Answer:
Part A:
This data is modeling an exponential function because the y-values are increasing at an increasing rate. For example, between station 1 and station 2, the time increased by 2 minutes, and between station 2 and station 3, the time increased by 4 minutes. The time between each station is increasing by a multiple of the time between the previous two stations. This indicates that the data follows an exponential curve.
Part B:
To represent this data as a function, we can use the formula y = ab^x, where a and b are constants and x is the input (station number).
Substituting in the values from the first data point, we get: 2 = ab^1
Substituting in the values from the second data point, we get: 4 = ab^2
We can then solve for a and b by dividing these equations:
4/2 = (ab^2)/(ab^1)
2 = b
Substituting this value back into the first equation, we get:
2 = a*2^1
1 = a
Therefore, the function that represents this data is y = 2^x.
Part C:
To find the average rate of change between station 2 and station 4, we can use the formula: (y2 - y1)/(x2 - x1).
Substituting in the values from the data, we get: (16 - 4)/(4 - 2) = 12/2 = 6.
Therefore, the average rate of change between station 2 and station 4 is 6.
4.4) Find the least number by which 768 must be multiplied so as to make it a perfect square
Answer:
3
Step-by-step explanation:
768 can be broken down to:
2×2×2×2×2×2×2×2×3
The part made up of twos is already a perfect square. The 3 needs a partner for it to be a perfect square also.
768 × 3 is 2304.
Sqrt2304 is 48.
Multiply 768 by 3 to make it a perfect square.
Refer To The Given Image
The table, the equation, and the graph show the rates at which three different students read in words per
minute. Which student reads faster?
The student that has the highest reading rate is Student C who has the highest rate of change of the number of words read of 158 words per minute.
What is the rate of change of a function?The rate of change of a function is the rate at which the output value changes per unit change in the input value.
The possible data and table obtained from a similar question on the website are presented as follows;
Student A
Number of minutes; [tex]{}[/tex]1 2 3 4
Number of words read; 150 [tex]{}[/tex]300 450 600
Student B
y = 158·x
Where;
x = The time duration in minutes
y = The number of words read by the student
Student C
The points on the graph representing the reading rate of student C are; (2, 280), (3, 420), (5, 700)
The first difference of the number of words read by Student 1 is constant, indicating that the relationship is a linear relationship, with the reading rate obtained by the rate of change of the number of words read as follows;
Reading rate for Student A = (300 - 150)/(2 - 1) = 150
The reading rate for Student A is 150 words per minute
The equation for the reading rate of Student B; y = 158·x, indicates that Student B reads 158 words per minute
The of the straight ling graph for the reading rate of Student C is found as follows;
Slope = (420 - 280)/(3 - 2) = 140
The slope indicates that the number of words read by Student C increases by 140 words every minute, therefore, the reading rate for Student C is 140 words per minute
The student that reads fastest is therefore, Student C who has a reading reading rate of 158 words per minute
Learn more about the slope of the graph of a function here: https://brainly.com/question/13434264
#SPJ1
Which graph represents a function?
Answer:
The fourth graph since it passes the vertical line test.
Each input has one output.
Hope this helps :)
Pls help! Step by step
Answer:
x = 4[tex]\sqrt{3}[/tex]
Step-by-step explanation:
using the cosine ratio in the right triangle and the exact value
cos30° = [tex]\frac{\sqrt{3} }{2}[/tex] , then
cos30° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{x}{8}[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex] ( cross- multiply )
2x = 8[tex]\sqrt{3}[/tex] ( divide both sides by 2 )
x = 4[tex]\sqrt{3}[/tex] ( exact value )
Step-by-step explanation:
SOHCAHTOA
CAH-
Cosine●= adj/hyp
cos30= y/8
0.8660=y/8
Cross multiply
0.8660×8=y
y=8×0.8660
y=6.928
A cell tower is located 3 miles east and 6 miles north of the center of a small town. The cell tower has a coverage radius of 4 miles.
Start by drawing a diagram of this situation. Your diagram might include a coordinate plane, the cell tower, and a circle representing the cell tower's coverage boundary.
