The equation representing the number of people, y, at the fair x hours after the gates open:
y = 68 * 1.5^(x-1)
Initial number of people: 68 (given)
Growth factor per hour: 1.5 (given)
Number of hours since gates opened: x
The equation uses the following logic:
Start with the initial number of people (68).
Multiply by the growth factor (1.5) to account for the increase after the first hour.
Since the growth factor applies after each hour, raise it to the power of (x-1) to account for the total number of times it's applied after x hours. This is because the first hour's growth is already accounted for in the initial number.
Therefore, the equation y = 68 * 1.5^(x-1) accurately represents the number of people at the fair x hours after opening.
Complete question:
When the county fair opened its gates, 68 people entered the fairgrounds. After one hour, there were 1.5 times as many people on the fairgrounds as when the gates opened. After two hours, there were 1.5 times as many people on the fairgrounds as the previous hour. If this pattern continues, write the equation representing the number of people, y, at the fair x hours after the gates open.
Four people are painting a house. Zachary paints 1/5 of the house, Alyssa paints 33% of the house, Chloe paints 0.3 of the house, and Nicholas paints 0.17 of the house. Which choice lists the people in order from least to greatest by the amount of the house each painted?
Answer:
Nicholas, Zachary, Chloe, Alyssa.
Step-by-step explanation:
Given that Four people are painting a house. Zachary paints 1/5 of the house, Alyssa paints 33% of the house, Chloe paints 0.3 of the house, and Nicholas paints 0.17 of the house.
As such we cannot compare their works to order from least to greatest
Hence we can convert each portion into a decimal thus enabling comparison easier.
Zachary paints [tex]\frac{1}{5} =0.20[/tex] of the house
Alyssa paints [tex]33%=\frac{33}{100} =0.33[/tex] of the house
Chloe paints 0.3 of the house and
Nicholas paints 0.17 of the house.
In ascending order these can be written as
0.17, 0.2, 0.3, 0.33
Hence Nicholas, Zachary, Chloe, Alyssa.
Which of the sets of ordered pairs represents a function? (4 points)
A = {(−4, 5), (1, −1), (2, −2), (2, 3)}
B = {(2, 2), (3, −2), (9, 3), (9, −3)}
you can do both or neither as well THX
What is the exact value of cos theta = squareroot 2 over 2?
x(x+8) = 256 square yards
solve for x
im having a lot of trouble please help
What is the x-intercept of a line that passes through the point (3, 4) and has a slope of 2?
PLEASE HELP
simplify the expression
2. 10r^(-7)t^3
Estimate the decimal factors, then multiply to estimate the product.
1. 5.3 rounded to the nearest whole number is ____ .
2. 7.9 rounded to the nearest whole number is ____ .
3. (5.3)(7.9) ≈ ____ .
Answer:
1. 5
2. 8
3. 40
Step-by-step explanation: So rounding the factors is an easy way to estimate the product of 5.3 and 7.9.
The real answer is 41.87 and 40 is a reasonable approximation, Your welcome.
Math Help??
What is the value of X?
The table below represents the distance a person runs as a function of time:
Time distance meters
x f(x)
10 60
13 78
16 96
19 114
he average rate of change of the function between x = 10 to x = 16 is m/s and represents the person's speed. (3 points)
which ordered pair is a solution of the equation y=x-4
Answer:
Step-by-step explanation:
y = x - 4
there are so many ordered pairs which are the solution of the given equation.
for example,
x = 0, y = -4
x = 1 , y = -3
x = 2, y = -2
x = 3, y = -1
x = 4, y = 0
x = - 1, y = - 5
x = - 2, y = - 6
x = - 3, y = - 7
x = - 4, y = - 8
Megan has a bag of beads. She uses 28 beads to make each necklace. She makes 12 necklaces. Megan has 135 beads left over.
1. Daniel served Dinner for table 14. The check came to $100. The customers tipped him 25%. How much was his tip?
2. Sammy served lunch for table 7. The total came to $55. The customers gave a 15% tip to Sammy. How much was his tip?
3. Cat served dessert for table 3 The total cost was $20. The customers give a tip of 12% to cat. How much was your tip?
At the Yum Yum Cafe , the waiters come binder tips and divide the total by the number of waiters. Today’s tip total is $132, and three waiters are working. How much money in tips does each waiter get?
