An auditorium is in the shape of an equilateral triangle. the stage extends from one vertex of the triancle to the midsegment, and the seating area extends from the midsegment to the resr wall. the rear wall measures 112 feet. what is the perimeter of the seating area.
Answers
Answer:
280 ft
Step-by-step explanation:
An auditorium is in the shape of an equilateral triangle with side length as 112 ft.
The stage extends from one vertex of the triangle to the mid-segment and the seating area extends from the mid-segment to the rear wall.
*The situation is represented in the attachment.
According to the midpoint theorem, the segment joining two sides of a triangle at the midpoints of those sides is parallel to the third side and is half the length of the third side.
Hence, the length of the mid-segment in this case is,
[tex]\dfrac{1}{2}\times 112=56\ ft[/tex]
Therefore, the perimeter of the seating area is,
[tex]=112+56+56+56=280\ ft[/tex]
The perimeter of the seating area of an auditorium shaped as an equilateral triangle with rear wall measuring 112 feet will be 224 feet.
Explanation:This is a Mathematics question related to Geometry. An equilateral triangle is a triangle where all sides are of equal length. Since the auditorium is in the shape of an equilateral triangle, all sides of the triangle will have identical measurements. In this case, it’s specified that the rear wall measures 112 feet. Thus, each side of the triangle will be 112 feet.
The question asks for the perimeter of the seating area which starts from the midsegment of the triangle and extends to the rear wall. The midsegment of an equilateral triangle splits the triangle into equivalent smaller equilateral triangles. Hence, the length of the midsegment to a vertex is half of the side of the triangle. So, the length of the seating area on each side is 112/2 = 56 feet.
Since, there are two sides that measure 56 feet (that is from the midsegment to the other two vertices of the triangle), and the rear side measures 112 feet, to calculate the perimeter, we sum up these sides. Hence, the perimeter of the seating area will be 56 + 56 + 112 = 224 feet.
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Related Questions
an advertiser will pay you $12 for every 100 viewers you have watching the show. based on the information above , how much will they give you?
Answers
Answer:
$17,600,000
Step-by-step explanation:
First, we need to count the amount of money we pay for each episode. If each episode costs you $200,000 to make, that would be subtracted from your total amount. If there are 150,000 viewers per episode, we can multiply 150,000 by 11, because there are 11 episodes. There are 1,650,000 people watching your show! Since the advertiser pays you $12 per person, we can simply multiply 12 times the number of people. You have earned $19800000. However, we need to subtract how much it took us to make the episodes, so we multiply the number of episodes, 11, by $200,000 and subtract the product from our total amount. Your amount of profit is $17,600,000.
Hope this helps! (Brainliest please!)
Answer:
$99 000
Step-by-step explanation:
(a) No. of episodes
There are 11 episodes per season.
No. = 0.5 × 11
No. = 5.5 episodes
=====
(b) No. of viewers
There are 150 000 viewers per episode
No. = 5.5 × 150 000/1
No. = 825 000 viewers
=====
(c) Payment
The advertiser pays $12 per 100 viewers.
Pay = 825 000 × 12/100
Pay = $99 000
The advertiser will pay you $99 000.
what is the mass of aluminum?
Answers
Answer:
The mass of aluminum is 26.982 g/mol.
Step-by-step explanation:
The molar mass of an element is the mass in grams of 1 mole of the element. It is determined by taking the atomic weight of the element on the periodic table, and writing it as g/mol.
The mass of aluminum will depend on the quantity and context. Given quantities in chemical compounds range from 26.98g in AlPO4 to 80.94g in Al2S3 (for 1 mol). For specific quantities or other situations, the mass should be calculated proportionally.
Explanation:The mass of aluminum can be determined using the specific heat and molecular absorption principles. A known quantity of aluminum in a compound like AlPO4 contains 1.000 mol or 26.98 g Al, while an Al2Cl6 molecule contains 1.994 mol or 53.74 g Al. When considering an Al2S3 molecule, it contains 3.00 mol or 80.94 g Al, which is the greatest mass of Al among the examples.
To calculate the mass for a different quantity of aluminum, you need to adjust these figures proportionally. For instance, if you have only half a mol of Al2S3, the mass would not be 80.94g, but half of that. Also, regarding mass of atoms, it is often represented in atomic mass units (amu) or in kilograms.
