All categories

2 years ago

GCSE MATHS PLEASE HELP

Mathematics

2 answers:

SpyIntel [72]2 years ago

3 0

Answer:

A) y = 16/(x^2), B) 4/5

Step-by-step explanation:

For A, we can plug in some of the table values to check it. I will try 2 and 3

2. 4 = 16 / (2^2)

16/4 = 4

3. 16/9 = 16 / (3^2)

16/9 = 16/9

B) We can just input y into the formula 25 = 16 / (x^2)

This leaves us with +-4/5

Arisa [49]2 years ago

3 0

Answer:

see explanation

Step-by-step explanation:

(a)

given y varies inversely as x² then the equation relating them is

y = $\frac{k}{x^2}$ ← k is the constant of variation

to find k substitute any ordered pair from the table into the equation

using (2, 4 ) , then

4 = $\frac{k}{2^2}$ = $\frac{k}{4}$ ( multiply both sides by 4 )

16 = k

y = $\frac{16}{x^2}$ ← equation of variation

(b)

when y = 25 , then

25 = $\frac{16}{x^2}$ ( multiply both sides by x² )

25x² = 16 ( divide both sides by 25 )

x² = $\frac{16}{25}$ ( take the square root of both sides )

x = ± $\sqrt{\frac{16}{25} }$ = ± $\frac{4}{5}$

the positive value of x is x = $\frac{4}{5}$

You might be interested in

A complex electronic system is built with a certain number of backup components in its subsystems. One subsystem has eight ident

Fudgin [204]

Answer:

a) 0.0486 = 4.86% probability that exactly two of the four components last longer than 1000 hours.

b) 0.9996 = 99.96% probability that the subsystem operates longer than 1000 hours.

Step-by-step explanation:

For each component, there are only two possible outcomes. Either they last more than 1,000 hours, or they do not. Components operate independently, which means that the binomial probability distribution is used 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.

One subsystem has eight identical components, each with a probability of 0.1 of failing in less than 1,000 hours.

So 1 - 0.1 = 0.9 probability of working for more, which means that $p = 0.9$

a. exactly two of the four components last longer than 1000 hours.

This is P(X = 2) when $n = 4$ . So

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

$P(X = 2) = C_{4,2}.(0.9)^{2}.(0.1)^{2} = 0.0486$

0.0486 = 4.86% probability that exactly two of the four components last longer than 1000 hours.

b. the subsystem operates longer than 1000 hours.

The subsystem has 8 components, which means that $n = 8$

It will operate if at least 4 components are working correctly, so we want:

$P(X \geq 4) = 1 - P(X < 4)$

In which

$P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)$

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

$P(X = 0) = C_{8,0}.(0.9)^{0}.(0.1)^{8} \approx 0$

$P(X = 1) = C_{8,1}.(0.9)^{1}.(0.1)^{7} \approx 0tex][tex]P(X = 2) = C_{8,2}.(0.9)^{2}.(0.1)^{6} \approx 0$

$P(X = 3) = C_{8,3}.(0.9)^{3}.(0.1)^{5} = 0.0004$

Then

$P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0 + 0 + 0 + 0.0004 = 0.0004$

$P(X \geq 4) = 1 - P(X < 4) = 1 - 0.0004 = 0.9996$

0.9996 = 99.96% probability that the subsystem operates longer than 1000 hours.

5 0

3 years ago

Please help me with this problem !!!

Alborosie

Answer:

all you have to do is select all numbers that are 0 or less

anything above 0 is wrong

Hope it Helps!

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

Evaluate 1/4c + 3d when c = 6 and d = 7

maxonik [38]

Answer:

22 1/2

Step-by-step explanation:

1/4×6=1 1/2

3×7=21

21+1 1/2=22 1/2

7 0

2 years ago

Read 2 more answers

Plz help 20 pts given for the question answered

xxMikexx [17]

Answer:

what question?

Step-by-step explanation:

7 0

3 years ago

Calculate the area of the shaded sector. 11.73 11.2 11.4 11.83

laiz [17]

The formula for the area of a circle is

A=πr²
plug in the data we know
A=π4²
A=16π

Since we only we need to find the area of the shaded section, we need to twerk this equation a bit. (remember that the shaded section is 84/360 of the original circle.)

A=84/360*16π
A=11.728
A=11.73 units²

answer: A=11.73 units²

4 0

3 years ago