The number of square units enclosed by the polygon is 18.
First, count the number of dots that are enclosed by the polygon (including those on the boundary). There are 14 such dots.Next, count the number of dots on the boundary of the polygon. There are 8 dots on the boundary.Each of the dots on the boundary corresponds to a line segment of the polygon.
So, the perimeter of the polygon is 8 units (the length of each of these line segments).Now, we can use Pick's theorem to find the area of the polygon. Pick's theorem states that A = i + b/2 - 1, where A is the area of the polygon, i is the number of dots inside the polygon, and b is the number of dots on the boundary of the polygon.
So, plugging in the values we have: A = 14 + (8/2) - 1 = 14 + 4 - 1 = 17
Therefore, the area of the polygon is 17 square units.However, we have to remember that the dots are spaced one unit apart, horizontally and vertically.
Therefore, each square that is enclosed by the polygon has an area of 1 square unit. We counted 17 such squares, so the total area enclosed by the polygon is 17 square units.
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suppose the amount of time (in minutes) per day that you spend watching netflix is in the 90th percentile of all account users. which interpretation(s) of this quantity are correct? select all that apply.
The correct interpretations of the given quantity are C and E.
C. Your daily viewing time is greater than 90% of all Netflix users.
E. 90% of all Netflix users viewing times per day are less than your daily viewing time.
To understand the correct interpretation, we need to first understand what the 90th percentile means. It refers to the value below which 90% of the data falls.
If your daily viewing time is in the 90th percentile of all Netflix users, it means that your viewing time is greater than 90% of all users. In other words, only 10% of users watch more Netflix than you, and your viewing time is greater than the viewing time of 90% of users.
Therefore, options C and E are the correct interpretations.
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Complete Question:
Suppose the amount of time (in minutes) per day that you spend watching Netflix is in the 90th percentile of all account users. Which interpretation(s) of this quantity are correct? Select ALL that apply.
A. You spend approximately 90 minutes per day watching Netflix.
B. 90% of all viewers spend more time on Netflix per day than you.
C. Your daily viewing time is greater than 90% of all Netflix users.
D. There is a 90% probability that a randomly selected viewer spends less time than you watching Netflix per day.
E. 90% of all Netflix user viewing times per day are less than your daily viewing time.
F. 90% of all Netflix user viewing times per day are less than or equal to your daily viewing time.
find the surface area of this figure
The Surface area of the given cuboid is found to be 872 sq, in.
Explain about the cuboid?Three-dimensional shapes with length, breadth, and height are called cuboids. Six of the cuboid's sides are referred to as faces.
Every corner of a cuboid's faces, which usually refer to as vertices, are at a 90-degree angle. Hence, a cuboid is any object that has the shape of a box.The only thing that cuboids have are straight angles. It is not a cuboid if it has additional kinds of angles. The same is true for cubes. A cube and even a cuboid have the same number of edges, faces, and vertices: 12 edges, 8 vertices, and 6 faces.Surface area of a cuboid is = 2(lw + 2lh + hw0
l= lengthw= width.h = heightS.A = 2[(17)*(8) + (8)*(12) +(12)*(17)]
S.A = 2*436
S.A = 872
Thus, the Surface area of the given cuboid is found to be 872 sq, in.
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Select the correct answer.
A graph with a y-axis and an x-axis in positive and negative planes. Two lines L I and I J are formed by connecting points (Negative 4,3), (5,3), and (5, Negative 3).
I(5, 3), J(5, -3), and L(-4, 3) are three vertices of rectangle IJKL. What are the coordinates of the fourth vertex, K, of rectangle IJKL?
A.
(-4, -3)
B.
(5, 3)
C.
(5, -3)
D.
(-4, 3)
The cοοrdinates οf the fοurth vertex K must be the reflectiοn οf the pοint L(-4,3) acrοss the οrigin, which is (4,-3).
Thus, οptiοn D is cοrrect.
