In a polygon with n sides, the sum of the measures of the interior angles, S, is
[tex] S = (n - 2)180 [/tex]
In a regular polygon with n sides, the measure of each interior angle, a, is the sum of the measures of the interior angles divided by the number of sides, or
[tex] a = \dfrac{(n - 2)180}{n} [/tex]
In this case, we know the measure of one angle, a = 157.5°, so we plug it into the second formula and solve for n.
[tex] a = \dfrac{(n - 2)180}{n} [/tex]
[tex] 157.5 = \dfrac{(n - 2)180}{n} [/tex]
[tex] 157.5n = (n - 2)180 [/tex]
[tex] 157.5n = 180n - 360 [/tex]
[tex] -22.5n = -360 [/tex]
[tex] n = 16 [/tex]
Answer: The polygon has 16 sides.
In order to find the number of sides for a regular polygon with an interior angle of 157.5°, we use the formula n = 360 / (180 - 157.5), which gives us n = 16. Hence, the polygon has 16 sides.
Explanation:In mathematics, the number of sides of a regular polygon can be found if the measure of an interior angle is known. Given that the interior angle is 157.5° we use the formula for calculating the measure of an interior angle in a regular polygon:
n = 360 / (180 - 157.5)
Where 'n' represents the number of sides in the polygon. Substituting 157.5 into the formula, the calculation becomes n = 360 / 22.5. By performing the calculation, we find that n = 16. Therefore, the regular polygon with an interior angle of 157.5° has 16 sides.
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What is 4.58+y=2.5? Thanks!
Isolate the y. Note the equal sign. What you do to one side, you do to the other. Subtract 4.58 form both sides
4.58 (-4.58) + y = 2.5 (-4.58)
y = 2.5 - 4.58
y = -2.08
-2.08 is your answer
hope this helps
the attendance at a rugby game is as follows no. of men:no. of women:no. of children = 17:9:12
Given that there are 3512 more men than women work out the number of children attending the game
Answer: Number of children is 5268
Step-by-step explanation:
Since we have given that
The ratio of men to women to children is given by
17:9:12
So,
Number of men be 17x
Number of women be 9x
Number of children 12x
According to question, we have there are 3512 more men than women ,
so,
[tex]17x-9x=3512\\\\8x=3512\\\\x=\frac{3512}{8}\\\\x=439[/tex]
So, Number of children is given by
[tex]12x=12\times 439=5268[/tex]
The number of children who attend the game are:
5268
Step-by-step explanation:The ratio of number of men to number of women to the number of children is given by:
17:9:12
Let x be a constant such that we may define:
Number of men are: 17x
Number of women are: 9x
and the number of children are: 12x
There are 3512 more men than women.
This means that:
17x-9x=3512
i.e. 8x=3512
i.e. x=439
Hence, the number of children who attend the game are:
12x=12×439
= 5268
What is a if 6= a/4+2
4+2=6 then you bring the 6 to the other side so you have combine like terms. 6-6=0 so its 0
A = 36
Check:
6 = 36/4 + 2
6 = 36/ 6
6 = 6 (True)
65 points, I will give brainliest.
What is the coefficient in the expression 3x/13 +4 ?
Enter your answer in the box.
Answer:
I'm pretty sure the co-efficient is 3 mainly because the 3 is in front of the 'x'Answer:
I believe it is 3/13
Im not sure...
Correct Me if im wrong...
Is 1x+4=10 20-11=11 7+10=17
True false or open?
The first equation is open, since it has an unsolvable variable. 1x could be anything!
The second equation is false, because 20 - 11 = 9 not 11.
The last equation is true, 7 + 10 does equal 17!
1x + 4 = 10
x = 10 - 4
x = 6 (true)
--------------------
20 - 11 = 11
20 - 11 = 9 (false)
-----------------------
7 + 10 = 17 (true)
A new cell phone costs $85, and the sales tax is 9%. what is the amount of sales tax?
This is a great life skill to learn and something you will use everyday. To find tax, multiply the cost by the tax rate as a decimal. Here is how it is done:
cost: $85
tax rate: 9%=0.09 as a decimal
85 times 0.09= 7.65
You will pay $7.65 in taxes on the new cell phone.
