The factorization of given expression would be,
(4a^2)^2 - (b^2)^2= (4a^2 + b^2)(4a^2 - b^2)
In this question, we have been given an expression 16a^4 − b^4
We need to factor given expression using the polynomial identity
(x^2 - y^2) = (x − y)(x + y)
We write given expression as,
16a^4 − b^4 = (4a^2)^2 - (b^2)^2
Using the above polynomial identity,
16a^4 − b^4
= (4a^2)^2 - (b^2)^2
= (4a^2 + b^2)(4a^2 - b^2)
Therefore, the factorization of given expression would be,
(4a^2)^2 - (b^2)^2= (4a^2 + b^2)(4a^2 - b^2)
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A rectangular garden must have a perimeter of 540 feet and and area of at least 12,000 square feet. Describe the possible lengths of the garden. round to the nearest whole number
I really need help with this, it is due soon, please help me!
The possible length of the rectangular garden is L ≥ 6225ft which has a perimeter of 540 feet,
What is a Rectangle?The interior angles of a four-sided polygon are all 90 degrees. At each corner or vertex, the two sides meet at a right angle. The rectangle varies from the square in that its two opposite sides are of equal length.
Let L represent the garden's length.
Let W represent the garden's width.
The perimeter is 540 feet.
The rectangle's perimeter is equal to 2(L + W) = 540
L + W = 270 ....(i)
W = 270 - L ....(ii)
The rectangle's area is equal to its length times its width, which is given 12000 square feet.
L × W ≤ 12000 ....(iiI)
Substitute the value of equation (ii) into (iii)
(270 - L)(L) ≤ 12000
270l - L² ≤ 12000
0 ≤ L² - 270l + 12000
L² - 270l + 1200 ≥ 0
Solving the quadratic inequality above, and we get
L ≥ 6225
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While driving at an average
velocity of 15.6 m/s down the
road, a driver slams on brakes to
avoid hitting a squirrel. The car
stops completely in 4.2 seconds.
What is the average acceleration
of the car?
The average acceleration is -3.71m/s². Any procedure where the velocity varies is referred to as acceleration.
What is acceleration ?Any procedure where the velocity varies is referred to as acceleration. There are only two ways to accelerate: changing your speed or changing your direction, or changing both. This is because velocity is both a speed and a direction.According to Newton's second law, a body's acceleration is the end outcome of all the forces that have been applied to it. The frequency at which a body's velocity changes is referred to as acceleration, a vector quantity.A vehicle accelerates in the direction of travel when it begins at a stop and moves at increasing speeds in a straight line.A linear acceleration is the acceleration of the car in the direction it is moving, and it causes the passengers to feel a force pushing them back into their seats. The acceleration that is used when shifting direction is known as radial acceleration.acceleration = change in velocity / Time taken
a = 0 - 15.6 / 4.2
= -15.6 / 4.2
= -3.71
The average acceleration is -3.71m/s²
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please help i need answers and i need them now!!!!
The evaluation of the quadratic equations are as follows;
Question 5
No solutionQuestion 6
Yes; (x - 8)² = 4Question 7
Sometimes; Factoring
Always; Quadratic formula
Always; Completing the square
Sometimes; Square root method
Sometimes; Factoring by group
Question 8
The numerator are;
(a) 8
4
(b) The denominator value;
4
(c) The roots are;
2
1
What is a quadratic equation?A quadratic equation is an equation of the form; a·x² + b·x + c = 0
Question 5
The quadratic equation, x² + 6·x + 10 = 0
The discriminant is 6² - 4×1×10 = -4
The discriminant < 0, therefore, the equation does not have solution
Question 7
Factoring;
Method of solving equations work more when the coefficient of x and the constant can be expressed as a + b and a·b
Where;
a·b = The constant
a + b = The coefficient of x
Therefore, factoring works sometimes
Sometimes; Factoring
Quadratic formula
The quadratic formula is an equation that involves the use of the constant and the coefficients of x
The quadratic formula therefore works all the time
Always; Quadratic formula
Complete the square
The completing the square method works by rearranging the equation in the form;
a·x² + b·x + c ⇒ a·(x + m)² + n
Where;
m = b/(2·a),
n = c - (b²/(4·a))
The method therefore works all the time
Always; Completing the square
Square root method
The square root method involves placing the square term of the equation on one side of the equation and the constant term on the other side
The square root method works for equations that can be expressed in the form x² = b
The method works sometimes
Sometimes; Square root method
Factoring by group
The method involves finding the common factors and grouping based on the common factors
The method only works when there are common factors
Sometimes; Factoring by group
Question 8
The equation is 2·x² - 5·x = x - 4,
Writing the equation so that we have;
2·x² - 5·x - x + 4 = 0
2·x² - 6·x + 4 = 0
x = (6 ± √((6² - 4× 2 × 4))/(2×2) =
Therefore;
x = 8/(2×2) or x = 4/(2×2)
The numerators are 8 and 4
8
4
(b) The denominator is (2 × 2) = 4
(c) The two roots of the quadratic equation are;
x = 8/4 = 2 and x = 4/4 = 1
2
1
Question 6
The equation, x² - 16·x + 64 = 4
The left side of the equation can be factored as follows;
x² - 16·x + 64 = 4
x² - 8·x - 8·x + 64 = 4
(x² - 8·x) + (64 - 8·x) = 4
x·(x - 8) - 8·(x - 8) = 4
(x - 8)·(x - 8) = (x - 8)² = 4
Yes; (x - 8)² = 4
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Tim’s mom filled the gas tank in her SUV and spent $72.00 for 22.5 gallons of unleaded gasoline. What is the constant of proportionality that relates the cost in dollars, y, to the number gallons of unleaded gasoline, x?
