Heights (cm) and weights (kg) are measured for 100 randomly selected adult males, and range from heights of 133 to 193 cm and weights of 40 to 150 kg. Let the predictor variable x be the first variable given. The 100 paired measurements yield x overbarequals167.90 cm, y overbarequals81.47 kg, requals0.228, P-valueequals0.023, and ModifyingAbove y with caretequalsnegative 105plus1.13x. Find the best predicted value of ModifyingAbove y with caret (weight) given an adult male who is 172 cm tall. Use a 0.05 significance level. The best predicted value of ModifyingAbove y with caret for an adult male who is 172 cm tall is nothing kg. (Round to two decimal places as needed.)

The weight of an adult male who is 172 cm tall is 89.36 kg.

Step-by-step explanation:

The regression equation representing the relationship between height and weight of a person is:

Here

y = weight of a person

x = height of a person

The information provided is:

The hypothesis to test the significance of the correlation between height and weight is:

H₀: There is no relationship between the height and weight, i.e. ρ = 0.

Hₐ: There is a relationship between the height and weight, i.e. ρ ≠ 0.

Decision rule:

If the p-value of the test is less than the significance level, then the null hypothesis will be rejected and vice-versa.

According to information provided:

p-value = 0.023 < α = 0.05

The null hypothesis was rejected at 5% level of significance.

Thus, concluding that there is a relationship between the height and weight.

Compute the weight of an adult male with height, x = 172 cm as follows:

Thus, the weight of an adult male who is 172 cm tall is 89.36 kg.

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be

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step-by-step explanation: