To find the radius of the sphere formed by melting five metal cubes with 7 cm sides, calculate the combined volume of the cubes and equate it to the volume of the sphere; then solve for the radius, which is approximately 7.24 cm.
To find the radius of the sphere formed by melting five metal cubes, we need to equate the total volume of the cubes to the volume of the sphere. The volume of a cube with a side length of 7 cm is found by the formula V = s³, where s is the side length of the cube. For one cube, this is V = 7 cm x 7 cm x 7 cm = 343 cm³. Since there are five cubes, the total volume is 5 x 343 cm³ = 1715 cm³.
The volume of a sphere is given by the formula V = 4/3 * π * r³, where r is the radius of the sphere. We must solve for r when the volume is 1715 cm³. Setting the volumes equal gives 4/3 * π * r³ = 1715 cm³. Solving for r yields:
r³ = (1715 cm³) / (4/3 * π)
r = (1715 cm³) / (4.14159)^√(1/3)
r ≈ 7.24 cm
Therefore, the radius of the sphere is approximately 7.24 cm.
A bag contains 40 tickets, each numbered between 1-40. If a ticket is drawn at random, find the probability of it being odd or less than 26
Answer:
you have a 50% chance of getting an odd number and a 60% chance of getting a number less than 26.
Step-by-step explanation:
Between 1 and 40 there are 20 odd numbers
20÷ 40 x 100=50, This means you have a 50% (20:20) chance of getting an odd number.
Between 1 and 40 there 25 numbers less than 26
15÷25 x 100=60, This means you have a 60% (25:15) chance of getting a number under 26.
Final answer:
The probability of drawing an odd ticket or a ticket numbered less than 26 from a bag containing 40 numbered tickets is 4/5 or 0.8, meaning there is an 80% chance to draw such a ticket.
Explanation:
To find the probability of drawing an odd ticket or a ticket numbered less than 26 from a bag containing tickets numbered 1-40, we need to consider the total number of favorable outcomes for each separate event and be careful not to double-count any outcomes that satisfy both conditions.
Firstly, there are 20 odd numbered tickets (1, 3, 5, ..., 39) which satisfy the first condition. For the second condition, there are 25 tickets that are numbered less than 26 (1, 2, 3, ..., 25).
However, half of the tickets less than 26 are odd (1, 3, 5, ..., 25), which we've already counted. So, we should only add the even numbered tickets that are less than 26 to get the total number of favorable outcomes. There are 12 even numbered tickets less than 26 (2, 4, 6, ..., 24).
Adding the odd numbered tickets (20) to the unique even numbered tickets less than 26 (12), we get a total of 32 favorable outcomes.
Since there are 40 tickets in total, the probability of drawing a ticket that is either odd or less than 26 is 32/40.
To simplify, divide both numerator and denominator by their greatest common divisor which is 8, giving us 4/5 or 0.8, which means there's an 80% chance of drawing a ticket that meets the criteria.
Which is equivalent to (3/125)*?
answer : a 1251/3x
Answer:
1/50
Step-by-step explanation:
Which expression is equivalent to 8g+2+4g-2-2g
Answer:
10g
Step-by-step explanation:
add 8g,4g and -2g to get 10g
add 2 and -2 to receive 0
the simplified expression would be 10g
The equivalent expression for 8g + 2 + 4g - 2 -2g after combining like terms is 10g.
The original expression given is 8g + 2 + 4g - 2 -2g. To find an equivalent expression, we need to combine like terms. We do this by adding or subtracting the coefficients of identical variables and also combining any constant terms.
In this case, we combine the coefficients of g:
8g + 4g - 2g = (8 + 4 - 2)g = 10g.
Next, we combine the constant terms: 2 - 2 = 0. Since adding or subtracting 0 does not change the value, we can ignore this part.
Thus, the equivalent expression is simply 10g.
What is 1/4y+3/4(y-8)
Answer: y-6
Step-by-step explanation:
1/4y+3/4(y-8)
1/4y+3/4y-6
1y-6
Just simplify the equation by distributing 3/4 to y and -8 then combine like terms
Determine the sine of
Answer:
The sine of the angle = the length of the opposite side. the length of the hypotenuse.
The cosine of the angle = the length of the adjacent side. the length of the hypotenuse.
The tangent of the angle = the length of the opposite side. the length of the adjacent side.
I'm not sure if this answers your question.
What is the slope of the line shown below?
Answer:
3, you can count the points, up 3 over one
Jasmine thinks that the images are the same because they are both isosceles triangles. Do you agree with Jasmine why or why not?
Answer:
No, images are not same as their dimensions are different although two sides in each of the two triangles are equal.
Step-by-step explanation:
Given: images of two isosceles triangles.
To check: if images are the same
Solution:
A triangle is a polygon made up of three sides.
An isosceles triangle is a triangle in which two sides are equal. Also, in an isosceles triangle, angles opposite to equal sides are equal.
The given images of two isosceles triangles A and B are not the same as their dimensions are different although two sides in each of the two triangles are equal.
The city aquarium got a new tank for their dolphins. The tank is 16 feet high with a radius of 28 feet. Answer these
questions about the new dolphin tank.
Approximately how much water will it take to fill the tank?
The aquarium needs to purchase a plastic cover for the tank. What should the approximate size of the cover be?
Answer:
I know the answer to the last one. Its D
Step-by-step explanation:
Approximately, the quantity of water it will take to fill this tank is equal to 39,413 cubic feet.
Given the following data:
Radius of cylinder = 28 feet.
Height of cylinder = 16 feet.
How to calculate the volume of this cylinder?Mathematically, the volume of a cylinder is calculated by using this formula:
V = πr²h
Where:
h is the height.r is the radius.Substituting the given parameters into the formula, we have;
V = 3.142 × 28² × 16
V = 39,413.248 ≈ 39,413 cubic feet.
For the cover size, we have:
Area = πr²
Area = 3.142 × 28²
Area = 2,463.328 ≈ 2,463 ft².
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4. Factor (2a - b)2 - 4a2
The answer is b(-4a+b)
In the diagram below, XY and YZ are tangent to O. What is the measure of XZ?
The measure of arc xz is 106 degrees.
What is Major and Minor Arc ?A small arc is one with a measure of fewer than 180 degrees. A major arc is one with a measure greater than 180 degrees. A semicircle is an arc that divides a circle in half and has a measure of 180 degrees.
An arc is a continuous segment of a circle. There are two sections, one of which is larger than the other. The major arc is the larger one, and the minor arc is the smaller one.
Given:
From diagram, m ∠xz = 254 degrees.
We know that whole circle = 360 degrees
So, measure of arc XZ = 360 - 254
= 106
Hence, the measure of arc xz is 106 degrees.
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Evaluate 5+ (-11) - (-11)
Answer:
5
Step-by-step explanation:
To solve a problem with negatives, we use the following rule.
If it is like
x+(-y), it is equivalent to x-y
If the equation is like
(-x)-(-y), it is equivalent to (-x)+y
So,
5+(-11)=5-11=-6
(-6)-(-11)=(-6)+11=5
Your answer is 5.
Find the mean, median, mode and range of 13, 18, 13, 14, 13, 16, 14, 21, 13
Answer:
Mean -
15
Median -
14
Mode -
13
Range -
8
Hope this helps!
Four fifths of 30 students finished the test early .How may students finished the test early?
Answer:
24
Step-by-step explanation:
count by sixes. Good luck
Answer:
24
Step-by-step explanation:
(4/5)*30=24
4/5=.8
(.8)*30=24
Help with mathematics
Answer:
no
Step-by-step explanation:
because
Answer:
vertical line: x = 1
horizontal line = y = -2
Step-by-step explanation:
It's easy, really. A vertical line will always have x in the equation, and a horizontal line will always have y. Then, you find what it's equal to by looking at the point's x and y values and it corresponds to the answer.
Which of the following is a statistical question?
A. How many books did Matt read?
B. How many jars are kept on the shelf?
C. How many pieces of candy does Rachel have?
D. How many runs did the baseball team score in each game this season?
Answer:
D
Step-by-step explanation:
It is asking overall
sams swim shop also owns a small beachside stand. the beachside stand profit is about 25% of the amount of the swim shop profit. If the stand profited $2,000 in march,then how much did the swim shop profit ??
Answer:
8000
Step-by-step explanation:
25% of x = 2000
x=8000
help me plz and thank you!!!!
Answer: A is the answer
Step-by-step explanation:
Fido weighs 26 pounds more than Fifi. Fifi weighs 12 pounds less than Rover. If the sum of their weights is 71, how much does Fifi weigh?
By setting up a system of linear equations using the given relationships and solving for Fifi's weight, we find that Fifi weighs 11 pounds.
Explanation:The question involves solving a system of linear equations to find the weight of Fifi. We are given three pieces of information:
Fido weighs 26 pounds more than Fifi.Fifi weighs 12 pounds less than Rover.The sum of their weights is 71 pounds.Let's denote Fifi's weight as F, Rover's weight as R, and Fido's weight as D. Based on the information provided, we can write the following equations:
D = F + 26F = R - 12F + R + D = 71To find Fifi's weight, we need to substitute the first two equations into the third one:
Substitute D from equation (1) into equation (3): F + R + (F + 26) = 71Substitute R from equation (2) into the new equation: F + (F + 12) + (F + 26) = 71Combine like terms: 3F + 38 = 71Now, solve for F:
3F = 71 - 383F = 33F = 11Therefore, Fifi weighs 11 pounds.
Determine the intercepts of the line
The Great Pyramid of Giza is an example of a square pyramid and is the last surviving structure considered a wonder of the ancient world. The builders of the pyramid used a measure called a cubit, which represents the length of the forearm from the elbow to the tip of the middle finger. One cubit is about 20 inches in length. The height of the great pyramid is?
Answer:
The height of the great pyramid is:
303.6 cubits approximately.Or:
5464.6 inches approximately.Step-by-step explanation:
The Great Pyramid of Giza could be said to have two heights: one at the time of being built and the other that can be currently measured, however, to answer the question, the current height has been used, which is 303.6 cubits (I give the answer in this unit because it was the one used by its builders).
There is a slight discrepancy with the values given in the exercise: one cubit equals 18 inches, not 20.
Answer: 3560 in
Step-by-step explanation: algebra nation told me so
true or false if two triangles have three pairs of congruent sides, then the triangles are not guarnteed to be congruent
Answer:
False
Step-by-step explanation:
Because when you have pairs of congruent shapes, then you have a guaranteed to be congruent.
Answer:
it is true on quiz 7.1.2 exam sem 1
Step-by-step explanation:
Mrs. Smith has 4 pounds of cat food. Her son gave her 5 more pounds. She feeds her cats 3/4 of a pound per day. How many days will Mrs. Smith be able to feed her cats with the cat food she has now? Group of answer choices 27 days 15 days 12 days 9 days
Answer:
12 days
Step-by-step explanation:
So 4 + 5 is 9. Then you divide 9 by 0.75 since that is equivalent to 3/4 and get 12.
Which of the following is a solution of y> |x| - 5?
(4,-1)
(-1,-4)
(-4, 1)
Answer:
(-4,1)
Step-by-step explanation:
Let us check the choices.
y > |x| - 5
- 1 > |4| - 5 = -1 NO (4,-1);
-4 > |-1| - 5 = -4 NO not(-1,-4)
1 > |-4| - 5 = -1 TRUE, yes (-4,1)
convert 64 km to miles
Answer:
39.68 miles
Step-by-step explanation:
1 km is roughly 0.62 miles
Multiply 0.62 by 64 to get the answer of 39.68
Answer:
39.768 miles
Step-by-step explanation:
1.60934 Km equals 1 miles so 64 divide by 1.60934 to get the answer, 39.768.
Find the perimeter of the square
With one side 2 1/2 yards
Answer:
12
Step-by-step explanation:
2.5*4=12
if each side of a square is the same length then yes my answer is correct
Final answer:
To find the perimeter of the square with a side length of [tex]2\frac{1}{2}[/tex] yards, the side length is converted to a decimal and multiplied by 4, resulting in a perimeter of 10 yards.
Explanation:
The student's question is about finding the perimeter of a square when given the length of one side, which is [tex]2\frac{1}{2}[/tex] yards.
Since a square has four equal sides, the perimeter (P) of a square is calculated by multiplying the length of one side (s) by 4, which can be expressed as P = 4s.
In this case, if we convert [tex]2\frac{1}{2}[/tex] yards to a decimal, we get 2.5 yards.
Therefore, the perimeter of the square is 4 × 2.5 yards, which equals 10 yards.
Help Me Out With This Question Plz!!
5 red flowers 10 yellow 75 total how many red
Answer
25 are red
Step-by-step explanation:
red I blue
5 I 10
10 I 20
15 I 30
20 I 40
25 I 50
Gio is standing at the base of his house. He measures the angle of elevation to the top of a nearby high rise to be
50°. He decides to go to the roof of his house standing in the same position and measures the elevation to the top
of the same high rise to be 25°. If the height of the high rise is 150 meters tall, how tall is the house? How much
taller is the high riser than the house? Draw a diagram
Answer:
the apartment building is 31.2 meters
Step-by-step explanation:
Find the area of the triangle below.
Answer:
90
Step-by-step explanation:
The formula for a triangle is base times height then dividing it by 2
So 15 times 12 is 180 and dividing it by 2 gets you 90.
Hope this helps!
Answer:
72 :)Step-by-step explanation:
To find the area of a triangle, multiply the base by the height, and then divide by 2. The division by 2 comes from the fact that a parallelogram can be divided into 2 triangles. For example, in the diagram to the left, the area of each triangle is equal to one-half the area of the parallelogram.Hope this helps
Ryan and Matt are playing a game by rolling two number cubes, with faces numbered 1 through 6, one after the other. Ryan gets a point when the number on the first cube is an odd number and the number on the second cube is an even number. Matt gets a point when the number on the first cube is 5. The table below shows all possible combinations of numbers on the cubes.
Who is more likely to get a point on the first roll of both the cubes?
A.
Ryan is more likely to get a point, because 13/36>9/36
B.
Matt is more likely to get a point, because 13/36 > 6/36
C.
Both are equally likely to get a point, because 6/36 = 6/36
D.
Ryan is more likely to get a point, because 9/36>6/36
Ryan is more likely to get a point than Matt on the first roll of both cubes.
The fraction of outcomes in which Ryan gets a point is 9/36, which simplifies to 1/4.
The fraction of outcomes in which Matt gets a point is 1/36.
Option A is the correct answer.
What is probability?It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
Example:
The probability of getting a head in tossing a coin.
P(H) = 1/2
We have,
To determine who is more likely to get a point, we need to count the number of outcomes that satisfy each condition and then compare the fractions.
Ryan gets a point if the first cube shows an odd number and the second cube shows an even number.
There are three odd numbers and three even numbers,
So there are 3 x 3 = 9 outcomes that satisfy this condition.
Matt gets a point if the first cube shows a 5.
There is only one outcome that satisfies this condition.
Therefore,
Ryan is more likely to get a point than Matt on the first roll of both cubes.
The fraction of outcomes in which Ryan gets a point is 9/36, which simplifies to 1/4.
The fraction of outcomes in which Matt gets a point is 1/36.
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