Answer:
7.65
Step-by-step explanation:
just did the lesson
How many 3/4 cup servings of trail mix are in a 8 cup bag?
Which product is negative?
−2⋅(−4)⋅8⋅(−1)
−7⋅(−3)⋅(−5)⋅(−8)
−3⋅(−4)⋅(−9)⋅0
6⋅(−2)⋅(−3)⋅1
When I had these kinds of problems, I'd count how many negatives there were. If there more or less negatives to positives, then it is negative. If there's the same amount of positives and negatives, then it's positive since they cancel out! The answer to this is A. (-2)(-4)(8)(-1)=-64.
In mathematics, the product −2⋅(−4)⋅8⋅(−1) is negative. This occurs because it has an odd number (three) of negative numbers being multiplied, leading to a negative product. The other options will give either a positive product or zero.
Explanation:In the realm of mathematics, when we multiply equal numbers of positive and negative values, we arrive at positive products. However, when we multiply an unequal number of positive and negative values, the product is negative. Let's apply this rule to the given products:
−2⋅(−4)⋅8⋅(−1): It contains three negative numbers, hence product will be negative.−7⋅(−3)⋅(−5)⋅(−8): It contains four negative numbers, hence product will be positive.−3⋅(−4)⋅(−9)⋅0: As one of the numbers is zero, the product will be zero.6⋅(−2)⋅(−3)⋅1: It has two negative numbers, so the product will be positive.
Among the provided choices, only the first product, −2⋅(−4)⋅8⋅(−1), will yield a negative product.
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Colton can rake 79/10 bags of leaves each hour. How many bags of leaves will colton rake and fill in 6 hours.
I need to know the steps to answering this.
Answer:
Colton will rake and fill [tex]\frac{237}{5}[/tex] bags of leaves.
Step-by-step explanation:
To solve this problem you must apply the proccedure shown below:
1. You have that Colton can rake [tex]\frac{79}{10}[/tex] bags of leaves each hour.
2. Then, to calculate the amount of bags of leaves that he will rake and fill in 6 hours (which you can call [tex]x[/tex]), you must multiply these hours by the amount of bags he can rake in 1 hour:
[tex]x=(6)(\frac{79}{10})\\x=\frac{474}{10}[/tex]
3. Simplify:
[tex]x=\frac{237}{5}[/tex] bags of leaves.
Colton can rake and fill 47.4 bags of leaves in 6 hours.
The student has asked how many bags of leaves Colton can rake in 6 hours if he can rake 79/10 bags of leaves each hour. To find the total bags Colton can rake, we need to multiply the number of bags Colton can rake per hour by the total number of hours he works. Here is the calculation step-by-step:
Identify the rate at which Colton can rake leaves: 79/10 bags per hour.Identify the total time Colton will be raking leaves: 6 hours.Multiply the rate by the total time to find the total amount of work done: 79/10 bags/hour *6 hours = 474/10 bags = 47.4 bags.Therefore, Colton can rake and fill 47.4 bags of leaves in 6 hours.
Marketing Chapter 3 Test Questions
1. A movie theater charges $5 per ticket and averages 300 customers each night. If prices are raised to $7 per ticket, the theater estimates that average nightly ticket sales will be $1,750. What is the percentage change in the average number of customers the theater has each night? (Express your answer in whole numbers; round decimals up or down).
Answer is 0.17
2. A movie theater charges $5 per ticket and averages 300 customers each night. If prices are raised to $7 per ticket, the theater estimates that average nightly ticket sales will be $1,750. What is the percentage change in ticket prices?
Answer is 0.40
3. A movie theater charges $5 per ticket and averages 300 customers each night. If prices are raised to $7 per ticket, the theater estimates that average nightly ticket sales will be $1,750. What is the elasticity of demand in this situation? (Hint: Elasticity of demand is determined by calculating the ratio of the percentage change in the quantity demanded over the percentage change in price.)
Answer is 0.425
4. Study the following data for a product:
Price Amount produced Amount demanded
$200 100,000 7,000
$100 80,000 35,000
$75 45,000 45,000
$50 30,000 70,000
$20 15,000 90,000
Find the market price. ________? Answer is $75
Step-by-step explanation:
1.) The average nightly ticket sales can be calculated as
Average sales = Average no. of customers per night x Charge per ticket
For the second night, we have
$1750 = (N)($7)
This gives us N = 250.
