I dont know if 1/2 + 1/3 equal 2/5

Answer: 36 inches

Step-by-step explanation:

The formula for the circumference of a circle is 2πr where r is the radius of the circle Therefore 2πr=72π so r=72/2 = 36 inches.

\(-2x+6=12\\2x=-6\\x=-3\)

The value of the trigonometric ratios  are;

sin A = 2/5

cos A = 3/5

tan A = 2/3

It is important to note that there are six different trigonometric identities and their ratios.

We have;

From the diagram shown, we have;

sin θ = opposite/hypotenuse

cos θ = adjacant/hypotenuse

tan θ = opposite/adjacent

Then,

sin A = 6/15 = 2/5

cos A = 9/15 = 3/5

tan A = 6/9 = 2/3

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The value of the trigonometric ratios  are;

sin A = 2/5

cos A = 3/5

tan A = 2/3

It is important to note that there are six different trigonometric identities and their ratios.

We have;

From the diagram shown, we have;

sin θ = opposite/hypotenuse

cos θ = adjacant/hypotenuse

tan θ = opposite/adjacent

Then,

sin A = 6/15 = 2/5

cos A = 9/15 = 3/5

tan A = 6/9 = 2/3

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The area of the shaded part of the figure is; 114.3ft²

From the task content:

The area of the square is;

The area of the quarter circle is;

A(quarter circle) = 50.3ft².

Ultimately, the area of the shaded part of the figure is; 50.3ft² + 64ft² = 114.3ft².

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Answer:

13.76

Step-by-step explanation:

I got it right :)

Answer:

Well, the smallest successive composites with gap 17, 73, 2, and 19 would have to be:

1. $341 = 11 \times 31$

2. $458 = 2 \times 299$

3. $460 = 2^2 \times 5 \times 23$

4. $479 = 13 \times 37$

The z-statistic test was conducted to determine the Deviation of RPM, ASM, and LF from the mean. The test indicates that RPM, ASM, and LF significantly deviate from the mean.

Report on the Analysis of American Airlines (Domestic) PerformanceThe quantitative analysis focused on three variables- load factors, revenue passenger miles, and available seat miles for American Airlines.

The Bureau of Transportation Statistics data for domestic flights from January 2006 to December 2012 was retrieved for the analysis. The quantitative analysis also focused on finding critical statistical values like mean, median, mode, standard deviation, variance, and minimum/maximum variables. The results of the data are summarized in Table 2. Revenue Passenger Miles (RPM) mean is 6,624,897, the median is 6,522,230, and mode is NONE. The minimum is 5,208,159 and the maximum is 8,277,155. The standard deviation is 720,158.571, and the variance is 518,628,367,282.42.

Load Factors (LF) mean is 82.934, the median is 83.355, and mode is 84.56. The minimum is 74.91, and the maximum is 89.94. The standard deviation is 3.972, and the variance is 15.762. The Available Seat Miles (ASM) mean is 7,984,735, the median is 7,753,372, and mode is NONE. The minimum is 6,734,620, and the maximum is 9,424,489. The standard deviation is 744,469.8849, and the variance is 554,235,409,510.06.Figure 1 above displays the performance of American Airlines (Domestic).

The mean RPM is 7,984,735, and the linear regression line is y = 50584x - 2.53E+8. The linear regression line indicates a positive relationship between RPM and year, with a coefficient of determination, R² = 0.6806. A coefficient of determination indicates the proportion of the variance in the dependent variable that is predictable from the independent variable. Therefore, 68.06% of the variance in RPM is predictable from the year. A one-way ANOVA analysis of variance test was conducted to determine the equality of means of three groups of variables; RPM, ASM, and LF. The null hypothesis is that the means of RPM, ASM, and LF are equal.

The alternative hypothesis is that the means of RPM, ASM, and LF are not equal. The level of significance is 0.05. The ANOVA results indicate that there is a significant difference in means of RPM, ASM, and LF (F = 17335.276, p < 0.05). Furthermore, a post-hoc Tukey's test was conducted to determine which variable means differ significantly. The test indicates that RPM, ASM, and LF means differ significantly.

