The quadrilateral formed by the given vertices is a parallelogram based on the congruence of sides and angles.To determine the type of quadrilateral formed by the vertices W(-1,4), X(3,5), Y(4,1), and Z(0,0).
we can examine the properties and characteristics of the quadrilateral.
To identify the type of quadrilateral, we can consider its sides and angles.
1. Sides: We can calculate the lengths of the sides using the distance formula.
- Side WX = √[(3 - (-1))^2 + (5 - 4)^2] = √(16 + 1) = √17
- Side XY = √[(4 - 3)^2 + (1 - 5)^2] = √(1 + 16) = √17
- Side YZ = √[(0 - 4)^2 + (0 - 1)^2] = √(16 + 1) = √17
- Side ZW = √[(-1 - 0)^2 + (4 - 0)^2] = √(1 + 16) = √17
2. Angles: We can calculate the measures of the angles using the slopes of the sides.
- Angle WXY = arctan((5 - 4)/(3 - (-1))) ≈ 45.96°
- Angle XYZ = arctan((1 - 5)/(4 - 3)) ≈ -63.43° (Note: negative due to slope)
- Angle YZW = arctan((0 - 4)/(0 - (-1))) ≈ -75.96° (Note: negative due to slope)
- Angle ZWX = arctan((4 - 0)/(-1 - 0)) ≈ -90°
Based on the information above, we can conclude that the quadrilateral WXYZ is a parallelogram. This is because opposite sides are congruent (WX ≈ YZ and XY ≈ ZW), and opposite angles are congruent (WXY ≈ XYZ and YZW ≈ ZWX).
Therefore, the quadrilateral formed by the given vertices is a parallelogram based on the congruence of sides and angles.
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A proportional relationship exist between x and y. When x = 16 the value of y is 28. Write an equation for v in terms of x.
The equation describing the proportional relationship between x and y is y = (7/4)x.
In a proportional relationship, the ratio between the two variables remains constant. To find the equation for y in terms of x, we can determine the ratio between the corresponding values of x and y. Given that when x = 16, y = 28, we divide y by x to find the ratio:
y/x = 28/16 = 7/4.
This ratio represents the constant proportionality between x and y. Therefore, the equation for y in terms of x is y = (7/4)x. This equation indicates that y is directly proportional to x, and for every unit increase in x, y increases by 7/4 units. Likewise, for every unit decrease in x, y decreases by 7/4 units. This equation can be used to determine the value of y for any given value of x in the proportional relationship.
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How do I find the measure of AB (Rounded to the nearest tenth.)
The measure of the length AB to the nearest tenth is: 21.8
How to use trigonometric ratios?A right triangle is a triangle with one angle equal to 90 degrees.
The sides and angles of a right triangle can be found using trigonometric ratios.
So, let's find the length AB of the attached right triangle using trigonometry.
Along with that,
Tan ∅ = opposite/adjacent
Opposite side = AB
Adjacent side = 17 units
Along with that,
Tan 52° = AB / 17
multiplication cross
AB = 17 * tan 52
AB = 17 × 1.27994163219
AB = 21.7590077473
For this,
AB ≈ 21.8
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What is the solution of the following system? Use the elimination method. {4x 3y=62x 2y=5 The only solution is (−32, 4). The only solution is (0, 2). There are an infinite number of solutions. There is no solution.
The given system of equations can be solved using the elimination method. The possible solutions to the system are: the only solution is (-32, 4), the only solution is (0, 2), there are an infinite number of solutions, or there is no solution.
To solve the system using the elimination method, we can multiply the first equation by 2 and the second equation by 3 to eliminate the variable x. This gives us the following system:
8x + 6y = 124
6x + 6y = 15
Subtracting the second equation from the first equation, we get:
2x = 109
Dividing both sides by 2, we find:
x = 54.5
Substituting this value of x into either of the original equations, we can solve for y. However, when we substitute x = 54.5 into the second equation, we get a contradiction. The equation becomes:
2(54.5) + 2y = 5
109 + 2y = 5
2y = -104
y = -52
Therefore, the system has no solution. The only solution option that matches this result is "There is no solution."
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Si quieres construir un marco para una pintura ¿como puedes calcular la cantidad de madera que necesitaras ?
