a) The vertex of the problem is given as follows: (220, -583), meaning that the minimum depth reached by the vertex is of 583 after 220 hours.
b) The submarine was submerged for 440.1 hours.
What is the quadratic function?The quadratic function in this problem is defined as follows:
d(t) = 0.012t² - 5.29t.
Which gives the depth of the submarine after t hours.
The coefficients of the equation are given as follows:
a = 0.012, b = -5.29.
Then the t-coordinate of the vertex is given as follows:
t = -b/2a = 5.29/(2(0.012)) = 220.
The minimum depth is then of:
d(220) = 0.012(220)² - 5.29(220) = -583.
This is a concave up parabola, which is the reason why the vertex is a minimum.
The roots of the function are given as follows:
0.012t² - 5.29t = 0
t(0.012t - 5.29) = 0.
Hence:
t = 00.012t - 5.29 = 0 -> t = 5.29/0.012 -> t = 440.1.Meaning that the submarine was submerged for 440.1 hours.
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Sophia had $112 in her bank account. After she bought some carne asada fries for her and her friends that cost $8 for each, she now has $64 in her account. How many carne asada fries did she buy?
Answer:
6
Step-by-step explanation:
1) Total-Amount left
112-64=48
So now we know how much money she spent on the carne asada fries. Now let's get on with the next step.
2) Amount Spent/Cost for carne asada fries
48/8=6
So they bought 6 carne asada fries
I hope this helps!!!
An electrician leans an extension ladder against the outside wall of a house so that it
reaches an electric box 28 feet up. The ladder makes an angle of 60° with the ground.
Find the length of the ladder. Round your answer to the nearest hundredth of a foot if
necessary.
A 31.2 foot ladder is required to access an electrical box that is 28 feet up.
Which ratios in trigonometry are there?
Sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant are the six trigonometric ratios (sec). A branch of mathematics called trigonometry in geometry deals with the sides and angles of a right-angled triangle.
A right-angled triangle is formed by the ladder, the distance from the wall to the ladder's base, and the distance from the ground to the electrical box.
The link between the sides and angles of a right-angled triangle is demonstrated through trigonometric ratios.
If x stands for the ladder's length, then:
28 feet/x for sin(64).
28 feet/sin x = (64)
x = 31.2 ft
Therefore, a 31.2-foot ladder is required to reach an electrical box that is 28 feet up.
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Consider the relation below
Is it a function?
Is the relation a one to one function?
Is the inverse of the relation below itself of function ?
Answer: Yes to all 3 questions
It is a function. The function is one-to-one.The function has an inverse, which is also a function.==================================================
Explanation:
VLT = vertical line test
HLT = horizontal line test
The given curve passes the VLT since it's not possible to draw a single vertical line through more than one point on the blue curve. Therefore, we have a function. Any input (x) leads to exactly one output (y).
The curve also passes the HLT through similar reasoning (use a horizontal line this time of course). This tells us the function is one-to-one. Each input leads to a unique output.
The keyword "unique" is important in the previous paragraph. It's needed to help set up the inverse. Since this curve passes the HLT, we know the inverse exists and it is a function. The inverse itself will pass the VLT.
Note: recall you reflect the given curve over the line y = x to form the inverse curve.
Please help, I'm very confused:
1. Give another name for plane p
2. Name a line that intersects the plane
3. Name two rays
4. Name three points in plane p
1.. Plane R and plane P intersect at AB.
2.. 3 points that are collinear are A, D and B.
3. Planes can be named indicating three points that are on the same plane yet not on the same line.
4. Coplanar points are three or more points that lie on the same plane.
What is Coplanar points?
When three points that are not on the same line can be used to describe a plane, it is said to be a plane. Line AB is the point where planes P and R intersect. Plane P is horizontal and Plane R is vertical. These two planes intersect at this point, so line AB is shared by both planes.
A, D, and B are the three collinear points. This occurs when three or more points are all aligned in a single straight line, as the name collinear suggests.
Three locations that are on the same plane but not on the same line might be termed as a plane. These points are not collinear, to put it another way. DBG or FAD are two ways to represent Plane R.
