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2 years ago

Solve the compound inequality for x and identify the graph of its solution.

Mathematics

1 answer:

RoseWind [281]2 years ago

8 0

Step-by-step explanation:

Given, 3x−2<2x+1

⇒3x−2x<1+2

⇒x<3orx∈(−∞,3)

The lines y=3x−2 and y=2x+1 both will intersect at x=3

Clearly, the dark line shows the solution of 3x−2<2x+1.

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What are the coordinates for a dilated triangle, A’B’C’, if the scale factor for the dilation is 0.75?

ycow [4]

Answer:

A’(–3.75, 0.75); B’(0, 1.5); C’(3, –1.5)

Step-by-step explanation:

Did this on edgenut and got it right

Hope this helps

6 0

2 years ago

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A recipe says it produced the best sweet tea. In addition to using tea bags, the recipe calls for ½ cup of sugar for every 1 ½ c

Sergio [31]

Answer:

The relationship between the number of cups of water and sugar in the recipe is w = ¹/₃(s)

Step-by-step explanation:

Given;

number of cups of sugar = s

number of cups of water = w

The relationship between the number of cups of water and sugar in this recipe is given as;

½ cup of sugar is proportional to 1 ½ cups of water

$\frac{1}{2} s = \frac{3}{2}w\\\\s= 3w\\\\w = \frac{s}{3}$

Therefore, the relationship between the number of cups of water and sugar in the recipe is w = ¹/₃(s)

7 0

2 years ago

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The initial population of a town is 4000 and it grows with a doubling time of 10 years what will the population be in 12 years

Doss [256]

Population in 12 years ≈10, 108 people

4 0

2 years ago

Western Athletic Club International (WACI) owns and operates a chain of fitness clubs. Currently WACI has 675 members at its Col

Ad libitum [116K]

Answer:

12%

Step-by-step explanation:

let x represent the actual number of members last year.

current members = 675 and with an increment of 13% over previous year

to find the increment

(675 - x) / x = 0.13

675 - x = 0.13x

collect the like terms

675 = 0.13x + x

675 = 1.13 x

x = approx 597 members were there last year

its hope to increase by the same number next year

percent increase = 675 - 597 / 675 = 78 / 675 = 0.12 = 12%

4 0

3 years ago

A marketing research firm wishes to compare the prices charged by two supermarket chains—Miller’s and Albert’s. The research fir

AVprozaik [17]

Answer:

a) $F=\frac{s^2_2}{s^2_1}=\frac{1.84^2}{1.4^2}=1.727 \approx 1.73$

b) For this case since we have a two tailed test we have two critical values, and we can find the two values since we need that on each tail the area would be $\alpha/2 =0.025$ , the distribution is the F with 9 df for the numerator and denominator, and we can use the following excel codes to find the critical values:

"=F.INV(0.025,9,9)"

"=F.INV(1-0.025,9,9)"

The two critical values are 0.248 and 4.026, so the rejection zone would be: $F>4.026 \cup F$ since our calculated value is not on the rejection zone we fail to rejec the null hypothesis

Step-by-step explanation:

Data given and notation

$n_1 = 10$ represent the sampe size for the Miller's Stores

$n_2 =10$ represent the sample size for the Albert's stores

$\bar X_1 =121.92$ represent the sample mean for Miller's store

$\bar X_2 =114.81$ represent the sample mean for Albert's store

$s_1 = 1.4$ represent the sample deviation for the Miller's store

$s_2 = 1.84$ represent the sample deviation for the Albert's stores

$s^2_2 = 12.25$ represent the sample variance for the utility stocks

$\alpha=0.05$ represent the significance level provided

Confidence =0.95 or 95%

F test is a statistical test that uses a F Statistic to compare two population variances, with the sample deviations s1 and s2. The F statistic is always positive number since the variance it's always higher than 0. The statistic is given by:

$F=\frac{s^2_2}{s^2_1}$

Solution to the problem

System of hypothesis

We want to test if the variation for th two groups is the same, so the system of hypothesis are:

H0: $\sigma^2_1 = \sigma^2_2$

H1: $\sigma^2_1 \new \sigma^2_2$

a) Calculate the statistic

Now we can calculate the statistic like this:

$F=\frac{s^2_2}{s^2_1}=\frac{1.84^2}{1.4^2}=1.727 \approx 1.73$

Now we can calculate the p value but first we need to calculate the degrees of freedom for the statistic. For the numerator we have $n_1 -1 =10-1=9$ and for the denominator we have $n_2 -1 =10-1=9$ and the F statistic have 9 degrees of freedom for the numerator and 9 for the denominator. And the P value is given by:

P value

$p_v =2*P(F_{9,9}>1.727)=0.428$

And we can use the following excel code to find the p value:"=2*(1-F.DIST(1.727,9,9,TRUE))"

b) Critical value

For this case since we have a two tailed test we have two critical values, and we can find the two values since we need that on each tail the area would be $\alpha/2 =0.025$ , the distribution is the F with 9 df for the numerator and denominator, and we can use the following excel codes to find the critical values:

"=F.INV(0.025,9,9)"

"=F.INV(1-0.025,9,9)"

The two critical values are 0.248 and 4.026, so the rejection zone would be: $F>4.026 \cup F$ since our calculated value is not on the rejection zone we fail to rejec the null hypothesis

Since our calcu

Conclusion

Since the $p_v > \alpha$ we have enough evidence to FAIL to reject the null hypothesis. And we can say that we don't have enough evidence to conclude that the two deviations are different at 5% of significance.

8 0

3 years ago