Consider the function f(x)=2x^3+24x^2−54x+9,−9≤x≤2 This function has an absolute minimum value equal to? and an absolute maximum value equal to ?

Answer:

  x = 4

Step-by-step explanation:

Add 8 to both sides of the equation:

  6x -8 +8 = 16 +8

  6x = 24

Divide both sides of the equation by 6:

  6x/6 = 24/6

  x = 4

For this case we have the following equation:

[tex]6x-8 = 16[/tex]

We must find the value of the variable "x":

Adding 8 to both sides of the equation we have:

[tex]6x = 16 + 8\\6x = 24[/tex]

Dividing between 6 on both sides of the equation we have:

[tex]x = \frac {24} {6}\\x = 4[/tex]

Thus, the solution of the equation is[tex]x = 4[/tex]

Answer:

[tex]x = 4[/tex]

Answer:

Step-by-step explanation:

n^2 is less than 2^n for n < 2 and for n > 4. The smallest size of n that is of interest is n=1. For that, n^2 = 1^1 = 1.

The n^2 algorithm will outperform the 2^n algorithm for n = 1. That problem size will take 1 day to solve.

_____

Please note that there are no algebraic methods for solving an inequality of the form x^2 < 2^x. We have solved it using a graphing calculator.

Final answer:

The smallest instance size where the n² days algorithm outperforms the 2n seconds algorithm is n=43200. However, it's not practical, as this size leads to a computation time of approximately 1.86496 × 10⁹ days for the first algorithm, showing that for any realistic value of n, the second algorithm is more efficient.

Explanation:

The student's question is about the comparison of the performance of two different algorithms. Specifically, the question asks at what size the algorithm, which takes n² days to solve an instance of size n, will outperform the 2n seconds algorithm.

To determine the smallest instance size at which the first algorithm outperforms the second, we must set the two times equal and solve for n. Let's denote the time taken by the first algorithm as T1 and the second algorithm as T2, where T1 = n² days and T2 = 2n seconds. We should convert both times to a common unit, which typically is seconds, as follows:

1 day = 24 hours = 86400 seconds

T1 in seconds: n²  times 86400 seconds/day

T2 is already in seconds: 2n seconds

Now equate the two to find the smallest n:

n²  times 86400 = 2n

n²  times 86400 / 2 = n

n = 86400 / 2 = 43200

Thus, the smallest instance size n is 43200. To find how long this instance takes to solve by the first algorithm:

T1 = 43200² days

T1 ≈ 1.86496 × 109 days

This is impractically large, indicating that for any realistic value of n, the second algorithm is more efficient.

Suppose [tex]y_2(x)=y_1(x)v(x)[/tex] is another solution. Then

[tex]\begin{cases}y_2=vx^3\\{y_2}'=v'x^3+3vx^2//{y_2}''=v''x^3+6v'x^2+6vx\end{cases}[/tex]

Substituting these derivatives into the ODE gives

[tex]x^2(v''x^3+6v'x^2+6vx)-x(v'x^3+3vx^2)-3vx^3=0[/tex]

[tex]x^5v''+5x^4v'=0[/tex]

Let [tex]u(x)=v'(x)[/tex], so that

[tex]\begin{cases}u=v'\\u'=v''\end{cases}[/tex]

Then the ODE becomes

[tex]x^5u'+5x^4u=0[/tex]

and we can condense the left hand side as a derivative of a product,

[tex]\dfrac{\mathrm d}{\mathrm dx}[x^5u]=0[/tex]

Integrate both sides with respect to [tex]x[/tex]:

[tex]\displaystyle\int\frac{\mathrm d}{\mathrm dx}[x^5u]\,\mathrm dx=C[/tex]

[tex]x^5u=C\implies u=Cx^{-5}[/tex]

Solve for [tex]v[/tex]:

[tex]v'=Cx^{-5}\implies v=-\dfrac{C_1}4x^{-4}+C_2[/tex]

Solve for [tex]y_2[/tex]:

[tex]\dfrac{y_2}{x^3}=-\dfrac{C_1}4x^{-4}+C_2\implies y_2=C_2x^3-\dfrac{C_1}{4x}[/tex]

So another linearly independent solution is [tex]y_2=\dfrac1x[/tex].