Three or more points on the same plane are referred to as coplanar points. Since planes are typically flat surfaces, any three or more points located there are considered coplanar points. The four coplanar points ACDE are located on plane P.
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help this nobody my friend
Answer:
t=2/f-5
Step-by-step explanation:
Multiply both sides by "t"subtract 5t from both sidesfactor out "t" from the expressiondivide both sides by "f-5"James and Bethany Morrison are celebrating their 10th anniversary by having a reception at a local reception hall. They have budgeted $3,500 for their reception. If the reception hall
charges a $50 cleanup fee plus $32 per person, find the greatest number of people that they may invite and still stay within their budget.
James and Bethany can invite at most people to the reception.
(Round down to the nearest whole person.),
Step-by-step explanation:
James and Bethany Morrison are celebrating their 10th anniversary by having a reception at a local reception hall. They have budgeted $3,500 for their reception. If the reception hall charges a $50 cleanup fee plus $32 per person, find the greatest number of people that they may invite and still stay within their budget. James and Bethany can invite at most people to the reception. (Round down to the nearest whole person).
3,500 = 32p + 50
subtract 50 from both sides:
3,450 = 32p
divide both sides by 32:
p = 107.8125
because you cannot invite part of a person, round down to 107 people.
Answer:
107
Step-by-step explanation:
You have $3,450 to work with and you divide that by 32, which is the cost per person, and you come up with 107.8... You can round up to 108, but you risk(because you are) being over budget.
Please help, I don't really understand.
Answer:
Step-by-step explanation:
The standard form of a linear equation is y=mx+b, where m is the slope and b is the y-intercept. Let's rewirite the given equation to match this format:
y = 6 - 6x
y = -6x + 6
The slope is -6 and the y-intercept is 6. The slope tells us the angle the line is taking. A negative slope such as this means that the line is angled down as it goes from left to right. The size of the number tells us just how steep the line is.
All parallel lines have the same slope. Any line with the format of y = -6 + b will be parallel. See the attached graph for proof. The graph shows several parallel lines to y=-6+b, including the three top lines, all with the same slope, but with three different values for b: +6, 0, and +10.
Perpendicular lines have a slope that is the negative inverse of the reference line, in this case y = -6x + 6. A perpendicular line will have a slope of -(1/-6) or 1/6 [the negative inverse of -6]. Perpendicular lines will have the form y = (1/6)x + b. See the attached graph. The three bottom equations are all perpendicular to y=-6x+6. All have the same slope (1/6), but differnt y-intercepts (b = 0, 6, and 10). The y-intercept numbers for both the parallel and perpendicular lines were randomly chosen, simply to illustrate the possibilities.
In summary,
"Slope of a parallel line" is -6, and
"Slope of perpendicular line" is (1/6)
The distribution of ages of licensed drivers shopping at the kalish county mall is normally distributed with mean 41 and standard deviation 7. A person will be selected at random. Round your answers to the nearest hundredth.
According to the given statement 16% is the probability that the person is age 48 or older.
How to interpret a standard deviation?A metric of a data set's deviation from the mean is referred to as "standard deviation" (or ""). While a high standard deviation indicates that the numbers are more spread, a smaller standard deviation suggests that the data are clustered around the mean.
Briefing:After calculating the z-score, we will look up the value in the table on page (718–719).
We will employ the equation, to determine the z-score.
z= x−μ / σ
How is x=48
μ=41
σ=7 the z-score is,
z = 48 - 47 /7
z = 7 / 7
z = 1
The value for z=1 in the table is 0.84130, meaning that the region below the curve represents people who are 48 years of age and older. However, we are looking at the area that represents people who are 48 years of age and older, hence,
1−0.8413
=0.1587≈0.16
=16%
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The complete question is-
The distribution of ages of licensed drivers shopping at the Kalish County Mall is normally distributed with mean 41 and standard deviation 7. A person will be selected at random. Round your answers to the nearest hundredth. What is the probability that the person is age 48 or older?
7 of 8
→
Given that A, O & B lie on a straight line segment, evaluate the size of the smallest angle.
