As per the concept of polygon,
a) The sum of the interior angles is 10,440° then the number of sides is 58
b) The value of each interior angle is 171°, then the number of sides is 36
A polygon is a two-dimensional geometric shape made up of straight lines and angles. The number of sides a polygon has is directly related to the sum of its interior angles.
a), we can use the formula for the sum of the interior angles of a polygon, which is (n-2) times 180 degrees, where n is the number of sides. To find n, we can rearrange the formula to
=> n = (sum of interior angles / 180) + 2.
Plugging in the value of 10,440 degrees for the sum of interior angles, we get
=> n = (10440 / 180) + 2 = 58.
Therefore, the polygon in item a) has 58 sides.
For item b), we can use the formula for the value of each interior angle of a regular polygon, we get
=> n = (180(n-2)) / 171 = (180n - 360) / 171.
Solving for n, we find that the polygon in item b) has 36 sides.
In conclusion, polygons with the angle values shown in items a) and b) have 58 and 36 sides respectively. These formulas can be applied to any polygon to find the number of sides based on its interior angle values.
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If a shopkeeper gives you a 15%discount on shirt of having total price 50. What price will you give after discount ?
If a shopkeeper gives you a 15% discount on shirt of having total price 50, the price you will give after the 15% discount is 42.5 dollars.
If the original price of the shirt is 50 dollars, and the shopkeeper gives a discount of 15%, then the discount amount is calculated by:
Discount = Original price x Discount rate
Discount = 50 x 0.15
Discount = 7.5 dollars
The discounted price is calculated by subtracting the discount from the original price:
Discounted price = Original price - Discount
Discounted price = 50 - 7.5
Discounted price = 42.5 dollars
The discount rate of 15% means that you will save 15% of the original price, which is 7.5 dollars in this case. The discounted price is the price after subtracting the discount amount from the original price.
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By rounding to one significant figure estimate the answer to 216x876
how do you do this? (Write an equivalent expression without parentheses. Then simplify the result
m-(8-3m)
The expression m - (8 - 3m) is equivalent to the expression 4m - 8.
What is an equivalent?The equivalent is the expression that is in different forms but is equal to the same value.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
The expression is given below.
⇒ m - (8 - 3m)
Simplify the expression, then we have
⇒ m - (8 - 3m)
⇒ m - 8 + 3m
⇒ 4m - 8
The expression m - (8 - 3m) is equivalent to the expression 4m - 8.
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Consider these functions:
f(x)=r² + 4
g(r)=9r - 12
What is the value of g(f(x))?
The value of g(f(x)) is 9r² + 24.
What is Function?A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.
Given are two functions.
f(r) = r² + 4
g(r) = 9r - 12
Composition of two functions f and g is the third function h such that f(g(x)) = h(x).
g(f(x)) = g(r² + 4)
= 9 (r² + 4) - 12
= 9r² + 36 - 12
= 9r² + 24
Hence the new function which is the composition of the two given function is 9r² + 24.
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Li-Ming has 20 ounces of lettuce, 12 ounces of chopped nuts, and 7 ounces of cranberries. What is the total weight of the salad?
Answer: 39
Step-by-step explanation: 20 + 12+7
pls help me i need this answer
solve for p pls
For the given algebraic expression, the value of p is 0.2 .
Linear Expression
A linear expression can be represented by a line. The standard form for this equation is: y=mx+b , for example, y=x+9. Where:
m= the slope.
b= the constant term that represents the y-intercept
For the given example: m=1 and b=9.
The exercise presents the following algebraic expression:
14=p*70 and it asks you the value of p. Thus, you should divide the number 14 by 70. See below.
14=p*70
p=14/70
p=2/10
p=0.2
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Ethan has pp pennies and nn nickels. He has no more than 20 coins altogether. Write this situation as an inequality.
Answer:
P+n<20
Step-by-step explanation:
The given situation can be expressed as an inequality as p + n ≤ 20.
What is Linear Inequalities?Linear inequalities are defined as those expressions which are connected by inequality signs like >, <, ≤, ≥ and ≠ and the value of the exponent of the variable is 1.
