assertion: if p and q are integers and is represented in the form of p/q then it is a rational number
reason: 17/3 is a rational number

The simplified form of the given expression is:

(cosx * (tanx + 1) + 1) / cosx

To solve the given expression, we can start by simplifying it using trigonometric identities.

Given expression: tanx / (1 + secx) + (1 + secx) / tanx

Step 1: Simplify denominators

We can rewrite secx as 1/cosx, and tanx as sinx/cosx. Using these identities, we get:

tanx / (1 + 1/cosx) + (1 + 1/cosx) / (sinx/cosx)

Step 2: Find the least common denominator (LCD)

The LCD is cosx, as it is the common denominator for both fractions.

Step 3: Combine the fractions

Using the LCD, we can combine the fractions:

[(tanx * cosx) + (1 + 1/cosx)(cosx)] / cosx

Step 4: Simplify the numerator

Multiplying through by cosx to simplify the numerator, we get:

[tanx * cosx + (cosx + 1)] / cosx

Step 5: Combine like terms

Combining like terms in the numerator, we get:

[tanx * cosx + cosx + 1] / cosx

Step 6: Factor out cosx

We can factor out cosx from the numerator:

cosx * (tanx + 1) + 1 / cosx

So, the simplified form of the given expression is:

(cosx * (tanx + 1) + 1) / cosx

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QUESTION IS - simplify . tanx/1+secx  +  1+secx/tan x

If you buy a ticket, you can expect to make a profit of approximately $0.96 on average.

To calculate the expected profit, we need to consider the probability of winning each prize and the value of each prize.

The probability of winning each prize can be calculated by dividing the number of winning tickets by the total number of tickets. There is 1 winning ticket for each prize, so the probability of winning each prize is:

$240 prize: 1/250

$130 prize: 1/250

$120 prize: 1/250

$70 prize: 1/250

The value of each prize is already given, so we can multiply the probability of winning each prize by its value and sum the results to find the expected profit:

Expected profit = (1/250 x $240) + (1/250 x $130) + (1/250 x $120) + (1/250 x $70) - ($16)

Expected profit = $0.96

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The quadrilateral is a type of "kite", as the pair of adjacent angles are equal.

A quadrilateral known as a kite has four sides that may be grouped into two adjacent pairs of equal-length sides, and the diagonals cross each other at right angles. The quadrilateral is a polygon with four sides.

Thus, the quadrilateral is a type of "kite", as the pair of adjacent angles are equal.

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Answer: 2

Step-by-step explanation:  0 1 1 2 2 3 3  order

011 2 middle one  233

Answer:

0.16%

Step-by-step explanation:

Imagine you are a politician who wants to increase taxes in your city. You decide to conduct a survey among 450 residents to see how many of them are against your proposal. You know that the probability of finding someone who is against increasing taxes is 0.38. You hope that the survey will show that most people support your idea, or at least that the opposition is not too strong. However, when you get the results, you are shocked to see that more than 180 people are against increasing taxes. How unlucky are you? Well, let's do some math. This is a binomial probability problem. The probability of success (being against increasing taxes) is p = 0.38 and the number of trials (residents surveyed) is n = 450. The question asks for the probability of more than 180 successes, which is equivalent to the probability of at least 181 successes. Using a binomial calculator, the answer is approximately 0.0016 or 0.16%. That means that there is only a 0.16% chance of getting at least 181 people against increasing taxes in a sample of 450 residents. That's very rare and unlucky indeed! You might want to reconsider your proposal or find a better way to convince people that paying more taxes is good for them.

If she will begin paying off the loan in 15 months, . The amount she will she owe when she begins making payments is: C. $12,496.52, since Alma is responsible for the interest on the loan that accrues before she starts making payments.

The formula to calculate the future value of a loan with monthly compounding interest is:

FV = PV * (1 + r/12)^n

where:

PV = present value of the loan

r = annual interest rate

n = number of months

Using this formula, we can calculate the amount that Alma will owe when she begins making payments:

PV = $10,925

r = 10.8% APR = 0.9% monthly interest rate

n = 15 months

FV = $10,925 * (1 + 0.009)^15 = $12,496.52

Therefore, the answer is C. Alma is responsible for the interest on the loan that accrues before she starts making payments, and she will owe $12,496.52 when she begins making payments.

