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2 years ago

The lines graphed below show the amounts of water in two tanks as they

Mathematics

1 answer:

maria [59]2 years ago

6 0

Answer:

Tank B

Step-by-step explanation:

Proportional relationships are relationships between two variables with equivalent ratios. For a proportional relationship, one variable is always a constant value times the other. A line is a proportional relationship if it starts from the origin, but if it does not start from the origin, it is not proportional.

From the two tanks, we can see that tank A have a y intercept whereas tank B starts from the origin. Therefore tank B shows a proportional relationship.

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(1) Cos AcosecA=cot A

Mashutka [201]

Answer:

The Basic Identities are :

$cosec(A) = \frac{1}{ \sin(A) }$

$\tan(A) = \frac{ \sin(A) }{ \cos(A) }$

$\cot(A) = \frac{1}{ \tan(A) } = \frac{ \cos(A) }{ \sin(A) }$

So for this question :

$\cos(A)cosec(A) = \cot(A)$

$l.s.h = \cos(A) \times \frac{1}{ \sin(A) }$

$l.s.h = \frac{ \cos(A) }{ \sin(A) }$

$l.sh = \cot(A) \: (proven)$

7 0

3 years ago

Which of the following is a solution of y - x > -3? (6, 2) (2, 6) (2, -1)?

SVEN [57.7K]

Hello :
(2, 6) is a solution of y - x > -3 because : 6-2> -3 ..... 4 > -3

7 0

2 years ago

The quotient of 17 and k

myrzilka [38]

The answer is 17/k because there is no exact way to divide so 17/k is the quotient. :)

8 0

3 years ago

the following equation represents the total distance (d) that the Benson family has traveled from their home, after traveling 10

Pani-rosa [81]

Answer:

The distance the Bensons had traveled from their home $3\frac{1}{2}$ hours after picking up their grand parents 292.5 miles

Step-by-step explanation:

The given equation for the distance the Benson family traveled from their home can be presented as follows;

d = 55·t + 100

Where;

d = The total distance that the Benson family has traveled from their home after traveling 100 miles to pick up their grandparents

t = The time duration the Benson family have been traveled from their grandparents home on the way to their vacation

To find how far from their home the Bensons will be after 3 1/2 hours of driving with their grand parents, we substitute t with 3 1/2 hours or 3.5 hours as follows;

d = 55·t + 100

When t = $3\frac{1}{2}$ hours, we get;

$d = 55 \times 3\frac{1}{2} + 100 = 292.5 \ miles$

Therefore, the distance the Bensons had traveled from their home $3\frac{1}{2}$ hours after picking up their grand parents = 292.5 miles.

7 0

3 years ago

Richard has just been given an l0-question multiple-choice quiz in his history class. Each question has five answers, of which o

myrzilka [38]

Answer:

a) 0.0000001024 probability that he will answer all questions correctly.

b) 0.1074 = 10.74% probability that he will answer all questions incorrectly

c) 0.8926 = 89.26% probability that he will answer at least one of the questions correctly.

d) 0.0328 = 3.28% probability that Richard will answer at least half the questions correctly

Step-by-step explanation:

For each question, there are only two possible outcomes. Either he answers it correctly, or he does not. The probability of answering a question correctly is independent of any other question. This means that we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

Each question has five answers, of which only one is correct

This means that the probability of correctly answering a question guessing is $p = \frac{1}{5} = 0.2$

10 questions.

This means that $n = 10$

A) What is the probability that he will answer all questions correctly?

This is $P(X = 10)$

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 10) = C_{10,10}.(0.2)^{10}.(0.8)^{0} = 0.0000001024$

0.0000001024 probability that he will answer all questions correctly.

B) What is the probability that he will answer all questions incorrectly?

None correctly, so $P(X = 0)$

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{10,0}.(0.2)^{0}.(0.8)^{10} = 0.1074$

0.1074 = 10.74% probability that he will answer all questions incorrectly

C) What is the probability that he will answer at least one of the questions correctly?

This is

$P(X \geq 1) = 1 - P(X = 0)$

Since $P(X = 0) = 0.1074$ , from item b.

$P(X \geq 1) = 1 - 0.1074 = 0.8926$

0.8926 = 89.26% probability that he will answer at least one of the questions correctly.

D) What is the probability that Richard will answer at least half the questions correctly?

This is

$P(X \geq 5) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)$

In which

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 5) = C_{10,5}.(0.2)^{5}.(0.8)^{5} = 0.0264$

$P(X = 6) = C_{10,6}.(0.2)^{6}.(0.8)^{4} = 0.0055$

$P(X = 7) = C_{10,7}.(0.2)^{7}.(0.8)^{3} = 0.0008$

$P(X = 8) = C_{10,8}.(0.2)^{8}.(0.8)^{2} = 0.0001$

$P(X = 9) = C_{10,9}.(0.2)^{9}.(0.8)^{1} \approx 0$

$P(X = 10) = C_{10,10}.(0.2)^{10}.(0.8)^{0} \approx 0$

$P(X \geq 5) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) = 0.0264 + 0.0055 + 0.0008 + 0.0001 + 0 + 0 = 0.0328$

0.0328 = 3.28% probability that Richard will answer at least half the questions correctly

8 0

3 years ago