the interval in which g(x) is positive is [3, ∞].
On what interval is the function positive?Here we have the function:
g(x) = ∛(x - 3)
The interval in which the function is positive is defined by:
g(x) > 0.
Then we have:
∛(x - 3) > 0.
We need to solve that inequality for x.
∛(x - 3) > 0
The cube root respects the sign of the argument, then:
x - 3 > 0
x > 3
Then the interval in which g(x) is positive is [3, ∞].
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Find the surface area of the prism.
Answer:
204
Step-by-step explanation:
6*10=60
6*6=36
6*8=48
2((10*6)/2)=60
60+60+36+48=204
Dexter is in charge of ticket sales at his town’s water park. He has to report to his boss how many tickets he sells and how much money the water park makes in ticket sales each day - adult tickets ($7), child tickets ($5). Today, Dexter has sold 100 adult and 125 child tickets. Yesterday, he sold 120 adult and 120 child tickets. Can Dexter write an expression to figure out today’s ticket sales, and use this to compare today’s sales to yesterday’s?
Dexter needs to write an expression to figure out the total money made from the 100 adult and 125 child tickets he sold today, compared to the 120 adult and 120 child tickets he sold yesterday. The adult tickets cost $7 and the child tickets cost $5
The expression to figure out today’s ticket sales is 7x+5y.
Today's ticket sale is less than that of yesterday's.
According to the question,
Adult tickets cost $7 each.
Child tickets cost $5 each.
Let the number of adult and child tickets sold be x and y respectively.
Expression for ticket sales= $(7x+5y)
Dexter has sold 125 kid's tickets and 100 adult tickets today.
Ticket sales = $(7*100+5*125) = $ 1325
He sold 120 adult tickets and 120 kid tickets yesterday.
Ticket sales = $(7*120+5*120) = $ 1440
Thus, from the expression it can be seen that yesterday' s ticket sale is greater than today's ticket sale.
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The price of a new car is £27000 In a sale, the price is reduced by 30% Brodie buys the car in the sale. He pays a £8000 deposit and pays the rest over 50 monthly payments. Find the cost of each monthly payment.
Answer:
£218
Step-by-step explanation:
price of the car = £27000
reduce 30% = 30/100 x 27000 = £8100
£27000 - £8100 = £18900
£18900 - £8000 = £10900
installment per month = £10900/50 = £218
Find the greatest common
factor of the following numbers.
24.34.567
23.36 52 11
37. 53. 72. 11². 13
Give your answer as a single number.
●
The greatest common factor for the following sets of numbers are as follows,
24, 34, 567 : 1
23, 36, 52, 11 : 1
37, 53, 72, 11², 13 : 1
1, 2, 3, 4, 6, 8, 12, and 24 make up the number 24.
1, 2, 17, and 34 make to the number 34.
1, 3, 7, 9, 21, 27, 63, 81, 189, and 567 make up the number 567.
Because of this, the case's greatest common factor is 1.
The elements of 11 are: 1, 11
The 23 factors are: 1, 23,
1, 2, 3, 4, 6, 9, 12, 18, and 36 make up the number 36.
The sum of 52's factors is: 1, 2, 4, 13, 26, and 52.
Therefore, 1 is the number that these numbers have the most in common, and thus, 1 is the greatest common factor here.
The elements of 13 are: 1, 13, and
These are the 37 factors: 1, 37
These are the components of 53: 1, 53
1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72 make up the number 72.
1, 11, and 121 make up the number 121.
Thus, the greatest common factor for 37, 53, 72, 121, 13 is again 1.
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For a project in her Geometry class, Chloe uses a mirror on the ground to measure
the height of her school's football goalpost. She walks a distance of 10.65 meters from
the goalpost, then places a mirror on flat on the ground, marked with an X at the
center. She then steps 1.2 meters to the other side of the mirror, until she can see the
top of the goalpost clearly marked in the X. Her partner measures the distance from
her eyes to the ground to be 1.75 meters. How tall is the goalpost? Round your answer
to the nearest hundredth of a meter.
