Round 16,360 to the nearest hundred.

The probability that exactly two of the three people selected also travel by train is 4/9

The probability of an event occurring is specified by the ratio of the number of  required outcomes to the number of possible outcomes.

The number of people that travelled from London to Manchester for the conference = 30

Number of people that traveled by train = 15

Number of people that travelled by plane = 9

Number of people that did not travel by travel by either train or plane = 12

Number of people chosen from those that traveled by plane = 3

The probability that two of those selected also traveled by train can be found as follows;

The number of people that traveled by either train of plane = 30 - 12 = 18

The number of people that traveled by plane and train = 15 + 9 - 18 = 6

The binomial probability distribution formula that can be used to find the probability of an event, p, occurring exactly r times is as follows;

P(p) = \(_nC_r\cdot p^r\cdot q^{n-r}\)

Where;

n = Number of people chosen = 3

r = Number of people chosen that also traveled by train = 2

p = Probability that a person chosen also traveled by train = 6/9 = 2/3

q = Probability that a person chosen did not travel by train = 3/9 = 1/3

Therefore;

\(P = _3C_2\times \left(\dfrac{2}{3}\right) ^2\times \left(\dfrac{1}{3} \right)^{3-2} = \dfrac{4}{9}\)

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Answer:

Sustitute the y-values into the equation.

For y=10,

2(10) + 3 (10 - 5)

20 + 3(5)

20+15

35

For y=57,

2(57) + 3 (57 - 5)

114 + 156

270

For y=35

2(35) + 3 (35 - 5)

70 + 3(30)

70 + 90

160

:)

Answer:

Step-by-step explanation:

monert

Answer:

rational

Step-by-step explanation:

Answer:

it's Rational Number

Step-by-step explanation:

since each integer can't be written in the fraction form or for this example it would be thus 5 so it would be a rational number

Answer:

-5.5m-4n+11.8

Step-by-step explanation:

Answer:

It would be the first option.

f(x) = -2 |x| + 1

The equation of the parabola is y = 2(x - 1)² + 3

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

Vertex = (1. 3)

Point = (2, 5)

These parameters can be expressed as

(h, k) = (1, 3)

(x, y) = (2. 5)

A parabola can be represented as

y = a(x - h)² + k

Substitute the known values in the above equation, so, we have the following representation

y = a(x - 1)² + 3

Next, we have

5 = a(2 - 1)² + 3

Evaluate the difference and the exponent

5 = a + 3

So, we have

a = 2

Substitute a = 2 in y = a(x - 1)² + 3

y = 2(x - 1)² + 3

Hence, the equation is y = 2(x - 1)² + 3

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Using the concept of probability, the probability that the first experiment is successful is 70.97%

To calculate the probability that the first experiment is successful, we use the relation thus :

Inserting the values into the formula :

Therefore, the probability value is 70.97%

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Answer:

x = - 2

Step-by-step explanation:

2x + 6 = 2

2x = 2 - 6

2x = -4

x = -4/2

x = - 2

Hope it helps ⚜

Considering the information about trees, The value of a is 5500

The value of r is calculated to be 0.92

In 1 October 2030 the number is 2022

A mathematical function called an exponential function is employed frequently in everyday life. It is mostly used to compute investments, model populations, determine exponential decay or exponential growth, and so on.

Exponential function is a type of function of the form: f(x) = a(b)^x. It is made up of  3 main parts

a = the starting or initial value

b = the base function

x = the exponents

Considering the given problem,  N = ar^t

the starting, a = 5500

the base, r =

the exponents = t

Solving for the base

N = ar^t

5500 = ar^t in 2018 t = 0

a = 5500

in 2019, t = 1

N = ar^t

5060 = 5500 * r

r = 5060/5500

r = 0.92

From 2018 to 2030 = 12 years, hence t = 12

N = 5500 * 0.92^12

N = 2,022.165132

N = 2022

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Answer:

do we put all numbers on one side

which is

-6=-6/4x

then we multiply by 4

-24=-6x

then divide by -6

x=4

Answer:

\(x=4\)

General Formulas and Concepts:

Step-by-step explanation:

Step 1: Define equation

\(2=8-\frac{6}{4} x\)

Step 2: Solve for x

Step 3: Check

Plug in x to verify it's a solution.

