In the following question, among the conditions given, Menu 1:Cost per person: $20, Total cost for 50 people: $20 x 50 = $1000, we can afford Menu 1 within our budget, and the total cost for the food, including sales tax and tip, is $1209.
First, we need to determine the total amount of the budget available after applying the 10% discount:
Budget after discount = $1200 - (10% x $1200) = $1080
Next, we need to consider the three menus offered by the catering company:
Menu 1:
Cost per person: $20
Total cost for 50 people: $20 x 50 = $1000
Menu 2:
Cost per person: $25
Total cost for 50 people: $25 x 50 = $1250
Menu 3:
Cost per person: $30
Total cost for 50 people: $30 x 50 = $1500
Since Menu 1 is the only option that fits within our budget, we will choose that menu.
Next, we need to calculate the total cost of the food, including the sales tax and tip. To do this, we'll need to add the sales tax and tip percentages to the original cost of the food:
Sales tax: 8.875%
Tip: 15%
Total cost per person after tax and tip = cost per person + (sales tax x cost per person) + (tip x cost per person)
Total cost per person after tax and tip = $20 + (8.875% x $20) + (15% x $20) = $24.18
Total cost for 50 people after tax and tip = $24.18 x 50 = $1209
Therefore, the total cost of the food, including sales tax and tip, for Menu 1 is $1209.
To summarize our calculations:
Budget after discount: $1080
Total cost for Menu 1: $1000
Total cost per person after tax and tip: $24.18
Total cost for 50 people after tax and tip: $1209
So, we can afford Menu 1 within our budget, and the total cost for the food, including sales tax and tip, is $1209.
For more such questions on Cost Calculation
https://brainly.com/question/20329337
#SPJ4
One year, the population of a city was 181,000. Several years later it was 150,230. Find the percent decrease.
Answer:
17%
Step-by-step explanation:
Calculate the difference in the population
181,000 - 150,230 = 30,770
Decrease is 30,770
Perecentage decrease = Decrease/ original population x 100%
30770/ 181,000 x 100 = 0.17 x 100
= 17%
Check 17% of 181,000
Deduct from 181,000 and you will get 150,230
You have one fair coin and one biased coin which lands Heads with a probability of 2/3. You pick one of the coins at random and flip it two times. Assume that the outcomes are independent given the picked coin. (a) Given that the picked coin lands Head all two times, what is the probability that the coin you picked is a biased coin? (b) Let H1 be the event that the outcome of the first flip is Head, and let H2 be the event that the outcome of the second flip is Head. Are the events H1 and H2 independent?
The events H1 and H2 are independent.
Let P(B) be the probability that the selected coin is the biased one. Since we're picking the coin at random, P(B) = 0.5. Now, suppose we get two heads in a row. Let's call this event E. If E happens and the coin we picked is the biased coin, then the probability of getting two heads in a row is given by the probability that the biased coin gives heads twice, which is (2/3)² = 4/9. Therefore, the probability that we picked the biased coin given that we got two heads in a row is: P(B|E) = P(E|B)P(B) / [P(E|B)P(B) + P(E|F)P(F)], where F is the event that the fair coin is chosen. Note that the probability of getting two heads in a row with the fair coin is 1/4. Hence, the above formula becomes P(B|E) = (4/9 x 0.5) / [(4/9 x 0.5) + (1/4 x 0.5)] = 16/29. Therefore, the probability that we picked the biased coin given that we got two heads in a row is 16/29. b) The outcomes are independent given the picked coin, hence P(H1 ∩ H2) = P(H1)P(H2). Therefore, the events H1 and H2 are independent.
Learn more about Probability
brainly.com/question/11034287
#SPJ4
The diameter of a circle is 3 ft. Find its area to the nearest whole number.
The area of the circle is 7 ft^2
What is a Circle?Circle is an closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “centre” which is measured in terms of its radius. It is also a closed shape formed by tracing a point that moves in a plane such that its distance from a given point is constant.
Area of a circle = πr^2 or π(d/2)^2
Where π = 22/7
Diameter = 3ft = 3ft/2 = 1.5 ft
Radius = 1.5ft
Area = 22/7 * (1.5)^2
Area = 22/7 * 2.25
Area = 7.07
Area = 7 ft^2 to nearest whole number
Read more about Circle
https://brainly.com/question/12298717
#SPJ1
Play the game Karappan Poochi: Algebra vs The Cockroaches
get to level six take a snip shop and post it in the comments
please help me
The solution to the equation x² + 2x = 18 is x = 4 ± √19.
Karappan Poochi: Algebra vs The Cockroaches is a math-based game designed to help students learn and practice algebra. The objective of the game is to help Karappan, a character in the game, solve algebraic equations. Players must solve equations by manipulating the variables and constants to reach the correct answer. To reach level six, the player must solve six equations correctly.
The equation for level six is x² + 2x = 18. To solve this equation, the player must first recognize that it is a quadratic equation and can be solved using the quadratic formula. The formula is: x = [-b ± √(b²-4ac)]/2a. For this equation, a = 1, b = 2, and c = -18. Plugging these values in, the player gets: x = [-2 ± √(2²-4(1)(-18))]/2(1). This simplifies to x = [-2 ± √76]/2, which simplifies to x = [8 ± √76]/2. Therefore, the solution to this equation is x = 4 ± √19.
Learn more about equation here:
https://brainly.com/question/10413253
#SPJ4
given f(x)=2x^2-3x+1 and g(x)= 4x^2+2x-3, evaluate (f-g)(x)
The value οf (f-g)(x) when [tex]f(x)=2x^2-3x+1[/tex] and[tex]g(x)= 4x^2+2x-3,[/tex] is equals to [tex]-2x^2 - 5x + 4.[/tex]
What is Function ?
Function can be defined in which it relates an input to output.
Tο evaluate (f-g)(x), we need to subtract the functiοn g(x) from f(x) for the same input value x:
(f-g)(x) = f(x) - g(x)
Given [tex]f(x) = 2x^2 - 3x + 1[/tex] and [tex]g(x) = 4x^2 + 2x - 3[/tex], we can substitute these intο the expression for (f-g)(x):
(f-g)(x) = f(x) - g(x)
[tex]= (2x^2 - 3x + 1) - (4x^2 + 2x - 3)[/tex]
To simplify this expressiοn, we first distribute the negative sign to the terms inside the parentheses:
[tex](f-g)(x) = 2x^2 - 3x + 1 - 4x^2 - 2x + 3[/tex]
Next, we cοmbine like terms:
[tex](f-g)(x) = -2x^2 - 5x + 4[/tex]
Therefore, The value of (f-g)(x) when [tex]f(x)=2x^2-3x+1[/tex] and [tex]g(x)= 4x^2+2x-3[/tex] , is equals to [tex]-2x^2 - 5x + 4.[/tex]
To learn more abοut Function from given link.
https://brainly.com/question/30721594
#SPJ1
the length of a rectangle is increasing at a rate of 5 cm/s and its width is increasing at a rate of 4 cm/s. when the length is 13 cm and the width is 4 cm, how fast is the area of the rectangle increasing (in cm2/s)?
The rate of increasing the area of the rectangle is 72cm²/s
We have, The length of a rectangle is increasing at a rate of 5 cm/s and its width is increasing at a rate of 4 cm/s. When the length is 13 cm and the width is 4 cm, we have to find how fast is the area of the rectangle increasing.
The area of a rectangle is given by, A = l × w
Where l is the length and w is the width.
Now we will differentiate the equation with respect to time t.
dA/dt = d/dt (l × w)
dA/dt = l(dw/dt) + w(dl/dt)
We can use this formula to calculate how fast the area of the rectangle increases when the length is 13 cm and the width is 4 cm.
Substituting the given values, l = 13 cm and dl/dt = 5 cm/s w = 4 cm and dw/dt = 4 cm/s
dA/dt = 13(4) + 4(5)
dA/dt = 72 cm²/s
Therefore, the area of the rectangle increasing at a rate of 72 cm²/s.
To know more about the "area of the rectangle": https://brainly.com/question/24571594
#SPJ11
what type of graph is best suited for displaying the number of hours spent watching television by people from different age ranges?
A bar graph or a histogram is best suited for displaying the number of hours spent watching television by people from different age ranges.
What is a bar graph?
A bar graph is a type of graph that uses bars or rectangles to represent data, with the height or length of each bar proportional to the value it represents.
Both types of graphs can easily show the distribution of data across different age groups and allow for easy comparison of the number of hours spent watching television.
