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3 years ago

Find an equation of the line perpendicular to the graph of 14x-7y=4 that passes through the point at (2,-9)

1 answer:

6 0

If it is perpendicular to the line 14x-7y=4, then we know our line has the opposite and inverse slope of that line. Solving for y of the first line, we get y=2x-(4/7). All we care about is the coefficient of the x term, because that will give us our slope. The slope of the first line is 2, so the slope of out line is the opposite and inverse of that slope, which -(1/2).

Plugging into our slope- point formula, where y1=(-9), x1=2, and m=(-1/2), then:

y-(-9)=(-1/2)(x-2)
y+9=(-1/2)x+1
y=(-1/2)x-8

Hope this helps!

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Q and r are independent events. if p(q) = 1/4 and p(r)=1/5, find p(q and r)

klasskru [66]

Answer:

(b) $\frac{7}{30}$

Step-by-step explanation:

When two p and q events are independent then, by definition:

P (p and q) = P (p) * P (q)

Then, if q and r are independent events then:

P(q and r) = P(q)*P(r) = 1/4*1/5

P(q and r) = 1/20

P(q and r) = 0.05

In the question that is shown in the attached image, we have two separate urns. The amount of white balls that we take in the first urn does not affect the amount of white balls we could get in the second urn. This means that both events are independent.

In the first ballot box there are 9 balls, 3 white and 6 yellow.

Then the probability of obtaining a white ball from the first ballot box is:

$P (W_{u_1}) = \frac{3}{9} = \frac{1}{3}$

In the second ballot box there are 10 balls, 7 white and 3 yellow.

Then the probability of obtaining a white ball from the second ballot box is:

$P (W_{u_2}) = \frac{7}{10}$

We want to know the probability of obtaining a white ball in both urns. This is: P( $W_{u_1}$ and $W_{u_2}$ )

As the events are independent:

P( $W_{u_1}$ and $W_{u_2}$ ) = P ( $W_{u_1}$ ) * P ( $W_{u_2}$ )

P( $W_{u_1}$ and $W_{u_2}$ ) = $\frac{1}{3}* \frac{7}{10}$

P( $W_{u_1}$ and $W_{u_2}$ ) = $\frac{7}{30}$

Finally the correct option is (b) $\frac{7}{30}$

3 0

3 years ago

What is the radius and diameter of the following circle?

alexandr1967 [171]

Diameter= 18cm

Radius is half of diameter

Radius=9cm

7 0

3 years ago

Convert the following radian angle into degrees.

NeTakaya

The degree of the radian angle 0.11 is $6.3^{\circ}$

Explanation:

It is given that the radian angle is 0.11

We need to determine the degrees of the radian angle.

To convert the radian into degrees, let us multiply the radian with $\left(\frac{180}{\pi}\right)$

Thus, we have,

$0.11\times\left(\frac{180}{\pi}\right)=\frac{19.8}{\pi}$

It is given that $\pi=3.14$

Substituting $\pi=3.14$ in the above expression, we have,

$\frac{19.8}{3.14} =6.303...$

Rounding off to the nearest tenth, we have,

$6.3^{\circ}$

Thus, the degree of the radian angle 0.11 is $6.3^{\circ}$

4 0

3 years ago

An activity has an optimistic time estimate of 25 days, a most likely estimate of 29 days, and a pessimistic estimate of 34 days

Margaret [11]

The expected duration of the activity is 29 days and 4 hours.

Step-by-step explanation:

Step 1:

The optimistic time, $t_{o}$ = 25 days,

The most likely estimate, $t_{m}$ = 29 days.

The pessimistic time, $t_{p}$ = 34 days.

According to PERT, the expected duration of the activity, $t_{e} = \frac{t_{0}+4t_{m} +t_{p} }{6}.$

Step 2:

By substituting the given values, we get $t_{e} = \frac{t_{0}+4t_{m} +t_{p} }{6} = t_{e} = \frac{25+4(29) +34 }{6} = \frac{175}{6} = 29.1666.$

0.1666 days = $0.1666 (24) = 3.9999 hours.$

29.1666 days approximately equal 29 days and 4 hours.

8 0

3 years ago

What is the domain and range? ex. (-4, infinity)

nevsk [136]

Answer:

Step-by-step explanation:

Domain for the bottom graph

D: [-6,0)

R: (-6,5]

7 0

3 years ago