These examples give a clear idea of how to determine the mass of aluminum in different situations. The specific condition determines which calculation or table to use.
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Is the error the zero’s?
Answers
Answer:
NO
Step-by-step explanation:
Because that just means they started off with 0
The error in the table is that the "total" value for miles = 40 and gallons = 8 is incorrect.
The error in the given ratio table is that the values in the "total" row are not calculated correctly based on the provided "miles" and "gallon" values.
The values in the "total" row do not match the sum of the "miles" and "gallon" values for each corresponding column.
When miles = 0 and gallons = 0, the total should also be 0.
When miles = 10 and gallons = 2, the total should be 12.
When miles = 20 and gallons = 4, the total should be 24.
When miles = 30 and gallons = 6, the total should be 36.
When miles = 40 and gallons = 8, the total should be 48 (not 49).
When miles = 50 and gallons = 10, the total should be 60.
The error occurs in the row where miles = 40 and gallons = 8. The "total" value is listed as 49 instead of the correct value, which should be 48. So, the error in the table is that the "total" value for miles = 40 and gallons = 8 is incorrect.
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a bag contains 2 red marbles, 3 green marbles, and 2 black marbles what is the probability of drawing out a black marble
Answers
Answer:
P (black) = 2/7
Step-by-step explanation:
We need to know the total amount of marbles.
2 red + 3 green + 2 black = 7 marbles
P ( black) = number of black marbles / total marbles
= 2 /7
Write two equations of lines in slope-intercept form that are parallel to the graph of the line in Part I. y=1/2x+5
Explain why the equations of the lines in Part I and Part II are parallel.
Answers
Answer:
The two equations are [tex]y=\frac{1}{2}x+5[/tex] and [tex]y=\frac{1}{2}x[/tex]
Step-by-step explanation:
we have given that : Part I= [tex]y=\frac{1}{2}x+5[/tex] equation of line
slope intercept form is y=mx+c
the slope of the line Part I is m=1/2
taken another equation of line Part II= [tex]y=\frac{1}{2}x[/tex]
whose slope of line Part II is m=1/2
since, both equation have same slope therefore these two equation Part II and Part I are parallel
It is also shown by the graph attached.
if a= b^2/3 and b= c^3/4; what is the relation between a and c?
a=c^1/2
c=a^1/2
a=c^-1/2
c=a^-1/2
a=c
Answers
Answer: a = c^(1/2) which is the first answer choice of the list
Work Shown:
a = b^(2/3) ... given equation
a = (c^(3/4))^(2/3) ... replace b with c^(3/4)
a = c^((3/4)*(2/3)) .... multiply exponents
a = c^(1/2) .... Simplify; note the 3's cancel, also 2/4 turns into 1/2
a school cafeteria has 40 tables 35% of the tables have eight chairs at each table their remaining 65% of the tables have six chairs at each table complete the model then complete the statement to find the total number of chairs in the cafeteria
Answers
Solve: √81/100
Will mark brainliest for fastest and correct response.
Answers
Answer:
[tex]\dfrac{9}{100}=0.09\ or\ \dfrac{9}{10}=0.9[/tex]
Step-by-step explanation:
[tex]\sqrt{a}=b\iff b^2=a\ for\ a\geq0\ and\ b\geq0\\\\\text{We have}\ \sqrt{81}:\\\\\sqrt{81}=9\ because\ 9^2=81.\ \text{Therefore}\\\\\dfrac{\sqrt{81}}{100}=\dfrac{9}{100}\\\\\text{If is}\ \sqrt{\dfrac{81}{100}},\text{then:}\\\\ \text{Use}\ \sqrt{\dfrac{a}{b}}=\dfrac{\sqrt{a}}{\sqrt{b}}\\\\\sqrt{\dfrac{81}{100}}=\dfrac{\sqrt{81}}{\sqrt{100}}=\dfrac{9}{10}=0.9\\\\\sqrt{81}=9\ because\ 9^2=81\\\sqrt{100}=10\ because\ 10^2=100[/tex]
Solve for x: 4 (1-x)+2x=-3 (x+1)
Answers
4(1-x)+2=-3(x+1 )
-4x +3x = -3 -6
-x=-9
x=9
Answer -7
Step-by-step explanation:
Which equation is a point slope form equation for line AB ? y+1=2/3(x−4) y+1=3/2(x−4) y+1=−2/3(x−4) y+1=−3/2(x−4) A graph with a line running through point A, with coordinates (4, -1), and point B, with coordinates (-2, 3)
Answers
Answer:
C) y + 1 = -2/3(x - 4)
Step-by-step explanation:
The given line passes through the points A (4, -1) and B (-2, 3)
Let's find the slope now.
