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sergiy2304 [10]
3 years ago
12

there are 400 pages-to be read from a book.yesterday you read 1/4 of the pages. today you read 2/3 of the remains pages from the

book.how many pages are left in the book
Mathematics
1 answer:
Black_prince [1.1K]3 years ago
6 0

Answer:

100 pages

Step-by-step explanation:

Yesterday, there were 400 pages left unread so you read 1/4 * 400 = 100 pages yesterday. Today, there are 400 - 100 = 300 pages left unread so today, you read 2/3 * 300 = 200 pages. This means that there are 300 - 200 =   100 pages left in the book.

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The fox population in a certain region has a continuous growth rate of 5% per year. It is estimated that the population in the y
kvasek [131]

Answer:

P(t) = A * (1 + r)^t ;

14,922 ;

Year 2013

Step-by-step explanation:

Given the following :

Continuous growth rate(r) = 5% = 0.05

Population in year 2000 = Initial population (A) = 10,100

Time(t) = period (years since year 2000)

A)

Find a function that models the population,P(t) , after (t) years since year 2000 (i.e. t= 0 for the year 2000).

P(t) = A * (1 + r)^t

Trying out our function for t = year 2000, t =0

P(0) = 10,100 * (1 + 0.05)^0

P(0) = 10,100 * 1.05^0 = 10,100

B.)

Use your function from part (a) to estimate the fox population in the year 2008.

Year 2008, t = 8

P(8) = 10,100 * (1 + 0.05)^8

P(8) = 10,100 * 1. 05^8

P(8) = 10,100 * 1.4774554437890625

= 14922.29

= 14,922

c) Use your function to estimate the year when the fox population will reach over 18,400 foxes. Round t to the nearest whole year, then state the year.

P(t) = A * (1 + r)^t

18400 = 10,100 * (1.05)^t

18400/10100 = 1.05^t

1.8217821 = 1.05^t

1.05^t = 1.8217821

In(1.05^t) = ln(1.8217821)

0.0487901 * t = 0.5998151

t = 0.5998151 / 0.0487901

t = 12.293787

Therefore eit will take 13 years

2000 + 13 = 2013

4 0
3 years ago
CHOOSE TO ANSWER EITHER QUESTION:
Ugo [173]

Answer:

First one: C. Second One:C.

Step-by-step explanation:

Kate purchased a car for $23,000. It will depreciate by a rate of 12% a year. What is the value of the car in 4 years?

a) $13,935.76

b) $12,874.57

c) $13,792.99

To solve this this is an exponential function. The price started at $23,000 and depreciates at 12% so the equation is f(x) = (23,0000)(1-0.12)^4. When calculated results with 13792.99328 which is C.

A rare coin is currently worth $450. The value of the coin increases 4% each year. Determine the value of the coin after 7 years.

a) $613.98

b) $546.78

c) $592.17

To solve this this is also an exponential function. The price started at $450 and  the coin increases 4% each year so the equation is f(x) = (450)(1+0.04)^7. When calculated results with 592.169300656 which is c.

4 0
2 years ago
A gardener is planting two types of trees:
ICE Princess25 [194]

Answer:

After 1 year, both the tress will be of the same height.

Step-by-step explanation:

Let us assume in x years, both trees  have same height.

Type A  is 7 feet tall and grows at a rate of 8 inches per year.

⇒The growth of tree A in x years = x times  ( Height growth each year)

                                                        = 8 (x)  = 8 x

⇒Actual height of tree A in x years  = Initial Height + Growth in x years

                                                             = 7 + 8 x

or, the height of tree A after  x years  = 7 + 8x

Type B is 9 feet tall and grows at a rate of 6 inches per year.

⇒The growth of tree B in x years = x times  ( Height growth each year)

                                                        = 6 (x)  = 6 x

⇒Actual height of tree B in x years  = Initial Height + Growth in x years

                                                             = 9 + 6 x

or, the height of tree B after  x years  = 9 + 6x

According to the question:

After x years, Height of tree A  =Height of tree B

⇒7 + 8x   = 9 + 6x

or, 8x - 6x = 9 - 7

or, 2 x  = 2

or, x  =  2/2  = 1    ⇒ x  = 1

Hence, after 1 year, both the tress will be of the same height.

5 0
3 years ago
What is the answer??
Dmitriy789 [7]

Answer:

the answer would be the second one

Step-by-step explanation:

a congruency symbol consists of a = and a ~

8 0
2 years ago
After the rocket has traveled a total distance of 300 feet, what is its vertical height above sea level? Round the distance to t
il63 [147K]
I added a screenshot with the complete question along with its diagram.

Answer:
vertical height is approximately 260 ft

Explanation:
We can note that the sea level, vertical height and the distance traveled by the rocket all form a right angled triangle.
This means that the special trig functions can be applied.
These functions are as follows:
sin θ = opposite / hypotenuse
cos θ = adjacent / hypotenuse
tan θ = opposite / adjacent

From the given we have:
θ = 60°
opposite is the vertical height that we want to find
hypotenuse = 300 ft

Applying the sin function, we can get the vertical height as follows:
sin (60) = opposite / 300
opposite = 300 * sin (60)
opposite = 259.807 which is approximately 260 ft

Hope this helps :)

3 0
3 years ago
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