if 124 people attend a concert and tickets for adults cost $2.5 while tickets for children cost $2 and total receipts for the concert was $274, how many of each went to the concert?

Answer:

(x - 3) (5x + 1)(x + 1).

Step-by-step explanation:

5x^3 - 9x^2 - 17x - 3

As the first coefficient is 5 and the last -3, so product is -15, we could try if (x-3) is a factor:

By the Factor Theorem, if x-3 is a factor then f(3) = 0.

f(3) = 5(3)^3 - 9(3)^2 - 17(3) - 3

= 135 - 81 - 51 - 3 = 0

So, x - 3 is a factor.

Now divide:

x - 3)5x^3 - 9x^2 - 17x - 3(5x^2 + 6x + 1 <------- Quotient

       5x^3 - 15x^2

                    6x^2 - 17x

                    6x^2 - 18x

                                    x - 3

                                    x - 3

                                     .......

Factoring 5x^2 + 6x + 1:

= (5x + 1)(x + 1)

So, the answer is:

(x - 3) (5x + 1)(x + 1).

8/13 x 3/1 = 24/13

24 - 13 =11

So, simplified answer is 1 11/13 or 24/13

Hope this helps!

Answer:

D

Step-by-step explanation:

(4,5)  is 5 units above the x axis.  So, D' will be 5 units below the x axis.  This would be the point (4 -5)

Answer: The answer is D A (4,05)

(4,5)  is 5 units above this x axis. because of that , D' will have 5 units below the x axis for this problem.  therefore the point is (4 -5)

The height of plant will be 7.56cm tall after 2 weeks

The original height of the plant is 6.2cm

The height increases by 11% each week

= 11/100

= 0.11

The increase of the plant in a week

= 0.11 × 6.2

= 0.682

The height of the plant after two weeks can be calculated as follows

= 0.682 + 0.682

= 1.364

= 6.2 + 1.364

= 7.56

Hence the height of the plant after 2 weeks is 7.56cm

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sin(40 + 2°) cosec(30 + 5°) = 1 we proved that by the values.

Given,

sin(40 + 2°) cosec(30 + 5°) = 1

To prove the trigonometry function equal to 1.

Now, According to the question:

We know that

Sin 42° = 0.66913061

Cosec 35° = 1.7434468

sin(40 + 2°) cosec(30 + 5°) = 1

sin 42° × cosec 35° = 1

Plug the values of sin and cosec in above function:

0.66913061 × 1.7434468

= 1.16659

But we take the before decimal value i.e., 1

Hence,  sin(40 + 2°) cosec(30 + 5°) = 1 we proved that by the values.

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Answer:

6.  Draw a vertical line that goes though points (4,7) and (4,9).  For a relation to be a function, each input has to have only one output.  The input 4 cannot have the output of 7 and 9.  This proves that this is not a function

7. The range is 91, 3, 6, 10 and 15)

Step-by-step explanation:

The range is the answer if you put in the x for range that they give you.

For example:

x ( x+ 1)/2  If I put in 1 for x, I will get

1(1+1)/2

2/2

1

When the input is 1, the output is one.  You that for each of the domains given and you will find the ranges (outputs) that I have written above.

The individual that has a greater rate of reading is Rhoni.

Rate measures how fast a person is reading a book. Rate is the total pages read per time. Rate is determined by dividing total pages read by the total time spent reading.

Division is the operation used in mathematics that is used to determine the quotient of two or more numbers. It entails grouping a number into equal parts using another number. The sign used to denote division is ÷. Division is one of the basic mathematical operations.

Rie's rate = pages read / time

195 / 3 = 65 pages per hour

325 / 5 = 65 pages per hour

Rie's rate is 65 pages per hour. While Rhoni's rate is 75 pages per hour. This means that Rhoni reads faster than Rie.

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It depends on the number of decimal points of the values from which we get the average.

Normally it must be rounded to the nearest tenth, 17.3

The average price in 1992 and 2013 was given. It is required to find the percentage increase in the average price over these years.

Recall that the formula for Percentage Increase is:

Substitute initial price=12500 and final price= 22000 into the formula:

Hence, the percent increase in the average price is 76%.

Answer:

depends on whether or not the dealerships are scammers

Step-by-step explanation:

Answer's

Step-by-step explant

Yes, you are right!

