Are the triangles similar, if so what postulate can you use to prove similarity? *

The volume of the given cylinder would be = 4300 in³

The formula that can be used to calculate the volume of a cylinder = V= πr²h

where,

π = 3.14

r = 14

h = 7

volume = 3.14× 14² × 7

= 3.14× 196× 7

= 4308.08

= 4300 in³

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The length PR is given as follows:

PR = 337.75 ft.

Similar triangles share these two features:

The similar triangles for this problem are given as follows:

PRE and POC.

Hence the equivalent side lengths are given as follows:

Then the proportional relationship among the equivalent side lengths is given as follows:

x/165 = (x + 125)/255.

Applying cross multiplication, the length PR, represented by x, is obtained as follows:

255x = 165(x + 125).

225x = 165x + 20625

60x = 20265

x = 20265/60

x = 337.75 ft.

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Answer:

7.66

Step-by-step explanation:

Properties of triangle

'One inch represents 2,000 feet' is a verbal type scale.

The link between a length unit on a map and its corresponding length on the ground is known as the map scale. It will be beneficial for you to carefully study this section because we will use map scale principles throughout the course.

We can use three distinct scales to relate a map to the ground:

'One inch represents 2,000 feet' is an example of a Verbal scale. The relationship between a map distance and a ground distance is expressed verbally using a verbal scale.

Here, it is inferred that one inch on the map corresponds to 2000 feet on the ground. Popular atlases and maps frequently use verbal scales.

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Answer:

Below

Step-by-step explanation:

The ENTIRE perimeter of a circle is  pi * d

 a semi circle circumference is 1/2 of this  1/2 pi * d   PLUS the diameter line

               1/2 pi * ( 2 mm)  + 2mm = 5.14 mm

The value of 'x' in the expression (1/2)(4x - 5) + 5/2 = 10 is, x = 5.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, An expression  (1/2)(4x - 5) + 5/2 = 10.

(1/2)(4x - 5) = 10 - 5/2.

(1/2)(4x - 5) = (20 - 5)/2.

(1/2)(4x - 5) = 15/2. ('2' on both sides of the denominator cancels)

4x - 5 = 15.

4x = 20.

x = 5.

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Answer:

[tex]\frac{1}{9}[/tex] or 11.11%

Step-by-step explanation:

P(A) = probability of an event

f = favored outcomes

N = number of total outcomes

[tex]P(A)=\frac{f}{N}[/tex]

In this equation there is one favored income, when the first counter is blue and the second one is green. There are also nine total outcomes. This means that the equation necessary is:

[tex]P(A)=\frac{1}{9}[/tex]

The probability that Mike takes a blue counter and then Ellie takes a green counter is [tex]\frac{1}{9}[/tex] or around 11.11%

The two numbers are 7/6 and 5 when the sum of two numbers is 3 more than four times the first number.

Let's call the two numbers x and y, where x is the first number and y is the second number.

The problem gives us two equations that relate the two numbers:

[tex]x + y = 3 + 4x\\y - x = 2y - 10[/tex]

We can substitute the expression for y from equation 1 into equation 2:

[tex]y - x = 2(3 + 4x) - 10[/tex]

Expanding the right side and simplifying, we get:

[tex]y - x = 6 + 8x - 10\\y - x = 8x - 4[/tex]

Adding x to both sides:

[tex]y = 9x - 4[/tex]

Substituting this expression for y into equation 1:

[tex]x + (9x - 4) = 3 + 4x[/tex]

Expanding and simplifying the right side:

[tex]10x - 4 = 3 + 4x[/tex]

Subtracting 4x from both sides:

[tex]6x - 4 = 3[/tex]

Adding 4 to both sides:

[tex]6x = 7[/tex]

Dividing both sides by 6:

[tex]x = 7/6[/tex]

Substituting this value of x back into the expression for y:

[tex]y = 9x - 4 = 9 * (7/6) - 4 = 63/6 - 4 = 9 - 4 = 5[/tex]

So the two numbers are 7/6 and 5.

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Part 1:

Domain = (-2, -1, 0, 2)

Range = (-4, -2, 2)

Part 2:

Domain = (-4, -2, 1, 4)

Range = (-2, 1, 4)

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,

Part 1:

From the function figure:

All the x values are domain and all the y values are codomain.

All the y values that are an image of an x value are called the range.

So,

Domain = (-2, -1, 0, 2)

Range = (-4, -2, 2)

Part 2:

From the table:

All the x values are domain and all the y values are range.

