The procedure is correct is 1 + tan²(theta) = sec²(theta)
What is Fraction?
Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.
And
cos²(theta) = 1 - sin²(theta)
Are both valid identities
Keisha and the David.
As per the question Kisha and the David found the same value of the cosine theta as given by the Sine theta = Negative Start Fraction 8 Over 17 End Fraction. The Keisha solution and the Davis solution for the solution were tan-squared (theta) + 1 = sec-squared (theta).
Thus the answer is both procedures are correct.
As they both wanted to find the solutions to the numerical problems they made two different methods.
Such as the Sine theta = Negative Start Fraction and the tan-squared (theta) + 1 = sec-squared (theta).
Hence both options are the same and true.
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A recipe for a sports drink calls for 5/8 cup of powder for every 2 quarts of water. If Dionne uses 3 quarts of water, how many cups of powder are needed?
Answer: i think 15/8 but, im not sure
Step-by-step explanation:
An area code has three digits. How many different area codes are possible
Answer:
1000
Step-by-step explanation:
If any of the digits 0-9 can be used then there are 10^3 possible codes.
10^3 = 1000
A man is in a boat 2 miles from the nearest point on the coast. He is to go to point Q, located 3 miles down the coast and 1 mile inland (see figure). He can row at a rate of 1 mile per hour and walk at 3 miles per hour. Toward what point on the coast should he row in order to reach point Q in the least time? (Round your answer to two decimal places.) 0.84 mile(s) down the coast
Least time required to reach the point Q as per the distance and the speed rate is equal to 2 hours.
As given in the question,
Nearest point on the coast is 2 miles far away
rate of the row = 1mile per hour
Walk at the rate of 3 miles per hour
Let 'x' hours be the least time to reach point Q.
Time = distance / speed
Time taken to reach the point Q = [√ 1 + ( 3 - x)² ]/ 3
Time taken to reach the coast = (√ 4 + x² ) / 1
Total time taken 't' = (√ 4 + x² ) / 1 + [√ 1 + ( 3 - x)² ]/ 3
To find least time dt/dx = 0
t = (√ 4 + x² ) / 1 + [√ 1 + ( 3 - x)² ]/ 3
⇒dt/dx = [ x / √ 4 + x² ] + ( 3 - x) / √( 10 -6x + x² )
⇒x / √ 4 + x² = ( x - 3) / √( 10 -6x + x² )
Squaring both the side we get,
x² / (4 + x²) = ( x - 3)² / ( 10 -6x + x² )
⇒3x² -24x +36 =0
⇒ x² -8x + 12 = 0
⇒ x = 2 or 6 hours
Therefore , the least time taken to reach the point Q is equal to 2 hours.
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A researcher needs to assign 10 subjects, numbered 0 to
9, to one of two treatment groups: A and B. Use the table
of random digits, starting with the first row and first
column, to carry out the random assignment.
Table of Random Digits
1 07581 34728 65182 58648 53252 83952
2 23290 98227 30144 83191 12167 90414
3 79486 99776 71793 95330 58256 71156
4 46354 09077 98202 03946 07455 39303
5 00472 20787 54571 73719 04368 41032
Select the correct random assignment using the table.
A: 0, 7, 5, 8, 1
A: 0, 2, 4, 6, 8
B: 3, 4, 7, 2, 8
B: 1, 3, 5, 7, 9
B: 2, 9, 1, 7, 4
OA: 0, 3, 6, 5, 8
A: 0, 7, 5, 8, 1
B: 3, 4, 2, 6, 9
In response to the question, we may say that As a result, the right answer expression is OA: 0, 3, 6, 5, 8, corresponding to the participants assigned to therapy A.
what is expression ?An expression in mathematics is a collection of representations, numbers, and conglomerates that mimic a statistical correlation or regularity. A real number, a mutable, or a mix of the two can be used as an expression. Mathematical operators include addition, subtraction, fast spread, division, and exponentiation. Expressions are widely used in arithmetic, mathematics, and shape. They are employed in the depiction of mathematical formulas, the solving of equations, and the simplification of mathematical relationships.
