What is the slope of this

A student who is training for a distance race jogged for thirty minutes and covered a distance of 7.5 km. What is the average sp

Tju [1.3M]

Answer:

<h2>Average speed is 15km/h</h2>

Step-by-step explanation:

Step one:

given data:

total distance =7.5km

time taken= 30 min= 0.5 hours

we know that the average speed is the average distance divided by time taken

Step two:

mathematically expressed as

speed=distance/time

substituting we have

speed=7.5/0.5

speed=15km/hour

Hence the average speed is 15km/h

3 0

3 years ago

A population of mice is increasing exponentially. On Monday there were 120 most. One month later there were 132 most. Ready func

djyliett [7]

Answer:

$y=120 * 1.1^x$ --- function

The monthly rate is 10%

Step-by-step explanation:

Given

Let

$x \to months$

$y \to mice$

So, we have:

$(x_1,y_1) = (0,120)$ --- Monday

$(x_2,y_2) = (1,132)$ --- One month later

Required

The function

The function is represented as:

$y=ab^x$

In $(x_1,y_1) = (0,120)$ , we have:

$120 = a * b^0$

$120 = a * 1$

$120 = a$

$a=120$

In $(x_2,y_2) = (1,132)$ , we have:

$132 = a * b^1$

$132 = a * b$

Substitute: $a=120$

$132 = 120 * b$

Solve for b

$b = \frac{132}{120}$

$b = 1.1$

So, the function is:

$y=ab^x$

$y=120 * 1.1^x$

To calculate the monthly rate (r), we have:

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

Compare to: $y =ab^x$

$1 + r = b$

Make r the subject

$r = b-1$

Substitute $b = 1.1$

$r = 1.1-1$

$r = 0.1$

Express as percentage

$r = 0.1*100\%$

$r = 10\%$

5 0

3 years ago

One sphere has a radius of 3 inches and another sphere has a radius of 6 inches. The volume of the larger sphere is about how ma

NikAS [45]

Answer:

8

Step-by-step explanation:

First off, we need to recognize that the formula for the volume of a sphere is $\frac{4}{3} \pi r^3$ .

Then, we can plug in our r values one at a time.

The volume for the sphere with a 6-inch radius is about 904.779.

The volume for the sphere with a 3-inch radius is about 113.097.

To find how much greater the larger sphere is, we simply create a ratio between the two numbers: $\frac{904.779}{113.097}$

Do the division to find that the volume of the larger sphere is about 8 times the volume of the smaller sphere.

8 0

2 years ago

You have 24 months left until you graduate and you plan on buying yourself a new $20,000 car on graduation day. If you invest $3

shusha [124]

Answer: No, the money won't be enough to buy the car

Step-by-step explanation:

you plan on buying yourself a new $20,000 car on graduation day and graduation day is 24 months time. If you invest $300 a month for the next 24 months.

The principal amount, p = 300

He is earning 4% a month, it means that it was compounded once in four months. This also means that it was compounded quarterly. So

n = 4

The rate at which the principal was compounded is 4%. So

r = 4/100 = 0.04

It was compounded for a total of 24 months. This is equivalent to 2 years. So

n = 2

The formula for compound interest is

A = P(1+r/n)^nt

A = total amount that would be compounded at the end of n years.

A = 300(1 + (0.04/4)/4)^4×2

A = 300(1 + 0.01)^8

A = 300(1.01)^8

A = $324.857

The total amount at the end of 24 months is below the cost of the car which is $20000. So he won't have enough money to buy the car

3 0

3 years ago

The constraints of a problem are listed below. What are the vertices of the feasible region?

Luda [366]

Answer: option 1.

Explanation:

feasible region is that region which is formed by the lines of constraints.

feasible region is shaded in the attached graph

inequalities becomes equalities to draw the graph

and lines will head towards the origin if constraint satisfied by putting x= 0, y=0

and on the contrary lines will move away from origin when condition of constraint does not satisfied.

3 0

3 years ago

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What is the slope of this ​

What is the slope of this