Answer:
The equation that models this situation correctly is C. y = 0.0025(x-90)² + 6.
Step-by-step explanation:
To find the quadratic equation that best models this equation, the only piece of information we need is "The lowest point of the cable is 6ft above the roadway and is a horizontal distance of 90 ft from the left bridge support."
The keyword lowest tells us the value is a minimum. Therefore, the parabola must be a positive one, because negative parabolas have maximum values. This disqualifies answer choices A and B because they have negative a values.
We also know the vertex occurs at (90, 6) because this is where the lowest point is. Therefore, the equation should be y = 0.0025(x-90)² + 6. (Note: the information about point (30, 15) is not relevant to the problem.)
the left and right page numbers of an open book are two consecutive integers whose sum is 329. Find these page numbers.
Follow below steps:
The student is seeking to find two consecutive integers whose sum is 329. This is a mathematics problem and involves understanding of even and odd numbers as well as basic algebra. Since the numbers are consecutive, we can represent them as n and n + 1. The sum of these numbers given in the problem is 329, so we have the equation n + (n + 1) = 329.
Solving this equation:
Combine like terms: 2n + 1 = 329
Subtract 1 from both sides: 2n = 328
Divide both sides by 2: n = 164
Thus, the two consecutive page numbers of the book are 164 and 165
Find the area of this figure. Please show work if you can!
suppose you want to buy three loaves of bread that cost $1•50 each and a jar of peanut butter that costs $4. A jar of jelly is $2•75, but you don't need any jelly. you have $10. how much money will you have left over
Mike earned $11.76 per hour for working 23.5 hours last week.How much money did Mike earn last week?
1. If one letter is chosen at random from the word combed, what is the probability that the letter chosen will be a "d"?
2. The sides of number cube have the numbers 2,4,8,9,4, and 7. If the cube is thrown once, what is the probability of rolling a 7?
3. A bag contains 12 red marbles, 10 green marbles, 2 yellow marbles, 19 blue marbles, and 9 purple marbles. What is the probability of pulling out a green marble?
Answer:
Probability that the chosen letter is d is [tex]\frac{1}{6}[/tex]Probability of rolling a 7 is [tex]\frac{1}{6}[/tex]Probability of picking a green is [tex]\frac{5}{21}[/tex]Step-by-step explanation:
Probability of choosing d in the word "combed"Given:
Alphabet: d
Word: combed
First, we note down the length of the word "combed";
The length is 6 characters
The we check the number of occurrence of d in the word "combed"
Occurrence of d = 1
Probability is then calculated as;
Probability of choosing d = [tex]\frac{Number of Occurrence}{Total Observation}[/tex]
By Substitution; Probability = [tex]\frac{1}{6}[/tex]
Probability of rolling a 7 in a cube of side numbers 2,4,8,9,4, and 7Given:
Roll number = 7
Sample Space= {2,4,8,9,4, 7}
Sample Size, n(S) = 6
We check the number of occurrence of 7 in the sample space
Number of occurrence = 1
Probability is then calculated as;
Probability of rolling a 7 = [tex]\frac{Number of Occurrence}{Sample Size}[/tex]
By Substitution; Probability = [tex]\frac{1}{6}[/tex]
Probability of pulling out a green marbleGiven
Red = 12
Green = 10
Yellow = 2
Blue = 19
Purple = 9
Total = 12 + 10 + 2 + 19 + 9 = 42
Probability of picking a green marble is then calculated as;
Probability of choosing d = [tex]\frac{Number of Green}{Total}[/tex]
By Substitution; Probability = [tex]\frac{10}{42}[/tex]
Probability = [tex]\frac{5}{21}[/tex]
find Two consecutive odd intergers such that 44 more than the lesser is three times the greater
Which of the following would be equivalent to 11 to the 8th power over 11 to the 3rd power?
A)11 to the 7th power over 11 to the 7th power
B)11 ⋅ 114
C)11 to the 0 power over 11 to the 5th power
D)110
Option: B is the correct answer.
[tex]B)\ 11\cdot 11^4[/tex]
Step-by-step explanation:We are given a numerical expression as:
11 to the 8th power over 11 to the 3rd power.
i.e. mathematically it is given by:
[tex]\dfrac{11^8}{11^3}[/tex]
Now, we know that if the numerator and the denominator terms are power terms such that both the terms are of same base then the resultant is the same base and the exponent of the base is: exponent of numerator minus exponent of denominator.
i.e.
[tex]\dfrac{a^m}{a^n}=a^{m-n}[/tex]
Here we have:
[tex]a=11,\ m=8\ and\ n=3[/tex]
Hence, we get:
[tex]\dfrac{11^8}{11^3}=11^{8-3}[/tex]
i.e.
[tex]\dfrac{11^8}{11^3}=11^5[/tex]
Now, this could also be written as:
[tex]\dfrac{11^8}{11^3}=11\cdot 11^4[/tex]
( since,
[tex]a^m\cdot a^n=a^{m+n}\\\\i.e.\\\\11^1\cdot 11^4=11^{4+1}=11^5[/tex] )
help me please I'm stuck
the answer to this question
Which are partial products for 89 × 25?
A. 9 X 2 = 18
B. 8 X 5 = 40
C. 9 X 5 = 45
D. 80 X 20
The sides of a hexagon are equal in length. The perimeter of the hexagon is at most 42 in. Find the possible side lengths of the hexagon
Tom went on a bike ride to the store 3 miles away if it took Time 1/2 hour to get there in 2/3 of an hour to get back what was his average rate of speed miles per hour for the entire trip
In order to achieve the times that he did in going to and from the store, Tom went at an average speed of 5.14 miles per hour.
