16 .Write an equation that represents the statement
below.
"Twelve less than a number, x, is 18."

The value of c such that the function f is a probability density function is 2

The density function is given as:

f(x) = cxe^(−x^2) if x ≥ 0

f(x) = 0 if x < 0.

We start by integrating the function f(x)

∫f(x) = 1

This gives

∫ cxe^(−x^2) = 1

Next, we integrate the function using a graphing calculator.

From the graphing calculator, we have:

c/2 * (0 + 1) = 1

Evaluate the sum

c/2 * 1 = 1

Evaluate the product

c/2 = 1

Multiply both sides of the equation by 2

c = 2

Hence, the value of c such that the function f is a probability density function is 2

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Answer:

2500

Step-by-step explanation:

1×10^6/10=10%

=1×10^5 then divide by 10 will give 10

=1×10^4 divide by 4 to get 2.5 of the original 10%

=2.5×10^3

=2500

Total sold at 4 games: 523 + 604 + 544 + 596 = 2,267

Mean is the average, multiply mean by total games to find total sold:

573 x = 5 = 2,865 total

Now subtract for the amount sold at the 5th game:

2865 - 2267 = 598 hotdogs sold at 5th game.

Answer:

Step-by-step explanation:

b·b·b= b³

Answer:

4.472135955

Step-by-step explanation:

Answer:

i think it's 1.7082039325

Step-by-step explanation:

One example of a nonempty subset u of R^2 such that u is closed under scalar multiplication, but u is not a subspace of R^2, is the set u = {(x, y) | x, y are rational numbers}.

This set is closed under scalar multiplication as if a and (x,y) are in u, a*(x,y) will also be in u because rational numbers are closed under multiplication.

A subset can be described with different properties, one of them is closure, a subset U is closed under an operation if the operation is applied to any two elements of U, and the result is also an element of U.

In mathematics, a subset is a set that is completely contained within another set. It is defined as a set U that is a part of a set S, such that every element of U is also an element of S. The notation used to indicate that U is a subset of S is U ⊆ S.

However, this set u is not a subspace of R^2 because it doesn't contain the zero vector (0,0) and it doesn't close under addition, as the sum of two rational numbers may not be a rational number.

Therefore, One example of a nonempty subset u of R^2 such that u is closed under scalar multiplication, but u is not a subspace of R^2, is the set u = {(x, y) | x, y are rational numbers}.

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The probability of rainfall actually occurring tomorrow is 0.3465. The correct answer is therefore 0.3465.

To solve this problem, you can use Bayes' Theorem. Bayes' Theorem is a way to calculate the probability of an event occurring based on prior knowledge of conditions that might be related to the event.

In this case, we are trying to find the probability of rainfall occurring tomorrow, given that it has been predicted. Let's call this probability P(R|P), where R is the event of rainfall occurring and P is the event of rain being predicted.

According to the problem statement, the probability of rain occurring on any given day during the summer is 2/10, or P(R) = 0.2.

The probability of rain not occurring is 1 - P(R) = 0.8.

The probability of rain being predicted, given that it does rain, is 0.7, or P(P|R). The probability of rain being predicted, given that it does not rain, is 0.33, or P(P|¬R).

Using Bayes' Theorem, we can calculate the probability of rain occurring tomorrow as follows:

P(R|P) = [P(P|R) * P(R)] / [P(P|R) * P(R) + P(P|¬R) * P(¬R)]

Substituting in the values from the problem statement, we get:

P(R|P) = [0.7 * 0.2] / [0.7 * 0.2 + 0.33 * 0.8]

Simplifying this expression gives us:

P(R|P) = 0.3465

So the probability of rainfall actually occurring tomorrow is 0.3465.

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Answer:

n= 21/2   or 10.5

Step-by-step explanation:

isolate the variables by dividing each side by factors that don't contain the variable.

:)

Answer:

\(\bold{f(x) = 375(2.5)^{-x}+ 33}\)

Step-by-step explanation:

An exponential function of form f(x) = ba^(-x) + c has a horizontal asymptote of y = c as x approaches infinity, and a y-intercept of (0, b + c). We can use the given information to set up a system of equations and solve for the unknowns.