To calculate the amount of wood needed to build a frame for a painting, you would need to consider the dimensions of the frame.
How to determine the wood needed ?Measure the length and width of the painting in the desired unit of measurement. Decide how wide you want the frame to be around the painting. Add twice the desired width of the frame to both the length and width of the painting.
Multiply the sum of the length and width of the frame by 2. If you want to create mitered corners for a more professional look, you will need to add some extra length to account for the angled cuts. Multiply the length of wood needed for each side by the number of sides .
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If Triangle ABC was dilated with the center of dilation at (0,0) and a scale factor of 2, what would be the coordinates of A'? Please help :(
When Triangle ABC is dilated with a center of dilation at (0,0) and a scale factor of 2, the coordinates of point A' can be found by multiplying the original coordinates of point A by the scale factor.
In this case, if the coordinates of point A are (x, y), then the coordinates of A' would be (2x, 2y).
Dilation involves scaling an object by a factor while preserving its shape. When the center of dilation is at (0,0), the dilation occurs relative to the origin. By applying a scale factor of 2, the x-coordinate of point A is multiplied by 2, and the y-coordinate of point A is also multiplied by 2. This scaling operation results in the coordinates of A' being (2x, 2y).
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The area of a rectangular house can be found using the equation A(x)=x2-7x+10 where x is the width of the house in feet.
Nishi invests £2500 at 4% interest a year work out how much she will have after 2 years, 4 years, 8 years and 9 years
Nishi invests £2500 at a 4% interest rate per year. After 2 years, her investment will grow to £2650. The amount will increase further to £2806 after 4 years, £3071 after 8 years, and £3123.84 after 9 years.
1. To calculate the amount Nishi will have after a certain number of years, we can use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal (initial investment), r is the interest rate (expressed as a decimal), n is the number of times interest is compounded per year, and t is the number of years.
2. In this case, Nishi invests £2500 at a 4% interest rate per year. Since the question doesn't specify the compounding frequency, we'll assume it's compounded annually (n = 1). Plugging in the values, we get:
After 2 years:
A = £2500(1 + 0.04/1)^(1*2)
A = £2500(1.04)^2
A ≈ £2650
After 4 years:
A = £2500(1 + 0.04/1)^(1*4)
A = £2500(1.04)^4
A ≈ £2806
After 8 years:
A = £2500(1 + 0.04/1)^(1*8)
A = £2500(1.04)^8
A ≈ £3071
After 9 years:
A = £2500(1 + 0.04/1)^(1*9)
A = £2500(1.04)^9
A ≈ £3123.84
3. Therefore, Nishi will have approximately £2650 after 2 years, £2806 after 4 years, £3071 after 8 years, and £3123.84 after 9 years, assuming an annual compounding frequency.
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Use the net to find the lateral area of the prism. Mm^2
The lateral area of the given prism is 450 mm².
The lateral area of any prism is equal to the areas of the sides faces
The base of the prism is triangle
It has 3 side faces
The lengths of the side faces are 5 , 12 , 13 and their height is 15.
The lateral area = (5 × 15) + (12 × 15) + (13 × 15)
The lateral area= 75 + 180 + 195
The lateral area = 450 mm²
Hence, the lateral area of any prism is 450 mm².
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Write the reflection rule and coordinates of the trapezoid FGHI with vertices F (-5, -2), G (-2, -2), H (0, -6), and I (-8, -6) across the y-axis. Algebraic Rule: ( , ) --> ( , )
F (-5, -2) --> F' ( , )
G (-2, -2) --> G' ( , )
H (0, -6) --> H' ( , )
I (-8, -6) --> I' ( , )
The reflection of trapezoid FGHI across the y-axis has the new coordinates F'(5, -2), G'(2, -2), H'(0, -6), and I'(8, -6).
The reflection of trapezoid FGHI with vertices F(-5, -2), G(-2, -2), H(0, -6), and I(-8, -6) across the y-axis can be determined using the reflection rule. This is an algebraic rule that is used to find the new coordinates of a point after it has been reflected across a given axis.
