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3 years ago

Which expression can be written as k square root 3 where k is an integer

Mathematics

1 answer:

Damm [24]3 years ago

8 0

Answer:

A simple expression is $\sqrt{48}$ = 4 $\sqrt{3}$

Step-by-step explanation:

Surds are irrational numbers expressed with respect to a square root. There are some basic rules required when dealing with surd.

Integers are numbers that do not have a decimal or fractional part i.e whole numbers. So, a simple expression that can be written as k square root 3 where k is an integer is $\sqrt{48}$ .

So that,

$\sqrt{48}$ = $\sqrt{16 * 3}$

= 4 $\sqrt{3}$

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The weights of newborn baby boys born at a local hospital are believed to have a normal distribution with a mean weight of 4016

hodyreva [135]

Answer:

Required Probability = 0.97062

Step-by-step explanation:

We are given that the weights of newborn baby boys born at a local hospital are believed to have a normal distribution with a mean weight of 4016 grams and a standard deviation of 532 grams.

Let X = weight of the newborn baby, so X ~ N( $\mu=4016 , \sigma^{2} = 532^{2}$ )

The standard normal z distribution is given by;

Z = $\frac{X-\mu}{\sigma}$ ~ N(0,1)

Now, probability that the weight will be less than 5026 grams = P(X < 5026)

P(X < 5026) = P( $\frac{X-\mu}{\sigma}$ < $\frac{5026-4016}{532}$ ) = P(Z < 1.89) = 0.97062

Therefore, the probability that the weight will be less than 5026 grams is 0.97062 .

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2 years ago

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Serga [27]

Answer:

Step-by-step explanation:

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1 year ago

How many integers are there that consist of four digits (from 1000 to 9999) where the first digit is a 5 or an 8 and the third d

Ostrovityanka [42]

Answer:

1600 integers

Step-by-step explanation:

Since we have a four digit number, there are four digit placements.

For the first digit, since there can either be a 5 or an 8, we have the arrangement as ²P₁ = 2 ways.

For the second digit, we have ten numbers to choose from, so we have ¹⁰P₁ = 10.

For the third digit, since it neither be a 5 or an 8, we have two less digit from the total of ten digits which is 10 - 2 = 8. So, the number of ways of arranging that is ⁸P₁ = 8.

For the last digit, we have ten numbers to choose from, so we have ¹⁰P₁ = 10.

So, the number of integers that can be formed are 2 × 10 × 8 × 10 = 20 × 80 = 1600 integers

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2 years ago

Find the sum of the following series. Round to the nearest hundredth if necessary,

Aneli [31]

Answer:

$sum = \frac{a( {r}^{n - 1} )}{r - 1} \\ : but \: l = a( {r}^{n - 1} ) \\ 49152 = 3( {2}^{n - 1} ) \\ 16384 = {2}^{n - 1} \\ {2}^{n} = 32768 \\ {2}^{n} = {2}^{15} \\ n = 15 \\ \therefore \: sum = \frac{3(2 {}^{15 - 1}) }{15 - 1} \\ = \frac{49152}{14} \\ = 3510.9$

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2 years ago

The function A = 15x - x2, where x is the width in yards, gives the area A of a llama pen in square yards. Make a table using 1/

Mnenie [13.5K]

Answer:

The width which gives the greatest area is 7.5 yd

Step-by-step explanation:

This is an application of differential calculus. Given the area as a function of the width, we simply need to differentiate the function with respect to x and equate to zero which yields; 15-2x=0 since the slope of the graph is zero at the turning points. Solving for x yields, x=7.5 which indeed maximizes the area of the pen

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2 years ago