How many integers between 160 and 279 inclusive, are divisible by 7?

Answers

Answer 1
Answer:

Answer:

17

Step-by-step explanation:

We can put this as an AP (arithmetic progression).

The first number, after 160, that is divisible by 7 is:

161

The last number before 279 that is divisible by 7 is:

273

We can use the formula:

t_n=a+(n-1)d

Where

tn is the nth term [here we take the last one, 273

a is the first term [161]

d is the common difference [7]

and n is the number of terms, we are trying to find this.

Substituting we get:

t_n=a+(n-1)d\n273=161+(n-1)(7)\n273=161+7n-7\n273=154+7n\n7n=119\nn=17

Hence, there are 17 integers


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Answers

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Step-by-step explanation:

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Suppose that a medical test has a 92% chance of detecting a disease if the person has it (i.e., 92% sensi- tivity) and a 94% chance of correctly indicating that the disease is absent if the person really does not have the disease (i.e., 94% specificity). Suppose 10% of the popu- lation has the disease. (a) What is the probability that a randomly chosen per- son will test positive

Answers

Answer:

14.6% probability that a randomly chosen person will test positive

Step-by-step explanation:

We have these following probabilities:

10% probability that a randomly selected person has the disease.

If a person has the disease, 92% probability of testing positive.

100-10 = 90% probability that a person does not have the disease.

If a person does not have the disease, 100-94 = 6% probability of testing positive.

What is the probability that a randomly chosen person will test positive

92% of 10% or 6% of 90%.

Then

p = 0.92*0.1 + 0.06*0.9 = 0.146

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What is the greatest common factor of 4xy2 and 20x2y4?4xy
4xy2
24xy
24xy2

Answers

The greatest common factor of 4xy² and 20x2y^4 is: 4xy².

What is the Greatest Common Factor?

Greatest common factor of a set of terms is the factor that all terms in the set share together.

Given:

4xy² and 20x2y^4

4xy² can divide both terms, meaning both terms share a factor.

Therefore, the greatest common factor of 4xy² and 20x2y^4 is: 4xy².

Learn more about greatest common factor on:

brainly.com/question/219464

The ratio of the interior angle of a regular polygon to the exterior angle is 13:2 . How many sides does it have?

Answers

Answer:

15

Step-by-step explanation:

Int angle : Ext angle : Total

13 : 2 : 15 (13+2)

We know that, int angle + ext angle = 180

Let's introduce a variable x to help solve this ratio

Our ratio is now - 13 x : 2 x : 15x

Use your total ratio and equate it to your total angle size

15 x = 180

x = 180 / 15 = 12

So,

Int angle = 13 x = 13 (12) = 156

Ext angle = 2 x = 2 × 12 = 24

Now, use this formula.

Ext angle = 360 / n

(n represents your number of sides)

24 = 360 / n

n = 360 / 24 = 15