The domain and range for the function for the maximum height of the rockets Kate fires is; h = 70·t - 16·t² are;
Domain; 0 ≤ t ≤ 4.375
Range; 0 ≤ h ≤ 39.06
What is a mathematical function?A function is a rule that defines the relationship between input variables and output variables, such that the each value from the set of input variables are assigned to exactly on variable from the set of output variables.
The possible specified function in the question is; h = 70·t - 16·t², and the possible required details is the domain and range that best represent the situation.
The domain of the above function is the set of possible input (t) values, which is found by the time it takes the rocket to land after flight as follows;
At ground level, h = 0, therefore;
h = 70·t - 16·t² = 0
(70 - 16·t)·t = 0
A possible solution is therefore, t = 0
The other solution is found as follows;
(70 - 16·t) = 0
70 = 16·t
16·t = 70
t = 70/16 = 4.375
The other solution or time at which the rocket is at ground level is t = 4.375
The domain is therefore; 0 ≤ t ≤ 4.375The range is the set of possible h values, which is obtained as follows;
The maximum point of the quadratic function, f(x) = a·x² + b·x + c, is the point, x = -b/2·a. Therefore, comparison between the function, f(x) = a·x² + b·x + c, and h = 70·t - 16·t², we get;
a = -16
b = 70
c = 0
The maximum height reached, therefore is obtained at the point, at which; t = -70/(2 × (-16)) = 2.1875
The maximum height, [tex]h_{max}[/tex], is therefore;
[tex]h_{max}[/tex] = 70 × 2.1875 - 16 × 2.1875² = 76.5625
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is f(x)=x+1/x+2 a function? Explain.
The equation represented as f(x) = x + 1/x + 2 is a function
How to determine if the equation is a functionFrom the question, we have the following parameters that can be used in our computation:
f(x) = x + 1/x + 2
The above equation is a rational equation whose numerator and denominator are linear functions
Equations with these properties are always functions
This is so because their x values do not have multiple y values
Hence, the equation f(x) = x + 1/x + 2 is a function
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On Thursday, the temperature in Spincich Lake, Michigan was 22F. By Friday, the temperature had dropped 35 degrees. What was the temperature on Friday?
Answer:
-13F
Step-by-step explanation:
since its negative, you could find the answer by doing 35-22
then, just adding a negative symbol in front!
this is because you are finding the difference by subtracting, and by doing this i find it a lot easier to get your answer
so, 35-22 is equal to 13. so, 22-35 is -13
i hope that makes sense
honestly, you can just use a calculator to figure it out too! just put 22-35
Which descriptions and equations could be the function rule? Select all that apply.
The table in the attached image shows some of the input and output values for a function rule.
For the given table of values the equation that could be the function rule is option 4: y = 3x - 2.
What is a function?
In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.
The table of input and output values are given for the function.
The slope-intercept form of an equation/function is - y = mx + b
To find the slope m use the formula -
(y2 - y1)/(x2 - x1)
Substituting the values in the equation -
[-2 - (-11)]/[0 - (-3)]
(-2 + 11)/(0 + 3)
9/3
3
So, the slope point is obtained as m = 3.
The equation becomes - y =3x + b
To find the value of b substitute the values of x and y in the equation -
-11 = 3(-3) + b
-11 = -9 + b
b = -11 + 9
b = -2
So, the value for b is -2.
Now, the equation becomes -
y = 3x - 2
The graph is plotted for the function.
Therefore, the equation is y = y = 3x - 2.
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a hybrid electric vehicle is a car with both a gasoline-powered motor and an electric motor. some hybrids achieve mileage ratings as high as 75 miles per gallon of gasoline. calculate this quantity in miles per liter and kilometers per liter.
The mileage rate of 75 miles per gallon is equal to 19.8 miles/liter or 31.9 km/liter. The result is obtained by converting the value of each unit.
How to convert the unit of mileage rate?The conversion value of
1 gallon = 3.785 L1 mile = 1.609 kmSome hybrids achieve mileage ratings as high as 75 miles per gallon of gasoline. Determine that quantity in:
Miles per literKilometers per literMultiply the number with the conversion value of each!
