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3 years ago

Given m/n find the value of x. 106° 470

Mathematics

1 answer:

Igoryamba3 years ago

3 0

Answer:

x = 106

Step-by-step explanation:

The angle with a measure of 106 degrees and the angle labeled "x" are opposite exterior angles

Opposite exterior angles are congruent

Hence, x = 106

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Please help: A box contains 5 yellow balls, 3 blue, and 1 red ball. Two balls are drawn at random. Find the probability that:

Y_Kistochka [10]

Answer:

a) 0.2778

b) 0.3611

c) 0.1389

d) 0.0833

Step-by-step explanation:

We have a total of 5 + 3 + 1 = 9 balls

a) First ball being yellow: we have 5 yellow balls, so P1 = 5/9

Second ball being yellow after one yellow was drawn: we have 4 yellows and 8 balls, so P2 = 4/8 = 1/2

Both yellows: P = P1 * P2 = 5/18 = 0.2778

b) Both blues:

P1 = 3/9 = 1/3

P2 = 2/8 = 1/4

P = P1 * P2 = 1/12 = 0.0833

Both yellows or both blues: 5/18 + 1/12 = 0.2778 + 0.0833 = 0.3611

c) First yellow: P1 = 5/9

Second red: P2 = 1/8

Pa = P1 * P2 = 5/72

First red: P3 = 1/9

Second yellow: P4 = 5/8

Pb = P3 * P4 = 5/72

P = Pa + Pb = 10/72 = 5/36 = 0.1389

d) First blue: P1 = 3/9 = 1/3

Second red: P2 = 1/8

Pa = P1 * P2 = 1/24

First red: P3 = 1/9

Second blue: P4 = 3/8

Pb = P3 * P4 = 1/24

P = Pa + Pb = 2/24 = 1/12 = 0.0833

8 0

3 years ago

A baseball coach is determining the batting order for the team. The team has 9 players, but the coach does not want the pitcher

Rus_ich [418]

Answer: 2.25

Step-by-step explanation:

6 0

2 years ago

dmitriy555 [2]

Answer:

Step-by-step explanation

Process capabilitty ration and process capability index are statistical tools which are often used to produced output within a limit.

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2 years ago

Math question down below

julsineya [31]

This data set has no outliers, because all of the numbers are close together.

6 0

2 years ago

The pesticide diazinon is in common use to treat infestations of the German cockroach, Blattella germanica. A study investigated

cluponka [151]

Answer:

We conclude that there is no difference in the proportion of cockroaches that died on each surface.

Step-by-step explanation:

We are given that a study investigated the persistence of this pesticide on various types of surfaces.

After 14 days, they randomly assigned 72 cockroaches to two groups of 36, placed one group on each surface, and recorded the number that died within 48 hours. On the glass, 18 cockroaches died, while on plasterboard, 25 died.

Let $p_1$ = proportion of cockroaches that died on glass surface.

$p_2$ = proportion of cockroaches that died on plasterboard surface.

So, Null Hypothesis, $H_0$ : $p_1-p_2$ = 0 {means that there is no difference in the proportion of cockroaches that died on each surface}

Alternate Hypothesis, $H_A$ : $p_1-p_2\neq$ 0 {means that there is a significant difference in the proportion of cockroaches that died on each surface}

The test statistics that would be used here Two-sample z proportion statistics;

T.S. = $\frac{(\hat p_1-\hat p_2)-(p_1-p_2)}{\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2} } }$ ~ N(0,1)

where, $\hat p_1$ = sample proportion of cockroaches that died on glass surface = $\frac{18}{36}$ = 0.50

$\hat p_2$ = sample proportion of cockroaches that died on plasterboard surface = $\frac{25}{36}$ = 0.694

$n_1$ = sample of cockroaches on glass surface = 36

$n_2$ = sample of cockroaches on plasterboard surface = 36

So, test statistics = $\frac{(0.50-0.694)-(0)}{\sqrt{\frac{0.50(1-0.50)}{36}+\frac{0.694(1-0.694)}{36} } }$

= -1.712

The value of z test statistics is -1.712.

Since, in the question we are not given with the level of significance so we assume it to be 5%. Now, at 5% significance level the z table gives critical values of -1.96 and 1.96 for two-tailed test.

Since our test statistics lies within the range of critical values of z, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.

Therefore, we conclude that there is no difference in the proportion of cockroaches that died on each surface.

8 0

3 years ago