Tickets to the zoo cost four dollars for Children, five dollars for teenagers and six dollars for adults. In the high season, 1200 people came to the zoo every day. On a certain day, the total revenue at the zoo was $5300. For every three teenagers, eight children went to the zoo. How many teenagers went to the zoo.
Answer:
300 teenagers
Step-by-step explanation:
Let
x -----> the number of children
y ----> the number of teenagers
z ----> the number of adults
we know that
x+y+z=1,200 ----> equation A
4x+5y+6z=5,300 ---> equation B
y/x=3/8
y=(3/8)x ----> equation C
Substitute equation C in equation A and equation B and solve for x,z
x+y+z=1,200 ----> x+(3/8)x+z=1,200 ---> (11/8)x+z=1,200 -----> equation D
4x+5y+6z=5,300 --> 4x+5(3/8)x+6z=5,300 --> (47/8)x+6z=5,300 --> equation E
Solve the system of equations D and equation E by graphing
(11/8)x+z=1,200 -----> equation D
(47/8)x+6z=5,300 --> equation E
The solution is the intersection point both graphs
The intersection point is (800,100)
see the attached figure
therefore
x=800 children
z=100 adults
Find the value of y
y=(3/8)x ----> y=(3/8)800=300 teenagers
The approximate value of 4 times 10 Superscript 9 divided by left parenthesis 1.5 times 10 Superscript 6 right parenthesis is
Answer:
[tex]\boxed{2.7 \times 10^{3}}[/tex]
Step-by-step explanation:
[tex]\dfrac{4 \times 10^{9}}{1.5 \times 10^{6}}[/tex]
1. Divide the coefficients and the exponentials separately
[tex]\dfrac{4 \times 10^{9}}{1.5 \times 10^{6}} = \dfrac{4}{1.5} \times \dfrac{10^{9}}{10^{6}}[/tex]
2. Divide the coefficients
[tex]\dfrac{4}{1.5} \approx 2.7[/tex]
3. Divide the exponential terms
Subtract the exponent in the denominator from the exponent in the numerator.
[tex]\dfrac{10^{9}}{10^{6}} = 10^{(9 - 6)} = 10 ^{3}[/tex]
4. Rejoin the new coefficient and the new exponential
[tex]\dfrac{4 \times 10^{9}}{1.5 \times 10^{6}} \approx \boxed{\mathbf{2.7 \times 10^{3}}}[/tex]
Answer:
2.7 x 10(3)
Step-by-step explanation:
Put the following steps for calculating net worth in the correct order
Step-by-step explanation:
1.List your assets (what you own), estimate the value of each, and add up the total.
2.List your liabilities (what you owe) and add up the outstanding balances.
3.Subtract your liabilities from your assets to determine your personal net worth.
The parking rates @ the hospital's parking garage are 50 cents for the first hour and 25 cents for each additional hour. If juan parks in the garage for 8 hours, how much will the total charge for parking be?
Answer:
$2.25Step-by-step explanation:
[tex]n-number\ of\ hours\\\\\text{The equation of the function:}\\\\f(n)=0.25(n-1)+0.50\\\\\text{for n = 8:}\\\\f(8)=0.25(8-1)+0.50=0.25(7)+0.50=1.75+0.50=2.25[/tex]
The quotient of 2 and the sum of a number and 1.
Answer:
2 / (x + 1).
Step-by-step explanation:
If the number is represented by x the expression is:
2 / (x + 1).
Answer:
2 / (x + 1).
Step-by-step explanation:
If the quotient of 2 and the sum of a number and 1 is 2 / (x + 1).
Yolanda's age is 5 years less than twice Marco's age. If Yolanda is 15 years old, how old is Marcus? Choose the answer below that is a viable solution to this problem. A. 10 B. 8 C. 5 D. 1
Answer:
(A) 10
Step-by-step explanation:
Let age of Marco's be "x" years
then according to question
Yolanda age will be "2x - 5"
Also in the question it is given that age Yolanda is 15 years.
then, 2x - 5 = 15
Adding 5 both sides of the equation, we will get
2x = 20
Dividing both sides of the equality by 2, we get
x = 10
therefore, Age of Marcus will be 10years
Option (A) is the correct option.
