Given that
y
= 6 cm and
θ
= 55°, work out
x
rounded to 1 DP.
x rounded to 1 decimal place is approximately 3.4 cm.
To work out the value of x, we can use the trigonometric function cosine (cos).
The cosine of an angle is defined as the ratio of the length of the adjacent side to the length of the hypotenuse in a right triangle.
In this case, the length of the adjacent side is
x, and the length of the hypotenuse is 6 cm.
The given angle θ is 55°.
Using the cosine function, we have:
\(cos(\theta ) =\frac{adjacent }{hypotenuse}\)
\(cos(55^{\circ}) =\frac{x}{6}\)
To solve for x, we can rearrange the equation:
\(x = 6 \times cos(55^{\circ})\)
Now we can calculate x using the given values:
\(x \approx 6 \times cos(55^{\circ})\)
\(x \approx 6 \times 0.5736\)
\(x \approx 3.4416\)
Therefore, x rounded to 1 decimal place is approximately 3.4 cm.
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Solve for the unknown angle
Answer:
30
Step-by-step explanation:
Orange gray produce 133,952 oranges. If a crate holds 92 oranges, how many crates were needed for shipping? (Write operation and answer) no links
Answer:
1,456 crates needed
Step-by-step explanation:
oranges = 133,952
crate capacity = 92
133,952 / 92 = 1,456 crates needed
Please answer the question will mark brainliest.., graph the equation
Answer:move the midle dot 1 left move the other one to the x
Step-by-step explanation:
Please help me on my assignment I have to do it before taking the test
Answer:
26
Step-by-step explanation:
w = 5 so 7w is 7 x 5 = 35 and x = 9 so it’s 35 - 9 which is 26
What Is The Inverse Function Of Lnx, And What Are Its Domain D And Range R ? What Is The Inverse Function Of Lnx ? (Type An Expression Using X As The Variable.) What Is The Domain D Of The Inverse Function Of Lnx ? D= (Simplify Your Answer. Type Your Answer In Interval Notation.) What Is The Range R Of The Inverse Function Of Lnx ? R= (Simplify Your Answer.
The inverse function of ln(x) is y = e^x, and its domain (D) is (-∞, +∞), and its range (R) is (0, +∞).
The inverse function of ln(x) is e^x. The domain (D) of the inverse function e^x is the range (R) of the original function ln(x), and the range (R) of the inverse function e^x is the domain (D) of the original function ln(x).
First, let's find the inverse function of ln(x) by swapping the roles of x and y and solving for y:
x = ln(y)
e^x = e^(ln(y))
e^x = y
So, the inverse function of ln(x) is y = e^x.
Now, let's determine the domain (D) and range (R) of the inverse function e^x:
The domain (D) of e^x is the set of all real numbers since the exponential function is defined for all real values of x.
The range (R) of e^x is the set of all positive real numbers (excluding zero) since the exponential function always yields positive values. In interval notation, the range is (0, +∞).
Therefore, the inverse function of ln(x) is y = e^x, and its domain (D) is (-∞, +∞), and its range (R) is (0, +∞).
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Which equations have a lower unit rate than the rate represented in this table?
х у
6 2
12 4
18 6
y=3/11x
y=2/5x
y=9/23x
y=4/13x
y=3/8x
Answer:
A and DStep-by-step explanation:
Find the unit rate of the data in the table:
y = kx2 = 6kk = 2/6k = 1/3The equation is:
y = 1/3xCompare this with the others:
A. 3/11 < 1/3 = 3/9 ⇒ yesB. 2/5 > 1/3 = 2/6 ⇒ noC. 9/23 > 1/3 = 9/27 ⇒ noD. 4/13 < 1/3 = 4/12 ⇒ yesE. 3/8 > 1/3 = 3/9 ⇒ noFind. rate
m=4-2/12-6m=2/6m=1/3Only first one and 4the one have lower unit rate
y=3/11xy=4/13xA dishonest shopkeeper marks his goods 40% above the cost price and gives a 25% discount to customers. at time of selling the goods uses a false 1kg of weight which actually weighs 800gm find his profit
The dishonest shopkeeper marks his goods with a 40% markup and offers a 25% discount to customers. The profit earned by the shopkeeper on this particular item is $105 - $100 = $5.
