Answer:
See explanation below
Answer is 1/8
Step-by-step explanation:
The expression is:
[tex]\left(\dfrac{1}{512}\right)^{\dfrac{1}{3}}[/tex]
A number x raised to the power [tex]\dfrac{1}{3}[/tex] means it is the cube root of that number or [tex]\mbox{\large \sqrt[3]{x} }[/tex]
Also [tex]\left(\dfrac{1}{x}\right)^a = \dfrac{(1)^a}{x^a}[/tex]
Combining these two facts we get
[tex]\left(\dfrac{1}{512}\right)^{\frac{1}{3}} = \dfrac{1^{\frac{1}{3}}}{512^\frac{1}{3}}= \dfrac{\sqrt[3]{1} }{\sqrt[3]{512} } = \dfrac{1}{\sqrt[3]{512} }[/tex]
[tex]\sqrt[3]{512} = 8[/tex]
So
[tex]\left(\dfrac{1}{512}\right)^{\dfrac{1}{3}} = \dfrac{1}{8}[/tex]
how to convert 0.24 as a fraction?
The value 0.24 as a fraction is 6/25. .
In mathematics, fractions are defined as part of a whole. A whole can be an object or a group of objects. In real life, if you cut a pie out of the whole pie, that piece becomes part of the pie. Fractions are words of Latin origin. "Fractus" means "broken" in Latin. In ancient times, rest was expressed in words. Later it was introduced in numerical form.
Fractions are also called parts or sections of any quantity. Represented by the symbol '/'. Bachelor/Bachelor For example, 2/4 is the numerator above and the fraction below the denominator. In this article, you will learn the definition of fractions in mathematics, types of fractions, how to convert fractions to decimals, and many solved examples and full explanations
to convert in fraction we will muliply and devide by 100.
0.24*100/100 =6/25
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Find the conditional probability calculator
Conditional probability can be calculated by using Bayes' theorem, P(A|B) = P(B|A) × P(A) / P(B)
To find the conditional probability, we need to know the probability of two events: the probability of the event we're interested in, and the probability of the condition. Then, we can use Bayes' theorem to calculate the conditional probability.
Bayes' theorem states that the probability of an event A given that event B has occurred is equal to the probability of B given A, multiplied by the probability of A, divided by the probability of B:
P(A|B) = P(B|A) × P(A) / P(B)
The steps to find the conditional probability:
1) Identify the events A and B.
2) Determine the probabilities of A and B.
3) Determine the conditional probability P(B|A)
4) Substitute the values into Bayes' theorem to find P(A|B)
5) Interpret the result.
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How do you calculate Riemann sums?
Riemann sums are calculated by dividing the area under a curve into subintervals and approximating the area in each interval using a rectangle.
Riemann sums are a method of approximating the area under a curve by dividing the area into smaller subintervals and approximating the area in each interval using a rectangle. The width of each rectangle is determined by the size of the subinterval, and the height of the rectangle is determined by the value of the function at a specific point within the subinterval.
The sum of the areas of all the rectangles gives an approximation of the total area under the curve. The accuracy of the approximation increases as the width of the subintervals decreases, and as the number of subintervals increases, the approximation approaches the exact value of the area under the curve.
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What is a measurable part of a line?
approximately what percent of the values in a distribution lie between the 25th percentile and the 75th percentile?
Approximately 50% of the values in a distribution lie between the 25th percentile and the 75th percentile.
The interquartile range (IQR) is the range between the 25th percentile (Q1) and the 75th percentile (Q3) of a distribution. The IQR contains the middle 50% of the data.
Therefore, approximately 50% of the values in a distribution lie outside the IQR, with 25% of the values below Q1 and 25% of the values above Q3. The remaining 50% of the values lie within the IQR, with approximately 25% of the values between Q1 and the median, and 25% of the values between the median and Q3.
