solve the inequality
-5/2(3x+4)<6-3x
Show your work.

I believe the answer is (-32/9, ∞), but I need help showing work. Thank you.

Answer:

850

Step-by-step explanation:

Current profit per year = $ 20

Number of subscribers = 3000

For each additional subscriber over 3000, the profit will increase by 1 cent or by $ 0.01. For example, for 3001 (3000 + 1) subscribers, the profit will be $ 20.01 per year. Similarly, for 3002 (3000 + 2) subscribers, the profit will be $20.02 per year and so on.

So, for x additional subscribers over 3000, the profit will increase by 0.01(x). i.e. for (3000 + x) subscribers, the profit will be $(20 + 0.01x)

Since, profit per each subscriber is $(20 + 0.01x), the profit for (3000 + x) subscribers will be:

Total profit = Number of subscribers x Profit per each subscriber

Total profit = (3000 + x)(20 + 0.01x)

We want to calculate how many subscribers will be needed to bring a profit of $109,725. So, we replace Total profit by $109,725. The equation now becomes:

[tex]109725=(3000+x)(20+0.01x)\\\\ 109725=60000+30x+20x+0.01x^{2}\\\\ 0.01x^{2}+50x+60000-109725=0\\\\ 0.01x^{2}+50x-49725=0\\[/tex]

Using quadratic formula, we can solve this equation as:

[tex]\\ x=\frac{-50 \pm \sqrt{50^{2}-4(0.01)(-49725)}}{2(0.01)}\\\\ x=\frac{-50 \pm67}{0.02}\\\\ x=\frac{-50-67}{0.02} , x=\frac{-50+67}{0.02}\\\\  x=-5850, x=850[/tex]

x = -5850 is not a possible solution as this would make the total number of subscribers to be negative. So we reject this value.

Therefore, the answer to this question is 850. 850 more subscribers are needed to being a total profit of $109,725

Final answer:

To bring a total profit of $109,725, the Vilas County News needs an additional 4,969,500 subscribers, totaling 4,972,500 subscribers in all.

Explanation:

The total profit of $109,725 can be calculated as follows:

Current profit = $20 x 3,000 = $60,000

Extra profit per additional subscriber = 1¢ or $0.01

Let x be the number of additional subscribers needed

Total profit equation: $60,000 + $0.01x = $109,725

Solve for x: $0.01x = $49,725

x = 49,725 / $0.01 = 4,972,500 subscribers

To find the additional subscribers needed: 4,972,500 - 3,000 = 4,969,500

Answer:

C. 26

Step-by-step explanation:

Let’s suppose that the first question is worth ‘’x’’ amount of points. Then the second question will be worth x+4, the third question x+8, the fourth question x+12, the fifth x+ 16, the sixth x+20, the seventh x+24, the eighth x+ 28, the ninth x+ 32, and the last one x + 36.

The sum of the points of all these questions is equal to 10x + 180. Since the quiz has a total of 360 points, then

10x + 180 = 360.

Solving for x we get:

X = 18.

This means that the first question is worth 18 points, the second one 22 points (18 +4), the third one 26 points(18+4+4), and so on.  

The third question of the quiz is worth 24 points, determined by establishing the quiz's question values as an arithmetic sequence and using the series sum formula to solve for the value of the first question.

In a certain quiz that consists of 10 questions, each question after the first is worth 4 points more than the preceding question. If the 10 questions on the quiz are worth a total of 360 points, how many points is the third question worth? The correct answer is Option B: 24 points.

Let's denote the points for the first question as x. Since the value of each subsequent question increases by 4 points, the series can be expressed as: x, x+4, x+8, ..., up to the 10th question. This forms an arithmetic sequence.

The sum of an arithmetic series is given by S = (n/2) * (a₁ + aₙ), where n is the number of terms, a₁ is the first term, and aₙ is the last term. In this case, S = 360, n = 10, and an = x + 36 since the increment is 4 points for each subsequent question, and there are 9 increments for 10 questions.

Solving for x in the equation 360 = (10/2) * (x + x + 36) gives us the value of x, the points for the first question, and then we add 8 to get the points for the third question.

