Solve for x in the drawing below.

Answer:

The answer is 7/2

Step-by-step explanation:

d=2r

7=2r

r=7/2

Truth tables are utilized to decide redundancies by assessing reality an incentive for every single imaginable mix. Both [(p ^ q) - > r] <-> [p - > (q - > r)] and [(p ∧ q) ^ (~q)] - > p were viewed as repetitions.

a. We should assemble reality table for [(p ^ q) - > r] <-> [p - > (q - > r)].

p | q | r | (p ^ q) - > r | p - > (q - > r) | [(p ^ q) - > r] <-> [p - > (q - > r)]

T | T | T | T | T | T, T | T | F | F | F | F, T | F | T | T | T | T, T | F | F | T | T | T,

F | T | T | T | T | T, F | T | F | T | T | T, F | F | T | T | T | T, F | F | F | T | T | T

Since every one of the qualities in the last segment are "T", the assertion [(p ^ q) - > r] <-> [p - > (q - > r)] is a redundancy.

b. We should construct reality table for [(p ∧ q) ^ (~q)] - > p.

p | q | ~q | (p ∧ q) ^ (~q) | [(p ∧ q) ^ (~q)] - > p

T | T | F | F | T, T | F | T | T | T, F | T | F | F | T, F | F | T | F | T

Since every one of the qualities in the last section are "T", the assertion [(p ∧ q) ^ (~q)] - > p is a repetition.

A repetition is a coherent explanation that is in every case valid, no matter what reality values doled out to its singular parts. To decide whether an assertion is a repetition, we can utilize a reality table which records generally potential blends of truth values for the parts and assesses reality worth of the whole assertion. In the event that reality worth of the assertion is generally "Valid" for every conceivable mix, then, at that point, the assertion is a redundancy. In the models given, the two explanations [(p ^ q) - > r] <-> [p - > (q - > r)] and [(p ∧ q) ^ (~q)] - > p were viewed as repetitions through truth tables.

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eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee

The volume common to the two spheres is V = 2 * (2/3) * pi * r^3 = (4/3) * pi * r^3.

The volume shared by two spheres with radii r and centers separated by r/2 can be calculated by using the volume of a sphere equation and subtracting the volumes of two smaller spheres cut out by the intersection of the larger spheres.

Assume that the two spheres are centered at (r/2,0,0) and (-r/2,0,0). Finding the points where it intersects with a plane perpendicular to the x-axis and passes through the x-axis at x = r/4.

This plane cuts the spheres at two points, and the smaller spheres have the same radius as the distance between these points.

The radius of these spheres can be found using the Pythagorean theorem:

r = sqrt(r^2 - (r/2)^2) = sqrt(3r^2/4)

The volume of each smaller sphere is given by:

V = (4/3) * pi * (r)^3 = (4/3) * pi * (sqrt(3r^2/4))^3 = (2/3) * pi * r^3

Therefore, the volume common to the two spheres is given by:

V = 2 * (2/3) * pi * r^3 = (4/3) * pi * r^3.

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The probability of rolling 1 (R), 1 (G), 1 (B) is 1/216, odd (R), even (G), any number (B) is 1/36, 6 or 5 (R), 4 or 3 (G), 1, 2 or 3 (B) is 1/18, no fives at all is 125/216, and a different number on each dice is 1/6.

a. The probability of rolling 1 (R), 1 (G), 1 (B) is 1/216. This is because there are 6 faces on each die, and 6 x 6 x 6 = 216 total possible outcomes. Since there is only one way to roll the dice and get 1 (R), 1 (G), 1 (B), the probability of this outcome is 1/216.

b. The probability of rolling odd (R), even (G), any number (B) is (3/6) x (3/6) x (1/6) = 1/36. This is because there are 3 odd numbers on the red die, 3 even numbers on the green die, and 6 numbers on the blue die, thus making the total number of outcomes (3/6) x (3/6) x (6/6) = 1/36.

