You roll a fair 666-sided die. What is \text{P(roll greater than 4})P(roll greater than 4)start text, P, left parenthesis, r, o, l, l, space, g, r, e, a, t, e, r, space, t, h, a, n, space, 4, end text, right parenthesis?

When k is a common multiple of 75, 98, and 140, the following statements are true:I. k is divisible by 9II. k is divisible by 49III.

k is greater than 14,000Option C: I and II only is the correct option. In order to find the common multiple of 75, 98 and 140, we first have to find the prime factorization of the given numbers. 75 = 3 × 5²98 = 2 × 7²140 = 2² × 5 × 7.

Hence, the common multiple of 75, 98 and 140 is the product of the highest powers of all prime factors in the prime factorization of these numbers. Hence, the common multiple of 75, 98 and 140 is 2² × 5² × 7² = 2450.I.

k is divisible by 9: 2450 is not divisible by 9. Hence, this statement is incorrect.II. k is divisible by 49: 2450 is divisible by 49. Hence, this statement is correct.III. k is greater than 14,000: 2450 is less than 14,000.

Hence, this statement is incorrect. Therefore, the correct option is C: I and II only.

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Answer: look below.

x = −1/2

Answer

x=-0.5

Step-by-step explanation:

4x-12x=32-28

-8x=4

x=-0.5

Answer:

The perimeter is 206.

Step-by-step explanation:

When given the area, height and side of the parallelogram, you would use the formula to find the perimeter: P=2a+2*A /h. a = side of the parallelogram, A = area, and h = height. When you plug in everything, you will get 206.

The equation \(\frac{5-3-2}{1+4+6+7+8+9}\)  = 0 is true

In arithmetic, a number expressed as a quotient, in which a numerator is divided by a denominator.

Using digits 0 to 9, no more than once each.

we want to place them in such a way that the division will be zero.

As we know that a quotient is equal to zero iff the numerator is equal to zero and the denominator other than zero.

So if we put some numbers on the numerator in such a way by adding them gives 0.

So, 5 - 3 - 2 = 0

Use all the other numbers in the denominator.

\(\frac{5-3-2}{1+4+6+7+8+9}\)  = 0

which is true.

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Answer:

r = $105.6

Step-by-step explanation:

Given,

Amount paid by Trevor for 4 nights = $528

Rate per day = r

Now,

We know that a 4-night stay in the hotel means 5 days to stay at MGM Grand.

Now,

Amount paid = Number of days x Rate per day

$528 = 5 r

\(r = \frac{528}{5}\)

r = $105.6

Hence, Trevor pays $105.6 to stay at the MGM Grand Hotel in Las Vegas for four nights.

The annual sales of the Hand & Foot Cream are increasing by 151,000 bottles per year. Based on the linear trend equation, the predicted annual sales for year 6 is 1,006,000 bottles.

According to the given linear trend equation F1 = 80 + 151, the constant term 80 represents the initial annual sales at the start of the trend. The coefficient of the independent variable t, which represents the number of years, is 151.

To determine whether the annual sales are increasing or decreasing, we look at the coefficient of t. Since the coefficient is positive (151), it indicates that the annual sales are increasing over time. The coefficient tells us that for every year that passes, the annual sales increase by 151,000 bottles. Therefore, the annual sales are experiencing positive growth.

To predict the annual sales for year 6, we substitute t = 6 into the equation. Plugging in the value, we have F6 = 80 + (151 * 6) = 80 + 906 = 986. Therefore, the predicted annual sales for year 6 is 986,000 bottles.

In conclusion, the annual sales of the Hand & Foot Cream are increasing by 151,000 bottles per year. Based on the linear trend equation, the predicted annual sales for year 6 is 986,000 bottles. This indicates that the product's popularity and demand are growing steadily.

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The distance between successive fourth roots of the complex number √3/2 - 1/2i on the unit circle is 5π/24 units.

To find the distance between successive fourth roots of a complex number on the unit circle, we can use the concept of the angle between the roots. Let's proceed step by step:

The given complex number is √3/2 - 1/2i. This complex number lies on the unit circle because its magnitude is equal to 1.

1. Convert the given complex number to trigonometric form:

  √3/2 - 1/2i = cos(θ) + i*sin(θ)

  By comparing the real and imaginary parts, we can determine the angle θ:

  cos(θ) = √3/2

  sin(θ) = -1/2

  Using the unit circle, we can find that θ = 5π/6 (or 150 degrees). This angle represents the position of the given complex number on the unit circle.

2. Find the angle between successive fourth roots:

  Since we are interested in the fourth roots, we divide the angle θ by 4:

  θ/4 = (5π/6) / 4 = 5π/24

  This angle represents the angular distance between two successive fourth roots on the unit circle.

3. Calculate the distance between the two points:

  To find the distance, we multiply the angular distance by the radius of the unit circle (which is 1):

  Distance = (5π/24) * 1 = 5π/24

  Therefore, the distance between successive fourth roots of the complex number √3/2 - 1/2i on the unit circle is 5π/24 units.

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The angle at the centre is twice the angle at the circumference.

