To find the ratio of edge lengths of two triangles given their area ratio, we need to take the square root of the area ratio.
Finding the volumeTo find the ratio of edge lengths of two figures given their volume ratio, you need to use the fact that volume is proportional to the cube of the edge length.
If we have two figures, Figure A and Figure B, with edge lengths a and b respectively, and their volumes are in the ratio of V(A) : V(B) = k, then we can set up the following equation:
(Volume of A) / (Volume of B) = (a^3) / (b^3) = k
We can then solve for the ratio of edge lengths:
a / b = (k)^(1/3)
Therefore, to find the ratio of edge lengths given the volume ratio, we need to take the cube root of the volume ratio.
This method works for any shape, as long as the volume formula for that shape involves the cube of the edge length. For example, this method works for cubes, rectangular prisms, cylinders, spheres, and so on.
For triangles, however, we cannot use this method directly because the volume of a triangle is not a function of its edge length. Instead, we can use similar triangles to find the ratio of their edge lengths.
If we have two similar triangles, with corresponding sides in the ratio of a : b, then their areas are in the ratio of (a^2) : (b^2). We can use this fact to find the ratio of their edge lengths:
a / b = sqrt(Area of first triangle / Area of second triangle)
So, to find the ratio of edge lengths of two triangles given their area ratio, we need to take the square root of the area ratio.
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The angle times three out of 10 of the circle what is the measure of the angle
The measure of the angle that turns through 3/10 of the circle is 108 degrees.
Define angleAn angle is a geometric figure that is formed by two rays that share a common endpoint, which is called the vertex of the angle. The rays are referred to as the sides or legs of the angle. Angles are typically measured in degrees, with a full circle measuring 360 degrees.
Angles can be classified based on their degree of measurement: acute angles are less than 90 degrees, right angles are exactly 90 degrees, obtuse angles are greater than 90 degrees but less than 180 degrees, and straight angles are exactly 180 degrees.
Since a full circle has 360 degrees, 3/10 of the circle can be represented as:
(3/10) x 360 degrees = 108 degrees
Therefore, the measure of the angle that turns through 3/10 of the circle is 108 degrees.
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The complete question is :
The angle turns through 3/10 of the circle. What is the measure of the angle?
What is the surface area of this right triangular prism?
i will give brainliest
Thus, the total surface area of the given right triangular prism is found as : 96 sq. in.
Explain about the right triangular prism:The bases of a prism, which can have up to n sides, are joined to one another by parallel lines that create planes. These bases plus planes would create right angles with one another in a right prism if they were perpendicular to one another.
surface area of right triangular prism S:
surface area of right triangular prism = base area + 2*triangle area + 2* rectangle area
surface area of right triangular prism = 4*8 + 2*(1/2*8*3) + 2*4*5
surface area of right triangular prism = 32 + 24 + 40
surface area of right triangular prism = 96
Thus, the total surface area of the given right triangular prism is found as : 96 sq. in.
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what is the next 3 numbers in this sequence 3, 2, 6, 5, 15, 14
Answer:
42, 41, 123
Step-by-step explanation:
3, 2, 6, 5, 15, 14
- 1 x3. - 1. x3. - 1
you just gotta look for the pattern thats the same in the sequence so the next three numbers would be x3, then - 1 then x3 again onto the numbers.
Answer:
The next three numbers are 42, 41, and 123
Step-by-step explanation:
3 - 1 = 2
2 * 3 = 6
6 - 1 = 5
5 * 3 = 15
15 - 1 = 14
The pattern is subtracting one and then multiplying by three.
14 * 3 = 42
42 - 1 = 41
41 * 3 = 123
A company sells snow globes made out of glass that are in the shape of hollow
spheres. Khloe measures the outer diameter of a snow globe to be 30 cm. If the glass
has a thickness of 0.35 cm, find the total volume of glass that makes up the globe.
Round your answer to the nearest hundredth if necessary. (Note: diagram is not
drawn to scale.)
The total volume of glass that makes up the snow globe is approximately 1,757.84 cubic centimeters.
What is the inner sphere?
The Inner Sphere is a region of interstellar space surrounding Earth to a radius of roughly 450 - 550 light-years, generally demarcated by the outer borders of the "Great Houses."
The outer sphere has a diameter of 30 cm, so its radius is 15 cm. The volume of the outer sphere is given by the formula:
V outer = (4/3)πr_outer³
V outer = (4/3)π(15 cm)³
V outer ≈ 14,137.17 cm³
The inner sphere has a diameter of 30 cm minus the thickness of the glass on both sides, so its diameter is:
30 cm - 2(0.35 cm) = 29.3 cm
Therefore, the radius of the inner sphere is:
r inner = 29.3 cm / 2 = 14.65 cm
The volume of the inner sphere is given by the formula:
V inner = (4/3)πr_inner³
V inner = (4/3)π(14.65 cm)³
V inner ≈ 12,379.33 cm³
Finally, the volume of glass that makes up the snow globe is the difference between the volumes of the outer and inner spheres:
V glass = V outer - V inner
V glass ≈ 1,757.84 cm³
Therefore, the total volume of glass that makes up the snow globe is approximately 1,757.84 cubic centimeters.
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from a group of seven candidates, a committee of six people is selected. in how many different ways can the committee be selected?
According to the informations, there are 7 different ways a committee of six people can be selected from a group of seven candidates.
How can we find this number?In this case, we must use the combination formula, which is expressed by:
nCr = n! / r!(n-r)!Where n is the total number of items in the set, r is the number of items being selected, and ! denotes the factorial function, which means multiplying a number by all the positive integers less than it.
Therefore, from a group of 7 candidates, a committee of 6 people can be selected in 7 different ways using the combination formula. The formula for the combination of n objects taken r at a time is C(n,r) = n!/r!(n-r)!, where n is the total number of objects and r is the number of objects to be chosen. In this case, we have n = 7 and r = 6, so the formula gives us C(7,6) = 7!/6!(7-6)! = 7 ways.
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Jason wants to find more information about the heights of players on his school's soccer team and his school's basketball team. Jason surveys 29 members of the soccer team and 16 members of the basketball team. The results of his study are shown in the dot plots below .
The average height of the soccer team is 77.45 inches, and the average height of the basketball team is 79 inches.
To find the average height of each team, we'll sum up the heights and divide by the number of players on each team.
Soccer team average height:
Sum of heights: 60+61+...+87+88 = 2,246 inches
Number of players: 29
Average height: 2246 / 29 = 77.45 inches
Basketball team average height:
Sum of heights: 72+73+...+86+87 = 1,264 inches
Number of players: 16
Average height: 1264 / 16 = 79 inches
So, the average height of the soccer team is 77.45 inches, and the average height of the basketball team is 79 inches.
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Soccer team heights (in inches):
60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88
Basketball team heights (in inches):
72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87
Jason wants to find more information about the heights of players on his school's soccer team and his school's basketball team. Jason surveys 29 members of the soccer team and 16 members of the basketball team. The heights of the soccer team and basketball team players are given above. What is the average height of the soccer team and the basketball team?
The length of a rectangle is 2 inches more than 2 times the width. If the area of the rectangle is 40
square inches, find the length and the width.
The length of the rectangle is 10 inches and the width is 4 inches.
What is the area of the rectangle?
To find the area of a rectangle, we multiply the length of the rectangle by the width of the rectangle.
Let's assume that the width of the rectangle is "x" inches.
From the given information, we can write an equation for the length "L" in terms of the width "x":
L = 2x + 2
We also know that the area of the rectangle is 40 square inches:
A = L * x = 40
Substituting the expression for "L" in terms of "x" into the area equation, we get:
(2x + 2) * x = 40
Expanding the left-hand side of the equation and simplifying, we get:
2x² + 2x - 40 = 0
Dividing both sides by 2, we get:
x² + x - 20 = 0
This is a quadratic equation that can be factored:
(x + 5)(x - 4) = 0
The solutions are x = -5 and x = 4. Since the width of the rectangle cannot be negative, the only valid solution is:
x = 4
Substituting this value for "x" into the equation for "L", we get:
L = 2x + 2 = 2(4) + 2 = 10
Therefore, the length of the rectangle is 10 inches and the width is 4 inches.
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Substitute the supplied value and simplify both sides of the equation, if necessary. Then decide if the supplied value is or is not a solution.
–2p – 17 = 3(p – 5) {–2}
Starting with the original equation:
-2p - 17 = 3(p - 5)
Distributing the 3 on the right side:
-2p - 17 = 3p - 15
Subtracting 3p from both sides:
-5p - 17 = -15
Adding 17 to both sides:
-5p = 2
Dividing by -5:
p = -2/5
Now, we can substitute this value of p back into the original equation and check if it is a solution:
-2(-2/5) - 17 = 3((-2/5) - 5)
4/5 - 17 = 3(-27/5)
-136/5 = -81/5
The left side does not equal the right side, so the supplied value of p = -2/5 is NOT a solution to the equation.
Hope this helps :)
If you open a bank account with 23,000 and its annual interest is compounded quarterly. What would the interest have to be for the amount to grow to $50,000 in 7 years?
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 50000\\ P=\textit{original amount deposited}\dotfill &\$23000\\ r=rate\to r\%\to \frac{r}{100}\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &7 \end{cases}[/tex]
[tex]50000 = 23000\left(1+\frac{ ~~ \frac{r}{100} ~~ }{4}\right)^{4\cdot 7} \implies \cfrac{50000}{23000}=\left( 1+\cfrac{r}{400} \right)^{28} \\\\\\ \cfrac{50}{23}=\left( \cfrac{400+r}{400} \right)^{28}\implies \sqrt[28]{\cfrac{50}{23}}=\cfrac{400+r}{400} \\\\\\ 400\sqrt[28]{\cfrac{50}{23}}=400+r\implies 400\sqrt[28]{\cfrac{50}{23}}-400=r\implies \stackrel{ \% }{11.25}\approx r[/tex]
Please help with study island!!
The total volume of the wall units is 108 cubic feet
How to find the volume of the wallThe volume of the wall is solved by dividing the figure to give the various dimensions represented in the form length x width x depth
first division has the dimensions as 3 x 4 x 8 second division has the dimensions as 3 x 2 x 2The volume of each is solved then added to get the total volume
first division: 4 x 4 x 8 = 96
second division: 3 x 2 x 2 = 12
The total volume is
= 96 + 12
= 108 cubic feet
so the total volume is solved to be 108 cubic feet
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34. What are the coordinates of the information
center? Explain.
Generally, coordinates are a way of specifying the position of something in space, usually using a system of latitude and longitude or x, y, and z axes.
What informs the coordinates of an information center?The coordinates of a physical location that serves as a hub for information, such as a data center or a library, then the answer will depend on the specific location you have in mind. To find the coordinates of such a place, you would need to use a mapping tool or geographic information system (GIS) to locate the facility and determine its latitude and longitude.
On the other hand, if you're asking about the "coordinates" of information in a more abstract sense, then this could refer to the ways in which information is organized or classified.
For example, a database might use a system of fields and tables to arrange information in a structured way, while a search engine might use algorithms to determine the relevance and ranking of different pieces of information based on factors like keywords, backlinks, and user behavior.
In conclusion, the coordinates of an information center is dependent on its nature in terms of its structural formation and the set goals to be accomplished by determining such coordinates.
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Does anybody know What is
11=4x
Answer:
2.75
Step-by-step explanation:
When you put that equation into a calculator, you get 2.75.
Answer:
Step-by-step explanation:
To solve for x in the equation 11=4x, we need to isolate x on one side of the equation.
We can start by dividing both sides of the equation by 4:
11/4 = (4x)/4
Simplifying the right side of the equation, we get:
11/4 = x
Therefore, x = 11/4 or 2.75.
a line passes through the point (-9,-5) an has a slope of -2/3.
Write an equation in slope -intercept form for this line.
The slope-intercept form of a linear equation with given point (-9,-5) and slope -2/3 is y = (-2/3)x - 11.
What is a slope of a line?The slope of a line is a measure of its steepness or incline, represented by the ratio of the vertical change between two points, known as the rise, to the change in horizontal part between the same two points, known as the run. It describes the rate at which the line is increasing or decreasing as it moves from left to right. The slope of a line can be positive, negative, zero, or undefined, and it plays a critical role in many mathematical applications, including calculus, geometry, and physics. It is commonly denoted by the letter m and is defined as m = (y₂ - y₁)/ (x₂ - x₁), where (x₁, y₁) and (x₂, y₂) are any two points on the line.
The slope-intercept form of a linear equation is y = mx + b, where m represents the slope of the line and b represents the y-intercept.
To find the equation of a line with a given slope and a point on the line, we can substitute the values into the equation and solve for the y-intercept, b.
Given that the line passes through the point (-9, -5) and has a slope of -2/3, we can substitute these values into the equation to find the value of b:
-5 = (-2/3) × (-9) + b
-5 = 6 + b
b = -11
Now that we know the value of b, we can write the equation of the line in slope-intercept form:
y = (-2/3)x - 11
Therefore, the equation of the line in slope-intercept form is y = (-2/3)x - 11.
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Monica has a dog food dispenser that can hold 25 cups of food. Sometimes, she likes to mix different flavors of food for her dog. This morning, Monica noticed there was some chicken-flavored food in the dispenser already. After Monica added 11 cups of beef-flavored food to the dispenser, it was completely full.
C - 11 = 25 or c + 11 = 25.
Answer:
I got you
Step-by-step explanation:
c-11=25
c=25+11
c=36
What’s the system of equations?
The solution set is {(x, y) | x = y + 2}, which represents a straight line with a slope of 1 passing through the point (2, 0).
Therefore, the correct answer is option 2, infinite solutions.
What is quadratic equation?Equations of the form ax2 + bx + c = 0, where a, b, and c are real numbers, and a 0, are known as polynomial equations in the variable x. Any equation that has the formula p(x) = 0, where p(x) is a polynomial of degree 2 with a single variable, is actually a quadratic equation.
The equation has the following form: ax2 + bx + c = 0, where x is the unknown variable and a, b, and c are constants, with "a" not equal to 0.
Numerous strategies, including factoring, completing the square, and the quadratic formula, can be used to solve quadratic equations.
To solve the system of equations:
x - y = 2 ---(1)
-3x + 3y = -6 ---(2)
We can use the first equation to isolate x in terms of y:
x = y + 2
-3(y + 2) + 3y = -6
Simplifying the equation, we get:
-3y - 6 + 3y = -6
Solving for y, we get:
0 = 0
For all values of y this equation is true-
So,the equations has infinite solutions.
To find the solution set, we can substitute the value of y into the expression for x:
x = y + 2
x = y + 2, for all values of y
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A right cylinder has a radius of 4 and a height of 11. What is its surface area?
OA. 152
units²
OB. 120 units²
OC. 88 units²
O D. 60 units²
The closest option among the given options is option B: 120 units².
What is cylinder?
A cylinder is a three-dimensional geometric shape that consists of two parallel circular bases of the same size and shape, and a curved lateral surface connecting the bases.
The formula for the surface area of a right cylinder is:
SA = 2πr² + 2πrh
where r is the radius and h is the height.
Substituting the given values, we get:
SA = 2π(4)² + 2π(4)(11)
SA = 2π(16) + 2π(44)
SA = 32π + 88π
SA = 120π
Using the approximation π ≈ 3.14, we can calculate the surface area to be:
SA ≈ 120(3.14)
SA ≈ 376.8
Therefore, the closest option among the given options is option B: 120 units².
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Mrs. Jenkins gifts 10 cookies to her six sons if they share the cookies equally how many cookies should each son get
Mrs. Jenkins could divide each cookie into six equal pieces, giving each son six pieces of cookies, which would add up to 10 cookies in total.
How to solve the question?
If Mrs. Jenkins gifts 10 cookies to her six sons, the number of cookies each son should get can be found by dividing the total number of cookies by the number of sons.
So, if we divide 10 cookies equally among six sons, we get:
10 / 6 = 1.6667
This means that each son should get approximately 1.67 cookies. However, since it is not possible to divide a cookie into fractions, the actual number of cookies each son would get may vary.
To distribute the cookies equally, Mrs. Jenkins can either give each son one cookie and then divide the remaining four cookies equally among the six sons. This would give each son one cookie and each son would get an additional 4/6 or 0.67 cookies.
Alternatively, Mrs. Jenkins could divide each cookie into six equal pieces, giving each son six pieces of cookies, which would add up to 10 cookies in total.
In any case, the important thing is to ensure that each son receives an equal share of the cookies.
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YOUR COMPLETE QUESTION IS :-
Mrs. Jenkins gifts 10 cookies to her six sons if they share the cookies equally how many cookies should each son get
Determine the rate of change of the function given by the table.
I WIL GIVE BRAINLYEST TO WHOEVER ANSWERS FIRST AND CORECTY
Answer:
Step-by-step explanation:
1
4. Which of the following angles is vertical to angle /DEB?
A
C
109°
E
D
B
Answer: Vertical angles are formed by the intersection of two lines and are always equal in measure. Therefore, to find the angle that is vertical to angle ∠DEB, we need to look for another angle that has the same measure as ∠DEB.
Unfortunately, we do not know the measure of angle ∠DEB, so we cannot determine which angle is vertical to it based on the given information.
Therefore, the correct answer is: None of the angles can be determined as vertical to angle ∠DEB without additional information.
Step-by-step explanation:
Find the mass of the triangular region with vertices (0, 0), (4, 0), and (0, 2), with density function ρ(x,y)=x^2+y^2.
The mass of the triangular region with density function ρ(x,y) = [tex]x^2 + y^2 is 136/375.[/tex]
What is a triangle?A triangle is a three-sided polygon made up of three line segments that connect at three endpoints, called vertices. The study of triangles is an important part of geometry, and it has applications in various fields such as engineering, architecture, physics, and computer graphics.
According to the given information:The mass of a 2D region with variable density can be calculated using the double integral formula:
m = ∬R ρ(x,y) dA
where R is the region of integration, ρ(x,y) is the density function, and dA is the area element.
In this case, we have a triangular region with vertices (0, 0), (4, 0), and (0, 2), and the density function is ρ(x,y) = [tex]x^2 + y^2.[/tex]To set up the double integral, we need to determine the limits of integration for x and y.
Since the triangular region is bounded by the lines y = 0, y = 2, and x = (2/5)y, we can set up the integral as follows:
m = ∫0 ∫[tex]0^[/tex](2/5)y ([tex]x^2 + y^2)[/tex] dxdy
Integrating with respect to x first, we get:
m = ∫[tex]0^2 [(x^3/3) + xy^2]_0^(2/5[/tex])y dy
m = ∫[tex]0^2 [(8/375)y^5 + (4/15)y^3][/tex]dy
Evaluating the integral, we get:
m = [tex][(2/1875)y^6 + (2/5)y^4]_0^2[/tex]
m = (64/1875) + (16/5)
m = 136/375
Therefore, the mass of the triangular region with density function ρ(x,y) = [tex]x^2 + y^2 is 136/375.[/tex]
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Consider the integral given below
Answer:
C ∫[-a,0] = -∫[0, a]
Step-by-step explanation:
You want an alternate representation of the given integral ...
∫(2x⁵ -5x³)dx
on the interval [-a, a].
Odd functionThe function f(x) = 2x⁵ -5x³ being integrated is an odd function. This means ...
f(-x) = -f(x) and f(0) = 0
Even functionAn even function is characterized by ...
f(-x) = f(x)
The integral F(x) of this odd function f(x) is an even function, so the parts either side of x=0 have the integrals ...
[tex]\displaystyle \int_{-a}^0{(2x^5-5x^3)}\,dx=F(0)-F(-a)=F(0) -F(a)[/tex]
[tex]\displaystyle \int_0^a{(2x^5-5x^3)}\,dx=F(a)-F(0)[/tex]
As we can see, these integrals are the opposites of each other, matching answer choice C.
__
Additional comment
The second attachment shows a numerical value for a=2.
Consider the information below for Postman Builders Inc. Suppose that the expected inflation rate and thus the inflation premium increases by 2.0 percentage points, and Postman acquires risky assets that increase its beta by the indicated percentage. What is the firm's new required rate of return? Beta 1.5, Required Return 10.2, RPm 6%, Percentage increase in beta 65
Therefore, Postman Builders Inc’s new required rate of return is 23.7%1.
SET A RATE?Rate might signify two different things. As a noun, it denotes an amount, frequency, or measure that is typically compared to another quantity or measure. Or, it can be used as a verb to indicate "assign a standard or value to" using a specific scale.
Postman Builders Inc. has a necessary return of 10.2% and a beta of 1.5, according to the information given.
We may get the new necessary rate of return as follows if Postman purchases risky assets that increase its beta by 65% and the predicted inflation rate and inflation premium increase by 2 percentage points.
New Required Rate of Return
= Risk-free rate + Beta * (Expected Market Return - Risk-free rate)
= 2% + (1.5 * (6% + 2% + (65% * 6%))) = 23.7%
New Required Rate of Return equals 8% plus 2.47 x (-2%) to 3.85%.
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Find the circumference of the circle. Round to the nearest tenth.
A. 148.4 m
B. 169.6 m
C. 84.8 m
D. 54.0 m
Answer:
251.2 in
Step-by-step explanation:
Circumference of circle = 2 · π · r
π = 3.14
r = 40 in
Let's solve
2 · 3.14 · 40 = 251.2 in
So, the circumference of the circle is 251.2 in
Q7: Use the image to determine the line of reflection.
An image of polygon VWYZ with vertices V at negative 9, 1, W at negative 9, negative 1, Y at negative 3, negative 1, and Z at negative 3, 1. A second polygon V prime W prime Y prime Z prime with vertices V prime at 7, 1, W prime at 7, negative 1, Y prime at 1, negative 1, and Z prime at 1, 1.
Reflection across y = 1
Reflection across x = −1
Reflection across the x-axis
Reflection across the y-axis
This line is the horizontal line y = 1. Therefore, the correct answer is "Reflection across y = 1".
How to solve the question?
The line of reflection is the line that serves as the mirror for the original polygon such that each point on the original polygon is reflected to a corresponding point on the reflected polygon such that the distance between the line of reflection and each point is the same as the distance between the line of reflection and its reflection.
In this case, we are given two polygons, one original and one reflected. We need to determine the line of reflection that maps each point of the original polygon to its corresponding point on the reflected polygon.
Looking at the two polygons, we can see that the corresponding vertices are equidistant from a line of reflection that passes through the midpoint of the line segment joining V and V prime. Therefore, the line of reflection is the line that passes through the midpoint of the line segment joining V and V prime.
This line is the horizontal line y = 1. Therefore, the correct answer is "Reflection across y = 1". The other options are incorrect because they do not pass through the midpoint of the line segment joining V and V prime and do not produce the corresponding points for the original and reflected polygons.
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A balloon filled with helium gas has a volume of 326 mL at a pressure of 1 atm. The balloon is released and reaches an altitude of 6.5 km, where the pressure is at 0.5 atm. Assuming that the temperature has remained the same, what volume does the gas occupy at the height? Answer in units of mL.
The volume of the gas at the height (i.e 6.5 Km) is 652 mL
Data obtained from the question[tex]\text{Initial volume} \ (\text{V}_1) = \text{326 mL}[/tex][tex]\text{Initial pressure} \ (\text{P}_1) = \text{1 atm}[/tex][tex]\text{Temperature = Constant}[/tex][tex]\text{Final pressure} \ (\text{P}_2) = \text{0.5 atm}[/tex][tex]\bold{Final \ volume \ (V_2) = \ ?}[/tex]The final volume of the gas can be obtained by using the Boyle's law equation as shown below:
[tex]P_1V_1 = P_2V_2[/tex]
[tex]1 \times 326 = 0.5 \times V_2[/tex]
[tex]326 = 0.5 \times V_2[/tex]
Divide both side by 0.5
[tex]V_2 = \dfrac{326}{0.5}[/tex]
[tex]\boxed{\bold{V_2 = 652 \ mL}}[/tex]
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Suzy can drive 53 miles in 1 hour. How many miles can she drive in 18 hours?
The total miles drive by Suzy in 18 hours when she can drive 53 miles in 1 hour is equal to 954 miles.
If Suzy can drive 53 miles in 1 hour,
Using the formula of speed based on distance and time we have,
Speed = Distance / Time
Substitute the values in the formula we get,
⇒ Speed = 53 miles / 1 hour
⇒ Speed = 53 miles/hour
Use this information to find out how far Suzy can drive in 18 hours we get,
Now, Speed = 53 miles/hour
Time = 18 hours
Distance = Speed x Time
Substitute the value of speed and time we get,
⇒ Distance = 53 miles/hour x 18 hours
⇒ Distance = 954 miles
Therefore, Suzy can drive 954 miles in 18 hours.
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Find the size of angle p. Give your answer
in degrees (°).
137⁰
60°
60°
112°
р
134
Not drawn accurately
PLEASE HELPPP
Answer:
76°
Step-by-step explanation:
The sum of the interior angles of any quadrilateral is 360°.
p = 360 - 60 - 134 - 90 = 76
all the fifth grade students go outside for exercise. one-half of the students are on the soccer fields. One-fourth of the students are on the basketball courts. One-eight of the students are jogging around the track. Twelve of the students are tossing footballs to each other. How many fifth grade students are outside for exercise? How many students are playing each sport? Show all your mathematical thinking
Answer: 96 fifth grade students outside for exercise. 48 students playing soccer, 24 students playing basketball, 12 students jogging around the track, and 12 students tossing footballs.
Step-by-step explanation:
Let x be the total number of fifth grade students.
- 1/2x are on the soccer fields
- 1/4x are on the basketball courts
- 1/8x are jogging around the track
- 12 students are tossing footballs
x = 1/2x + 1/4x + 1/8x + 12
x = 4/8x + 2/8x + 1/8x + 12
x = 7/8x + 12
1/8x = 12
x = 12*8
x = 96
Therefore, there are 96 fifth grade students outside for exercise.
Soccer fields: 1/2x = 1/2 * 96 = 48 students
Basketball courts: 1/4x = 1/4 * 96 = 24 students
Jogging around the track: 1/8x = 1/8 * 96 = 12 students
Tossing footballs: 12 students (as given in the problem)
There are 48 students playing soccer, 24 students playing basketball, 12 students jogging around the track, and 12 students tossing footballs.
Answer:
96 students in general
Step-by-step explanation:
I drew an Euler circle to make it more clear. so we can see that 1/8 class = 12
so 1/4 class is 12×2=24
1/2 class is 12×4=48
12+12+24+48=96
I hope this helped
which expresions are equivalent to 1/2³
1/8
(1/2)^3 1^3 2^3 1/8 or:(1/2)^3 (1/2) (1/2)(1/2)1×1×1/2×2×1/8
A rectangular patio has a length of (1 + 2x) yards and a width of (2 - 3x) yards. Which correctly describes the area and perimeter of the patio?
Area of the patio is -6x² + x + 2 square yards and perimeter of the patio is 6 - 2x yards.
What is a yard?A yard is a unit of measurement used to measure length or distance in both the US customary system and the British imperial system. One yard is equal to 3 feet or 36 inches. In the US customary system, a yard is equal to 0.9144 meters, while in the British imperial system, it is equal to 0.9144 meters or 3 feet. Yards are commonly used for measuring larger distances, such as in construction or landscaping, as well as in some sports like American football and cricket.
The area of the rectangular patio is given by multiplying its length by its width, so the area is:
A = (1 + 2x)(2 - 3x)
Now using distributive property we get,
A = 2 - 3x + 4x - 6x²
Simplifying further, we get:
A = -6x² + x + 2
Therefore, the area of the patio is described by the quadratic equation -6x² + x + 2.
To find the perimeter of the patio, we add up the lengths of all four sides. The length and width are given as (1 + 2x) and (2 - 3x), respectively, so the perimeter is:
P = 2(1 + 2x) + 2(2 - 3x)
Simplifying this expression, we get:
P = 2 + 4x + 4 - 6x
P = 6 - 2x
Therefore, the perimeter of the patio is described by the linear equation 6 - 2x.
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