In miles per liter,
75 miles/gallon = 75 × 1/3.785 miles/liter
75 miles/gallon = 19.8 miles/liter
In kilometers per liter,
75 miles/gallon = 75 × 1.609 × 1/3.785 km/liter
75 miles/gallon = 31.9 km/liter
Hence, 75 miles per gallon is equal to 19.8 miles/liter or 31.9 km/liter.
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A rectangular rug has a perimeter of 240 yards. The width of the rug is 2 yards more than two times the length. Find the length and the width
The length of a rectangular rug is 84 yards and the width is 36 yards
Let 'l' represents the length of the rectangular rug and 'w' represents the width of a rectangular rug.
The length of the rug is 12 yards more than two times the width.
So, we get an equation,
l = 12 + 2w
Also, a perimeter of a rectangular rug is 240 yards
We know that the formula for the perimeter of rectangle:
P = 2(w + l)
Using this formula the perimeter of a rectangular rug would be,
P = 2 × [w + (12 + 2w)]
240 = 2 (12 + 3w)
120 = 12 + 3w
108 = 3w
w = 118/3
w = 36
And the length would be,
l = 2 + 2( 36)
l = 84 yards
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The complete question is:
A rectangular rug has perimeter 240 yards. The length is 12 yards more than twice the width. Find the length and width of the rug.
suppose you have a column of experimental data in column j and a column of positions for each experimental point in column k. what formula would you put in cell location h10 to find the numerical derivative at position 10 of column k of the data found in j? write your answer in your word document.
The formula would you put in cell location h10 to find the numerical derivative at position 10 of column k of the data found in j is =DERIVXY(h10, k10, j)
The term called derivative is defined as the process to determine the rate of change of a quantity with respect to another changing quantity
Here we have to write the formula for the cell location h10 to find the numerical derivative at position 10 of column k of the data found in j.
As from the definition, the general form derivative function is written as,
=> =DERIVXY(x, y, p, [options])
where x a vector of the points x-coordinates and y corresponding vector of the points y-values and p the point at which to compute the derivative.
Here we have the values of x as h10, y as k10 and p as j
Then the formula is written as,
=> =DERIVXY(h10, k10, j)
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steven makes a base monthly salary of $2700. as a vendor, be must sell $17000 worth of items per month. he also makes a 10% commission on all sales beyond the monthly quota. there is also an additional 5% bonus on top of the normal commission rate for any sales beyond $25000. if steven made $4800 this month, how much did he sell to the nearest dollar?
If Steven made $4,800 this month, the value of his sales for the month is $51,000.
How the sales value is determined:Steven's base monthly salary on sales of $17,000 = $2,700
First sales commission above $17,000 sales = 10%
Second bonus commission above $25,000 sales = 5%
Total earnings for the month = $4,800
Commissions:First sales commission = $800 ($25,000 - $17,000 x 10%)
Additional bonus commission = $1,300 ($4,800 - $2,700 - $800)
$1,300 = 5%
Sales above $25,000 = $26,000 ($1,300/5%)
Sales value = $51,000 ($25,000 + $26,000)
Thus, we can assert that Steven generated Sales of $51,000 to earn a total of $4,800 for the month.
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3. Find the value of h.
h
2h
60°
30°
120°
15°
2h
h
(1 point)
The value of the variable, h is 60 degrees
How to determine the value of hThe properties of a trapezium are expressed as;
It is a 2-Dimensional shapeThe bases of a trapezium are parallel to each otherLength of both the diagonals is equalDiagonals of a trapezium always intersect each otherAdjacent interior angles sum up to 180°Sum of all the interior angles in a trapezium is always 360°If the size of the angles of the trapezium are 2h, 2h, h and h
Then, it is represented as;
Add all the angles
2h + 2h + h + h
Equate the angles to the sum of the interior angles of a trapezium, we get
2h + 2h + h + h = 360
Now, add the like terms
6h = 260
Divide both sides by the coefficient of h, we get;
6h/6 = 630/6
h = 60 degrees
Hence, the value is 60 degrees
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Please answer this question within 10 min! Information in the picture.
The area of triangle A(F) D is 42.44 units²
How to find the area of the triangle?