Answer:

It's quite easy

Step-by-step explanation:

people less than 30 years = frequency of people 0 to 15 + 15 to 30 = 8+15 =23

Therefore there are 23 people less than 30 years old.

pls mark me as brainliest pls.

The APR, or stated rate, is calculated as the annualized interest rate expressed as a percentage.

The APR, or stated rate, represents the annualized interest rate on a loan or investment, expressed as a percentage.

To calculate the APR, we need to consider the nominal interest rate and the compounding frequency. The formula to calculate the APR is:

APR = (1 + nominal interest rate/compounding periods)^(compounding periods) - 1

The nominal interest rate is the stated rate without taking compounding into account.

The compounding periods refer to the number of times interest is compounded in a year, typically based on daily, monthly, or quarterly periods.

By applying the formula and considering the appropriate compounding periods, we can determine the APR.

The APR is an important metric as it allows for easy comparison of interest rates across different financial products.

It helps consumers and investors understand the true cost or yield associated with a loan or investment and enables them to make informed decisions.

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Answer:

$7.20

Step-by-step explanation:

7.208

Step-by-step explanation: 20 % x 36.04  is equal to 7.208 because it's multiplying.

Answer:

imma celeb chek

Step-by-step explanation:

The area of a rectangle is given by:

where l is the length and w is the width. In this case we know that the area is 153 square ft and the width is 9 ft, plugging these values and solving for l we have:

Therefore, the length of the shed is 17 ft.

The value of x for the given expression of angles of a triangle is 2.

When a triangle is inscribed in a circle, there are several angle properties that can be derived from the relationship between the sides of the triangle and the angles formed at the points where the sides touch the circle. An angle inscribed in a semicircle is a right angle.

The sum of the two angles is 90°.

11x -4 + 16x + 40 = 90

27x + 36 = 90

27x = 54

x = 2

Therefore, the value of x for the given angles will be 2.

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The function g(x) = \(e^x^/^3\) has a fixed point x* by applying the Intermediate Value Theorem.

To show the existence of a fixed point, we can create a root-finding problem f(x) = 0, where f(x) = x - g(x). This problem is equivalent to finding a point x such that x = g(x), which represents the fixed point condition.

Let's consider the function f(x) = x - g(x). We want to show that there exists a value c such that f(c) = 0, which would imply the existence of a fixed point.

First, we observe that f(x) is continuous over the entire real line because both x and g(x) are continuous functions. Additionally, we can see that f(x) is negative for x < 0 and positive for x > 0.

Now, let's consider the values of f(x) at x = 0 and x = 1. We have f(0) = 0 - g(0) = 0 - \(e^0^/^3\) = 0 - 1 = -1, and f(1) = 1 - g(1) = 1 - \(e^1^/^3\) > 0.

Since f(x) is continuous and changes sign between x = 0 and x = 1, the Intermediate Value Theorem guarantees that there exists a value c between 0 and 1 such that f(c) = 0. This value of c represents the fixed point x* of the function g(x).

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Answer: 4

Step-by-step explanation:

Use the triangle to the right to find the measure of the side the two triangles share. That side is 8.06 roughly and squared it’s 65. I used the 65 to solve for b in a^2 + b^2 = c^2

65 + b^2 = 81

b^2 = 16

b = 4

Here is the answer:

75 - 40 = t

Brainliest pls

Answer:

75=T+40

35

Step-by-step explanation:

75=T+40 subtract 40 from both sides and we get 35

The longest possible altitude of the third altitude (if it is a positive integer) is 83.

According to statement

Let h is the length of third altitude

Let a, b, and c be the sides corresponding to the altitudes of length 12, 14, and h.

