x
Find the value
of x. Show
3
10
your work.

Answer:

see details in graph and below

Step-by-step explanation:

There are many ways to generate the function.

We'll generate a function whose first derivative f'(x) satisfies the required conditions, say, a quadratic.

1. f(x) has a local minimum at x = -3, and

2. a local maximum at x = 3

Therefore f'(x) has to cross the x-axis at x = -3 and x=+3.

Furthermore, f'(x) must be increasing at x=-3 and decreasing at x=+3.

f'(x) = -x^2+9

will satisfy the above conditions.

Finally f(x) must be decreasing at x= -5, which implies that f'(-5) must be negative.

Check: f'(-5) = -(-5)^2+9 = -25+9 = -16 < 0  so ok.

f(x) can then be obtained by integrating f'(x) :

f(x) = integral of -x^2+9 = -x^3/3 + 9x = 9x - x^3/3

A graph of f(x) is attached, and is found to satisfy all three conditions.

A function is differentiable at [tex]x = a[/tex], if the function is continuous at [tex]x = a[/tex]. The function that satisfy the given properties is [tex]f(x) = 9x - \frac{x^3}{3} + 3[/tex]

Given that:

The function decreases at [tex]x = -5[/tex] means that: [tex]f(-5) < 0[/tex]

The local minimum at [tex]x = -3[/tex] and local maximum at [tex]x = 3[/tex] means that:

[tex]x = -3[/tex] or [tex]x = 3[/tex]

Equate both equations to 0

[tex]x + 3 = 0[/tex] or [tex]3 - x = 0[/tex]

Multiply both equations to give y'

[tex]y' = (3 - x) \times (x + 3)[/tex]

Open bracket

[tex]y' = 3x + 9 - x^2 - 3x[/tex]

Collect like terms

[tex]y' = 3x - 3x+ 9 - x^2[/tex]

[tex]y' = 9 - x^2[/tex]

Integrate y'

[tex]y = \frac{9x^{0+1}}{0+1} - \frac{x^{2+1}}{2+1} + c[/tex]

[tex]y = \frac{9x^1}{1} - \frac{x^3}{3} + c[/tex]

[tex]y = 9x - \frac{x^3}{3} + c[/tex]

Express as a function

[tex]f(x) = 9x - \frac{x^3}{3} + c[/tex]

[tex]f(-5) < 0[/tex] implies that:

[tex]9\times -5 - \frac{(-5)^3}{3} + c < 0[/tex]

[tex]-45 - \frac{-125}{3} + c < 0[/tex]

[tex]-45 + \frac{125}{3} + c < 0[/tex]

Take LCM

[tex]\frac{-135 + 125}{3} + c < 0[/tex]

[tex]-\frac{10}{3} + c < 0[/tex]

Collect like terms

[tex]c < \frac{10}{3}[/tex]

[tex]c <3.33[/tex]

We can then assume the value of c to be

[tex]c=3[/tex] or any other value less than 3.33

Substitute [tex]c=3[/tex] in [tex]f(x) = 9x - \frac{x^3}{3} + c[/tex]

[tex]f(x) = 9x - \frac{x^3}{3} + 3[/tex]

See attachment for the function of f(x)

Read more about continuous and differentiable function at:

https://brainly.com/question/19590547

Answer:

y= -0.8x + 4

Midpoint is 0,4

Answer:

7

Step-by-step explanation:

it's simply 13 - 6

7 it the answer, that was easy

Answer: 8

Step-by-step explanation:

Given: A bag contains three red marbles, two green ones, one lavender one, two yellows, and two orange marbles.

Total marbles other than green = 8

Total marbles other than green and yellow = 6

Then the number of sets of seven marbles include at least one yellow one but no green ones:-

[tex]^{2}C_1\times^{6}C_6+ ^2C_2\times^6C_5\\\\= 2\times 1+1\times6\\\\=2+6=8[/tex]

Number of sets of seven marbles include at least one yellow one but no green ones = 8

Answer: -1.33 .

Step-by-step explanation:

Formula to find the Z-score :

[tex]Z=\dfrac{\text{Expected value - Mean}}{\text{Standard deviation}}[/tex]

Given: Mean = 191  and Standard deviation = 21

Then , the z-score corresponding to the expected value of 163 will be :

[tex]Z=\dfrac{163-191}{21}\\\\=\dfrac{-28}{21}\approx-1.33[/tex]

Hence, the z score corresponding to selling 163 inhalers is -1.33 .

Complete Question

Pennsylvania Refining Company is studying the relationship between the pump price of gasoline and the number of gallons sold. For a sample of 14 stations last Tuesday, the correlation was 0.65.At the 0.01 significance level Can the company conclude that the correlation is positive

Answer:

Yes the company conclude that the correlation is positive

Step-by-step explanation:

From the question we are told that

   The  sample size is  n =  14

    The correlation is  r =  0.65

The  null hypothesis is  [tex]H_o : r < 0[/tex]

The  alternative hypothesis is  [tex]H_1 : r > 0[/tex]

Generally the standard deviation is mathematically evaluated as

       [tex]Sr = \sqrt{1- r}[/tex]

       [tex]Sr = \sqrt{1- 0.65}[/tex]

       [tex]Sr = 0.616[/tex]

The  degree of freedom for the one-tail test is

       [tex]df = n- 2[/tex]

        [tex]df = 14- 2[/tex]

        [tex]df = 12[/tex]

The standard error is evaluated as

        [tex]SE = \frac{0.616}{ \sqrt{12} }[/tex]

        [tex]SE =0.1779[/tex]

The test statistics  is evaluated as

      [tex]t = \frac{r }{SE}[/tex]

       [tex]t = \frac{0.65 }{0.1779}[/tex]

        [tex]t = 3.654[/tex]

The p-value of of  t is obtained from the z table, the value is  

        [tex]p-value = P(t < 3.654) = 0.00012909[/tex]

Given that [tex]p-value < \alpha[/tex]  then we reject the null hypothesis

           Hence the company can conclude that the correlation is positive

Answer:

James town is 5 meters higher than Takoradi​ .

Step-by-step explanation:

Given:

Height of James town = 2 meters below sea level

Height of Takoradi town = 7 meters below sea level

To find:

How much higher is James town that Takoradi = ?

Solution:

As we can see the standard of height is how much the town is below the sea level.

So, the height of town having lesser value will be at a higher level.

Value of Height of James town is lesser than that of Takoradi town.

Therefore, James town is at a higher level.

Difference of height = 7 meters - 2 meters = 5 meters

So, the answer is:

James town is 5 meters higher than Takoradi.

Answer:

Step-by-step explanation:

Initial population of wolf = 850 wolves

If the wolves increases by 7% each year, yearly increment will be 7% of 850

=  7/100 * 850

= 7*8.5

= 59.5 wolves.

This shows that the wolves increases by 59.5 each year.

After 7 years, increment will be equivalent  to 59.5 * 7 = 416.5

The wolf population after 7 years = Initial population + Increment after 7 years

= 850 + 416.5

= 1266.5

≈ 1267 wolves

Hence the population of the wolves after 7 years is approximately 1,267 wolves

Answer:

800700

Step-by-step explanation:

800000 + 00000 + 0000 + 000 + 00 + 0

000000 + 00000 + 0000 + 700 + 00 + 0

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

= 800700

Answer:

Hey there!

800000+700=800700

Hope this helps :)

Answer:

  A.  1,162.5

Step-by-step explanation:

Write the next two terms and add them up:

  S5 = 600 +300 +150 +75 +37.5 = 1162.5 . . . . matches choice A

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

Explanation:

{600, 300, 150, ...} is a geometric sequence starting at a = 600 and has common ratio r = 1/2 = 0.5, this means we cut each term in half to get the next term. We could do this to generate five terms and then add them up. Or we could use the formula below with n = 5

Sn = a*(1-r^n)/(1-r)

S5 = 600*(1-0.5^5)/(1-0.5)

S5 = 1,162.5

-----------

Check:

first five terms = {600, 300, 150, 75, 37.5}

S5 = sum of the first five terms

S5 = 600+300+150+75+37.5

S5 = 1,162.5

Because n = 5 is relatively small, we can quickly confirm the answer. With larger values of n, a spreadsheet is the better option.

Answer:

D

Step-by-step explanation:

The fastest way to solve this probelm would be to plug in each x value into these equations untill it outputs the correct two y values.

When you plug 3 into equation D the entire right side it will become.

y-1=0

y=1, which is true.

When you plug 6 into that equation.

y-1=5

y=6 which is also true.

im sorry but the thing is i cant translate these words but the answer is D

Answer:

H₀: μ = 93.29 vs. Hₐ: μ ≠ 93.29.

Step-by-step explanation:

In this case we need to test whether the claim made by BC financial aid is true or not.

Claim: The average textbook at BC bookstore costs $93.29.

A null hypothesis is a sort of hypothesis used in statistics that intends that no statistical significance exists in a set of given observations.  

It is a hypothesis of no difference.

It is typically the hypothesis a scientist or experimenter will attempt to refute or discard. It is denoted by H₀.

Whereas, the alternate hypothesis is the contradicting statement to the null hypothesis.

The alternate hypothesis describes direction of the hypothesis test, i.e. if the test is left tailed, right tailed or two tailed.

It is also known as the research hypothesis and is denoted by Hₐ.

The hypothesis to test this claim can be defined as follows:

H₀: The average textbook at BC bookstore costs $93.29, i.e. μ = 93.29.

Hₐ: The average textbook at BC bookstore costs different than $93.29, i.e. μ ≠ 93.29.

Answer:

The chi - square test can be [tex]\approx[/tex] 0.667

Step-by-step explanation:

From the given data :

The null hypothesis and the alternative hypothesis can be computed as:

Null hypothesis: The number of customers does  follow  a uniform distribution

Alternative hypothesis: The number of customers does not  follow  a uniform distribution

We learnt that: Carl recorded the number of customers who visited his new store during the week:

Day              Customers

Monday               17

Tuesday              13

Wednesday         14

Thursday              16

The above given data was the observed value.

However, the question progress by stating that : He expected to have 15 customers each day.

Now; we can have an expected value for each customer  as:

                      Observed Value                   Expected Value

Day                 Customers                        

Monday                17                                          15

Tuesday               13                                          15

Wednesday          14                                          15

Thursday               16                                         15

The Chi square corresponding to each data can be determined by using the formula:

[tex]Chi -square = \dfrac{(observed \ value - expected \ value )^2}{expected \ value}[/tex]

For Monday:

[tex]Chi -square = \dfrac{(17 - 15 )^2}{15}[/tex]

[tex]Chi -square = \dfrac{(2)^2}{15}[/tex]

[tex]Chi - square = \dfrac{4}{15}[/tex]

chi - square = 0.2666666667

For Tuesday :

[tex]Chi -square = \dfrac{(13- 15 )^2}{15}[/tex]

[tex]Chi -square = \dfrac{(-2)^2}{15}[/tex]

[tex]Chi - square = \dfrac{4}{15}[/tex]

chi - square = 0.2666666667

For Wednesday :

[tex]Chi -square = \dfrac{(14- 15 )^2}{15}[/tex]

[tex]Chi -square = \dfrac{(-1 )^2}{15}[/tex]

[tex]Chi -square = \dfrac{(1 )}{15}[/tex]

chi - square = 0.06666666667

For Thursday:

[tex]Chi -square = \dfrac{(16- 15 )^2}{15}[/tex]

[tex]Chi -square = \dfrac{(1 )^2}{15}[/tex]

[tex]Chi -square = \dfrac{(1 )}{15}[/tex]

chi - square = 0.06666666667

                   Observed Value   Expected Value    chi - square

Day                 Customers                        

Monday                17                     15                       0.2666666667

Tuesday               13                     15                       0.2666666667

Wednesday          14                     15                       0.06666666667

Thursday               16                    15                       0.06666666667

Total :                                                                        0.6666666668

The chi - square test can be [tex]\approx[/tex] 0.667

At level of significance ∝ = 0.10

degree of freedom = n - 1

degree of freedom = 4 - 1

degree of freedom = 3

At ∝ = 0.10 and df = 3

The p - value for the chi - square test statistics is 0.880937

Decision rule: If the p - value is greater than the level of significance , we fail to reject the null hypothesis

Conclusion: Since the p - value is greater than the level of significance , we fail to reject the null hypothesis and conclude that there is insufficient evidence to show that the number of customers does not follows a uniform distribution.

Answer:.67

Step-by-step explanation:

Answer:

sine and tangent

will be positive.

Answer:

Lori will pay $12 more if she makes monthly payments

Step-by-step explanation:

to find how much she will pay for 6 months, we have to multiply 12 by 6 to get $72

subtracting the amount she would pay as a down payment

$72 - $60 is $12

Lori will pay $12 more if she makes monthly payments

Complete Question

The complete question is shown on the first uploaded image

Answer:

The 95% confidence interval is  [tex]49.85 < \mu < 54.15[/tex]

This means that there is 95% chance that the true population mean is within this interval

Step-by-step explanation:

From the question we are told that

    The  sample size is n = 30  

    The sample mean is  [tex]\= x = 52[/tex]

    The population standard deviation is  [tex]\sigma = 6[/tex]

Given that the confidence level is 95% then the level of confidence is evaluate as

             [tex]\alpha = 100 - 95[/tex]

            [tex]\alpha = 5\%[/tex]

            [tex]\alpha = 0.05[/tex]

Next we obtain the critical value of  [tex]\frac{\alpha }{2}[/tex] from the normal distribution table , the values is

                 [tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]

Generally the margin of error is mathematically represented as

           [tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]

substituting values

            [tex]E = 1.96 * \frac{ 6 }{\sqrt{30} }[/tex]

           [tex]E = 2.147[/tex]

The  95% confidence interval is mathematically represented as

          [tex]\= x - E < \mu < \= x + E[/tex]

substituting values

         [tex]52 - 2.147 < \mu < 52 + 2.147[/tex]

         [tex]49.85 < \mu < 54.15[/tex]

Answer:

The respiratory system extends from the nose and upper airway to the alveolar surface of the lungs, where gas exchange occurs. Inhaled tobacco smoke moves from the mouth through the upper airway, ultimately reaching the alveoli. As the smoke moves more deeply into the respiratory tract, more soluble gases are adsorbed and particles are deposited in the airways and alveoli. The substantial doses of carcinogens and toxins delivered to these sites place smokers at risk for malignant and nonmalignant diseases involving all components of the respiratory tract including the mouth.

Answer:  2.5 seconds

Step-by-step explanation:

x refers to time. Since we want to know how long it is in the air, we need to find the time (x) for the ball to land on the ground (y = 0)

0 = -10x² + 25x

0 = -5x(2x - 5)

0 = -5x     0 = 2x - 5

[tex]0 = x\qquad \dfrac{5}{2}=x[/tex]

x = 0 seconds is when the ball was kicked

x = 5/2 --> 2.5 seconds is when the ball landed on the ground

Answer:

C) w+4

Step-by-step explanation:

w=the variable

+4= increased by 4

HOPE THIS HELPS!!!!!! :)

<33333333333

Answer:

The question is incomplete, below is a possible match for the complete question:

You make $85,000 per year and your company matches 50 cents for every dollar you deposit into your 401k plan, up to 8% of your salary. Complete parts (a) through (c) below.

(a) If you contribute $200 every month to your 401k, what will your company contribute each month?

The company will contribute $ (Type an integer or a decimal rounded to two decimal places as needed.)

(b) If you contribute $830 every month to your 401k, what will your company contribute each month?

The company will contribute $ (Type an integer or a decimal rounded to two decimal places as needed.)

(c) What is the maximum amount of money the company will contribute to your 401k each year?

The maximum amount that the company will contribute each year is $

(Type an integer or a decimal rounded to two decimal places as needed.)

Answer:

a.) The company will contribute $100

b.) The company will contribute $415

c.) maximum amount the company will be willing to contribute = $6,800 per year

Step-by-step explanation:

First, let us calculate the maximum amount the company will be willing to pay into the 401k plan yearly:

Annual salary = $85,000

Monthly salary = $7083.3333

maximum amount = 8% = 8/100 = 0.08 of salary

maximum amount = 0.08 × 7083.3333 = $566.67

a.) If you contribute $200 every month.

Since $200 is less than the maximum amount that the company will be willing to contribute, let us calculate how much the company is willing to contribute:

Company matches 50 cents for every dollar you deposit

1 dollar deposited = 50 cents from company

but 1 cent = $0.01

∴ 50 cents = 0.01 × 50 = $0.5

$1 deposited = $0.5 from company

∴ $200 deposited = 0.5 × 200 = $100 contributed by company

Therefore, if you contribute $200 every month, your company will contribute $100 each month.

from this example, we can see that the company is willing to contribute half of every amount you deposit every month ($100 = half of $200), hence, subsequently, we will use this for calculations.

b.) If you contribute $830 every month, the company will be willing to contribute half this amount, which is:

half of $830 = 830 ÷ 2 = $415

Therefore, if you contribute $830 per month, your company will contribute $415 per month.

c.) The maximum amount the company will be willing to contribute each year = 8% of salary per year

= [tex]= \frac{8}{100}\times 85,000 \\ =0.08\ \times\ 85,000 = \$6,800[/tex]

Therefore, the company will be willing to contribute $6,800 per year.

Answer:

The answer is 1/14w-8

Complete Question

The  complete question is shown on the first uploaded image

Answer:

The 90% confidence interval is  [tex][108.165 ,112.895][/tex]

The  95%  confidence interval is [tex][107.7123 ,113.3477][/tex]

The  correct option is  D

Step-by-step explanation:

From the question we are told that

    The sample size is  n =  48

     The sample  mean is  [tex]\= x = \$ 110.53[/tex]

    The standard deviation is  [tex]\sigma = \$ 9.96[/tex]

Considering first question

  Given that the confidence level is  90% then the level of significance is mathematically represented as

            [tex]\alpha = (100 - 90)\%[/tex]

           [tex]\alpha = 0.10[/tex]

The  critical value  of  [tex]\frac{\alpha }{2}[/tex] from the  normal distribution table is  

          [tex]Z_{\frac{\alpha }{2} } = 1.645[/tex]

Generally the margin of error is mathematically represented as

            [tex]E = ZZ_{ \frac{x}{y} } * \frac{\sigma}{ \sqrt{n} }[/tex]

             [tex]E = 1.645 * \frac{9.96}{ \sqrt{ 48} }[/tex]

             [tex]E = 2.365[/tex]

The  90% confidence interval is  

       [tex]\= x - E < \mu < \= x + E[/tex]

=>    [tex]110.53 - 2.365 < \mu < 110.53 + 2.365[/tex]

=>    [tex]108.165 < \mu < 112.895[/tex]

Considering second question

  Given that the confidence level is  95% then the level of significance is mathematically represented as

            [tex]\alpha = (100 - 95)\%[/tex]

           [tex]\alpha = 0.05[/tex]

The  critical value  of  [tex]\frac{\alpha }{2}[/tex] from the  normal distribution table is  

          [tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]

Generally the margin of error is mathematically represented as

            [tex]E = Z_{ \frac{x}{y} } * \frac{\sigma}{ \sqrt{n} }[/tex]

             [tex]E = 1.96 * \frac{9.96}{ \sqrt{ 48} }[/tex]

             [tex]E = 2.8177[/tex]

The  95% confidence interval is  

       [tex]\= x - E < \mu < \= x + E[/tex]

=>    [tex]110.53 - 2.8177 < \mu < 110.53 + 2.8177[/tex]

=>    [tex]107.7123 < \mu < 113.3477[/tex]

Answer:

5x+4f-1(x)=3 this is short answer

Answer:

x∈[2nπ−5π/6, 2nπ−π/6]∪{(4n+1)π/2}, n ϵ I

Step-by-step explanation:

1−2sin2  x≤−sin x    ⇒    (2sin x+1)(sin x−1)≥0

sin x≤−1/2    or    sin x≥1

−5π/6+2nπ≤x≤−π/6+2nπ    or    , n ϵ I x=(4n+1)π/2, n ϵ I⇒    -5π6+2nπ≤x≤-π6+2nπ    or    , n ϵ I x=4n+1π2, n ϵ I     (as sin x = 1 is valid only)

In general⇒    In general    x∈[2nπ−5π/6, 2nπ−π/6]∪{(4n+1)π/2}, n ϵ I

Answer:

Step-by-step explanation:

The graph tells you the zeros of the function are x=-3/4 and x=4.

The y-intercept is the constant in the function: 12.

The maximum is 22.5625 at x = 1.625.

Answer:

time taken for trip 2nd half >  time taken for trip 1st half

Step-by-step explanation:

Let the total distance of Joy's trip be = D

Then, the first half distance travelled = D/2

The rate (speed) at which Joy travels during first half = x

So, time taken to travel first half  = Distance / Speed

= (D/2) / x = D / 2x

Let the rate (speed) at which Joy travels during second half = x'

As given, x' (second half speed) < x (first half speed)

So, time taken to travel first half =  Distance / Speed  

(D/2) / x' =  D / 2x'

As  x' < x : D / 2x'  > D / 2x .

Trip 1st half Time taken trip < 2nd half ; or trip 2nd half time taken > 1st half

Answer:

c(x)=(3/4)^x

(3/4)^-2= 16/9

(3/4)^-1 =4/3

(3/4)^0=1

(3/4)^1 = 3/4

(3/4)^2= 9/16

Answer:

x= 5.5

Step-by-step explanation:

(segment piece) x (segment piece) =    (segment piece) x (segment piece)

x*4 = 11*2

4x = 22

Divide each side by 4

4x/4 = 22/4

x =5.5

Answer:

please mark my answer brainliest

Step-by-step explanation:

question is unclear to give u correct answer