What is the cοοrdinate geοmetry?Cοοrdinate geοmetry is a branch οf mathematics that deals with the study οf geοmetry using the principles οf algebra.
The rectangle IJKL is fοrmed by cοnnecting the pοints I, J, K, and L in a clοckwise οr cοunterclοckwise manner. Since I and J have the same x-cοοrdinate and are οn οppοsite sides οf the x-axis, and L and K have the same y-cοοrdinate and are οn οppοsite sides οf the y-axis, it fοllοws that the diagοnals οf the rectangle IJKL intersect at the οrigin (0,0).
Therefοre, the cοοrdinates οf the fοurth vertex K must be the reflectiοn οf the pοint L(-4,3) acrοss the οrigin, which is (4,-3).
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A student was asked to factor
During bracket off, when 6x⁴ * 6x⁴= 36x⁸ instead of 36x¹⁶ using Perfect square method.
When 4y² * 4y² = 16y^4 instead of 25y⁴⁴ gotten in the question. To correct the error, using the perfect square method, it can be corrected.
The answer will be (6x⁸ - 5y²)(6x⁸ + 5y²)The last error found is sign rule-4y^2 x -4y^2 = +16y⁴ instead of -4y² * +4y² = -16y⁴
What is a Perfect Square?Perfect square is is a number that is generated by multiplying two equal integers by each other.
Given 36x¹⁶ - 25y⁴
The rule = A difference of two perfect squares, A² - B²² can be factored into (A+B) x (A-B)36x¹⁶ is a perfect square = 6₂ * x⁸2)= (6x⁸)^225y⁴ is also a perfect square= 5² * x²(2)= (5x²)²
Using the rule for Perfect square,
When A² - B² = (A + B) x (A - B)
So,(6x⁸)₂ - (5x²)²
=(6x⁸ + 5x²) * (6x⁸ - 5x²)
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a town doubles its size every 38 years. if the population is currently 6,790, what will the population be in 76 years?
Population will be 43,160 in 76 years if a town doubles its size every 38 years if the current population is 6,790.
Since the town doubles in size every 38 years, we can use the formula:
P = P0 * 2^(t/T)
where P0 is the initial population, P is the population after time t, and T is the doubling time (38 years in this case).
We know that the current population is P0 = 6,790, and we want to find the population in 76 years, which is t = 76. Plugging these values into the formula, we get:
P = 6,790 * 2^(76/38)
P = 6,790 * 2^2
P = 6,790 * 4
P = 27,160
Therefore, the population of the town will be 27,160 in 76 years.
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Find and explain the error in the student’s work below.
Solve 2x² - 5x -12 = 0 using the Quadratic Formula.
The error made by the student is in simplifying the expression inside the square root.
What is the quadratic equation?
The solutions to the quadratic equation are the values of the unknown variable x, which satisfy the equation. These solutions are called roots or zeros of quadratic equations. The roots of any polynomial are the solutions for the given equation.
The student made an error in simplifying the expression inside the square root.
The expression should be simplified as follows:
25 + 4(2)(-12) = 25 - 96 = -71
So the correct expression inside the square root is -71, not 121.
Therefore, the correct solution using the Quadratic Formula is:
x = (-(-5) ± √((-5)² - 4(2)(-12)))/(2(2))
x = (5 ± √(25 + 96))/4
x = (5 ± √121)/4
x = (5 ± 11)/4
Hence, the solutions are x = -3 and x = 4/2, which simplifies to x = 2.
Therefore, the error made by the student is in simplifying the expression inside the square root.
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all the edges of a cube are expanding at a rate of 4 4 in. per second. how fast is the volume changing when each edge is 10in. 10 in. long?
Answer:
Step-by-step explanation:
every second we are increasing the sides by 4.4 in all 3 dimensions. This must mean that we need to do 4.4x4.4x4.4 to get
85.184in^3 per second
your cousin says that if two fractions have the same numerator,then the fraction with the greater denominator is the greater fraction. is your cousin correct explain
It is not always true that if two fractions have the same numerator, then the fraction with the greater denominator is the greater fraction.
