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2 years ago

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A meteorologist is studying the monthly rainfall in a section of the Brazilian rainforest. She recorded the monthly rainfall, in

inches, for last year. They were:
10.4, 10.3, 11.7, 11.1, 8.0, 4.4, 2.6, 1.8, 2.5, 4.4, 7.3, 9.5

Calculate the following for the data set:

1 answer:

mario62 [17]2 years ago

7 0

Answer:

Mean = 7

Median = 7.65

Mode = 4.4

Range = 9.9

Step-by-step explanation:

The question is incomplete as it doesn't state what to find. Lets complete the question first. The complete question states that:

Calculate the following for the data set

Mean

Median

Mode

Range

<h3>A) Mean</h3>

Mean = sum of values/ total number of values

Mean = 84/12

Mean = 7

<h3>B) Median</h3>

Arrange the data in ascending order

1.8, 2.5, 2.6, 4.4, 4.4, 7.3, 8.0, 9.5, 10.3, 10.4, 11.1, 11.7

Median = Average of middle values

Median = (7.3+8.0) / 2

Median = 7.65

<h3>C) Mode</h3>

Mode = number which appears most = 4.4

<h3>D) Range</h3>

Range = Max value - Min value

Range = 11.7 - 1.8

Range = 9.9

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Jar A contains four liters of a solution that is 45% acid. Jar B contains five liters of a solution that is 48% acid. Jar C cont

castortr0y [4]

Answer:

k= 80%

Step-by-step explanation:

Jar A contains 4*0.45 L acid, and 4 L of a solution of acid.

Jar B contains 5*0.48 L acid., and 5 L of a solution of acid.

Jar C contains 1*k/100 = k/100 acid, and 1 L of a solution.

50% = 0.5

For jar A.

(2/3)*k/100 L acid is added to jar A.

Now jar A contains 4*0.45 L + (2/3)*k/100 L acid, and it has (4+2/3)L of a solution.

L solute/L solution = 0.5

[4*0.45 L + (2/3)*k/100 L]/(4+2/3)L = 0.5

[1.8 + (2k/300)]/[(12+2)/3] = 0.5

[1.8 + (2k/300)]/[14/3] = 0.5

[1.8 + (2k/300)]= 0.5*(14/3)

(2k/300) = 0.5*(14/3) - 1.8

2k = (0.5*(14/3) - 1.8)*300

k = (0.5*(14/3) - 1.8)*300/2 =80

k= 80%

We also can find k using jar B.

(1/3)k/100 L acid is added to jar B.

Now jar B contains 5*0.48 L+ (1/3)k/100 L acid, and it has (5+1/3) L of a solution.

L solute/L solution = 0.5

[5*0.48 L+ (1/3)k/100 L ]/(5+1/3)L= 0.5

[5*0.48 + (1/3)k/100 ]/(5+1/3)= 0.5

This equation also gives k=80%

Check.

We can check at least for jar A.

Jar A has 4L solution and 4*0.45=1.8 L acid.

2/3 L of the solution from jar C was added, and now we have 4 2/3 L of solution.

(2/3)* 80%= (2/3)*0.8 acid was added from jar C.

Now we have [1.8 +(2/3)*0.8] L acid in jar A.

L solute/L solution = [1.8 +(2/3)*0.8] L /(4 2/3) L = 0.5 or 50% as it is given that jar A has 50% at the end.

7 0

2 years ago

What is the slope of the line through ( − 5 , − 10 ) (−5,−10)left parenthesis, minus, 5, comma, minus, 10, right parenthesis and

nikdorinn [45]

Answer:

3.75

Step-by-step explanation:

We have to find the slope of a straight line through points (-5,-10) and (-1,5).

Now. we know the slope of a straight line through the points ( $x_{1},y_{1}$ ) and ( $x_{2},y_{2}$ ) is given by $[\frac{y_{2} - y_{1} }{x_{2} - x_{1}} ]$ .

So, in our case ( $x_{1},y_{1}$ ) ≡ (-5,-10) and ( $x_{2},y_{2}$ ) ≡ (-1,5).

Therefore, the slope of the line is $\frac{5 - (- 10)}{- 1 - (- 5)} = \frac{15}{4} = 3.75$ (Answer)

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2 years ago

A researcher gathers data on the length of essays (number of lines) and the SAT scores received for a sample of students enrol

LenaWriter [7]

Answer:

(C) The slope of the regression equation is not significantly different from zero

Step-by-step explanation:

Let's suppose that we have the following linear model:

$y= \beta_o +\beta_1 X$

Where Y is the dependent variable and X the independent variable. $\beta_0$ represent the intercept and $\beta_1$ the slope.

In order to estimate the coefficients $\beta_0 ,\beta_1$ we can use least squares estimation.

If we are interested in analyze if we have a significant relationship between the dependent and the independent variable we can use the following system of hypothesis:

Null Hypothesis: $\beta_1 = 0$

Alternative hypothesis: $\beta_1 \neq 0$

Or in other wouds we want to check is our slope is significant.

In order to conduct this test we are assuming the following conditions:

a) We have linear relationship between Y and X

b) We have the same probability distribution for the variable Y with the same deviation for each value of the independent variable

c) We assume that the Y values are independent and the distribution of Y is normal

The significance level is provided and on this case is $\alpha=0.05$

The standard error for the slope is given by this formula:

$SE_{\beta_1}=\frac{\sqrt{\frac{\sum (y_i -\hat y_i)^2}{n-2}}}{\sqrt{\sum (X_i -\bar X)^2}}$

Th degrees of freedom for a linear regression is given by $df=n-2$ since we need to estimate the value for the slope and the intercept.

In order to test the hypothesis the statistic is given by:

$t=\frac{\hat \beta_1}{SE_{\beta_1}}$

The confidence interval for the slope would be given by this formula:

$\hat \beta_1 + t_{n-2, \alpha/2} \frac{\sqrt{\frac{\sum (y_i -\hat y_i)^2}{n-2}}}{\sqrt{\sum (X_i -\bar X)^2}}$

And using the last formula we got that the confidence interval for the slope coefficient is given by:

$-0.88 < \beta_1$

IF we analyze the confidence interval contains the value 0. So we can conclude that we don't have a significant effect of the slope on this case at 5% of significance. And the best option would be:

(C) The slope of the regression equation is not significantly different from zero

6 0

2 years ago

Which ordered pair minimizes the objective function C = 60x + 85y?. (0, 160). (55, 70). (80, 50). (170, 0)

dangina [55]

Step-by-step explanation:

The given objective function is $C = 60x + 85y$

To check that which ordered pair is minimizing the objective function-we will substitute all the ordered pair one by one in the given function and we will calculate the value of C. The ordered pair which will give the minimum value will be the answer.

For (0, 160)

$C=60\times 0+85\times 160=13600$

For (55, 70)

$C=60\times 55+85\times 70=9250$

For (80, 50)

$C=60\times 80+85\times 50=9050$

For (80, 50)

$C=60\times 170+85\times 0=10200$

Hence the ordered pair which minimizes the objective function is (80, 50)

3 0

2 years ago

Read 2 more answers

Carla and Jonah are working together to determine if quadrilateral CDEF with coordinates C(2, 3), D(1, 2), E(4, 1), and F(5, 3)

mart [117]

Answer:

A. Carla is on the right track because she is finding the slopes of consecutive sides to check for perpendicular sides.

Step-by-step explanation:

Only adjacent sides can be perpendicular, so Jonah's approach of finding slopes of opposite sides cannot work.

Carla is on the right track; choice A.

4 0

2 years ago