The set W represents the x-axis and y-axis in the plane. Any vector with one of its components equal to 0 will satisfy the equation x⋅y = 0, and these vectors lie on either the x-axis or y-axis.
(a) The set W is closed under standard scalar multiplication in the plane. This is because for any scalar c and any vector u = (x,y) in W, the product of the components of cu = (cx,cy) is (cx)(cy) = c2(xy) = c2(0) = 0, so cu is also in W.
(b) The set W is not closed under standard vector addition in the plane. For example, the vectors u = (1,0) and v = (0,1) are both in W, but their sum u + v = (1,1) is not in W because the product of its components is 1(1) = 1, which does not satisfy the equation x⋅y = 0.
Since the set W is not closed under standard vector addition, it does not form a vector space. A set must be closed under both scalar multiplication and vector addition in order to be a vector space.
Geometrically, the set W represents the x-axis and y-axis in the plane. Any vector with one of its components equal to 0 will satisfy the equation x⋅y = 0, and these vectors lie on either the x-axis or y-axis.
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O is the center of the regular nonagon below. Find its perimeter. Round to the nearest tenth if necessary.
The perimeter of the regular octagon with an apothem of 4 units will be 26.51 units.
What is the perimeter of the regular polygon?All the sides of the regular polygon are congruent to each other. The perimeter of the regular polygon of n sides will be the product of the number of the side and the side length of the regular polygon.
P = (Side length) x n
The Apothem of a regular octagon is 5 units. Then the side length of the regular octagon is given as,
tan (360° / (2 × 8)) = (n/2) ÷ 4
tan 22.5° = n / 8
n = 3.3137
Then the perimeter is given as,
P = 8 x 3.3137
P = 26.51 units
The perimeter of the regular octagon with an apothem of 4 units will be 26.51 units.
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One leg of a right triangle measures 7 feet. If the other leg is 1 foot shorter than the hypotenuse, find the dimensions of the triangle.
One leg of a right triangle measures 7 feet. If the other leg is 1 foot shorter than the hypotenuse, the dimensions of the right triangle will be 7 feet, 24 feet, and 25 feet.
To find the dimensions of the right triangle, we can use the Pythagorean Theorem, which states that for any right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two legs. The formula for the Pythagorean Theorem is a² + b2 = c2, where a and b are the lengths of the legs and c is the length of the hypotenuse.
We are given that one leg of the triangle measures 7 feet, and the other leg is 1 foot shorter than the hypotenuse. Let's call the length of the other leg x and the length of the hypotenuse x + 1. We can plug these values into the Pythagorean Theorem to find the dimensions of the triangle:
72 + x2 = (x + 1)2
49 + x2 = x2 + 2x + 1
48 = 2x
x = 24
So the other leg of the triangle measures 24 feet, and the hypotenuse measures 24 + 1 = 25 feet. The dimensions of the right triangle are 7 feet, 24 feet, and 25 feet.
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Find the missing lengths. Give your answers in both simplest radical form and as approximations correct to two decimal places.
Create drawings as needed.
Given: ΔABC with m∠A = m∠B = 45° and BC = 6
Find: AC and AB
The missing lengths are AC = 3√2 ≈ 4.23 and AB = 3√2 ≈ 4.23.
To find the missing lengths of ΔABC, we can use the properties of a 45-45-90 triangle. A 45-45-90 triangle is a special type of right triangle in which the two legs are congruent and the angles are 45°, 45°, and 90°. The ratio of the sides in a 45-45-90 triangle is 1:1:√2, where the hypotenuse is √2 times the length of each leg.
Since we are given that BC = 6 and ∠A and ∠B are both 45°, we can conclude that ΔABC is a 45-45-90 triangle. Therefore, the lengths of AC and AB are both equal to the length of BC, which is 6.
