Find the surface area of the rectangle prism. 3cm 9cm and 6cm

Answer:

See explanation

Step-by-step explanation:

Prove that

[tex]1^2+2^2+3^3+...+n^2=\dfrac{1}{6}n(n+1)(2n+1)[/tex]

1. When [tex]n=1,[/tex] we have

2. Assume that for all [tex]k[/tex] following equality is true

[tex]1^2+2^2+3^3+...+k^2=\dfrac{1}{6}k(k+1)(2k+1)[/tex]

3. Prove that for [tex]k+1[/tex] the following equality is true too.

[tex]1^2+2^2+3^3+...+(k+1)^2=\dfrac{1}{6}(k+1)((k+1)+1)(2(k+1)+1)[/tex]

Consider left part:

[tex]1^2+2^2+3^2+...+(k+1)^2=\\ \\=(1^2+2^2+3^3+...+k^2)+(k+1)^2=\\ \\=\dfrac{1}{6}k(k+1)(2k+1)+(k+1)^2=\\ \\=(k+1)\left(\dfrac{1}{6}k(2k+1)+k+1\right)=\\ \\=(k+1)\dfrac{2k^2+k+6k+6}{6}=\\ \\=(k+1)\dfrac{2k^2+7k+6}{6}=\\ \\=(k+1)\dfrac{2k^2+4k+3k+6}{6}=\\ \\=(k+1)\dfrac{2k(k+2)+3(k+2)}{6}=\\ \\=(k+1)\dfrac{(k+2)(2k+3)}{6}[/tex]

Consider right part:

[tex]\dfrac{1}{6}(k+1)((k+1)+1)(2(k+1)+1)=\\ \\\dfrac{1}{6}(k+1)(k+2)(2k+3)[/tex]

We get the same left and right parts, so the equality is true for [tex]k+1.[/tex]

By mathematical induction, this equality is true for all n.

Answer:

0.275

Step-by-step explanation:

We want to write 11 out of 40 batters as a decimal.

We can write 11 out of 40 as a fraction to get:

[tex] \frac{11}{40} [/tex]

Note that:

[tex] \frac{11}{40} = \frac{1}{4} \times \frac{11}{10} [/tex]

This implies that:

[tex] \frac{11}{40} = 0.25 \times 1.1[/tex]

This gives us

[tex] \frac{11}{40 } = 0.275[/tex]

Answer: 30

Step-by-step explanation:5(Z+4) + 5(2-Z).

Open the brackets by multiplying true by the number out of the bracket.

5Z + 20 + 10 - 5Z

Now, collect like terms, we have.

5Z - 5Z + 20 + 10. Now we have

0 + 30 = 30//

Answer:

Ducks = 8

Horses = 17

Step-by-step explanation:

From the question;

We are required to determine the number of ducks and horses;

We need to know that;

A duck has two legs while a horse has four legs;

Assuming there were x ducks and y horses

Then;

x + y = 25 ................................Eqn 1

And;

2x + 4y = 84 .............................Eqn 2

Solving the two equations simultaneously we can get the number of each animal.

x + y = 25

2x + 4y = 84

Multiplying the first equation by 2, we get

2x + 2y = 50

2x + 4y = 84

Subtracting the two equations;

2x + 2y = 50

2x + 4y = 84

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

      - 2y = -34

          y = 17

Solving for x

x = 25 -17

    = 8

Therefore; there were 8 ducks and 17 horses in the field

It should take the student 1.75 minutes to complete 35 multiplication facts.

To determine how long it will take the 5th grade student to complete 35 multiplication facts at the same rate as 20 facts in 1 minute, we can set up a proportion or use unit rates. Since the student can complete 20 facts in 1 minute, we find the time per fact by dividing the total time by the number of facts:

1 minute / 20 facts = 0.05 minutes per fact

Then, we multiply the rate by the number of new facts:

0.05 minutes per fact * 35 facts = 1.75 minutes

Therefore, it should take the student 1.75 minutes to complete 35 multiplication facts.