Can you explain to me what is 20% of 150, and how to get it?
Answer:
30
Step-by-step explanation:
20% = 20/100= 1/5
It is 1/5 of the number 150
Taking the problem what is 20% of 150
Is means equals and of means multiply
what is 20% of 150
W = 20% * 150
Change 20% to a decimal
W = .20 * 150
W = 30
Answer:
20% of 150 is 30
Step by Step Solution:
To find percentage of any number, we must change the percent to a decimal.
Step 1: Move the decimal place in 20% to the left by two place so that it ends up being .20
Step 2: Now that 20% is now .20, We simply 150 by .20
Conclusion: 20% of 150 is 30
two more than the product of a number and 5 equals 9. use variable x for the unknown number
Answer:
[tex]x=\frac{7}{5}[/tex]
Step-by-step explanation:
The question states product so we know that we're multiplying.
A number and 5, and since the unknown variable is now [tex]x[/tex] we have [tex]5x[/tex] so far.
Then we need to make it so that it is 2 more.
[tex]5x+2[/tex]
Equals 9.
[tex]5x+2=9[/tex]
Solve for the unknown number.
[tex]5x=7[/tex]
[tex]x=\frac{7}{5}[/tex]
Transforming the problem into the equation 5x + 2 = 9, where 'x' is the unknown number, we solve for 'x' by subtracting 2 from both sides and then dividing by 5, yielding 'x' = 7/5, or 1.4.
Explanation:The mathematics problem described can be solved using simple algebra. The problem is stated as: two more than the product of a number and 5 equals 9. If we use the variable 'x' to represent the unknown number, then we can write the algebraic equation to represent this problem as 5x + 2 = 9. The next step would be to solve this equation to find the value of 'x'. In order to isolate 'x', you would first subtract 2 from both sides of the equation, yielding 5x = 7. To find 'x', you would then divide both sides of the equation by 5. The solution to the equation, and therefore the value of the unknown number 'x', would thus be 7/5 or 1.4.
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Find the value of the combination. 16 C 14
Answer:
16C14 = 120
Step-by-step explanation:
we need to find the value of the combination 16C14.
The formula used is [tex]nCr= \frac{n!}{r!(n-r)!}[/tex]
in the given question
n = 16
and r = 14
Putting values and solving:
[tex]16C14= \frac{16!}{14!(16-14)!}\\16C14= \frac{16!}{14!2!}\\16!\,\,can\,\,be\,\,written\,\,as\,\, 16*15*14!\\16C14= \frac{16*15*14!}{14!2!}\\16C14= \frac{16*15}{2*1}\\16C14= \frac{240}{2}\\16C14 = 120[/tex]
So, 16C14 = 120
Answer:
120
Step-by-step explanation:
Using the definition of n[tex]C_{r}[/tex] = [tex]\frac{n!}{r!(n-r)!}[/tex]
where n ! = n(n - 1)(n - 2)...... × 3 × 2 × 1
16[tex]C_{14}[/tex]
= [tex]\frac{16!}{14!2!}[/tex]
= [tex]\frac{16(15)14!}{14!(2)(1)}[/tex] ← cancel 14 !
= [tex]\frac{16(15)}{2}[/tex] = [tex]\frac{240}{2}[/tex] = 120
Let f(w) = 2w^3 - 5. What is f(4)?
Answer:
f(4) =123
Step-by-step explanation:
first your going to put in 4 for every w
then, think of PEMDAS.
after you solve your parenthesis, then exponents Multiply/devide Then, add/subtract.
2(4)^3 -5
2* 64 -5
128 - 5
123 = f(4)
Question 2 of 10
2 Points
The temperature is 45°F. The temperature will decrease by 2°F each hour. Let
h be the number of hours.
When will the temperature be below 32°F?
Write an inequality for this problem.