The angle in a semicircle is a right angle.

Angles in the same segment are equal.

Opposite angles in a cyclic quadrilateral sum to 180°

Answer:

2+2b

Explanation:

To expand the given expression, we divide each term in the parenthesis by the number outside. For the final step, we sum the results.

Multiplying each term by 2 gives

adding the two results gives

which can be written as

Which is our answer!

Answer:One pint and 16 quarts or one pint and four gallons

Step-by-step explanation:there are two pints in a quart and there are 4 quarts in a gallon.

\( = \frac{3}{4} \times \frac{1}{2} \\ \)

\( = \frac{3}{8} \\ \)

Answer:

y = 22x+10

Step-by-step explanation:

There cost of parking is 10 and tickets cost 22 dollars each.  If x people are attending, the total cost y is

y = 10+22x

y = 22x+10

Answer:

divide, 2x+9

Step-by-step explanation:

got it right

The correct option is C. Isolating a variable in one of the equations.

The first step in solving a system of nonlinear equations by substitution is to isolate a variable in one of the equations.

A set of two or more equations in two or more variables that includes at least one nonlinear equation is referred to as a system of nonlinear equations.

The method to solve a system of nonlinear equations by substitution is-

The importance of systems of nonlinear equations are-

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The complete question is-

Which is most likely the first step in solving a system of nonlinear equations by substitution?

A. Substituting a number for one of the variables

B. Substituting one equation into the other equation

C. Isolating a variable in one of the equations

D. Taking the square root of both sides of one of the equations

Answer:

Isolating a variable in one of the equations.

Step-by-step explanation:

Answer:

its abt 45 degrees I think

Step-by-step explanation:

Answer:

45 degrees

Step-by-step explanation:

could you make this answer brainliest please?

Answer:

18 units

Step-by-step explanation:

since the y- coordinates are equal then the 2 points lie on a horizontal line and the distance (d) between them is the absolute value of the x- coordinates, that is

d = | - 4 - 14 | = | - 18 | = 18

or

d = |  14 - (- 4) | = | 14 + 4 | =   18  = 18

Answer: The value of the expression at x = -2 and y = 3 will be negative 18.

What is the value of the expression?

When the relevant factors and natural laws of a mathematical model are given values, the outcome of the calculation it describes is the expression's outcome.

PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.

The expression is given below.

⇒ 3x - 4y

The value of the expression at x = -2 and y = 3 will be

⇒ 3(-2) - 4(3)

⇒ - 6 - 12

⇒ - 18

The value of the expression at x = -2 and y = 3 will be negative 18.

Step-by-step explanation:

Given:-

Solution:-

\( \: \)

\( \: \)

\( \: \)

\( \: \)

hope it helps! :)

Based on the bar graph, the most reasonable estimate for the number of Gamin Middle School athletes whose favorite sport is hockey is 10.

A chart type known as a bar graph uses rectangular bars to show data. The length or height of each bar, which is usually evenly spaced along a horizontal or vertical axis, correlates to the value of the data being displayed. The relative sizes or frequencies of several categories or groups in a data collection are frequently compared using bar graphs. Since they offer a clear and straightforward approach to depict complicated information, bar graphs are helpful for data visualisation.

Based on the bar graph, the most reasonable estimate for the number of Gamin Middle School athletes whose favorite sport is hockey is 10.

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The solution to the initial value problem is:

y(t) = (-3/4) * e^(-4t+4) + (3/8) * e^(2t+8)

To solve a second-order linear homogeneous differential equation the equation is y′′ 2y′-8y = 0.

Given initial conditions: y(102) = 3 and y′(102) = -12.

To solve this differential equation, we can use the characteristic equation: r^2 + 2r - 8 = 0

Factoring this equation, we get: (r + 4)(r - 2) = 0

So the roots of the characteristic equation are r = -4 and r = 2.

The general solution to the differential equation is:

y(t) = c1 * e^-4t + c2 * e^2t

To find the values of c1 and c2, we can use the initial conditions.

We know that y(102) = 3, so we can substitute t = 2 into the general solution:

3 = c1 * e^-8 + c2 * e^4

We also know that y′(102) = -12, so we can take the derivative of the general solution and substitute t = 2:

y′(t) = -4c1 * e^-4t + 2c2 * e^2t

y′(102) = -4c1 * e^-8 + 2c2 * e^4 = -12

Solving for c1, we get:

c1 = (-3/4) * e^4 + (3/4) * e^-8

Solving for c2, we get:

c2 = (3/8) * e^8 - (3/8) * e^-4

Therefore, the solution to the initial value problem is:

y(t) = (-3/4) * e^(-4t+4) + (3/8) * e^(2t+8)

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The specific function that will be called by the function call square(23.4) cannot be determined without knowing the definitions of the four functions.

The answer depends on the function signatures and parameter types of the defined functions.

To determine which function will be called, we need to consider the parameter types and function signatures of the four defined functions. If one of the functions has a parameter that matches the type of the argument passed (in this case, 23.4), that function will be called.