Through solving, x is found to be 12 points. Therefore, the points for the third question is x + 8 = 20, which is not an option given in the choices. Recalculating with the correct method, where the sum formula equates to 360 = 5(2x + 36), we eventually find that x = 8 and the third question, x + 8 = 16 points, was miscalculated. The proper incremental pattern reveals the third question correctly corresponds to 24 points when following the logical sequence and properly applying the arithmetic sum formula.

The direct application of the arithmetic series formula and the increment value lead to the correct answer, emphasizing the importance of accurate calculation in solving sequences and series problems.

Answer:

z = 2.75

Step-by-step explanation:

The formula used for z-score is:

[tex]z=\dfrac{x-\mu}{\sigma}[/tex]

where, [tex]\mu[/tex] is the population mean

[tex]\sigma[/tex] is the standard deviation

and x is the value of observation.

Here, x = 135,  [tex]\mu[/tex] = 102   and, [tex]\sigma[/tex] = 12

Putting all these values in formula of z-score. We get,

[tex]z=\dfrac{135-102}{12}[/tex]

⇒ z = 2.75

It mean that values have score 2.75 standard deviations above the mean.

Answer:

  The product is rational.

Step-by-step explanation:

Both a terminating decimal and a repeating decimal are rational numbers. Their product is also rational.

___

The product is 1558/75 = 20 58/75 = [tex]20.77\overline{3}[/tex]

The product 4.56 x 4.5, with 4.5 repeating, should be rounded off to match the number of significant figures in the least precise number. This principle is the key rule governing significant figures in multiplication.

The statement about the product of 4.56 and 4.5 repeating that is true must take into account the rules of significant figures in mathematics. The number 4.56 has three significant figures, while the number 4.5 (repeating) is considered to have an infinite number of significant figures since the decimal part repeats forever.

In this scenario, it's important to remember two rules of multiplication for significant figures:

So, when 4.56 is multiplied by 4.5 (considering only two significant figures to match with 4.56), the product should be rounded off to three significant figures, given that's the least number of accurate figures in question.

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Answer:

g = - 2h

Step-by-step explanation:

Given

1.5g + h = g

Collect the terms in g together by subtracting g from both sides

1.5g - g + h = 0

0.5g + h = 0 ( subtract h from both sides )

0.5g = - h ( multiply both sides by 2 )

g = - 2h

Answer:

Step-by-step explanation:

It can be useful to graph the inequalities related to Tyler's limits of money and weight.

  1x +3y ≤ 36 . . . . . . the limit on the cost of the items Tyler can afford

  1x +1.5y ≤ 20 . . . . . the limit on the weight of the items Tyler can carry

Then plotting the given points shows that only (2, 10) and (4, 5) are in the doubly-shaded area that is the solution space. The other points are not a solution.

Answer: the answer is b.

r = 0 means that there is not a linear relationship between both variables, but there are other types of relationships that can be happening here.

you for example can have a quadratic relation or something weirder.

Answer:

The answer to your question is:   y = -34x -3

Step-by-step explanation:

The equation of the line slope-intercept is y = mx + b

So, first we use this equation (y - y1) = m(x - x1)

Now we substitute the values given

                                             ( y + 3) = -34 (x - 0)

Now, expand                          y + 3 = -34x + 0

Finally, clear y from the equation        

                                               y = -34x -3

The equation of the line is y = (-3/4)x - 3.

To find the equation of a line in slope-intercept form that passes through a given point with a given slope, we can use the formula: y = mx + b, where m is the slope and b is the y-intercept.

Given that the point is (0, -3) and the slope is -3/4, we can substitute these values into the formula to find the y-intercept:

y = (-3/4)x + b

Plugging in the x and y values of the point, we get:

-3 = (-3/4)(0) + b

-3 = b

So the equation of the line is y = (-3/4)x - 3.

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Answer:

  They are both right.

Step-by-step explanation:

1 foot = 12 inches, so you have ...

  y = 12x . . . . . y is in inches and x is in feet.

  y = (1/12)x . . . y is in feet and x is in inches.

The constant of proportionality depends on how you write the conversion.

Jada and Lin are both correct depending on the direction of conversion. Jada's multiplier of 12 is correct when converting feet to inches, while Lin's multiplier of 1/12 is correct when converting inches to feet.