Let's consider the cost price of an item to be $100. The shopkeeper marks it up by 40%, which results in a selling price of $140. However, the shopkeeper then offers a 25% discount on this inflated price, bringing the price down to $105.
Now, regarding the weight manipulation, the shopkeeper falsely claims that the weight of the item is 1kg. However, in reality, it weighs only 800g. Since the selling price is determined based on weight, the customer is paying the price of 1kg while receiving only 800g of the item.
To calculate the profit, we need to subtract the cost price from the selling price. The selling price, taking into account the discount and weight manipulation, is $105. The cost price is $100. Hence, the profit earned by the shopkeeper on this particular item is $105 - $100 = $5.
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Find the length of side x in simplest radical form with a rational denominator. URGENT HELP 50 PTS
Answer: x = 2√3.
Step-by-step explanation:
\(x^{2} +6^{2} =(2x)^{2}\\\\x^{2} +36=4x^{2} \\\\4x^{2}-x^{2} -36=0\\\\3x^{2} -36=0\\\\3(x^{2} -12)=0\\\\x^{2} -12=0\\\\x^{2} =12\\\\x=\sqrt{12} =2\sqrt{3}\)
Finding the missing length in a figure
Answer:
6 ft
Step-by-step explanation:
Marian Plunket owns her own business and is considering an investment. if she undertakes the investment, it will pay $28,000 at the end of each of the new 3 years. the opportunity requires an initial investment of $7,000 plus an additional investment at the end of the second year of $35,000. what is the NPV of this opportunity if the interest rate is 8% per year? Should Marian take it?
The NPV is positive, it is worth taking the Investment.
Net Present Value (NPV) is an assessment method that determines the attractiveness of an investment. It is a technique that determines whether an investment has a positive or negative present value.
This method involves determining the future cash inflows and outflows and adjusting them to their present value. This helps determine the profitability of the investment, taking into account the time value of money and inflation.The formula for calculating NPV is:
NPV = Σ [CFt / (1 + r)t] – CIWhere CFt = the expected cash flow in period t, r = the discount rate, and CI = the initial investment.
The given problem can be solved by using the following steps:
Calculate the present value (PV) of the expected cash inflows:
Year 1: $28,000 / (1 + 0.08)¹ = $25,925.93Year 2: $28,000 / (1 + 0.08)² = $24,009.11Year 3: $28,000 / (1 + 0.08)³ = $22,173.78Total PV = $72,108.82
Calculate the PV of the initial investment: CI = $7,000 / (1 + 0.08)¹ + $35,000 / (1 + 0.08)²CI = $37,287.43Calculate the NPV by subtracting the initial investment from the total PV: NPV = $72,108.82 – $37,287.43 = $34,821.39
Since the NPV is positive, it is worth taking the investment.
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Can someone help me I really don’t understand this..
Answer:
this would be the answer 4.66666667 but when rounded it would be 5 or 4.7
Step-by-step explanation:
brainliest ???
1)
2 points
A school lunch menu is posted in the cafeteria as shown below. Phoebe selects 1
food item and 1 drink at random. What is the probability she chooses a hamburger
with juice?
Food
hamburger
pizza
chicken nuggets
Drinks
milk
juice
Your answer
Answer:
81
Step-by-step explanation:
If i have 2 lemons and i give 1 away. how many do i have now?
.The first term of a sequence along with a recursion formula for the remaining terms is given below. Write out the first ten terms of the sequence.
a1 = 1, an+1 = nan/n+3
The first term of a sequence along with a recursion formula for the remaining terms is given below: a1 = 1, an+1 = nan/n+3.
We need to write out the first ten terms of the sequence.