A house is located 7 miles north of the center of the town and is to the east of the cell tower. If the house lies on the boundary of the cell tower's coverage, how far east of the center of the town is the house?
The house is located 6.87 miles to the east of the cell tower.
What is Pythagoras theorem?“In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“.
Given:
Let the center of the town represent the origin (0,0).
Also 1 unit = 1 mile.
Since the cell tower is located 3 miles east and 6 miles north of the center of a small town, it is represented by A(3, 6)
The cell tower has a coverage of radius 4 miles. This can be represented by a circle with equation:
(x - a)² + (y - b)² = r². where (a,b) is the center of the circle and r is the radius.
Then, (x - 3)² + (y - 6)² = 4²
(x - 3)² + (y - 6)² = 16
b) The house is 7 miles north. It can be represented by y = 5 line.
To find the distance east of the house we have to substitute y = 5 and solve for x,
(x - 3)² + (y - 6)² = 16
(x - 3)² + (5 - 6)² = 16
(x - 3)² + 1 = 16
(x - 3)² = 15
(x - 3) = ±3.87
x= 3 ±3.87
x= 6.87 or 0.87.
Hence, the house is located 6.87 miles to the east.
Learn more about Pythagoras theorem here:
https://brainly.com/question/21926466
#SPJ1
Ian is taking a true/false quiz that has four questions on it. The correct sequence of answers
is T, T, F, T. Ian has not studied and yet guesses all answers correctly- He decides he wants
to determine how likely this is to happen using a simulation. He decides to use a fair coin to
do the simulation.
Describe the design of a simulation that would allow Ian to determine how likely it would
be to guess all answers correctly on this quiz.
The design of a simulation that would allow Ian to determine how likely it would
be to guess all answers correctly on this quiz can be Illustrated through a coin.
How to design the simulation?Ian can design a simulation to determine the likelihood of guessing all answers correctly on the quiz by using a fair coin. He can flip the coin four times, with each flip representing a guess on the quiz. If the coin lands heads up, he marks it as a true answer, and if it lands tails up, he marks it as a false answer.
He can repeat this process a large number of times (e.g. 1000) and count the number of times that the sequence T, T, F, T is generated. The proportion of times that this sequence is generated out of the total number of simulations will be an estimate of the probability of guessing all answers correctly on the quiz by chance.
Learn more about simulation on:
https://brainly.com/question/15892457
#SPJ1
I need help with this PLEASE!!!
Answer:
See the image for marked congruences.
1. JM ≅ LM | Given
2. △JML is isosceles | definition of isosceles
3. ∠MJL ≅ ∠MLJ | isosceles triangle theorem
4. m∠MJL = m∠MLJ | definition of ≅
5. JK ≅ LK | Given
6. △JKL is isosceles | definition of isosceles
7. m∠KJL = m∠KLJ | isosceles triangle theorem
8. m∠MJL + m∠KJM = m∠KJL | adjacent angle theorem
9. m∠MLJ + m∠KMJ = m∠KLJ | adjacent angle theorem
10. m∠MJL + m∠KJM = m∠MLJ + m∠KLM | transitive property of =
11. m∠MJL + m∠KJM = m∠MJL + m∠KLM | substitution
12. m∠KJM = m∠KMJ | subtraction
13. ∠KJM ≅ ∠KLM | definition of ≅
14. △KJM ≅ △KLM | SAS theorem
15. ∠JKM ≅ ∠LKM | CPCTC
16. KM bisects ∠JKL | definition of bisector
100 POINTS PLEASE HELP!!! PICTURE IS ATTACHED.
The simplified expression is [tex]c^2 d^2 e^6 / b^8[/tex]
How simplification of an expression work?The given expression is [tex](a^0 b^-4 cde^3)^2[/tex]
We know that any number raised to the power of 0 is 1.
Therefore,[tex]a^0 = 1[/tex].
Also, any number raised to the power of -1 is its reciprocal.
