- Trace has 453 trading cards,

Mrs. Adesso wants to take her class on a trip to either the science center or natural history museum. The science center charges

BartSMP [9]

Answer:

25

Step-by-step explanation:

When we write expressions for the total cost of each field visit and set them equal, we find the solution to be the ratio of the difference in fixed cost to the difference in variable cost.

y = 75 +7x . . . . . cost for x students to visit the science center

y = 50 +8x . . . . cost for x students to visit the natural history museum

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Subtracting the first equation from the second, we get ...

0 = -25 +x

25 = x . . . . . add 25; the number of students such that costs are equal

The cost will be the same either place for 25 students.

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<em>Additional comment</em>

Here, the fixed cost difference is 75-50=25, and the variable cost difference is 8-7=1. The ratio of these costs is ...

$25/($1 /student) = 25 students.

This relationship only holds when the higher fixed cost is associated with the lower variable cost. Charges are such that one place caters to larger numbers of students (science center), and one prefers fewer students (natural history museum).

4 0

2 years ago

More people leave Anytown, AL each year than move into it. The population over the past 20 years is shown in the table. Use tech

Phoenix [80]

The equation that models the exponential decline is y = 46348587109809610(0.9861)ˣ if the population over the past 20 years is provided.

A mathematical notion called the line of the best fit connects points spread throughout a graph. It's a type of linear regression that uses scatter data to figure out the best way to define the dots' relationship.

Let's suppose the equation that models the exponential decline is:

$\rm y = a(b^x)$

From the data given, we can calculate the value of a and b:

a = 46348587109809610

b = 0.9861

y = 46348587109809610(0.9861)ˣ

Thus, the equation that models the exponential decline is y = 46348587109809610(0.9861)ˣ if the population over the past 20 years is provided.

Learn more about the line of best fit here:

brainly.com/question/14279419

#SPJ1

6 0

2 years ago

Find the x- and y-intercepts of the graph of the linear equation −x+8y=4

Andreyy89

First set the equation equal to y by adding x to each side, then divide everything by 8. then set x to zero and solve to find the y - intercept of 1/2 which is just 4/8 reduced. you get this answer because x/8 becoming 0/8 is just 0 leaving you with only 1/2. then reset the equation with x and set y to zero and solve for x to get the x- intercept of -4. you get this by subtracting 1/2 from both sides leaving you -1/2=x/8 and multiply by 8 to get -4=x

4 0

3 years ago

Erica is a sheep farmer. She is having a problem with wolves attacking the flock. She starts with an initial 200 sheep and notic

Free_Kalibri [48]

The equation for the situation is $y=200(\frac{2}{3})^{x}$

It will take around 9 years for her to have around 5 sheep

Step-by-step explanation:

The exponential decay growth/decay equation is $y=a(b)^{x}$ , where

a is the initial value
b is the growth/decay factor
If b > 1, then it is a growth factor
If 0 < b < 1, then it is a decay factor

Erica is a sheep farmer. She is having a problem with wolves attacking the flock. She starts with an initial 200 sheep and notices that the population is two-thirds of the previous year

∵ The population is decreased

∴ The equation is decay

∵ The population is two-thirds of the previous year

∴ The decay factor is $\frac{2}{3}$