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3 years ago

Two apples and three peaches cost $1.65. three apples and two peaches cost $1.60. what is the cost of one peach

2 answers:

8 0

Let a = cost of an apple and p = cost of a peach

From the two statements we can create the following system of equations:
2a + 3p = 1.65
3a + 2p = 1.60

Since we want to know the cost of a peach, let's eliminate the "a" terms by creating opposites. The LCM for 2 and 3 is 6 so I will multiply the top equation by 3 and the bottom equation by -2. This will create opposites to cancel "a" terms.
3(2a + 3p = 1.65) → 6a + 9p = 4.95
-2(3a + 2p = 1.60) → -6a - 4p = -3.20
The result of adding → 5p = 1.75
The result of ÷ 5 → p = .35
This means one peach cost .35 or 35 cents

Lyrx [107]3 years ago

7 0

Let number of apples be a and peaches be p.
Number of apples = a
Number of peaches = p

Two apples and three peaches cost $1.65
⇒2a + 3p = 1.65

Three apples and two peaches cost $1.60
⇒3a + 2p = 1.60

System Equations :
 $\begin{cases}&2a + 3p = 1.65 ---- (1) \\&3a + 2p = 1.60 ---- (2)\end{cases}$

$\begin{cases}&\text{Equation (1}) \times3: 6a + 9p = 4.95 ---- (1a) \\&\text{Equation (2}) \times2: 6a + 4p = 3.20 ---- (2a)\end{cases}$

Equation (1a) - (2a) :
$\begin{aligned} &5p = 1.75 \\&p = 0.35&\end{aligned}
$

Answer: $0.35

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4 years ago

A random sample of 20 individuals who graduated from college five years ago were asked to report the total amount of debt (in $)

Gekata [30.6K]

Answer:

a. As college debt increases current investment decreases.

b. Y= 68778.2406 - 1.9112X

Every time the college debt increases one dollar, the estimated mean of the current investments decreases 1.9112 dollars.

c. There is a significant linear relationship between college debt and current investment because the P-value is less than 0.1.

d. Y= $59222.2406

e. R²= 0.9818

Step-by-step explanation:

Hello!

You have the information on a random sample of 20 individuals who graduated from college five years ago. The variables of interest are:

Y: Current investment of an individual that graduated from college 5 years ago.

X: Total debt of an individual when he graduated from college 5 years ago.

To see the relationship between the information about the debt and the investment is it best to make a scatterplot with the sample information.

As you can see in the scatterplot (attachment) there is a negative relationship between the current investment and the debt after college, this means that the greater the debt these individuals had, the less they are currently investing.

The statement that best describes it is: As college debt increases current investment decreases.

The population regression equation is Y= α + βX +Ei

To develope the regression equation you have to estimate alpha and beta:

a= Y[bar] -bX[bar]

a= 44248.55 - (-1.91)*12829.70

a= 68778.2406

b= $\frac{sumXY-\frac{(sumX)(sumY)}{n} }{sumX^2-\frac{(sumX)^2}{n} }$

b= $\frac{9014653088-\frac{(256594)(884971)}{20} }{4515520748-\frac{(256594)^2}{20} }$

b= -1.9112

∑X= 256594

∑X²= 4515520748

∑Y= 884971

∑Y²= 43710429303

∑XY= 9014653088

n= 20

Means:

Y[bar]= ∑Y/n= 884971/20= 44248.55

X[bar]= ∑X/n= 256594/20= 12829.70

The estimated regression equation is:

Y= 68778.2406 - 1.9112X

Every time the college debt increases one dollar, the estimated mean of the current investments decreases 1.9112 dollars.

The hypotheses to test if there is a linear regression between the two variables are two tailed:

H₀: β = 0

H₁: β ≠ 0

α: 0.01

To make this test you can use either a Student t or the Snedecor's F (ANOVA)

Using t= b - β = -1.91 - 0 = -31.83

Sb 0.06

The critical region and the p-value for this test are two tailed.

The p-value is: 0.0001

The p-value is less than the level of signification, the decision is to reject the null hypothesis.

Using the

$F= \frac{MSTr}{MSEr}= \frac{4472537017.96}{4400485.72} =1016.37$

The rejection region using the ANOVA is one-tailed to the right, and so is the p-value.

The p-value is: 0.0001

Using this approach, the decision is also to reject the null hypothesis.

The conclusion is that at a 1% significance level, there is a linear regression between the current investment and the college debt.

The correct statement is:

There is a significant linear relationship between college debt and current investment because the P-value is less than 0.1.

To predict what value will take Y to a given value of X you have to replace it in the estimated regression equation.

Y/X=$5000

Y= 68778.2406 - 1.9112*5000

Y= $59222.2406

The current investment of an individual that had a $5000 college debt is $59222.2406.

To estimate the proportion of variation of the dependent variable that is explained/ given by the independent variable you have to calculate the coefficient of determination R².

$R^2= \frac{b^2[sumX^2-\frac{(sumX)^2}{n} ]}{sumY^2-\frac{(sumY)^2}{n} }$

$R^2= \frac{-1.9112^2[4515520748-\frac{(256594)^2}{20} ]}{43710429303-\frac{(884971)^2}{20} }$

R²= 0.9818

This means that 98.18% of the variability of the current investments are explained by the college debt at graduation under the estimated regression model: Y= 68778.2406 - 1.9112X

I hope it helps!