A box contains 5 orange pencils, 8 yellow pencils, and 4 green pencils.
Two pencils are selected, one at a time, with replacement.
Find the probability that the first pencil is green and the second pencil is yellow.
Express your answer as a decimal, rounded to the nearest hundredth.

Answer:

See Explanation

Step-by-step explanation:

Required

Proportion problems

An example is:

y is directly proportional to x such that: y=4 when x = 2;

Derive the equation

For direct proportions, we have:

[tex]y\ \alpha\ x[/tex]

This gives:

[tex]y = kx[/tex]

Make k the subject

[tex]k = y/x[/tex]

So:

[tex]k = 4/2 =2[/tex]

So, the equation is:

[tex]y = kx[/tex]

[tex]y = 2x[/tex]

Assume the above question is for inverse proportion

The variation will be:

[tex]y\ \alpha\ \frac{1}{x}[/tex]

This gives:

[tex]y\ = \frac{k}{x}[/tex]

Make k the subject

[tex]k =x*y[/tex]

[tex]k =2* 4 = 8[/tex]

So, the equation is:

[tex]y\ = \frac{k}{x}[/tex]

[tex]y = \frac{8}{x}[/tex]

Answer:

Step-by-step explanation:

Given system:

Substitute x into the second equation:

Find x:

Answer:

x = 2 and y = -2

Step-by-step explanation:

Given system :-

y + 4 = x

10x + 2y = 16

Solve the system by substitution:-

Let,

y + 4 = x ...(1)

10x + 2y = 16 ...(2)

Solve for y;

Substitute y + 4 as x in the eq.(2)

10( y + 4 ) + 2y = 16

10y + 40 + 2y = 16

12y + 40 = 16

12y = 16 - 40

12y = -24

12y / 12 = -24/12

Hence, y = -2

Solve for x.

-2 + 4 = x

Hence, 2 = x

Answer:

It will take 15 days for the same crew to clear the entire plot of 2 1/2 acres.

Step-by-step explanation:

Given that a crew clears brush from 1/3 acre of land in 2 days, to determine how long will it take the same crew to clear the entire plot of 2 1/2 acres, the following calculation must be performed:

1/3 = 0.333

1/2 = 0.5

0.333 = 2

2.5 = X

2.5 x 2 / 0.333 = X

15 = X

Therefore, it will take 15 days for the same crew to clear the entire plot of 2 1/2 acres.

Answer:

happy person in the village

Answer:

B. There is not sufficient evidence to support the claim that the proportion of male golfers is less than 0.6.

Step-by-step explanation:

The proportion of male golfers is less than 0.6.

At the null hypothesis, we test if the proportion is of at least 0.6, that is:

[tex]H_0: p \geq 0.6[/tex]

At the alternative hypothesis, we test if the proportion is of less than 0.6, that is:

[tex]H_1: p < 0.6[/tex]

Fail to reject the null hypothesis.

This means that there is not sufficient evidence to conclude that the proportion is less than 0.6, and thus the correct answer is given by option B.

Answer

13

Step-by-step explanation:

We are essentially being asked to find f(10), so let's evaluate this function at 10 by plugging this in for x.

f(10)=10/2+8=5+8=13

Answer:

f(x) = 40

Step-by-step explanation:

f(x) = x / 2 * 8

x = 10

f(x) = (10 / 2) * 8

     = 5 * 8

     = 40

Answer:

You can go ahead with option D

Step-by-step explanation:

Answer:

16

Step-by-step explanation:

[tex]x^2 - 2xy + y^2 = (x -y)^2 \\[/tex]

                   [tex]= 4^2 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [ \ given : x - y= 4 \ ]\\\\= 16[/tex]

The value of x^2-2xy+y^2

will be 16 .

Explanation is in the attachment .

hope it is helpful to you ☺️

9514 1404 393

Answer:

  23.4 ft³

Step-by-step explanation:

In terms of the perimeter of the square base, the volume of a pyramid can be found using the formula ...