Given that,
Ethan has p pennies and n nickels.
Number of pennies = p
Number of nickels = n
Total number of coins is no more than 20.
This means that the combined total of pennies and nickels does not exceed 20.
sum of p and n is less than or equal to 20.
p + n ≤ 20
Hence the required inequality expression is p + n ≤ 20.
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two angles are supplementary if the sum of their measures is 180. angles A and B are supplementary. if the measure of angle A is 78 write and solve an addition equation to find the measure of angle B.
Answer:
78° + B = 180°
B = 102°
Step-by-step explanation:
"Supplementary" means angle A and B added together are 180°.
We know A is 78, but we don't know B
Write an equation:
A + B = 180°
Fill in what we know.
78° + B = 180° this is the equation the question is asking for.
To solve, subtract 78 from both sides of the equation.
B = 102°
What are the measures of angles B and C?
In a parallelogram, the opposite angles have equal measures. Therefore, 2n + 32 = 4n - 2
32 = 2n - 2
34 = 2n
17 = n
help with this theres a lot of points in it for you
The measure of angles from the given figure A, B, C, D, E, F, G and H are 61°, 130°, 58°, 50°, 84°, 85°, 146° and 145° respectively.
What is an angle?An angle is formed when two straight lines or rays meet at a common endpoint. The common point of contact is called the vertex of an angle.
1) By using the angle sum property of triangle
∠A+58°+61°=180°
∠A+119°=180°
∠A=61°
2) ∠B+50°=180° (Adjacent angles)
∠B=130°
3) ∠A=∠C (Angles of same segment)
∠C=58°
4) ∠D=50° (Vertically opposite angles)
5) 111°+90°+75°+∠E=360° (Sum of interior angles of quadrilateral)
∠E= 84°
6) 111°+84°+130°+130°+x=540° (Sum of interior angles of pentagon)
∠F=x=85°
∠F= 85°
7) 70°+50°+y=180° (angle sum property of triangle)
y=60°
70°+84°+60°+∠G=360° (Sum of interior angles of quadrilateral)
∠G=146°
8) ∠G+∠A+58°+130°+∠H=540°
146°+61°+58°+130°+∠H=540°
∠H=145°
Hence, ∠A=61°, ∠B=130°, ∠C=58°, ∠D=50°, ∠E= 84°, ∠F= 85°, ∠G=146° and ∠H=145°.
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Answer:
Step-by-step explanation:
A: 61°
B:130°
C: 58°
D: 50°
E: 84°
F: 85°
G:146°
H: 145°
Compute finance charges for installment purchases
1. If Sal saves $55 per month, express his total savings for x years as an
expression in terms of x.
2. Jean bought a $1,980 snow thrower on an installment plan. The installment agreement included a 10% down payment and 18 monthly payments of $116 each.
a. How much is the down payment?
b. What is the total amount of the monthly payments?
c. How much did Jean pay for the snow thrower on the installment plan?
d. What is the total finance charge?
Down payment = $198, total monthly payment = $2088, installment price = $2286, finance charge = $1782
What is down payment?Down payment is the amount of money that a purchaser needs to pay at the early stage of purchasing an expensive goods.
How to calculate down payment, total monthly payment and total finance charge?
Given, purchasing price = $1980, 18 monthly payments of $116 each.
down payment = 10%
amount of down payment = $1980 × 10/100
= $198
Total amount of monthly payment = $116 × 18 = $2088
Total paid for the snow thrower on the installment plan = Down payment + all monthly payment = $198 + $2088
Total installment price = $2286
total finance charge = Stated purchased price - down payment
= $1980 - $198
= $1782
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If Sal saves $55 per month, the expression for his total savings for x years is 55x.
What is amount?Amount is a term used to describe the total sum of money, quantity, or value of something. It is usually used to refer to a specific figure or a set of figures, such as the amount of money in a bank account, the number of items in a store, or the total cost of a purchase. Amount can also be used to describe the amount of time, energy, or effort put into something.
a. The down payment is 10% of $1,980, which is $198.
b. The total amount of the monthly payments is 18 x $116, which is $2,088.
c. Jean paid a total of $1,980 + $198 = $2,178 for the snow thrower on the installment plan.
d. The total finance charge is $2,088 - $2,178 = $90.
If Sal saves $55 per month, the expression for his total savings for x years is 55x.
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A boat traveled 165 miles each way downstream and back. The trip downstream took 11 hours.
The trip back took 15 hours. What is the speed of the boat in still water? What is the speed of
the current?
The speed of the boat in still water is 20.625 km/hr. and the speed of the current is 66 km/hr.
What is the relation of speed and distance?The speed formula is speed = distance / time.
Consider x= speed of current and y = speed of still water
The speed of the boat in still water can be calculated by dividing the total distance traveled by the total time taken;
(165 km x 2 = 330 km)
(5 hours + 11 hours = 16 hours).
Therefore, the speed of the boat in still water
330 km/16 hours = 20.625 km/hr.
The speed of the current can be calculated by dividing the total distance traveled by the total time taken for the downstream trip ;
(165 km x 2 = 330 km)
(5 hours).
Therefore, the speed of the current = 330 km/5 hours = 66 km/hr.
Hence,
speed of still water = 20.625 km/hr.
speed of current = 66 km/hr
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Write an equation that represent the linear relationship between x-values and y-values?
X
0
2
4
6 y -1
4
9
14
Answer: y = 5x - 1 ( look at the image for the solution )
Step-by-step explanation:
we have two fractions 5/12 and 3/4 and we want to rewrite them so they have a common denominator
Answer:
Below
Step-by-step explanation:
So you need to find a denominator that both will divide 'evenly' into...
12 would work.....4 will divide into it 'evenly' = 3
You do to need to do anything to the '5/12 ' ....
So change 3/4 to 12ths by multiplying by ' 1 ' in the for 3/3
3/4 * 3/3 = (3* 3 ) / ( 3*4 ) = 9 / 12 Done.
B - 2 is greater than equal to -1
The inequality B -2 ≥ -1 gives the value for B ≥ 1.
What is Inequality?Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
Given:
B - 2 is greater than equal to -1
Writing the mathematical inequality is
B -2 ≥ -1
B ≥ -1 + 2
B ≥ 1
So, the value of B should be greater than 1.
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There are 2 questions.
Answer:
27) #3 --> 12x - 24 = 60
29) 2x^2 + x - 15
Step-by-step explanation:
27) If x represents the number of boxes, and there are 12 cookies in each box, multiplying 12 by x results in the total number of cookies Kendal bought. However, she kept 2 boxes for herself, which is the same as 2(12) = 24 cookies. Kendal ended up with 60 cookies at the party, so subtracting 24 cookies from the total number of cookies (12x) equals 60 cookies.
29) (3 + x)(2x - 5)
3 * 2x = 6x
3(-5) = -15
x * 2x = 2x^2
x(-5) = -5x
6x - 15 + 2x^2 - 5x =
2x^2 + x - 15
you lease a car vauled at 23495 for 3 years
at 429.95/month
The amount of interest paid over the 3-year lease is $4,643.64 for a car.
What is a monthly payment?A monthly payment is a payment made every month to disburse loans or advances.
First, we need to calculate the total amount paid over the 3-year lease.
The monthly payment is $429.95, and there are 36 months in the lease, so:
Total lease payments = 36 x $429.95 = $15,478.20
The down payment of $500 is separate from the lease payments, so we don't include it in this calculation.
Next, we need to calculate the interest paid over the 3-year lease. We are told that interest is 30% of the monthly payment, so:
Monthly interest = 30% of $429.95 = $128.99
To find the total interest paid over the 3-year lease, we can simply multiply the monthly interest by the number of months in the lease:
Total interest paid = 36 x $128.99 = $4,643.64
Therefore, the amount of interest paid over the 3-year lease is $4,643.64.
