Suppose that a single die with 19 sides (numbered 1, 2, 3, ... , 19) is rolled once. What is the probability of getting an even number.

Kevin's solution is incorrect. He found the area of the triangle as [tex]bh[/tex], not [tex]\frac{1}{2}bh[/tex].

The correct area of the triangle is [tex]\frac{1}{2}(8)(5)=20 \text{ in}^2[/tex].

Factorization of  6ax - 15x is 3x.(2a - 5)

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Given expression,

6ax - 15x

It can be written as

3×2 . a . x - 3×5 . x

Factoring out common factor

3x.(2a - 5)

Hence, 3x.(2a - 5) is the factorization of 6ax - 15x.

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The exponential function from the table is f(x) = 2 [tex](0.5)^x[/tex].

The graph is given below.

Option D is the correct answer.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

The exponential function is given as,

f(x) = m[tex]a^x[/tex]

Now,

From the table,

2 = m[tex]a^0[/tex]

m = 2

1 = m[tex]a^1[/tex]

m = 1/a ____(1)

0.5 = m[tex]a^2[/tex]

m = 0.5/[tex]a^2[/tex] _____(2)

Now,

From (1) and (2).

1/a = 0.5/[tex]a^2[/tex]

a = 0.5

Now,

f(x) = 2 [tex](0.5)^x[/tex]

Thus,

The exponential function is f(x) = 2 [tex](0.5)^x[/tex].

The graph is given below.

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x = 15/2

do u need an explanation?

Answer:

Step-by-step explanation

Sort the data: 41, 41, 43, 43, 45, 50, 52, 53, 54, 62, 63, 63, 67, 75, 97

Find the median (Q2): 53

Split the data set into two parts: Q1 (25th percentile) and Q3 (75th percentile)

Q1: 41, 41, 43, 43, 45, 50, 52, 53

Q3: 54, 62, 63, 63, 67, 75, 97

Find the median (Q1) of Q1 and the median (Q3) of Q3:

Q1 = 45

Q3 = 63

Finally, calculate the IQR by subtracting Q1 from Q3:

IQR = Q3 - Q1 = 63 - 45 = 18

So, the interquartile range of the given data set is 18. This means that 50% of the data falls within a range of 45 + 18 = 63 and 45 - 18 = 27.  

AB vector is a vector whereas AB bar is a line segment.

What is a vector ?

The vectors are described as an object containing both significance and course. Vector describes the motion of an item from one point to any other. Vector math may be geometrically picturised via the directed line segment.

The duration of the phase of the directed line is known as the value of a vector and the angle at which the vector is inclined shows the path of the vector. The start line of a vector is referred to as “Tail” and the finishing factor (having an arrow) is referred to as “Head.”

The difference is in their names itself.

AB vector is a vector whereas AB bar is a line segment.

A vector has a direction and a magnitude while a line segment ( scalar ) has only magnitude.

Therefore, AB vector is a vector whereas AB bar is a line segment.

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Answer:

3734.24100725

Step-by-step explanation:

This is related for all problems like this, not just this one:

When you see the key words below, this is what it means, and you can craft an equation from it:

Per = division

Of = multiplication

Using this above, we can replace the words with an equation:

The question is asking the amount of money per person.

Remember above, per means division:

Money/person

We know the amount of money and the number of people, so let's plug it in:

1,130,000,000/302,605

After division:

3734.24100725, final answer.

Hope this helps :D

The area of the given rectangle will be A = 9x² - 64 yards².

What is a rectangle?

Rectangles are quadrilaterals having four right angles in the Euclidean plane of geometry. Various definitions include an equiangular quadrilateral, A closed, four-sided rectangle is a two-dimensional shape. A rectangle's opposite sides are equal and parallel to one another, and all of its angles are exactly 90 degrees.

The area of the rectangle is A = a*b

Given is l =(3x+8) yards

b = (3x-8)yards

So the area of the rectangle is A = l*b

A = (3x+8)(3x-8)

A = 3x² - 8²

A = 9x² - 64

hence the area of the given rectangle will be A = 9x² - 64 yards².

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The difference in rainfall between the wettest and driest months is 3.97 inches.

A bar graph is a graphical depiction of information, amounts, or numbers using bars or strips. They are utilized to contrast and compare various data types, frequencies, or other measurements of several categories of data.

On the graph, there are two axes. The numerical data is displayed against the category data on one axis, which is used to depict the numerical values.

