Overall, the article has given me a deeper appreciation for the role that statistics plays in the political landscape.
One statistical discussion that stood out to me was the concept of margin of error. This is a measure of the accuracy of a poll and is calculated by taking into account the sample size and the variability in responses. I now have a better understanding of how pollsters use this measure to determine the reliability of their results.
Additionally, the article highlighted the importance of understanding statistical significance, which refers to the likelihood that a particular result occurred by chance. This is an essential concept in statistics that helps to determine whether a particular result is reliable or not.
It has also emphasized the need to interpret polling data with caution and to be mindful of the potential for errors and biases.
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which expression is equivalent to 2(a-3)+4a
The expression is equivalent to 2(a -3) + 4a will be 6a - 6. Then the correct option is A.
What is an equivalent?The equivalent is the expression that is in different forms but is equal to the same value.
The expression is given below.
⇒ 2(a -3) + 4a
Simplify the expression, then we have
⇒ 2(a -3) + 4a
⇒ 2a - 6 + 4a
⇒ 6a - 6
The expression is equivalent to 2(a -3) + 4a will be 6a - 6. Then the correct option is A.
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The missing options are given below.
A. 6a - 6
B. 6a - 1
C. a - 6
D. None of the above
Which of the following sequences are geometric?
Check all that apply.
Answer: A and C
Step-by-step explanation:
- Geometric sequences are sequences where there is a constant number being multiplied or divided.
- In A, we are dividing by 2 each time. In C, we are multiplying by 3
each time.
- B is not multiplication or division. Neither is D.
(っ◔◡◔)っ ♥
Hope this helps.
MM4343
A rectangle is divided up into four smaller rectangles/ The length of each segment is a whole number of cm. The areas of three rectangles is given in the diagram. Find the number of sq. cm in the total area of rectangle ACEG
The solution is, The value of N is 12 sq cm.
What is area of a rectangle?Area of a rectangle (A) is the product of its length (l) and width (w).
A= l. w
here, we have,
1. Find the greatest common factor of 35 and 42 to find the length (horizontal). The GCF is 7.
2. The horizontal length of the 35 and 42 sq cm is 7, and the heights are 5 and 6 respectively.
3. Moving on tot he 10 sq cm rectangle,
since the height of just that one rectangle is and 10/5 is 2, the horizontal length is 2.
4. For n, the horizontal length is 2 and the height is 6.
2 X 6 is 12 sq cm.
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Which statements are true about the angles in the figure? Select two options.
Angle x and angle y are supplementary angles.
Angle W and angle Z are a linear pair.
Angle W and angle Y are adjacent angles.
Angle X and Angle Z are vertical angles.
Angle Z and angle Y are complementary angles angles.
The true statements are ∠X and ∠Y are supplementary angles, ∠W and ∠Z are a linear pair and ∠Y and ∠Z are complementary angles. The solution has been obtained by using angles and line.
What are angles and line?
Lines having little depth or width are said to be straight. Lines can be perpendicular, intersecting, transversal, and many more various forms. A figure in which two rays emanate from the same point is referred to be an angle.
We know that angles on a straight line add up to 180° and such angles are called supplementary angles.
Therefore, ∠X and ∠Y are supplementary angles.
Similarly, we know that angles on a straight line form a linear pair.
Therefore, ∠W and ∠Z are a linear pair.
Also, we know that two angles are complementary when their sum is 90°.
We can see from the figure that ∠Z and ∠Y add up to 90°.
Therefore, ∠Y and ∠Z are complementary angles.
Hence, the above provided statements are true about the angles.
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The figure of the question is attached below
Gail is selling Girl Scout cookies. This week Mrs. Martin bought 3 boxes, Mr. Leesville bought 4 boxesm, and her friend Carroll bought 1 box. Mr. Millbrook cannot eat cookies so he gave a $7 donation to Gail's troop. If Gail sold 10 boxes last week and the amount of money she collected last week equals the amount of money she collected this week, write and solve an equation to determine how much each box of cookies costs.