The choice between a bar graph or a histogram depends on the nature of the data and the desired level of detail.
A bar graph is appropriate when the data is categorical (e.g., age ranges) while a histogram is used when the data is continuous (e.g., number of hours).
To know more about histogram visit:
https://brainly.com/question/16819077
#SPJ1
Your math teacher is planning a test for you. The test will have 30 questions. Some of the questions will be worth 3 points and the others will be worth 4 points. The total number of points on the test will be 100 points. How many 3-point questions and how many 4-point questions will be on the test?
Identify the problem: _______
a.Do I know the material?
b.How many 3-point questions and how many 4 point questions will be on the test?
c.Did I study?
d.What will my score be?
Answer:
B
Step-by-step explanation:
This is just the prosses of elmiation. How is A even possablie, C doesnt make sense, and D is also a non logical or solvable question. Thus its b.
The Amazon selling fee is 15%. Amazon’s fulfillment fee is 20%. The brand’s cost of goods sold is 20%. The brand wants their advertising budget to be 35% of net sales. If gross sales are $50,000, what should their advertising budget be?
The advertising budget of the brand should be $12,250. This can be calculated using the following equation:
What is budget?A budget is a financial plan for how much money will be earned, saved, and spent over a given period of time. It is a tool that helps individuals and organizations plan for their financial future and manage their current finances. A budget outlines expected income, expenses, and savings goals. It can also be used to track past spending and evaluate how successful a person or organization was in achieving their financial goals.
Gross Sales x 15% (Amazon Selling Fee) x 20% (Amazon Fulfillment Fee) x 20% (Cost of Goods Sold) x 35% (Advertising Budget) = Advertising Budget
$50,000 x 15% x 20% x 20% x 35% = $12,250
To learn more about budget
https://brainly.com/question/25169847
#SPJ1
AD and EC are diameters of 0. OB is a radius. Classify each statement as true or false. AOE = 50
Applying the definition of a diameter, we can conclude that m<AOE = 80 degrees. Therefore, m<AOE = 50 is FALSE.
What is a Diameter and a Radius?The diameter is the longest chord passing through the center of a circle, while the radius is the distance from the center to any point on the circumference. The diameter forms two semicircles or divides the circle into two halves.
We are given that AD and EC are diameters of the circle O. This means that EOC is a straight angle or semicircle, which is equal to 180 degrees. Therefore:
m<EOC - m<AOB - m<BOC = m<AOE
Substitute:
180 - 50 - 50 = m<AOE
80 = m<AOE
m<AOE = 80°
Therefore, the statement, m<AOE = 50 is FALSE.
Learn more about diameter on:
https://brainly.com/question/30959895
#SPJ1
If QS = 7, what is TU?
[tex]TU = 2QS = 2(7)[/tex]
[tex]\implies \bf TU = 14[/tex]
Given: ABCD is a parallelogram, E is the midpoint of overline AB and F is the midpoint of overline DC. Prove: overline DE ≌ overline FB.
Therefore , the solution of the given problem of parallelograms comes out to be s intended, overline DE and overline FB are congruent.
How do parallelograms function?In Euclidean mathematics, a simple quadrilateral of two sets of equal distances is referred to as a parallelogram. In a specific kind of quadrilateral known as a parallelogram, both set of opposite sides are straight and equal. There are four types of parallelograms, 3 of which are each mutually exclusive. Rhombuses, parallelograms, squares, but also rectangles are the four distinct shapes.
Here,
We can use the midpoint theorem and the fact that the opposing sides of a parallelogram are parallel and congruent to demonstrate that overline DE is congruent with overline FB.
The midpoint theory tells us that DE EA because we first know that E is the midpoint of overline AB.
The midpoint theory tells us that BF FC because we also know that F is the midpoint of overline DC.
As a result, overline DE and overline BC are parallel, and overline BF and overline AD are parallel.
DE EA and BF FC resulted in:
=> FC = EA Plus DE (Preserving equality by adding identical lengths)
If we replace FC with EA and DE with BF, we get:
=> BF + FC = DE + DE
If we simplify, we get:
=> 2DE = 2BF
When you divide both parts by 2, you get:
=> DE = BF
We have thus demonstrated that, as intended, overline DE and overline FB are congruent.
To know more about parallelograms visit:
https://brainly.com/question/29147156
#SPJ1
i think of a number ,i double it,and subtract two.I get nine
What is the number?
let the number be x, next perform calculations on it
double : 2x
subtract 2 : 2x - 2
2x - 2 = 9
2x = 9 + 2
x = 11 ÷ 2 = 5.5
so the number is 5.5
Suppose you want to purchase a house. Your take-home pay is $3160 per month, and you wish to stay within the recommended guidelines for mortgage amounts by only spending 1414 of your take-home pay on a house payment. You have $16,400 saved for a down payment and you can get an APR from your bank of 4.35%, compounded monthly. What is the total cost of a house you could afford with a 15-year mortgage? Round your answer to the nearest cent, if necessary.
The total cost of the house we can afford is $242,139.78.
What is compound interest?
Compound interest is when you earn interest on both the money you've saved and the interest you earn.
First, we need to determine the maximum monthly payment we can afford based on the recommended guidelines. If we can only spend 1414 of our take-home pay on a house payment, then:
Monthly payment = 0.45 × take-home pay
1414 = 0.45 × 3160
1414 = 1422
Therefore, we can afford a maximum monthly payment of $1422.
Next, we can use the present value formula to find the maximum loan amount we can afford:
Loan amount = (monthly payment / monthly interest rate) × (1 - (1 + monthly interest rate)^(-n))
where monthly interest rate = 4.35% / 12 = 0.003625, and n = 15 years × 12 months/year = 180 months.
Substituting the values, we get:
Loan amount = (1422 / 0.003625) × (1 - (1 + 0.003625)^(-180))
Loan amount = $225,739.78
Therefore, the maximum cost of the house we can afford with a 15-year mortgage is $225,739.78 + $16,400 (down payment) = $242,139.78. Rounded to the nearest cent, the total cost of the house we can afford is $242,139.78.
Hence, the total cost of the house we can afford is $242,139.78.
To learn more about compound interest visit:
https://brainly.com/question/3989769
#SPJ1
A kite is flying 85 ft off the ground, and its string is pulled taut. The angle of elevation of the kite is 58 . Find the length of the string. Round your answer to the nearest tenth.
The length of the string which is pulled taut as described in the task content is; 100.2 ft.
What is the length of the string?As evident in the task content; the kite is flying 85 ft off the ground, and the angle of elevation is; 58°.
It therefore, follows from trigonometric ratios that the ratio which holds true is;
sin (58°) = 85 / l
where l = Length of the string.
Therefore;
Multiply both sides by l;
l sin (58) = 85
Divide both sides by sin (58);
l = 85 / sin (58)
I = 100.2 ft (nearest tenth)
Ultimately, the length of the string as described in the task content is; 100.2 ft.
Read more on trigonometric ratios;
https://brainly.com/question/16853912
#SPJ1
Which rectangle has side lenghths of 5 units and 6 units
The area of a rectangle is [tex]30cm^{2}[/tex] , so let know more about rectangle and also know about Quadrilaterals.
What is Rectangle?Rectangle is a plane figure that differs from a square by having four adjoining sides that are not equal and 4 consecutive sides.
A rectangle is a type of quadrilateral that has r opposed sides that are equally long and parallel.
A quadrilateral is a closed object in geometry that is created by connecting 4 points, any 3 of which are not collinear. A quadrilateral, often known as a square, rectangle, or rhombus, is a polygon with 4 sides.
from the question
Given, Length, l = 6 cm, Breadth, b = 5cm
[tex]area of rectangle : A= length * breadth =6 * 5= 30 cm ^{2}[/tex]
To learn more about Rectangle, visit:
https://brainly.com/question/25986613
#SPJ1
all the whole numbers that re greater than -4 but less than 3
Answer: -3, -2, -1, 0, 1 and 2
Answer:
0, 1, and 2
Step-by-step explanation:
A whole number is any number that does not contain a fraction, decimal, or negative value. For example, 1, 25, and 365 are whole numbers. Whereas the values of -3, 100.01, 365 ¼, and 2006.3 are not.
PLEASE SHOW WORK!!!!!!!!!
