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emmasim [6.3K]
2 years ago
14

A bicycle manufacturing company makes a particular type of bike. Each child bike requires 4 hours to build and 4 hours to test.

Each adult bike requires 6 hours to build and 4 hours to test. With the number of workers, the company is able to have up to 120 hours of building time and 100 hours of testing time for a week. If c represents child bikes and a represents adult bikes, determine which system of inequality best explains whether the company can build 20 child bikes and 6 adult bikes in the week. (2 points) No, because the bike order does not meet the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100 No, because the bike order does not meet the restrictions of 4c + 4a ≤ 120 and 6c + 4a ≤ 100 Yes, because the bike order meets the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100
Mathematics
1 answer:
Leokris [45]2 years ago
6 0

Answer:a

Step-by-step explanation:

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For a polygon to be convex means that all of its interior angles are less than 180 degrees. Prove that for all integers n ≥ 3, t
Alexeev081 [22]

Answer: check explanation

Step-by-step explanation:

Let K(n) be the sum of the interior angles in any n-sided convex polygon which is exactly 180(n −2)

degrees.

CASE: n = 3. A 3-sided polygon is a triangle, whose interior angles were shown always to sum to be 180 degree

INDUCTION HYPOTHESIS: Suppose that K(b) holds for some b ≥ 3. Which means that the interior angles in any b-sided convex

polygon is exactly 180(n −2) degrees.

INDUCTION STEP: We need to show that K(n is greater than or equals to 3) . That is, the interior angles of any b+1-sided convex polygon

is exactly 180(b−2) = 180(b −1) degrees,

Let X be any (b+1)-vertex convex polygon, say with successive vertices x1, x2,..., xb+

Now Y is also a convex polygon , so by the induction hypothesis K(b), the sum of the interior

angles of Y is 180(k −2).

Now let T be the triangle with vertices xk , xb+1, x1. The sum of the interior angles in X is the sum of those

in Y plus the sum of those in T .

So the sum of the interior angles in X is

180(b −2)+180 = 180((b +1)−2) = 180(b −1).

Since X was arbitrary, we conclude that the sum of the interior angles of any (b +1)-sided convex polygon

is 180((b−2)+1) = 180(b−1). That is, P(b +1) holds.

And which means that n is greater or equals to 3

8 0
2 years ago
At a desert resort, the temperature at 7 a.m. was 3°C. The temperature increased by an average of 3.4°C each hour until it reach
11Alexandr11 [23.1K]

Answer: It will take 8 hours to reach this temperature.

Step-by-step explanation:

Given: At a desert resort, the temperature at 7 a.m. was 3°C.

The temperature increased by an average of 3.4°C each hour until it reached 30.2°C.

Let x be the number of hours taken to reach 30.2°C..

As per given ,

Initial temperature +(average increase in temperature) (Number of hours) = 30.2

⇒3+3.4x=30.2

⇒3.4x=30.2-3

⇒3.4x=27.2

⇒ x=8    [Divide both sides by 3.4]

Hence, it will take 8 hours to reach this temperature.

6 0
1 year ago
If the egress rate for a stadium is 5,500 fans per hour and it takes fans about one-third less time for fans to exit a game as i
Marina CMI [18]

Answer:

1833 fans per hour

Step-by-step explanation:

Ingress is entering and Egress is exiting.

Since exiting time is 1/3rd less than entering time, we have 5500 people exiting, so ingessing would be 1/3rd that.

Thus,

Ingress Rate = 5500/3 = 1833.33

Rounding to whole number, we have 1833 fans per hour

4 0
2 years ago
Read 2 more answers
Elliot has a total of 26 books. He has 12 more fiction books than nonfiction books. Let x represent the number of fiction books
AlladinOne [14]

<u>Answers</u>

19 fiction books

7 nonfiction books


<u>Explanation</u>

x + y = 26  ............................................. (i)

x – y = 12  ............................................ (ii)

Elliot added the two equations and the result was

2x = 38.

Dividing both sides by 2;

x = 19

There are 19 fiction books.

Substituting x in equation (i),

x + y = 26             when x = 19

19 + y = 26

y = 26 - 19

   = 7

There are 7 nonfiction books

4 0
2 years ago
Read 2 more answers
According to Net Market Share, Microsoft's Internet Explorer browser has 53.4% of the global market. A random sample of 70 users
Natalija [7]

Answer:

Probability that 32 or more from this sample used Internet Explorer as their browser is 0.9015.

Step-by-step explanation:

We are given that according to Net Market Share, Microsoft's Internet Explorer browser has 53.4% of the global market.

A random sample of 70 users was selected.

Let \hat p = <u><em>sample proportion of users who used Internet Explorer as their browser.</em></u>

The z score probability distribution for sample proportion is given by;

                            Z  =  \frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }  ~ N(0,1)

where, p = population proportion of users who use internet explorer = 53.4%

           \hat p = sample proportion = \frac{32}{70} = 0.457

           n = sample of users = 70

Now, probability that 32 or more from this sample used Internet Explorer as their browser is given by = P( \hat p \geq 0.457)

      P( \hat p \geq 0.457) = P( \frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } } \geq \frac{0.457-0.534}{\sqrt{\frac{0.457(1-0.457)}{70} } } ) = P(Z \geq -1.29)

                            = P(Z \leq 1.29) = <u>0.9015</u>

The above probability is calculated by looking at the value of x = 1.29 in the z table which has an area of 0.9015.

4 0
2 years ago
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