The sum of the 5 terms in the arithmetic series is 40.

Step-by-step explanation:

Step 1;  First we need to determine the three values between a1= -14 and a5=30. The difference between the first and fifth value = 30 - (-14) = 30 + 14 = 44.

Since there are 4 values after a1 we divide the difference by the number of terms, the difference between each term = 44 / 4 = 11. So the difference between each term is 11.

Step 2; To find out the terms we just add the difference to the previous number.

a1 = -14.

a2 = -14 + 11 = -3.

a3 = -3 + 11 = 8.

a4 = 8 + 11 = 19.

a5 = 19 + 11 = 30.

So a1 + a2 + a3 + a4 + a5 = -14 -3 + 8 + 19 + 30 = 40.

The sum of the first 5 terms in this arithmetic series is 40, calculated based on the formulas for an arithmetic series involving the first term, the fifth term, and the common difference.

In an arithmetic sequence or series, the difference between each term (the common difference) is constant. We can represent this as: an = a1 + (n - 1) * d, where d is the common difference. Given in this problem that a1 = -14, a5 = 30, and n = 5.

First, we can find the common difference d using the formula: d = (a5 - a1) / (5 - 1) . So, d = (30 - (-14)) / (5 - 1) = 44 / 4 = 11.

Then, we can find the sum of the first 5 terms using the formula: Sn = n / 2 * (2a1 + (n - 1) * d). That gives us: S5 = 5 / 2 * (2(-14) + (5 - 1) * 11) = 5 / 2 * (-28 + 44) = 5 / 2 * 16 = 40.

https://brainly.com/question/31366683

#SPJ3

Answer:

The correct option is A

Therefore the quadrilateral in the option A can be inscribed in a circle.

Step-by-step explanation:

Given:

Four Quadrilateral, A ,B ,C ,D in the figure below.

For a quadrilateral to be inscribed in a circle we required opposite angles must be supplementary, that is it should add up to 180°.

So from the four given quadrilateral we have only in quadrilateral A the opposite angles are supplementary.

Quadrilateral A :

Consider the quadrilateral PQRS where

∠SPQ = 91°

∠PQR = 101°

∠QRS = 89°

∠SPQ  and ∠QRS  are opposite angles and their sum is 180°

[tex]\angle SPQ+\angle QRS = 91+89 =180[/tex]

Others in option B, C , and D opposite angles are not supplementary hence cannot inscribe in a circle.

Therefore the quadrilateral in the option A can be inscribed in a circle.

Answer:

c Mark me as the brainiest

Step-by-step explanation:

A quadrilateral that can be inscribed in a circle has vertices that lie on a single circle. A distinguishing property of such quadrilaterals is that they have opposite angles adding up to 180°. Non-rectangular parallelograms cannot be inscribed in circles, because their opposite angles are equal rather than supplementary.

Answer:

-4/3

Step-by-step explanation:

-4/3 is equal to -1 1/3 which is greater than just -1

Answer: -1 is ;larger

Answer:

1/4

Step-by-step explanation:

15 out of the 20 books are horses. 5 of those are nature. 5/20 is the fraction, but can be simplified to 1/4

Shira has 5 out of 20 books about nature on her bookshelf, which simplifies to a fraction of 1/4 of her books being about nature.

Shira has 20 books in total on her bookshelf. Out of these, she has 15 books about horses, meaning the remaining books are about nature.

To find the fraction that represents the nature books, we need to subtract the number of horse books from the total number of books.

So, the number of nature books is 20 total books - 15 horse books = 5 nature books. The fraction of books about nature would therefore be the number of nature books divided by the total number of books, which is 5/20.

This fraction can be simplified by dividing both the numerator and the denominator by 5, resulting in 1/4. Therefore, 1/4 of Shira's books are about nature.

Answer:

b. investing in various types of investments

Step-by-step explanation:

i hope this helps!

brainliest is appreciated... :}

Answer:

1. diversification is the process of allocating capital in a way that reduces the exposure to any one particular asset or risk.

