What is the area of the beach ball with a diameter of 14 in. ?

Geometric series means

Lets spot out common ratio

Its less than 1

Hence series converges

Sum:-

Answer:

Series converges

Sum = 192

Step-by-step explanation:

General form of geometric series:   [tex]a_n=ar^{n-1}[/tex]

where:

Given series:  48, 36, 27, 81/4, ...

[tex]\implies a = 48[/tex]

[tex]\implies r=\dfrac{a_2}{a_1}=\dfrac{36}{48}=\dfrac34[/tex]

Geometric series converges when |r| < 1

Geometric series diverges when |r| ≥ 1

[tex]\textsf{As }r=\dfrac34\ \implies|\dfrac34| < 1\:\implies\:\textsf{series converges}[/tex]

Sum of an infinite geometric series:

[tex]S_\infty=\dfrac{a}{1-r}\quad\textsf{for}\:|r| < 1[/tex]

Substituting values of a and r:

[tex]\implies S_\infty=\dfrac{48}{1-\frac34}=192[/tex]

Answer:

B

Step-by-step explanation:

the opposite angles of the quadrilateral ABDC are supplementary , that is

∠ BDC + 40° = 180° ( subtract 40° from both sides )

∠ BDC = 140°

Answer:

A

Step-by-step explanation

math

[tex]\sf\large\underline{\star Given:-}[/tex]

[tex]\rightarrow[/tex] Length(l) of map = [tex]\sf\red{\frac{7}{8}m.}[/tex]

[tex]\rightarrow[/tex] Width(w) of map = [tex]\sf\red{\frac{3}{4}m.}[/tex]

[tex]\sf\large\underline{\star To \: Find:-}[/tex]

[tex]\rightarrow[/tex] Area of map.

[tex]\sf\large\underline{\star Solution:-}[/tex]

[tex]\rightarrow[/tex] From the above given dimensions we can conclude that map is in the shape of rectangle. So, we can find the area of map by using the formula: [tex]\sf\blue{Length×Width}[/tex]

So, let's begin

[tex]\rightarrow[/tex] Area of rectangular map = [tex]\sf{Length×Width}[/tex](putting the value of length and width from the above given)

[tex]\rightarrow[/tex][tex]\sf{=\:\frac{7}{8}×\frac{3}{4}}[/tex]

[tex]\rightarrow[/tex][tex]\sf{=\:\frac{21}{32}m^2}[/tex] Or,

[tex]\rightarrow[/tex][tex]\sf{=\: 0.65m^2}[/tex]

Therefore the area of the Mason map [tex]\sf\purple{=\: 0.65m^2}[/tex]or [tex]\sf\purple{\frac{21}{32}m^2}[/tex]

________________________________

Hope it helps you:)

Hope the picture will help you...

Answer:

1 1/8

Step-by-step explanation:

One half of 2 cups is 1 cup

One half of 1/4 cup is 1/8 cup

Answer = 1 + 1/8 = 1 1/8 cup

Another method

2 1/4 = (4×2+1)/4 = 9/4

Half of 9/8 = 1 1/8

Answer:

half of 2 1/4 as a fraction is 1 1/8

Answer: 864

Step-by-step explanation:

The formula is 4/3 pie radius ^3 but since it says 3 just use three. Now the radius is 6. So you do 4/3 times 3 times 6^3 and you get 864. I hope this helps.

Answer:

28 in2

Step-by-step explanation:

2×2÷2 + 2×2÷2 + 4×6

2in square +

2in square +

24in square=

28in squarr

The for formula for finding the area of a triangle is width times length divided by 2, and the formula for finding the area of a square is width times length.

F(51)

===========================================================

Explanation:

The very large numbers are likely put there as a distraction. They aren't needed. Adding any two adjacent Fibonacci numbers will lead to the next term in the sequence. This is simply based on how the special number sequence is defined or set up.

This means F(49)+F(50) = F(51) i.e. adding the 49th and 50th terms will generate the 51st term.

In general,

F(n) + F(n+1) = F(n+2)

where n is a positive integer.

Answer:

x = - 11

x + 7 = -4

Step-by-step explanation:

[tex]3(x + 7) = - 12 [/tex]

Multiply each term in parentheses by 3

[tex]3x + 3 \times 7 = - 12[/tex]

Multiply 3 and 7

[tex]3x + 21 = - 12[/tex]

Move the constant to the right side and change the sign

[tex]3x = - 12 - 21[/tex]

Find the sum of negative numbers

[tex]3x = - 33[/tex]

Divide both side by the same number

[tex]x = - 11[/tex]

= x + 7

= -11 + 7

Add the term - 11 + 7

= -4

Hey ! mate

Answer:

Step-by-step explanation:

In this question we have given an equation that is 3( x + 7 ) = -12 and we have asked to find the value of x + 7 and x .

