Evaluate the following

-(-4)+3

V is parallel to a normal direction vector to the plane P containing the terminal endpoints of a, b, and c.

The given vectors are a, b, and c. We are asked to prove that the vector v = (a × b) + (b × c) + (c × a) is parallel to a normal direction vector to the plane P containing the terminal endpoints of a, b, and c.

To prove this, we need to show that the vector v is perpendicular to the vectors a, b, and c. This can be done by taking the dot product of v with each of the given vectors and showing that the result is zero.

First, let's take the dot product of v with a:

v · a = [(a × b) + (b × c) + (c × a)] · a

= (a × b) · a + (b × c) · a + (c × a) · a

= 0 + 0 + 0

= 0

Similarly, we can take the dot product of v with b and c and show that the result is also zero:

v · b = [(a × b) + (b × c) + (c × a)] · b

= (a × b) · b + (b × c) · b + (c × a) · b

= 0 + 0 + 0

= 0

v · c = [(a × b) + (b × c) + (c × a)] · c

= (a × b) · c + (b × c) · c + (c × a) · c

= 0 + 0 + 0

= 0

Since the dot product of v with each of the given vectors is zero, we can conclude that v is perpendicular to a, b, and c. Therefore, v is parallel to a normal direction vector to the plane P containing the terminal endpoints of a, b, and c.

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The E(T) is 4 when A and B, two players, alternately toss a fair coin (A tosses the coin first, then B tosses the coin, then A, then B and so on).

Given that,

A and B, two players, alternately toss a fair coin (A tosses the coin first, then B tosses the coin, then A, then B and so on). The heads and tails are recorded in order. The game is over and the winner is the person who throws the tail if there is a head followed by a tail (HT sub-sequence).

We have to find what is the anticipated game length. Let the game continue for T number of coin tosses. Find E (T).

We know that,

Here,

E(T )=first time sequence HT occurs

E(T) = P(first H)× P(expected number till 1st T |first H)+ P(first T)× P(expected number till 1st HT |first T)

E(T) =0.5×(1+2)+0.5×(1+E(T))

0.5×E(T)=0.5×4

E(T) =4

Therefore, The E(T) is 4 when A and B, two players, alternately toss a fair coin (A tosses the coin first, then B tosses the coin, then A, then B and so on).

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Answer:

\(y = -1x + 3\)

Step-by-step explanation:

Finding the y-intercept

The y-intercept is the point where the line crosses the y-axis. As we can see, there is a point at the y-axis. (0, 3) is our y-intercept.

Finding the slope

Using two points:

Formula: \(\frac{y_2-y_1}{x_2-x_1}\)

The two points we see on the graph, we can use those points to find the slope.

(0, 3)

(4, -1)

Plug these points into the formula; solve:

\(\frac{-1-3}{4-0}\)

\(=\frac{-4}{4}\)

\(=-1\)

Therefore, m = -1, and b = 3. Hence, the equation for the graph is y = -1x + 3.

Answer:

x = 88

The measurement of the other unknown angle is = 44°

Step-by-step explanation:

The sum of interior angles in a triangle is equal to 180°

48 + x + x - 44 = 180 add like terms

4 + 2x = 180 subtract 4 from both sides

2x = 176 divide both sides by 2

x = 88

Now to find the measure of two other angles we replace x with 88

In the case of coinciding lines with the same y-intercept, the number of solutions to the equation system is unlimited.

An equation is a mathematical statement that contains the symbol "equal to" between two expressions with identical values. as in 3x + 5 = 15, for example.

There are many different types of equations, such as linear, quadratic, cubic, etc.

Equations are statements in mathematics that have two algebraic expressions on either side of the equals (=) sign.

It shows that the expressions printed on the left and right sides have an equal relationship. In any mathematical equation, we have LHS = RHS (left hand side = right hand side).

Equations can be solved to find the value of an unknown variable that represents an unknown quantity. If there is no "equal to" symbol in the sentence, it is not an equation.