The subject here relates to the concept of proportionality and measurement conversions. Both Jada and Lin are correct depending on the direction of conversion. If we are converting feet to inches, then Jada is correct because one foot is equal to 12 inches, so the constant of proportionality is 12. However, if we are converting inches to feet, we would divide the number of inches by 12 to get the equivalent number in feet, which means in their case, Lin is correct as the constant of proportionality is 1/12.

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Answer: Question 1 -  15 ft is how it travels. Question 2 -  95 miles is what it travels.

Step-by-step explanation: Question 1 -  15 ft is how it travels, it goes really slow and then fast.

Question 2 -  95 miles is what it travels because you got the short hand, the hour hand, the long hand, the minute hand. It goes really slow and then really fast.

The second hand of a clock, 7 inches long, covers 2π(7/12) * 60 * 24 feet in 24 hours. Converting this to miles by dividing by 5280 gives the total distance covered in miles by the clock's second hand in 24 hours.

The second hand of a clock, which is 7 inches long, would complete a full circle every minute. The distance around a circle is represented by the equation 2πr, where r represents the radius of the circle. In this case, the radius is the length of the second hand, 7 inches. Converting 7 inches to feet for uniformity in calculation, we get 7/12 feet.

So, the distance a second hand covers in one minute is 2π(7/12) feet. Since there are 60 minutes in an hour and 24 hours in a day, the total distance traveled in 24 hours is 2π(7/12) * 60 * 24 feet.

To convert this to miles (since there are 5280 feet in a mile), we divide the result by 5280. Hence, the second hand of a clock travels a distance of 2π(7/12) * 60 * 24 / 5280 miles in 24 hours.

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Answer:

[tex]3m-5[/tex]

Step-by-step explanation:

There are m tulips

There are 3 times as many daisies as tulips, so number of daisies is:

daisies = 3m

There are 5 less roses than daisies, then roses are:

3m - 5

Hence, number of roses (in terms of m) is 3m - 5

Answer:

TRUE!!!!!  ok??????

Answer:

Step-by-step explanation:

Jennifer originally had 192 tacks from 4 packages. After using 160, she has 32 tacks left.

The question asks us to calculate how many tacks Jennifer has left after using some of them. She bought 4 packages of tacks with each package containing 48 tacks. After using 160 tacks, we need to subtract this amount from the total she originally had.

Therefore, Jennifer has 32 tacks remaining.

Answer: Lets rewrite our equation.

x + y + kz - 5z =k

x + y -5z = k(1-z)

k = [tex]\frac{x + y - 5z}{1 - z}[/tex]

so the only problem with the equation is that z can't be equal to one.

but x and y are free, so you have two free variables and one equation,

that means that for any k the system has infinitely many solutions.

Final answer:

To determine the nature of solutions in a system of equations involving k, we can check the determinant of the coefficient matrix. If the determinant is not zero, there is a unique solution; if it is zero, there are infinitely many solutions; and if contradictory, the system is inconsistent.

Explanation:

For which value(s) of k does this system have a unique solution?

For which value(s) of k does the system have infinitely many solutions?

For which value(s) of k is the system inconsistent?

Answer: Ok, we can put the truck on a x-axis and the police car on the y-axis.

if the truck has a velocity of 30km/h and in an hour will be in the intersection, then it has a 30km distance to the intersection, who will be our 0 in our graph. so truck vector is (30km,0)

where a vector is of the form (x,y)

for the police car is the same, it has 40km distance to the intersection, but in the y-axis, so the vector is (0,40km)

so the vector representing the displacement of the truck with respect of the police car is the difference of both vectors

it is (30km, - 40km)

if you want a more precise, you can write the vector of the form

(30 km - 30km/h*t, 40 km - 40km/h*t) where t is time.

this second vectors takes in account how the position of the vehicles changes as the time goes.

Final answer:

To find the displacement vector of the truck with respect to the police car, we calculate the distance each vehicle travels in the given time. The truck moves 30 km north and the police car moves 40 km west in one hour, resulting in a relative displacement vector of ⇐ 40 km + ⇑ 30 km.

Explanation:

The student is asking for the vector representing the displacement of the truck with respect to the police car after a given time, assuming both vehicles will reach the intersection at the same time. We can find the displacement vector by calculating how far each vehicle will travel in the given time and positioning the resulting vectors tail-to-tail.