From Area of triangle

A = 1/2*B*H

Substitute the values in it

A = 1/2*a*12

a = 2A / 12 -(1)

Then

A = 1/2*b*14

b = 2A / 14 -(2)

Then

A = 1/2*c*h

c = 2A / h -(3)

Now, we will use the triangle inequalities:

2A/12 < 2A/14 + 2A/h

Solve it and get

h<84

2A/14 < 2A/12 + 2A/h

Solve it and get

h > -84

2A/h < 2A/12 + 2A/14

Solve it and get

h > 6.46

From all the three inequalities we get:

6.46<h<84

So, the longest possible altitude of the third altitude (if it is a positive integer) is 83.

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N(t) approaches 550.

The equation N(t) = 550 / (1 + 49e^(-0.7t)) models the number of people in a town who have heard a rumor after t days. The equation describes the growth of the number of people who have heard the rumor over time. The e^(-0.7t) term in the denominator represents the rate of decay or the slowing down of the spread of the rumor as t increases. As t increases without bound, the exponential term approaches 0, so the fraction approaches 550 / (1 + 49 * 0) = 550 / 1 = 550.

This means that as time goes on, the number of people who have heard the rumor will approach 550, the limit or maximum value of N(t). This value is not limited by any of the factors mentioned in the options (b) to (e).

The number of people who started the rumor is not given in the equation and cannot be determined from the information provided.

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Lol i forgot how to do this. Sorrryyy.

The net growth of of population of butterflies led to 560 butterflies.

We know that the population of butterflies is 500.

The population experiences a net growth of 12%.

The net growth can be defined as increase in number of individuals in a population .

So, the gain in the population of butterflies = 12% of 500= (12/100) × 500= 60 Butterflies

So, the new population of butterflies after the gain is 500 + 60 = 560 Butterflies.

This can be calculated by another method which is

112% of 500= (112/100)*500 = 560 butterflies

Hence, the required answer is 560 butterflies.

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We have reached an equation that is not true: 290 = 360. This means that our assumptions were incorrect and there is no solution to this system of equations that satisfies all the constraints

How to measure an angle?

a) To find the measure of angles B, C, and D, we can start by drawing a diagram of the bridge and labeling the angles:

      A

     / \

    /   \

   /     \

  /       \

 /         \

/           \

B             C

\           /

 \         /

  \       /

   \     /

    \   /

     \ /

      D

Since the bridge is perpendicular to the two towers, we know that angles B and C are both 90 degrees. Therefore, we can use the fact that the angles in a triangle add up to 180

degrees to find the measure of angle D:

angle D = 180 - angle A - angle B - angle C

       = 180 - 35 - 90 - 90

       = 180 - 215

       = -35

This is an invalid result, since angles cannot be negative. We made a mistake in assuming that angles B and C are both 90 degrees. In fact, they are not necessarily equal to each other, since the bridge may not be perfectly symmetrical. Let's call the measure of angle B x and the measure of angle C y. Then we can use the fact that the angles in a triangle add up to 180 degrees

to get an equation

:

angle A + angle B + angle C + angle D = 180

35 + x + y + angle D = 180

We also know that the sum of the angles around each tower is 360 degrees. Let's call the measure of angle E on one side of the bridge, and the measure of angle F on the other side. Then we can set up two more equations:

angle B + angle D + angle E = 360

x + angle D + angle F = 360

We have three equations and three unknowns (x, y, and angle D), so we can solve for them using

algebra

. First, we can rearrange the first equation to solve for angle D:

angle D = 180 - 35 - x - y

Then we can substitute this expression for angle D into the other two equations:

x + (180 - 35 - x - y) + angle F = 360

(180 - 35 - x - y) + angle E + 90 = 360

Simplifying these equations, we get:

145 - y + angle F = 360 - angle E

145 - x - y + angle E = 270

Now we have two equations and two unknowns (x and y), which we can

solve using

algebra. Let's rearrange the first equation to solve for angle F:

angle F = 360 - 145 + y - x

Substituting this expression for angle F into the second equation, we get:

145 - x - y + (180 - 35 - x - y) + 360 - 145 + y - x = 270

140 - 2x = 0

x = 70

Now we can substitute this value for x into the other equations to get:

angle D = 180 - 35 - x - y

      = 180 - 35 - 70 - y

      = 75 - y

angle F = 360 - 145 + y - x

      = 215 + y - 70

      = 145 + y

145 - y + angle F = 360 - angle E

145 - y + (145 + y) = 360 - angle E

290 = 360

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Answer:

D

Step-by-step explanation:

in this case, because it is being dilated by a factor of 2 this means that figure A´B´C´ will be double the size of its pre-image ABC.

each side will now be its double which means:

side A´C´= 10

side B´C´= 6

and side A´B´= 8

since the figure is only increasing its sides the angles of the right triangle remain the same.