C
A
(3a + 8)
0°
(60 - a)
O
(4a-38)
The diagram is not drawn to scale.
D
B
Answer:
smallest angle = 35
Step-by-step explanation:
the 3 angles lying on the straight line AOB sum to 180° , then
3a + 8 + 60 - a + 4a - 38 = 180 , that is
6a + 30 = 180 ( subtract 30 from both sides )
6a = 150 ( divide both sides by 6 )
a = 25
Then
3a + 8 = 3(25) + 8 = 75 + 8 = 83°
60 - a = 60 - 25 = 35°
4a - 38 = 4(25) - 38 = 100 - 38 = 62°
the smallest angle is 35°
Factorise the following:
x² 18x + 81
Answer:
(x+9)(x+9)
Step-by-step explanation:
Let's factor x2+18x+81
x2+18x+81
hope this help xxx
The points on the line are ____ of the equation.
Answer choices:
1) Solution
2) Points
3) Answers
Answer: 2/ Points
Step-by-step explanation:
The points can't make up the answer to the equation, so it can't be 3!
I don't think it is the solution, because on a table points are just points of an equation!
Write a linear equation in slope intercept form to represent the number of miles each car can drive on one tank of gas. State the domain and range.
car #1: y=28x+607.6
car #2: y=80x+568
car #3: y=20x+528.4
How do I find my domain and range for these equations?
The domain and range of the equations for the three cars using the hypothetical condition that x represents additional gas added to the tank are;
Car #1
Domain; 0 ≤ x < ∞
Range; 607.8 ≤ y < ∞
Car #2
Domain; 0 ≤ x < ∞
Range; 568 ≤ y < 0
Car #3
Domain; 0 ≤ x < x
Range; 528.4 ≤ y < ∞
What is an equation?An equation is a statement that indicates that two expressions be equivalent by joining them with an equals sign.
The specified equations for three cars are;
Car #1: y = 28·x + 607.6
Car #2: y = 80·x + 568
Car #3: y = 20·x + 528.4
The domain of a function is the set of possible input values (x-values) of the function
The range is the set of possible output values (y-values) of the function
Let y represent the number of miles driven and let x represent the additional gas added to the car, we get;
The domain of car #1
The additional number of gallons of gas car #1 can drive receive has a domain of 0 ≤ x < ∞
The range for car #1
The total number of miles car #1 can drive = 607.6 ≤ y < ∞
The domain for car #2
The additional amount of gas car #2 receives is; 0 ≤ x < ∞
The range for car #2
The distance car #2 can drive is; 568 ≤ y < ∞
The domain for car #3
The additional volume of gas car #3 receives is; 0 ≤ x < ∞
The range of the function for car #3
The number of miles car #3 can drive is; 528.4 ≤ y < ∞
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What i the volume of the following rectangular prim? Volume ==equal unit^3 3 cubed
Since the side length is three units, the specified rectangular prism's volume will be 27 units.
What is volume?Each thing in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity. The capacity of an object is measured by its volume. For instance, a cup's capacity is stated to be 100 ml if it can hold 100 ml of water in its brim. The quantity of space occupied by a three-dimensional object can also be used to describe volume.
Here,
Length of side=3 units
Volume=(side)³
=3³ unit
=27 unit³
The length of side is 3 unit, so the volume of the given rectangular prism will be 27 unit.
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In the diagram of a gate, the horizontal bars are parallel and the vertical bars are parallel. Find x and y.
Complete the explanation Indicating which postulates and/or theorems were used to find the values.
Answer:
x = 6y = 1718x +2y = 142 by the corresponding angles theorem, and3x +2y = 52 by the alternate interior angles theoremStep-by-step explanation:
Given a set of parallel lines with a transversal and angles marked, you want to find the values for x and y consistent with the markings.
SetupAlternate interior angles are congruent, so the marked acute angles have the same measure:
3x +2y = 52
Corresponding angles are congruent, so the marked obtuse angles have the same measure:
18x +2y = 142
SolutionSubtracting the first equation from the second gives ...