Hence, In the case of coinciding lines with the same y-intercept, the number of solutions to the equation system is unlimited.

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Complete question-

Using the equation y = 2/3 x - 5, describe how to create a system of linear equations with an infinite number of solutions.

True. In 2016, the percentage of the ageing population (55 years or older) in state prisons surpassed the percentage of people aged 18-24 for the first time.

This trend reflects the overall growth of the ageing population within the United States and is a result of various factors such as longer life expectancy, harsher sentencing laws, and an increase in older individuals being convicted of crimes.
As the ageing population in state prisons continues to grow, it poses several challenges for the correctional system. These challenges include providing appropriate healthcare and accommodations for older inmates and addressing the specific needs of this population, such as mobility assistance and specialized medical care.
In conclusion, the shift in the age demographics of state prisons has significant implications for the management and administration of correctional facilities. It is crucial to address the unique needs of the ageing population within these institutions and adapt policies and practices accordingly to ensure the well-being and fair treatment of all inmates, regardless of their age.

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Work Shown:

f(x) = -x - 6

f(-x) = -(-x)-6

f(-x) = x-6

g(x) = f(-x)

g(x) = x-6

Explanation:

I replaced every x with -x to reflect the point over the y axis.

For example, the point (2,3) reflects to (-2, 3)

Step-by-step explanation:

n=an-a

n=1--15

n=16

this might be helpful for you of it isnt I am super sorry

Answer:

hiiiiiiiii

burrgerry.com

Answer:

3:9

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

27:81

= 27/81

=3/9

=3:9

it could be reduced to 1:3 but because the alternatives does not include, it 3: 9

please reward me by marking me as the brainliest.

The density of the tank is  D. 0.37 goldfish per cubic foot.

To find the density of the tank, we need to divide the number of goldfish by the volume of the tank. In this case, we have 19 goldfish and a tank volume of 52 cubic feet. So, the density of the tank can be calculated as follows:

Density = Number of goldfish / Volume of tank

Density = 19 / 52

Density = 0.365

Therefore, the density of the tank is 0.37 goldfish per cubic foot, which is option d.

The density is a measure of the amount of matter (in this case, goldfish) that is present in a given volume (in this case, the tank). A higher density means that there are more goldfish per unit volume, while a lower density means that there are fewer goldfish per unit volume.

In this case, we can see that the density is relatively high, meaning that there are a significant number of goldfish in the tank. This could potentially be a problem, as overcrowding can lead to poor water quality and health problems for the fish. It's important to monitor the density of fish in a tank and ensure that it stays at a healthy level. Therefore the correct option is D.

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Answer:

82 because 102.50/1.25=82

please mark as brainliest and have a good day

Step-by-step explanation:

Answer:

4/3

Step-by-step explanation:

Slope is calculated by \(\frac{y1-y2}{x1-x2}\) so now you pul the points (10,2) and (19,14) into that.

\(\frac{14-2}{19-10}\) = \(\frac{12}{9}\)

12/9 can be simplified to be 4/3

Answer:

4/3

Step-by-step explanation:

Given,

Two points are (10,2) and (19,14)

To find the slope of the line passing through these points.

Answer:

D be because 2 +4 -5

Step-by-step explanation:

Answer:

which number to solve, it kinda seem difficult

Answer: True, False, False, True, False

Step-by-step explanation: Fractions are easy.

5x - 17 = 48

5x − 17 + 17 = 48 + 17

5x = 65

x = 13

180 - 48 = 132

y = 132

Answer:

x = 8.5

Step-by-step explanation:

In this question, we are to calculate the value of x.

To calculate this, we shall be utilizing one of the important properties of parallelogram.

This property is that opposite angles of a parallelogram are equal.

This means that mQSR = mSPQ = 4x + 90

Now to finally calculate x, we make use of another important parallelogram property which is that angles of parallelogram which faces each other are supplementary.