The constant of proportionality that relates the cost in 72 dollars as y, to the number of gallons of unleaded gasoline in 22.5 gallons of unleaded gasoline as x is $3.20 per gallon of unleaded gasoline.
The constant of proportionality is the ratio of the so-called proportional relationship that relates two given values to each other.
Other names for the constant of proportionality are constant ratio, constant rate, unit rate, variable constant, and even rate of change.
The relationship between two variables, X and Y, is directly proportional if it can be expressed in terms of Y/X = k or Y = Xk.
y/x = k
k is the constant of proportionality.
Given that:
y = $72 and x = 22.5 gallons.
So, the value of the constant of proportionality (k) = 72/22.5
=> k = 720/225
Dividing both by the numerator and denominator by 45. We get,
=> k = 16/5
The value of the constant of proportionality (k) = $3.20 per gallon of unleaded gasoline.
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a workbook contains a list of houses and the months that they were sold in several cities in florida in june. you are interested in determining the average price of sold houses in ft. lauderdale. what function is best suited for this calculation? (1 point) maxifs averageifs sumif averageif
As per the statement the function which is best suited for this calculation is averageif.
What is averageifs?In Microsoft Office Excel, averageifs may be a function that helps to determine the average of cells that follow different criteria. Averageif is one among many functions under the "Statistic" category. the standards for averageifs can be words or a range of numbers which allows more diverse analysis compared to other average functions.While averaging the equation this option is very easy to implement. you need not recall any formula just go for the formulas option at tabs in excel there are many formulas such as SUMIF, MAXIFS ETC.To know more about averageifs visit:
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is there a statistically significant relationship between money spent on advertising and sales? test at the 5% level of significance and explain your approach (including hypotheses).
We can see that the p-value for above test is less than α=0.05 and it indicates that we have very strong evidence against H(0) to reject it and we can conclude that there is highly significant relationship between money spent on advertising and sales.
In the given question we have to find is there a statistically significant relationship between money spent on advertising and sales.
Here we have Sales(in $1000) as dependent variable (y) and spend on Advertising (in $1000) as independent variable (x).
The significance of relationship between x and y is given by the significance of regression coefficient of regression of y of x.
So we have to test
H(0): β1=0
H(1): β1≠0
From the table that is given below, we have;
b(1)=3.778221987
se(b(1)) =0.563520732
The test statistic to test the above hypothesis is
t=b(1)/se(b(1))
From the given output, we already have
t=6.704672556
p-value=0.0000146
We can see that the p-value for above test is less than α=0.05 and it indicates that we have very strong evidence against H(0) to reject it, so we reject the H(0) and we can conclude that there is highly significant relationship between money spent on advertising and sales.
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consider the sequence {20, 17, 14, 11, 8, 5, 2...}. what is the value of sum from n equals 3 to 6 of a subscript n?
The value of the sum of the arithmetic sequence from a₃ to a₆ is 38
What is an arithmetic sequence?An arithmetic sequence is a sequence in which the difference between two consecutive terms is a constant.