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The surface area of the figure, given the diameter of the base and the height, would be 353.43 square millimeters.

We can use the formula for the surface area of a cone:

Surface Area = πr² + πr√(r² + h²)

where r is the radius of the base and h is the height of the cone.

Since the diameter of the base is 9mm, the radius is half of that, or 4.5mm. The height of the cone is 20mm. Plugging these values into the formula, we get:

Surface Area = π(4.5)² + π(4.5)√(4.5² + 20²)

Surface Area = π(20.25) + π(4.5)√(436.25)

Surface Area = 353.43 millimeters²

Therefore, the surface area of the cone is approximately 353.43 square millimeters.

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Answer:

C. 15 + 18x ≥ 95

Step-by-step explanation:

Given: She has $15 saved so far

She earns $18.00 for each lawn she mows (each lawn she mows = x)

The inequality has to be greater or equal to $95.00, so she can have enough to buy a pair of shoes.

15 + 18x ≥ 95

The solution for the given quadratic equation is √27.

What is a quadratic equation?

A quadratic equation is any algebraic equation that can be written in the standard form as where variable 'x' is an unknown number and where a, b, and c are known values, with a ≠ 0.

We are given a quadratic equation in variable 'w' as 3[tex]w^{2}[/tex] + 9 = 90.

Now, on solving the given equation , we get

⇒ 3[tex]w^{2}[/tex] + 9 = 90

⇒ 3[tex]w^{2}[/tex] = 81

⇒ [tex]w^{2}[/tex] = 27

⇒ w = √27

Hence, the solution for the given quadratic equation is √27.

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The complete question has been attached below.

Since h(-x) = -h(x), the function is odd.

The given function is h(x) = 2x³ + 9x.

To determine whether the function is even, odd, or neither, we need to analyze the behavior of the function when x is replaced by -x:

h(-x) = 2(-x)³ + 9(-x) = -2x³ - 9x.

Since h(-x) = -h(x), the function is odd.

Odd functions have origin symmetry, which means that if you rotate the graph 180 degrees around the origin, it remains unchanged. In other words, the graph has symmetry with respect to the origin, which occurs when the point (x, y) on the graph implies the point (-x, -y) is also on the graph.

So, the function h(x) is odd and has origin symmetry.

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Answer:

[tex]S = \dfrac{v^2 - u^2}{2a}[/tex]

Step-by-step explanation:

We can solve for S using algebraic manipulation.

[tex]v^2 = u^2 + 2aS[/tex]

↓ subtract [tex]u^2[/tex] from both sides

[tex]v^2 - u^2 = 2aS[/tex]

↓ divide both sides by [tex]2a[/tex]

[tex]\dfrac{v^2 - u^2}{2a} = S[/tex]

[tex]\boxed{S = \dfrac{v^2 - u^2}{2a}}[/tex]

[tex]\sf \boxed{\sf S=\dfrac{v^{2}-u^{2} }{2a}}[/tex]

[tex]\sf v^{2} =u^{2} +2aS[/tex]

[tex]\sf v^{2}-u^{2} =u^{2} +2aS-u^{2}\\ \\v^{2}-u^{2} =2aS[/tex]

[tex]\sf \dfrac{v^{2}-u^{2} }{2a} =\dfrac{2aS}{2a} \\ \\ \\\dfrac{v^{2}-u^{2} }{2a} =S\\ \\ \\\boxed{\sf S=\dfrac{v^{2}-u^{2} }{2a}}.[/tex]

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The candy company's package can be modeled as a right circular cone with a height of 13 inches and a base diameter of 9 inches.

The circular base of the cone holds the chocolates, while the curved surface extends up to a point at the top. To calculate the surface area, we need to find the area of the circular base and the area of the curved surface. The formula for the area of a circle is pi times the radius squared, so the radius of the base is 4.5 inches.

The area of the base is pi times the radius squared, or approximately 63.62 square inches. The formula for the curved surface area of a cone is pi times the radius times the slant height, which is the square root of the height squared plus the base radius squared. Substituting the given values into the formula, the curved surface area is approximately 207.35 square inches. Thus, the approximate surface area of the package is the sum of the area of the base and the curved surface area, or approximately 271.97 square inches.

