What is the value of 6x² -- 9 when x = 2?

A) 3

B) 33

C) 15

D) 55​

The number of people that attended the game in each cost category is Faculty: 7,000,Alumni: 18,000,Public: 18,000,Veterans: 4,000

To determine the number of people that attended the game in each cost category,  to consider the given information and set up a system of equations to solve for the unknowns. Let's break down the problem step by step.

Let's denote the number of people in each cost category as follows:

Faculty: F

Alumni: A

Public: P

Veterans: V

The number of alumni is 11,000 more than the faculty, so we have the equation:

A = F + 11,000

The number of public plus alumni together was 10 times the number of veterans, so  the equation:

P + A = 10V

The number of faculty plus alumni together was the same as the number of veterans, so we have the equation:

F + A = V

The total number of people attending the game is the sum of the people in each category, so  the equation:

F + A + P + V = 100,000

Now, use these equations to solve for the unknowns.

First, substitute equation 1 into equations 2 and 3:

P + (F + 11,000) = 10V

F + (F + 11,000) = V

Simplify these equations:

P + F + 11,000 = 10V

2F + 11,000 = V

Next, substitute these equations into equation 4:

F + (F + 11,000) + P + (2F + 11,000) = 100,000

Simplify and combine like terms:

4F + 22,000 + P = 100,000

Subtract 22,000 from both sides:

4F + P = 78,000

Now a system of two equations:

P + F + 11,000 = 10V

4F + P = 78,000

solve this system of equations to find the values of F, P, and V.

By solving the system,

F = 7,000

P = 18,000

V = 4,000

Finally, substitute these values back into equation 1 to find the value of A:

A = F + 11,000 = 7,000 + 11,000 = 18,000

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Answer:

2

Step-by-step explanation:

Answer:

Step-by-step explanation:  will u be my friend

To find the percentage, we can use the following formula:

Percentage = (Part / Whole) * 100

So, $131,701.32 is approximately 16.67% of $790,207.91.

In this case, the part is $131,701.32 and the whole is $790,207.91.

Percentage = ($131,701.32 / $790,207.91) * 100

Calculating the value:

Percentage ≈ 0.1667 * 100

Percentage ≈ 16.67%

Therefore, $131,701.32 is approximately 16.67% of $790,207.91.

Alternatively, we can calculate the percentage by dividing the part by the whole and multiplying by 100:

Percentage = ($131,701.32 / $790,207.91) * 100 ≈ 0.1667 * 100 ≈ 16.67%

So, $131,701.32 is approximately 16.67% of $790,207.91.

If you have any further questions, feel free to ask!

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the volume of the cone is 94.2 cubic feet

The solution of the system goes to infinity as t gets large.

Consider the given system of differential equations: dx/dt = 3x + 4ydy/dt = −x − 2yNow, find the solution of the system:(2)   dx/dt + 2 dy/dt = 7xObserve the second equation and multiply it by 2:2  dy / dt = −2x − 4y(3)   dx/dt + 2 dy/dt = 3x − 4ySubstitute the value of dy/dt from (3) into (2):(2)   dx/dt + 3x − 4y = 7xSimplify this equation:dx/dt − 4x = 4yTake the laplace transform of both sides: Laplace{dx/dt − 4x} = Laplace{4y} ⇒ sX(s) − x(0) − 4X(s) = 4Y(s) ⇒ X(s) = {4Y(s)}/{s − 4}Now, find the Laplace transform of y(s):(1)   dy/dt = −x − 2y ⇒ Laplace{dy/dt} = −Laplace{x} − 2Laplace{y} ⇒ sY(s) − y(0) = −X(s) − 2Y(s) ⇒ Y(s) = {−X(s)}/{s + 2}Substitute the value of X(s) in the above equation, we get:Y(s) = {−4Y(s)}/[(s − 4)(s + 2)]Simplify this equation:Y(s) = {A}/{s − 4} + {B}/{s + 2}Now, find the values of A and B:Multiplying the above equation by (s − 4) and (s + 2), we get:Y(s) = A(s + 2) + B(s − 4)Simplify this equation:Y(s) = (A + B)s + 2A − 4BAs per the equation (3), we can say A + B = 0, 2A − 4B = −4On solving, we get A = 2, B = −2Therefore, the value of Y(s) is:Y(s) = {2}/{s − 4} − {2}/{s + 2}Now, substitute the value of X(s) and Y(s) in the following equation:dx/dt − 4x = 4yThe solution of the above differential equation is:x(t) = {2}/{3}e^{4t} − {5}/{3}e^{-2t}The above is the general solution of the given system of differential equations.Now, find what happens to the system as t gets large?As t gets large, the term {5}/{3}e^{-2t} will tend to zero and {2}/{3}e^{4t} will tend to infinity.

