solve each of the following equations for x . equation solution x 7=18 5x 4=14 12−4x=−36

log 7

log (7x2/3) + log (11/5) - log (11x2/5x3) [ log laws ]

log 7 + log 2 - log 3 + log 11 - log 5 - [ log 11 + log 2 - (log 5 + log 3)]

log 7 + log 2 - log 3 + log 11 - log 5 - [ log 11 + log 2 - log 5 - log 3]

log 7 + log 2 - log 3 + log 11 - log 5 - log 11 - log 2 + log 5 + log 3

{ + log 3 - log 3 gets cancelled + log 2 - log 2 gets cancelled + log 11 - log 11 gets cancelled + log 5 - log 5 gets cancelled }

log 7

Answer:

C.17+6x

Step-by-step explanation:

2+3 (2X +5)

Distribute the 3 to each term in the parentheses.

2+3*2X +3*5

2 + 6x+15

Combine like terms.

6x+17

c.17+6×

Answer:

c. 17+6×

Step-by-step explanation:

2+3(2×+5) = 2+6×+15=17+6×

a) The domain of g is U between 0 and n, since the integral is taken over the domain of f(x), which goes from 0 to n. The range of g can be estimated by looking at the area of the region below the graph of f(x) and above the x-axis. It is seen that this area is positive but less than 2; therefore, the range og is (0,2).

b) The maximum of g is achieved when the graph of f(x) is highest, which occurs at x = 3. The minimum of g is achieved when the graph of f(x) is lowest, which occurs at x = 1.

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The progress reports may be given verbally to immediate supervisors, management, and users.

The above statement is False.

Progress reports are reports in which you update project information. Progress reports allow management and clients to stay informed of project status and to modify or adjust tasks, schedules and budgets.

Progress reports are important beyond simply tracking and managing various projects happening at the same time. Progress reports also provide valuable insight into how your team can complete projects more efficiently.

In addition to providing an overview of ongoing projects, well-structured progress report templates allow project managers to identify critical issues affecting team productivity and project progress.

Although progress reports may be given orally to immediate supervisors, they are usually communicated in writing to management and users.

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46,536 is the possible number of codes if repeats are not allowed and the second letter must be 'g' and the first digit must be '3'.

If repeats are not allowed, and the second letter must be 'g', and the first digit must be '3', then we have to find the number of codes that can be possible.

Solution: Here we have to calculate the total number of possible codes if repeats are not allowed and the second letter must be 'g' and the first digit must be '3'.

The given conditions:

First digit = 3

Second letter = g

We know that a code is usually formed by combining letters, numbers or both.

Thus, for the formation of the code, the remaining 4 digits are free to choose any digit or alphabet, except the two already selected ones.

We know that the number of codes that can be formed by n objects taken k at a time, without repetition is given by:P(n, k) =n!/(n−k)!

Here, n = 25, as we have to select 25 letters, starting from A to Y.

We exclude G from these, as it has already been selected as the second letter.

k = 4 as we need to select 4 remaining characters.

We have to find the number of possible codes that can be formed without repetition, and with the conditions specified.

Here, we have 1 fixed number (3) and one fixed alphabet (g) and four spaces for the remaining digits:

Thus, the number of ways of selecting the remaining four characters = 24 × 23 × 22 × 21

Total number of codes possible = 1 × 1 × 24 × 23 × 22 × 21 = 46,536, which is our answer.

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In the limit, the deck of cards will be perfectly shuffled, in the sense that any of the n! possible orderings are equally likely.

The question is asking to show that, in the limit, a deck of n cards will be perfectly shuffled if each number from 1 to n is randomly chosen and the chosen card is placed in position 1. This can be shown as follows:

Let us denote the initial ordering of the deck of cards by P1, P2, ..., Pn. Suppose the first card chosen is Pi, and thus it is put in position 1. Now the ordering is Pi, P1, ..., Pn.

Suppose the next card chosen is Pj. Thus the ordering is now Pj, Pi, P1, ..., Pn. By repeating this process, the ordering of the deck is changing.

As each of the numbers 1, 2, ..., n is equally likely to be chosen, the probability of any particular ordering is the same. This means that, in the limit, the deck of cards will be perfectly shuffled, in the sense that any of the n! possible orderings are equally likely.

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The cοrrect answer tο this questiοn is x = 89°.Tο sοlve this questiοn, we must first calculate the sum οf the interiοr angles οf a clοsed figure, which is always equal tο 360°.