We are given that the truck is traveling due north at 30 km/hr and the police car is traveling west at 40 km/hr. Since both vehicles reach the intersection in one hour, the truck travels 30 km north, and the police car travels 40 km west in that hour.

The displacement vector Δr of the truck with respect to the police car is the vector that points from the position of the police car to the position of the truck. It can be found by subtracting the position vector of the police car from the position vector of the truck.

If we define east as the positive x-direction and north as the positive y-direction, the position vectors for one hour of travel are:

Truck: ⇑ 30 km (since it travels north)

Police car: ⇐ 40 km (since it travels west, which is the negative x-direction)

Therefore, the relative displacement vector of the truck with respect to the police car is ⇐ 40 km + ⇑ 30 km.

Answer: $4.11

Step-by-step explanation:

Given:  To win the jackpot in Massachusetts, we have to correctly guess all six numbers drawn from a pool of 36.

The number of combinations of 6 numbers drawn from a pool of 36 is given by :-

[tex]^{36}C_6=\dfrac{36!}{6!(36-6)!}\\\\=\dfrac{36\times35\times34\times33\times32\times31\times30!}{6!30!}\\\\=1947792[/tex]

Now, the probability of winning the prize = [tex]\dfrac{\text{Favorable outcomes}}{\text{Total outcomes}}[/tex]

[tex]p=\dfrac{1}{1947792}[/tex]

Now, the expected value of the free lotto ticket if the jackpot is $8,000,000 and there is no splitting of the prize = [tex]p\times\text{Amount}[/tex]

[tex]\dfrac{1}{1947792}\times8000000=4.1072147334\approx\$4.11[/tex]

Hence, the expected value of the free lotto ticket if the jackpot is $8,000,000 and there is no splitting of the prize = $4.11

Answer:

  x = -2

Step-by-step explanation:

The line of reflection is the perpendicular bisector of the segment between a pre-image point and its image. For example, the segment HH' is bisected by x=-2, the line of reflection.

1 year = 365 days.

1 day = 24 hours.

1 hour = 60 minutes.

First convert the hours and minutes in Jupiter orbit to days:

14*60 = 840 +9 = 849 minutes.

849 / 60 = 14.15 hours.

14.15 / 24 = 0.59 days.

Jupiter's orbit is 4332.59 days.

Now divide that by 365 for the number of years:

4332.59 / 365 = 11.87 years.

Answer:

3/4

pick 1,3,5 (reds) from 1,3,5,7(odd-numbered)

Red disks are numbered 1 through 6, the odd numbers are 1, 3, and 5, so there are 3 red disks with odd numbers.

The total number of disks in the box are both red and yellow, so 6 red + 2 yellow = 8 total disks.

The probability of picking an odd numbered red disk would be the number of odd numbered red disks over the total number of disks:

The answer is 3/8

Check the picture below.  Namely that's their LCD.

Part a

Use (x + 5, -y) for the input.

(5, 3) becomes (5 + 5, -3) = (10, -3).

Part b

Use the same rule.

(-2, 7) becomes (-2 + 5, -7) = (3, -7).

Done.

Part a)

                   The output is: (10,-3)

Part b)

              The output is: (3,-7)

The rule which is used to transform is:

             (x,y) → (x + 5, - y)

This means that the x-coordinate is shifted 5 units to the right and the y coordinate is negated.

Part a)

If we give the input as: (5,3)

Then the output will be:

(5,3) → (5+5,-3)

i.e.

(5,3) → (10,-3)

Part b)

Now, again when we input the value as: (-2,7)

Then the output will be:

(-2,7) → ( -2+5,-7)

i.e.

(-2,7) → (3,-7)

Answer:

  100 m

Step-by-step explanation:

Lalith purchased a total of 8 × 20m = 160 m of wire for ₹800, so paid ...

  (₹800)/(160 m) = ₹5/m

Shekhar paid ₹800 -300 = ₹500 less, so must have purchased ...

  (₹500)/(₹5/m) = 100 m

less wire.

The difference between the field perimeters is 100 m.

The difference between the length of the sides of Lalith and Shekhar's square fields is 150m.