The horizontal asymptote is given as y = 33, so we have:

c = 33

The y-intercept is given as (0, 408), so we have:

b + c = 408

Substituting c = 33, we get:

b + 33 = 408

b = 375

So the function we're looking for is of the form:

\(\bold{f(x) = 375a^{-x}+ 33}\)

To find a, we use the fact that the function passes through P(2, 93):

93 = 375a^(-2) + 33

60 = 375a^(-2)

a^2 = 375/60

a^2 = 6.25

a = \(\sqrt{6.25 } =2.5\)

Therefore, the exponential function that satisfies the given conditions is:

\(\bold{f(x) = 375(2.5)^{-x}+ 33}\)

Answer:

The slope is 2.5

Step-by-step explanation:

y = 2.5x + 5   or

y =   5/2x + 5

When x=0, y = 5

When y=0, x = -2

Answer:

slope  = 5/2

\(y = \frac{5}{2}x + 5\)

Step-by-step explanation:

(x₁ ,y₁) = (-4 , -5)    & (x₂, y₂) = (2 , 10)

\(Slope=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\\\=\frac{10-[-5]}{2-[-4]}\\\\=\frac{10+5}{2+4}\\\\=\frac{15}{6}\\\\=\frac{5}{2}\\\\= 2.5\)

m = 5/2 ;  (-4 , -5)

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

                \(y - [-5] = \frac{5}{2}*(x - [-4])\\\\y + 5 = \frac{5}{2}(x + 4)\\\\y + 5 =\frac{5}{2}x + \frac{5}{2}*4\\\\y + 5 = \frac{5}{2}x + 5*2\\\\y + 5 = \frac{5}{2}x + 10\\\\ y = \frac{5}{2}x + 10 - 5\\\\ y = \frac{5}{2}x + 5\)

Answer: 1/5

Step-by-step explanation:

given data;

chances of winning = 1/3

chances of losing = 1/3

chances of tying in a given round = 1/3

solution:

probability that you would win atleast 2 in any 3 matches without a tied match is

1/3 /  ( 2 - 1/3 )

= 1/3 / 5/3

= 1/5

the probability of winning 2 of 3 games without a tie is 1/5

Answer:

the value of x is 18

Step-by-step explanation:

4x+17+91=180(Liner pair)

4x=180-108

4x=72

x=72/4

so,x=18

Answer:

GHJKL

Step-by-step explanation:

VBNM,

Face Value of Promissory Note: $1,200.00

1. Determine the interest value of the promissory note.

  Interest = Maturity Value - Principal Amount

  Interest = $1,190.03 - Principal Amount

2. Calculate the interest rate for four months.

  Interest Rate = (Interest / Principal Amount) * (12 / Number of Months)

  50% p.a. = (Interest / Principal Amount) * (12 / 4)

3. Substitute the calculated interest rate into the equation and solve for the Principal Amount.

  0.5 = (Interest / Principal Amount) * 3

  Principal Amount = Interest / (0.5/3)

4. Substitute the given maturity value into the equation and solve for the Principal Amount.

  $1,190.03 = Principal Amount + Interest

  Principal Amount = $1,190.03 - Interest

5. Equate the Principal Amounts obtained from steps 3 and 4, and solve for the interest value.

  Interest / (0.5/3) = $1,190.03 - Interest

  Interest = $1,190.03 * (0.5/3) / (1 + 0.5/3)

6. Substitute the calculated interest value into step 2 and solve for the Principal Amount.

  50% p.a. = (Interest / Principal Amount) * (12 / 4)

  Principal Amount = Interest / (0.5/3) * (4 / 12)

7. The Principal Amount obtained from step 6 is the face value of the promissory note.

  Face Value = Principal Amount

Therefore, the face value of the four-month promissory note dated May 20, 2018, with a 70 50% p.a. interest rate and a maturity value of $1,190.03 is $1,200.00.

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At any time, there are about 29.4 users on the developer's site

Little's law states that: If users log on to a website at an average rate of

r users per minute and each stays on the site for an average time of T minutes, the average number of users on the website, N, at any one

time is given by the formula N= rT

Given that:

196 users per hour log on to a site

Each user spends an average of 9 minutes on the site

This implies:

r = 196 users per hour =  196/60  = 49/15 users per minute

T = 9 minutes

N = rt

N = 49/15 × 9

N = 29.4 users

Therefore, at any time, there are about 29.4 users on the developer's site

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When substituting y = 11 into the equation y = 1/2(x) - 25, we find that x = 72, confirming that (23.5, 11) is a valid point of intersection.

Given that x is 23.5, it is required to prove that it is an intersection point for the equation y = 1/2(x) - 25 when y is equal to 11.

