Type the correct answer in each blank. Use numerals instead of words. If necessary, use / for the fraction bar(s). John hosts an art workshop on the weekends. He has an average of 14 students in each session and charges a fee of $12 per session. He estimates that for every $2 increases in the fee, the average number of students reduces by 1. Complete the equation that models this scenario, where c(x) is the revenue generated and x is the number of $2 fee increases.
c(x) =_x^2 +_x+_

A standard form equation representing the weightlifting situation is 45x + 10y = 260. If eight 10-pound plates are used, the number of 45-pound plates used is 4.

The situation given can be translated mathematically to an equation in standard form as follows: 45x + 10y = 260. This equation signifies that the total weight lifted (260 pounds) is equal to the sum of the weight of the 45

pound plates

(which each weighs 45 pounds multiplied by the number of plates, represented by x) and the 10 pound plates (which each weighs 10 pounds multiplied by the number of plates, represented by y). In the second part of the question, we're told that the weightlifter uses eight 10-pound weights, so y=8. Substituting y=8 into the equation from above, it simplifies to 45x + 80 = 260, which solves to x = 4. So, if the weightlifter uses eight 10 pound plates, then he uses four 45 pound plates.

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Nan and Soto used a total of 45 tiles. However, to cover a coffee table that has an area of 36 inches by 24 inches, they need 54 tiles, so they will need to acquire 9 more tiles.

1A. Nan uses 30 tiles and Soto uses half as many, which means Soto uses 15 tiles. So, they used a total of 45 tiles (30 + 15).1B. The area of the coffee table is 36 inches by 24 inches, which equals 864 square inches (36 x 24). Each tile is a four-inch square, so it covers an area of 16 square inches (4 x 4).

To find out how many tiles are needed, we divide the total area of the table by the area of one tile: 864/16 = 54 tiles. Since Nan and Soto have only 45 tiles, they need an additional 54 - 45 = 9 more tiles to cover the table.

GivEn:

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To find:

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Solution:

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☯ Let two adjacent sides of parallelogram be 2x and 5x.

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⋆ Refrence of image is shown in diagram:

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[tex]\setlength{\unitlength}{1 cm}\begin{picture}(0,0)\thicklines\qbezier(1,1)(1,1)(6,1)\put(0.4,0.5){\bf D}\qbezier(1,1)(1,1)(1.6,4)\put(6.2,0.5){\bf C}\qbezier(1.6,4)(1.6,4)(6.6,4)\put(1,4){\bf A}\qbezier(6,1)(6,1)(6.6,4)\put(6.9,3.8){\bf B}\put(0.7,2.5){\sf 2x}\put(3,0.5){\sf 5x}\end{picture}[/tex]

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[tex]\underline{\bigstar\:\boldsymbol{According\:to\:the\:question\::}}\\ \\[/tex]

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[tex]\dag\;{\underline{\frak{We\;know\;that,}}}\\ \\[/tex]

[tex]\star\:{\boxed{\sf{\purple{Perimeter_{\;(parallelogram)} = 2 \times (sum\:of\: adjacent\:sides)}}}}\\ \\[/tex]

[tex]:\implies\sf 2 \times (2x + 5x) = 70\\ \\[/tex]

[tex]:\implies\sf 2 \times 7x = 70\\ \\[/tex]

[tex]:\implies\sf 14x = 70\\ \\[/tex]

[tex]:\implies\sf x = \cancel{ \dfrac{70}{14}}\\ \\[/tex]

[tex]:\implies{\boxed{\sf{\pink{x = 5}}}}\;\bigstar\\ \\[/tex]

Therefore,

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[tex]\therefore[/tex] Hence, Adjacent sides of parallelogram are 10 cm and 25 cm.

Answer:

Adding and subracting change from one polynomial to another by combining like terms, when multiplying and dividing don't do that.

we are given

[tex](4x\sqrt{5x^2} +2x^2\sqrt{6} )^2[/tex]

we can expand it

[tex](4x\sqrt{5x^2} +2x^2\sqrt{6} )^2=(4x\sqrt{5x^2} +2x^2\sqrt{6} )(4x\sqrt{5x^2} +2x^2\sqrt{6} )[/tex]

we can simplify it

[tex](4x\sqrt{5x^2} +2x^2\sqrt{6} )^2=(4x\sqrt{5}x +2x^2\sqrt{6} )(4x\sqrt{5}x +2x^2\sqrt{6} )[/tex]