AC = 6
AB = 6
To find the lengths in simplest radical form, we can multiply the lengths of AC and AB by √2/√2 to get:
AC = 6 * √2/√2 = 6√2/2 = 3√2
AB = 6 * √2/√2 = 6√2/2 = 3√2
To find the approximations correct to two decimal places, we can use a calculator to find the decimal values of 3√2:
AC ≈ 3 * 1.41 = 4.23
AB ≈ 3 * 1.41 = 4.23
Therefore, the missing lengths are AC = 3√2 ≈ 4.23 and AB = 3√2 ≈ 4.23.
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A triangle has angle measurements of 3°, 35°, and 142°. What kind of triangle is it?
The triangle is an obtuse triangle.
What is a valid triangle?
A valid triangle is a geometric figure with three sides and three angles. To be considered a valid triangle, it must satisfy the following conditions:
1. The sum of the lengths of any two sides must be greater than the length of the third side. This is known as the Triangle Inequality Theorem, and it ensures that the three sides can form a closed figure.
2. The measure of each angle must be less than 180 degrees. This is known as the Angle Sum Theorem, and it ensures that the three angles can fit inside a two-dimensional plane.
The sum of the angles of any triangle is always 180 degrees.
So, if a triangle has angle measurements of 3°, 35°, and 142°, we can add them up to check whether they add up to 180 degrees:
3° + 35° + 142° = 180°
Since the sum of the angles is 180 degrees, the triangle is a valid triangle.
Now, we can classify the triangle based on the measure of its angles. Since the measure of one angle (142°) is greater than 90 degrees, the triangle is an obtuse triangle.
We cannot determine the length of the sides of the triangle based on the angle measures provided. So, we cannot classify the triangle based on the length of its sides.
Therefore, the triangle is an obtuse triangle.
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Help me!
Apply the inscribed angle theorem.
What is the measure of angle C?
What is the measure of angle B?
What is the measure of angle BSD?
What is the measure of angle CSE?
What is the measure of angle E?
What is the measure of arc BC?
The solution is, the measure of the, inscribed angle: 30°, and,
central angle: 60°.
The solution are,
the measure of angle C is 52°
the measure of angle B is 52°
the measure of angle BSD is 71°
the measure of angle CSE is 71°
the measure of angle E is 57°
the measure of arc BC 57°.
What is an angle?In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle. The two rays are called the sides of an angle, and the common endpoint is called the vertex.
here, we have,
from the given figure, we get,
The central angle is double the inscribed angle for the same intercepted arc.
Since doubling the angle adds 30° to it,
the original inscribed angle must be 30°.
so, we get,
Then the central angle is 30°+30° = 2·30° = 60°.
The solution are,
the measure of angle C is 52°
the measure of angle B is 52°
the measure of angle BSD is 71°
the measure of angle CSE is 71°
the measure of angle E is 57°
the measure of arc BC 57°.
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Help is greatly appreciated :). Will mark brainliest !:D
Answer:
The volume of a rectangular solid is given by the formula V = LWH, where L is the length, W is the width, and H is the height.
In this case, we have:
W = x + 3
L = x + 2
H = x
So the volume is:
V = (x + 2)(x + 3)(x)
V = x(x + 2)(x + 3)
V = x(x^2 + 5x + 6)
V = x^3 + 5x^2 + 6x
Therefore, the volume of the rectangular solid is given by the polynomial expression x^3 + 5x^2 + 6x.
help me PLEASEEEEEEEEEEEEEEEEEEEE
25 POINTS!
The resulting amount should be zero, indicating that all the money was spent. The unknown quantity in this context is the number of players 'p', which we can solve for by rearranging the equation.
What is Algebraic expression ?
Algebraic expression can be defined as combination of variables and constants.
The amount raised by the lacrosse team is $2080.50.
They rented a bus for $970.50.
For each player, they budgeted $74 for meals.
Let's represent the number of players as 'p'.
The equation that represents the context is:
2080.50 - 970.50 - 74p = 0
Or we can represent it in the tape diagram as follows:
_______
| |
| $2080.50|
|_______|
_______
| |
| -$970.50|
|_______|
_______
| |
| -$74p |
|_______|
_______
| |
| $0 |
|_______|
This tape diagram shows that the total amount raised by the team was reduced by the cost of the bus rental and the cost of meals for each player.
Therefore, The resulting amount should be zero, indicating that all the money was spent. The unknown quantity in this context is the number of players 'p', which we can solve for by rearranging the equation
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RADICALS AND QUADR Applying the quadrati Jse the quadratic formula to 9x^(2)-3x-1=0 If there is more than one sol
The quadratic formula is used to solve equations of the form ax^(2) + bx + c = 0. The formula is given by:
x = (-b ± √(b^(2) - 4ac))/2a
In this case, the coefficients are a = 9, b = -3, and c = -1. Plugging these values into the formula gives:
x = (-(-3) ± √((-3)^(2) - 4(9)(-1)))/2(9)
Simplifying the expression gives:
x = (3 ± √(9 + 36))/18
x = (3 ± √45)/18
x = (3 ± 3√5)/18
Simplifying further gives:
x = (1 ± √5)/6
So the two solutions to the equation are:
x = (1 + √5)/6 ≈ 0.62
and
x = (1 - √5)/6 ≈ -0.29
Therefore, the two solutions to the equation 9x^(2)-3x-1=0 are x ≈ 0.62 and x ≈ -0.29.
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What is the volume of a sphere with a diameter of 8.6 m, rounded to the nearest
tenth of a cubic meter?
Answer:
The volume of a sphere with a diameter of 8.6 m = 333.0 m^3
Step-by-step explanation:
1. A factory uses 2 machines, A and B, to produce wafers. Suppose machine A produces 70% of the wafers, of which 5% are defective, while machine B produces 30% of the wafers, of which 6% are defective. Find the probability that a randomly selected wafer is (a) produced by machine A and not defective (b) defective given that it is produced by machine B (c) defective (d) not defective
2. At Sam's tune-up and brake repair shop, the manager found that a car will require a tune-up with a probability of 0.6, a brake job with a probability of 0.02.
a) what is the probability that a car requires either a tune-up or a brake job?
b) what is the probability that a car requires a tune-up but not a brake job?
c) what is the probability that a car requires neither types of repair?
d) are the events "car requires a tune-up" and "car requires a brake job" independent and mutually exclusive?
1. (a) The probability that a randomly selected wafer is produced by machine A and not defective is 0.665 or 66.5%.
(b) The probability that a wafer is defective given that it is produced by machine B is 0.06 or 6%.
(c) The probability that a wafer is defective is 0.053 or 5.3%.
(d) The probability that a wafer is 0.947 or 94.7%.
2. (a) The probability that a car requires either a tune-up or a brake job is 0.608 or 60.8%.
(b) The probability that a car requires a tune-up but not a brake job is 0.588 or 58.8%.
(c) The probability that a car requires neither types of repair is 0.392 or 39.2%.
(d) The events "car requires a tune-up" and "car requires a brake job" are independent because the probability of one event occurring does not affect the probability of the other event occurring. They are not mutually exclusive because a car can require both a tune-up and a brake job at the same time.
We can find the probability using this calculation:
The probability that a randomly selected wafer is produced by machine A and not defective is 0.7 x 0.95 = 0.665 or 66.5%.
The probability that a wafer is defective is (0.7 x 0.05) + (0.3 x 0.06) = 0.035 + 0.018 = 0.053 or 5.3%.
The probability that a wafer is not defective is 1 - 0.053 = 0.947 or 94.7%.
The probability that a car requires either a tune-up or a brake job is 0.6 + 0.02 - (0.6 x 0.02) = 0.608 or 60.8%.
(b) The probability that a car requires a tune-up but not a brake job is 0.6 x (1 - 0.02) = 0.588 or 58.8%.
(c) The probability that a car requires neither types of repair is 1 - 0.608 = 0.392 or 39.2%.
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When an airplane accelerates down a runway at 3.20 m/s2 to 5.41 m/s2 for 28 s until is finally lifts off the ground calculate its acceleration before it takes off.
