Suppose f left parenthesis x right parenthesis right arrow 150f(x)→150 and g left parenthesis x right parenthesis right arrow 0g(x)→0 with ​g(x)less than<0 as x right arrow 3x→3. Determine modifyingbelow lim with x right arrow 3 startfraction f left parenthesis x right parenthesis over g left parenthesis x right parenthesis endfractionlimx→3 f(x) g(x).

Answer:

-5/2(3x+4)<6-3x

2•-5/2(3x+4)<2(6-3x)

-5(3x+4)<2(6-3x)

-15x-20<12-6x

-15x+6x-20<12-6x+6x

-9x-20<12

+20 +20

-9x<32

-9 -9

x>32/-9 or -3.5 recurring

Answer:

see explanation

Step-by-step explanation:

let y = f(x) and rearrange making x the subject, that is

y = [tex]\frac{2x-3}{x+1}[/tex] ← multiply both sides by (x + 1)

y(x + 1) = 2x - 3 ← distribute left side

xy + y = 2x - 3 ( subtract y from both sides )

xy = 2x - 3 - y ( subtract 2x from both sides )

xy - 2x = - 3 - y ← factor out x from each term on the left side

x(y - 2) = - 3 - y ← divide both sides by y - 2

x = [tex]\frac{-3-y}{y-2}[/tex] factor out - 1 on numerator and denominator

x = [tex]\frac{-(3+y)}{-(2-y)}[/tex]

Change y back into terms of x, thus

[tex]f^{-1}[/tex](x) = [tex]\frac{3+x}{2-x}[/tex] = [tex]\frac{x+3}{2-x}[/tex]

Answer:

f-1(x) = (x + 3)/ (2 - x) or -(x + 3 / (x - 2).

Step-by-step explanation:

Let y = (2x - 3)/(x + 1)

We find x in terms of y:

Cross multiply:

y(x + 1) = 2x - 3

xy + y = 2x - 3

y + 3  =  2x - xy

x(2 - y) = y + 3

x =  (y + 3) / (2 - y)

Now replace x by f-1(x) and y by x, we get:

f-1(x) = (x + 3)/ (2 - x).

Your answer was correct. You  found the same result written in a different form.

If we multiply  the above by -1 / -1 we get

-(x + 3) / -(2 - x)

= -(x + 3) / (x - 2).

Answer:  2.4 miles

Step-by-step explanation: law of cosines

Let's call the distance between Brielle and Eduwa's cottages x. As the angle btw them is 43°, we can use:

x² = 3.5² + 2.8² - 2*3.5*2.8*cos43

x² = 5.755

x = 2.4 miles

Answer:

Q(2, 6 )

Step-by-step explanation:

Using the midpoint formula

let the coordinates of Q = (x, y ), then

0.5(x + 10) = 6 ( multiply both sides by 2 )

x + 10 = 12 ( subtract 10 from both sides )

x = 2

and

0.5(y + 6) = 6 ( multiply both sides by 2 )

y + 6 = 12 ( subtract 6 from both sides )

y = 6

Coordinates of Q = (2, 6 )

Answer:

Mars: 0.103 *(Real weigh)

Venus: 0.9 * (Real weigh)

Jupiter 2.53 * (Real weigh)

Step-by-step explanation:

The formula is this:

GM/r**2

M= Mass

r = radius

You do not need G for comparing between different masses or planets.

Answer: Hello!

So the list of ingredients in the sauce are:

{onions,​ garlic, carrots,​ broccoli, shrimp,​ mushrooms, zucchini, green​ pepper}

there are 8 possible elements in the sauce, so we need to see the combinations for this elements in the sauce.

let's count!

0 ingredients; there is only one combination with 0 ingredients.

1 ingredient: there are 8 combinations with 1 ingredient, one for each.

2 ingredients: now star playing with combinatorics, so the combinatory between A and B is: [tex]\frac{A!}{B!(A-B)!}[/tex], so for 8 and 2 we get:

[tex]\frac{8!}{2!(6)!} = 8*7/2 = 28[/tex]

3 ingredients: Similar as before; the combinatory for 8 and 3 is: [tex]\frac{8!}{3!*5!} = 8*7 =56[/tex]

4 ingredients: for 8 and 4 we have: [tex]\frac{8!}{4!*4!} = \frac{8*7*6*5}{4*3*2} = 2*7*5 = 70[/tex]

5 ingredients: You can think that now we are counting the combinations of 3 ingredients that we are not using, so the combinations are the same as for 3 ingredients: 56

6 ingredients: Similar as before, here are the combinations of the two ingredients that we are not using: 28

7 ingredients: there are 8 options if we decide to not use only one ingredient.

8 ingredient: there is 1 option in this case, same as the case with no ingredients

And now, we need to add all those combinations:

so C = 1 +8 +  28 + 56+ 70+ 55 + 28 +8 +1 = 512 total combinations.

Through the application of combinations in Probability theory, we can determine that there are 256 potential ways to order pasta with tomato sauce, considering the inclusion or exclusion of eight possible ingredients.

