Measurements made by a surveyor with a total station carry errors. Based on previous measurements and when the weather is sunny, the errors made by a surveyor follow a lognormal distribution with a mean value of 5 mm and a standard deviation of 2 mm. When it is rainy, the measurement errors made by the surveyor are normally distributed with a mean of 6 mm and a standard deviation of 3 mm. For a particular construction project, errors of more than 10 mm during the measurement stage will result in extra costs from adjustments in materials and design. It is expected that the 35% of the time there will be rainy conditions during the measurement stage. Answer the following: a) Calculate the probability that measurement errors will result in extra costs (7 marks). b) If extra costs occur due to measurement errors, what is the probability that the measurements occurred during a sunny day? (3 marks). Note: to get full marks you must correctly answer all questions showing all your working and calculations not just your final answers.

Here are the matching pairs for the given question:

1. The smallest multiple that two or more given numbers have in common multiple

2. A number resulting from multiplying a given number by an integer solution

3. The least common multiple of two or more denominators Solve

4. The value(s) of a variable that will make an algebraic sentence true Least common denominator

5. The process for finding the solution(s) to an algebraic equation Least common multiple

1. Common Multiple - The smallest multiple that two or more given numbers have in common is known as the common multiple of those numbers.

2. Multiple - A number that results from multiplying a given number by an integer solution is known as a multiple.

3. Least Common Multiple - The least common multiple of two or more denominators is the smallest number that is a multiple of each denominator.

4. Least Common Denominator - The smallest common multiple of the denominators of two or more fractions is known as the least common denominator.

5. Least Common Multiple - The process for finding the solution(s) to an algebraic equation is known as the least common multiple.

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The present value, or the amount Jerry would need to deposit today, is approximately $47,120.23.

To calculate the amount Jerry would need to deposit today, we can use the formula for present value:

Present Value = Future Value / (1 + Interest Rate)ⁿ

Where:

Future Value is $85,000

Interest Rate is 8% (or 0.08 as a decimal)

n is the number of years, which is 9

Plugging in these values into the formula, we have:

Present Value = $85,000 / (1 + 0.08)⁹

Simplifying the expression:

Present Value = $85,000 / (1.08)⁹

Calculating this expression using a calculator or spreadsheet software, we find that the present value, or the amount Jerry would need to deposit today, is approximately $47,120.23.

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Answer:

Step-by-step explanation:

B. Because your domain is the number of songs someone will purchase

Answer:

y = - \(\frac{28}{5}\)

Step-by-step explanation:

Given y varies inversely with x then the equation relating them is

y = \(\frac{k}{x}\) ← k is the constant of variation

To find k use the condition y = 7 when x = - 4, then

7 = \(\frac{k}{-4}\) ( multiply both sides by - 4 )

- 28 = k

y = \(\frac{-28}{x}\) ← equation of variation

When x = 5 , then

y = \(\frac{-28}{5}\) = - \(\frac{28}{5}\)

As a result, if the two angles' measurements are (3y+11) and (11y+15) and they are congruent, then y must equal -1/2.

An angle is a geometric figure formed by two rays that have a common endpoint, called the vertex. The rays are also known as the sides or legs of the angle. Angles are typically measured in degrees, with a full circle measuring 360 degrees. Angles can also be measured in radians, which are another unit of angular measurement used in mathematics and physics. One radian is equal to the angle subtended by an arc of a circle that has a length equal to the radius of the circle. The size of an angle is determined by the amount of rotation that occurs between the two rays. This is typically measured relative to the positive x-axis, with counterclockwise rotations being considered positive and clockwise rotations being considered negative. Angles are used in a wide range of mathematical and scientific applications, including geometry, trigonometry, physics, engineering, and architecture. They are also used in many everyday situations, such as measuring the size of an opening or the angle of incidence of sunlight on a surface.

Here,

If the two angles are congruent, then they must have the same measure.

