Distribute and simplify these radicals. √12•(-1+√5) O-4√3 O-2√3+2√15 O 4√3 06√3

NewPop produces their brand of soda drinks in a factory where they claim that the

Citrus2011 [14]

Answer:

a) 14960 bottles

b) 502 bottles

Step-by-step explanation:

Given that:

Mean (μ) = 24 ounces, standard deviation (σ) = 0.14 ounces

a) From empirical rule (68−95−99.7%) , 68% of the population fall within 1 standard deviation of the mean (μ ± 1σ).

Therefore 68% fall within 0.14 ounces of the mean

the number of bottle = 22,000*68% = 14960 bottles

b) To solve this we are going to use the z score equation given as:

$z=\frac{x-\mu}{\sigma}$ where x is the raw score = 23.72

$z=\frac{x-\mu}{\sigma}=\frac{23.72-24}{0.14} =-2$

From the normal probability distribution table: P(X < 23.72) = P (Z < -2) = 0.0228

The number of rejected bottles = 22000 × 0.0228 = 502 bottles

8 0

3 years ago

Find the circumference of a circle whose area is 24

zalisa [80]

The answer is: " 17.35 " .

__________________________________

→ The circumference of the circle is: " 17.35 units " .

__________________________________

The area, "A", of a circle:

A = $\pi$ * r² ;

Note: $\pi = 3.14$ .

The area of the circumference, "C", of a circle:

C = 2 $\pi$ r .

__________________________________________

Given:

A = 24 ;

Use the formula for the area, "A" of a circle, to find the radius, "r" .

Then, plug the value obtained for "r" into the formula for the circumference, "C" , of a circle:

C = 2 $\pi$ r l

To solve for the circumference, "C", of the circle.

________________

A = $\pi * r^{2}$ ;

24 = 3.14 * r² ;

↔ 3.14 * r² = 24 ;

Divide each side of the equation by "(3.14)" ;

[3.14 * r²] / 3.14 = (24) / (3.14) ;

to get:

→ r² = 7.64331210191 ;

Take the positive square root of each side of the equation;

to isolate "r" on one side of the equation; & to solve for the radius, "r" ;

→ ⁺√(r²) = ⁺√(7.64331210191) ;

to get:

→ r = 2.76281034802 ;

____________________________

Now, plug this "obtained value" for the radius, "r" into the equation for the formula for the circumference, "C" of a circle:

→ C = 2 $\pi$ * r ;

to solve for the circumference, "C", of the circle:

→ C = 2 * (3.14) * (2.76281034802) ;

= (6.28) * (2.76281034802) ;

= 17.3504489856 ;

→ round to: " 17.35 units" .

__________________________________

The answer is: " 17.35 " .

__________________________________

→ The circumference of the circle is: " 17.35 units " .

__________________________________

6 0

3 years ago

What is the rate of change between (2,2) and (17,7)

choli [55]

Answer:

1/3

Step-by-step explanation:

(7-2)/(17-2)=5/15=1/3

5 0

3 years ago

If point C lies between two points A and B such that AC=BC, then

professor190 [17]

Answer:

If point C lies between two points A and B such that AC=BC, then point C is the bisector of A and B, that means it is at right the centre.

3 0

2 years ago

Typing errors in a text are either nonword errors (as when "the" is typed as "teh") or word errors that result in a real but inc

nordsb [41]

Answer:

a) X is binomial with n = 10 and p = 0.3

Y is binomial with n = 10 and p = 0.7

b) The mean number of errors caught is 7.

The mean number of errors missed is 3.

c) The standard deviation of the number of errors caught is 1.4491.

The standard deviation of the number of errors missed is 1.4491.

Step-by-step explanation:

For each typing error, there are only two possible outcomes. Either it is caught, or it is not. The probability of a typing error being caught is independent of other errors. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

10 word errors.

This means that $n = 10$

(a) If X is the number of word errors missed, what is the distribution of X ?

Human proofreaders catch 70 % of word errors. This means that they miss 30% of errors.

So for X, p = 0.3.

The answer is:

X is binomial with n = 10 and p = 0.3.

If Y is the number of word errors caught, what is the distribution of Y ?

Human proofreaders catch 70 % of word errors.

So for Y, p = 0.7.

The answer is:

Y is binomial with n = 10 and p = 0.7

(b) What is the mean number of errors caught?

$E(Y) = np = 10*0.7 = 7$

The mean number of errors caught is 7.

What is the mean number of errors missed?

$E(X) = np = 10*0.3 = 3$

The mean number of errors missed is 3.

(c) What is the standard deviation of the number of errors caught?

$\sqrt{V(Y)} = \sqrt{np(1-p)} = \sqrt{10*0.7*0.3} = 1.4491$

The standard deviation of the number of errors caught is 1.4491.

What is the standard deviation of the number of errors missed?

$\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{10*0.3*0.7} = 1.4491$

The standard deviation of the number of errors missed is 1.4491.

6 0

2 years ago