Multiply the polynomial 4x(2x+3) (show work pls)

Answer:

a) The mean number of radioactive atoms that decay per day is 81.485.

b) 0% probability that on a given day, 50 radioactive atoms decayed.

Step-by-step explanation:

Poisson distribution:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

[tex]P(X = x) = \frac{e^{-\lambda}*\lambda^{x}}{(x)!}[/tex]

In which

x is the number of sucesses

e = 2.71828 is the Euler number

[tex]\lambda[/tex] is the mean in the given interval.

a. Find the mean number of radioactive atoms that decayed in a day.

29,742 atoms decayed during 365 days, which means that:

[tex]\lambda = \frac{29742}{365} = 81.485[/tex]

The mean number of radioactive atoms that decay per day is 81.485.

b. Find the probability that on a given day, 50 radioactive atoms decayed.

This is P(X = 50). So

[tex]P(X = 50) = \frac{e^{-81.485}*(81.485)^{50}}{(50)!} = 0[/tex]

0% probability that on a given day, 50 radioactive atoms decayed.

Answer:

x = 960.4

Step-by-step explanation:

980 = 1000[tex]e^{kt}[/tex]

.98 = [tex]e^{10 k}[/tex]

ln(.98) = 10k ln(e)

k = ln(.98)/10

k=-0.00202

~~~~~~~~~~~~~~

x = 1000[tex]e^{20 *-.00202}[/tex]

x = 960.4

The amount of the material right after 20 years will be x = 960.4.

Powers can simply be expressed in concise form using exponential expressions. The exponent shows how many times the base has been multiplied. Since 2 is the "base" and 5 is the "exponent," it can be represented as 2x2x2x2=25 for the number 32. This phrase should be understood as "two to the fifth power."

Given that radioactive material is known to decay at a yearly rate proportional to the amount at each moment. There were 1000 grams of the material 10 years ago. There are 980 grams right now.

The amount of the material will be calculated as,

980 = 1000

[tex]0.98 = e^{10k}[/tex]

ln(.98) = 10k ln(e)

k = ln(.98)/10

k=-0.00202

The value after 20 years will be,

[tex]x = 1000e^{20\times 0.00202}[/tex]

x = 960.4

Therefore, the amount of the material right after 20 years will be x = 960.4.

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Answer:

18

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Step-by-step explanation:

Step 1: Define

Identify

b = 3

y = -3

5b - y

Step 2: Evaluate

Step-by-step explanation:

The graph of Fx), shown below in pink, has the same shape as the graph of G(x)-x, but it is shifted to the right two units. Complete its equation below Enter exponents using the caret (a), for example, enter x as x 4. Do not include Fx)-in your answer. .5 5 F(x) = Answer: 0

The equation of the graph is,

⇒ G (x) = (x - 3)⁴

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given that;

The graph of function G (x) is shown in image.

Here, The graph is 3 units left to function F (x) = x⁴.

Hence, The equation of the graph is,

⇒ G (x) = (x - 3)⁴

Thus, The equation of the graph is,

⇒ G (x) = (x - 3)⁴

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Answer:

answer is 1 2 3 and 4 respectively of given match the following

Answer:

let inverse f(x) be m:

[tex]m = \frac{1}{2x + 1} \\ 2x + 1 = \frac{1}{m} \\ 2x = \frac{1 - m}{m} \\ x = \frac{1 - m}{2m} [/tex]

substitute x in place of m:

[tex]{ \bf{ {f}^{ - 1}(x) = \frac{1 - x}{2x } }}[/tex]

If X ~ Exponential(µ), then the mean of X is 1/µ. So if the mean of X is twice the mean of Y, then the mean of Y is 1/(2µ), so that Y ~ Exponential(2µ).

We're given that

P(X > 50) = 1 - P(X ≤ 50) = 1 - Fx (50) ≈ 0.7788

==>   Fx (50) = P(X ≤ 50) ≈ 0.2212

where Fx is the CDF of X, which is given for 0 ≤ x < ∞ to be

Fx (x) = 1 - exp(-µx)

Solve for µ :

1 - exp(-50µ) ≈ 0.2212   ==>   µ ≈ -ln(0.7788)/50 ≈ 0.005

Then we have

P (Y > 40) = 1 - P (Y ≤ 40) = 1 - Fy (40)

where Fy is the CDF of Y,

Fy (y) = 1 - exp(-2µy)

so that

P (Y > 40) ≈ 1 - exp(-2 × 0.005 × 40) ≈ 0.3297

Answer:

[tex]d = \frac{4c}{3x + 4} [/tex]

Step-by-step explanation:

[tex]3x = \frac{4(c - d)}{d} [/tex]

Multiply both sides by d:

[tex]3xd = 4(c - d)[/tex]

Expand:

[tex]3xd = 4c \: - 4d[/tex]

+4d on both sides:

[tex]3xd + 4d = 4c[/tex]

Factorise d out of the left-hand side:

[tex]d(3x + 4) = 4c[/tex]

Divide both sides by (3x +4):

[tex]d = \frac{4c}{3x + 4} [/tex]

Answer:

0.15866

Step-by-step explanation:

6-7/1

=-1

p(x>-1)=1-p(x<1)

=0.15866

Answer:

t = 13.56915448 hrs.

Step-by-step explanation:

500 = 300 [tex]e^{2k}[/tex]

5/3 = [tex]e^{2k}[/tex]

ln(5/3) = 2k ln(e)

k = ln(5/3)/2

k= 0.255412812