The skewness test was conducted to determine the symmetry of the distribution of RPM, ASM, and LF. The test indicates that the distribution of RPM, ASM, and LF is not symmetrical (Skewness > 0).

Additionally, the z-statistic test was conducted to determine the deviation of RPM, ASM, and LF from the mean. The test indicates that RPM, ASM, and LF significantly deviate from the mean.

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(b) The probability that the call is not for medical assistance = 0.37

(c) The probability that two successive calls will both be for medical assistance = 0.3969

(d) The probability that the first is for medical assistance and the second is not for medical assistance = 0.2331

(e) The probability that exactly one of the next two calls is going to be for medical assistance = 0.4662

The probability of an event is the proportion of favourable outcomes to all other possible outcomes. The symbol x can be used to denote how many successful outcomes there were in an experiment with 'n' outcomes. The formula below can be used to determine a given event's probability:

Probability (Event) = Positive Results/Total Results

                                 = x/n

Given P (call for medical assistance) = 0.63

This means that out of all incoming calls to the fire station, the probability that the call is for medical assistance is 0.63 or 63%. The complement of this event, which is the probability that an incoming call is NOT for medical assistance, is:

P (Not Medical Assistance) = 1 - P (Medical Assistance)

                                            = 1 - 0.63

                                            = 0.37

Now, assuming that successive calls are independent of one another, the probability that two successive calls will both be for medical assistance will be:

P (2 calls for medical assistance)

= 0.63 × 0.63

= 0.3969

The probability that the first is for medical assistance and the second is not for medical assistance will be:

P (1st for medical assistance × 2nd for not medical assistance)

= 0.63 × 0.37

= 0.2331

The probability that exactly one of the next two calls is going to be for medical assistance will be:

P (Exactly 1 call for medical assistance)

= (0.63×0.37) + (0.63×0.37)

= 0.2331 + 0.2331

= 0.4662

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Answer:

\(x=11\)

Step-by-step explanation:

Angle EFB = 180 - 147 = 33 (Angles on a straight line add up to 180 degrees)

Angle FEB = 180 - 4x (Angles on a straight line add up to 180 degrees)

Since the angles in a triangle add up to 180 degrees ,

\(33+(180-4x)+x=180\)

Remove brackets:

\(33+180-4x+x=180\)

Add/Subtract:

\(213-3x=180\)

Subtract 213 from both sides:

\(213-3x-213=180-213\)

\(-3x=-33\)

Divide both sides by -3:

\(\frac{-3x}{-3}=\frac{-33}{-3}\)

\(x=11\)

Answer:

\(P(B) = 0.55\)

Step-by-step explanation:

Given

\(P(A\ or\ B) = 0.8\)

\(P(A) = 0.4\)

\(P(A\ and\ B) = 0.15\)

Required

Find P(B)

In probability, we have:

\(P(A\ or\ B) = P(A) + P(B) - P(A\ sd B)\)

Substitute values

\(0.8 = 0.4 + P(B) - 0.15\)

Collect Like Terms

\(P(B) = 0.8 - 0.4 + 0.15\)

\(P(B) = 0.55\)

3.375

hope it helps...!!

Answer:

Ángulo de 125 grados Cómo se llama

Este ángulo es obtuso porque 120 es un número mayor que 90 y menor que 180. Es decir, la amplitud de este ángulo mide entre los 90º y los 180º: 90º < 120º < 180º.

Step-by-step explanation:

On solving the provided question, we can say that -  here in graph we have on solving equation  \(2x^2+ 9y^2 \\\) = \(8 + 9 = 17\)

An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.

here,

from graph, x= 2

y = 1

\(2x^2+ 9y^2 \\\)

\(8 + 9 = 17\)

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The diameter of the tin in the picture is  \(3d/5\) where 'd' is the diameter of the tin in reality.