The equation is given as y = 1/2(x) - 25

When y = 11, we can substitute the value of y in the equation to obtain 11 = 1/2(x) - 25

This can be simplified as 11 + 25 = 1/2(x)36 = 1/2(x)

On solving, x = 72Thus, when y is equal to 11 and x is equal to 72, the given point of intersection is valid.

Therefore, it can be concluded that x = 23.5 is a point of intersection for the equation y = 1/2(x) - 25 when y is equal to 11.

In summary, when given an equation with two variables, we can find the point of intersection by setting one of the variables to a given value and solving for the other variable. In this case, when y is equal to 11, we can solve for x and obtain the point of intersection as (72,11).

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The area of the blue-shaded region is 19.95 m²

Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.

Given that, a rectangle with length 14 m, and diagonal 15.5 m, a parallelogram has been cut out of it, we need to find the area remaining,

Using the Pythagoras theorem,

15.5² = 14²+w² [width]

w² = 240.25-196

w² = 44.25

w = 6.65

Therefore, the width of the rectangle is 6.65 m

That mean, the height of the parallelogram is 6.65 m,

The area of the blue-shaded region, is calculated by subtracting the area of the parallelogram by the area of the rectangle,

Area of the remaining region = 14×6.65-11×6.65

= 6.65(14-11) = 6.65×3

= 19.95 m²

Hence, the area of the blue-shaded region is 19.95 m²

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Answer:

Generally the constraint that sets next week are shown below

Generally the constrain that sets next week maximum production of connecting rod for 4 cylinder  to  W_4 or  0 is  

     \(x_4 \le W_4 *  s_4\)

    \(x_4 \le 5000 *  s_4\)

Generally the constrain that sets next week maximum production of connecting rod for 6 cylinder  to  W_6 or  0  is  

     \(x_6 \le W_6 *  s_6\)

     \(x_6 \le 8,000 *  s_6\)

Generally the constrain that limits the production of connecting rods  for both 4 cylinder and 6 cylinders  is

     \(x_4 \le W_4 *  s_6\)

=>   \(x_4 \le 5000 *  s_6\)

     \(x_4 \le W_6 *  s_4\)

=>    \(x_4 \le 8000 *  s_4\)

     \(s_4 + s_6 = 1\)

The minimum cost of production for next week is  

   \(U  =  M_4 *  x_4 + M_6 * x_6 + C_4 * s_4 + C_6 * s_6\)

=>  \(U  =  13x_4 + 16x_6 + 2000 s_4 + 3500 s_6\)

Step-by-step explanation:

The cost for the four cylinder production line is  \(C_4 =  \$2,100\)

The cost for the six cylinder production line is  \(C_6 = \$3,500\)

The manufacturing cost for each four cylinder is  \(M_4= \$13\)

 The manufacturing cost for each six cylinder is \(M_6= \$16\)

  The weekly production capacity for 4 cylinder connecting rod is \(W_4 = 5,000\)

   The weekly production capacity for 6 cylinder connecting rod is \(W_6 = 8,000\)

Generally the constraint that sets next week are shown below

Generally the constrain that sets next week maximum production of connecting rod for 4 cylinder  to  W_4 or  0 is  

     \(x_4 \le W_4 *  s_4\)

    \(x_4 \le 5000 *  s_4\)

Generally the constrain that sets next week maximum production of connecting rod for 6 cylinder  to  W_6 or  0  is  

     \(x_6 \le W_6 *  s_6\)

     \(x_6 \le 8,000 *  s_6\)

Generally the constrain that limits the production of connecting rods  for both 4 cylinder and 6 cylinders  is

     \(x_4 \le W_4 *  s_6\)

=>   \(x_4 \le 5000 *  s_6\)

     \(x_4 \le W_6 *  s_4\)

=>    \(x_4 \le 8000 *  s_4\)

     \(s_4 + s_6 = 1\)

The minimum cost of production for next week is  

   \(U  =  M_4 *  x_4 + M_6 * x_6 + C_4 * s_4 + C_6 * s_6\)

=>  \(U  =  13x_4 + 16x_6 + 2000 s_4 + 3500 s_6\)

Answer:

A.

Step-by-step explanation:

Let's think of this as a clock.  We can see that the 2 lines start in the same place, around 3 o'clock.  Next, one of the line segments shifts down to around 6 o'clock.  Next, it shifts to about 9 o'clock.  Logically, the next step (in a clock) would be 12 o'clock, making A the correct choice.

We can also just use a regular circle, with one of the line segments moving 90 degrees each time.

