5 Determine the intervals on which the function f(x) = is continuous 2 4 ... Choose the correct answer below. O A. (-00,-2).(-2,2),(2,00) O B. (-00,4),(4.00) C. (-0,5),(5,00) OD. (-00,00)

permutations and combinations, the various ways in which objects from a set may be selected, generally without replacement, to form subsets. This selection of subsets is called a permutation when the order of selection is a factor, a combination when order is not a factor.

The factorial function (symbol: !) just means to multiply a series of descending natural numbers.

a) The number of four people committees that can be selected from a group of 16 people is:

no. of committees are possible = 16!/ 4!

(16x15x14x13)/(1x2x3x4)=1820

b)Given that

One person is the chair, and the rest are general members

n! / (n − r)!

where n is the number of things to choose from,

Pick a chairman:: 16 ways

Pick 3 others:: 15C3 = 455 ways

Ans: 16×455 = 7200

c)

Each committee has a chair, a secretary, a refreshment person and a cleanup person.

The number of combinations of assignments within each committee is: 4x3x2x1=24.

The total number of committees with each committee member’s responsibility is: 1820x24=43680.

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Calculi is the plural of calculus. It alludes to the study of mathematics and how it can be used to address issues with change, motion, and other ideas.

The plural of calculus is calculi. Calculus is the study of mathematics and how to use it to solve problems involving change, motion, and other concepts. Calculi is the plural form of calculus. Mathematicians who study calculus focus on the study of change and motion. It makes it possible for us to compute solutions to problems involving rates of change, area, and volume. Calculus is the technique of solving problems by dividing them into smaller, more manageable components. This entails examining the issue, dissecting it into smaller parts, and then applying mathematical ideas and operations to each piece individually. Problems involving derivatives, integrals, and limits are solved using calculus.

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Since Tony is self-employed, he will have to pay all of the tax himself.

Take his adjusted earnings times the tax rate

58238.74 * 2.9%

58238.74 * .029

1688.92346

Rounding to the nearest cent

1688.92

The expressions for dz/du and dz/dv are as follows:

dz/du = 4x siny

dz/dv = -6y cosx

To find the expressions for dz/du and dz/dv, we need to differentiate the given function z = 2x^2 - 3y with respect to u and v, respectively.

1. dz/du:

Since u = x^2 siny, we can express z in terms of u by substituting x^2 siny for u in the original function:

z = 2u - 3y

Now, we differentiate z with respect to u while treating y as a constant:

dz/du = d/dx (2u - 3y)

      = 2(d/dx (x^2 siny)) - 0 (since y is constant)

      = 2(2x siny)

      = 4x siny

Therefore, dz/du = 4x siny.

2. dz/dv:

Similarly, we express z in terms of v by substituting 2y cosx for v in the original function:

z = 2x^2 - 3v

Now, we differentiate z with respect to v while treating x as a constant:

dz/dv = d/dy (2x^2 - 3v)

      = 0 (since x^2 is constant) - 3(d/dy (2y cosx))

      = -6y cosx

Therefore, dz/dv = -6y cosx.

In summary, the expressions for dz/du and dz/dv are dz/du = 4x siny and dz/dv = -6y cosx, respectively.

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Answer:

a 4 b 5 c 7 d 6

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

The line that passes through the point (-2,-1) and has a slope of 5. The equation of the line is y + 1 = 5(x + 2).

A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate. Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by y and x, respectively. The ratio of the increase in elevation between two points to the run in elevation between those same two points is referred to as the slope.

Using the slope and 1 point format:   (y- y₁) = m(x - x₁)  

where m = slope = 5, and point is (x₁, y₁). In this case point (x₁, y₁) = (-2, -1)

x₁ = -2,  y₁ = -1

Using: (y- y₁) = m(x - x₁)

y - -1 = 5(x - -2)

y + 1 = 5(x + 2).

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Answer:

$240

Step-by-step explanation:

to find out how much Sue has put down we want to work out 20% of $300

the easiest way to do this is by finding 10% first, in order to find 10% we want to divide our number by 10 like this:

$300 / 10 = $30

this means that 10% of $300 = $30

now she paid 20%, not 10% so how do we get to 20% from 10%?

we double it!

