Rewrite sin 15 degree in terms of a 75 degree angle and in terms of the reciprocal of a trigonometric function.

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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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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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

1 meter = 1000 mm

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

Answer:

Your answer will be D.

Step-by-step explanation:

I did it on the test and got it correct.

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:

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:

[tex](-5,2)[/tex]

Step-by-step explanation:

We have been given that a figure has a vertex at (5,2). The figure has line symmetry about the y-axis.

We know that if a figure is symmetric about y-axis, then its x-coordinate changes to opposite sign and y-coordinate remains same.

We can see that x-coordinate of our given point is 5, so x-coordinate of another vertex of the figure would be -5.

Therefore, the point [tex](-5,2)[/tex] is symmetric about y-axis for our given point.

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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volume = pi x r^2x h

100 = 3.14 x 2^2 x h

100 =3.14 x 4 x h

100 = 12.56 x h

h = 100/12.56 = 7.9617

the height is approximately 8 inches tall

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

Final answer:

To determine the number of adult tickets sold for the school play, a system of equations is set up and solved, revealing that 275 adult tickets were sold.

Explanation:

To find the number of adult tickets sold for the school play, we need to set up a system of equations based on the information given. Let x represent the number of adult tickets and y represent the number of student tickets. According to the problem, the following two statements are true:

The total number of tickets sold is 487: x + y = 487

There were 63 fewer student tickets sold than adult tickets: y = x - 63

We can substitute the second equation into the first to find the value of x:

x + (x - 63) = 487

2x - 63 = 487

2x = 487 + 63

2x = 550

x = 275

Therefore, 275 adult tickets were sold.

Answer:

Any rational number.

Step-by-step explanation:

∴ [tex]x+0.5[/tex] is rational if and only if x is rational.

To proveL:  we proceed as follows:

Suppose that  [tex]x+0.5[/tex] is rational.

Then there are some integers p , q with [tex]q\neq 0[/tex] such that

[tex]x+\frac{1}{2}=\frac{p}{q}[/tex]

Subtract both sides by [tex]\frac{1}{2}[/tex], we get

[tex]x=\frac{p}{q}-\frac{1}{2}=\frac{2p-q}{2q}[/tex] which is rational.

Conversely, if x is rational, then there are integers a,b with b>0 such that    [tex]x=\frac{a}{b}[/tex]  then we have,  

[tex]x+\frac{1}{2}=\frac{a}{b}+\frac{1}{2}=\frac{2a+b}{2b}[/tex] which is also a rational.

Answer:

5y-y =360

4y =360

y= 90 sandwiches by Pete's deli

x= 5(90) = 450 sandwiches by Bills Roast Beef

Step-by-step explanation:

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