The fifth term of the given sequence is: a₅ = 63
How to find the nth term of a sequence?We are told the formula for the nth term of the sequence is given as:
aₙ = aₙ₋₁ + 6(n - 1) for n ≥ 2
We are given:
a₁ = 3
a₂ = 9
a₃ = 21
a₄ = 39
Thus:
a₅ = a₅₋₁ + 6(5 - 1)
a₅ = a₄ + (6 * 4)
a₅ = 39 + 24
a₅ = 63
Read more about nth term of a sequence at: https://brainly.com/question/7882626
#SPJ1
Melvin has twice as many pencils as Ali. Zachary has four times as many pencils as Ali. If Ali has 3 pencils, how many pencils do the three boys have in all?
SHOW YOUR WORK
24
21
12
6
Answer:
[tex]\huge\boxed{\sf 21 \ pencils}[/tex]
Step-by-step explanation:
Ali has 3 pencils.
Melvin:Melvin has twice.
So,
Melvin pencils = 2 × 3
= 6 pencilsZachary:Zachary has four times as many pencils as Ali.
So,
Zachary' pencils:
= 4 × 3
= 12 pencilsSo:
Total pencils:= 3 + 6 + 12
= 21 pencils[tex]\rule[225]{225}{2}[/tex]
Which is the difference in price?? Please help
Answer:
the left one is cheaper, the difference is 4.2 pounds cheaper
Step-by-step explanation:
If the correlation coefficient r is equal to 0.521,
find the coefficient of nondetermination.
a) 0.729
b) 0.720
c) 0.396
d) 0.271
The correct option is d. If the correlation coefficient r is equal to 0.521, the coefficient of non-determination is 0.271.
Correlation is a term used to describe the relationship between two variables in a statistical context. The correlation coefficient is a measure of the strength and direction of the relationship between two variables.
The coefficient of non-determination is used in statistics to refer to the proportion of variability in one variable that is not accounted for by another variable. It is equal to 1 - r², where r is the correlation coefficient between the two variables.
So, the coefficient of non-determination can be found using the formula:
Coefficient of non-determination = 1 - r²Given that the correlation coefficient, r = 0.521, substitute the value in the formula to find the coefficient of non-determination:
Coefficient of non-determination = 1 - (0.521)²= 1 - 0.271 = 0.729
Hence, the answer is (a) 0.729.
You can learn more about correlation coefficients at: brainly.com/question/15577278
#SPJ11
At the Great Lakes Medieval Faire, 12% of the entertainers have red hair. If there are a total of 150 entertainers, how many of them do NOT have red hair?
HeLP Im iN cLAsS
There are 132 entertainers who do not have red hair.
What is Percentage?
Percentage is a way of expressing a number or quantity as a fraction of 100. It is represented by the symbol "%". Percentages are commonly used to express the proportion or ratio of one quantity to another.
Percentages are widely used in many fields, including mathematics, science, finance, and economics, among others. They are a convenient way to express a relative quantity or change in quantity, and are easy to compare and interpret.
If 12% of the entertainers have red hair, then 100% - 12% = 88% do not have red hair.
To find out how many entertainers do not have red hair, we can calculate 88% of the total number of entertainers:
88% = 88/100 = 0.88
Number of entertainers without red hair = 0.88 x 150 = 132
Therefore, 132 entertainers do not have red hair.
To learn more about Percentage, visit the link:
https://brainly.com/question/24877689
#SPJ1
Dry concrete can be made by mixing sand, gravel and cement in the ratio 1: 2: 3. If you want 1200 kg of dry concrete, how much of each will you need? Give your answers in kilograms (kg).
By answering the presented question, we may conclude that As a result, 200 kilograms of cement, 400 kg of sand, and 600 kg of gravel are required to produce 1200 kg of dry concrete in the 1:2:3 ratio.
what is ratio?In mathematics, ratios demonstrate how often one number is included in another. If there are 8 oranges and 6 lemons in a fruit bowl, the ratio of oranges to lemons is 8 to 6. In a similar vein, the ratio of oranges to whole fruit is 8, whereas the ratio of lemons to oranges is 6:8. A ratio is an ordered pair of integers a and b represented as a / b, where b is not equal to zero. A ratio is an equation that equals two ratios. For example, if there is 1 male and 3 girls (for every boy she has 3 girls), 3/4 are girls and 1/4 are boys.
One component cement, two parts sand, and three parts gravel are required to build dry concrete in the 1:2:3 ratio. This indicates that for every 1 kg of cement, 2 kg of sand and 3 kg of gravel are required.