Determining the diameter of tin:

Since there is no indication of dimensions, represent the diameter with a variable 'd' and find the diameter of the tin according to the given condition in the problem.

Here we have assumed that the diameter of the tin is 'd' in reality and the diameter of the tin picture can be calculated as given below.  

Here we have

A ricoffy tin container with no dimensions indicated

Let d and h be the diameter and height of the tin

Given that the container is 2/5 times smaller than d

then the diameter of the tin in the picture \(= d - 2/5(d)\)

\(= [5d - 2d]/5 = 3d/5\)

Therefore, The diameter of the tin in the picture is  \(3d/5\) where 'd' is the diameter of the tin in reality.

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Answer:

360

Step-by-step explanation:

To solve to volume you need to times the width, length, height. so 3 times 6 is 18 and 18 times 20 is 360.

The y-coordinate of -3f(x-1) when x = 0 is -63

From the question, we have the following parameters that can be used in our computation:

The table of values

So, we have

-3f(x - 1)

When x = 0, we have

y = -3f(0 - 1)

This gives

y = -3f(-1)

From the table, we have

y = -3 * 21

Evaluate

y = -63

Hence, the y-coordinate is -63

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The base area of the prism is 2x² + 5x - 18

From the question, the given parameters are

Volume = 2 x cubed + 9 x squared minus 8 x minus 36

Height =  x + 2

Rewrite properly as

Volume = 2x³ + 9x² - 8x - 36

Height =  x + 2

The base area is calculated as

Base area = Volume/Height

Using the synthetic division, we have

Set the divisor to 0

x + 2 = 0

This gives

x = -2

So, we have the representation to be

-2 | 2   9  - 8  - 36

Write out 2

So, we have

-2 | 2   9  - 8  - 36

     2

Multiply 2 and -2

This gives

-2 | 2   9  - 8  - 36

          -4

     2

So, we have

-2 | 2   9  - 8  - 36

          -4

     2    5

Repeat the process

So, we have

-2 | 2   9  - 8  - 36

          -4  -10

     2    5   -18

Repeat the process

So, we have

-2 | 2   9  - 8  - 36

          -4  -10   36

     2    5   -18    0

This means that

Base area = 2x² + 5x - 18

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Answer:

perimeter

Step-by-step explanation:

Perimeter is the distance around a two dimensional shape, a measurement of the distance around something; the length of the boundary.

Answer:

(-1,3)

Step-by-step explanation:

Elimination makes solving for the system of equations much easier if it is the faster route. In this case, it is already done for you, and no multiplication is required.

First, we want to eliminate the x values completely because they are opposites and therefore cancel out. Next, you want to add the y-values and sum (20 and 10) so that you get the new equation \(10y=30\). To isolate you need to divide by 10 on each side which will give you \(y=3\).

Now that you have your y-value, you can plug in your value to either of the equations and find what x is. I will use the equation 4x + 8y = 20 to solve for x. We first want to substitute in our y-value so that we get \(4x+8(3)=20\) which is simplified to \(4x+24=20\) now subtract by 24 on both sides to get 4x by itself to get \(4x=-4\). Lastly, isolate x by dividing by 4 on each side to get \(x=-1\)

Answer:

11

Step-by-step explanation:

we know this because there are 5 people saying they have 3 and 6 people saying they have between 4-7

The numerical value of x in the similar pair of triangle is 10.

A ratio is simply the relation between two amounts showing how many times a value is contained within another value.

From the diagram,

Side A of the small triangle = 10

Side B of the small triangle = x + 2

Side A of the Big triangle = 10 + x

Side B of the big triangle = x + 14

Hence;

Ratio of Side A to Side B of the small triangle = 10 / x + 2

Ratio of Side A to Side B of the Big triangle = 10 + x / x + 14

Since the triangle area similar, equate the two ratio and solve for x.