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The question seems incomplete, the complete question would be as:
You lease a car valued at 23,495 for 3 years at $429.95/month with a $500 down payment. If interest is 30% of the payment, how much interest is paid over the 3 years?
What is the result of multiplying the first equation by 2 and adding to the second equation?
6x − y = 7
2x + y = 5
A. 14x + 3y = 19
B. 14x + y = 19
C.14x - y = 19
please help
The result of the operation is 14x - y = 19
How to determine the result of the operationFrom the question, we have the following parameters that can be used in our computation:
6x − y = 7
2x + y = 5
The operation is given as
Multiplying the first equation by 2 Adding to the second equationUsing the above as a guide, we have the following:
12x − 2y = 14
+ 2x + y = 5
Evalaute the sum
14x - y = 19
Hence, the solution is 14x - y = 19
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The a-value for the quadratic equation x² - 7x - 18.5 = 0 is 1.
The b-value for the quadratic equation x² - 7x - 18.5 = 0 is -7.
The c-value for the quadratic equation x² - 7x - 18.5 = 0 is -18.5.
The a-value for the quadratic equation 2x² + 15x + 12 = 0 is 2.
The b-value for the quadratic equation 2x² + 15x + 12 = 0 is 15.
The c-value for the quadratic equation 2x² + 15x + 12 = 0 is 12.
What is a quadratic equation?In Mathematics, a quadratic equation can be defined as a mathematical expression that can be used to define and represent the relationship that exists between two or more variable on a graph.
In Mathematics, the standard form of a quadratic equation is given by;
ax² + bx + c = 0
Mathematically, the quadratic formula is modeled or represented by this mathematical expression:
[tex]x = \frac{-b\; \pm \;\sqrt{b^2 - 4ac}}{2a}[/tex]
For the quadratic equation x² - 7x - 18.5 = 0, we have:
[tex]x = \frac{-(-7)\; \pm \;\sqrt{(-7)^2 - 4(1)(-18.5)}}{2(1)}[/tex]
For the quadratic equation 2x² + 15x + 12 = 0, we have:
[tex]x = \frac{-(5)\; \pm \;\sqrt{(5)^2 - 4(2)(12)}}{2(2)}[/tex]
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Consider the distance formula d = rt.
A boat travels 5 hours at a constant speed of 45 km/h. How far does the boat travel? Show your work
i will give brainlyst
Answer: 225 km/h
Step-by-step explanation: If distance = rate multiplied by time, then you are just multiplying 45 x 5.
45 x 5= 225
Which of the following is a binomial experiment?
Flipping a coin until it comes up tails
Flipping a coin until 8 heads are recorded
Flipping a coin 10 times and recording if it comes up heads
Flipping a coin by 10 different people and recording the age of each person
Flipping a coin 10 times and recording if it comes up heads is an example of binomial experiment. Option (c) is correct.
Further Explanation:
Given:
The options are follows,
(a). Flipping a coin until it comes up tails.
(b). flipping a coin until 8 heads are recorded
(c). flipping a coin 10 times and recording if it comes up heads
(d). flipping a coin by 10 different people and recording the age of each person
Explanation:
Conditions for binomial experiment are as follows,
(1). The experiment should be independent means that the probability of successive trial will not be affected by the previous trial.
(2). The experiment should have a finite number of trials.
(3). The probability of success will remain same for each trial.
(4). The experiment should have only two outcomes.
Flipping a coin has only two outcomes head or tail.
Flipping a coin 10 times and recording if it comes up heads is an example of binomial experiment. Option (c) is correct.
Option (a) is not a binomial experiment as the experiment is not for finite number of times.
Option (b) is not a binomial experiment as the experiment is not for finite number of times.
Option (c) is a binomial experiment.
Option (d) is not a binomial experiment as the experiment doesn’t have the same probability of occurrence.
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Answer details:
Grade: College
Subject: Statistics
Chapter: Binomial experiment
Keywords: binomial experiment, flipping a coin, tails, heads, recorded, 10 different people, probability, each person.
This experiment has a fixed number of trials (10), each trial has only two possible outcomes (heads or tails), the probability of success (heads) is the same for each trial (0.5), and there is no interdependence between the trials.