So we can set the expressions for the measures of the two angles equal to each other and solve for y:

3y + 11 = 11y + 15

Subtracting 3y from both sides:

11 = 8y + 15

Subtracting 15 from both sides:

-4 = 8y

Dividing both sides by 8:

y = -1/2

Therefore, if the measure of the two angles is (3y+11) and (11y+15) and they are congruent, then y must equal -1/2.

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Answer: 7.25/1

I think you are simplifying fractions so this should be the answer

Answer:

just do 4+2 then 6x9 the you get your top number then put 4 as the bottem number

Step-by-step explanation:

Answer:

∠ BAE = 29.5°

Step-by-step explanation:

the secant- secant angle BAE is half the difference of the measures of the intercepted arcs, that is

∠ BAE = \(\frac{1}{2}\) (BE - CD) = \(\frac{1}{2}\) (88 - 29)° = \(\frac{1}{2}\) × 59° = 29.5°

The total surface area of a rectangular prism with a base of 7, a height of 9, and another height of 3 can be calculated. The specific value will be provided in the explanation.

To find the total surface area of a rectangular prism, you need to calculate the sum of the areas of all its faces. A rectangular prism has six faces: a top face, a bottom face, two side faces, a front face, and a back face.

To calculate the area of each face, you multiply the length of one side by the length of an adjacent side. Given that the base has a length of 7, the height has a length of 9, and another height has a length of 3, you can calculate the areas of the faces.

The top and bottom faces have areas of 7 * 9 = 63 square units each. The two side faces have areas of 7 * 3 = 21 square units each. The front and back faces have areas of 9 * 3 = 27 square units each.

To find the total surface area, you add up the areas of all the faces: 63 + 63 + 21 + 21 + 27 + 27 = 222 square units.

Therefore, the total surface area of the rectangular prism is 222 square units.

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Answer:

37.5%

Step-by-step explanation:

Answer:

37.5%

Step-by-step explanation:

Answer:

62.5 miles per hour

Step-by-step explanation:

Assuming she had the same speed the whole time and never stopped, just divide the miles driven by the time to get miles per hour. 437.5/7 = 62.5, so she drove 62.5 miles per hour.

Hopefully this helps- let me know if you have any questions!

Answer:

0.67  cents

Step-by-step explanation:

Answer:

230 text messages

Answer:

Volume of wheat = 147.26 m³ (check the explanation)

Step-by-step explanation:

The question still lacks some details such as the size of the silo. We will go forward by assuming the size of the silo to aid our calculation. Silos are cylindrical storage structures that range from 3 - 27 m in diameter and 10 - 90 m in height. For the purpose of this question, let's assume that the size of the silo is 5 m (diameter) by 15 m (height).

Let's list out the parameters to be used:

diameter (D) = 5 m; r = D ÷ 2 ⇒ r = 5/2 = 2.5 m,

height (h) = 15 m

Volume of silo = πr²h = π * 2.5² * 15

V (silo) = 294.52 m³

The silo is half full ⇒ ½ * V

Volume of wheat stored is given by half of the silo volume, since the silo is half-full

V (wheat) = ½ * 298.52

V (wheat) = 147.26 m³

Part a

Let \(a=2\). Then, we have that

\(7+2=\sqrt{7b+c}\\\\81=7b+c\)

We can let \(b=11\) and \(c=4\), meaning the equation is \(x+2=\sqrt{11x+4}\).

Part b

\(x+2=\sqrt{11x+4}\\\\x^2 +4x+4=11x+4\\\\x^2 -7x=0\\\\x(x-7)=0\\ \\ x=0, 7\)

Substituting both of these values into the equation, we see they are both solutions.

Part c

\(x+10=\sqrt{10x+219}\)

Answer:

20:10 10 hours

Step-by-step explanation:

10:5 * 2 = 20:10 or 10:5 / 5 : 2:1 * 20 = 20:10

The volume of the remaining portion of the sphere is 2.096 cubic units.