The function definition must explicitly state a parameter of the appropriate type to match the argument. Without knowledge of the function definitions and their parameter types, it is not possible to determine which specific function will be called by the function call square(23.4).

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if the average time to serve a customer is 3 minutes, then the service rate is 3 per hour. group of answer choices is False.

If the average time to serve a customer is 3 minutes, then the service rate is actually 20 customers per hour, not 3 per hour. This is because there are 60 minutes in an hour, so in one hour, there are 60/3 = 20 sets of 3 minutes, each of which can serve one customer.

what is  average time?

Average time refers to the sum of all the times divided by the total number of observations or events. It is a measure of central tendency that provides information about the typical or representative time for a certain process or event.

For example, if the times to complete a task are 2 seconds, 4 seconds, 6 seconds, and 8 seconds, the average time would be:

(2 + 4 + 6 + 8) / 4 = 5 seconds

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(i) Yes, it is even and divisible by 3 as 1 + 0 + 2 = 3

(ii) No, it does not end in 5 or 0

What are Divisibility Rules?

Divisibility criteria can be used to determine whether or not to diminish a fraction. The rules are based on patterns seen while listing the multiples of any integer.

Solution:

(i) 102 is divisible by 6 - TRUE

It is because 102 is even number thus, it is divisible by 2 and since the sum of digits 1 + 0 + 2 is 3 therefore, it is divisible by 3

- Yes, it is even and divisible by 3 as 1 + 0 + 2 = 3

(ii) 102 is divisible by 5 - FALSE

It is because any number to be divisible by 5 it should always end with 5 or 0 at ones place.

- No, it does not end in 5 or 0

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Answer:

C.

There is no repeated x or y values

We know that a relation is a function, when each input of x value gives exactly one output of y-value.

In a function two or more x-coordinates can give same y-value, but one x-value cannot give two y-values.

We can see that in our given set each x-value corresponds to exactly one y-value, therefore, the given set represents a function.

Step-by-step explanation: Hopefully this helped, if not HMU and I will get you a better answer

-Have a great day! :)

To find the indefinite integral of the function x²(x² - 25)³/² dx, we can use the trigonometric substitution x = 5sec(θ).

This substitution involves replacing x with 5sec(θ), which allows us to express the expression in terms of trigonometric functions. The resulting integral will involve trigonometric functions and their derivatives, which can be evaluated using trigonometric identities and integration techniques.

To use the trigonometric substitution x = 5sec(θ), we start by expressing x² - 25 in terms of sec(θ). From the identity sec²(θ) - 1 = tan²(θ), we have sec²(θ) = tan²(θ) + 1. Rearranging this equation, we obtain sec²(θ) - 1 = tan²(θ), which implies sec²(θ) = tan²(θ) + 1.

Substituting x = 5sec(θ), we have x² - 25 = (5sec(θ))² - 25 = 25sec²(θ) - 25 = 25(tan²(θ) + 1) - 25 = 25tan²(θ).

Therefore, the integral becomes ∫ 25tan²(θ) * 5sec(θ) * 5sec(θ) * sec(θ) dθ.

Simplifying further, the integral becomes ∫ 125tan²(θ)sec³(θ) dθ.

Using the trigonometric substitution x = 5sec(θ), we can rewrite the expression in terms of trigonometric functions. This allows us to evaluate the integral using trigonometric identities and integration techniques specific to trigonometric functions.

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The integral: S1 0 (-x³ - 2x² - x + 3)dx is -1/12

An integral is a mathematical operation that calculates the area under a curve or the value of a function at a specific point. It is denoted by the symbol ∫ and is used in calculus to find the total amount of change over an interval.

To evaluate the integral:

\($ \int_0^1 (-x^3 - 2x^2 - x + 3)dx $\)

We can integrate each term of the polynomial separately using the power rule of integration, which states that:

\($ \int x^n dx = \frac{x^{n+1}}{n+1} + C $\)

where C is the constant of integration.

So, we have:

\($ \int_0^1 (-x^3 - 2x^2 - x + 3)dx = \left[-\frac{x^4}{4} - \frac{2x^3}{3} - \frac{x^2}{2} + 3x\right]_0^1 $\)

Now we can substitute the upper limit of integration (1) into the expression, and then subtract the result of substituting the lower limit of integration (0):

\($ \left[-\frac{1^4}{4} - \frac{2(1^3)}{3} - \frac{1^2}{2} + 3(1)\right] - \left[-\frac{0^4}{4} - \frac{2(0^3)}{3} - \frac{0^2}{2} + 3(0)\right] $\)

Simplifying:

\($ = \left[-\frac{1}{4} - \frac{2}{3} - \frac{1}{2} + 3\right] - \left[0\right] $\)

\($ = -\frac{1}{12} $\)

Therefore,

\($ \int_0^1 (-x^3 - 2x^2 - x + 3)dx = -\frac{1}{12} $\)

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Answer:

false

Step-by-step explanation:

Answer:

D.

Step-by-step explanation:

pint slope form:

(y-y1)=m(x-x1)

do just olug in the point and the slope into the equation

(y-4)= -8/7 (x-4)