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3 years ago

Find the GCF of 27, 45, 36

Mathematics

1 answer:

LuckyWell [14K]3 years ago

7 0

Answer:

9 is the right answer and the way I know that is because it is the highest factor their could be between both of them.

27-9and 3

45-9 and 5

36- 9 and 4

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Which is the solution to the equation solved for p? (q + p)q = (s + r)s

Brums [2.3K]

Answer:

Option B

Step-by-step explanation:

$(q + p)q = (s + r)s$

Lets open the brackets of L.H.S.

$=> q^2 + pq = (s+ r)s$

Lets substract q² from both the sides.

$=> q^2 + pq - q^2 = (s + r)s - q^2$

$=> pq = (s + r)s - q^2$

Lets divide both the sides by q.

$=> \frac{pq}{q} = \frac{(s + r)s - q^2}{q}$

$=> p = \frac{(s + r)s }{q} - \frac{q^2}{q} = \frac{(s + r)s}{q} - q$

7 0

3 years ago

In a program designed to help patients stop smoking. 192 patients were given to sustained care, and 80.2% of them were no longer

stira [4]

Answer:

We conclude that 80% of patients stop smoking when given sustained care.

Step-by-step explanation:

We are given that in a program designed to help patients stop smoking. 192 patients were given to sustained care, and 80.2% of them were no longer smoking after one month.

Let p = percentage of patients stop smoking when given sustained care.

So, Null Hypothesis, $H_0$ : p = 80% {means that 80% of patients stop smoking when given sustained care}

Alternate Hypothesis, $H_A$ : p $\neq$ 80% {means that different from 80% of patients stop smoking when given sustained care}

The test statistics that would be used here One-sample z test for proportions;

T.S. = $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ~ N(0,1)

where, $\hat p$ = sample proportion of patients who stop smoking when given sustained care = 80.2%

n = sample of patients = 192

So, the test statistics = $\frac{0.802-0.80}{\sqrt{\frac{0.802(1-0.802)}{192} } }$

= 0.07

The value of z test statistics is 0.07.

Also, P-value of the test statistics is given by the following formula;

P-value = P(Z > 0.07) = 1 - P(Z $\leq$ 0.07)

= 1 - 0.52790 = 0.4721

Now, at 0.05 significance level the z table gives critical values of -1.96 and 1.96 for two-tailed test.

Since our test statistic 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 80% of patients stop smoking when given sustained care.

8 0

3 years ago

In a random sample of 600 cars making a right turn at a certain intersection, 157 pulled into the wrong lane. Test the hypothesi

nevsk [136]

Answer:

The statistic value |Z| = 2.053 > 1.96 at 0.05 Level of significance

Null hypothesis is rejected

Alternative hypothesis is Accepted

Actually 30% of all drivers make not this mistake at the given intersection

b)

The test statistic value |Z| = 2.053 >2.576 at 0.01 Level of significance

Null hypothesis is Accepted

Actually 30% of all drivers make this mistake at the given intersection

Step-by-step explanation:

Step(i):-

Given Population proportion = 30% or 0.30

Given data In a random sample of 600 cars making a right turn at a certain intersection, 157 pulled into the wrong lane

sample proportion

$p^{-} = \frac{x}{n} = \frac{157}{600} = 0.2616$

Null hypothesis:- H₀: p = 0.30

Alternative hypothesis : H₁:p≠0.30

Step(ii):-

Test statistic

$Z = \frac{p^{-}-P }{\sqrt{\frac{p(1-p)}{n} } }$

$Z = \frac{0.2616-0.30 }{\sqrt{\frac{0.30(1-0.30)}{600} } }$

Z = -2.053

|Z| = |-2.053| = 2.053

Level of significance = 0.05

Z₀.₀₅ = 1.96

The calculated value |Z| = 2.053 > 1.96 at 0.05 Level of significance

Null hypothesis is rejected

Alternative hypothesis is Accepted

Conclusion:-

Actually 30% of all drivers make not this mistake at the given intersection

b)

Given level of significance = 0.01

Z₀.₀₁ = 2.576

The calculated value |Z| = 2.053 >2.576 at 0.01 Level of significance

Null hypothesis is Accepted

Actually 30% of all drivers make this mistake at the given intersection

7 0

3 years ago

Ten less the quotient of a number and three

Anettt [7]

Answer:

(x/3) - 10

Step-by-step explanation:

quotient = divide

it's ten less than what the quotient is.

7 0

3 years ago

At 11 am one one share of Starbucks stock was $18. By 4 pm the price was $23. The rate the Starbucks stock value was changing is

ziro4ka [17]

The changing is $1 per hour

7 0

3 years ago