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3 years ago

Simplify the radicals

Mathematics

1 answer:

alukav5142 [94]3 years ago

7 0

Answer:

The Answer is a:) (20,3)

Step-by-step explanation:

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Although bats are not known for their eyesight, they are able to locate prey (mainly insects) by emitting high-pitched sounds an

Sergeu [11.5K]

Answer:

$Mean = 48.6364$

$s^2 = 331.8545$ -- Sample Variance

$s = 18.2169$ --- Sample Standard Deviation

Step-by-step explanation:

Given

$n = 11$

$Data: 24, 41 ,25 ,68 ,53 ,83 ,43 ,63 ,56 ,34 ,45$

Solving (a): The sample mean

$Mean = \frac{\sum x}{n}$

So:

$Mean = \frac{24 +41 +25 +68 +53 +83 +43 +63 +56 +34+ 45}{11}$

$Mean = \frac{535}{11}$

$Mean = 48.6364$

Solving (b): Sample variance (s^2)

This is calculated as:

$s^2 = \frac{\sum (x - \bar x_i)^2}{n - 1}$

Where:

$\bar x = 48.6364$

So:

$s^2 = \frac{(24 -48.6364)^2 +(41 -48.6364)^2 +......................+( 45 -48.6364)^2}{11-1}$

$s^2 = \frac{3318.54545456}{10}$

$s^2 = 331.8545$

Solving (c): Sample Standard Deviation (s)

This is calculated as:

$s = \sqrt {s^2$

$s = \sqrt{331.8545$

$s = 18.2169$

8 0

3 years ago

What must be added to f(x) = 4x4 + 2x3 -2x2 +x - 1, so that the resulting polynomial is divisible by g(x) = x2 +2x -3?

s344n2d4d5 [400]

Answer:

p(x) = -4*x^4 - 2*x^3 + 3*x^2 + 1*x - 2

Step-by-step explanation:

We want to find a polynomial p(x), such that if we add that polynomial to:

f(x) = 4*x^4 + 2*x^3 - 2*x^2 + x - 1

we get:

g(x) = x^2 + 2*x - 3

This is:

f(x) + p(x) = g(x)

Notice that f(x) is a polynomial of degree 4 and g(x) is a polinomial of degree 2, so p(x) must be also a polynomial of degree 4.

p(x) = a*x^4 + b*x^3 + c*x^2 + d*x + e

Then we get:

(4*x^4 + 2*x^3 - 2*x^2 + x - 1) + (a*x^4 + b*x^3 + c*x^2 + d*x + e) = x^2 + 2*x - 3

We can simplify the left side to:

(4 + a)*x^4 + (2 + b)*x^3 + (-2 + c)*x^2 + (1 + d)*x + (-1 + e) = x^2 + 2*x - 3

Because in the right side we do not have terms with exponent 4 and 3, we must have that:

4 + a = 0

2 + b = 0

and for the other exponents of x we just match the exponent in the left side with the correspondent one in the right side:

(-2 + c) = 1

(1 + d) = 2

(-1 + e) = -3

Solving the 5 equations we get:

a = -4

b = -2

c = 1 + 2 = 3

d = 2 - 1 = 1

e = -3 + 1 = -2

Then the equation for p(x) is:

p(x) = -4*x^4 - 2*x^3 + 3*x^2 + 1*x - 2

6 0

3 years ago

0.008 is 1/10 of what

sp2606 [1]

0.008 x 1/10 = 0.0008

8 0

3 years ago

Is algebra.

True [87]

The GFC is 7
The factors need to add up to 49x
They need to multiply to -56

7 0

3 years ago

How many intersections are there of the graphs of the equations below?

kipiarov [429]

Answer:

The number of intersections = ∞

Step-by-step explanation:

Given the system of equations:

0.5 x + 5y = 6

3x + 30y = 36

By multiplying the first equation by 6

∴ 6 (0.5 x + 5y) = 6 * 6

∴ 3x + 30y = 36

So, Those equations are "Dependent", because they are really the same equation, just multiplied the first equation by 6.

So, the two equations are identical

Therefore: They have infinity number of solutions.

See the attached figure.

0.5 x + 5y = 6 ⇒ in black color

3x + 30y = 36 ⇒ in red color

6 0

3 years ago