Find the area of a circle with a diameter of 2 feet. Use 3.14 for π.

Recall that to determine if a table represents a probability distribution, the sum of the probabilities must add up to 1, and all the probabilities have to be positive numbers less or equal to 1.

Now, notice that:

From the table, we notice that all the given probabilities are positive numbers between 0 and 1. Therefore, we can conclude that the given table represents a probability distribution.

Yes, it is a probability distribution.

Answer:

$ 27.6.

Step-by-step explanation:

Let the cost of tea be C.

Let the mass of tea be M

From the question given, we were told that the cost of tea varies directly with the mass. This can be expressed as:

C & M

C = KM

K is called constant of proportionality.

C is the cost of the tea.

M is the mass of tea.

Next, we shall determine the constant of proportionality, K.

Cost (C) = $ 10.35

Mass (M) = 4.5 kg

Constant (K) =..?

C = KM

10.35 = K × 4.5

Divide both side by 4.5

K = 10.35/4.5

K = 2.3

Finally, we shall determine the cost of 12kg of tea as follow:

Mass (M) = 12 kg

Constant (K) = 2.3

Cost (C) =..?

C = KM

C = 2.3 × 12

C = $ 27.6

Therefore, the cost of 12 Kg of tea is $ 27.6

Answer:

$27.6

Step-by-step explanation:

10.35 divided by 4.5 = 2.3

$2.3 for 1 kg

2.3 times 12= 27.6

The surface area of the cylinder with height 7cm and radius 4cm is approximately 88π cm²

Surface area is the measure of the total area that the surface of an object occupies. It includes the area of all faces, sides, and curves.

a cylinder is a three-dimensional shape with a circular base and straight parallel sides that connect to a circular top. Its volume can be calculated as the product of the base area and height.

According to the given information :

To find the surface area of a cylinder using a net, we need to "unwrap" the cylinder into a flat shape, which will consist of a rectangle and two circles. The area of the rectangle will be the lateral area of the cylinder, and the area of the two circles will be the top and bottom areas of the cylinder.

The lateral area of the cylinder is given by the formula:

Lateral Area = 2 x π x r x h

where r is the radius of the cylinder, and h is the height of the cylinder.

The top and bottom areas of the cylinder are each given by the formula:

Top/Bottom Area = π x r²

where r is the radius of the cylinder.

Using the given dimensions, we can calculate the surface area of the cylinder as follows:

Lateral Area = 2 x π x 4cm x 7cm = 56π cm²

Top/Bottom Area = π x 4cm² = 16π cm²

Total Surface Area = Lateral Area + 2 x Top/Bottom Area

Total Surface Area = 56π cm² + 2 x 16π cm² = 88π cm²

Therefore, the surface area of the cylinder with height 7cm and radius 4cm is approximately 88π cm²

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Answer:

Decreasing

Step-by-step explanation:

We are given two points, A (-3,2) and B (1,-5).

We want to know if the line passing through these two points is increasing, decreasing, vertical, or horizontal.

To do that, we should find the slope (m) of the line.

Recall that the slope of the line can be found using the formula \(m=\frac{y_2-y_1}{x_2-x_1}\) where \((x_1,y_1)\) and \((x_2,y_2)\) are points.

Although we already have two points, we can label the values of the points to help reduce confusion and mistakes.

\(x_1=-3\\y_1=2\\x_2=1\\y_2=-5\)

Now, substitute these values into the formula.

\(m=\frac{y_2-y_1}{x_2-x_1}\)

\(m=\frac{-5-2}{1--3}\)

\(m=\frac{-5-2}{1+3}\)

\(m=\frac{-7}{4}\)

So, the slope of this line is negative, so the line passing through the points is decreasing.

Answer:

The probability of rolling an odd number or a two on a six-sided die is 1/2 + 1/6 = 2/3. This means that if you roll a six-sided die 300 times, you can expect to roll an odd number or a two approximately 200 times

Step-by-step explanation:

Answer: 400 TIMES

Step-by-step explanation:

1/6 +1/2

4/6

2/3

The rectangle in the example has a 173.70 cm perimeter.

The perimeter of a form is the space surrounding its edge. you can find the perimeter of various forms by summing the lengths of their sides.

Given, In a rectangle, the diagonal amount with the base is 72. The diagonal is 2 cm bigger than the base.

Since the Diagonal is 72 cm

and also given base = diagonal - 2

Base = 70

Because Diagonal ² = base² + height²

height² = 72² - 70²

Height² = 284

Height = 16.85

Thus the perimeter = 2*(base + height)

Perimeter of rectangle = 2 * (70 + 16.85)

the perimeter of the rectangle = 173.70

Therefore, the perimeter of the given Rectangle is 173.70 cm.

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Answer:

I believe it is a total of 73.188

Answer:

Different scientists might perform the experiment differently

Step-by-step explanation:

Answer: If the results are the same, replication of the investigation helps to confirm the results.

Step-by-step explanation:

Answer:

The paint mixer should use 3 1/3 gallons of 15% gloss paint and 1 2/3 gallons of 30% gloss paint.

Step-by-step explanation:

To make a paint of 20% gallon, the quantity of gloss in 5 gallons of 20% gloss.

0.2 × 5 = 1 gallon.

To get 1 gallon from a combination of 15% gallon and 30% gallon.

Let x rep the volume of 15% gallon.

The volume of 30% gallon can be given as;

5-x.

And we can interpret to form the equation below.

0.15x + 0.3(5-x) = 1

0.15x+1.5-0.3x = 1

-0.15x = 1-1.5 = -0.5

x = -0.5/-0.15

x = 10/3 = 3 1/3

5-x = 5-10/3 = 5/3 = 1 2/3

Therefore, the gallons of 15% = 3 1/3

And the gallons of 30% = 1 2/3

The statement [1,5] = { 1, 2, 3, 4, 5 is False.

In mathematics, there are two ways of representing a set of elements: by using curly braces {} or square brackets []. The curly braces {} are commonly used to represent sets, while square brackets [] are used to represent lists or arrays.

[1,5] is a list, which means it is ordered and has duplicates allowed. On the other hand, {1,5} is a set, which means it is unordered and has no duplicates allowed.

Therefore, [1,5] is not equal to {1, 2, 3, 4, 5} because the former is a list of two elements, while the latter is a set of five distinct elements.

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There 5 5 dollars in the amount given by the teller to Neka

What is the  total value of a single denomination?

The total value of a single denomination is the number of that denomination received by Neka multiplied by the value of each denomination

In other words, the total value of 50-dollar is $50 multiplied by 2 since there 2 50- dollar bills, the same applies all other bills.

Total amount=($50*2)+($20*6)+($5*f)

total amount=$245

$245=($50*2)+($20*6)+($5*f)

$245=$100+$120+($5*f)

$245=$220+($5*f)

$245-$220=$5*f

$25=$5*f

f=$25/$5

f=5

In essence, there are 5 5 dollar bills

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By using previous years' population data and calculating the annual growth rate, we can estimate the population of the United States in 2010, assuming the population trend continued in the same manner.

To estimate the population of the United States in 2010, we can use the population growth trend from previous years. Here's a step-by-step explanation:

1. Collect population data: Find the population of the United States in previous years, preferably as close to 2010 as possible. For example, we can use the population data from 2000 and 2005.

2. Calculate the annual growth rate: Subtract the population in 2000 from the population in 2005, and divide the result by the population in 2000. Then, divide the result by the number of years between the two data points (5 years in this case) to get the average annual growth rate.

3. Apply the growth rate to the 2005 population: Multiply the population in 2005 by the annual growth rate, and then add the result to the 2005 population to get an estimate of the population in 2006. Repeat this process for each subsequent year until you reach 2010.

4. The estimated population in 2010: The result of step 3 for the year 2010 will be the reasonable estimation of the population in 2010, assuming the population trend continued in the same manner.

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Answer:

386+20m = 344+35m

Step-by-step explanation:

a. The contingency table for the given data is attached file below.

b. The proportion of lizards that were either species A or B is 0.605.

c. The probability that a species C lizard in this study did not survive is 0.4667.

a.

