what is the mean of -2, -6, -7, -3

To estimate the volume using the Midpoint Rule with \(\displaystyle n=5\), we need to divide the interval \(\displaystyle 0\leq x\leq 1\) into \(\displaystyle n\) subintervals of equal width. Since \(\displaystyle n=5\), each subinterval will have a width of \(\displaystyle \Delta x=\frac{1-0}{5}=\frac{1}{5}\).

Now, let's calculate the volume using the Midpoint Rule. The formula for the volume obtained by rotating about the y-axis is:

\(\displaystyle V\approx 2\pi \sum _{i=1}^{n}y_{i}\Delta x\)

where \(\displaystyle y_{i}\) represents the value of the function \(\displaystyle y=\sqrt{1+x^{3}}\) evaluated at the midpoint of each subinterval.

First, let's find the midpoints of the subintervals. Since the width of each subinterval is \(\displaystyle \Delta x=\frac{1}{5}\), the midpoint of the \(\displaystyle i\)-th subinterval is given by:

\(\displaystyle x_{i}=\frac{\Delta x}{2}+\left( i-\frac{1}{2}\right) \Delta x=\frac{1}{10}+\left( i-\frac{1}{2}\right) \frac{1}{5}\)

Substituting \(\displaystyle x_{i}\) into the function \(\displaystyle y=\sqrt{1+x^{3}}\), we obtain:

\(\displaystyle y_{i}=\sqrt{1+\left( \frac{1}{10}+\left( i-\frac{1}{2}\right) \frac{1}{5}\right) ^{3}}\)

Now, we can calculate the approximate volume using the Midpoint Rule:

\(\displaystyle V\approx 2\pi \sum _{i=1}^{5}y_{i}\Delta x\)

Substituting the values of \(\displaystyle y_{i}\) and \(\displaystyle \Delta x\) into the formula, we can evaluate the sum and compute the estimated volume.

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

Answer:

3,2,6

Step-by-step explanation:

if you divide 10,398 by all numbers 3,2 and 6 have whole numbers:)

Answer: The answer is false!

Step-by-step explanation: You may think its true but NO, its not true!

Answer: false

Step-by-step explanation:

the correct answer is a dialect of spanish, chilean spanish.

Answer:

1/2p - 1/4p - 4.

Step-by-step explanation:

1/2p - (1/4p + 4)

= 12p - 1/4p - 4

≠ 1/2p + 1/2p - 4

Instead of writing -1/4p, Tim wrote 1/2p

Answer:

75 hairs/ day =  525 hairs / week

Step-by-step explanation:

so your base question for this is 75 hairs/ day =? h/ week. how? if the dog is losing 75 hairs per day, then you would do 75 x 7 becuase there are 7 days in a week. the answer to that would give you how many hairs the dog was losing per week. (see attached image for reference)

Hope this helps!

#MRS

Answer:

The answer is 30

Step-by-step explanation:

Answer:

6 and 18

6+6=12

18+6=24

12x2=24

Unless a number is given it is mainly trial and error so guessing numbers that fit the first part of Ax3=B

Step-by-step explanation:

Answer:

(b) t/5=17, so t is about 85 seconds

Step-by-step explanation:

The question is saying , the distance of the strike(17) is the number of seconds(t) divided by 5

Answer: -3x+8

Step-by-step explanation:

Answer:

Collect like terms

(−2x−x)+8

Simplify

and then the answer will be

−3x+8

Hope this helps

love

Step-by-step explanation:

To design a spinner with the given probabilities, we can use the following sectors:

A sector covering 60 degrees for the number 1, with probability 1/6.

A sector covering 120 degrees for the number 3, with probability 1/3.

A sector covering 180 degrees for the number 7, with probability 1/2.

A sector covering 180 degrees for the odd numbers (1 and 3), with probability 1.

To create the spinner, draw a circle and divide it into four equal sectors. Color one sector red for the number 1, color two adjacent sectors green for the number 3, color one remaining sector blue for the number 7. Finally, color half of the blue sector green to represent the odd numbers.