Hope this helps! :)

Based on the intersecting secants theorem:

a. CG*CE = CH*CD

b. length of DH = 10 in.

When an exterior point is formed by two secant segments to a circle, the product of the length of one secant segment and its external segment will always be equal to the product of the length of the other secant segment and its external segment, according to the intersecting secants theorem.

a. Based on the intersecting secants theorem, the relationship that describes the lengths of the segments formed by the two secants is:

CG*CE = CH*CD

b. Given the following lengths:

CG = 3 in, CH = 2 in, and GE = 5 in

CE = CG + GE = 3 + 5 = 8 in.

CD = CH + DH = 2 + DH

Substitute into CG*CE = CH*CD:

3*8 = 2*(2 + DH)

24 = 4 + 2DH

24 - 4 = 2DH

20 = 2DH

20/2 = DH

DH = 10 in.

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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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Answer:

\(\huge\boxed{\sf \frac{2\sqrt{7}-4 }{3}}\)

Step-by-step explanation:

This is a rationalizing denominator question.

\(= \displaystyle \frac{2}{2+\sqrt{7} } \\\\Multiply \ and \ divide \ by \ conjugate \ 2 - \sqrt{7} \\\\= \frac{2}{2+\sqrt{7} } \times \frac{2-\sqrt{7} }{2-\sqrt{7} } \\\\\underline{\sf Using \ formula:}(a+b)(a-b)=a^2-b^2\\\\= \frac{2(2-\sqrt{7}) }{(2)^2-(\sqrt{7})^2 } \\\\= \frac{4-2\sqrt{7} }{4-7} \\\\= \frac{4-2\sqrt{7} }{-3} \\\\= \frac{-(4-2\sqrt{7}) }{3} \\\\= \frac{2\sqrt{7}-4 }{3} \\\\\rule[225]{225}{2}\)

To find the exact value of (7π/6) using the unit circle, locate the angle (π/6) on the unit circle in the second quadrant, determine the coordinates, and adjust the y-coordinate to be negative. The final answer is (√3/2, -1/2). This answer is obtained by understanding the reference angle and using the coordinates of the point where the angle intersects the unit circle.

To find the exact value of (7π/6) using the unit circle, follow these steps:

1. Start by understanding the reference angle. The reference angle for (7π/6) is (π/6).

2. Locate the angle (π/6) on the unit circle. This angle lies in the second quadrant.

3. Determine the coordinates of the point where the angle intersects the unit circle. For (π/6), the x-coordinate is √3/2 and the y-coordinate is 1/2.

4. Since (7π/6) lies in the second quadrant, the x-coordinate will remain the same, but the y-coordinate will be negative. Therefore, the coordinates for (7π/6) are (√3/2, -1/2).

5. The exact value of (7π/6) is (√3/2, -1/2).

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Answer:

60³

Step-by-step explanation:

Hi again.

This time we are working with a triangular prism which is a bit trickier than a rectangular prism but it is still pretty easy once you know the formula.

The formula for a triangular prism is :

V = 1/2 x b x h x l

Or in full terms :

Volume = 1/2 x Base x Height x Length

So basically we are going to plug in the base , height, and width like we did before but this time at the end we are going to divide it in half.

So like last time, lets look at what we are given :

Base = 5

Height = 3

Length = 8

And now we put these numbers into the formula :

Volume = 1/2 x Base x Height x Length

Volume = 1/2 x 5 x 3 x 8

Lets save the 1/2 for last and do the others first.

So we can do 5 x 3 and get 15.

Then 15 x 8 and we get 120.

Now the equation is literally :

Volume = 1/2 x 120

(This is the same as 120 / 2 just in multiplication terms)

So lets do this :

120 / 2

=

60

So now we have your answer :

Volume = 60³

(Don't forget the little 3)

Again, I hope this helps!

Any questions or concerns please comment or message me ofc :)

I got this answer off of

Answer:

D

y = |x-3| -5

(- 5) shifts the graph 5 units down

( - 3) shifts the graph 3 units to the right

Answer:

The function is:

y = |x - 3| -5

The total volume is the one in option C, 708 cubic centimeters.

We know that this prism can be divided into two prisms, and remember that the volume of a prism is equal to the product between its dimensions.

Then the volume of the first prism is:

V = 8cm*6cm*13cm = 624 cm³

And the volume of the second prism is:

v' = 3cm*4cm*7cm = 84 cm³

Adding that we will get:

total volume =  624 cm³+  84 cm³ = 708 cm³

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