The formula to calculate the area of a triangle with base b and height h is given by:
Area = 1/2(bh)
In ΔA(F) D, the base is (F)D and A(F) is the height
Using trigonometric ratio:
sin 30° = A(F) /AD (opposite/hypotenuse)
0.5 = A(F) /14
A(F) = 7 units
(F)D = √(14²-7²) = 7√3 units (Pythagoras theorem)
Area of ΔA(F) D = 1/2 × (F) D × A(F)
Area of ΔA(F) D = 1/2 × 7√3 × 7
Area of ΔA(F) D = (49√3)/2
Area of ΔA(F) D = 42.44 units²
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Let f(x) = 2x^2 + x - 3 and g(x) = x - 1. Perform the indicated operation, then find the domain. (f - g)(x)
A) x^2 - 4; domain: positive real numbers
B) 2x^2 - 4; domain: all real numbers
C) x^2 - 4; domain: all real numbers
D) 2x^2 - 2; domain; all real numbers
Let f(x) = 2x^2 + x - 3 and g(x) = x - 1. Perform the indicated operation, then find the domain. (f * g)(x)
A) 2x^3 - x^2 - 4x + 3; domain: all real numbers
B) 2x^3 + x^2 - 3x; domain: all real numbers
C) 2x^3 + x^2 + 4x - 3; domain: negative real numbers
D) 2x^2 + x - 3x + 3; domain: positive real numbers
=============================================
Work shown for problem 1
[tex](f - g)(\text{x}) = f(\text{x}) - g(\text{x})\\\\(f - g)(\text{x}) = (2\text{x}^2+\text{x}-3)-(\text{x}-1)\\\\(f - g)(\text{x}) = 2\text{x}^2+\text{x}-3-\text{x}+1 \\\\(f - g)(\text{x}) = 2\text{x}^2-2\\\\[/tex]
This leads to choice D as the final answer.
The domain is the set of all real numbers since the result is a polynomial. Any polynomial function has the domain "all real numbers". This is because we don't have anything like a division by zero error. We also don't have to worry about square roots of negative values.
------------------------
Work shown for problem 2
[tex](f * g)(\text{x}) = f(\text{x}) * g(\text{x})\\\\(f * g)(\text{x}) = (2\text{x}^2+\text{x}-3) * (\text{x}-1)\\\\(f * g)(\text{x}) = \text{x}(2\text{x}^2+\text{x}-3)-1(2\text{x}^2+\text{x}-3)\\\\(f * g)(\text{x}) = 2\text{x}^3+\text{x}^2-3\text{x}-2\text{x}^2-\text{x}+3\\\\(f * g)(\text{x}) = 2\text{x}^3-\text{x}^2-4\text{x}+3\\\\[/tex]
This leads to choice A as the final answer.
The domain is the set of all real numbers for the exact same reasoning as problem 1.
Mia estimated 5/8 + 1/9 by replacing 5/8 with 1 and 1/9 with 0. Her
estimated sum was 1 + 0 = 1. Explain why Mia's estimate is Not accurate?
NOT accurate.
Estimation done by Mia is not accurate, as the accurate estimated sum of the given expression 5/8 + 1/9 is equal to ( 1/2).
Estimation done by Mia is not accurate:
Replaced 5 /8 with 1.
But accuracy represents:
0 < (1 /4 ) < ( 1 /2 ) < (5 /8 ) < ( 3 / 4 ) < 1
( 5 / 8 ) is more close to ( 1 /2 ).
Estimated value of ( 5 / 8 ) is ( 1 / 2 )
0 < ( 1 / 9 ) < ( 1 / 4 )
So , estimated value of ( 1 / 9 ) is 0
Estimated sum = ( 1 / 2 ) + 0
= ( 1 / 2 )
≠ 1
Therefore, accurate estimated sum of 5/8 + 1/9 is equal to ( 1 /2 ).
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2x is greater than 5 + 2
Answer:
x = greater than or equal to 3.5 x = 3≥
Step-by-step explanation:
any number that is greater than or is 3.5 will make 2x greater than 5 + 2 which equals 7
How would paying off the lowest outstanding balance credit card first be beneficial over paying off the one with the highest?
Paying off the lowest outstanding balance credit card first will not be beneficial over paying off the one with the highest. Instead, it's beneficial to pay the highest outstanding balance first.
