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3 years ago

I need help with this...

Mathematics

1 answer:

solniwko [45]3 years ago

4 0

This can be represented as the equation
x/48 + 1/3 = 47/48

In order to solve this we need to siolate x ( get x in one side of the equation by itself and the rest in the other)

We can do that by subtracting 1/3 from both sides of the equation, by doing this we eliminate 1/3 from the left side of the equation and since we did it on both sides of the equations, it still is an equation ( one side equals the other )

x/48 + 1/3 - 1/3 = 47/48 - 1/3
1/3 - 1/3 cancel out, so we get
x/48 = 47/48 - 1/3
To subtract 47/48 - 1/3 ( and all other equations), the denominator of all fractions need to be the same. We can make the denominators equal by setting 1/3 as 16/48, which is the same thing as 1/3.

x/48 = 47/48 - 16/48
x/48 = 31/48

Now to fully isolate x, we can just multiply both sides by 48, so the x/48 turns into 48/48x or just x, and the 31/48 just turns into 31.
x = 31 x 48/48
x = 31

so 31/48 + 1/3 = 47/48
This was quite long but I hope it helps if you didnt understand how to solve equations
:)

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In a study of pleas and prison sentences, it is found that 6060% of the subjects studied were sent to prison. Among those sent

Dovator [93]

Answer:

a. 40 %

b. 34.3 % ( approx )

Step-by-step explanation:

Let S is the event of the subjects studied that were sent to prison,

S' is the event of the subjects studied that won't sent to prison,

G is the event of pleading guilty,

G' is the event of not pleading guilty,

According to the question,

P(S) = 60% = 0.6 ⇒ P(S') = 1 - P(S) = 1 - 0.6 = 0.4,

P(S∩G) = 46% of 60% = 0.46 × 0.60 = 0.276,

P(S'∩G) = 36% of 40% = 0.36 × 0.40 = 0.144,

P(G) = P(S∩G) + P(S'∩G) = 0.276 + 0.144 = 0.42

a. The of getting someone who was not sent to prison, P(S') = 0.4,

b. the probability that this person was not sent to prison when it is given that the subject entered a guilty plea,

$P(\frac{S'}{G})=\frac{P(S'\cap G)}{P(G)}=\frac{0.144}{0.42}\approx 0.343=34.3\%$

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4 years ago

47 = 77 - b; 20, 30, 40

stiv31 [10]

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3 years ago

Find the area of the given figure.<br> show your work please!

ICE Princess25 [194]

Answer:

30.3m^2

Step-by-step explanation:

I started off by finding the area of the semi circle. The formula πr^2 divided by 2. The radius of the circle is 2 because it is half of the diameter which is 4. So π(2)^2 divided by 2 is 6.3.

Next I broke apart the the shape into a rectangle and a triangle for simplicity sake. So doing this I had to know where to cut and if you look at the top of the figure it shows 2m for the length at the top. So I put a vertical line there. Thus changing the 10m on the bottom to a 8m section and a 2m section. So the rectangle's area will be the length times the height which is 2x4=8.

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3 years ago

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4 years ago

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David started across a lake 15 miles wide in his fishing boat at 10 miles per hour. He had to row the rest of the way at only 5

schepotkina [342]

Answer:

Total time = 2hrs

Step-by-step explanation:

Firstly, to outline some variables, with which we can construct some equations:

x = the time taken to cross the river at 10mph (in hrs)

y = the time taken to cross the river at 5mph (in hrs)

t = total time taken to cross the river (in hrs)

a = distance travelled at speed 10mph (in miles)

b = distance travelled at speed 5mph (in miles)

Then,

a + b = 15

t = x + y

y = ¹/₂(t) ∴ t = 2y, so,

x + y = 2y ∴ x = y

Secondly, we know speed = distance/time, so,

10 = a/x ⇒ x = a/10

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So,

a/10 = b/5 ∴ a = 2b

Thirdly, if a + b = 15, then,

2b + b = 15 ⇒ 3b = 15 ⇒ b = 5

[a = 2b ∴ a = 10]

Fourthly, x = b/5, so,

x = 5/5 = 1,

Since x = y, y = 1 and since t = 2y,

t = 2(1) = 2

The whole trip, therefore, took 2hrs.

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