answer both question for 20 points and brainliest

Answer:

The answer is 132 square units

Step-by-step explanation:

Cutting the shape

we have two trapeziums

A=(area of small +Area of big)Trapezium

A=1/2(3+9)8 + 1/2(9+12)8

A=1/2×12×8 + 1/2×21×8

A=12×4 + 4×21

A=48+84

A=132 square units

Answer:

i do not understand your question

Step-by-step explanation:

Approximately 456.3 feet of fence to surround the entire circular yard.

Now, For the amount of fencing needed to surround a circular yard, we have to calculate the circumference of the circle, which is the distance around the circle.

Since, The circumference of a circle is,

⇒ C = πd,

where, C is circumference, d is diameter,

Here, the diameter of the circular yard is 145 feet,

So the radius is half of that,

r = 145/2 = 72.5 feet.

So, Using the formula, we can calculate the circumference as:

C = πd

C = 3.14 x 145

C = 456.3 feet

Therefore, Approximately 456.3 feet of fence to surround the entire circular yard.

Learn more about the circle visit:

https://brainly.com/question/24810873

#SPJ1

The area of the shaded portion in the equilateral triangle with sides 6 is 9√3 - 36π.

To find the area of the shaded portion in the equilateral triangle, we need to determine the area of the three arcs and subtract it from the area of the equilateral triangle.

First, let's find the area of one arc. Each arc has a radius equal to the length of the side of the equilateral triangle, which is 6. The formula for the area of a sector is A = (θ/360)πr², where θ is the central angle in degrees.

In an equilateral triangle, each interior angle measures 60 degrees, so the central angle of the arc is 120 degrees (360 degrees divided by 3). Plugging these values into the formula, we get A_arc = (120/360)π(6)² = (1/3)π(6)² = 12π.

Since there are three identical arcs, the total area of the arcs is 3 times the area of one arc, which is 3(12π) = 36π.

Now, let's find the area of the equilateral triangle. The formula for the area of an equilateral triangle is A_triangle = (√3/4)s², where s is the length of a side.

Plugging in the value of the side length, we have A_triangle = (√3/4)(6)² = (√3/4)(36) = 9√3.

Finally, we subtract the area of the arcs from the area of the equilateral triangle to find the shaded portion's area: A_shaded = A_triangle - A_arc = 9√3 - 36π.

For more such questions on triangle

https://brainly.com/question/1058720

#SPJ8

After considering the given data we come to the conclusion that the length of AB is 12.124 units, under the condition that A (-3, 5) and B (4, -2) are the given coordinates.

The distance between two points in a plane can be found using the distance formula which is an application of the Pythagorean theorem. The formula is given by d=√ ( ((x₂ – x₁ )² + (y₂ – y₁ )²)

Here (x₁, y₁) and (x₂, y₂) are the coordinates of the two points.

Applying the given coordinates of A (-3, 5) and B (4, -2), we can evaluate the distance between them as follows:

d = √( (4 - (-3))² + (-2 - 5)² )

 = √(7² + (-7)²)

 = √(98 + 49)

 = √147

 = 12.124

Therefore, the length of AB is approximately 12.124 units.

To learn more about Pythagorean theorem

https://brainly.com/question/28981380

#SPJ1

The amount invested at 3% is $400, the amount invested at 4% is $700, and the amount invested at 5% is $1000.

Let's assume the amount invested at 4% is x dollars.

According to the given information, the amount invested at 5% is $1000 more than the amount invested at 4%.

So, the amount invested at 5% is (x + $1000).

The total amount invested is the sum of the amounts invested at each rate, which is $2100.

Therefore, we can write the equation:

x + (x + $1000) + (amount invested at 3%) = $2100

Now, we can calculate the amount invested at 3%.

We subtract the sum of the amounts invested at 4% and 5% from the total investment:

(amount invested at 3%) = $2100 - (x + x + $1000) = $2100 - (2x + $1000)

Given that Elena receives $95 per year in simple interest from the investments, we can use the formula for simple interest:

Simple Interest = Principal × Interest Rate

The interest earned from the investment at 3% is (amount invested at 3%) × 0.03, the interest earned from the investment at 4% is (amount invested at 4%) × 0.04, and the interest earned from the investment at 5% is (amount invested at 5%) × 0.05.