Interiοr angles are angles inside a clοsed shape such as a triangle, quadrilateral, pentagοn, hexagοn οr any οther pοlygοn. These angles are fοrmed by twο lines that intersect inside the shape.

Sum of Interior angle of polygons is given by:

(n − 2) × 180°

Here, n is number of sides = 6

So,

(6 − 2) × 180°

720°

That gives us

149° + 161° + 135° + 59° +127 + x = 720°

631 + x = 720°

x = 720° - 631

x = 89°

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The probability of an event occurring when the odds against it are 10 to 1 is approximately 9.1%, while the probability of an event occurring when the odds against it are 5 to 1 is approximately 16.7%.

For two rolls of a fair n-sided die for an arbitrary n instead of 6 is given below;The given is an arbitrary number n, this means we cannot write an equation. This is because, for each arbitrary number n, we cannot calculate the values for each side of the die.For the second question, given below, we can calculate the probability from the given odds:Odds against an event occurring are 10 to 1.The chance of the event is given by,P(E) = (1/(10+1))×100%= (1/11)×100% ≈ 9.1%The chance of the event occurring is approximately 9.1%What if the odds were 5 to 1 against?The chance of the event is given by,P(E) = (1/(5+1))×100%= (1/6)×100% ≈ 16.7%The chance of the event occurring is approximately 16.7%Therefore, the probability of an event occurring when the odds against it are 10 to 1 is approximately 9.1%, while the probability of an event occurring when the odds against it are 5 to 1 is approximately 16.7%.

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Answer: The answer would be A

Step-by-step explanation:

Answer:

Step-by-step explanation:

The shape of the histogram used to show the birth month of the students is uniform distribution.

The histogram displaying the birth months of the students in the professor's class shows a uniform distribution. In a uniform distribution, each birth month has an equal number of occurrences resulting in a relatively flat and consistent histogram.

This suggests that the students' births are evenly spread across the months with no specific month having significantly more or fewer students born in it compared to others. Such a pattern is common when there is no specific seasonal trend or preference for a particular birth month among the students in the class.

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The circumference of the circle based on the area given is 14π.

The circumference of a shape is simply the total length of the boundary that the shape has. The area of a shape simply means the total space that is taken by the shape. It simply expresses the extent of the region on a particular plane as well as a curved surface.

It should be noted that area of a circle is πr² and this is given as 98π.

The radius will be:

πr² = 98π

r² = 98π / π × 1/2

r² = 49.

r = ✓49

r = 7

The circumference will be:

= 2πr

= 2 × 7π

= 14π

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A linear-time algorithm that can be used to find the number of paths from s to t in a DAG G = (V, E) is the dynamic programming algorithm.

This algorithm works by computing the number of paths from s to each vertex in the graph, and then using this information to compute the number of paths from s to t.

The steps of the algorithm are as follows:

1. Initialize an array P of size |V|, where P[i] represents the number of paths from s to vertex i.

2. Set P[s] = 1, since there is exactly one path from s to itself.

3. For each vertex u in the graph, in topological order: a. For each edge (u, v) in the graph: i. Add P[u] to P[v], since any path from s to u can be extended to a path from s to v.

4. Return P[t], which is the number of paths from s to t. The algorithm runs in O(|V| + |E|) time, since it iteratively processes each vertex and edge in the graph. Therefore, it is a linear-time algorithm.

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The birthplace of humans is believed to be in Africa, specifically in the eastern and southern regions of the continent. This is based on evidence from archaeological and genetic studies.

According to the theory of evolution, humans evolved from earlier primates over millions of years through a process of natural selection. The earliest human ancestors were likely small, tree-dwelling primates that lived in Africa about 6-7 million years ago.

Over time, some of these primates evolved into bipedal creatures that walked upright on two legs. One of the most well-known early human ancestors is Australopithecus, which lived about 4-2 million years ago and is known for its distinctive skull shape.

Later, other species of human ancestors, such as Homo erectus and Homo neanderthalensis, appeared and spread to different parts of the world. Modern humans, Homo sapiens, emerged about 300,000 years ago in Africa, and eventually migrated to other parts of the world.

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For part a, the vector x can be expressed as a linear combination of a1 and a2 as x = -a1 - 2a2. For parts b, c, d, no linear combination of the given vectors can express x. For part e, x = a1 - 2a2 + 2a3 with constants k1=1, k2=-2, and k3=2.

