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2 years ago

Please Help Timed Question. Picture provided below.

Mathematics

1 answer:

Jobisdone [24]2 years ago

6 0

Answer:

17.67 mpg

Step-by-step explanation:

The fuel efficiency is given by :

$\eta=1.437+0.541\times s$

We need to find the fuel efficiency for a speed of 30 mph

Put the value of s equals 30 mph in the above equation.

$\eta=1.437+0.541\times 30\\\\\eta=17.67\ mpg$

So, the required fuel efficiency is equal to 17.67 mpg.

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A researcher conducted an Internet survey of 500 students at a particular college to estimate the average amount of money studen

bonufazy [111]

Answer:

The margin of error is $ME = 2.2962$

Step-by-step explanation:

From the question we are told that

The number of student is $n = 500$

The highest amount is $A =$ $200

The lowest amount is $B =$ $75

The sample mean is $x =$ &140

The Standard deviation of this set is mathematically evaluated as

$s = \frac{A-B}{4}$

Substituting values

$s = \frac{200-75}{4}$

$s = 31.25$

The margin of error (ME) is mathematically evaluated as

$ME = t_{n-1}__{\alpha }} * \frac{s}{\sqrt{n} }$

Where $t_{n-1}__{\alpha }}$ is the critical value for $\alpha = 0.05$ i.e the significance level

From the critical value table this is $t_{n-1}__{\alpha }} = 1.649$

$ME = 1.649 * \frac{31.25}{\sqrt{500} }$

$ME = 2.2962$

6 0

3 years ago

Determine whether each equation is True or False. In case you find a "False" equation, explain why is False.

elixir [45]

Answer:

(1) TRUE.

(2) FALSE.

(3) FALSE.

(4) TRUE.

(5) FALSE.

Step-by-step explanation:

(1) $\sqrt{32} = 2^{\frac{5}{2} }$

$2^{\frac{5}{2} } = (\sqrt{2} )^5 = (\sqrt{2} \ \times \ \sqrt{2} \ \times \ \sqrt{2} \ \times \ \sqrt{2} \ \times \ \sqrt{2}) = 4\sqrt{2}\\\\\sqrt{32} = \sqrt{16 \ \times \ 2}\ = \ \sqrt{16} \ \times \ \sqrt{2} \ = \ 4\sqrt{2}$

Thus, the equation is TRUE.

(2) $16^{\frac{3}{8} } = 8^2$

$16^{\frac{3}{8} } =(2^4)^{\frac{3}{8} } = 2^\frac{3}{2} }= (\sqrt{2} )^3 = (\sqrt{2} \ \times \ \sqrt{2} \ \times \ \sqrt{2}) = 2\sqrt{2} \\\\8^2 = 64$

Thus, the equation is FALSE.

(3) $4^{\frac{1}{2} } = \sqrt[4]{64}$

$4^{\frac{1}{2} }= \sqrt{4} = 2\\\\\sqrt[4]{64} = (64)^{\frac{1}{4} } = (2^6)^{\frac{1}{4} }= 2^{\frac{6}{4} } = 2^{\frac{3}{2} }=(\sqrt{2} )^3 = (\sqrt{2} \times \sqrt{2} \times \sqrt{2} ) = 2\sqrt{2}$

Thus, the equation is FALSE.

(4) $2^8 = (\sqrt[3]{16} )^6$

$2^8 = 256\\\\ (\sqrt[3]{16} )^6 = (16)^{\frac{6}{3} } = (2^4)^{\frac{6}{3} } = (2)^{\frac{24}{3} } = 2^8 = 256$

Thus, the equation is TRUE.

(5) $(\sqrt{64} )^{\frac{1}{3} } = 8^{\frac{1}{6} }\\\\$

$8^{\frac{1}{6} } = (2^3)^{\frac{1}{6} } = 2^{\frac{3}{6} } = 2^{\frac{1}{2} } = \sqrt{2} \\\\(\sqrt{64} )^{\frac{1}{3} } = (2^6)^{\frac{1}{3} } = 2^{\frac{6}{3} } = 2^2 = 4$

Thus, the equation is FALSE.

4 0

2 years ago

You’re in charge of your country currency which is backed by gold standard unfortunately gold production is dropping sharply and

Alex17521 [72]

Change the entire currency system

8 0

2 years ago

There are 10 cards. Each card has one number between 1 and 10, so that every number from 1 to 10 appears once.

pychu [463]

Answer:

When a card is chosen at random with replacement five times, X is the number of times a prime number is chosen. Here the card is chosen with replacement. This implies probability for choosing a prime number remains the same as the previously drawn card is replaced.

The sample space= {1,2,3,4,5,6,7,8,9,10}

Prime numbers = {2,3,5,7}

Prob for drawing prime number = 4/10 = 0.4

is the same when replacement is done.

Also there are two outcomes either prime or non prime. Hence in this case, X the no of times a prime number is chosen, is binomial with p =0.4 and q = 0.6 and n=5

When a card is chosen at random without replacement three times, X is the number of times an even number is chosen.

Prob for an even number = 0.5

But after one card drawn say odd number next card has prob for even number as 5/9 hence each draw is not independent of the other. Hence not binomial.

When a card is chosen at random with replacement six times, X is the number of times a 3 is chosen.

Here since every time replacement is done, probability of drawing a 3 remains constant = 1/10 = 0.3

i.e. each draw is independent of the other and there are only two outcomes , 3 or non 3. Hence here X is binomial.

When a card is chosen at random with replacement multiple times, X is the number of times a card is chosen until a 5 is chosen

Here X is the number of times a card is chosen with replacement till 5 is chosen. This is not binomial. Here probability for drawing nth time correct 5 is P(non 5 in the first n-1 draws)*P(5 in nth draw) = 0.1^(n-1) (0.9)

Because nCr is not appearing i.e. 5 cannot appear in any order but only in the last draw, this is not binomial.

Step-by-step explanation:

6 0

2 years ago

Out of the 125 children at summer camp 45 signed up for swimming and 38 signed up for arts and crafts twelve students who signed

kap26 [50]

Add 48, 38, and 12 together to get your answer

5 0

3 years ago