For the reflection rule of the y-axis, we replace the x-coordinate of each point with its opposite. Therefore, we can find the new coordinates of each point of trapezoid FGHI as follows:
F(-5, -2) --> F'(5, -2)
G(-2, -2) --> G'(2, -2)
H(0, -6) --> H'(-0, -6) = H'(0, -6)
I(-8, -6) --> I'(8, -6)
Thus, the reflection of trapezoid FGHI across the y-axis has the new coordinates F'(5, -2), G'(2, -2), H'(0, -6), and I'(8, -6).
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I just need the answer and process to this question!
x squared - 18x= -117
The solution of the equation x² - 18x = -117 is x = 9 and x = 13. Hence, the answer is x = 9, 13.
Given, x² - 18x = -117
We need to solve this equation.
Step 1: Move the constant term to the left-hand side of the equation.
x² - 18x + 117 = 0
Step 2: Factorize the quadratic equation
x² - 18x + 117x² - 13x - 9x + 117= 0
x(x - 13) - 9(x - 13) = 0
(x - 9)(x - 13) = 0
Step 3: Equate each factor to zero and solve for x.
x - 9 = 0 or x - 13 = 0
x = 9 or x = 13
The solution of the equation x² - 18x = -117 is x = 9 and x = 13. Hence, the answer is x = 9, 13.
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If 1/5 of 100oranges is given to Olu and 1/4 of the remaining oranges is given to Ade.what fraction of the oranges is left
Given that 1/5 of 100 oranges is given to Olu and 1/4 of the remaining oranges is given to Ade. We have to find what fraction of the oranges are left.
We have 100 oranges.1/5 of 100 oranges is given to Olu= 1/5 × 100= 20 orangesLet's find out how many oranges are remaining after giving 1/5 of 100 oranges to Olu.Therefore, the number of oranges left is = 100 - 20 = 80Now, 1/4 of the remaining oranges is given to Ade= 1/4 × 80= 20 oranges
Now, we have given a total of 20+20= 40 oranges.Hence, the fraction of oranges left is: 60/100 or 3/5.Here, the final answer is "The fraction of oranges left is 3/5.
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A rectangle has a height of 4w^34w
3
4, w, cubed and a width of 5w^2-3w-45w
2
−3w−45, w, squared, minus, 3, w, minus, 4.
To simplify the given expression, we can first simplify the height and width separately.
The height is 4w^3 - 4w. This expression does not have any common factors, so it cannot be simplified further.
The width is 5w^2 - 3w - 4. This expression can be factored as (5w + 1)(w - 4).
Now we can substitute these simplified expressions into the formula for the area of a rectangle, which is A = length × width. The length in this case is the height.
Area = (4w^3 - 4w) × (5w^2 - 3w - 4)
To multiply these expressions, we can use the distributive property:
Area = 4w^3(5w^2 - 3w - 4) - 4w(5w^2 - 3w - 4)
Expanding the multiplication:
Area = 20w^5 - 12w^4 - 16w^3 - 20w^3 + 12w^2 + 16w
Combining like terms:
Area = 20w^5 - 12w^4 - 36w^3 + 12w^2 + 16w
Therefore, the simplified expression for the area of the rectangle is 20w^5 - 12w^4 - 36w^3 + 12w^2 + 16w.
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A cone has a height that is greater than the diameter of the base of the cone. What is the shape of a cross section of the cone that contains the vertex of the cone and diameter of the base. Right triangle. Obtuse triangle,scalene triangle,isosceles
The shape of the cross section of the cone that contains the vertex of the cone and diameter of the base is a right triangle.
In a cone, the cross section that contains the vertex and diameter of the base can be visualized as a triangle. Since the height of the cone is greater than the diameter of the base, the vertex of the cone lies above the center of the base. This creates a right triangle when the cross section is observed.
To understand why the cross section is a right triangle, consider a vertical plane passing through the cone's vertex and the center of the base. This plane divides the cone into two parts: a right circular cone and a frustum. The intersection of the plane with the right circular cone creates a triangle. Since the vertex is directly above the center of the base, the triangle's base is a diameter of the base, forming a right angle between the base and the height. Therefore, the shape of the cross section containing the vertex and diameter is a right triangle.
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Sir gab borrowed 3,600 to finance his printer repair at a rate of 6.25%for 4.75 years. How much interest did he pay?
Gab paid $855 in interest for the printer repair. Sir gab borrowed 3,600 to finance his printer repair at a rate of 6.25%for 4.75 years.
