Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval? f(x) = 4x2 − 3x + 2, [0, 2]

Answers

Answer 1

Answer:

Yes , it satisfies the hypothesis and  we can conclude that c = 1 is an element of [0,2]

c = 1 ∈ [0,2]

Step-by-step explanation:

Given that:

[tex]f(x) = 4x^2 -3x + 2, [0, 2][/tex]

which is read as the function of x = 4x² - 3x + 2 along the interval [0,2]

Differentiating the function with respect to x is;

f(x) = 8x - 3

Using the Mean value theorem to see if the function satisfies it, we have:

[tex]f'c = \dfrac{f(b)-f(a)}{b-a}[/tex]

[tex]8c -3 = \dfrac{f(2)-f(0)}{2-0}[/tex]

since the polynomial function is differentiated in [0,2]

[tex]8c -3 = \dfrac{(4(2)^2-3(2)+2)-(4(0)^2-3(0)+2)}{2-0}[/tex]

[tex]8c -3 = \dfrac{(4(4)-3(2)+2)-(4(0)-3(0)+2)}{2-0}[/tex]

[tex]8c -3 = \dfrac{(16-6+2)-(0-0+2)}{2-0}[/tex]

[tex]8c -3 = \dfrac{(12)-(2)}{2}[/tex]

[tex]8c -3 = \dfrac{10}{2}[/tex]

8c -3  = 5

8c = 5+3

8c = 8

c = 8/8

c = 1

Therefore, we can conclude that c = 1 is an element of [0,2]

c = 1 ∈ [0,2]


Related Questions

Find the distance between (-8, 4) and (-8, -2).
10 units
2 units
6 units
8 units​

Answers

Answer:

10

Step-by-step explanation:

I don’t understand this, may I get some help?

Answers

Answer
B. 8.0023 10(tiny 4)

Explain
In scientific notation, the goal is to get any select number between the numbers 1 and 10. To find the answer quickly, i find where the decimal is (in this case it would be at the end of the number because there are no decimal numbers) and count how many numbers it takes to get between 1 and 10 (diagram below to show what i mean)

●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●

Hi my lil bunny!

❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙

80,023 written in scientific notation is [tex]8,0023[/tex] x [tex]10^4[/tex].

Step 1

To find a, take the number and move a decimal place to the right one position.

Original Number: 80,023

New Number: 8.0023

Step 2

New Number: 8 . 0 0 2 3

Decimal Count:   1 2 3 4

Now, to find b, count how many places to the right of the decimal.

There are 4 places to the right of the decimal place.

Step 3

Building upon what we know above, we can now reconstruct the number into scientific notation.

Remember, the notation is: a x 10^b

a = 8.0023

b = 4

Now the whole thing:

8.0023 x 104

Step 4

Check your work:

10^4 = 10,000 x 8.0023 = 80,023

❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙

●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●

Have a great day/night!

❀*May*❀

(Algebra) PLZ HELP ASAP!

Answers

Answer: Its everthing except irrational

Step-by-step explanation:

A father is three times as old as his son. After fifteen years the father will be twice as old as his son's age at that time. Hence the father's present age is

Answers

Answer:

Step-by-step explanation:

let present age of father=y

present age of son=x

then y=3x

after 15 years age of father=y+15

and age of son=x+15

∴y+15=2(x+15)

y+15=2x+30

y-2x=30-15

y-2x=15

∴3x-2x=15

x=15

y=3x=15×3=45

father's present age=45 years

Question:
If V7 - y = 6, then y =
A. -29
B. -5
C. 1
D. 29
[tex] \sqrt{7 - y = 6} [/tex]

Answers

Answer:

-29

Step-by-step explanation:

[tex] {\sqrt{7 - y }}^{2} = {6}^{2} [/tex]

[tex]7 - y = {6}^{2} [/tex]

y = 7-36

y = -29

Explain the difference between using the sine ratio to solve for a missing angle in a right triangle versus using the cosecant ratio. You must use complete sentences and any evidence needed (such as an example) to prove your point of view. (10 points)

Answers

Answer:

The sine ratio is the ratio between the opposite side over hypotenuse. The cosecant ratio is the ratio between the hypotenuse over the opposite side, therefore cosecant is the reciprocal of sine.

To find a missing angle using sine, you would need to use the inverse of sine. For example,  if the sine was  [tex]\frac{30}{40}[/tex], to find the angle you would need to find sin⁻¹ of  [tex]\frac{30}{40}[/tex] which is x =  sin⁻¹ (0.75). Therefore x equals approximately 49°.  

The mean salary of federal government employees on the General Schedule is $59,593. The average salary of 30 state employees who do similar work is $58,800 with \sigmaσσ= $1500. At the 0.01 level of significance, can it be concluded that state employees earn on average less than federal employees? What is the critical value? Round your answer to the nearest hundredths.

Answers

Answer:

Yes it can be concluded that state employees earn on average less than federal employees

  The critical value is  [tex]Z_{\alpha } = - 2.33[/tex]

Step-by-step explanation:

From the question we are told that

   The  population mean is  [tex]\mu = \$ 59593[/tex]

   The sample size is  n =  30

    The  sample mean is [tex]\= x = \$ 58800[/tex]

     The  standard deviation is  [tex]\sigma = \$ 1500[/tex]

     The significance level is  [tex]\alpha = 0.01[/tex]

   

The null hypothesis is  [tex]H_o : \mu = \$ 59593[/tex]

 The  alternative hypothesis is  [tex]H_a : \mu < \$ 59593[/tex]

The critical value of [tex]\alpha[/tex] from the normal distribution table is  [tex]Z_{\alpha } = - 2.33[/tex]

 Generally the test statistics is  mathematically evaluated as

            [tex]t = \frac{\= x - \mu}{ \frac{ \sigma }{ \sqrt{n} } }[/tex]

=>         [tex]t = \frac{ 58800 - 59593 }{ \frac{ 1500 }{ \sqrt{30} } }[/tex]  

=>          [tex]t = -2.896[/tex]

The  p-value is obtained from the z-table

   [tex]p-value = P(t < -2.896) = 0.0018898[/tex]

Since [tex]p-value < \alpha[/tex] , we reject the null hypothesis, hence it can be concluded that state employees earn on average less than federal employees  

   

Annie has 3/2 pounds of cookie dough. If she needs 1/16 of a pound of cookie dough to make one cookie, how many cookies can she make

Answers

Answer:

[tex]\boxed{\sf 24\ cookies}[/tex]

Step-by-step explanation:

1 cookie = 1/16 of a pound of cookie

If we want to find how many cookies can be made by 3/2 pounds ( 1.5 pounds) then we need to divide 3/2 pounds by 1/16

=> [tex]\frac{3}{2} / \frac{1}{16}[/tex]

=> [tex]\frac{3}{2} * 16[/tex]

=> 3*8

=> 24 cookies

Answer:

24 cookies

Step-by-step explanation:

3/2= 1.5 and 1/16= 0.0625

if you divide the amount of dough you have by the amount needed for each cookie you will have 24

1.5/0.0625=24

Simply. Who ever answers this will be marked Brainlist.

Answers

Answer:

Step-by-step explanation:

Hello,

[tex]r^3s^{-2}\cdot 8r^{-3}s^4\cdot 4rs^5\\\\=r^{3-3+1}s^{-2+4+5}\cdot 8\cdot 4\\\\\boxed{=32\cdot r\cdot s^7}[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

I need some help pls! I'm getting stuck!

Answers

Answer: 3 pounds.

Step-by-step explanation:

We have two metals:

One that contains 20% nickel, let's call it metal A.

One that contains 80% nickel, let's call it metal B.

We have 6 pounds of metal B, in those 6 punds we have:

0.80*6lb = 4.8lb of nickel.

Now, if we add X pounds of metal A, then we will have:

X + 6lb in total weight.

4.8lb + 0.2*X of nickel.

And we want to have exactly 60% of nickel, so we must have that the quotient between the amount of nickel and the total weight is equal to 0.6

(4.8lb + 0.2*X)/(6lb + X) = 0.6

now we solve it for X:

(4.8lb + 0.2*X) = 0.6*(6lb + X) = 3.6lb + 0.6*X

4.8lb - 3.6lb = 0.6*X - 0.2*X

1.2lb = 0.4*X

1.2lb/0.4 = 3lb = X

We should use 3 pounds of the metal with 20% of nickel.

PLEASE HELP!!! The question is.. [tex]163-y=-5[/tex] ANSWER GETS BRAINLIEST

Answers

Answer:

y = 168Step-by-step explanation:

[tex]163 -y =-5\\Collect\:Like\:terms\\163+5 = y\\Simplify\\168 =y\\\\y = 168[/tex]

Hello There!

Answer: [tex]163-168=-5[/tex]Explanation:

[tex]163-y=-5[/tex]

To solve your equation, you can just change the -5 to 5 and move it to where y is. After that, change the minus sign to addition.

[tex]163+5=y[/tex]

Now all you have to do is sum it up.

[tex]163+5=168[/tex]

So y = to 168

So your answer is

[tex]163-168=-5[/tex]

Hope this Helps!

i need help will rate you branliest

Answers

Answer D. the bottom one is the answer, because hyperbola is two curves that curve infinitely

Hope

Answer:

D. the bottom one is the answer, because hyperbola is two curves that curve infinitely

An architectural drawing lists the scale as 1/4" = 1'. If a bedroom measures 6 3/4" by 4 1/2" on the drawing, how large is the bedroom? Please Help! (No other information was given.)

Answers

1 inch = four 1/4’s

1 inch = 4 feet

6 X 4 = 24 feet

3/4 inches = 3 feet.

6 3/4 inches = 27 feet

4 x 4 = 16

1/2 inch = 2 feet

4 1/2 inches = 18 feet

Room is 27 feet x 18 feet

Find the minimum and maximum values of 3 sin^2x – 2 cos^2x + 9

Answers

838373838393 7373hshjd

An observer standing on a cliff 320 feet above the ocean measured angles of depression of the near and far sides of an island to be 16.5 and 10.5 respectively. How long is the island ?

Answers

Answer:

154.10 Feets

Step-by-step explanation:

Given the following :

Height (h) of cliff = 320 feet

Angle of depression of near side = 16.5°

Angle of depression of far side = 10.5°

Using trigonometry :

We can obtain x and y as shown in the attached picture :

Tanθ = opposite / Adjacent

Adjacent = height of cliff = 320 Feets

For the near side :

Tanθ = opposite / Adjacent

Tan (16.5°) = x / 320

0.2962134 = x / 320

x = 0.2962134 * 320

x = 94.788318 Feets

For the far side :

Tanθ = opposite / Adjacent

Tan (10.5°) = x / 320

0.1853390 = x / 320

x = 0.1853390 * 320

x = 59.308494 Feets

Length of island = (59.308494 + 94.788318) feet

= 154.10 Feets

A professional soccer player kicked a ball across the field. The ball’s height, in meters, is modeled by the function graphed below. What's the average rate of change between the point when the ball reached its maximum height and the point where it hit the ground?

Answers

Answer:

Hey there!

You can think of the rate of change as the slope of a quadratic function- here we see that it is 9/-3, or - 3.

Let  me know if this helps :)

Answer:

–3 meters per second

Step-by-step explanation:

There were 18,652 geese on a lake. What is this number rounded to the ten
thousands place?​

Answers

Answer:

20,000

Step-by-step explanation:

To round a number to the nearest ten thousands place, we have to look at the thousand place and see whether it crosses the "hill" of 5 as it's digit.

The thousand digit is 8, so it will round UP, making 18,652 become 20,000.

Hope this helped!

Answer:

[tex]\boxed{20,000}[/tex]

Step-by-step explanation:

Hey there!

Well the ten thousands number is 1 and the 1rst thousands place number is 8 so since 8 is more than 5 we have to round 1 UP to 2,

so the answer is 20,000.

Hope this helps :)

Suppose that prices of a certain model of new homes are normally distributed with a mean of $150,000. Use the 68-95-99.7 rule to find the percentage of buyers who paid: between $150,000 and $152,400 if the standard deviation is $1200.
A. 68%
B. 99.7%
C. 47.5%
D. 34%

Answers

Answer:

C. 47.5%

Step-by-step explanation:

The  summary of the given statistics include:

mean =150000

standard deviation: 1200

The  objective is to use tributed with a mean of $150,000. Use the 68-95-99.7 rule to find the percentage of buyers who paid: between $150,000 and $152,400

The z score formula can be use to calculate the percentage of the buyer who paid.

[tex]z = \dfrac{X - \mu}{\sigma}[/tex]

For the sample mean x = 150000

[tex]z = \dfrac{150000 - 150000}{1200}[/tex]

[tex]z = \dfrac{0}{1200}[/tex]

z = 0

For the sample mean x = 152400

[tex]z = \dfrac{152400 - 150000}{1200}[/tex]

[tex]z = \dfrac{2400 }{1200}[/tex]

z  = 2

From the standard normal distribution tables

P(150000 < X < 152400) = P(0 < z < 2 )

P(150000 < X < 152400) =P(z<2) -P(z<0)

P(150000 < X < 152400) =0.9772 -0.5

P(150000 < X < 152400) = 0.4772

P(150000 < X < 152400) = 47.7%  which is close to 47.5% therefore option C is correct

This question is based on concept of  statistics. Therefore, correct option is C i.e. 47.5% of buyers who paid: between $150,000 and $152,400 if the standard deviation is $1200.

Given:

Mean is $150,000, and

Standard deviation is $1200.

We need to determined the percentage of buyers who paid: between $150,000 and $152,400 as per given mean and standard deviation.

By using z score formula can be use to calculate the percentage of the buyer who paid,

[tex]\bold{z=\dfrac{x-\mu }{\sigma}}[/tex]

As given in question sample mean i.e. X= 150,000

[tex]z=\dfrac{150000-150000}{1200} \\\\z= \dfrac{0}{1200}\\\\z=0[/tex]

Now for the sample mean X = 152,400 ,

[tex]z=\dfrac{152400-150000}{1200} \\\\\\z= \dfrac{24000}{1200}\\\\\\z=2[/tex]

By using standard normal distribution table,

P(150000 < X < 152400) = P(0 < z < 2 )

P(150000 < X < 152400) =P(z<2) -P(z<0)

P(150000 < X < 152400) =0.9772 -0.5

P(150000 < X < 152400) = 0.4772

P(150000 < X < 152400) = 47.7%  which is close to 47.5%

Therefore, correct option is C that is 47.5%.

For further details, please prefer this link:

https://brainly.com/question/23907081


Megan’s room is expanded so the width is 150% of 3 meters. What is the new width?

Answers

Answer: 4.5 meters

Work Shown:

The keyword "of" means "multiply".

150% = 150/100 = 1.5

150% of 3 = 1.5*3 = 4.5

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Required percentage value = a

total value = b

Percentage = a/b x 100

100% = 3 meters

150% = 4.5 meters

The new width is 4.5 meters.

What is a percentage?

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

Megan’s room is expanded so the width is 150% of 3 meters.

This means,

100% = 3 meters

Multiply 150/100 on both sides.

150% = 150/100 x 3

150% = 4.5 meters

Thus,

The new width is 4.5 meters.

Learn more about percentages here:

https://brainly.com/question/11403063

#SPJ2

An economist is interested in studying the spending habits of consumers in a particular region. The population standard deviation is known to be $1,000. A random sample of 50 individuals resulted in an average expense of $15,000. What is the width of the 99% confidence interval for the mean of expense? a. 364.28 b. 728.55 c. 329.00 d. 657.99

Answers

Answer:

The  width is  [tex]w = \$ 729.7[/tex]

Step-by-step explanation:

From the question we are told that

   The population standard deviation is  [tex]\sigma = \% 1,000[/tex]

    The  sample size is  [tex]n = 50[/tex]

    The sample mean  is  [tex]\= x = \$ 15,000[/tex]

Given that the confidence level is  99% then the level of significance is mathematically represented as  

               [tex]\alpha = 100 - 99[/tex]

=>            [tex]\alpha = 1\%[/tex]

=>             [tex]\alpha = 0.01[/tex]

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

             [tex]Z_{\frac{\alpha }{2} } = Z_{\frac{0.01 }{2} } = 2.58[/tex]

Generally margin of error is mathematically represented as

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

substituting values

              [tex]E = 2.58 * \frac{1000 }{\sqrt{50} }[/tex]

              [tex]E = 2.58 * \frac{1000 }{\sqrt{50} }[/tex]

               [tex]E = 364.9[/tex]

The width of the 99% confidence interval is mathematically evaluated as

         [tex]w = 2 * E[/tex]

substituting values

          [tex]w = 2 * 364.9[/tex]

          [tex]w = \$ 729.7[/tex]

Evaluate 1 + (-2/3) - (-m) where m = 9.2.

Answers

Answer:

9.533

Step-by-step explanation:

1+(-2/3)-(-9.2)

1-2/3--9.2

1-2/3+9.2=9.533

Answer: See below

Explanation:

1 + (-2/3) - (-m)
m = 9.2

1 - 2/3 + m
= 1 - 2/3 + 9.2
= 3/3 - 2/3 + 9.2
= 1/3 + 9.2
= 1/3 + 27.6/3
= 28.6/3

Find the volume of the cylinder. Round your answer to the nearest tenth.

Answers

Answer:

716.75 m^3

Step-by-step explanation:

Volume of a cylinder:

=> PI x R^2 x H

H = Height

R = Radius

=> PI x 3.9^2 x 15

=> PI x 15.21 x 15

=> PI x 228.15

=> 228.15 PI

           or

=> 228.15 x 3.14159

=> 716.75 m^3

Construct a polynomial function with the following properties: fifth degree, 4 is a zero of multiplicity 3, −4 is the only other zero, leading coefficient is 4. setup problem so I can solve, thanks!!

Answers

Answer:

Step-by-step explanation:

Hello,

degree 5

4 is a zero of multiplicity 3 -> (x-4)^3 is a factor

-4 is the only other zero, so the multiplicity is 5-3=2 -> (x+4)^2 is a factor

leading coefficient is 4 so we can write

[tex]\boxed{4(x-4)^3(x+4)^2}[/tex]

If there is something that you do not understand or you are blocked somewhere let us know what / where.

Thank you.

EXAMPLE 5 If F(x, y, z) = 4y2i + (8xy + 4e4z)j + 16ye4zk, find a function f such that ∇f = F. SOLUTION If there is such a function f, then

Answers

If there is such a scalar function f, then

[tex]\dfrac{\partial f}{\partial x}=4y^2[/tex]

[tex]\dfrac{\partial f}{\partial y}=8xy+4e^{4z}[/tex]

[tex]\dfrac{\partial f}{\partial z}=16ye^{4z}[/tex]

Integrate both sides of the first equation with respect to x :

[tex]f(x,y,z)=4xy^2+g(y,z)[/tex]

Differentiate both sides with respect to y :

[tex]\dfrac{\partial f}{\partial y}=8xy+4e^{4z}=8xy+\dfrac{\partial g}{\partial y}[/tex]

[tex]\implies\dfrac{\partial g}{\partial y}=4e^{4z}[/tex]

Integrate both sides with respect to y :

[tex]g(y,z)=4ye^{4z}+h(z)[/tex]

Plug this into the equation above with f , then differentiate both sides with respect to z :

[tex]f(x,y,z)=4xy^2+4ye^{4z}+h(z)[/tex]

[tex]\dfrac{\partial f}{\partial z}=16ye^{4z}=16ye^{4z}+\dfrac{\mathrm dh}{\mathrm dz}[/tex]

[tex]\implies\dfrac{\mathrm dh}{\mathrm dz}=0[/tex]

Integrate both sides with respect to z :

[tex]h(z)=C[/tex]

So we end up with

[tex]\boxed{f(x,y,z)=4xy^2+4ye^{4z}+C}[/tex]

Megan has 12 pounds of cheesecake. On Monday, she and her friends eat 4 pounds. On Tuesday, she and her friends eat another 3 pounds. On Wednesday, her friend Mark gives her some more cheesecake so that she has 3 times as much as she had at the end of Tuesday. On Thursday, some of her cheesecake goes bad, so she has the amount that she had at the end of Wednesday, but divided by 5. On Friday, she gives 3 pounds to her dog. On Saturday, her mom gives her one more pound. On Sunday, how many pounds of cheesecake does Megan have left?

Answers

Answer:

Step-by-step explanation:

First we start with 12 pounds

On Monday, she and her friends eat 4 pounds. So we have 8 now.

On Tuesday, she and her friends eat another 3 pounds. So we gave 5 now.

On Wednesday, her friend Mark gives her some more cheesecake so that she has 3 times as much as she had at the end of Tuesday. 5 * 3 = 15

On Thursday, some of her cheesecake goes bad, so she has the amount that she had at the end of Wednesday, but divided by 5. She had 15 at the end of Wednesday. 15/5 = 3.

On Friday, she gives 3 pounds to her dog. 5 - 3 = 2.

On Saturday, her mom gives her one more pound. 2 + 1 = 3.

On Sunday, she finally has 3 pounds.

Answer:

nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn

Step-by-step explanation:

Actual time in seconds recorded when statistics students participated in an experiment t test their ability to determine when one minute 60 seconds has passed are shown below.Find the mean median mode of the listed numbers. 55 51 70 64 68 60 49?49

Answers

Step-by-step explanation:

mean add upp all the numbers and divide by how many they are

A bag contains two six-sided dice: one red, one green. The red die has faces numbered 1, 2, 3, 4, 5, and 6. The green die has faces numbered 1, 2, 3, 4, 4, and 4. A die is selected at random and rolled four times. You are told that two rolls were 1's and two were 4's. Find the probability the die chosen was green.

Answers

Answer:

the probability the die chosen was green is 0.9

Step-by-step explanation:

Given that:

A bag contains two six-sided dice: one red, one green.

The red die has faces numbered 1, 2, 3, 4, 5, and 6.

The green die has faces numbered 1, 2, 3, 4, 4, and 4.

From above, the probability of obtaining 4 in a single throw of a fair die is:

P (4  | red dice) = [tex]\dfrac{1}{6}[/tex]

P (4 | green dice) = [tex]\dfrac{3}{6}[/tex] =[tex]\dfrac{1}{2}[/tex]

A die is selected at random and rolled four times.

As the die is selected randomly; the probability of the first die must be equal to the probability of the second die = [tex]\dfrac{1}{2}[/tex]

The probability of two 1's and two 4's in the first dice can be calculated as:

= [tex]\begin {pmatrix} \left \begin{array}{c}4\\2\\ \end{array} \right \end {pmatrix} \times \begin {pmatrix} \dfrac{1}{6} \end {pmatrix} ^4[/tex]

= [tex]\dfrac{4!}{2!(4-2)!} ( \dfrac{1}{6})^4[/tex]

= [tex]\dfrac{4!}{2!(2)!} \times ( \dfrac{1}{6})^4[/tex]

= [tex]6 \times ( \dfrac{1}{6})^4[/tex]

= [tex](\dfrac{1}{6})^3[/tex]

= [tex]\dfrac{1}{216}[/tex]

The probability of two 1's and two 4's in the second  dice can be calculated as:

= [tex]\begin {pmatrix} \left \begin{array}{c}4\\2\\ \end{array} \right \end {pmatrix} \times \begin {pmatrix} \dfrac{1}{6} \end {pmatrix} ^2 \times \begin {pmatrix} \dfrac{3}{6} \end {pmatrix} ^2[/tex]

= [tex]\dfrac{4!}{2!(2)!} \times ( \dfrac{1}{6})^2 \times ( \dfrac{3}{6})^2[/tex]

= [tex]6 \times ( \dfrac{1}{6})^2 \times ( \dfrac{3}{6})^2[/tex]

= [tex]( \dfrac{1}{6}) \times ( \dfrac{3}{6})^2[/tex]

= [tex]\dfrac{9}{216}[/tex]

The probability of two 1's and two 4's in both dies = P( two 1s and two 4s | first dice ) P( first dice ) + P( two 1s and two 4s | second dice ) P( second dice )

The probability of two 1's and two 4's in both die = [tex]\dfrac{1}{216} \times \dfrac{1}{2} + \dfrac{9}{216} \times \dfrac{1}{2}[/tex]

The probability of two 1's and two 4's in both die = [tex]\dfrac{1}{432} + \dfrac{1}{48}[/tex]

The probability of two 1's and two 4's in both die = [tex]\dfrac{5}{216}[/tex]

By applying  Bayes Theorem; the probability that the die was green can be calculated as:

P(second die (green) | two 1's and two 4's )  = The probability of two 1's and two 4's | second dice)P (second die) ÷ P(two 1's and two 4's in both die)

P(second die (green) | two 1's and two 4's )  = [tex]\dfrac{\dfrac{1}{2} \times \dfrac{9}{216}}{\dfrac{5}{216}}[/tex]

P(second die (green) | two 1's and two 4's )  = [tex]\dfrac{0.5 \times 0.04166666667}{0.02314814815}[/tex]

P(second die (green) | two 1's and two 4's )  = 0.9

Thus; the probability the die chosen was green is 0.9

The domain of the following relation has how many elements?
[(1/2, 3.14/6), (1/2, 3.14/4), (1/2, 3.14/3), (1/2,3.14/2)]

a. 0
b. 1
c. 4​

Answers

Answer:

b. 1

Step-by-step explanation:

All first coordinates are 1/2.

Answer: b. 1

Calcule o valor de x nas equações literais: a) 5x – a = x+ 5a b) 4x + 3a = 3x+ 5 c) 2 ( 3x -a ) – 4 ( x- a ) = 3 ( x + a ) d) 2x/5 - (x-2a)/3 = a/2 Resolva as equações fracionárias: a) 3/x + 5/(x+2) = 0 , U = R - {0,-2} b) 7/(x-2) = 5/x , U = R - {0,2} c) 2/(x-3) - 4x/(x²-9) = 7/(x+3) , U = R - {-3,3}

Answers

Answer:

1) a) [tex]x = \frac{3}{2}\cdot a[/tex], b) [tex]x = 5-3\cdot a[/tex], c) [tex]x = -a[/tex], d) [tex]x = \frac{5}{2}\cdot a[/tex]

2) a) [tex]x = -\frac{3}{4}[/tex], b) [tex]x = -5[/tex], c) [tex]x = 3[/tex]

Step-by-step explanation:

1) a) [tex]5\cdot x - a = x + 5\cdot a[/tex]

[tex]5\cdot x - x = 5\cdot a + a[/tex]

[tex]4\cdot x = 6\cdot a[/tex]

[tex]x = \frac{3}{2}\cdot a[/tex]

b) [tex]4\cdot x + 3\cdot a = 3\cdot x + 5[/tex]

[tex]4\cdot x - 3\cdot x = 5 - 3\cdot a[/tex]

[tex]x = 5-3\cdot a[/tex]

c) [tex]2\cdot (3\cdot x - a) - 4\cdot (x-a) = 3\cdot (x+a)[/tex]

[tex]6\cdot x -2\cdot a -4\cdot x +4\cdot a = 3\cdot x +3\cdot a[/tex]

[tex]6\cdot x -4\cdot x -3\cdot x = 3\cdot a -4\cdot a +2\cdot a[/tex]

[tex]-x = a[/tex]

[tex]x = -a[/tex]

d) [tex]\frac{2\cdot x}{5} - \frac{x-2\cdot a}{3} = \frac{a}{2}[/tex]

[tex]\frac{6\cdot x-5\cdot (x-2\cdot a)}{15} = \frac{a}{2}[/tex]

[tex]\frac{6\cdot x - 5\cdot x+10\cdot a}{15} = \frac{a}{2}[/tex]

[tex]2\cdot (x+10\cdot a) = 15 \cdot a[/tex]

[tex]2\cdot x = 5\cdot a[/tex]

[tex]x = \frac{5}{2}\cdot a[/tex]

2) a) [tex]\frac{3}{x} + \frac{5}{x+2} = 0[/tex]

[tex]\frac{3\cdot (x+2)+5\cdot x}{x\cdot (x+2)} = 0[/tex]

[tex]3\cdot (x+2) + 5\cdot x = 0[/tex]

[tex]3\cdot x +6 +5\cdot x = 0[/tex]

[tex]8\cdot x = - 6[/tex]

[tex]x = -\frac{3}{4}[/tex]

b) [tex]\frac{7}{x-2} = \frac{5}{x}[/tex]

[tex]7\cdot x = 5\cdot (x-2)[/tex]

[tex]7\cdot x = 5\cdot x -10[/tex]

[tex]2\cdot x = -10[/tex]

[tex]x = -5[/tex]

c) [tex]\frac{2}{x-3}-\frac{4\cdot x}{x^{2}-9} = \frac{7}{x+3}[/tex]

[tex]\frac{2}{x-3} - \frac{4\cdot x}{(x+3)\cdot (x-3)} = \frac{7}{x+3}[/tex]

[tex]\frac{1}{x-3}\cdot \left(2-\frac{4\cdot x}{x+3} \right) = \frac{7}{x+3}[/tex]

[tex]\frac{x+3}{x-3}\cdot \left[\frac{2\cdot (x+3)-4\cdot x}{x+3} \right] = 7[/tex]

[tex]\frac{2\cdot (x+3)-4\cdot x}{x-3} = 7[/tex]

[tex]2\cdot (x+3) -4\cdot x = 7\cdot (x-3)[/tex]

[tex]2\cdot x + 6 - 4\cdot x = 7\cdot x -21[/tex]

[tex]2\cdot x - 4\cdot x -7\cdot x = -21-6[/tex]

[tex]-9\cdot x = -27[/tex]

[tex]x = 3[/tex]

What is the range of g?

Answers

Answer:

R: {y∈R | -1 ≤ y ≤ 5}

Step-by-step explanation:

the lowest point is -1 and the highest point is 5.

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