Answer: 15.53
Step-by-step explanation:
Let the height of the goalpost be y. Then,
[tex]\frac{y}{10.65}=\frac{1.75}{1.2}\\\\y \approx 15.53[/tex]
Can someone please help me with question 4 and 5. I’ve been having so much trouble we these type of questions. Thank you!
Answer:
question 4:
the smaller building is 262.31 metres tall
Step-by-step explanation:
see the diagram attached:
1. draw a diagram:
as ive done below, it is easiest to solve this type of equation if you draw it out as a diagram2. as you can see in the diagram, a right angled triangle has been created.
assuming you understand basic trigonometry, you will see that as we know 1 angle (3 degrees, 21 minutes), and 1 side length (46m), we can now solve for the other sides, which is what the question is asking us to do. the side length we have been given (46m) is opposite the right angle (90°) and is the longest side of the triangle, making it the hypotenuse. So we know:hypotenuse = 46mas we are trying to find the difference between the heights of the buildings, we are trying to find the side opposite the given angle (3°21'). As it is opposite from the given angle, it is referred to in trigonometry as the opposite. As we don't yet know the length of the Opposite, i have labelled it x in the diagram. known angle = 3°21'opposite = x3. convert the known angle from degrees and minutes to degrees.
3 degrees 21 minutes = 3 degrees + 21 minutes (there are 60 minutes in a degree, so to convert the 21 minutes into degrees, divide 21 by 60)21 minutes / 60 = 0.35 degrees4. Identify which trigonometry ratio to use:
sin = [tex]\frac{opposite}{hypotenuse}[/tex]
cos = [tex]\frac{adjacent}{hypotenuse}[/tex]
tan = [tex]\frac{opposite}{adjacent}[/tex]
as we know the hypotenuse, and we want to know the opposite, the will use Sin.5. insert known values into the equation:
sin θ [tex]\frac{opposite}{hypotenuse}[/tex]we know the hypotenuse = 46we know the given angle = 3.35°we have labelled the opposite side xtherefore our new equation looks like:sin (3.35) = [tex]\frac{x}{46}[/tex]as we know the denominator (bottom value of the fraction), we multiply it by the angle to find the length of the unknown side (x):46 x sin (3.35) = 2.688 (use a calculator for this step)we now know the length of the unknown side (x):x = 2.688 metres6. Interpreting the question with new knowledge:
as can be seen in the diagram, the unknown side (x), was the difference between the heights of the building. we can now replace side x with 2.688To find the height of building 2, simply subtract the difference between the buildings (2.688m), from the height of the tallest building (265m) to find the height of the smallest building. 265 - 2.688 = 262.312 m (height of building 2)the question says only to 2 decimal places so we can round the height to 262.31 metres.the height of building 2 is 262.31 metres.
How many 5-digit numbers can be created
using the digits 2, 3, 5, 7, and 8 without
repeating any digits within that 5-digit
number?
Answer:
120.
Step-by-step explanation:
That would be factorial 5, written 5!.
That is 5*4*3*2*1
= 120.
Answer:
120
Step-by-step explanation:
We have 5 digits that can be used to create different 5 digit numbers. We are also not allowed to repeat any numbers. Let's say we have 5 boxes to put the 5 numbers in.
Box 1
Box 2
Box 3
Box 4
Box 5
In the first box, we have 5 different choices. Since we aren't allowed to repeat any digits, the second box only has 4 different choices. And so on...
Box 1 --> 5 choices
Box 2 --> 4 choices
Box 3 --> 3 choices
Box 4 --> 2 choices
Box 5 --> 1 choice
Therefore the amount of 5 digit numbers that can be created is:
[tex]5\times4\times3\times2\times1[/tex] or 5 factorial (a factorial is all the product of all the positive integers equal to and less than the number), which is equivalent to:
120 5-digit numbers
Suppose it costs $43 to roll a pair of dice. you get paid $6 times the sum of the numbers that appear on the dice. is it a fair game?
The game is not fair as 6 times the expected sum is less than the cost, $43.
In the question, we are asked if the game is fair.