~~~~~~~~~~~~

9600 = 300 [tex]e^{0.255412812 t}[/tex]

32= [tex]e^{0.255412812 t}[/tex]

ln(32) = [tex]0.255412812 t[/tex] ln(e)

t = ln(32)/0.255412812

t = 13.56915448 hrs.

Answer:

A is the equation in standard form

Step-by-step explanation:

Answer:

A. (1, -5), (2, -1), (-1, 7)

Step-by-step explanation:

Reflecting a function over the x-axis:

When a function is reflected over the x-axis, the x-value stays the same, while y changes the signal, so the transformation rule is:

[tex](x,y) \rightarrow (x,-y)[/tex]

To find the range:

We apply the transformation to the points in the domain. Thus:

[tex](1,5) \rightarrow (1,-5)[/tex]

[tex](2,1) \rightarrow (2,-1)[/tex]

[tex](-1,-7) \rightarrow (-1,-(-7)) = (-1, 7)[/tex]

Thus the correct answer is given by option a.

Answer:

It is letter A and please give me brainliest

Step-by-step explanation:

Answer:

a) The margin of error for a 98% confidence interval is of 3.388 people.

b) The 98% confidence interval for the population mean is between 20.61 people and 27.39 people.

Step-by-step explanation:

We have the standard deviation for the sample, which means that the hypergeometric distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 15 - 1 = 14

98% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 14 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.98}{2} = 0.99[/tex]. So we have T = 2.624

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}} = 2.624\frac{5}{\sqrt{15}} = 3.388[/tex]

In which s is the standard deviation of the sample and n is the size of the sample. This means that the answer to question a is of 3.388.

Question b:

The lower end of the interval is the sample mean subtracted by M. So it is 24 - 3.39 = 20.61 people

The upper end of the interval is the sample mean added to M. So it is 24 + 3.39 = 27.39 people.

The 98% confidence interval for the population mean is between 20.61 people and 27.39 people.

Answer:

The forth option

It forms a right angle with the segment.

Answer:

9 hours

Step-by-step explanation:

Let

x = number of hours it would take Seth to work by himself

He would paint 1/x in 1 hour

x + 2 = number of hours it would take Ted to work by himself

He would paint 1/(x + 2) in 1 hour

Seth and Ted = 5 hours

They would paint 1/5 in 1 hour

The equation is this:

1/x + 1/(x + 2) = 1/5

(x + 2)+x/x(x+2) = 1/5

x+2+x / x(x+2) = 1/5

2x + 2 / x(x+2) = 1/5

2x + 2 = x(x + 2)1/5

2x + 2 = (x² + 2x)1/5

5(2x + 2) = x² + 2x

10x + 10 = x² + 2x

x² + 2x - 10x - 10 = 0

x² - 8x - 10 = 0

x = -b ± √b² - 4ac/2a

= -(-8) ± √(-8)² - 4(1)(-10) / 2(1)

= 8 ± √64 - (-40) / 2

= 8 ± √64 + 40) / 2

= 8 ± √104 / 2

= 8 ± 2√26 / 2

= 8/2 ± 2√26/2

= 4 ± √26

= 4 ± 5.0990195135927

= 4 + 5.0990195135927 or 4 - 5.0990195135927

= 9.0990195135927 or -1.Answer:

Step-by-step explanation:

Let

x = number of hours it would take Seth to work by himself

He would paint 1/x in 1 hour

x + 2 = number of hours it would take Ted to work by himself

He would paint 1/(x + 2) in 1 hour

Seth and Ted = 5 hours

They would paint 1/5 in 1 hour

The equation is this:

1/x + 1/(x + 2) = 1/5

(x + 2)+x / x(x+2) = 1/5

x+2+x / x(x+2) = 1/5

2x + 2 / x(x+2) = 1/5

Cross product

2x + 2 = x(x + 2)1/5

2x + 2 = (x² + 2x)1/5

Cross product

5(2x + 2) = x² + 2x

10x + 10 = x² + 2x

x² + 2x - 10x - 10 = 0

x² - 8x - 10 = 0

x = -b ± √b² - 4ac/2a

= -(-8) ± √(-8)² - 4(1)(-10) / 2(1)

= 8 ± √64 - (-40) / 2

= 8 ± √64 + 40) / 2

= 8 ± √104 / 2

= 8 ± 2√26 / 2

= 8/2 ± 2√26/2

= 4 ± √26

= 4 ± 5.0990195135927

= 4 + 5.0990195135927 or 4 - 5.0990195135927

= 9.0990195135927 or -1.0990195135927

Approximately,

x = 9 hours or -1 hour

It can't take Seth negative hours to work

Therefore,

x = number of hours it would take Seth to work by himself = 9 hours

Answer: hi your question is incomplete below is the complete question

Suppose we increase the overall number of doctors in the U.S. in all fields and specialties of medical practice by equal percentages, which would shift the supply curves in all the respective medical practice markets. Suppose we were to analyze two separate medical practice markets: Plastic Surgery Cardiology Which markets' price would be most impacted by this increase in the supply of doctors? Which markets' quantity would be most impacted by this increase in the supply of doctors?

answer :

Change in Market price = Cardiology

Change in Quantity = Plastic surgery

Step-by-step explanation:

Given that we are analyzing two separate markets with different levels of importance .

The demand for plastic surgery is more elastic when compared with Cardiology and this is due to the importance of Cardiology over plastic surgery.

The market price that will be affected by the increase in doctors supply is Cardiology market price while the Market quantity that would be affected by the increase is quantity of  Plastic surgery

Answer:

71

Step-by-step explanation:

The measure of angle WXY will be thee ame as the measure of the intercepted arc, 109°.

W and Y are both tangent to the circle; this means angle XWZ and angle XYZ are both 90°.

Every quadrilateral has a total measure of 360°; to find the measure of WZY, we subtract:

360-90-90-109 = 71°

The measure of angle WZY (∠WZY) is; 71°

From the attached image, we can say that the measure of ∠WXY will be the same as the measure of the intercepted arc, 109°.

Now, W and Y are both tangent to the circle and this means that ∠XWZ and ∠XYZ are both equal to 90°.

Now, every quadrilateral has a total internal sum of angles as 360°.

Thus,  ∠WZY is gotten from;

∠WZY = 360 - (90 + 90 + 109)

∠WZY = 71°

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Answer:

B.

Step-by-step explanation:

f(x) = 4(1/2)^x

Let's find the value of the function for x = 0 and for x = 1.

f(0) = 4(1/2)^0 = 4(1) = 4

f(1) = 4(1/2)^1 = 4(1/2) = 2

The only graph that has both points (0, 4) and (1, 2) is the second graph.

Answer: B.

Answer:

Answer to the following question is as follows.

Step-by-step explanation:

Given:

a = 12500000

b = 0.00125

c = 1120000​

Calculate (ab) ÷ (c)

Given:

d) Express the interval [-1.5, 4] as an inequality and then graph

Computation:

(ab) ÷ (c) = (a)(b) / c

(ab) ÷ (c) = (12500000)(0.00125) / (1120000​)

(ab) ÷ (c) = 25 / 1,792

Express the interval [-1.5, 4]

{x : -1.5 < x ≤ 4}

Graph.

._________._________.

-1.5              0                  4

Explanation:

It's most effective to use a contingency table because we have two variables here: 1) the responses, and 2) the party affiliation.

We can have the responses along the rows and the party affiliation along the columns, or vice versa.

See the example below. The values are completely random simply for the purpose of the example (and not drawn from any real life data source).

As per the given options, the appropriate for the displaying these data will be contingency table. Hence, option D is correct.

A pie chart is a visual depiction of information in the shape of a pie, where the pieces of the pie represent the magnitude of the data. To depict data as a pie chart, you need a list of quantitative variables as well as categorical variables.

As per the given information in the question,

A contingency table in statistics is a particular kind of matrix-style table that shows the frequency of the variables. They are extensively utilized in scientific, engineering, business intelligence, and survey research.

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Answer:

The total amount due after five years is $57,000.