O
A. 45 + 2h 32
B. 45 + 2h< 32
O c. 45 - 2h<32
O
D. 45 - 2hs 32
Answer:
45-2(h-1)<32
Step-by-step explanation:
This is a problem related to arithmetic progression. The formula we use is that of for nth term
[tex]a_{n}=a+(n-1)d[/tex]
Here
[tex]a=45 , d=-2 ,n=h , a_{n}=a_{h}[/tex]
[tex]a_{h}=45+(h-1)(-2)\\a_{h}=45-2(h-1)\\[/tex]
Now we have to analyse a situation when our temperature comes below 32
or
[tex]a_{h}<32[tex]
[tex]45-2(h-1)<32\\45-2h+2<32\\45-2h<32-2\\45-2h<30\\[/tex]
This is our inequality
Solving this
[tex]45-2h<30\\-2h<30-45\\-2h<-15\\h>7.5\\[/tex]
Hence in 8th hours the temperature will be below 32F
Express ‘y’ in term of ‘x’ in the solution 5y-3x-10=0
What is this can someone please help?
Answer:
x= 6
Step-by-step explanation:
You need to set up a proportion
12/8 = 9/x
Then you do Cross Product Property
8*9=72
12*x=12x
12x=72
divide 72 by 12
72/12=6
x=6
Answer:
A
Step-by-step explanation:
The ratios of corresponding sides are equal, that is
[tex]\frac{XZ}{DF}[/tex] = [tex]\frac{XY}{DE}[/tex], that is
[tex]\frac{12}{8}[/tex] = [tex]\frac{9}{x}[/tex] ( cross- multiply )
12x = 72 ( divide both sides by 12 )
x = 6
x = DE = 6 → A
Convert 30 days to weeks and days
Answer:
4 weeks and 2 days
Step-by-step explanation:
There are 7 days in one week.
To convert 30 days into weeks and days, divide 30 by 7.
The biggest number you can divide it by is 4 [without going over 30]
7 x 4 = 28.
30 - 28 = 2.
So 30 days = 4 weeks and 2 days.
I hope this helps! :)
Answer:
4 weeks and 2 days
Step-by-step explanation:
What is the domain of the function Y = In(x+2)?
044-2
Α
x -2
442
22
Answer:
x>-2
Step-by-step explanation:
I can't read or understand your choices... But you can only take log of positive numbers....
That is you need x+2 is to be positive.
That is as an inequality you need x+2>0
Solving x+2>0 gives you x>-2
what happens to the value of the expression b-1 as b increases
Answer:
It increases
Step-by-step explanation:
if b increases and the only other part of the equation is a constant it should increase as well. for example (the first value is b and the second is b-1) : (1,0) (2,1) (3,2) (4,3) (5,4)...
Answer:
The value increases
Step-by-step explanation:
Thinking process:
Let the expression be: b - 1
Let's say the value of b was 0, then the function will be: 0 - 1 = -1
Let the value of b be increased to 1, the expression will be 1 - 1 = 0
Let the value of b be increased to 2, the expression will be 2 - 1 = 1
Let the value of b be increased to 3, the expression will be 3 - 1 = 2
From the simulation, as the value of b increases, the net value becomes large.
Please help guys I don’t get it thank you so much to whoever answers :)
Lainey paid 30 cents (equivalent to $0.30) for each marker in the set.
To find the cost of 1 marker, you can divide the total cost by the number of markers.
Cost of 1 marker = Total cost / Number of markers
In this case, the total cost is $6, and the number of markers is 20.
Cost of 1 marker = $6/20
Simplifying the expression:
Cost of 1 marker=$0.30
Therefore, the cost of 1 marker is $0.30.
Think of the cost as being divided equally among all 20 markers. By dividing the total cost ($6) by the number of markers (20), we find the share of the cost for each marker ($0.30).
Question:
What is the value of a in the equation 3 a + b = 54, when b=9
To solve this plug in 9 for b and solve for a like so...
