(04.04 LC)

The functions f(x) = −2x + 30 and g(x) = 3x + 10 are shown in the graph.

graph of f of x equals negative 2 times x plus 30 and g of x equals 3 times x plus 10

Determine the approximate ordered pair for f(x) = g(x).

a
(4, 22)

b
(22, 4)

c
(4, 18)

d
(18, 4)

Answer:

OK so I'm not that good at math but the answer should be.. $175?

Step-by-step explanation:

I  don't know if that's right answer or not so... :/

Answer:

The probability of this occurring is 1/7

Step-by-step explanation:

Okay, here is a probability question.

From the question, we can identify the following;

Total number of socks = 2 + 4 + 2 = 8 socks

Since we are not given the order in which the socks was worn, we can assume any order.

Let’s say the right leg socks was worn first.

From the question, the socks on the right leg is a brown one.

So now let’s calculate the probability of selecting a brown socks out of the mix

That would be ;

number of brown socks/ total number of socks = 4/8 = 1/2

Now, for the left foot, we are having white sock here.

Kindly recall that since we already have a sock on the right foot, we have 7 socks left to pick from.

Now we need the probability of picking a white sock from the total 7. That would be ; 2/7

So the probability of both action occurring is simply the product of both probabilities and that is ;

1/2 * 2/7 = 1/7

The deceleration through the box is -531.25 m/s^2 and the time taken to get through the box is 0.96 seconds.

Given data:

Initial velocity of bullet,

u = 345 m/s

Final velocity of bullet, v = 260 m/s

Thickness of box,

s = 5.5 cm

 = 0.055 m

Now, we can use the formula for deceleration:

deceleration = (v - u)/td

                     = (v - u)/t

Substituting the given values, we get:

d = (260 - 345)/t

  = -85/t

Now, we can use the formula for time:

time = s/vt = s/v

Substituting the given values, we get:

t = 0.055/345

 = 0.00016 hours

 = 0.96 seconds

Therefore,

the deceleration through the box is -531.25 m/s^2 (negative sign indicates deceleration) and the time taken to get through the box is 0.96 seconds.

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A boxplot is a visual display that provides information about the distribution of a dataset. When we want to determine the percentage of data that falls within a certain range, we need to look at the boxplot and find the interquartile range (IQR). The IQR is the difference between the first and third quartiles, which contains the middle 50% of the data. So, approximately 50% of the data lie between 4 and 8 hours.

A boxplot shows the median, quartiles, and possible outliers. To determine the percentage of data that falls between two values, we need to calculate the proportion of the IQR that corresponds to this range. For example, if the IQR is from 2 to 10, and we want to know the percentage of data between 4 and 8, we need to calculate the proportion of the IQR that corresponds to this range. This can be done by subtracting the lower value of the range from the upper value and dividing by the IQR:

Proportion = (8 - 4) / (10 - 2) = 4 / 8 = 0.5

Therefore, approximately 50% of the data lie between 4 and 8 hours. The answer is (C) about 50%.

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The number of positive integers which are less than 1992 and  not factorial tails  are 396.

Let for some positive integer with exactly n zeros be m

Number at the end of zeros of m! be f(m)

f(m) = ( m /5 ) + ( m /25 ) + ( m /125 ) + ( m /625 ) + ....

Here 'm' is multiple of 5

So ,f(m) = f( m + 1) = f( m + 2) = f( m + 3 ) = f( m + 4 )

And f(m) ≤ ( m /5 ) + ( m /25 ) + ( m /125 ) + ( m /625 ) +...

              = m / 4.03

              = m / 4

Value of m greater than 7964 such that f(m) = 1991

f( 7975 ) = 1991

Number of distinct positive integer 7975 / 5 = 1595 less than 1992

Number of positive integers less than 1992 and they are not factorial tails  are equal to

= 1991 - 1595

= 396.

Therefore, there are 396 positive integers which are less than 1992 and  are not factorial tails.

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Answer:

y = 130

Step-by-step explanation:

(4x+8) + (3x-19) + (x+7) = 180

4x + 8 + 3x - 19 + x + 7 = 180

(4x + 3x + x) + (8 -19 + 7) = 180

8x - 4 = 180

8x -4 +4 = 180 +4

8x = 184

8x/8 = 184/8

x = 23

3(23) - 19 = 50

50 + y = 180

180 - 50 = y

y = 130

Answer:

31

Step-by-step explanation:

A straight line has the angle 180 and this one is split by line segment BO. The 180 is now split into 149+x=180, so subtract 149 from both sides to get x=31

The completed statement based on two-dimensional motion in the x-y plane can be presented as follows;

The two-dimensional motion in the x-y plane, the x part of the motion and the y part of the motion are independent, whether or not there is an acceleration in any direction. The correct option is therefore;

D) Whether or not there is an acceleration in any direction

Two-dimensional motion in the x-y plane can be analyzed by separating them into its horizontal (x) and vertical (y) components, and analyze each component using the one dimensional equations of motion.