This means that they add up to be 180

Since mQSR faces mQRS

This means that;

4x + 90 + 9x -20 = 180

13x + 70 = 180

13x = 110

x = 110/13 which is approximately 8.5

The current in an rlc circuit is described by d²i/dt² + 10di/dt + 25i = 0 if i(0) = 10 a and di(0)/dt = 0, then for t > 0, where a = 10 , b = 5 , and s = -5.

The given differential equation is:

d²i/dt² + 10di/dt + 25i = 0

The characteristic equation is:

r² + 10r + 25 = 0

Solving this quadratic equation, we get:

r = (-10 ± √(100 - 4*25))/2

r = -5

Since the roots are equal, the general solution of the differential equation is:

i(t) = (a + bt) \(e^{-5t}\)

Now, using the initial conditions i(0) = 10 and di(0)/dt = 0, we get:

i(0) = a = 10

di/dt = -5(a + bt)e \(e^{-5t}\) + b* \(e^{-5t}\)

At t=0, di/dt = 0

So, 0 = -5a + b

b = 5a

Substituting the value of a and b, we get:

i(t) = (10 + 5t) \(e^{-5t}\)

Therefore, for t > 0, i(t) = (10 + 5t) \(e^{-5t}\).

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A) The derivative of dy/dx is -1 / (6 sin(6y)) using implicit differentiation.

B) The slope of the curve at the point (0, π/12) is -1/3.

A) To find the derivative dy/dx using implicit differentiation, we differentiate both sides of the equation with respect to x, treating y as a function of x:

d/dx (cos(6y)) = d/dx (x)

Using the chain rule and product rule, we can simplify this as:

-6 sin(6y) dy/dx = 1

Then, we can solve for dy/dx to get:

dy/dx = -1 / (6 sin(6y))

B) To find the slope of the curve at the point (0, π/12), we substitute these values into our equation for dy/dx:

dy/dx = -1 / (6 sin(6y))

     = -1 / (6 sin(6π/72))

     = -1 / (6 sin(π/12))

     = -1 / (6 (1/2))

     = -1/3

Therefore, the slope of the curve at the point (0, π/12) is -1/3.

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Answer:

i need the rest of the problem to figure it out sorry

Step-by-step explanation:

Answer:

60 ounces

Step-by-step explanation:

got i t on edmentum

Answer:

1) The difference between the temperatures in Miami and Anchorage is calculated by subtracting the temperature in Anchorage from the temperature in Miami. In this case, the temperature in Anchorage is -28°F and the temperature in Miami is 65°F. To find the difference, we subtract -28°F from 65°F.

65°F - (-28°F) = 65°F + 28°F = 93°F

Therefore, the difference between the temperatures in Miami and Anchorage is 93°F.

2) To find the temperature in Miami on a day when Anchorage was -14°F and Miami was 73°F warmer, we need to add the temperature difference to the temperature in Anchorage. In this case, the temperature in Anchorage is -14°F and Miami is 73°F warmer.

-14°F + 73°F = 59°F

Therefore, the temperature in Miami on this day is 59°F.

3) To find the temperature in Anchorage at the end of a three-hour period, we need to subtract the decrease in temperature from the starting temperature. In this case, the starting temperature is 6°F and the temperature decreases by 2.5°F every hour for three hours.

Starting temperature: 6°F

Decrease per hour: 2.5°F

Number of hours: 3

6°F - (2.5°F * 3) = 6°F - 7.5°F = -1.5°F

Therefore, the temperature in Anchorage at the end of the three-hour period is -1.5°F.

4) To find the temperature at sunset in Miami on a specific day, we need to calculate the changes in temperature throughout the day. In this case, the temperature at sunrise is 52°F, and it increases by 8°F, then increases by another 17°F, and finally decreases by 12°F.

Temperature at sunrise: 52°F

Temperature increase 1: 8°F

Temperature increase 2: 17°F

Temperature decrease: 12°F

52°F + 8°F + 17°F - 12°F = 65°F

Therefore, the temperature at sunset in Miami on this day is 65°F.