10% = 30

multiply by 2

20% = $60

this is how much Sue has paid.

now to get the amount Sue has remaining to pay we are going to subtract the total payment from Sue's payment like so:

$300 - $60 = $240

this is the amount Sue has left to pay, $240.

hope this helps :D

Answer:

y= ⅓x +2

Step-by-step explanation:

Since the graph is a linear graph, let's use the slope-intercept form to find its equation.

Slope-intercept form

y= mx +c, where m is the slope and c is the y-intercept.

The y-intercept is the point at which the graph cuts through the y-axis. In this case, the y-intercept is 2.

Thus, y= mx +2.

Let's find the slope of the graph.

First, identify 2 pairs of coordinates from the graph:

(0, 2) and (3, 3)

Next, substitute these coordinates into the slope formula below:

\(\boxed{ \text{slope} = \frac{y _{1} - y_2 }{x_1 - x_2} }\)

slope

\( = \frac{3 - 2}{3 - 0} \)

\( = \frac{1}{3} \)

Thus, the equation of the graph is y= ⅓x +2.

Student is wrong  An exterior angle of a triangle can be adjacent to the right angle of a right triangle, so an exterior angle can be a right angle.

The Exterior Angle is the angle between any side of a shape, and a line extended from the next side.

The student make an error he states that the exterior angle of a triangle can never be a right angle.

The correct answer will be option D that is An exterior angle of a triangle can be adjacent to the right angle of a right triangle, so an exterior angle can be a right angle.I have also attached the diagram of the triangle for better understanding.

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Answer:

The answer is 7x²+5x

Step-by-step explanation:

\(\sf{}\)

♛┈⛧┈┈•༶♛┈⛧┈┈•༶

Answer:

"If I passed the test, then I got a 90%"

Step-by-step explanation:

A passing score is 70 or above.

So, scores like 71, 80, or 90 would also make you pass the test.

A counterargument for this could be "If I passed the test, then I got a 90%" because 90 is also passing, not just 70.

If you passed the test you would have 90%.

Answer:

\(x = \frac{7 + \sqrt{65}}{2} \ , \ x = \frac{7 - \sqrt{65}}{2}\)

Step-by-step explanation:

\(x^2 = 7x + 4 \\\\x^2 - 7x - 4 = 0\\\\ a = 1 \ , \ b = - 7 , \ c \ = \ - 4 \\\\x = \frac{-b \pm \sqt{b^2 - 4ac }}{2a}\\\\Substitute \ the \ values : \\\\x = \frac{7 \pm \sqrt{7^2 - (4 \times 1 \times -4)}}{2 \times 1}\\\\x = \frac{7 \pm \sqrt{49 + 16}}{2 }\\\\x = \frac{7 \pm \sqrt{65}}{2 }\\\\x = \frac{7 + \sqrt{65}}{2}\ , \ x = \frac{7 - \sqrt{65}}{2}\)

Answer:

a) y = 11x

b) y = $660

Step-by-step explanation:

a) For 10 people is $110, so simply divide.

110/10 = $11 per person.

y = 11x

b) So using that, substitute 60 for x.

y = 11(60)

y = $660

In this case, p = 1/4 ≤ 1. According to the p-series test, when p ≤ 1, the series diverges.  given series diverges. Theorem 9.11, also known as the p-series test, helps us determine the convergence or divergence of a series of the form ∑(n=1 to ∞) 1/n p, where p is a positive constant.

According to the p-series test, if p > 1, the series converges. If p ≤ 1, the series diverges. In the given series, we have \(1 + 1/(8)^(1/4) + 1/(27)^(1/4) + 1/(64)^(1/4) + 1/(125)^(1/4)...\)

To apply the p-series test, we need to express the terms in the form 1/np. Let's rewrite the series using the power of 1/4 for each term:   Now, we can see that p = 1/4. Since p = 1/4 is a positive constant, we can compare it to 1 to determine the convergence or divergence of the series.