We are starting our solution from here :

[tex] \longmapsto \: 3( x + 7 ) = -12 [/tex]

Transposing 3 to right hand side :

[tex] \longmapsto \: x + 7 = \frac{ - 12}{3} [/tex]

Now , dividing -12 by 3 :

[tex] \longmapsto \: \blue{\boxed{x + 7 = -4}}[/tex]

Now ,

[tex] \longmapsto \:x + 7 = - 4[/tex]

Transposing 7 to right hand side :

[tex] \longmapsto \:x = - 4 - 7[/tex]

[tex] \longmapsto \: \blue{ \boxed{x = - 11}}[/tex]

Length= 14inches and breadth= 10inches

We know, Perimeter of rectangle= 2(Length+Breadth)

[tex]2(14 + 10) \\ = 2 \times 24 \\ = 48 \: \text{inches}[/tex]

We know, Area of rectangle= Length × Breadth

[tex]14 \times 10 \\ = 140 \: \text{in} ^{2}[/tex]

Answer:

10,11.25,15

Step-by-step explanation:

we use linear scale factor you had mentioned that the triangles are similar so the smallest side in the first triangle is 8 and in tje other triangle it is 10

those two sides are equal which means 8 is equal to ten so if 8 is equal to 10 what about 9.if you cross multiply you get 11.25 then you do the same for 12 and get 15

8=10

9=11.25

12=15

Answer:

  $1650

Step-by-step explanation:

Each payment is applied first to the amount of interest that is due, then to the remaining principal.

__

For the first monthly payment, the interest due is ...

  I = Prt = $1800(0.10)(1/12) = $15.00

So, the amount of the payment that gets applied to the principal is ...

  payment - interest = $165 -15 = $150

The new balance is ...

  $1800 -150 = $1650.00 . . . . new principal after the first payment

__

The attachment shows the balance after each payment. Each interest amount is rounded to cents. The negative balance after the last payment is the amount of excess that last payment represents.

Answer:

The answer is 5^4

Step-by-step explanation:

You are given the expression 5^18 times 5^6 while all over (5^10)^2

First, let's simplify the numerator

Whenever you multiply exponents with the same base, which is 5 in this case, you have to add the exponents or powers

Keep the base the same and 18 and 6 together

So, 5¹⁸ ° 5⁶ = 5¹⁸⁺⁶ = 5²⁴

you have 5²⁴ in the numerator

now let's work on simplifying the denominator

Whenever you have number that has a power and is taken to another power, you multiply the powers

We call this the power of the power rule

So, (5¹⁰)² = 5¹⁰ˣ² = 5²⁰

Now the denominator is 5^20

We have 5^24/5^20

Now you just subtract the powers 24-20=4

And you get 5^4

Hope this helps

The maximum height of the kite is 13 meters while the minimum height is 12.44 meters.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let h represent the height of the kite. Hence:

At an angle of 56°, the height is:

sin(56) = h/15

h = 12.44 m

At an angle of 60°, the height is:

sin(60) = h/15

h = 13 m

The maximum height of the kite is 13 meters while the minimum height is 12.44 meters.

Find out more on equation at: https://brainly.com/question/1214333

Answer:

Area = 26 sq units

Step-by-step explanation:

If you put the points on a graph then you can see what you are working with. The parallelogram you can just count the squares to find the base and height. base = 6 and height = 1.

A = b • h = 6•1 = 6

To find the lengths of the sides for the rectangle you must use distance formula or pythagorean theorem. I have shown this using Pythagorean theorem. The short side of the rectangle is marked x and calculated to have length sqroot10. See image.

The graph shows the length is twice as long. But I showed a separate calculation also using pythag.thm. to find the length of y, the long side is sqroot40.

Area of rectangle is:

A = b•h OR L×W

A=sqrt10×sqrt40

=20 See image.

Add the areas to get your final answer.

Answer:

First u get the Y by itself then you read the less than or equal to or greater than or equal to.

Step-by-step explanation:

hope it helps

Answer:

(-4,3)

Step-by-step explanation:

Answer:

Option 1 :  (-4,3)

Step-by-step explanation:

When doing coordinates we always go across first the up or down.

Since it goes 4 to the left, our x coordinate is -4 and since it goes 3 up, our y coordinate is 3.

Therefore our answer must be (-4,3)

Step-by-step explanation:

Q = msdt

or, 940 = m* 0.780* 15

or, 940 = 11.7m

or, 940/11.7 = m

m = 80.341

Therefore the mass of the metal is 80.341g.

