Answer:
• 800 pavilion seats
• 800 lawn seats
Step-by-step explanation:
Let p represent the number of pavilion seats sold. Then 1600-p is the number of lawn seats sold. Total revenue is ...
25p +20(1600 -p) = 36000
5p + 32000 = 36000
5p = 4000
p = 800 . . . . . . . . . . number of pavilion seats sold
1600-p = 800 . . . . . number of lawn seats sold
_____
You can work these problems in your head. Consider that all seats were sold at the lower price. Then revenue would be 1600·20 = 32000. It was 36000 -32000 = 4000 more than that. The difference in ticket price is 25 -20 = 5 dollars, so there must have been 4000/5 = 800 higher-priced tickets sold. (Compare this working to the math above. You will find it substantially similar.)
Miguel and Grace started collecting rare coins at the same time. Back then, they had the same number of rare coins. Miguel has been collecting 5 coins each week and he now has 38 coins. Grace has been collecting 3 coins each week and she now has 24 coins. How many rare coins did they have altogether when they started collecting?
A) 3
B) 6
C) 7
D) 14
The correct answer is 6
Answer:
Option B is the correct answer
Step-by-step explanation:
Both collections follow arithmetic progression.
Back then, they had the same number of rare coins, which means their first term of AP is same. Let it be a.
Miguel's AP have a common difference 5 and Grace's AP have a common difference 3.
Let the number of weeks completed be n.
We have
a + ( n-1 )x 5 = 38 -------- eqn 1
a + ( n-1 )x 3 = 24 -------- eqn 2
eqn 1 - eqn 2
a + ( n-1 )x 5 - (a + ( n-1 )x 3) = 38 - 24
( n-1 )x 2 = 14
n-1 = 7
n = 8
Substituting in eqn 1
a + ( 8-1 )x 5 = 38
a = 38 - 35 =3
So at starting they both have 3 rare coins.
Total rare coins = 3 + 3 = 6
Option B is the correct answer
Find the median of the data set: 475, 500, 450, 450, 500
Answer:
475
Step-by-step explanation:
Answer:
450
Step-by-step explanation:
Please answer right away
Answer:
199 a 426 students
Step-by-step explanation:
first to see what amount we are talking about in each case, let's see how many students each percentage represents
22% of students: (22 * 1420 students) /100 = 312.4 students
8% of students: (8*1420 students)/100 = 114.6 students
that is, that the average number of students who work part time is 312.4 students. And that number can vary up to 114.6 students above and up to 114.6 students below
that can be expressed as
22% + 8% = 312.4 + 113.6 = 426 students
and
22% -8% = 312.4-113.6 = 198.8≅ 199 students
(3x – 1)(2x2 + 4x + 3)
Answer: (3x-1)(4x+7)
For this case we make the product of the following expression:
[tex](3x-1) (2x ^ 2 + 4x + 3)[/tex]
To make the product we must apply distributive property that by definition establishes that:
[tex](a + b) (c + d) = ac + ad + bc + bd[/tex]
So:
[tex](3x-1) (2x ^ 2 + 4x + 3) =\\6x ^ 3 + 12x ^ 2 + 9x-2x ^ 2-4x-3 =[/tex]
We group similar terms:[tex]6x ^ 3 + (12x ^ 2-2x ^ 2) + (9x-4x) -3 =\\6x ^ 3 + 10x ^ 2 + 5x-3[/tex]
Answer:
[tex]6x ^ 3 + 10x ^ 2 + 5x-3[/tex]
ILL GIVE BRAINLIEST HELPP
What is the solution to the equations of lines A and B?
A graph is shown with x- and y-axes labeled from 0 to 6 at increments of 1. A straight line labeled A joins the ordered pair 2, 6 with the ordered pair 6, 2. Another straight line labeled B joins the ordered pair 0, 3 with the ordered pair 4.5, 6.