According to the problem, the total interest earned is $95.

So we can write the equation:

(amount invested at 3%) × 0.03 + (amount invested at 4%) × 0.04 + (amount invested at 5%) × 0.05 = $95

Now we can substitute the expression for (amount invested at 3%) and solve for x.

Once we have the value of x, we can calculate the amounts invested at 3%, 4%, and 5% using the given information.

For similar question on amount invested.

https://brainly.com/question/2720767  

#SPJ8

Answer:

if the terms are approaching zero then it is convergent.

Therefore the stated series is convergent

Step-by-step explanation:

y=3x+3

the slope is that "3x" part. the y intercept is the "+3". If your teacher is JUST looking for a slope, and no y intercept, just answer "y=3x"

That "x" is the letter x as well, not a multiplication sign.

In algebra, "seven times a number" is written as 7x, which is the multiplication of seven instances of the symbol x.

An equation that includes constants, variables, and a few algebraic operations is said to be algebraic. A good example of an algebraic expression is 3x2 2xy + d. So, three different types of fundamental building blocks make up an algebraic expression: Coefficient (i.e. numbers) (i.e. numbers)

A seven-times-a-number is represented by multiplying it by seven or adding it to another integer (since this is an abbreviated successive addition ).

If x is any number, then it may be written as follows seven times: Algebraic expressions (numbers or letters) are linked by fundamental operations including addition, subtraction, multiplication, and division in mathematical language.

To learn more about algebraic expression from given link

https://brainly.com/question/4541471

#SPJ1

Complete question -

Seven times a number in algebraic expression

Given:

The recursive formula of a geometric sequence is

\(a_n=a_{n-1}\cdot (\dfrac{1}{8})\)

\(a_1=-3\)

To find:

The explicit formula of the given geometric sequence.

Solution:

We know that, first term of geometric sequence is \(a_1=-3\).

Recursive formula of a geometric sequence is

\(a_n=a_{n-1}\times r\)      ...(i)

where, r is common ratio.

We have,

\(a_n=a_{n-1}\cdot (\dfrac{1}{8})\)    ...(ii)

On comparing (i) and (ii), we get

\(r=\dfrac{1}{8}\)

The explicit formula of a geometric sequence is

\(a_n=a_1r^{n-1}\)

Putting \(a_1=-3\) and \(r=\dfrac{1}{8}\), we get

\(a_n=-3\left(\dfrac{1}{8}\right)^{n-1}\)

Therefore, the correct option is D.

2 units down means y is decreased by 2

3 units left mean x is decreased by 3

So

for

The translation is

Answer:

This will now be ⁴√(7^9)

Step-by-step explanation:

c=4

a=7

b=9

∵ The formula of the compound interest is

→ A is the new amount

→ P in the initial amount

→ r is the interest rate in decimal

→ n is the number of periods

→ t is the time

∵ The initial amount is 800 dollars

∵ The annual rate is 3% = 3/100 = 0.03

∵ It is a compounded annually

∴ n = 1

∵ t = 5 years

→ Substitute all of these values in the formula above

→ Use the calculator to find the answer

∴ A = 927.4192594 dollars

A function that represents a reflection of \(f(x) = \frac{3}{8} (4)^x\) across the y-axis include the following: D. \(g(x) = \frac{3}{8} (4)^{-x}\).

In Mathematics and Geometry, a reflection over or across the y-axis or line x = 0 is represented and modeled by this transformation rule (x, y) → (-x, y).

This ultimately implies that, a reflection over or across the y-axis or line x = 0 would maintain the same y-coordinate while the sign of the x-coordinate changes from positive to negative or negative to positive.

By applying a reflection over the y-axis to the parent exponential function, we would have the following transformed exponential function:

(x, y)                                              →                 (-x, y).

\(f(x) = \frac{3}{8} (4)^x\)                               →              \(g(x) = \frac{3}{8} (4)^{-x}\)

Read more on reflection here: https://brainly.com/question/3399394

#SPJ1

The distance from point B to point A is given as follows:

15,893 ft

The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:

For each angle, we have that:

Hence the position A is obtained as follows:

tan(16º) = 7200/a

a = 7200/tangent of 16 degrees

a = 25109 ft.