To express x=(-3,-6) as a linear combination of a1=[1,4] and a2=[-2,3], we need to find constants k1 and k2 such that x = k1 * a1 + k2 * a2. Solving for k1 and k2, we get:

-3 = k1 * 1 + k2 * (-2)

-6 = k1 * 4 + k2 * 3

Solving this system of equations, we get k1=-6 and k2=1. Therefore, x can be expressed as:

x = -6 * [1,4] + [ -2,3] = [-8, 9]

x = -a1 - 2a2

To express x=[5,9,5) as a linear combination of a1=[2,1,4), a2=[1,-1,3), and a3=[3,2,5), we need to find constants k1, k2, and k3 such that x = k1 * a1 + k2 * a2 + k3 * a3. Solving for k1, k2, and k3, we get:

5 = k1 * 2 + k2 * 1 + k3 * 3

9 = k1 * 1 - k2 * 1 + k3 * 2

5 = k1 * 4 + k2 * 3 + k3 * 5

Solving this system of equations, we get k1=1, k2=0, and k3=1. Therefore, x can be expressed as:

x = 1 * [2,1,4] + 0 * [1,-1,3] + 1 * [3,2,5] = [5,3,9]

To express x=[2,-1,4) as a linear combination of a1=[3,6,2] and a2=[2,10,-4], we need to find constants k1 and k2 such that x = k1 * a1 + k2 * a2. Solving for k1 and k2, we get:

2 = k1 * 3 + k2 * 2

-1 = k1 * 6 + k2 * 10

4 = k1 * 2 + k2 * (-4)

This system of equations has no solution, since the second equation implies that k2 is negative, but the third equation implies that k2 is positive. Therefore, x cannot be expressed as a linear combination of a1 and a2.

To express x=(2,2,3] as a linear combination of a1=[6,-2,3), a2=[0,-5,-1), and a3=[-2,1,2], we need to find constants k1, k2, and k3 such that x = k1 * a1 + k2 * a2 + k3 * a3. Solving for k1, k2, and k3, we get:

2 = k1 * 6 + k2 * 0 + k3 * (-2)

2 = k1 * (-2) + k2 * (-5) + k3 * 1

3 = k1 * 3 + k2 * (-1) + k3 * 2

Solving this system of equations, we get k1=1, k2=1, and k3=1. Therefore, x can be expressed as:

x = 1 * [6,-2,3] + 1 * [0,-5,-1] + 1 *[-2,1,2]

To express x = [17,2,3], as linear combination of a1 = [1, -2,3), a2 = [5, -2,6], a3 = [4,0,3], We need to find constants k1, k2, and k3 such that:

x = k1a1 + k2a2 + k3*a3

Substituting the given values:

[17, 2, 3] = k1[1, -2, 3] + k2[5, -2, 6] + k3[4, 0, 3]

This gives us the following system of linear equations:

k1 + 5k2 + 4k3 = 17

-2k1 - 2k2 = 2

3k1 + 6k2 + 3k3 = 3

Solving for k1, k2, and k3, we get:

k1 = 1, k2 = -2, k3 = 2

Therefore, we can express x as a linear combination of a1, a2, and a3 as:

x = a1 - 2a2 + 2a3

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Answer: The formula for the length of an arc is L = rθ, where L is the length of the arc, r is the radius of the circle, and θ is the central angle of the arc in radians.

To solve this problem, we need to convert the measure of the central angle from degrees to radians. Since 360 degrees is equal to 2π radians, we have:

125 degrees = (125/360) * 2π radians

125 degrees = (5/18) * π radians

So, the central angle θ is (5/18) * π radians, and the length of arc RS is given as:

L = (25π/9)

Now we can use the formula for arc length to find the radius r:

L = rθ

(25π/9) = r * (5/18)π

r = (25π/9) / (5/18)π

r = (25/9) * (18/5)

r = 5 * 6

r = 30

Therefore, the radius of the circle is 30 units.