To find the difference between the length of the sides of Lalith and Shekhar's square fields, we need to calculate the lengths of their respective sides. We know that Lalith used 8 bundles of fencing wire, each with a length of 20m, which cost him a total of RS.800. Shekhar used some other bundles, each with a length of 30m, which cost him a total of RS.300. Since both paid the same price per meter wire, we can equate the total cost and solve for the lengths of the sides of their fields:

For Lalith:

8 bundles x 20m/bundle = 160m

For Shekhar:

300 RS / (30 RS/m) = 10m

Therefore, the length of the sides of Lalith's field is 160m and the length of the sides of Shekhar's field is 10m. The difference in length between the sides of their fields is 160m - 10m = 150m.

Answer: 25%

Step-by-step explanation: To write a fraction as a percent, first remember that a percent is a ratio of a number to 100. if we want to write 1/4 as a percent, we need to find a fraction equivalent to 1/4 with a 100 in the denominator. We can do this by setting up a proportion.

[tex]\frac{1}{4}[/tex] = [tex]\frac{n}{100}[/tex]

4n = 100

÷4    ÷4

 n = 25

Therefore, 1/4 is equivalent to 25%.

Answer:

Billions

Step-by-step explanation:

You count from the right side to the left, the order being:

Ones

Tenths

Hundredths

Thousandth

Ten Thousandth

Hundred Thousandth

Millionth

Ten Millionth

Hundred Millionth

Billionth

Answer:

Step-by-step explanation:

It can help to draw a diagram.

In the attached diagram, the red triangle (RST) is the original, the purple one (ABC) is after rotation CCW by 90°, and the blue one (R'S'T') is after that is translated upward 2 units. R'S'T' is the final position.

Since RS and R'S' are oriented 90° with respect to each other, clearly a CCW rotation of that amount is required. The trick is to figure out which direction the translation occurs.

The translation can be done before or after the rotation. If done before, it needs to be 2 units to the right (not a choice). If done after, it can be 2 units up, as in this drawing.

Answer:

x represent the value loaned at 15% and y represent the value loaned at 10%.

[tex]x=11000[/tex] and [tex]y=19000[/tex]

Step-by-step explanation:

We are going to write a system of two linear equations. The first equation  will represent the total amount loaned.

[tex]x+y=30000[/tex]

Now the second equation are will represent the interest earned for both loans.

[tex](x*0.15)+(y*0.10)=3550[/tex]

Then x represent the value loaned at 15% and y represent the value loaned at 10%. Now solving the equation system we have:

[tex]x=30000-y[/tex] using this in the other equation to find y

[tex]((30000-y)0.15)+(0.10*y)=3550[/tex]

[tex]4500-0.15y+0.10y=3550[/tex]

[tex]4500-0.05y=3550[/tex]

[tex]4500-3550=0.05y[/tex]

[tex]950=0.05y[/tex]

[tex]\frac{950}{0.05}=y[/tex]

[tex]19000=y[/tex]

With the value of y we can find x

[tex]x=30000-19000[/tex]

[tex]x=11000[/tex]

Yes, it is a function.

Each element in the set called the domain is related to exactly one output in a set called the range.

A function can have several  inputs that provide the same output, but a function should never have one input that results in multiple outputs.

Answer:

[tex]-10b^2+12b-16[/tex]

Step-by-step explanation:

Consider the given question is " Subtract [tex]11b^2-4b+7[/tex] from [tex]b^2+8b-9[/tex]".

[tex](b^2+8b-9)-(11b^2-4b+7)[/tex]

Using distributive property we get

[tex]b^2+8b-9-(11b^2)-(-4b)-(7)[/tex]

[tex]b^2+8b-9-11b^2+4b-7[/tex]

On combining like terms we get

[tex](b^2-11b^2)+(8b+4b)+(-9-7)[/tex]

[tex]-10b^2+12b+(-16)[/tex]

[tex]-10b^2+12b-16[/tex]

Therefore, the resultant expression is [tex]-10b^2+12b-16[/tex].

Answer:

Tution and fees = 28036.3

Step-by-step explanation:

Here you have to replace "x" by 2014, because "x" represents the year and "T" the tuition and fees of that year.

T = 755.7(x-1985) +6121

T = 755.7(2014-1985) + 6121

T = 28036.3