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Answer:

Step-by-step explanation:

Given the equation sec(x)cot(x)= -2 on the interval [0,2π]. In order to get the value of x, the following steps must be followed.

sec(x)cot(x)= -2

From trigonometry identity, sec(x)= 1/cos(x) and cot(x)= 1/tan(x) = cos(x)/sin(x)

subsituting this expressions in the given equation we have;

1/cos(x)*cos(x)/sin(x) = -2

1/sin(x) = -2

sin(x) = -1/2

\(x = sin^{-1}-1/2\\ x = -30^{0}\)

Since sin is negative in the 3rd and 4th quadrant,

In the 3rd quadrant, x = 180+30 = 210°

In the 4th quadrant, x = 360-30 = 330°

Converting the values to radian;

since 180° =  πrad

210° = 210π/180 rad

210° = 7π/6 rad

Similarly, 330° = 330π/180 rad

330° = 11π/6 rad

The solutions are 7π/6 and 11π/6

The cost of the jersey that Charlotte, who is visiting Brazil, in U.S. dollars based on the exchange rate is B. $16.39.

The exchange rate is the rate at which two nations' currencies are exchanged in the foreign exchange market.

The exchange rate depends on the purchasing power of each currency.

Cost of jersey = Br. 89

Exchange rate = $1 : Br. 5.43

Cost of jersey in US dollars = $ (Br. 89/Br. 5.43)

Thus, the cost of the jersey that Charlotte in U.S. dollars based on the exchange rate is B. $16.39.

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There will be 221 highway signs on the road trip.

What is Total Length?

Whole Length (TL) is the measurement taken in a straight line, with the fish lying on its side, from the tip of the snout to the end of the tail (caudal fin).

The total length of the road trip is 13.2 hours.

Highway signs are posted every 0.06 hours. To find out how many highway signs are on the road trip, we can divide the total length of the road trip by the interval between each sign and then add one more sign for the end of the road trip:

(number of signs) = (total length of road trip) / (interval between signs) + 1

Substituting the values, we get:

(number of signs) = 13.2 / 0.06 + 1

(number of signs) = 220 + 1

(number of signs) = 221

Therefore, there will be 221 highway signs on the road trip.

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Answer: {5, -7, -19, -27, -35}

Step-by-step explanation:

In order solve this, we need to plug in the values of x into the table.

For spaces on the left of the equals sign, you need to write each x from the domain. You can then match that x-value with its function value by putting that on the right side.

For each equation, we are simply plugging a number from the domain into the function and replacing the x-value:

\(f(-1) = -4(-1) + 1 = 5\\f(2) = -4(2) + 1 = -7\\f(5) = -4(5) + 1 = -19\\f(7) = -4(7) + 1 = -27\\f(9) = -4(9) + 1 = -35\)

I hope this helps. If you need any extra explanation on how the functions are set up, please let me know.

Answer:

15.09%

Step-by-step explanation:

Sum of frequencies = 53

Probability = 8

53

=0.1509

Expressing as a percentage

>> 15.09%

The area of the cutout and the coin is as follows:

(A) 9mm²

(B) 293 mm²

The size of a patch on a surface is determined by its area.

Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.

The area of a plane figure is the area that its perimeter encloses.

The quantity of unit squares that cover a closed figure's surface is its area.

Square units like cm² and m² are used to measure area.

Area of the cutout:

A = s²

A = 3²

A = 9mm²

Area of the coin:
A = πr²

A = π9.8²

A = π9.8²

A = π96.04

A = 301.5656

Then,

301.5656 - 9

292.5656

Rounding off: 293 mm²

Therefore, the area of the cutout and the coin is as follows:

(A) 9mm²

(B) 293 mm²

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The statement cross-tabulation with two variables is known as twice-tabulation is false because there is no such term as "twice-tabulation" in the context of statistical analysis.

Cross-tabulation, also known as contingency table analysis, involves the analysis of categorical variables by creating a table that shows the frequency or distribution of one variable based on the levels of another variable.

