43. Consider the equation 4(x-8)+y=9(x-2)

[Part 1]

Find an expression for y of the form ax+b expression for y such that the equation has infinitely many solutions. Is there more than one such solution? Explain your reasoning using complete sentences.


[Part 2]
Find an expression for y of the form ax+b expression for y such that the equation has no real solutions. Is there more than one such solution? Explain your reasoning using complete sentences.

The amount the gambler can win in this fractional game that pays a 10 to 1 with a 1/12 chance of winning is $2,500.

A fractional betting or game allows the gambler to calculate the winning from their betting when it is compared with their stake.

The number on the left-side represents the winning, while the number on the right side of the fractional odds represents the stake (investment).

When the gambler wins, they receive 10x their stake.  The expected amount to be won is computed as the total stakes, multiplied by the winning probability and the fractional odds.

Fractional odds of winning = 10/1

Chance of winning = 1/12

Number of independent games played = 150 times

Bet each time = $20

Total bets = $3,000 ($20 x 150)

Amount won = $2,500 ($3,000 x 1/12 x 10/1)

Thus, the amount the gambler can win in this fractional game that pays a 10 to 1 with a 1/12 chance of winning is $2,500.

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How much do you expect to win?

The outcome of the product is 4 + 2/24, so the correct option is B.

Here we want to solve:

(4 + 2/3)*(7/8)

Using the distributive property of the product we get:

4*(7/8) + (2/3)*(7/8)

28/8 + 14/24

Now we can multiply the first fraction by (3/3) (it does not change the fraction).

(3/3)*28/8 + 14/24

84/24 + 14/24 = 98/24  

Now we can rewrite it as:

98/24 = (96/24) + (2/24)  =4 + 2/24

Then the correct option is B.

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The number of half page advertisements that Michael purchased is 4 while the full page advertisements is 11.

The elimination approach involves taking one variable out of the system of linear equations by utilising addition or subtraction together with multiplication or division of the variable coefficients.

Let the number of half page ads be represented by h

Let the number of full page ads be represented by f.

Total number of advertisements = 15

h + f = 15 ....... (i)

h = 15 - f

Therefore, the system of equations to represent the situation will be:

60h + 100f = 1340 ........ (ii)

Put the value of h into equation (ii)

60(15 - f) + 100f = 1340

[tex]\Rightarrow[/tex]  900 - 60f + 100f = 1340

Collect like terms

    100f-60f  = 1340-900

[tex]\Rightarrow[/tex]              40f = 440

[tex]\Rightarrow[/tex]                   f = 11

The number of full-page advertisements that Michael purchased is 11.

Since h + f = 15

[tex]\Rightarrow[/tex]    h + 11 = 15

[tex]\Rightarrow[/tex]       h = 15 - 11

[tex]\Rightarrow[/tex]      h = 4

The number of half page advertisements that Michael purchased is 5.

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Around 298 people can sing together with the same relative intensity to achieve a loudness of 80 decibels.

Given Information

Loudness of sound is given as, l = 10 log₁₀r

Here, r is the relative intensity.

Relative intensity of a single person when singing = 10

Loudness to be achieved, L = 10 decibels

Calculating the Number of People

Let the number of people with relative intensity 10 singing together be n decibels, then to produce a loudness of 80 decibels, we have,

80 = 10 log₁₀(r × n)

80 = 10 log₁₀(10 × n)  [∵ r = 10]

log₁₀(10 × n) = 8

10n ≈ 2980

n = 298

Therefore, 298 people, each with a relative intensity of 10 decibels can sing together to achieve a loudness of 80 decibels.

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The maximum possible length of the rectangular front of the building is 23 feet

The complete question is attached

Let the length of the rectangular front be x and the height be y.

So, we have:

x = 2y

The building has 4 congruent sides.