c. The probability of rolling 6 or 5 (R), 4 or 3 (G), 1, 2 or 3 (B) is (2/6) x (2/6) x (3/6) = 1/18. This is because there are 2 faces with a 6 or 5 on the red die, 2 faces with a 4 or 3 on the green die, and 3 faces with a 1, 2, or 3 on the blue die, thus making the total number of outcomes (2/6) x (2/6) x (3/6) = 1/18.

d. The probability of rolling no fives at all is (5/6) x (5/6) x (5/6) = 125/216. This is because there are 5 faces on each die that do not have a 5, thus making the total number of outcomes (5/6) x (5/6) x (5/6) = 125/216.

e. The probability of rolling a different number on each dice is (6/6) x (5/6) x (4/6) = 1/6. This is because there are 6 different numbers on the red die, 5 different numbers on the green die, and 4 different numbers on the blue die, thus making the total number of outcomes (6/6) x (5/6) x (4/6) = 1/6.

In conclusion, the probability of rolling 1 (R), 1 (G), 1 (B) is 1/216, odd (R), even (G), any number (B) is 1/36, 6 or 5 (R), 4 or 3 (G), 1, 2 or 3 (B) is 1/18, no fives at all is 125/216, and a different number on each dice is 1/6.

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If Auberon swim 52 meters in five minutes then at this rate the number of meters would he swim in 10 minutes & 12 minutes are respectively,

104 meters & 124.8 meters

The distance covered by the object is equal to the product of the speed at which the object is moving and time taken for covering the distance.

Distance = Time × Speed

Since Auberon swim 52 meters in 5 minutes,

you can find his average rate of swimming by dividing the distance by the time:

Rate = 52 meters / 5 minutes

        = 10.4 meters per minute

To find the distance he would swim in 10 minutes, you can multiply his average rate by the time:

Distance in 10 minutes = 10.4 meters per minute x 10 minutes

                                      = 104 meters

To find the distance he would swim in 12 minutes, you can multiply his average rate by the time:

Distance in 12 minutes = 10.4 meters per minute x 12 minutes

                                      = 124.8 meters

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The probability that "Relaxation Through Mathematics" is first to review is 1/k, and the probability that "Relaxation Through Mathematics" and "The Joy of Calculus" are next to each other in the stack is (1/k)*(1/(k-1)).

A) The probability that "Relaxation Through Mathematics" is first to review is 1/k. This is because there are k documents to review, and the order in which they are reviewed is random with each ordering being equally likely. Therefore, the probability that any given document is chosen first is 1/k.

B) The probability that "Relaxation Through Mathematics" and "The Joy of Calculus" are next to each other in the stack is (1/k)*(1/(k-1)). This is because there are k documents to review, and the probability that the first document is "Relaxation Through Mathematics" is 1/k. Then, since there are k-1 documents remaining in the stack, the probability that the second document is "The Joy of Calculus" is 1/(k-1). Therefore, the probability that both documents are next to each other is (1/k)*(1/(k-1)).

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I really think it's option A because it's more than 90° and less than 180°

Answer:

A

Step-by-step explanation:

An obtuse triangle is a triangle in which one of the interior angles measures more than 90° degrees

formula for finding obtuse triangle is 1/2 *base*height

Answer:

[tex]\displaystyle P(x)=-\frac{1}{10}(x-3)^2(x+2)[/tex]

Step-by-step explanation:

Multiplicity is basically how much of a factor of a polynomial appears. In this case, if we disregard the y-intercept, we can show a multiplicity of 2 at x = 3 and a multiplicity of 1 at x=-2 with [tex]y=(x-3)^2(x+2)[/tex].

Of course, there will need to be a scale factor for the function so that the y-intercept will be at y = -1.8, so we can solve the following:

[tex]-1.8=a(0-3)^2(0+2)\\-1.8=a(3)^2(2)\\-1.8=a(9)(2)\\-1.8=18a\\-0.1=a[/tex]

Thus, we can write the function as [tex]\displaystyle P(x)=-\frac{1}{10}(x-3)^2(x+2)[/tex]. See below for a visual.