A. Stock market volatility is arguably one of the most misunderstood concepts in investing.

(B i) Stocks.

(ii) Bounds

(III) mutual funds

(iv) index funds

(C). Bank Savings.

Certificates of Deposit (CDs) ...

Treasury Securities. ...

Money Market Accounts. ...

Stable Value Funds. ...

Fixed Annuities. ...

Immediate Annuities

You'll make 14 dollars.

7% of 50 is 3.5.

If you add 3.5 four times you'll get 14.

200 - 7% is 186.

200 - 14 is 186.

Answer:

$14

Step-by-step explanation:

Well, first find 7% of 50.  To do this you need to make the percent a decimal by moving the decimal that is already(7 is the whole number, if there were any fractions it would be 7.00%) there two space to the left, adding zeros as needed.  

0.07 x 50 = x

3.5 = x

Now you can multiply it by whatever you want.  In this case it would be 4 since 50 time 4 is 200.

3.5 x 4 = 14

So the amount of money that you would make would be $14.

Hope this helped you out.

Answer:

A, E

Step-by-step explanation:

I think it is obtuse and scalene, but I don't think that is the only answer. Hope that can help a little.

The triangle is an isosceles and an obtuse triangle.

A triangle with two sides of equal length is an isosceles triangle. The isosceles triangle has three acute angles, meaning that the angles are less than 90°. The sum of three angles of an isosceles triangle is always 180°.

In an isosceles triangle, the two equal sides are called legs, and the remaining side is called the base. The angle opposite the base is called the vertex angle

The three types of Isosceles Triangles are :

Isosceles acute triangle

Isosceles right triangle

Isosceles obtuse triangle

Given data ,

Let the triangle be represented as ΔABC

Now , the measure of ∠ABC = 120°

So , it is an obtuse triangle with angle > 90°

Now , the measure of sides AB = measure of BC

So , an isosceles triangle, the two equal sides are called legs, and the remaining side is called the base

Therefore , it is an Isosceles obtuse triangle

Hence , the triangle is isosceles

Answer:

58 ounces

Step-by-step explanation:

16 x 4=64 - 6=58 ounces

Final answer:

After converting the weight of the cleats from ounces to pounds, the new weight of Bill's baseball bag is determined to be 3.625 pounds by subtracting 0.375 pounds (weight of the cleats in pounds) from the original 4 pounds.

Explanation:

The subject of this question is Mathematics, specifically dealing with unit conversion and simple subtraction of weights. To determine the new weight of Bill's baseball bag after removing the cleats that weigh 6 ounces, we need to first convert the ounces to pounds, since the weight of the bag is given in pounds.

There are 16 ounces in one pound. Therefore, 6 ounces is equivalent to 6 ounces \/ 16 ounces per pound = 0.375 pounds. Starting with the original weight of the bag which is 4 pounds, subtracting the weight of the cleats in pounds will give us the new weight of the bag.

4 pounds - 0.375 pounds = 3.625 pounds. This is the weight of Bill's baseball bag after the cleats are removed.

Answer:

4.3π or 13.51 = r

Step-by-step explanation:

C=2πr To find the circumference of a circle, you must have the formula

8.6π = 2πr      Substitute the C for 8.6π

4.3π = r           Divide both sides by 2π

13.51 = r         Simplify 4.3π if needed

Answer:

Part 1) [tex]y=-4x+4[/tex]

Part 2) The graph in the attached figure

Step-by-step explanation:

Part 1)

we know that

The linear equation in slope intercept form is equal to

[tex]y=mx+b[/tex]

where

m is the slope

b is the y-intercept

we have

[tex]m=-4\\point\ (2,-4)[/tex]

substitute in the linear equation

[tex]-4=-4(2)+b[/tex]

solve for b

[tex]-4=-8+b\\b=8-4\\b=4[/tex]

substitute

[tex]y=-4x+4[/tex]

Part 2) Draw the equation

we know that

To graph a line we need two points

we have the y-intercept (0,4) and (2,-4)

Plot the points, connect them and join to draw the line

see the attached figure

Answer:

(2*246)-(2*3)-194=492-6-194=292

Step-by-step explanation:

Final answer:

To find the flooded area after 6 minutes, calculate the number of 1/5-minute intervals in 6 minutes, which is 30. Then, multiply by the area flooded in each interval. The flooded area after 6 minutes would be 1500 square feet.