For the game to be fair, 6 times the expected sum for the pair from the game has to be greater than or equal to $43, that is,
6E(X) ≥ 43.
The expected sum for the pair, E(X) can be calculated using the formula,
E(X) = ∑x.p(x),
or, E(X) = 1/18 + 1/6 + 1/3 + 5/9 + 1/6 + 7/9 + 10/9 + 1 + 5/6 + 11/18 + 1/3,
or, E(X) = 107/18.
Now, 6E(X) = 6*(107/18) = 107/3 = 35.67.
Since, the total return from the game is $35.67, which is less than the cost of $43, the game is not fair.
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The first 5 terms of a sequence are 2 8 14 20 26 Find the nth term
Answer: [tex]\Large\boxed{a_n=6n-4}[/tex]
Step-by-step explanation:
Given sequence
2, 8, 14, 20, 26
Determine the pattern
2 + 6 = 8
8 + 6 = 14
14 + 6 =20
20 + 6 = 26
For each term, add 6 to get the next term
Determine the type of sequence
Since it continuously adds 6, the common difference is 6, which means it is an arithmetic sequence
Given the arithmetic sequence formula
aₙ = a₁ + d (n - 1)
a₁ = 1st term of a sequenceaₙ = nth term of a sequencen = nth positiond = Common differenceSubstitute values into the formula
aₙ = (2) + (6) (n - 1)
aₙ = 2 + 6 (n - 1)
aₙ = 2 + 6n - 6
aₙ = 2 - 6 + 6n
[tex]\Large\boxed{a_n=6n-4}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Given sequence :-
2 , 8 , 14 , 20 , 26...Solution :-
We need to calculate the nth term of the given sequence.
Common difference (d) = 8 - 2 => 6First term of sequence (a) = 2We know that,
tn = a + (n - 1) dApplying the values here.
>> tn = 2 + (n - 1) 6
>> tn = 2 + (n - 1) × 6
>> tn = 2 + 6n - 6
>> tn = 6n - 4
Therefore, nth term of the sequence is (6n - 4).
The data in the table can be entered into a calculator to determine a linear equation of best fit where x represents the number of years with a company and y represents an employee’s salary in dollars.
What conclusion can be drawn from the correlation coefficient associated with this linear equation?
Based on the given table which shows the number of years with a company in relation to the employee salary, the conclusion that can be drawn is There is a weak positive correlation between the variables.
What is the correlation between the values?When two variables are said to be positively correlated, then it means that when one variable increases, the other variable would increase as well.
If the correlation between them is strong, then the increase between the variables would be more uniform i.e. we can tell with higher accuracy, how the increase in one variable would affect the other.
In the table, we see that with every increase in the number of years with the company, there is an increase in the salary. This means that there is a positive correlation.
The increase is not uniform however. Sometimes it increases by $1,000, and other times by $7,000. As the increase is not uniform, it means that the correlation is weak.
In conclusion, there is a weak positive correlation between number of years and salary.
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The go fish game tank contains 30 fish the probability of catching a purple fish is 1/3 the probability of catching a green fish
Answer:
2/3
Step-by-step explanation:
since they are just two colors of fish inside, since the probability is always 1.. so we have to minus 1/3 from 1,which is 1-1/3=2/3
Drag and drop an answer to each box to correctly explain the derivation of the formula for the volume of a pyramid.
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be PLEASE NEED HELP
moved by dragging with a mouse.
The ratio of the volume of a pyramid to the volume of a prism with the same base and height is Response area. Because the formula for the volume of a prism is V=Bh, where B is the area of the base and h is the height, the formula for the volume of a pyramid is Response area.
The ratio of the volume of a pyramid to the volume of a prism with the same base and height is 1 to 3; the formula for the volume of a pyramid is V = 1/3Bh.
Volume of pyramidVolume of prism, V = BhVolume of pyramid, V = 1/3Bhwhere,
B = the area of the base and h = the heightVolume of prism : Volume of pyramid
Bh : 1/3Bh
Therefore, the ratio of the volume of a pyramid to the volume of a prism with the same base and height is 1 to 3.