The meaning of the motion on the x-y plane is that the x-direction motion of an object exclusive or excludes the effect of the motion of the object in the y-direction, vis a vis, the y-direction motion.

The horizontal and vertical components of the motion can be analyzes individually or by themselves, by making use of the equations of motion for a one-dimensional motion, whether or not there is an acceleration in any direction as the acceleration are also evaluated using one dimensional equations.

The possible options in the question from a similar question on the internet are;

A) When there is no acceleration in any direction

B) When there is no acceleration in one direction

C) Only when an acceleration is present in both directions

D) Whether or not there is an acceleration in either direction

E) Only when the acceleration is in the y-direction

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The Length AB of the triangle ABC is 31.079m

Area is the total amount of space filled by a flat (2-D) surface or an object's shape.

A planar figure's area is the space that its perimeter encompasses.  Square units like cm²and m² are used to measure area. The area of a form is a two-dimensional quantity.

Area of oblique triangle: S(CAB)=AC*BC*sin(ACB)/2

Substituting the values;

AC=8.4m

S(ΔCAB)=100m²

(∠ACB)=40°

S(ΔCAB)=(8.4×BC×Sin40°)/2

100=(8.4×BC×Sin40°)/2

BC=37.041m

Law of cosines:

AB²=AC²+BC²-2AC×BC×cos(∠ACB)

Substitute  the values,

AC=8.4m, ∠ACB=40 ° , BC=37.041 we get:

AB²=8.4²+37.041²-2×8.4×37.041×cos40°

AB=31.079m

Hence, The Length AB of the triangle ABC is 31.079m.

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Answer:

4+3x

Step-by-step explanation:

4+3x

The SI units of the proportionality constant G is Newton \(Kg^{-2} m^2\)

Gravitational force is given by Newton's law of gravitation which states that every particle of matter in the cosmos is drawn to every other particle by a force of attraction that varies directly with the product of their masses and is inversely proportional to the square of the distance or degree of separation from each other.

F = G \($ \frac{m_1 m_2}{r^2}\)

Upon rearranging the terms we get,

G = \($\frac{F r^2}{m_1 m_2}\)

Where F is the gravitational force, \(m_{1}\) and \(m_{2}\) are masses, and r is the length.

Force has the SI units kg · m/s2

The SI units of the proportionality constant G

SI Unit of G = \($\frac{(\text { Newton })\left(\mathrm{m}^2\right)}{\mathrm{kg} ^2}\)

= Newton \(Kg^{-2} m^2\)

Therefore the units are Newton \(Kg^{-2} m^2\)

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Newton's law of universal gravitation is represented by F = G \($ \frac{m_1 m_2}{r^2}\) where F is the gravitational force, \(m_{1}\) and \(m_{2}\) are masses, and r is a length. force has the SI units kg· m/s2. what are the SI units of the proportionality constant G?

The three points to plot for the equation 2y = 3x + 11 are (0, 5.5), (1, 7), and (-1, 4).

To graph the equation 2y = 3x + 11, we can choose any three points that satisfy the equation. Let's select three points and plot them on a coordinate plane:

Point 1:

Let's set x = 0 and solve for y:

2y = 3(0) + 11

2y = 0 + 11

2y = 11

y = 11/2 = 5.5

So, the first point is (0, 5.5).

Point 2:

Let's set x = 1 and solve for y:

2y = 3(1) + 11

2y = 3 + 11

2y = 14

y = 14/2 = 7

The second point is (1, 7).

Point 3:

Let's set x = -1 and solve for y:

2y = 3(-1) + 11

2y = -3 + 11

2y = 8

y = 8/2 = 4

The third point is (-1, 4).

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The area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

Area of regular polygon = 1/2 × apothem × perimeter

perimeter = (s)side length of octagon × (n)number of side.

apothem = s/[2tan(180/n)].

11 = s/[2tan(180/12)]

s = 11 × 2tan15

s = 5.8949

perimeter = 5.8949 × 12 = 70.7388

Area of dodecagon = 1/2 × 11 × 70.7388

Area of dodecagon = 389.0634 in²

Area of pentagon = 1/2 × 5.23 × 7.6

Area of pentagon = 19.874 in²

Therefore, the area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

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Answer:

14 grams

Step-by-step explanation:

20/100=x/70

70 * 20/100=x

14=x

Answer:

your anwser is 1085

Step-by-step explanation:

Answer:

164.85 m

Step-by-step explanation:

You have a right triangle with 60 as the side opposite the 20° angle and you are looking for the adjacent side to that angle.

