What is the area of the trapezoid at the right

Note the derivative rule

[tex]\\ \boxed{\star\bf \dfrac{d}{dx}(x^n)=nx^{n-1}}[/tex]

Let's see

[tex]\\ \rm\Rrightarrow \dfrac{d}{dx}(2^{x+1}-2^{x-1})[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{d}{dx}2^{x+1}-\dfrac{d}{dx}2^{x-1}[/tex]

[tex]\\ \rm\Rrightarrow (x+1)2^{x+1-1}-(x-1)2^{x-1-1}[/tex]

[tex]\\ \rm\Rrightarrow (x+1)2^x-(x-1)2^{x-2}[/tex]

[tex]\\ \rm\Rrightarrow (x+1)2^x-(x-1)2^x/2^2[/tex]

[tex]\\ \rm\Rrightarrow (x+1)2^x-(x-1)2^x2^{-2}[/tex]

[tex]\\ \rm\Rrightarrow 2^x(x+1-(x-1)2^{-2})[/tex]

[tex]\\ \rm\Rrightarrow 2^x(x+1-x/4-1/4)[/tex]

Answer:

It is called the test statistic

Step-by-step explanation:

Hope this helps:)...if not then sorry for wastign your time and may God bless you:)

Answer:

Exact Form:

3√5

Decimal Form:

6.70820393

Step-by-step explanation:

Answer:

Distance = 3√5 or 6.708203932,,,

Step-by-step explanation:

Find the distance between the y-values and x-values which in this case would be 6 and 3. Use the Pythagorean theorem.

[tex]3^2 + 6^2 = 45[/tex]

Simplify.

[tex]\sqrt{45} = 3\sqrt{5}[/tex]

===========================================================

Explanation:

The given statement is claiming something like [tex]P(X < 2)[/tex] produces a different result compared to [tex]P(X \le 2)[/tex]. The subtle difference of course is the "or equal to".

When talking about continuous random variables, the two values are the same. Why? Because probability of selecting *exactly* X = 2 is going to be zero. Think of a very very thin strip of height P(X = 2) and the width is approaching zero. The width is doing this because we're trying to pinpoint X = 2 itself. As you can see, this skinny rectangle will have its area approach 0. Ultimately, whether we compute [tex]P(X < 2)[/tex] or [tex]P(X \le 2)[/tex], it doesn't matter. They both produce the same result.

If you are a visual learner, consider the standard normal distribution. Now consider the task if shading to the left of z = 2. This area describes both probabiltiies mentioned above.

If X is a continuous random variable, then [tex]P(X < 2) = P(X \le 2)[/tex] and we can change the "2" to any number we want to have the same outcome.

Therefore, the original claim is false.

-------------------------

Extra info:

Now if X was discrete (say from the binomial distribution), then the two probabilities would be different. This is because

[tex]P(X < 2) = P(0) + P(1)\\\\P(X \le 2) = P(0) + P(1) + P(2)\\\\P(X < 2) \ne P(X \le 2) \ \text{only if X is discrete}[/tex]

We can see in this case that the second line has P(2) while the first one does not.

So the original claim would be true if we changed "continuous" to "discrete".

Answer:

1. 8000mm is the same as 8 metres. So 8km is greater than 8000mm

2. 5000m is the same as 5 km. So 50 km is greater than 5000m

3. 100cm is the same as 1 m. So 10m is greater than 100cm

4. 40 cm is the same as 400mm. So 4mm is less than 40cm.

Answer:

125 ways

Step-by-step explanation:

5 x 25 = 125

Hope this helps!

Answer:

2-5f ≤ 52, so -5f ≤ 50

f≥-10, because we flip the sign when multiplying or dividing by a neg number for inequalities.

Draw a closed circle on -10 and in the direction all the way towards the right arrow.

Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. The cost of 500 shares of Delta Air is $25,305.

Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. For example, 3 × 4 means 3 is added to itself 4 times, and vice versa for the other number.

The cost of a single share is $50.61, therefore, the cost of 500 shares will be,

Cost of 500 shares = 500 × cost of single share

                                 = 500 × $50.61

                                 = $25,305

Hence, the cost of 500 shares of Delta Air is $25,305.

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answer:62.5

a dozen=12 eggs

12× 2 eggs=300

5 eggs=x

cross multiply

24x=1500

thus x=62.5

Answer:

x = -17y/2+y

Step-by-step explanation:

Reorder the terms -7y = 2x + xy + 10y

Move the terms -7y = 2x + yx + 10y

Rewrite collect like terms -2x - yx = 10y + 7y

Divide both sides (-2 - y)x = 17y

simplify x = 17y/-2-y

Solution x = -17y/2+y

Have a good day <3

Answer:

x*5.5 + y* 7.25 = 45.5

x + y = 7

Step-by-step explanation:

every Espresso cost 5.5 => x*5.5

And the total cost is 45.5 so the sum should be 45.5

there are 7 coffees. means that the number of Espresso and latte is 7

Answer:

[tex]y=-2x+2[/tex]

Step-by-step explanation:

Answer:

y = -2x +2 I think

Step-by-step explanation:

The line of best fit shows that Luther can expect the speed to be 51 miles/hour when he throws 80 pitches and 64 miles/hour when he throws 54 pitches.

The average speed of Luther's pitches when he throws 80 pitches will be:

y = -0.511x + 91.636

= -0.511(80) + 91.636

= 50.756

= 51

Also, the number of pitches that Luther can throw when the speed is 64 miles per hour will be:

y = -0.511x + 91.638

64 = -0.511x + 91.638

0.511x = 91.638 - 64

0.511x = 27.636

x = 54

Therefore, the number of pitches will be 54.