To calculate the weight of one part, divide the entire weight of dry concrete (1200 kg) by the total number of parts (6). 1200 kg ÷ 6 = 200 kg.
Cement: 1 component cement (200 kilograms) = 200 kg
2 pieces sand 200 kilogram/part = 400 kg
Gravel: 600 kg = 3 parts gravel 200 kg/part
As a result, 200 kilograms of cement, 400 kg of sand, and 600 kg of gravel are required to produce 1200 kg of dry concrete in the 1:2:3 ratio.
To know more about ratio visit:
https://brainly.com/question/29467965
#SPJ1
What is the following product?
Steve goes from Birmingham to Coventry by bus. He takes 9 minutes to walk from his house to the bus stop in Birmingham. He takes 12 minutes to walk from the bus stop in Coventry to work. Steve has to get to work by 10 am. What is the latest time Steve should leave his house to get to work on time?
Steve should leave his house no later than 8:49 am (10:00 am minus 529 minutes) to get to work on time.
Minutes or minutes is correct?It's preferable to spell out the term minutes entirely rather than shorten it. Sixty seconds make up one minute, which is a measure of time. Minutes are a noun that also refers to the records of a formal meeting. The abbreviation "min" is frequently used.
Let's call the hour Steve needs to leave his house to leave for work "x".
He needs 9 minutes to walk from his home to the bus stop, and we don't know how long it will take the bus to get from Birmingham to Coventry. Call the length of the bus ride "t" for now.
Steve needs 12 minutes to walk to work from the bus stop in Coventry.
So, Steve's commute to work takes a total of:
Walking from the bus stop in Coventry to work takes 12 minutes, and it takes 9 minutes to go to the bus stop in Birmingham, thus the total time is 21 + t minutes.
Steve needs to arrive at work by 10 a.m., or 10 x 60 = 600 minutes.
Thus, we can formulate the equation shown below:
x + 21 + t <= 600
After finding x, we obtain:
x <= 579 - t
This indicates that Steve must leave his home no later than 579 minutes before 10 am, rounded to the nearest minute, minus the time it will take him to take the bus there and back (t).
For instance, if the bus ride takes 50 minutes, Steve should leave his house no later than:
x <= 579 - 50 = 529
In order to arrive at work on time, Steve must leave his residence no later than 8:49 am (10:00 am minus 529 minutes).
To know more about Minutes visit:
https://brainly.com/question/15600126
#SPJ1
Joanna is filling bags with beans each bag holds 2/3 pound of beans Johanna has 3 1/3 of beans how many bags can Johanna fill
Answer: 5 bags
Step-by-step explanation: convert the proper fraction (3 1/3) into improper fractions (10/3)
then do 10 / 2 because the denominators are the same
5 bags
Answer:
Step-by-step explanation:
Describe the situation with a division equation
The coordinates of the point M are (4, -8) and the coordinates of point N
are (-8,-8). What is the distance, in units, between the point M and point
N?
The distance between point M and point N is 12 units.
What are coordinates?Coordinates are a set of numbers or vaIues that describe the position or Iocation of a point in space. In two-dimensionaI space (aIso known as the Cartesian pIane), coordinates are typicaIIy represented by two vaIues, usuaIIy denoted as (x, y), that describe the horizontaI and verticaI position of a point reIative to a set of axes.
What is distance formuIa?The distance formuIa is a mathematicaI formuIa used to find the distance between two points in a two- or three-dimensionaI space.
d = √[(x₂ - x₁)² + (y₂ - y₁)²]
The distance formuIa is based on the Pythagorean theorem, which states that in a right triangIe, the square of the Iength of the hypotenuse (the side opposite the right angIe) is equaI to the sum of the squares of the Iengths of the other two sides.
In the given question,
We can use the distance formuIa to find the distance between point M and point N:
d = √[(x₂ - x₁)²+ (y₂ - y₁)²]
where (x₁, y₁) are the coordinates of point M and (x₂, y₂) are the coordinates of point N.
PIugging in the given vaIues, we have:
d = √[(-8 - 4)² + (-8 - (-8))²]
d = √[(-12)² + 0²]d = √[144]
d = 12
Therefore, the distance between point M and point N is 12 units.
To know more about coordinates, visit:
brainly.com/question/29132913
#SPJ9
Calculate the perimeter of the following.
