Which ordered pair is a solution of y = x – 4?

A. (–3, 7)

B. (3, –7)

C. (–3, –7)

D. (3, 7)

The correct option is the last one, the mean will decrease.

For a set of N values {x₁, x₂, ..., xₙ} the mean is defined as the sum of the N values divided by N, this is:

mean = (x₁ + x₂ + ... + xₙ)/N

Now, here the mean is 3, and a family with 7 children (more than the mean) moves away.

That will cause a decrease in the mean, because we are removing one of the larger values.

The correct option is the last one.

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x = -6.

[tex]\sf \dfrac{3x+4}{3} -\dfrac{2x}{x-3} =x[/tex]

Applying the distributive property of multiplication on the left hand side:

[tex]\sf (3)(\dfrac{3x+4}{3} -\dfrac{2x}{x-3}) =x(3)\\ \\ \\{3x+4} -\dfrac{(3)2x}{x-3}=3x\\ \\ \\{3x+4} -\dfrac{6x}{x-3}=3x[/tex]

Applying the distributive property of multiplication:

[tex]\sf (x-3)({3x+4} -\dfrac{6x}{x-3})=3x(x-3)\\ \\ \\(x-3)({3x+4}) -6x=3x(x-3)\\ \\ \\(x)(3x)+(x)(4)+(-3)(3x)+(-3)(4) -[6x]=3x(x-3)\\ \\ \\[/tex]

Check the image below to see an illustration of this process.

[tex]\sf 3x^{2} +4x-9x-12 -[6x]=3x(x-3)\\ \\ \\3x^{2} +4x-9x-12 -6x=3x(x-3)\\ \\ \\3x^{2} -11x-12 =3x(x-3)[/tex]

Now simplifying on the right hand side (applying the same logic as last step).

[tex]\sf 3x^{2} -11x-12 =3x(x-3)\\ \\ \\3x^{2} -11x-12 =(3x)(x)+(3x)(-3)\\ \\ \\3x^{2} -11x-12 =3x^{2}-9x[/tex]

[tex]\sf 3x^{2} -11x-12+9x =3x^{2}-9x+9x\\ \\ \\3x^{2} -2x-12 =3x^{2}[/tex]

[tex]\sf 3x^{2} -2x-12-3x^{2} =3x^{2}-3x^{2}\\ \\ \\-2x-12 =0[/tex]

[tex]\sf -2x-12+12=0+12\\ \\ \\-2x=12[/tex]

[tex]\sf \dfrac{-2x}{-2} =\dfrac{12}{-2} \\ \\ \\x =-6[/tex]

If "x= -6" is the correct answer, substituting "x" by "-6" on the original equation should return the same value on both sides of the equal (=) symbol. Let's test!

[tex]\sf \dfrac{3(-6)+4}{3} -\dfrac{2(-6)}{(-6)-3} =(-6)\\ \\-6=-6[/tex]

That's correct!

x = -6 is the corect answer.

Answer:

B) Wx is equal to WX.

When a shape is rotated 90 degrees, the length of its sides and angles do not change. Therefore, the length of Wx in the original trapezoid will be the same as the length of WX in the rotated trapezoid.

The two trends on the graph are:

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

The graph

The two trends on the graph are:

For the positive correlation, we have

Upward trend from January till August

This is because the function values increase approximately in this domain

For the negative correlation, we have

Upward trend from August till December

This is because the function values decrease approximately in this domain

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Let's say there are $v$ varsity players and $j$ JV players.

The problem tells us that 2/3 of the varsity players are partnered with 3/5 of the JV players. So the number of varsity players partnered with a JV player is:

$\sf\implies\:(2/3)v$

And the number of JV players partnered with a varsity player is:

$\sf\implies\:(3/5)j$

Since these two numbers represent the same group of paired players, they must be equal:

$\sf\implies\:(2/3)v = (3/5)j$

To find the fraction of players who are partnered, we can divide the total number of paired players by the total number of players:

$\implies\:\frac{(2/3)v}{v} = \frac{2}{3}$ of the varsity players are paired

$\implies\:{\sf{\frac{(3/5)j}{j}} = \frac{3}{5}}$ of the JV players are paired

So the total fraction of players who are paired is:

$\sf\implies\:\frac{2}{3} + \frac{3}{5} - \frac{2}{15}$ (since some players will be counted in both fractions)

Simplifying:

$\sf\implies\:\frac{10}{15} + \frac{9}{15} - \frac{2}{15} = \frac{17}{15}$

Therefore, the fraction of players who are partnered for training is $\frac{17}{15}$, which is greater than 1. This means that the problem may have been set up incorrectly, or there may be additional information missing.