So,

Domain = (-4, -2, 1, 4)

Range = (-2, 1, 4)

Thus,

The domain and range are given above.

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The area of the garden will be = 1512 square meters.

The formula for calculating the area of a rectangle.

Rectangle surface area. A = l × b.

Once the length and breadth of a rectangle are determined, the area is computed.

The area of a rectangle may be calculated by multiplying its length and width.

Let's assume the length of the garden is 6x meters and the width is 7x meters, where x is a positive value that we need to find.

From the given ratio, we have:

6x + 7x = 78

13x = 78

x = 6

So the length of the garden is 6 * 6 = 36 meters and the width is 7 * 6 = 42 meters.

The area of the garden can be calculated as: 36 * 42 = 1512 square meters.

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Above 700: 5%, Above 550: 34%, Between 400 and 550: 26%, Below 400: 16%, Below 550: 55%.

To calculate the fraction of students who scored above 700, we can use the z-score formula, which is (x - μ) / σ, where x is the score, μ is the mean, and σ is the standard deviation. In this case, μ = 500 and σ = 100. Plugging in 700 for x, we get (700 - 500) / 100 = 2. This corresponds to a z-score of 2, which is .9772, meaning that 97.72% of the scores are below 700. This means that 5% are above 700. To calculate the fraction of students who scored above 550, we can use the same formula, but with 550 for x. This gives us (550 - 500) / 100 = .5, which corresponds to a z-score of .5, meaning that 84% of the scores are below 550. This means that 34% are above 550. To calculate the fraction of students who scored between 400 and 550, we can subtract the z-score of 400 from that of 550. This gives us .84 - .2 = .64, meaning that 64% of the scores are below 550. This means that 26% are between 400 and 550.

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Answer:y

=

93

−

q

a

q

−

67

Step-by-step explanation:

Tthe population of the colony after 2 hours is 64a

From the question, we have the following parameters that can be used in our computation:

Rate = doubles every 20 minutes

Represent the initial population with a

So, we have the following representation

f(t) = a(2)^t

Where t is the number of 20 minutes in the time

The time is given as 2 hours

So, we have

t = 2 hours/20 minutes

Evaluate

t = 6

The function becomes

f(t) = a(2)^6

Evaluate

f(t) = 64a

hence, the population is 64a

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The value of the rationalization is 5√2

Surds are described as the nth root of a number, say x and a  number r which, when raised to the power n

Given that;

n is a positive integer or  the degree of the root.

It is also seen as an expression that includes a square root, a cube root or other roots.

They are used to write irrational numbers only.

Given the surds;

10/√2 × √2/ √2

Multiply the values

10√2/2

Divide the values

5√2

Hence, the value is 5√2

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The radius of the sphere is 42 feet.

The correct option is D.

Space occupied by an object in three dimensional space is called as volume of an object. In simple words space is taken by object.

Given:

A sphere has a volume of 2304π cubic feet.

The volume of sphere = 4/3 π r³

4/3 π r³ = 2304π

r³ = 1728

r = 41.6

r ≈ 42 feet.

Thererfore, the radius is 42 feet.

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The mean height of the four boys is 157657.75 centimeters.

The three main methods for identifying the average value of a set of integers are mean, median, and mode.

Adding the numbers together and dividing the result by the total number of numbers in the list yields the arithmetic mean.

The middle value in a list that is arranged from smallest to greatest is called the median.

The value that appears the most frequently on the list is the mode.

Given, Four boys have heights of 155155cm, 156156cm, 158158cm, and 162162cm.

Therefore, The mean height of the boys is the sum of the heights of boys divided by the total number of boys which is,

= (155155 + 156156 + 158158 + 162162)/4.

= 630631/4.

= 157657.75 cm.

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Let's call the number of hours spent on a job as "h". Then, the fee charged to the client can be represented as a function of "h" as follows:

f(h) = 30h + 40

This means that for any value of "h" (representing the number of hours spent on a job), the function f(h) gives the corresponding fee charged to the client.

Function notation is a mathematical notation used to express a mathematical function, which assigns a unique output to each input of a set. The function is represented by a symbol, usually a letter (such as f or g), followed by a variable in parentheses.

For example, the function f(x) = x^2 assigns the value x^2 to the input x. The input is usually referred to as the argument of the function. The function notation is commonly used in calculus, algebra, and other branches of mathematics.