Therefore , the solution of the given problem of area comes out to be Formula for Square Area is = length * length.

Its surface area provides a good estimate of its overall size. When computing a right triangle's squared, the surroundings are taken into consideration. The surface area of everything determines its overall size. The sum of the volumes on each of the six horizontal sides makes up the volume of water inside a cuboid. Utilize the following formula to get the box's dimensions: In 2lh, 2lw, and 2hw, the region is the same (SA). The flexible shape's total area serves as a representation of the area.

Here,

To fill the blank space in the given problem is

Formula for Square Area

We are aware that Side Side equals the area of a square.

7 7 Equals 49 when the side length of 7 cm is substituted.

As a result, the square's area is 49 cm2.

Therefore , the solution of the given problem of area comes out to be Formula for Square Area is = length * length.

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The total area of the garden is given as follows:

52 ft².

The area of a rectangle of length l and width w is given by the multiplication of these dimensions, as follows:

A = lw.

For the new rectangle, the dimensions are given as follows:

Hence the area of the new part is of:

A = 4 x 8

A = 32 ft².

Considering the previous part of 20 ft², the total area is given as follows:

32 + 20 = 52 ft².

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The algebraic expression that Danielle should write is 2x - 4

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

4 less than twice a number

Represent the number with x

So, we have the following representation

4 less than twice x

Twice x means 2x

So, we have

4 less than 2x

Less than here means minut

So, we have the following representation

2x - 4

Hence, the expression is 2x - 4

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The formula for the tangent line to f(x) = ln(x) at x = 2 is 2y = x − 2.

We must first differentiate f(x).

The derivative of ln(x) is 1/x

The slope of the tangent at a point x = a on the function f(x) is given by evaluating f'(a).

Hence, the slope of the tangent is 1/x = 1/2

The function passes through,

(1/2, ln1)=(2, 0).

Now, we can use point slope form to find the equation of the tangent.

y − y1 = m( x− x1)

y − 0 = 1/2( x− 2 )

2y = x - 2

Thus, the equation of the tangent is 2y = x − 2.

The straight line that "just touches" the curve at a given position is known as the tangent line to a plane curve at that location. It was described by Leibniz as the path connecting two points on a curve that are infinitely near together.

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Answer:

Let's call the number of $5 child tickets sold "x".

According to the problem, the number of $adult tickets was 14 less than twice the number of child tickets, so the number of $adult tickets sold can be represented as 2x - 14.

The total revenue from ticket sales was $728, so we can set up an equation:

5x + 20(2x - 14) = 728

Expanding the second term on the left side of the equation:

5x + 40x - 280 = 728

Combining like terms:

45x = 1008

Dividing both sides of the equation by 45:

x = 22.4

So the number of child tickets sold was 22 and the number of adult tickets sold was 2 * 22 - 14 = 36.

The expressions of the sale price is as follows:

Expression B: 0.8p

Expression D: p - 0.2p

The regular price of an item at a store is p dollars. The item is on sale for 20% off the regular price.

Therefore, the expression that represent the sale price in dollars of the items can be calculated as follows:

original price = p

Therefore, let's find the percent off the price.

price off = 20% of p

price off = 20 / 100 p

price off = 0.2p

Therefore,

sale price = p - 0.2p

sale price = 0.8p

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Answer:

Step-by-step explanation:

A. The total cost after t hours can be represented by the linear equation C(t) = 50 + 190/4 * t, where C(t) is the total cost after t hours.

B. The electrician charges 190/4 = $47.5 per hour.

Answer:

$30,029.78

Step-by-step explanation:

NPV = Cash flow / (1 + i)^t – initial investment (assuming initial investment =$1).

solve NPV

$30,029.78

The equation of the velocity is v(t) = 24t² - 24t - 288 and the time where velocity is equal to zero is t = -3 and t = 4.