Answer:
Let's assume that the cost of each box of cookies is "x" dollars.
Based on the given information, Gail sold a total of 3 + 4 + 1 = 8 boxes of cookies this week, and Mr. Millbrook gave a $7 donation. Therefore, the total amount of money collected this week is:
8x + 7
Since we know that Gail sold 10 boxes of cookies last week and collected the same amount of money, we can set up an equation:
10x = 8x + 7
Solving for x, we get:
2x = 7
x = 3.50
Therefore, each box of Girl Scout cookies costs $3.50.
Step-by-step explanation:
15 pts pls help me TvT
Chords AB and CD intersect at E and AE= EB is Semi circle is drawn with diameter CD. EF perpendicular to CD meet this semi circle at F then AE= EF
What is Circle?A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.
Let M be the midpoint of AB, so EM is perpendicular to AB.
Since OF is a diameter of the circle, angle EOF is a right angle.
Triangles EOF and EMA are similar, since they both have a right angle and angle EFM is congruent to angle EAM, being alternate interior angles of parallel lines.
The corresponding sides are proportional:
EF / EA = EO / EM.
EM is half the length of AB, which is the diameter of the semicircle,
EO must be equal to the radius of the semicircle.
Therefore, we have EF / EA = radius / (diameter / 2) = 2 / 2 = 1,
EF = EA.
Hence, chords AB and CD intersect at E and AE= EB is Semi circle is drawn with diameter CD. EF perpendicular to CD meet this semi circle at F then AE= EF
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How do you factor with a leading coefficient greater than 1?
Factoring polynomials with a leading coefficient greater than 1 is to use the factoring by grouping technique or quadratic formula.
Factoring a polynomial with a leading coefficient greater than 1 can be more challenging than factoring a polynomial with a leading coefficient of 1. However, there are several methods and techniques that can be used to factor such polynomials.
One common method for factoring polynomials with a leading coefficient greater than 1 is to use the factoring by grouping technique. This involves grouping the terms of the polynomial in pairs and factoring out the greatest common factor of each pair.
The resulting expressions can then be further factored or combined to obtain the final factorization of the polynomial.
Another method for factoring polynomials with a leading coefficient greater than 1 is to use the quadratic formula, which can be used to find the roots of a quadratic polynomial. Once the roots are found, the polynomial can be factored as a product of linear factors.
In some cases, it may also be helpful to use a combination of these techniques, along with other algebraic manipulations, such as completing the square or long division.
Overall, factoring a polynomial with a leading coefficient greater than 1 may require more patience and creativity than factoring a polynomial with a leading coefficient of 1, but with practice and persistence, it is possible to develop the skills and techniques needed to factor such polynomials efficiently and accurately.
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Helppp i need to find the transformations needed.
The transformations from the function f(x) to g(x) is horizontal shift: Right 4 Units and vertical shift: Up 1 Units.
What is a transformation?A transformation is a general term for four specific ways to manipulate the shape and/or position of a point, a line, or geometric figure. The original shape of the object is called the Pre-Image and the final shape and position of the object is the Image under the transformation.
The given functions are f(x)=x³ and g(x)= -(x-4)³+1.
To find the transformation, compare the function to the parent function and check to see if there is a horizontal or vertical shift, reflection about the x-axis or y-axis, and if there is a vertical stretch.
Horizontal Shift: Right 4 Units
Vertical Shift: Up 1 Units
Reflection about the x-axis: None
Reflection about the y-axis: Reflected
Vertical Compression or Stretch: None
Therefore, the transformations from the function f(x) to g(x) is horizontal shift: Right 4 Units and vertical shift: Up 1 Units.
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If the diameter of the pie is ten inchefls, what is the approximate arc length of one slice of pie?
A. 1.67 inches
B. 13.08 inches
C. (c) 3.14 inches
D. D 5.24 inches
The approximate arc length of one slice of pic is 5.24 inches according to the circle circumference.