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The two equations that have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p include the following:

B. 2.3p – 10.1 = 6.49p – 4

C. 230p – 1010 = 650p – 400 – p

From the information provided, we have the following equation:

2.3p – 10.1 = 6.5p – 4 – 0.01p

Next, we would simplify the given equation by collecting like terms as follows;

2.3p - 10.1 = 6.5p - 0.01p - 4 = 6.49p - 4

2.3p - 10.1 = 6.49p - 4

In Mathematics, the multiplication property of equality states that both sides of an equation will remain the same and equal, when both sides of the equations are multiplied by the same number.

By multiplying both sides of the given equation by 100, we have the following;

100 × (2.3p - 10.1) = 100 × (6.5p - 4 - 0.01p)

230p - 1010 = 650p - 400 - p

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Answer:

the car's angular speed is 72,000π radians per hour.

the car's linear speed is approximately 100.53 miles per hour.

Step-by-step explanation:

To find the car's angular speed in radians per hour, we can start by finding the angular speed in radians per second.

The formula for angular speed is:

ω = 2πf

where ω is the angular speed in radians per second, and f is the frequency or rate of rotation in revolutions per second.

In this case, the wheel is spinning at a rate of 10 revolutions per second, so:

ω = 2π(10) = 20π radians per second

To convert this to radians per hour, we can multiply by the number of seconds per hour:

20π radians per second × 3600 seconds per hour = 72,000π radians per hour

To find the car's linear speed in miles per hour, we can use the formula:

v = rω

where v is the linear speed, r is the radius of the wheel, and ω is the angular speed in radians per second.

The radius of the wheel is half the diameter, or 9 inches. To convert this to miles, we can divide by 12 and then by 5280:

9 inches ÷ 12 inches per foot ÷ 5280 feet per mile = 0.000142045 miles

Now we can substitute the values we have found:

v = (0.000142045 miles) × (18/2 inches) × (20π radians per second)

v ≈ 100.53 miles per hour

Answer:

(i) 10 revolutions = 10(2π) = 20π radians

10 revolutions/sec =

(20π radians/sec)(3,600 sec/hr) =

72,000π radians/hr

(ii) C = 18π inches

10 revolutions × 18π inches =

180π inches

(180π in./sec)(3,600 sec/hr) =

(648,000π in./hr)(1 mi./63,360 in.)

= 225π/22 miles/hour

= about 32.13 miles/hour

Answer:

It is a graphical representation that discusses the relationship between two or more quantities or things

Step-by-step explanation:

The graphical method is used to optimize the two-variable linear programming. If the problem has two decision variables, a graphical method is the best method to find the optimal solution. In this method, the set of inequalities are subjected to constraints. Then the inequalities are plotted in the XY plane.

Answer:

It is a graphical representation that discusses the relationship between two or more quantities or things

Step-by-step explanation:

The graphical method is used to optimize the two-variable linear programming. If the problem has two decision variables, a graphical method is the best method to find the optimal solution. In this method, the set of inequalities are subjected to constraints. Then the inequalities are plotted in the XY plane.

Graphical methods are commonly used for determining whether the data support an interpretation of mixing of two potential sources or fractionation of a single source.

A graphic solution can be done by hand (on graph paper), or with the use of a graphing calculator. Graphing a system of linear equations is as simple as graphing two straight lines. When the lines are graphed, the solution will be the (x,y) ordered pair where the two lines intersect (cross).

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For the given function the value of f(x) when x = 2 is 0.5, option (d) is correct.

The given function f(x) = 2/x² represents a hyperbolic curve with a vertical asymptote at x=0 and a horizontal asymptote at y=0. As x approaches infinity or negative infinity, the value of the function approaches 0.

The given function is:

f(x) = 2 ÷ x²

We are asked to find the value of f(x) when x = 2.

