the exact derivative of f(x)=x^3 at x=5
​

Let's simplify step-by-step.

3(2x+1)−2(x+1)

Distribute:

=(3)(2x)+(3)(1)+(−2)(x)+(−2)(1)

=6x+3+−2x+−2

Combine Like Terms:

=6x+3+−2x+−2

=(6x+−2x)+(3+−2)

=4x+1

4x+1 is the answer to the question

Answer:

The  probability is  [tex]P[ D n R] = 0.196[/tex]

Step-by-step explanation:

  From the question we are told that

     The number of Democrats is  [tex]D = 8[/tex]

       The number of republicans is  [tex]R = 8[/tex]

The  number of ways of selecting selecting two Democrats and four Republicans.

         [tex]N = \left {D} \atop {}} \right. C_2 * \left {R} \atop {}} \right. C_1[/tex]

Where C represents combination

substituting values

           [tex]N = \left {8} \atop {}} \right. C_2 * \left {8} \atop {}} \right. C_1[/tex]

           [tex]N = \left {8} \atop {}} \right. C_2 * \left {8} \atop {}} \right. C_1 = \frac{8!}{(8-2)! 2!} * \frac{8! }{(8-4)! 1 !}[/tex]

=>        [tex]N = \left {8} \atop {}} \right. C_2 * \left {8} \atop {}} \right. C_1 = \frac{8!}{(6)! 2!} * \frac{8! }{(6)! 1 !}[/tex]

=>        [tex]N = \left {8} \atop {}} \right. C_2 * \left {8} \atop {}} \right. C_1 = \frac{8 * 7 * 6!}{(6)! 2!} * \frac{8*7 *6! }{(6)! 1 !}[/tex]

=>        [tex]N = \left {8} \atop {}} \right. C_2 * \left {8} \atop {}} \right. C_1 = \frac{8 * 7 }{ 2*1 } * \frac{8*7 }{ 1 *1 }[/tex]

=>      [tex]N = 1568[/tex]

The total number of ways of selecting the committee of six people is  

          [tex]Z = \left {D+R} \atop {}} \right. C_6[/tex]

substituting values

           [tex]Z = \left {8+8} \atop {}} \right. C_6[/tex]

            [tex]Z= \left {16} \atop {}} \right. C_6[/tex]

substituting values

             [tex]Z= \left {16} \atop {}} \right. C_6 = \frac{16! }{(16-6) ! 6!}[/tex]

           [tex]Z= \left {16} \atop {}} \right. C_6 = \frac{16 *15 *14 * 13 * 12 * 11 * 10! }{10 ! 6!}[/tex]

           [tex]Z= \left {16} \atop {}} \right. C_6 = \frac{16 *15 *14 * 13 * 12 * 11 }{6* 5 * 4 * 3 * 2 * 1}[/tex]

           [tex]Z= \left {16} \atop {}} \right. C_6 = 8008[/tex]

The probability of selecting two Democrats and four Republicans  is  mathematically  represented as

           [tex]P[ D n R] = \frac{N}{Z}[/tex]

substituting values

           [tex]P[ D n R] = \frac{1568}{8008}[/tex]

            [tex]P[ D n R] = 0.196[/tex]

Answer:

Step-by-step explanation:

Let x represent the smaller integer.

Let y represent the larger integer.

A positive integer is 2 less than another. It means that

y = x + 2

If the sum of the reciprocal of the smaller and twice the reciprocal of the larger is 11/15, it means that

1/x + 2/y = 11/15- - - - - - - - - - 1

Substituting y = x + 2 into equation 1, it becomes

1/x + 2/(x + 2) = 11/15

Considering the left hand side of the equation, it becomes

(x + 2 + 2x)/x(x + 2)

Therefore,

(3x + 2)/(x² + 2x) = 11/15

Cross multiplying, it becomes

15(3x + 2) = 11(x² + 2x)

