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3 years ago

Choose all numbers that are divisible by 3

Mathematics

1 answer:

Aleks04 [339]3 years ago

3 0

Answer:

A 61377

B 87405

Step-by-step explanation:

If sum of the digits of a number is divisible by 3, then that number is also divisible by 3.

Option A:

Given number is: 61377

Sum of the digits = 6+1+3+7+7 = 24

24 is divisible by 3, hence 61377 is also divisible by 3.

Option B:

Given number is: 87405

Sum of the digits = 8+7+4+0+5 = 24

24 is divisible by 3, hence 87405 is also divisible by 3.

Option C:

Given number is: 30898

Sum of the digits = 3+0+8+9+8 = 28

28 is not divisible by 3, hence 30898 is also not divisible by 3.

Similarly, sum of the digits of the numbers in options D, E and F are 8, 22 and 26 respectively, which are not divisible by 3, hence the numbers 6020, 29830 and 75932 are also not divisible by 3.

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16 Use the Empirical Rule. (Do not use technology. Technology will give a slightly different answer.)

kotykmax [81]

Answer:

a)8.4kg to 10.6kg

b)7.3 kg to 11.7kg

c)16%

d) 95%

e) 0.15%

Step-by-step explanation:

The empirical rule formula states that:

68% of data falls within 1 standard deviation from the mean - that means between μ - σ and μ + σ .

95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ .

99.7% of data falls within 3 standard deviations from the mean - between μ - 3σ and μ + 3σ

From the question,

Mean(μ) = 9.5 kg,

Standard Deviation (σ) = 1.1 kg.

a) 68% of the data is between which 2 values?

68% of data falls within 1 standard deviation from the mean - that means between μ - σ and μ + σ .

μ - σ

= 9.5kg - 1.1kg

= 8.4kg

μ + σ

= 9.5kg + 1.1kg

= 10.6kg

Therefore, 68% of the data is between 8.4kg to 10.6kg

(b) 95% of the data is between which 2 values?

95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ .

μ - 2σ

9.5kg - 2(1.1)kg

9.5kg - 2.2 kg

= 7.3kg

μ + 2σ

9.5kg + 2(1.1)kg

9.5kg + 2.2 kg

= 11.7kg

Therefore, 95% of the data is between 7.3 kg to 11.7kg

We need to find how many standard deviations from the mean 8.4kg is, in order to know the percentage it falls under

μ - xσ = 8.4kg

= 9.5kg - 1.1x = 8.4kg

9.5 - 8.4 = 1.1x

1.1 = 1.1x

x = 1.1/1.1

x = 1

Hence, the percentage it falls under according to Empirical rule = 68%

The percentage of the data that is less than 8.4 kg is calculated as:

100 - 68/2 = 32/2 = 16%

(d) What percentage of the data is between 7.3 kg and 11.7 kg?

We have to find the Standard deviation that they fall under

For 7.3 kg

μ - xσ = 7.3kg

= 9.5kg - 1.1x = 7.3kg

9.5 - 7.3 = 1.1x

2.2 = 1.1x

x = 2.2/1.1

x = 2

μ + xσ = 11.7kg

= 9.5kg + 1.1x = 11.7kg

11.7 - 9.5 = 1.1x

2.2 = 1.1x

x = 2.2/1.1

x = 2

Therefore, based on the calculation above and the empirical formula rule, the percentage of the data is between 7.3 kg and 11.7 kg is 95%

(e) What percentage of the data is more than 12.8 kg?

μ + xσ = 12.8kg

9.5kg + 1.1x = 12.8kg

= 12.8- 9.5 = 1.1x

3.3 = 1.1x

x = 3.3/1.1

x = 3

Hence, the percentage it falls under according to Empirical rule = 99.7%

The percentage of the data that is more than 12.8kg is calculated as:

100 - 99.7/2 = 0.3/2 = 0.15%

5 0

3 years ago

An exterior angle of a regular polygon cannot have the measure Select one: a. 90 b. 120 c. 50 d. 40 e. 30

Otrada [13]

Answer: c. 50

Step-by-step explanation:

1. By definition, when you add the exterior angles of a regular polygon, you obtain 360 degrees and the number of sides of that polygon can be calculated by dividing 360 degrees by the measure of the exterior angle of it.

2. As you know, the number of sides cannot be fractions, therefore, if you make the folllowing division:

360°/50°=36/5

You obtain a fraction.

3. Then, an exterior angle of a regular polygon cannot have the measure is 50°.

7 0

4 years ago

Read 2 more answers

Determine whether the ordered pair is a solution of the given system. (3,10); y greater than 2xplus3 y less than 3xplus1 Is

-BARSIC- [3]

Answer:

(3,10) is not a solution of the given system.

Step-by-step explanation:

Testing the point (3,10) for the system of inequalities, where 3 is the x coordinate, and 10 the y-coordinate, then:

$\left\{\begin{matrix}y &> 2x+3 & \\y& 2(3)+3\Rightarrow 10>9 \: False\\10>3(3)+1\Rightarrow 10 >10 \: False$

So the point (3,10) is not a solution of the given system.

5 0

4 years ago

What does -m+8=4m-7<br>equal <br>

Olegator [25]

Answer:

Step-by-step explanation:

-m+8=4m-7

8=4m-(-m)-7

8=4m+m-7

8=5m-7

5m=8+7

5m=15

m=15/5

m=3

5 0

3 years ago

Read 2 more answers

A patient is given a 100-milligram dosage of a drug that decays exponentially at a rate of 11% per hour. The doctor wants to kno

I am Lyosha [343]

Answer:

This is an example of exponential decay (somewhat similar to half-life).

If it decays at 11% per hour we can calculate its half-life by this formula:

half life = [ time • ln (2) ] ÷ ln (beginning amount ÷ ending amount)

where "ln" means natural log

half life =[ 1 hour * .69315] / ln (100 / 89)

half life =[.69315] / ln (1.1235955056)

half life =[.69315] / 0.11653381624

half life = 5.9481 hours

We need "lambda" "λ" (the decay constant) which equals

λ = ln(2) / half-life = .693147 / 5.9481 = 0.1165325062

Now we need a formula for the time required:

time = ln (Nt ÷ N0) ÷ -λ where No = beginning amount (100 milligrams) Nt = ending amount (15 milligrams)

time = ln (15 ÷ 100) ÷ -0.1165325062

time = ln (.15) / -0.1165325062

time = -1.8971199849 / -0.1165325062

time = 16.2797492885 hours

Source: https://www.1728.org/halflif2.htm

Step-by-step explanation:

4 0

3 years ago