Derivatives concept:
Exercises using the definition of derivatives:

(Full development)

Hi

let's call X amount of second going and Y the height reach by the ballon.

so Y=8X+94

f(x) = 8X+94

If you want to know how high will the ballon be in 25 seconds, remplace X by 25 and do the math. Have fun .

Answer: Angle LMN = 45

Step-by-step explanation:

The line MN will be parallel to the side Line JK

And LJ will be transversal

Therefore

Angle LMN = LJK (Corresponding angles)

ATQ

⇒3 + 6x = 101 - 8x

⇒6x + 8x = 101 -3

⇒14x = 98

⇒x = 98/14

⇒x = 7

Angle LMN = 3 + 6x

= 3 + 6(7)

= 3 + 42

= 45

Therefore Angle LMN will be 45°

Must click thanks and mark brainliest

For each customer, there are only two possible outcomes. Either they will order an alcoholic beverage, or they will not. The probability of a customer ordering an alcoholic beverage is independent of any other customer, which means that the binomial probability distribution is used to solve this question..

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

At a Noodles & Company restaurant, the probability that a customer will order a nonalcoholic beverage is .50

This means that [tex]p = 0.5[/tex]

Sample of 14 customers

This means that [tex]n = 14[/tex]

Probability that at least 7 will order a nonalcoholic beverage

This is:

[tex]P(X \geq 7) = 1 - P(X < 7)[/tex]

In which

[tex]P(X < 7) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6)[/tex]

Then

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{14,0}.(0.5)^{0}.(0.5)^{14} = 0.0001[/tex]

[tex]P(X = 1) = C_{14,1}.(0.5)^{1}.(0.5)^{13} = 0.0009[/tex]

[tex]P(X = 2) = C_{14,2}.(0.5)^{2}.(0.5)^{12} = 0.0056[/tex]

[tex]P(X = 3) = C_{14,3}.(0.5)^{3}.(0.5)^{11} = 0.0222[/tex]

[tex]P(X = 4) = C_{14,4}.(0.5)^{4}.(0.5)^{10} = 0.0611[/tex]

[tex]P(X = 5) = C_{14,5}.(0.5)^{5}.(0.5)^{9} = 0.1222[/tex]

[tex]P(X = 6) = C_{14,6}.(0.5)^{6}.(0.5)^{8} = 0.1833[/tex]

So

[tex]P(X < 7) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) = 0.0001 + 0.0009 + 0.0056 + 0.0222 + 0.0611 + 0.1222 + 0.1833 = 0.3954[/tex]

[tex]P(X \geq 7) = 1 - P(X < 7) = 1 - 0.3954 = 0.6046[/tex]

0.6046 = 60.46% probability that at least 7 will order a nonalcoholic beverage.

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Answer:

Step-by-step explanation:

Using V as a substitute for √ is misleading. Better to write “square root of x”.

AC = BD = √170

Answer:

Natural numbers,integers, rational numbers, irrational numbers.

9514 1404 393

Answer:

  480

Step-by-step explanation:

The expression evaluates to ...

  160·243^(1/5) = 160·(3^5)^(1/5) = 160·3 = 480

Answer: 17/20

Step-by-step explanation:

0.85 = 85/100 = 17/20

The number 0.85 can be written using the fraction 85/100 which is equal to 17/20 when reduced to lowest terms.

Answer:

[tex]14a[/tex]

Step-by-step explanation:

Combining like-terms gives us [tex]12a+2a=14a[/tex]

Hope this helped!

Answer:

14a

Step-by-step explanation:

Answer:

Please display full question . your question is incomplete ..

Answer:

Step-by-step explanation:

Please display a picture

Step-by-step explanation:

41a+11a-2b+3c

52a-2b+3c

Step-by-step explanation:

(41a-2b+3c) +11a

open the bracket

41a-2b+3c+11a

collect like terms

41a+11a-2b+3c

52a-5bc

so final answer is 52a-5bc

because they are not like terms they are unlike terms

Determining how much money will be in the account of Maite at the end of each year, we use an exponential growth factor, since this is a geometric sequence.

1. This situation represents a geometric  sequence.

A geometric sequence increases by a common exponential growth factor.

2. The common exponential factor is 1.03 (which gives a growth rate of 3% annually).  See how this factor is determined below.