The first term of the sequence is 20, the common difference is 17 - 20 = 14 - 17 = 11 - 14 = 8 - 11 = 5 - 8 = 2 - 5 = -3
The sum from n = 3 to n = 6 of aₙ is found as follows;
The sequence is an arithmetic progression of the form aₙ = a + (n - 1)·d
Where;
aₙ is the value of the nth term
a = The first term
d = The common difference
From the sequence, we have;
a = 20, d = -3, from which we have;
aₙ = 20 + (n - 1) × (-3) = 20 - 3·(n - 1)
aₙ = 20 - 3·(n - 1)
From which we have;
a₃ = 20 - 3×(3 - 1) = 14
a₄ = 20 - 3×(4 - 1) = 11
a₅ = 20 - 3×(5 - 1) = 8
a₆ = 20 - 3×(6 - 1) = 5
a₃ + a₄ + a₅ + a₆ = 5 + 8 + 11 + 14 = 38
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what equations could i use with 1 2 3 4 5 to get 35
You could use
2x((2x5)+5+2)+1
the caspian sea is 92 feet below sea level. sea level is considered 0 feet. what number presents this height in feet of the caspian sea
Caspian Sea is elevated at 92 feet (or 28 meters) below sea level. (globally preferred unit is meters)
On the scale of sea levels, a certain height has been assigned zero elevation. This acts as a reference point for rest of the measurements and is called Mean Sea Level (MSL). It is also known as still water level.
Caspian Sea at 92 feet below sea level means it is 92 feet below MSL. Thus, its elevation is considered 92 feet below sea level.
Global MSL is calculated using the spatial average of the complete ocean's level.
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The Hernandez family is on a road trip. They have been driving for 3 1/2 hours. They have listened to 4 CDs of equal length.
Part A
How long was each CD?
Part B
If the family has 1 hour of their drive left, how many CDs will they be able to listen to in the final hour?
Part A: The length (number of hours) of each CD is 0.875 hours.
Part B: The Hernandez family can listen each for 0.875 hours
Given that,
The Hernandez family is on a road trip. They have been driving for 3 1/2 hours. They have listened to 4 CDs of equal length.
What is an equation?
An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Part A
Let the length (number of hours) of each CD be x.
Now, x = 7/2 = 3.5/4 = 0.875
= 0.875 hours
Part B
If the family has 1 hour of their drive left, still they can listen 4 CDs.
Therefore, the Hernandez family can listen each for 0.875 hours.
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if you randomly select a card from a well-shuffled standard deck of 52 cards, what is the probability that the card you select is a spade or queen?
Answer:
The answer is [tex]\frac{4}{13}[/tex].
Step-by-step explanation:
Additive rule:
According to this rule, the probability that events A or B will occur is given by the formula,
[tex]P(A\cup B)=P(A)+P(B)-P(A\cap B)[/tex]
Here,
[tex]P(A\cup B)[/tex] means the probability of either event A occurring or B occurring.P(A) is the probability of event A.P(B) is the probability of event B.[tex]P(A\cap B)[/tex] means the probability of both event A and event B occurring.We know that there are 13 spades and 4 queens in a deck of 52 cards. Also, there is only one queen of a spade.
Then,
[tex]\begin{aligned}P(S)&=\frac{13}{52}\\P(Q)&=\frac{4}{52}\\P(S\cap Q)&=\frac{1}{52}\end{aligned}[/tex]
Therefore, the probability that the card you select is a spade or queen is given by,
[tex]\begin{aligned}P(S\cup Q)&=P(S)+P(Q) -P(S\cap Q)\\&=\frac{13}{52}+\frac{4}{52}-\frac{1}{52}\\&=\frac{16}{52}\\&=\frac{4}{13}\end{aligned}[/tex]
Therefore, the answer is [tex]\frac{4}{13}[/tex].
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Simplify & state any excluded values x^2-x-6/x^2+7x+10 show work
After using the Simplification method we will get the value (x - 3) / (x + 5)
What is Simplification?
To simplify simply means to make anything easier. In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler. Calculations and problem-solving techniques simplify the issue. We can —
By eliminating all common elements from the numerator and denominator and putting the fraction in its simplest/lowest form, fractions can be made simpler.
By combining and grouping like terms, mathematical expressions can be made simpler. This makes the phrase simple to comprehend and to solve.
Given,
(x^2-x-6) / (x^2+7x+10)
This equation can be separated into two parts, the top and the bottom, which we can simplify further.
