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olasank [31]
3 years ago
5

Nedra purchased apples and oranges at the grocery store. Apples are $0.55 each and oranges are $0.75 each. If she spent a total

of $12.65 for 19 pieces of fruit, which two linear equations can be used to find the number of apples and oranges? Then determine how many pieces of each fruit she purchased.
Mathematics
1 answer:
Thepotemich [5.8K]3 years ago
6 0

Answer:

The two linear equation

x + y = 19.... Equation 1

0.55x + 0.75y = 12.65... Equation 2

Nedra purchased

9 Apples and 11 Oranges

Step-by-step explanation:

Nedra purchased apples and oranges at the grocery store. which two linear equations can be used to find the number of apples and oranges?

Let the number of apples be represented by x

The number of oranges by represented by y.

Hence,

Apples are $0.55 each and oranges are $0.75 each. If she spent a total of $12.65 for 19 pieces of fruit,

Hence:

x + y = 19..... Equation 1

x = 19 - y

$0.55 × x + $0.75 × y = $12.65

0.55x + 0.75y = 12.65.....Equation 2

Hence: we substitute 19 - y for x in Equation 2

0.55(19 - y) + 0.75y = 12.65

10.45 - 0.55y + 0.75y = 12.65

-0.55y+ 0.75y = 12.65 - 10.45

0.20y = 2.2

y = 2.2/0.20

y = 11 oranges

x = 19 - y

x = 19 - 11

x = 8 Apples

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3 years ago
Twenty students from Sherman High School were accepted at Wallaby University. Of
nydimaria [60]

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.

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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

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We would set up the hypothesis.

The null hypothesis is

H0 : μw = μo H0 : μw - μo = 0

The alternative hypothesis is

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

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From the information given,

xw = 1099.375

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so = 140.89

nw = 8

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

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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

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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

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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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