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2 years ago

Which is the solution to this system of equations?

Mathematics

2 answers:

DENIUS [597]2 years ago

7 0

The 1st one is the one that is the Answer

vivado [14]2 years ago

5 0

A graphing calculator shows the only solution to be ...
(0, 3)

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Set A of six numbers has a standard deviation of 3 and set B of four numbers has a standard deviation of 5. Both sets of numbers

Alenkinab [10]

Given:

$\sigma_A=3$

$n_A=6$

$\sigma_B=5$

$n_B=4$

$\overline{x}_A=\overline{x}_B$

To find:

The variance. of combined set.

Solution:

Formula for variance is

$\sigma^2=\dfrac{\sum (x_i-\overline{x})^2}{n}$ ...(i)

Using (i), we get

$\sigma_A^2=\dfrac{\sum (x_i-\overline{x}_A)^2}{n_A}$

$(3)^2=\dfrac{\sum (x_i-\overline{x}_A)^2}{6}$

$9=\dfrac{\sum (x_i-\overline{x}_A)^2}{6}$

$54=\sum (x_i-\overline{x}_A)^2$

Similarly,

$\sigma_B^2=\dfrac{\sum (x_i-\overline{x}_B)^2}{n_B}$

$(5)^2=\dfrac{\sum (x_i-\overline{x}_B)^2}{4}$

$25=\dfrac{\sum (x_i-\overline{x}_B)^2}{4}$

$100=\sum (x_i-\overline{x}_B)^2$

Now, after combining both sets, we get

$\sigma^2=\dfrac{\sum (x_i-\overline{x}_A)^2+\sum (x_i-\overline{x}_B)^2}{n_A+n_B}$

$\sigma^2=\dfrac{54+100}{6+4}$

$\sigma^2=\dfrac{154}{10}$

$\sigma^2=15.4$

Therefore, the variance of combined set is 15.4.

7 0

2 years ago

Which statement best describes g(x) = 3x + 6 - 8 and the parent function f(x) = } ?

kumpel [21]

Answer:

In general gf(x) is not equal to fg(x)

Some pairs of functions cannot be composed. Some pairs of functions can be composed only for certain values of x.

Only with they can be composed some values of x are the ranges of g(x) and f(x) are the same, and their domains are also the same. Or else lies inside it.

Step-by-step explanation:

g(x) = 3x + 6 - 8, f(x) = √x.

The domain of a composed function is either the same as the domain of the first function, or else lies inside it

The range of a composed function is either the same as the range of the second function, or else lies inside it.

Or vice versa

Now only positive numbers, or zero, have real square roots. So g is defined only for numbers

greater than or equal to zero. Therefore g(f(x)) can have a value only if f(x) is greater than or

equal to zero. You can work out that

f(x) ≥ 0 only when x ≥3/2

3 0

2 years ago

Alfie sells flooring for playgrounds.

dexar [7]

area of playground= 9×15= 135m^2

area of lawn= 3×4=12m^2

total flooring area= 135-12= 123m^2

cost=36×123=$4428

6 0

2 years ago

A line passes through the point (10,5) and has a slope of 3/2. Write and equation in slope intercept form

ehidna [41]

$\bf \begin{array}{lllll}
&x_1&y_1\\
% (a,b)
&({{ 10}}\quad ,&{{ 5}})\quad 
\end{array}
\\\\\\
% slope = m
slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{3}{2}
\\\\\\
% point-slope intercept
\stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-5=\cfrac{3}{2}(x-10)\implies y-5=\cfrac{3}{2}x-15
\\\\\\
y=\cfrac{3}{2}x-15+5\implies y=\cfrac{3}{2}x-10$

8 0

3 years ago

Evaluating algebraic expressions <br><br><br> B3 - 3a5

lutik1710 [3]

Answer:

3B-15a

Step-by-step explanation:

B3=3B

3a5=15a

3B-15a

8 0

2 years ago