Answer: The first number is 2000 times greater than second number.

Step-by-step explanation:

Let the first number be 'x' and second number be 'y'

We are given:

x = [tex]8\times 10^{-3}[/tex]

y = [tex]4\times 10^{-6}[/tex]

To calculate the times, number 'x' is greater than number 'y', we divide the two numbers:

[tex]\frac{x}{y}=\frac{8\times 10^{-3}}{4\times 10^{-6}}\\\\\frac{x}{y}=2\times 10^3\\\\x=2000y[/tex]

Hence, the first number is 2000 times greater than second number.

The number [tex]8\times 10^{-3}[/tex] is [tex]2000[/tex] times grater than the number [tex]4\times 10^{-6}[/tex].

Given information:

The number [tex]8 \times 10^{-3}[/tex]

And number [tex]4\times 10^{-6}[/tex]

Now , consider the first number as [tex]x[/tex] and number second as [tex]y[/tex].

So, according to the information given in the question we can write as:

[tex]\frac{x}{y} =\frac{8\times 10^{-3}}{4\times 10^{-6}}[/tex]

[tex]\frac{x}{y} = 2\times 10^3\\x=2000y[/tex]

Hence, We can conclude that the number [tex]8\times 10^{-3}[/tex] is [tex]2000[/tex] times the number [tex]4\times 10^{-6}[/tex].

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Answer: There are 26000 miles that will both be due at the same time.

Step-by-step explanation:

Since we have given that

Number of miles required by new vintage = 400

Number of miles if these services have must been performed by the dealer = 13000

We need to find the number of miles from now that will both be due at the same time.

We would use "LCM of 400 and 13000":

As we know that LCM of 400 and 13000 is 26000.

So, there are 26000 miles that will both be due at the same time.

Answer: 0.9713

Step-by-step explanation:

Given : Mean : [tex]\mu = 5.2\text{ day}[/tex]

Standard deviation : [tex]\sigma = 1.7\text{ days}[/tex]

The formula of z -score :-

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

At X = 2 days

[tex]z=\dfrac{2-5.2}{1.7}=-1.88235294118\approx-1.9[/tex]

Now, [tex]P(X>2)=1-P(X\leq2)[/tex]

[tex]=1-P(z<-1.9)=1- 0.0287166=0.9712834\approx0.9713[/tex]

Hence, the probability of spending more than 2 days in recovery = 0.9713

Answer:

There is a 98.54% probability of spending more than 2 days in recovery.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

[tex]\mu = 5.7, \sigma = 1.7[/tex]

What is the probability of spending more than 2 days in recovery?

This probability is 1 subtracted by the pvalue of Z when X = 2. So:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{2 - 5.7}{1.7}[/tex]

[tex]Z = -2.18[/tex]

[tex]Z = -2.18[/tex] has a pvalue of 0.0146.

This means that there is a 1-0.0146 = 0.9854 = 98.54% probability of spending more than 2 days in recovery.

Answer:

Part a) The amount of hardwood floor is [tex]480\ ft^{2}[/tex]

Part b) The amount of trim to buy is [tex]78\ ft[/tex]

Part c) The amount of paintable space is [tex]1,297\ ft^{2}[/tex]

Part d) The amount of paint needed is [tex]7.41\ gallons[/tex]

Step-by-step explanation:

Part a) You want to put down hard wood floors in your master bedroom. How much hard wood flooring would you need to buy?

Find the area of the floor

[tex]A=(10+5+3)(10+5+10)+(2+6+2)(3)[/tex]

[tex]A=(18)(25)+(10)(3)[/tex]    

[tex]A=480\ ft^{2}[/tex]

Part b) You also want to put a trim on the bottom of each wall, except in front of the french doors, sliding doors, or hallway. How much trim should you buy?  

step 1

Find the perimeter of the  master bedroom

[tex]P=2(25)+2(18)+2(3)[/tex]

[tex]P=50+36+6[/tex]

[tex]P=92\ ft[/tex]

step 2

Subtract the front of the french doors, sliding doors and hallway from the perimeter

[tex]92-(5+6+3)=78\ ft[/tex]

Part c) You want to paint your new bedroom. How much paintable space is there in the room?

step 1

Find the area of the ceiling

we know that

The area of the floor is equal to the area of the ceiling

so

The area of the ceiling is equal to [tex]A=480\ ft^{2}[/tex]

step 2

Find the area of the walls

Multiply the perimeter by the height

[tex]92*10=920\ ft^{2}[/tex]  

step 3

Subtract 73 square feet of surface that does not get painted (windows and sliding doors ) and the area of the hallway

The amount of paintable space is equal to

[tex]A=480+920-73-3(10)=1,297\ ft^{2}[/tex]

Part d) How many gallons of paint would you need to buy?

we know that

One gallon of paint covers 350 square feet

Multiply the area by two (because You want to put on two coats of paint on every paintable surface)

so

[tex]1,297*(2)=2,594\ ft^{2}[/tex]

using proportion

[tex]1/350=x/2,594[/tex]

[tex]x=2,594/350[/tex]

[tex]x=7.41\ gallons[/tex]

[tex]|\Omega|={_{16}C_5}=\dfrac{16!}{5!11!}=\dfrac{12\cdot13\cdot14\cdot15\cdot16}{120}=4368\\|A|={_{12}C_5}=\dfrac{12!}{5!7!}=\dfrac{8\cdot9\cdot10\cdot11\cdot12}{120}=792\\\\P(A)=\dfrac{792}{4368}=\dfrac{33}{182}\approx18\%[/tex]

The probability of the event is defined as the ratio of the number of cases favourable to an occurrence, and the further calculation can be defined as follows:

4 of the 16 modems are defective, while the remaining 12 are not.

P(accepting shipment) = P (all 5 modems work)

[tex]\bold{^{12}C_{5}}[/tex] methods could be used to choose 5 non-defective modems from a pool of 12 non-defective modems.

[tex]\to \bold{^{12}C_{5} = \frac{12!}{ (12 -5)! \times 5! }}[/tex]

             [tex]\bold{ = \frac{12!}{ 7! \times 5!}}\\\\\bold{ = \frac{12 \times 11 \times 10 \times 9 \times 8 \times 7!}{ 7! \times 5!}}\\\\\bold{ = \frac{12 \times 11 \times 10 \times 9 \times 8}{5 \times 4 \times 3 \times 2 \times 1}}\\\\\bold{ =11 \times 9 \times 8}\\\\\bold{=792}[/tex]

The total number of methods to choose 5 modems from a pool of 16 modems is [tex]\bold{^{16}C_{5}}[/tex].

[tex]\to \bold{^{16}C_{5} = \frac{16!}{ (16 -5)! \times 5! }}[/tex]

             [tex]\bold{ = \frac{16!}{ 11! \times 5!}}\\\\\bold{ = \frac{16 \times 15 \times 14 \times 13 \times 12 \times 11 !}{ 11! \times 5!}}\\\\\bold{ = \frac{16 \times 15 \times 14 \times 13 \times 12}{ 5!}}\\\\\bold{ = \frac{16 \times 15 \times 14 \times 13 \times 12}{ 5\times 4\times 3 \times 2 \times 1}}\\\\\bold{ = 8 \times 3 \times 14 \times 13 }\\\\\bold{ = 4368 }\\\\[/tex]

P(accepting shipment) = P(all 5 modems work):

[tex]= \bold{\frac{^{12}C_5}{ ^{16}C_{5}}}[/tex]

[tex]\bold{=\frac{792}{4368}}\\\\\bold{=0.18131}\\\\\bold{=0.18131 \times 100= 18.131 \approx 18.131\%}\\\\[/tex]

Therefore, the final answer is "18.131%".

