The table shows the annual consumption of cheese per person in the United States for selected years in the 20th century. Let x = number of years since 1900, and y = pounds per person. What cubic model best fits this data? YearPounds Consumed. 19021.959. 19246.373. 19467.29. 198215.817. A. y = 0.00989x3 - 0.0000872x2 + 1.192x + 0.403. B. y = -0.0000872x3 + 0.00989x2 - 0.403x - 1.192. C. y = -0.0000872x3 - 0.00989x2 - 0.403x + 1.192. D. y = 0.0000872x3 - 0.00989x2 + 0.403x + 1.192

Answers

Answer 1

Answer: To see what model best represents this data we have to plug in the values for x and y:
Model D :
x = 2, y = 1.959
y = 0.0000872 · 2³ - 0.00989 · 2² + 0.403 · 2 + 1.192 = 1.968
.... ...
x = 82, y = 15.817
y = 0.000873 · 82³ - 0.00989 · 82² + 0.403 · 82 + 1.192 = 15.818
Answer:
D ) y = 0.0000872 x²- 0.00989 x² + 0.403 x + 1.192

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Find the exponential function that satisfies the given conditions: Initial value = 31, increasing at a rate of 10% per year f(t) = 10 ⋅ 1.1t
f(t) = 31 ⋅ 1.1t
f(t) = 31 ⋅ 0.1t
f(t) = 31 ⋅ 10t

Answers

Option 2: $f(t) = 31.(1.1)^t$ is the correct answer.

Step-by-step explanation:

Let t be the independent variable time and f(t) be the function that will be used to represent the exponential growth

The general form of an exponential function is given by:

$y = a(1+r)^t$

Here

a is the initial value of the function while r is the growth rate

and t is the number of years

Given

Initial value = 31

Growth rate = 10% per year

We have to convert the growth rate in decimal

So,

$r = (10)/(100) = 0.1$

Putting the values in the general form

$f(t) = 31 . (1+0.1)^t\nf(t) = 31 . (1.1)^t$

Hence,

Option 2: $f(t) = 31.(1.1)^t$ is the correct answer.

Keywords: Functions, exponential functions

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203% as a fraction ??

Answers

Answer:

.20301

Step-by-step explanation:

203/1000

HELP ME OUT WITH THIS PLEASE

Answers

Equivalent rational numbers are generated by multiplying both the numerator and denominator by the same nonzero integer. These were calculated for -6/4, -4/12, and -12/10. The given numbers were then graphed on a number line and ordered from least to greatest.

For the first part of the question, equivalent rational numbers can be generated by multiplying both numerator and denominator by the same nonzero integer.

Therefore, equivalent rational numbers for -6/4 are: -12/8, -9/6, and -3/2. For -4/12, we have: -8/24, -2/6, and -1/3. For -12/10, we have: -24/20, -6/5, and -3/2.5.

The second part involves graphing the given numbers on a number line and then ordering them. The order from least to greatest would be: -9/5, -3.2, -3, 13/10, 2.5, and 4.

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Marc is looking at the plans for his new garage. the length of the garage is 8 metres. the scale on the drawing is 1:50. what will the length of the garage be on the drawing?

Answers

The answer is 16 cm (or 0.16 m).

The scale is the ratio of the model to the real thing.
So, in the scale 1:50, the model is 1, while the real thing is 50.
Now, just make a proportion:
the model : the real thing = the model dimension : the real thing dimension
1 : 50 = x : 8m

From here:
x = 8m * 1 / 50 = 0.16 m = 0.16 * 100 cm = 16 cm.

The product of two integers is 50. one integer is twice the other. find the integers.

Answers

(1) -5*(-10)=50
(2) 5*10=50

use what they are telling.

a*b=50 (one integer times the other give you a product of 50. we're randomly calling these integers "a" and "b")

2a=b (one integer is twice the amount of the other. we're randomly selecting "b" to be twice the amount of "a")

plug in what we know

a*(2a)=50 (we replaced "b" with "2a" because we know from the info they gave us that b=2a)

now solve for "a"

a*2a=50
2a²=50
a²=50/2
a²=25
√a²=√25
a=5

which because 2a=b we know that b=10

Given A(2, 3), B(8, 7), C(6, 1), which coordinate will make line AB perpendicular to line CD?D(9, 3)
D(4, 4)
D(3, 3)
D(8, 4)

Answers

Answer:

The correct option is;

D(4, 4)

Step-by-step explanation:

The given coordinates of the points are, A(2, 3) B(8, 7), C(6, 1), therefore, the coordinates of the point D that will make CD perpendicular to AB will have a slope = -1/m, where, m = the slope of the line segment AB

The formula for finding the slope, m, of a segment, given the coordinates of two points on the straight line segment (x₁, y₁), (x₂, y₂)

$Slope, \, m =(y_(2)-y_(1))/(x_(2)-x_(1))$