How many students rank themselves as introverts? Demonstrate your work!!

Answer:

[tex]\displaystyle f(x)=\frac{3}{2}x^3-\frac{27}{2}x^2+36x-21[/tex]

Where:

[tex]\displaystyle a=\frac{3}{2}, \, b=-\frac{27}{2}, \, c=36, \text{and } d=-21[/tex]

Step-by-step explanation:

We are given a cubic function:

[tex]f(x)=ax^3+bx^2+cx+d[/tex]

And we want to find a, b, c and d such that the  function has a relative maximum at (2, 9); a relative mininum at (4, 3); and an inflection point at (3, 6).

Since the function has a relative maximum at (2, 9), this means that:

[tex]f(2)=9=a(2)^3+b(2)^2+c(2)+d[/tex]

Simplify:

[tex]8a+4b+2c+d=9[/tex]

Likewise, since it has a relative minimum at (4, 3):

[tex]f(4)=3=a(4)^3+b(4)^2+c(4)+d[/tex]

Simplify:

[tex]64a+16b+4c+d=3[/tex]

We can subtract the first equation from the second. So:

[tex](64a+16b+4c+d)-(8a+4b+2c+d)=(3)-(9)[/tex]

Simplify:

[tex]56a+12b+2c=-6[/tex]

Divide both sides by two. Hence:

[tex]28a+6b+c=-3[/tex]

Relative minima occurs only at the critical points of a function. That is, it occurs whenever the first derivative equals zero.

Find the first derivative. We can treat a, b, c and d as constant. Hence:

[tex]f'(x)=3ax^2+2bx+c[/tex]

Since it has a minima at (2, 9), it means that:

[tex]f'(2)=3a(2)^2+2b(2)+c=0[/tex]

Thus:

[tex]12a+4b+c=0[/tex]

(We will only need one of the two points to complete the problem.)

Inflection points occurs whenever the second derivative of a function equals zero. Find the second derivative:

[tex]f''(x)=6ax+2b[/tex]

Since there is a inflection point at (3, 6):

[tex]18a+2b=0\Rightarrow 9a+b=0[/tex]

Solve for b:

[tex]b=-9a[/tex]

Substitute this into the above equation:

[tex]12a+4(-9a)+c=0[/tex]

Solve for c:

[tex]c=24a[/tex]

Substitute b and c into the previously acquired equation:

[tex]28a+6(-9a)+(24a)=-3[/tex]

Solve for a:

[tex]\displaystyle -2a=-3\Rightarrow a=\frac{3}{2}[/tex]

Solve for b and c:

[tex]\displaystyle b=-9\left(\frac{3}{2}\right)=-\frac{27}{2}\text{ and } c=24\left(\frac{3}{2}\right)=36[/tex]

Using either the very first or second equation, solve for d:

[tex]\displaystyle 8\left(\frac{3}{2}\right)+4\left(-\frac{27}{2}\right)+2(36)+d=9[/tex]

Hence:

[tex]d=-21[/tex]

Hence, our function is:

[tex]\displaystyle f(x)=\frac{3}{2}x^3-\frac{27}{2}x^2+36x-21[/tex]

Answer:

Third one.

BO is not 7.8 cm

Step-by-step explanation:

Answer:

1.55

2.66

1.631

Step-by-step explanation:

Given :

x: 0 1 2 3 4 5

P(x): .27 .28 .20 .15 .08 .02

The expected mean, E(X) = Σ(x*p(x))

E(X) = (0*0.27)+(1*0.28)+(2*0.20)+(3*0.15)+(4*0.08)+(5*0.02)

E(X) = 1.55

The expected variance :

Σx²*p(x) - E(X)

(0^2*0.27)+(1^2*0.28)+(2^2*0.20)+(3^2*0.15)+(4^2*0.08)+(5^2*0.02) - 1.55

4.21 - 1.55 = 2.66

The standard deviation :

√variance = √2.66 = 1.631

Answer:

Step-by-step explanation:

The percentage of the number 80 is 40 will be 50%.

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates for one hundred percent. It is symbolized by the character '%'.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

The percentage is given as,

P = [(80 - 40) / 80] x 100

P = (40 / 80) x 100

P = 0.50 x 100

P = 50%

The percentage of the number 80 is 40 will be 50%.

More about the percentage link is given below.

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Answer:

32

Step-by-step explanation:

18 : 6 = 3

therefore, x : 3 has to equal 3.