Explanation:

The question is asking to calculate the area that would be flooded by a water pipe after 6 minutes, given that the pipe floods 50 square feet every 1/5 of a minute. To find the answer, we need to determine how many 1/5-minute intervals are in 6 minutes, and then multiply that number by the area flooded in each interval.

First, calculate the number of intervals: 6 minutes × (5 intervals/minute) = 30 intervals.

Next, multiply the number of intervals by the area flooded per interval: 30 intervals × 50 square feet/interval = 1500 square feet.

Therefore, after 6 minutes, the flooded area would be 1500 square feet.

Answer:

The length of the side of the triangles are;

First side = 38 ft

Second side = 19 ft

Third side =24 ft

Step-by-step explanation:

To solve the question we are going to take;

Second side is x ft

Since, the first side is 2 times the second side then;

First side of the triangle is 2x ft

Since the third side is 5 ft less than the second side, then;

The third side is (x+5) ft

But, the perimeter of the triangle is 81 ft

Perimeter of a triangle is given by the sum of sides;

Therefore;

x + 2x +(x +5) = 81 ft

4x + 5 = 81

4x = 76

    x = 19 ft

Therefore;

Second side = 19 ft

First side = 38 ft

Third side = 24 ft

Step-by-step explanation:

[tex]146 + 8 \frac{1}{5} \\ \\ = 146 + \frac{8 \times 5 + 1}{5} \\ \\ = \frac{146 \times 5 + 40 + 1}{5} \\ \\ = \frac{730 + 41}{5} \\ \\ = \frac{771}{5} \\ \\ = 154 \frac{1}{5} \\ \\ thus \\ \\ \huge \orange{ \boxed{146 + 8 \frac{1}{5} = 154 \frac{1}{5}}}[/tex]

Answer:

56.76923076...

Step-by-step explanation:

738 divided by 13 should be [tex]\frac{738}{13}[/tex] as an improper fraction.

As a mixed fraction, it is: [tex]56\frac{10}{13}[/tex]

And as a decimal it is approximately 56.769

I did this problem on a calculator after doing some written work on it.

a. It spends 2.04 hours going 55 mph.

b. It will spend 1 hour going 35 mph.

c. The trip will take 3.64 hours.

Step-by-step explanation:

Given equation is;

55x + 35y = 200

Where

x represent the time when speed is 55 mph

y represent the time when speed is 35 mph

a. If the car spends 2.5 hours going 35mph on the trip, how long does it spend going 55mph?

Putting y=2.5 in given equation

[tex]55x+35(2.5)=200\\55x+87.5=200\\55x=200-87.5\\55x=112.5\\[/tex]

Dividing both sides by 55

[tex]\frac{55x}{55}=\frac{112.5}{55}\\x=2.04\ hours[/tex]

It spends 2.04 hours going 55 mph.

b. If the car spends 3 hours going 55mph on the trip, how long does it spend going 35mph?

Putting x=3 in given equation

[tex]55(3)+35y=200\\165+35y=200\\35y=200-165\\35y=35[/tex]

Dividing both sides by 35

[tex]\frac{35y}{35}=\frac{35}{35}\\y=1[/tex]

It will spend 1 hour going 35 mph.

c. If the car spends no time going 35mph, how long would the trip take?