So, approximately 50% of the values in a distribution lie outside the IQR, and approximately 50% of the values lie within the IQR, which includes the values between the 25th and 75th percentile.
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You deposit $600 in an account earning 7% coumpound interest for 2 years. Find the future value and the interest earned for each of the following compounding frequencies. Use the Bankers' Rule for daily compounding.
Answer: in two years you'll have 686.94
there is one line on the graph and its asking what is in the solution set?
Answer: you
Step-by-step explanation:
Two angles of a quadrilateral measure 120° and 10°. The other two angles are in a ratio of 5:18. What are the measures of those two angles?
The two angles in the ratio of 5:18 are 50° and 130° respectively. To determine this, we can use the fact that the sum of the angles in any quadrilateral is 360°.
Therefore,
120° + 10° + x + y = 360°where x and y are the two angles in the ratio of 5:18.
We can then solve for x and y by setting up the proportion
5/18 = x/360 and 18/5 = y/360and then solving for x and y.
This gives us
x = 50 and y = 130.Therefore, the two angles in the ratio of 5:18 are 50° and 130°.
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A triangle has sides with lengths of 42 millimeters, 56 millimeters, and 70 millimeters. Is it a right triangle?
Right triangle side lengths can be achieved in a few different ways. You can utilise various relationships or laws to discover the remaining side depending on what is offered.
Presented with two sides
The simplest way is to use the Trigonometry if you are aware of two additional right triangle sides:
a² + b² = c²
If leg an is the omitted side, change the equation such that an is still on one corner and compute the scale factor of that number:
a = √(c² - b²)
Leg b is equal to (c2 - a2) if foot b is unknown.
The formula for a deficient hypotenuse is c = (a2 + b2).
A right triangle has one symmetry boundary line if it is isosceles, meaning that its two different sides have an identical length. Otherwise, the triangle won't have any symmetries lines.
However, not all right-angled triangles are identical. If all of their angles have the same length as well as the relation of two among their angles is the same, then they are similar.
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the teacher workroom has a small room used for the meetings that it shaped like a square . if one wall measures 8 feet what is the area of the floor of that meeting room
The area of the teacher workroom is 64 feet squared
In the screenshots it shows directions answer for each number
1) All the angles are,
∠ 1 = 72°
∠ 2 = 54°
∠ 3 = 54°
∠ 4 = 72°
2) All the angles are,
∠1 = 59°
∠2 = 90°
∠3 = 90°
∠ 4 = 31°
3) All the angles are,
∠ 1 = 22°
∠ 2 = 68°
∠ 3 = 68°
∠ 4 = 90° (right angle)
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
1) From first figure,
⇒ ∠ 3 = 54° (Two sides are equal hence two angles are also equal)
Hence, We get;
∠3 + ∠4 + 54° = 180°
54° + ∠4 + 54° = 180
∠4 = 180 - 108
∠4 = 72°
Hence, We get;
∠ 1 = ∠ 4
∠ 1 = 72°
And, ∠2 = ∠3 = 54°
2) From second figure,
∠ 4 = 90 - 59°
= 31°
And, We have;
∠1 = 59°
And, Diagonal bisect each other.
Hence,
∠ 2 = ∠ 3 = 90°
3) From third figure,
∠ 2 = 68°
Hence, 2 ∠ 1 = 180 - 136°
2 ∠ 1 = 44°
∠ 1 = 22°
And, We have;
Since, ∠ 2 = 68°
Hence, ∠ 3 = 68°
And. ∠ 4 = 90° (right angle)
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Solve the following equation for A.
-BA+g² = MA
Answer: To solve for A in the equation -BA + g² = MA, we can start by isolating the A variable on one side of the equation.