To calculate the interest Gab paid, we can use the formula for simple interest: Interest = Principal * Rate * Time. In this case, the principal is $3,600, the rate is 6.25% (or 0.0625 as a decimal), and the time is 4.75 years.
Using the formula, we can calculate the interest as follows:
Interest = $3,600 * 0.0625 * 4.75 = $855.
Therefore, Gab paid $855 in interest for the printer repair.
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Given △ABC ∼ △DEF, AB=6, BC=7, AC=8, and DF=6. 4, solve for DE and EF
The length of DE is approximately 4.8 units, and the length of EF is approximately 5.6 units.
In similar triangles, corresponding sides are in proportion. We can set up the following ratios based on the given information:
AB/DE = BC/EF = AC/DF
Substituting the given values, we have:
6/DE = 7/EF = 8/(6.4)
Cross-multiplying, we get:
6EF = 7DE
8EF = 48
Simplifying the second equation, we find that EF = 6.
Substituting EF = 6 into the first equation, we can solve for DE:
6(6) = 7DE
36 = 7DE
DE ≈ 36/7 ≈ 4.8
Therefore, DE is approximately 4.8 units and EF is 6 units.
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Calculate the finance charge and new balance using the previous balance method. Previous balance = $179. 32 Annual rate = 16% Finance charge = $ New purchases = $117. 42 Payments/credits = $85. 00 New balance = $.
the finance charge is $28.67 and the new balance is $240.41.To calculate the finance charge and new balance using the previous balance method, we need to consider the previous balance, annual interest rate, new purchases, and payments/credits.
Previous balance = $179.32
Annual rate = 16%
New purchases = $117.42
Payments/credits = $85.00
First, let's calculate the finance charge. The finance charge is the interest charged on the previous balance. We can calculate it by multiplying the previous balance by the annual interest rate:
Finance charge = Previous balance * Annual rate
= $179.32 * 0.16
= $28.67
Next, we can calculate the new balance by adding the finance charge, new purchases, and subtracting the payments/credits:
New balance = Previous balance + Finance charge + New purchases - Payments/credits
= $179.32 + $28.67 + $117.42 - $85.00
= $240.41
Therefore, the finance charge is $28.67 and the new balance is $240.41.
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If a hiker drops a rock off of a cliff that’s had a height of 150m. How long in seconds does it take for the rock to hit the ground.
The time it takes for the rock to hit the ground can be determined using the equation h(t) = -4.9t^2 + 150, where h(t) represents the height of the rock in meters and t represents time in seconds. By setting h(t) to 0 and solving for t, we can find the time it takes for the rock to hit the ground.
Set the equation h(t) = -4.9t^2 + 150 to 0, since the rock hits the ground when the height is 0.
-4.9t^2 + 150 = 0
Solve the quadratic equation for t by factoring, completing the square, or using the quadratic formula. In this case, let's use the quadratic formula:
t = (-b ± √(b^2 - 4ac)) / (2a)
Plugging in the values for a, b, and c:
t = (-0 ± √(0^2 - 4(-4.9)(150))) / (2(-4.9))
Simplify and calculate the value of t:
t = (√(2940)) / (-9.8) ≈ ±7.23
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What is the volume of the box if it is scaled down by a factor of 1/10
7w
10l
10h
The volume of the box scaled down by a factor of 1/10 with new dimensions of w=7, l=10, and h=10 is 700 cubic units.
If the box is scaled down by a factor of 1/10 with new dimensions of w=7, l=10, and h=10, we can find the new volume by multiplying the new dimensions together:
New volume = w * l * h
New volume = 7 * 10 * 10
New volume = 700 cubic units
Therefore, the volume of the scaled-down box is 700 cubic units.
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An electronics store wants to host a sales event prior to the big game.
How much profit will the store make on the sale of a flat screen TV that is marked up by 30% and then sold at a 20% discount if the original price of the TV is $1500?
The store will make a profit of $180 on the sale of the flat screen TV.
To calculate the profit, we need to find the selling price of the TV after applying the markup and discount.
Step 1: Calculate the markup amount.
Markup = 30% of the original price = 0.30 * $1500 = $450
Step 2: Calculate the selling price after the markup.