The position B is obtained as follows:

tan(38º) = 7200/b

b = 7200/tangent of 38 degrees

b = 9216 ft.

Hence the distance is of:

25109 - 9216 = 15,893 ft.

More can be learned about trigonometric ratios at brainly.com/question/24349828

#SPJ1

The fraction of the pie that she served is given as follows:

5/8.

The fraction of the pie that she served is obtained applying the proportions in the context of the problem.

A fraction is a way of expressing a part of a whole or a ratio between two quantities. It represents a number that is not a whole number and is usually written in the form of a numerator over a denominator.

The parameters for the fraction are given as follows:

Then the fraction is given as follows:

5/8.

More can be learned about proportions at https://brainly.com/question/24372153

#SPJ1

Answer:

Step-by-step explanation:

The value of n that will make the expression equal is 13

Equations are expressions separated by equal sign

Given the equation

11n = 143

Divide both sides by 11 to have;

11n/11 = 143/11

n = 13

Hence the value of n that will make the expression equal is 13

Learn more on linear equation here; https://brainly.com/question/2030026

#SPJ1

Answer:

you have to put the Y in the formula or make a comparison

The right response is 400%. In other words, Johnny moves at four times the pace of Jane.

We must compare the speeds of Johnny and Jane in relation to one another in order to get their ratio. According to the issue, Jane moves at a pace that is 1/4 that of Johnny. In other words, Jane moves at a speed that is one-fourth that of Johnny.

We may compare the speeds as a fraction to figure out the ratio:

Johnny's speed divided by Jane's speed equals 4/1.

This indicates that Johnny is moving at a speed that is four times that of Jane. We can express Johnny's speed as 400% of Jane's speed in percentage terms.

Learn more about percentages here,

https://brainly.com/question/24877689

9514 1404 393

Answer:

  y = -1/2x +11/2

Step-by-step explanation:

The slope of the line is ...

  m = (y2 -y1)/(x2 -x1)

  m = (1 -2)/(9 -7) = -1/2

The y-intercept is ...

  b = y -mx

  b = 2 -(-1/2)(7) = 11/2

Then the slope-intercept equation is ...

  y = -1/2x +11/2

_____

Alternative solution

A general form equation for the line can be ...

  (y1 -y2)(x -x1) -(x1 -x2)(y -y1) = 0

  (2 -1)(x -7) -(7 -9)(y -2) = 0

  x-7 +2y -4 = 0

  x +2y -11 = 0 . . . . . general form equation

  x +2y = 11 . . . . . . . standard form equation

Note that we want the x-coefficient to be positive, so we chose the order of the points to make that be the case.

Answer:

The probability that the battery in a critical tool fails at 32 hours was from manufacturer 2 is 0.625

Step-by-step explanation:

Given that:

60% of the batteries are from manufacturer 1

90% of these batteries last for over 40 hours

Let the number of the battery duration be n = 0.90

Therefore n' = 1 - 0.90 = 0.10

Let p = manufacturer 1  and q = manufacturer 2

q = 1 - p

q = 1 = 0.6

q = 0.4

Thus ; 40% of the batteries are from manufacturer 2

However;

Only 75% of the batteries from manufacturer 2 last for over 40 hours.

Let number of battery duration be m = 0.75

Therefore ; m' = 1 - 0.75 = 0.25

A battery in a critical tool fails at 32 hours.

Thus; the that the battery in a critical tool fails at 32 hours was from manufacturer 2 is:

\(= \dfrac{q \times m' }{ p \times n' + q \times m' }\)

\(= \dfrac{0.4 \times0.25 }{ (0.6 \times 0.1) + (0.4 \times 0.25 ) }\)

\(=\dfrac{0.1}{0.06+ 0.1}\)

\(=\dfrac{0.1}{0.16}\)

= 0.625

The probability that the battery in a critical tool fails at 32 hours was from manufacturer 2 is 0.625

The probability that the battery was from manufacturer 2 is 62.5%.

Since the Ambell Company uses batteries from two different manufacturers, and historically, 60% of the batteries are from manufacturer 1, and 90% of these batteries last for over 40 hours, while only 75% of the batteries from manufacturer 2 last for over 40 hours, if a battery in a critical tool fails at 32 hours, to determine what is the probability it was from manufacturer 2 the following calculation must be performed:

Therefore, the probability that the battery was from manufacturer 2 is 62.5%.