Answer:
-87.786
Step-by-step explanation:
Given:
Acceleration 1 = 3.20 m/s²
Acceleration 2 = 5.41 m/s²
Time = 28 s
To find: Acceleration before takeoff
Initial velocity = Average acceleration x time + 0.5 x acceleration 1 x time²
Initial velocity = 3.20 m/s² x 28 s + 0.5 x 3.20 m/s² x (28 s)²
Initial velocity = 2460.8 m
Acceleration before takeoff = (0 m/s - 2460.8 m/s) / 28 s
Acceleration before takeoff = -87.886 m/s²
Therefore, the acceleration before takeoff is -87.886 m/s².
There are 25 white tiles in a box. What percent of the tiles will Ally use to tile her laundry room floor.
The percentage of white tiles used out of 25 tiles in Ally's laundry room floor is 32%.
What is meant by percentage?A figure or ratio stated as a fraction of 100 is called a percentage. Frequently, it is indicated with the per cent sign, "%". If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The percentage, therefore, refers to a component per hundred. Per 100 is what the word per cent means. As there is no unit of measurement for percentages, they are dimensionless numbers. This is because we divide numbers with the same units in percentage calculation.
From the figure,
We can see that the total number of tiles used for flooring= 16
Out of this, 8 tiles used are white tiles.
Now it is said that the total number of white tiles is 25.
We are asked to find what percentage of 25 tiles are used on the laundry room floor.
We will use a fraction to describe the proportion of white tiles in the box to those used for the floor and then multiply it by 100 to find the percentage.
Percentage = ( white tiles used / Total number of white tiles ) * 100
= 8/25 * 100 = 32%
Therefore the percentage of white tiles used out of 25 tiles in Ally's laundry room floor is 32%.
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Minh has 2 cups of sesame seed one recipe calls for 1/3 cup of sesame seeds how many batches of the recipe Minh make
The number of batches of the recipe Minh makes is 6
What is proportion?A proportion can be described as a mathematical comparison that is between two numbers.
These numbers can represent a comparison between things or people.
Also, proportions can also be written as two equivalent fractions. They are represented with the equality sign '=' or the equivalent sign ':'
From the information given, we have that;
For one recipe, one uses 1/3 cup of sesame seeds
Minh has 2 cups of sesame seeds
Then,
If 1/3 cup of sesame seeds = 1 recipe
Then 2 cups of sesame seeds = x
cross multiply
c = 2 × 3/1
c = 6 recipes
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Which polynomial would be classified as a cubic trinomial?
a) -5x^2-4x
b) -3x^4+2x^3-8
c) 5x^3-4x+2
d) 7x^4-3x^^3
Answer: C
Step-by-step explanation: What is an example of cubic trinomial?
Cubic Trinomials of the Form Ax^3 + Bx+^2 + Cx
For example, the greatest common factor of the trinomial 3x^3 - 6x^2 - 9x is 3x, so the polynomial is equal to 3x times the trinomial x^2 - 2x -3, or 3x*(x^2 - 2x - 3).
Which of the following is the graph of the piecewise function f of x is equal to the piecewise function of the quantity square root of negative x minus 1 if x is less than or equal to negative 1 and the function negative x over the quantity x squared minus x minus 2 end quantity if negative 1 is less than x is less than 2 and the function log in base 2 of the quantity x minus 1 end quantity if x is greater than or equal to 2 question mark
The graph of the piece-wise function is given by the image presented at the end of the answer.
What is a piece-wise function?A piece-wise function is a mathematical function that is defined by different formulas or expressions over different intervals or pieces of its domain, that is, the function has different definitions based on it's input.
The intervals for which the function has different definitions are given as follows:
x ≤ -1.-1 < x < 2.x ≥ 2.The definitions for each interval are given as follows:
x ≤ -1 -> f(x) = sqrt(x - 1). -> outside domain of square root, hence does not show up on graph-1 < x < 2 -> f(x) = -x/(x² - x - 2).x ≥ 2. -> f(x) = log2(x - 1).Hence the graph of the function, containing these three definitions, is given by the image presented at the end of the answer.