(18x +2y) -(3x +2y) = (142) -(52)
15x = 90
x = 6
The value of y can be found from either equation. We choose to use the first:
3(6) +2y = 52
9 +y = 26 . . . . . . . . divide by 2
y = 17 . . . . . . . . . subtract 9
Summaryx = 6y = 1718x +2y = 142 by the corresponding angles theorem, and3x +2y = 52 by the alternate interior angles theoremThe boss told the management team some sad news too. “I’m cutting your hourly pay. You now get paid per project you finish. I will give you $10 for each finished schedule you create and $20 for each meeting you complete! You cannot make more than $100 per day! Also you must make more than twice as many schedules as meetings!”
Create a system of linear inequalities to model the situation above, where x is the number of schedules made and y is the number of meetings completed.
The system of linear inequalities to model the situation is 10x + 20y ≤ 100 and y > 2x
How to create a system of linear inequalities to model the situationFrom the question, we have the following parameters that can be used in our computation:
Each finished schedule = $10Each meeting = $20Amount to make = Not more than $100You must make more than twice as many schedules as meetingsUsing the following representations:
x = the number of schedules madey = the number of meetings completedWe have the following system of inequalities from the given statements
10x + 20y ≤ 100
y > 2x
Hence, the system of inequalities is 10x + 20y ≤ 100 and y > 2x
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Given the ytem of equation: 3x − 3y = 6 2x 6y = 12 Solve for (x, y) uing elimination
The values of x and y after solving the equations by using elimination method are :- 3 and 1
What is a system of equations?A group of equations involving one or more variables is known as a system of equations. The variable mappings that satisfy each component equation, or the points where all of these equations intersect, are the solutions to systems of equations.
What are the 3 ways to solve system of equations?There are three ways to solve systems of linear equations in two variables: graphing. substitution method. elimination method
In the above equations
Multiplying equation 1 with 2 and adding it to equation 2 we get
X= 3
Y=1
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A jar contains 7 red jelly beans, 2 black jelly beans and 6 green jelly beans. you draw one jelly bean. what is the probability of drawing a red bean?
a. startfraction 7 over 15 endfraction
b. 1
c. startfraction 1 over 15 endfraction
d. startfraction 1 over 7 endfraction
7/15 is the probability of drawing a red bean .
What is the simple definition of probability?
A probability is a number that expresses the possibility or likelihood that a specific event will take place.
Probabilities can be expressed as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.
Total beans = 7 + 2 + 6 = 15
Now out of these 15 only 7 are red.
Probability is normally written as a fraction.
= 7/15
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Please help!! Find the measure of numbered angles 1 and 2
Answer:
Step-by-step explanation:
the adjacent angles are congruent
angle 1 = 51°
the sum of the angles is 360°
51 · 2 + 2 · angle (2) = 360
102 + 2angle(2) = 360
2angle (2) = 360 - 102
2 angle (2) = 258
angle (2) = 258/2
angle (2) = 129°
angle (3) = 129°
Which equations are true for x = –2 and x = 2? Select two options x2 – 4 = 0 x2 = –4 3x2 + 12 = 0 4x2 = 16 2(x – 2)2 = 0
The equations that are true for x = -2 and x = 2 are x^2 - 4 = 0 and 2(x - 2)^2 = 0.
For x = -2, the equation x^2 - 4 = 0 becomes (-2)^2 - 4 = 0, which simplifies to 4 - 4 = 0, and therefore this equation is true when x = -2.
Similarly, for x = 2, the equation 2(x - 2)^2 = 0 becomes 2((2 - 2)^2) = 0, which simplifies to 2(0)^2 = 0, and therefore this equation is also true when x = 2.