It allows for the examination of the relationship between two variables, highlighting any associations or patterns that may exist. Each cell in the cross-tabulation table represents the count or proportion of observations that fall into specific combinations of categories from the two variables.

The term "twice-tabulation" does not exist in statistical literature and is not commonly used to refer to cross-tabulation with two variables. The correct term to describe this statistical technique is simply cross-tabulation or contingency table analysis.

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The rate at which the angle between the ladder and the wall changes is 30√75 ft/sec and the rate at which the base of the ladder slides away from the wall at this instant is 13.2 ft/sec.

When a 10-foot ladder slides down a wall at a rate of 3 ft/sec, the rate at which the (acute) angle between the ladder and the wall changes when the foot of the ladder is 5 feet from the wall and the rate at which the base of the ladder slides away from the wall are required to be calculated.

Let's mark the length of the ladder as ‘l’ and the distance of the ladder from the wall as ‘x’.If the ladder has slid x feet down the wall at time t, the triangle formed by the ladder, the wall, and the ground is such that l² = x² + y². The angle is θ, then sin θ = y/l, cos θ = x/l, and tan θ = y/x.

Thus, we have the following equation:(l)² = (x)² + (y)²Differentiate with respect to t.2(l)(dl/dt) = 2(x)(dx/dt) + 2(y)(dy/dt)

Solve for dy/dt when x = 5ft and dx/dt = 3 ft/sec.dy/dt = (l/x)(dx/dt)√[l² - x²]dy/dt = (10/5)(3)√[10² - 5²]dy/dt = 30√75 ft/sec

Now, let's differentiate the equation l² = x² + y² with respect to time:2l(dl/dt) = 2x(dx/dt) + 2y(dy/dt)

We have already calculated the value of dy/dt from the previous step. Substituting, l = 10, x = 5 and dx/dt = 3, we get: 20(dl/dt) = 10(3) + 2(5)(30√75)dl/dt = 13.2 ft/sec

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Answer:

she not with him tonight

she not with Jim tonight

she in the gym tonight

Answer:yes

Step-by-step explanation:

Control limits are based on multiples of the sample statistic's standard deviation, hence the assertion is false that "control limits are based on multiples of the process standard deviation".

A control chart is made up of many different parts. There are two control limitations. The top dashed line represents the upper control limit (UCL), and the bottom dashed line represents the lower control limit (LCL).The solid middle line denotes the statistic's average for the plot.

The horizontal lines known as control limits in a control chart show the upper and lower limits of the acceptable range of results for a process. When plotted data goes over a control limit, a process is out of control and requires management action. The control limits are defined as three standard deviations on either side of the mean.

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A. The units of these decision variables are in quantities (pieces).

B. Maximize Profit = 20x1 + 85x2 + 35x3

The objective function calculates the total revenue by multiplying the unit selling price of each product with its corresponding quantity (decision variable). The goal is to maximize this total profit.

a) Decision Variables:

Let's define the decision variables as follows:

x1: The number of fabric necklaces produced.

x2: The number of bags produced.

x3: The number of scarves produced.

The units of these decision variables are in quantities (pieces).

b) Objective Function:

The objective function represents the goal or objective to be optimized. In this case, the objective is to maximize the total profit generated from the sale of necklaces, bags, and scarves. The objective function can be written as follows:

Maximize Profit = 20x1 + 85x2 + 35x3

The objective function calculates the total revenue by multiplying the unit selling price of each product with its corresponding quantity (decision variable). The goal is to maximize this total profit.

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Answer:

12

Step-by-step explanation:

Answer:

I believe it is answer B if it's wrong I'm very sorry/

Step-by-step explanation:

there are 24 small cubes painted on exactly 3 faces.

The rectangular cube has dimensions of 4 cm × 4 cm × 4 cm. If we remove two straight tunnels of 4 cubes each, we are left with a solid shape that has dimensions of 4 cm × 4 cm × 2 cm (since we have removed 2 layers of cubes along one dimension).

In order to find the number of small cubes painted on exactly 3 faces, we need to count how many cubes touch an exposed face of the solid shape.

The solid shape has 6 faces in total. Each face has dimensions of 4 cm × 4 cm, and is made up of 16 small cubes, so there are a total of 6 × 16 = 96 small cubes on all the faces combined.