Step-by-step explanation:

Recall that simple interest is given by the formula:

[tex]\displaystyle A=P(1+rt)[/tex]

Where A is the final amount, P is the principal amount, r is the rate, and t is the time (in years).

Since we are investing a principal amount of $38,000 at a rate of 10.0% for five years, P = 38000, r = 0.1, and t = 5. Substitute:

[tex]\displaystyle A=38000(1+(0.1)(5))[/tex]

Evaluate. Hence:

[tex]\displaystyle A=\$ 57,000[/tex]

The total amount due after five years is $57,000.

Answer:

B. 88

Step-by-step explanation:

the total data = 1+2+4+5 = 12

the median is (a6+a7) /2

a6 = 87, a7 = 89

so, the median = (87+89)/2 = 88

Answer:

B. 88

--

the median is (a6+a7) /2

a6 = 87, a7 = 89

so, the median =[tex]\frac{87+89}{2}[/tex]= 88

Answer:

2. 2200 m²

3. 703 m²

Step-by-step explanation:

2. Given,

Base (b) = 45m

Top (a) = 35m

Height (h) = 55m

Area = (a+b)*h/2

= (45+35)*55/2

= 85*55/2 = 2200 m²

3. Given,

Base (b) = 19m

Height (h) = 37m

Area = b*h

= 19*37

= 703 m²

(The * sign represents the multiplication sign)

Answered by GAUTHMATH

Answer:

2. area = 2200 m²

3. area = 703 m²

Step-by-step explanation:

2. Find the area of a trapezium shaped field with a base of 45m, top is 35m and with a height of 55m applying the

formula for trapezium = 0.5 * (b+a) * h

Given:

Base= 45 m

Top (a) = 35 m

Height = 55 m

area = 0.5 * (b+a) * h

area = 0.5 * (45 m + 35 m) * 55 m

area = 2200 m²

3. Find the area of a Parallelogram shaped field where the base measures 19m and with a h of 37m.

Applying the formula for parallelogram = b * h

Given:

Base= 19 m

Height= 37 m

area = b * h

area = 19 m * 37 m

area = 703 m²

Answer:

The domain is "all real numbers" and the range is x more than -3

Answer:

2 hours

Step-by-step explanation:

Since Tory and Emilio's motorboats travel at the same speed, they are traveling at the speed of 30 km/h. Therefore, it should take Tory two hours to travel 60 km.

Tory took 2 hours to navigate the 60 kilometers.

Velocity is the pace and direction of an item's movement, whereas speed is the time rate at which an object is travelling along a route.

Given:

Tory pilots her boat 60 km before docking.

Emilio continues for another 4 hours traveling, a total of 120 km before docking.

The speed of Emilio's boat = 120 / 4 = 30 kilometers per hour.

Tory and Emilio's motorboats travel at the same speed.

Tory's boat speed,

= 60/30 = 2 hours.

Therefore, Tory takes 2 hours.

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Answer:

2TRN

Let me know if this is wrong!

233115555532224444432

Answer:

4.32 = k

Step-by-step explanation:

8/k = 5/2.7

We can solve using cross products

8* 2.7 = 5k

21.6 = 5k

Divide each side by 5

21.6/5 = k

4.32 = k

Answer: 5k = 21.6 and k = 4.32

there you go have a good day bye

Step-by-step explanation:

Answer:

0.0337 = 3.37% probability of finding two defects.

Step-by-step explanation:

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.

What is the probability of finding two defects in a Binomial distribution, with a sample size of 30, and probability of 0.2?

This is [tex]P(X = 2)[/tex], with [tex]n = 30[/tex] and [tex]p = 0.2[/tex]. So

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

[tex]P(X = 30) = C_{30,2}.(0.2)^{2}.(0.8)^{28} = 0.0337[/tex]

0.0337 = 3.37% probability of finding two defects.

Answer:

B

Step-by-step explanation:

I'm not really sure tho

Answer:

[tex]hright =12[/tex]

Step-by-step explanation:

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

The formula to find the area of a triangle is  [tex]A=\frac{1}{2}bh[/tex]  where [tex]b[/tex] stands for the base and [tex]h[/tex] stands for the height.

But we already know the area and the base. So to find the height, let's substitute 72 for [tex]A[/tex] and 12 for [tex]b[/tex], and solve.

[tex]72=\frac{1}{2}(12)(h)[/tex]

[tex]72=6h[/tex]

Here, divide both sides by 6

[tex]12=h[/tex]

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

Hope this is helpful.

Answer:

height = 12

Step-by-step explanation:

.............