45x + 30 = 11x² + 22x

11x² + 22x - 45x - 30 = 0

11x² - 23x - 30 = 0

11x² + 10x - 33x - 30 = 0

x(11x + 10) - 3(11 + 10) =℅0

(x - 3)(11x + 10) = 0

x - 3 = 0 or 11x + 10 = 0

x = 3 or x = - 10/11

Since it us a positive integer, the smaller integer is 3 and the larger integer is 3 + 2 = 5

Answer: Let x represent the smaller integer.Let y represent the larger integer.A positive integer is 2 less than another. It means that y = x + 2 If the sum of the reciprocal of the smaller and twice the reciprocal of the larger is 11/15, it means that 1/x + 2/y = 11/15- - - - - - - - - - 1Substituting y = x + 2 into equation 1, it becomes 1/x + 2/(x + 2) = 11/15Considering the left hand side of the equation, it becomes(x + 2 + 2x)/x(x + 2) Therefore,(3x + 2)/(x² + 2x) = 11/15Cross multiplying, it becomes15(3x + 2) = 11(x² + 2x)45x + 30 = 11x² + 22x11x² + 22x - 45x - 30 = 011x² - 23x - 30 = 011x² + 10x - 33x - 30 = 0x(11x + 10) - 3(11 + 10) =℅0(x - 3)(11x + 10) = 0x - 3 = 0 or 11x + 10 = 0x = 3 or x = - 10/11Since it us a positive integer, the smaller integer is 3 and the larger integer is 3 + 2 = 5

Step-by-step explanation:

Answer:

6.96x10^-3

Step-by-step explanation:

0.00696

We move the decimal point to between 6 and 9

since the number with the decimal point should be between 0 and 9.

Then we count the numbers.

6.96x10^-3.

Hope this helps. ❤❤❤

Answer: 6.96 * 10^(-3)

Step-by-step explanation:

In scientific notation, you multiply a number that has a value in the ones place and no value in the tens place by 10 raised to an exponent.

Hope it helps <3

Answer:

B

Step-by-step explanation:

Using the cosine ratio in the right triangle

cos54° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{AC}{AB}[/tex] = [tex]\frac{39}{AB}[/tex] ( multiply both sides by AB )

AB × cos54° = 39 ( divide both sides by cos54° )

AB = [tex]\frac{39}{cos54}[/tex] ≈ 66.35 → B

Answer:

[tex]\Large \boxed{-\dfrac{5}{4}(x+3)(x+1)(x-2)}[/tex]

Step-by-step explanation:

Hello,

Based on the indication, we can write this polynomial as below, k being a real number that we will have to identify (degree = 3 and we have three zeroes -3, -1, and 2).

   [tex]\Large \boxed{k(x+3)(x+1)(x-2)}[/tex]

We know that the point (1,10) is on the graph of this function, so we can say.

[tex]k(1+3)(1+1)(1-2)=10}\\\\4*2*(-1)*k=10\\\\-8k=10\\\\k=\dfrac{10}{-8}=-\dfrac{5}{4}[/tex]

Then the solution is:

[tex]\large \boxed{-\dfrac{5}{4}(x+3)(x+1)(x-2)}[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

  7 units, 8 units

Step-by-step explanation:

Apparently, the cross section of each prism is a rectangle 1 unit by 2 units. Hence the total length will be ...

  (30 units³)/((1 unit)(2 units)) = 15 units

Two numbers that differ by 1 and have a sum of 15 are 7 and 8.

The lengths of the prisms are 7 units and 8 units.