The following features of the binomial experiment apply:
There are a set number of trials in the experiment.In a trial, there are only two possible outcomes: success or failure.The likelihood of success is the same for every trial.The trials run separately from one another.These traits allow us to identify the following characteristics of the binomial experiment:
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What is Math 220 at UIUC?
Math 220 at UIUC is a calculus course offered at the University of Illinois at Urbana-Champaign.
It is designed to introduce students to the fundamental concepts of calculus, including limits, differentiation, and integration. The course also covers applications of these concepts to real-world problems, such as optimization and modeling.
Students are expected to have a strong foundation in algebra and trigonometry before taking Math 220. The course is typically taken by students in the College of Engineering and the College of Liberal Arts and Sciences.
The textbook for the course is the 8th edition of Calculus: Early Transcendentals by James Stewart. Additionally, Math 220 students must obtain access to the online homework system MyMathLabPlus and a copy of the textbook (hard copy or eBook).
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Milly bakes cookies to sell for a fundraiser. Her goal is to raise $500. The first day, she reaches 38 of her goal. On the second day, she raises 50% of the remaining money needed to meet her goal. How much money does Milly still need to make to reach her goal?
Answer:
$231
Step-by-step explanation:
500-38=462
50% of 462= 231
So she needs to make $231 more to reach her goal
what is 8.75 as a fraction?
The number 8.75 is equivalent to the fraction 35/4 in its simplest form.
To convert 8.75 to a fraction, we can write it as a fraction with a denominator of 1. We then multiply both the numerator and denominator by 100 to get rid of the decimal point. This gives us:
8.75 = 8.75/1
= 875/100
Next, we want to get rid of the decimal point, which we can do by multiplying both the numerator and denominator by a power of 10 that moves the decimal point of the numerator to the right until it disappears. In this case, we can multiply both the numerator and denominator by 100, which gives us:
8.75/1 x 100/100 = 875/100
We can simplify this fraction by dividing both the numerator and denominator by their greatest common factor, which is 25. This gives us:
875/100 = (875/25) / (100/25) = 35/4
Therefore, we conclude that 8.75 is equivalent to the fraction 35/4 in its simplest form.
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what is 600 hours in days?
Answer: 25 days
Step-by-step explanation:
Convert the unit for 600 hours
1 day = 24 hours
divide 600 hours with 24 hours as 24 hours = 1 day
600 ÷ 24 = 25
SOMEONE PLS HELP FASTT
pic below
Answer:
the correct answer is Tim
Hi can someone help me please and thank you
What is truth table in discrete mathematics?
In discrete mathematics, a truth table is a table that lists all possible combinations of truth values for a given set of logical variables and shows the resulting truth values of a compound proposition.
In discrete mathematics, a truth table is a table that lists all possible combinations of truth values (usually either true or false) for a given set of logical variables and shows the resulting truth values of a compound proposition (a logical expression formed by combining the variables using logical operators such as AND, OR, and NOT). Each row of the truth table represents one possible combination of truth values, and the columns represent the variables and the various intermediate steps of the logical calculation. Truth tables are often used to determine the truth values of complex propositions and to test the validity of logical arguments.
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Chuck bought 13 pounds of gummy worms.
Each pound cost $1.95. How much did Chuck
spend on gummy worms?
Answer:
Step-by-step explanation:
1.95 times 13= 25.35
Using trigonometric identities to simplify the following expression:
tan(θ)cot(θ)
Answer:
Step-by-step explanation:
The expression tan(θ)cot(θ) can be simplified using the trigonometric identity:
tan(θ) = sin(θ) / cos(θ)
cot(θ) = cos(θ) / sin(θ)
So,
tan(θ)cot(θ) = (sin(θ) / cos(θ)) x (cos(θ) / sin(θ))
= sin(θ) x cos(θ) / (cos(θ) x sin(θ))
= sin^2(θ) / sin^2(θ)
= 1
Therefore, tan(θ)cot(θ) = 1.