Actually, paying the one with the highest interest rate is logically the right thing to do because you can shorten the amount that you spend on interest or charges by month, but paying the lowest outstanding balance credit card first makes more sense if you could transfer the highest interest balance into a low or maybe no interest rate that is being offered to another card, only if you are so certain that you will pay the remaining balance or on before its due.
It should be remarked that paying off the lowest outstanding balance credit card first cannot be beneficial over paying off the one with the highest interest rate.
It's significant to pay the one that has the highest interest rate. This is because it'll assist in shortening the amount the person will pay as interest.
In conclusion, it's important to pay the highest Interest rate.
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In statistics, a population is a set of similar items or events which is of interest for some question or experiment and a sample is a set of data collected from a population by a defined procedure. In the following examples of statistical studies, identify the population of interest and the sample and provide the sample size.
An employee at the local ice cream parlor asks eight customers if they like unicorn ice cream.
Population:
Sample size:
The population of interest and the sample size include the following:
Population: all potential customers of the parlor.
Sample size: 8.
What is a population?In Statistics and science, a population can be defined as a set of similar items or events that comprises every member of a group and from which a researcher, scientist, or experimenter, obtains or generates data for a statistical study.
What is a sample?In Statistics and science, a sample can be defined as a set of data that is collected from a population based on a well-defined sampling procedure.
In this scenario, we can logically deduce that sample is the eight customers that were selected and questioned by an employee at the local ice cream parlor.
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Determine weather the mean value theorem can be applied to f(x)= sqrt(5-x) on (-4,5) find all values of c in (-4,5) such that f’(c)= f(b)-f(a)/b-a if possible
Answer:2.75 (or 11/4, they are equal).
Step-by-step explanation: The graph of f(x) is continuous on the closed interval and differentiable on the open interval. Now we need to find the average slope over the interval, which is [0-3]/[5-(-4)] = -3/9 = -1/3. The goal is to find a place where f'(c) = -1/3, so basically anywhere where the derivative equals -1/3. First we need to find the derivative of the function which can be rewritten as (5-x)^(1/2). Differentiating this using the chain rule gives you -1/(2*sqrt(5-x)). Set this equal to -1/3. The numerator is -1, so really we just need to find where the denominator, 2sqrt(5-x), is equal to 3. Divide by 2 and get sqrt(5-x) = 3/2. Square both sides and get 5-x = 9/4. Subtract 5 and get -x = -2.75, so x = 2.75. This means c = 2.75.
Lorena and Karla are creating an art project in the shape of a right triangle. They have a 92 cm long piece of wood, which is to be used for the hypotenuse. The two legs of the triangular support are of equal length. Approximately how many more centimeters of wood do they need to complete the supports?
The amount of wood that they need to complete the supports is given as follows:
130.10 cm.
How to obtain the amount of wood needed?First we must obtain the side lengths of the right triangle.
The equal side lengths of the right triangle are obtained applying the Pythagorean Theorem, hence:
x² + x² = 92²
2x² = 92²
x² = 4232
x = square root of 4232
x = 65.05 cm.
They have two sides of 65.05 cm, hence the amount of wood needed is obtained as follows:
2 x 65.05 = 130.10 cm.
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d. tickets to the zoo cost $25 for adults and $10 for children. the total ticket sales one day were $47,750. the number of children, c, who visited the zoo was 270 more than 6 times the number of adults, a, who visited. write and solve a system of equations to find the total number of visitors to the zoo that day.
The total number of visitors to the zoo that day=3980.
Given:
cost of each ticket for an adult=$25
cost of each ticket for an adult=$10
Total ticket sales one day=$47,750.
⇒$25+$10=47,750
⇒25+10=47,750-----(1)
Also,
c=6a+270
6a-c=-270------(2)
multiplying eq(2) with 10 we get:
60a-10c=-2700----(3)
Adding eq(1) and eq(3) we get
25a+10c=47,750
60a-10c=-2700
--------------------------
85a=45050
--------------------
To calculate a value just divide 45050 by 85 we get
a=45050/85
a=530
Now to get the value of c substitutes a value.
c=60(530)+270
c=3450
Number of Adult visitors=530
Number of children visitors=3450
Total Number of visitors=3980.
