$x-3y-27=0\\
y^2=4x\\\\
x-3y-27=0\\
x=\frac{y^2}{4}\\\\
\frac{y^2}{4}-3y-27=0\\
y^2-12y-108=0\\
y^2-12y+36-144=0\\
(y-6)^2=144\\
y-6=-12 \vee y-6=12\\
y=-6 \vee y=18\\\\
x=\frac{(-6)^2}{4} \vee x=\frac{18^2}{4}\\
x=\frac{36}{4} \vee x=\frac{324}{4}\\
x=9 \vee x=81\\\\
\boxed{(9,-6),(81,18)}
$

4 0

3 years ago

Read 2 more answers

An exit poll of 1000 randomly selected voters found that 515 favored measure A. a. Construct a 99% confidence interval for the s

never [62]

Answer:

Step-by-step explanation:

Given that an exit poll of 1000 randomly selected voters found that 515 favored measure A.

Sample proportion p = $\frac{515}{1000} =0.515$

$q=1-0.515 =0.485\\n =1000\\SE = \sqrt{\frac{pq}{n} } \\=0.158\\$

Margin of error 99% = 2.58*SE

= $2.58*0.0158\\=0.0408$

99% confidence interval = $(0.515-0.0408, 0.515+0.0408)\\= (0.474, 0.556)$

------------------------

$H_0: p =0.5\\H_a: p >0.5\\$

(Right tailed test)

STd error = $\sqrt{\frac{0.5*0.5}{1000} } \\=0.0158$

Test statistic Z = p diff/std error = $\frac{0.015}{0.0158} \\\\=0.9487$

p value = 0.1714

6 0

3 years ago

Consider two identical iron nails: one nail is heated to 95 °c, the other is cooled to 15 °c. the two nails are placed in a coff

Angelina_Jolie [31]

The heat released or absorbed by a substance is calculated through the equation,
H = mcpdT

where H is teh heat,
m is the mass,
Cp is the specific heat, and
dT is the temperature difference

In this item, since both nails are identical, m and cp for both nails are equal such that the equation can be expressed as,
mcp(95 - x) = mcp(x - 15)

where x is the final temperature. Solving for the value of x from the equation derived above will give us a final answer of 55 degrees C.

Answer: 55°

3 0

3 years ago