Translating the new coordinate up by 2 units and 5 units to the left will given a final coordinate at X''''(10, 1), Y''''(-4, 15) and Z''''(4, 19)

This is a technique used to change the position or size of an object on the xy plane.

Given the coordinate points X(2, 4), Y(5,-3) and Z(-7, 1)'

If the coordinate points is rotated 90 degrees clockwise, then the resulting coordinate will be at X(4, -2), Y(-3,-5) and Z(1, 7)

If the resulting coordinate is dilated by by a scaling factor of 2, then the new coordinate points wil be at X''(8, 4), Y''(-6, -10) and (2, -14)

If the resulting coordinate is reflected over the x-axis, then the new coordinate points wil be at X'''(8, -4), Y''(-6, 10) and (2, 14)

Finally, translating the new coordinate up by 2 units and 5 units to the left will given a resulting coordinate at X''''(10, 1), Y''''(-4, 15) and Z''''(4, 19)

Learn more on transformation here:

https://brainly.com/question/4289712

Answer:

Step-by-step explanation:

Darnell gives his friends

Remaining pie

Answer:

[tex]\huge\boxed{\bf{Leftover\:Daniel\:pie = 1\frac{1}{8}pie}}[/tex]

Step-by-step explanation:

Given:-

To find: -

Ans:-

The first step is to find a lot of cakes that will be given to five of Daniel's friends

Finally we determine the rest of Daniel's pie

Therefore leftover Daniel pie is = [tex]\frac{9}{8}[/tex]pie or [tex]1\frac{1}{8}[/tex]pie

[tex]\:[/tex]

[tex]\huge\colorbox{skyblue}{BlackPain}[/tex]

Answer:

Perimeter = 30 in

Step-by-step explanation:

Pythagoras' Theorem: a² + b² = c²

(where a and b are the legs, and c is the hypotenuse, of a right triangle)

Given:

Substitute given values into the formula and solving for a:

⇒ a² + 12² = 13²

⇒ a² + 144 = 169

⇒ a² = 25

⇒ a = 5 in

Therefore, perimeter = a + b + c

                                   = 5 in + 12 in + 13 in

                                   = 30 in

Final Answer:

[tex]\fbox{perimeter \: of \: triangle = 30 \: in.}[/tex]

Step by Step explanation:

Data achieved from diagram:

The given triangle is a right angle triangle

Hypotenuse of triangle = 13 in.

Base of triangle = 12 in.

To find:

Perimeter of triangle = ?

Solution:

We need length of all three sides (Altitude) of triangle,

let's find out the measure of length of Altitude using Pythagoras theorem!

[tex]{Hypotenuse}^2 = {Base}^2 + {Altitude}^2 \\ {13}^{2} = {12}^{2} + {A}^{2} \\ {A}^{2} = 169 - 144 \\ {A}^{2} = 25 \\ {A} = \sqrt{25 } \\ \fbox{A = 5 \: in.}[/tex]

Now we have all three sides of triangle,

[tex]perimeter \: of \: triangle = Hyp. + Base + Alt. \\perimeter \: of \: triangle = 13 + 12 + 5 \\ \fbox{perimeter \: of \: triangle = 30 \: in.}[/tex]

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The scale factor of 0.75 would ensure that the new fence has a smaller area

The total cost of fencing the smaller area is $1610.28

From the complete question, we have the following parameters:

Start by calculating the perimeter of the smaller area using:

Smaller Area = Perimeter * Scale factor * k

Where k represents the number of units on the smaller area

So, we have:

Smaller Area = 28 yards * 0.75 * 12

Evaluate the product

Smaller Area = 252 yards

The total cost is then calculated as:

Total cost = Unit cost * Smaller Area

This gives

Total cost = 6.39 * 252

Total cost = $1610.28

Hence, the total cost of fencing is $1610.28

Read more about scale factors at:

https://brainly.com/question/3457976

Answer:

An equation for the slope and y-intercept would be y=-3/5x-3

Step-by-step explanation:

Remember the formula for this, y=mx+b, in which the m stands for the slope and the x would be next to the slope always because the slope is ever changing, and the b stands for the y-intercept or in other words, where the line crosses the y-axis not the x-axis.

Answer:

y = -3/5x - 3

Explanation:

The format of slope-intercept is:

[tex]\sf{y = mx + b}[/tex]

Where:

So to write the equation, I just plug the data into y = mx + b:

[tex]\sf{y=-\dfrac{3}{5}x+(-3)}\\\\\sf{y=-\dfrac{3}{5}x-3}[/tex]

Hence, the equation is y = -3/5x - 3.

180+72=252

Step-by-step explanation:

an angel can be a large or as wide up to 360 then it is a circle

from the center out one way is 180

the same from the center the other way is 180