Substituting x = 2, we get:

f(2) = 2 ÷ 2²

= 2 ÷ 4

= 1/2

= 0.5

Alternatively, we can use the fact that 2² = 4 and simplify the expression as follows:

f(x) = 2 ÷ x²

= 2 ÷ 4

= 1/2

Then, substituting x = 2, we get the same result:

f(2) = 1/2

f = 0.5

Hence, option (d) is correct.

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The distance between the two lines is about 6/√17 units, which is approximately 1.46 units

To find the distance between two parallel lines, we need to find the length of the perpendicular segment that connects them.

Both lines have the same slope (4), so they are parallel and never intersect.

The shortest distance between them will be the perpendicular distance between any point on one line and the other line.

Let's choose a point on the first line, say (0, -1), and find the perpendicular distance from this point to the second line.

We can use the formula for the distance between a point (x₁, y₁) and a line in slope-intercept form y = mx + b:

Distance = |m(x₁) - y₁+ b| /√m² + 1

Plugging in the values for the second line, we get:

Distance = |4(0) - (-1) + 5| / √4² + 1

Distance = 6 / sqrt(17)

Therefore, the distance between the two lines is about 6/√17 units, which is approximately 1.46 units

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The value of the given functions are:

(a) (f + g)(x) = (x -8 + 14) = x + 6

(b) (f-g)(x) = (x -8 - 14) = x - 22

(c) (f • g)(x) = (x - 8 (14)) = 14x - 112

(d) (f/g)(x) = (x - 8)/ 14

An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

We have the functions are as follows:

f(x)=x - 8,

g(x)=5 + 9

To solve :

a. (f + g)(x),

b. (f-g)(x),

c. (f • g)(x), and

d. (f/g)(x)

Now,

(a) (f + g)(x) = (x -8 + 14) = x + 6

(b) (f-g)(x) = (x -8 - 14) = x - 22

(c) (f • g)(x) = (x - 8 (14)) = 14x - 112

(d) (f/g)(x) = (x - 8)/ 14

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The given question is incomplete, complete question is:

For the functions f and g find a. (f+ g)(x), b. (f-g)(x), c. (f• g)(x), and d. (f/g)(x) f(x)=x - 8, g(x)=5 + 9

Answer:

x = 5√2, x = 3√2

Step-by-step explanation:

Question 1:

Using the 30-60-90 triangle properties, YX = WX /√3.

YX = 5√3 /√3 = 5.

Using the 45-45-90 triangle properties, x = YX *√2.

x = 5 *√2 = 5√2.

Question 2:

Using the 45-45-90 triangle properties, BC = AB *√2.

BC = 6 *√2 = 6√2.

Using the 30-60-90 triangle properties, x = BC / 2.

x = 6√2 / 2 = 3√2.

Answer: 50 pounds

Step-by-step explanation:

The maximum weight of the luggage a passenger can bring without charge is 50 pounds.

Mary Ellen has decided to weigh each item as she packs her bag.

weight of Suitcase = 3.65 lbs

weight of clothing = 4.35 lbs

weight of shoes = 8.67 lbs

weight of toiletries = 11.35 lbs

weight of extras = 21.63 lbs

Now we will add the weights of each items

Total weight = 3.65 + 4.35 + 8.67 + 11.35 + 21.63 = 49.65

Rounding to the nearest to the one pound will be = 50 lbs

(Since 0.65 is greater than 0.5 so by rounding off 0.65 will become 1.)

Therefore the estimated weight is 50 pounds.

Answer:

10000

otra solución es: 10⁴

Answer:

B) The other number is even.

The number of packing materials the Amelia will need = 2.4

From the diagram given above, the formula for the volume of a right rectangular prism = Length×width ×height.

Where;

Length = 10in

Width = 6 in

Height = 8 in

The volume = 10×6×8 = 480 in³

But one bag = 200in³

The amount of bag that the music box can contain = 480/200 = 2.4

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Applying mathematical operations, the greatest number of necklaces Georgia can make is 26.

The total number of beads available for making bracelets and necklaces is an addition operation between the beginning inventory of beads and the additional units purchased.

A subtraction operation is performed to determine the remainder after making bracelets.

Finally, a division operation determines the greatest number of necklaces to make.