However, each tunnel removes 4 cubes from the interior of the solid shape. Since there are 2 tunnels, a total of 8 cubes have been removed from the inside. Therefore, the total number of small cubes in the solid shape is:

4 cm × 4 cm × 2 cm / (1 cm)^3 = 32 small cubes

So, the number of small cubes that touch an exposed face is:

32 - 8 = 24 small cubes

Each of these 24 small cubes touches exactly 3 faces (one face is part of the tunnel and is not painted). Therefore, the number of small cubes painted on exactly 3 faces is:

24 small cubes

Hence, there are 24 small cubes painted on exactly 3 faces.

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Answer:

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

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = \(\frac{1}{2}\) so

y = \(\frac{1}{2}\) x + c ← is the partial equation

To find c substitute (4, 6) into the partial equation

6 = 2 + c ⇒ c = 6 - 2 = 4

y = \(\frac{1}{2}\) x + 4 ← equation of line

Since the provided equation is inconsistent, it cannot intersect.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign. A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

Here,

we can see that the second set of equation,

4x+2y=12

20x+10y=30

4/20=2/10≠12/30

1/5=1/5≠2/5

The given equation is inconsistent so it does not intersect.

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Answer:

Part 1:

4. The slope is -4.

5. The slope is 17/4.

6. The slope is -2/3.

Part 2:

4. y = -4x - 11

y-intercept is (-11/4, 0)

5. y = 17/4x - 12

6. y = -2/3x + 4/3

Step-by-step explanation:

Answer:

0.1

Step-by-step explanation:

Just take 24/24 which is 1 and move the decimal one place to the left because there is an extra 0 on the denominator

The answer of the given question based on the triangle is , - 15.75 ,  this is not possible as the length cannot be negative.

We are given:

In ΔCDE, the measure of ∠E = 90°, CD = 9.2 feet, and DE = 8.3 feet.

To find:

The measure of ∠C to the nearest tenth of a degree.

Solution:

In ΔCDE, applying Pythagoras theorem:

CE² + CD² = DE²CE² + (9.2)² = (8.3)²

CE² = (8.3)² - (9.2)²CE²

= 68.89 - 84.64CE²

= - 15.75

This is not possible as the length cannot be negative.

Hence, the given values are not possible.

So, there is no such triangle ΔCDE, which satisfies the given conditions.

Hence, we cannot find the measure of ∠C.

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Answer:  Check out the diagram below.

Explanation:

Use a calculator to find that:

\(A = \sqrt{18} \approx 4.24\\\\B = \sqrt{73} \approx 8.54\\\\C = \sqrt{30} \approx 5.48\\\\D = \sqrt{52} \approx 7.21\\\\E = \sqrt{7} \approx 2.65\\\\\)

You'll then plot those decimal approximate values on the number lines given.

For example, 4.24 will go somewhere between 4 and 5. It's closer to 4 than it is to 5. The other values are handled the same way. The placement of the points doesn't have to be perfect.

Check out the diagram below. I made one single number line and plotted all the values on it. However, you'll have 5 separate number lines (one value per number line).

Answer:

300

Step-by-step explanation:

1 year -> 12 mths

12÷6=2

2x150=300

The acutal width of the picnic area by using proportion if the scale used is 3 inches : 2 yards will be 60 yards.

Let the actual width of the picnic area be x yards.

According to the given question.

Laura measured a picnic area near the river and made a scale drawing.

The scale she used was 3 inches : 2 yards.

⇒ The scale is 3 inches : 2 yards

The width of the picnic area in the drawing is 90 inches.

As we know that, a proportion is a fraction of a total amount, and the measures are related using a rule of three.

Thereofore, the acutal width of the picnic area by using proportion if the scale used is 3 inches : 2 yards is given by

3inches : 2 yards = 90inches : x

⇒ 3x = 180

⇒ x = 60yards

The acutal width of the picnic area by using proportion if the scale used is 3 inches : 2 yards will be 60 yards.

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Answer:

1.5

Step-by-step explanation:

I think

The frequency distribution is shown below.

Frequency tables or charts are used to represent frequency distributions. Frequency distributions can display the proportion of observations or the actual number of observations that fall inside each range. The distribution is known as a relative frequency distribution in the latter case.

We have,

Two of the sectors say, "0 points," three say, "1 point," two say, "2 points," and one says, "5 points."

So, the frequency distribution is

Outcome       0 pts  1 pts  2 pts  5 pts

Probability     2/8      3/8    1/8      1/8

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