Which equation represents the line that passes through the points (3, 7) and ( - 1, - 1)?

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:

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)

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

False. The sample size needed to estimate the population distribution should not always be at least 10% of the population size.

False. The statement that the sample size needed to estimate the population distribution should always be at least 10% of the population size is not true. The size of the sample needed depends on various factors such as the original population, the level of confidence desired, and the margin of error allowed. For example, if the population is large and diverse, a smaller sample may still provide a reliable estimate of the population distribution. It is important to consider statistical concepts such as normal distribution and sampling techniques when determining the appropriate sample size.

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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.

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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Using algebra, we find that 225 adult tickets were sold out of a total of 504 tickets.

Let's denote the number of adult tickets as x. Since there were 54 more student tickets sold than adult tickets, we can represent the number of student tickets as x + 54. The total number of tickets sold is 504, so we set up the equation x + (x + 54) = 504.

Combining like terms, we get 2x + 54 = 504. Subtracting 54 from both sides gives us 2x = 450. Finally, dividing both sides by 2 gives us x = 225.

Therefore, 225 adult tickets were sold.

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Answer:

Your answer will be D.

Step-by-step explanation:

I did it on the test and got it correct.

234 x 2 = 468 scoops

156 x 3 = 468 scoops

468 + 468 = 936 total scoops

936 x 3 = 2808 ounces

  16 ounces = 1 pound

2808/16 = 175.5 pounds

175.5/10 = 17.55 tubs

 round answer as needed

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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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

divide them:

3.6/28.8 = 0.125

0.125 = 12.5%

The expression 33 • 32 + 12 ÷ 4 simplifies to 1059.

To simplify the expression 33 • 32 + 12 ÷ 4, we follow the order of operations - performing multiplication and division before addition.

Now we can add the results: 1056 + 3 = 1059.

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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