We can start by adding BA to both sides of the equation:
-BA + BA + g² = MA + BA
Simplifying the left side by cancelling the -BA and +BA terms:
g² = MA + BA
Next, we can factor out the A variable from the right side:
g² = A(M + B)
Finally, we can divide both sides by (M + B) to isolate the A variable:
g² / (M + B) = A
So the solution for A is:
A = g² / (M + B)
Step-by-step explanation:
Kolton and Kynslee are taking ice skating lessons. They want to compete in the local ice skating winter show. To participate, they must sell items for the fundraiser. The ice rink is selling winter hats and they are selling t shirts with their logo on it. If Kolton sells 10 hats and 1 shirts for $104 and Kynslee sells 12 hats and 3 shirts for $132, how much are they selling the winter hats for and how much are they selling each t shirt for?
I think for the shirts it's 32 and the t-shirts for 50 .
Step-by-step explanation:
a rectangular room is 3 meters longer than it is wide, and its perimeter is 30 meters. find the dimension of the room.
A regular pentagon has an area of 118.25 square meters, and each side of the pentagon measures 4.3 meters.
What is the length of an apothem of the pentagon?
Answer: 11
Step-by-step explanation: Just took the test
The length of the apothem of the pentagon is approximately 11 meters.
What is a polygon?Polygon is defined as a geometric shape that is composed of 3 or more sides these sides are equal in length, and an equal measure of angle at the vertex,
Examples of polygons, equilateral triangles, squares, pentagons etc.
Here,
To solve this problem, we can use the formula for the area of a regular pentagon:
A = (5/2) × s × a
Where A is the area of the pentagon, s is the length of one side, and a is the apothem (the distance from the center of the pentagon to the midpoint of a side).
We know that the area of the pentagon is 118.25 square meters and the length of one side is 4.3 meters. We can substitute these values into the formula and solve for the apothem:
118.25 = (5/2) × 4.3 × a
Divide both sides by (5/2) x 4.3:
a = 118.25 / ((5/2) × 4.3)
= 118.25 / 10.75 ≈ 11 meters
Therefore, the length of the apothem of the pentagon is approximately 11 meters.
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In ΔSTU, s = 56 cm, u = 94 cm and ∠U=79°. Find all possible values of ∠S, to the nearest degree.
Answer:
∠S possibility is 65 degrees and 115 degrees
Step-by-step explanation:
∠S + ∠T + ∠U = 180
Substituting the given values, we get:
∠S + ∠T + 79 = 180
Simplifying, we get:
∠S + ∠T = 101
We also know that the sides of a triangle are related to the angles opposite them by the law of sines:
a/sin A = b/sin B = c/sin C
In this case, we can use the following ratio:
ST/sin S = UT/sin U
Substituting the given values, we get:
ST/sin S = UT/sin 79
ST = s = 56 cm
UT = u = 94 cm
Solving for sin S, we get:
sin S = (ST × sin 79) / UT
sin S = (56 × sin 79) / 94
sin S ≈ 0.906
Taking the inverse sine, we get:
∠S ≈ 65 degrees or ∠S ≈ 115 degrees
Therefore, the possible values of ∠S are approximately 65 degrees and 115 degrees, to the nearest degree.
Two numbers have a total of 26. The larger number is 10 more than triple the smaller number. What are the two numbers?
Let's call the smaller number "x" and the larger number "y".
We know that:
y + x = 26 (since the total of the two numbers is 26)
and
y = 10 + 3x (since the larger number is 10 more than triple the smaller number)
We can substitute the second equation into the first equation to get:
(10 + 3x) + x = 26
Simplifying, we get:
4x + 10 = 26
Subtracting 10 from both sides, we get:
4x = 16
Dividing both sides by 4, we get:
x = 4
Now that we know x is 4, we can use the second equation to find y:
y = 10 + 3x
y = 10 + 3(4)
y = 22
Therefore, the two numbers are 4 and 22.
what is definition of orthogonal?
In mathematics, the term "orthogonal" refers to a relationship between two objects where they are perpendicular or at right angles to each other.