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The probability of each team winning the tournament is A= 0,2 B= 0,2     C= 0,4 D=0,2

We know that only one team can win, so the sum of each probability of winning  is one

P(A)+P(B)+P(C)+P(D)=1

then we know that the probability of Team A and B are the same, so

P(A)=P(B)

And that the probability that either team A or team C wins the tournament is 0.6, so P(A)+Pc)= 0,6, then P(C)= 0.6-P(A)

Also, we know that team C is twice as likely to win the tournament as team D, so P(C)= 2 P(D) so P(D) = P(C)/2= (0.6-P(A))/2

Now if we use the first formula:

P(A)+P(B)+P(C)+P(D)=1

P(A)+P(A)+0.6-P(A)+(0.6-P(A))/2=1

0,5 P(A)+0.9=1

0,5 P(A)= 0,1

P(A)= 0,2

P(B)= 0,2

P(C)=0,4

P(D)=0,2

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Suppose that 90% of  batteries that are supplied from the certain supplier have acceptable voltages, probability that among all the batteries supplied least nine will work is 26 and 0.3076 .

M: Math

P: Physics

S: Statistic

n(Math) = 24

n(Physics) = 29

Formula:

Putting the values, we get,

Thus, 26 students took statistic.

Probability is basically  based on the possible chances or the chances of happening of something. The theoretical probability is a type of probability that is  mainly based on the reason behind that probability. For example, if a coin is tossed, the theoretical probability or the outcome of getting a head will be ½.

Probability is the branch of mathematics that basically concern about  the occurrence of a random event or the chances of favorable outcome and  there are mainly four  types of probability exist: classical, empirical, subjective and axiomatic.

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The bearing of the airport from the plane is calculated as; 245 degrees

The parameter given is that the bearing from the airport to the plane is 65 degrees.

From the the diagram I have attached, since the bearing from airport to plane is 65 degrees, we see that the bearing is calculated from North.

Thus, the 360° covering the North to the south in the clockwise direction is 180°

When the bearing required is from plane to bearing , the angle will be;

180 + 65 = 245 degrees

So the bearing from plane to airport will be = 245 degrees

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Answer:

The total average decrease in the stock after 8 weeks is -10 - 8 = -2 dollars.

Step-by-step explanation:

Answer:

you count from the top to the bottem

The area of triangle NOP is given as follows:

1416 cm².

The area of a triangle, given two side lengths and the angle between them, is given by the multiplication of the side lengths and the sine of the angle between them.

The parameters for this problem are given as follows:

Hence the area of the triangle is given as follows:

A = 92 x 23 x sine of 138 degrees

A = 1416 cm².

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There are a total of 10 different combinations for each of the four-letter words.

If reiteration is permitted

There are 10 possible combinations for each of the four letters, making a total of 104 four-letter words.

If reiteration is prohibited

The first letter has 10 potential outcomes, followed by 9 for the second, 8 for the third, and 8 for the fourth, for a total of 10 * 9 * 8 * 7 outcomes.

If the first letter must be A, there is only one alternative for that letter and ten possibilities for each of the following three letters, for a total of 103.

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The coordinates of another point with the same y-value are (10, 10).

The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.

The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.

We have,

f(x) = |x|

For (-10, 10)

i.e,

x = -10

f(-10) = |-10| = 10

So,

(-10, 10) is on the graph.

Now,

For x = 10,

f(10) = |10| = 10

This means,

(10, 10) is also on the graph.

We see that,

(-10, 10) and (10, 10) has the same y-value.

Thus,

The coordinates of another point are (10, 10).

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The number of permutations for the remaining hours is 6 hours.

Permutation is a mathematical concept that refers to the arrangement of objects or elements in a specific order. It is used to find the number of possible combinations of a given set of elements.

Let's assume that she takes exactly three hours of classes on Monday, two on Thursday, and one on Friday. Now, we have three hours left for Tuesday, Wednesday, and the rest of the week.

To find the number of permutations for the remaining hours, we can use the permutation formula, which is:

P(n, r) = n! / (n-r)!

Where n is the total number of items and r is the number of items being selected. In this case, n = 3 (hours left for Tuesday, Wednesday, and the rest of the week) and r = 3 (hours being selected).

So, the number of permutations for the remaining hours is:

P(3, 3) = 3! / (3-3)! = 6

Now, we have found the number of permutations for the remaining hours.

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Answer:

153.86

Explanation:

using 3.14 as pi and 7 as radius

type (3.14)7^2 into calculator