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Answer:

In Triangle FGH, m<F = 42 and an exterior angle at vertex H as a measure of 104. What is the measure of <G?

Step-by-step explanation:

Answer:

82 units

Step-by-step explanation:

look at the paper...

Answer: x>=200

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

[tex](-1 (\frac{2}{3} - 4)) / (5/6)[/tex]

Let's solve for the numerator first:

PEMDAS says parenthesis first so...

2/3 - 4, we'll turn 4 into an improper fraction so it's easier

2/3 - 12/3 = -10/3

-1(-10/3) = (+)10/3

Now, we replace this as the numerator:

(10/3) / (5/6)

To divide, we multiply the first fraction by the reciprocal of the second:

(10/3) * (6/5) = 60/15

now simplify.....

60/15 = 4 or in other words, {15 * 4 = 60}

So, the answer is 4!

Answer:

3,500

Step-by-step explanation:

700,000/200

7,000/2

3,500

Answer:

A. 3,703 inches squared

Step-by-step explanation:

I took the test and got it right. #platofam

Probability helps us to know the chances of an event occurring. The probability that a person will be a female and prefer suspense movies is 0.047.

Probability helps us to know the chances of an event occurring.

[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]

The total number of people who were surveyed are:

Total Number of people = 82 + 94 +18 + 46 + 48 + 91 = 379

Also, it is mentioned in the table that the number of females who prefers suspense movies is 18. Therefore, the probability that a person will be a female and prefer suspense movies will be,

[tex]\rm Probability = \dfrac{\text{Number of females who prefers suspense movies}}{\text{Total Number of people}}\\\\Probability = \dfrac{18}{379} = 0.047[/tex]

Hence, the probability that a person will be a female and prefer suspense movies is 0.047.

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Step-by-step explanation:

normal 100 part sale 15 part saple price 85 part

85/100 = 272000/normal price

normal price = 272000 × 100/85

= 320000

Answer:

312800

Step-by-step explanation:

You could do 272000 times 15% then add the discount price

which is 272000 + 40800 = 312800

x=2

_______

x= [tex]\frac{1}{3}[/tex]

Answer:

0.5s

Step-by-step explanation:

His initial mean would be calculated by:
His minimum race time = 19.8s

The maximum race time = 19.8 + 5.6 = 25.4s

Since the mode is also 25.4, there are 2 25.4s races.

Since the median is 23.8s and the number of race times is even, the final race time can be calculated by:

25.4- 23.8s = 1.6s

23.8-1.6 = 22.2s

So the race times are 19.8s, 22.2s, 25.4s and 25.4s.

This means that his initial mean was (19.8+22.2+25.4+25.4)/4 = (42+50.8)/4= 92.8 /4 = 23.2s

With the new race time, the equation will change to (92.8+25.7)/(4+1)= 118.5/5= 23.7s

So the mean change would be 23.7 - 23.2 = 0.5 s.

Hope this helps!

Answer: $15.49.

Step-by-step explanation: So far, her pizza already costs $13.99 because she chose large.  However, she also ordered two toppings for $0.75 each, which is $1.50.  We need to add $13.99 and $1.50 to find out the total cost of her custom pizza.

$13.99 + $1.50 = $15.49.

Therefore, the total cost of her pizza is $15.49.

Have a great day! :)

Answer:

a) growth

b) $500

c) 6% = 0.06

d) [tex]f(x)=500(1.06)^x[/tex]

e) $595.51

Step-by-step explanation:

Part (a)

Exponential GROWTH, since interest is applied to the account each year.

Part (b)

Initial amount = $500

Part (c)

Growth factor = 6% = 0.06 (in decimal form)

Part (d)

General form of exponential growth function:

[tex]f(x)=a(1+r)^x[/tex]

where:

Given:

[tex]\implies f(x)=500(1+0.06)^x[/tex]

[tex]\implies f(x)=500(1.06)^x[/tex]

Part (e)

when x = 3

[tex]\begin{aligned}\implies f(3) & =500(1.06)^3\\ & = 595.51\: \sf(nearest\:hundredth)\end{aligned}[/tex]

Ty total compensation for the week where he earns a base rate of $12 per hour and receive a weekly attendance award of $20 is $500.

Rate is the ratio between two related quantities in different units.

Therefore, he earn a base rate of $12 per hour and receives a weekly attendance award of $20.

If he works 40 hours a week, his compensation will be as follows:

let

y = total compensation

x = number of hours worked

Hence,

y = 12x + 20

y = 12(40) + 20

y = 480 + 20

y = $500

Therefore, Ty total compensation is $500.

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Answer:

$15.00

Step-by-step explanation:

Just did the quiz

By evaluating the piecewise function, we will see that the brother owes $15.

The piecewise function is:

y = 26,   if 0 < h < 4

y = 26 + 5*(h - 4),  if 4 < h < 8

y = 60, if 8 < h

Barbara uses it for 3 hours, so we only need to use the first part for her, so she needs to pay $26.

Then the brother uses it for 4 hours (and we need to add the 3 hours that Barbara used it, so we have h = 7).

Then for the 7 hours the two brothers need to pay:

y = $26 + $5*(7 - 4) = $41

If we subtract the part that Barbara needs to pay we get.

$41 - $26 = $15

This means that the correct option is $15.

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