Answer: The cost of adult ticket is $6.1 and that of student ticket is $2.44
Step-by-step explanation:
Let the cost of adult ticket be 'x' and cost of student ticket be 'y'
From the question, the equations formed are:
[tex]662.5=85x+65y[/tex] .....(1)
[tex]x=2.5y[/tex] ......(2)
Putting value of 'y' from equation 2 to equation 1:
[tex]662.5=85(2.5x)+65y\\\\662.5=271.5y\\\\y=\frac{662.5}{271.5}=\$ 2.44[/tex]
Now, solving for 'x', we get:
[tex]x=2.5(2.44)=\$ 6.1[/tex]
Hence, the cost of adult ticket is $6.1 and that of student ticket is $2.44
The following functions give the populations of four towns with time tt in years.
(i) P=600(1.12)^t
(ii) P=1,000(1.03)^t
(iii) P=200(1.08)^t
(iv) P=900(0.90)^t
Which town has the largest percent growth rate? What is the percent growth rate?
Solution :
Transforming given equations :
[tex]1)\ P = 600( 1 + \dfrac{12}{100})^t\\\\2)\ P = 1000( 1 + \dfrac{3}{100})^t\\\\3)\ P = 200( 1 + \dfrac{8}{100})^t\\\\4)\ P = 900( 1 - \dfrac{10}{100})^t[/tex]
From above equations we can see that equation 1) has largest percentage growth rate and the percent growth rate is 12% .
Hence, this is the required solution.
Answer: (i), 12%
Step-by-step explanation:
Given
The Population of four towns is given
(i) [tex]P=600(1.12)^t[/tex] i.e.
[tex]\Rightarrow P=600(1+0.12)^t\\\Rightarrow P=600(1+12\%)^t[/tex]
rate=12%
(ii) [tex]P=1000(1.03)^t[/tex]
[tex]\Rightarrow P=1000(1+0.03)^t\\\Rightarrow P=1000(1+3\%)^t[/tex]
rate=3%
(iii) [tex]P=200(1.08)^t[/tex]
[tex]\Rightarrow P=300(1+0.08)^t\\\Rightarrow P=300(1+8\%)^t[/tex]
rate=8%
(iv) [tex]P=900(0.90)^t[/tex]
[tex]\Rightarrow P=900(1-0.10)^t\\\Rightarrow P=900(1-10\%)^t[/tex]
rate=10% fall
So, the largest growth rate is for town (i) i.e. 12%
what is the vertex of y=x²+14x-9
help
Sadie needs 3.1 yards to make one costume for each choir member in the play. How much fabric will she need if she has to make 5 costumes?
A.
15.5 yards
B.
10.5 yards
C.
18.6 yards
D.
16.5 yards
Answer:
A. 15.5 yards
Step-by-step explanation:
3.1 ×5=15.5
Find the volume of the prism.
What is
(481x10")(1.1x 10-4) in scientific notation?
5.291x 10-64
5.291x10
5.291x1012
5.291x1020
Answer:
5.291 * 10^4
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If A = {x x is an even integer), B = {xx is an odd integer), C = {2, 3, 4, 5), and D = {8, 9, 10, 11), list the element(s) of the following set.
AND
An D= { } (Use a comma to separate elements in the set.)
Answer:
AnD = {8,10}
Step-by-step explanation:
A = {2, 4, 6, 8 ,10 ...}
B = {1, 3, 5, 7 ,9 ...}
C = {,2 ,3 ,4 ,5 ...}
D = { 8, 9 ,10 ,11 ...}
AnD = {8, 10}
A number pattern was created by dividing the previous term by 4. If the starting value for the pattern was 576, which of the following shows the resulting pattern?
A.
576, 144, 72, 9...
B.
576, 144, 36, 9...
C.
576, 144, 72, 5...
D.
576, 144, 36, 5...
Answer:
The answer is B!!!!!!!!!!!!
WILL MARK YOU IF YOU CAN HELP ME
Answer:
x= 62
first take linear pair angle with any line then once again with x then you're done
Answer:
x value is 62 degree
because they are vertically opposite angles
Please help please and thanks
6x+3y=24
3x-4y=-21
What is the solution of system of equations
Answer:
i don't know if it is correct or not, sorry if i were mistaken
The value of x and y for the given system of equations is 1 and 6 respectively.
What is system of equations?
A system of equations is a collection of two or more equations with a same set of unknown variables.
What is solution to the system of equation?A solution to a system of equations is a set of values for the variable that satisfy all the equations simultaneously.
What is substitution method?The substitution method is a method to solve simultaneous linear equations. In which the value of one variable from one equation is substituted in the other equation.