Let's take the volume of the remaining portion of the sphere = V

The volume of the sphere = \(\frac{4}{3}\) * π * \(r^3\)

The volume of the sphere with radius 1  = 4/3 * π

The volume of the cylinder = π * \(r^2\) * h

The volume of the cylinder with height 2 and radius 1 = π * \(r^2\) * h = 2 * π.

The difference between the volume of the sphere and the cylinder is

V = 4/3 * π - 2 * π = 4/3 * π - 2 * π = 2/3 * π.

By taking π = 3.14

V = \(\frac{2}{3}\) * 3.14

V= 2.096.

So, the volume of the remaining portion of the sphere is 2.096 cubic units.

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Answer:

number of 1 pointers = 19

number of 2 point shots = 35

Step-by-step explanation:

let the number of 1 point shots be x

let the number of 2 point shots be y

x+y=54 (1)

x+2y=89(2)

Subtract (1) from (2)

y = 35

from (1)x = 54 - y = 54-35 = 19

checking : 19 + 35 = 54 ; and 19 + 2*35 = 89

Brainliest? ^^

Answer:

x^2 + 6x + 8

Step-by-step explanation:

area of blue = x^2

area of pink= 2x

area of green=4x

area of brown=8

Adding all the area.

we get : x^2 + 6x +8

Answer:

IM NOT SURE SHAWTY BAE

Step-by-step explanation:

Answer:

hmm very diffecult.

Step-by-step explanation:

if f (x) = StartRoot

The net of a triangular prism consists of two triangles and three rectangles.

In the net of a triangular prism, we can observe two types of polygons: triangles and rectangles.

First, let's discuss the triangles.

A triangular prism has two triangular faces, which are congruent to each other.

These triangles are equilateral triangles, meaning they have three equal sides and three equal angles.

Each of these triangles contributes two polygons to the net, one for each face.

Next, we have the rectangles.

A triangular prism has three rectangular faces that connect the corresponding sides of the triangular bases.

These rectangles have opposite sides that are parallel and equal in length.

Each rectangle contributes one polygon to the net, resulting in a total of three rectangles.

To summarize, the net of a triangular prism consists of two equilateral triangles and three rectangles.

The triangles represent the bases of the prism, while the rectangles form the lateral faces connecting the bases.

Altogether, there are five polygons in the net of a triangular prism.

It's important to note that the dimensions of the polygons may vary depending on the specific size and proportions of the triangular prism, but the basic shape and number of polygons remain the same.

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Answer:

10th number in the sequence is 786432

n = 4

Step-by-step explanation:

Multiply the following number by 4 (starting at #4) until you reach the 10th number in the sequence

Answer:

Los números son:

43 y 165

Step-by-step explanation:

Planteamiento:

a + b = 208

a - b = 122

Desarrollo:

de la segunda ecuación del planteamiento:

a = 122 + b

sustituyendo este último valor en la primer ecuación del planteamiento:

(122+b) + b = 208

2b = 208 - 122

2b = 86

b = 86/2

b = 43

a = 122 + b

a = 122 + 43

a = 165

Comprobación:

165 + 43 = 208

165 - 43 = 122

Answer:

There are 2 solutions to square root x = 9

They are 3, and -3

Step-by-step explanation:

The square root of x=9 has 2 solutions,

The square root means, for a given number, (in our case 9) what number times itself equals the given number,

Or, squaring (i.e multiplying with itself) what number would give the given number,

so, we have to find the solutions to \(\sqrt{9}\)

since we know that,

\((3)(3) = 9\\and,\\(-3)(-3) = 9\)

hence if we square either 3 or -3, we get 9

Hence the solutions are 3, and -3

For the growth model function is given by f(x) = 0.01(2)ˣ , average rate of change for the difference from day 8 to 3 is f(8) - f(3) = 2.48.