Apart from integration, differentiation is one of the two key ideas in calculus. A technique for determining a function's derivative is differentiation. Mathematicians use a process called differentiation to determine a function's instantaneous rate of change based on one of its variables. The most typical illustration is velocity, which is the rate at which a distance changes in relation to time. Finding an antiderivative is the opposite of differentiation.

The function for the velocity can be found by differentiating the equation for the motion for the particle.

s(t) = 8t³ - 12t² - 288t

v(t) = d/ dt s(t)

v(t) = 24t² - 24t - 288

Velocity is zero for:

v(t) = 0

24t² - 24t - 288 = 0

t² - t - 12 = 0

t² - 4t + 3t -12 = 0

t(t - 4) + 3(t - 4) = 0

(t + 3)(t - 4) = 0

t = -3 and

t = 4

Hence, the equation of the velocity is v(t) = 24t² - 24t - 288 and the time where velocity is equal to zero is t = -3 and t = 4.

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[tex]~\hfill \stackrel{\textit{\large distance between 2 points}}{d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}}~\hfill~ \\\\[-0.35em] ~\dotfill\\\\ A(\stackrel{x_1}{-2}~,~\stackrel{y_1}{-2})\qquad B(\stackrel{x_2}{4}~,~\stackrel{y_2}{3}) ~\hfill AB=\sqrt{(~~ 4- (-2)~~)^2 + (~~ 3- (-2)~~)^2} \\\\\\ ~\hfill AB=\sqrt{( 6)^2 + ( 5)^2} \implies \boxed{AB=\sqrt{ 61 }} \\\\\\ B(\stackrel{x_1}{4}~,~\stackrel{y_1}{3})\qquad C(\stackrel{x_2}{3}~,~\stackrel{y_2}{4}) ~\hfill BC=\sqrt{(~~ 3- 4~~)^2 + (~~ 4- 3~~)^2}[/tex]

[tex]~\hfill BC=\sqrt{( -1)^2 + ( 1)^2} \implies \boxed{BC=\sqrt{ 2 }} \\\\\\ C(\stackrel{x_1}{3}~,~\stackrel{y_1}{4})\qquad A(\stackrel{x_2}{-2}~,~\stackrel{y_2}{-2}) ~\hfill CA=\sqrt{(~~ -2- 3~~)^2 + (~~ -2- 4~~)^2} \\\\\\ ~\hfill CA=\sqrt{( -5)^2 + (-6)^2} \implies \boxed{CA=\sqrt{ 61 }} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \stackrel{\textit{two equal sides}}{\textit{\LARGE Isosceles}}~\hfill[/tex]

We need 32.65 W power to maintain the temperature at 197°C.

In order to discover the wattage to maintain a temperature of 197°C for the crystals, we need to start by substituting that value into the function:

T(x) = 0.1w² + 2.157w + 20

197 = 0.1w² + 2.157w + 20

and set the equation equal to zero by subtracting 197 from both sides:

0.1w² + 2.157w - 177 = 0

To solve this equation we make use of the quadratic formula, which in this case will be:

[tex]w = \frac{- b (+/-)\sqrt{b^{2}-4ac } }{2a}[/tex]

in this case:

a=0.1

b=2.157

c=-177

which come from the equation according to their position in the equation with the form ax²+bx+c = 0.

so we substitute them into the formula like this:

[tex]w = \frac{- 2.157(+/-)\sqrt{2.157^{2}-4*(0.1)*(-177) } }{2*0.1}[/tex]

w= -54.22W and w=32.65W

we use the positive answer since that means that the power is being input into the system, a negative answer would mean you are retrieving power from the system which would cool the system down.

So we need 32.65W power to maintain the temperature at 197°C.