Simplifying the top part
x² - x - 6
This can be factored into the following:
x² + 2x - 3x - 6
x(x + 2) - 3(x + 2)
(x + 2)(x - 3)
Now, Simplifying the bottom part
x²+7x+10
x² + 2x + 5x + 10
x(x + 2) + 5(x + 2)
(x + 2)(x + 5)
Now, we can write the new numerator and denominator
(x + 2)(x - 3) / (x + 2)(x + 5)
(x - 3) / (x + 5)
Hence, (x - 3) / (x + 5) is the answer when simplifying
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What kind of a number is √-9
Answer:√(9) is a rational number.
Step-by-step explanation:
Answer:This is a rational numer because it can be expressed in the form of p/q
Step-by-step explanation:If a number can be expressed int he form of p/q then its rational.
what is 2.085x10^5 in scientific notation
The number in scientific notation is 2.1×10⁵.
What is rounding a number?Adjusting a number's digits so that it produces an approximation of a result is known as rounding.
The given number is 2.085×10⁵.
Round the number 2.085 to the nearest tenth:
2.085 ≈ 2.1
Therefore, the number in scientific notation is 2.1×10⁵.
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tissues cost $3.48 per box . how many boxes did nancy buy if she spent $17.40? Write an equation and solve .
Answer:
She purchased 5 boxes
Step-by-step explanation:
17.40 ÷ 3.48 = 5
the proportion of heads is 0.49 in 100 tosses. what is the difference between the number of heads and half the number of tosses?
Using the difference, the difference between the number of heads and half the number of tosses is 1.
In the given question,
The proportion of heads is 0.49 in 100 tosses.
We have to find the difference between the number of heads and half the number of tosses.
The proportion of heads=0.49
Total tosses =100
So the total number of heads
=0.49*100
=49
Since we have to find the difference between the total number of head and half the number of tosses.
So the half on the number of tosses=Total number of tosses/2
The half on the number of tosses=100/2
The half on the number of tosses=50
So, The difference=The half on the number of tosses−Total number of heads
The difference=50−49
The difference=1
Hence, the difference between the number of heads and half the number of tosses is 1.
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solve the compound inequality-4x≤x-5<16
The solution to the compound inequality is 1 ≤ x < 21
Compound inequalityCompound inequality are type of inequality that has two or more parts.
In order to solve these simultaneous inequalities, we need to write them as two separate inequalities, and find the values of x that satisfy both of them
(-4x [tex]\leq[/tex]x-5 -------------------------------Equation 1
(x-5< 16) --------------------------------Equation 2
Move all the term to the left side
(-4x +(-x+5) ≤ (x-5) +(-x+5) ---------Equation 3
(x-5) +(-16) < 16+(-16)------------------Equation 4
We need to get rid of expression interval. If there is a negative sign in front of it, each term within the expression changes sign
(-4x -x +5 ≤x-5-x+5)-------------------Equation 5
( X-5 -16 < 16 -16) ----------------------Equation 6
Rearrange and Simplify equation (5 & 6)
(-5x+5 ≤ ) ---------------------------------Equation 7
(x -21 < 0)----------------------------------Equation 8
We need to get rid of expression interval and subtract 5 from equation (7) and add 21 to equation (8)
(-5x ≤ -5) ---------------Equation (9)
(x < 21)------------------Equation (10)
Divide equation (9) by 5 on both sides and flip the sign because of the negative
5x/ 5 ≥ 5/ 5
( x ≥ 1 )
(x < 21 )
Therefore the solution to the compound inequality is 1 ≤ x < 21
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how many different three-letter initials are there that end with the letter z (using the upper case characters in the english alphabet)?
A total of 676 different three-letter initials combinations end with the letter Z using the uppercase characters in English alphabets.
We have three letters which have to be filled in.
English alphabets consist of 26 letters (A-Z). Let's suppose A1, A2 & A3 are the three initials.
For A1, we have 26 alphabets to choose from i.e. A-Z
For A2, we again have 26 alphabets to choose from i.e. A-Z
For A3, we have only one option i.e. Z
Thus, total different three-letter initials combinations for "**Z" pairings are:
26 x 26 x 1 = 676
Please note that combinations allow repetition of values. If one wants to avoid repetition, permutation needs to be calculated.
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a large office desk has an area of 42ft4. if the width is 3.5 feet, write an equation to represent the area
The equation to represent the area of the.large office is 3.5l = 42.
What is a equation?An equation is simply used to illustrate the relationship between the variables given.
In this case, the large office desk has an area of 42ft² anz the width is 3.5 feet. It should be noted that the area is calculated as:
= Length × Width
Therefore, l × w = 42
where w = 3.5
l × 3.5 = 42
3.5l = 42
Therefore, the equation is 3.5l = 42
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Round 55 to the nearest ten
this is due in 30 min :(
Answer: 55 rounded to the nearest tenth is 60.
Step-by-step explanation: Hope this helps!!!
Answer: 60
Step-by-step explanation
help meeeeeeeeeeee pleaseee rnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
534,000
Step-by-step explanation:
12 days pass from may 10 to may 22 so we replace x with 12
190,000(1.09)^12
190,000(2.81266)
534406.309
But rounded to the nearest thousands
534,000
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The sum of a number, it’s square, and it’s square root is 93. What is the number
Answer:
The answer is 9How I got the answer:
93 doesn't have an exact square root. So, we need to try numbers that fit with the equation.
x will be less than the square root of 93. Since the square root of 93 is between 9 and 10. The largest perfect square that we can try is 9. Let us see if that number works.
x + x² + √x = 93
9 + 9² + √9 = 93
9 + 81 + 3 = 93
93 = 93 ✔
It does work.
So the number is 9.
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james bond is on an island 6 miles from the nearest point a on a beach with a straight shoreline. he desperately needs to get to the point which is 10 miles up the beach from a. if he can swim 6 miles an hour and run 12 miles an hour, where on the beach should he come ashore in order to reach b in the least possible time?
James bond should come ashore 3.464 miles from point A to reach B in least time.
Calculus is defined as a branch of mathematics concerned with the calculation of instantaneous rates of change (differential calculus) and the summation of infinitely many small factors to determine some whole (integral calculus).
Let's say the James bond travels x miles from point A.
We are aware that time = distance / speed
Total time taken by James bond to reach B is
t(x) = √(x^2+36)/6 + (10-x)/12
dt/dx = x/(6√(x^2+36)) - 1/12
for critical point dt/dx =0
= x/(6√(x^2+36)) - 1/12 = 0
√(x^2+36) = 2x
Squaring on both sides we get
X2 + 36 = 4x2
X2 = 12
X2 = 2√3
T(0) = √(0^2+36)/6 + (10-0)/12 = 41/6
= 6.833 hours
T(2√3) = √(12+36)/6 + (10-2√3)/12 = (5+3√3)/6
= 1.699 hours
T(0) = √(10^2+36)/6 + (10-10)/12 = √34/3
= 1.94 hours
Therefore James bond should come ashore 3.464 miles from point A to reach B in least time
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seith's age is 3 years more twice his brother's age. The sum of their ages is 24. Find each of their ages
g(x)= 4 - x
fog(x)= 11 - 2x
f(x) = ?
When the function g(x) = 4 - x and fog (x) = 11 - 2x then the function f(x) is
f(x) = 2x + 3How to solve the required expressionWhen a function is expressed in terms of another function it can be called a composite function
if g(x) = 4 - x and fog (x) = 11 - 2x
let f(x) = ax + b
fog = f(g(x))
11 - 2x = f((4 - x) + b)
11 - 2x = a(4 - x) + b
11 - 2x = 4a - ax + b
grouping by coefficients
11 - 2x = (4a + b) - ax
equating the coefficients
11 = 4a + b
-2x = -ax
a = 2
plugging a = 2 into 11 = 4a + b
11 = 4 * 2 + b
11 = 8 + b
b = 3
if a = 2 and b = 3 then f(x) = 2x + 3
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The coordinates of the midpoint of $\overline{gh}$ are $m\left(4,\ 3\right)$ and the coordinates of one endpoint are $g\left(5,-6\right)$ . the coordinates of the other endpoint are ( , ).
The coordinates of the midpoints of GH are M (4,3) and the coordinates of one endpoints are G (5,-6) the coordinates of the other endpoints are
The co - ordinates of another end point is
(x,y) = (3, 12)
mid point formula:-
Let [tex](x_{1}, y_{1}) and (x_{2}, y_{2})[/tex] be any two end points
Mid point of two given points are
[tex](\frac{x_{1}+ x_{2}}{2}, \frac{y_{1}+ y_{2}}{2} )[/tex]
let (x,y ) be the another end point
given one end point is (5,-6)
now by using mid-point formula , we get
[tex](\frac{x+5}{2} ,\frac{y-6}{2})[/tex] this is equating to given mid-point is M(4,3)
now [tex](\frac{x+5}{2}, \frac{y-6}{2}) = (4,3)[/tex]
simplify , we get
[tex]\frac{x+5}{2} = 4 and \frac{y-6}{2} = 3[/tex]
cross multiplication and simplify
x+5 = 8 and y-6 = 6
so x = 3 and y = 12
Hence the another point is (x,y) = (3,12)
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What is the value of y in the solution to the system of equations?
1/3x + 1/4y =1
2X - 3y = -30
A. -8
B. -3
C. 3
D. 8
Answer:
D. 8
Step-by-step explanation:
Given system of equations:
[tex]\begin{cases}\dfrac{1}{3}x+\dfrac{1}{4}y=1\\\\2x-4y=-30\end{cases}[/tex]
Multiply the first equation by -6:
[tex]\implies -6 \cdot \dfrac{1}{3}x+-6 \cdot \dfrac{1}{4}y=-6 \cdot 1[/tex]
[tex]\implies -2x-\dfrac{3}{2}y=-6[/tex]
Add this to the second equation to eliminate x:
[tex]\begin{array}{rrcccl}&2x &- &3y& = &-30\\\phantom{\dfrac12}+ &(-2x& - &\frac{3}{2}y &= &\;\;-6)\\\cline{2-6} \phantom{\dfrac12}&0&-&\frac{9}{2}y&=&-36\\ \cline{2-6}\end{array}[/tex]
Solve the equation for y:
[tex]\implies -\dfrac{9}{2}y=-36[/tex]
[tex]\implies \dfrac{9}{2}y=36[/tex]
[tex]\implies 9y=72[/tex]
[tex]\implies y=\dfrac{72}{9}[/tex]
[tex]\implies y=8[/tex]
Given that sin 2π/3= cos y, first express 2π/3 as a sum of π/2 and angle and then apply a trigonometric identity to determine the measure of angle y.
Answer:
[tex]y=\frac{\pi}{6}[/tex]
Step-by-step explanation:
Given that:
[tex]\sin(\frac{2\pi}{3})=\cos y[/tex]
Substitute the value [tex]\frac{2\pi}{3}=\frac{\pi}{2}+\frac{\pi}{6}[/tex].
[tex]\sin(\frac{\pi}{2}+\frac{\pi}{6})=\cos(y)[/tex]
(Using the formula: [tex]\sin(\alpha+\beta)=\sin\alpha\cos\beta+\cos\alpha\sin\beta[/tex])
[tex]\sin\frac{\pi}{2}\cos\frac{\pi}{6}+\cos\frac{\pi}{2}\sin\frac{\pi}{6}=\cos y[/tex]
Using [tex]\sin\frac{\pi}{2}=1, \cos\frac{\pi}{2}=0[/tex], we obtain:
[tex]1\times\cos\frac{\pi}{6}+0\times \sin\frac{\pi}{6}=\cos y[/tex]
This is equivalent to:
[tex]\cos\frac{\pi}{6}=\cos y[/tex]
Applying cos inverse on both sides, we get:
[tex]y=\frac{\pi}{6}[/tex]
Nolan is blocking off several rooms in a hotel for guests coming to his wedding. The hotel can reserve small rooms that can hold 3 people, and large rooms that can hold 5 people. Nolan booked a total of 25 rooms which can accommodate 99 guests altogether. Determine the number of small rooms reserved and the number of large rooms reserved.
The number of small rooms reserved is 13 and the number of large rooms reserved is 12.
Given, Nolan is blocking off rooms for the guests. We will solve the problem using the linear equation. The number of small rooms is x and number of large rooms is y.
There are total of 25 rooms, which can be written as,
x+y=25 ------(1)
Small room can accommodate 3 people and large room 5 people, which can be written as follows,
3x+5y=99 --------(2)
Multiplying the equation 1 by 3, we get
3x+3y=75
Substracting equation 1 and 2, we get
3x+5y=99
3x+3y=75
- - -
---------------
0x+2y=24
2y=24
y=12
x+12=25
x=25-12
x=13
Therefore, the number of small rooms is 13 and large rooms is 12.
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Express the following ratio as a unit rate. Round to the nearest tenth, if necessary. 5 inches of rain in 24 hours
0.21 inches of rain for one hour for ratio of 5 inches of rain in 24 hours
What is Division?A division is a process of splitting a specific amount into equal parts.
Given,
5 inches of rain in 24 hours
We need to find the unit rate.
For this we need to use the division.
Divide five by twenty four
5/24
Zero point two zero eight
0.208
Zero point two one
0.21
Hence 0.21 inches of rain for one hour for ratio of 5 inches of rain in 24 hours
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