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what is x in x +10 =2000
Answer:
x=1990
Step-by-step explanation:
x+10=2000
x=2000-10
x=1990
Answer:
therefore x = 1990
Step-by-step explanation:
x+10 = 2000
= x = 2000-10
= x = 1990
THE FIRST PERSON TO ANSWER GETS BRAINLIEST!!! A student traveled to a foreign country on an airplane. It took 18 hours to arrive at his destination, and the plane was traveling 900 kilometers per hour. When returning home, the same trip took only 15 hours going at a speed of 1,080 kilometers per hour. If t represents time and s represents the speed of the plane, which statement is true about this relationship?
(answer choices are below)
Answer:
4
Step-by-step explanation:
the time it takes for a plane to travel a distance varies directly as the speed of the plane because ts=16,200
math help pleasee!!!!
Hello and Good Morning/Afternoon:
Let's take this problem step-by-step:
Since this is an algebraic problem
⇒let's solve it like one
[tex]2*3^{x+5} < 14\\3^{x+5} < 7\\ x+5 < log_37\\x < -5 + log_37\\x < -3.2288[/tex]
Answer: x < -3.2288
Hope that helps!
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The appropriate test for a comparison a group of 10 dogs and group of 10 cats is:_____.
The appropriate test for a comparison a group of 10 dogs and group of 10 cats is called independent sample t-test.
In this question,
The independent samples t test (also called the unpaired samples t test) is the most common form of the T test. It helps you to compare the means of two sets of data.
The Independent samples t test compares the means of two independent groups in order to determine whether there is statistical evidence that the associated population means are significantly different.
The independent sample t-test is a useful statistical method of hypothesis testing when an organization wants to determine whether there is a statistical difference between two categories, groups, or items and, furthermore, if there is a statistical difference, whether that difference is significant.
From the definition, the independent sample t-test is the appropriate test for a comparison a group of 10 dogs and group of 10 cats.
Hence we can conclude that the appropriate test for a comparison a group of 10 dogs and group of 10 cats is called independent sample t-test.
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Quick algebra 1 question for 10 points!
Only answer if you know the answer, quick shout-out to tariqareesha2 and MrBrainly, tysm for the help!
Answer:
See image
Step-by-step explanation:
Using a graphing calculator, first press the Y= button at the top left.
Then enter the equation given in the question.
Next, press 2nd then graph, and you will get the table. Put in whatever values for x to get y.
So your answer is 48, 18, 0, -6, 0, -18, 0, 48
1) The ratio of the number of Mary's stickers to Anne's is 4:7. Mary has 48 stickers. If
Mary buys another 8 stickers, what will be the new ratio of the number of Mary's
stickers to Anne's?
Answer:
2:3
Step-by-step explanation:
ratio = 4:7
4 parts = 48
1 part = 12
Mary has 48
Anne has 84
Mary will have 56
56:84 = 2:3
Point M is on line segment \overline{LN}
LN
. Given LN=2x-5,LN=2x−5, MN=x-1,MN=x−1, and LM=3,LM=3, determine the numerical length of \overline{LN}.
LN
.
Considering the relation built the presence of point M on line LN, the numerical length of LN is of 9 units.
What is the relation from the presence of point M on the line LN?Point M splits line LN into two parts, LM and MN, hence the total length is given by:
LN = LM + MN.
From the given data, we have that:
LN = 2x - 5.LM = 3.MN = x - 1.Hence we first solve for x.
LN = LM + MN.
2x - 5 = 3 + x - 1
x = 7.
Hence the total length is:
LN = 2x - 5 = 2 x 7 - 5 = 14 - 5 = 9 units.
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Which answer choice below correctly identifies the 205th term in the sequence 5, 10, 15, 20, 25 …?
Answer:
1025
Step-by-step explanation:
y=5x
y=5(205)
y=1025
The 205th term in the arithmetic sequence is 1025.