Therefore, [tex]b^-4 = 1/b^4[/tex]
Simplifying the above expression we get
[tex](1*1/b^4 * cde^3)^2 = (cde^3/b^4)^2[/tex]
Now, we apply the rule that [tex](a^m * a^n) = a^(m+n)[/tex]
So, [tex](cde^3/b^4)^2 = c^2 d^2 e^6 / b^8)[/tex]
Hence the simplified expression is [tex]c^2 d^2 e^6 / b^8[/tex]
Please note, when an exponent is raised to another exponent, we can multiply the exponents, so [tex](a^m)^n = a^(m*n)[/tex]
To know more about simplification visit: https://brainly.com/question/28996879
#SPJ1
what is the slope of the table below? 3/8 15/12 9/10 0/7
The slope of the table below? 3/8 15/12 9/10 0/7 is 23.8
What is slope?Slope is defined as the rate of change of y with respect to x. Invariably, it it the rise in y over the run in x. put differently, slope is increase over increase in x
The slope of a line is defined
S= (increase in y)/(Increase in x) = Δy/Δx
Slope = (0/7 - 18/12) ÷ (9/10 -3/8)
Slope = 15/12 ÷ 42/80
Simplify the fractions to have
Slope = 15/12 * 80/42
The slope = 1200/504
Slope of the table is given as 23.4
Conclusively, the table gives us a slope approximately 23
Learn more about slope on https://brainly.com/question/3605446
#SPJ1
I need help with this?
The first equation will be multiplied by 3 and that of the second by 4.
What is an elimination method?An elimination method is a process of solving a system of linear equation, in this we make coefficients of the one variable equal and subtract the equations.
Given that are two equations to be solved by using elimination method,
-4x+4y = 32.....(i)
3x-y = 12......(ii)
To eliminate x, we will multiply eq(i) by 3 and eq(ii) by 4
-12x+12y = 96.....(iii)
12x-4y = 48....(iv)
Solving the equations, we get,
8y = 144
y = 18
Put y = 18 in eq (ii)
3x-18 = 12
3x = 30
x = 10
Hence, the first equation will be multiplied by 3 and that of the second by 4.
Learn more about elimination method, click;
https://brainly.com/question/12090959
#SPJ1
[tex] \: \: \: \: \: \rm \: 25x {}^{2} = - 25 + 50x[/tex]
Find possible values of x
Answer:
[tex]\boxed{\boxed{\sf x=1}}[/tex]
Step-by-step explanation:
[tex]\sf 25x^2=-25+50x[/tex]
Simplify both sides of the equation:-
[tex]\sf 25x^2-50x=-25[/tex]
Subtract 50x-25 from both sides:-
[tex]\sf 25x^2-(50x-25)=50x-25-(50x-25)[/tex]
[tex]\sf 25x^2-50x+25=0[/tex]
Factor left side of equation:-
[tex]\sf 25(x-1)(x-1)=0[/tex]
Set factors equal to 0:-
[tex]\sf x-1=0\: or\: x-1=0[/tex]
[tex]\sf x=1[/tex]
___________________
Hope this helps!
Have a great day!
Mona loves the ocean, so she was thrilled to visit the beach and collect some seashells. The function g(x) gives the number of seashells Mona found after x minutes of searching.
What does g(30)≥20 tell you?
The inequality g(30) ≥ 20 us that: D. Mona found no more than 20 seashells in the first 30 minutes.
What is an inequality?In Mathematics, an inequality simply refers to a mathematical relation that can be used to compare two (2) or more numerical values, numbers, and variables in an algebraic equation, especially based on any of the following inequality symbols:
Greater than or equal to (≥).Greater than (>).Less than (<).Less than or equal to (≤).How to determine the required function?Assuming the variable g represents the total number of seashells and the variable x represents the total number of time (minutes), an inequality which would model the situation is given by;
g(x) ≥ x
when x = 30, we have;
g(30) ≥ 20
Therefore, Mona found no more than (less than or equal to) 20 seashells in the first 30 minutes.
Read more on inequality here: brainly.com/question/27166555
#SPJ1
Complete Question:
Mona loves the ocean, so she was thrilled to visit the beach and collect some seashells. The function g(x) gives the number of seashells Mona found after x minutes of searching.
What does g(30) ≥ 20 tell you?