Slope (m) = (y2 - y1)/(x2 - x1)
= (3 - (-1)) / (-2 - 4)
= (3 + 1)/-6
= 4/-6
Slope (m) = -2/3
The equation of line y - y1 = m (x - x1)
y - (-1) = -2/3(x - 4)
y + 1 = -2/3(x - 4)
Answer: C) y + 1 = -2/3(x - 4)
Thank you.
Answer:
answer is c)
Step-by-step explanation:
:)
How would you simplify (log 27/logx) x (log x^2/log3)? I don’t think I did this correctly.
Answers
Answer:
6
Step-by-step explanation:
logx 27 * log3 x^2
The first step is to convert to base 10
(log 27/logx) * (log x^2/log3)
27 = 3^3 so we can rewrite this
(log 3^3/logx) * (log x^2/log3)
log a^b = b log a
(3 log 3/logx) * (2log x/log3)
We can cancel the log x in the numerator and denominator and the log 3 in the numerator and denominator
3 * 2
6
Write the explicit formula for the geometric sequence.
64, 32, 16, 8, ...
A) an = 8 · 4n-1
B) an = 8 · 2n-1
C) an = 32 · 0.5n-1
D) an = 64 · 0.5n-1
Which answer?
Answers
Answer:
Option D is correct.
Explicit formula for the geometric sequence is, [tex]a_n = 64 \cdot (0.5)^{n-1}[/tex]
Step-by-step explanation:
Geometric sequence states that a sequence of numbers in which the ratio between consecutive terms is constant,
we can write a formula for the nth geometric sequence in the form of:
[tex]a_n = a_1r^{n-1}[/tex] .....[1] where [tex]a_1[/tex] is the first term and r is the common ratio between successive term.
Given the sequence: 64, 32, 16 , 8......
Here, first term ([tex]a_1[/tex]) = 64.
Common ratio(r) = 0.5
Since,
[tex]\frac{32}{64} =0.5[/tex]
[tex]\frac{16}{32} = 0.5[/tex] ,
[tex]\frac{8}{16} = 0.5[/tex] ......
Substitute the value of a and r in [1] we get;
[tex]a_n = 64 \cdot (0.5)^{n-1}[/tex]
therefore, the explicit formula for the geometric sequence is, [tex]a_n = 64 \cdot (0.5)^{n-1}[/tex]
What is $0.8\%$ of $125\%$ of $8128$? Express your answer as a decimal.
Answers
Answer:
The correct answer is $81.28
Step-by-step explanation:
In order to find this, we simply treat the word of as a multiplication symbol.
0.8% of 125% of $8128
Now change the percentages to decimals
0.008 * 1.25 * 8128 = 81.28
Answer:
81.28Step-by-step explanation:
To solve this kind of problem, we must remember that the word "of" means multiplication in math language, and all percentages numbers can be expressed as a fraction where the denominator is 100. Applying all this, we have
[tex]0.8\%\times 125\%\times 8128\\\frac{0.8}{100}\times \frac{125}{100} \times 8128\\ 0.008(1.25)(8128)=81.28[/tex]
Therefore, all those percentages of 8128 results in 81.28
Can anyone answer this??
OPTIONS:
1. first, second
2. 3,9,-3,-9
3. first, second
4. is not, is
Answers
Unable to determine the subject of the question due to lack of information.
Explanation:The arithmetic operations described pertain to the addition and multiplication of numbers and the result of their signs. For instance:
When two positive numbers add or multiply, the result is also positive (e.g., 3 + 2 = 5 and 2 x 3 = 6).