Here is the solution;
First term, a1 = 1
Second term, a2 = a1+1 = (a1*n)/(n+3) = (1*n)/(n+3) = n/(n+3)
Third term, a3 = a2+1 = (a2*n)/(n+3) = (n/(n+3)*n)/(n+3) = n²/((n+3)²)
Fourth term, a4 = a3+1 = (a3*n)/(n+3) = (n²/((n+3)²)*n)/(n+3) = n³/((n+3)³)
Similarly, we continue to get the next term as a5 = (n^4)/((n+3)^4)a6 = (n^5)/((n+3)^5)a7 = (n^6)/((n+3)^6)a8 = (n^7)/((n+3)^7)a9 = (n^8)/((n+3)^8)a10 = (n^9)/((n+3)^9)
Thus, the first ten terms of the sequence are: a1 = 1a2 = n/(n+3)a3 = n²/((n+3)²)a4 = n³/((n+3)³)a5 = (n^4)/((n+3)^4)a6 = (n^5)/((n+3)^5)a7 = (n^6)/((n+3)^6)a8 = (n^7)/((n+3)^7)a9 = (n^8)/((n+3)^8)a10 = (n^9)/((n+3)^9)
A recursion formula, also known as a recursive formula or recurrence relation, is a mathematical equation or definition that expresses the terms of a sequence or function in terms of previous terms. It is a way to define a sequence or function recursively, where each term depends on one or more previous terms.
Recursion formulas can also be used to define functions recursively. In this case, the recursion formula expresses the value of the function at a given point in terms of its values at previous points.
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Identify the coordinates of triangle ABC when it is dilated by a scale factor of 2 from the origin (0,0).
Answer:
\(A' = (-4,4)\)
\(B' = (2,6)\)
\(C' = (2,0)\)
Step-by-step explanation:
Given [Missing from the question]
\(A = (-2,2)\)
\(B= (1,3)\)
\(C= (1,0)\)
\(k = 2\) --- scale factor
Required
The new coordinates
The new coordinate is calculated by:
\(New = Old * k\)
So, we have:
\(A' = A * 2\)
\(A' = (-2,2) * 2\)
\(A' = (-4,4)\)
\(B' = B * 2\)
\(B' = (1,3) * 2\)
\(B' = (2,6)\)
\(C' = C * 2\)
\(C' = (1,0) * 2\)
\(C' = (2,0)\)
help me
I need someone..
plsss..
please help me please help me
Answer:
the answer is 1
Step-by-step explanation:
(√4 / √6) + (√6 / √4)
(2 / 2√3) + (2√3 / 2)
√3 / √3
= 1
Draw an enhanced entity-relationship diagram for the following case.
AutoPlanet is a company that sells and services cars and light trucks through a nationwide network of dealerships. Each dealership is authorized to both sell and service both cars and light trucks. AutoPlanet intends to develop a new information system to improve its competitiveness.
Each dealership is identified by a unique dealership number assigned by AutoPlanet. The company also wants to store the dealership’s address, phone number, and the name of its general manager. AutoPlanet want to have good relations with the cities in which its dealerships are located. For each such city, identified by state and city names, it wants to store the name of its mayor, the address of its city hall, and its main telephone number. There can be more than one AutoPlanet dealership in a city.
AutoPlanet wants to keep track of each dealership’s employees. AutoPlanet assigns each employee an employee number that is unique across the country. It also wants to maintain each employee’s name, home address, and cell phone number. Employees have dependents (spouse and children) and the company stores their names, ages (for insurance purposes), and gender. Some employees have no dependents.
There are several categories of employees, two of which are salesperson and mechanic. It is possible than an employee functions in more than one category. In addition to the common data about employees, AutoPlanet wants to store the year a salesperson was hired and the salesperson’s sales commission percentage. Some salespersons are sales managers who manage other salespersons while also selling cars, themselves. All mechanics are required to attend periodic training programs. These programs are identified by a unique name, cost, and length in days. AutoPlanet wants to maintain the dates that a mechanic took a particular course and the grade that the mechanic received at the end of it.
There are only two types of mechanics: car mechanics and light truck mechanics. All mechanics are restricted to working only on the type of vehicles (i.e. cars or light trucks) that they specialize in. For car mechanics, the company wants to record the mechanic’s current salary; for light truck mechanics the company wants to record the mechanic’s skill rating.