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Answer:

x = -3

Step-by-step explanation:

-3x - 8 = 1

-3x = 9

3x = -9

x = -9/3

x = -3

Answer:

It's 59 degrees

The macrostate s of two six-sided dice can be defined as the sum of the top faces of the dice.

The macrostate of a system refers to a comprehensive description of the system in terms of its properties and variables that are used to characterize it. In the case of two six-sided dice, the macrostate is described by the sum of the numbers on the top faces of the two dice, which determines the total score or outcome. This macrostate, represented by the variable "s", is a measurable quantity that summarizes the state of the system, providing information about the distribution of the outcomes over all possible configurations of the two dice.

It's important to note that a macrostate does not specify the exact configuration of the system, but rather provides a probabilistic description of it. In other words, the macrostate "s" only describes the sum of the two dice and does not specify which number is on each die. In thermodynamics, macrostates are used to characterize the thermodynamic properties of a system, such as its temperature, pressure, and entropy. The study of macrostates and their distributions helps us to understand the behavior of complex systems and make predictions about their future behavior.

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Answer: 77

Step-by-step explanation:

From the given rates, the unit rates are as follows 9/1 and 10:1. That is option D and E.

A unit rate of a measurement of the distance of a traveling vehicle or of a moving object is the rate for per one of the value of interest.

A unit rate can only be two figures that shows the relationship that exists between them and a whole value.

Therefore the given rates that shows unit rate are 9/1 and 10:1

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A system of equations to represent this situation include the following:

2x + 2y = 4.40

3x + 4y = 7.80

In order to write a system of equations that model this situation, we would assign variables to the number of bagels and the number of cups of coffee respectively, and then translate the word problem into algebraic equation as follows:

Next, we would translate the word problem into algebraic equation as follows:

Since 2 bagels and 2 cups of coffee cost $4.40, we would have:

2x + 2y = 4.40    .....equation 1.

Additionally, 3 bagels and 4 cups of coffee cost $7.80:

3x + 4y = 7.80    .....equation 2.

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B. No, the reduced row echelon form of the augmented matrix is which is an inconsistent system. In this case, the vector u is [0 26 8] and the matrix A is [5 -3 1; -3 7 1].

To check if u is in the plane spanned by the columns of A, we can form the augmented matrix by appending u to A, and attempt to reduce it to the reduced row echelon form.

If the resulting augmented matrix is an inconsistent system (i.e. the last row has a non-zero coefficient in the last column and a zero in the right-hand side), then u cannot be written as a linear combination of the columns of A, and thus it is not in the plane spanned by the columns of A.

In this case, the reduced row echelon form of the augmented matrix is an inconsistent system, which means that u cannot be written as a linear combination of the columns of A, and thus it is not in the plane spanned by the columns of A.

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The correct answer is option C. In a research proposal, the Data Collection method discusses the types of scales to be used for data collection.

The Data Collection Method section of a research proposal is where the various scales for data collection are discussed. The types of scales (such as Likert scales, qualitative scales, etc.) and specific research instruments (such as surveys, interviews, questionnaires, or focus groups) typically are described in this section. that will be applied to the measurement of the variables. The target population and the definition of the sample size might also be discussed in the sample design section.

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The length of EH is determined as 10.72.

The length of EH can be determined if the length of the each side is properly identified as shown below.

In the given figure, H is the circumcenter of triangle BCD,

Triangle BHD is isosceles, therefore BH = HD

Point E is midpoint of BC, therefore BE = ¹/₂ of BC

Using Pythagorean, calculated the value of EH as follows;

EH = √ (BH² - BE²)

EH = √ ( 14² -  ( 18 /2) ² )

EH = √ ( 196 - 81 )

EH = √115 = 10.72

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The side length of BE is 40 units

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

H is the circumcenter.

BD= 80 and HB=50

Using the above as a guide, we have the following:

BE = 1/2 * BD

Substitute the known values in the above equation, so, we have the following representation

BE = 1/2 * 80

Evaluate

BE = 40 units

Hence, the side length of BE is 40 units

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