The store was 3 miles away which means that the distance of the entire trip is:
= Distance going + Distance coming
= 3 + 3
= 6 miles in total
The time he took was:
= Time going + Time coming
= 1/2 hours + 2/3 hours
= 0.5 + 0.67
= 1.17 hours
His average speed for the entire journey is:
= Distance / Time
= 6 / 1.17
= 5.14 miles per hour
In conclusion, Tom's average speed was 5.14 miles per hour.
Find out more at https://brainly.com/question/14523120.
7.4p - 9.2p = -2.6 + 5.3
List three numbers that are divisible by 3, 4 and five
To find numbers divisible by 3, 4, and 5, we need to find common multiples of these three numbers. One example is 30, and other possible numbers include 60 and 90.
Explanation:When we need to find numbers that are divisible by 3, 4, and 5, we can look for numbers that are common multiples of these three numbers. In other words, we need to find numbers that can be divided evenly by 3, 4, and 5 without any remainder. Let's take a look at the first few numbers and see if they satisfy this condition.
15: 15 is divisible by 3 (15 ÷ 3 = 5), divisible by 5 (15 ÷ 5 = 3), but not divisible by 4 (15 ÷ 4 = 3 remainder 3), so it is not a solution.20: 20 is not divisible by 3 (20 ÷ 3 = 6 remainder 2), not divisible by 4 (20 ÷ 4 = 5 remainder 0), but divisible by 5 (20 ÷ 5 = 4), so it is not a solution.30: 30 is divisible by 3 (30 ÷ 3 = 10), divisible by 4 (30 ÷ 4 = 7 remainder 2), and divisible by 5 (30 ÷ 5 = 6), so it is a solution.From our analysis, we found that the number 30 is divisible by 3, 4, and 5. We can list two more numbers by finding common multiples of these three numbers.
6090Customers at an ice-cream shop took a survey. The results showed that 144 customers rates the shop as being "very satisfactory." This number represented 45% of the total number of customers who took the survey. What was the total number of customers who took the survey ? explaination plz
The total number of customers who took the survey is 320 customers
let
x = total number of customers
percentage of "very satisfactory" customers = 45%
Number of "very satisfactory" customers = 144
So,
Number of "very satisfactory" customers = percentage of "very satisfactory" customers × total number of customers
144 = 45% × x
144 = 0.45 × x
144 = 0.45x
x = 144/0.45
x = 320
Therefore, the total number of customers who took the survey is 320
Learn more about percentage:
https://brainly.com/question/843074
Two more than a certain number is 15 less than the product of 7/8 and the number
Final answer:
The algebraic equation derived from the statement is solved by isolating 'x' after moving terms to either side of the equation and combining like terms. The solution to the equation is x = -136, which represents the certain number in question.
Explanation:
Solving the Algebraic Equation
The question can be translated into an algebraic equation. Let's call the certain number 'x'. According to the problem, 'two more than a certain number is 15 less than the product of 7/8 and the number'. We can write this as:
x + 2 = (7/8)x - 15
To solve for x, we can start by moving all terms involving x to one side of the equation and the constant terms to the other side, aiming to isolate x:
Subtract (7/8)x from both sides to get x - (7/8)x + 2 = -15.
Combine like terms, remembering that x is the same as (8/8)x, which results in (1/8)x + 2 = -15.
Subtract 2 from both sides to get (1/8)x = -17.
Multiply both sides by 8 to find x. Therefore, x = -136.
The certain number in the equation is -136.
four of these points lie on a straight line. which one is the odd one out?
(-3,-3) (-2,-1) (2,5) (4,11) (5,13)
Suppose you have developed a scale that indicates the brightness of sunlight each category in the table is five times brighter than the category above it for example a day that is dazzling is five times brighter than a day that is radian how many times brighter is a dazzling day then a dim day
Dim=2
Illuminated=3
Radiant=4
Dazzling=5
Answer:
Basicly all you do is Multiply Dazzling 4 times by 5, so 5*5*5*5 and your answer is 125.
EXAMPLE ;
IF it was 2 times brighter you would count the catagories. There are 4. So you would do 2*2*2*2 and you answer is 16.
There 22,869 children,49,563 men and 2,872 more women than men st the fair.how many people were at the fair?
Jasmine has a budget of $800 for catering. The catering company charges $12.50 per person. Write and solve an inequality to show the number of guests Jasmine can invite.
I have been stuck on this for days someone pls help!!!!
How is mode different from the median?
1/2 +2/3=?
What's the answer?
The volume of a drop of a certain liquid 0.000047 liter write the volume of the drop of liquid in scientific notation
Use the function f(x) = 2 - 5x to fill in the blanks in the table.
x f(x)
-2
-1
0
1
2
2-5(-2)=12
2-5(-1)=7
2-5(0)=2
2-5(1)=-3
2-5(2)=-8
write 45% as a fraction in simplest form
Which following best express this population
The average polar bear weighs 1,200 pounds. The average grizzly bear weighs 800 pounds. The average black bear weighs 400 pounds. The average polar bear weighs how many times more than the average black bear?
The wait time of a line t hours after a store opens is given by the expression.
40x−12x+2340x−1 x+23
What does the value 23 represent?
A.the total number of people in line
B. the total rate of change in people per hour
C.the rate at which people join the line
D.the number of people in line when the store opened
What is the answer to 3/8r=15/16