So, the average number of customers decreased as a result of the price increase.
To calculate the percentage change, we use the following formula:
% change = [tex]\frac{250 -300}{300} X 100[/tex]
We have -17% change in the average number of customers the theater has each night. The negative sign indicates a decrease in the number, which is consistent with our calculations.
2.) % change in prices = [tex]\frac{Final price - Initial price}{Initial price} X100[/tex]
Therefore, we have 40% change in the cost of ticket per person, which reflects an increase in the prices.
3.) Elasticity of Demand = [tex]\frac{ percentage change in quantity demanded}{percentage change in price}[/tex]
Hence, we have [tex]\frac{-17}{40}[/tex] = -0.425
This stands consistent with the Law of Demand - as the price increases, the quantity demanded decreases.
4.) Market price is obtained by looking for a point where the quantity supplied equals the quantity demanded. From the table we see that at $75 price, there is a demand for 45,000 units of that product in that market, which the suppliers are willing to supply. Hence, that defines the market price for that product.
a new car that costs $22575 depreciates at a rate of 11% per year. The car's value can be modeled by the equation V(x)=22,575(0.89)x. evaluate the function over the domain (2,5,7) and interpet the results
Answer: The values of the function V(x) over the domain (2, 5, 7) are 17881.66, 12,606.01 and 9985.224.
Explanation:
The cost of car is $22575 and the value of car depreciate at a rate of 11% per year.
The value of car can be modeled by the equation,
[tex]V(x)=22,575(0.89)^x[/tex]
Where is number of years after purchase of car or the age of car. We have to find the value of the function over the domain (2,5,7), so put x=2,
[tex]V(x)=22,575(0.89)^2=17881.66[/tex]
It means the value of car will be $17881.66 after two years.
put x=5,
[tex]V(x)=22,575(0.89)^5=12,606.01[/tex]
It means the value of car will be $12,606.01 after five years.
put x=7,
[tex]V(x)=22,575(0.89)^7=9985.224[/tex]
It means the value of car will be $9985.224 after seven years.
when you subtract one square number from another the answer is 7 what are the two square numbers
16 and 9 since 16 - 9 = 7
-65/64 as a mixed number
-1 1/64
Hope that helps!!
[tex]- \frac{65}{64}[/tex] as a mixed nombre, The correct answer is [tex]-1 \frac{1}{64}[/tex]
Is this statement true or false the only objects you can find the perimeter of are squares triangles and rectangles true or false
false
hope this helps :)
Translate equation:
The sum of twice a number six is the same as three subtracted from the number itself.
Hello...
The sum of twice a number six is the same as three subtracted from the number itself.
Answer - 2x + 6 = 3 - x
What ordered pair represents the point where the x-axis and y-axis intersecf? What is the name of this
point?
Answer:
The answer is A.
Step-by-step explanation:
the ratio of the length of an airplane wing to its width is 6 to1 . if the length of a wing is 12.5 meters ,how wide must it be
If you set up a proportion, this will make sense.
[tex]\frac{6}{1}= \frac{12.5}{x}[/tex]
Now, Cross Multiply
6x = 12.5
x = 25/12
The image from rotating a figure in the first quadrant 180 degree clockwise.
When rotating a figure in the first quadrant 180 degrees clockwise, the x-coordinates and y-coordinates of the points are negated.
Explanation:When an object in the first quadrant is rotated 180 degrees clockwise, its position is reflected across both the x-axis and y-axis. This means that the x-coordinates are negated and the y-coordinates are also negated.
For example, if a point A is located at (3, 4) in the first quadrant, after rotating it 180 degrees clockwise, it will be reflected across the x-axis and y-axis to the position (-3, -4).
Therefore, all points in the figure will have their coordinates negated when rotated 180 degrees clockwise in the first quadrant.
What is equivalent to 4.321 × 10−4 ?
A) 43210
B) 4321
C) 0.004321
D) 0.0004321
Answer:D
Step-by-step explanation:
what is the distance between -15 to 20
The distance between -15 and 20 on the number line is 35 units, calculated by taking the absolute difference between the two numbers.