When two negative numbers add or multiply, the result is negative when adding and positive when multiplying (e.g., -4 + (-2) = -6 and (-4) x (-3) = 12).
For numbers with opposite signs, in addition, subtract the smaller number from the larger number and give the result the sign of the larger number, while in multiplication, the result will have a negative sign (e.g., -5 + 3 = -2 and (-3) x 2 = -6).
Regarding quantum numbers, the sets of quantum numbers provide information about the state of an electron in an atom. Each set of numbers must follow specific rules:
The principal quantum number n must be a positive integer.
The azimuthal quantum number l must be an integer ranging from 0 up to n - 1.
The magnetic quantum number mē must range from -l to +l.
The spin quantum number ms must be either +1/2 or -1/2.
Therefore, for the given quantum numbers a. {4, 2, -2, 1} is not an allowed set because the spin quantum number must be either +1/2 or -1/2, not 1. Similarly, set b. {3, 1, 0, -1/2} is a possible set because it follows all the designated rules for quantum numbers.
I WILL GIVE BRAINLIEST, PLZ HELP! 3 out of 4 students in a class play a team sport. There are 28 students in the class. How many play a team sport?
Answers
Answer:
21.
Step-by-step explanation:
As 3/4 of the students play, we just have to multiply 3/4 by the total number of students.
3/4 * 28 = 84/4, or 21. 21 students play a team sport.
A nutrition label states that there are 36g of carbohydrates in each serving. This accounts for 12% of a daily value. How many grams of carbohydrates are recommended per day?
Answers
The recommended daily intake of carbohydrates is 300 grams per day based on a daily value of 12%.
To determine how many grams of carbohydrates are recommended per day based on a daily value of 12%, you can use the following calculation:
First, calculate what 1% of the daily value would be:
1% of daily value = 36 grams / 12% = 3 grams
Now, to find the recommended daily intake, simply multiply this by 100 since you want to find the recommended intake for 100% of the daily value:
Recommended daily intake = 3 grams/1% * 100% = 300 grams
So, the recommended daily intake of carbohydrates is 300 grams per day based on a daily value of 12%.
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kevin correctly answered 75% of his 32 test questions. how many questions would kevin have to answer to get more that 80% correct?
Answers
Kevin needs to answer at least 26 questions correctly out of 32 to exceed an 80% success rate, which means he needs to get 2 more questions right than he previously did.
Kevin correctly answered 75% of his 32 test questions, which is 24 questions. To achieve more than an 80% correct rate, Kevin needs to answer more than 80% of 32, which is more than 25.6 questions. Since Kevin can't answer a fraction of a question, he must answer at least 26 questions correctly. To find the number of additional questions he needs to answer correctly to exceed 80% when he has already answered 24 correctly, we subtract 24 from 26, resulting in 2 more questions that Kevin needs to answer correctly to exceed an 80% success rate.
Solve using elimination.
5x-4y=-21
-2x+4y=18
Answers
Answer:
(-1,4)
x=-1,y=4
Step-by-step explanation:
To solve by elimination, add the two equations together to eliminate y.
5x-4y=-21
-2x+4y=18
-----------------
3x = -3
Divide by 3
3x/3 = -3/3
x=-1
Now we still need to find y
-2x + 4y = 18
-2(-1) +4y =18
2+4y =18
Subtract 2 from each side
-2+2 + 4y = 18-2
4y = 16
Divide by 4
4y/4 = 16/4
y =4
There are 325 children at the zoo . If 64% of children are boys and the
rest are girls, how many children at the zoo are girls?
Answers
Answer:
117 Girls
Step-by-step explanation:
If 64% of the kids are boys, then 36% are girls 64% + 36% = 100%
.36 x 325 = 117 girls
Proof
.64 x 325 = 208 boys
208 + 117 = 325
There are 117 girls at the zoo.
To determine how many children at the zoo are girls, we start by understanding that 64% of the 325 children are boys. Let's go through the steps to find out the number of girls.
Calculate the number of boys by multiplying 64% by 325.
Percentage to decimal conversion: 64% = 0.64. So, 0.64 × 325 = 208 boys.
Subtract the number of boys from the total number of children to find the number of girls: 325 - 208 = 117 girls.