Putting y=0 in given equation

[tex]55x+35(0) = 200 \\55x+0=200\\55x=200[/tex]

Dividing both sides by 55

[tex]\frac{55x}{55}=\frac{200}{55}\\x=3.636[/tex]

Rounding off

x = 3.64

The trip will take 3.64 hours

Keywords: linear equation, division

Learn more about linear equations at:

#LearnwithBrainly

Answer:

slope = 1/5

Step-by-step explanation:

[tex]\frac{0-(-3)}{11-(-4)} =\frac{3}{15} =1/5[/tex]

D and E are the only ones true.

Answer:

E

Step-by-step explanation:

You simplify the fraction by dividing both top and bottom by 5

35÷5=7

80÷5=16

Answer:

The correct option for this is C.) The mean and median age are more likely to be the same for the students in Math 1.

Step-by-step explanation:

i) The median age of the students is Math 1 is less than the median age of the students in Math 2.

This statement is NOT TRUE as the median age of students in Math 1 = median age of students in Math 2 = 19

ii) The mean and median age are most likely the same for both sets of data.

   This statement is NOT TRUE. The mean age of students in Math 2 should be greater than mean age of students in Math 1.

iii) The mean and median age are more likely to be the same for the students in Math 1.

  This statement is TRUE.

Answer:

The mean and median age are more likely to be the same for the students in Math 1.

Step-by-step explanation:

The median age of the students for the student is Math 1 is less than the median age of the students in Math 2.

The statement is not true as the median age of students in Math 1 is equal to the median age of the students in Math 2 = 19.

Also, the mean and median age are the most likely to be the same for both sets of data.

The above statement is also not true as the mean age of students in Math 2 should be greater than the mean age of students in Math 1.

Answer:424

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

when you write them down and draw a diaganal line from 7,2 to 5,5 it passes 4 intersections, so it would be 4 units. When you round if it is 4 or less it stays the same and if it is 5 or more then it changes so it would still be 4.

Stay Safe

Answer:

answer choice b is the correct answer

Step-by-step explanation:

5/8 times 2 1/2

1 3/4

1 3/4 > 1 1/4

Answer:

  V = (4/3)πr³

Step-by-step explanation:

The formula usually used to find the volume of a sphere is ...

  [tex]V=\dfrac{4}{3}\pi r^3[/tex]

where r represents the radius of the sphere.

The actual math involved will depend on what information about the sphere you are given. If you are given the radius or diameter (twice the radius), then this formula will be directly useful.

To determine the volume of a sphere, use the formula V = ([tex]\frac{4}{3}[/tex])πr³. Measure the radius, cube it, multiply by pi, and then multiply by 4/3.

To find the volume of a sphere, you use the formula:

V = ([tex]\frac{4}{3}[/tex])πr³

Here, V stands for volume, r represents the radius of the sphere, and π (pi) is approximately 3.14159.

Step-by-Step Explanation:

Answer:

Therefore,

The Height of Cylinder is 11 meters.

Step-by-step explanation:

Given:

Cylindrical Shape

Radius = r = 7 meter

Volume of Pipe = 539π

To Find:

Height = ?

Solution:

Formula for Volume of Cylinder is given by

[tex]\textrm{Volume of Cylinder}=\pi (Radius)^{2} \times Height[/tex]

Substituting the given values we get

[tex]539\pi=\pi(7)^{2}\times Height\\\\Height=\dfrac{539}{49}=11\ meter[/tex]

Therefore,

The Height of Cylinder is 11 meters.

The actual length of car is 42.857 foot

Solution:

Given that,

The scale of a railroad train set is 3.5 mm to 1 foot

The link of the model car in this it is 150 mm

To find: Length of actual car

Let "x" be the length of actual acr

From given,

Scale is:

3.5 mm : 1 foot

Then, given that link of the model car in this it is 150 mm

Then we get,

3.5 mm : 1 foot

150 mm : x foot

This forms a proportion and we can solve the sum by cross multiplying

[tex]3.5 \times x = 1 \times 150\\\\x = \frac{150}{3.5}\\\\x = 42.857[/tex]

Thus the actual length of car is 42.857 foot