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2 years ago

Explain why the following expression is false. |x| < -4

Mathematics

1 answer:

levacccp [35]2 years ago

8 0

Step-by-step explanation:

Whenever we put a negative number inside a modulus function it will give us the positive output. For example , |-3| = 3 , |-6|=6, |5|= 5 ,etc.

So a modulus function i.e. |x| is always greater than zero ( positive ) when x is any number except 0 and it is equal to zero when the value of x is 0.

So |x| can't be less than -4 as |x| is always positive . So the statement is false.

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Guidelines for the jolly blue giant health insurance company say that the average hospitalization for a triple hernia operation

lidiya [134]

To solve this problem, we make use of the t statistic. So what we have to do is to calculate for the t score in this case and using the standard distribution tables, we locate for the p value using the t score value.

The formula for t score is given as:

t = (x – μ) / (σ / sqrt(n))

Where,

x = statistical mean of the sample = 40

n=number of individuals in the sample = 16

s=standard deviation = 20

μ=Population Mean = 30

Substituting the given values:

t = (40 – 30) / (20 / sqrt 16)

t = 10 / 5

t = 2

Using the standard distribution tables at degrees of freedom = n – 1 = 15, the value of p to the right is:

p = 0.032

6 0

2 years ago

Which expression is equivalent to 3 256x^10y^7

Leviafan [203]

$3 \sqrt{256 \ \times x^{10} y^{7} }$

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square root of 256 is 16 :
------------------------------------
$= 48 \sqrt{x^{10} y^{7}}$

------------------------------------
√10¹⁰ = 10⁵ :
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$= 48x^5 \sqrt{ y^{7}}$

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√y⁶ = y³ :
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$= 48x^5y^3 \sqrt{ y}}$

3 0

2 years ago

A cylinder is filled up with water to 3 4 its total capacity. The solid sphere is dropped completely into the cylinder. How high

Olenka [21]

Answer:

30.3 cm

Step-by-step explanation:

Suppose the height is h after the sphere is full submerged.

4/3 $\pi$ R³ = $\pi$ r²(h-30) The volume of the sphere is equal to the volume

4/3 $\pi x$ (10/2)³= $\pi$ × (14/2)²(h-30) of the water surface rising

4/3 × 125 = 49 × (h-30)

h - 30 = 49 × 3/4 × 125

h - 30 = 0.3

h = 30 + 0.3

h = 30.3 cm

8 0

2 years ago

(a) The function k is defined by k(x)=f(x)g(x). Find k′(0).

Brut [27]

Answer:

(a) k'(0) = f'(0)g(0) + f(0)g'(0)

(b) m'(5) = $\frac{f'(5)g(5) - f(5)g'(5)}{2g^{2}(5) }$

Step-by-step explanation:

(a) Since k(x) is a function of two functions f(x) and g(x) [ k(x)=f(x)g(x) ], so for differentiating k(x) we need to use product rule,i.e., $\frac{\mathrm{d} [f(x)\times g(x)]}{\mathrm{d} x}=\frac{\mathrm{d} f(x)}{\mathrm{d} x}\times g(x) + f(x)\times\frac{\mathrm{d} g(x)}{\mathrm{d} x}$

this will give k'(x)=f'(x)g(x) + f(x)g'(x)

on substituting the value x=0, we will get the value of k'(0)

{for expressing the value in terms of numbers first we need to know the value of f(0), g(0), f'(0) and g'(0) in terms of numbers}{If f(0)=0 and g(0)=0, and f'(0) and g'(0) exists then k'(0)=0}

(b) m(x) is a function of two functions f(x) and g(x) [ $m(x)=\frac{1}{2}\times\frac{f(x)}{g(x)}$ ]. Since m(x) has a function g(x) in the denominator so we need to use division rule to differentiate m(x). Division rule is as follows : $\frac{\mathrm{d} \frac{f(x)}{g(x)}}{\mathrm{d} x}=\frac{\frac{\mathrm{d} f(x)}{\mathrm{d} x}\times g(x) + f(x)\times\frac{\mathrm{d} g(x)}{\mathrm{d} x}}{g^{2}(x)}$