Hence, p = 1/4 ≤ 1. Therefore, the given series diverges.

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Answer:

A) 17

Step-by-step explanation:

3x3=9x2=18-1=17

you start with parenthasis, then exponents, then mulitplication/division, and finally addition/subtraction

Answer:

17

Step-by-step explanation:

2 • 3² - 1

= (2 • 3²) - 1

= (2 • 9) - 1

= 18 - 1

= 17

Rember to use the PEMDAS order, where,

P = Parentheses

E = Exponents

M = Multiplication

D = Division

A = Addition

S = Subtraction

_____

Hope it helps ⚜

The answer is:

Work/explanation:

To solve the inequality, multiply each side by 13.

This is done to clear the fraction on the left side and isolate x.

\(\bullet\phantom{333}\bf{\dfrac{x}{13} > 1}\)

\(\bullet\phantom{333}\bf{x > 1\times13}\)

\(\bullet\phantom{333}\bf{x > 13}\)

The perimeter of the triangle is 170 inches.

To solve for the perimeter, we first need to find the length of the perpendicular height. We can do this using the sine function:

sin(35°) = 46/x

x = 46/sin(35°) = 65 inches

Now that we know the length of the perpendicular height, we can find the length of the base of the triangle using the cosine function:

cos(35°) = 65/x

x = 65/cos(35°) = 75 inches

The perimeter of the triangle is the sum of the lengths of the three sides, so the perimeter is:

P = 65 + 75 + 30

= 170 inches

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Answer:

oOoOoO what's brainliest?, can i have it?

Step-by-step Explanation:

Area of the region enclosed by one loop of the curve is pi/288.

To find the area of the region enclosed by one loop of the curve, we can use the formula for the area of a polar region:

A = 1/2 * ∫(r^2)dθ

We can use this formula with the equation for r given:

A = 1/2 * ∫(sin^2(6θ))dθ

This integral can be simplified by noting that sin^2(x) = (1/2)(1 - cos(2x))

Thus,

A = 1/2 * ∫(1/2)(1 - cos(12θ))dθ

This integral can be solved by noting that the antiderivative of (1/2)(1 - cos(12θ)) is (1/24)(sin(12θ) + θ).

Therefore, the area enclosed by one loop of the curve is

A = 1/2 * ((1/24)(sin(12θ) + θ)) evaluated from 0 to pi/6

A = (1/48)(sin(2pi) + pi/6)

   = (1/48)(0 + pi/6)

   = pi/288

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Answer : (-2, -8)

Step-by-step explanation:

Refer to attachment.

Hope it helps.

If points d and f are on side ab and points e and g are on side ac then line segments de and fg are parallel

What are parallel lines?

Parallel lines are those lines that do not meet at any point. If we draw a triangle ABC and plot points d and f are marked on side ab and points e and g are marked on side ac then the line segment fg is parallel to de because both the line segments are drawn from the points which are on the sides opposite to each other. We have assumed a simple triangle because no description is given for the triangle

Hence the line segment fg is parallel to de if drawn points d and f marked on ab and points e and g are marked on ac.

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If you multiply or divide both sides of an inequality by a negative number, you must reverse the inequality sign.

A statement that upholds the equality of two mathematical expressions is known as an equation. An identity is a statement that is true regardless of the value of each variable. A conditional equation is one that only holds true for certain values of one or more variables.

On the other hand, an inequality is a claim that indicates that one quantity has a greater or lesser value than another using the symbols > for greater than or for lesser than. An inequality has values for every variable, much like an identity. It concentrates on two-variable inequalities with a single exponent.

If both sides of an inequality are multiplied or divided by a negative value, the inequality sign must be reversed. This is due to the fact that adding or subtracting a negative integer causes the numbers on the number line to appear in reverse order.

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The mean is $1.60 greater than median So, Option B is correct

Adding the numbers together and dividing the result by the total number of numbers in the list yields the arithmetic mean. An average is most frequently used to refer to this.