Therefore, there are 117 girls at the zoo.
what property does the number sentence show on 8+0=8
Answers
Answer:
The property for 8 +0 = 8, Additive Identity Property
What is the absolute value of point D? A.-6 B.9 C.7 D.-7
Answers
The absolute value of a number is its distance from zero on the number line, which is always positive or zero. If point D is -7, its absolute value would be 7, matching option D in the given choices.
Explanation:The absolute value of a number is the distance of that number from zero on the number line, regardless of direction. Therefore, it is always a positive value or zero. In this case, whether point D is -6, 9, 7, or -7, the absolute value would be the positive counterpart of that number.
To find the absolute value of point D, we look for the option that falls in line with the definition of absolute value. For option A (-6), the absolute value is 6; for option B (9), the absolute value remains 9; for option C (7), the absolute value remains 7; and for option D (-7), the absolute value is 7.
Thus, considering point D is given a negative value in the question, the correct answer for the absolute value of point D is 7, which corresponds to choice C if the value of D is 7 or D if the value of D is -7.
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The number 900 has an interesting property in that the only primes that divide into it evenly are 2, 3, and 5. What are the next two numbers after 900 that also have this property?
Answers
900 = 2 · 2 · 3 · 3 · 5 · 5
Next numbers:
2 · 2 · 2 · 3 · 3 · 3 · 5 · 5 · 5 = 900 · 15 = 13,500
2 · 2 · 2 · 2 · 3 · 3 · 3 · 3 · 5 · 5 · 5 · 5 = 13,500 · 15 = 202,500
202,500 · 15 = 3,037,500
3,037,500 · 15 = 45,562,500
....
What's 3.7 in a fraction
Answers
Answer:
3 7/10
Hope that helped!
Answer:
3.7 converted into a fraction is [tex]\frac{37}{10}[/tex]
Step-by-step explanation:
what is 6÷2/3 in simplest form A.4 B.8 C.9 D. 12
Answers
Answer:
The correct answer is 9.
Step-by-step explanation:
Answer:
the answer is C hope this helps
Step-by-step explanation:
Can someone please hep me with this problem thank you.
Answers
Answer:
the desired equation is y = (1/6)x + 3/2.
Step-by-step explanation:
From the graph you can see immediately that the y-intercept is (0,3/2).
This is "b" in y = mx + b.
Focus on point (-3,1). Substitute -3 for x in y = mx + 3/2 and then 1 for y:
1 = m(-3) + 3/2
Clear this result of fractions by mult. all three terms by 2:
2 = m(-6) + 3. Solving for m, -6m = 2 - 3, or -6m = -1. Then m = 1/6, and the
desired equation is y = (1/6)x + 3/2.
[tex]x - 6y = - 9[/tex]
3 - 6(2) = -9
3 - 12 = -9
If you plug the numbers in for x and y and end up with the correct solution then you'll know you've got the right equation.
Jones Manufacturing offers chain discounts of 5/4/2 to many of its preferred customers. Rowly Dress Shop purchased 40 dresses that had a total list price of $1,400. What was the net price paid by Rowly? What was the amount of trade discount? Use the net price equivalent rate and single equivalent discount rate in your calculations. Round final answers to nearest cent.
Answers
Answer:
1.What was the net price paid by Rowly
by 5/4/2 percentage 137000 cents,138400 cents,141200 cent
2.What was the amount of trade discount
by 5/4/2 percentage 7000 cents,5600 cents,2800 cents
Step-by-step explanation:
list price= $1,400
percentage discounts=5%
4%
and
2%
we have to find net price=?
we will calculate discount one by one
5% of 1400=[tex]\frac{5}{100}[/tex]×1400
5% of 1400=70
amount of trade discount for 5 %=70 dollar
we know that
1 dollar=100 cent
we will convert dollar into cents
7o dollar=70*100=7000 cent
Net amount paid for 5% discount=1440-70=1370 dollar
1370 dollar=1370*100=137000 cent
4% of 1400=[tex]\frac{4}{100}[/tex]×1400
4% of 1400=56
amount of trade discount for 4 %=56 dollar
56 dollar=56*100=5600 cent
Net amount paid for 4% discount=1440-56=1384 dollar
1384 dollar=1384*10138400 cent
2% of 1400=[tex]\frac{2}{100}[/tex]×1400
2% of 1400=28
amount of trade discount for 2%=28 dollar
28 dollar=28*100=2800 cent
Net amount paid for 2% discount=1440-28=1412 dollars
1412 dollar=1412*100=141200 cent
-3x+y=-10 what does x equal?