<A= 37 degrees

The length of A'B' is, 8 units and the measure of angle A' is, 37 degree.

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

ΔABC is dilated by a factor of 2 to produce ΔA'B'C'.

Now, When the triangle undergoes dilation, the length of its sides gets multiplied by 2 (dilation factor) but the angles remain the same ( since, the shape has to remain same).

Thus, The length of A'B' is,

= 4 x 2

= 8

And, the measure of angle A' is, 37 degree.

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Approximately 34% of American adults have a mobile phone but not a landline, based on the given proportions from the study conducted by the Centers for Disease Control.

The proportion of American adults who have a mobile phone but not a landline, we need to subtract the proportion of those who have both a mobile phone and a landline from the proportion of those who have a mobile phone.

Let's denote the proportion of American adults who have a mobile phone as P(M), the proportion who have a landline as P(L), and the proportion who have neither as P(N).

Given information:

P(M) = 89% (proportion with a mobile phone)

P(L) = 57% (proportion with a landline)

P(N) = 2% (proportion with neither)

We can now calculate the proportion of adults who have a mobile phone but not a landline using the following equation:

P(M and not L) = P(M) - P(M and L)

To find P(M and L), we can subtract P(N) from P(L) since those who have neither are not included in the group with a landline:

P(M and L) = P(L) - P(N)

P(M and L) = 57% - 2%

P(M and L) = 55%

Now we can substitute the values back into the equation to find P(M and not L):

P(M and not L) = P(M) - P(M and L)

P(M and not L) = 89% - 55%

P(M and not L) = 34%

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Answer:

0.7 0.73 0.81 0.9

Step-by-step explanation:

hope this helps

The ratio (3 - 5)/(4 - 1) in the simplified form is -2/3.

Comparing two amounts of the same units and determining the ratio tells us how much of one quantity is in the other. Ratios can be divided into two categories. The part-to-whole ratio is one, and the part-to-part ratio is another. The part-to-part ratio illustrates the relationship between two separate entities or groupings.

Mathematicians use the term "ratio" to compare two or more numbers. It serves as a comparison tool to show how big or tiny an amount is in relation to another.

The given ratio is

(3 - 5)/ (4 - 1)

When we subtract a bigger number from a smaller number, we subtract the small number from the bigger one and put the sign before the result the sign of the bigger number. So,

= - 2 / 3

So, the simplified form of (3 - 5)/ (4 - 1) is -2/3.

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Given a linear operator T on a vector space V and an ordered basis {3}, we need to compute the matrix representation [T] with respect to this basis. Once we have the matrix [T], we can find its eigenvectors and eigenvalues

To address your question, we first need to understand the concepts involved:

1. A linear operator (T) is a function that maps a vector space V to itself, while preserving the structure of the space.
2. An ordered basis is a linearly independent set of vectors that spans the vector space V.
3. [T] is the matrix representation of the linear operator T with respect to the ordered basis.
4. Eigenvectors are non-zero vectors that satisfy the equation T(v) = λv, where λ is a scalar called an eigenvalue.

. If the eigenvectors of T form a basis for the vector space V (i.e., they are linearly independent and span the space), then we can say that F3 is a basis consisting of eigenvectors of T.

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Answer:

Step-by-step explanation:

The correct answer is:

the initial height of the plant

The y-intercept represents the point where the graph intersects the y-axis. In the context of a relationship between plant growth and time, the y-intercept would represent the initial height of the plant, which is the height of the plant at the start of the experiment, before any growth has occurred.