The statement that if two fractions have the same numerator, then the fraction with the greater denominator is the greater fraction is not always correct. This is because the value of a fraction is determined by both its numerator and denominator, and if the denominators of two fractions with the same numerator are different, then the fractions are not directly comparable.
Consider the fractions 3/4 and 3/5. Both have a numerator of 3, but the denominator of the first fraction is greater than the denominator of the second fraction. However, 3/5 is actually the greater fraction because it represents a larger portion of the whole.Consider the fractions 5/7 and 5/9. Both have a numerator of 5, but the denominator of the second fraction is smaller than the denominator of the first fraction. Therefore, 5/7 is the greater fraction because it represents a larger portion of the whole.
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subtract 13 5/8 - 3 2/3
Answer:
9 23/24
Step-by-step explanation:
Change both mixed fractions to improper fractions
13 5/8=109/8
3 2/3=8
Now substract: 109/8 - 8/3= 10 23/24.
Hope this helps!!
A Venn Diagram comparing swimmers and weightlifters is shown below:
An image of a Venn diagram is shown labeled swimmers and weightlifters. The label in the swimmer's portion is B. The label in the intersection of the two circles is A. The label in the weightlifter's portion is C. The label outside the circles is D.
Which area represents elements contained in open parentheses swimmers intersection weightlifters close parentheses complement?
A
D
B, C, D
A, B, C
Answer:
The area that represents elements contained in the complement of the intersection of swimmers and weightlifters is the region outside the circles labeled as D. Therefore, the answer is D.
Step-by-step explanation:
chatgpt
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If a = 3 square root of 3 in the right triangle below, what is the value of b?
In 1962, an automobile worker was paid an annual salary of $8,400. Each year the worker's pay went up by 5% of the previous year's salary. What is the total amount that the worker will have earned from the beginning of 1962 through the end of 1980?
the worker will have earned $231,584.10 from the period of beginning 1962 through the end 1980.
To solve this problem, we can use the formula for the sum of a geometric series:
S = a(1 - rⁿ)/(1 - r)
where S is the sum of the series, a is the first term, r is the common ratio, and n is the number of terms.
In this case, the first term is $8,400 and the common ratio is 1.05 (since the worker's salary increases by 5% each year). We need to find the sum of the series from 1962 to 1980, which is 19 years. So, the total amount that the worker will have earned from the beginning of 1962 through the end of 1980 is:
S = 8,400(1 - 1.05¹⁹)/(1 - 1.05)
S ≈ $231,584.10
Therefore, the worker will have earned approximately $231,584.10 during this period.
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Describe a series of transformations that moves the blue figure to the red figure. If there is a : Translation - show number and direction Reflection - give axis of reflection
Rotation - give direction (clockwise or counterclockwise) and degree amount
Translation: The blue figure can be moved to the red figure by a translation of three units to the right and one unit down.
Reflection: The blue figure can be moved to the red figure by a reflection over the x-axis.
Rotation: The blue figure can also be moved to the red figure by a rotation of 90 degrees counterclockwise.
What is transformation?Transformation in mathematics is the process of changing an object or figure in some way. This includes changing the size, position, rotation or reflection of an object. Transformations can also be used to move a figure from one coordinate system to another. Common transformations include translation, rotation, reflection and scaling.
To demonstrate this transformation, imagine the blue figure being shifted three units to the right and one unit down, such that it is now completely overlapping the red figure.
This transformation can be visualized by imagining the figure being flipped along the x-axis, so that the right side of the figure is now on the left side and vice versa.
To demonstrate this transformation, imagine the blue figure being spun 90 degrees counterclockwise, so that the top of the figure is now on the left side and the bottom is on the right side. This rotation will align the figure with the red figure.
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Down below are the coordinates after dilation but it says its wrong
Answer:
For the original triangle:
A is at (-3, 6), B is at (1, 2), C is at (-5, 1).
