MATHEMATICS COLLEGE

There are 15 pieces of fruit in the fruit in a bowl and 6 of them are apples. What percentage of the pieces of the fruit in the bowl are apples0.06%

0.4

6%

40%

Answers

Answer 1
Answer: The answer is 0.4 because 6/15 is 2/5 which is 0.4 as a decimal

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T-3 ≥ 2;T=10




Please answer

Answers

Answer:

  True

Step-by-step explanation:

Substitute for T and evaluate:

  10 -3 ≥ 2

  7 ≥ 2 . . . . . . . true; T=10 is a member of the solution set

Solve the system of equation by elimination. x+2y= -7
-x-2y=8

A. (8,7)
B. No solution
C. (-7,8)
D. (-8,7)

If you can, please explain step by step:)

Answers

Answer: D

Step-by-step explanation:
D. (-8,7) just do it

What is the sum of 18 23/30+ 2/3

Answers

Answer:

See image

Step-by-step explanation:

The Pacific halibut fishery has been modeled by the differential equation dy dt = ky 1 − y K where y(t) is the biomass (the total mass of the members of the population) in kilograms at time t (measured in years), the carrying capacity is estimated to be K = 6×107 kg, and k = 0.78 per year. (a) If y(0) = 2×107 kg, find the biomass a year later. (Round your answer to two decimal places.) .52 Incorrect: Your answer is incorrect. ×107 kg (b) How long will it take for the biomass to reach 4×107? (Round your answer to two decimal places.) years

Answers

Answer:

a. The biomass weighs 2.30 * 10^7 kg after a year

b. It'll take 2.56 years to get to 4*10^7kg

Step-by-step explanation:

a.

k = 0.78,K = 6E7 kg

Given

dy/dt = ky(1- y/K)

Make ky dt the subject of formula

ky dt = dy/(1-y/K) --- make k dt the subject of formula

k dt = dy/(y(1-y/K))

k dt = K dy / y(K-y)

k dt = ((1/y) + (1/(K-y)))dy ---- integrate both sides

kt + c = ln(y/(K-y))

Ce^(kt) = y/(K-y)

Substitute the values of k and K

Ce^(0.78t) = y/(6*10^7 - y) ----- (1)

Given that y(0) = 2 * 10^7kg

(1) becomes

Ce^(0.78*0) = (2 * 10^7)/(6*10^7 - 2*10^7)

Ce° = (2*10^7)/(4*10^7

C = 2/7

Substitute 2/7 for C in (1)

2/7e^0.78t = y/(6*10^7 - y) ---(2)

We're to find the biomass a year later

So, t = 1

2/7e^0.78 = y/(6*10^7 - y)

0.62 = y/(6*10^7 - y)

y = 0.62(6*10^7 - y)

y = 0.62*6*10^7 - 0.62y

y + 0.62y = 0.62*6*10^7

1.62y = 0.62*6*10^7

1.62y = 3.72 * 10^7

y = 2.30 * 10^7kg.

Hence, the biomass weighs 2.30 * 10^7 kg after a year

b.

Here, we're to calculate the time it'll take the biomass to get to 4*10^7 kg

Substitute 4*10^7 for y in (2)

2/7e^0.78t = 4*10^7/(6*10^7 - 4*10^7)

2/7e^0.78t = 4*10^7/2*10^7

2/7e^0.78t = 2

e^0.78t = (2*7)/2

e^0.78t = 2

t = 2 * 1/0.78

t = 2.56 years

Hence, it'll take 2.56 years to get to 4*10^7kg

1-1 Relations and Functions Marcus drives 32 miles to work each day. He records the number of minutes it takes him to drive and writes his average speed as the input and the number of minutes as the output. He recorded his information in a table, like the one shown below. Speed (mph) Time (minutes) 60 32 45 43 55 35 50 38 62 31 If Marcus drives no faster than 65 miles per hour, what is the domain that includes all possible average speeds using interval notation? O A. [0, 65] B. [65,-) O C. (0, 65) D. (65,-)​

Answers

Answer:

A. [0, 65]

Step-by-step explanation:

Given that

Distance that Marcus drives every day = 32 miles.

The table having average speed as input and time taken as output is shown below in the table format:

\begin{center}\begin{tabular}{ c c}Speed(mph) & Time(minutes) \n 60 & 32 \n 45 & 43 \n 55 & 35 \n 50 & 38 \n 62 & 31 \n\end{tabular}\end{center}

To find:

The domain that includes all possible average speeds using interval notation = ?

Solution:

First of all, let us understand what is a domain of a function.

Domain of a function is set of valid input values that can be provided to the function so that it has a valid output.

If a function is written as:

y=f(x) then values of x are the input given to the function.

In the given question statement, we are given that maximum Average speed attained by Marcus is 65 miles per hour.

That means domain has a maximum value of 65.

Let us learn something about interval notation.

( or ) means the value is not inclusive.

[ or ] means the value is inclusive.

Here 65 will be inclusive.

On the left side of comma, lower value is written and on the right side of comma, larger value is written.

So, domain for the current situation will be:

[0, 65]

0 is taken as the minimum value of domain here, because average speed value can not be negative.

This interval will contain all the possible values of input (average speed) as shown in the above table of values.

-5+i/2i how do I break this down?​

Answers

Answer:

i2 = -1

Step-by-step explanation:

5i ⋅i⋅(−2i)= −

10 ⋅ i2 ⋅ i= − 10 ⋅ (−1) ⋅ i = 10i
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