X : 3 = 3

X = 3 × 3

X = 9

To verify:

18 : 6 = 9 : 3

3 = 3

It's true that X = 9, so now just replace the X with 9 in the next equation

5 + 3(9) = 32

Answer:

32

Step-by-step explanation:

18 :  6 = x : 3

Product of means  =  Product of extremes

6 * x = 3*18

     x = [tex]\frac{3*18}{6}[/tex]

     x = 3*3

x = 9

Now plugin x = 9 in the expression

5 + 3x = 5 + 3*9

          = 5 + 27

          = 32

[tex]_____________________________________[/tex]

[tex]\sf\huge\underline\red{SOLUTION:}[/tex]

Use formula:

[tex]\sf{V = \pi(\frac{d}{2})^2h}[/tex]

Solving for diameter:

[tex]\sf d = 2 \times \sqrt{ \frac{V}{\pi h} } \\ \sf = 2 \times \sqrt{ \frac{40}{\pi \times 1800} } \approx0.16821 \\ = \sf \large\boxed{\sf{\green{d = 0.17}}}[/tex]

[tex]\sf\huge\underline\red{FINAL \: ANSWER}[/tex]

[tex]\large\boxed{\sf{\green{d=0.17}}}[/tex]

[tex]_____________________________________[/tex]

✍︎ꕥᴍᴀᴛʜᴅᴇᴍᴏɴǫᴜᴇᴇɴꕥ

✍︎ᴄᴀʀʀʏᴏɴʟᴇᴀʀɴɪɴɢ

Answer:

D, E, and F

Step-by-step explanation:

✔️Statement D is true:

Rationale: m<4 is more than 90°, while m<2 is less than 90°. Therefore m<4 is greater than m<2

✔️Statement E is true:

Rationale: m<4 is more than 90°, while m<1 is less than 90°. Therefore m<4 is greater than m<1

✔️Statement F is true:

Rationale:

m<4 is an external angle of the triangle.

m<1 and m<2 are interior angles that are opposite to m<4. Therefore, based on the external angle theorem of a triangle,

m<4 = m<1 + m<2

Answer:

12

Step-by-step explanation:

Answer:13

Step-by-step explanation:11

Answer:

Inconsistent system

Step-by-step explanation:

Given

The attached graph

Required

The type of system

When two lines are parallel, it means they have the same slope and as such, the system has no solution.

Equations with the same slope are:

[tex]y = 2x + 6[/tex]

[tex]y = 2x- 8[/tex]

Both have a slope of 2

Such system are referred to inconsistent system.

Hence, (c) is correct.

Answer:

[tex] \frac{1}{12} [/tex]

Step-by-step explanation:

[tex] \frac{2}{9} \div \frac{8}{3} \\ = \: \frac{1}{12}[/tex]

So, if you divide 2/9 by 1/12, you'll get 8/3

Answered by GAUTHMATH

Answer:

So, the initial number of apples is 7.

Step-by-step explanation:

The number of apples of An, Binh, and Chi are the same. An gave away 17 apples, Chi gave away 19 apples, so now Chi's apples are 5 times higher than the total remaining apples of An and Binh. How many apples did each of you have at first? (Solve the above problem by equation or system of equations)

Let the initial numbers of apples is a.

An gave 17 apples

Chi gave 19 apples

So,

x - 19 = 5 (x - 17 + x)

x - 19 = 5 (2x - 17)

x - 19 = 10 x - 85

9 x = 66

x = 7

Step-by-step explanation:

The horizontal stretch or compression for a function f(x) is given by  g = f(bx) where b is a constant. If b> 0 then the graph of a function is compressed.

As it is given in the question that the function is transformed by a compression factor of 3.

Given function

The value of k will be 3 if the function is transformed by a compression factor of 3

Answer:

36

Step-by-step explanation:

(6^2)^4

(6)^2+4

6^6

36

simplify the expression : (6²)⁴= (36)⁴= 1679616

Or

[tex]{6}^{2 \times 8} = 1679616[/tex]

Answer:

P(X < 995) = 0.4761

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

CNBC recently reported that the mean annual cost of auto insurance is 1013 dollars. Assume the standard deviation is 284 dollars.

This means that [tex]\mu = 1013, \sigma = 284[/tex]

Find the probability that a single randomly selected value is less than 995 dollars.

This is the p-value of Z when X = 995. So

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

[tex]Z = \frac{995 - 1013}{284}[/tex]

[tex]Z = -0.06[/tex]

[tex]Z = -0.06[/tex] has a p-value of 0.4761. So

P(X < 995) = 0.4761

Answer:

x2 - 4x - 5 factored form is (x - 5)(x + 1)

Answer:

(x − 5)(x + 1)

Step-by-step explanation:

The answer above is correct.

1km = 0.621371miles

195 km= ?

cross multiplication

= 121.167 miles

25 miles= 1hour

121.167miles = ?hours

121.167=25x

divide by 25x both sides

=4.84 hours

approx 5hours

She must ride for 5 hours if she wants to bike 195 km.

Average speed is defined as the ratio of the total distance traveled by a body to the total time taken for the body to reach its destination.

Given that cyclist rides at an average speed of 25 miles per hour.