Beyond what has been described above, AutoPlanet wants to focus on car sales for now and will add light truck sales at a later time. Each car is uniquely identified by its vehicle identification number (VIN), plus its model and year of manufacture. Customers are identified by a unique customer number assigned by AutoPlanet, plus their name, address, and telephone number. AutoPlanet wants to record which salesperson sold which car to which customer, including the date of the sale and the selling price.
The enhanced entity-relationship (EER) diagram for AutoPlanet's information system includes entities such as Dealership, City, Employee, Dependent, Category, Training Program, Mechanic, Car, Customer, and more. The diagram also includes attributes for each entity, capturing relevant information like addresses, phone numbers, employee numbers, and sales commission percentages.
The enhanced entity-relationship (EER) diagram for AutoPlanet's information system captures the entities and relationships involved in the system. The main entities in the diagram are Dealership, City, Employee, Dependent, Category, Training Program, Mechanic, Car, Customer, and Salesperson.
The Dealership entity is identified by a unique dealership number and stores information such as address, phone number, and the name of the general manager. The City entity is identified by state and city names and stores data about the mayor, city hall address, and telephone number.
The Employee entity has attributes like employee number, name, home address, and cell phone number. Employees can have dependents, represented by the Dependent entity, which stores their names, ages, and gender. The Category entity represents the different employee categories, such as salesperson and mechanic.
The relationships between entities include Employee-Dependent (one-to-many), Employee-Category (many-to-many), Salesperson-Car (many-to-many), Mechanic-Training Program (many-to-many), and more.
The Car entity is identified by its vehicle identification number (VIN) and includes attributes for model and year of manufacture. The Customer entity is identified by a unique customer number and stores information like name, address, and telephone number. The Salesperson entity is linked to the Car and Customer entities, capturing data about which salesperson sold a car to a customer, along with the sale date and selling price.
The EER diagram provides a visual representation of the entities, relationships, and attributes in AutoPlanet's information system, allowing for a better understanding of the system's structure and data flow.
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write the equation of the line from the given information. through (-3,5) & (4,-2)
Answer:
y = -x + 2
Step-by-step explanation:
(-3,5) and (4,-2)
Slope: (-2-5)/(4 - - 3) = -7/7 = -1
y-intercept= -2 - (-1)(4) = -2 + 4 = 2
300X256+350=
HELP ME FASTTTT
Answer: 77150
300*256+350 = 77150
Hope this helped =)
Answer: 77150300*256+350 = 77150
Step-by-step explanation: hope this helps <3
what does the following indicate in a genogram:
1. square
2. circle
3. solid horizontal line
4. broken line
5. X through a square/circle
6. solid verticle line
In a genogram, various symbols and lines represent different aspects of a person's familial relationships and attributes. Here's a breakdown of the symbols you mentioned:
1. Square: A square in a genogram indicates a male individual. It represents the person's gender and is used to distinguish between male and female family members.
2. Circle: A circle in a genogram indicates a female individual. It represents the person's gender and is used to distinguish between male and female family members.
3. Solid horizontal line: A solid horizontal line in a genogram represents a marital relationship between two individuals. The line connects a square (male) and a circle (female) to show that they are married or in a committed partnership.
4. Broken line: A broken line in a genogram represents a non-blood relationship, such as an adoptive parent-child relationship or a step-sibling connection. It is used to show relationships that are not based on biological ties.
5. X through a square/circle: An X through a square or a circle indicates that the individual is deceased. This symbol is used to show that the person has passed away and is no longer living.
6. Solid vertical line: A solid vertical line in a genogram represents a parent-child relationship. It connects an individual (either a square or circle) to their parent(s), showing the biological connection between the family members.
These symbols and lines help provide a visual representation of a person's family history and relationships, making it easier to analyze and understand the various connections within a family tree.
Overall, a genogram is a visual representation of a family tree that includes important information about relationships, health issues, and other relevant details. By understanding the various symbols and indicators used in a genogram, it is possible to gain a deeper understanding of family dynamics and relationships, as well as potential risk factors for various health conditions. As such, genograms are an important tool for healthcare providers, therapists, and other professionals working with individuals and families.
