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Which of the following numbers are rational?

ololo11 [35]

Answer:

402

Step-by-step explanation:

2(109) plus 2(92) equals 402

6 0

3 years ago

The speeds of cars on a given i street we are normally distributed with a mean of 72 miles per hour and a standard deviation of

Ostrovityanka [42]

Answer: 72.78% of the drivers are traveling between 70 and 80 miles per hour based on this distribution.

Step-by-step explanation:

Let X be a random variable that represents the speed of the drivers.

Given: population mean : M = 72 miles ,

Standard deviation: s= 3.2 miles

The probability that the drivers are traveling between 70 and 80 miles per hour based on this distribution:

$P(70\leq X\leq 80)=P(\frac{70-72}{3.2}\leq \frac{X-M}{s}\leq\frac{80-72}{3.2})\\\\= P(-0.625\leq Z\leq 2.5)\ \ \ \ \ [Z=\frac{X-M}{s}]\\\\=P(Z\leq2.5)-P(Z\leq -0.625)\\\\\\ =0.9938-0.2660\ \ \ [\text{Using p-value calculator}]\\\\=0.7278$

Hence, 72.78% of the drivers are traveling between 70 and 80 miles per hour based on this distribution.

3 0

3 years ago

Evaluate the expression: for y = 2 + 3x when x=4. What does y=?

lora16 [44]

Answer:

y = 14

Step-by-step explanation:

Plug in 4 as x into the equation:

y = 2 + 3x

y = 2 + 3(4)

Simplify:

y = 2 + 12

y = 14

So, when x = 4, y = 14.

4 0

3 years ago

Given the functions f(x) = 2x + 5 and g(x) = x2 + 8, which of the following functions represents f(g(x)] correctly?

lakkis [162]

Answer:

Choice 4.

Step-by-step explanation:

f(g(x))

Replace g(x) with x^2+8 since g(x)=x^2+8.

f(g(x))

f(x^2+8)

Replace old input,x, in f with new input, (x^2+8).

f(g(x))

f(x^2+8)

2(x^2+8)+5

Distribute:

f(g(x))

f(x^2+8)

2(x^2+8)+5

2x^2+16+5

Combine like terms:

f(g(x))

f(x^2+8)

2(x^2+8)+5

2x^2+16+5

2x^2+21

7 0

3 years ago

You and your friend mix water and cirtic acid. You add 3 cups of citrtic acid for every 16 cups of water Your friend adds 2 cups

Vlad [161]

Answer:

A's mixture is more acidic.

Step-by-step explanation:

Given:

Two friends mix water and citric acid.

One (Let A) add 3 cups of citric acid for every 16 cups of water and another (Let B)adds 2 cups of citric acid for every 12 cups of water.

Now, we have to find that whose mixture is more acidic means:-

Solution:

A add 3 cups of citric acid for every 16 cups of water, the ratio = $\frac{3}{16}$

B adds 2 cups of citric acid for every 12 cups of water = $\frac{2}{12}$

Now, to find that who mix more citric acid in the mixture, firstly we will equalize the denominator of both fraction by taking LCM so that can be compare easily.

LCM of 16 and 12:- 48

16 - 16, 32, 48, 64, 80, 96....

12 - 12, 24, 36, 48, 60, 72.......

For friend A - $\frac{3\times3}{16\times3} =\frac{9}{48}$

For friend B - $\frac{2\times4}{12\times4} =\frac{8}{48}$

We found that in terms of 48 cups of water, friend A mixes 9 cups of acid while friend B mixes 8 cups of acid, means A is adding more acid than B and hence friend A's mixture is more acidic.

4 0

3 years ago