Determine the domain of the function. f as a function of x is equal to the square root of two minus x.

To evaluate the limit of (x + h)³ - x³h as h approaches 0, we can expand the expression using the binomial theorem and simplify. The resulting expression can be factored to show that as h approaches 0, the entire expression becomes 0. Therefore, the limit is 0.

To evaluate the given limit, we can start by expanding the expression (x + h)³ using the binomial theorem. This gives us (x³ + 3x²h + 3xh² + h³) - x³h. Simplifying further, we can cancel out the x³ terms and obtain 3x²h + 3xh² + h³ - x³h. Now, we can factor out h from the expression to get h(3x² + 3xh + h² - x³). As h approaches 0, the entire expression becomes 0, since h is being multiplied by a polynomial that does not contain h. Therefore, the limit is 0.

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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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Answer:

Direct variation states that the relationship between two variables in which one is a constant multiple of the other one.

In other words, when one variable changes the other one changes in proportion to the first.

i.e, if y is directly proportional to x then, the equal will be of the form is, y= kx where k is the constant of variation.

Given: y varies directly with x, and y = 8 when x = –6

By definition of direct variation,

y = kx

Substitute the  values of x = -6 and y=8 to solve for k;

8 = -6k

Divide both sides by -6 we get;

[tex]k = -\frac{8}{6} = -\frac{4}{3}[/tex]

Now, to find the value of y when x = 2 we have;

[tex]y = -\frac{4}{3}x[/tex]

Substitute the given value of x =-2 we have;

[tex]y = -\frac{4}{3} \cdot -2 = \frac{8}{3}[/tex]

Therefore, the direct variation related x and y is, [tex]y = -\frac{4}{3}x[/tex]

and the value of [tex]y =\frac{8}{3}[/tex] when x = -2

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.

divide them:

3.6/28.8 = 0.125

0.125 = 12.5%

Answer:

2 × 10³ cm³

Step-by-step explanation:

Given data

Considering the crate is a cuboid, its volume (V) is:

V = length × width × height

Since

area of the base = length × width

We get

V = area of the base × height

V = 6 cm² × 4 × 10² cm

V = 2.4 × 10³ cm³ ≈ 2 × 10³ cm³ (we round off to 1 significant figure)

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 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 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  

1 meter = 1000 mm

 so 5 meters = 5 x 1000 = 5,000 millimeters

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: $54

Step-by-step explanation:

The equation to show the direct variation in two quantities x and y  is given by :-

[tex]\dfrac{x_1}{y_1}=\dfrac{x_2}{y_2}[/tex]

The tax on a $500 item is $30.

Let 'x' be the sales tax on a $900 item.

Then , we have the following equation:-

[tex]\dfrac{x}{900}=\dfrac{30}{500}\\\\\Rightarrow\ x=\dfrac{900\times30}{500}\\\\\Rightarrow\ x=54[/tex]

Hence, the sales tax on a $900 item = $54

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