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Help please asap please and thank you
Answer:
The second one
Step-by-step explanation:
the second one
The 15 Point Project Viability Matrix works best within a _____ structure.
A. DMADV
B. DMAIC
C. Manufacturing
D. Service
The 15 Point Project Viability Matrix is a tool used to assess the feasibility and viability of a project. It consists of 15 key factors that should be considered when evaluating a project's potential success., the 15 Point Project Viability Matrix works best within a DMAIC structure.
DMAIC is a problem-solving methodology used in Six Sigma that stands for Define, Measure, Analyze, Improve, and Control. The DMAIC structure provides a framework for identifying and addressing problems, improving processes, and achieving measurable results. By using the 15 Point Project Viability Matrix within the DMAIC structure, project managers can systematically evaluate the viability of a project, identify potential risks and challenges, and develop strategies to overcome them. This approach can help ensure that projects are successful and deliver value to the organization.
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can someone please help me i dont know the answer.
What is the sum of 9 of the interior angles of a regular dodecagon?
Answer:
1350
Step-by-step explanation:
A regular dodecagon has 12 congruent sides.
Find the sum of the interior angles:
180∘⋅ (12−2)= 180∘ ⋅10
= 1800 /12 = 150∘
Divide the sum of the interior angles by the number of interior angles
Multiply by 9:
150 ∘ ⋅9= 1350
The sum of 9 angles of a regular dodecagon is 1350
The sum of 9 interior angles of the dodecagon is A = 1350°
What is the sum of the interior angles of a polygon?The sum of the interior angles of a polygon is given by the formula
Sum of Interior angles of a polygon with n sides is
nθ = 180 ( n - 2 )
where n is the number of sides
θ = angle in degrees
Given data ,
Let the polygon be represented as P
Now , P = dodecagon
The number of sides for P = 12 sides
And , sum of interior angles = (n - 2) x 180° , where n is the number of sides
The sum of interior angles = (12 - 2) x 180°
The sum of interior angles = 10 x 180°
The sum of interior angles = 1800°
To find the sum of 9 of the interior angles, we can divide the total by 12 (the number of angles in the dodecagon) and then multiply by 9:
The sum of 9 interior angles = (9/12) x 1800°
The sum of 9 interior angles = 1350°
Hence , the sum of 9 of the interior angles of a regular dodecagon is 1350°
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What is the distance between 4.5 and - 3.75
The volume of the large cube is 125 cubic inches. The volume of the small cube is 27 inches. What is the difference between the length of one side of the large cube and the length of one side of the small cube?
Answer:
2cmStep-by-step explanation:
Step one:
given data
for the large cube
the volume= 125cm^3
we know that volume = l*l*l
volume=l^3
we want to find l, so we have to cube both sides
125=l^3
l=∛125
l=5cm
Step two:
given data
for the large cube
the volume= 27cm^3
we know that volume = l*l*l
volume=l^3
we want to find l, so we have to cube both sides
27=l^3
l=∛27
l=3cm
The difference between the length of one side of the large cube and the length of one side of the small cube=5-3= 2cmlim x→π/6 {x^2/tanx}
The limand is continuous at x = π/6, so by direct substitution
\(\displaystyle \lim_{x\to\pi/6} \frac{x^2}{\tan(x)} = \frac{\left(\frac\pi6\right)^2}{\tan\left(\frac\pi6\right)} = \frac{\pi^2}{36\times\frac1{\sqrt3}} = \boxed{\frac{\pi^2}{12\sqrt3}}\)
Answer the following.(a) A certain solution has a hydrogen ion concentration of 0.00000896 moles per liter. Write this number in scientific notation.(b) A humpback whale can weigh up to 1.1 * 10^5 pounds. Write this number in standard notation.
Given:
Two statements (a) and (b) are given.
Find:
we have to write the answers of both statments (a) and (b).
Explanation:
(a) A certain solution has a hydrogen ion concentration of 0.00000896 moles per liter
The scientific notation of 0.00000896 is
\(8.96×10^{-6}\)......................................................................................................................................
(b) A humpback whale can weigh up to 1.1 * 10^5 pounds
The standard form of the given number is given as below
\(1.1\times10^5=110000\)