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The sum of two consecutive integers is 85. Find the integers.
(Enter your answers as a comma-separated list.)
The sum of two consecutive integers 42 and 43 is 85.
The sum of two consecutive integers is 85. This means that we need to find two integers that are next to each other on the number line and add up to 85. We can write this as an equation:
x + (x + 1) = 85
Simplifying the equation gives us:
2x + 1 = 85
Subtracting 1 from both sides gives us:
2x = 84
Dividing both sides by 2 gives us:
x = 42
This means that the first integer is 42. Since the two integers are consecutive, the second integer is 42 + 1 = 43. Therefore, the two integers are 42 and 43.
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Bill's SUV is 6 feet 4 inches tall. If he puts a 2 -foot 9 -inch box on top of his SUV, what is the total height of the SUV and the box (in feet and inches)?
Answer: The total height of the SUV and the box is 9 feet 1 inch.
Step-by-step explanation:
To solve this problem, we first convert the height of the SUV and the box from feet and inches to inches. The height of the SUV is 6 feet 4 inches, which is equal to 76 inches. The height of the box is 2 feet 9 inches, which is equal to 33 inches. We then add the heights of the SUV and the box to get the total height:
76 inches + 33 inches = 109 inches
To convert this back to feet and inches, we divide by 12 to get 9, with a remainder of 1. Therefore, the total height of the SUV and the box is 9 feet 1 inch.
Determine the intercepts of the line.
Do not round your answers.
2
�
+
5
�
=
−
6
2x+5y=−6
The intercepts of the line are (-3, 0) and (0, -6/5).
What is intercepts ?
In mathematics, intercepts refer to the points at which a line or curve intersects the x-axis or the y-axis of a coordinate plane.
To find the x-intercept, we need to set y = 0 and solve for x:
2x + 5(0) = -6
2x = -6
x = -3
Therefore, the x-intercept is (-3, 0).
To find the y-intercept, we need to set x = 0 and solve for y:
2(0) + 5y = -6
5y = -6
y = -6/5
Therefore, the y-intercept is (0, -6/5).
Thus, the intercepts of the line are (-3, 0) and (0, -6/5).
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The following are body mass index (BMI) scores measured in 9 patients who are free of diabetes and participating in a study of risk factors for obesity. Body mass index is measured as the ratio of weight in kilograms to height in meters squared.
25 27 31 33 26 28 38 41 24
What is the standard deviation of BMI?
Therefore, the standard deviation of BMI for the 9 patients in the study is 5.67.
To find the standard deviation of BMI for the 9 patients in the study, we need to follow these steps:
Find the mean of the BMI scores: (25 + 27 + 31 + 33 + 26 + 28 + 38 + 41 + 24) / 9 = 29.67
Subtract the mean from each BMI score to find the deviation: -4.67, -2.67, 1.33, 3.33, -3.67, -1.67, 8.33, 11.33, -5.67
Square each deviation: 21.81, 7.13, 1.77, 11.09, 13.45, 2.79, 69.43, 128.51, 32.15
Find the mean of the squared deviations: (21.81 + 7.13 + 1.77 + 11.09 + 13.45 + 2.79 + 69.43 + 128.51 + 32.15) / 9 = 32.12
Take the square root of the mean of the squared deviations to find the standard deviation: √32.12 = 5.67
Therefore, the standard deviation of BMI for the 9 patients in the study is 5.67.
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Mrs. Hernandez bought several soccer uniforms. She spent $57 in all. Write an equation to find the number of soccer uniforms she bought * each uniform cost $9.50
the answer is 6 uniforms. 57/9.5=6
There is an equal amount of yellow, blue, green, and red marbles in a bag of 32 marbles. If Ed draws 4 marbles out of the bag with replacement, predict how many of the 4 marbles drawn should be blue.