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Answer:

[tex]\large\boxed{x=\sqrt6-3}[/tex]

Step-by-step explanation:

[tex]Domain:\\2x+3\geq0\to x\geq-1.5[/tex]

[tex]f(x)=\sqrt{2x+3},\ g(x)=x^2\\\\f(g(x))-\text{substitute x = g(x) in}\ f(x):\\\\f(g(x))=f(x^2)=\sqrt{2x^2+3}\\\\g(f(x))-\text{substitute x = f(x) in}\ g(x):\\\\g(f(x))=g(\sqrt{2x+3})=(\sqrt{2x+3})^2=2x+3\\\\f(g(x))=g(f(x))\iff\sqrt{2x^2+3}=2x+3\qquad\text{square of both sides}\\\\(\sqrt{2x^2+3})^2=(2x+3)^2}\qquad\text{use}\ (\sqrt{a})^2=a\ \text{and}\ (a+b)^2=a^2+2ab+b^2\\\\2x^2+3=(2x)^2+2(2x)(3)+3^2\\\\2x^2+3=4x^2+12x+9\qquad\text{subtract}\ 2x^2\ \text{and 3 from both sides}[/tex]

[tex]0=2x^2+12x+6\qquad\text{divide both sides by 2}\\\\x^2+6x+3=0\qquad\text{add 6 to both sides}\\\\x^2+6x+9=6\\\\x^2+2(x)(3)+3^2=6\qquad\text{use}\ (a+b)^2=a^2+2ab+b^2\\\\(x+3)^2=6\iff x+3=\pm\sqrt6\qquad\text{subtract 3 from both sides}\\\\x=-3-\sqrt6\notin D\ \vee\ x=-3+\sqrt6\in D[/tex]

Answer:

  28 mi

Step-by-step explanation:

The cars are separating at the rate of 52 mi/h - 45 mi/h = 7 mi/h. Then after 4 hours, their separation distance will be ...

  (7 mi/h)(4 h) = 28 mi

The two cars will be 28 miles apart after 4 hours.

To find the distance between the two cars after 4 hours, we need to calculate the distance traveled by each car. The formula to find distance is speed multiplied by time. The first car travels at an average speed of 45 mph for 4 hours, so its distance traveled is 45 mph * 4 hours = 180 miles.

The second car travels at an average speed of 52 mph for 4 hours, so its distance traveled is 52 mph * 4 hours = 208 miles. Therefore, the two cars will be 208 miles - 180 miles = 28 miles apart after 4 hours.

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Answer:

22 yd

Step-by-step explanation:

Length is four times its width   ----->    L=4W

area of rectangle is 196           ----->   196=LW

Plug L=4W into 196=LW giving you 196=(4W)W

Simplify a bit 196=4W^2

Divide both sides by 4:   196/4=W^2

Simplify a bit:   49=W^2

Square root both sides:  7 or -7=W

The width is 7 yd

The length is 4(7)=28 yd

Now its final part is for you to find the perimeter of this rectangle.  The rectangle is a 7 yd by 4 yd rectangle.

Double both then add.. 14+8=22 yd

Answer:

21 yd

Step-by-step explanation:

Length of a rectangle is four times its width =

L = 4 × w

The area of the rectangle is 196

L = 4W

A = L*W = 196

---

4W*W = 196

W*W = 196/4

W*W = 49

W = 7

L = 28

---

Answer:

P = 2(L + W)

P = 2(28 + 7)

P = 14 + 7

P = 21 yd

Answer:

  (1/3(5-√34), 1/27(-205+32√34)) and (1/3(5+√34), 1/27(-205-32√34))

Step-by-step explanation:

The slope of the given line is the x-coefficient, 4. Then you're looking for points on the f(x) curve where f'(x) = 4.

  f'(x) = 3x^2 -10x +1 = 4

  3x^2 -10x -3 = 0

  x = (5 ±√34)/3 . . . . . x-coordinates of tangent points

Substituting these values into f(x), we can find the y-coordinates of the tangent points. The desired tangent points are ...

  (1/3(5-√34), 1/27(-205+32√34)) and (1/3(5+√34), 1/27(-205-32√34))

_____

The graph shows the tangent points and approximate tangent lines.

To find where the tangent line to the function f(x)=[tex]x^3-5x^2+x[/tex] is parallel to the line y=4x+23, we need to find where the derivative of the function is equal to the slope of the given line.

In the field of mathematics, the problem asks us to find at which points the tangent line to function f(x)=[tex]x^3-5x^2+x[/tex] is parallel to the line y=4x+23. A line is tangent to a function at a point where the derivative of that function equals the slope of the line. The first step in solving this problem is to calculate the derivative of function f(x).