Given the graph which shows the rainfall of the wettest and driest months,

here red blocks are for the driest months and blue blocks show the wettest months,

From the graph, we can see that the wettest month has a rainfall height of 2.3 inches

The driest month has a rainfall of -1.67 inches

So the difference between the two will be;

2.3 - (-1.67)

=  2.3 + 1.67 = 3.97 inches

Hence the difference is 3.97 inches.

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The complete question is,

The bar graph shows the differences in a city’s rainfall from the historical average. What is the difference in rainfall between the wettest and the driest months? Write your answer as a decimal.

The difference in rainfall between the wettest and the driest months is inches.

Answer: D. [tex]5\sqrt{3}[/tex]

Step-by-step explanation:

[tex]\tan 30^{\circ}=\frac{x}{15}\\\\x=15 \tan 30^{\circ}\\\\x=5\sqrt{3}[/tex]

The surface area of the pyramid, given the height and base of the triangles, and the area of the hexagonal base, is 439. 8 square inches

Let's determine the area of the six isosceles triangles using the formula;

= 6 x 1 /2 x base x height

= 6 x 1 / 2 x 10 x 6

= 180 square inches

The surface area of the pyramid is therefore;

= Area of triangles + Area of hexagonal base

= 180square inches + 259.8 square inches.

Add the values, we get;

= 439. 8 square inches

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Answer: 439.8

Step-by-step explanation:

x > -2

Inequalities compare the values of 2 expressions.

Solving for x

To solve the inequality, we need to isolate x. First, add 4 to both sides.

Then, divide by 5.

Finally, divide both sides by -1. When multiplying or dividing an inequality by a negative, switch the direction of the sign.

Interpreting the Answer

Verbally, the answer is that x is greater than or equal to -2. This means that any x-value greater than -2 (including -2 itself) will make the original inequality, −5x−4 ≤ 6, true. For example, let's plug in 0.

This statement is true, which proves our answer is correct.

answer is 2 because if we expand the bracket we get 2x–8y+3y which is 2x–5y but if it was 2(x+4y) it would be equal to 2x+8y+3y therefore being 2x+11y

Answer: 58.5

Step-by-step explanation: 65.00 - 10% = 58.5

Answer: $58.50

Step-by-step explanation: Orignal Price: $65.00

10% discount = -$6.50

$65.00 - $6.50 = $58.50.

Answer:

The length of 5 inches should be counted 1 time.

Step-by-step explanation:

The 5 inches between the triangle and rectangle is inside the shape. So, it doesn't count as perimeter.

Answer:

<YTZ

Step-by-step explanation:

Vertical angles are congruent.

<VTW measures 40°.

<YTZ is vertical to angle VTW.

m<YTZ = m<VTW

m<YTZ = 40°

Answer: <YTZ

The horizontal distance which the car must have travelled is equal to 450 meters.

Mathematically, the gradient (slope) of a geometric figure or line can be calculated by using this formula:

Pitch (slope) = V/H

Where:

Based on the given image, we have the following distances and gradient (slope):

Rising vertical distance = 60

Horizontal distance (Run) = x

Gradient (slope) = 2/15

Substituting the given parameters into the formula, we have;

2/15 = 60/x

2x = 900

x = 450

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The area for this figure is given as follows:

38.13 cm².

The composite area of the figure is obtained by the sum of the areas of each component of the figure.

The figure is composed as follows:

The area of the rectangle is given by the multiplication of the dimensions, hence:

Ar = 6 x 4 = 24 cm².

The area of the semicircle is given by half the multiplication of π = 3.14 by the radius square, hence:

As = 0.5 x 3.14 x 3² = 14.13 cm².

Hence the total area is given as follows:

A = Ar + As

A = 24 + 14.13

A = 38.13 cm².

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Answer:

x intercept: (0,0)

Step-by-step explanation:

y intercept: (0,0)

The required graph of the equation is given by y=x/2

Linear equations help in representing the relationship between variables such as x, y, and z, and are expressed in exponents of one degree. In these linear equations, we use algebra, starting from the basics such as the addition and subtraction of algebraic expressions.

Given here: A graph proportional to the line that passes through the point.

Now one of the graph has the equation y= x/2

we can treat this line as some proportional equation with 1/2 as the constant.

And it also passes through the point (2,1)

Hence, The required graph of the equation is given by y=x/2

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The options containing the graph are attached

The amount invensted at 5% and 7% are 3500 and 4500 respectively.

A set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.