The contingency table for the given data is attached file below.

b.

The proportion of lizards that were either species A or B can be calculated as:

P(A or B) = (15+8)/(15+8+6+9+4)

P(A or B) = 23/38

P(A or B) = 0.605

c.

The probability that a species C lizard in this study did not survive can be calculated as:

P(Not survive| C) = 7/15

= 0.4667

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Answer:

B

Step-by-step explanation:

cut tghe shape into one rectangle and a two cimi circles

area of a rect. is b x h --> 7x14 = 98ft^2

now make the two cimi circles a whoal and find the area of a circle

pie r^2 --> 3.14x3.5^2 = 38.48

add both getting about 136.48

Answer:

136.48 ft^2 (B)

Step-by-step explanation:

First, we need to find the area of a rectangle.

A(rectangle) = l * w

  = 14 ft * 7 ft

  = 98 ft^2

Next we need to find the area of the two semicircles.

A(semicircle) * 2 = πr^2/2 * 2

                           = π(3.5 ft)^2

                           = 12.25π ft^2

                           = 38.48 ft^2

Finally, you add the two areas:

98 ft^2 + 38.48 ft^2 = 136.48 ft^2

Hope this helps!

Answer:

$250*C + $180*G = $950

Step-by-step explanation:

Solving for G, it is G = (950 - 250C)/180

Solving for C, it is C = (950 - 180G)/250

The dimensions of the triangle are;

Base = 21 yards

Height of the triangle = 16 yards

It is important to note that the formula for determining the area of a triangle is expressed as;

Area = 1/2bh

Given that;

From the information given, we have that;

Base = 5 + h

Area =  168 square yards.

Now, substitute the values

168 = 1/ 2 (5 + h) h

expand the bracket

168 = 1/ 2 5h + h²

cross multply

5h + h² = 336

h² + 5h - 336 = 0

h² + 21h - 16h - 336 = 0

h( h + 21) - 16( h + 21) = 0

Then,

h = 16

h = -21

Base = 5 + h = 5 + 16 = 21 yards

Height = 16 yards

Hence, the values are 16 and 21 yards

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Therefore , the solution of the given problem of equation comes out to be a.60 , b.20 and c.21.

An equation in mathematics is a representation of two equal variables, one on each side of a "equals" sign. To tackle common issues, equations can be used. We commonly seek pre algebra help to overcome obstacles in real life. Math fundamentals are covered in pre-algebra lessons.

Here,

9(x - y) = 30,

or (x-y) =30/9

To find :  

a) 18(x - y) = ?

=> 2(9(x - y))

=> 2(30)

=> 60

b)6x - 6y = ?

=> 6(x-y) = 6(30/9)

=> 2*30/3

=> 20

c) 9(x-y)-9

=> 30 -9

=>21

Therefore , the solution of the given problem of  equation comes out to be a.60 , b.20 and c.21.

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On solving the provided question, we can say that the inequality provided is  -s < 6  he values that stratifies will be = 0-6

An inequality in mathematics is a relationship between two expressions or values that is not equal. Thus, imbalance leads to inequality. An inequality creates the link between two values that are not equal in mathematics. Egality is distinct from inequality. When two values are not equal, most commonly use the not equal sign (). Different inequalities are used to contrast values, no matter how little or large. Many simple inequalities may be resolved by modifying the two sides until the variables are all that remain. But a number of things contribute to inequality: Negative values on both sides are divided or added. Trade off the left and right.

the inequality provided is

-s < 6

the values that stratifies will be = 0-6

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Answer:

The middle term is negative but should be positive

Step-by-step explanation:

Let's walk through doing it:

\(-3x^2(4x^2 - 5x + 7)\\= -12x^4 + 15x^6 - 21x^2\)

Answer:

-0.329

Step-by-step explanation:

The formula for Geometric ratio is

an = ar^n - 1

Where

a = First term = 18

r = Common ratio = ?

n = Number of term= 6

Hence

a6 = 18 × r^6-1

From the question

a6 = -2/29

Hence:

-2/29 = 18 × r^6-1

-2/29 = 18 × r⁵

Divide both sides by 18

-2/29 ÷ 18 = 18 × r⁵/18

-2/29 × 1/18 = r⁵

r⁵ = -1/261

Take the fifth root of both sides

⁵√(r⁵) = ⁵√(-1/261)

r = -0.3286032834

Approximately = -0.329

Therefore, Common ratio = -0.329

Answer:

x=12

Step-by-step explanation:

4x+16=64

to isolate x, take 16 from both sides

4x+ 16(-16)=64-16

4x=48

divide 4 on each side

4x/4=x

48/4=12

x=12

The solution of the equation 4x+16= 64 is x = 12.

