The variable z is directly proportional to x and inversely proportional to y. When x is 12 and y is 18 z has the value 2 what is the value of z when x = 19 and y = 22

To decrease the concentration of a 15% alcohol solution to 7%, 16 mL of water needs to be added to the original 14 mL solution.

The problem involves using the concept of concentration dilution that is C1V1 = C2V2, where C1 is the initial concentration, V1 is the initial volume, C2 is the final concentration, and V2 is the final volume.

First, we need to convert the percentage to decimal so, C1=0.15 (15% as a decimal) and C2=0.07 (7% as a decimal). We know V1=14 mL (the starting volume of the 15% alcohol solution) and we are solving for V2.

Insert the known values into the equation and solve for V2: (0.15)(14) = (0.07)(V2). After calculation, V2 is approximately 30 mL.

To figure out how much water should be added to reduce the concentration from 15% to 7%, subtract the initial volume from the final volume: 30 mL - 14 mL = 16 mL.

So 16 mL of water needs to be added to the 15% alcohol solution to reduce the concentration to 7%.

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The cube root of 0 is 0; this is because 0 multiplied by itself three times is 0.

The cube root of 0 is simply 0. This is because any number, when multiplied by itself three times, which is what we are doing when we take the cube of a number, that results in 0, must have been 0 to start with. The cube root operation is asking us what number, when cubed, gives us the original number, and in the case of 0, 0³ equals 0. Therefore, the cube root of 0 is 0.

Answer:

advance booking is cheaper by 400 bahts or $10.

Step-by-step explanation:

Car rental cost in advanced booking = $35 per day

and

when the rented locally it is charged = 1800 bahts per day

it is given that,

$1 is equal to 40 bahts.

now,

Car rental cost in advanced booking =  35  × 40

                                                              = 1400 bahts

hence, when booking is done advance

  the cost is cheaper  by  1800 - 1400 = 400 bahts

hence, advance booking is cheaper by 400 bahts or $10.

63-57 = 6 inches in 2 days

6/2 = 3 inches per day

17-5 = 12

12*3 =36 inches in 12 days

57-36 = 21 inches after 17 days

Answer with explanation:

Principal = $ 1000

Time = 2 years

Rate of Interest = 7 %

Since of rate of interest is compounded monthly,

then, [tex]R=\frac{7}{12}\\\\T=2 \times 12 =24[/tex]

Amount after 2 years

 [tex]=P\times [1 +\frac{R}{100}]^T\\\\=1000 \times [1+\frac{7}{1200}]^{24}\\\\=1000 \times [\frac{1207}{1200}]^{24}\\\\=1000 \times (1.00583)^{24}\\\\=1000\times 1.14972\\\\=1149.72[/tex]

Amount after 2 years, when rate of interest, is compounded monthly=$ 1149.72  

Answer:  The required probability is 50%.

Step-by-step explanation: Given that Tommy has a piece of toast that has butter on one side.

The first two times dropped the piece, it landed with the butter side up.

We are to find the probability that the piece will have landed butter side up a total of three times, if he drops it two more times.

For the butter side to be landed up three times, one of the last two drops must land butter side up.

Let, 'S' denotes the sample space for the experiment of dropping the piece for the last two times, then

n(S) = 2.

Let, 'B' be the event of getting one of the last two drops landed butter side up, then

n(B) = 1.

Therefore, the probability of  getting one of the last two drops landed butter side up will be

[tex]P(B)=\dfrac{n(B)}{n(S)}=\dfrac{1}{2}=50\%.[/tex]

Thus, there is 50% probability of landing butter side up a total of three times.

 To solve the following problems, we use the binomial probability equation:

P (r) = [n!/(n-r)! r!] p^r q^(n-r)

where,

n = total number of households = 8

r = number of sample

p = probability of success = 65% = 0.65

q = probability of failure = 0.35

A. r = 5

P (r=5) = [8! / 3! 5!] 0.65^5 0.35^3

P (r=5) = 0.28

B. r >5

P (r=6) = [8! / 2! 6!] 0.65^6 0.35^2

P (r=6) = 0.26

P (r=7) = [8! / 1! 7!] 0.65^7 0.35^1

P (r=7) = 0.14

P (r=8) = [8! / 0! 8!] 0.65^8 0.35^0

P (r=8) = 0.03

Therefore total is:

P (r>5) = 0.26 + 0.14 + 0.03 = 0.43

C. r ≤ 5

P (r ≤ 5) = 1 - P (r>5)

P (r ≤ 5) = 1 – 0.43

P (r ≤ 5) = 0.57

there would be 3 kings left and 51 cards left

 so it would be a 3/51 which reduces to 1/17 probability

The probability of drawing a king from a 52-card deck on the second draw, given that a king was drawn on the first draw and was not replaced, is 1 in 17.

The question pertains to the concept of probability, specifically with regards to sampling without replacement in a 52-card deck. First, let's identify the elements: there are 4 kings in a 52-card deck. When one king is drawn and not replaced, there are now 51 cards left with 3 kings.

The probability of drawing a king on the second draw, with the first king not replaced, is the number of favorable outcomes (drawing a king) divided by the total number of outcomes (total cards left). Hence, the probability is 3/51 = 1/17.

This means that there is 1 chance in 17 of drawing a king on the second draw if a king has been drawn on the first draw and not replaced.

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To calculate the salesperson's total annual pay, we add the commission earned from the total sales to the base salary. The commission is $12,500, and the base salary is $36,000, resulting in a total pay of $48,500.

The question asks us to determine the total pay for a salesperson with a base salary and a commission percentage on total sales. To find the salesperson's total pay for a year, we calculate the commission earned from total sales and add it to the base salary. The salesperson's commission is 2 1/2% of $500,000, which can also be written as 0.025. We calculate the commission by multiplying 0.025 by $500,000, which equals $12,500. Therefore, the total pay for the salesperson for that year is the sum of the base salary of $36,000 plus the commission of $12,500, which gives us $48,500.

The width of the rectangular garden is 6 feet with a perimeter of 36 feet.

We know the perimeter of any 2D figure is the sum of the lengths of all the sides except the circle and the area of a rectangle is the product of its length and width.

Given, A rectangular garden has a length of 12 feet.

Assuming the width of the garden to be x feet.

We know the perimeter of a rectangle is 2(length + width).

∴ 2(12 + x) = 36.

24 + 2x = 36.

2x = 12.

x = 6 Or the width is 6 feet.

learn more about rectangles here :

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Answer:

The correct option is A.

Step-by-step explanation:

The general form of an ellipse is

[tex]\frac{x^2}{a^2}+\frac{y^2}{b^2}=1[/tex]

Where, (0,0) is the center of ellipse, (±a,0) are x-intercepts and (0,±b) are y-intercepts.

From the given graph it is clear that the center of ellipse is (0,0), (±2,0) are x-intercepts and (0,±4) are y-intercepts. So, the equation of ellipse is

[tex]\frac{x^2}{(2)^2}+\frac{y^2}{(4)^2}=1[/tex]

[tex]\frac{x^2}{4}+\frac{y^2}{16}=1[/tex]

The shaded region is inside the ellipse, (0,0) lie in the solution set and the points lie on the ellipse are included in the solution set, therefore the sign of inequality is ≤.

[tex]\frac{(0)^2}{4}+\frac{(0)^2}{16}\leq 1[/tex]

[tex]0\leq 1[/tex]

This statement is true. The required inequality is

[tex]\frac{x^2}{4}+\frac{y^2}{16}\leq 1[/tex]

Therefore, the correct option is A.

divide them:

3.6/28.8 = 0.125

0.125 = 12.5%