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sp2606 [1]
3 years ago
8

In this figure of a protractor , which angle is a right angle?

Mathematics
1 answer:
blsea [12.9K]3 years ago
6 0
CQE is a right angle. Hope this helps!!!
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The Pacific halibut fishery has been modeled by the differential equation dy dt = ky 1 − y K where y(t) is the biomass (the tota
Dafna1 [17]

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

8 0
3 years ago
Write and solve a proportion to answer the question. 30% of what number is 9? ​
Vikentia [17]

Answer:

The answer would be 30.

Step-by-step explanation:

Calculating 9×100÷30 equals 30 and that would be your answer.

8 0
2 years ago
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A​ true/false test has 8080 questions. Suppose a passing grade is 5252 or more correct answers. Test the claim that a student kn
Makovka662 [10]
<h2>Answer with explanation:</h2>

Let p be the proportion of the correct answers.

As per given , we have

H_0: p=0.50

H_a: p>0.50 , since the alternative hypothesis is right tailed , so the test is a one -tailed test.

If the student gets 52 answers correct out of 80.

i.e. the proportion of correct answers : \dfrac{52}{80}=0.65

Test statistic : z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}

z=\dfrac{0.65-0.50}{\sqrt{\dfrac{0.50(0.50)}{80}}}\approx2.68

P-value : P(z>2.68)=0.0037   [ by using p-value table for z (right-tailed)]

Since the p-value(0.0037) is less than the significance level (0.05), so we reject the null hypothesis.

Results : We have enough evidence to support the claim that a student knows more than half of the answers and is not just guessing.

8 0
3 years ago
Please answer it’s important thanks
Veseljchak [2.6K]

Answer:

3.14

Step-by-step explanation:

Hello! To get the formula we must first use the formula!

The formula is pi * r^2. In this case since r = 1, we know 1 * 1 = 1.

And since we are going to use 3.14 for pi, we can do 1 * 3.14 which is 3.14.

Hoped this helped ya :)

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3 years ago
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Gloria enjoys playing Skee ball — an arcade game where players toss a ball so it rolls up a ramp and falls into one of several s
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Answer:27

Step-by-step explanation:

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