The solution of an equation refers usually to the values of the variables involved in that equation which if substituted in place of those variable would give a true mathematical statement.

For this case, we've to solve for x, the equation \(4x + 16 = 64\)

Subtracting 16 from both the sides:

\(4x + 16 - 16 = 64 - 16\\4x + 0 = 48\\4x = 48\)

4x is actually 4 times x, and is written in short, where the multiplication sign is hidden. This is usually done when variables like x,y are there.

Dividing both the sides by 4, we can get x on one side, and rest of the constant values on the other side.

\(\dfrac{4x}{4} = \dfrac{48}{4}\\\\1 \times x = 12\\x = 12\)

(since 1 times any number is that number itself, and as x represents a number, so we got 1 times x =x).

Thus, the solution of the equation 4x+16= 64 is x = 12.

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\(f(x)=3x^2-5\)

Substitute x = -11 in the equation.

\(f(-11)=3(-11)^2-5\\f(-11)=3(121)-5\\f(-11)=363-5\\f(-11)=358\)

Thus, the answer is 358 aka the second choice.

Answer:

Below.

Step-by-step explanation:

1 / secA+tanA =  1 / [1/cosA+sinA/cosA))]

= 1/ [(1 + sinA)/cosA]

= cosA/(1+sinA)

Now check if this is identical to 1-sinA/cosA:

1-sinA/cosA = cosA/(1+sinA)

Cross multiply:

(1-sinA)(1+sinA) = cos^2A

1 - sin^2A = cos^2A

sin^2A + cos^2A = 1  

This is a known idenity.

So the original identity is true.

Answer:

D) 15/4+5.4

Step-by-step explanation:

Answer:

Area(path)=7456sqm

Area(green)=196,544 sqmeters

Step-by-step explanation:

See image. The long path is

8×600=4800sqm

The short path is

8×340=2720sqm

But we've included the center square twice. So we should remove the redundancy by subtracting 64.see image

Area(paths)

=4800+2720-64

= 7456 sq meters

Area of the entire park= 600×340

=204,000 sq meters

Area(park not incl roads)=

204000 - 7456

=196,544 sq meters

The circumference of the circular test track is 3.3 km. When a car travels around the track from the southernmost point to the northernmost point, it covers the entire circumference of the track.

To calculate the distance traveled by the car, we can use the formula: distance = circumference.

In this case, the distance traveled by the car is equal to the circumference of the track, which is 3.3 km.

So, when the car completes one full lap around the track, it will have traveled a distance of 3.3 km.

If the car completes multiple laps around the track, the total distance traveled will depend on the number of laps. For example:

- If the car completes 2 laps, the total distance traveled will be 2 times the circumference, which is 2 * 3.3 km = 6.6 km.
- If the car completes 3 laps, the total distance traveled will be 3 times the circumference, which is 3 * 3.3 km = 9.9 km.

Therefore, the distance traveled by the car around the circular test track depends on the number of laps completed.

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A plane cannot be named by any three points in the plane because there are infinitely many planes that can pass through those points. By specifying only three points, we do not have enough information to uniquely identify a single plane.

To uniquely define a plane, we need to use three noncollinear points. Noncollinear points are points that do not lie on the same line. By choosing three noncollinear points, we can determine a unique plane that passes through those points. The combination of these three points creates a plane that is different from any other plane passing through any other set of three noncollinear points.

In summary, naming a plane requires three noncollinear points because this combination uniquely identifies a plane, whereas three points alone are not sufficient for this purpose.

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