The question pertains to combinations in Probability theory, specifically involving pasta with options to include or exclude eight different sauce ingredients: onions, garlic, carrots, broccoli, shrimp, mushrooms, zucchini, and green pepper. For each ingredient, we have two choices - either to include it or not, giving us 28 options, where 8 is the total number of ingredients.

To calculate the number of combinations, we use the formula for combinations which is 2n, where 'n' is the number of items. In this case, n equals eight as there are eight ingredients. Therefore, plugging into the formula, we get 28 = 256. So, there can be a total of 256 combinations when ordering pasta with tomato sauce considering the options of eight ingredients to include or not.

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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:

  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:

216

Step-by-step explanation:

72 + (72×2)=

72 + 144 =

216

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:

Step-by-step explanation:

When I am dealing with fractions I put them in money wise so 2 1/4 would be like 2.25 and 3/8 would be like 0.75.

So that means you divide 2.25 by 0.75 and that will give you three.

Therefore Kia can make 3 small bags of candies.

have a nice day

please follow

Answer:

The probability of choosing exactly 2 male and 4 female students =[tex]\frac{\binom{16}{2}\times \binom{19}{4}}{\binom{35}{6}}[/tex]

Step-by-step explanation:

We are given that a class has 35 students

Number of male=16

Number of female=19

We have to choose 6 students for committee

We have to find the probability that exactly 2 male students are selected

Probability=P(E)=[tex]\frac{number\;of\;favorable\;cases}{total\;number\;of\;cases}[/tex]

If we have to choose total 6 student in which 2 male and 4 female

Combination formula:

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

Using the formula

The probability of choosing exactly 2 male and 4 female students =[tex]\frac{\binom{16}{2}\times \binom{19}{4}}{\binom{35}{6}}[/tex]

Answer: B. 3,276,000

Step-by-step explanation:

Given : A student number system for a county requires that the student number be 6 characters.

Number of digits (0,1,2,3,4,5,6,7,8,9)=10

Number of letters in English alphabet = 26

When repetition of things is not allowed then we use Permutations.

Number of permutations of m things taking n at a time =[tex]^mP_n=\dfrac{m!}{(m-n)!}[/tex]

Similarly, Number of permutations of 10 numbers taking 4 at a time :

[tex]^{10}P_4=\dfrac{10!}{(6)!}=\dfrac{10\times9\times8\times7\times6!}{6!}=5040[/tex]

Number of permutations of 26 letters taking 2 at a time :

[tex]^{26}P_2=\dfrac{26!}{(2)!}=\dfrac{26\times25\times24!}{24!}=650[/tex]

Now, the possible number of numbers can be make = [tex]5040\times650=3,276,000[/tex]

Hence, the correct answer is options (b).

Answer:

∠A = 99°

Step-by-step explanation:

Complementary angles sum to 180°, thus

∠A + ∠B = 180 ← substitute values

2x - 23 + x + 20 = 180

3x - 3 = 180 ( add 3 to both sides )

3x = 183 ( divide both sides by 3 )

x = 61

Hence

∠A = 2x - 23 = (2 × 61) - 23 = 122 - 23 = 99°

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:

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]

Answer:

The answer to your question is: 24 561 104 bacteria

Step-by-step explanation:

every 16 minutes bacteria population double

There are 6140276 bacteria at 9:15 AM

estimate bacteria at 9:47

First calculate the minutes : 47 - 15 = 32 minutes

                                               and 32 / 16 = 2

then 2 times the bacteria population double

So,

          first time = 6140276 x 2 = 1 2280552 bacteria

          second time = 1 2280552 x 2 = 24561104 bacteria

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.

The probability of not choosing a white marble from a bag containing 10 marbles of different colors is 80%.

To find the probability that you will NOT choose a white marble from a bag containing 1 blue, 4 yellow, 3 red, and 2 white marbles (10 marbles in total), follow these steps. First, calculate the total number of marbles that are not white. There is 1 blue, 4 yellow, and 3 red marbles, summing up to 8 marbles that are not white. The probability of picking a marble that is not white is therefore the number of marbles that are not white divided by the total number of marbles.

Probability = Number of marbles that are not white / Total number of marbles
Probability = 8 / 10
Probability = 0.8 or 80%

Thus, the probability of choosing a marble that is not white is 80%.

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:

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:

  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.

Answer:

=20.5

Step-by-step explanation:

1. use the Pythagorean theorem: a^2+ b^2=c^2  (arms+legs squared=hypotenuse)

2. plug in the numbers to the equation:

14^2+15^2=c

225+196=c^2

421=C^2

the square root of 421 is 20.5 which is the hypotenuse of the triangle

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:

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:

B

Step-by-step explanation:

6 machines complete the job in 12 days;

the more machine you have faster the job will be done, inverse proportion

6 machines ---  12 days

x machines -- 8 days

you reduce the number of days by a factor of 1.5 (12/1.5)

sou you hvae to increase the number of machines by 1.5

6 x 1.5 = 9, so you will need 3 additional machines

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:

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: 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?