Step-by-step explanation:

The slope of the straight line are 3/5, -6, -1, 3/2

4. To determine the slope of the straight line, we need to take two points along the line and use the formula;

m = y2 - y1 / x2 - x1

The points are;

A(2, 2) and B(-3, -1)

m = -1 - 2 / -3 - 2

m = -3 / -5

m = 3/5

5. The points are P(-1, 8) and Q(0, 2)

m = y2 - y1 / x2 - x1

m = 2 - 8 / 0 - (-1)

m = -6/ 1

m = -6

7. The points are A(0, 4) and B(2, 2)

m = y2 - y1 / x2 - x1

m = 2 - 4 / 2 - 0

m = -2 / 2

m = -1

8. The point are A(1, 5) and B(3, 8)

m = y2 - y1 / x2 - x1

m = 8 - 5 / 3 - 1

m = 3 / 2

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The estimated simple linear regression equation comes down when the sum of the squared deviations for each y value from the line.

The above statement is false.

Simple linear regression is a linear regression model with a single variable. That is, it takes two-dimensional sample points with one independent variable and one dependent variable, and finds a linear function (a non-vertical straight line) that predicts the value of the dependent variable as the independent variable as accurately as possible.

Simple linear regression is used for estimating the relationship between two quantitative variables. The Simple linear regression is used for:

(1) How strong is the relationship between two variables (such as the relationship between rainfall and soil erosion).

(2) The value of the dependent variable is relative to a value of the independent variable (For example, the amount of soil erosion under a certain amount of precipitation).

Regression models describe the relationship between variables by fitting a line to observed data. Linear regression models use straight lines, while logistic and nonlinear regression models use curved lines. Regression allows you to estimate how the dependent variable changes when the independent variable changes.

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The perimeter of the sector is 16 + π cm (or approximately 22.28 cm if we use 3.14 as an approximation for π).

To find the perimeter of the sector, we need to add the lengths of the two radii and the arc length of the sector.

If the sector has an angle of 45 degrees and a radius of 8 cm, then the arc length of the sector can be calculated as:

Arc Length = (angle/360) x 2πr

Arc Length = (45/360) x 2π(8)

Arc Length = π

The perimeter of the sector is then:

Perimeter = 2r + Arc Length

Perimeter = 2(8) + π

Perimeter = 16 + π

A sector of a circle is a region bounded by two radii and an arc, where the arc is a portion of the circle. The sector is determined by the central angle that subtends the arc.

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The measure of the angle HCW inscribed in the circle is equals to 161 degrees.

HRWC is inscribed in the circle E,

The angles of the quadrilateral must add up to 360 degrees.

Measure of angle HCW

= ( 360 degrees ) - ( sum of the measures of the other three angles )

⇒ m(HCW) = 360 - (m(RHC) + m(HRW) + m(HWC))

⇒ m(HCW) = 360 - [(6x + 41) + (8x + 51) + (5x + 12)]

⇒ m(HCW) = 360 - (19x + 104)

⇒ m(HCW) =  256 - 19x

Round to the nearest hundredth by plugging in an approximate value of x.

For example, let x = 5, we get,

m(HCW) = 256 - 19(5)

⇒  m(HCW) = 256 - 95

⇒ m(HCW) = 161

Therefore, the measure of angle HCW is approximately 161 degrees.

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Answer:

tan 45° = 1

Step-by-step explanation:

45° is a Special angle,so tan 45° = 1

or it's like the identity of tan

tan 45= sin45° ÷ cos45°

=√2/2 ÷ √2/2

=1

Answer:

Step-by-step explanation:

This word problem involves solving a set of two equations for two unknowns: M (cost of 1 thin mint), and T (cost of 1 trefoil).

First customer: 3*M + 2*T = 1.35

Second customer: 5*M + 1*T = 1.55

Solving the second equation for T:     T = 1.55 - 5*M

Then, we can plug this into the first equation:

3*M + 2*(1.55 - 5*M) = 1.35

3*M + 3.1 - 10*M = 1.35

-7*M = 1.35 - 3.1

-7*M = -1.75

M = -1.75/-7

M = 0.25 --> one thin mint costs $0.25

Now that we have one price, we can solve for the other one.

T = 1.55 - 5*M = 1.55 - 5*(0.25)

T = 1.55 - 1.25 = 0.30 --> one trefoil costs $0.30

As we have proved that the Fourier transform F(ω), with the only difference being the sign of ω

Firstly, let us recall what the Fourier transform is. It is a mathematical technique that decomposes a function into its frequency components. The Fourier transform is defined as:

F(ω) = ∫ f(t) [tex]e^{(-iwt)}[/tex]dt

where f(t) is the function being transformed, ω is the frequency, i is the imaginary unit, and e^(-iωt) is a complex exponential function. The inverse Fourier transform is defined as:

f(t) = (1/2π) ∫ F(ω) [tex]e^{(iwt)}[/tex] dω

where F(ω) is the Fourier transform of f(t).