Therefore, the total number of visitors to the zoo that day=3980.
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What is the range of h Choose 1 answer - 4 <= h(x) < 6 The x h(x)-vabuc5-4.0.2.and 4 The x h(x)- sqrt 3 locs-4-2 2,4,and l; - 5 <= h(x) < 4
The range of h include the following: A. -4 ≤ h(x) ≤ 6.
What is a range?In Mathematics, a range can be defined as the set of all real numbers that connects with the elements of a domain.
How to identify the range of this graph?Generally speaking, the vertical extent of a graph represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.
By critically observing the graph shown, we can reasonably and logically deduce the following:
Range = [-4, 6]
In mathematical notation, the range of this graph can be rewritten as -4 ≤ h(x) ≤ 6.
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A right rectangular prism is shown.
What is the length of DH¯¯¯¯¯¯ to the nearest tenth of an inch?
Drag and drop the answer into the box.
The length of DH (diagonal) in the rectangular prism is approximately 3.5 inches.
How to Find the Measure of the Diagonal of a Right Rectangular Prism?A rectangular prism has three dimensions: length, width, and height. The diagonal of a rectangular prism is the distance between two opposite corners of the prism.
To find the diagonal of a rectangular prism, you can use the Pythagorean theorem, which states that the square of the diagonal is equal to the sum of the squares of the length, width, and height.
In this case, the length is 1.5 inches, the width is 1 inch, and the height is 3 inches. So, you can use the formula:
d² = 1.5² + 1² + 3²
d² = 2.25 + 1 + 9
d² = 12.25
Then take the square root of the d²
d = √12.25
d ≈ 3.5 inches.
Therefore, the measure of the diagonal of the rectangular prism is approximately 3.49 inches.
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Answer:
3.5
Step-by-step explanation:
I took the quiz
proviion of a weekend tay in ydney valued at $1,000 which included flight to the value of $300, meal to the value of $200 and accommodation to the value of $500, a a chritma gift in december 2022. need to calculate the FBT liability
the total FBT liability for this benefit is $329 ($700 x 47% = $329).
Fringe Benefits Tax (FBT) is imposed by the Australian Taxation Office (ATO) on certain non-cash benefits provided to employees. If a company provides a weekend stay in Sydney valued at $1,000 as a Christmas gift in December 2022, the FBT liability is calculated as follows:
The taxable value of the benefit is calculated by deducting the expenses that are not subject to FBT, i.e. $300 (flight) from the total value of the gift, i.e. $1,000. This leaves a taxable value of $700 ($1,000 - $300 = $700).
The FBT liability is then calculated by multiplying the taxable value, i.e. $700, by the FBT rate which is currently 47% (as of 2021). This results in an FBT liability of $329.
Therefore, the total FBT liability for this benefit is $329 ($700 x 47% = $329).
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What is the value of f(m) = 55?
Answer:
Step-by-step explanation:The exponent of a number shows how many times the number is multiplied by itself.
According to the rules of exponents,
We know that, am ÷ an = am − n
(5m ÷ 5−3) = 55
5m−(−3) = 55
5m + 3 = 55
The bases are the same on both the sides, so their exponents must be equal.
∴ m + 3 = 5
⇒ m = 5 − 3
⇒ m = 2
20. MP MODELING REAL LIFE The plate for a microscope has a circumference of
100 millimeters. What is the area of the plate?
The area of the plate of the microscope with a circumference of
100mm is 2500/π mm².
What is the area of the circle?A circle is simply a closed 2-dimensional curved shape with no corners or edges.
The area of a circle is expressed mathematically as;
A = πr²
The circumference of a circle is expressed as 2πr.
Given the data in the question;
Circumference of the plate C = 100 mmRadius r = ?Area A = ?First, we determine the radius of the plate.
Circumference C = 2πr
100 = 2πr
r = 100/2π
r = 50/π
Now, calculate the area of the plate.
A = πr²
A = π ( 50/π )²
A = π × 2500/π²
A = 2500π / π²
A = 2500/π mm²
Therefore, the area of the plate is 2500/π mm².
