The height of the tail post is 13.74 m.
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
Given that, after travelling 11.45 metres from her school, she lays a flat mirror on the ground in the center, with an x drawn on it. When she can clearly see the top of the goalpost depicted in the x.
She moves 1.25 metres to the other side of the mirror. Her spouse calculates that there are 1.15 metres between her eyes and the earth.
Suppose the height of the tail post is x,
The geometric relation is,
1.5/1.25 = x/11.45
Apply cross multiplication
1.5×11.45=1.25x
17.175=1.25x
Divide both sides by 1.25
x=13.74
Hence, if she moves 1.25 metres to the other side of the mirror. Her spouse calculates that there are 1.25 metres between her eyes and the earth. The height of the tail post is 13.74 m.
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3(2x+4) = 6x + 8
3(2x + 4) = 6x + 8
6x + 12 = 6x + 8
-6x -6x
12 = 8
no solution??
Answer: no solution
Step-by-step explanation:
Correct, there is no solution as any values of x and y will make the equation false
A railroad's track can be determined using the following graph.
Linear function increasing from the left in quadrant 3 passing through the point negative 8 comma 0 and 0 comma 5.
Several different roadways are in the same region as the railroad.
Part A: A highway's path can be found using the equation 2x − 3y = 21. Use the graphs of the functions to determine the number of intersections there will be between the railroad and the highway, and explain completely. (5 points)
Part B: A turnpike's route is determined by the equation y equals one third times x squared period Prove algebraically how many intersections there will be between the railroad and the turnpike, showing all necessary work. (5 points)
a) The number of intersections between the railroad and the highway is of: One.
b) The number of intersections between the railroad and the turnpike is of: Two.
How to define the linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which the parameters are listed as follows:
m is the slope, representing by how much y changes when x is increased by one.b is the intercept, representing the value of y when x = 0.The points for the railroad are given as follows:
(-8, 0) and (0,5).
When x = 0, y = 5, hence the intercept is of:
b = 5.
When x increases by 8, y increases by 5, hence the slope is of:
m = 5/8.
Thus the equation for the railroad is of:
y = 5/8x + 5.
Then the number of intersections with the highway is of one, as they are linear functions with different slopes.
With the turnpike, the intersection is given as follows:
5/8x + 5 = x²/3
x² -1.875x - 15 = 0.
The discriminant is of:
(-1.875)² - 4(1)(-15) = 63.5.
Which is positive, hence they have two intersections.
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From Book 5
As a man in a distant field, no hearthfires near,
will hide a fresh brand in his bed of embers
to keep a spark alive for the next day;
so in the leaves Odysseus hid himself.
What is being compared to what?
The way Odysseus hides himself in the leaves to sleep is compared to the way a burning coal is buried deep in the embers to preserve a spark for the next day.
Odyssey, epic poem in 24 books traditionally attributed to the ancient Greek poet Homer. The poem is the story of Odysseus, king of Ithaca, who wanders for 10 years (although the action of the poem covers only the final six weeks) trying to get home after the Trojan War. On his return, he is recognized only by his faithful dog and a nurse. With the help of his son, Telemachus, Odysseus destroys the insistent suitors of his faithful wife, Penelope, and several of her maids who had fraternized with the suitors and reestablishes himself in his kingdom.
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Find the 56th term of the following arithmetic sequence 7,10,13,16
The 56th term of the following arithmetic sequence 7,10,13,16 is 172.
What is the arithmetic sequence?
A series of numbers called an arithmetic progression or arithmetic sequence has a constant difference between the terms.
Here, we have
Given
Arithmetic sequence 7,10,13,16.
We have to find the 56th term.
The common difference between terms: 10 - 7 = 3
Using the arithmetic progression formula:
nth term = first term + (n-1)* common difference
56th term = 7 +(56-1) 3
56th term = 7 + 55×3
56th term = 7 + 165
56th term = 172
Hence, the 56th term of the following arithmetic sequence 7,10,13,16 is 172.