Answer:
The solution is the point (3,5)
The graph in the attached figure
Step-by-step explanation:
step 1
Line A ----> (2,6),(6,2)
Find the equation of the line A
Find the slope
m=(2-6)/(6-2)
m=-1
Find the equation of the line into point slope form
The equation is equal to
y-y1=m(x-x1)
we have
m=-1
point (2,6)
substitute
y-6=-1(x-2)
y=-x+2+6
y=-x+8 ------> equation of the line A
step 2
Line B ----> (0,3),(4.5,6)
Find the equation of the line B
Find the slope
m=(6-3)/(4.5-0)
m=(2/3)
Find the equation of the line into point slope form
The equation is equal to
y-y1=m(x-x1)
we have
m=(2/3)
point (0,3)
substitute
y-3=(2/3)(x-0)
y=(2/3)x+3 ------> equation of the line B
step 3
Solve the system of equations by graphing
Remember that the solution of the system of equations is the intersection point both lines
The solution is the point (3,5)
see the attached figure
Its DE and ik its too late but the points is good. oof
What is the value of y?
The sum of all angles is 180 degrees. Which means.
[tex]
2y+y+10+50=180
[/tex]
Now just solve for y.
[tex]
3y+60=180 \\
3y=120 \\
y=\boxed{40}
[/tex]
The value of y is 40 therefore option B.
Hope this helps.
r3t40
For this case we have by definition, that the sum of the internal angles of a triangle is 180 degrees. Then, according to the figure we have:
[tex]y + 10 + 2y + 50 = 180[/tex]
We add similar terms:
[tex]y + 2y + 10 + 50 = 180\\3y + 60 = 180[/tex]
We subtract 60 from both sides of the equation:
[tex]3y = 180-60\\3y = 120[/tex]
We divide between 3 on both sides of the equation:
[tex]y = \frac {120} {3}\\y = 40[/tex]
Thus, the value of "y" is 40 degrees.
ANswer:
Option B
What is the value of x in this figure?
14√3
28√3
28√2
28
Answer:
x=28 (Yup you're correct)
Step-by-step explanation:
As this problem is involving the Opposite angle and the Hypotenuse, we can use the sin function in order to solve this. The setup is as follows
[tex]sin(30)=\frac{14}{x}[/tex]
Now we can solve for x
[tex]sin(30)=\frac{14}{x}\\\\x=\frac{14}{sin(30)}[/tex]
Now we can plug it into a calculator to get
[tex]x=28[/tex]
Answer:
28Step-by-step explanation:
(Look at the picture)
We have the triangle 30° - 60° - 90°. The sides are in ratio 1 : √3 : 2.
We have a = 14. Therefore x = 2a ⇒ x = 2(14) = 28
2 Ella, James, and Ray's grandmother gave them $24 to divide equally. They spent the
money during a 4-day vacation. They spent the same amount of money each day.
How much did each person spend each day?
A $1
B $2
C $4
D $8
3 kids and $24 will give each 24/3=$8 each
$8 for 4days is 8/4=$2 a day they spent
Jonathan conducted a survey among random boys in his grade to learn their shoe sizes. He found that the mean shoe size of the sample was size 10 and the median was size 8. Which statement is true based on the results of Jonathan’s survey?
Answer: his shoe size was 11
Step-by-step explanation:
Answer:
I hope this helps
Step-by-step explanation:
Solve this equation.
0>p-5
Answer:
p < 5
Step-by-step explanation:
The only "solving" you can do here is to solve for p:
Add 5 to both sides, obtaining 5 > p, which is equivalent to p < 5.
0>p-5
/ \
+5 +5
add 5 to both sides of the equation to make it disappear
so the answer is 5>p
Simplify
[tex] {x}^{5} \div {y}^{2} \times {x}^{3} \times {y}^{5} [/tex]
And animexcartoons209 please don't use PHOTOMATH...
[tex]\bf ~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] ~\dotfill\\\\ x^5\div y^2\times x^3\times y^5\implies \cfrac{x^5}{y^2}\cdot x^3\cdot y^5\implies x^5\cdot y^{-2}\cdot x^3\cdot y^5 \\\\\\ x^{5+3}y^{-2+5}\implies x^8y^3[/tex]
Answer:
x⁸y³
Step-by-step explanation:
x⁵ ÷ y² × x³ × y⁵
It will be easier to solve this problem if you first rearrange the expression to associate like terms.
