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kondor19780726 [428]
2 years ago
5

What is the solution to 3/2b + 5 < 17? Explain How.

Mathematics
2 answers:
jek_recluse [69]2 years ago
8 0
<h3>3/2b + 5 < 17</h3>

<em>We subtract 5 from both sides of the inequality.</em>

<h3>3/2b + 5 - 5 < 17 - 5</h3><h3>3/2 b < 12</h3>

<em>Multiply both sides by 2/3.</em>

<h3>( 2/3) * (3/2b) < (2/3) * 12</h3><h3>b < 8</h3>

<em>Therefore, the </em><em>correct option</em><em> is </em><em>alternative "A".</em>

<em>We would think that it is </em><em>option B,</em><em> but the only difference is that it changes the</em><em> direction of the sign.</em>

Over [174]2 years ago
4 0

Answer:  [A]: " b < 8 " .
_____

Step-by-step explanation:

Given:
Find the solution to:   " 3/2b + 5 < 17 " ; and choose from the answer choices.

So; we have:  

 (3/2)b + 5 < 17  ;

 Now, subtract "5" from each side of this inequality:
 (3/2)b + 5 − 5  <  17 − 5  ;

   To get:
  (3/2)b  <  12 ;

Now, let's multiply Each Side of this inequality by "2" ;

 to get rid of the fraction:

    "  2*(3/2)b  <   12*2 "  ;

{Note: " 2 *\frac{3}{2}=\frac{2}{1}*\frac{3}{2} " } ;

Note:  To simplify:  " \frac{2}{1} * \frac{3}{2} " ;
   Note the "2" in the denominator in the "first term" ;  

   And:  The "2" in the denominator in the "second term" ;

      Both "cancel out" to "1" ;  since:  "[ 2 / 2 = 2÷2 = 1 ]" ;

   And:  we have:  " \frac{1}{1}*\frac{3}{1}= 1 *3 = 3 " };

_____
and rewrite:
   " 3b < 24 "  ;

Now, divide Each side of the inequality by "3" ;

 to isolate "b" on one side of the inequality;

and to solve for "x" ;
_____
 " 3b/3 < 24/3 " ;

 to get:

_____

   " b < 8 " ; which corresponds to the correct answer:

Answer choice:  [A]:  " b < 8 " .
_____

Hope this is helpful to you! Best wishes!
_____

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62% of U.S. adults have very little confidence in newspapers. You randomly select 10 U.S. adults. Find the probability that the
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Answer:

a) 0.1829

b) 0.6823

c) 0.0413

Step-by-step explanation:

We are given the following information:

We treat adult having little confidence in the newspaper as a success.

P(Adult have little confidence) = 62% = 0.62

Then the number of adults follows a binomial distribution, where

P(X=x) = \binom{n}{x}.p^x.(1-p)^{n-x}

where n is the total number of observations, x is the number of success, p is the probability of success.

Now, we are given n = 10

a) exactly 5

P(x =5)\\\\=\binom{10}{5}(0.62)^5(1-0.62)^5\\\\=0.1829

0.1829 is the probability that exactly 5 out of 10 U.S.adults have very little confidence in newspapers.

b) atleast six

P(x \geq 6)\\\\ = P(x = 6) + P(x = 7)+P(x = 8)+P(x = 9)+P(x=10)\\\\= \displaystyle\sum \binom{10}{n}(0.62)^n(1-0.62)^{10-n}, n =6,7,8,9,10\\\\= 0.6823

0.6823 is the probability that atleast 6 out of 10 U.S. adults have very little confidence in newspapers.

c) less than four

P(x

0.0413 is the probability that less than 4 out of 10 U.S. adults have very little confidence in newspapers.

8 0
3 years ago
The surface area of a sphere can be approximated as follows:
notsponge [240]

<em><u>Question:</u></em>

The surface area of a sphere can be approximated as follows:

Surface area = 4πr2;

where r is the radius of the sphere;

π is a constant that is roughly equal to 3.

Calculate the surface area of a sphere with a radius of 7 meters using the simple approximation above.

<em><u>Answer:</u></em>

<h3>The surface area of a sphere  is 588 square meter</h3>

<em><u>Solution:</u></em>

<em><u>The surface area of a sphere is given as:</u></em>

Surface\ area = 4 \pi r^2

Where, "r" is the radius of sphere

π is a constant that is roughly equal to 3

From given,

Radius = 7 meter

<em><u>Substitute r = 7 in given formula</u></em>

Surface\ Area = 4 \times 3 \times 7^2\\\\Surface\ Area = 4 \times 3 \times 49\\\\Surface\ Area = 12 \times 49\\\\Surface\ Area = 588

Thus the surface area of a sphere  is 588 square meter

6 0
3 years ago
Read 2 more answers
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