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Answer:

58

Step-by-step explanation: You add them all together

If Mariana needs to surround the garden with a stone-path, then she would need 20 feet of stone, Option (d) is correct.

The "Perimeter" of a rectangle is defined as the "total-length" of the outer boundary.

The length of the rectangle can be calculated as the difference between the x-coordinates of the vertices on the same vertical side.

In this case, the "x-coordinates" of vertices on same vertical side are 4 and -2.

So, the length of the rectangle is = 4 -(-2) = 6 feet.

Similarly, the width of rectangle is calculated as difference between "y-coordinates" of vertices on same horizontal side.

In this case, the "y-coordinates" of vertices on same horizontal side are 1 and -3.

So, the width of the rectangle is = 1 -(-3) = 4 feet,

To surround rectangle with a stone path, Marina need to add length of stone needed for the perimeter of rectangle, which is sum of all four sides.

The perimeter (P) is ⇒ P = 2(length + width),

Substituting the values,

We get,

⇒ P = 2(6 + 4) = 2(10) = 20 feet

Therefore, the correct option is (d).

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The given question is incomplete, the complete question is

Marina is drawing a plan for a new garden. The rectangle with the vertex (4,1) , (4,-3) , (-2,-3) , (-2,1)in the coordinate plane represents the garden, measured in feet. To surround the garden with a stone path, how many feet of stone does she need?

(a) 4 feet

(b) 6 feet

(c) 10 feet

(d) 20 feet

Answer:

20 feet because ik from experience

The equation of this circle in general form is: (x - 1)^2 + (y - 3)^2 = 36

To find the equation of a circle in general form, we need to complete the square for both x and y terms.

x^2 + y^2 - 2x - 6y - 26 = 0

First, we will complete the square for x terms:

x^2 - 2x + y^2 - 6y - 26 = 0

(x - 1)^2 - 1 + y^2 - 6y - 26 = 0

(x - 1)^2 + y^2 = 27

Now, we will complete the square for y terms:

(x - 1)^2 + (y - 3)^2 = 36

Therefore, the equation of this circle in general form is: (x - 1)^2 + (y - 3)^2 = 36

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Answer:

x2+y2−2x−6y−26=0

Step-by-step explanation:

Just took the test.

The 10,000 cubic yards of snow were spread evenly over the rectangular football field, the layer of snow would be approximately 1.56 yards deep.

To determine how many yards deep the layer of snow would be if spread evenly over the rectangular football field, we need to know the volume of the snow and the area of the football field.

First, let's find the area of the football field. Assuming standard dimensions for a football field, we have:

Length = 120 yards

Width = 53.3 yards

Area = Length x Width

Area = 120 yards x 53.3 yards

Area = 6,396 square yards

Now, let's find the volume of the snow. We are given that 10,000 cubic yards of snow were removed from the downtown area, so the volume is:

Volume = 10,000 cubic yards

Finally, to find the depth of the layer of snow, we can divide the volume of the snow by the area of the football field:

Depth = Volume / Area

Depth = 10,000 cubic yards / 6,396 square yards

Depth ≈ 1.56 yards

Therefore, if the 10,000 cubic yards of snow were spread evenly over the rectangular football field, the layer of snow would be approximately 1.56 yards deep.

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Answer:

Quadrant III

Step-by-step explanation:

The point has a negative x AND y value, so it would be in Quadrant III

Taking a look at the quadrant graph will help you.

The resulting histogram would show the distribution of the grades on the exam, with the bins and frequency of data points clearly displayed. The title, axis labels, and scales would provide context for the graph and make it easy to interpret the data.

In mathematics and computer science, a graph is a collection of points, called vertices or nodes, that are connected by lines, called edges or arcs. Graphs can be used to model and analyze relationships between objects or data, such as social networks, transportation systems, or web pages.

Here,

Part A:

The best graphical representation to display the given data is a histogram. A histogram is a bar graph-like representation of data that divides the data into intervals or bins and shows the frequency of each interval. Histograms are appropriate for displaying continuous data, which the grades on the exam can be considered as, and can also show the distribution of the data.

Part B:

To create a histogram of the given data, follow these steps:

Choose the number of bins or intervals. In this case, we can choose a reasonable number of bins, such as 6-8, to display the distribution of the grades.