It took at least 20 minutes for Mona to find 30 seashells.
Mona found at least 20 seashells in the first 30 minutes.
It took at least 30 minutes for Mona to find 20 seashells.
Mona found no more than 20 seashells in the first 30 minutes.
In triangle ABC, angle A is 37° and angle B is 24*. Select all triangles which are similar to triangle ABC.
D triangle DEF where angle Dis 37° and angle E is 24
• triangle GHI where angle G is 37" and angle I is 34°
O triangle JKL where angle J is 35" and angle L is 125*
• triangle MNO where angle Nis 24* and angle E is 119
O triangle POR where angle O is 24° and angle R is 30
Answer:
Triangles DEF and JKL are similar to triangle ABC because they have corresponding angles with the same measure.
Step-by-step explanation:
•Triangles DEF and JKL are similar to triangle ABC because they have corresponding angles with the same measure.
•The Triangle GHI is not similar to triangle ABC because the measure of angle G does not match the measure of angle A.
•The Triangle MNO is not similar to triangle ABC because the measure of angle N does not match the measure of angle B.
• The Triangle POR is not similar to triangle ABC because the measure of angle R does not match the measure of angle A or B.
To learn more about traingles :-
https://brainly.com/question/21752738?referrer=searchResults
https://brainly.com/question/8141142?referrer=searchResults
A triangle has dimensions 9ft by 12ft if you wanted to increase the size of the triangle by a scale factor of 10 over three what would the area of the new triangle be
The area of the new triangle is 600ft²
How determine the area of the new triangle?To increase the size of a triangle by a scale factor of 10/3, multiply each dimension of the triangle by 10/3.
The new dimensions of the triangle will be:
10/3 × 9ft = 30ft
10/3 × 12ft = 40ft
The area of a triangle is given by the formula A = 1/2 × b ×h,
where b is the length of the base and h is the height of the triangle.
Thus, the area of the new triangle will be:
A = 1/2 × 30 × 40 = 600ft²
Learn more about area of a triangle on:
https://brainly.com/question/639390
#SPJ1
Find, rounded to the nearest hundredth, the diagonal of a rectangle whose sides are 6 and 11.
WHAT IS THE ANSWER. I NEED IT ASAP
Answer:
The length of the diagonal is 12.53
Step-by-step explanation:
Since we have a rectangle, the diagonal is the hypotenuse of a right triangle. So we can use Pythagorean Theorem.
a^2 + b^2 = c^2
We know the two legs are 6 and 11, so we can find the hypotenuse (which is the diagonal) see image.
See image.
Complete the table using the function c = 12m - 17.
Step-by-step explanation:
c = 12m - 17
m = 2
c = 12×2 - 17 = 24 - 17 = 7
m = 4
c = 12×4 - 17 = 48 - 17 = 31
m = 8
c = 12×8 - 17 = 96 - 17 = 79
If f(x)=2(x)^2+5square root (5+2) complete the following statement f(2)= blank
The complete statement is f(2) = 8+5√7
What are functions?Function, in mathematics, is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given here f(x)=2x²+5√7
Thus f(1) = 2×4+5√7
= 8+5√7
Hence, The complete statement is f(2) = 8+5√7
Learn more about functions here:
https://brainly.com/question/28303908
#SPJ1
-15 POINTS-
A.
B.
C.
Answer:
Trapezoid
Step-by-step explanation:
The math
Worked Example:
Select all the expressions that have the same value as 4 1/2% of 50.
A. 0.045x50
B. 4.5%x50
C. 43%x50
D. 4.5x50
E. 0.45x50
F. 412x50
Answer:
Options A and B------------------------------------------
4 1/2% of 50 is 4.5% of 50 which is same as:
4.5% × 50or substituting % with 1/100,
4.5/100 × 50 = 0.045 × 50The matching choices are A and B.
i feel like im doing something wrong here it's in order of operation
(3+5)5-20(2+5) when i put it in a calculator it says the answer is 27 but when i work out the problem out i get out 0
We will solve the expression:
(3 + 5)*5 - 20*(2 + 5)
Step by step, and we will get the solution -100.