The linear transformation T: 3() → 3

To determine if the linear transformation T is invertible, we need to check if T is both injective (one-to-one) and surjective (onto).

To check injectivity, we can examine the kernel of T. The kernel of T consists of all vectors in 3() that map to the zero vector in the codomain. In this case, we want to find vectors (x, y, z, c) such that T(x, y, z, c) = (0, 0, 0). Using the rule for T, we have:

T(x, y, z, c) = (x, 2 - 3y, y + 2z + 5c) = (0, 0, 0)

From the first component, we have x = 0. From the second component, we have 2 - 3y = 0, which implies y = 2/3. Finally, from the third component, we have y + 2z + 5c = 0.

Therefore, the kernel of T consists of the zero vector only, which means T is injective.

To check surjectivity, we need to determine if T maps to every vector in the codomain, which is 3(). Since the third component of T(x, y, z, c) is y + 2z + 5c, we can see that any vector in 3() can be obtained by choosing appropriate values for y, z, and c. Therefore, T is surjective.

Since T is both injective and surjective, it is invertible.

To find the rule for T, we can simply rewrite the transformation in terms of the input variables:

T(x, y, z, c) = (x, 2 - 3y, y + 2z + 5c)

This rule represents the linear transformation T on 3().

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The correct answer is B) a subdivision plat map.

A subdivision plat map is a detailed map that shows the layout, sizes, and locations of streets, lots, and other features within a subdivision. It provides an overview of the entire subdivision and is commonly used for planning and development purposes.

Here is the LaTex code snippet for the answer:

\(\textbf{B) a subdivision plat map.}\)

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On a hot summer day, you visit an ice cream shop that offers 15 ice cream flavors, 3 types of cones, and 8 toppings. If you want one ice cream flavor, one cone, and one topping, there are a total of 360 possible combinations you can create.

To find the total number of possible combinations, you simply multiply the number of options for each category. In this case, you have 15 ice cream flavors, 3 types of cones, and 8 toppings.

So, the total combinations would be: 15 (flavors) × 3 (cones) × 8 (toppings) = 360 possible combinations. You can create 360 different ice cream combinations at the shop on a hot summer day.

This is calculated by multiplying the number of ice cream flavors (15) by the number of cone types (3) and the number of toppings (8), which equals 360. So, there are plenty of delicious options to choose from to cool off on a hot summer day.

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The maximum value of f on the interval [0, 2] occurs at x=(pi)^(1/3), and its value is approximately 0.923. So the answer is (C) 1.465.

To find the maximum value of the function f on the interval [0, 2], we need to find the critical points of f within the interval and then check their values to determine which one is the maximum.

First, we need to find the critical points by finding where the derivative of f is equal to zero or undefined. In this case, we have:

f'(x) = sin(x^3)

To find the critical points, we need to solve the equation sin(x^3) = 0, which occurs when x^3 = n*pi for any integer n. However, we are only interested in the solutions within the interval [0, 2]. The first solution is when n=0, which gives x=0. The next solution occurs when n=1, which gives x=(pi)^(1/3). Since (pi)^(1/3) is approximately 1.464, this solution lies within the interval [0, 2]. There are no more solutions within the interval.

Next, we need to check the values of f at the critical points and the endpoints of the interval to determine which one is the maximum. We have:

f(0) = 0

f((pi)^(1/3)) = integral from 0 to (pi)^(1/3) of sin(x^3) dx

Unfortunately, there is no closed form for this integral, so we need to use numerical methods to estimate its value. Using a numerical integration method like Simpson's rule with a large number of subintervals, we can estimate that f((pi)^(1/3)) is approximately 0.923.

f(2) = integral from 0 to 2 of sin(x^3) dx

Again, there is no closed form for this integral, so we need to use numerical methods to estimate its value. Using Simpson's rule with a large number of subintervals, we can estimate that f(2) is approximately -0.499.

Therefore, the maximum value of f on the interval [0, 2] occurs at x=(pi)^(1/3), and its value is approximately 0.923. So the answer is (C) 1.465.

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