The resulting spinner will have the desired probabilities: P(1) = 1/6, P(3) = 1/3, P(7) = 1/2, P(odd number) = 1.

Answer:

(a)

(b)

Step-by-step explanation:

First pic is a second is b

The expectation to play the game is $2.5 and the fair price to play is $7.5.

The expectation is defined as the weighted average value of the random variable which is the product of the value of the random variable and its possibility.

Expectation= ∑P(win)*amount of win or loss of random variable

=∑x*P(x)

Here given that there are only two possible outcomes $5 and $10. And the possibility of every outcome is the same which is 0.5 as they occupy the same area.

As we know

Expectation= ∑P(win)*amount of win or loss of random variable

= 0.5(5-5) +0.5(10-5)

=0.5*0 + 0.5*5

=0+2.5

=$2.5

As fair price= expectation + cost of play

⇒fair price= $2.5 + $5

⇒fair price= $7.5

Therefore the expectation to play the game is $2.5 and the fair price to play is $7.5.

Learn more about expectation

here: https://brainly.com/question/10675141

#SPJ2

ANSWER:-

Yes,

There is a direct proportional relationship

between the cost of items before tax and the

cost of items after tax.

5.0

STEP-BY-STEP EXPLANATION:-

Given - A city has a 5% sales tax.

To find - Is there a proportional relationship

between the cost of items

before tax and the cost of items after

tax?

PROOF:-

Yes, the cost of items before tax is directly

proportional to the cost of items after tax.

REASON:-

With the increase in the sales tax, there is

increase in the cost of items after tax, therefore,

there is a direct relation between the cost of items

before tax and cost of items after tax

Answer:

D

Step-by-step explanation:

A. 2(2) - (-2)= 4+2=6

B. 2(2) - (-1) = 4+1=5

C. 2(7) - (4) = 14 - 4= 10

   2(7) - 2(4) = 14 - 8 = 6 doesn't = 4

D. 2(8) - (6) = 16 - 6= 10

   2(8) - 2(6) = 16 - 12 = 4 = 4

1. 4/1

2. 1/2

3. 2/5

4. 1/1

Answer:

x = -2 , x = -1/2 , x = 1

Step-by-step explanation:

Answer:

x=-2 , x=-1/2, x=1

Step-by-step explanation:

Not going to lie to you, I grabbed my phone and took a photo on a math app on my phone to solve this. It gave me three different answers. I hope this is what you were looking for.

Answer:

a) 3400g

b) 5000ml

c) 6.20m

d) 400cm

e) 70ml

f) 3.8km

Step-by-step explanation:

a) There are 1000g (gram) in every 1kg (kilogram)

b) There are 1000ml (millilitre) in every 1l (litre)

c) There are 100cm (centimetre) in every 1m (metre)

d) There are 10ml (millilitre) in every 1cl (centilitre)

e) There are 1000m (metre) in every 1km (kilometre)

Answer:

B

Step-by-step explanation:

Answer:

8.88

Step-by-step explanation:

...

2 ⇒ 1

3 ⇒ 3

4 ⇒ 2

5 ⇒ 1

6 ⇒ 3

7 ⇒ 5

8 ⇒ 2

9 ⇒ 4

10 ⇒ 0

11 ⇒ 2

12 ⇒ 2

Hope my answer helps you✌️

Mark BRAINLIEST

Answer:

21 \(\frac{1}{3}\)

Step-by-step explanation:

Don't really know how to explain this over a computer, other than use a calculator.

Hope that this helps!

Answer:

To find the first four terms of the series, we can substitute the values of n from 1 to 4 in the given formula and simplify:

n=1: -4(2/3)^0 = -4(1) = -4

n=2: -4(2/3)^1 = -4(2/3) = -8/3

n=3: -4(2/3)^2 = -4(4/9) = -16/9

n=4: -4(2/3)^3 = -4(8/27) = -32/27

So the first four terms of the series are -4, -8/3, -16/9, -32/27.

To determine if the series converges or diverges, we need to find the common ratio r, which is the ratio of any term to its preceding term:

r = (-4(2/3)^n) / (-4(2/3)^(n-1)) = 2/3

Since the absolute value of the common ratio is less than 1, the series converges.