10 / ( x + 2 ) = ( 10 + x ) / ( x + 14 )

Cross multiply

10( x + 14 ) = ( 10 + x )( x + 2 )

Expand using FOIL method

10x + 140 = 10x + 20 + x² + 2x

10x + 140 = x² + 12x + 20

x² + 12x + 20 = 10x + 140

x² + 12x + 20 - 10x - 140 = 0

x² + 2x - 120 = 0

Factor the left side of the equation

( x - 10 )( x + 12 ) = 0

Hence;

x - 10 = 0 and x + 12 = 0

x = 10 and x = -12

Since the dimension of the triangle cannot be negative,

x = 10

Therefore, the value of x is 10.

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Answer:

-5

Step-by-step explanation:

Using the equation -30/xy, plug in given values for x and y

-30 / (-3 * -2)

Multiply Denominator

-30 / 6

Divide

-5

The graph of the feasible region is attached

From the question, we have the following parameters that can be used in our computation:

\(\left\{ \begin{array}{lr} y + 7x \ge 10 \\ 8y + 2x \ge 20 \\ y + x \ge 4 \\ y + x\le 10 \\ x \ge 0 \\ y \ge 0\end{array}\)

To plot the graph of the feasible region, we plot each inequality in the domain x ≥ 0 and y ≥ 0

Using the above as a guide, the graph is attached

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Answer:

To convert euros to pounds, we have to multiply the amount in euros by the exchange rate. So, the sunglasses cost 90 * 0.875 = 78.75 pounds.

To use a suitable approximation, we can round the exchange rate to the nearest hundredth, which is 0.88. This makes the calculation easier and gives a close estimate of the actual value.

Using the rounded exchange rate, the sunglasses cost 90 * 0.88 = 79.2 pounds.

We can see that both the exact and the approximate values are greater than 70 pounds, so Elyas is wrong. The sunglasses cost more than 70 pounds

Step-by-step explanation:

Answer: y < 2

Step-by-step explanation:

The word problem for given equation is : When 3 is multiplied with x and subtracted by 2 multiplied by y , the number obtained is 13. Solve the equation for x =1 .

The complete equation will be 3x - 2y =13

When an algebraic expression is equated by an equal sign to a constant or any other algebraic expression , then an equation is formed .

The equation given in the question is

3x-2y =13

When 3 is multiplied with x and subtracted by 2 multiplied by y , the number obtained is 13. Solve the equation for x =1 .

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Answer:

Step-by-step explanation:

The line segment joining two points P and Q can be represented by the equation of a straight line in the form y = mx + b, where m is the slope and b is the y-intercept.

To find the equation of the line, we need to find the slope, which can be calculated using the formula:

m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the points P and Q, respectively.

In this case, the coordinates are:

P = (-3, 2) and Q = (5, 7)

So, the slope is:

m = (7 - 2) / (5 - (-3)) = 5 / 8

Next, we can use either of the points to find the y-intercept. Let's use point P:

b = y - mx, where y and x are the y and x coordinate of the point, respectively.

In this case,

b = 2 - m * (-3) = 2 - (5/8) * (-3) = 2 + 15/8 = 89/8

So, the equation of the line joining the points P and Q is:

y = (5/8)x + 89/8

Now, to find the point where the line crosses the y-axis, we need to find the x-coordinate of the point where y = 0.

So, we have:

0 = (5/8)x + 89/8

Solving for x, we get:

x = -(89/8) / (5/8) = -89 / 5

This means that the line crosses the y-axis at the point (-89/5, 0). To find the ratio in which the line segment is divided by the y-axis, we need to find the ratio of the distance from the y-axis to point P to the distance from the y-axis to point Q.

Let's call the point of intersection with the y-axis R. The distances are then:

PR = (3, 2) and QR = (5 - (-89/5), 7)

The ratio of the distances is then:

PR / QR = (3, 2) / (5 - (-89/5), 7) = 3 / (5 + 89/5) = 3 / (94/5) = 15/47

So, the line segment joining the points P and Q is divided by the y-axis in the ratio 15:47.