  V = (1/48)P²h . . . . . where P is the base perimeter and h is the height

  V = (1/48)(10.7 ft)²(9.8 ft) ≈ 23.4 ft³

_____

Additional comment

The relevant formulas usually used are ...

  P = 4s . . . . perimeter of a square with side length s

  A = s² . . . . area of a square with side length s

  V = (1/3)Bh . . . . . volume of a pyramid with base area B and height h

Solving the perimeter equation for s, and using that result in the other formulas, we get ...

  s = P/4

  B = (P/4)² = P²/16

  V = 1/3(P²/16)h = (1/48)P²h . . . . the formula used above

Using this result saves the effort of computing the intermediate values of side length and base area.

Answer:

x<-12

Step-by-step explanation: hope this helps!

The perimeter of the whole garden would be 66m.

Hope this helps! :)

Answer:

[tex]P(X = 0) = 0.03125[/tex]

[tex]P(X = 1) = 0.15625[/tex]

[tex]P(X = 2) = 0.3125[/tex]

[tex]P(X = 3) = 0.3125[/tex]

[tex]P(X = 4) = 0.15625[/tex]

[tex]P(X = 5) = 0.03125[/tex]

Step-by-step explanation:

For each toss, there are only two possible outcomes. Either it is tails, or it is not. The probability of a toss resulting in tails is independent of any other toss, 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.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

Fair coin:

Equally as likely to be heads or tails, so [tex]p = 0.5[/tex]

5 tosses:

This means that [tex]n = 5[/tex]

Probability distribution:

Probability of each outcome, so:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{5,0}.(0.5)^{0}.(0.5)^{5} = 0.03125[/tex]

[tex]P(X = 1) = C_{5,1}.(0.5)^{1}.(0.5)^{4} = 0.15625[/tex]

[tex]P(X = 2) = C_{5,2}.(0.5)^{2}.(0.5)^{3} = 0.3125[/tex]

[tex]P(X = 3) = C_{5,3}.(0.5)^{3}.(0.5)^{2} = 0.3125[/tex]

[tex]P(X = 4) = C_{5,4}.(0.5)^{4}.(0.5)^{1} = 0.15625[/tex]

[tex]P(X = 5) = C_{5,5}.(0.5)^{5}.(0.5)^{0} = 0.03125[/tex]

Answer:

This is a multiplication of functions g and f, and these functions have no restrictions(such as a even root or a fraction), and thus [tex](g \mult f)(0) = g(0)f(0) = -4(1) = -4[/tex]

Step-by-step explanation:

We are given the following functions:

[tex]f(x) = 1[/tex]

[tex]g(x) = x - 4[/tex]

Can you evaluate (g•f)(0)?

This is a multiplication of functions g and f, and these functions have no restrictions(such as a even root or a fraction), and thus [tex](g \mult f)(0) = g(0)f(0) = -4(1) = -4[/tex]

Answer:

To evaluate the composition, you need to find the value of function f first. But, f(0) is 1 over 0, and division by 0 is undefined. Therefore, you cannot find the value of the composition.

You must evaluate the function f first.

Division by 0 is undefined.

The composition cannot be evaluated.

Answer:

D. The y-intercept of the new graph would shift down 2 units.

Step-by-step explanation:

y = -9x + 3 has a y-intercept of 3 (0, 3).

y = -9x + 1 has a y-intercept of 1 (0, 1).

3 - 1 = 2

So, down two units.

Answer:

3:2, 6;4 hope this helps

Answer:

C, D

Step-by-step explanation:

If you multiply both numbers of a ratio by the same number, you get an equivalent ratio.

A.  Divide both numbers by 10

40:30 = 4:3 No

B. 10:0 No

C. Multiply both numbers by 10

3:2 = 30:20 Yes

D. Multiply both numbers by 5

6:4 = 30:20 Yes

Step-by-step explanation

n^3-n.