Daniel, Sammy, and Cat receive $25, $8.25, and $2.40 respectively in tips. The total tip amount for the day is $132, and with three waiters working, each waiter gets an equal share of $44 in tips.
Calculating Tips for Waiters
To calculate the tip for each waiter, we will multiply the total bill amount by the percentage of the tip and then convert that percentage into a decimal. Here are the step-by-step solutions for each waiter:
Daniel's Tip: For Table 14, the bill was $100. A 25% tip is calculated as $100 x 0.25 = $25.
Sammy's Tip: For Table 7, the bill was $55. A 15% tip is calculated as $55 x 0.15 = $8.25.
Cat's Tip: For Table 3, the bill was $20. A 12% tip is calculated as $20 x 0.12 = $2.40.
To find out how much each waiter gets from the total tips, we add up all the tips: $25 + $8.25 + $2.40 = $35.65. Since the total tip amount for the day is $132, we divide this by the number of waiters working, which is three: $132 / 3 = $44. Therefore, each waiter gets $44 in tips.
The relation of this set of points is a function. True or false.
{(−2, 6), (4, 5), (3, −3), (6, 9), (4, −4)}
Question 1 options:
True
False
Save
There are currently 58 million cars in a certain country, increasing exponentially by 5.5% annually. how many years will it take for this country to have 79 million cars? round to the nearest year.
Find the sum of all numbers below 1000 that are divisible by 3 or 5
First of all, stop thinking on the number 10001000 and turn your attention to the number 990990 instead. If you solve the problem for 990990 you just have to add 993,995,996993,995,996 & 999999 to it for the final answer. This sum is (a)=3983(a)=3983
Count all the #s divisible by 33: From 33... to 990990 there are 330330 terms. The sum is 330(990+3)/2330(990+3)/2, so (b)=163845(b)=163845
Count all the #s divisible by 55: From 55... to 990990 there are 198198 terms. The sum is 198(990+5)/2198(990+5)/2, so (c)=98505(c)=98505
Now, the GCD (greatest common divisor) of 33 & 55 is 11, so the LCM (least common multiple) should be 3×5=153×5=15.
This means every number that divides by 1515 was counted twice, and it should be done only once. Because of this, you have an extra set of numbers started with 1515 all the way to 990990 that has to be removed from (b)&(c).
Then, from 1515... to 990990 there are 6666 terms and their sum is 66(990+15)/266(990+15)/2, so (d)=33165(d)=33165
The answer for the problem is: (a)+(b)+(c)−(d)=233168(a)+(b)+(c)−(d)=233168
Simple but very fun problem.
solve this inequality 2(4x-3)≥-3(3x)+5x?
Answer:
x ≥0.5
Step-by-step explanation:
Given : 2(4x-3)≥-3(3x)+5x.
To find : solve this inequality.
Solution : We have given that
2(4x-3)≥-3(3x)+5x.
Distributes 2 over (4x-3) and -3 over 3x.
8x - 6 ≥ -9x + 5x .
8x - 6 ≥ -4x .
On adding both side by 4x
8x + 4x - 6 ≥ 0 .
12 x - 6 ≥ 0
On adding both sides by 6.
12 x ≥ 6.
On dividing both sides by 12.
x ≥ [tex]\frac{6}{12}[/tex] .
x ≥ [tex]\frac{1}{2}[/tex] .
x ≥0.5.
Therefore, x ≥0.5
Graph ƒ(x) = -x + 2. Click on the graph until the graph of ƒ(x) = -x + 2 appears.
Answer with Step-by-step explanation:
We have to graph f(x) = -x + 2
When x=0 , f(x) = 2
When f(x)=0 , x=2
Hence, the graph passes through the points:
(0,2) and (2,0)
So, the correct graph of f(x) = - x + 2 is the last one which is shown below
which blood type was donates by the largest percent of people?
The total number of people at a football game was 5600. field-side tickets were 40 dollars and end-zone tickets were 20 dollars. if the total amount of money received for the tickets was 132000 how many of each kind of ticket were sold.
What is the volume if something measures 6.2 cm x 13.7 cm x 26.9 cm?
The calculated volume is 2284.886 cubic centimeters.