We have,
To find the 205th term in the sequence 5, 10, 15, 20, 25 ..., we can use the formula for an arithmetic sequence:
The nth term of an arithmetic sequence can be represented as:
[tex]a_n = a_1 + (n - 1) ~d[/tex]
Where:
[tex]a_n[/tex] is the nth term,
[tex]a_1[/tex] is the first term,
n is the position of the term we want to find, and
d is the common difference between consecutive terms.
In this sequence, the first term [tex]a_1[/tex] is 5, and the common difference (d) is 10 - 5 = 5.
Now, let's find the 205th term ([tex]a_{205}[/tex]):
= 5 + (205 - 1) * 5
= 5 + 204 * 5
= 5 + 1020
= 1025
Thus,
The 205th term in the arithmetic sequence is 1025.
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h(x)=
8
1
x
3
−x
2
h, left parenthesis, x, right parenthesis, equals, start fraction, 1, divided by, 8, end fraction, x, cubed, minus, x, squared
What is the average rate of change of hhh over the interval -2\leq x\leq 2−2≤x≤2minus, 2, is less than or equal to, x, is less than or equal to, 2?h(x)=
8
1
x
3
−x
2
h, left parenthesis, x, right parenthesis, equals, start fraction, 1, divided by, 8, end fraction, x, cubed, minus, x, squared
What is the average rate of change of hhh over the interval -2\leq x\leq 2−2≤x≤2minus, 2, is less than or equal to, x, is less than or equal to, 2?
The average rate of change of the function over −2 ≤ x ≤ 2 is 1/2
How to determine the average rate of change?The function is given as:
[tex]h(x) = \frac 18x^3 - x^2[/tex]
The interval is given as:
−2 ≤ x ≤ 2
Calculate h(2) and h(-2)
[tex]h(2) = \frac 18 * 2^3 - (2)^2[/tex]
h(2) = -3
[tex]h(-2) = \frac 18 * (-2)^3 - (-2)^2[/tex]
h(-2) = -5
The average rate of change is then calculated as:
[tex]m = \frac{h(-2) - h(2)}{-2-2}[/tex]
This gives
[tex]m = \frac{-5 + 3}{-4}[/tex]
Evaluate
m = 1/2
Hence, the average rate of change of the function over −2 ≤ x ≤ 2 is 1/2
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Complete question
[tex]h(x) = \frac 18x^3 - x^2[/tex]
What is the average rate of change of h over the interval −2 ≤ x ≤ 2
10.
JKLM is a rhombus KLN is a triangle. Find MKN.
Answer:
65°
Step-by-step explanation:
JM = JK (all sides of a rhombus are equal)
Angle JKM = 25° (isosceles triangle)
Angle JKL = 50° (consecutive angles of rhombus)
Angle MKL = 25° (angle subtraction)
Angle MLK = 130° (opposite angles of a rhombus)
Angle KLN = 50° (angles on a straight line)
Angle LKN = 40° (angle sum of triangle)
Angle MKN = 65° (angle addition)
Describe how to simplify the expression startfraction 3 superscript negative 6 baseline over 3 superscript negative 4 baseline endfraction.
The simplified fraction expression results into [tex]\frac{1}{9}[/tex].
What is fraction?
A number that is stated mathematically as a quotient, where the numerator and denominator are divided. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.
A number that represents a rational number is called a common fraction. The three main sorts of fractions are as follows. Proper fractions, incorrect fractions, and mixed fractions are these three types.
Given,
Expression = [tex]\frac{3^{-6}}{3^{-4}}[/tex]
= [tex]3^{-6-(-4)}[/tex]
= [tex]3^{-6+4}[/tex]
= [tex]3^{-2}[/tex]
= [tex]\frac{1}{3^2}[/tex]
= [tex]\frac{1}{9}[/tex]
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The purpose of statistical inference is to make estimates or draw conclusions about a.
When we make estimates of or draw conclusions about one or more characteristics of a population based upon the sample, we are using the process of statistical inference.
To estimate this sample to sample variance or uncertainty is the goal of statistical inference.What is the purpose of statistical inferences ?