The derivative of the function f(x) is f'(x) =[tex]3x^2 - 10x +1[/tex]. Next, we set this equal to the slope of the given line, which is 4. Solving this quadratic equation will give us the x-values where the tangent line is parallel to y=4x+23.

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Answer:

It diverges to positive infinity  

Step-by-step explanation:

I see it was 4/(x-6)^3 not 4(x-6)^3... but still can't make out everything else.

[tex] \int_6^8 \frac{4}{(x-6)^3} dx [/tex]

The integrand does not exist at x=6.

[tex] \int_6^8 \frac{4}{(x-6)^3} dx [/tex]

[tex] \lim_{z \rightarrow 6^{+} } \int_z^8 4(x-6)^{-3} dx [/tex]

[tex] \lim_{z \rightarrow 6^{+} }\frac{4(x-6)^{-2}}{-2} |_z^8dx [/tex]

[tex] \lim_{z \rightarrow 6^{+} }[\frac{4(8-6)^{-2}}{-2} -\frac{4(z-6)^{-2}}{-2} ] [/tex]

[tex] \frac{1}{-2} - -\infty [/tex]

[tex] \infty [/tex]

So it diverges

Answer:

I could not properly read this but here was what I could make out

Step-by-step explanation:

Find the difference.

LaTeX: -\frac{5}{6}-\frac{17}{18}-\left(-\frac{2}{9}\right)Find the difference.

LaTeX: -\frac{5}{6}-\frac{17}{18}-\left(-\frac{2}{9}\right)Find the difference.

LaTeX: -\frac{5}{6}-\frac{17}{18}-\left(-\frac{2}{9}\right)Find the difference.

LaTeX: -\frac{5}{6}-\frac{17}{18}-\left(-\frac{2}{9}\right)Find the difference.

LaTeX: -\frac{5}{6}-\frac{17}{18}-\left(-\frac{2}{9}\right)Find the difference.

LaTeX: -\frac{5}{6}-\frac{17}{18}-\left(-\frac{2}{9}\right)Find the difference.

LaTeX: -\frac{5}{6}-\frac{17}{18}-\left(-\frac{2}{9}\right)Find the difference.

LaTeX: -\frac{5}{6}-\frac{17}{18}-\left(-\frac{2}{9}\right)Find the difference.

LaTeX: -\frac{5}{6}-\frac{17}{18}-\left(-\frac{2}{9}\right)Find the difference.

LaTeX: -\frac{5}{6}-\frac{17}{18}-\left(-\frac{2}{9}\right)

home this helped ;)

Answer:

n = 1067

Step-by-step explanation:

Since nothing is known, we would assume that 50% of the computers use the new operating system.

So, standard error = 0.5/SQRT(n)

Z-value for a 95% CI = 1.9596

So, margin of error = 1.9596 x 0.5 / SQRT(n) = 0.03

So, n = 1067 (approx.)

This will be your approximate answer : n = 1067

Answer: 2401

Step-by-step explanation:

Formula to find the sample size is given by :-

[tex]n= p(1-p)(\dfrac{z_{\alpha/2}}{E})^2[/tex]

, where p = prior population proportion.

[tex]z_{\alpha/2}[/tex] = Two -tailed z-value for [tex]{\alpha[/tex]

E= Margin of error.

As per given , we have

Confidence level : [tex]1-\alpha=0.95[/tex]

⇒[tex]\alpha=1-0.95=0.05[/tex]

Two -tailed z-value for [tex]\alpha=0.05 : z_{\alpha/2}=1.96[/tex]

E= 2%=0.02

We assume that nothing is known about the percentage of computers with new operating systems.

Let us take p=0.5  [we take p= 0.5 if prior estimate of proportion is unknown.]