The volume of a rectangular prism (or box) is calculated using the formula:
Volume = length x width x height
For the given measurements:
Length (l) = 6.2 cmWidth (w) = 13.7 cmHeight (h) = 26.9 cmPlug the values into the formula:
Volume = 6.2 cm x 13.7 cm x 26.9 cm
First, calculate the product of the length and width:
6.2 cm x 13.7 cm = 84.94 cm²
Next, multiply this result by the height:
84.94 cm² x 26.9 cm = 2284.886 cm³
Therefore, the volume of the object is 2284.886 cubic centimeters.
Given: -7x < -21.
Choose the solution set.
A. {x | x < -3}
B. {x | x > -3}
C. {x | x < 3}
D. {x | x > 3}
You were assigned to read 5⁄8 of your book. how many sixteenths is that? fraction
n Monday, Elsbeth’s bank account balance was -$16.75. On Tuesday, she deposited a check for $5.72. On Thursday, she deposited $16.75. What is her new balance? -16.75 + (5.72 + 16.75) Use the commutative property to get: -16.75 + (16.75 + 5.72) Use the associative property to get: (-16.75 + 16.75) + 5.72 On Friday, Elsbeth deposited her pay check for $872.56. What was the account’s final total? -$866.84 $878.28 $895.03 $903.10
Answer:
Option B. $878.28
Step-by-step explanation:
On Monday, Elsbeth's bank account balance was = $-16.75
She deposited a check = $5.72
On Thursday, she deposited = $16.75
Her new balance = -16.75+( 5.72 + 16.75)
= $5.72
On Friday Elsbeth deposited her pay check for = $872.56
The account's final total = 872.56 + 5.72 = $878.28
Elsbeth's account's final total was $878.28.
Option B. $878.28.
Do the dimensions of 9 cm, 40 cm, and 41 cm form a right triangle? explain.
Segment AB is rotated to form A'B'¯¯¯¯¯¯¯ . The coordinates of point A are (1, 5) and the coordinates of point B are (−6, 4) . Which clockwise rotation around the origin results in the transformation of AB¯¯¯¯¯ to form A'B'¯¯¯¯¯¯¯ ?
Which of the following properties is 5(3 + 2) = 15 + 10 an example of?
associative property
commutative property
multiplicative identity
distributive property
Answer: Distributive property
Step-by-step explanation:
Associative property states that either in addition or multiplication we can changes the position of parenthesis.
That is, a.(b.c) = (a.b).c or a+(b+c) = (a+b)+c
Commutative property states that in addition or multiplication we can change the order.
That is, a.b = b.a or a+b = b+a
Multiplicative identity is an element that gives the same number after multiplication.
That is, a × 1/a = 1 ⇒ 1/a is the multiplicative identity of a.
Distributive property lets us multiply a sum by multiplying each addend separately and then add the products.
That is, a(b+c) = a.b + a.c
Thus, it is clear that ,
5(3 + 2) = 5× 3+ 5×2 = 15 + 10 is the example of distributive property.
If inflation is 4% a year compounded annually, what will it cost in 20 years to buy a house currently valued at $75,000.00?
Compound interest is the interest that is made from the principal and the interest as well in consecutive years.
The cost of the house in 20 years valued currently at $75,000 is $1,64,250.
What is compound interest?Compound interest is the interest that is made from the principal and the interest as well in consecutive years.
The formula for amount compounded anually:
A = P [tex](1 + \frac{R}{100})^{n}[/tex]
We have,
Principal = $75,000
Rate = 4%
Time = n = 20 years
The amount after 20 years:
A = P [tex](1 + \frac{R}{100})^{n}[/tex]
A = 75,000 [tex](1 + 0.04)^{20}[/tex]
A = 75,000 x [tex]1.04^{20}[/tex]
A = 75,000 x 2.19
A = $1,64,250
Thus,
The cost of the house in 20 years valued currently at $75,000 is $1,64,250.
Learn more about compound interest here:
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PLZ HELPP ME WITH THIS MATH PROBLEM
Which of the following are the factors of t4 – 81? A. (t – 3)(t + 3)(t2 + 9) B. (t – 3)2(t + 3)2 C. (t – 3)(t + 3)2 D. (t2 – 9)(t2 – 9)
The function y = h(x) is defined as follows:
h(1) =
and h(4) =