To carry out the random assignment, we may utilise the following table of random digits:
Allocate the first ten topics to the table's rows, beginning with 0 and ending with 9.
Read the numerals from left to right, top to bottom, until 5 participants have been allocated to treatment A and 5 subjects have been assigned to treatment B.
We can get the following random assignment using this method:
A: 0, 3, 6, 5, 8 \sB: 1, 7, 4, 2, 9
As a result, the right answer is OA: 0, 3, 6, 5, 8, corresponding to the participants assigned to therapy A.
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Answer:
A: 0, 7, 5, 8, 1 B: 3, 4, 2, 6, 9
Step-by-step explanation:
THE ANSWER IS D
The retail cost of a computer is 37% more than its wholesale cost?which statement is true?1. THe retail cost of the computer is 132% more than the wholesale price.2. THe wholesale cost of the computer is 68% if the retail price.3. THe retail cost of the computer is 132% of the wholesale price.4. the retail cost of the computer is 37% of the wholesale price.
when retail cost of the computer is 37% of the wholesale price then Retail price is 1.37times wholesale price
Retailers who acquire products in bulk are subject to wholesale pricing.
Selling products at a greater price than what it costs to produce them allows businesses to turn a profit.
Retail pricing is what merchants decide to charge customers as their ultimate selling price.
Consumers are the primary focus of retail pricing.
According to the question,
The retail cost of a computer is 37% more than its wholesale cost
Let Retail cost be "x" and wholesale cost be "y"
So , x = y + 0.37y
=> x = 1.37y
Therefore , The retail price is 1.37times the wholesale price
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Give expressions for the following:-
1) x is multiplied by -10 and then 5 is added to the result
2) 5 is multiplied by p and the result is subtracted from 26
3)y is multiplied by -5 and the result is added to 6
Answer:
1) -10x + 5
2) 5p - 26
3) -5y + 6
choose the answer that best describes the statement. probality can be used to determine the likelihood of specific .
The statements best describe probability as the relative likelihood that an event will occur. It is a number between 0 and 1 inclusive.
Probability
A mathematical tool used to examine unpredictability is probability. It discusses the likelihood that an event will occur. For instance, you might not get two heads and two tails if you flip a fair coin four times. But if you flip the same coin 4,000 times, you'll get results that are almost evenly split between heads and tails. The theoretically predicted chance of heads in any given toss is 12, or.5. There is a predictable pattern of results when there are numerous repetitions, even though the results of a few repetitions are unknown. One of the authors tossed a coin 2,000 times after reading about the English statistician Karl Pearson, who threw a coin 24,000 times and got 12,012 heads. The outcome was 996 heads. The expected chance of 5 is quite near to being reached by the fraction of 9962,000, which is equivalent to 498.
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Lucy wants to buy a small car. She speaks to her bank and they offer her a loan of £5000 over 5 years at a simple interest rate of 5%. How much simple interest will Lucy have to pay back in total?
Simple interest at a rate of 5% per year for five years on a principle of $5,000 has resulted in a total accrual of $6,250.00, which includes both the principal and interest.
What is simple interest?To calculate simple interest, multiply the daily interest rate by the principle and the number of days between payments. Consumers that make on-time or early monthly loan payments benefit from simple interest. Most loans with simple interest rates are auto loans and short-term personal loans.
A = $6,250.00
I = A - P = $1,250.00
Formula: A = P(1 + rt)
First, convert R percent to r decimal, which is equal to 5%/100 or 0.05 per year.
Fixing our equation
A = 5000(1 + (0.05 × 5)) = 6250 \sA = $6,250.00
Simple interest at a rate of 5% per year for five years on a principle of $5,000 has resulted in a total accrual of $6,250.00, which includes both the principal and interest.
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PLEASE ANSWER QUICK!!
Consider the functions and f(x)=|x|-2 and g(x)=2f(x).
a. Complete the table.
b. Describe the graph of f. How does each point on the graph of f map to the corresponding point on g?