(x⁵ × x³) × (y⁵ ÷ y²)
Now, you can use the rules of exponents: When multiplying, you add exponents; when dividing, you subtract exponents.
x⁵ × x³ = x⁵⁺³ = x⁸
y⁵ ÷ y² = y⁵⁻² = y³
Thus,
(x⁵ × x³) × (y⁵ ÷ y²) = x⁸y³
In rhombus ABCD, AB=14 and AC=19. Find the area of the rhombus to the nearest tenth. A 190.7 B 228.3 C 195.4 D 179.8
Answer:
C
Step-by-step explanation:
The triangle ABC has two sides that are 14 and 1 side that is 19. We can use Heron's formula to Calculate ABC.
s = (a + b + c)/2
s = (14 + 14 + 19)/2 = 23.5
s - a = 23.5 - 14 = 9.5
s - b = 23.5 - 14 = 9.5
s - c = 23.5 - 19 = 4.5
=================
Area = sqrt(s * (s - a) * (s - b) * (s - c) )
Area = sqrt(23.5 * 9.5 * 9.5 * 4.5)
Area = sqrt(9543,9)
Area = 97.69
But ABC is only 1/2 the rhombus. The area is twice that amount.
Area = 2 * 97.69 = 195.4
Given: BD is a diameter
m 1 = 100°
m BC= 30°
m ADB=
160
280
330
Answer:
280
Step-by-step explanation:
<1=100 <4=150 <3=30
mADB=100+150+30=280
Answer with explanation:
Given
m∠1=100°
[tex]m \widehat{BC}=30 ^{\circ}[/tex]
To Find:---m∠A D B
Solution
In Δ A OD
Represent the center of circle by O.
→ m∠1=100°
→OD=O A----------Radii of Circle
→∠ADO=∠D A O--------If opposite sides are equal angle opposite to them are equal.
In ΔA OD, Using Angle Sum property of Triangle
→∠ADO+∠D A O+∠A OD=180°
→2 ∠ADO+100° =180°-------------------[∠ADO=∠D A O]
→2∠ADO=180° -100°
→2∠ADO=80°
Dividing both sides by , 2 we get
⇒∠ADO=40°
⇒⇒⇒∠A DB=40°
≡⇒If you are asking about
[tex]m \widehat{ADB}=180 ^{\circ}[/tex]
Because Angle in a semicircle is Right Angle.Diameter B D divides the circle into two equal arc measure of each arc being 180 degree.
⇒⇒If you are asking about Angle made by Major arc ADB, then
[tex]m \widehat{ADB}=\angle AOD + \widehat{BOD}\\\\=100 ^{\circ}+180 ^{\circ}=280 ^{\circ}[/tex]
Option B
Which function represents g(x), a reflection of f(x) = (3)x across the y-axis?
g(x) = 2(3)x
g(x) = −(3)x
g(x) = (3)−x
g(x) = 2(3)−
Answer: [tex]g(x)=(3)^{-x}[/tex]
Step-by-step explanation:
We know that if a figure is reflected across y axis then its y coordinate remains same but the x coordinate changes its polarity.
i.e. the function [tex]f(x)[/tex] will become [tex]f(-x)[/tex] .
Now, the given function :[tex]f(x)=(3)^x[/tex]
Then , after reflection across y axis the new function will become:
[tex]g(x)=f(-x)=(3)^{-x}[/tex]
if cosec theta = 3/2, then find the value of 2 ( cosec2 theta + cot2 theta )
Answer:
7
Step-by-step explanation:
Using the trigonometric identity
• 1 + cot²x = cosec²x, then
2(cosec²Θ + cosec²Θ - 1 )
= 2(2cosec²Θ - 1)
= 4cosec²Θ - 2
= 4 × ([tex]\frac{3}{2}[/tex] )² - 2
= 4 × [tex]\frac{9}{4}[/tex] - 2
= 9 - 2
= 7
Find the range and interquartile range of the data. Round to the nearest tenth.
183, 339, 284, 111, 134, 344, 133
A. Range=211; interquartile range= 206
B. Range=233; interquartile range= 206
C. Range= 233; interquartile range= 156
D. Range= 211; interquartile range= 156
Answer:
It's B.
Step-by-step explanation:
The range is 344 - 111
= 233.
Arranging the data in ascending order:
111 133 134 183 284 339 344
The lower quartile = 133 and the upper quartile = 339.
So the interquartile range = 339 - 133
= 206.
We first need to list the following Data Set:
111, 133, 134, 183, 284, 334, 339
Range = highest value - lowest value =
Range = 339 - 111 = 228
Interquartile range = upper quartile - lower quartile =
(or IQR = interquartile range, another term)
Interquartile range = 334 - 133 = 201
Evaluate -4a + 8z if a=8 and z=3.