Using the Chain Rule, we have: dy/dx = f'(g(x)) * g'(x) = 1 * 1 = 1.The derivative of y with respect to x is 1.

When we compose a function, it may be possible to write it in a variety of different ways. Differentiating such functions can result in different derivatives, but the Chain Rule indicates that the derivatives of the compositions should be the same regardless of how the function is written, if the function is continuous and differentiable.For instance, consider the function f(x) = sin(x²). It can be written as f(g(x)) where g(x) = x² and f(x) = sin(x). Furthermore, it can be written as f(h(x)) where h(x) = x² and f(x) = sin(x). These are both compositions of functions, but they are different compositions that lead to different derivatives.However, if the function is a composite of differentiable functions, the Chain Rule tells us that the derivative of a composite function is the derivative of the outer function multiplied by the derivative of the inner function.

To find dy/dx if y = x using the Chain Rule with y as a composite of the following functions, we must first rewrite y as a composite function: y = f(g(x)) where g(x) = x and f(x) = x. This composite function can be written in a variety of different ways, such as y = f(h(x)) where h(x) = x and f(x) = x, or y = f(k(x)) where k(x) = x and f(x) = x. However, regardless of how we write it, the Chain Rule tells us that the derivative of y is equal to the derivative of the outer function (f(x) = x) multiplied by the derivative of the inner function (g(x) = x).

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Answer:

\(\int {7 \sec(\theta) } \, d\theta = 7\ln(\sec(\theta) + \tan(\theta)) + c\)

Step-by-step explanation:

The question is not properly formatted. However, the integral of \(\int {7 \sec(\theta) } \, d\theta\) is as follows:

\(\int {7 \sec(\theta) } \, d\theta\)

Remove constant 7 out of the integrand

\(\int {7 \sec(\theta) } \, d\theta = 7\int {\sec(\theta) } \, d\theta\)

Multiply by 1

\(\int {7 \sec(\theta) } \, d\theta = 7\int {\sec(\theta) * 1} \, d\theta\)

Express 1 as: \(\frac{\sec(\theta) + \tan(\theta) }{\sec(\theta) + \tan(\theta)}\)

\(\int {7 \sec(\theta) } \, d\theta = 7\int {\sec(\theta) * \frac{\sec(\theta) + \tan(\theta) }{\sec(\theta) + \tan(\theta)}} \, d\theta\)

Expand

\(\int {7 \sec(\theta) } \, d\theta = 7\int {\frac{\sec^2(\theta) + \sec(\theta)\tan(\theta) }{\sec(\theta) + \tan(\theta)}} \, d\theta\)

Let

\(u = \sec(\theta) + \tan(\theta)\)

Differentiate

\(\frac{du}{d\theta} = \sec(\theta)\tan(\theta) + sec^2(\theta)\)

Make \(d\theta\) the subject

\(d\theta = \frac{du}{\sec(\theta)\tan(\theta) + sec^2(\theta)}\)

So, we have:

\(\int {7 \sec(\theta) } \, d\theta = 7\int {\frac{\sec^2(\theta) + \sec(\theta)\tan(\theta) }{u}} \,* \frac{du}{\sec(\theta)\tan(\theta) + sec^2(\theta)}\)

Cancel out \(\sec(\theta)\tan(\theta) + sec^2(\theta)\)

\(\int {7 \sec(\theta) } \, d\theta = 7\int {\frac{1}{u}} \,du}}\)

Integrate

\(\int {7 \sec(\theta) } \, d\theta = 7\ln(u) + c\)

Recall that: \(u = \sec(\theta) + \tan(\theta)\)

\(\int {7 \sec(\theta) } \, d\theta = 7\ln(\sec(\theta) + \tan(\theta)) + c\)

Answer:

\(\huge\boxed{\sf 18^{-3}}\)

Step-by-step explanation:

\(\displaystyle \frac{18^4}{18^7}\)

So, the expression becomes:

= \(18 ^{4-7}\)

= \(18^{-3}\)

\(\rule[225]{225}{2}\)