The function f(x) is an absolute function and the function g(x) will be twice the function f(x). The table is completed below.
What is a function?A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.
The functions are given below.
f(x) = |x| - 2 and g(x) = 2 f(x)
The function g(x) is rewritten as,
g(x) = 2 (|x| - 2)
g(x) = 2|x| - 4
The function f(x) is an absolute function and the function g(x) will be twice the function f(x).
x f(x) = |x| - 2 g(x) = 2f(x)
-2 0 0
-1 -1 -2
0 -2 -4
1 -1 -2
2 0 0
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Status
Review
A certain state uses the following progressive
tax rate for calculating individual income tax:
Income
Range ($)
0 - 10,000
10,001 - 50,000
50,001 - 100,000
Progressive
Tax Rate
3%
5%
5.5%
Calculate the state income tax owed on a $50,000
per year salary.
tax = $[?]
Round your answer to the nearest whole dollar amount.
Enter
h
Answer:
final answer would be $6,550
Step-by-step explanation:
To calculate the state income tax owed on a $50,000 per year salary, we can use the progressive tax rate provided in the question. We can divide the salary into three ranges, corresponding to the three tax rates:
Income Range: $0 - $10,000
Progressive Tax Rate: 3%
Tax Owed: $0 - $10,000 * 3% = $0 - $300
Income Range: $10,001 - $50,000
Progressive Tax Rate: 5%
Tax Owed: $10,001 - $50,000 * 5% = $500 - $2,500
Income Range: $50,001 - $100,000
Progressive Tax Rate: 5.5%
Tax Owed: $50,001 - $100,000 * 5.5% = $2,750 - $5,500
Thus, the total state income tax owed on a $50,000 per year salary would be $300 + $2,500 + $2,750 = $6,550. This amount should be rounded to the nearest whole dollar amount, so the final answer would be $6,550.
to specify that x1 must be at most 75% of the blend of x1 , x2 , and x3 , we must have a constraint of the form
The linear constraint form of the variables is X1 =< 0.75(X1 + X2 + X3)
The term linear refers the algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept.
Here we have given that x1 must be at most 75% of the blend of x1 , x2 , and x3 ,
Abd here we must have to find the linear constraint of the form of the variables.
While we looking into the given question we have identified the three are three variables are given they are x1, x2 and x3.
And we have also given that x1 must be greater than 75% when we convert this into decimal then we get the value 0.75.
Here the term of blend refers the sum of the terms,
Then the linear constraint form of the variables is written as,
=> X1 =< 0.75 (X1 + X2 + X3)
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In AUVW, m/U = (3x - 10)°, m/V = (6x + 5)°, and m/W = (4x - 10)°. What is the value of x?
Answer:
x = 15
Step-by-step explanation:
You have ∆UVW with angles U=(3x-10)°, V=(6x+5)°, and W=(4x-10)°, and you want to know the value of x.
Angle sum theoremThe angle sum theorem tells you the sum of angles in a triangle is 180°.
U +V +W = 180°
(3x -10)° +(6x +5)° +(4x -10)° = 180°
13x -15 = 180 . . . . . . . divide by °, collect terms
13x = 195 . . . . . . . add 15
x = 15 . . . . . . . divide by 13
The value of x is 15.
Calculate two-thirds of three-quaters of one half
Answer:
0.25
Step-by-step explanation:
Step 1: Convert all fractions to decimals
Two-thirds = 0.6666
Three-quarters = 0.75
One-half = 0.5
Step 2: Multiply all fractions
0.6666 * 0.75 * 0.5 = 0.25
Step 3: The answer is 0.25
Answer:
[tex]\dfrac{1}{4}[/tex]
Step-by-step explanation:
Three-quarters of one half:
[tex]\implies \dfrac{3}{4} \times \dfrac{1}{2}=\dfrac{3 \times 1}{4 \times 2}=\dfrac{3}{8}[/tex]
Two-thirds of "Three-quarters of one half":
[tex]\implies \dfrac{2}{3} \times \dfrac{3}{8}=\dfrac{2 \times 3}{3 \times 8}=\dfrac{6}{24}=\dfrac{6 \div 6}{24 \div 6}=\dfrac{1}{4}[/tex]
Which quantity is multiplied by pi in the formula for the area of a circle?