How to solve the expression?Here we want to solve the following expression:
(3 + 5)*5 - 20*(2 + 5)
The first thing that you need to solve when working in these type of problems, are the operations inside the parenthesis, then we will get:
(3 + 5)*5 - 20*(2 + 5) = (8)*5 - 20*(7)
Now we need to solve the two products, we will get:
(8)*5 - 20*(7) = 40 - 140 = -100
Thus, the solution of that expression is -100.
Learn more about solving expressions:
https://brainly.com/question/723406
#SPJ1
which value of s makes the following true 7s < 42
The value of s that makes the inequality true is 6
What is an inequality?An inequality can simply be defined as a mathematical relation that makes a non-equal comparison between two variables, numbers, ratios or other mathematical expressions.
It is used in comparing two numbers on the number line on the basis of their size.
The inequality signs are;
Greater than: >Less than: <Greater than or equal to: ≥Less than or equal to: ≤From the expression given, we have;
7s < 42
Make 's' the subject by dividing both sides by 7, we have;
s > 42/7
s> 6
Hence, the value is greater than 6
Learn more about inequality here:
https://brainly.com/question/25275758
#SPJ1
Please Click The Screenshot.
Answer:
Step-by-step explanation:
70%=0.7
90 X 0.7 = 63
ANSWER IS 63
Make equivalent fractions with the LCD of 12:
5/6 + 1/4 =
5/12 + 1/12 =
10/12 + 3/12 =
7/12 + 4/12 =
11/12 + 5/12 =
Which one?
Answer:
All four are equivalent fractions with the LCD of 12
Step-by-step explanation:
Round 0.2275 to the nearest hundredth
Answer:
0.23 is the answer
I wish you luck in your assignments.
What is 17 divided by 9
How many ounces each of a 63% acid solution and a 33% acid solution must be mixed to produce 100 ounces of a 39% acid solution?
Answer:
20 ounces of the 63% solution and 80 ounces of the 33% solution.
Step-by-step explanation:
Let x = number of ounces of 63% solution.
Let y = number of ounces of 33% solution.
The total solution to be made is 100 oz.
x + y = 100
x ounces of 63% solution is 0.63x ounces of acid.
y ounces of 33% solution is 0.33y ounces of acid.
100 ounces of 39% solution is 39 ounces of acid
0.63x + 0.33y = 39
The system of equations is
x + y = 100
0.63x + 0.33y = 39
Multiply the both sides of the first equation by -0.33. Then add it to the second equation.
-0.33x - 0.33y = -33
+ 0.63x + 0.33y = 39
---------------------------------
0.3x = 6
x = 6/0.3
x = 20
x + y = 100
20 + y = 100
y = 80
Answer:
20 ounces of the 63% solution and 80 ounces of the 33% solution.
The first modern Olympic games were held in Greece 1896. The 2004 Olympic games in Athens had 202 participating countries. The number of countries in the 2004 Olympic games was more than 14 times the number of countries in the 1896 games. How many countries participated in the 1896 Olympic games?
Answer: To solve this problem, we can use the information provided to set up and solve an equation. Let x be the number of countries that participated in the 1896 Olympic games.
According to the problem, we know that the number of countries in the 2004 Olympic games was more than 14 times the number of countries in the 1896 games. So we can write the following equation:
x * 14 < 202
To solve for x, we can divide both sides of the inequality by 14:
x < 202/14
x < 14.43
x is the number of countries, it must be an integer.
so x = 14
Therefore, 14 countries participated in the 1896 Olympic games.
Step-by-step explanation:
44x46 ayuda plssss speak spanish plssssss
Answer:2024
Step-by-step explanation: 44x46
How do you write 0.00000000090 in scientific notation?
Answer:
Step-by-step explanation:
9.0 × 10-10 I think.....
A woman has 31 coins in her pocket, all of which are dimes and quarters. If the total value of the coins is $ 5.20, how many dimes and how many quarters does she have?
Answer:
D+Q = 31
10D + 25Q = 595
10D + 10Q = 310
subtract to get
15Q = 285 Q = 285/15 = 19 quarters D = 31-19 = 12 dimes