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a) If the gradient of a line, A, is 4, what is the gradient of the line
which is perpendicular to A?
a test consists of 10 true/false questions. if a student guesses on each question, what is the probability that thestudent will answer at least7questions correctly.
The probability that the student will answer at least7questions correctly then the probability is = [tex]\frac{120}{128}[/tex]
A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.
Given that,
A test consists of 10 true/false questions.
If a student guesses on each question
The probability that the student will answer at least7questions correctly.
The probability that the student answers each question correctly is 1/2, and
The probability that the student answers each question correctly is also 1/2
{Bernoalli trail}
Bernoalli trail for at least 7 times,
Probability P = [tex]C7_{10} (\frac{1}{2}) ^{7} (\frac{1}{2}) ^{7}[/tex]
Using the formula nCr = n!(n−r)!r!
= 10!(10−7)!7!
Subtract 7 from 10.
= 10!(3)!7!
Simplify 10!(3)!7!.
Rewrite 10! as (10⋅9⋅8⋅7!)
= (10⋅9⋅8⋅7! / (3)!7!)
Cancel the common factor of 7!.
Cancel the common factor.
= 10⋅9⋅8⋅7! / (3)!7!
Rewrite the expression.
= 10⋅9⋅8 / (3)!
Multiply 10 by 9.
= 90⋅8 / (3)!
Multiply 90 by 8.
= 720 / (3)!
Expand (3)! to 3⋅2⋅1.
= 720 / 3⋅2⋅1
Multiply 3 by 2.
= 720 / 6⋅1
= 720 / 6
Divide 720 by 6
= 120
So,
We can write,
P = [tex]\frac{120}{2^{7} }[/tex]
P = [tex]\frac{120}{128}[/tex]
Therefore,
The probability that the student will answer at least7questions correctly then the probability is = [tex]\frac{120}{128}[/tex]
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Suppose that a quiz consists of 20 true-false questions. A student hasn't studied for the exam and will just randomly guesses at all answers (with true and false equally likely). How would you find the probability that the student will get 8 or fewer answers correct?.
The required probability that the student will get 8 or fewer answers is 0.2475.
What is binomial distribution for probability?Binomial distribution is a typical probability dissemination that models the likelihood of getting one of two results under a given number of boundaries. It sums up the quantity of preliminaries whenever every preliminary has a similar possibility accomplishing one explicit result.
According to question:By using binomial distribution for calculating the probability of getting 8 or less than 8 correct answer in the quiz.
Formula ; ⁿCₓ × pˣ × qⁿ⁻ˣ
We have, n = 20 p = 0.5, q = 1 - p = 1 - 0.5 = 0.5
Then,
P(x=0)=20C0*0.5^0*0.5^20=1/1048576
P(x=1)=20C1*0.5^1*0.5^19=5/262144
P(x=2)=20C2*0.5^2*0.5^18=95/524288
P(x=3)=20C3*0.5^3*0.5^17=285/262144
P(x=4)=20C4*0.5^4*0.5^16=4.621*10^-3
P(x=5)=20C5*0.5^5*0.5^15=969/65536
P(x=6)=20C6*0.5^6*0.5^14=0.03696
P(x=7)=20C7*0.5^7*0.5^13=4845/65536
P(x=8)=20C8*0.5^8*0.5^12=0.1201
Then, p(x≤8) = P(x=0)+.......+P(x=8) = 0.2475
Thus, required probability of answers ia 0.2475.
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joy needs to mix a 20% alcohol solution with a 40% alcohol solution to create 200 millileters of a 20% solution. how many millileters of each solution must joy use?
In linear equation, X = 200 millileters of each solution must joy use .
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.
