All categories

3 years ago

Help please!

Mathematics

2 answers:

oksian1 [2.3K]3 years ago

8 0

Answer:

y= -4x^2 + 15x - 14

Step-by-step explanation:

Anna71 [15]3 years ago

4 0

Answer:

y= -4x^2 + 15x - 14

Step-by-step explanation:

A parabola is always in the form y = ax^2 + bx + c.

Substitute each point to produce different equations:

-14 = 0a + 0b + c = c

so c = -14

-3 = a1^2 + b1 + c = a + b - 14

so a + b = 11

0 = a2^2 + b2 + c = 4a + 2b -14 = 0

so 4a + 2b = 14

if we double a + b = 11 we get 2a + 2b = 22

Subtract this from 4a + 2b = 14 and we get 2a = -8 so a= -4 and b = 11 - a = 15

We don't need to use the (3,5) points as we have all the information we need.

You might be interested in

Ashlyn is selling boxes of cookies for a fundraiser. If she raised $26 selling eight boxes, how much will she raise if she sells

allochka39001 [22]

She raises thirteen dollars

6 0

3 years ago

Read 2 more answers

A shark is swimming 28 ft below sea level. If the angle of depression from a boat on the water to the shark is 19 degrees, what

Orlov [11]

Answer:

81,3 ft to the nearest tenth.

Step-by-step explanation:

Tan 19 = 28 / h where h = the horizontal distance.

h = 28 / tan 19

h = 81.3 ft.

3 0

3 years ago

Seventy-two percent of the light aircraft that disappear while in flight in a certain country are subsequently discovered. Of th

Anton [14]

Answer:

a) 0.105 = 10.5% probability that it will not be discovered if it has an emergency locator.

b) 0.522 = 52.2% probability that it will be discovered if it does not have an emergency locator.

c) 0.064 = 6.4% probability that 7 of them are discovered.

Step-by-step explanation:

For itens a and b, we use conditional probability.

For item c, we use the binomial distribution along with the conditional probability.

Conditional Probability

We use the conditional probability formula to solve this question. It is

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

In which

P(B|A) is the probability of event B happening, given that A happened.

$P(A \cap B)$ is the probability of both A and B happening.

P(A) is the probability of A happening.

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.

a) If it has an emergency locator, what is the probability that it will not be discovered?

Event A: Has an emergency locator

Event B: Not located.

Probability of having an emergency locator:

66% of 72%(Are discovered).

20% of 100 - 72 = 28%(not discovered). So

$P(A) = 0.66*0.72 + 0.2*0.28 = 0.5312$

Probability of having an emergency locator and not being discovered:

20% of 28%. So

$P(A cap B) = 0.2*0.28 = 0.056$

Probability:

$P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.056}{0.5312} = 0.105$

0.105 = 10.5% probability that it will not be discovered if it has an emergency locator.

b) If it does not have an emergency locator, what is the probability that it will be discovered?

Probability of not having an emergency locator:

0.5312 of having. So

$P(A) = 1 - 0.5312 = 0.4688$

Probability of not having an emergency locator and being discovered:

34% of 72%. So

$P(A \cap B) = 0.34*0.72 = 0.2448$

Probability:

$P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.2448}{0.4688} = 0.522$

0.522 = 52.2% probability that it will be discovered if it does not have an emergency locator.

c) If we consider 10 light aircraft that disappeared in flight with an emergency recorder, what is the probability that 7 of them are discovered?

p is the probability of being discovered with the emergency recorder:

0.5312 probability of having the emergency recorder.

Probability of having the emergency recorder and being located:

66% of 72%. So

$P(A \cap B) = 0.66*0.72 = 0.4752$

Probability of being discovered, given that it has the emergency recorder:

$p = P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.4752}{0.5312} = 0.8946$

This question asks for P(X = 7) when $n = 10$ . So

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

$P(X = 7) = C_{10,7}.(0.8946)^{7}.(0.1054)^{3} = 0.064$

0.064 = 6.4% probability that 7 of them are discovered.

8 0

3 years ago

Evaluate 5x – 2y + (7x – y) for x = 7 and y = –2

Lynna [10]

Answer:

Step-by-step explanation:

5x – 2y + (7x – y)

Combine like terms

12x -3y

Let x = 7 and y = -2

12(7) -3(-2)

84 +6

6 0

3 years ago

Read 2 more answers

What is the surface area of the prism in square inches?

Kay [80]

<u>Given</u>:

Given that the triangular prism with height 10 inches.

The side lengths of the base of the triangle are 12 inches, 13 inches and 5 inches.

We need to determine the surface area of the prism.

<u>Surface area of the prism:</u>

The surface area of the prism can be determined using the formula,

$SA=bh+(s_1+s_2+s_3)H$

where b is the base and h is the height of the triangle.

s₁, s₂, s₃ are the side lengths of the triangle and

H is the height of the prism.

Substituting b = 12, h = 5, s₁ = 12, s₂ = 5, s₃ = 13 and H = 10 in the above formula, we get;

$SA=(12)(5)+(12+5+13)(10)$

$SA=60+(30)(10)$

$SA=60+300$

$SA=360 \ in^2$

Thus, the surface area of the triangular prism is 360 square inches.

Hence, Option b is the correct answer.

8 0

3 years ago