So, the area of the 4 sides is

A = 4 * (x * y)

This gives

A = 4 * (x * 2x)

Evaluate

A = 8x²

For the triangular roof, we have:

Slant height, l = y

Base, b = x

So, the area of the 4 triangular faces is

A = 0.5 * 4 * xy

This gives

A = 2xy

Recall that:

x = 2y

Make y the subject

y = 1/2x

So, we have:

A = 2x * 1/2x

A = x²

The cost of designing the buildings is

C = 25 * 8x² + 50 * x²

C = 200x² + 50x²

C = 250x²

This gives

250x² = 500000

Divide both sides by 250

x² = 2000

Square both sides

x = 45

Recall that:

y = 1/2x

This gives

y = 1/2 * 45

y = 23

Hence, the maximum possible length of the rectangular front of the building is 23 feet

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The probability of getting tails on the coin and an even number on the number cube is 1/4

Probabilities are used to determine the chances, likelihood, possibilities of an event or collection of events

The sample space of a coin is:

S = {H, T}

The sample space of a die is:

S = {1, 2, 3, 4, 5, 6}

The above means that:

A coin has 2 faces, one of which is the tail.

So, we have:

P(Tail) = 1/2

A number cube has 6 numbers, 3 or which are even.

So, we have

P(Even) = 3/6

The required probability is

P = P(Tail) * P(Even)

This gives

P = 1/2 * 3/6

Evaluate

P = 1/4

Evaluate the quotient

P = 0.25

Hence, the probability of getting tails on the coin and an even number on the number cube is 1/4 or 0.25

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Using it's concept, the relative frequency of business majors in the sample is of 0.16 = 16%.

A relative frequency is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, there are 337 students, of which 30 + 24 = 54 students are business majors, hence the relative frequency is:

r = 54/337 = 0.16 = 16%.

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Step-by-step explanation:

the volume of a 3D object is always calculated in some way by multiplying the 3 dimensions with each other.

so, if every dimension is then changed by a factor f (4 in our case), then the volume changes by f×f×f = f³, as the factor has to be included in the calculation for each dimension. and as they are multiplied with each other, so are the scaling factors in each case.

in our case the prism is dilated by the factor 4.

that means that every side length, every height, ..., each dimension is increased by the factor 4.

and therefore, the volume increases by the factor 4³ = 64.

so, the volume of the new image is

244 × 64 = 15,616 cm³

Volume changes by f × f × f = f³

Volume increases by the factor of 4³ = 64

The volume of the new image exists 244 × 64 = 15616 cm³.

The volume of a 3D object exists always computed in some form by multiplying the 3 dimensions by each other.

The volume changes by f × f × f = f³, as the factor, contains to be included in the calculation for each dimension and as they exist multiplied with each other, so exist the scaling factors in each case.

Here, the prism exists dilated by factor 4 which indicates that every side length, every height and each dimension exists increased by factor 4.

Volume increases by the factor of 4³ = 64

The volume of the new image exists 244 × 64 = 15,616 cm³.

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The surface area of the composite figure is 444m²

Given a composite figure which is shown in the question.

The  area of ​​a shape (in square units) is the number of unit squares required to cover the entire area without gaps or overlaps. If a hologram has planes, those faces are called faces. Area is the sum of the areas of the faces.

Firstly, we will find the area of front and end triangles by using the formula

Area=(1/2)×b×h and we will multiply this area by 2 because we are finding the area of two same triangles.

Here, h=6 and b=16 and substitute these values in the formula, we get

A₁=2×(1/2)×16×6

A₁=2×8×6

A₁=96m²

Now, we will find the area of the left and right side rectangles which joined both the triangles.

We will find the area by using the formula Area=l×b and we will multiply this area by 2 because we are finding the area of two same rectangles.

here, l=10 and b=5 and substitute these values in the formula, we get

A₂=2×10×5

A₂=100m²

Further, we will find the area of the front and end side rectangles that joined both by the base of the triangles.

We will find the area by using the formula Area=l×b and we will multiply this area by 2 because we are finding the area of two same rectangles.

here, l=16 and b=4 and substitute these values in the formula, we get

A₃=2×16×4

A₃=128m²

Furthermore,  we will find the area of the left and right side rectangles which joined by the front and end rectangles.

We will find the area by using the formula Area=l×b and we will multiply this area by 2 because we are finding the area of two same rectangles.

here, l=4 and b=5 and substitute these values in the formula, we get

A₄=2×4×5

A₄=40m²

Now, we will find the area of the base of the composite figure which is rectangle.

We will find the area by using the formula Area=l×b.

here, l=16 and b=5 and substitute these values in the formula, we get

A₅=16×5

A₅=80m²

So, the surface area of the given composite figure will be

Surface area=A₁+A₂+A₃+A₄+A₅

Surface area=96m²+100m²+128m²+40m²+80m²

Surface area=444m²

Hence, the surface area of the given composite figure is 444m².

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The domain of the exponential function given is the set of all real numbers while the range of the exponential function is the set of all real numbers greater than zero.

As with other exponential functions, it follows that the domain of the exponential function given is the set of all real numbers while the range of the exponential function is the set of all real numbers greater than zero.

Additionally, by observation, the function has a positive variable correlation, hence;

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Answer:

7

Step-by-step explanation:

Perpendicular lines have slopes that are negative reciprocals of each other. For example, if line A has a slope of 2, then line B, perpendicular to line A, will have a slope of -0.5.

The solution to the system of inequalities is (-3.375, 1.75)

The system of inequalities is given as:

3y > 2x+12

2x+y ≤ -5

Next, we plot the graph of the system using a graphing tool

From the graph, both inequalities intersect at

(-3.375, 1.75)

Hence, the solution to the system of inequalities is (-3.375, 1.75)

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Answer:

10x-6y-11

Step-by-step explanation:

3(3x+y) = 3(3) +×-3y=-2

9x + 3y = 9 + x -3y =-2

9x+x = -3y-3y =-2-9

10x = -6y =-11

10x-6y-11

The 15 foot ramp must make an angle 19.45° with the ground to reach the same window.

Since the height of the window above ground remains constant in both cases, it follows that by means of trigonometric identity sine; we have;

10sin30° = 15sinx

sinx = 5/15 = 0.333

x = sin-¹(0.333)

x = 19.45°.

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Hello,

an other method

Pythagorean theorem :

x² + x² = 6²

2x² = 36

x² = 36/2

x² = 18

x = √18 (and not -√18 because x ≥ 0)

x = √(9 × 2)

x = √(3² × 2)

x = 3√2

Answer A

The graphed function, F(x), has a value greater than 0 over the intervals (-0.7, 0.76) and (0.76,  ∞) . F(x) > 0 over the intervals (-0.7, 0.76) and (0.76, ∞) is the correct statement [Fourth choice].

About a Graphed Function

The function graph of an object F stands for the set of all points in the plane that are (x, f(x)). The graph of f is also known as the graph of y = f. (x). The graph of an equation is thus a specific example of the graph of a function. A graphed function is a function that has been drawn out on a graph.

It is evident from the attached graph that the supplied function exceeds 0 for the following range:

-0.7 < F(x) < 0.76

And, 0.76 < F(x) < ∞

As a result, the intervals for which the given graphed function, F(x) is greater than 0 are as follows,

(-0.7, 0.76) and (0.76, ∞)

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The complete table of values for the function rule y = -2x +9 is

x -4 -2   0  2  4

y 17    13  9 5  1

Linear equations are equations that have constant average rates of change, slope or gradient

From the question, the function rule is given as:

y = -2x +9

The table of values is given as:

x -4 -2 0 2 4

y 17

Next, we substitute the other values of x in the equation y = -2x +9

y = -2(-2) +9 = 13

y = -2(0) +9 = 9

y = -2(2) +9 = 5

y = -2(4) +9 = 1

So, the complete table of values is

-4     -2   0  2  4

y 17    13  9 5  1

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Using a system of equations, it is found that she has 9 picture books.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the variables are:

The ratio of the number of picture books encyclopedias, and fairy tale books Annette had is 3:4:5, hence:

[tex]\frac{x}{y} = \frac{3}[4}, \frac{x}{z} = \frac{3}{5}, \frac{y}{z} = \frac{4}[5}[/tex]

She gave half of her encyclopedias to her brother and he gave her 5 books of fairytales. Now she has 14 more books of fairy tales than encyclopedias, hence:

z + 5 - 0.5y = 14.

z - 0.5y = 9

From the ratios, we have that:

[tex]y = \frac{4}{3}x, z = \frac{5}{3}x[/tex]

Hence we solve for x to find the number of picture books:

[tex]z - \frac{y}{2} = 9[/tex]

[tex]\frac{5}{3}x - \frac{2}{3}x = 9[/tex]

x = 9.

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The average height is [tex]5feet[/tex] and [tex]11.5[/tex] inches if Allen is [tex]5 feet 9 inches[/tex] tall and Terrel is [tex]6 feet 2 inches[/tex] tall.

How to find the average height ?

Allen height is [tex]5feet ,9inches[/tex]

Terrel height is [tex]6feet,2inches[/tex]

And we know that [tex]1feet=12inches[/tex]

So Allen height is

[tex]=5*12+9\\=60+9\\=69 inches[/tex]

And Terrel height is

[tex]=6*12+2\\=72+2\\=74inches[/tex]

Average of the Allen and Terrel height is

[tex]\frac{69+74}{2\\} \\=143/2\\=71.5inches[/tex]

And average height in feet is  [tex]5feet,11.5inches[/tex]

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Answer:

Step-by-step explanation:

6 and 9

Answer: 16 girls and 22 boys

Step-by-step explanation:

This can be solved with simple algebra.

Let's say that the number of girls is x.

Since there are 10 less than twice as many boys as girls, the number of boys would be 2x-10. (2x for twice as many, and -10 for ten less.)

The total number of students is 38. Adding the girls, the equation is now 3x-10=38.

3x=48

x=16.

2x-10=the number of boys, as said earlier. SO, 32-10=22=the number of boys.

To check our work, add 16+22. This equals 38.

Answer:

D. [tex]\displaystyle{\dfrac{5^8}{9^8}}[/tex]

Step-by-step explanation:

The law of exponent defines that:

[tex]\displaystyle{\left(\dfrac{a}{b}\right)^n = \dfrac{a^n}{b^n}}[/tex]

In word, you simplify the expression by expanding an exponent to both numerator and denominator.

So from the expression [tex]\displaystyle{\left(\dfrac{5}{9}\right)^8}[/tex], you expand the exponent 8 in both numerator and denominator then you'll end up with D choice!

If you have any questions then please let me know in comment!

Answer:

250,000 Meters

Step-by-step explanation:

1 Km = 1000 meters

250x1000= 250,000 meters

Answer:

acute angle and angle between zero and 90 degrees right angle and 90 degree angle obtuse angle and angle between 90 and 180

Answer:

what kind of people are the best division

Answer:

D

Step-by-step explanation:

The red line starts with a filled in circle that mean that the number -12 is included.  The graph is saying that x can be -12 or any number above -12.  The line under the > is telling you that 12 is included.

Answer:

16

Step-by-step explanation:

We can use the binomial distribution formula to find the probability of flipping three coins tails, four coins tails, and five coins tails. This is because the probability of P(x=3) is going to give the same result if we had defined the entire set, counted how many had 3, and then divided that by the entire set. So we can use this to find how much % of the data set is going to have at least 3.

So the binomial distribution formula is defined as: [tex]P_x=(^n_x)p^x(1-p)^{n-x}[/tex], where n=number of trials, x=how many successes (in this case it will be 3, 4, and 5) and p=probability of success.