Answers
Step-by-step explanation:
First , Subtract y from both sides:
−3x = −10 −y
Second, Divide both sides by −3
x = [tex]\frac{-10-y}{3}[/tex]
That's ur answer
Hope this helped u!!!
Good luck!!
Solve the system of equations using the substitution method. y = 7x – 16, y = 2(2x – 5) What is the solution? (, )
Answers
Answer:
Solving the system of equations using the substitution method, the solution is: x=2 and y=-2
Step-by-step explanation:
(1) y=7x-16
(2) y=2(2x-5)
Substituting "y" of the equation (1) in the equation (2)
(2) 7x-16=2(2x-5)
Applying the distributive property to eliminate the parentheses on the right side of the equation:
7x-16=2(2x)-2(5)
Multiplying:
7x-16=4x-10
Solving for x: Subtracting 4x and adding 16 both sides of the equation:
7x-16-4x+16=4x-10-4x+16
3x=6
Adding like terms:
Dividing by 3 both sides of the equation:
3x/3=6/3
x=2
Replacing x by 2 in the equation (1):
(1) y=7(2)-16
y=14-16
y=-2
Solution: x=2 and y=-2
Answer:
Solve the system of equations using the substitution method. y = 7x – 16, y = 2(2x – 5) What is the solution? (, )Step-by-step explanation:
if f(×)=2x^2-5 and g(×)=3×+3 find (f-g)(×)
a.3x-2x^2-2
b.2x^2-3x-2
c.-x^2-7
d.2x^2-3x-8
Answers
[tex]2 {x}^{2} - 5 - 3x - 8 = 2 {x}^{2} - 3x - 8[/tex]
Answer:
d. 2x^2 -3x -8
Step-by-step explanation:
if f(×)=2x^2-5 and
g(×)=3×+3
(f-g)(×)=
I like to line them up vertically
2x^2-5
-(3x+3)
-------------------
Distribute the minus sign
2x^2-5
-3x-3
-------------------
Line up the powers
2x^2+ 0x -5
-3x-3
-------------------
2x^2 -3x -8
In May, 2018 a store had a furniture with a listed price of $550, having a sales tax of 3% on the listed price. Next month the price increased by 33 1/3 %. What sales tax should be paid in dollars on the new price?
Answers
Answer: $ 22
Step-by-step explanation:
[tex]\boxed{\$ 22}[/tex] of sales tax should be paidon the new price.
Further Explanation:
Calculation:
The given listed price of furniture in the month of May is [tex]\$550.[/tex]
The sales tax is of [tex]3\%[/tex] on the listed price of the furniture.
The price of the month May is increased by [tex]33\dfrac{1}{3}\%.[/tex]
The increased price of the furniture can be obtained as follows,
[tex]\begin{aligned}{\text{Increased price}} &= 550 + \left( {33\frac{1}{3}\% \times 550} \right)\\&= 550 + \left( {\frac{{33.34}}{{100}} \times 550} \right)\\&= 550 + 0.3333 \times 550\\&= 550 + 183.32\\&= 733.32 \\\end{aligned}[/tex]
The new price of the furniture in dollars is [tex]\$ 733.32.[/tex]
The sales tax is of [tex]3\%[/tex] on the listed price.
The sales tax on the new price can be obtained as follows,
[tex]\begin{aligned}{\text{Sales tax}}&= 3\% {\text{ of new price}}\\&= \frac{3}{{100}} \times 733.32\\&= \$ 22\\\end{aligned}[/tex]
[tex]\boxed{\$ 22}[/tex] of sales tax should be paid in dollars on the new price.
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Answer details:
Grade: High School
Subject: Mathematics
Chapter: Sales Tax
Keywords: May, 2018, store, furniture, listed, price, listed price, $550, sales, sales tax, 3%, tax on listed price, next month, price increased, increased price, month, 33 1/3%, paid, dollars, new price.