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3 years ago

What is the real numbers for a, radical a squared

Mathematics

1 answer:

Wittaler [7]3 years ago

5 0

Answer:

$\sqrt{a^{2}}$ = a

Step-by-step explanation:

We have to evaluate the expression, 'Radical a squared'.

Now, radical means square root.

So, our expression becomes, 'Square root of 'a' square'.

That is, the expression is $\sqrt{a^{2}}$ .

We know that, the square root of some squared value is the value itself.

So, $\sqrt{a^{2}}$ = a

Hence, the real number for 'radical a squared' i.e. $\sqrt{a^{2}}$ is 'a'.

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a sock drawer has 6 red socks and 4 blue socks. what is the probability or picking two blue socks without replacement

nalin [4]

It is 4/10 times 3/9 which is 12/90.12/90 is equivalent to 4/30, or 2/15 chance.

8 0

3 years ago

At a branch office of the company, 350 people are polled and 125 indicate they are in favor of using a corporate American Expres

AlladinOne [14]

Answer:

The P-value is Less than 0.0005%.

Step-by-step explanation:

We are given that at a branch office of the company, 350 people are polled and 125 indicate they are in favor of using a corporate American Express card.

A recent survey at the main corporate headquarters revealed that the 400 employees who responded to the survey indicated that 350 wanted to stay with the American Express Card.

Let $p_1$ = proportion of employees at the headquarters who want the American Express Card.

$p_2$ = proportion of employees at the branch office who want the American Express Card.

So, Null Hypothesis, $H_0$ : $p_1\leq p_2$ {means that the percentage of employees at the headquarters who want the American Express Card is smaller or equal to the percentage of employees at the branch office}

Alternate Hypothesis, $H_A$ : $p_1>p_2$ {means that the percentage of employees at the headquarters who want the American Express Card is greater than the percentage of employees at the branch office}

The test statistics that would be used here Two-sample z proportion statistics;

T.S. = $\frac{(\hat p_1-\hat p_2)-(p_1-p_2)}{\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2} } }$ ~ N(0,1)

where, $\hat p_1$ = sample proportion of employees at the headquarters wanted to use the American Express Card = $\frac{350}{400}$ = 0.875

$\hat p_2$ = sample proportion of employees at the branch office wanted to use the American Express Card = $\frac{125}{350}$ = 0.357

$n_1$ = sample of people at the main corporate headquarters = 400

$n_2$ = sample of people at a branch office = 350

So, the test statistics = $\frac{(0.875-0.357)-(0)}{\sqrt{\frac{0.875(1-0.875)}{400}+\frac{0.357(1-0.357)}{350} } }$

= 16.99

The value of z test statistics is 16.99.

Now, P-value of the test statistics is given by;

P(Z > 16.99) = Less than 0.0005%

6 0

3 years ago

A triangle has an area of 42 cm2. The height of the triangle is 14 centimeters. What is the length of the base of the triangle.

pentagon [3]

Answer:

6 centimeters

Step-by-step explanation:

Area of a triangle is A = height x base / 2

So plug in what you know.

42 = (14 x b)/2 get rid of the 2 by multiplying both sides by 2 which gives:

84 = 14 x b get rid of the 14 by dividing both sides by 14

b = 84/14

b=6 cm

7 0

2 years ago

Fred has 96 muffins, which he needs to box up. He needs 12 muffins in each box. 7 of the muffins are blueberry. How many boxes d

Ivenika [448]

Answer: the answer should be 14 but i can’t confirm that it is

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

Find both the number of combinations and the number of permutations for the given number of objects.

Nikitich [7]

Answer:

First, if we have a set of K elements, such that are ordered as:

{x₁, x₂, ...}

The total number of permutations for the K elements can be found in the next way.

For the first element in the set, we have K options.

For the second element in the set, we have (K - 1) options (because we already choose one)

For the third element we have (K - 2) options, and so on.

The total number of permutation is equal to the product between the numbers of options for each position's element, then the number of permutations for K elements is:

permutations = K*(K - 1)*(K - 2)*....*2*1 = K!

Now suppose that we have a set of N elements, and we want to make groups of K elements.

The total number of different combinations of K elements is given by the equation:

$C(N, K) = \frac{N!}{(N - K)!*K!}$

In this case we have 15 objects (then N = 15) and we take 7 at the time (Then K = 7)

Where we need to take in account the number of combinations and also the permutations for each combination.

Then the total number of different sets is:

C(15*7)*7!

First, the total number of combinations will be:

$C(15,7) = \frac{15!}{(15 - 7)!7!} = \frac{15!}{8!*7!} = \frac{15*14*13*12*11*10*9}{7*6*5*4*3*2*1} = 6,435$

So we have 6,436 combinations, and each one of these combinations has 7! permutations.

permutations = 7! = 7*6*5*4*3*2*1 = 5,040

if we combine these we get:

Combinations*Permutations = 6,435*5,040 = 32,432,400

5 0

3 years ago