The trig function to use is the tangent of an angle = opp/adj

Let x = distance from you to the base of plateau

So,  tan 20 = 60/x

x tan 20 = 60

x = 60/tan 20

x = 164.85 m

You must memorize the definitions all of the trig functions so you can do a problem like this one. OK?

The probability that a  randomly selected bolt will have a diameter greater than 19.705 mm is 0.9812.

Given that:

mean = 19.0

standard deviation = 0.3

P(18.295 < x < 19.705)

The ratio of good outcomes to all possible outcomes of an event is known as the probability. The number of positive results for an experiment with 'n' outcomes can be represented by the symbol x. The probability of an event can be calculated using the following formula.

Probability(Event) = Positive Results/Total Results = x/n

= P[(18.295 - 19.0)/0.3) < (x-mean)/standard deviation < (19.705-19.0)/0.3)]

= P(-2.35 < z < 2.35)

= P(z<2.35)-P(z<-2.35)

= 0.9906 - 0.0094

= 0.9812

Probability = 0.9812

Hence we get the required probability.

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Answer:

240

Step-by-step explanation:

15% of 54=8.1

15% of 240=36

15% of 360=54

15% of 540=81

so the answer is 240

36 is 15 percent of 240.

We have,

To find out what number 36 is 15% of, we can set up the equation:

36 = 0.15x

Here, x represents the unknown number we are trying to find.

To solve for x, we divide both sides of the equation by 0.15:

36 / 0.15 = x

Simplifying the right side gives:

240 = x

Therefore,

36 is 15 percent of 240.

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The age of the person who entered the room is 26.

From the information, the ages of the people are

23 , 19 , 12 , 21 , 13. Therefore the addition of the ages will give 88.

When another person entered, the person enters the room, the mean age of the 6 people is now 19. Therefore, the total ages will be:

= 19 × 6

= 114

Therefore, the age of the last person will be:

= 114 - 88

= 26

Therefore, the age of the person who entered the room is 26.

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The type of graph described, where the bars are positioned in order of decreasing height, is a Pareto chart. Option C

A Pareto chart is a specific type of vertical bar graph that displays data in descending order of frequency or magnitude. It is named after Vilfredo Pareto, an Italian economist who introduced the concept of the 80/20 rule, also known as the Pareto principle.

In a Pareto chart, the vertical bars represent different categories or groups, while the height of each bar represents the frequency or magnitude of the data associated with that category. The bars are arranged in descending order, with the tallest bar positioned on the left, gradually decreasing in height towards the right.

The purpose of a Pareto chart is to highlight the most significant factors or categories that contribute the most to a particular outcome. It allows for easy visual identification of the most important elements or issues, helping in decision-making and problem-solving processes.

Unlike a pie chart (option D) or a stem-and-leaf plot (option B), which represent data in different ways, a Pareto chart specifically focuses on ranking and ordering categories by their frequency or magnitude. Therefore, "pareto chart," is the most appropriate choice for the described graph. So  option C is correct.

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To calculate the standard error of the proportion, we can use the formula:

Standard Error = sqrt((p*(1-p))/n)

where p is the proportion of young adults in Generation Y who pay their monthly bills on time (which is given as 0.58), and n is the sample size (which is 210).

Plugging in these values, we get:

Standard Error = sqrt((0.58*(1-0.58))/210)
              = sqrt((0.2436)/210)
              = 0.031

Therefore, the standard error of the proportion is 0.031.

It's worth noting that the standard error is a measure of the variability of the sample proportion from one sample to another. It tells us how much we can expect the sample proportion to vary if we were to take multiple random samples of the same size from the population. In this case, a standard error of 0.031 indicates that we can expect the sample proportion of young adults in Generation Y who pay their monthly bills on time to vary by around 3.1 percentage points from one sample to another.

In conclusion, if we take a random sample of 210 people from Generation Y, the standard error of the proportion of young adults who pay their monthly bills on time is 0.031.

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The average acceleration of Train A over the interval 2 ≤ t ≤ 8 is -40 meters per minute squared.

Explanation:

The average acceleration of a body over a given time interval is defined as the change in velocity divided by the time interval. In this case, we are given the velocity function vA(t) for Train A, and we want to find its average acceleration over the interval 2 ≤ t ≤ 8.

To find the change in velocity over this interval, we can subtract the velocity at t=2 from the velocity at t=8:

Δv = vA(8) - vA(2) = (-120) - 100 = -220 meters per minute

To find the time interval, we can subtract 2 from 8:

Δt = 8 - 2 = 6 minutes

Now we can use the formula for average acceleration:

a = Δv/Δt = (-220)/6 = -40 meters per minute squared

Therefore, the average acceleration of Train A over the interval 2 ≤ t ≤ 8 is -40 meters per minute squared.

