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SIZIF [17.4K]
2 years ago
14

Suppose a certain company sell reg keyboards for $82 and wireless $110 last week the store sold three times as many regular keyb

oards as wireless. If the total sales were 4628 how many was sold?
Mathematics
1 answer:
shutvik [7]2 years ago
3 0

Answer:

3,471 regular keyboards sold

1,157 wireless keyboards sold

Step-by-step explanation:

To represent this scenario use this system of equations:

x + y = 4628

x = 3y

x = regular keyboards

y = wireless keyboards

The first equation represents how many regular and wireless keyboards were sold to equal 4,628 units of keyboards.

The second equation represents how there are three times as many regular keyboards sold than wireless.

Solve this by plugging in x in the second equation to the first equation:

(3y) + y = 4628

4y = 4628                        Add the y's together to get 4y

y = 1,157

Therefore, 1,157 wireless keyboards were sold

To find how many regular keyboards were sold, plug y back into the second equation:

x = 3(1157)

x = 3,471

The final answer to this problem is that 3,471 regular keyboards were sold and 1,157 wireless keyboards were sold.

Hope this helps!! If you have any questions about the work please let me know!

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Answer:

Data provide convincing evidence of a difference in SAT scores  between students with and without a military scholarship is explained below in details.

Step-by-step explanation:

This is a quiz of 2 autonomous groups. The population model differences are not understood. it is a two-tailed examination. Let w be the index for scores of students with army research and o be the index for scores of students without army research.

Therefore, the population means would be μw and μo.

The irregular variable is x w - xo = variation in the sample mean records of students with military accomplishments and students without.

For students with military accomplishments,

n = 8

Mean = (850 + 925 + 980 + 1080 + 1200 + 1220 + 1240 + 1300)/8

Mean = 1099.375

Standard deviation = √(summation(x - mean)/n

Summation(x - mean) = (850 - 1099.375)^2 + (925 - 1099.375)^2 + (980 - 1099.375)^2 + (1080 - 1099.375)^2 + (1200 - 1099.375)^2 + (1220 - 1099.375)^2 + (1240 - 1099.375)^2 + (1300 -1099.375)^2 = 191921.875

Standard deviation = √(191921.875/8 = 154.89

For students without military scholarship,

n = 12

Mean = (820 + 850 + 980 + 1010 + 1020 + 1080 + 1100 + 1120 + 1120 + 1200 + 1220 + 1330)/12

Mean = 1073.83

Summation(x - mean) = (820 - 1073.83)^2 + (850 - 1073.83)^2 + (980 - 1073.83)^2 + (1010 - 1073.83)^2 + (1020 - 1073.83)^2 + (1080 - 1073.83)^2 + (1100 - 1073.83)^2 + (1120 - 1073.83)^2 + (1120 - 1073.83)^2 + (1200 - 1073.83)^2 + (1220 - 1073.83)^2 + (1330 - 1073.83)^2 = 238199.4268

Standard deviation = √(238199.4268/12 = 140.89

We would set up the hypothesis.

The null hypothesis is

H0 : μw = μo H0 : μw - μo = 0

The alternative hypothesis is

Ha : μw ≠ μo Ha : μw - μo ≠ 0

Since sample standard deviation is recognized, we would analyis the examination statistic by using the t examination. The formula is

(xw - xo)/√(sw²/nw + so²/no)

From the information given,

xw = 1099.375

xo = 1073.83

sw = 154.89

so = 140.89

nw = 8

no = 12

t = (1099.375 - 1073.83)/√(154.89²/8 + 140.89²/12)

t = 0.37

The formula for determining the degree of freedom is

df = [sw²/nw + so²/no]²/(1/nw - 1)(sw²/nw)² + (1/no - 1)(so²/no)²

df = [154.89²/8 + 140.89²/12]²/(1/8 - 1)(154.89²/8)² + (1/12 - 1)(140.89²/12)² = 21650688.37/1533492.15

df = 14

We would get the probability count from the t test calculator. It becomes

p value = 0.72

Since the level of importance of 0.05 < the p value of 0.72, we would not neglect the null hypothesis.

Therefore, these data do not present an acceptable indication of a difference in SAT scores between students with and without a military scholarship.

Part B

The formula for getting the confidence interval for the difference of two population means is expressed as

z = (xw - xo) ± z ×√(sw²/nw + so²/no)

For a 95% confidence interval, the z score is 1.96

xw - xo = 1099.375 - 1073.83 = 25.55

z√(sw²/nw + so²/no) = 1.96 × √(154.89²/8 + 140.89²/12) = 1.96 × √2998.86 + 1654.17)

= 133.7

The confidence interval is

25.55 ± 133.7

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Answer:

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Step-by-step explanation:

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