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3 years ago

1) 12x - 18 < 14x + 4

Mathematics

2 answers:

ycow [4]3 years ago

5 0

Answer:

x > - 11

Step-by-step explanation:

Isolate the variable, x. Note the <, treat it like a equal sign, what you do to one side, you do to the other.

First, subtract 14x and add 18 to both sides:

12x (-14x) - 18 (+18) < 14x (-14x) + 4 (+18)

12x - 14x < 4 + 18

-2x < 22

Next, isolate the variable, x. Divide -2 from both sides. Note that when you divide by a negative number, you must flip the sign:

(-2x)/-2 < (22)/-2

x < (22/-2)

x > -11

x > - 11 is your answer.

cluponka [151]3 years ago

5 0

Answer: x > - 11

Step-by-step explanation:

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3 years ago

Please help me its timed -H.M

VladimirAG [237]

Answer:

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Step-by-step explanation:

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3 years ago

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LekaFEV [45]

Answer:

Yes, there is evidence that more than 50% of likely voters will likely vote for the incumbent.

Step-by-step explanation:

We are given that in order to estimate the proportion of all likely voters who will likely vote for the incumbent in the upcoming city’s mayoral race, a random sample of 267 likely voters is taken, finding that 65% state they will likely vote for the incumbent.

The polling agency wishes to test whether there is evidence that more than 50% of likely voters will likely vote for the incumbent.

Let p = proportion of voters who will likely vote for the incumbent

SO, Null Hypothesis, $H_0$ : p $\leq$ 50% {means that less than or equal to 50% of likely voters will likely vote for the incumbent}

Alternate Hypothesis, $H_A$ : p > 50% {means that more than 50% of likely voters will likely vote for the incumbent}

The test statistics that will be used here is One-sample z proportion statistics;

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

where, $\hat p$ = sample proportion of voters who will likely vote for the incumbent in a sample of 267 voters = 65% or 0.65

n = sample of voters = 267

So, test statistics = $\frac{0.65-0.50}{{\sqrt{\frac{0.65(1-0.65)}{267} } } } }$

= 5.139

Since in the question we are not given the level of significance so we assume it to be 5%. Now at 0.05 significance level, the z table gives critical value of 1.6449 for right-tailed test. Since our test statistics is more than the critical value of z so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.

Therefore, we conclude that the more than 50% of likely voters will likely vote for the incumbent. The strength of the evidence is 95%.

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olga55 [171]

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