3a + 9 = 54
9 must be combined with 54. To do this you must subtract 9 from both sides. This will cancel out 9 from the left and bring it over to the right
3a + (9 - 9) = 54 - 9
3a + 0 = 45
3a = 45
Now we must isolate the a. To do this you have to divide 3 to both sides. This will make 3 on the left side 1 and bring 3 over to the other side
3a/3 = 45/3
1a = 15
a = 15
Hope this helped!
~Just a girl in love with Shawn Mendes
Identify the inverse g(x) of the given relation f(x).
f(x) = {(8,3), (4, 1), (0, -1), (-4, -3)}
g(x) = {(-4, -3), (0, -1), (4, 1), (8,3)}
g(x) = {(-8, -3), (-4, 1), (0, 1), (4,3)}
g(x) = {(8, -3), (4, -1), (0.1), (-4,3)}
g(x) = {(3.8), (1,4),(-1,0), (-3,-4)}
Answer:
D
Step-by-step explanation:
Given (x, y) is a point on f(x), then the corresponding point on the inverse g(x) is (y, x)
Hence
(8, 3) → (3, 8)
(4, 1) → (1, 4)
(0, - 1) → (- 1, 0)
(- 4, - 3) → (- 3, - 4)
That is the last set of points represents g(x)
Solve (x + 9)2 = 25
1. Apply the square root property of equality
2 Isolate the variable
Itx+95, then
If x +92 +5, then
Answer:
x = - 14, x = - 4
Step-by-step explanation:
Given
(x + 9)² = 25 ( take the square root of both sides )
x + 9 = ± [tex]\sqrt{25}[/tex] = ± 5
Subtract 9 from both sides
x = - 9 ± 5, that is
x = - 9 - 5 = - 14 or x = - 9 + 5 = - 4
Ush financial is examining the use of it midtown Atm machine. Here are the numbers of transactions made per day at this atm during the past 9days 53,21,46,33,9,46,8,10,8 find the range of the data set
Answer:
8 to 53;45
Step-by-step explanation:
This is because 8 is the smallest and 53 is the biggest and the difference of 53-8 = 45
(please give brainliest)
Solve: x + 2.5 = 1.5
Answer:
x = -1
Step-by-step explanation:
x + 2.5 = 1.5
- 2.5 -2.5
x = -1
Help me out here please
Tom has 2 8-foot long boards he needs to cut pieces that are 15 inches long. How many 15 inch pieces can he cut from the two boards?
Answer:
Tom can cut 12 (15 inch pieces) from the two boards.
Step-by-step explanation:
We're first given foot measurements and we're asked to find the answer in inches. That means we must convert 8 feet to inches, which is a 1:12 inches conversion. 8 times 12 will give you 96, so now you will multiply that value by 2 because Tom has 2 8-foot long boards. That will give you 192 inches. Since the question is asking for 'how many 15 inch pieces he can cut from the two boards?', you will need to divide 192 inches by 15 to find the answer. This will give you 12.8 boards. Because you can't have parts of an object, the answer will be 12 whole boards.
Scenario:
Susan wants to make 2 square flags to sell at a crafts fair. the fabric she wants to buy is 3 meters wide. she doesn't want any fabric left over. What's the least amount of fabric she should buy?
Question:
Which equation will help Susan solve her problem?
Note: Let X represent the length of 1 side of the flag.
Options:
1) 3x^2 -2x =0
2) 2x^2 =3x
3) 2 * 2 = 2 * 2
4) 6 +2x = 2(4x)
Answer:
B) 2x² = 3x
Step-by-step explanation:
Answer:
Option 2 - [tex]x^2=3x[/tex]
Step-by-step explanation:
Given : Susan wants to make 2 square flags to sell at a crafts fair. The fabric she wants to buy is 3 meters wide. she doesn't want any fabric left over.
To find : What's the least amount of fabric she should buy?
Solution :
If she doesn't want any fabric left over.
The fabric purchased should have same area of the flags.
So, let x be the length of 1 side of the flag.