The middle value in a list that is arranged from smallest to greatest is called the median. The value that appears the most frequently on the list is the mode.

According to the question,

Five year data is given:

For calculating mean,

Total number of year = 5

Sum of all year = 896 + 925 + 880 + 963 + 914

=> 4573

Mean = sum / total number

=> mean = 4578/5

=> 915.6

For calculating Median,

Arrange all the data in a ascending order

880 , 896 , 914 , 925 , 963

The middle value is 914

Therefore , median = 914

Difference of mean and median = 915.6 - 914

=> 1.6

Hence , Mean is $1.60 greater than median

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To determine whether Melissa can apply two coats of paint to the entire sculpture with a can of spray paint that covers 6,500 square centimeters need to consider the surface area of the sculpture and the amount of paint required for two coats.

Let's assume the sculpture has a total surface area of S square centimeters.

To apply one coat of paint to the entire sculpture, Melissa would need approximately S square centimeters of paint.

The can of spray paint covers 6,500 square centimeters, it would be sufficient to cover the sculpture with one coat.

A second coat of paint, Melissa would need an additional S square centimeter of paint.

The first coat has already covered the sculpture, the second coat would only require coverage of any missed spots or areas that need additional touch-up.

The amount of paint required for the second coat would generally be less than the amount required for the first coat.

Considering these factors, it is likely that Melissa can apply two coats of paint to the entire sculpture with a can of spray paint that covers 6,500 square centimeters.

The actual feasibility would depend on the size and complexity of the sculpture, as well as the efficiency of Melissa's painting technique.

If the sculpture has a significantly larger surface area than 6,500 square centimeters, or if it has intricate details that require a substantial amount of touch-up, Melissa may require additional cans of spray paint to achieve two coats.

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Answer: x = 17/9

Step-by-step explanation: Lets solve for x.

9x - 5 = 12

9x - 5 + 5 = 12 + 5

9x = 17

9x/9 = 17/9

x = 17/9

Answer:

You can expand this with this rule:

\(a(b+c)=ab+ac\)

Similarly,

\(\frac{1}{4}(4x+8) =\frac{1}{4}*4x+\frac{1}{4}*8\)

\(\frac{1}{4}*4x+\frac{1}{4}*8=x+2\)

Answer:

x = 11

Step-by-step explanation:

The two angles are consecutive interior angles so they add up to 180

13x -26 + 5x + 8 = 180

13x + 5x -26 + 8 = 180

18x - 18 = 180
18x = 180 + 18

18x = 198

x = 11

The solution to the system of equations that includes functions f(x) and g(x) is given by: (1,7).

A linear function is modeled by:

y = mx + b

In which:

The linear function g(x) goes through point (0,5), hence the y-intercept is of 5. The function also goes through point (1,7), hence the slope is of 2 and the function is:

g(x) = 5 + 2x.

The solution to the system of equations is found as follows:

f(x) = g(x)

2x² + x + 4 = 5 + 2x

2x² - x - 1 = 0

Which is a quadratic equation with coefficient a = 2, b = -1, c = -1, hence:

When x = 1, f(x) = g(x) = 7, hence the solution of the system is of (1,7).

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Answer:

D. (1,7)

Step-by-step explanation:

I took the exam

(a) The number 72% is a D. statistic.

(b) The unknown true percentage of American citizens who like ''real TV'' is a C. parameter.

It is related to statistics and parameters.

(a) The number 72% is a statistic because it represents a summary measure of the sample of individuals who participated in the phone-in poll.

A statistic is a numerical value calculated from a sample of data, and it is used to make inferences about the population from which the sample was drawn.

(b) The unknown true percentage of American citizens who like ''real TV'' is a parameter.

A parameter is a numerical characteristic of a population, such as a mean, proportion, or standard deviation, and it is typically unknown and estimated from sample data.

In this case, the percentage of all American citizens who like ''real TV'' is unknown and cannot be directly observed, so it is considered a parameter.

The phone-in poll only represents a sample of individuals who called in to the newspaper and cannot be used to estimate the parameter for the entire population.

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