According to the given question
we have a system of equations
[tex]6x + 3y = 24..(i)[/tex]
and, [tex]3x -4y = -21..(ii)[/tex]
From equation (i)
[tex]6x + 3y = 24[/tex]
⇒ [tex]2x + y = 8[/tex]
⇒ [tex]y = 8-2x[/tex]
Substitute the value of y in equation (ii)
⇒[tex]3x - 4(8-2x)=-21[/tex]
⇒[tex]3x-32+8x =-21[/tex]
⇒[tex]11x = 32-21[/tex]
⇒[tex]11x = 11[/tex]
⇒ [tex]x =1[/tex]
Substitute, x = 1 in either the equations (i) and (ii)
⇒[tex]3(1)-4y =-21[/tex]
⇒[tex]3 -4y=-21[/tex]
⇒[tex]-4y = -21-3[/tex]
⇒-4y = -24
⇒[tex]y =6[/tex]
Hence, the value of x and y for the given system of equations is 1 and 6 respectively.
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The sum of two numbers is 69. One number is 15 less than the other. Find the numbers.
Answer:
58+-43=15
Step-by-step explanation:
I need help with #1 . Please help. I have to show all work so please explain
Answer:C=10
Step-by-step explanation:
Follow along with the picture below
The formula for this type of problem is a^2+b^2=c^2
We know that 6=a and 8=b so we fill in the formula and square them
we then add the two values we got which get us to 100=c^2
we want to get rid of that square with we square root bothe sides and get c and the square root of 100 is 10.
So C=10
What is the factored form of this expression?
4x to the third power– 8x to the second power– 9x+ 18
In the circle below, the measure of arc QT is 50 and the measure of angle P is 55,
What is the measure of arc RS?
Answer:
C. 160degrees
Step-by-step explanation:
Find the diagram attached
From the diagram;
<P = 1/2(arcRS - arcQT)
Given the following
arcQT = 50degrees
<P = 55 degrees
Required
arcRS
55 = 1/2(arcRS - 50)
2*55 = arcRS - 50
110 = arcRS - 50
arcRS = 110 + 50
arcRS = 160degrees
Hence the measure of arcRS is 160degrees
5-2(3-x)=4x+10
can anyone help me, if i cant give you the brainliest answer i will.
Answer:
-11/2 = x
Step-by-step explanation:
5-2(3-x)=4x+10
Distribute
5 - 6 +2x = 4x+10
Combine like terms
-1 +2x = 4x+10
Subtract 2x from each side
-1 +2x-2x= 4x-2x+10
-1 = 2x+10
Subtract 10 from each side
-1-10 = 2x+10-10
-11 = 2x
Divide by 2
-11/2 = 2x/2
-11/2 = x
Answer:
See below
Step-by-step explanation:
5 - 2 * (3 - x) = 4x + 10
5 - 6 + 2x = 4x + 10
-2x = 11
x = -5.5
PT=3x+3 and TQ=6x-6
Use the figure to the right to find the value of PT. T is the midpoint of PQ
Answer:
PT = 12 units
Step-by-step explanation:
Given that,
PT=3x+3 and TQ=6x-6
T is the midpoint of PQ.
If T is mindpoint of PQ, it means,
PT = TQ
Substitute all the values,
3x+3 = 6x-6
Taking like terms together,
3x-6x = -6-3
-3x = -9
x = 3
So,
PT = 3x+3
= 3(3) + 3
= 9+3
= 12
So, the value of PT is equal to 12 units.
The length of a rectangle is six times its width.
If the perimeter of the rectangle is 84 in, find its area.
Answer:
6yd=W The width of the rectangle is 6 yards. L=6W=6(6yd)=36 yards The length is 36 yards. A=36yd*6yd=216 sq yd ANSWER: The area is 216 square yards...The area of a given rectangle is 216 square inches.
Given that, the perimeter of the rectangle is 84 inches.
We need to find the area of a rectangle.
What is the perimeter of a rectangle?The perimeter of a rectangle is the total distance of its outer boundary. It is twice the sum of its length and width and it is calculated with the help of the formula: Perimeter = 2(length + width).
Let the width of a rectangle be x.
Given, that the length of a rectangle is six times its width. So, length=6x.
Now, 84=2(6x+x)
⇒14x=84
⇒x=6 inches
Then, length=6x=36 inches.
Area of a rectangle= Length×width=36×6=216 square inches
Therefore, the area of a given rectangle is 216 square inches.
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Eric borrowed a total of $3000 from two student loans. One loan charged 4% simple interest and the other charged 3.5% simple
interest, both payable after graduation. If the interest he owed after 2 years was $215, determine the amount of principal for each
loan.
Answer:
$ 500 was the principal of the loan at 4%, and $ 2,500 was the principal of the loan at 3.5%.
Step-by-step explanation:
Given that Eric borrowed a total of $ 3000 from two student loans, and one loan charged 4% simple interest and the other charged 3.5% simple interest, both payable after graduation, if the interest he owed after 2 years was $ 215, to determine the amount of principal for each loan, the following calculation must be performed:
4 x 2 = 8
3.5 x 2 = 7
1500 x 0.08 + 1500 x 0.07 = 225
1400 x 0.08 + 1600 x 0.07 = 224
100 x 0.08 + 2900 x 0.07 = 211
500 x 0.08 + 2500 x 0.07 = 215
Therefore, $ 500 was the principal of the loan at 4%, and $ 2,500 was the principal of the loan at 3.5%.
Instructions: Find the area of the sector. Round your answer to the nearest tenth.