Answer:
-8
Step-by-step explanation:
-4a + 8z
= -4(8)+8(3)
= -32+24
= -8
use the substitution method
-4a+8z
-4(8)+8(3)
-32+24 Negative number times (*) and positive number=negative number
=-8
Answer is -8
Can you guys please help me
Answer: A?
Step-by-step explanation:
Find the 29th term of the following sequence. 2, 13, 24, 35,....
321
Look for a pattern: The term is 11 more than the number before. this means 11 is added each time.
Since you start with 2 and the number goes up by 11 per term, the equation you would use to find the nth term would be 11n+2
To find the 29th term, simply plug in 29
11n+2
11(29)+2
321
The 29th term is 321.
First you have to find the rate of change. It would be 11 because 35 - 24 = 11, 24 - 13 = 11 and 13 - 2 = 11.
These are the first 4 terms so just keep adding on 11 until you get 29 terms.
2, 13, 24, 35, 46, 57, 68, 79, 90, 101, 112, 123, 134, 145, 156, 167, 178, 189
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
200, 211, 222, 233, 244, 255, 266, 277, 288, 299, 310
19 20 21 22 23 24 25 26 27 28 29
Your final answer would be 310.
the inequality 1/2x+3<2x-6 is equivalent to) A. x<-5/6 B. x<6 C. x>-5/6 D. x>6 explain and show work please
Answer:
D. x > 6Step-by-step explanation:
[tex]\dfrac{1}{2}x+3<2x-6\qquad\text{multiply both sides by 2}\\\\2\!\!\!\!\diagup^1\cdot\dfrac{1}{2\!\!\!\!\diagup_1}x+2\cdot3<2\cdot2x-2\cdot6\\\\x+6<4x-12\qquad\text{subtract 6 from both sides}\\\\x<4x-18\qquad\text{subtract 4x from both sides}\\\\-3x<-18\qquad\text{change the signs}\\\\3x>18\qquad\text{divide both sides by 3}\\\\x>6[/tex]
Use the elimination method to solve the following system of equations. x+y=1 and x-y=-6
.
The system has a single solution. The solution set is (X,Y)
(Type an ordered pair, using integers or fractions.)
B.
There are infinitely many solutions. The solution set is (Type an equation. Type your answer in standard form.)
C.The solution set is the empty set.
[tex]\bf \begin{array}{llll} x+y=1&\times(-1)\implies &\begin{matrix} -x \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~-y&=-1\\ x-y=-6&&\begin{matrix} x \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~~~ -y&=-6\\ \cline{3-4}\\ &&~\hfill -2y&=-7 \end{array} \\\\\\ y=\cfrac{-7}{-2}\implies \blacktriangleright y=\cfrac{7}{2} \blacktriangleleft \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf \stackrel{\textit{substituting on the 1st equation}}{x+\left( \cfrac{7}{2} \right)=1\implies x=1-\cfrac{7}{2}}\implies \blacktriangleright x=-\cfrac{5}{2} \blacktriangleleft \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \left(-\frac{5}{2}~~,~~\frac{7}{2} \right)~\hfill[/tex]
The elimination method shows that the system of equations x + y = 1 and x - y = -6 has a single solution, which is the ordered pair (-5/2, 7/2).
To solve the system of equations x + y = 1 and x - y = -6 using the elimination method, we can add the two equations together to eliminate y. The resulting equation would be:
2x = -5
Dividing both sides by 2 gives us x = -5/2. We can then substitute the value of x back into either of the original equations to find y. Using the first equation x + y = 1:
-5/2 + y = 1
Adding 5/2 to both sides gives us y = 1 + 5/2, which simplifies to y = 7/2.
The solution set is therefore (-5/2, 7/2).
This system of equations has a single solution, so the correct answer is A, and the solution set is written as an ordered pair.
Alex is selling tickets to a school play. An adult ticket costs $6.50 and a student ticket costs $4.00. Alex sells x adult tickets and 12 student tickets. Write a function, f (x), to represent how much money Alex collected from selling tickets.
Answer:
[tex]f(x)=6.50x+48.00[/tex]
Step-by-step explanation:
Let
x ----> the number of adult tickets
f(x) ----> amount of money collected
To find the amount collected multiply the number of adult tickets by the cost and multiply the number of student tickets by the cost, and then sum the two quantities
The linear equation that represent this problem is
[tex]f(x)=6.50x+4.00(12)[/tex]
[tex]f(x)=6.50x+48.00[/tex]
Answer:
Step-by-step explanation:
F(x)=6.50x+48.00
the product of -5 and x
Answer:
-5x
Step-by-step explanation:
you multiply them together
(-5)(x)= -5x
Answer:
-5x
Step-by-step explanation:
-5 * X =
Let f(x)=x^2−10x−11 .
