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xxMikexx [17]
3 years ago
5

Find the equation of the line that is perpendicular to y = 1/4x – 2 and passes though the point (5, –2). A) y = –1/4x + 18 B) y

= –1/4x – 22 C) y = –4x + 18 D) y = –4x – 22
Mathematics
1 answer:
Mashcka [7]3 years ago
7 0

Since our line is perpendicular to this line, the slope of

our line is the negative reciprocal of 1/4, which is -4/1.

Remember, negative reciprocal is just a fancy way

of saying flip the fraction and change the sign.

So the slope of our line is -4/1 and we use this slope along

with our given point to write the equation of our line.

Start with the point-slope formula.

Y - y1 = m(x - x1).

~Substitute

Y - -2 = -4/1(x - 5).

Minus a negative is plus a positive.

Y + 2 = -4/1x + 20.

Subtract 2 from both sides.

Y = -4/1x + 18

So, our answer is C.

You might be interested in
A blackjack player at a Las Vegas casino learned that the house will provide a free room if play is for four hours at an average
marysya [2.9K]

Answer:

a) player’s expected payoff is $ 240

b) probability the player loses $1000 or more is 0.1788

c)  probability the player wins is 0.3557

d) probability of going broke is 0.0594

Step-by-step explanation:

Given:

Since there are 60 hands per hour and the player plays for four hours then the sample size is:

n = 60 * 4 = 240

The player’s strategy provides a probability of .49 of winning on any one hand so the probability of success is:

p = 0.49

a)

Solution:

Expected payoff is basically the expected mean

Since the bet is $50 so $50 is gained when the player wins a hand and $50 is lost when the player loses a hand. So

Expected loss =  μ

                        = ∑ x P(x)

                        = 50 * P(win) - 50 * P(lose)

                        = 50 * P(win) + (-50) * (1 - P(win))

                         = 50 * 0.49 - 50 * (1 - 0.49)

                        = 24.5 - 50 ( 0.51 )

                        = 24.5 - 25.5

                        = -1

Since n=240 and expected loss is $1 per hand then the expected loss in four hours is:

240 * 1 = $ 240

b)

Using normal approximation of binomial distribution:

n = 240

p = 0.49

q = 1 - p = 1 - 0.49 = 0.51

np = 240 * 0.49 = 117.6

nq = 240 * 0.51 = 122.5

both np and nq are greater than 5 so the binomial distribution can be approximated by normal distribution

Compute z-score:

z = x - np / √(np(1-p))

  = 110.5 - 117.6 / √117.6(1-0.49)

  = −7.1/√117.6(0.51)

  = −7.1/√59.976

  = −7.1/7.744417

  =−0.916789

Here the player loses 1000 or more when he loses at least 130 of 240 hands so the wins is 240-130 = 110

Using normal probability table:

P(X≤110) = P(X<110.5)

             = P(Z<-0.916)

             = 0.1788

c)

Using normal approximation of binomial distribution:

n = 240

p = 0.49

q = 1 - p = 1 - 0.49 = 0.51

np = 240 * 0.49 = 117.6

nq = 240 * 0.51 = 122.5

both np and nq are greater than 5 so the binomial distribution can be approximated by normal distribution

Compute z-score:

z = x - np / √(np(1-p))

  = 120.5 - 117.6 / √117.6(1-0.49)

  = 2.9/√117.6(0.51)

  = 2.9/√59.976

  = 2.9/7.744417

  =0.374463

Here the player wins when he wins at least 120 of 240 hands

Using normal probability table:

P(X>120) = P(X>120.5)

              = P(Z>0.3744)  

             =  1 - P(Z<0.3744)

             = 1 - 0.6443

             = 0.3557

d)

Player goes broke when he loses $1500

Using normal approximation of binomial distribution:

n = 240

p = 0.49

q = 1 - p = 1 - 0.49 = 0.51

np = 240 * 0.49 = 117.6

nq = 240 * 0.51 = 122.5

both np and nq are greater than 5 so the binomial distribution can be approximated by normal distribution

Compute z-score:

z = x - np / √(np(1-p))

  = 105.5 - 117.6 / √117.6(1-0.49)

  = -12.1/√117.6(0.51)

  = -12.1/√59.976

  = -12.1/7.744417

  =−1.562416

Here the player loses 1500 or more when he loses at least 135 of 240 hands so the wins is 240-135 = 105

Using normal probability table:

P(X≤105) = P(X<105.5)

             = P(Z<-1.562)

             = 0.0594

7 0
3 years ago
Need help with this math problem
grandymaker [24]

Answer:

m<1 = 87

m<2 = 45

m<3 = 45

m<4 = 52

Step-by-step explanation:

if BC intersects <ACD then that means angle 2 and 3 = 90

so that being angle 2 and 3 are the same

now you do 180-(45+48) = 87

now same thing but 180-(45+83) = 52

3 0
3 years ago
A gift box is a rectangular prism. The box measure 8 inches by 10 inches by 3 inches. What is it’s surface area?
MakcuM [25]

Answer:

the answer is 80 i think

Step-by-step explanation:

bc dependng on  2lw+2lh+2hw, formula 8 and 10 would be length and width

Lets say

8=width

10=lenght

3in=height

u would do

2 x l x w   + 2 x l h + 2 x h x w=

2 x 10 x 8 + 2 x 10 x 3 + 3 x 8=

160 +            60       +      48+=

268 is the sa

pls brainliest and more points :0

8 0
3 years ago
3)
Wewaii [24]

Answer:

For covering  1 unit area of the entire playground, the amount of sand required is equal to volume of 3 buckets of sand.

Step-by-step explanation:

Given -

\frac{1}{3} volume of sand in bucket is able to cover \frac{1}{9} area of the entire playground

Thus,

For covering  \frac{1}{9} unit area of the entire playground, the amount of sand required is equal to  \frac{1}{3}  of the total volume of sand in bucket

For covering  1 unit area of the entire playground, the amount of sand required is equal to

\frac{\frac{1}{3} }{\frac{1}{9} } \\\\\frac{1}{3}  * \frac{9}{1} \\\frac{9}{3}\\= 3

For covering  1 unit area of the entire playground, the amount of sand required is equal to volume of 3 buckets of sand.

4 0
3 years ago
There are 3ft in 1 yard. This is equivalent to 12ft in 4yrds.Which proportion can be used to represent this?
harina [27]

You could use the proportion 3:1.

Per 3 feet, there is 1 yard.

For every 3 feet, there is an additional yard.

The ratio is 3 to 1, or 3:1


5 0
3 years ago
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