I’ll mark brainliest please help me
Answer:
[tex]area \: = \frac{165}{360} \times \pi {8}^{2} \\ = 92.1533845053 \\ = 92 \: in^{2} [/tex]
Identify the location of the point (-3, -2).
2x + 5y = 17
what is x
what is y
Answer:
x = (17 - 5y)/2
y = (17 - 2x)/5
Step-by-step explanation:
nothing else can be done here.
if you are looking for actual numbers as solution, then you have forgotten to put something important here.
to solve a system with 2 variables we need 2 equations. it cannot be solved with only 1 equation.
State if the two triangles are congruent. If they are, prove by using a two column proof!!!
Answer:
you can prove that they are congruent if their angles are the same.
What is the complementary number of 16
I
Answer:
2
Step-by-step explanation:
Pls Pls Pls help! Simplify the equation: [tex]\sqrt{\frac{1}{9} x^{2}y^{10}[/tex]
for what values of x are these functions defined x - 1
Answer:
The function is defined for all real numbers.
which can be denoted as >> R
The domain of a function is what?
The domain is all possible x values, specified for that function.
Calculate the total cost, total depreciation, and annual depreciation for the following assets by using the straight-line method. Cost Shipping Charges Setup Charge Total Cost Salvage Value Estimated Useful Life (years) Depreciation Total Annual
1. $5,600 $210 $54 ______ $600 6
2. $16,900 $310 0 ______ $1900 4
Answer:
a. For Asset 1, we have:
Total cost = $5,864
Total depreciation = $5,264
Annual depreciation = $877.33
b. For Asset 2, we have:
Total cost = $17,210
Total depreciation = $15,310
Annual depreciation = $3,827.50
Step-by-step explanation:
Note: The data in this question are merged together. They are therefore sorted before answering the question. See the attached pdf for the complete question with the sorted data.
Also note: See the attached excel file for the presentation of the data in the question with the answers (in bold red color).
The explanation of the answers is now given as follow:
Straight line method is a method of calculating depreciation and amortization of an asset by dividing the difference between the total cost and salvage value of an asset by its estimated useful life.
Therefore, wee have:
a. For Asset 1, we have:
Total cost = Cost + Shipping Charges + Setup Charge = $5,600 + $210 + $54 = $5,864
Total depreciation = Total cost - Salvage Value = $5,864.00 = $600 = $5,264
Annual depreciation = Total depreciation / Estimated Useful Life = $5,264 / 6 = $877.33
b. For Asset 2, we have:
Total cost = Cost + Shipping Charges + Setup Charge = $16,900 + $310 + $0 = $17,210
Total depreciation = Total cost - Salvage Value = $17,210 - $1,900 = $15,310
Annual depreciation = Total depreciation / Estimated Useful Life = $15,310 / 4 = $3,827.50
PLEASE HELP ASAPPP!!!!!
Three coins are flipped. What is the probability that there will be two tails and one head?
Given: In this figure, `/_AED` and `/_BEC` form a pair of vertical angles. Prove: `/_AED ~= /_ BEC `. Match each statement to its corresponding reason. Drag the items on the left to the correct location on the right.
Answer:
Step-by-step explanation:
The matched statement to its corresponding reason for the given alternate interior angles as:
Given: Let points A, B, and C form a triangle.
definition: Let stackrel(harr)(DE) be a line passing through B, parallel to "bar(AC)", with angles labeled as shown.
Congruent angles: m∠1=m∠4, m∠3 = m∠5
Linear pair theorem: m∠4+m∠2+m∠5 = 180°
As per the shown figure,
Given:
Let points A, B, and C form a triangle.
Defining a parallel line and labeling angles:
Let stackrel(harr)(DE) be a line passing through B, parallel to "bar(AC)", with angles labeled as shown.
Alternate Interior Angles Theorem:
∠1=∠4
∠3 = ∠5
Congruent angles have equal measures:
m∠1=m∠4
m∠3 = m∠5
Definition of a straight angle and angle addition:
m∠4+m∠2+m∠5 = 180°
Substitution:
m∠1 + m∠2 +m ∠3 = 180°
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Find the value of x to the nearest tenth
Answer:
a^2+b^2=c^2
6^2+6^2=72
square root of 72
=8.49(3sf)
c^2-b^2=a^2
=3
x=3
answer : 3
step by step:
this may seem hard but it is easy.
the first thing to do is to look at the bottom of the shape it shows a right triangle that is missing the hypotenuse lets see how to solve for that:
name the hypotenuse x
then write the equation
x^2= 6^2 + 6^2
x^2= 72
take both the square root of them
x = 8.5
next part is the rectangle and we see that it has been split into 2 right triangles which are the same but the cool part is that if we solve for one of the triangles we solve for the other we are going to do the same steps again notice now we are solving for the right angle that's not labeled if we solve that then that means we solve for the other triangle that is labelled x
first off we know that the hypotenuse is 9 and one angle is 8.5 so here is the equation:
x^2 = 9^2 - 8.5^2
x^2 = 8.75
take square root of both
x = 3
