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3 years ago

Is the simplified form of 2 square root of 3 minus 2 square root of 3 rational?

Mathematics

1 answer:

EastWind [94]3 years ago

4 0

Yes because its equal to 0 and zero is whole number.its rational

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Match each square root to its closest integer approximation.

Phoenix [80]

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7 0

3 years ago

Find three consecutive even integers if three times the first integer is two times the third.

drek231 [11]

Using a system of equations, it is found that the three consecutive even integers are -8, -6 and -4.

<h3>What is a system of equations?</h3>

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the three consecutive even integers are represented by:

n, n + 2, n + 4

The first integer is two times the third, hence:

n = 2(n + 4)

2n + 8 = n

n = -8

Thus:

n = -8

n + 2 = -8 + 2 = -6

n + 4 = -8 + 4 = -4

The integers are -8, -6 and -4.

To learn more about system of equations, you can take a look at brainly.com/question/26650649

6 0

2 years ago

Read 2 more answers

Fill in the blank with the correct number.

liberstina [14]

Answer:

and it is correct because it is

8 0

3 years ago

The manager of a music store has kept records of

Marysya12 [62]

Answer:

(a) $P(x\le 3) = 0.75$

(b) $P(x\le 3) = 0.75$

(d) $P(x = 1\ or\ 2) = 0.55$

(e) $P(x > 2) = 0.45$

Step-by-step explanation:

Given

$\begin{array}{ccccccc}{CDs} & {1} & {2} & {3} & {4} & {5} & {6\ or\ more}\ \\ {Prob} & {0.30} & {0.25} & {0.20} & {0.15} & {0.05} & {0.05}\ \ \end{array}$

Solving (a): Probability of 3 or fewer CDs

Here, we consider:

$\begin{array}{cccc}{CDs} & {1} & {2} & {3} \ \\ {Prob} & {0.30} & {0.25} & {0.20} \ \ \end{array}$

This probability is calculated as:

$P(x\le 3) = P(1) + P(2) + P(3)$

This gives:

$P(x\le 3) = 0.30 + 0.25 + 0.20$

$P(x\le 3) = 0.75$

Solving (b): Probability of at most 3 CDs

Here, we consider:

$\begin{array}{cccc}{CDs} & {1} & {2} & {3} \ \\ {Prob} & {0.30} & {0.25} & {0.20} \ \ \end{array}$

This probability is calculated as:

$P(x\le 3) = P(1) + P(2) + P(3)$

This gives:

$P(x\le 3) = 0.30 + 0.25 + 0.20$

$P(x\le 3) = 0.75$

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Solving (c): Probability of 5 or more CDs

Here, we consider:

$\begin{array}{ccc}{CDs} & {5} & {6\ or\ more}\ \\ {Prob} & {0.05} & {0.05}\ \ \end{array}$

This probability is calculated as:

$P(x \ge 5) = P(5) + P(6\ or\ more)$

This gives:

$P(x\ge 5) = 0.05 + 0.05$

$P(x \ge 5) = 0.10$

Solving (d): Probability of 1 or 2 CDs

Here, we consider:

$\begin{array}{ccc}{CDs} & {1} & {2} \ \\ {Prob} & {0.30} & {0.25} \ \ \end{array}$

This probability is calculated as:

$P(x = 1\ or\ 2) = P(1) + P(2)$

This gives:

$P(x = 1\ or\ 2) = 0.30 + 0.25$

$P(x = 1\ or\ 2) = 0.55$

Solving (e): Probability of more than 2 CDs

Here, we consider:

$\begin{array}{ccccc}{CDs} & {3} & {4} & {5} & {6\ or\ more}\ \\ {Prob} & {0.20} & {0.15} & {0.05} & {0.05}\ \ \end{array}$

This probability is calculated as:

$P(x > 2) = P(3) + P(4) + P(5) + P(6\ or\ more)$

This gives:

$P(x > 2) = 0.20+ 0.15 + 0.05 + 0.05$

$P(x > 2) = 0.45$

3 0

3 years ago

An orange juice producer buys oranges from a large orange grove that has one variety of orange. The amount of juice squeezed fro

strojnjashka [21]

Answer:

a) 0.10565

b) The two values = 4.61712 and

4.78288

c) 4.64088

Step-by-step explanation:

The z score formula we use to solve when given a random number of samples=

The formula for calculating a z-score is is z = (x-μ)/σ/√n

where x is the raw score

μ is the population mean

σ/√n is standard error

σ is the population standard deviation

n = random number of samples

a. What is the probability that the sample mean amount of juice will be at least 4.60 ounces?

z = (x-μ)/σ/√n

x = 4.60

μ = 4.70

σ = 0.40

n = 25

z = 4.60 - 4.70/0.40/√25

z = -0.10/0.40/5

z = -1.25

P-value from Z-Table:

P(x ≤ 4.60)

= P(x ≤ 4.60)

= P(z = -1.25)

= 0.10565

Therefore, the probability that the sample mean amount of juice will be at least 4.60 ounces is 0.10565

b. The probability is 70% that the sample mean amount of juice will be contained between what two values symmetrically distributed around the population mean?

The probability of 70% = 0.70

The z score for 0.70 = 1.036

This means, -1.036 and +1.036 gives a probability (0.70) or confidence level of 70%

We are to find x(raw score)

We solve using z score formula

For z = +1.036

z = (x-μ)/σ/√n

x = ?

μ = 4.70

σ = 0.40

n = 25

1.036 = x - 4.70/0.40/√25

1.036 = x - 4.70/0.08

Cross Multiply

1.036 × 0.08 = x - 4.70

0.08288 = x - 4.70

0.08288 + 4.70 = x

x = 4.78288

For z = -1.036

z = (x-μ)/σ/√n

x = ?

μ = 4.70

σ = 0.40

n = 25

-1.036 = x - 4.70/0.40/√25

-1.036 = x - 4.70/0.08

Cross Multiply

-1.036 × 0.08 = x - 4.70

-0.08288 = x - 4.70

-0.08288 + 4.70 = x

= 4.61712

Therefore, the two values = 4.61712 and

4.78288

c. The probability is 77% that the sample mean amount of juice will be greater than what value?

We are told to find the value that the sample mean is greater than

The z score for a P(x > z)

= P(x > 0.77)

= -0.739

Using z score formula, we find x first

z = (x-μ)/σ/√n

x = ?

μ = 4.70

σ = 0.40

n = 25

-0.739 = x - 4.70/0.40/√25

-0.739 = x - 4.70/0.08

Cross Multiply

-0.739 × 0.08 = x - 4.70

-0.05912 = x - 4.70

-0.05912 + 4.70 = x

x = 4.64088

Therefore, the value that the probability is 77% that the sample mean amount of juice will be greater than is 4.64088

5 0

3 years ago