First of all, we will subtract [tex]5[/tex] from each side.

Then we multiply both sides by [tex]4[/tex].

Then add [tex]3[/tex] to each side.

Finally, we divide each side by [tex]2[/tex].

[tex]\boldsymbol{\sf{\cfrac{2x-3}{4}+5=10 }}[/tex]

Multiply the two sides of the equation by 4.

2x - 3+20 = 40

Add −3 and 20 to get 17.

2x+17 = 40

It remains 17 on both sides.

2x = 40−17

Subtract 17 of 40 to get 23.

2x = 23

Divide both sides by 2.

[tex]\boldsymbol{\sf{x=\dfrac{23}{2} \ \ \longmapsto \ Answer }}[/tex]

Answer:

C- below the mean by a distance equal to 2 standard deviations

Step-by-step explanation:

Calculating the sine, cosine and tangent of the angle pi/6 (that is, 30°), we have that:

Answer:

woooooowwoowww your terrible

Step-by-step explanation:

gude

The improper fraction equivalent of the fraction 2 1/4 is 9/4.

Improper fraction:

Basically, the improper fraction is also the fraction where the numerator is greater than or equal to the denominator.

Given,

Here we have the mixed fraction 2 1/4.

And we have to convert this mixed fraction into improper fraction.

The conversion from mixed fraction to an improper fraction will follow the following formula,

numerator = (denominator × whole number) +  numerator of mixed fraction

Based on the this rule, the numerator of the improper fraction is,

=> numerator = (4 x 2) + 1

=> numerator = 8 + 1

=> numerator = 9

The denominator will remain same.

Therefore, the resulting improper fraction is 9/4.

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Answer: the Equation is y-3=0.4(x-1) or y-5=0.4(x-6).

Step-by-step explanation: I hope this helps.

Answer:36

Step-by-step explanation:

f(x)=12-3*(-8)

=36

The factors of the quadratic equation are found as the 7 and -3/2

For the given question, the quadratic equation is give as;

2x² - 11x - 21 = 0

Find the factors of -21×2 = 42 such that on subtraction it gives -11.

2x² - 14x + 3x - 21 = 0

Take 2x common from the first two terms and 3 from the last two terms.

2x(x - 7) + 3(x - 7) = 0

Take (x - 7) common from the terms.

(x - 7)(2x + 3) = 0

Then,

x - 7 = 0

x = 7

and, 2x + 3 = 0

x = -3/2

Thus, the factors of the quadratic equation are found as the 7 and -3/2.

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Step-by-step explanation:

79 degrees plus X would make 180 degrees, because these two angles make up a straight angle.

So, 79 + X = 180

    -79          -79

         X=101 degrees.

Y is 79 degrees because it is an alternate interior angle to the other 79 degree angle.

Z is 101 degrees because X and Z are corresponding angles, which means they are equal.

If Z is 101 degrees, Y must be 79 degrees because Y and X make up a straight angle.

Answer:

X is 101 degrees. Y is 79 degrees. Z is 101 degrees.

Hope this helped! :)

Answer: 84 minutes for 32 songs= 42 minutes for 16 songs.

Step-by-step explanation: All I had to do was divide 84 by two and divide 32 by 2.

84/2=42

32/2= 16 songs.

Answer: 16 songs.

84 dived by 2 equals 42.

Do 32 divided by 2 and it gives us 16.

Answer:

Trapezoid

Step-by-step explanation:

The area of this parallelogram is its height (half-height of the trapezoid) times its base (sum of the bases of the trapezoid)

Answer:

w = 27

Step-by-step explanation:

Solve for w: -6 = -2/9w

-6 = -2/9w

divide both sides by -2/9:

-6/(-2/9) = -2/9w/(-2/9)

27 = w

Answer:

Step-by-step explanation:

Solve each  inequality:

or

The answer is: m < 7 or m ≥ 8

Updated Probabilities are: P(L1/W) = 0.341 & P(L1/w) = 0.949

Let W be the event that the robot's camera observes a window

It is given that the Probability of observing a window there is no window at its location is given 0.2

P(W/ L1) = 0.2 ( L1 which does not have a window)

Also, probability of observing a window is 0.9

P(W/ L2) = 0.9 ( L2 has window)

Now we have to find updated probabilities for the robot being in L1 i.e:- P(L1/W) & P(L1/w)

w means the camera does not observe a window.