Required sample size will be :-

[tex]n= 0.5(1-0.5)(\dfrac{1.96}{0.02})^2\\\\ 0.25(98)^2=2401[/tex]

Hence, the number of computer must be surveyed = 2401

Answer: Third Option

[tex]f(t)=21,386[/tex]

Step-by-step explanation:

We know that the equation that models the number of trees in the forest is:

[tex]f(t)=\frac{32,000}{1+12.8e^{-0.065t}}[/tex]

Where t represents the time elapsed in years

To calculate the number of trees after 50 years substitute [tex]t = 50[/tex] in the equation

[tex]f(t)=\frac{32,000}{1+12.8e^{-0.065(50)}}[/tex]

[tex]f(t)=21,386[/tex]

Answer:

[tex]\sqrt[3]{17}= 2.57128=257128[/tex]×[tex]10^{-5}[/tex]

Step-by-step explanation:

We need to find: [tex]\sqrt[3]{17}[/tex] in decimals. To do this, we are going to need the help of a calculator. After plugging the values, we get that:

[tex]\sqrt[3]{17}= 2.57128 = 257128[/tex]×[tex]10^{-5}[/tex]

In this case, I just considered 5 significant figures!

Answer: 0.8186

Step-by-step explanation:

Given: Mean : [tex]\mu=1.01\text{ inch}[/tex]

Standard deviation :  [tex]\sigma=0.003\text{ inch}[/tex]

Sample size :  [tex]n=9[/tex]

The formula to calculate z-score :-

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

For x=1.009 inch

[tex]z=\dfrac{1.009-1.01}{\dfrac{0.003}{\sqrt{9}}}=-1[/tex]

For x=1.012 inch

[tex]z=\dfrac{1.012-1.01}{\dfrac{0.003}{\sqrt{9}}}=2[/tex]

Now, The p-value =[tex]P(-1<z<2)=P(2)-P(-1)=0.9772498-0.1586553=0.8185945\approx0.8186[/tex]

Hence, the required probability = 0.8186

Answer:

P (Math or English) = 0.90

Step-by-step explanation:

* Lets study the meaning of or , and on probability

- The use of the word or means that you are calculating the probability

  that either event A or event B happened

- Both events do not have to happen

- The use of the word and, means that both event A and B have to

  happened

* The addition rules are:

# P(A or B) = P(A) + P(B) ⇒ mutually exclusive (events cannot happen

  at the same time)

# P(A or B) = P(A) + P(B) - P(A and B) ⇒ non-mutually exclusive (if they  

   have at least one outcome in common)

- The union is written as A ∪ B or “A or B”.  

- The Both is written as A ∩ B or “A and B”

* Lets solve the question

- The probability of taking Math class 71%

- The probability of taking English class 77%

- The probability of taking both classes is 58%

∵ P(Math) = 71% = 0.71

∵ P(English) = 77% = 0.77

∵ P(Math and English) = 58% = 0.58

- To find P(Math or English) use the rule of non-mutually exclusive

∵ P(A or B) = P(A) + P(B) - P(A and B)

∴ P(Math or English) = P(Math) + P(English) - P(Math and English)

- Lets substitute the values of P(Math) , P(English) , P(Math and English)

 in the rule

∵ P(Math or English) = 0.71 + 0.77 - 0.58 ⇒ simplify

∴ P(Math or English) =  0.90

* P(Math or English) = 0.90

To find the probability that a randomly selected student is taking a math class or an English class, use the principle of inclusion-exclusion. The probability is 90%.

To find the probability that a randomly selected student is taking a math class or an English class, we can use the principle of inclusion-exclusion. We know that 71% of students are taking a math class, 77% are taking an English class, and 58% are taking both.

To find the probability of taking either math or English, we add the probabilities of taking math and English, and then subtract the probability of taking both:

P(Math or English) = P(Math) + P(English) - P(Math and English)

= 71% + 77% - 58%

= 90%

Therefore, the probability that a randomly selected student is taking a math class or an English class is 90%.

Answer:

792

Step-by-step explanation:

₁₂C₅ = (12!) / (5! (12-5)!)

₁₂C₅ = (12!) / (5! 7!)

₁₂C₅ = 792

There are 792 different selections are​ possible.

Each of the different groups or selections can be formed by taking some or all of a number of objects, irrespective of their arrangments is called a combination.

We are given that in a Power Ball​ lottery, 5 numbers between 1 and 12 inclusive are drawn. These are the winning numbers.

Therefore, the selections are​ possible as;

₁₂C₅ = (12!) / (5! (12-5)!)

₁₂C₅ = (12!) / (5! 7!)

