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3 years ago

What is the solution to this system? 3x+2y=45 4x+-y=5

Mathematics

1 answer:

hodyreva [135]3 years ago

5 0

(I) $3x + 2y = 45$

(II) $4x - y = 5$

Get $y$ alone in equation (II)

$4x - y = 5\\y = 4x - 5$

Insert new equation (II) in equation (I)

$3x + 2(4x - 5) = 45\\3x + 8x - 10 = 45\\3x + 8x = 45 + 10\\11x = 55\\x = 5$

Insert $x = 5$ in equation (II)

$y = 4 \cdot 5 - 5\\y = 20 - 5\\y = 15$

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The length of human pregnancies from conception to birth follows a distribution with mean 266 days and standard deviation 15 day

Katena32 [7]

Answer:

a) 81.5%

b) 95%

c) 75%

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 266 days

Standard Deviation, σ = 15 days

We are given that the distribution of length of human pregnancies is a bell shaped distribution that is a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

a) P(between 236 and 281 days)

$P(236 \leq x \leq 281)\\\\= P(\displaystyle\frac{236 - 266}{15} \leq z \leq \displaystyle\frac{281-266}{15})\\\\= P(-2 \leq z \leq 1)\\\\= P(z \leq 1) - P(z < -2)\\= 0.838 - 0.023 = 0.815 = 81.5\%$

b) a) P(last between 236 and 296)

$P(236 \leq x \leq 281)\\\\= P(\displaystyle\frac{236 - 266}{15} \leq z \leq \displaystyle\frac{296-266}{15})\\\\= P(-2 \leq z \leq 2)\\\\= P(z \leq 2) - P(z < -2)\\= 0.973 - 0.023 = 0.95 = 95\%$

c) If the data is not normally distributed.

Then, according to Chebyshev's theorem, at least $1-\dfrac{1}{k^2}$ data lies within k standard deviation of mean.

For k = 2

$1-\dfrac{1}{(2)^2} = 75\%$

Atleast 75% of data lies within two standard deviation for a non normal data.

Thus, atleast 75% of pregnancies last between 236 and 296 days approximately.

7 0

3 years ago

2y+8×=2 identify the table that would correctly graph this equation

lys-0071 [83]

We have

$2y+8x=2$

In order to obtain easily the table, we need to clear y

$\begin{gathered} 2y=-8x+2 \\ y=\frac{-8x+2}{2} \\ y=-4x+1 \end{gathered}$

then we evaluate for values of x

if x=0

y=-4(0)+1=1

y=1

if x=1

y=-4(1)+1=-3

y=3

if x=2

y=-4(2)+1=-7

y=-7

if x=3

y=-4(3)+1=-11

y=-11

So the table for the given equation is

x y

0 1

1 -3

2 -7

3 -11

3 0

1 year ago

Find the slope and reduce of p=(3/4,1 1/4) q=(-1/2,-1)

sergij07 [2.7K]

$\bf \begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
p&({{ \frac{3}{4}}}\quad ,&{{ \frac{1}{4}}})\quad 
% (c,d)
q&({{ -\frac{1}{2}}}\quad ,&{{ -1}})
\end{array}$

$\bf slope = {{ m}}= \cfrac{rise}{run} \implies 
\cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{-1-\frac{1}{4}}{-\frac{1}{2}-\frac{3}{4}}\quad \cfrac{\leftarrow LCD=4}{\leftarrow LCD=4}
\\\\\\
\cfrac{\frac{-4-1}{4}}{\frac{-2\cdot 1-3}{4}}\implies \cfrac{\frac{-5}{4}}{\frac{-5}{4}}\implies \cfrac{-5}{4}\cdot \cfrac{4}{-5}\implies 1$

7 0

3 years ago

Help!<br><br> I fallen and can’t get up.

Gnom [1K]

I miss when everyone always said this

good times but ty for the points

7 0

3 years ago

Read 2 more answers

Dos rectas son paralelas, una de ellas es 3x+2y−4=0 y la otra pasa por el punto (4,5); Encuentra la ecuación general de la otra

____ [38]

Step-by-step explanation:

la respuesta está en la imagen de arriba .si necesita ayuda, no dude en preguntar