By Bayes Rule,

P(L1/W) = P(L1)P(W/L1)/P(L1)P(W/L1)+P(L2)P(W/L2)

            = (0.7x 0.2)/ (0.7x0.2) + (0.3x0.9)

            = (0.14)/ 0.14+0.27

            ≈0.341 (rounded to 3. decimal places)

Thus  the probability of being in L1 if the camera observes a window is nearly 0.341.

P(L1/w) = P(L1)P(w/L1)/P(L1)P(w/L1)+P(L2)P(w/L2)

As P(W/L1) = 0.2;

P(w/L1) = 1 - P(w/L1) = 1-0.2 = 0.8

Also P(W/L2) = 0.1;

P(w/L2) = 1 - P(w/L2) = 1-0.9 = 0.1

P(L1/w) = (0.7 X 0.8)/ (0.7X0.8) + (0.3X0.1)

           =(0.56)/ (0.56+0.03) = (0.56/ 0.59)

           ≈ 0.949 (rounded to 3 decimal places).

Thus the probability of being in L1 if observe not the window is nearly 0.949.

Updated Probabilities are: P(L1/W) = 0.341 & P(L1/w) = 0.949

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Paper towels are being ordered by a restaurant. The data table compares the number of cases to the quantity of paper towel rolls. 1:12 ratio does the proportionality constant appear at in the data table.

Given that,

There is a table.

Paper towels are being ordered by a restaurant. The data table compares the number of cases to the quantity of paper towel rolls.

We have to find what ratio does the proportionality constant appear at in the data table.

The table is

Number of cases ordered     |      Number of rolls of paper towels

1                                               |      12

3                                               |      36

5                                               |      60

10                                              |      120

Therefore, 1:12 ratio does the proportionality constant appear at in the data table.

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Answer: 4,800,000

Step-by-step explanation: 2 times 24 is 48 then there is 3 zeros in 2000 and 2 zeros in 2400 so just add those on to the end of 48 and then you get your final answer of 4,800,000.

Jon's bathtub exists rectangular and its base exists 18 ft². The water level rising if Jon is filling the tub at a rate of 0.2 ft³/min is 0.011 ft/min.

A differential equation in mathematics exists an equation that links the derivatives of one or more unknown functions. Applications often involve functions that reflect physical quantities, derivatives that depict the rates at which those values change, and a differential equation that establishes a connection between the three.

If we take a look at a rectangular bathtub, the volume of the bathtub can be expressed as:

Volume (V) = length × breadth × height

where; base = length × breadth = 18ft²

The volume of the rectangular bathtub = 18h ......... (1)

Using differentiation to differentiate 18h with respect to t implicitly, then:

[tex]$\frac{\mathrm{dV}}{\mathrm{dt}}=18 \frac{\mathrm{dh}}{\mathrm{dt}}$$[/tex]

When the rate of rising of the volume is 0.2 ft² / min

[tex]$0.2=18 \frac{\mathrm{dh}}{\mathrm{dt}}$$[/tex]

substitute the values in the above equation, we get

[tex]$\frac{\mathrm{dh}}{\mathrm{dt}}=\frac{1}{18} \times(0.2)$$[/tex]

[tex]$\frac{\mathrm{dh}}{\mathrm{dt}}=0.011 \mathrm{ft} / \mathrm{min}$$[/tex]

Therefore, we can conclude that the rate at which the water level rises if Jon is filling the tub at 0.2 ft³/min exists 0.011 ft/ min.

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Answer:

140

Step-by-step explanation:

A) A function rule for the total cost T, including the mandatory examination, for a dog to stay at the hotel for n days is; T = 25n + 15

B) The total cost to stay for 6 nights is; $165

C) No, 3 night does not cost half as much as the cost for 6 nights due to the addition mandatory cost of $15.

We are told that a pet hotel charges $25 per night to keep a dog. We are also told that there is a mandatory $15 examination fee when the dog arrives there.

A) If the number of nights spent is n, then the function rule here for the total cost  is;

T = 25n + 15

B) We are told that the number of nights is 6 nights. Thus, we will just plug in 6 for n into the total cost equation to get;

T(6) = 25(6) + 15

T(6) = $165

C) The cost of 3 nights would be;

T(3) = 25(3) + 15

T(3) = $90

This is more than half of the cost of 6 nights.

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