As given in the question,

Growth model of investing money is given by function:

f(x) = 0.01(2)ˣ

Where 'x' is the number of days

Approximately the average rate of change for the difference from day 8 to 3

f(8) - f(3)

= 0.01(2)⁸ - 0.01(2)³

= 0.01 (2)³(2)⁵ - 0.01(2)³

= 0.01(2)³ [ 2⁵ -1]

= 0.01(2)³ [ 32 -1]

= 0.01 × 8 × 31

= 2.48

Therefore, for the growth model function is given by f(x) = 0.01(2)ˣ , average rate of change for the difference from day 8 to 3 is equal to  f(8) - f(3) = 2.48.

The complete question is:

Terrance has invested money in a technology stock its growth is modeled by the function f(x) = 0.01(2)ˣ, where x represents number of days. Calculate the approximate average rate of change from day 3 to day 8.

0.496

2.016

2.48

5

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We can put the values in the equation to find the bearing: SBx = cot(98°20'06'') + cot(38°36'38'') / tan(50°54'26'') x tan(75°47'12'')SBx = 1.0802⇒ SBx = 47°06'05''So, the bearing of BCD is SB47∘06′05′′.Hence, option (c) is the correct answer.

The angle at point B.ABC = angle at B = 66∘36′10′′Azimuth AB = 343∘26′14′′, thus angle from South in a clockwise direction is 180 - 343∘26′14′′ = 16∘33′46′′. Given that the bearing of AB = SB 3∘08′24′′ W. Thus angle between AB and SB = 90° - 3∘08′24′′ = 86∘51′36′′. Using the Law of sines we can calculate the distance BD sin(BDC) = BD / BDC sin(180° - ABC - BDC) = BD / BC. Calculating BC Because BC is common, so we will use the angle BCD and angle ABCBD = BC x [sin(180° - ABC - BDC) / sin(BDC)]BD = BC x [sin(ABC + BDC) / sin(BDC)]BD = BC x BD = BC x BD = BC x [sinABCcotBDC + cosABC].

To calculate the required bearing, we need to calculate angle ABD.ABD = 180° - angle ABC - angle BCDABD = 180° - 66∘36′10′′ - 38∘36′38′′ABD = 75∘47′12′′Now we can calculate the bearing of BD. Let SBx be the bearing of BD, then⇒ tanSBx = BD / AB⇒ tanSBx = BC x [sinABCcotBDC + cosABC] / ABtanSBx = sinABCcotBDC + cosABC / cosABC / sinABCtanSBx = cotBDC + cotABC / tanABCcotSBx = 1 / (tanABCtanBDC)

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The eye color of people on commercial aircraft flights is not a random variable.

What is random variable?

Random variables are variables that can take on different values based on the outcome of a random event or experiment.

However, eye color is a characteristic of individuals and does not vary randomly within a specific context, such as being on a commercial aircraft flight. Eye color is determined by genetic factors and does not change during a flight or as a result of being on a flight.

Eye color is a categorical variable that represents the color of an individual's eyes, such as blue, green, brown, or hazel. While it is not a random variable in the context of commercial aircraft flights, it can still be observed and recorded as a characteristic of the passengers on the flight.

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The equation to estimate a person's height (in cm) at any given age x (in years) after age 30:

h(x) = h(30) - 0.06(x - 30)

What is the rate?

A rate is a measure of the amount of change of one quantity with respect to another quantity. It is expressed as a ratio of two different units, and it indicates how fast or slow one quantity is changing in relation to another quantity.

If we assume that a person's height decreases by 0.06 cm per year starting at age 30,

we can use the following equation to estimate a person's height (in cm) at any given age x (in years) after age 30:

h(x) = h(30) - 0.06(x - 30)

where h(30) represents the person's height at age 30.

This equation assumes that the rate of height decrease is constant and linear over time.

Hence, the equation to estimate a person's height (in cm) at any given age x (in years) after age 30:

h(x) = h(30) - 0.06(x - 30)

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Answer: 4.15 degrees

Step-by-step explanation:

-6 + 6.5 + 3.9 - 4/25 = -6 + 6.5 + 3.9 - 0.25 = 4.15 degrees (assuming that the am in the fourth sentence is a typo)