The student needs to apply the formula for the volume of a pyramid, V = 1/3 * a² * h. Since the height is 3 cm less than the side length, this introduces a variable in the equation, (x - 3), to solve for x.
Explanation:The question relates to pyramid volume and the formulation of mathematical equations. First, it requires understanding that the volume of a pyramid is derived using the formula V = 1/3 * a² * h, where V is the volume, a is the length of the side of the square base, and h is the height of the pyramid. Since the height is stated as 3 cm less than the base (x), we can interpret this in the formula as h = x - 3.
Replacing these values in the volume formula gives us V = 1/3 * x² * (x-3). As the volume given is 162 cubic centimeters, this forms the equation: 162 = 1/3 * x² * (x-3). Simplifying this equation would provide the base length x in cm.
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Guys please help me please...
Phineas is the lead research scientist in a lab and responsible for ordering supplies and equipment. The lab is out of petri dishes, so Phineas orders 185 of them. The lab uses 12 petri dishes each day.
Answer:
The relationship is between the days that have gone by and the number of petri dishes. The point (0, 185) means that if 0 days have gone by there are 185 petri dishes. The number of petri dishes decreases by 12 each day, so the slope is –12. Use the slope-intercept form to write the equation y = –12x + 185.
Thats the actual answer from edge
It costs Marie $25 overhead and then an additional $1.25 to make each barrette. She charges $3.50 for each one. Write a function to model Marie's profit?
Given is the Overhead charges = 25 dollars.
Making charge of each barrette = 1.25 dollars.
Let's assume the number of barrette that she makes = x
So the Cost function would be, C(x) = 1.25x + 25.
She sell each piece for 3.50 dollars.
So the Revenue function would be, R(x) = 3.50x
We know the Profit function is given by the difference of Revenue function and Cost function.
Profit function = Revenue function - Cost function
P(x) = R(x) - C(x)
P(x) = 3.50x - (1.25x + 25)
P(x) = 3.50x - 1.25x - 25
P(x) = 2.25x - 25
Hence, Marie's Profit would be P(x) = 2.25x - 25.
The number of right-handed students in a math class is nine times the number of left-handed students. The total number of students in the class is 30. How many left-handed students are in the class?
The number of left-handed students in the class is 3.
Explanation:The problem involves understanding and solving a simple algebraic equation. From the problem, we know that the number of right-handed students is nine times the number of left-handed students. We can use 'x' to represent the number of left-handed students, meaning 9x represents the number of right-handed students. The total number of students is given as 30.
So, we set up the equation: x + 9x = 30. Simplifying this gives 10x = 30. Solving for 'x', we find x = 3. So, there are 3 left-handed students in the class.
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Ty borrowed $500 from his parents.The graph shows how much he owes them each month if he pays back a certain amount each amount each month. How long will it take Ty to pay back his parents?
Joey has 8 pairs of socks in his drawer 5 of them are white. what percent of colored socks does Joey have
How is a ratio table used to graph equivalent ratios?? Best Answer Will Be Rewarded As Brainliest!
A ratio table organizes equivalent ratios, aiding in systematic plotting of points to graphically represent the relationships between different quantities.
A ratio table is a useful tool in graphing equivalent ratios by providing a systematic and organized way to identify corresponding pairs of values. To use a ratio table for graphing equivalent ratios, follow these steps:
Identify the Original Ratio:
Start with the given ratio or pair of values. For example, if the original ratio is 2:3, write this pair in the first row of the ratio table.
Generate Equivalent Ratios:
Expand the ratio by multiplying or dividing both parts by the same factor. For instance, if you multiply both parts of the original ratio by 2, you get an equivalent ratio of 4:6. Record these equivalent ratios in subsequent rows of the table.
Create an Ordered Pair:
Pair each value from the ratio table to create ordered pairs. For the ratio 2:3, the pairs would be (1, 1.5), (2, 3), (3, 4.5), and so on.