Answer:

45

Step-by-step explanation:

The n th term of a GP is

[tex]a_{n}[/tex] = a[tex]r^{n-1}[/tex]

where a is the first term and r the common ratio

Given a₂ = 6 and a₅ = 48, then

ar = 6 → (1)

a[tex]r^{4}[/tex] = 48 → (2)

Divide (2) by (1)

[tex]\frac{ar^4}{ar}[/tex] = [tex]\frac{48}{6}[/tex] , that is

r³ = 8 ( take the cube root of both sides )

r = [tex]\sqrt[3]{8}[/tex] = 2

Substitute r = 2 into (1)

2a = 6 ( divide both sides by 2 )

a = 3

Thus

3, 6, 12, 24 ← are the first 4 terms

3 + 6 + 12 + 24 = 45 ← sum of first 4 terms

Answer:

46 customers

Step-by-step explanation:

If the number of original customers is n, we can write the following equation:

98 = 2n + 6

92 = 2n

46 = n

Answer:

Hey there!

Pythagorean Theorem:

[tex]a^2+b^2=c^2\\[/tex]

Let 6 be a, and 11 be b.

[tex]6^2+11^2=c^2\\[/tex]

[tex]36+121=c^2\\[/tex]

[tex]157=c^2[/tex]

[tex]\sqrt{157} =c[/tex]

Hope this helps :)

Answer:

[tex]12.529[/tex]

Step-by-step explanation:

[tex] {a}^{2} + {b}^{2} = {c}^{2} \\ {6}^{2} + {11}^{2} = {c}^{2} \\ 36 + 121 = {c}^{2} \\ 157 = {c}^{2} \\ \sqrt{157} = {c}^{2} \\ c = 12.529[/tex]

[tex]hope \: it \: helps \: < 3[/tex]

Answer:

they divied the turkey into 14 pices

Step-by-step explanation:

Answer:

not just you

Step-by-step explanation:

Answer:

111.33667

Step-by-step explanation:

You add percentages just like you would any other number.

122.9%   +   108.46%  +   102.65% = 334.01%

334.01%/3 = 111.33667

Answer:

(d-5-√15)(d-5+√15)

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

1 ÷ 1 = 1

2 ÷ 1 = 2

3 ÷ 1 = 3

4 ÷ 1 = 4

5 ÷ 1 = 5

6 ÷ 1 = 6

7 ÷ 1 = 7

8 ÷ 1 = 8

9 ÷ 1 = 9

10 ÷ 1 = 10

Answer:

The world smallest number that is divisible by all the numbers 1,2,3,4,5,6,7,8,9,10 means that all the above numbers can divide that number without a remainder.

From the question the world smallest number that is divisible by the above numbers is

Hope this helps you

Answer:

The answer is 15.6/31 or 1/2

Step-by-step explanation:

The data in the question is sufficient to find an answer for it.

1. I look at the temperature and rainfall chart for Brighton, United Kingdom.

2. Check for rainy season and dry season.

3. The rainy season lasts approximately 5 months while the dry season (which still has some rainfall) lasts approximately 7 months. All together, 12 months of the calendar year.

4. July happens to fall within the dry season. The temperature and rainfall statistics are observed.

The number of rainfall days is 15.6 and we know there are 31 days in July.

If the approximate number of days it rains in Brighton, in July, is 15.6 then the probability of rainfall in the month is 15.6/31 which is = 0.503 or 0.5

Therefore, there's a 50% chance of having rainfall in Brighton, on any day in the month of July.

In fraction, 0.5 = 1/2

They left off the equation but we can know it's

y(t) =  h₀ - g t² / 2

That's

y(t) = 144 - 16 t²

It hits the ground when

0 = 144 - 16 t²

16 t² = 144

t² = 144 / 16 = 9

t = 3 seconds

Answer: 3 seconds

Answer:  a. read, question, summarize, practice

Step-by-step explanation:

This may be subjective, but the most efficient method usually is:

> Read:

Obviously the first step is read, if there is something that you do not understand, keep reading (but take note of all the things that you don't understand), is important that you have a complete overview on the topic that you are studying

> Question:

Now is time to ask about the things that you did not understand in the first read, always when you do not fully understand something, is a good habit to ask about it, this is the best and easiest way to learn.

> Summarize:

Now that you understand all the text (or at least most of it) is the moment to summarize your new knowledge: Write all the new equations that you learned, also write for what they are for, when they can be useful, etc.

This is what you will use to solve exercises, so you should be clear when writing.

> Practice:

This is one of the most important parts, here is where you put in practice your new knowledge. Here you may find some problematic situations where you need to be inventive with your equations, which will allow you to learn new ways to use your equations, so this is a really important step.

So the correct option is A.

Answer:

278 feet.

Step-by-step explanation:

S = 350 - 16t^2 + vt

t =2; v = -4.

S = 350 - 16 * (2)^2 + 2 * (-4)

S = 350 - 16 * 4 - 8

S = 350 - 64 - 8

S = 350 - 72

S = 278 feet.

Hope this helps!

Answer:

204.4(repeating) degrees

Step-by-step explanation:

The equation to go from F to C, is (F-32)×5/9. So 400-32 is 368.

368×5=1840

Than 1840/9=204.44 degrees. The 4 is repeating at the end.

Answer:

the length of DF = 3/4 AC

see below for explanation

Step-by-step explanation:

ABC is said to be approximately equal to DEF

The scale factor from ABC to DEF = 3/4

From the question, we can tell the original and new shape is a triangle because the lettering to indicate the vertices for both are 3.

We can deduce from the question, ΔABC was dilated to form ΔDEF

In dilation, the length of each of the corresponding side of the new figure is equal to the multiplication of each of the corresponding sides of the old figure and thee scale factor.

In the absence of cordinates for each vertices and length of each sides, ΔABC has 3 sides :

AB, BC and AC

ΔDEF has 3 sides : DE, EF and DF

If AB corresponds to DE

BC corresponds to EF

AC corresponds to DF

Then:

length DE = scale factor × AB = 3/4 AB

length EF = scale factor × BC = 3/4 BC

length DF = scale factor × AC = 3/4 AC

Therefore, the length of DF = 3/4 AC

Answer:

Option B

Step-by-step explanation:

The margin of error describes how many percentage points the results will differ from the real population value, thus 'the margin of error for a 95% confidence interval is given as plus or minus 7 milligrams per deciliter of blood (mg/dl)' can be interpreted as 'The study used a method that gives a results within 7 mg/dl of the truth about the population in 95% of all samples.'

Answer:

672 chairs

Step-by-step explanation:

24 × 28 = 672

hope this helps

Answer:

{ } or empty set.

Step-by-step explanation:

The solutions should be where the two lines intersect, but in this case, the parallel lines never intersect. That means that they have no solutions.

Hope this helps!

Answer:

{ } or empty set

Step-by-step explanation:

It's because these lines are parallel so they don't intersect to give you a coordinate.

Answer:

See below

Step-by-step explanation:

images attached showing all working

a) The possible values of X are as follows

X = {0,1,2,3,4}

P(x) = P(X=x)

b) The cdf in this case, as in the F(x), comes out to be a step function graph on the basis of values obtained from the probability mass function.

c) To find out the probability when more women are interviewed than me, add together the matrices from when value of X is equal to 2, 3 and 4 (from part a).

Answer:

D (13,5)

Step-by-step explanation:

X 2 3 4 5

Y 2 5 9 13

So the ordered pairs are (2,2),(3,5), (4,9), (5,13)

and the ordered pairs for the inverse are

(2,2),(5,3), (9,4), (13,5)

from which D (13,5) is found among the options.

Answer:

b

Step-by-step explanation:

Answer:

731`55

Step-by-step explanation:

*Step-by-step explanation:*

The given sequence:

88511, 16351, ?, 10251

To find, the missing number (?) = ?

The pattern follow:

1. To Add the first 2 digits in the number .

2. Subtract digit 3 from Digit 2 .

3. The multiply digit 3 and 4 .

4. To  divide digit 4 by 3.

16351 ⇒ 8 + 8 = 16,   8 - 5 = 3, 5 × 1 = 5 and \dfrac{1}{1} =111=1

= 16351

? ⇒ 1 + 6 = 7, 6 - 3 = 3, 3 × 5 = 15 and \dfrac{5}{1}15 = 5

= 73155

10251  ⇒ 7 + 3 = 10, 3 - 1 = 2,  1 × 5 = 5 and \dfrac{5}{5}55 = 1

=  10251

∴ The missing number of the given sequence = 73155

Thus, the missing number of the given sequence is 73155.

The third number in the sequence is : 73155

The given sequence is:

88511, 16351, ?, 10251

Now the pattern to find the missing value is:

Add, subtract, multiply and then divide.

These patterns are applied on the previous number's double digits to get the next number of the sequence.

Example:

Take 88511.

First pair (8,8): Add them: 16

Second pair (8,5): Subtract them: 8-5 = 3

Third pair: (5,1): Multiply them: 5

Fourth pair(1,1): Divide them: 1/1 = 1

Thus the next number of the sequence we get is 16351.

Similarly, doing it on 2nd term (16351) to find the missing third term:

Add (1,6): 7

Subtract (6,3): 3

Multiply (3,5): 15

Divide (5,1): 5

Thus the third number in the sequence is : 73155

Learn more here:

https://brainly.com/question/3000144

Answer:

Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 11.80

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > 11.80

Step-by-step explanation:

We are given that you have a sample of 40 14-year-old children with antisocial tendencies and you are particularly interested in the emotion of surprise. The average 14-year-old has a score on the emotion recognition scale of 11.80.

Assume that scores on the emotion recognition scale are normally distributed.

Let [tex]\mu[/tex] = true average score on the emotion recognition scale

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 11.80

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > 11.80

This a right-tailed test because the higher the score on this scale, the more strongly an emotion has to be displayed to be correctly identified. Therefore, higher scores indicate greater difficulty recognizing the emotion.

We can evaluate this hypothesis using One-sample t-test statistics or One-sample z-test statistics depends on the information given in the question.

If the z-test statistic is used, then the critical region at 0.05 level of significance will be an area more than the critical value of 1.645.

And if the t-test statistic is used, then the critical region at 0.05 level of significance with 39 degrees of freedom will be an area more than the critical value of 1.685.

The null hypothesis should be considered as the [tex]H_0: \mu = 11.80[/tex]

The alternative hypothesis should be considered as the [tex]H_A: \mu > 11.80[/tex]

It is the right-tailed test.

Since The average 14-year-old has a score on the emotion recognition scale of 11.80.

So here the null hypothesis should be [tex]H_0: \mu = 11.80[/tex]

And, here it is the right-tailed test since there should be higher the score on the given scale, due to this it should strongly an emotion that represent for rightly identified. Also high scores represent the high difficults for recording the emotion.

Learn more about hypothesis here: https://brainly.com/question/18831983

Answer:

work is shown and pictured

Answer:

RS = 8

Step-by-step explanation:

Given:

Secant QU = internal secant segment PU + external secant segment PQ = 7 + 9 = 16

Secant QS = internal secant segment RS + external secant segment RQ = (3x - 5) + 8

To find the measure of RS, we need to find the value of x.

Thus, recall the "Two Secant Theorem"

According to the theorem,

(RS + RQ)*RQ = (PU + PQ)*PQ

Thus,

[tex] (3x - 5 + 8)*8 = (7 + 9)*9 [/tex]

[tex] (3x + 3)*8 = (16)*9 [/tex]

[tex] 24x + 24 = 144 [/tex]

Subtract 24 from both sides

[tex] 24x + 24 - 24 = 144 - 24 [/tex]

[tex] 24x = 120 [/tex]

Divide both sides by 24

[tex] \frac{24x}{24} = \frac{120}{24} [/tex]

[tex] x = 5 [/tex]

Plug in the value of x into (3x - 5) to find the measure of RS

RS = 3(5) - 5 = 15 - 7

RS = 8