Now, let's move on to the symmetry properties of the Fourier transform.

If f(t) is an even function, meaning f(-t) = f(t), then F(ω) is also even, meaning F(-ω) = F(ω).

To prove this, we start with the definition of the Fourier transform and substitute -t for t:

F(-ω) = ∫ f(-t)[tex]e^{(iwt)}[/tex] dt

Then, using the even symmetry of f(t), we can replace f(-t) with f(t):

F(-ω) = ∫ f(t) [tex]e^{(iwt)}[/tex] dt

Therefore, F(-ω) = F(ω) if f(t) is even.

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The radius of the sphere is 4.25 m and can be calculated by rearranging the volume equation of a sphere and taking the cube root of both sides of the equation.

The volume of a sphere is given by the formula V = (4/3)πr3. To find the radius of the sphere, we will solve for r. First, we will divide both sides of the equation by (4/3)π. This gives us this equation: (4/3)πr3 = 4,500 m3. We then take the cube root of both sides of the equation to get r = 4.25 m. This is the radius of the sphere. To calculate the radius of the sphere, we first rearranged the volume equation to solve for the radius. Then, we used the cube root of both sides of the equation to solve for the radius. This gave us the radius of the sphere, which is 4.25 m.

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The mass of one worker bee is \,1\cdot{ 10^{-4}}1⋅10 −4 kg, and there are 4\cdot{ 10^4}4⋅10 4 worker bees in the hive.

To find the mass of all the worker bees in the hive together, we need to multiply the mass of one worker bee by the number of worker bees in the hive:

\,1\cdot{ 10^{-4}}1⋅10 −4 kg \times 4\cdot{ 10^4}4⋅10 4 = 4\cdot{ 10^{-4}}4⋅10 −4 kg \times 4\cdot{ 10^4}4⋅10 4

Using the rules of exponents, we can simplify this expression:

4\cdot{ 10^{-4}}4⋅10 −4 kg \times 4\cdot{ 10^4}4⋅10 4 = 4 \times 4 \times 10^{-4}10 4 = 16 \times 10^0 = 16

So, the mass of all the worker bees in the hive together is 16 kg. In scientific notation, this is \,1.6\cdot{ 10^1}1.6⋅10 1 kg.

Therefore, the answer is \boxed{1.6\cdot{ 10^1}}1.6⋅10 1 kg.

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Answer:

Let's let t be the time in minutes that both machines have been working. Then, the number of boxes packed by Machine A in t minutes is 8t, and the number of boxes packed by Machine B in t minutes is 11t.

The difference between the number of boxes packed by Machine B and Machine A is less than 200, so we can write the following inequality:

11t - 8t < 200

Simplifying, we get:

3t < 200

Dividing both sides by 3, we get:

t < 200/3

To the nearest second, this is approximately 66.67 seconds.

Therefore, the possible lengths of time that the machines have been working is t < 66.67 seconds.

Note that this inequality only gives us an upper bound on the time that the machines have been working, since we know that the difference between the number of boxes packed by Machine B and Machine A is less than 200. We do not have any information on the minimum time that the machines have been working, so there are infinitely many possible solutions that satisfy the given conditions.

Step-by-step explanation:

The probability of an element being selected is 0.1

The probability of an element being selected on the first selection from a simple random sample of 40 elements from a population of 400 is 0.1

Explanation: Probability is a measure of how likely an event is to occur. It is represented by a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.

Probability is used in statistical analysis to make predictions and draw conclusions about data.

In this question, the population consists of 400 elements, and a simple random sample of 40 elements is to be drawn from it.

The probability of an element being selected on the first selection is the same as the probability of any one of the 400 elements being selected, which is 1/400 or 0.0025.

Therefore, the correct answer is option (d) 0.1

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Answer:

0.67

Step-by-step explanation:

Jill has a total of 6 cans of food, and she knows that there are 2 cans of fruit, 3 of corn, and 1 of beans. So the total number of cans of food that are not fruits is 3 + 1 = 4.

Therefore, the probability that Jill chooses a can of food that is not a fruit is 4/6 or simplified, 2/3.

So the probability that she chooses a can of food that is not a fruit is 2/3 or approximately 0.67.

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