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3 years ago

Tell whether each table represents a linear relationship...

Mathematics

1 answer:

grigory [225]3 years ago

8 0

Yes it is you are constantly
adding 2 (x) for every 1 (y)

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The table displays data for Nutrition Guides of a single serving of particular foods. Assuming there exists a correlation betwee

xz_007 [3.2K]

Answer:

The linear regression model that will determine approximate Fat Grams (y) as a function of Calories (x) is given by

y = 0.054 x - 2.105

Hence the correct option is B.)

Step-by-step explanation:

Step 1: Find X⋅Y and as it was done in the table below.

Step 2: Find the sum of every column:

ΣX = 1560, ΣY = 67, ΣX.Y = 14860 , ∑( $\textbf{X}^{2}$ ) = 337600

Step 3: Use the following equations to find a and b:

a = = -2.105

b = $\frac{n.\sum{XY} - \sum{X}.\sum{Y}}{n.\sum{(X^{2})}- (\sum{X})^{2} }$ = 0.054

Step 4: Substitute a and b in regression equation formula

y = a + b⋅x= −2.105 + 0.054⋅x

The linear regression model that will determine approximate Fat Grams (y) as a function of Calories (x) is given by

y = 0.054 x - 2.105

Hence the correct option is B.)

7 0

3 years ago

The length of an aquarium, which has the form of a rectangular solid, is equal to 5 decimeters, and the width is 4/5 the length.

Oksanka [162]

Answer:

Given the statement: The length of an aquarium, which has the form of a rectangular solid, is equal to 5 decimeters, and the width is 4/5 the length.

Since, aquarium is in the form of a rectangular solid.

Length of an aquarium(l) = 5 dm

Width of an aquarium(w)= $\frac{4}{5}\times 5 = 4 dm$

It is also given that when you put 40 liters of water into the aquarium, it was full to $\frac{2}{3}$ its volume.

Volume of Rectangular solid(V) is given by;

$V = l \times b \times h$ where l is the length , w is the width and h is the height of the rectangle respectively.

Volume(V) of an aquarium = $\frac{3}{2} \times 40 = 60$ liter.

Using volume formula to calculate the height(h);

$60 = 5 \times 4 \times h$

$60 = 20h$

Divide both sides by 20 we get;

h = 3 dm [ 1 liter = 1 cubic dm]

We have to find the what part of length makes up the height of the aquarium.

$h = \frac{3}{5} l$ where l = 5 dm

therefore, $\frac{3}{5}$ part of the length makes up the height of the aquarium.

8 0

4 years ago

If f(x) is 4x-3 what is (f^-1of) (10)

muminat

$f(x)=4x-3\\
y=4x-3\\
4x=y+3\\
x=\frac{1}{4}y+\frac{3}{4}\\
f^{-1}(x)=\frac{1}{4}x+\frac{3}{4}\\\\
f^{-1} \circ f=\frac{1}{4}(4x-3)+\frac{3}{4}\\
f^{-1} \circ f=\frac{4x}{4}-\frac{3}{4}+\frac{3}{4}\\
f^{-1} \circ f=x$