The other equations, x^2 = -4, 3x^2 + 12 = 0, and 4x^2 = 16, are not true for x = -2 or x = 2. For example, for x = -2, the equation 3x^2 + 12 = 0 becomes 3(-2)^2 + 12 = 0, which simplifies to -24 + 12 = -12, and therefore this equation is not true when x = -2. Similarly, for x = 2, the equation 4x^2 = 16 becomes 4(2)^2 = 16, which simplifies to 16 = 16, and therefore this equation is true when x = 2. However, since the problem asks for equations that are true for both x = -2 and x = 2, the equation 4x^2 = 16 is not a correct answer because it is only true when x = 2.
helppp pleaseeeeeeeeeeeeeee
Answer:
the answer is d
Step-by-step explanation:
x is -2 and y is
4(8x-1)=2(2x-2)
explain
Answer:
0
Step-by-step explanation:
4(8x–1) = 2(2x–2)
32x–4 = 4x–4
32x–4x = –4+4
28x = 0
x=0/28
x= 0
Answer:
x=0
Step-by-step explanation:
4(8x-1)=2(2x-2)
Step 1) 32x-4=4x-4
Step 2) 28x=0
Step 3) x=[tex]\frac{0}{28\\}[/tex]
Step 4) x=0
find the slope and y intercept for the graph of : 2x+4y=20
you can either graph it or solve it algebraically
move the parts of the equation to fit the sctructure of y = mx + b
2x + 4y = 20
4y = -2x + 20
divide by 4 on both sides to get 'y' by itself
y = -2/4x + 20/4
y = -1/2x + 5
this equation tells you the 'y intercept' and the slope
slope; -1/2
y intercept; 5
Which graph represents the solution to the inequality 0.25 is less than the product of a number and −0.5?
number line with closed circle on 0.5 with arrow shaded right
number line with open circle on point on negative 0.5 with arrow shaded left
number line with closed circle on negative 2 with arrow shaded right
number line with open circle on 2 with arrow shaded left
Which of the following is true regarding the relationship between a catalyst and a chemical reaction?
Catalysts are not specific to reactions.
A single catalyst can initiate many different types of reactions.
Many catalysts are often involved in a single chemical reaction.
Each reaction has its own unique catalyst.
The true option regarding the relationship between a catalyst and a chemical reaction is D. Each reaction has its own unique catalyst.
What is a catalyst?A catalyst is a substance that accelerates the rate of a chemical reaction without affecting the end product. They only have an effect on the rate of the reaction, not the yield.
Catalysts offer an alternative reaction pathway with lower activation energy than uncatalyzed reactions. It raises the frequency of collision and, as a result of the increased collision, lowers the activation energy of the reaction.
A chemical reaction is a process that converts one or more substances, known as reactants, to one or more different substances, known as products. Chemical elements or compounds are examples of substances.
A chemical reaction rearranges the constituent atoms of the reactants to produce various products. The properties of the products differ from the properties of the reactants. It is distinct from physical changes, which include state changes such as ice melting to water and water evaporating to vapor.
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The data from car crash tests for four different vehicle size categories (Small, Midsize, Large, and SUV) with measured amounts of left leg ferur force (kN) results in the
following Minitab display. Using a 0. 05 significance level, test the claim that the four vehicle size categories have the same mean force on the femur of the left leg. Does size
of the car appear to have an effect on the force on the left femur in crash tests?
Analysis of Variance
Source DF Adj SS Adj MS F-Value P-value
3 0. 6165 0,2055 0. 52 0. 670
Determine the test statistic.
The test statistic is
(Round to two decimal places as needed. )
Determine the P-value
Size
Do not reject H0 there is not sufficient evidence at a 0.05 significance level to warrant rejection of the claim that the four vehicle size categories have the same mean force on the left femur in crash tests.
What is Null hypothesis?
A statistical hypothesis known as a null hypothesis asserts that no statistical significance can be found in a collection of provided observations. Using sample data, hypothesis testing is performed to judge a theory' veracity. It is sometimes referred to as just "the null," and its symbol is H0.
from given outpout
Null hypothesis
H0:u1=u2=u3=u4
Alternative Hypothesis
H1: not all means are equal
Test statistic =F=0.49
P value=0.691
Pvalue>0.05 alpha level of significance
We fail to reject null hypothesis
Conclusion =
Do not reject H0 there is not sufficient evidence at a 0.05 significance level to warrant rejection of the claim that the four vehicle size categories have the same mean force on the left femur in crash tests.
