Answer:
In 2008.
Step-by-step explanation:
The function:
[tex]y=4.2\sqrt{0.28x-1}[/tex]
Models the annual number of visitors to an amusement park, where y is the number of visitors (in millions) and x is the number of years since 1975.
We want to determine the first year in which the amusement park had 12 million visitors.
So, we will set y equal to 12 and solve for x. This yields:
[tex]12=4.2\sqrt{0.28x-1}[/tex]
By dividing both sides by 4.2, we acquire:
[tex]\displaystyle \frac{12}{4.2}=\frac{120}{42}=\frac{20}{7}=\sqrt{0.28x-1}[/tex]
And by squaring both sides:
[tex]\displaystyle \frac{400}{49}=0.28x-1[/tex]
Adding 1 to both sides produces:
[tex]\displaystyle \frac{400}{49}+1=\frac{449}{49}=0.28x[/tex]
And finally, dividing both sides by 0.28 gives us the approximation:
[tex]\displaystyle x=\frac{449}{49}\cdot \frac{1}{.28}=\frac{11225}{343}\approx32.72\approx33[/tex]
So, 33 years after 1975, the amusement park will have 12 million annual visitors.
Therefore, the first year in which the amusement park will have 12 million annual visitors is in the year 2008.
On a college test, students receive 4 points for every question answered correctly and lose 7 points for every question answered incorrectly. On a particular test, Terry answered 87 questions correctly and 46 questions incorrectly. What was his score on the test? Show your work.
Answer:
26
Step-by-step explanation:
correct answers:87
so do 87x4=348
46*7=322
do this because he got some incorrect
348-322=26
so her score is 26
Marcus can drive his boat 36 miles down the river in 3 hours but takes 4 hours to return upstream. Find the rate of the boat
in still water and the rate of the current.
Answer:
With river 12 miles per hour
Against river 9 miles per hour
wv = water velocity vsw = boat velocity in still water
vsw +wv = 12 mph
vsw -wv = 9 mph
2 * vsw = 21 mph
boat velocity in still water = 10.5
Since vsw + wv = 12 then
water velocity = 1.5 mph
Step-by-step explanation:
Answer:
speed in still water: 10.5 Current: 1.5
Step-by-step explanation:
The equation for line g can be written as y = x + 5. Parallel to line g is line h, which passes through the point (-6, -4). What is the equation of line h? SHOW WORK PLEASE
Answer:
y=x+2
Step-by-step explanation:
we know the slopes have to be equal because the lines are parallel, so the slope is 1, or written as x. plug the point given, (-6,-4), and the slope, 1, into the y=mx+b equation to find the y-intercept. then solve. then put the slope and y-intercept together for the equation of line h.
y=mx+b, m=1, x=-6, y=-4
-4=(1)(-6)+b
-4=-6+b
2=b
y=x+2
-) Write 32 + 24 as a product of two factors using the GCF
and the distributive property.
32 + 24
?
+
?
Answer:
8 (4+3)
Step-by-step explanation:
32 + 24 as a product of two factors using the GCF is 8(4 + 3).
Greatest common factor (GCF)?The greatest common factor (GCF) of two number is the largest number which can divide both the numbers completely.
Given,
The expression is 32 + 24 .
The greatest common factor of 24 and 32 can be found using the following method.
Common factors of 24 and 32 are:
2, 4, and 8
Out of all the common factors 8 is the largest number.
Therefore greatest common factor of 24 and 32 is equal to 8.
Taking the GCF out we get:
8(3 + 4)
Hence, 32 + 24 as a product of two factors using the GCF is 8(4 + 3).
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Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution.
Answer:
only one solution
Step-by-step explanation:
Complete question:
Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. 2x − y = 2 3x + y = −6 one and only one solution infinitely many solutions no solution Find the solution, if one exists. (If there are infinitely many solutions, express x and y in terms of the parameter t. If there is no solution, enter NO SOLUTION.) (x, y) =
Given the expression
2x − y = 2 .... 1
3x + y = −6 ..... 2
We are to determine the number of solution the equation has:
Add equation 1 and 2
2x + 3x = 2 - 6
5x = -4
x = -4/5
Substitute x = -4/5 into 1
From 1: 2x − y = 2 .... 1
2(-4/5) - y = 2
-8/5 - y = -2
-y = -2+8/5
-y = -10+8/5
-y = -2/5
y = 2/5
Since the value of x and y are just 1 hence the system of equations has ine solution
What do we put in the first boxes
Answer:
What BOXES?
Step-by-step explanation:
The admission tickets to an exhibition at $5 for an adult and $2 for a child. A family of 3 adults and 4 children visited the exhibition. What would be the charge if $50 note was used to buy the tickets?
Given :
The admission tickets to an exhibition at $5 for an adult and $2 for a child.
A family of 3 adults and 4 children visited the exhibition.
To Find :
What would be the charge if $50 note was used to buy the tickets.
Solution :
Charge of 3 adult ticket is, A = $( 5 × 3 ) = $15 .
Charge of 4 children ticket is, C = $( 4 × 2 ) = $8 .
Total amount to pay is :
T = $( 15 + 8 )
T = $23
Therefore, they get $( 50 - 23 ) = $27 change.
I need help with this problem, I’d appreciate it if someone helped.
Answer:
answer A looks good
Step-by-step explanation:
what is the domain of the function y= cube root x-1
Answer:
A on edge
Step-by-step explanation:
just took the test
Your bill at pizza hut is $30. You leave 20% tip. Whats is the amount of tip?
You gave $30.
[$30 * 0.20] (tip % amount) = $6.
You left $6 in tips.
A ball is dropped from a height of 9 meters. On each bounce, it rises to 35% of its previous height.
When it hits the ground for the sixth time, how far has it traveled?
Round your answer to the nearest hundredth.
List three different combinations of coins, each with a value of 30% of a dollar.
Answer:
1. 3 dimes
2. 1 quarter and a nickel
3. 30 pennies
Step-by-step explanation:
i hope this is it and i hope this helped <3
Answer:
3 nickels, 1 quarter and 5 pennies, and 30 pennies
Step-by-step explanation:
30% of a dollar is 30 cents. those all equal 30 cents
what fraction is equivalent to -3/2
Answer:
-1 1/2
Step-by-step explanation:
60
70
50
Find angle x
Answer:
Where is the pictureeeeeeee
Answer:
picture??
Step-by-step explanation:
At 9 a.m., Jessica started riding on the Red Mountain Parkway at the 40-mile marker.
At the same time, Kate started riding on the Red Mountain Parkway at the 10-mile
marker. Jessica rides her motorcycle at a rate of 30 miles per hour. Kate rides her
motorcycle at a rate of 40 miles per hour. If they are both riding in the same direction,
which graph shows the number of hours after 9 a.m. when Jessica and Kate will be in
the same position on the parkway?
Answer:
See below
Step-by-step explanation:
Start time = 9 A.M.
JessicaStart point- 40 milesSpeed - 30 mphEquation:
y = 40 + 30xKateStart point- 10 milesSpeed - 40 mphEquation:
y = 10 + 40xNote. There is no graph but see the attached. It should be similar graph for this case
The will meet after 3 hours at 130 miles mark
Solving the system of equations we get:
40+30x = 10 + 40x10x = 30x = 3And y is:
y = 40+3*30 = 130(3, 130) is the intersection of lines
Since it takes 3 hours for Jessica and Kate, it happens at 12 A.M.
PLEASE HELP THIS IS TIMED!!!! I WILL GIVE BRAINLIESTTTTTT
The table below represents a linear function f(x) and the equation represents a function g(x):
x f(x)
−1 −3
0 0
1 3
g(x)
g(x) = 7x + 2
Part A: Write a sentence to compare the slope of the two functions and show the steps you used to determine the slope of f(x) and g(x). (6 points)
Part B: Which function has a greater y-intercept? Justify your answer. (4 points)
(10 points)
Answer
Given: Sorry the images are at the bottom.
To find:
Part A: Write a sentence to compare the slope of the two functions and show the steps you used to determine the slope of f(x) and g(x).
Part B: Which function has a greater y-intercept? Justify your answer.
Solution:
On inspection of values of x and f(x) it is clear that f(x) is a linear function
i.e.
1)Slope of f(x) and y-intercept of f(x):
Convert the function in slope intercept form and calculate the slope.
Slope intercept form:
Here,
Slope of f(x)=1,
y-intercept of f(x)=(0,0)
2) Slope and y-intercept of g(x):
Slope of g(x)=7
Y-INTERCEPT of g(x) =(0,2)
Part A:
Slope of f(x) is 1 and slope of g(x) is 7.
Part B:
g(x) has a greater y-intercept.
Hope it helps you.
newibfib
bewbhbhdcwebcwbch
Step-by-step explanation:
Peter Piper picked a pack of pickled peppers. If Peter Piper picked a pack of pickled peppers, How many packs of pickled peppers did Peter Piper pick?
a. tan2 -sin= sin2 tane
Step-by-step explanation:
tan²θ - sin²θ
= sin²θ/cos²θ - sin²θ
= sin²θ * (1/cos²θ - 1)
= sin²θ * (csc²θ - 1)
= sin²θ * tan²θ. (shown)
you play tennis against a player that you have a 20% chance of winning. what is the probability g
Question:
You play tennis against a player that you have a 20% chance of winning. What is the probability that you win no game out of 6 games?
Answer:
[tex]Probability = 0.262144[/tex]
Step-by-step explanation:
Represent the probability of winning with P(Win)
[tex]P(Win) = 20\%[/tex]
Required
Determine the probability of not winning 6 games
First, we calculate the probability of not winning a game.
Opposite probability add up to 1.
So, we have:
[tex]P(Win) + P(Lose) = 1[/tex]
[tex]P(Lose) = 1 - P(Win)[/tex]
[tex]P(Lose) = 1 - 20\%[/tex]
[tex]P(Lose) = 100\% - 20\%[/tex]
[tex]P(Lose) = 80\%[/tex]
The sample space of losing 6 games is:
Lose Lose Lose Lose Lose Lose
Therefore, the probability is:
[tex]Probability = 80\% *80\% *80\% *80\% *80\% *80\%[/tex]
[tex]Probability = 0.80*0.80*0.80*0.80*0.80*0.80[/tex]
[tex]Probability = 0.262144[/tex]
One-third of Olivia's age, increased by 12, is equal to twice her age, decreased by 3. How old is Olivia?
Answer:
Olivia is 9 years old.
Step-by-step explanation:
1/3 of o (Olivia's age) increased by 12, is twice of o minus 3. The equation for this would be 1/3o + 12 = 2o - 3. (The left side could be o/3 as well.)
1/3o + 12 = 2o - 3
Subtract 2o from both sides
-5/3o + 12 = -3
Subtract 12 from both sides
-5/3o = -3 - 12
Subtract 12 from -3 to get -15
-5/3o = -15
Multiply both sides by -3/5, the reciprocal of -5/3
o = -15 (-3/5)
Express -15(-3/5) as a single fraction
o = -15 (-3)/5
Multiply -15 by -3 to get 45
o = 45/5
Divide 45 by 5 to get 9.
o = 9
To make sure this works, substitute 9 for o.
1/3(9) + 12 = 2(9) - 3
3 + 12 = 18 - 3
15 = 15
Both sides match each other, so o equals 9.
Olivia is 9 years old
Let the age of olivia be "x"One-third of Olivia's age is expressed as 1/3xIf it is increased by 12, the expression becomes 1/3 x + 12Twice her age decreased by 3 is expressed as 2x - 3
Equate both expressions and find x
1/3x + 12 = 2x - 3
1/3x - 2x = -3-12
(x-6x)/3 = -15
-5x = -45
x = 9
Hence Olivia is 9 years old
Learn more on equations here; https://brainly.com/question/2972832
Please helllp meeee !!!
