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3 years ago

I will give brainliest to whoever can answer this question. It’s due in 40 min Please help me )):

Mathematics

1 answer:

Aleonysh [2.5K]3 years ago

5 0

Given:

$m\angle L=m\angle Z=70^\circ$

$m\angle N=m\angle Y=90^\circ$

To find:

The value of $m\angle 1$ .

Solution:

In triangle XYZ,

$m\angle Y=m\angle N=90^\circ$ (Given)

$m\angle Z=m\angle L=70^\circ$ (Given)

$m\angle X+m\angle Y+m\angle Z=180^\circ$ [Angle sum property]

$m\angle 1+90^\circ+70^\circ=180^\circ$

$m\angle 1+160^\circ=180^\circ$

$m\angle 1=180^\circ-160^\circ$

$m\angle 1=20^\circ$

Therefore, the $m\angle 1$ is 20°.

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3 years ago

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3 years ago

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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.

Let X = apartment rents in Minneapolis

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

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

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

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.

(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

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.

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

(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

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.

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

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.

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2 years ago