The perimeter of the figure is 52 cm
How to determine the perimeter of the figureFrom the question, we have the following parameters that can be used in our computation:
The composite figure
The perimeter of the figure is the sum of the side lengths of the figure
So, we start by calculating the missing lengths as follows
Missing = 12 cm/4
Missing = 3 cm
Using the above as a guide, we have the following:
Perimeter = 12 + 9 + 3 + 3 + 3 + 3 + 3 + 3 + 7 + 9 - 3
Evaluate
Perimeter = 52
Hence, the perimeter is 52 cm
Read more about perimeter at
https://brainly.com/question/24571594
#SPJ1
Find sin2x, cos2x, and tan2x if sinx = - 1/ √5 square root 10 and x terminates in quadrant III
sin(2x) is 4/5 cos(2x) is 3/5 and tan(2x) is -2/3.
Given that, sin(x) = −1/√5
We know that sin x = y/r, where y is the opposite side and r is the hypotenuse. Since x is in the third quadrant, y is negative and r is positive, so we can draw a triangle in the third quadrant like the one below:
[asy]
unitsize(2cm);
pair A = (-1,0);
pair B = (-0.6,-0.8);
pair C = (0,-0.8);
draw(A--B--C--A);
draw(rightanglemark(A,C,B,2.5));
draw(Circle((0,0),1));
label("$x$",(C+B)/2,E);
label("$r$",(C)/2,NW);
label("$y$",(A)/2,S);
[/asy]
Here, $y=-1$, $r=\sqrt{5}$ and $x$ is the angle opposite to the side $y$. Using the Pythagorean theorem, we can find that the adjacent side is $x = -\sqrt{5 - 1} = -\sqrt{4} = -2$. Therefore,
$$
\cos(x) = \frac{x}{r} = \frac{-2}{\sqrt{5}} = -\frac{2\sqrt{5}}{5}
$$
Using the double angle formulas for sine and cosine,
$$
\begin{aligned}
\sin(2x) &= 2\sin(x)\cos(x)\\
&= 2\cdot \left(-\frac{1}{\sqrt{5}}\right) \cdot \left(-\frac{2\sqrt{5}}{5}\right)\\
&= \frac{4}{5}\\
\\
\cos(2x) &= 1 - 2\sin^2(x)\\
&= 1 - 2\cdot \left(-\frac{1}{\sqrt{5}}\right)^2\\
&= \frac{3}{5}\\
\\
\tan(2x) &= \frac{2\tan(x)}{1-\tan^2(x)}\\
&= \frac{2 \cdot \left(-\frac{1}{2}\right)}{1-\left(-\frac{1}{2}\right)^2}\\
&= \frac{-2}{3}
\end{aligned}
$$Therefore, sin(2x) is 4/5, cos(2x) is 3/5 and tan(2x) is -2/3.
Learn more about trigonometry
brainly.com/question/29002217
#SPJ4
unit 10 m homework 1 parts of a circle
1. The parts of the circle identified are as explained below. 2. Area = 153.94 m²; Circumference ≈ 43.98 m; 3. Area ≈ 706.86 ft²; Circumference ≈ 94.25 ft; 4. Area ≈ 326.85 in.; Circumference = 64.09 in.
What is a Circle?A circle is a closed two-dimensional shape that consists of points that are equidistant from a central point called the center.
1. An example of each part using the diagram of the circle given would be:
a. a center is K
b. One radius is JK
c. A chord is JL
d. Diameter is JI
e. Secant is GI
f. Tangent is GJ
g. Point of tangency is J
h. A minor arc is IL
i. A major arc is HIL
j. Semicircle is JLI
k. A central angle is <JKL
l. An inscribed angle is <HIJ
Use the area and circumference formula to calculate each required measure for each circle.
2. Area = πr² = π*7² = 153.94 m²
Circumference = 2πr = 2·π·7 ≈ 43.98 m
3. Area = πr² = π·15² ≈ 706.86 ft²
Circumference = 2·π·15 ≈ 94.25 ft
4. Area = πr² = π·10.2² ≈ 326.85 in.²
Circumference = 2·π·10.2 ≈ 64.09 in.
5. Area = πr² = π·9² ≈ 254.47 mm²
Circumference = 2·π·9 ≈ 56.55 mm
Learn more about circle on:
https://brainly.com/question/20489969
#SPJ1