Determine the range of the data. The lowest grade is 60 and the highest is 99, so the range is 99-60 = 39.

Calculate the bin size. The bin size is calculated by dividing the range by the number of bins. For example, if we choose 6 bins, the bin size would be 39/6 ≈ 6.5. Since it is difficult to have bins that are fractions of a point, we can round the bin size up to the nearest whole number to get a bin size of 7.

Create the bins. Starting from the lowest grade, create intervals or bins of size 7 that cover the range of the data. For example, the first bin would be 60-66, the second bin would be 67-73, and so on.

Count the frequency of data points that fall into each bin. For example, there are 2 data points in the first bin, 3 data points in the second bin, and so on.

Draw the histogram. On the horizontal axis, label and scale the bins. On the vertical axis, label and scale the frequency of data points in each bin. Draw a rectangle above each bin with a height equal to the frequency of data points in that bin.

Title: Grades on Recent 8th Grade Mathematics Exam

X-axis label: Grades

Y-axis label: Frequency

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By probability, the likelihood that a candidate chosen at random played an electric guitar and wore sequins is 0.3.

Using probabilities, one can determine how likely something is to occur.. It is represented by a number between 0 and 1, with 1 denoting a certain event and 0 an impossibility.

For instance, you can get either heads or tails when you flip a coin. There is only one way to get heads and two outcomes, hence the probability of receiving heads is 0.52.

The likelihood that a competitor played an electric guitar is 0.8, the likelihood that they were wearing sequins is 0.4, and the combined likelihood that they both played an electric guitar and wore sequins is 0.91.

The following formula can be used to determine the likelihood that a competitor chosen at random played an electric guitar and wore sequins:

P(A and B) equals P(A) times P(B|A)

where there are two events, A and B.

In this instance, A stands for the competitor who played an electric guitar, and B is for the person who wore sequins.

P(A) is known to equal 0.8. and P(B) = 0.4.

We also know that P(A or B) = 0.9.

Using the following equation to determine the likelihood of two events occurring together:

P(A or B) = P(A) + P(B) - P(A and B)

we can find P(A and B):

P(A and B)

           = 0.8 + 0.4 - 0.9

           = 0.3

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Answer:

x=162

Step-by-step explanation:

55+x-87+50=180

x+18=180

x=162

Answer:

e = - [tex]\frac{1}{2}[/tex] q + [tex]\frac{1}{3}[/tex]

Step-by-step explanation:

- 12e = 6q - 4 ( divide through by - 12 )

e = [tex]\frac{6}{-12}[/tex] q - [tex]\frac{4}{-12}[/tex] , that is

e = - [tex]\frac{1}{2}[/tex] q + [tex]\frac{1}{3}[/tex]

Value of matrix X=[tex]\left[\begin{array}{ccc}-31/135 & 1/45 \\14/135&1/45 \\ \end{array}\right][/tex]

Matrices are a type of mathematical object that consists of a rectangular array of numbers or other mathematical objects, such as variables, functions, or even other matrices. Matrices are widely used in mathematics, science, engineering, computer graphics, and other fields to represent and manipulate data, perform transformations, and solve systems of equations.

A matrix can be represented using a set of ordered pairs, where each pair represents a specific element of the matrix, and the position of the element is determined by its row and column indices. For example, a 3x3 matrix can be represented as:

| a11 a12 a13 |

| a21 a22 a23 |

| a31 a32 a33 |

 Given matrix;

A=[tex]\left[\begin{array}{ccc}-1&-2 \\2&2 \\ \end{array}\right][/tex]

B=[tex]\left[\begin{array}{ccc}-6&5 \\2&-1 \\ \end{array}\right][/tex]

C=[tex]\left[\begin{array}{ccc}-3&1 \\2&0 \\ \end{array}\right][/tex]

Solving the equation

(A-4B)X=C

[tex]\left[\begin{array}{ccc}-1&-2 \\2&2 \\ \end{array}\right][/tex]-  4 [tex]\left[\begin{array}{ccc}-6&5 \\2&-1 \\ \end{array}\right][/tex]X=[tex]\left[\begin{array}{ccc}-3&1 \\2&0 \\ \end{array}\right][/tex]

[tex]\left[\begin{array}{ccc}23&-22 \\-6&6 \\ \end{array}\right][/tex] X=[tex]\left[\begin{array}{ccc}-3&1 \\2&0 \\ \end{array}\right][/tex]

Taking the inverse and multiplying it with RHS,  we get

X=[tex]\left[\begin{array}{ccc}-31/135 & 1/45 \\14/135&1/45 \\ \end{array}\right][/tex]

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we are 95% confident that the true proportion of people with brown hair in the U.S. falls between 0.532 and 0.728.