1
4
8
32
We predict that Ed should draw about 1 blue marble out of the 4 draws. The closest option is 1.
What is probability?
Probability is a branch of mathematics in which the chances of experiments occurring are calculated. It is by means of a probability, for example, that we can know from the chance of getting heads or tails in the launch of a coin to the chance of error in research.
There are 4 colors of marbles, each with 8 marbles in the bag, so the probability of drawing a blue marble on any given draw is:
P(blue) = 8/32 = 1/4
Since Ed is drawing 4 marbles with replacement, the probability of drawing a blue marble on each individual draw is the same:
P(blue) = 1/4
The probability of drawing a blue marble exactly k times out of 4 draws can be calculated using the binomial probability formula:
P(k blue out of 4) [tex]= (4 choose k) * (1/4)^k * (3/4)^{(4-k)[/tex]
where (4 choose k) is the binomial coefficient, which gives the number of ways to choose k blue marbles out of 4 draws.
E(number of blue) = Σ(k * P(k blue out of 4)), summed over all possible values of k from 0 to 4.
This calculation can be done directly or by using the formula:
E(number of blue) = n * P(blue)
where n is the total number of draws (4 in this case) and P(blue) is the probability of drawing a blue marble on each draw.
Using this formula, we get:
E(number of blue) = 4 * (1/4) = 1
Therefore, we predict that Ed should draw about 1 blue marble out of the 4 draws. The closest option is 1.
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Determine the finance charge on a $15,820 car loan if monthly payments were $325 for 60 months.
The finance charge on a $15,820 car loan if monthly payments were $325 for 60 months is: $3,680.
How to find the finance charge?The total amount paid over 60 months is:
Total amount paid = $325/month x 60 months
Total amount paid = $19,500
The amount of interest paid is:
Amount of interest = $19,500 - $15,820
Amount of interest = $3,680
Therefore, the finance charge on the car loan is $3,680.
Therefore the finance charge is $3,680.
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What is the variable if
the trinomial a^2+7a+6 and the binomial a+1 have the same value?
The variable that satisfies the condition that the trinomial a^2 + 7a + 6 and the binomial a + 1 have the same value is a = -5 or a = -1.
How is a variable determined?Setting the trinomial and binomial equal to one another and then solving for the variable will help us identify the variable that satisfies the stated criteria. Which is:
a^2 + 7a + 6 = a + 1
By putting all the terms to one side and grouping like terms, we may make this equation simpler:
a^2 + 6a + 5 = 0
The quadratic expression on the left-hand side can now be factored:
(a + 5)(a + 1) = 0
To make each factor equal to zero, we can use the zero product property:
a + 5 = 0 or a + 1 = 0
In each equation, we can solve for a to obtain:
a = -5 or a = -1
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what is 7.5= to in mm?
Answer:
7.5 inches is equal to 190.5 millimeters (mm).
To convert from inches to millimeters, we can use the conversion factor of 1 inch = 25.4 millimeters.
So, 7.5 inches x 25.4 millimeters/inch = 190.5 millimeters.
The difference in the x-coordinates of two points is 3, and the difference in the y-coordinates of the two points is 6. What is the slope of the line that passes through the points?
The slope of the line that passes through the two points is 2.
What is point slope form?The equation of the straight line that is inclined at a specific angle to the x-axis and passes at a specific point may be found using the point slope form. A line's equation is an equation that each and every point on the line can solve. Hence, a line may be represented by a linear equation with two variables. Depending on the information at hand, a line's equation can be discovered using a variety of techniques. Among the techniques are: Slope form at a point. Slope-intercept pattern
The equation of the slope is given as:
slope = (change in y-coordinates) / (change in x-coordinates)
Here, for the given condition we have:
slope = (6) / (3) = 2
Therefore, the slope of the line that passes through the two points is 2.
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Review Question Simplify the expression. (8d^((3)/(2))*7h^((5)/(6)))(7h^((3)/(2))*8d^((5)/(6)))
To simplify the expression (8d^((3)/(2))*7h^((5)/(6)))(7h^((3)/(2))*8d^((5)/(6))), we need to use the distributive property and the laws of exponents.