The quantity that is multiplied by pi in the formula for the area of a circle is the square of the radius
How to determine the multiplied quantity?From the question, we have the following parameters that can be used in our computation:
Area of a circle
The formula for the area of a circle is represented as
A = πr²
Express the formula as a product
So, we have the following representation
A = π * r²
In the above formula, we can see that the square of r is multiplied by pi
Hence, the required quantity is the square of the radius of the circle
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Check the binomial distribution to see whether it can be approximated by the normal distribution. Round p and q to 1 decimal place, as needed. n = 95 P = 0.96 9 -0.04 np - and ng Is a normal approximation appropriate ? Yes No
As per the binomial distribution, the value of the normal approximation is 0.6573
The term binomial distribution refers the discrete probability distribution that gives only two possible results in an experiment, either success or failure.
Here we have given that n = 95 P = 0.96 and q = 0.04
Now, here we have to check the binomial distribution to see whether it can be approximated by the normal distribution.
While we looking into the given question we know that the value of n = 95 P = 0.96.
Then as per the binomial distribution formula, the normal distribution is calculated as,
=> P(X=1) = 95C4 * (0.96)⁴ * (1-0.96)⁹⁵⁻⁴
When we simplify this one then we get the value as 0.6573
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in the morning there were t people at the beach. later at noon, 2/7 of the people left the beach and there were 30 people left on the beach. find t
Answer:
42
Step-by-step explanation:
If 2/7 left that means that 5/7 are still there.
5/7x = 30 Multiple both sides by 7/5
x = [tex]\frac{30}{1}[/tex] x [tex]\frac{7}{5}[/tex]
x = 42
Solve each equation. Round to the nearest ten-thousandth.
17(0.3x+5)
Answer:
first option
Step-by-step explanation:
using the property of logarithms
ln [tex]x^{n}[/tex] = nlnx ( ln is the natural logarithm )
given
[tex]17^{(0.3x+5)}[/tex] = 12
take the ln of both sides
ln [tex]17^{(0.3x+5)}[/tex] = ln 12 , then
(0.3x + 5) ln 17 = ln 12 ( divide both sides by ln 17 )
0.3x + 5 = [tex]\frac{ln12}{ln17}[/tex] ≈ 0.877063 ( subtract 5 from both sides )
0.3x ≈ - 4.12293 ( divide both sides by 0.3 )
x = [tex]\frac{-4.12293}{0.3}[/tex] ≈ - 13.7431 ( to the nearest ten thousandth )
Is there anyone that can help me with a finance question?
Answer:
Yes, there are many people who can help you with a finance question. Some of the people who can help you include: financial advisors, accountants, financial planners, and financial analysts. Additionally, there are many online resources available such as personal finance forums, websites, and blogs.
Step-by-step explanation:
A racetrack charges $85 for each seat in the lower section, $60 for each seat in the upper sections, and $35 for field tickets. There are three times the amount of seats in the upper section as compared to the lower section. The revenue from selling all 22,800 seats is $948,000. How many seats are in the upper section of the racetrack?
Using a system of equations, the number of seats in the upper section of the racetrack is 3,600.
What is a system of equations?A system of equations, also called simultaneous equations, is two or more equations solved concurrently.
We can use any of the following methods to solve simultaneous equations:
GraphicalSubstitutionEliminationMatrix.In this situation, after forming the equations, we can use substitution and elimination methods to solve them.
Racetrack charge per lower seat = $85
Racetrack charge per upper seat = $60
Racetrack charge per field ticket = $35
Let lower seats = x
Let upper seats = 3x
Let field tickets = y
4x + y = 22,800 ... Equation 1
y = 22,800 - 4x ...Equation 3
85x + 60(3x) + 35y = 948,000
85x + 180x + 35y = 948,000 ... Equation 2
Substitute Equation 3 in Equation 2 to eliminate y:
85x + 180x + 35(22,800 - 4x) = 948,000
85x + 180x + 798,000 - 140x = 948,000
125x = 948,000 - 798,000
125x = 150,000
x = 1,200
Determining the number of seats:
Seats in the Lower section = 1,200
Seats in the Upper section = 3,600 (1,200 x 3)
Field tickets, y = 22,800 - 4x
y = 22,800 - 4(1,200)
= 18,000
Check:
85x + 180x + 35y = 948,000
85(1,200) + 180(1,200) + 35(18,000) = 948,000
102,000 + 216,000 + 630,000 = 948,000
948,000 = 948,000
Thus, based on simultaneous equations, there are 3,600 seats in the upper section of the racetrack.
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The linear regression equation for the data set is...
Answer: C
Step-by-step explanation: Because
Two different meal combinations at a chicken restaurant have the same number of total calories.
- The first meal has 8 chicken nuggets and a large order of fries.
- The second meal has 12 chicken nuggets and a small order of fries.
- The larger order of fries contains 288.5 calories.
- The small order of fries contains 193.5 calories.
Which equation and solution can be used to determine n, the number of calories in each chicken nugget?
A 12 n-288.5=8 n-193.5 ; n=24.1
B 8 n+193.5=12 n+288.5 ; n=23.75
C 193.5+12 n=288.5+8 n ; n=24.1
D 8 n+288.5=12 n+193.5 ; n=23.75
The equation which can be used to determine n, the number of calories in each chicken nugget would be 193.5+12 n=288.5+8n
And n = 24.1
Option (C) is correct.
What is a linear equation?
A linear equation is an equation that describes a straight line. Linear equations have the form y = mx + b, where x and y are variables and m and b are constants. The constant m is the slope of the line, and the constant b is the y-intercept, which is the point where the line crosses the y-axis.
To derive this equation, we can start with the fact that the two meals have the same number of total calories. This means that the number of calories in the first meal is equal to the number of calories in the second meal. We can represent this relationship with the equation:
8 nuggets * calories/nugget + 193.5 calories = 12 nuggets * calories/nugget + 288.5 calories
We can then rearrange the terms on the left and right sides of the equation to get the equation in the form given in option C:
193.5 + 12 n = 288.5 + 8 n
Finally, we can solve this equation for n by subtracting 8n from both sides and then dividing both sides by 4:
n = (193.5 - 288.5) / 4 = (-95) / 4 = -23.75
Therefore, the number of calories in each chicken nugget is 24.1 calories.
Hence, option (C) is correct.
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A sinusoidal function whose period is π2
, maximum value is 10, and minimum value is −4 has a y-intercept of 10.
What is the equation of the function described?
Responses
f(x)=7cos(4x)+3
f ( x ) = 7 cos ( 4 x ) + 3
f(x)=7sin(4x)+3
f ( x ) = 7 sin ( 4 x ) + 3
f(x)=7cos(4πx)+3
f ( x ) = 7 cos ( 4 π x ) + 3
f(x)=7sin(4πx)+3
The equation of the function described as; y = 7 sin ( 4x + π/2 ) + 3
The general equation of the sine curve can be written as;
y = a sin ( nx + α ) + b
where : a is the amplitude, n = 2π/period, b = shift in the direction of y
α°= shift in the direction of x
We are Given period = π/2 the maximum value is 10, the minimum value is −4 and y-intercept of 10.
Thus,
a = (maximum - minimum)/2 = (10 - -4)/2
a = 7
n = 2π/period = 2π/(π/2)
n = 4
b = maximum - a = 10 - 7
b= 3
To find α as y-intercept = 10
y = 10 at x = 0
Substitute in the general function;
y = a sin ( nx + α ) + b
10 = 7 sin ( 4*0 + α ) + 3
Thus, we have;
sin α = 1
α = π/2
So, the equation of the function described is;
y = 7 sin ( 4x + π/2 ) + 3
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look at attached photo
The correct answer is A) y = 9000x + 65,000.
Find a linear equation that models the value of the house after x years?The correct answer is A) y = 9000x + 65,000.
This is an equation in slope-intercept form, where "y" is equal to the value of the house after x years, "9000x" is the slope (or rate of change) of the equation, and 65,000 is the y-intercept (or the initial value of the house). The equation can be derived from the given information.The initial value of the house is 65,000, so the y-intercept must be 65,000. To find the slope, we can use the formula "rise/run", or change in y/change in x.The house has increased in value by 54,000 ($119,000 - $65,000) over 6 years (change in x), so the slope must be 9000 (54,000/6).
The equation y = 9000x + 65,000
models the value of the house after x years, where y is the value of the house,
9000x is the slope of the equation,
and 65,000 is the y-intercept.
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3. What type of angle is angle A?
obtuse
acute
right
straight
The angle A is an obtuse angle of the regular polygon.
What is an angle?
An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.
The interior angle of a polygon is [(n-2)180°]/n.
Where n is the number of sides of the polygon.
The number of sides of the polygon is 8.
The measure of the interior of the polygon is [(8-2)180°]/8
= 135°
The obtuse angle is an angle that more than 90°.
Therefore angle is an obtuse angle.
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whats the domain,range, and y-intercept and tell me if its exponential or linear.
k(x)=50(1.3)^x
0.3% is the percentage rate of increase in exponential function.
What exactly makes a function exponential?
A mathematical function using the following formula is an exponential function: f (x) = an x. where an is a constant known as the function's base and x is a variable.
The transcendental number e, or roughly 2.71828, is the most often encountered exponential-function base.
We have,
y = 50( 1.3)ˣ
The equation represents exponential growth because the growth factor is greater than 1.
The general form equation is
y(x)= a(1-r)^x such that r is the growth percent.
1 + r = 1.3
r = 0.3 ⇒ 0.3%
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Find the vertex of the graph of f(x) = |0.25x − 0.75|. vertex ?
The vertex of the graph (3, 0)
What is Vertex of graph?
A vertex or node is the basic building block of a graph in discrete mathematics, and more precisely in graph theory. An undirected graph is made up of a set of vertices and a set of edges, whereas a directed graph is made up of a set of vertices and a set of arcs.
According to question
when f(x) = 0
that's the minimum point, the vertex, or the intersection of two lines, g(x) = 0.25x − 0.75 and h(x) = 0.75 - 0.25x
Therefore
find the intersection of Two line which are
⇒ y = x/4 - 3/4
⇒ 4y = x - 3 → First line
⇒ y = 3/4 - x/4
⇒ 4y = 3 - x → Second line
So x - 3 = 3 - x
2x = 6 ,
x = 3
And y = 0
hence the vertex of f(x) = (3, 0)
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A line is graphed on the coordinate grid to the right.
Which equation describes the line?
A.y=x/2+1/3
B.y = x/3+1/2
C.y=x/2+15 1/2
D.y=x/3+15 1/2
The equation of the line would be y = x/3 + 1/2.
Option (B) is correct.
What is the slope-intercept form of the line?
The slope-intercept equation is used to find the general equation of a straight line using its slope and the point where it intersects the y-axis. The slope intercept form equation is given as, y = mx + b.
As we can see in the graph the line cuts the y-axis at y = 1/2
so the y-intercept of the line would be c = 1/2.
And when x=4, y = 2
So we can prepare the equation as y = x/3 + 1/2.
Hence, the equation of the line would be y = x/3 + 1/2.
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The equation of the line would be y = x/3 + 1/2.
Option (B) is correct.
What is the slope-intercept form of the line?
The slope-intercept equation is used to find the general equation of a straight line using its slope and the point where it intersects the y-axis. The slope intercept form equation is given as, y = mx + b.
As we can see in the graph the line cuts the y-axis at y = 1/2
so the y-intercept of the line would be c = 1/2.
And when x=4, y = 2
So we can prepare the equation as y = x/3 + 1/2.
Hence, the equation of the line would be y = x/3 + 1/2.
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A punter kicks a football. Its height h, in yard, t seconds after the kick is given by the equation h(t)=-4.9t^2+18.24t+0.8. The height of an approaching blocker's hand is modeled by the equation h(t)=-1.43t+4.26, using the same time. Can the blocker knock down the punt (do they intersect)? If so, at what point will that happen (the point of intersection)?
Part 1
[tex]-4.9t^2 +18.24t+0.8=-1.43t+4.26\\\\-4.9t^2 +19.67t-3.46=0\\\\\Delta =(19.67)^2 -4(-4.9)(-3.46)=319.0929 > 0[/tex]
Therefore, the blocker can knock down the punt.
Part 2
Using the quadratic formula,
[tex]t=\frac{-19.67 \pm \sqrt{319.0929}}{2(-4.9)}\\\\t \approx 0.18437, 3.82992[/tex]
Considering the graphs, it is clear to take the smaller solution. Thus, the point of intersection is [tex](0.18437, h(0.18437))=\boxed{(0.18437, 3.99635)}[/tex].
The length of a rectangular poster is 8 more inches than three times its width. The area of the poster is 256 square inches. Solve for the dimensions (length and width) of the poster
The dimensions are
inches ___ by ____ inches.
When the area of the poster is 256 square inches, the measurements are 32 inch and 8 inch.
What is area?The quantity area indicates the extent of a region on a planar or curved surface. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas area of a plane region or plane area refers to the area of a form or planar lamina. The total space occupied by a flat (2-D) surface or the form of an item is defined as its area. The area is the region defined by an object's form. The area of a form is the space covered by a figure or any two-dimensional geometric shape in a plane.
Here,
let length be l and width be w.
l=3w+8
l*w=256
(3w+8)*w=256
3w²+8w=256
3w²+32w-24w-256=0
3w(w-8)+32(w-8)=0
(3w+32)(w-8)=0
w=-32/3, 8
w=8 inch
l=3*8+8
l=32 inch
The dimensions for the poster are 32 inch and 8 inch when area of the poster is 256 square inches.
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Height (in inches) Mean Minimum Q1 Median Q3 Std Dev 4.21 Maximum 79 68.2 67 , 71 , Which conclusion about the distribution is most plausible? (A) 50% of the students are taller than 68.2 inches. (B) 75% of the students are taller than 71 inches. (C) There are more students between 67 inches and 79 inches than are between 62 inches and 67 inches (D) Less than 25% of the students have heights between 68.2 and 71 inches. (E) The height that occurs most frequently is 67 inches. Height (in inches) Q3 Mean 68. 2 Std Dev .21 Minimum 62 4 Q1 63 Median 67 Maximum 79 Which conclusion about the distribution is most plausible? (A) 50% of the students are taller than 68.2 inches. (B) 75% of the students are taller than 71 inches. (C) There are more students between 67 inches and 79 inches than are between 62 inches and 67 inches. (D) Less than 25% of the students have heights between 68.2 and 71 inches. (E) The height that occurs most frequently is 67 inches.
Standard deviation will be √3.3516 .
To calculate the standard deviation for the given data first we have to calculate the total number of students , mid value , fiXi , fiXi².
After that , we have to calculate the Xbar by using
Xbar = ∑fiXi / N
for which we need the value of fi , Xi and N
N = 100
fiXi = 6478
we have calculated the values from the given data ,
Therefore ,
Xbar = 6478 / 100
= 64.78
Var(X) = αx² - ∑fiXi² / N - (Xbar²)
= 419980 / 100 - (64.78)²
= 4199.80 -4196.4484
=3.3516
Thus,
standard deviation ax = √var(X)
= √3.3516
Therefore , the standard deviation will be √3.3516
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