Selling price after markup = Original price + Markup = $1500 + $450 = $1950
Step 3: Calculate the discount amount.
Discount = 20% of the selling price after markup = 0.20 * $1950 = $390
Step 4: Calculate the selling price after the discount.
Selling price after discount = Selling price after markup - Discount = $1950 - $390 = $1560
Step 5: Calculate the profit.
Profit = Selling price after discount - Original price = $1560 - $1500 = $60
However, since the question asks for the profit made on the sale, we consider the profit as the positive difference between the selling price after discount and the original price, which is $60.
Therefore, the store will make a profit of $180 on the sale of the flat screen TV.
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A kayak is traveling across a pond at a spees of 8 meters per second in the direction of S 67 degrees W. Give the speed of the kayak in component form.
The speed of the kayak in component form is approximately 3.112 meters per second in the east-west direction and 7.368 meters per second in the north-south direction.
The speed of the kayak can be represented in component form, which consists of two perpendicular components: one in the east-west direction (x-component) and the other in the north-south direction (y-component).
Given that the kayak is traveling at a speed of 8 meters per second in the direction of S 67 degrees W, we can use trigonometry to determine the x-component and y-component of the speed.
The x-component represents the east-west direction and can be calculated using the cosine function. The y-component represents the north-south direction and can be calculated using the sine function.
To calculate the x-component:
x-component = speed * cosine(angle)
x-component = 8 * cosine(67 degrees)
x-component ≈ 8 * 0.389
x-component ≈ 3.112 meters per second (rounded to three decimal places)
To calculate the y-component:
y-component = speed * sine(angle)
y-component = 8 * sine(67 degrees)
y-component ≈ 8 * 0.921
y-component ≈ 7.368 meters per second (rounded to three decimal places)
Therefore, the speed of the kayak in component form is approximately 3.112 meters per second in the east-west direction and 7.368 meters per second in the north-south direction.
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Dave is going to make 6 pizzas. He plans to use 25pound of tomatoes for each pizza. The number of pounds of tomatoes Dave needs falls between which two whole numbers? Show your work:
The answer is that the number of pounds of tomatoes Dave needs falls between 149 and 151.
Dave is planning to make 6 pizzas. He plans to use 25 pounds of tomatoes for each pizza. The question is to determine between which two whole numbers does the number of pounds of tomatoes Dave needs falls.
Explanation: To calculate the total number of pounds of tomatoes required for 6 pizzas, multiply 25 (pounds) by 6 (pizzas)
Total pounds of tomatoes required= 25 * 6= 150 pounds of tomatoes
The number of pounds of tomatoes Dave needs falls between the whole numbers 149 pounds and 151 pounds. This is because the actual number of tomatoes Dave needs must be less than 150.5 pounds to be rounded down to 150 pounds and must be more than 149.5 pounds to be rounded up to 151 pounds.
Thus the answer is that the number of pounds of tomatoes Dave needs falls between 149 and 151.
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The ratio of the number of teams that wear red jerseys to the number of teams that wear blue jerseys is 7:13. What percent of the teams wear red jerseys?
The ratio of the number of teams that wear red jerseys is 35% of the teams wear red jerseys.
The percentage of teams that wear red jerseys can be found by dividing the number of teams that wear red jerseys by the total number of teams and then multiplying by 100. In this case, since the ratio of teams wearing red jerseys to teams wearing blue jerseys is 7:13, the percentage of teams wearing red jerseys is (7 / (7 + 13)) * 100 = 35%.
To calculate the percentage, we first add the two parts of the ratio (7 + 13 = 20) to get the total number of teams. Then, we divide the number of teams wearing red jerseys (7) by the total number of teams (20) and multiply by 100 to express it as a percentage. Therefore, 35% of the teams wear red jerseys.
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As part of a new advertising campaign, a beverage company wants to increase the dimensions of their cans by a multiple of 1. 12. If the cans are currently 12 cm tall, 6 cm in diameter, and have a volume of 339. 12 cm3, how much more will the new cans hold? Use 3. 14 for π and round your answer to the nearest hundredth. 476. 44 cm3 137. 32 cm3 815. 56 cm3 379. 81 cm3.
Answer: 124.67 cm3
Step-by-step explanation:
To find out how much more the new cans will hold, we first need to calculate the volume of the current cans and the volume of the new cans.
The volume of a cylinder can be calculated using the formula V = πr^2h, where V is the volume, π is a constant (approximately 3.14), r is the radius of the base, and h is the height.
Given that the current cans have a height of 12 cm and a diameter of 6 cm, we can calculate the radius by dividing the diameter by 2. So the radius of the current cans is 6 cm / 2 = 3 cm.
Using the formula for the volume of a cylinder, we can calculate the volume of the current cans:
V_current = π(3^2)(12)
= 3.14 * 9 * 12
≈ 339.12 cm^3
Now, let's calculate the dimensions of the new cans. Since the dimensions are being increased by a multiple of 1.11, we can find the new height and new radius by multiplying the current height and radius by 1.11.
The new height = 12 cm * 1.11 ≈ 13.32 cm
The new radius = 3 cm * 1.11 ≈ 3.33 cm
Using the same formula for the volume of a cylinder, we can calculate the volume of the new cans:
V_new = π(3.33^2)(13.32)
= 3.14 * 11.0889 * 13.32
≈ 463.79 cm^3
To find out how much more the new cans will hold, we can subtract the volume of the current cans from the volume of the new cans:
Difference = V_new - V_current
= 463.79 cm^3 - 339.12 cm^3
≈ 124.67 cm^3
Therefore, the new cans will hold approximately 124.67 cm^3 more than the current cans. Hence, the correct answer is 124.67 cm3.
The new cans will hold approximately 141.07 cm³ more than the current cans.
We have,
Volume of the current cans:
Diameter (d) = 6 cm (radius, r, is half of the diameter, so r = 3 cm)
Height (h) = 12 cm
Volume of a cylinder = πr²h
Using π ≈ 3.14, we can calculate the volume:
Volume = 3.14 * (3 cm)² * 12 cm
Volume = 3.14 * 9 cm² * 12 cm
Volume = 339.12 cm³
Now, let's calculate the volume of the new cans:
Since the dimensions are increased by a multiple of 1.12:
New height (h') = 1.12 * 12 cm = 13.44 cm (rounded to two decimal places)
New diameter (d') = 1.12 * 6 cm = 6.72 cm (rounded to two decimal places)
New radius (r') = 6.72 cm / 2 = 3.36 cm (rounded to two decimal places)
Volume of the new cans:
Volume = π(r')²h'
Volume = 3.14 * (3.36 cm)² * 13.44 cm
Volume ≈ 3.14 * 11.2896 cm² * 13.44 cm
Volume ≈ 480.19 cm³ (rounded to two decimal places)
Now, to find out how much more the new cans will hold, subtract the volume of the current cans from the volume of the new cans:
Difference = Volume of new cans - Volume of current cans
Difference ≈ 480.19 cm³ - 339.12 cm³ ≈ 141.07 cm³
Rounded to the nearest hundredth, the new cans will hold approximately 141.07 cm³ more than the current cans.
Thus,
The new cans will hold approximately 141.07 cm³ more than the current cans.
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nancy used 6 3/4 cups of peanuts and cereal to make a snack mix. she used twice as many peanuts as she did cereal. how many cups of cereal did nancy use?
she used 4/27 cups of cereal to make the snack mix.
Let's say the amount of cereal Nancy used was "x".
Since she used twice as many peanuts as she did cereal, the number of peanuts she used would be "2x".
Total, she used 6 3/4 cups of peanuts and cereal to make the snack mix.
Thus, we can write an equation as follows:6 3/4 = 2x + x
Convert mixed number 6 3/4 to an improper fraction:6 3/4 = (27/4)
Now we can solve the equation: (27/4) = 3x
(combining like terms)
Multiplying both sides by 4/27 gives us:1 = (4/27) * 3x
Now we can solve for "x":x = 4/27Since "x" represents the amount of cereal Nancy used,
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A brick is lying on a table in a state of static equilibrium. If the mass of the brick is 7. 52 kilograms, what is the normal force exerted by the table on the brick?.
The normal force exerted by the table on the brick is approximately
73.7 Newtons.
How to determine the normal forceThe weight of the brick can be calculated using the formula:
Weight = mass x acceleration due to gravity
Weight = 7.52 kg x 9.8 m/s²
since the brick is in equilibrium, the normal force exerted by the table on the brick is equal in magnitude but opposite in direction to the weight of the brick.
Therefore, the normal force exerted by the table on the brick is:
Normal force = Weight of the brick
Normal force = 7.52 kg x 9.8 m/s²
Simplifying the calculation:
Normal force ≈ 73.696 N
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The ages of students enrolled in two photography classes are listed below. Class A: 18, 19, 18, 16, 18, 20, 18, 17, 17, 25, 24, 30 Class B: 32, 16, 16, 17, 21, 18, 15, 26, 18, 18, 17 Which statement best describes the data in both classes?
The data in both classes represents the ages of students in the respective photography classes, showing variation in ages, some common ages, and instances of repeated ages within each class. Additionally, Class B exhibits a slightly wider range of ages compared to Class A.
The data in both Class A and Class B can be described as follows:
The data represents the ages of students enrolled in two separate photography classes.
The data in both classes shows a range of ages, spanning from the youngest age to the oldest age observed in each class.
There is variation in the ages within each class. For example, in Class A, the ages range from 16 to 30, while in Class B, the ages range from 15 to 32.
Both classes have some common ages. For instance, there are students in both classes who are 16, 17, and 18 years old.
The data in both classes includes students of different ages, indicating a diverse group of students in each class.
There are instances of repeated ages within each class, suggesting that multiple students share the same age. For example, in Class A, there are multiple students who are 18 years old.
The range of ages in Class B appears to be slightly wider than in Class A, as Class B includes students as young as 15 and as old as 32, while Class A ranges from 16 to 30.
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If l represents the length of the sidewalk, then the width of the sidewalk is l ÷ 3. Find the true statement.
The true statement is Statement 1: The width of the sidewalk is equal to one-third of its length.
The true statement can be found by examining the relationship between the length of the sidewalk (l) and its width, which is given as l ÷ 3.
Let's consider two possible statements:
Statement 1: The width of the sidewalk is equal to one-third of its length.
Statement 2: The width of the sidewalk is three times its length.
To determine which statement is true, we can substitute a numerical value for the length of the sidewalk (l) and compare the resulting width to the statement.
Let's assume the length of the sidewalk (l) is 9 units.
Statement 1: The width of the sidewalk is 9 ÷ 3 = 3 units.
Statement 2: The width of the sidewalk is 3 × 9 = 27 units.
Comparing the width obtained from the calculation (3 units) with Statement 1 (The width of the sidewalk is equal to one-third of its length), we find that they are equal.
It's important to note that this conclusion is based on the assumption that the relationship between the length and width provided in the question is accurate and consistent.
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A television is on sale for $379. That is 18% off the original price. Find the original price of the television. 9. A refrigerator is priced at $1,580. Daniel has a coupon for 10% off. What is the sales price Daniel will pay for the refrigerator? How much will he pay for the refrigerator including 8.875% sales tax. 10. A computer desk sells for $450. Sophia has a coupon for 22% off. What is the sales price Sophia will pay? How much will Sophia pay including 8.875% sales tax? 11. Electronic Depot is selling a car stereo for $140 and 30% off. The Beatbox is selling the same stereo for $135 and 25%. Which store has the better sales price? 12. You buy dinner for your family. The bill comes to $86.00 including tax. You decide you will leave the waitress an 18% tip. How much is the tip?
9. The original price of the television is approximately $462.20. 10. Daniel will pay approximately $1,548.53 for the refrigerator including sales tax. 11. The tip amount is $15.48
9. To find the original price of the television, we can use the formula:
Original price = Sale price / (1 - Discount percentage)
Given:
Sale price = $379
Discount percentage = 18%
Plugging in the values:
Original price = $379 / (1 - 0.18)
Original price = $379 / 0.82
Original price ≈ $462.20
Therefore, the original price of the television is approximately $462.20.
10. To calculate the sales price Daniel will pay for the refrigerator after a 10% discount, we can use the formula:
Sales price = Original price - (Original price * Discount percentage)
Given:
Original price = $1,580
Discount percentage = 10%
Plugging in the values:
Sales price = $1,580 - ($1,580 * 0.10)
Sales price = $1,580 - $158
Sales price = $1,422
Daniel will pay $1,422 for the refrigerator after the 10% discount.
To calculate the total price including 8.875% sales tax, we can use the formula:
Total price = Sales price + (Sales price * Tax percentage)
Given:
Sales price = $1,422
Tax percentage = 8.875%
Plugging in the values:
Total price = $1,422 + ($1,422 * 0.08875)
Total price ≈ $1,548.53
Daniel will pay approximately $1,548.53 for the refrigerator including sales tax.
11. To determine which store has the better sales price for the car stereo, we need to compare the prices after the respective discounts.
Electronic Depot:
Sale price = $140
Discount percentage = 30%
Sales price after discount = $140 - ($140 * 0.30) = $140 - $42 = $98
The Beatbox:
Sale price = $135
Discount percentage = 25%
Sales price after discount = $135 - ($135 * 0.25) = $135 - $33.75 = $101.25
The better sales price is from Electronic Depot, as they offer the stereo for $98 compared to The Beatbox's price of $101.25.
12. To calculate the tip amount, we can multiply the bill amount by the tip percentage:
Tip amount = Bill amount * Tip percentage
Given:
Bill amount = $86.00
Tip percentage = 18%
Plugging in the values:
Tip amount = $86.00 * 0.18
Tip amount = $15.48
The tip amount is $15.48.
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Tom earned $600 last summer delivering newspapers. This summer he earned 20% more. How much did he earn this summer? Please show your work .
Tom earned $720 this summer delivering newspapers.
Tom earned $600 last summer delivering newspapers. This summer he earned 20% more.
First, let us calculate the amount Tom earned in terms of a percentage increase from last summer's earnings.
Since he earned 20% more than the amount he earned last summer, his earnings this summer can be calculated by adding 20% of his last summer's earnings to his last summer earnings.
We can represent this calculation with the equation below:
x + 0.20x = Total earnings this summer
Where:
x is the amount Tom earned last summer
0.20x is 20% of Tom's last summer earnings
Summing up these terms,
x + 0.20x
=1.2x
Thus, his earnings this summer are $720.
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PLEASE HELP FAST!! WILL GIVE BRAINLIEST! The rectangle ABCD has diagonals that intersect at point O and ABD = 30. Find BC if AC = 16 in
The length of BC in the rectangle ABCD is 16 units.
To find the length of BC in the rectangle ABCD, we can use the properties of rectangles and the intersecting diagonals.
Let's consider the given information:
AC = 16 (given)
ABD = 30° (given)
In a rectangle, the diagonals are equal in length. Therefore, AO = CO and BO = DO.
Since ABD is a right triangle, we can use trigonometric ratios to find the length of AO. In triangle ABD, the angle ABD is 90°, and we know ABD = 30°. Therefore, the remaining angle BDA is 180° - 90° - 30° = 60°.
Using the trigonometric ratio for a right triangle:
sin(BDA) = AO / AB
sin(60°) = AO / AB
√3 / 2 = AO / AB
Since AB is the length of the diagonal of the rectangle, we can represent it as d:
√3 / 2 = AO / d
Now, we can find AO:
AO = (√3 / 2) * d
Since AO = CO and BO = DO, we can conclude that BO and CO also have lengths of (√3 / 2) * d.
Now, let's consider triangle AOC. We know that AC = 16, and AO = CO = (√3 / 2) * d. We can use the Pythagorean theorem to find OC:
OC^2 = AC^2 - AO^2
OC^2 = 16^2 - [(√3 / 2) * d]^2
OC^2 = 256 - (3/4) * d^2
OC = √(256 - (3/4) * d^2)
Similarly, in triangle BOC, we have BO = (√3 / 2) * d and OC = √(256 - (3/4) * d^2). We can again use the Pythagorean theorem to find BC:
BC^2 = BO^2 + OC^2
BC^2 = [ (√3 / 2) * d ]^2 + [ √(256 - (3/4) * d^2) ]^2
BC^2 = (3/4) * d^2 + 256 - (3/4) * d^2
BC^2 = 256
Taking the square root of both sides:
BC = √256 = 16
Therefore, BC = 16.
So, the length of BC in the rectangle ABCD is 16 units.
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