Let us assume that the pic is equally cut into 6 pieces. Also given that the diameter of the pie is 10 inches.
Diameter (D)=10.
So the radius will be D/2.
Radius (R)=10/2=5.
The pie's circumference is given by:
C=2πR
C=2π*5
C= 10π (in)
Because the pie is divided into six pieces, the circumference of the pie is divided into six equal-length arcs. So,
Length of Arc (L)= 10π/6
L = 5π/3
L= 5(3.14)/3
L=5.234=5.24
Therefore the approximate arc length of one slice of pie is 5.24 inches.
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pls help i dont know how to do it i've been out sick
Please find the missing side length using trig
Answer:
13.0898597466511 or 13.09
Step-by-step explanation:
a heavy rope, 30 ft long, weighs 0.7 lb/ft and hangs over the edge of a building 80 ft high. (a) how much work w is done in pulling the rope to the top of the building?
A heavy rope, 30 ft long, weighs 0.7 lb/ft and hangs over the edge of a building 80 ft high, the work done in pulling the rope to the top of the building is 1785 ft-lb.
To calculate the work done in pulling the rope to the top of the building, we need to use the formula:
W = F x d
where W is the work done, F is the force applied, and d is the distance over which the force is applied.
In this problem, we can calculate the force required to pull the rope as the product of its weight per unit length (0.7 lb/ft) and the length of the rope (30 ft). Thus, the force required is:
F = 0.7 lb/ft x 30 ft = 21 lb
To calculate the distance over which the force is applied, we need to calculate the total length of the rope that needs to be lifted. This can be found using the Pythagorean theorem, as follows:
l = √(30^2 + 80^2) = 85 ft
So the distance over which the force is applied is 85 ft.
Now we can substitute the values for F and d into the formula for work to get:
W = F x d = 21 lb x 85 ft = 1785 ft-lb
This calculation shows how the formula for work can be used to calculate the energy required to lift an object against gravity over a given distance.
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Andrew ran 0.75 miles at basketball practice.
Write 0.75 miles as a fraction in simplest form.
of a mile
Write 0.75 miles as a percent.
% of a mile
Answer:
Fraction 3/4 percent 75%
Step-by-step explanation:
.75 in simplest form is 3/4
The volume of a cylinder is given by the formula V = ²h
where r represents the length of the radius of the base of
the cylinder and h represents the height of the cylinder.
A cylinder has a volume of 54 m³ and a radius of 3 m.
What is its height, h?
Answer: 0.95m or 3/π
Step-by-step explanation:
Volume of cylinder = 2π[tex]r^{2}[/tex]*h
54 = 2π*9*h
divide 2π*9 on both sides
54/2π*9 = h
54/18π = h
3/π = h
h = 0.95 m
Mr. Mackinson has to choose 2 students to lead the class field trip. If he draws from a list of 6 boys and 6 girls, what is the probabilty that the names of 2 girls will be drawn?
The required probability of Mr. Mackinson choosing the names of 2 girls is approximately 0.2273.
What is probability?Probability can be defined as the ratio of favorable outcomes to the total number of events.
Here,
The total number of ways to choose any 2 students from a group of 12 is given by the combination formula:
C(12,2) = 12! / (2! * 10!) = 66
This means there are 66 total ways for Mr. Mackinson to choose any 2 students from the class.
To calculate the probability of choosing 2 girls, we need to count the number of ways to choose 2 girls from the group of 6 girls. We can use the combination formula again:
C(6,2) = 6! / (2! * 4!) = 15
This means there are 15 ways for Mr. Mackinson to choose any 2 girls from the class.
So the probability of Mr. Mackinson choosing 2 girls is:
P(2 girls) = number of ways to choose 2 girls / total number of ways to choose 2 students
= C(6,2) / C(12,2)
= 15 / 66
= 0.2273
Therefore, the probability of Mr. Mackinson choosing the names of 2 girls is approximately 0.2273.
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Blake purchased a new car in 1990 for \$15,200$15,200. The value of the car has been depreciating exponentially at a constant rate. If the value of the car was \$10,000$10,000 in the year 1992, then what would be the predicted value of the car in the year 2001, to the nearest dollar?
Answer:
$3,000
Step-by-step explanation:
To find the predicted value of the car in 2001, we need to use the exponential decay formula:
V(t) = V0 * e^(-kt)
where V0 is the initial value of the car ($15,200), t is the time in years since 1990, and k is the exponential decay constant. We can find k using the value of the car in 1992:
V(2) = $10,000 = $15,200 * e^(-2k)
Solving for k, we get:
k = -ln(0.654) / 2
Now that we have k, we can find the value of the car in 2001:
V(11) = $15,200 * e^(-11k)
To the nearest dollar, the predicted value of the car in 2001 is $$3,000$.
prove by induction that if we remove the root of a k-th order binomial tree, it results in k binomial trees of the smaller orders. you can only use the definition of bk. per the definition, bk is formed by joining two bk−1 trees.
To prove that removing the root of a k-th order binomial tree results in k binomial trees of smaller orders, we will use mathematical induction.
Base case: For k = 1, removing the root of a 1st order binomial tree results in zero smaller binomial trees, which is true.
Inductive hypothesis: Assume that removing the root of a k-th order binomial tree results in k binomial trees of smaller orders, for some positive integer k.
Inductive step: We want to prove that removing the root of a (k+1)-th order binomial tree results in (k+1) binomial trees of smaller orders.
By definition, a (k+1)-th order binomial tree, denoted by B(k+1), is formed by joining two k-th order binomial trees, denoted by Bk, with one of them as the leftmost child of the root of the other. Let us remove the root of B(k+1) to obtain a new binomial tree, denoted by B'.
Since B(k+1) is formed by joining two k-th order binomial trees, we can apply the inductive hypothesis to each of them to obtain that removing their roots results in k smaller binomial trees each. Let these smaller binomial trees be denoted by B1, B2, ..., Bk and C1, C2, ..., Ck,
respectively.
Now, consider B' and observe that it is a k-th order binomial tree, since it has k children, each of which is a smaller binomial tree. Moreover, B' is obtained from B(k+1) by removing the root, which is the parent of the two k-th order binomial trees Bk and Ck. Thus, we have decomposed B' into k smaller binomial trees, namely B1, B2, ..., Bk and C1, C2, ..., Ck.
Therefore, we have shown that removing the root of a (k+1)-th order binomial tree results in (k+1) binomial trees of smaller orders, which completes the induction.
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Alex is putting away bowls in the school cafeteria. He must stack the bowls so they will all fit in the cupboard, but each stack can be only five bowls high.
If Alex has 287 bowls to put away, what is the minimum number of stacks he will have to make?
Answer:
heyyyyy
Step-by-step explanation:
whatssss goooddd
Quadrilateral A'B'C'D' is a translation of quadrilateral ABCD. What is
the length of B'C?
The length of B'C' after the translation of the original object is; B'C' = 3 units
How to interpret translation in transformation?Translation in transformation is simply defined as the displacement of a figure or a shape from one place to another. In translation, a figure can move upward, downward, right, left or anywhere in the coordinate system. In translation, only the position of the object changes, its size remains the same.
Now, from the attached image, we see that;
AB = 7 units
BC = 3 units
CD = 4 units
DA = 5 units
Now, by virtue of the definition of translation, it means that the translated object will retain the same dimensions. Thus;
B'C' = 3 units
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3. Meenakshi bought 12 books, each costing 250.75, if she gave the shopkeeper ₹ 4000. How much money will returned?
ans
4. One crayon set costs 25. How many crayon sets can be bought for rupees 2750
ans
5. Manu goes to buy a new bicycle in an exchange offer. The price of the new bicycle is bike on exchange is he pays for his new bike?
ans
pls put the questin number and give the answer
3. The amount that should be returned to Meenaski for buying 12 books worth R250.75 each and giving the shopkeeper R4,000, using mathematical operations, is R991.
4. The number of crayon sets that can be bought for R2,750 if one set costs R25, using division operation, is 110.
5. Manu will pay R1,700, exchanging his old bike for a new bike.
What are the mathematical operations?The four basic mathematical operations include addition, subtraction, division, and multiplication.
These mathematical operations are performed to solve algebraic problems using the relevant mathematical operands and rules.
Books:The number of books bought = 12
The unit cost of each book = R250.75
The total cost of the 12 books = R3,009 (R250.75 x 12)
The amount advanced to the cashier = R4,000
The balance to be returned = R991 (R4,000 - R3,009)
Crayon:The cost of a set of crayon = R25
The amount of money for the purchase = R2,750
The number of crayon sets that can be bought with R2,750 = 110 (R2,750/R25).
Bicycle:The price of the new bicycle = R2,500
The value of the old bike for exchange = R800
The amount to be paid = R1,700 (R2,500 - R800)
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Question Completion:The price of the new bicycle is R2,500. The bike on exchange is worth R800. How much does he pay for his new bike?
A submarine starts at the depth of -15 meters and then dives down 0.5 meter every second
The linear function representing the depth of the submarine after t seconds is given as follows:
d(t) = -15 - 0.5t.
How to obtain a linear function?
The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
The slope m represents the rate of change.The intercept b represents the value of y when x = 0.The parameters for this problem are given as follows:
b = -15 -> initial depth of the submarine.m = -0.5 -> each second, the height decays by 0.5.Hence the function is given as follows:
d(t) = -15 - 0.5t.
Missing InformationThe problem asks for the linear function representing the depth of the submarine after t seconds.
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The cylinder shown here has a height of 7 centimeters and a radius of 4 centimeters.
1. What is the area of the base of the cylinder? Express your answer in terms of .
2. How many cubic centimeters of fluid can fill this cylinder? Express your answer in terms of .
3. Give a decimal approximation of your answer to the second question using 3.14 to approximate n.
Answer:
1) 16pi square cm
2) 112pi cubed cm
3) 351.68 cubed cm
Step-by-step explanation:
Question 1: The base of a cylinder is a circle. To find the area of a circle, we can use the formula A = pi(r^2). the radius is 4 centimeters. 4^2 = 16.
The answer to the question is 16pi square cm
Question 2: This question is asking for the volume of the cylinder. To find the volume of the cylinder, we must multiply the area of the base by its height. we know the area of the base is 16pi. 16pi x 7(the height) = 112 pi.
The answer to the question is 112 pi cubed cm
Question 3: If pi were to be 3.14, we just need to substitute pi in the equation for question two with 3.14:
16(3.14) x 7 = 351.68
The answer is 351.68 cubed cm
Samir bought snacks for his team's practice. He bought a bag of popcorn for $1.67 and a 24-pack of juice bottles. The total cost before tax was $31.19. Write and solve an equation which can be used to determine
x, how much each bottle of juice cost.
Answer:
Step-by-step explanation:
is this in deltamath or bigideas? lol
(31.19-1.67)/24=x
"/" means divide.
Is either x=8 or x=10 solution 4x < 34
Answer:
x=8 is true for the this condition
Step-by-step explanation:
4x<34
if x=8
4*8<34
32<34
which is true
if x=10
40 is not greater than 34, so it not satisfied the condition
solve for x
13x-64=-2x+86
Answer:
x=10
Step-by-step explanation:
Answer:
x=10
Step-by-step explanation:
In this figure, lines a and b intersect a transversal, c. What is the relationship between ∠1 and ∠5?
m∠1 = m∠5, because alternate exterior angles are congruent.
What are angles of parallel lines?Angles formed by intersecting two parallel lines with a transversal are known as angles in parallel lines.
Given:
lines a and b intersect a transversal, c.
The pair of angles on the outside of the two parallel lines but on the other side of the transversal are known as alternate exterior angles.
m∠1 = m∠5 (Alternate exterior angles are congruent)
m∠1 = m∠5, because alternate exterior angles are congruent.
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The Complete Question is attached below.
which set or sets the number below belongs to: natural numbers, whole numbers, integers, rational numbers, irrational numbers, or real numbers.
19
Natural numbers are sometimes known as counting numbers. Numbers that can be counted but not zero. Whole numbers are a modest extension of natural numbers and include Zero.
Are a set of natural numbers and a set of integers the same thing?A subset of the natural numbers are the positive integers, often known as non-negative integers. Here are a few instances: 1, 2, 3, 4, 5, 6,... In other words, the "natural numbers" are the collection of all whole numbers that do not include 0.
What are a few examples in groups?There are just a limited amount of parts to it. Example: A = 1, 2, 3, and 4. An infinite set has unlimited items. All entire numbers are in a set called whole numbers.
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Wendell purchased a hot dog and 3 orders of french fries for $6.00. If the hot dog cost $2.25, what was the cost of each order of french fries?
The cost of each order of french Fries is $1.75.
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
Wendell purchased a hot dog and 3 orders of French fries for $6.00.
If the hot dog cost $2.25.
Then the cost of Hot dog
= 6 - 2.25
= 3.75
and, the cost of each order of French Fries
= 3.75 / 3
= $1.25
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Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the high temperature of 80 degrees occurs at 5 PM and the average temperature for the day is 60 degrees. Find the temperature, to the nearest degree, at 3 AM.
The temperature at 3 AM is about 53 degrees Fahrenheit.
How would you define temperature?The average kinetic energy of the particles in a medium, such as a gas, liquid, or solid, is measured by its temperature. It is a basic physical characteristic that governs the rate and amount of heat transmission between two bodies that are in thermal contact.
A thermometer is commonly used to measure temperature. It does this by detecting changes in a substance's physical characteristics that change with temperature, such as the expansion or contraction of a liquid or the resistance of a wire.
We are aware that a sinusoidal function models temperature, and the following information is crucial:
A high of 80 degrees is reached at 5 PM, or 17:00 in a 24-hour period.
The day's average temperature is 60 degrees.
We're looking for the temperature at three in the morning, or three in 24-hour time.
We can utilize the fact that the temperature moves through one full cycle in a 24-hour day to determine the frequency. As the time frame is 24 hours, the frequency is:
B = 2π/24 = π/12
To find the phase shift, we can use the fact that the high temperature occurs at 5 PM, which is 8 hours after noon (when the temperature starts to rise). So the phase shift is:
C = (8/24) * 2π = (1/3)π
To find the amplitude, we can use the fact that the temperature swings 10 degrees above and below the average. So the amplitude is:
A = 10
Finally, we can use the formula to find the temperature at 3 AM:
f(x) = A sin(B(x - C)) + D
f(3) = 10 sin(π/12(3 - (1/3)π)) + 60
f(3) ≈ 53.4
So the temperature at 3 AM is about 53 degrees Fahrenheit.
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The sales tax rate is 6%. If Sally buy sarowboat priced at $842,how much tax will she pay?
If the sales tax rate is 6% and if Sally buy rowboat priced at $842, the amount of tax she will pay, $50.52
What is the percentage?Percentage is a way to express a number as a fraction of 100. It is often used to represent ratios and proportions in a more convenient and understandable form, especially in financial and statistical contexts. For example, 50% means 50 per 100, or half of a given quantity. It is denoted using the symbol "%".
To calculate the sales tax on the purchase of a sailboat priced at $842 with a sales tax rate of 6%, you can follow these steps:
1. Convert the sales tax rate from a percentage to a decimal by dividing by:
= 100: 6% ÷ 100
= 0.06.
2. Multiply the price of the sailboat by the sales tax rate to find the amount of tax:
= $842 × 0.06
= $50.52.
Therefore, Sally will pay $50.52 in sales tax for the purchase of the sailboat.
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