₁₂C₅ = 792

Hence, there are 792 different selections are​ possible.

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Answer: Hello your in college please help me with my latest problem please :(

Step-by-step explanation:

Answer:

The 1st & 2nd option

Step-by-step explanation:

Ans1: 16/3

Ans2: 30

Ans3: 11/7×surd6

Ans4: 2/3×surd11

Rational number is a number that can be expressed in ratio (quotient)

It can be expressed in the form of repeating or terminating decimal

Example:

16/3 is equal to

5.3333333333....(repeating decimal)

thus it is a rational number

1/4 is equal to

0.25 (terminating decimal)

thus it is a rational number

Answer:

II. Angle C cannot be a right angle.

III. Angle C could be less than 45 degrees.

The given altitude of triangle ABC is h, is located inside the triangle and

extends from side AB to the vertex C.

The true statements are;

I. Triangle ABC could be a right triangle

II. Angle C cannot be a right angle

Reasons:

I. Triangle ABC could be a right triangle

The altitude drawn from the vertex C to the line AB = h

The length of h = AB

Where, triangle ABC is a right triangle, we have;

The legs of the right triangle are; h and AB

The triangle ABC formed is an isosceles right triangle

Therefore, triangle ABC could be an isosceles right triangle; True

II. Angle C cannot be a right angle: True

If angle ∠C is a right angle, we have;

AB = The hypotenuse (longest side) of ΔABC

Line h = AB is an altitude, therefore, one of the sides of ΔABC is hypotenuse to h, and therefore, longer than h and AB, which is false

Therefore, ∠C cannot be a right angle

III. Angle C could be less than 45 degrees; False

The minimum value of angle C is given by when triangle ABC is an isosceles right triangle. As the position of h shifts between AB, the lengths of one of the sides of ΔABC increases, and therefore, ∠C, increases

Therefore, ∠C cannot be less than 45°

The true statements are I and II

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Answer:

  a) growth will reach a peak and begin declining after about 42.6 days. 5000 people will be infected at that point

  b) the infected an uninfected populations will be the same after about 42.6 days

Step-by-step explanation:

We have assumed you intend the function to match the form of a logistic function:

[tex]P(t)=\dfrac{Kpe^{rt}}{K+p(e^{rt}-1}[/tex]

This function is symmetrical about its point of inflection, when half the population is infected. That is, up to that point, it is concave upward, increasing at an increasing rate. After that point, it is concave downward, decreasing at a decreasing rate.

a) The growth rate starts to decline at the point of inflection, when half the population is infected. That time is about 42.6 days after the start of the infection. 5000 people will be infected at that point

b) The infected and uninfected populations will be equal about 42.6 days after the start of the infection.

f(x) = 3x^2 - 5x +2

Let me show you the picture below and the answer is (0 , 2)

Answer:

(0,2)

Step-by-step explanation:

the y-intercept of the function, f(x) = 3x² -5x + 2 when : x = 0

f(0) = 3(0)² - 5(0)+2 = 2

Answer:

Step-by-step explanation:

Anwer -1

Answer:

-1

Step-by-step explanation:

You could solve for x... or just plug those values in to see which would make the inequality true

Let's check x=3

-3(3-4)>6(3-1)

-3(-1)>6(2)

3>12  this is false  so not x cannot be 3

Let's check x=-1

-3(-1-4)>6(-1-1)

-3(-5)>6(-2)

15>-12 this is true so x can take on the value -1

Let's check x=7

-3(7-4)>6(7-1)

-3(3)>6(6)

-9>36 is false so x cannot be 7

Let's check x=2

-3(2-4)>6(2-1)

-3(-2)>6(1)

6>6 is false so x cannot be 2

For this case we have the following expression:

[tex](\frac {-27x ^ 0 * y ^ {- 2}} {54x ^ {- 5} * y ^ {- 4}}) ^ {- 2} =[/tex]

By definition we have to:

[tex]a^0 = 1[/tex]

So:

[tex](\frac {-27y ^ {- 2}} {54x ^ {- 5} * y ^ {- 4}}) ^ {- 2} =[/tex]

Simplifying:

[tex](\frac {-y ^ {- 2}} {2x ^ {- 5} * y ^ {- 4}}) ^ {- 2} =[/tex]