For the new triangle:
A' will be at (-3 - 3, -(6 + 2)) = (-6, -8)
B' will be at (1 - 3, -(2 + 2)) = (-2, -4)
C' will be at (-5 - 3, -(1 + 2)) = (-8, -3)
What is the volume of the composite figures?
Total volume of the composite figure using volume of cuboid formula is = 120ft³.
Define volume?A cuboid's volume is a measurement of how much room it occupies. A three-dimensional shape with dimensions of length, breadth, and height is the cuboid. We can keep stacking them, starting with a rectangular sheet, until we achieve a shape with a particular length, breadth, and height.
The shape of this stack of sheets is a cuboid, which has 6 faces, 12 edges, and 8 vertices. The (unit)³ is used to represent a cuboid's volume.
In the given figure,
Length of cuboid = 6ft.
Breadth of cuboid = 3ft.
Height of cuboid = 5ft.
Length of second cuboid = 4ft.
Height of second cuboid = 5ft.
Breadth of second cuboid = 3ft.
Volume of first cuboid = length × breadth × height.
= 6 × 3 × 5
= 90ft³
Volume of second cuboid = 4 × 3 × 5
= 60ft³
Now the second cuboid is half.
So, volume becomes = 60/2
= 30ft³.
So, total volume of the figure = 90 + 30 = 120ft³.
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Use the given scale factor and the side lengths of the scale drawing to determine the side lengths of the real objects.
Using the scale factor of 4:1, the side lengths of the real objects are:
B. Side a is 5 inches long and side b is 4.5 inches long.
What is a Scale Factor?A scale factor is a number that represents the ratio of the size or dimensions of an object in relation to another object. It is a proportional relationship between two similar objects, where the scale factor is the ratio of any corresponding lengths or dimensions.
Thus, given that the scale factor is 4:1, it means 4 inches of the scale drawing represents 1 inch of the real object.
Therefore, the sides would be:
Side a = 20/4 = 5 in.
Side b = 18/4 = 4.5 in
The answer is B.
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a restaurant offers a special pizza with any 6 toppings. if the restaurant has 16 topping from which to choose, how many different special pizzas are possible?
To calculate the number of different special pizzas possible with any 6 toppings out of 16, we can use the combination formula:C(16,6) = 16! / (6! * (16-6)!) = (161514131211) / (654321) = 8008
there are 8,008 different special pizzas possible with any 6 toppings out of 16.
To calculate the number of different special pizzas possible with any 6 toppings out of 16, we need to use the combination formula, which is given by:
C(n, k) = n! / (k! * (n - k)!)
where n is the total number of items to choose from, and k is the number of items we want to choose.
In this case, n = 16 (the total number of toppings available), and k = 6 (the number of toppings we want to choose).
Plugging these values into the formula, we get:
C(16, 6) = 16! / (6! * (16 - 6)!)
= (16 * 15 * 14 * 13 * 12 * 11) / (6 * 5 * 4 * 3 * 2 * 1)
= 8008
Therefore, there are 8,008 different special pizzas possible with any 6 toppings out of 16.
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please answer!! A rectangle is 1/3 yards long and 2/3 yards wide.
What is the area of the rectangle?
Enter your answer as a fraction in simplest form by filling in the boxes
Answer:
2/9yd²
Step-by-step explanation:
We know that area is calculated by length × width, so we will do the same here. To get the area, we must multiply 1/3 by 2/3.
1/3 × 2/3 is 2/9. So, the area of the rectangle is 2/9yd². :D
The 15 Chihuahua puppies ate 63 cups of food last week. If each puppy ate the same amount of food, how many cups of puppy food did each puppy eat?
15 StartLongDivisionSymbol 63.0 EndLongDivisionSymbol minus 60 = a remainder of 30 and a quotient of 4.blank.
How many cups of food did each puppy eat?
4 cups
4.1 cups
4.2 cups
4.ModifyingAbove 2 with bar cups
Answer:c 4.2 cups
Step-by-step explanation:
just do 63 divided 15
PLEASE HELP NEED IT DONE RN !!
Answer: rectangleular pyramid
Step-by-step explanation:
A rectangle has an area of 717. 8m2. One of the sides is 7. 4m in length. Work out the perimeter of the rectangle
The perimeter of the rectangle is approximately 208.9 meters.
To find the perimeter of the rectangle, we need to know the length of the other side.
Let's use the formula for the area of a rectangle:
area = length x width
We know that the area is 717.8 m^2 and one of the sides (width) is 7.4 m. So we can rearrange the formula to solve for the length:
length = area / width
length = 717.8 / 7.4
length ≈ 97.05 m
Now we have both the length and width of the rectangle, so we can find the perimeter:
perimeter = 2 x (length + width)
perimeter = 2 x (97.05 + 7.4)
perimeter = 2 x 104.45
perimeter = 208.9 m
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does the confidence interval suggest that the difference, if any, observed in this sample will also generalize to the larger population?
In the following question, Yes, the confidence interval suggests that the difference observed in this sample will also generalize to the larger population.
What is a confidence interval? A confidence interval is a probability statement that provides an interval of plausible values that are likely to contain the value of a population parameter. It is a way to infer the population parameter value from sample data.
A confidence interval is calculated as a range of values that are predicted to include the unknown population parameter, based on the sample statistic. The confidence interval suggests that the difference, if any, observed in this sample will also generalize to the larger population.
A confidence interval with a high level of confidence (e.g. 95%) would have a wider range of values and a higher probability of including the population parameter. The interpretation of the confidence interval is that we are 95% confident that the actual population parameter falls within the calculated interval. Therefore, it implies that the sample data is likely to be representative of the population data.
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Lori bought a bond with a face value of $20,000 and a coupon rate of 9.5%. the bond will mature in 20 years. how much interest will she receive semiannually?
Lori will receive a semiannual interest of $950 from the bond with a face value of $20,000 and a coupon rate of 9.5%, which will mature in 20 years.
To calculate the semiannual interest that Lori will receive from the bond, we need to use the following formula:
Semiannual interest = (Coupon rate x Face value) / 2
Substituting the given values, we get:
Semiannual interest = (9.5% x $20,000) / 2
Semiannual interest = ($1,900) / 2
Semiannual interest = $950
Therefore, Lori will receive a semiannual interest of $950 from the bond. This means that she will receive a total of $1,900 in interest every year until the bond matures in 20 years.
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the number of weaving errors in a twenty-foot by ten-foot roll of carpet has a mean of 0.5 . what is the probability of observing exactly 4 errors in the carpet? round your answer to four decimal places.
The probability of observing exactly 4 errors in the carpet is 0.0165 or 1.65%.
The number of weaving errors in a twenty-foot by ten-foot roll of carpet follows a Poisson distribution with a mean of 0.5. We can use the Poisson probability distribution formula to find the probability of observing exactly 4 errors in the carpet:
[tex]P(X = 4) = (e^{-0.5} * 0.5^4) / 4![/tex]
where X is the random variable representing the number of weaving errors. Plugging in the values, we get:
[tex]P(X = 4) = (e^{-0.5} * 0.5^4) / 4! = 0.0165[/tex] (rounded to four decimal places)
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PLEASE HELP!
Solve and explain
1) The price of one senior citizen ticket is $16 and the price of one student ticket is $8.
2) The price of one adult ticket is $12 and the price of one student ticket is $6.
3) The cost of one hasta is $180 and the cost of one shrub is $302.
4) The cost of one daylily is $10.40 and the cost of one bunch of ornamental grass is $10.
5) The cost of one daylily is $6.88 and the cost of one bunch of ornamental grass is $3.67.
What is algebra?Algebra uses symbols to represent unknown values, and equations to describe the relationships between those values. It is used to solve for those unknown values in order to perform calculations and solve real-world problems.
These answers can be determined by using basic algebraic equations to solve for the unknown variables. In the first example, the equation can be written as: 7S + 7C = 112, where S is the cost of one student ticket and C is the cost of one senior citizen ticket. Solving for S, we can get: S = (112-7C)/7. The same technique can be used for the other examples. This process of solving equations is useful in determining the prices of items when given certain information. It is also important for businesses to use this technique when pricing items, in order to maximize their profits.
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By using system of equations, following are the solutions:
1) The price of one senior citizen ticket is $3 and the price of one student ticket is $13.
2) The price of one adult ticket is $4 and the price of one student ticket is $6.
3) The cost of one hosta is $10 and the cost of one shrub is $12.
4) The cost of one daylily is $12 and the cost of one bunch of ornamental grass is $8.
5) The cost of one daylily is $10 and the cost of one bunch of ornamental grass is $3.
What is algebra?Algebra uses symbols to represent unknown values and variables, and equations to describe the relationships between those values. It is used to solve for those unknown values in order to perform calculations and solve real-world problems.
1) Assume that the cost for the senior citizen tickets is x and for the students is y.
On the first day: 7x + 7y = 112 [eq. 1]
On second day: 4x + 7y = 103 [eq. 2]
By solving, 7x + 7y = 112
x = (112 - 7y)/7
We have,
x = (112/7) - y
Now substitute the value of x in [eq. 2]
4[(112/7) - y] + 7y = 103
4[(112/7) - y] = 103 - 7y
y = 13
Place the value of y in one of the above equations:
4x + 7(13) = 103
4x = 103 - 91
4x = 12
x = 3
2) Assume that the cost for the adult tickets is x and for the students is y.
On the first day: 3x + 6y = 48 [eq. 1]
On second day: 3x + 3y = 30 [eq. 2]
By solving, 3x + 6y = 48
3x = 48 - 6y
We have,
x = (48/3) - 2y
Now substitute the value of x in [eq. 2]
3[(48/3) - 2y] + 3y = 30
3[(48/3) - 2y] = 30 - 3y
3[(48/3) - 2y] = 3(10 - y)
(48/3) - 2y = 10 - y
y = 6
Place the value of y in one of the above equations:
3x + 3y = 30
3x + 3(6) = 30
3x = 30 -18
x = 4
3) Assume the price of hostas to be x and shrubs to be y.
For Ashley: 3x + y = 42 [eq. 1]
For Asanji: 7x + y = 82 [eq. 2]
By solving, 3x + y = 42
y = 42 - 3x
Now substitute the value of y in [eq. 2]
7x + (42 - 3x) = 82
4x = 40
x = 10
Place the value of x in one of the above equations:
7x + y = 82
7(10) + y = 82
y = 82 - 70
y = 12
4) Assume the price of dailylily to be x and ornamental grass to be y.
For Ashley: x + 5y = 52 [eq. 1]
For Kali: 5x + 5y = 100 [eq. 2]
By solving, x + 5y = 52
x = 52 - 5y
Now substitute the value of x in [eq. 2]
5(52 - 5y) + 5y = 100
5(52 - 5y) = 5(20 - y)
52 - 5y = 20 - y
y = 8
Place the value of y in one of the above equations:
x + 5y = 52
x + 5(8) = 52
x = 12
5) Assume the price of dailylily to be x and ornamental grass to be y.
For Dan: 8x + 6y = 50 [eq. 1]
For Kali: x + 6y = 22 [eq. 2]
By solving, x + 6y = 22
x = 22 - 6y
Now substitute the value of x in [eq. 1]
8(22 - 6y) + 6y = 50
126 = 42y
y = 3
Place the value of x in one of the above equations:
x + 6y = 22
x + 6(3) = 22
x = 10
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It takes 2 ounces of paint to completely cover all 6 sides of a rectangular prism box, which holds 15 cups of sugar. Double the dimensions of the box. Hint: given k, areas are scaled by ____ and volumes are scaled by ____ Approximately how much paint would the new box need? How much sugar would it hold?
The new box would need approximately 8 ounces of paint and would hold 120 cups of sugar.
To find out how much paint the new box would need and how much sugar it would hold, follow these steps:
1. The original box holds 15 cups of sugar, and it takes 2 ounces of paint to cover it completely. When you double the dimensions of the box, areas are scaled by [tex]k^2[/tex] (k is the scale factor), and volumes are scaled by[tex]k^3.[/tex]
2. Since you double the dimensions, the scale factor k is 2.
3. The surface area of the box will be scaled by [tex]k^2, which is 2^2 = 4.[/tex]So, the new box will need 4 times the amount of paint that the original box needed. Since the original box needed 2 ounces of paint, the new box will need 2 × 4 = 8 ounces of paint.
4. The volume of the box will be scaled by [tex]k^3, which is 2^3 = 8[/tex]. So, the new box will hold 8 times the amount of sugar that the original box held. Since the original box held 15 cups of sugar, the new box will hold 15 × 8 = 120 cups of sugar.
In conclusion, the new box would need approximately 8 ounces of paint and would hold 120 cups of sugar.
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eight different flavors are analyzed in a blind ice cream taste test. a participant is given four different ice cream samples and asked to sort them based on preference. in how many different ways can they be sorted?
There are 24 different ways that the participant can sort the four ice cream samples.
Since the participant is given 4 different ice cream samples, there are 4 ways in which they can place their first preference. Once they have chosen their favorite ice cream sample, there are 3 remaining options for their second preference. Similarly, there are 2 options for their third preference, and only one option for their least favorite ice cream sample. Here we have to use the principle of counting
Therefore, the number of ways the participant can sort the ice cream samples based on preference is
4 x 3 x 2 x 1 = 24
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GIVING BRAINLIEST FOR RIGHT ANSWER (provide proof please i need to know how you got the answer)
Answer:
x > 3
Step-by-step explanation:
This is an open circle, meaning there will be no equal sign.
The line is going to the right of 3, meaning x > 3
So, our inequality is x > 3
Shirts are on sale for 30% off the oringal price of one shirt is 15 what is the total cost of 2 of these shirts at the sales price including a 7% sales tax
The sales price of the two shirt with 30%off on original price and 7% sales tax is equal to $22.47.
Original price of one shirt = $15
Number of shirts bought = 2
Sale discount = 30% off on original price
Sale price of one shirt = Original price - 30% of the original price
Substitute the value we get,
⇒Sale price of one shirt = 15 - (0.30)(15)
⇒Sale price of one shirt = $10.50
The cost of two shirts is equal to,
2 x $10.50 = $21.00
Sales tax = 7% of the total cost.
Substitute the value we have,
⇒Sales tax = 0.07 x $21.00
= $1.47
Total cost of two shirts = Cost of two shirts + Sales tax
⇒ Total cost of two shirts = $21.00 + $1.47
⇒ Total cost of two shirts = $22.47
Therefore, the total cost of two shirts at the sale price including the 7% sales tax is $22.47.
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show that 2 2/3/6=4/9
2 and 2/3 divided by 6 equals 4/9.
So, 2 and 2/3 divided by 6,
we can simplify it step by step as follows:
First, we need to convert the mixed numbers 2 and 2/3 to an improper fraction:
2 and 2/3 = (2 × 3 + 2) / 3 = 8/3
Therefore, the expression becomes:
8/3 ÷ 6
To divide fractions, we need to invert the second fraction and multiply:
8/3 ÷ 6 = 8/3 × 1/6
Simplifying the multiplication of fractions:
8/3 × 1/6 = (8 × 1) / (3 × 6) = 8/18
Now, we can simplify the fraction 8/18 by dividing both the numerator and denominator by their greatest common factor, which is 2:
8/18 = (8 ÷ 2) / (18 ÷ 2) = 4/9
Therefore, 2 and 2/3 divided by 6 equals 4/9.
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