Hope this will help you :) <3

Step-by-step explanation:

total number of students are :4x 3 = 12

Fraction that's boys are : 3÷12

Answer:

Step-by-step explanation:

I assume that you mean y = x²/(x²+1), not y = x²/x²+1.

x²+1 = 0

x² = -1

x = ±√(-1) = ±i

deleted: deleted by user

Answer:

0.0060 = 0.6% probability that the proportion of counterfeits in a sample of 686 Persian carpets would differ from the population proportion by greater than 3%

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

A carpet expert believes that 9% of Persian carpets are counterfeits.

This means that [tex]p = 0.09[/tex]

Sample of 686:

This means that [tex]n = 686[/tex]

Mean and standard deviation:

[tex]\mu = p = 0.09[/tex]

[tex]s = \sqrt{\frac{0.09*0.91}{686}} = 0.0109[/tex]

What is the probability that the proportion of counterfeits in a sample of 686 Persian carpets would differ from the population proportion by greater than 3%?

Proportion lower than 9% - 3% = 6% or higher than 9% + 3% = 12%. The normal distribution is symmetric, thus these probabilities are equal, so we can find one of them and multiply by 2.

Probability it is lower than 6%

p-value of Z when X = 0.06. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.06 - 0.09}{0.0109}[/tex]

[tex]Z = -2.75[/tex]

[tex]Z = -2.75[/tex] has a p-value of 0.0030

2*0.0030 = 0.0060

0.0060 = 0.6% probability that the proportion of counterfeits in a sample of 686 Persian carpets would differ from the population proportion by greater than 3%

Answer:

A, C, D, F

Step-by-step explanation:

Given the expression : (3/5)³

Recall :

a^b where, a = base ; b = exponent

In ; (3/5)^3

Base = 3/5 ; exponent = 3

Similarly ;

a^b = a in b places

(3/5)^3 = (3/5) * (3/5) * (3/5)

(3/5) * (3/5) * (3/5) = (3*3*3) / (5*5*5) = 27/125

Hence, A, C, D and F are all correct

Answer:

I think the choose (B)

5x/x + 3/x

Answer:

I thinkchoose no.3

5x+3

5x+3x

Answer:

all counting numbers except one

Answer:

x = 80

Step-by-step explanation:

3x/2=120°

3x=240°

x=80°

Answered by GAUTHMATH

first speed --- x mph

return speed -- x+16 mph

6/x + 6/(x+16) = 1

times each term by x(x+16)

6(x+16) + 6x = x(x+16)

x^2 + 4x - 96 = 0

(x-8)(x+12) = 0

x = 8 or x is a negative

her first speed was 8 mph

her return speed was 24 mph

check:

6/8 + 6/24 = 1 , that's good!

40% of 15 L = 6 L of acid

20% of 25 L = 5 L of acid

This means the mixture contains a total of 11 L of acid, and with a total volume of 15 L + 25 L = 40 L, that means the mixture is at a concentration of

(11 L acid) / (40 L solution) = 0.275 = 27.5%

Answer:

Number of pineapples = 10

Number of pears = 10 + 9 = 19

Number of kiwis = 10 - 2 = 8

Step-by-step explanation:

Money = $ 13.5

Cost of a pear = $ 0.5

Cost of a pineapple = $ 1.5

Cost of a kiwi = $ 0.3

let the number of pineapple = p  

Number of pears = p + 9

Number of kiwis = p - 2

Cost is

0.5 (p + 9) + 0.15 p + 0.3 (p - 2) = 13.5

0.5 p + 4.5 + 0.15 p + 0.3 p - 0.6 = 13.5  

0.95 p = 9.6

p = 10

So, number of pineapples = 10

Number of pears = 10 + 9 = 19

Number of kiwis = 10 - 2 = 8  

Answer:

3 pineapples  12 pears  10 kiwis

Answer:

?????????????????

Step-by-step explanation:

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Answer:

A and F

Step-by-step explanation:

A and F both represent instances of division of 14/5

B represent multiplication

C represent the reciprocal of the problem, 5/14

D represent addition

Answer:

A. false B. true C. false D. true

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