Answer:
B
Step-by-step explanation:
8/5=1.6
Answer:
b
Step-by-step explanation:
8/5=1.6
Please help! Question posted above ^
Answer:
( x^2 - 6 )^2
Step-by-step explanation:
x^4 -12x^2 +36Find one factorFactor by grouping(x^2 - 6x) (x^2 - 6x)*solution* ( x^2 - 6 )^2
Need help with this one.
Answer:
7.82
Step-by-step explanation:
4x−5 for x=10
Please, I really need the answer.
Answer:
4(10)-5=35
Step-by-step explanation:
4(10)=40-5=35
4(10) is the same as 4x10
So think about it like 4x10-5
I hope this helps ;}
Marquis started at an elevation of 3000 feet and hiked down a mountain at a constant rate. His elevation decreased 500 feet per hour.
Graph the relationship between Marquis’ elevation and time as he hiked down the mountain.
Answer:
if u divide it then slop it u will get your answer
Step-by-step explanation:
Use the diagram showing m || n, as well as the relationships between interior and exterior angles of ΔABC, to answer the questions.
Angle B is the linear pairs with 60°, so the size is 180-60=120°
Angle ABC is the linear pair with 120°, so the size is 180-120-60°
Angle A corresponds to angle 60°, so they are equal
Angle BAC is the linear pair with angle A and angle 70°, so 180-(60+70)=50°
Angle ACB is 180-(50+60) = 70°
Answer: ABC is 60
BAC is 50
ACB is 70
Step-by-step explanation: welcome
A bottle contains 24oz of liquid medication.If the average dose is 2/3oz. How many dose does the bottle contain
Answer:
36
Step-by-step explanation:
keep, flip, change...
24 ÷ [tex]\frac{2}{3}[/tex] would be the same as [tex]\frac{24}{1}[/tex] × [tex]\frac{3}{2}[/tex] which is equal to [tex]\frac{72}{2}[/tex] (36 if you simplify it)
The number of dose of 2/3oz of liquid medication does the bottle contain is 36.
What is the fraction number?Fraction number is the number which is a part of a whole number. It is written with a numerator and denominator. Fraction number are written as,
[tex]\dfrac{a}{b}[/tex]
Here (a) is the numerator and (b) is the denominator.
A bottle contains 24oz of liquid medication and the average dose is 2/3oz.
Let suppose the number of dose does the bottle contain is n. There is total 24oz of liquid medication in the bottol.
As the average dose is 2/3oz. Thus the number of dose in the bottle which has 24oz of liquid medication is,
[tex]n=24\div\dfrac{2}{3}\\n=24\times\dfrac{3}{2}\\n=36[/tex]
Thus, the number of dose of 2/3oz of liquid medication does the bottle contain is 36.
Learn more about the fraction number here:
https://brainly.com/question/78672
The feet of a poem can easily be compared to _______.
a heartbeat
footsteps
a musical beat
a drum beat
Answer:
its a heartbeat.
Step-by-step explanation:
sorry for late answer, just answering for any future people.
What is the answer to: −12x−16≥32
Answer:
hello there mate
Step-by-step explanation:
Answer:
x≤−4
Step-by-step explanation:
if you want me to explain how I got the answer reply yes
this is for literal equations
A=4 πr2 (r2)
i think you solve for r2
Answer:
[tex]r^2=\dfrac{A}{4\pi}[/tex]
Step-by-step explanation:
The given equation is A=4 πr².
We need to solve the above equation for r².
We have,
A=4πr²
Dividing both sides by 4π, we get :
[tex]\dfrac{A}{4\pi}=\dfrac{4\pi r^2}{4\pi}\\\\r^2=\dfrac{A}{4\pi}[/tex]
Hence, the value of r² is equal to [tex]\dfrac{A}{4\pi}[/tex].