REASONING The table shows the weights (in pounds) and the prescribed dosages (in milligrams) of medicine for six patients.

Weight (lb), x Dosage (mg), y
94 72
119 90
135 103
150 115
185 140
202 156
a. Find an equation of the line of best fit. Round the slope and the $y$ -intercept to the nearest tenth, if necessary.

y=

Identify the correlation coefficient. Round your answer to the nearest thousandths.

Interpret the correlation coefficient.

b. Interpret the slope of the line of best fit.

c. A patient who weighs 140 pounds is prescribed 135 milligrams of medicine. How does this affect the line of best fit? Explain.

first off, let's notice that "x" and "y" are encapsulating a function in terms of time or namely "t", and that dy/dt is decreasing at a rate of 3 cm/s, since the rate is decreasing, that makes the rate negative, thus is changing at -3 cm/s.

[tex]xy=12\implies \stackrel{product~rule}{\cfrac{dx}{dt}y~~ + ~~ x\cfrac{dy}{dt}}~~ = ~~0\implies \cfrac{dx}{dt}y~~ + ~~x(-3)~~ = ~~0 \\\\\\ \cfrac{dx}{dt}y=3x\implies \left. \cfrac{dx}{dt}=\cfrac{3x}{y} \right|_{(\stackrel{x}{4},\stackrel{y}{3})}\implies \cfrac{3(4)}{3}\implies 4[/tex]

Answer:

A,C and E

Step-by-step explanation:

For every 3ml of vinegar we have 8ml of oil

This implies that

For case (A):

80ml of oil with 30ml of vinegar

dividing the amount of vinegar by 3 and multiplying the result by 8 gives 80 I.e

[tex]8ml (oil)\alpha 3ml(vinegar) \\ \frac{30ml(vinegar)}{2} = 10 \\ multiplying \: by \: 8 \: gives \: 80ml(oil)[/tex]

hence that's it

Answer:

16 percent of times are between 6 and 22

Answer: c I think. Sorry I'm wrong. Might be a.

Step-by-step explanation:

The measure of angle J is 19.8°, and the correct option is D.

The law of cosine or cosine rule in trigonometry is a relation between the side and the angles of a triangle. Suppose a triangle with sides a, b, c and with angles cosC.

The following formula is used to find the angle j is;

[tex]\rm j^2 = h^2 + i^2 -2hicosC[/tex]

Triangle HIJ has side lengths h=12, i = 17, j = 7.

Substitute all the values in the formula;

[tex]\rm j^2 = h^2 + i^2 -2hicosJ\\\\(7)^2=(12)^2+(17)^2-2 \times 12 \times 17 cosJ\\\\49=144+289-408cosJ\\\\144+289 -49 =408cosJ\\\\384 =408cosJ\\\\cosJ=\dfrac{384}{408}\\\\cosj = 0.94\\\\J =cos^{-1}(0.94)\\\\J=19.8[/tex]

Hence,  the measure of angle J is 19.8°, and the correct option is D.

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Answer:

Two shapes are similar when they have the same shape while their sizes may be the same or different

Therefore, two similar shapes are shapes that have a relationship such that the dimensions of one of the shapes can be obtained from the dimensions of the other shape by multiplying by a scale factor

All circles have the same shape and are defined by their center and radius

Given circle with center at 'x' and radius 'r' and circle with center 'y' and radius 's', then there exist a scale factor a = s/r such that we have;

r × a = s

Where a = s/r, we get;

r × s/r = s

We can therefore, obtain a circle with with the same size as the circle with center 'y' and radius 's' by multiplying the radius of the circle with center at 'x' and radius 'r' by a

Therefore the circle with center at 'x' and radius 'r' is similar to the circle with center 'y' and radius 's'Step-by-step explanation:

Answer:

21.4 I think, I might be wrong though

Answer:

12

Step-by-step explanation:

12=1

4=3

11=4

3=2

0=3

13=3

2=2

6=1

10=2

9=1

Answer:

I believe the answer is 200 feet squared

Step-by-step explanation:

Answer:

:)

Step-by-step explanation:

For simplicity I will substitue [tex]x[/tex] for β.

[tex]1-sin(2x)=(cosx-sinx)^2\\1-2sin(x)cos(x)=cos^2x-2sin(x)cos(x)+sin^2x\\1=cos^2(x)+sin^2(x)\\1=1[/tex]

In the first step I used the identity

[tex]sin(2x)=2sin(x)cos(x)[/tex]

And I factored out [tex](cosx-sinx)^2[/tex]

Then it's just simple algebra to cancel till the 3rd step where we used another identity derived from the Pythagorean Theorem.

[tex]cos^2(x)+sin^2(x)=1[/tex]

That's it!