[tex](4x\sqrt{5x^2} +2x^2\sqrt{6} )^2=(4x^2\sqrt{5} +2x^2\sqrt{6} )(4x^2\sqrt{5} +2x^2\sqrt{6} )[/tex]

now, we can FOIL it

we get

[tex](4x\sqrt{5x^2} +2x^2\sqrt{6} )^2=(4x^2\sqrt{5})^2 +2*2x^2\sqrt{6} *4x^2\sqrt{5} +(2x^2\sqrt{6} )^2[/tex]

now, we can simplify it

[tex]=4^2\cdot \:5x^4+16\sqrt{30}x^4+2^2\cdot \:6x^4[/tex]

[tex]=80x^4+16\sqrt{30}x^4+24x^4[/tex]

now, we can combine like terms

[tex]\mathrm{Add\:similar\:elements:}\:80x^4+24x^4=104x^4[/tex]

[tex]=104x^4+16\sqrt{30}x^4[/tex]

so, option-D.............Answer

Answer: D

Step-by-step explanation:

To find the probability that at most 75 bicycles sold are mountain bikes, use the binomial distribution formula with a success probability of 0.70, 100 trials, and a binomial calculator to find the cumulative probability of 0 to 75 mountain bike sales. Round the answer to four decimal places.

To find the approximate probability that at most 75 bicycles sold are mountain bikes, we can use the binomial distribution formula. In this case, the success is getting a mountain bike sale and the probability of success is 0.70. The number of trials is 100, which represents the randomly selected bike purchases. We can use a binomial calculator or software to find the probability.

The probability can be calculated as follows:

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The scenario represents a binomial probability problem. To solve, we'd calculate binomial probabilities for k from 0 to 75 (for 'at most 75' mountain bikes), where k is the count of successes, and  then sum up these probabilities. This calculation involves advance statistic methods

The subject of the question falls under probability in mathematics. Specifically, this question requires the use of the binomial distribution to find the probability of a certain event occurring. A binomial distribution is relevant because we know the probability of success (a bike sold being a mountain bike) is 70%, or 0.70, and we are looking at a fixed number of events (100 bike purchases).

In order to solve the problem, we calculate the binomial probability using the formula: [tex]P(X=k) = C(n, k)*(p^k)*((1-p)^{(n-k)})[/tex] where n = number of trials (100 in this case), k = number of successes we're looking at (75 in this case), p = probability of success on any given trial (0.70 in this case), and C(n, k) = combination of n items taken k at a time.

However, the question asks for the probability that 'at most 75 are mountain bikes'. So we also have to compute and sum up the probabilities from 0 to 75 to get the answer.

This can be quite laborious to calculate by hand, so we often use statistical software or a calculator capable of such operations to find the exact value. Hence, it is often a procedure performed in a College level Statistics class.

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John take longer time.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Time John practice = 500 seconds

And, Time bill practice = 8 minutes

                                   = 8 x 60 second

                                    = 480 second

Therefore, We get;

⇒ 500 > 480

So, John practice more time.

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We have been given that Olga’s family traveled 942 kilometers on the first day.

And 894.5 kilometers on the second day.

We need to find how many more meters did Olga’s family travel on the first day.

Therefore, we must subtract the distance traveled in first day to the distance traveled in the second day of the trip.

Hence, the difference is given by

[tex]942-894.5\\ \\ 45.5[/tex]

Thus, Olga’s family travel 45.5 km more on the first day.

Find the range of the following data. 5.3, 6.2, 3.1, 4.8, 7.3

Solution:

In Statistics, Range is the difference between the lowest and highest values.

Or, Range= Maximum Value-Minimum Value

In the given set :5.3,6.2,3.1, 4.8, 7.3

Let us arrange in increasing order first

3.1, 4.8, 5.3, 6.2, 7.3

So, The Lowest value in the set=3.1

And, The Highest value in the set=7.3

So, Range= Highest Value- Lowest Value

Range=7.3-3.1

Range=4.2

Answer: Range=4.2

An angle coterminal with 480° can be found by subtracting multiples of 360° from 480°. Two examples of such angles are 120° and -240°.

To find an angle that's coterminal with a given angle, we can add or subtract multiples of 360° (since a full circle is 360°). So, to find an angle coterminal with 480°, we can subtract 360° from 480°, which gives us 120°. Therefore, 120° is an angle that is coterminal with 480°. It's worth noting that there can be infinite coterminal angles, both positive and negative, for any given angle. For example, if we subtract 360° again from 120°, we get -240°, which is also coterminal with 480°.

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