3. At the end of the seventh year, Maite will have $1,194.05 in the account.  See the calculation below.

Data and Calculations:

Year    Amount

1       $1,000.00

2      $1,030.00

3      $1,060.90

4      $1,092.73

5       $1,125.51

6      $1,159.27 ($1,125.51 * 1.03)

7      $1,194.05 ($1,159.27 * 1.03)

The common exponential factor = 1.03 (1 + 0.03)

To obtain the common exponential factor, subtract Year 2 account balance from Year 1 account balance.  Divide the result by Year 1 account balance. This operation can also be carried out with Year 2 and Year 3 balances or Year 4 and Year 5 balances.

To determine how much money will be in the account of Maite at the end of Year 6, using Year 5 as a base = (Year 5 account balance * Exponential Factor)

= $1,159.27 ($1,125.51 * 1.03)

To determine Year 7 account balance, we use Year 6 above as the base

= $1.194.05 ($1,159.27 * 1.03)

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Answer:

This situation represents a geometric sequence.

The common ratio is 1.03

At the end of the seventh year, Maite will have $1,194.06 in the account.

Step-by-step explanation:

Plato

Split up the interval [1, 9] into n subintervals of equal length (9 - 1)/n = 8/n :

[1, 1 + 8/n], [1 + 8/n, 1 + 16/n], [1 + 16/n, 1 + 24/n], …, [1 + 8 (n - 1)/n, 9]

It should be clear that the left endpoint of each subinterval make up an arithmetic sequence, so that the i-th subinterval has left endpoint

1 + 8/n (i - 1)

Then we approximate the definite integral by the sum of the areas of n rectangles with length 8/n and height [tex]f(x_i)[/tex] :

[tex]\displaystyle \int_1^9 (x^2-4x+6) \,\mathrm dx \approx \sum_{i=1}^n \frac8n\left(\left(1+\frac8n(i-1)\right)^2-4\left(1+\frac8n(i-1)\right)+6\right)[/tex]

Take the limit as n approaches infinity and the approximation becomes exact. So we have

[tex]\displaystyle \int_1^9 (x^2-4x+6) \,\mathrm dx = \lim_{n\to\infty} \sum_{i=1}^n \frac8n\left(\left(1+\frac8n(i-1)\right)^2-4\left(1+\frac8n(i-1)\right)+6\right) \\\\ = \lim_{n\to\infty} \frac8n \sum_{i=1}^n \left(1+\frac{16}n(i-1)+\frac{64}{n^2}(i-1)^2-4-\frac{32}n(i-1)+6\right) \\\\= \lim_{n\to\infty} \frac8{n^3} \sum_{i=1}^n \left(64(i-1)^2-16n(i-1)+3n^2\right) \\\\= \lim_{n\to\infty} \frac8{n^3} \sum_{i=0}^{n-1} \left(64i^2-16ni+3n^2\right) \\\\= \lim_{n\to\infty} \frac8{n^3} \left(64\sum_{i=0}^{n-1}i^2 - 16n\sum_{i=0}^{n-1}i + 3n^2\sum{i=0}^{n-1}1\right) \\\\= \lim_{n\to\infty} \frac8{n^3} \left(\frac{64(2n-1)n(n-1)}{6} - \frac{16n^2(n-1)}{2} + 3n^3\right) \\\\= \lim_{n\to\infty} \frac8{n^3} \left(\frac{49n^3}3-24n^2+\frac{32n}3\right) \\\\= \lim_{n\to\infty} \frac{8\left(49n^2-72n+32\right)}{3n^2} = \boxed{\frac{392}3}[/tex]

The engagement score in 4 months would be 7.69

We are to determine the future value of engagement score in 4 months

The formula for calculating future value:

FV = P (1 + r)^n

FV = Future value  

P = Present value = 4.89  

R = rate of increase = 12%

N = number of months = 4

4.89 ( 1.12)^4 = 7.69

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Answer:

[tex]y = 7 - 7x \\ y + 7x = 7 \\ 7x + y = 7[/tex]

Answer:

7x + y = 7

Step-by-step explanation:

The equation of a line in standard form is

Ax + By = C ( A is a positive integer and B, C are integers )

Given

y = 7 - 7x ( add 7x to both sides )

7x + y = 7 ← in standard form

Answer:

24,32,40

Step-by-step explanation:

side 1: side2: side3: total

3            4         5         3+4+5=12

The total is the perimeter = 96

96/12 = 8

Multiply each term by 8

side 1: side2: side3: total

3*8       4*8      5*8    12*8

24         32       40        96

Let the sides of the triangle ABC be 3x , 4x and 5x.