To construct a 95% confidence interval for the proportion of people with brown hair in the U.S., we can use the following formula:

[tex]Confidence Interval = p± z \sqrt{\frac{p(1-p)}{n} }[/tex]

where p is the proportion of people with brown hair in our sample, z is the critical value for a 95% confidence level (which is 1.96), and n is the sample size.

In this case, our sample proportion is , and our sample size is 100. Plugging these values into the formula, we get:

[tex]Confidence Interval = 0.63  ± 1.96\sqrt{\frac{0.63(1-0.63)}{100} }[/tex]

Simplifying the expression inside the square root, we get:

[tex]Confidence Interval= 0.63 ± 0.098[/tex]

Therefore, the 95% confidence interval for the proportion of people with brown hair in the U.S. is:

[tex]\frac{63}{100}  = 0.63[/tex](0.532, 0.728)

This means that we are 95% confident that the true proportion of people with brown hair in the U.S. falls between 0.532 and 0.728.

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Answer:

Therefore, the answer is: The graph of the equation is a straight line passing through the points (0, -2), (7, 2), and (-7, -6).

Step-by-step explanation:

The given equation is y = (4/7)x - 2.

To graph this equation, we need to plot points on a coordinate plane. We can do this by choosing values of x and then finding the corresponding values of y using the equation.

Let's choose some values of x and find the corresponding values of y:

When x = 0, y = (4/7)(0) - 2 = -2

When x = 7, y = (4/7)(7) - 2 = 2

When x = -7, y = (4/7)(-7) - 2 = -6

We now have three points: (0, -2), (7, 2), and (-7, -6). We can plot these points on a coordinate plane and draw a line through them to get the graph of the equation.

Answer:18

Step-by-step explanation:

If each row behind the "row-A" has 6 more seats than row immediately in front of it, then there are (b) 46 seats in "Row-G".

The number of seats in "Row A" is = 10 seats,

We know that, each row behind the "row-A" has 6-more seats than the row immediately in front of it.

So, Number of seats in "Row-B" are =  10 + 6 = 16 seats,

Number-of-seats in "Row-C" are = 16 + 6 = 22 seats,

Number of seats in "Row-D" are = 22 + 6 = 28 seats,

Number of seats in "Row-E" are = 28 + 6 = 34 seats,

Number of seats in "Row-F" are = 34 + 6 = 40 seats,

So, According to the pattern,

Number of seats in "Row-G" will be = 40 + 6 = 46 seats.

Therefore, there are 46 seats in "Row-G", Option (b) is correct.

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If a large cube is made up of 27 equal-sized smaller cubes, and all faces of the large cube are painted, then the cubes on the interior of the large cube will not have any paint on any of their faces.

The large cube consists of 27 smaller cubes arranged in a 3x3x3 pattern. The smaller cubes on the exterior faces of the large cube will have some of their faces painted, while the smaller cubes on the interior will not have any of their faces painted.

To calculate the number of smaller cubes that will not have any paint on any of their faces, we need to subtract the smaller cubes on the exterior faces from the total number of smaller cubes in the large cube.

The number of smaller cubes on the exterior faces of the large cube can be calculated as follows:

There are 9 smaller cubes on each of the six faces of the large cube (3x3=9), for a total of 54 smaller cubes on the exterior faces.

So, the total number of smaller cubes in the large cube is 27, and the number of smaller cubes on the exterior faces is 54. Therefore, the number of smaller cubes that will not have any paint on any of their faces is:

27 - 54 = -27

Since we cannot have a negative number of cubes, the correct answer is 0. There will be 0 smaller cubes that will not have any paint on any of their faces.

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Answer:

9m^3

Step-by-step explanation:

since there is a square root remove it and find it square which is 9