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3 years ago

Which expression is equivalent to 3√50 × √22 ?

Mathematics

1 answer:

8_murik_8 [283]3 years ago

5 0

$\longrightarrow{\green{C.\:30 \sqrt{11} }}$ ✔

$\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}$

$3 \sqrt{50} \times \sqrt{22} \\ \\ = 3 \sqrt{50 \times 22} \\ \\ = 3 \sqrt{1100} \\ \\ = 3 \sqrt{2 \times 2 \times 5 \times 5 \times 11} \\ \\ = 3 \sqrt{ {2}^{2} \times {5}^{2} \times 11} \\ \\ = 3 \times 2 \times 5 \sqrt{11} \\\\ = 30 \sqrt{11}$

$\bold{ \green{ \star{ \orange{Mystique35}}}}⋆$

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16. A telemarketer makes six phone calls per hour and is able to make a sale on 30% of these contacts. During the next two hours

Reika [66]

Answer:

a) 23.11% probability of making exactly four sales.

b) 1.38% probability of making no sales.

c) 16.78% probability of making exactly two sales.

d) The mean number of sales in the two-hour period is 3.6.

Step-by-step explanation:

For each phone call, there are only two possible outcomes. Either a sale is made, or it is not. The probability of a sale being made in a call is independent from other calls. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

A telemarketer makes six phone calls per hour and is able to make a sale on 30% of these contacts. During the next two hours, find:

Six calls per hour, 2 hours. So

$n = 2*6 = 12$

Sale on 30% of these calls, so $p = 0.3$

a. The probability of making exactly four sales.

This is P(X = 4).

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 4) = C_{12,4}.(0.3)^{4}.(0.7)^{8} = 0.2311$

23.11% probability of making exactly four sales.

b. The probability of making no sales.

This is P(X = 0).

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{12,0}.(0.3)^{0}.(0.7)^{12} = 0.0138$

1.38% probability of making no sales.

c. The probability of making exactly two sales.

This is P(X = 2).

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 2) = C_{12,2}.(0.3)^{2}.(0.7)^{10} = 0.1678$

16.78% probability of making exactly two sales.

d. The mean number of sales in the two-hour period.

The mean of the binomia distribution is

$E(X) = np$

$E(X) = 12*0.3 = 3.6$

The mean number of sales in the two-hour period is 3.6.

4 0

4 years ago

I need help with number 30

yanalaym [24]

Answer:

220

Step-by-step explanation:

5 0

4 years ago

Write in slope-intercept form an equation of the line that passes through the points (−4, 2) and (6,−3).

asambeis [7]

Answer:

24,3

Step-by-step explanation:

4x6 3x2

3 0

3 years ago

What is the value of X? 80 cm 20 cm 12 cm 10 cm

dangina [55]

Answer:

$x=12cm$

Step-by-step explanation:

Triangle DEF is similar to triangle HGF.

Therefore the corresponding sides are proportional.

We can write the following equations for the corresponding sides.

$\frac{DF}{HF}=\frac{EF}{GF}$

This implies that,

$\frac{16+40}{40}=\frac{x+30}{30}$

This gives us,

$\frac{7}{5}=\frac{x+30}{30}$

We cross multiply to get,

$7\times 30=5(x+30)$

We divide through by 5 to get,

$7\times 6=(x+30)$

We multiply to get,

$\Rightarrow 42=x+30$

Grouping like terms gives,

$\Rightarrow 42-30=x$

We simplify to obtain,

$\therefore x=12cm$

The correct answer is C

6 0

3 years ago

Read 2 more answers

This cone has a height of 27 centimeters and a diameter of 32 centimeters. What is the volume, in cubic centimeters, of the cone

Bezzdna [24]

Answer:

The area of cone is 7240cm³.

Step-by-step explanation:

Given that the diameter is 2 times greater than radius.

So the radius of this cone will be 16cm.

Next, we have to apply volume formula, V = (1/3)×(area of circle)×height.

Formula for area of circle is A = π×r² :

$V = \frac{1}{3} \times \pi \times {r}^{2} \times h$

$V = \frac{1}{3} \times \pi \times {16}^{2} \times 27$

$V = 7240 { \: cm}^{3} \: \: (3sf)$

7 0

3 years ago