Use part 1 of the fundamental theorem of calculus to find the derivative of the function. g(x) = x e2t2 − 4t dt 4

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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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

Maria bought 8 daisies and 4 tulips in the bouquet.

Let's assume that Maria bought x daisies and y tulips. Since the total number of flowers in the bouquet is 12, we can write the equation: x + y = 12.

Also, the total cost of the bouquet is $12.52. Using the cost per flower, we can write another equation: 0.99x + 1.15y = 12.52.

Now we have a system of equations that we can solve. Multiplying the first equation by 0.99, we get 0.99x + 0.99y = 11.88. Subtracting this equation from the second equation eliminates the x term, giving us 0.16y = 0.64. Dividing both sides by 0.16, we find that y = 4.

Substituting this value back into the first equation, we can solve for x: x + 4 = 12, x = 8.

Therefore, Maria bought 8 daisies and 4 tulips in the bouquet.

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:

Let each of the equal small angles be x.

The sum of three small angles is 145 degrees. One of these small angles is 65  degrees.

Now let us substitute the given information in an equation.

[tex]2x+65=145[/tex]

After subtracting 65 from both sides of equation we get

[tex]2x=80[/tex]

Dividing both sides of equation with 2 we get

[tex]x=\frac{80}{2}=40[/tex]

Therefore measure of each of the remaining angles is 40 degrees.

The measure of the other two smaller angles, given that they are equal would be 40 degrees.

Let's denote the measure of the other two smaller angles as "x."

We know that the sum of the three angles should be equal to the original 145-degree angle. Therefore, we can set up the equation:

65 + x + x = 145

Simplifying the equation:

65 + 2x = 145

Next, we can isolate "x" by subtracting 65 from both sides of the equation:

2x = 145 - 65

2x = 80

Finally, we divide both sides of the equation by 2 to solve for "x":

x = 80 / 2

x = 40

So, the measure of the other two smaller angles is 40 degrees each.

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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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Tan(135°) is -1 because it lies in the second quadrant with sine positive and cosine negative, whereas tan(-135°) is 1 as it falls in the third quadrant with both sine and cosine negative. Thus, tan(135°) = -1 and tan(-135°) = 1.

1.  The tangent of an angle is defined as the ratio of the sine to the cosine of that angle: tan(θ) = sin(θ) / cos(θ). The tangent function is also periodic with a period of 180 degrees, meaning tan(θ) = tan(θ + 180°).

2. First, let’s find the value of tan(135°). Since 135° is in the second quadrant where sine is positive and cosine is negative:

3. Therefore, tan(135°) = (√2/2) / (-√2/2) = -1.

4. Next, we consider tan(-135°). Since -135° is in the third quadrant where both sine and cosine are negative:

5. So, tan(-135°) = (-√2/2) / (-√2/2) = 1.

In summary, tan(135°) = -1 and tan(-135°) = 1.

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.

Answer:

4.7 ft.

Step-by-step explanation:

Let x represent the distance of the bottom of the ladder from the base of the house.

We have been given that Eric leans a ladder against the roof of his house so that the ladder forms a 70 angle with the ground. The roof of the house is 13 feet above the ground.

Upon looking at our attached graph we can see that ladder and wall of house forms a right triangle with respect to ground, where x is adjacent and side with 13 ft length is opposite side to the angle of 70 degrees.

We know that tangent relates opposite side of a right triangle with adjacent, so we can set an equation as:

[tex]\text{tan}=\frac{\text{Opposite}}{\text{Adjacent}}[/tex]

[tex]\text{tan}(70^{\circ})=\frac{13}{x}[/tex]

[tex]x=\frac{13}{\text{tan}(70^{\circ})}[/tex]

[tex]x=\frac{13}{2.747477419455}[/tex]

[tex]x=4.7316\approx 4.7[/tex]

Therefore, the bottom of ladder is 4.7 feet away from the base of the house.

Answer: 49/100 is correct

( that other answer was bothering me )

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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