The binomial coefficient is defined as: [tex](^n_x)=\frac{n!}{k!(n-x)!}[/tex].

So let's define the variables.

x = 3, 4, 5 since we want to find the probability of getting at least 3. This means we want the probability of getting 3, 4, or 5 tails, and then we simply add up these probabilities.

n = 5, since Paul is flipping the coin 5 times

p = 0.5 since the probability of flipping tails is 0.50

So let's plug the information in!

[tex]P_{x\ge3} = P_3 + P_4 + P_5[/tex]

[tex]P_3=\frac{5!}{3!2!}*0.5^30.5^2 = 0.3125[/tex]

[tex]P_4=\frac{5!}{4!1!}*0.5^4*0.5^1=0.15625[/tex]

[tex]P_5 = \frac{5!}{5!0!}0.5^50.5^0 = 0.03125[/tex]

Now let's add up all these probabilities to get:

[tex]0.3125 + 0.15625 + 0.03125 = 0.5[/tex]

This means 50% of the time Paul will flip three or more tails.

To translate this to the number of ways, we need to find how many combinations there are which can generally be defined as: [tex]options^{length}[/tex] and in this case options = tails and heads so 2, and the length is 5. So we get: [tex]2^5 = 32[/tex]

Now multiply the 32 by the 0.5 and you get 16, which is the amount of ways he can flip at least three tails

Answer:

16

Step-by-step explanation:

In order to determine the number of different groups of three players that are possible for Coach Bennet to select from, we would use a mathematical model referred to as combination.

Mathematically, combination is given by this mathematical equation:

[tex]_nC_r = \frac{n!}{r!(n-r)!}[/tex]

Where:

Substituting the given parameters into the formula, we have;

Number of groups = (⁶C₃ × ⁸C₀) + (⁶C₂ × ⁸C₁) + (⁶C₁ × ⁸C₂) + (⁶C₀ × ⁸C₃)

Number of groups = 20 + 120 + 168 + 56

Number of groups = 364 different groups.

Therefore, there are 364 different groups of three players possible for Coach Bennet to select.

In conclusion, we can infer and logically deduce that this is a combination because the order in which the players are selected isn't important.

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Complete Question:

In this activity, you will apply your understanding of permutations and combinations to calculate probabilities. Use the information in this scenario to answer the questions that follow. Coach Bennet’s high school basketball team has 14 players, consisting of six juniors and eight seniors. Coach Bennet must select three players from the team to participate in a summer basketball clinic.

How many different groups of three players are possible for Coach Bennet to select?

Answer:

The slope is -3, in a y=mx+b equation the x coefficient is the slope

The interquartile range is 55.

The interquartile range is the difference between the upper quartile and the lower quartile. In example 1, the IQR = Q3 – Q1 = 87 - 52 = 35. The IQR is a very useful measurement. It is useful because it is less influenced by extreme values as it limits the range to the middle 50% of the values.

Interquartile range = higher quartile - lower quartile

Given data,    50,25,80,10

To arrange the given data in ascending order 10,25,50,80.

Now, we will find the median for the given data.

The median is obtained by first arranging the data in ascending order and applying the following rule.

If the number of observations is even, then the median is [tex]\frac{n}{2}th[/tex] term.

In given data the number of observations is '4'(even)

If the number of observations is even, then the median is [tex]\frac{4}{2} th[/tex] means 2nd term. So median for the given data is 25. It means the value of lower quartile is 25 .

Interquartile range = higher quartile - lower quartile

                                 = 80-25

                                = 55  

Thus, interquartile range  for the given data is 55.

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The above question is not complete.

by taking the quotient between the volume in the pot and the volume of each serving, we conclude that there are 12 servings.

The number of servings is given by the quotient between the volume in the pot and the volume of each serving, so we have:

N = (3/4)*/(1/16) = 12

So there are 12 servings in the pot.

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