The distance between two points on a number line can be found by taking the absolute difference between those points. To find the distance between -15 and 20, you subtract the smaller number from the larger one and take the absolute value:
|20 - (-15)| = |20 + 15| = |35| = 35
Therefore, the distance between -15 and 20 is 35 units.
What is
[tex]4x {}^{2} \times - 3x[/tex]
Hey there!!
Given equation :
... 4x² ( -3x )
... We know, 4 times -3 would be -12 and x² times x would be x³.
Hence,
the answer of 4x² × -3x is
... -12x³
Hope my answer helps!!
14 is a blank of 7 and 14
14 is a multiple of 7 and 14.
It is also the least common multiple of 7 and 14.
14 is a multiple of 7 and 14
The statement that "14 is a multiple of 7 and 14" is accurate because 14 can be evenly divided by both 7 and 14. A multiple of a number is the result of multiplying that number by any integer. In this case, 7 multiplied by 2 equals 14, making 14 a multiple of 7. Similarly, 14 multiplied by 1 equals 14, making it a multiple of itself.
Regarding the claim that "14 is the least common multiple of 7 and 14," it is actually incorrect. The least common multiple (LCM) of two numbers is the smallest number that is a multiple of both. In this case, the LCM of 7 and 14 is 14, not 14 itself.
The correct statement would be that 14 is a common multiple of 7 and 14, but it is not the least common multiple. The LCM is the smallest positive integer that is divisible by both numbers, and in this case, it is 14.
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Apples cost $0.89/pound. How much will 25 pounds cost?
$22.25 will be your answer for this one
Answer:
Your answer will be 22.25 because 0.89 times 25 equals that
Step-by-step explanation:
Is x = -3 a solution to the equation -3X^2=-27
Yes it is.
-3(-3)^2 = -27
-3(9) = -27
-27 = -27
Need help on 16 please!!!!!!!
What is the value of f(-3)
F(x)={ -2 if x<-3
4x if -3 _^< x _^<-1
X^2 if x >-1
[tex]f(x)=\left\{\begin{array}{ccc}-2&if&x < -3\\4x&if&-3\leq x\leq-1\\x^2&if&x > -1\end{array}\right\\\\-3\leq-3\leq-1\to f(x)=4x\\\\f(-3)=4(-3)=-12[/tex]
Gavin is thinking of a number.8 more than the product of 7 and the number is 120. find the number.
7x + 8 = 120
Subtract 8 from both sides.
7x = 112
Divide both sides by 7.
x = 16
what is the answer N= (3×5²×X³)
N= (3×5²×X³)
N = 75 * X³
N = 75 X³
Comment.
Just write out all the factors.
N = 3*5*5 * x*x*x
Note that the "x"s don't combine with anything but themselves. The numbers do.
3*5*5 = 75
N = 75 * x³ Answer
A probability experiment consists of rolling a fair 6-sided die. Find the probability of the event below. Rolling a number greater than 2
Answer:
The numbers are 1, 2 ,3, 4, 5 and 6.
Therefore 4 of the 6 numbers are greater than 2 so the probability is 4 out of 6 or 2/3.
Step-by-step explanation:
The question relates to probability while rolling a six-sided die for a number greater than 2. There are four favorable outcomes; 3, 4, 5, or 6. Therefore, the probability of this event is 4/6 or 2/3.
Explanation:The question you asked pertains to the concept of probability, specifically within the context of a fair, six-sided die. In this experiment, there are 6 equally likely outcomes: 1, 2, 3, 4, 5, or 6. When asked for the probability of rolling a number greater than 2, the outcomes we consider favorable are 3, 4, 5, and 6. That's 4 favorable outcomes. So, to calculate the probability of this event, you must divide the number of favorable outcomes by the total number of possible outcomes. Thus, the probability of rolling a number greater than 2 on a six-sided die is 4/6 or reducing to its simplest form becomes 2/3.
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evaluate -5/11+ -4/11 writing your answer as a simplified fraction
The answer would be -9/11 because since the denominator is the same, we can ignore it for now. Just add -4 and -5, you get -9. Finally, add the denominator of 11 back to get the answer