 72 = 9 x 8

Hence, she should buy 9 packs of pens, so she will have 9 x 8 = 72 pens.

And she should buy 8 packs of pencils, she will have 8 x 9 = 72 pencils.

7 0
4 years ago
PLESE HELPPP!!!!!!!!!!!!!!!!
zzz [600]

Answer:

B. \frac{6}{2x^{2}  - 5x}

Step-by-step explanation:

The product of the ratioal expressions given above can be found as follows:

= \frac{2}{x} * \frac{3}{2x - 5}

Multiply the denominators together, and the numerators together, separately to get a single expression

\frac{2(3)}{x(2x - 5)}

= \frac{6}{x(2x) - x(5)}

= \frac{6}{2x^{2}  - 5x}

The product of the expression \ = \frac{2}{x}*\frac{3}{2x - 5} = \frac{6}{2x^{2}  - 5x}

The answer is B.

8 0
3 years ago
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