You have 12 of chocolate to make holiday candy . The first batch used 1/3 of the chocolate. How much chocolate was used ?

A pink crayon is made with 12 mL of red wax for every 5 mL of white wax.

Answer:c

Step-by-step explanation:

7 0

3 years ago

In Illinois, 10 % of all drivers arrested for DUI (Driving Under the Influence) are repeat offenders; that is, they have been ar

docker41 [41]

Answer:

a) P(X=5) = 0.065

b) P(X≥1) = 0.928

c) The mean number of repeat offenders is 3.

d) The standard deviation of the number of repeat offenders is 2.

Step-by-step explanation:

n = 25

p = 10% = 0.10

q = 1-p

= 1-0.1

q=0.9

a) Find P(X =5)

Using the binomial distribution formula:

P(X = x) = ⁿCˣ pˣ qⁿ⁻ˣ

where p = probability of success

q = probability of failure

n = total number of trials

x = no. of successful trials

P(X=5) = ²⁵C₅ (0.1)⁵ (0.9)²⁵⁻⁵

= 0.0645 ≅ 0.065

P(X=5) = 0.065

b) We need to find the probability that at least one person is a repeat offender which means at most there can be 25 repeat offenders hence, we need to compute the probability for all values ranging from 1 to 25. The easy way to solve this problem is to find out the probability of less than one repeat offender and then subtract the value from the total probability (i.e. 1).

P(X≥1) = 1 - P(X<1)

= 1 - P(X =0)

= 1 - ²⁵C₀ (0.1)⁰ (0.9)²⁵⁻⁰

= 1 - 0.072

P(X≥1) = 0.928

c) The mean of the binomial distribution is:

μ = np

So, the mean number of repeat offenders can be computed as:

μ = (25)(0.10)

μ = 2.5 ≅ 3

The mean number of repeat offenders is 3.

d) The standard deviation of the binomial distribution is:

σ = √npq

So, the standard deviation of the number of repeat offenders can be computed as:

σ = √(25)(0.1)(0.9)

= √2.25

σ = 1.5 ≅ 2

The standard deviation of the number of repeat offenders is 2.

7 0

2 years ago

I need help fast please!!

kaheart [24]

Solution set is: ( $7,\frac{13}{3}$ )

Option B is correct

Step-by-step explanation:

We need to find the solution to system of equations

$y=\frac{1}{3}x+2\\y=\frac{4}{3}x-5$

Let:

$y=\frac{1}{3}x+2\,\,\,eq(1)\\y=\frac{4}{3}x-5\,\,\,eq(2)$

Putting value of y from eq(2) into eq(1)

$\frac{4}{3}x-5=\frac{1}{3}x+2\\Combining\,\,like\,\,terms:\\\frac{4}{3}x-\frac{1}{3}x=2+5\\Taking\,\,LCM\\\frac{4x-1x}{3}=7\\\frac{3x}{3}=7\\x=7$

So, value of x=7

Putting value of x into equation 1 to find the value of y:

$y=\frac{1}{3}x+2\\y=\frac{1}{3}(7)+2\\y=\frac{7}{3}+2\\Taking\,\,LCM\\y=\frac{7+2*3}{3}\\y=\frac{7+6}{3}\\y=\frac{13}{3}$

So, value of y = $\frac{13}{3}$

Solution set is: ( $7,\frac{13}{3}$ )

Option B is correct

Keywords: System of equations

Learn more about system of equations at:

#learnwithBrainly

3 0

3 years ago

There were 442 students at Deerlake Middle School who voted on a theme for the spring carnival. Those who voted represent 76% of

never [62]

Answer:

Option C is correct.

Step-by-step explanation:

Number of students of Deerlake middle school that voted = 442

Percentage of student that voted = 76%

Let x be the total number of student.

According to the Question,

$\frac{76}{100}\times x=442$

$x=442\times\frac{100}{76}$

$x=582$

Therefore, Option C is correct.

7 0

3 years ago

6x+12y+5+2y+8 what’s the coefficient of y and what’s the constant

Rudik [331]

The coefficient of y is 14 and the constant is 13.

You can find this by combining like terms first.

6x + 12y + 5 + 2y + 8

6x + 14y + 5 + 8

6x + 14y + 13

Now the coefficient is the number next to y. The constant is the number on its own.

4 0

2 years ago