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Given:
f(x)=x²- 5x+7 and g(x)=3x² + 4x - 2
Find:
(f- g)(x)
(g-f)(x)
(f + g)(x)
Polynomials
The following are solutions to the given problems given f(x)=x²- 5x+7 and g(x)=3x² + 4x - 2;
(f- g)(x) = -2x² - 9x + 9
(g-f)(x) = 2x² + 9x - 9
(f + g)(x) = 4 x² - x + 5
What is a function?A function can be defined as a relation between a set of inputs having one output each. In other words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and co-domain (range). A function is generally denoted by f(x) where x is the input.
The general mathematical representation of a function is y = f(x).
f(x)=x²- 5x+7
g(x)=3x² + 4x - 2
(f- g)(x) = x²- 5x+7 - (3x² + 4x - 2)
(f- g)(x) = x²- 5x+7 - 3x² - 4x + 2
(f- g)(x) = -2x² - 9x + 9
(g-f)(x) = 3x² + 4x - 2 - (x²- 5x+7)
(g-f)(x) = 3x² + 4x - 2 - x² + 5x - 7
(g-f)(x) = 2x² + 9x - 9
(f + g)(x) = x²- 5x+7 + 3x² + 4x - 2
(f + g)(x) = 4 x² - x + 5
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six thirty children had gallon of lemonade to share. if each child had the same amount, what portion of the gallon did each child have to drink?
If each child consumed the same quantity, then each would need to drink (63)x(4/n) of a gallon.
The US fluid ounce is equal to 1/128 of a US gallon since there are four quarts in a gallon, two pints in a quart, and 16 US fluid ounces in a US pint. The US gallon is accepted to be equivalent to around 3.785 L or 231 in inches, but the Imperial gallon is accepted to be equal to 4.54609 L. The liter is the unit of volume used by the great majority of people in the world. a volume measurement equal to eight pints.
An imperial gallon (Britain, Canada) is exactly 4.54609 liters. (US) 3.785 liters or around 231 cubic inches for liquids (a "U.S. liquid gallon")
Here gallon of lemonade to share = 63
let each children has 1 gallon of lemonade
so gallon=63
so portion =63/1
Formula = gallon to share x (4 parts of gallon shape / number of gallon)
which means if each one have n gallon then portion = (63)x(4/n)
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Each child would need to eat 63*4/n of a gallon if they all consumed the same amount.
Since there are four quarts in a gallon, two pints in a quart, and 16 US fluid ounces in a US pint, one US fluid ounce is equivalent to 1/128 of a US gallon. The Imperial gallon is acknowledged to be equal to 4.54609 L, but the US gallon is accepted to be about 3.785 L or 231 in. The vast majority of people in the world measure volume in litres. a volume that is eight pints in size.
In Britain and Canada, an imperial gallon equals precisely 4.54609 litres. 3.785 litres (US) or around 231 cubic inches (a "U.S. liquid")
Here, six thirty kids were sharing a gallon of lemonade.
each youngster should drink a gallon of lemonade.
Gallon = 63.
Hence part = 63/1
It indicates that the fraction is equal to 63*4/n if each has n gallons.
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Note: The complete question would be as bellow,
six thirty children had gallon of lemonade to share. if each child had the same amount, what portion of the gallon did each child have to drink?
Maria is 5 feet 3 inches tall. Marla is 4 feet 11 inches tall, Mandy is 5 feet 2 inches tall
and Marilyn is 4 feet 8 inches tall.. What is the average height of these 4 friends? Explain
how you found your answer.
Answer:
the average height is 5 feet 0 inches
Step-by-step explanation:
To find the average height of Maria, Marla, Mandy and Marilyn, we need to add up their individual heights and divide by the number of people in the group.
First, we need to convert all the heights to a common unit of measurement. Since inches are the smallest unit of measurement, we will convert all the heights to inches.
Maria: 5 feet 3 inches = 63 inches
Marla: 4 feet 11 inches = 59 inches
Mandy: 5 feet 2 inches = 62 inches
Marilyn: 4 feet 8 inches = 56 inches
Now we can add up the heights:
63 inches + 59 inches + 62 inches + 56 inches = 240 inches
To find the average, we divide the total height by the number of people:
240 inches / 4 people = 60 inches
So the average height of these four friends is 60 inches or 5 feet, which is the same as 5 feet 0 inches.