Perimeter of triangle = 3x + 4x + 5x

[tex] \bf \rightarrow \: 96 \: = \: 12x[/tex]

[tex]\bf \rightarrow \: \frac{96}{12} \: = \: x \\ [/tex]

[tex]\bf \rightarrow \: \cancel\frac{96}{12} \: ^{8} \: = \: x \\ [/tex]

[tex]\bf \rightarrow \: x \: = \: 8[/tex]

[tex] \bf \implies \: 3x \: = \: 3 \: \times \: 8 \: = 24[/tex]

[tex]\bf \implies \: 4x \: = \: 4 \: \times \: 8 \: = 32[/tex]

[tex]\bf \implies \: 5x \: = \: 5 \: \times \: 8 \: = 40[/tex]

Hence , the sides of the triangle are 24 , 32 and 40.

Step-by-step explanation:

A = 12.25cm2

P perimeter 14cm

Answer:

A=12.25cm²

P=14

Answer:

Step-by-step explanation:

? = -4, 9, or -5

The solution is, b.) y = 2(x+9) ( x - 4) and, c.) y = - 2(x+9) ( x - 4), these function's graph has a zeros at (4,0) and (-9,0).

The zero of the function is where the y-value is zero. The zero of a function is any replacement for the variable that will produce an answer of zero. Graphically, the real zero of a function is where the graph of the function crosses the x‐axis; that is, the real zero of a function is the x‐intercept(s) of the graph of the function.

here, we have,

from the given the information , we get,

If one zero is x= 4, then one factor of the expression would be (x - 4).

Similarly if another zero is x=-9, then another factor of the expression would be (x+9)

We have two answers with these two factors and both are possible. So, the answers are b and c.

Hence, The solution is, b.) y = 2(x+9) ( x - 4) and, c.) y = - 2(x+9) ( x - 4), these function's graph has a zeros at (4,0) and (-9,0).

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complete question:

Which function's graph has a zeros at (4,0) and (-9,0)?

Answer:

bajskalakbskajalabsnsja

Answer:

-pi/3

Step-by-step explanation:

To convert from degree to radians, multiply by pi/180

-60 * pi/180 =  -60/180 *pi = -pi/3

Answer:

D. -pi/3

Step-by-step explanation:

degree to radians formula: x=degree, x*pi/180

x=-60

-60*pi/180=-pi/3

Answer:

3x^2+x+2

Step-by-step explanation:

Let's simplify step-by-step.

2x2+3x−1+x2−2x+3

=2x2+3x+−1+x2+−2x+3

Combine Like Terms:

=2x2+3x+−1+x2+−2x+3

=(2x2+x2)+(3x+−2x)+(−1+3)

Answer:

A

Step-by-step explanation:

lemme meh knw if it was helpful..

Answer:

Step-by-step explanation:

A right triangle has one right angle and two acute angles.

A and B are the acute angles.

A+B =  90°

One acute angle is 45 less than twice the other acute angle.

A = 2B-45°

(2B-45°) + B = 90°

3B = 135°

B = 45°

A = 45°

Answer

0.3

Step-by-step explanation:

Answer:

This is so hard for me. I can't understand. I am in grade 9 now.

You = her*1.1

her = you/1.1 = you*0.9090...

her = you - you*(1 - 0.9090...) = you - you*0.0909...

--> 9.09% younger

x = 9.09

HOPE SO IT HELPS YOU

The required value of x is 0.909.

A percentage is a value that indicates 100th part of any quantity.

A percentage can be converted into a fraction or a decimal by dividing it by 100.

Given that,

The husband is 10% older than wife.

And, the wife is x% younger than husband.

Suppose the age of husband is h and of wife be w.

The following equations can be written for the given case,

(h - w)/w × 100 = 10                    (1)

And, (h - w)/h × 100 = x              (2)

Divide both equations to get,

h/w = 10/x

Equation (1) can be written as,

h/w - 1 = 10

=> 10/x - 1 = 10

=>  10/x = 11

=> x = 10/11

=> x = 0.909

Hence the value of x for the given case is 0.909.

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Answer:

1/256

Step-by-step explanation:

[tex]4^{-4}[/tex]

[tex](1/4)^{4}[/tex]

=> 1/256