Area of the flag is
[tex]A=s^2[/tex]
[tex]A=x^2[/tex]
Area of 2 square flags is [tex]A=2x^2[/tex]
Now, Area of fabric is
[tex]A=l\times b[/tex]
[tex]A=x\times 3[/tex]
[tex]A=3x[/tex]
According to question,
Area is same so,
[tex]x^2=3x[/tex]
Therefore, Option 2 is correct.
HELP ASAP
What is the circumference of the circle? Use 3.14 for PIE
A)51.81 cm
B)102.3 cm
C)103.62 cm
D)207.24 cm
Answer:
D
Step-by-step explanation:
Circumference of a circle:
[tex]\pi \times d[/tex]
and pie is 3.14
therefore
[tex]3.14 \times 33 = 103.62[/tex]
Henry invested $4,300 in an account paying an interest rate of 3.6% compounded quarterly. Assuming no deposits or withdrawals are made, how long would it take, to the nearest year, for the value of the account to reach $6,730?
Answer:
12.67 years
Step-by-step explanation:
Follow below steps;
To find out how long it takes for the value of the account to reach $6,730:
Calculate the formula for compound interest: A = P(1 + r/n)^(nt)
Plug in the values: $6,730 = $4,300(1 + 0.036/4)^(4t)
Solve for time(t): approximately t = 10.35 years, which rounded to the nearest year is 10 years
What is the midpoint of (-1,5) (5,5)
To find the midpoint, add the two X values and divide by 2 and add the two Y values and divide by 2.
-1 + 5 = 4/2 = 2
5 +5 = 10 /2 = 5
Midpoint = (2,5)
Answer:
(2,5)
Step-by-step explanation:
The points are on the same y, which is 5, so we only have to find the distance between the x values.
Distance formula = [tex]M = \frac{x_{1} + x_{2} }{2}[/tex]
[tex]M = \frac{-1 + 5}{2}[/tex]
Mid = \frac{4}{2} [tex]
Mid = 2
Which values are within the range of the piecewise-defined function?
F(x)={2x+2,x<-3{x,x=-3{-x-2,x>-3
Answer: y < 1
Step-by-step explanation:
[tex]\begin{array}{c|c||l}\underline{x; x<-3}&\underline{y=2x+2}&\\-5&2(-5)+2=-8&\\-4&2(-4)+2=-6&\\-3&2(-3)+2=-4&\text{approaching but not including -4}\\&&&\underline{x; x=-3}&\underline{\qquad y=x\qquad}&\\-3&-3&\\&&&\\\underline{x; x>-3}&\underline{y=-x-2}&\\-3&-(-3)-2=1&\text{approaching but not including 1}\\-2&-(-2)-2=0&\\-1&-(-1)-2=-1&\end{array}[/tex]
The first function has the range of y < -4
The second function has the range of y = -3
The third function has the range of y < 1
The largest y-value is 1 and the smallest y-value is -∞, therefore the range (y-values) are from -∞ to 1 → y < 1
Answer:
y=-6
y=-4
y=-3
y=0
Step-by-step explanation:
Help me... :/
Find the measure of each exterior angle of a regular 45-gon.
Answer:
7740° / 45
Step-by-step explanation:
The sum of the interior angles is given by this formula: (n - 2) * 180°. So a regular 45-gon would have interior angles that add up to: (45 - 2) * 180°. = 43 * 180°. = 7740°. Now divide that by the 45 angles to find the measure of one interior angle
hope that helped :(
The measure of each exterior angle of a regular 45-gon is calculated using the formula: Exterior Angle = 360° / Number of Sides. Hence, each exterior angle of a 45-gon measures 8°.
Explanation:In mathematics, the measure of each exterior angle of a regular polygon can be found using the formula: Exterior Angle = 360° / Number of Sides. So, to find the measure of an exterior angle in a 45-sided shape, or 45-gon, you would perform the calculation: 360° / 45 = 8°.
This indicates that each exterior angle of a regular 45-gon measures 8 degrees. This is a key concept to remember when working with regular polygons, as it can be used to determine other characteristics of the shape such as the sum of the exterior angles, which in any polygon is always 360°.
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