To be able to make inferences about a population based on data from a sample is the goal of statistical inference. The process of statistical inference involves selecting a sample, gathering data from that sample, calculating a statistic from the data, and drawing conclusions about the population from that statistic.How is statistical inference used to draw conclusions?
Estimation and hypothesis testing are components of statistical inference (evaluating a notion about a population using a sample) (estimating the value or potential range of values of some characteristic of the population based on that of a sample).
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5. On the way to the museum, 50% of the students rode on the first bus.
What fraction of the students rode on the second bus? Show your work
in the space below. Remember to check your solution.
Answer:
1/2
Step-by-step explanation:
50% = 50/100 = 1/2
1/2 of the students rode the first bus.
1 - 1/2 = 1/2
1/2 of the students rode the second bus.
2 [{2-2(2÷2-2)} ÷2]÷2
Answer:
read below or other answer
Step-by-step explanation:
2 [{2-2(2÷2-2)} ÷2]÷2
2 [ { 2 - 2 ( 1 - 2 ) } ÷ 2 ] ÷ 2
2 [ { 2 - 2 ( - 1 ) } ÷ 2 ] ÷ 2
2 [ { 2 + 2 } ÷ 2 ] ÷ 2
2 [ 4 ÷ 2 ] ÷ 2
2 ( 2 ) ÷ 2
4 ÷ 2
2 divided by 2
Answer: 2
Step-by-step explanation:
i don’t understand graphs
Answer:
y ≤ 2.5x + 5
Step-by-step explanation:
first step is to obtain the equation of the line in slope- intercept form
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 2, 0) and (x₂, y₂ ) = (0, 5) ← 2 points on the line
m = [tex]\frac{5-0}{0-(-2)}[/tex] = [tex]\frac{5}{0+2}[/tex] = [tex]\frac{5}{2}[/tex] = 2.5
the line crosses the y- axis at (0, 5 ) ⇒ c = 5
y = 2.5x + 5 ← equation of line
since the line is solid then inequality will be ≤
the solution to the inequality is the blue region below the line , then
y ≤ 2.5x + 5 ← inequality represented by graph
exponential growth and decay real-world word problems
The examples of exponential growth include bacteria population growth and compound interest and a real life example of exponential decay is radioactive decay.
What is exponential growth?Exponential growth is the pattern of data that shows sharper increases over time. Savings accounts with a compounding interest rate can show exponential growth.
There are many real-life examples of exponential decay. An example, is thatsuppose that the population of a city was 100,000 in 1980. Then every year after that, the population has decreased by 3% as a result of heavy pollution. This is an example of exponential decay.
One of the best examples of exponential growth is the observed in bacteria. It takes bacteria roughly an hour to be able to reproduce through prokaryotic fission. In this case, if we placed 100 bacteria in an environment and recorded the population size each hour, we would observe an exponential growth.
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Sarmad has a backyard pool that is filled with 10800 gallons of water the pool has a leak and is loseing about 2 gallons of water every second
a) Write an expression to represent that amount of water in the pool assume the pool starts with a full quantity of 10800 gallons.
b) How much water is the pool after 187 seconds
11) describe the transformations that have been applied to the function y=x Use proper mathematical terminolgy.
a) y=-2x b) y=x-2
The function that represents the amount of water is y = -2x + 10800 while the water in the pool after 187 seconds is 10426 gallons
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
A linear equation is in the form:
y = mx + b
Where m is the slope and b is the y intercept
Let y represent the amount of water in the pool after x seconds, hence:
y = -2x + 10800
After 187 s:
y = -2(187) + 10800 = 10426 gallons
The function that represents the amount of water is y = -2x + 10800 while the water in the pool after 187 seconds is 10426 gallons
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25) Every month the cafeteria orders 120 gallons of milk and 220 gallons of chocolate milk. What is the ratio of milk to chocolate milk as a fraction in simplest form?
Answer:
Step-by-step explanation:
120:220
2 will go into 120 60 times and go into 220 110 times. So your answer comes down to;
60:110
10 will go into 60 6 times and go into 110 11 times So your answer comes down to;
6:11
That is your final answer 6:11