First, we can distribute the 8d^((3)/(2)) and 7h^((5)/(6)) to the 7h^((3)/(2)) and 8d^((5)/(6)):
= (8d^((3)/(2))*7h^((3)/(2)))*(7h^((5)/(6))*8d^((5)/(6)))
Next, we can use the laws of exponents to simplify the expressions with the same base:
= (8^2*d^((3)/(2)+(5)/(6))*7^2*h^((5)/(6)+(3)/(2)))
= (64*d^((11)/(6))*49*h^((9)/(6)))
Finally, we can simplify the exponents and multiply the constants:
= (3136*d^((11)/(6))*h^((3)/(2)))
Therefore, the simplified expression is 3136*d^((11)/(6))*h^((3)/(2)).
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Can someone help me I need it quick
Thank in the shape of a cylinder that contains 54,000 gallons of water in the tank is over 60% food how many gallons of water can the tank hold
The tank can hold up to average 90,000 gallons of water, since it is already filled with 54,000 gallons and 60% of that is food.
Volume = πr2h
= 3.14 x (15 feet)2 x 18 feet
= 15,444.4 cubic feet
15,444.4 cubic feet x 7.48 gallons/cubic feet = 115,511.17 gallons
115,511.17 gallons - 54,000 gallons = 61,511.17 gallons
61,511.17 gallons + 54,000 gallons = 115,511.17 gallons
115,511.17 gallons is the total capacity of the tank.
The tank is able to hold up to 90,000 gallons of water, since it already contains 54,000 gallons and 60% of that is food. This means that the tank can still hold up to 36,000 gallons of water, giving it a total capacity of 90,000 gallons. This is possible because the tank is in the shape of a cylinder, which means that the volume of the tank is determined by the formula V = πr2h, where V is the volume, r is the radius, and h is the height. This means that the tank can be adjusted accordingly to increase or decrease the amount of water it can hold. In this case, the tank is able to hold up to 90,000 gallons of water because the capacity of the tank is determined by the size of its radius and height, and can be adjusted accordingly to increase or decrease the amount of water it can hold.
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(Write down the formula to calculate the distance between (x₁, y₁) and (x2. y2).) Ans: d =
The requried distance formula to calculate the distance between points (x₁, y₁) and (x₂, y₂) is d = √((x₂ - x₁)² + (y₂ - y₁)²)
What is Distance?Distance is defined as the length of measure between two points on the coordinate plane.
Here,
The formula to calculate the distance between two points in a two-dimensional Cartesian coordinate system is:
d = √((x₂ - x₁)² + (y₂ - y₁)²)
Where (x₁, y₁) and (x₂, y₂) are the coordinates of the two points, and sqrt represents the square root function.
This formula is derived from the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In this case, the two points represent the endpoints of the hypotenuse, and the distance between them is the length of the hypotenuse. Therefore, we can use the Pythagorean theorem to calculate the distance between the two points.
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Suppose you have 22 units of Virtual Currency and John takes 21 of them. How many units of Virtual Currency would you need to purchase Bloxburg on the rablax platform?
a. 1 unit of Virtual Currency (insufficient for Bloxburg purchase)
b. 25 units of Virtual Currency (sufficient for Bloxburg purchase)
c. 1 extra large unit of Virtual Currency (sufficient for Bloxburg purchase)
d. 62 units of Virtual Currency (insufficient for Bloxburg purchase)
In response to the aforementioned query, we may say that The right equation response is b. 25 virtual currency units (sufficient for Bloxburg purchase).
What is equation?A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.
You presently have 22 units of virtual currency, and John takes 21, according to the facts provided. You now only have 1 unit of virtual currency.
Consequently, to acquire Blox , you would require an additional 24 units of virtual currency.
The right response is b. 25 virtual currency units (sufficient for Bloxburg purchase).
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