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Westkost [7]
3 years ago
15

Phil strung two sets of lights around the window of his store. The first set of lights blinks every 30s and the second every 45s

. How often do the sets of lights blink at the same time?
Mathematics
1 answer:
Amiraneli [1.4K]3 years ago
5 0

Answer:

Every 90 seconds, the two sets of light blink together.

Step-by-step explanation:

Given that there are two sets of lights.

First light blinks at every 30s and

Second light blinks at every 45s

To find:

How often the sets of lights blink together?

Solution:

As per given statement,

First light blinks after 30s, 60s, <u>90s</u>, 120s, 150s, <u>180s</u>, ........

Second light blinks after 45s, <u>90s</u>, 135s, <u>180s</u>, .....

If we look at the common time, shown by underlining it, the two sets of light blink at the same time after 90s, 180s, ...... and so on.

So, the two lights blink together after every 90s.

This can also be solved by finding LCM (Least Common Multiple) of the two numbers i.e. 30 and 45.

Let us have a look at the factors of 30 and 45.

30 = 2 \times <u>3</u> \times <u>5</u>

45 = 3 \times <u>3</u> \times <u>5</u>

<u />

So, LCM = 2 \times 3 \times 3 \times 5 = <em>90</em>

<em></em>

So, after every <em>90s, </em>the lights will blink together.

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Jen earns $35,650 a year working for an electronics supplier. She is single with no
Kobotan [32]

Answer: 5% approximately

Step-by-step explanation:

Jen earns $35,650 a year working for an electronics supplier and pays $1,749.80 in state income tax each year. To calculate the income tax rate, we divide the amount paid as tax by her annual income and then multiply by 100. This will be:

= 1749.80/35650 × 100

= 4.91%

= 5% approximately

The state's tax rate is 5%.

7 0
3 years ago
Which statements are true based on the diagram? Check all that apply.
GrogVix [38]
First statement: False. Points K, M and N form a triangle.
Second statement: True. Points J, K, and Q are on the same line.
Third statement: False. KN and MQ intersect at N, not at R.
Fourth statement: False. JQ and KM intersect at K, but MQ does not pass through it.
Fifth statement: True. By definition, there is always only 1 line that can be drawn between 2 given points.
6 0
3 years ago
Read 2 more answers
Geometric Series assistance
Levart [38]

we have been asked to find the sum of the series

\sum _{n=1}^5\left(\frac{1}{3}\right)^{n-1}

As we know that a geometric series has a constant ratio "r" and it is defined as

r=\frac{a_{n+1}}{a_n}=\frac{\left(\frac{1}{3}\right)^{\left(n+1\right)-1}}{\left(\frac{1}{3}\right)^{n-1}}=\frac{1}{3}

The first term of the series is a_1=\left(\frac{1}{3}\right)^{1-1}=1

Geometric series sum formula is

S_n=a_1\frac{1-r^n}{1-r}

Plugin the values we get

S_5=1\cdot \frac{1-\left(\frac{1}{3}\right)^5}{1-\frac{1}{3}}

On simplification we get

S_5=\frac{121}{81}

Hence the sum of the given series is \frac{121}{81}

5 0
3 years ago
I need help with my algerbra
Molodets [167]
I can help you what problem??
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3 years ago
Kevin is 3 years older than daniel. Two years ago, Kevin was 4 times as old as Daniel. Let k be Kevin’s age and let d be Daniels
bezimeni [28]

Answer:

Daniel (now) is 3 years old,  (2 years ago) is 1 year old.

Kevin (now) is 6 years old,   (2 years ago) is 4 years old.

Step-by-step explanation:

Now:

-Kevin: k = d + 3

-Daniel: d

2 years ago:

-Kevin: k - 2 = 4(d - 2)

-Daniel: d - 2

We have the equation:

(k - 2) + 2 = k

4(d - 2) + 2 =  d + 3

4d - 8 + 2 = d + 3

3d - 6 = 3

3d = 9

d = 3

k = d + 3 = 3 + 3 = 6

8 0
3 years ago
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