X is the amount of the 20% saline solution
Y is the amount of the 40% saline solution
X + Y = 200
0.2X + 0.4Y = 0.20 * 200 = 40
Solving the first equation for Y and multiplying
the second equation by 10 to clear away the decimals
Y = 200 - X
2x + 4y = 400
2x + 4(200 - x) = 400
2x + 800 - 4x = 400
0 = 400 - 2x - 800 + 4x
0 = 2x - 400
400 = 2x
x = 200
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What is the term to term rule for this sequence ? 625,125,25,5,1
The required expression for the term of the given sequence is aₙ = 625 × (1/5)ⁿ⁻¹.
How to know whether a given sequence is geometric?In order to check a geometric sequence, find the ratios of the consecutive terms of the given sequence. If they are equal, the given sequence is geometric.
The given sequence is as follows,
625, 125, 25, 5, 1
The first term is given as a₁ = 625
And, the ratio of the consecutive terms are,
125/625 = 1/5
25/125 = 1/5
Since the ratio of two consecutive terms are equal, the given sequence is a geometric sequence.
The nth term of a geometric sequence is given as aₙ = a₁rⁿ⁻¹.
Thus, the expression for the given sequence is aₙ = 625 × (1/5)ⁿ⁻¹.
Hence, the term for the given sequence can be written in general form as aₙ = 625 × (1/5)ⁿ⁻¹.
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HELP ME ASAP!!!!!!!!!!!!!!!!!!!
Answer:
Statement 2 is a lie
Step-by-step explanation:
Statement 1 = TRUE
[tex]13^{2} * 13^{x} = 13^{6} \\13^{2+x} =13^{6}\\2 + x = 6\\x = 6 - 2\\x = 4[/tex]
x = 4 is True
Statement 3 = TRUE
[tex]5^{y} * 5^{6} =5^{12} \\5^{y+6} = 5^{12} \\y+6 = 12\\y=12 -6\\y =6[/tex]
y = 6 is True
Statement 2 = LIE
[tex]m^{y} *m^{z} = m^{x} \\m^{6} *m^{z} = m^{4}\\m^{6+z} = m^{4}\\6 + z = 4\\z= 4-6\\z= -2[/tex]
z = -2 is Lie
Please check your answer cause this is my last question
The interest rate would be 13%.
What is the simple interest?
Simple Interest (S.I.) is the method of calculating the interest amount for a particular principal amount of money at some rate of interest. For example, when a person takes a loan of Rs. 5000, at a rate of 10 p.a. for two years, the person's interest for two years will be S.I. on the borrowed money.
To find the interest rate, we can use the formula for simple interest:
I = Prt
where I is the amount of interest earned, P is the principal (the initial amount of money deposited), r is the interest rate, and t is the time in years.
In this case, we know that I = $3,900, P = $10,000, and t = 3 years. We can use this information to solve for r:
I = Prt
$3,900 = $10,000r3
r = $3,900/($10,000*3)
r = 0.13 or 13%
Hence, the interest rate is 13%.
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Which of the following is a point on the line defined by the parametric equations below?
[x(t)=t+7
y(t) = 5-2t
○ (3,10)
○ (7,0)
O (8,3)
O (2,1)
The following are five different examples of parametric models: exponential distributions, poisson distributions, normal distributions, the Weibull distribution, and linear regressions.
What is an example of a parametric equation?Well, a parametric equation is an equation where the variables (usually x and y) are expressed in terms of a third parameter, usually expressed as t. For example: Consider the equation of a circle with radius r and center at (0,0) : x2+y2=r2 x 2 + y 2 = r 2 .parametric equation, a type of equation that employs an independent variable called a parameter (often denoted by t) and in which dependent variables are defined as continuous functions of the parameter and are not dependent on another existing variable. More than one parameter can be employed when necessary.If there are m free variables in the homogeneous equation, the solution set can be expressed as the span of m vectors: x = s1v1 + s2v2 + ··· + smvm. This is called a parametric equation or a parametric vector form of the solution.Types of Parametric test–
Two-sample t-test.Paired t-test.Analysis of variance (ANOVA)Pearson coefficient of correlation.To learn more about parametric refer to:
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In angle JKL, if angle L is thirteen more than angle k and angle j is seven more than six times angle k, find the measure of each angle
The measure of Angle JKL mJ = 159.4°, mK = 3.8°, and mL = 16.8°.
What is the measure if Angle JKL?A ray is rotated about its endpoint, or vertex, to create an angle. The rotational difference between a ray's starting and ending positions is what is measured by an angle's degree.
If x = mJ, y = mK, and z = mL, then
Angle L exceeds Angle K by thirteen, hence z = y + 13 is the result (1)
Since angle J exceeds angle K by a factor of 7, x = 7(6y) = 42y (2)
X + Y + Z = 180 because the triangle's angles add up to 180°.
In place of (1) and (2) (3).
42y + y + (y + 13) = 180
44y + 13 = 180
44y = 167
y = 3.8°
x = 42y = 159.4°
z = y + 13 = 16.8°
The answer is that mJ = 159.4°, mK = 3.8°, and mL = 16.8°.
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Four boards were given to Sam to build a triangular picture frame for a large painting.
32 feet
21 feet
8 feet
12 feet
Which of these boards could be used for his project?
The sum of any two sides of a triangle must be greater than the other thus 32 feet,21 feet, and 12 feet will be the correct so options (A),(B), and (D) are correct.
What is a triangle?A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.
As per the given,
To be a triangle of three side polygon the sum of any two sides must be greater than the third side.
If we take 32 feet,21 feet, and 8 feet.
21 + 8 = 29 < 32 so it will not form any triangle.
Thus, 8 cannot be taken. now let's take 32,21 and 12 here 21 + 12 = 33 > 32 so it will form a triangle this will be used for the project.
Hence "The right answer will be 32 feet, 21 feet, and 12 feet because the sum of any two sides of a triangle must be bigger than the other".
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Rewrite 177+ 563 = 740 using the Commutative Law of Addition.
O(177 +563) = 740
563 +177 740
740 563 = 177
563 = 177 + 740
Answer: The Commutative Law of Addition states that the order in which numbers are added does not affect the result. This means that for any two numbers a and b, we have a + b = b + a.
We can use the Commutative Law of Addition to rewrite the equation 177 + 563 = 740 as follows:
177 + 563 = 740
563 + 177 = 740
Both of these equations are equivalent to the original equation, because they represent the same mathematical statement.
Note that in the first equation, we simply reordered the terms of the original equation. In the second equation, we added the numbers in a different order, but the result is still the same.
The other equations you provided are not equivalent to the original equation and do not use the Commutative Law of Addition.
Which table of values represents the equation y = 7x - 3?
The table of values which represent the equation y = 7x - 3 is: table D.
What is an ordered pair?In Mathematics, an ordered pair can be defined as a pair of two (2) elements or points that are commonly written in a fixed order within parentheses as (x, y), which represents the x-coordinate or x-axis (abscissa) and the y-coordinate or y-axis (ordinate) on the coordinate plane of any graph.
In order to determine the true ordered pair that is a solution for the given linear equation, we would have to test the ordered pair contained in each table by substituting it into the linear equation as follows;
For ordered pair (-2, -1), we have:
y = 7x - 3
-1 = 7(-2) - 3
-1 = -14 - 3
-1 = -17 (False).
For ordered pair (-2, -19), we have:
y = 7x - 3
-19 = 7(-2) - 3
-19 = -14 - 3
-19 = -17 (False).
For ordered pair (-2, -15), we have:
y = 7x - 3
-15 = 7(-2) - 3
-15 = -14 - 3
-15 = -17 (False).
For ordered pair (-2, -17), we have:
y = 7x - 3
-17 = 7(-2) - 3
-17 = -14 - 3
-17 = -17 (True).
In this context, we can logically deduce that all of the coordinates in table D represents the equation y = 7x - 3.
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The residents of a city voted on whether to raise property taxes. The ratio of yes votes to no votes was 5 to 3. If there were 4296 total votes, how many no votes were there?
Answer: 1611 no votes
Explanation:
4296/8=537
537*3=1611
Write the equation for the line in standard form passing through (5, 7) and (3, 1).
standard form for a linear equation means
• all coefficients must be integers, no fractions
• only the constant on the right-hand-side
• all variables on the left-hand-side, sorted
• "x" must not have a negative coefficient
[tex](\stackrel{x_1}{5}~,~\stackrel{y_1}{7})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{1}-\stackrel{y1}{7}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{5}}} \implies \cfrac{ -6 }{ -2 } \implies 3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{7}=\stackrel{m}{ 3}(x-\stackrel{x_1}{5})[/tex]
[tex]y-7=3x-15\implies y=3x-8\implies -3x+y=-8\implies {\Large \begin{array}{llll} 3x-y=8 \end{array}}[/tex]
Let g(x) be a horizontal compression of f(x) = -x + 4 by a factor of 0.5. Write the
rule for g(x).
g(x) = 4x+4
g(x)=x-4
g(x)=0.5x-4
g(x)=-2x+4
1 pts
There is no correct answer given.
Horizontal compression of f(x) = -x + 4 by a factor of 0.5 will be -2x + 4.
What is a horizontal function?A horizontal line that a function's graph looks to coincide with but does not really do so is said to be its horizontal asymptote. The final behavior of the function is determined using the horizontal asymptote.
Given, g(x) is a horizontal compression of function f(x) = - x + 4 by a factor of 0.5. Hence,
g(x) = -x / 0.5 + 4
g(x) = -2x + 4
Therefore, By a factor of 0.5, the horizontal compression of the function (f(x)) is -x + 4 will result in -2x + 4.
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What is the value of x?
Enter your answer in the box.
The value of x in the intersecting line is 54.
How to find angles in intersected lines?When lines intersect, angle relationships are formed such as vertically opposite angles, linear angles angles on a straight lines.
Therefore, angle 2x + 2 is vertically opposite to the angle 3x - 52 .
Vertically opposite angles are congruent to each other.
Vertical Angles are the angles opposite each other when two lines cross. in other words, vertical angles are formed when two lines meet each other at a point.
Hence,
2x + 2 = 3x - 52
2x - 3x = -52 - 2
- x = -54
Therefore,
x = 54
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831 is divisible by 3.
Answer:
yes
Step-by-step explanation:
The answer to your question is yes. We have calculated all the numbers that 831 is evenly divisible by. The numbers that 831 is divisible by are 1, 3, 277, and 831.
Write the
equation
of the line In
Slope-Intercept
Form.
Type your
answer here.
Answer:y=2x+3
Step-by-step explanation:
The slope intercept form is y=mx+b
m equals to slope
b equals the y-intercept
the slop of this equation is 2
The y-intercept is at (0, 3)
y=2x+3
What is the major difference between the alternate hypothesis and the null hypothesis?.
While the alternative hypothesis states your research's prediction of an effect or relationship, the null hypothesis of a test always predicts no effect or no relationship between variables.
What is alternative hypothesis?
The alternative to your research topic is represented by the alternative hypothesis (Ha). It asserts that there is a population-wide impact.
Frequently, your study hypothesis and alternate hypothesis are the same. Alternatively said, it's the assertion that you anticipate or hope will be accurate.
What is meant by a null hypothesis?
A common statistical theory called the null hypothesis asserts that there is no statistical relationship or significance between two sets of observed data and measured events for a given single observed variable.
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Billy’s mom bought pizza for 4 boys. The boys ate 3 pizzas. If each boy ate the same amount, how much did each eat
Answer:
If there are 4 boys and they ate 3 pizzas, and each boy ate the same amount, then each boy ate 3/4 of a pizza. If you want to express this as a fraction, it would be 3/4 of a pizza per boy. If you want to express it as a decimal, it would be 0.75 pizzas per boy. If you want to express it as a percentage, it would be 75% of a pizza per boy.
Punch recipe. Orange juice, 3, 1/3. Grape juice six and 1/2. Cherry juice. 4 and 1/8. Club soda, one and 1/4. About how much fruit juice,(orange, grape, and cherry) is used in the punch.
answers.
11 cups
12 cups
13 cups
14 cups
Answer:
14 cups
Step-by-step explanation:
3 + 6 = 9
9 + 4 = 13
13 + 1 = 14
14 plus fraction
A seed company planted a floral mosaic of a national flag. The perimeter of the flag is 2,340 ft Determine the flag's width and length if the length is 410 ft greater than the width.
Answer:
Hope this helps good luck! :)
Step-by-step explanation:
[tex]2340=2l+2w\\l= w+410\\2340=2(w+410) +2w\\\\2340= 2w+820+2w\\1520=4w\\\\w=380\\\\l=380+410\\l= 790[/tex]
to avoid a possible collision with a manned airplane, you estimate that your small ua climbed to an altitude greater than 600 feet agl. to whom must you report the deviation? group of answer choices
We must report the deviation to Upon request of the Federal Aviation Administration.
What is Deviation?
The deviation is a metric used to determine the discrepancy between an observed variable's value and its predicted value. The deviation can be defined as the distance from the centre point.
Concept:
Each remote PIC who deviates from a Part 107 rule shall, upon request from the FAA administrator, submit a written report of such deviation.
Who is in charge of providing the participants with information on emergency procedures while utilising a small unmanned airplane in a commercial operation? The commander of the remote pilot. A person may fly an unmanned aerial system for profit even without a Part 107 remote pilot certificate: under the immediate control of a Remote PIC.
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Joe i reponible for reerving hotel room for a company trip. Hi company change plan and increae how many people are going on the trip, o they need at leat 505050 total room. Joe had already reerved and paid for 161616 room, o he need to reerve additional room. He can only reerve room in block, and each block contain 888 room and cot \$900$900dollar ign, 900. Let BBB repreent the number of additional block that Joe reerve. 1) Which inequality decribe thi cenario?
Chooe 1 anwer:
The bare minimum required is $4500 to reserve 5 blocks totaling at least 34 rooms.
What is inequality?In mathematics, a relationship between two expressions or values that are not equal to each other is called "inequality".
Here,
The number of rooms Joe company needs is 50. Let the number of rooms needed be n, this can be represented by the inequality:
n ≥ 50
Joe has already reserved 16 rooms, therefore the number of additional rooms needed to be reserved = 50 - 16 = 34 rooms. At least 34 rooms have to be reserved, if B is the number of additional blocks that Joe reserves, the inequality is:
B ≥ 34
Each block contains 8 rooms therefore the minimum number of block (a) needed to be reserved = 34/8 = 4.25 = 5 to the next whole number. Therefore the minimum number of blocks needed is given as:
a ≥ 5
Since each block cost $900, let c represent the minimum amount of money needed, therefore the least amount of money needed is given as:
c = $900(5) = $4500
c ≥ $4500
The least amount of money needed is $4500 for booking 5 blocks that will reserve at least 34 rooms.
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To find the area of a square,
use the formula A = s2. If the side of
a square is b5, what is the area of
the square?
Answer:
25
Step-by-step explanation:
When you're figuring out the area of a square, you're measuring the size of its surface. You can think of it as finding how many square units make up the entire surface. For squares, the formula for determining area is A = s2, or A = side x side.=
While looking at some reports, a store manager notes that televisions that retail for $475 and up costing customers $513 once the sales tax is ended, what is the sales tax percentage?
The sales tax percentage of the store manager report is 7.41%
How to solve for the sales tax percentageCustomers are subject to a charge known as sales tax when they buy goods and services.
It is a pass-through tax, which means you must collect it from clients and send the money to your state or local government. the seller do not contribute sales tax.
The sales tax is first calculated by
= price after tax - price before tax
= 513 - 475
= 38
sales tax percentage is calculated using the formula
= (Tax amount / Price before tax) × 100%
= (38 / 513) * 100
= 7.4074
= 7.41%
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