Plot the Points:
Use the ordered pairs to plot points on a coordinate plane. Each point represents a pair of equivalent values.
Connect the Points:
Draw a line or curve that passes through all the plotted points. This line represents the graph of the equivalent ratios.
By systematically generating equivalent ratios and plotting the corresponding points, a ratio table facilitates the visualization of patterns and relationships, helping in the creation of a coherent graph.
A ratio table is used to graph equivalent ratios by listing pairs of numbers that maintain the same product and graphing those pairs as points on a coordinate graph. These points should line up to form a straight line, indicating equivalent ratios. Understanding the reciprocal of the numbers is key in constructing a clear and accurate graph.
Explanation:How to Use a Ratio Table to Graph Equivalent Ratios
A ratio table is a tool that helps us understand the relationship between quantities. It is particularly useful for visualizing equivalent ratios and can be used to graph these ratios. When you use a ratio table, you list pairs of numbers that form equivalent ratios. By selecting values that multiply to a constant number, such as 10, you ensure that the ratios are equivalent.
For instance, if the ratio is 2:5, we know that any other pair of numbers that multiplies to 10 (like 4:2.5, 1:5, or 5:2) will be equivalent to this ratio. Once you have a set of equivalent ratios, you can graph them by plotting the pairs of numbers as points on a coordinate graph. The resulting points should form a straight line, which represents the constant relationship between the two quantities.
To effectively use a ratio table and subsequently graph equivalent ratios, it is important to understand the concept of the reciprocal and how it relates to the ratios. For example, the reciprocal of 8 is thought of as '1.25-like', which means it shares a fundamental relationship (125) despite the actual placement of the decimal point. This approach aids in easily identifying the patterns in the ratios and transferring them to a graph.
Bar graphs are also a vital tool in comparing quantities across different categories. By employing bar graphs, you can visually compare the relationships between different sets of data, such as population sizes or the number of students falling into different categories. Effective use of colors, legibility, and orderly display are essential features to ensure clarity in bar graphs.
The density of gold is 19.32 grams per cubic centimeters. Jimmy Jackson built a pyramid made out of pure gold about 2.13 meters tall with a mass of 298.7 kilograms. If the base of the pyramid is a square, what are the dimensions of the base of the pyramid?
Final answer:
By calculating the volume of the gold pyramid using the given mass and density of gold, and then applying the volume of a pyramid formula, we find that the dimensions of the square base are approximately 14.75 cm by 14.75 cm.
Explanation:
To find the dimensions of the base of the pyramid made out of pure gold, we need to calculate the volume of the gold pyramid using the known mass and density of gold then use that volume to find the base area and, consequently, the dimensions of the base.
The density (d) of gold is given as 19.32 g/cm³, and the mass (m) of the pyramid is 298.7 kg. First, we convert the mass from kilograms to grams (since the density is in grams per cubic centimeter):
m = 298.7 kg * 1000 g/kg = 298700 g
Next, we use the formula for density d = m/V to find the volume (V) of the gold pyramid. Rearranging the formula to solve for V gives:
V = m/d
V = 298700 g / 19.32 g/cm³
V ≈ 15461.8 cm³
Since the base of the pyramid is a square and the pyramid is 2.13 meters tall, we can use the volume of a pyramid formula V = (1/3) * base area * height to find the base area. We first convert the height from meters to centimeters:
height = 2.13 m * 100 cm/m = 213 cm
Now applying the pyramid volume formula and solving for the base area, we have:
base area = 3V / height
base area = 3 * 15461.8 cm³ / 213 cm
base area ≈ 218.2 cm²
To find the dimensions of the square base, we take the square root of the base area:
side length = √(base area) ≈ √(218.2 cm²) ≈ 14.75 cm
Therefore, the dimensions of the base of the gold pyramid are approximately 14.75 cm by 14.75 cm.
there are 8 rows of chairs in the auditorium.three of the rows are empty. what fraction of the rows are empty?
Please I need help with questions 2-4 and it’s very hard and I’m struggling with it and if you need to see the picture big then click on it and it will be big
Convert the ratio of sheep to pigs below to the ratio of the pigs to total animals (sheep and pigs) 5:9
Answer:
The ratio of pigs to total animals is 9:14 or 9/14.
Step-by-step explanation:
Given that the total number of sheep = 5
The total number of pigs = 9
From that, the given ration of sheep to pigs is 5:9
Now, the total number of animals = no. of pigs + no. of sheep = 5+9 = 14.
So, to express the ratio of pigs to the total number of animals =
no. of pigs: total no. of animals = 9:14.
Therefore, the ratio of pigs to the total number of animals is 9:14.
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Write 30/80 as a percent
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Mr shen likes for his homework assignment to have 2 addition problems for every 3 subtraction problems
Answer:
Options B, C and D are correct choices.
Step-by-step explanation:
Please consider the complete question.
Mr. Shen likes for his homework assignments to have 2 addition problems for every 3 subtraction problems.
Which of the following homework assignments could
Mr. Shen create?
Choose 3 answers:
A. 3 addition problems and 4 subtraction problems .
B. 6 addition problems and 9 subtraction problems .
C. 16 addition problems and 24 subtraction problems.
D. 8 addition problems and 12 subtraction problems.
E. 15 addition problems and 10 subtraction problems.
To solve our given problem, we need to find the number that have same ratio.
Let us compare each ratio.
A. [tex]\frac{3}{2}\neq \frac{4}{3}[/tex]
Since the ratio of corresponding numbers is not same, therefore, option A is incorrect.
B. [tex]\frac{6}{2}=\frac{9}{3}[/tex]
[tex]3=3[/tex]
Since the ratio of corresponding numbers is same, therefore, option B is the correct choice.
C. [tex]\frac{16}{2}=\frac{24}{3}[/tex]
[tex]8=8[/tex]
Since the ratio of corresponding numbers is same, therefore, option C is the correct choice.
D. [tex]\frac{8}{2}=\frac{12}{3}[/tex]
[tex]4=4[/tex]
Since the ratio of corresponding numbers is same, therefore, option D is the correct choice.
E. [tex]\frac{15}{2}\neq \frac{10}{3}[/tex]
Since the ratio of corresponding numbers is not same, therefore, option E is incorrect.
what is 3^4
a.9
b.81
c.43
b.27
sarah is training for a bike race. she rides her bike 5 3/4 miles in 1/3 hour. what is sarahs's rate in miles per hour?
Cam is going to roll a fair 6-sided die 2,400 times. What is the best prediction for the number of times that cam will roll the number 4?
Answer:
Close to 400 times not exactly 400.
Polygon ABCDE is the result of a reflection of polygon LMNOP over the line. Which line segment in the image corresponds to OP¯¯¯¯¯ in the pre-image?
EA¯¯¯¯¯
DE¯¯¯¯¯
BC¯¯¯¯¯
CD¯¯¯¯¯
AB¯¯¯¯¯
Answer: [tex]\overline{DE}[/tex]
Step-by-step explanation:
Given: Polygon ABCDE is the result of a reflection of polygon LMNOP over the line.
Since reflection preserves the size of the figure and maps a congruent image .
Therefore, polygon ABCDE is congruent to polygon LMNOP
Also, we know that if two polygons are congruent then their corresponding sides are equal.
Then, LM=AB
MN=BC
NO=CD
OP=DE
AE=LP
So , the line segment in the image corresponds to [tex]\overline{OP}[/tex]in the pre-image is [tex]\overline{DE}[/tex]. [Last two letters of the name of polygons]
Answer:
(B) DE
Step-by-step explanation:
Given: Polygon ABCDE is the result of a reflection of polygon LMNOP over the line.
To find: A line segment in the image corresponds to OP in the pre-image.
Solution: It is given that Polygon ABCDE is the result of a reflection of polygon LMNOP over the line.
Also, we know that reflection maps a congruent image, therefore polygon ABCDE is congruent to polygon LMNOP.
And, if two polygons are congruent then their corresponding sides are congruent, thus
LM=AB
MN=BC
NO=CD
OP=DE
AE=LP
Hence, the line segment in the image corresponds to [tex]\overline{OP}[/tex] in the pre-image is [tex]\overline{DE}[/tex].
Therefore, option B is correct.
Three ballet dancers are positioned on stage. Shereen is straight behind Haley and directly left of Eric. If Haley and Shereen are 4 feet apart, and Eric and Haley are 7 feet apart, what is the distance between Shereen and Eric? If necessary, round to the nearest tenth.
The distance between Shereen and Eric is approximately 8.0623 feet.
Explanation:To find the distance between Shereen and Eric, we can use the information given in the question. Since Haley and Shereen are 4 feet apart, and Eric and Haley are 7 feet apart, we can calculate the distance between Shereen and Eric using the Pythagorean theorem. Let's label the distance between Shereen and Eric as 'x'. Based on the information, we have a right triangle with one leg of 4 feet and the other leg of 7 feet. Using the Pythagorean theorem, we can calculate the hypotenuse, which is the distance between Shereen and Eric: x^2 = 4^2 + 7^2. Solving for 'x', we find that the distance between Shereen and Eric is approximately 8.0623 feet.
The distance between Shereen and Eric is 3 feet.
Explanation:To find the distance between Shereen and Eric, we can use the given information about the distances between the dancers. Let's assume the distance between Shereen and Eric is 'd' feet. Since Haley and Shereen are 4 feet apart and Eric and Haley are 7 feet apart, we can set up the following equations:
Haley - Shereen = 4Haley - Eric = 7To solve these equations, we can use substitution. Rearrange the first equation to isolate Haley: Haley = Shereen + 4. Substitute this expression for Haley in the second equation: Shereen + 4 - Eric = 7. Simplify the equation:
Shereen - Eric = 3.
So, Shereen and Eric are 3 feet apart.
Denise and Stacey went to a carnival. The admission fee was $6 per person. Each ride at the carnival costs c dollars. The game booths charged g dollars for each game. Both Denise and Stacey went on 7 rides each. Stacey played 3 games, while Denise played 2 games. Which expression represents the total amount of money that Denise and Stacey spent at the carnival
The correct answer is Option D. [tex]14c+5g+12[/tex]. The expression [tex]14c+5g+12[/tex], which represents the total amount of money that Denise and Stacey spent at the carnival.
To calculate the total amount of money Denise and Stacey spent at the carnival, we need to consider the admission fee, the cost of rides, and the cost of games for both of them.
Admission Fee: Since both Denise and Stacey went to the carnival, we need to include the admission fee for each of them. The admission fee per person is $[tex]6[/tex]. So, for both Denise and Stacey, the total admission fee is [tex]2*6=12[/tex] dollars.
Rides: Both Denise and Stacey went on [tex]7[/tex] rides each. Since the cost of each ride is c dollars, the total cost for rides for each of them is [tex]7c[/tex]. So, for both Denise and Stacey, the total cost for rides is [tex]2*7c=14c[/tex] dollars.
Games: Stacey played [tex]3[/tex] games, and Denise played [tex]2[/tex] games. The cost of each game is g dollars. So, the total cost for games for Stacey is [tex]3g[/tex] dollars, and for Denise, it's [tex]2g[/tex] dollars.
Putting it all together, the expression representing the total amount of money that Denise and Stacey spent at the carnival is:
Combining these costs, we get [tex]14c+5g+12[/tex], which represents the total amount of money that Denise and Stacey spent at the carnival.
COMPLETE QUESTION:
Denise and Stacey went to a carnival. The admission fee was $[tex]6[/tex] per person. Each ride at the carnival costs c dollars. The game booths charged g dollars for each game. Both Denise and Stacey went on [tex]7[/tex] rides each. Stacey played [tex]3[/tex] games, while Denise played [tex]2[/tex] games. Which expression represents the total amount of money that Denise and Stacey spent at the carnival?
A. [tex]7c+5g+6[/tex]
B. [tex]7c+5g+12[/tex]
C. [tex]14c+5g+6[/tex]
D. [tex]14c+5g+12[/tex]
A table shaped like a solid cube needs to painted. All six faces of the table must be painted. The edge length of the table is 1.2 m. What is the total surface area that will be painted? Drag and drop the correct answer into the box. 7.21.7288.645.76 m²
Answer:
8.64 is the answer. I put 7.2 and got it wrong. :)
8.64
Step-by-step explanation:
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Final answer:
Since the area of one side is 1.44 m², the total surface area is 8.64 m².
Explanation:
To find the total surface area that will be painted on a cube-shaped table with an edge length of 1.2 m, we use the formula for the surface area of a cube, which is 6 times the area of one side.
Calculating the area of one side (1.2 m × 1.2 m) gives us 1.44 m². Multiplying this by 6 (6 × 1.44 m²) gives the total surface area which is 8.64 m². Therefore, the correct answer to drag and drop into the box is 8.64 m².
Which of the fraction below is equivalent to 1/3? Show why that fraction is equivalent to 1/3. 4/5, 4/6, 4/9, 4/12
To determine which fraction is equivalent to 1/3, we can compare each fraction to 1/3 and simplify if necessary. The fraction that is equivalent to 1/3 is 4/12.
Explanation:To determine which fraction is equivalent to 1/3, we can compare each fraction to 1/3 and simplify if necessary. Let's go through each option:
4/5: This fraction is not equivalent to 1/3 because 4/5 is greater than 1/3.4/6: To simplify this fraction, we can divide both the numerator and denominator by their greatest common factor, which is 2.Therefore, the fraction that is equivalent to 1/3 is 4/12.
Aubrey is painting a mural of an ocean scene. The triangular sail on a sailboat has a base of 4 feet and a height of 6 feet. Aubrey will paint the sail using a special white paint. A can of this paint covers 10 square feet. How many cans of white paint will Aubrey need?
Final answer:
Aubrey requires 2 cans of white paint to cover the triangular sail with an area of 12 square feet, given that one can covers 10 square feet.
Explanation:
Aubrey is painting a triangular sail as part of a mural with a base of 4 feet and a height of 6 feet. To calculate the area of the triangle, the formula is 1/2 × base × height. Thus, the area is 1/2 × 4 × 6, which equals 12 square feet. One can of special white paint covers 10 square feet. Therefore, Aubrey will need to use 2 cans of paint to cover the entire sail, since you can't purchase a fraction of a can.
1. Could the number 0000 appear in a table of random digits? How likely is this?
Yes,
probability = favorable outcomes/ total outcomes
to calculate the probability for this to occur, we use nCr ( nCr = n!/r!)
there are total 10 digits
so probability of the number 0000 appear in a table of random digits=
(1*1*1*1)/(10C1 * 10C1 * 10C1 * 10C1)
= 1/10000
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Lisa built a rectangular flower garden that is 4 feet wide and has a perimeter of 26 feet. what is the length of Lisa's flower garden?
janet lit a 12-inch candle. she noticed that it was getting an inch shorter every 30 minutes in how many hours will the candle burn out support your answer with a reason
Two complementary angles have the measurements of 2x + 8 and 3x - 13. What is the value of x?
from the top of a lighthouse 210 feet high, the angle created by the line of sight to a boat is 27°. find the distance of the boat to the light house.
what is 5cm × 8cm × 10cm