Answer:

10:25

Step-by-step explanation:

What do we know so far:

  *we converted the number of laps into improper fractions

        [tex]2\frac{2}{3} = \frac{8}{3}[/tex]

We want to know the number of laps in an hour

  ⇒ so we must find the rate which ⇒ lap/hour

   [tex]lap/hour =\frac{8/3laps}{4/15hours} =\frac{8}{3}*\frac{15}{4} =\frac{8}{4} *\frac{15}{3} =2*5=10laps/hour[/tex]

So William can run ⇒ 10 laps in one hour

Hope that helps!

The number of shares could he buy is 63.19 and 126.38. Then the profit gained by Bob is $764.68.

Bob Orleans invested $3,000 and borrowed $3,000 to purchase shares in Verizon Communications.

At the time of his investment, Verizon was selling for $47 a share.

If Bob paid a $30 commission, then the number of shares could he buy if he used only his own money and did not use margin.

[tex]\rightarrow \dfrac{3000- 30}{47}\\\\\rightarrow \dfrac{2970}{47}\\\\\rightarrow 63.19[/tex]

If Bob paid a $60 commission, then the number of shares could he buy if he used his $3,000 and borrowed $3,000 on margin to buy Verizon stock will be

[tex]\rightarrow \dfrac{6000 - 60 }{47}\\\\\rightarrow \dfrac{5940}{47}\\\\\rightarrow 126.38[/tex]

Assume Bob did use margin and paid a $60 total commission to buy his Verizon stock. Also, assume he paid another $60 to sell his stock and sold the stock for $54 a share. Then the profit will be

[tex]\rightarrow (126.38 \times 54 - 60) - (6000)\\\\\rightarrow (6824.68 - 60) - 6000\\\\\rightarrow 6764.68 - 6000\\\\\rightarrow \$764.68[/tex]

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Answer:

13.8

Step-by-step explanation:

Let us use tan theta to find the value of x.

tan Θ = Opposite ÷ Adjacent

Given that,

Opposite ⇒ 12

Let us solve it now.

tan Θ = Opposite ÷ Adjacent

tan 41 = 12 ÷ x

0.8692 = 12 ÷ x

x = 12 ÷ 0.8692

x = 13.80

x ≈ 13.8

Answer:

1st Part: Infinitely many solutions

2nd Part: Exactly one solution

3rd Part: No Solutions

Step-by-step explanation:

First Part: 4(x - 1) = 4x - 4

Distribute. 4x - 4 = 4x - 4

Because the equations are the same, any value can be substituted for x and both the equations' values would still be equivalent.

2nd Part:

x + 4 = 4(x + 1)

x + 4 = 4x + 4

Minus 4 both sides

x = 4x

Only 0 can make this equation true, meaning it only has ONE solution.

Third Part:

4x + 1 = 4(x - 1)

Distribute.

4x + 1 = 4x - 1

Subtract 4x both sides

1 = -1

Obviously, 1 and -1 are not equivalent, meaning there are no value that can be substituted for x to make this equation true.

Answer:

24

Step-by-step explanation:

just MultiplMultiply 8 times 3 and 24

Answer:

81

Step-by-step explanation:

Average | x = 81

Count | n = 5

Sum | Sum = 405

Solution:

The average (mean) is equal to the sum of all the data values divided by the count of values in the data set.

Average = Sum / Count

= 405 / 5

= 81

The cost for the contractor to have all the dirt hauled away for a foundation of 12 feet long, 9 feet wide and 6 feet deep is $720

volume of a rectangular prism = lwh

where

Therefore,

l = 12 ft

w = 9 ft

h = 6 ft

volume of the foundation = 12 × 9 × 6

volume of the foundation = 648 ft³

Therefore, the contractor pays $180 per load for the trucks remove the dirt.

648 cubic feet = 24 cubic yard

6 cubic yards = 1 truck load

24 cubic yard =

cross multiply

number of truck load = 24 / 6 = 4 truck loads

Hence,

1 truck load = $180

4 truck load =?

cross multiply

cost = 4 × 180 = $720

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Answer:

answer your own

brainliest me now

Answer:

B. 8.35

Step-by-step explanation:

3.5 x 1.7 = 5.95

5.95 + 2.4 = 8.35

You multiply first because of PEMDAS.

P=parenthesis

E=exponents

M=multiply
D=divide
A=add
S=subtract

Answer:

When a figure is dilated by a scale factor of a/b, then the new perimeter is a/b of the original perimeter and the new area is a 2 b 2 of the original area. Therefore, if the hexagon is dilated by a scale factor of , then the new perimeter is of the original perimeter.

Answer:

(49,-56)

Step-by-step explanation:

I not sure but scale factor show the magnitude therefore you multiply by the scale factor to get the image.

Answer:

c : they will have both saved 97

Step-by-step explanation:

7*6 = 42 + 55(base) = 97

12*6 = 71 = 25(base) =97

Answer:

Dosage strength

250mg = 1.5mL

Answer:

B

Step-by-step explanation:

The -2 reflects across the x -axis

The + 1   shifts it up one unit