The ratio of the width to the length of a rectangular garden is 2 to 3. Which of the following could be the width and length of the garden?A. Width = 12 feet, length = 13 feet.
B. Width = 18 feet, length = 12 feet.
C. Width = 24 feet, length = 39 feet.
D. Width = 12 feet, length = 18 feet.

Answers

Answer 1
Answer: The only one has a ratio of 2:3 is D. 

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Indicate in standard form the equation of the line passing through the given points. P(6, 2), Q(8, -4)

Answers

If you solve it into point-slop form, the equation is y = -3x + 20, then put into standard form is 3x + y = 20. That's your answer.

What's 32 to the power of negative 2/5

Answers

32^{-(2)/(5)}=\sqrt[5]{32}^(-2)=2^(-2)=((1)/(2))^2=(1)/(4)

15% of what number equals 12?

Answers

percent means parts out of 100
15%=15/100=0.15
'of' means multiply

therefor
15% of x equals 12 means
0.15 times x=12
divide both sides by 0.15
x=80



the number is 80

Which two numbers add up to 6 and multiply to 21

Answers

None.  The numbers adding to 6 with the greatest product are 3 and 3, and 3*3=9, which is not large enough.

Quadrilateral ABCD is located at A(−2, 2), B(−2, 4), C(2, 4), and D(2, 2). The quadrilateral is then transformed using the rule (x − 2, y + 8) to form the image A'B'C'D'. What are the new coordinates of A', B', C', and D'? Describe what characteristics you would find if the corresponding vertices were connected with line segments.

Answers

The new coordinates are A(-4, 10), B (-4, 12), C (0, 12) and D (0, 10). If you were to connect these, it would take the shape of a rectangle. 

A manufacturer of matches randomly and independently puts 23 matches in each box of matches produced. The company knows that one-tenth of 8 percent of the matches are flawed. What is the probability that a matchbox will have one or fewer matches with a flaw?

Answers

Answer:

0.9855 or 98.55%.

Step-by-step explanation:

The probability of each individual match being flawed is p = 0.008. The probability that a matchbox will have one or fewer matches with a flaw is the same as the probability of a matchbox having exactly one or exactly zero matches with a flaw:

P(X\leq 1)=P(X=0)+P(X=1)\nP(X\leq 1)=(1-p)^(23)+23*(1-p)^(23-1)*p\nP(X\leq 1)=(1-0.008)^(23)+23*(1-0.008)^(23-1)*0.008\nP(X\leq 1)=0.8313+0.1542\nP(X\leq 1)=0.9855

The probability  that a matchbox will have one or fewer matches with a flaw is 0.9855 or 98.55%.