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3 years ago

8

Shelby and her classmates placed colored blocks on a scale during a science lab. The green block weighed 9.2 pounds and the oran

ge block weighed 0.34 pounds. How much more did the green block weigh than the orange block?

1 answer:

12345 [234]3 years ago

7 0

The green block weighed 8.86 more

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By the way, that system of equations has no solution.

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Find the balance in the account. $800 principal earning 7%, compounded annually, after 4 years $1,048.64 $1,024.00 $1,920,800.00

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Find the equation of the line that passes through (0, -3) and is parallel to

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Hey there!

$\\$

Answer:

$\green{\boxed{\red{\bold{\sf{y = \dfrac{7}{6}x - 3}}}}}$

$\\$

Explanation:

To find the equation of a line, we first have to determine its slope knowing that parallel lines have the same slope.

Let the line that we are trying to determine its equation be $\: \sf{d_1} \:$ and the line that is parallel to $\: \sf{d_1} \:$ be $\: \sf{d_2} \:$ .

$\sf{d_2} \:$ passes through the points (9 , 2) and (3 , -5) which means that we can find its slope using the slope formula:

$\sf{m = \dfrac{\Delta y}{\Delta x} = \dfrac{\green{y_2} - \orange{y_1}}{\red{x_2} - \blue{x_1 }}}$

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⇒Subtitute the values :

$\sf{(\overbrace{\blue{9}}^{\blue{x_1}}\: , \: \overbrace{\orange{2}}^{\orange{y_1}}) \: \: and \: \: (\overbrace{\red{3}}^{\red{x_2}} \: , \: \overbrace{\green{-5}}^{\green{y_2}} )}$

$\implies \sf{m = \dfrac{\Delta y}{\Delta x} = \dfrac{\green{-5} - \orange{2}}{\red{ \: \: 3} - \blue{9 }} = \dfrac{ - 7}{ - 6} = \boxed{ \bold{\dfrac{7}{6} }}}$

$\sf{\bold{The \: slope \: of \: both \: lines \: is \: \dfrac{7}{6}}}$ .

Assuming that we want to get the equation in Slope-Intercept Form, let's substitute m = 7/6:

Slope-Intercept Form:

$\sf{y = mx + b} \\ \sf{Where \: m \: is \: the \: slope \: of \: the \: line \: and \: b \: is \: the \: y-intercept.}$

$\implies \sf{y = \bold{\dfrac{7}{6}}x + b}$ $\\$

We know that the coordinates of the point (0 , -3) verify the equation since it is on the line $\: \sf{d_1} \:$ . Now, replace y with -3 and x with 0:

$\implies \sf{\overbrace{-3}^{y} = \dfrac{7}{8} \times \overbrace{0}^{x} + b} \\ \\ \implies \sf{-3 = 0 + b} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \implies \sf{\boxed{\bold{b = -3}} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

Therefore, the equation of the line $\: \bold{d_1} \:$ is $\green{\boxed{\red{\bold{\sf{y = \dfrac{7}{6}x - 3}}}}}$

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Small sample: During an economic downturn, companies were sampled and asked whether they were planning to increase their workfor

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Complete Question

The complete question is shown on the first uploaded image

Answer:

The confidence level interval is $0.016 \le C \le 0.404$

Step-by-step explanation:

The sample size is $n = 20$

The number planning to increase workforce is $x = 3$

The confidence level is $c = 98$ %

The value of proportion for a plus 4 method is

$p = \frac{x+2}{n+4}$

substituting values

$p = \frac{3+2}{20+4}$

$p =0.21$

The z-critical value at confidence level of 98% is

$z_{c}=z_{0.98} = 2.33$

This values is obtained from the standard normal table

The confidence level interval can be mathematically represented as

$C =p \ \pm z_{c} * \sqrt{\frac{p(1-p)}{n+4} }$

substituting values

$C = 0.21 \pm 2.33 * \sqrt{\frac{0.21(1- 0.21)}{20 +4} }$

$C = 0.21 \pm 0.194$

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