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musickatia [10]
3 years ago
11

Write an equation in point-slope form for the line that has the given slope and that contains the given point. slope 4/5 ,(8,2)

Mathematics
1 answer:
Novosadov [1.4K]3 years ago
6 0
Hello,

The equation is y-2=4/5(x-8)==>y=4/5x-22/5 or 4x-5y=22
=========================================
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M/PF Research, Inc. lists the average monthly apartment rent in some of the most expensive apartment rental locations in the Uni
xz_007 [3.2K]

Answer:

(a) $1,020 or more = 0.2358

(b) Between $880 and $1,130 = 0.7389

(c) Between $830 and $940 = 0.3524

(d) Less than $770 = 0.0294

Step-by-step explanation:

We are given that According to M/PF Research, Inc. report, the average cost of renting an apartment in Minneapolis is $951.

Suppose that the standard deviation of the cost of renting an apartment in Minneapolis is $96 and that apartment rents in Minneapolis are normally distributed.

<em>Let X = apartment rents in Minneapolis</em>

So, X ~ Normal(\mu=$951,\sigma^{2} =$96^{2})

The z score probability distribution for normal distribution is given by;

<em>                  </em>    Z  =  \frac{X-\mu}{\sigma}  ~ N(0,1)

where,  \mu = average cost of renting an apartment = $951

            \sigma = standard deviation = $96

(a) Probability that the price is $1,020 or more is given by = P(X \geq $1,020)

    P(X \geq $1,020) = P( \frac{X-\mu}{\sigma} \geq \frac{1,020-951}{96} ) = P(Z \geq 0.72) = 1 - P(Z < 0.72)

                                                               = 1 - 0.76424 = 0.2358

<em>The above probability is calculated by looking at the value of x = 0.72 in the z table which gives an area of 0.76424.</em>

<em />

(b) Probability that the price is between $880 and $1,130 is given by = P($880 < X < $1,130) = P(X < $1,130) - P(X \leq 880)

    P(X < $1,130) = P( \frac{X-\mu}{\sigma} < \frac{1,130-951}{96} ) = P(Z < 1.86) = 0.96856

     P(X \leq $880) = P( \frac{X-\mu}{\sigma} \leq \frac{880-951}{96} ) = P(Z \leq -0.74) = 1 - P(Z < 0.74)

                                                         = 1 - 0.77035 = 0.22965

<em>The above probability is calculated by looking at the value of x = 1.86 and x = 0.74 in the z table which gives an area of 0.96856 and 0.77035 respectively.</em>

<em />

Therefore, P($880 < X < $1,130) = 0.96856 - 0.22965 = 0.7389

<em />

(c) Probability that the price is between $830 and $940 is given by = P($830 < X < $940) = P(X < $940) - P(X \leq 830)

    P(X < $940) = P( \frac{X-\mu}{\sigma} < \frac{940-951}{96} ) = P(Z < -0.11) = 1 - P(Z \leq 0.11)

                                                          = 1 - 0.5438 = 0.4562

     P(X \leq $830) = P( \frac{X-\mu}{\sigma} \leq \frac{830-951}{96} ) = P(Z \leq -1.26) = 1 - P(Z < 1.26)

                                                         = 1 - 0.89617 = 0.10383

<em>The above probability is calculated by looking at the value of x = 0.11 and x = 1.26 in the z table which gives an area of 0.5438 and 0.89617 respectively.</em>

<em />

Therefore, P($830 < X < $940) = 0.4562 - 0.10383 = 0.3524

(d) Probability that the price is Less than $770 is given by = P(X < $770)

    P(X < $770) = P( \frac{X-\mu}{\sigma} < \frac{770-951}{96} ) = P(Z < -1.89) = 1 - P(Z \leq 1.89)

                                                         = 1 - 0.97062 = 0.0294

<em>The above probability is calculated by looking at the value of x = 1.89 in the z table which gives an area of 0.97062.</em>

8 0
3 years ago
9) -1 +5n&gt;-26 and 7n-25 &lt;12<br> How do you solve this?
DIA [1.3K]

Answer:

n > -5 and n < 37/7

Step-by-step explanation:

Just move the values with n to one side....where it would state that...

5n > -26 + 1 and 7n < 25 + 12

5n > -25 and 7n < 37

;n > -5 and n < 37/7

8 0
3 years ago
Solve for x. (PLEASE HELP)
nexus9112 [7]

9514 1404 393

Answer:

  x = 6

Step-by-step explanation:

The parallel lines divide the sides proportionally. So, we can write the equation ...

  x/4 = (x +3)/6

  3x = 2(x +3) . . . . . multiply by 12

  x = 6 . . . . . . . . . . . subtract 2x

7 0
3 years ago
Which of the following ratios is not proportional to the others
atroni [7]
2 to 3 is the answer             
8 0
3 years ago
Read 2 more answers
A. 1
dimulka [17.4K]

Step-by-step explanation:

Given equation of circle (in general form) is:

8 {x}^{2}  + 8 {y}^{2}  - 16x - 32y + 24 = 0 \\  \\ dividing \: throughout \: by \: 8 \: we \: find :  \\  {x}^{2}  + {y}^{2}  - 2x - 4y + 3 = 0  \\ equating \: it \: with :  \\  {x}^{2}  +  {y}^{2}  + 2gx + 2fy + c = 0 \\ 2g =  - 2 \implies \: g =  -  1\\  2f =  - 4 \implies \: f =  - 2 \\ c = 3 \\   \therefore \:center =  ( - g, \:  \:  - f) = (1, \:  \: 2) \\  \\ radius \: r =  \sqrt{ {g}^{2} +  {f}^{2}  - c }  \\  =  \sqrt{ {1}^{2}  +  {2}^{2}  - 3}  \\  =  \sqrt{1 + 4 - 3}  \\  =  \sqrt{5 - 3}  \\  =  \sqrt{2}  \: units

7 0
3 years ago
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