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PLEASE HELP Clinical trials involved treating flu symptoms with a new medicine. Among 724 patients treated with the medicine, 72 experienced a side effect of nausea. The claim is that the rate of nausea is greater than the 6% rate experienced by flu patients given a placebo. Find a test statistic of the proportion.
z = 4.47
z = –1.41
z = 4.53
z = 1.41
The test statistic of the proportion is given as follows:
z = 4.47.
How to calculate the test statistic for the proportion?The equation that gives the test statistic for a proportion is given as follows:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
In which:
[tex]\overline{p}[/tex] is the sample proportion.p is the expected proportion from the population, or the test proportion.n is the sample size.In the context of this problem, the values of these parameters are given as follows:
[tex]p = 0.06, n = 724, \overline{p} = \frac{72}{724} = 0.0994[/tex]
Hence the test statistic for the proportion is calculated as follows:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
[tex]z = \frac{0.0994 - 0.06}{\sqrt{\frac{0.06(0.94)}{724}}}[/tex]
z = 4.47.
Meaning that the first option is correct.
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PLS HELP Which has the greatest rate
After solving the equation the greatest rate is y=x. therefore, the correct option is D
What does rate in math mean?
In mathematics, the term 'rate' usually refers to a ratio or a comparison between two different values. It is defined as the amount of one quantity with respect to another, and is most commonly expressed as a fraction, with one value being the numerator and the other being the denominator. For example, "the rate of increase" is a comparison between the amount of increase in an item over time, such as the rate of inflation over a period of time. Additionally, the term 'rate' can also be used to describe a rate of change, such as the rate of growth of a population. In this case, the rate of change describes how quickly the population is changing over time.
Given that:
For rate we have to differentiate all the function first
A) y = 3/4x + 1
dy/dx = 3/4
B) y = -x
dy/dx = -1
C) y = 1/2x +2
dy/dx = 1/2
D) y = x
dy/dx = 1
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A tore i intructed by corporate headquarter to put a markup of 11% on all item. An item coting $18 i diplayed by the tore manager at a elling price of $2. A an employee, you notice that thi elling price i incorrect. Find the correct elling price. What wa the manager' likely error?
When the actual selling price is $20, the store manager is showing a $18 item with a $2 price tag.
What does Percentage mean?One can calculate the percentage by dividing the value by the total value and multiplying the result by 100. (Value/Total Value)100% is the formula for calculating percentages.
To convert a decimal number, such as 0.57, to a percentage, just multiply it by 100. Therefore, 0.57 times 100 equals 57. Therefore, 0.57 is a percentage that equals 57%. Another example is 0.03 x 100 = 3%. Percentages are just fractions with a denominator of 100. To show that a number is a percentage, we place the percent sign (%) next to it.
For instance, if you properly answered 75 out of 100 questions on a test, you would have received a 75% grade (75/100).
Here,
Item cost is $18.
Price to Sell = 18 + 11% ×18
= $19.98
= $20
The store manager is displaying an item that cost $18 for a selling price of $2 when the true selling price is $20.
So,
When the actual selling price is $20, the store manager is showing a $18 item with a $2 price tag.
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Ms Hoblin needs to buy 452 prizes to fill up the prize bins.If 14 Prizes comes in each pack,how many packs will she need to purchase to completely fill up the prize bins.
Answer:
32 Packs
Step-by-step explanation:
Ms Hoblin will need to buy 452/14 = <<452/14=32>>32 packs of prizes.
Alternatively, you could divide 452 by 14 and then round up to the nearest whole number to determine the number of packs that she needs to buy. In this case, 452/14 = 32.64, so she would need to buy 33 packs of prizes.
On average, Jonathan drink 2/3 of a 10-ounce gla of water in 2 4/5 hour. How much water doe he drink, in glae per hour?
In linear equation,(10/21) glasses of water does she drink, in glae per hour.
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
3/4 of hour she drinks (2/3) of a glass
So, in 1 hour she drinks (2/3)×(5/14) of a glass
So, in 1 hour she drinks (10/21) glasses of water.
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