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Ainat [17]
3 years ago
11

Five times the sum of one-half and a number

Mathematics
1 answer:
yawa3891 [41]3 years ago
7 0
5(\frac{1}{2} + x) would be your answer. The 5 and the parenthesis imply multiplication, and inside the parenthesis is one-half and a number being added.)
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We are throwing darts on a disk-shaped board of radius 5. We assume that the proposition of the dart is a uniformly chosen point
Vlad1618 [11]

Answer:

the probability that we hit the bullseye at least 100 times is 0.0113

Step-by-step explanation:

Given the data in the question;

Binomial distribution

We find the probability of hitting the dart on the disk

⇒ Area of small disk / Area of bigger disk

⇒ πR₁² / πR₂²

given that; disk-shaped board of radius R² = 5, disk-shaped bullseye with radius R₁ = 1

so we substitute

⇒ π(1)² / π(5)² = π/π25 = 1/25 = 0.04

Since we have to hit the disk 2000 times, we represent the number of times the smaller disk ( BULLSEYE ) will be hit by X.

so

X ~ Bin( 2000, 0.04 )

n = 2000

p = 0.04

np = 2000 × 0.04 = 80

Using central limit theorem;

X ~ N( np, np( 1 - p ) )

we substitute

X ~ N( 80, 80( 1 - 0.04 ) )

X ~ N( 80, 80( 0.96 ) )

X ~ N( 80, 76.8 )

So, the probability that we hit the bullseye at least 100 times, P( X ≥ 100 ) will be;

we covert to standard normal variable

⇒ P( X ≥  \frac{100-80}{\sqrt{76.8} } )

⇒ P( X ≥ 2.28217 )

From standard normal distribution table

P( X ≥ 2.28217 ) = 0.0113

Therefore, the probability that we hit the bullseye at least 100 times is 0.0113

3 0
3 years ago
Solve the equation. Check for extraneous solutions. 9|9 – 8x| = 2x + 3
Bad White [126]
The answers of this equation are 39/37 and 6/5. To get the answers, the equation of the problem becomes 9(9-8x)=2x+3 and 9(8x-9)=2x+3. Then next step is to simplify first equation 1,
<span>81=74x+3.
After, equation 2 is simplified
</span><span>70x=3+81</span>
7 0
3 years ago
The equation of a line is 5x − 3y = 6. Which is the y-intercept of the line?
oksian1 [2.3K]

Answer:

y - intercept. = 2.

Step-by-step explanation:

Given  : The equation of a line is 5x − 3y = 6.

To find : Which is the y-intercept of the line.

Solution : We have given  5x − 3y = 6.

Equation of line y = mx +b

Where , m = slope , y intercept = b

Now we convert the  5x − 3y = 6 in line form y = mx +b

5x − 3y = 6

On subtracting both sides by 5x

-3x = - 5x + 6

On dividing both sides by - 3.

x = \frac{5x}{3}+2.

We cans see m = \frac{5}{3} , y - intercept. = 2.

Therefore, y - intercept. = 2.

7 0
3 years ago
Can you please help me with number 4. 15 points and if you don't know the answer don't say anything please.
iVinArrow [24]
You know the product will be greater than the two factors because multiplication always makes the numbers greater. So 2x12 is 24 and that is greater than the two factors
6 0
3 years ago
Read 2 more answers
Simplify the following rational expression.
Jet001 [13]

9514 1404 393

Answer:

  (x-8)/(4x-4)  x ≠ 1 or 8

Step-by-step explanation:

Common factors can be cancelled, but cannot be ignored when it comes to determining where the function is undefined.

  \dfrac{x^2-16x+64}{4x^2-36x+32}=\dfrac{(x-8)^2}{4(x-8)(x-1)}=\boxed{\dfrac{x-8}{4x-4}}

The function is undefined for x=1 and x=8, the values of x that make the original denominator zero.

8 0
3 years ago
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