Since 1 km = 0.621371 miles

So 195 km = 121.167 miles

The speed of the cyclist (s)  = 24 miles per hour.

Distance covered by the rider = 195 km

Distance covered by the rider (d) = 121.167 miles

By using the formula,  time taken by a body, we calculate the time,

⇒ t = d/s

Substitute the value of d and s in above the equation

⇒ t = 121.167/ 24

Apply the division operation,

⇒ t = 5

Hence, she must ride for 5 hours if she wants to bike 195 km.

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Answer:

y = x + 6

Step-by-step explanation:

rise = 1

run = 1

slope = rise/run = 1

y-intercept = 6

y = mx + b

y = x + 6

Answer:

(A - B) - C = { 1 , 4 , 6 , 7 }

Step-by-step explanation:

A = { 1 , 2 , 3 , 4 , 5 }

B = { 4 , 5 , 6 , 7 }

A - B = { 1 , 2, 3 ,6 , 7 }

C = { 2 , 3 , 4 }

(A - B) - C = { 1 , 4 , 6 , 7 }

Answer:

main age = total age/total people

if Main age is = 27

[tex]27 = \frac{ \times }{5} [/tex]

and x = 135

Total age is = 135

then main age is 35

[tex][35 = \frac{y}{6} [/tex]

and y = 210

first main age - second main age = age of the person participating

210 - 135 = 75

HAVE A NİCE DAY

Step-by-step explanation:

GREETINGS FROM TURKEY

Answer:

A. false B. true C. false D. true

Whope you all like this answer

Answer:

Anything to the power of zero (with the exception of zero itself) is equal to one.

So 3⁰ = 1

Answer:

P(X < 3) = 0.14254

Step-by-step explanation:

We have only the mean, which means that the Poisson distribution is used to solve this question.

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^{-\mu}*\mu^{x}}{(x)!}[/tex]

In which

x is the number of sucesses

e = 2.71828 is the Euler number

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

On weekend nights, a large urban hospital has an average of 4.8 emergency arrivals per hour.

This means that [tex]\mu = 4.8[/tex]

What is the probability P(X < 3)?

[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]

So

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

[tex]P(X = 0) = \frac{e^{-4.8}*4.8^{0}}{(0)!} = 0.00823[/tex]

[tex]P(X = 1) = \frac{e^{-4.8}*4.8^{1}}{(1)!} = 0.03950[/tex]

[tex]P(X = 2) = \frac{e^{-4.8}*4.8^{2}}{(2)!} = 0.09481[/tex]

So

[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.00823 + 0.03950 + 0.09481 = 0.14254[/tex]

P(X < 3) = 0.14254

9514 1404 393

Answer:

  assumed accuracy from overly precise numbers

Step-by-step explanation:

Except when counting large sums of money or considering definitions, most real-world numbers are not accurate beyond about 6 significant figures. When considering survey or sample results, the accuracy can be considerably less than that, often not even good to 3 significant figures. (Margin of error is usually some number of percentage points greater than 1.)

Expressing the given ratios to 10 significant figures substantially misstates their accuracy. (10^-9 television is less than 1 day's accumulated dust).

Answer:

80 panels

Step-by-step explanation

Answer:

you need a photo my dude

Step-by-step explanation:

Answer:

AC = (20+ 10q)

Step-by-step explanation:

Given that,

Total cost, TC = 20q + 10q²

We need to find AC i.e. average cost.

It can be solved as follows :

[tex]AC=\dfrac{TC}{q}\\\\AC=\dfrac{20q + 10q^2}{q}\\\\AC=\dfrac{q(20+ 10q)}{q}\\\\AC={(20+ 10q)}[/tex]

So, the value of AC is (20+ 10q).

Answer:

The interval is [98,132]

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Normal with mean 115 and standard deviation 25.

This means that [tex]\mu = 115, \sigma = 25[/tex]

Determine the interval of values that is centered at the mean and for which 50% of the students have IQ's in that interval.

Between the 50 - (50/2) = 25th percentile and the 50 + (50/2) = 75th percentile.

25th percentile:

X when Z has a p-value of 0.25, so X when Z = -0.675.

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

[tex]-0.675 = \frac{X - 115}{25}[/tex]

[tex]X - 115 = -0.675*25[/tex]

[tex]X = 98[/tex]

75th percentile:

X when Z has a p-value of 0.75, so X when Z = 0.675.

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

[tex]0.675 = \frac{X - 115}{25}[/tex]

[tex]X - 115 = 0.675*25[/tex]

[tex]X = 132[/tex]

The interval is [98,132]

Answer: a continuous random​ variable

Step-by-step explanation:

Can you count the distance it traveled? You can't, so it couldn't be discrete because you can count discrete variables.

Can you measure the distance it traveled? You sure can, that makes it a continuous random variable.

Do you know the exact distance it's going to travel? You won't, therefore it's a random variable since you don't know the value beforehand.