Therefore, the average height of these four friends is 5 feet 0 inches.
Consider the solid obtained by rotating the region bounded by the given curves about the x-axis. Y = 4 - 1/2x text(, ) y = 0 text(, ) x = 0 text(, ) x = 1 Find the volume V of this solid. V = Sketch the region, the solid, and a typical disk or washer. (Do this on paper. Your instructor may ask you to turn in this work. )
The volume of the solid is approximately 32π/3 cubic units.
The volume of the solid obtained by rotating the region bounded by the curves y = 4 - 1/2x, y = 0, x = 0, and x = 1 about the x-axis can be found using the method of disks/washers. The formula for the volume is given by:
V = π * ∫[a,b] (R^2 - r^2) dx
where R is the outer radius (4 - 1/2x), r is the inner radius (y = 0), a and b are the limits of x (x = 0 and x = 1), and dx represents a small slice of the solid.
Evaluating the definite integral:
V = π * ∫[0,1] (16 - x^2 - x^2) dx = π * ∫[0,1] (16 - 2x^2) dx = π * (16x - 4/3 x^3) evaluated at x = 1 - x = 0 = π * (16 - 4/3) = 32π/3 cubic units.
So the volume of the solid is approximately 32π/3 cubic units.
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Could someone please help! been struggling on these for a few mins !
The simplification of the logarithm expression are as shown below
How to simply logarithm expressions?A logarithm expression is a mathematical statement that involves logarithms. It is an expression that contains logarithmic functions, such as log, ln, logₐ, etc. These expressions can include logarithms with different bases, numbers in logarithm form, and exponents.
The logarithm expressions can be simplified as follow:
1. since logₐa = 1,
log₄4 = 1
2. Since logₐ1 = 0,
log₁₀1 = 0
3. since logₐ(M × N) = logₐM - logₐN and logₐa = 1
log₃4 × 3 = log₃4 + log₃3 = log₃4 + 1
4. since logₐxⁿ = n logₐx and logₐa = 1
log₄4³ = 3 log₄4 = 3 × 1 = 3
5. since logₐxⁿ = n logₐx and logₐa = 1
logₓx⁰ = 0 logₓx = 0 × 1 = 0
6. since logₐxⁿ = n logₐx and logₐa = 1
logₓx³ = 3 logₓx = 3 × 1 = 3
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If a jogger runs 84 laps in 28 minutes, what is the rate at which this jogger runs?
3 laps for every 12 minutes.
4 laps for every 3 minutes.
4 laps every 1 minute.
3 laps every 1 minute.
Answer:
3 laps every 12 minutes
Step-by-step explanation:
Different between adding and subtracting linear
Therefore, the method (addition or subtraction) used to combine or separate the terms is the primary distinction between adding and subtracting linear expressions.
Another difference is that when we subtract linear expressions, we get a smaller expression, whereas when we add them, we get a larger one.
What exactly are linear expressions?A mathematical expression that results from the linear combination of variables and constants is known as a linear expression.
Linear expressions can be combined or separated using two distinct operations: adding and subtracting.
By keeping the same variable while adding the coefficients (the numerical part) to linear expressions, like terms are combined. If we wanted to add 2x and 3x, for instance, we would get 5x.
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After traveling 70 meters in its dive, the submarine is at a depth of 25 meters. About what will the submarine’s depth be if it continues its dive for another 110 meters? Round to the nearest whole number A) 40m
B) 64m
C) 18m
D) 4m
About 40 meters the submarine’s depth be if it continues its dive for another 110 meters. So the option A is correct.
Since it is essentially a ratio problem, we can use the information given and apply the Rule of Three assuming that the submarine is moving at a constant speed.
In this rule, the depth after 110 meters is obtained by simply multiplying the ratio's diagonal values and dividing by the last value.
70min = 25 m
110min = x m
x = (110 × 25)/70
x = 2750/70
x = 39.28
x = 40(approx)
We can see that at 110 minutes, the depth would have been approximately 40 meters, but since the submarine travelled further during this time, we must add this measurement to the original 25 meters to determine the submarine's total depth.
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