The beginning inventory of beads = 322

The units purchased = 38 beads

The total number of beads that Georgia has = 360 (322 + 38)

The number of beads required to make bracelets = 120

The remainder after making bracelets = 240 (360 - 120)

The number of beads required for each necklace = 9

The greatest number of necklaces Georgia can make = 26 (240 ÷ 9)

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Answer:

Time = Distance / Speed

Time is taken from home to park = d / 10

Abel cycled back from the park to his home at an average speed of 8 km/h. The time taken for this part of the journey can be calculated using the same formula:

Time = Distance / Speed

Time is taken from park to home = d / 8

According to the given information, the total time taken for the whole journey is 1 1/5 hours, which is equivalent to 6/5 hours.

Total time is taken = Time from home to park + Time from park to home

6/5 = d/10 + d/8

To simplify the equation, let's find the least common multiple (LCM) of 10 and 8, which is 40:

(6/5) * 40 = (d/10) * 40 + (d/8) * 40

48 = 4d + 5d

48 = 9d

d = 48/9

d = 16/3 km

Now, to find the time taken from the park to Abel's home, we substitute the distance value:

Time from park to home = (16/3) / 8

Time from park to home = (16/3) * (1/8)

Time from park to home = 16/24

Time from park to home = 2/3 hour

Since 2/3 of an hour is equal to 40 minutes, Abel took 40 minutes to cycle from the park to his home.

Therefore, Abel took 40 minutes (or 2/3 of an hour) to cycle from the park to his home.

Answer:

To calculate the speed of the airplane, we need to subtract the speed of the headwind from the speed of the tailwind.

To calculate the speed of the airplane, we need to subtract the speed of the headwind from the speed of the tailwind. Speed of airplane = (Speed of tailwind) - (Speed of headwind)

To calculate the speed of the airplane, we need to subtract the speed of the headwind from the speed of the tailwind. Speed of airplane = (Speed of tailwind) - (Speed of headwind)Speed of airplane = (150 mph) - (100 mph)

To calculate the speed of the airplane, we need to subtract the speed of the headwind from the speed of the tailwind. Speed of airplane = (Speed of tailwind) - (Speed of headwind)Speed of airplane = (150 mph) - (100 mph)Speed of airplane = 50 mph

To calculate the speed of the airplane, we need to subtract the speed of the headwind from the speed of the tailwind. Speed of airplane = (Speed of tailwind) - (Speed of headwind)Speed of airplane = (150 mph) - (100 mph)Speed of airplane = 50 mphTherefore, the speed of the airplane would be 50 mph.

Here is a tree diagram to represent the sample space of Jill tossing a coin three times:

      H               T

    /   \           /   \

   H     T         H     T

 /  \   /  \     /  \   /  \

H   T  H   T    H   T  H   T

The concept of the sample space is fundamental to the calculation of probabilities because it defines the set of all possible outcomes that we are interested in measuring the likelihood of. By specifying the sample space, we can define events (subsets of the sample space) and assign probabilities to those events.

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Probability that event A or B takes place is, P(A or B) = 16/21.

Here from the Venn diagram we can obtain that,

Probability of occurring event A = 2/21 + 4/21 = (2 + 4)/21 = 6/21

Probability of occurring event B = 10/21 + 4/21 = (10 + 4)/21 = 14/21

Probability of occurring event A and event B both = 4/21

So, P(A) = 6/21

P(B) = 14/21

P(A and B) = 4/21

We know that the union of events formula,  

P(A or B) = P(A) + P(B) - P(A and B)

P(A or B) = 6/21 + 14/21 - 4/21

P(A or B) = (6 + 14 - 4)/21

P(A or B) = 16/21

Hence the value of P(A or B) = 16/21.

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The inverse statement of M implies N is a negation of both the conclusion and the hypothesis.

An inverse statement is one in which both the hypothesis and the conclusion are negated. Let us assume a statement with the hypothesis and conclusion as follows: If they annul the law, we will drive carelessly.

The inverse of this statement will be: If they do not annul the law, we will not drive carelessly. So, both the hypothesis and the conclusion are rewritten in negative terms.

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Check the picture below.

Answer:

Earned = 25 + 18h

Earned = 151

Step-by-step explanation:

The amount earned is the travel time plus the amount per hour times the hours

Earned = 25 + 18h

She works 7 hours

Earned = 25 + 18*7

Earned = 25 + 126

Earned = 151

Answer:

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The probability of catching a carp is 40% since 40% of the fish are carp.

We assume the fish is replaced each time so the probability of three carps is: