The volume of the triangular solid is 128/3 cubic units.
The cross-sections of the triangular solid along the y-axis are equilateral triangles with side length equal to the width of the triangular base at that y-coordinate. The width of the triangular base at y = h is equal to 8 - 4h/4. So, the side length of the equilateral triangle at y = h is 8 - 4h/4.
Let's call the height of the equilateral triangle at y = h as "x". Then, using the Pythagorean theorem, we can find the relationship between x and the side length:
x^2 = (8 - 4h/4)^2 - (x/2)^2
Expanding and simplifying the right-hand side:
x^2 = 64 - 16h + h^2/16 - x^2/4
Multiplying both sides by 4:
4x^2 = 256 - 64h + h^2 - x^2
Solving for x^2:
3x^2 = 256 - 64h + h^2
Taking the square root of both sides:
x = √(256 - 64h + h^2)/√3
So, the height of the equilateral triangle at y = h is equal to x = √(256 - 64h + h^2)/√3.
The volume of the triangular solid can be found by integrating the cross-sectional area over the height of the triangular base:
V = (1/3) ∫[0, 4] x^2(y) dy
= (1/3) ∫[0, 4] (√(256 - 64h + h^2)/√3)^2 dh
= (1/3) ∫[0, 4] (256 - 64h + h^2)/3 dh
Evaluating the definite integral:
V = (1/3) * [(256h/3 - 32h^2/2 + h^3/3) |_0^4]
= (1/3) * [(256/3 * 4 - 32/2 * 4^2 + 4^3/3) - (256/3 * 0 - 32/2 * 0^2 + 0^3/3)]
= (1/3) * (256 - 128 + 64/3)
= 128/3.
Correct Question :
The base of s is the triangular region with vertices (0, 0), (8, 0), and (0, 4). Cross-sections perpendicular to the y-axis are equilateral triangles. What is the volume of the triangular solid.
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What is 4.25 in expanded form?
Answer:
4 + 0.2 + 0.05
Step-by-step explanation:
Need help understanding this question
Answer:
The number of large bars of chocolate sold is:
1/4 x 208 = 52
The number of small bars of chocolate sold is:
208 - 52 = 156
The total amount of money earned from selling the large bars of chocolate is:
52 x e1 = e52
The total amount of money earned from selling the small bars of chocolate is:
156 x 60p = £93.60
To convert e52 to pounds, we need to multiply by the exchange rate. Let's assume that the exchange rate is £1 = e1.20.
So, e52 = £52 x 1.20 = £62.40
Therefore, the total amount of money earned from selling all 208 bars of chocolate is: £62.40 + £93.60 = £156
Write an algebraic expression to represent the following situation: "Greg has nickels and pennies in his pocket. The number of pennies is 7 less than twice the number of nickels. Let N represent the number the nickels. Write an expression for the number of pennies."
Algebraic expression to represent the given situation would be, P = 2N - 7
What is algebraic expression?
When we utilize numbers and words to solve a mathematical problem, we are using algebraic expressions.
Let P represent the number of pennies in Greg's pocket.
We know that the number of pennies is 7 less than twice the number of nickels, which can be written as:
P = 2N - 7
This expression represents the number of pennies in terms of the number of nickels.
Therefore, Algebraic expression to represent the given situation would be, P = 2N - 7
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how to convert milliliters to ounces?
From the given data by doing unit conversion, 250 mL is approximately equal to 8.4535 fluid ounces.
Unit conversion is the process of converting a given quantity from one unit of measurement to another.
To convert milliliters (mL) to fluid ounces (fl oz), you can use the following conversion factor:
1 mL = 0.033814 fl oz
To convert, simply multiply the number of milliliters by 0.033814 to get the equivalent volume in fluid ounces.
For example, if you want to convert 250 mL to fluid ounces, you can use the conversion factor as follows:
250 mL × 0.033814 fl oz/mL = 8.4535 fl oz (rounded to four decimal places)
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14. 15x5y
= -20
-3x + y = 4
Answer:
The answer is: y=4+3x
Step-by-step explanation:
I know this because I believe we are solving for the system of equations or solving by the system of subtraction.
I will say I am not completely sure this is right but I hope I helped out a little :)
Find the value of each variable provide proofs
The value of x is 18.
The value of y is 15.6.
What is the Pythagorean theorem?Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
We have,
From the figure,
Sin 30 = 9/x
1/2 = 9/x
x = 9 x 2
x = 18
Now,
Using the Pythagorean theorem.
x² = 9² + y²
18² = 81 + y²
y² = 325 - 81
y = √244
y = 15.6
Thus,
x = 18
y = 15.6
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The lengths of two sides of a triangle are 4 inches and 7 inches.
What is a possible length, in inches, of the third side?
A possible length, in inches, of the third side is equal to 4 inches.
What is the triangle inequality theorem?In Euclidean geometry, the Triangle Inequality Theorem states that the sum of any two sides of a triangle must be greater than or equal (≥) to the third side of the triangle.
Mathematically, the Triangle Inequality Theorem is represented by this mathematical expression:
b - c < n < b + c
Where:
n, b, and c represent the side lengths of this triangle.
By applying the Triangle Inequality Theorem, the possible side lengths of the triangle's third side is given by:
b - c < n < b + c
7 - 4 < n < 7 + 4
3 < n < 11.
Therefore, n could be 4, 5, 6, 7, 8, 9, and 10 inches.
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What is the area of the shape for the quilt block? ninety-four and one half in2 one hundred sixty-six and one half in2 189 in2 333 in2
The area of the shape for the quilt block is 166.5 in²
What is an area?The area is the region bounded by the shape of an object. The space covered by the figure or any two-dimensional geometric shape, in a plane, is the area of the shape
Given that, a quilt has blocks of design on it, we need to find the area of the block,
To find the area of the block = sum of the areas of the right triangle and the rectangle,
Area of the block = 16 × 9 + 6 × 7.5 × 1/2 = 166.5 in²
Hence, the area of the shape for the quilt block is 166.5 in²
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The figure is unavailable is the question is solved for the figure attached
Solve 1/11 divided by 4
a
one forty fourth
b
44
c
four forty fourths
d
one fifteenth
Answer:
a ) one by forty fourth
Step-by-step explanation:
1/11 ÷ 4
= 1/11 x 1/4
= 1/44
therefore, the answer is one by forty fourth
Hope it's helpful..
I think I have the answer, but it keeps saying I'm incorrect.
Answer:
B.
D.
Step-by-step explanation:
B is actually 141, not 14.1
(204 plus 98) is more than 250.7
This means that multiplying it by 8.3 would not even make it near 250.7
It would actually be 2506.6
Answer: Your answers are B and D.
Find the coordinates of the circumcenter of ABC with vertices A(-9, -4),
B(-9, 8), and C(-1,0).
The coordinates of the circumcenter are?
Answer:
Step-by-step explanation: 32 because 9 x4 lol
Sarah needs to earn a C in her Algebra class. Her current test scores are 69, 75, 65, and 83. Her final exam is worth 4 test scores. In
order to earn a C Sarah's average must lie between 70 and 79 inclusive. What range of scores can Sarah receive on the final exam to
earn a C in the course?
s final exam scores[
(Type an integer or a simplified fraction.)
Answer:
Sarah must get between a 67 and 85.
Step-by-step explanation:
69 + 75 + 65 + 83 = 292
70 ≥ 1/8(292 + 4x) ≥ 79
70 ≥ 0.5x + 36.5 ≥ 79
67 ≥ x ≥ 85
Find the 11th term of the geometric sequence 7, 35, 175
11th term of the given geometric sequence is [tex]a_{n} = 7(5^{n-1})[/tex]
What is Geometric sequence?In a Geometric Sequence each term is found by multiplying the previous term by a constant.
Given geometric sequence = 7,35,175
Nth term of the geometric sequence [tex]a_{n}=a_{1} .r^{n-1}[/tex]
[tex]a_{1}=7[/tex]
[tex]r= \frac{35}{7} =5[/tex]
Nth term of the geometric sequence
[tex]a_{n} = 7(5^{n-1})[/tex]
Hence, the Nth term of the given geometric sequence is [tex]a_{n} = 7(5^{n-1})[/tex]
A ping-pong ball rolls forward 6 meters, and bounces backward 3 meters. It traveled a total distance of:.
The distance traveled by the ping-pong ball as it rolls forward 6 meters and bounces backward 3 meters is 3 meters.
Distance is a concept that is important to understand in physics and mathematics. It refers to the amount of space between two points. In this scenario, we will be discussing the distance traveled by a ping-pong ball as it rolls forward and bounces backward.
When the ping-pong ball rolls forward, it covers a distance of 6 meters. This can be represented mathematically as d1 = 6 meters.
When the ball bounces backward, it covers a distance of 3 meters. This can be represented as d2 = -3 meters which means the negative sign indicates that it is moving in the opposite direction.
The total distance traveled by the ball can be found by adding the distance traveled in each direction. This can be represented as
=> d = d1 + d2 = 6 + (-3) = 3 meters.
In other words, the total distance traveled by the ball is 3 meters, which is the net distance covered after taking into account both the forward and backward movements.
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help fast need done pls.
my brain is playing not smart on me right now
Special Triangle Segments......
3. Find the value of the variable given the triangles are similar. Answer the additional questions. Show all work. Name the property you used in your problem.
The value of x is 20 and the property is similar triangle
What are similar triangles?Similar triangles are triangles that have the same shape, but their sizes may vary. All equilateral triangles, squares of any side lengths are examples of similar objects. In other words, if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.
Since ∆ ADC and IJH are similar, the ratio of their corresponding sides are equal.
Therefore,1.2/12 = 2/x
1.2x= 12×2
x = 24/1.2
x = 20
Therefore the value of x is 20
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What is the answers to 3/4 x 3/4
Answer: 9/16
Step-by-step explanation: Also known as (3/4)^2
1. 3x3/4x4
2. 9/4x4
3. 9/16
You can't simplify anymore because it is in the simplest form already.
write a explicit formula in slope intercept form.
an=-3+5(n-1)
An explicit formula in slope intercept form for the given expression is aₙ = 5n - 8.
What is the slope-intercept form?Mathematically, the slope-intercept form of the equation of a straight line is given by this mathematical expression;
y = mx + c
Where:
m represents the slope or rate of change.x and y are the points.c represents the y-intercept or initial value.Based on the information provided above, we can logically deduce that an equation in slope-intercept form that models the situation is given by:
aₙ = -3 + 5(n - 1)
aₙ = -3 + 5n - 5
aₙ = 5n - 8
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Can someone pls help me
Answer:10 or 25
Step-by-step explanation:
just add both or times them
5+5 or 5x5
This circle iS centered at the origin, and the length of its radius iS 5. What is
the equation of the circle?
Answer:
25
Step-by-step explanation:
The equation of a circle centered at the origin with radius r is given by:
(x^2) + (y^2) = r^2
In this case, the circle is centered at the origin and has a radius of 5, so the equation is:
x^2 + y^2 = 25
Therefore, the equation of the circle is: x^2 + y^2 = 25
how to calculating rf values?
Answer:
Step-by-step explanation:
Rf values (retention factor values) are used in thin layer chromatography (TLC) to measure the separation of components in a mixture. They are calculated as follows:
Rf = (distance traveled by the solute) / (distance traveled by the solvent)
The distance traveled by the solute is measured from the origin (the spot where the sample was applied) to the final position of the solute on the TLC plate. The distance traveled by the solvent is measured from the origin to the solvent front (the point where the solvent stops moving up the plate).
It is important to note that Rf values are unique to each solute and are dependent on the solvent used, the type of TLC plate, and the conditions of the experiment (such as the temperature and humidity). To ensure accurate comparison of Rf values, it is necessary to standardize the conditions of the experiment.
Calculating Rf values is a crucial step in the interpretation of TLC data, as it allows for the identification of the components of a mixture based on the unique Rf values of each solute.
2. An apartment is 8m in length, 5m in width and 3M in height. How many people can be invited to a party if each person requires 5m³ of air space?
The apartment can accommodate 24 people if each person requires 5 cubic meters of air space.
Solution:
Given,
Dimension of apartment
l = 8m
b = 5m
h = 3m
So, the volume of the apartment will be,
l*b*h = 8*5*3 = 120 cubic meters
Each person requires 5 cubic meters of air space,
Hence, the total number of persons = 120/5 = 24
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A zookeeper is preparing to care for snakes in an exhibit. For every
feeding, she needs three mice and an additional two mice for each
snake. How many mice are needed if the number of the snakes is:
A- 10
B-6
C- x
The number of mice needed is given as follows:
a) 10 snakes: 23 mice.
b) 6 snakes: 15 mice.
c) x snakes: (3 + 2x) mice.
How to define the linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
m is the slope, representing the rate of change.b is the intercept, representing the value of y when x = 0.For every feeding, she needs three mice and an additional two mice for each snake, hence the slope and the intercept of the function are given as follows:
m = 2, b = 3.
The function is then defined as follows:
y = 2x + 3.
For 10 snakes, the number of mice is given as follows:
y = 2(10) + 3
y = 23 mice.
For 6 snakes, the number of mice is given as follows:
y = 2(6) + 3
y = 15 mice.
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Can someone please help me with this?
Show work please
The closet square inch that is needed to cover the cuboid is 208 inches ( option A)
What is surface area of a cuboid?A cuboid is defined as a three-dimensional shape, that has six rectangular faces, eight vertices and twelve edges.
The surface area of cuboid is given as;
SA = 2(lb+lh+bh)
lb = 33/4 × 4 = 33 in
lh = 23/4 × 4 = 23 in
bh = 23/4 × 33/4 = 759/16
SA = 2( 23+33+759/16)
SA = 46+66+47.44
SA = 207 in
therefore the closet square inches is 208 in²
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What is the slope of a line perpendicular to a horizontal line?
The slope of a horizontal line perpendicular to a horizontal line is infinity or undefined.
The slope of a line is the that of the inclination that is makes with a horizontal line.
So, the slope of horizontal line is 1 because the value of tam(0 degrees) is also 1.
A line that is perpendicular to the horizontal line will have a the value of angle to be 90 degrees and we know that,
tan (90 degrees) = undefined/infinity
So, here we are concluding that the slope of any line that is being lying perpendicularly on any horizontally lying line is infinity or undefined.
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Mr. Lee's house has two stories and an attic. The first floor is
9½ feet high, the second floor is 8 3/4 feet high, and the entire
house is 24 7/12 feet high. What is the height of the attic?
The height of the attic in Mr. Lee's house is 6 1/3
What is an equation?An equation is an expression that shows the relationship between numbers and variables using mathematical operators like addition, subtraction, multiplication and division. Equations can be linear, quadratic.
Mr. Lee's house has two stories and an attic. Therefore:
Height of entire house = height of first floor + height of second floor + height of attic
The first floor is 9½ feet high, the second floor is 8 3/4 feet high, and the entire house is 24 7/12 feet high
9 1/2 = 19/2; 8 3/4 = 27/4; 24 7/12 = 295/12. Let x represent the height of the attic. Substituting:
x + 19/2 + 35/4 = 295/12
x = 19/3
x = 6 1/3
The height of the attic is 6 1/3
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A video game randomly chooses your
car color and type. The probability of
getting a red car is 0.25, and the probability of getting a convertible is 0.40.
Event A = You get a red car.
Event B = You get a convertible.
B A and B are independent events if
• A. The probability of getting a red car or a convertible is 0.10.
• B. The probability of getting a red convertible is 0.
•
C. The probability of getting a red convertible is 0.10.
• D. The probability of getting a red car or a convertible is 0.65.
A and B are independent events if, the probability of getting a red convertible is 0.10
What is probability?Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.
Given that, in a video game, the probability of getting a red car is 0.25 (event A), and the probability of getting a convertible is 0.40 (event B).
We need to identify the condition for events A and event B being independent events.
We know that,
The events in probability two are independent if event one does not affect the other one.
The formula for independent events =
P(A∩B) = P(A) x P(B).
So,
P(A) = 0.25 and P(B) = 0.40
P(A∩B) = P(A)xP(B)
= 0.25 x 0.4
= 0.10
Hence, the events A and B are independent events if, the probability of getting a red convertible is 0.10
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can u help me with I J and L please!!!
Teacher's name Height with the heels Height without the heels
Ms. Mathey 190 cm 182.4 cm
Mrs. Meansy 162.5 cm 156 cm
Ms. Cool 140 cm 134.4 cm
Miss Petite cm 155.1 cm
Ms. Lora cm
159.8 cm
The required complete table of heights of teachers is shown in the image attached.
What is the percentage?The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.
Here,
To calculate the height without heels, we need to subtract 4% of the height with heels from the height with heels. This can be done by multiplying the height with heels by 0.96 (which is equivalent to subtracting 4%):
Height without the heels = Height with the heels x 0.96
Using this formula, we can fill in the chart for each teacher.
Thus, the required complete table has been shown in the image attached.
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In a perfectly symmetrical distribution:
a. the range equals the interquartile range.
b. the interquartile range equals the mean.
c. the median equals the mean.
d. the variance equals the standard deviation.
In a perfectly symmetrical distribution, the median equals the mean. This means that half of the values in the distribution fall below the mean and half fall above it. So , the correct option is C.
In a perfectly symmetrical distribution, the median equals the mean. This means that half of the values in the distribution fall below the mean and half fall above it. The mean and median are both measures of the central tendency of a distribution and in a symmetrical distribution, they are the same value.
Option (a) is false because the range is the difference between the largest and smallest values in a distribution, whereas the interquartile range is the difference between the first quartile (25th percentile) and the third quartile (75th percentile), which are measures of variability.
Option (b) is false because the interquartile range is always smaller than the mean in any distribution, symmetrical or not.
Option (d) is false because in a symmetrical distribution, the variance and standard deviation may be equal, but this is not always the case.
So , the correct option is c.
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