Enter the x-intercepts of the quadratic function in the boxes.
ANSWER
The y-intercept is (0,-11)
The x-intercepts are:
(-1,0) and (11,0)
EXPLANATION
The given function is
[tex]f(x) = {x}^{2} - 10x - 11[/tex]
To find the y-intercept, we put x=0 into the function.
[tex]f(0) = {0}^{2} - 10(0) - 11[/tex]
[tex]f(0) = - 11[/tex]
The y-intercept is (0,-11)
To find the x-intercepts, we put f(x)=0.
[tex]{x}^{2} - 10x - 11 = 0[/tex]
[tex](x + 1)(x - 11) = 0[/tex]
This implies that,
[tex]x = - 1 \: or \: x = 11[/tex]
The x-intercepts are:
(-1,0) and (11,0)
For Future Reference____
-1 & 11 are the X Intercepts
A bag contains 1 yellow ball and 9 red balls. A ball is chosen at random from the bag. What is the BEST answer for the probability of drawing the yellow ball?
A) impossible
B) unlikely
C) very likely
D) certain
Answer
so it is answer B
Step-by-step explanation:
since the sample space is 10, the chance of selecting theyellow ball is 1/10
which is unliekly
B) unlikely
it’s a 10% chance to get a yellow ball and a 90% chance to get a red ball
today only, a suit is being sold at a 29% off (discount). The sale price is $284. What was the original price?
If the original price is X, then(1-29%)X=284, so X=284/(1-0.29)=400
The original price of the suit is $400.
How to find the original price?To find the original price, we must multiply the discounted value with the reciprocal of the percentage that it represents.
The original price can be found as shown below:The discounted price is $284.
The percentage of discount is 29%.
Therefore, the percentage which represents the price is 100 - 29 which is 71%.
Therefore, we can find the original cost by multiplying the discounted price by the reciprocal of 71/100. This can be done as shown below:
The original price = 284 * 100/71
= $400.
We have found the original price. The original price is found to be $400.
Therefore, we have found that the original price of the suit is $400.
Learn more about percentages here: https://brainly.com/question/24304697
#SPJ2
if I have 40 ft of cloth how many dresses can I make if each dress is 2 ft and 6 in
Answer:
16 dresses
Step-by-step explanation:
you can make 16 because when you divide the length of cloth (40 ft) by 2.5 (2 ft 6in) you get 16
Answer:
16
Step-by-step explanation:
We know 6 inches is .5 of a foot
1 ft = 12 inches
6 inches /12 inches = 1/2 ft
We have 40 ft of cloth and each dress is 2.5 ft long
Take 40 ft and divide by 2.5
40 ÷ 2.5 =16
We can make 16 dresses
What is the range please?
Answer:
28.8
Step-by-step explanation:
Range = Highest number - Lowest number
Highest number: 42
Lowest number: 13.2
42 - 13.2 = 28.8
I hope this helps! :D
28.8 because the range is the biggest minus the smallest so 42 - 13.2
If a triangle has an angle of 20 and an angle of 40 what is the other angle
Answer:
120
Step-by-step explanation:
A triangles angles always add to 180 degrees.
180=20+40+x
180-20=160
160-40=120
120=x
Answer:
120
Step-by-step explanation:
20+40=60
180-60
120
Zucker Enterprises manufactures painted porcelain dolls. Zucker conducted a time study of the painting task. The painters took from ½-hour to 1½ hours to paint one doll. Zucker Enterprises pays its painters $18.00 per hour. The company also pays $11.00 per doll for materials. It wants to spend no more than $24.50 in prime costs. What is the longest time a painter should spend painting a doll?
Answer:
45 mins
Step-by-step explanation:
The question is how much time should the painter spend on painting a doll for the costs to still be equal or lower to $24.50
We can make this equation, representing the raw materials + the painting job (at $18/h):
$11 + $18x = $24.50
18x = 13.50
x = 13.5 / 18 = 0.75
So, the painter should spend at most 3/4 of an hour (or 45 mins) painting a doll to keep the cost at or below $24.50 per doll.