By definition of power properties we have to:

[tex](a ^ n) ^ m = a ^ {n * m}[/tex]

So, rewriting the expression we have:

[tex](-1)^{-2}\frac{-y^{-2*-2}}{2^{-2}*x^{-5*-2}*y^{-4*-2}}=\\\frac{1}{(-1)^2}*\frac{-y^{4}}{2^{-2}x^{10}*y^{8}}=[/tex]

SImplifying:

[tex]+1*\frac{y^{4-8}}{2^{-2}x^{10}}=\\\frac{y^{-4}}{2^{-2}x^{10}}=\\\frac{2^2}{x^{10}y^{4}}[/tex]

Answer:

[tex]\frac{4}{x^{10}y^{4}}[/tex]

Answer: 0.9887

Step-by-step explanation:

Given : The true probability of a baby being a boy : [tex]0.527[/tex]

The number of selected births : [tex]7[/tex]

Now, the when next seven randomly selected births in the​ country, then the probability that at least one of them is a girl​ is given by :_

[tex]\text{P(at least one girl)=1-P(none of them girl)}\\\\=1-(0.527)^7=0.988710510435\approx0.9887[/tex]

Hence, the probability that at least one of them is a girl​ =0.9887

Final answer:

The probability of at least one girl being born among seven births in a country where a boy has a 0.527 chance of being born is calculated by subtracting the probability of all seven being boys from 1.

Explanation:

The question asks about the probability of at least one girl being born among the next seven randomly selected births in a country where the true probability of a baby being a boy is 0.527. To find this, we can use the complement rule, which focuses on the probability that all seven births will be boys, the opposite of what we want to find.

First, we find the probability of all seven being boys:

P(all boys) = (0.527)⁷

Next, we subtract this from 1 to get the probability of at least one girl:

P(at least one girl) = 1 - P(all boys)

This gives us the probability that at least one of the next seven births will be a girl.

The probability that a randomly selected dropout aged 16 to 17 is white, given the provided statistics, is 67.39%.

The student is asking a question related to conditional probability in the field of Mathematics. The question prompts us to find out the probability that a randomly selected high school dropout in the age range of 16 to 17 is white. To find the answer, we use the following formula:

P(A|B) = P(A ∩ B) / P(B)

Where:
P(A|B) is the probability of event A happening given that event B has occurred.
P(A ∩ B) is the probability of both event A and event B happening together.
P(B) is the probability of event B happening.

From the problem statement, we know that P(B), the percentage of dropouts who are 16-17 years old, is 9.2%. Also, P(A ∩ B), the percent of dropouts who are both white and 16-17 years old, is given as 6.2%. We are supposed to find P(A|B), the probability that a dropout is white given that they are 16-17 years old.

Therefore, by substituting these values into the formula, we get:

P(A|B) = 6.2% / 9.2% = 67.39%

Rounded to two decimal places, the answer is 67.39%. So, there is approximately a 67.39% chance that a random high school dropout aged 16-17 is white.

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Answer:

  use a suitable calculator

Step-by-step explanation:

For finding values related to a normal probability distribution function, it is convenient to use a suitable calculator or spreadsheet. (See below)

___

If all you have is a z-table, you must calculate the corresponding z-value and look it up in the table.

  z = (X -µ)/σ = (56 -54)/8 = 1/4

You are interested in the area above z=1/4. The table in the second attachment gives the area between z=0 and z=1/4. So, the area of interest is the table value subtracted from 0.5 (the total area above z=0.):

  0.5000 -0.0987 = 0.4013

Answer:

the number to be expected is 1,000

Step-by-step explanation:

you multiply 100,000 by 1% which give you 1,000

Answer:   1000

Step-by-step explanation:

Given : The proportion of the defective widgets manufactured by XYZ corp= 1%

= 0.01   [we divide a percent by 100 to convert it into decimal to perform further calculations]

If the total number of widgets manufactured by XYZ = 100000

Then, the number of defective widgets is expected to be

(proportion of defective widgets) x (number of widgets manufactured by XYZ)

= 0.01 x 100000

= 1000

Hence, the number of defective widgets is expected to be 1000 .