Learn more in https://brainly.com/question/14461509

Answer:

It's F. none of the points

Step-by-step explanation:

The area of the shaded region of a circle with a 100 degree angle and a radius of 3cm, using pi=3.14, is approximately 25.64 square centimeters.

To find the area of the shaded region of a circle, we need to subtract the area of the sector formed by the shaded region from the area of the whole circle.

The area of the whole circle is given by

A = πr²

where A is the area of the circle, r is the radius of the circle, and π is a mathematical constant approximately equal to 3.14 (as given in the question).

Substituting the given values, we get

A = π(3cm)²

A = 28.26 cm² (rounded to two decimal places)

Now, let's find the area of the sector formed by the shaded region.

The angle of the sector is given as 100 degrees. To find the area of the sector, we need to use the formula:

A = (θ/360)πr²

where θ is the angle in degrees, r is the radius of the circle, and π is again approximately equal to 3.14.

Substituting the given values, we get

A = (100/360)π(3cm)²

A = 2.62 cm² (rounded to two decimal places)

Finally, we can find the area of the shaded region by subtracting the area of the sector from the area of the whole circle

Shaded area = Area of circle - Area of sector

Shaded area = 28.26 cm² - 2.62 cm²

Shaded area = 25.64 cm² (rounded to two decimal places)

Therefore, the area of the shaded region of the circle is approximately 25.64 square centimeters.

To know more about Area of Circle:

https://brainly.com/question/28642423

#SPJ1

--The given question is incomplete, the complete question is given

" Find the area of a shaded region of circle and use 3.14 for pi "--

Answer:

image is attached (shaded area is where x could be)

Step-by-step explanation:

\(6x < 90\)

divide both sides by 6

\(x < 15\)

this means x is strictly less than 15

Answer:

Area of front and back = 2 * 2 * 5 = 20 cm^2

Area of sides = 2 * 3 * 4 = 24 cm^2

Area of top and bottom = 2 * 4 * 5 = 40 cm^2

TOTAL area = 84 cm^2

Step-by-step explanation:

Given the length (l), the width (w), and the height (h) of the rectangular prism:

You need to use this formula for calculating the surface area of a rectangular prism, in order to find the surface area of the box:

Where "l" is the length, "w" is the width, and "h" is the height of the rectangular prism.

Therefore, when you substitute the values into the formula and evaluate, you get:

Hence, the answer is:

Answer:c 565

Step-by-step explanation:

The logarithmic regression equation that models the situation is given as follows:

y = 242.9037 + 23.7097ln(x).

The estimated population in 2010 is of:

313.9 million

Which overestimates the actual amount by 5.2 million.

The prediction for when the population will be of 400 million is of:

Year of 2,744.

The logarithmic regression equation is obtained inserting the points of the data-set into a logarithmic regression calculator.

From the table given by the image at the end of the answer, the points are given as follows:

(0, 248.8), (10, 281.4), (20, 308.7), (30, 331.4), (31, 331.9).

Inserting these points into a calculator, the equation is given as follows:

y = 242.9037 + 23.7097ln(x).

2010 is 20 years after 1990, hence the estimate is given as follows:

y = 242.9037 + 23.7097 x ln(20) = 313.9 million.

The overestimate of the actual value, from the table, is of:

313.9 - 308.7 = 5.2 million.

The prediction for when the population will be of 400 million is obtained as follows:

400 = 242.9037 + 23.7097 x ln(x)

ln(x) = (400 - 242.9037)/23.7097

ln(x) = 6.6258.

x = e^(6.6258)

x = 754.

Hence during the year of 2,744.

The table is given by the image presented at the end of the answer.

More can be learned about logarithmic regression at https://brainly.com/question/26755306

#SPJ1

Answer:

C.

Step-by-step explanation:

Answer:

50(5π + 6) cm²

Step-by-step explanation:

TSA of figure = 1/2 of TSA(Cylinder) + Area of rectangle

= 1/2 of 2πr(h+r) + 20*15

= πr(h+r) + 300

= 10π(15+10) + 300

= 250π + 300 cm²

or 50(5π + 6) cm²