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Answer:

\(f(-2) = -20\)

Step-by-step explanation:

Plug -2 into the function for x.

\(f(x) = 7x - 6\)

For \(x=-2\):

\(f(-2) = 7(-2) - 6\)

\(f(-2) = -14 - 6\)

\(f(-2) = -20\)

(a) The probability distribution of the number of machines not running, and the mean of this distribution is 0.899.

(b)The expected fraction of time that the repair technician will be busy is 88.9% of the time.  

(a) Let X be the number of machines not running. At that point, X can take on values 0, 1, 2, 3, or 4. We will discover the likelihood conveyance of X as takes after:

P(X = 0) = P(all machines are running) = \(e^(-84)^4\)/4! = 0.302

P(X = 1) = P(one machine isn't running) = (4)(\(e^(-84)^3\)/3!) = 0.393

P(X = 2) = P(two machines are not running) = (6)(\(e^(-84)^2\)/2!) = 0.236

P(X = 3) = P(three machines are not running) = (4)(\(e^(-84)^1\)/1!) = 0.067

P(X = 4) = P(all machines are not running) = \(e^(-8*4)^0\)/0! = 0.002

The cruel(mean)  of this dispersion is E(X) = (0)(0.302) + (1)(0.393) + (2)(0.236) + (3)(0.067) + (4)(0.002) = 0.899.

(b) Let Y be the division of time that the repair specialist is active. At that point, Y can be communicated as

Y = T/(T + R),

where T is the full time that machines are not running

and R is the entire time that went through on repairs.

We know that

T has an Erlang dispersion with parameters

n = 4 and λ = 1/8 (since the running time of each machine has exponential dissemination with cruel 8 hours).

Subsequently, the anticipated esteem of T is E(T) = n/λ = 32 hours.

Additionally, R has an exponential dispersion with cruel 4 hours,

so E(R) = 4 hours. In this way, we have:

E(Y) = E(T/(T + R))

= E(T)/E(T + R)

= 32/(32 + 4)

= 0.889.

In this manner, ready to anticipate the repair professional to be active around 88.9% of the time. 

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The value of f(g(x)) is x^2 + 1/x

A function is an expression that describes the relationship between an independent variable and dependent variable.

Given the functions;

f(x) =

\( \sqrt[3]{x} \)

g(x) =

\( \frac{ x+ 1}{ {x}^{3} } \)

How to determine the function

Substitute the value do x as the value of the function g(x)

f(g(x)) =

\( \sqrt[3]{ \frac{x + 1}{ {x}^{3} } } \)

Find the cube root of the expression

f(g(x)) =

\( \frac{ {x}^{3} + {1}^{3} }{x} \)

Find the cube of the values

f(g(x)) =

\( \frac{ {x}^{3} + 1 }{x} \)

Divide through by x, we have;

f(g(x)) = x^2 + 1/x

Thus, the value of f(g(x)) is x^2 + 1/x

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By constructing a regular expression or a finite automaton that recognizes the set of strings containing the substring "aaa", we have shown that this set is regular.

To show that the set of all strings over Σ = {a, b} that include a substring "aaa" in them is regular, we can construct a regular expression or a finite automaton that recognizes this set.

1. Regular Expression:

A regular expression that represents the set of strings containing the substring "aaa" can be constructed as follows:

(aa)*aaa(aa)* + (aa)*aaa(aa)*b + (aa)*aaa(aa)*bb* + b*(aa)*aaa(aa)*

In this regular expression, the (aa)* represents any number (including zero) of consecutive "a" characters, and the (aa)*aaa(aa)* part represents the "aaa" substring surrounded by any number of "a" characters on both sides. The different possibilities after and before the "aaa" substring are accounted for using the alternatives (+) and the Kleene star (*) operator.

2. Finite Automaton:

A finite automaton can also be constructed to recognize the set of strings containing the substring "aaa". The automaton will have states representing different stages of reading the input string and transition between states based on the input symbols "a" and "b". The automaton will have a final state that is reached when the substring "aaa" is encountered.

By constructing a regular expression or a finite automaton that recognizes the set of strings containing the substring "aaa", we have shown that this set is regular.

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Answer:

it has an error of 15 more then the actual temperature

Step-by-step explanation:

to find the change all you have to do is just subtract 340 -325 that is 15 so if the oven was 100 it would show 115

Answer:

(0.4,1)

Step-by-step explanation:

I hope that this is for homework and not a quiz or test.

Since we already know the value of y which is 1, we can substitute it into the equation above it.

-5x+3=1

-5x=-2

x=2/5=0.4

So in (x,y) format (0.4,1)

Answer:

64 x 0.15 = 9.6

Step-by-step explanation: