Die A has 4 red faces and 2 black faces. Die B has 2 red faces and 4 black faces. A coin is flipped once. If it were heads, only die A is used (die B is discarded). If it were tails, only die B is used (die A is discarded). We do not get to know which die was chosen.
a) The first roll of the chosen die gives red. What is the probability that the second roll (with the same die) will be red?
b) The first two rolls of the die were both red. What is the probability that the third roll (with the same die) will be red?

Answer:

f(x) = x³ - 4x + 6

f'(x) = 3x² - 4

a) f'(2) = 3(2²) - 4 = 12 - 4 = 8

6 = 8(2) + b

6 = 16 + b

b = -10

y = 8x - 10

b) 3x² - 4 = 0

3x² = 4, so x = ±2/√3 = ±(2/3)√3

= ±1.1547

f(-(2/3)√3) = 9.0792

f((2/3)√3) = 2.9208

c) 3x² - 4 = 8

3x² = 12

x² = 4, so x = ±2

f(-2) = (-2)³ - 4(-2) + 6 = -8 + 8 + 6 = 6

6 = -2(8) + b

6 = -16 + b

b = 22

y = 8x + 22

f(2) = 6

y = 8x - 10

The equation perpendicular to the tangent is y = -1/8x + 25/4

-The smallest slope on the curve is 2.92

The curve has the smallest slope at the point (1.15, 2.92)

The equations at tangent points are y = 8x + 16 and  y = 8x - 16

From the question, we have the following parameters that can be used in our computation:

y = x³ - 4x + 6

Differentiate

So, we have

f'(x) = 3x² - 4

The point is (2, 6)

So, we have

f'(2) = 3(2)² - 4

f'(2) = 8

The slope of the perpendicular line is

Slope = -1/8

So, we have

y = -1/8(x - 2) + 6

y = -1/8x + 25/4

We have

f'(x) = 3x² - 4

Set to 0

3x² - 4 = 0

Solve for x

x = √[4/3]

x = 1.15

So, we have

Smallest slope = (√[4/3])³ - 4(√[4/3]) + 6

Smallest slope = 2.92

So, the smallest slope is 2.92 at (1.15, 2.92)

Here, we set f'(x) to 8

3x² - 4 = 8

Solve for x

x = ±2

Calculate y at x = ±2

y = (-2)³ - 4(-2) + 6 = 6: (-2, 0)

y = (2)³ - 4(2) + 6 = 6: (2, 0)

The equations at these points are

y = 8x + 16

y = 8x - 16

Read more about tangent lines at

https://brainly.com/question/21595470

#SPJ1

Experimental probability refers to the likelihood of an event occurring based on actual experimental results. If a group of students in a communications course is required to start a blog on a topic of their choice, and many have already begun blogging, and the three categories are: pop culture, literature, and business.

The following details and explanation help to find the probability of the blog being about pop culture, which is a topic of the group's choice.There are three categories, including pop culture, literature, and business.

The next blog will be about pop culture. That is, there is one successful result, which is the number of blogs that have been written about pop culture so far.

There is a total of five blogs written on pop culture, literature, and business. Hence, the experimental probability of the next blog being about pop culture can be obtained as follows:The experimental probability formula is:P(event) = number of successful outcomes ÷ total number of possible outcomesTherefore, P(event) = 5 ÷ 10= 1/2= 0.5 (as a decimal)

Therefore, the experimental probability that the next blog started will be about pop culture is 0.5, which is the chance that the blog will be about pop culture based on actual experimental results. This means that there is a 50% chance that the next blog started will be about pop culture.

For more such questions on pop culture

https://brainly.com/question/30653877

#SPJ8

The solution of the integral by variable change is equal to (1 / 6) · √(2 · x + 3)³ - (3 / 2) · √(2 · x + 3).

In this problem we find the definition of an integral, whose solution must be found by variable change, that is, a kind of algebraic substitution. First, write the complete expression:

∫ [x / √(2 · x + 3)] dx

Second, use algebraic substitution to simplify the expression:

u = 2 · x + 3

x = (u - 3) / 2

dx = du / 2

(1 / 2) ∫  [(u - 3) / (2 · √u)] du

(1 / 4) ∫ [(u - 3) / √u] du

(1 / 4) ∫√u du - (3 / 4) ∫ du / √u

Third, solve the integral:

(1 / 6) · √u³ - (3 / 2) · √u

Fourth, revert the algebraic substitution:

(1 / 6) · √(2 · x + 3)³ - (3 / 2) · √(2 · x + 3)

To learn more on indefinite integrals: https://brainly.com/question/28036871

#SPJ1

When you divide two numbers the answer is called the quotient.

Divide the dividend by the divisor to find the quotient of a division problem.

This may be accomplished by using repeated subtraction or lengthy division.

The quotient of two numbers, two fractions, or two algebraic expressions can be found.

According to the remainder theorem, when a polynomial p(x) is divided by (x – a), the remainder Equals f. (a). This is demonstrated by Euclid’s Division Lemma. Using this, p(x) = q(x) (x – a) + r if q(x) is the quotient and r is the remainder.

To learn more about quotient  to refer:

https://brainly.com/question/27796160

#SPJ1

Answer:

dlgSHJKAGDHFDKFKDK

Step-by-step explanation:

Answer:

-1

Step-by-step explanation:

12 + -13 = -1

Benny (B) would win the election using the plurality method.

To determine the winner using the plurality method, we need to calculate the total number of first-place votes for each candidate and see which candidate receives the most votes.

According to the given preference schedule, the number of first-place votes for each candidate is as follows:

Abe (A): 1st - 20 votes, 3rd - 2 votes (from the 2nd preference of voter 1)

Benny (B): 1st - 19 votes, 2nd - 5 votes

Chloe (C): 1st - 5 votes, 2nd - 19 votes, 3rd - 3 votes (from the 1st and 2nd preferences of voter 1)

Now, let's calculate the total number of first-place votes for each candidate:

Abe (A): 20 + 2 = 22 votes

Benny (B): 19 + 5 = 24 votes

Chloe (C): 5 + 0 + 3 = 8 votes

Based on the plurality method, the candidate with the highest number of first-place votes wins.

In this case, Benny (B) received the most first-place votes with a total of 24 votes.

Therefore, Benny (B) would win the election using the plurality method.

Learn more about plurality method click;

https://brainly.com/question/32003097

#SPJ1

7. Radius of circle P = 2       Radius of circle Q = 1

Coordinates of the point of tangency (4,2)

The equation of the tangency line is x = 4

8. AB is not a tangent. BC² ≠ AB² + AC²

9. The three radii of the circle are; CB, CF and CD

A diameter of the circle is BD

A tangent of the circle is GE

A chord of the circle is BD

A secant of the circle is AD

A point of tangency is F

7. To find the radius, identify the diameter of the circle. For the diagram, it can be said that the diameter of the circle P is 4.

The radius then is 4/2 = 2.

The radius of circle q is 2/2 = 1

You could also use the formula

Distance = sqrt((x2 - x1)² + (y2 - y1)²)

8. √4² + √12² = √160

√13 = 169

Therefore AB is not tangent. It is less than BC

9. The line that cuts the circle into two halves is the diameter. The lines than further cuts the diameter into equal parts are the radii's

Find more exercises on finding diameter and radius;

https://brainly.com/question/23891151

#SPJ1

Answer:

6Y

Step-by-step explanation:

We need to solve the statement ' Thrice the product of two and "Y" '.

Thrice means 3 times and product means multiply. It means we have to multiply 3,2 and Y.

Let the result is R. It can be calculated as follows :

\(R=3\times 2\times Y\)

We know that, 3×2 = 6

So,

\(R=6Y\)

Hence, Thrice the product of two and "Y" is 6Y.

Step-by-step explanation:

2 hrs 45 min + 3 hrs 35 min

= 5 hrs 80 min

60 min = 1 hr

*80 min = 1 hr + 20 min

5hrs 80 min

= 5 hrs + 1 hr + 20 min

= 6 hrs 20 min

Answer:

6 hour 20 minutes

Step-by-step explanation:

Add the two time measurements separately.

2 hours  +  3 hours  =  5 hours

35 minutes  +  45 minutes  =  80 minutes

Now, simplify the measurements to the lowest terms.  You can simplify the minutes by subtracting 60 from the value.  60 minutes is 1 hour.  The number you get after subtracting is how many minutes there are.

80 - 60 = 20

80 minutes  =  1 hour 20 minutes

Now add the two measurements together.

5 hours  +  1 hour 20 minutes  =  6 hour 20 minutes

Won 75%

then

a) team lose 25%

b) Find 25% of 12 games. Its a fourth part

Divide 12/4 = 3

Then answ er is

Team lose 3 games, this year.

Using linear function concepts, it is found that the slopes and intercepts of the functions are given as follows:

a) -4.

b) P = 25.

c) 2.

d) P = 5.

A linear function is modeled by: y = mx + b

m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.

b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.

The demand is given by:

D = 100 - 4P.

Hence the slope is -4. The demand is equals to zero when:

100 - 4P = 0 -> P = 25.

The supply is given by:

QS = -10 + 2P.

Hence the slope is 2. The supply is equal to zero when:

-10 + 2P = 0 -> P = 5.

Learned about linear function at

brainly.com/question/24808124

#SPJ1

There is a total of 720 students are in Ridgewood Junior High School.

5% of students brought their lunch.

36 students brought their lunch.

the percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

Let there be x students in the Ridgewood Junior High School.

5% of students brought their lunch and equal to 36

so 5% of x = 36

5/100 * x = 36

x = 36*100/5

x = 36*20

x = 720

There is a total of 720 students are in Ridgewood Junior High School.

Answer: 16 pounds of grain.

Step-by-step explanation: 36 divided by 9 is 4, which means we have to multiply bin C by how much bin J was multiplied by, which is 4, so 4x4 is 16.

(let me know if you would like me to explain more on this)

C

y=e^x

x=log base e

same as

16=2^x

x=log 16 base 2

Answer:

C

Step-by-step explanation:

You have to convert them from logarithm to exponential.

The first one becomes x = 2^16

The second one becomes 2 = 16^x

The third one becomes 16 = 2^x

The fourth one becomes x = 16²

The third one is your answer.

Answer:

B and H.

Step-by-step explanation:

By the triangle inequality, any two sides of a triangle must be greater than the remaining side.

Triangle 1)

The side lengths are 9, 40, and 41.

We only need to check the two smaller sides. 9 + 40 = 49 which is indeed greater than 41. Therefore, this is indeed a triangle.

Remember that if:

\(c^2=a^2+b^2\)

We have a right triangle.

\(c^2>a^2+b^2\)

We have an obtuse triangle.

And if:

\(c^2<a^2+b^2\)

We have an acute triangle.

In all of these, c is the longest side.

Therefore, we will substitute 41 for c and 9 and 40 for the others:

\(41^2\text{ }?\text{ }40^2+9^2\)

Evaluate:

\(1681=1681\)

Since the two values are equivalent, the first triangle is a right triangle.

Triangle 2)

Again, adding up the two smaller sides gives that 8 + 10 = 18.

However, 18 is less than 21, so it does not satisfy the triangle inequality.

Therefore, the given side lengths cannot form a triangle.

Answer:

Step-by-step explanation:

67

Alijah's taxable income puts him in the first tax bracket, over $8,350 but not surpassing $33,950. Hence, his tax due is a base of $835 plus 15% of the income that exceeds $8,350. This results in a total tax payable of $850. Option B is the correct answer.

Alijah's taxable income falls within the first bracket of the tax table given, being over $8,350 but not over $33,950.

This bracket requires him to pay a tax of $835.00 plus 15% of the amount over $8,350.

He has a surplus of $100 over the $8,350 threshold (i.e., $8,450 - $8,350), and 15% of $100 equals $15.

Therefore, the total tax he owes would be the fixed amount of $835.00 plus the $15.00 calculated, which sums up to $850.00.

Thus, looking at the provided options, option B ($850.00) would be the correct answer.

Learn more about Income Tax here:

https://brainly.com/question/34135935

#SPJ2

Answer:

right π/2

Step-by-step explanation:

The function f(x) = 2sin(x - π/2) is a sine function with a period of 2π, an amplitude of 2, and a phase shift of π/2. The phase shift of π/2 causes the graph of the function to be shifted π/2 units to the right. .

Therefore, the correct answer is right π/2

Answer:

Remaining amount of the element = 31.5 mg

Step-by-step explanation:

Half life of radioactive Iodine is \((T_{\frac{1}{2}})\) = 60 days

Formula to get the remaining element after t days is,

\(N=N_0(e)^{\lambda.t}\)

Where \(\lambda\) = decay constant of the radioactive element

t = duration of the decay (in days)

\(N_0\) = Initial amount of the element

N = final amount after decay

For half life period 't' = 60 days

\(\frac{N_0}{2}=N_0(e)^{\lambda\times 60}\)

\(e^{60\lambda}=0.5\)

\(ln(e^{60\lambda})=ln(0.5)\)

\(60\lambda =-0.069315\)

\(\lambda=-0.0115524\)

Remaining amount of the element after 40 hours,

N = \(50(e^{40\lambda} )\)

   = \(50(e)^{-(0.0115524)\times 40}\)

   = 50(0.62996)

   = 31.49

   ≈ 31.5 mg

Therefore, remaining amount of the element after 40 days is 31.5 mg.

Answer:

In 40 days, there would be approximately 31.5 mg remaining.

Step-by-step explanation:

Answer:

-200.5

Step-by-step explanation:

that’s just the right answer lol

b) The 99% confidence interval for the population proportion is given as follows: (0.57, 0.68).

A confidence interval of proportions has the bounds given by the rule presented as follows:

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which the variables used to calculated these bounds are listed as follows:

The confidence level is of 99%, hence the critical value z is the value of Z that has a p-value of \(\frac{1+0.99}{2} = 0.995\), so the critical value is z = 2.575.

The parameters for this problem are given as follows:

\(n = 520, \pi = \frac{325}{520} = 0.625\)

Then the lower bound of the interval is given as follows:

\(0.625 - 2.575\sqrt{\frac{0.625(0.375)}{520}} = 0.57\)

The upper bound of the interval is given as follows:

\(0.625 + 2.575\sqrt{\frac{0.625(0.375)}{520}} = 0.68\)

More can be learned about the z-distribution at https://brainly.com/question/25890103

#SPJ1

The value of x is -1 which makes the model true

The equation from the given model will be 5x+6=1

We have to find the value of x

5x+6=1

Subtract 6 from both sides

5x=-5

Divide both sides by 5

x=-1

Hence, the value of x is -1 which makes the model true

To learn more on Equation:

https://brainly.com/question/10413253

#SPJ1

The calculated bill for a person who uses 600kWh in a month is $80

From the question, we have the following parameters that can be used in our computation:

b(x) = 0.10x, x ≤ 200

b(x) = 0.15(x - 200) + 20, x > 200

For a person that uses 600kWh per month, we make use of the function

b(x) = 0.15(x - 200) + 20

This is because it is valid for x > 200

Substitute the known values in the above equation, so, we have the following representation

b(600) = 0.15(600 - 200) + 20

Evaluate

b(600) = 80

Hence, the bill for a person who uses 600kWh in a month is $80

Read more about piecewise function at

brainly.com/question/27262465

#SPJ1

The Future value of an annuity due of $200 each quarter for 2 1 2 years at 13%, compounded quarterly is $10263.734 ..

The future value of an annuity is the value of a group of regular payments at some point in the future. It assumes a particular rate of return, or discount rate. The higher the discount rate, the greater the annuity's future value.

P = PMT× ((1+r)ⁿ −1)/r

where:

P---> Future value of an annuity stream

PMT---->Dollar amount of each annuity payment

r -->Interest rate (also known as discount rate)

n--->Number of periods in which payments will be

We have given that

Present value for an Annuity = $200

compounded rate , r = 13%

but compounded quarterly, then, r = 13%/4

= 0.13/4 = 0.325

Number of years , n = 2 + 1/2 = 5/2

then change into quarterly, n = 5/2 × 4 = 10

Future value formula ,

F.V = PMT ( (1+i)ⁿ - 1)/r

=> Future value = 200((1+0.325)^10/0.325)

=> F.V = 10263.734

Hence, the future value of an annuity is $10263.734..

To learn more about Future value, refer:

https://brainly.com/question/20813161

#SPJ4