Given that, an amount $8000, is invested at 5% and 7%, with annual interest is $490,

For this we will establish the a system of equations,

x + y = 8000......(i)

0.05x + 0.07y = 490

Multiplying by 100,

5x + 7y = 49000.....(ii)

Multiplying eq(i) by 5,

5x + 5y = 40000

Subtract eq(i) from eq(ii)

2y = 9000

y = 4500

Put y = 4500 in eq(i)

x = 8000 - 4500

x = 3500

Hence, the amount invensted at 5% and 7% are 3500 and 4500 respectively.

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The result of the product for the following pairs of number is irrational for 1. Option d √2(4). 2. Option a. 3. Option d. 4. Option b.

A real number that cannot be stated as a ratio of integers is said to be irrational; an example of this is the number √2. Any irrational number, such as p/q, where p and q are integers, q≠0, cannot be expressed as a ratio. Once more, an irrational number's decimal expansion is neither ending nor recurrent.

1. The product of the numbers are:

a. √2 (√8) = √16 = 4

b. √49 (∛ 8) = 14

c. √3 (2/ √3) = 2

d. √2(4)

Option d is the correct answer.

Similarly, taking the product:

2. Option a is correct.

3. Option d is correct.

4. Option b is correct.

Hence, the result of the product for the following pairs of number is irrational for 1. Option d √2(4). 2. Option a. 3. Option d. 4. Option b.

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Answer:The length of AC to one decimal place in the trapezium is 18.1 cm

Step-by-step explanation: Using Pythagoras theorem, we can find the length AC

Pythagoras theorem

c² = a² + b²

Therefore, draw a line from the point B to the line AD and call it line BX.

BX ║ CD

Therefore,

16² - 7² = BX²

256  - 49 = BX²

BX² = 207

BX = √207

BX = 14.3874945699

BX = 14.4 cm

Therefore,

11² + 14.4² = AC²

121 + 207.36 = AC²

AC = √328.36

AC = 18.120706388

AC = 18.1 cm

The difference in rainfall between the wettest and driest months is the amount of precipitation.

Precipitation refers to any form of moisture that falls from the atmosphere to the ground, including rain, snow, sleet, hail, and other forms of precipitation. Precipitation is an important aspect of the Earth's water cycle, as it provides the water that replenishes rivers, lakes, and aquifers, and sustains the growth of plants and animals.

The amount of precipitation that falls in a given area can vary widely, depending on many factors such as geography, temperature, and prevailing weather patterns. For example, areas near the equator tend to receive more rainfall than areas located closer to the poles, and areas with high elevations tend to receive more snow than areas that are closer to sea level.

The distribution of rainfall and other forms of precipitation across a region can also be affected by the prevailing winds, air masses, and topographical features. For example, mountainous areas may receive more rainfall due to the prevailing winds and the way that air masses interact with the terrain.

The difference in rainfall between the wettest and driest months is the amount of precipitation that occurs in the wettest month minus the amount of precipitation that occurs in the driest month. This difference can vary greatly depending on the location and climate of a region.

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Answer:

Nope

Step-by-step explanation:

No, because if you add the angles of B and C (since they're asking for line BC), they must equal the angles of A and D (Since the other line was AD)

The sum of B and C is 90+45 which = 135

The sum of A and D is 90+135 which = 225

135 =/= 225

Answer:

The base is 8 and the height is 3. Multiply.

8 * 3 = 24

You will then multiply your product by 1/2.

24 * 1/2 = 12

The area is 12 inches squared.

Step-by-step explanation:

Hope it helps! =D

Answer:

[tex] {12cm}^{2} [/tex]

Step-by-step explanation:

Given

[tex]a = \frac{1}{2} bh[/tex]

b= 8in

h= 3in

8x3 = 24

24 ÷ 2 (Same as multiplying by half)

The potential energy increases as the charges or the poles get further apart.

Static charges does not build up by polarization.

A field force is a force that acts on a particle without physical contact. It arises from the presence of a field, such as an electric field, magnetic field, or gravitational field.

The field exerts a force on a particle based on its charge, mass, or other property, and the strength of the force is determined by the field intensity and the properties of the particle. For example, an electric field exerts a force on a charged particle, while a gravitational field exerts a force on a mass.

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Answer:

A

Step-by-step explanation:

please memorize this formula for area of sphere

A=4π r²

so d = 22, which means r=11

so A = 4* π*11² = 4*121*π =484π = 1519.76