To find the sum of the series, we can use the formula for the sum of an infinite geometric series:

S = a / (1 - r)

where a is the first term and r is the common ratio. Substituting the values we found:

S = -4 / (1 - 2/3) = -4 / (1/3) = -12

So the sum of the infinite geometric series is -12.

Answer:

a)  The first four terms of the series are:

    -4, -8/3, -16/9, -32/27

b)  The series converges.

c)  The sum of the infinite geometric series is -12.

Step-by-step explanation:

Given infinite geometric series:

\(\displaystyle \sum^{\infty}_{n=1} -4 \left(\dfrac{2}{3}\right)^{n-1}\)

Therefore, the formula for the nth term of the sequence is:

\(a_n=-4 \left(\dfrac{2}{3}\right)^{n-1}\)

where:

Calculate the first four terms of the series by substituting the n-values 1 through 4 into the nth term formula.

\(a_1 = -4 \left(\dfrac{2}{3}\right)^{1-1} = -4 \left(\dfrac{2}{3}\right)^{0}=-4\)

\(a_2 = -4 \left(\dfrac{2}{3}\right)^{2-1}= -4 \left(\dfrac{2}{3}\right)^{1}=-\dfrac{8}{3}\)

\(a_3 = -4 \left(\dfrac{2}{3}\right)^{3-1}= -4 \left(\dfrac{2}{3}\right)^{2}=-4 \left(\dfrac{4}{9}\right)=-\dfrac{16}{9}\)

\(a_4 = -4 \left(\dfrac{2}{3}\right)^{4-1}= -4 \left(\dfrac{2}{3}\right)^{3}= -4 \left(\dfrac{8}{27}\right)=-\dfrac{32}{27}\)

A geometric series converges if the absolute value of its common ratio is less than 1. As r = 2/3 and |2/3| < 1, the series converges.

Use the infinite geometric series sum formula to find sum of the infinite series.

\(\boxed{\begin{minipage}{5.5 cm}\underline{Sum of an infinite geometric series}\\\\$S_{\infty}=\dfrac{a}{1-r}$,\;\;for\;$|r| < 1$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\ \phantom{ww}$\bullet$ $r$ is the common ratio.\\\end{minipage}}\)

Substitute a = -4 and r = 2/3 into the formula to find the sum of the infinite series:

\(\begin{aligned}\implies S_{\infty}&=\dfrac{-4}{1-\frac{2}{3}}\\\\ &=\dfrac{-4}{\frac{1}{3}}\\\\&=-4 \cdot \dfrac{3}{1}\\\\&=-\dfrac{12}{1}\\\\&=-12\end{aligned}\)

Therefore, the sum of the given infinite geometric series is -12.

Answer:

Step-by-step explanation:

Answer:

The school is 3 km west of Robert's house.

Hope this helps.

Answer:

192 hours per day / 8 hours per person per day = 24 people

Step-by-step explanation:

Assuming each person works for 8 hours a day, the total number of hours needed to complete the project is:

720 person-days x 8 hours = 5,760 hours

To complete the project in 30 days, the total number of hours needed per day is:

5,760 hours / 30 days = 192 hours per day

Answer:

The final atmospheric pressure is 5.19 · 10⁴ Pa

Step-by-step explanation:

Assuming that the temperature of the air does not change, we can use Boyle's law, which states that for a gas kept at constant temperature, the pressure of the gas is inversely proportional to its volume. In formula,

pV = const.

where p is the gas pressure and V is the volume

The equation can also be rewritten as

p₁ V₁ = p₂ V₂

where in our problem we have:

p₁ = 1.03 · 10₅ Pa is the initial pressure (the atmospheric pressure at sea level)

V₁ = 90.0L is the initial volume

p₂ is the final pressure

V₂ = 175.0L is the final volume

Solving the equation for p2, we find the final pressure:

p₂ = p₁ v₁ divided by V₂ = (1.01 · 10⁵)(90.0) divided by 175.0 = 5.19 · 10⁴ Pa