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Calculate the average rate of change of the function f(x) = 3x2 over the interval 1 ≤ x ≤ 5.

rewona [7]

Average rate of change is delta y / delta x

(f(5)-f(1))/(5-1)

(75-3)/4

72/4

18

8 0

2 years ago

The table below shows the number of cups of coffee people drink a day

Effectus [21]

The mean of a distribution is the sum of the data elements divided by the count of the dataset.

The mean of the distribution is 4

The complete table is given as

$\left[\begin{array}{cc}People & Frequency &0 - 2 & 5 & 3 - 5 & 25 & 6 - 8 & 5\end{array}\right]$

The complete question requires that, we calculate the mean of the dataset

First, we calculate the class midpoint

This is the average of the class interval

For interval 0 - 2,

$x_1 = \frac{0 + 2}{2} = 1$

For interval 3 - 5,

$x_2 = \frac{3 + 5}{2} = 4$

For interval 6 - 8

$x_3 = \frac{6 + 8}{2} = 7$

So, the table becomes

$\left[\begin{array}{ccc}People & x & Frequency &0 - 2 &1 & 5 & 3 - 5 & 4& 25 & 6 - 8& 7 & 5\end{array}\right]$

The mean is then calculated as:

$\bar x = \frac{\sum fx}{\sum f }$

This gives

$\bar x = \frac{5 \times 1 + 25 \times 4 + 5 \times 7}{5 + 25 + 5}$

$\bar x = \frac{140}{35}$

$\bar x = 4$

Hence, the mean of the distribution is 4

Read more about mean at:

brainly.com/question/17060266

4 0

2 years ago

Read 2 more answers

The Intelligence Quotient (IQ) test scores for adults are normally distributed with a population mean of 100 and a population st

saveliy_v [14]

Answer:

The probability is 0.6796

Step-by-step explanation:

Given

Population Mean - 100

Population Standard Deviation - 25

As we know

z = x-μ/σ, where:

z is the standard score

x is the raw score

μ is the population mean

σ is the population standard deviation

Z value for mean of sample = 95

z1 = -100+95/25 = -5/25 = -0.2

P value for Z = -0.2 is 0.2912

Z2 = 100-105/25 = 0.2

P(z > 0.2 = 1 - P(z ≤ 0.2) = 1 - 0.0294 = 0.9706

P(-0.2 < z < 0.2) = 0.9706 - 0.2912= 0.6796

The probability is 0.6796

5 0

2 years ago

Write in form y=mx+b I will give brainiest to correct answer

Viktor [21]

Step-by-step explanation:

y=mx+b (m is the slope, b is the y-intercept)

To come with sope choose two points from the graph (6,20), (4,30)

Then

m=(Y2-Y1)/(X2-X1) =(4-6)/(30-20)=-1/5

b= 50 (y-intercept)

SO y=-1/5x-50

I hope this helps

5 0

2 years ago

Read 2 more answers

What is a simple way to solve for the sum and difference of 2 cubes? For example, 27+64<img src="https://tex.z-dn.net/?f=x%5E3"

salantis [7]

Answer:

(3 + 4x)(9 - 12x + 16x²) = 0

(4m - 1)(16m² + 4m + 1) = 0

Step-by-step explanation:

Here we have to solve the sum of two cubes which is $27 + 64x^{3}$

Now, the equation is $27 + 64x^{3} = 0$

⇒ 3³ + (4x)³ = 0

⇒ (3 + 4x)[3² - 3(4x) + (4x)²] = 0

⇒ (3 + 4x)(9 - 12x + 16x²) = 0

So, (3 + 4x) = 0 or (9 - 12x + 16x²) = 0

Therefore, from the above two relation we can solve for x.

One root will be $- \frac{3}{4}$ and the others we will get by applying Sridhar Acharya Formula, which will give a pair of conjugate imaginary roots of the equation.

Again, we have to solve the difference of two cubes which is $64m^{3} - 1$

Now, the equation is $64m^{3} - 1 = 0$

⇒ (4m)³ - 1³ = 0

⇒ (4m - 1)[(4m)² + 4m(1) + 1²] = 0

⇒ (4m - 1)(16m² + 4m + 1) = 0

So, (4m - 1) = 0 or (16m² + 4m + 1) = 0

Therefore, from the above two relation we can solve for m.

One root will be $\frac{1}{4}$ and the others we will get by applying Sridhar Acharya Formula, which will give a pair of conjugate imaginary roots of the equation. (Answer)

8 0

3 years ago