More generally, it refers to a relationship where two objects are independent or uncorrelated with each other. For example, in Euclidean geometry, two lines are orthogonal if they meet at a right angle. In linear algebra, two vectors are said to be orthogonal if their dot product (also known as inner product) is zero. Similarly, in statistics, two variables are said to be orthogonal if they have a correlation coefficient of zero, indicating that they are uncorrelated.
The term "orthogonal" is also used in various other fields, such as signal processing, computer science, and quantum mechanics, with similar meanings of independence, uncorrelatedness, or perpendicularity.
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need help with this question
The explicit formula for the nth term of the sequence 14,16,18,... is aₙ = 2n + 12.
What is an explicit formula?
The explicit equations for L-functions are the relationships that Riemann introduced for the Riemann zeta function between sums over an L-complex function's number zeroes and sums over prime powers.
Here, we have
Given: the sequence 14,16,18,….
First term a₁ = 14
Common difference d = 16 - 14 = 2
Now, plug the values into the above formula and simplify.
aₙ = a₁ + d( n - 1 )
aₙ = 14 + 2( n - 1 )
aₙ = 14 + 2n - 2
aₙ = 14 - 2 + 2n
aₙ = 2n + 12
Hence, the explicit formula is aₙ = 2n + 12.
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ssume the weight of a randomly chosen american passenger car is a uniformly distributed random variable ranging from 1,749 pounds to 4,039 pounds. (a) what is the mean weight of a randomly chosen vehicle?
The mean weight of a randomly chosen vehicle is 3500 pounds.
What is Z-score?A Z-score helps us to understand how far is the data from the mean. It is a measure of how many times the data is above or below the mean.
We are given that the weight of a randomly chosen american passenger car is a uniformly distributed random variable ranging from 1,749 pounds to 4,039 pounds.
Let X= weight of the passenger car
a/q, X is u(1,749, 4,039)
we know that mean= a+b/2
so a=1,749, b=4,039
hence, mean=1,749 +4,039/2
mean=3500 pounds
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what is left skewed histogram?
A left-skewed histogram is a frequency distribution in which the data is concentrated towards the right side of the histogram, with a tail stretching towards the left.
A left-skewed histogram is a kind of frequency distribution where the data is concentrated towards the right side of the histogram, with a tail extending towards the left. It is otherwise called a negatively skewed histogram or a left-tailed histogram. In a left-skewed histogram, the mean is not exactly in the middle, demonstrating that the information is slanted toward the lower end of the conveyance. This can happen when the information has a lower bound or a base worth, which makes the tail of the dispersion be pulled towards the left. Left-skewed histograms can be helpful in examining information that has a characteristic lower cutoff or floor, for example, response times, reaction rates, or pay levels.
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imagine a line segment ts of length 10000000 and point g moving from t=10000000 toward s=0
At the end of the fourth minute, the point 'g' would be at the position of 9605961 on the line segment TS.
As per the question, at the end of the first minute, g covers 1/100th of the remaining segment, which is 1/100 × 10000000 = 100000 units. Therefore, the position of point g would be at 10000000 - 100000 = 9900000 at the end of first minute.
At the end of second minute, g covers another 1/100th of the remaining segment, which is 1/100 × 9900000 = 99000 units. So, the position of point g would be now 9900000 - 99000 = 9801000.
On the third minute's end , g would covers another 1/100th of the remaining segment, which is 1/100 × 9801000 = 98010 units. Therefore, the position of point g would be at 9801000 - 98010 = 9702990.
For fourth minute's end, point g covers another 1/100th of the next remaining segment, which is 1/100 × 9702990 = 97029 units. Therefore, the final position of point g would be at 9702990 - 97029 = 9605961 units.
Therefore, at the end of the fourth minute, point g would be finally at the position of 9605961 on the line segment TS.
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The correct question is :
imagine a line segment ts of length 10000000 and point g moving from t=10000000 toward s=0, so that it cuts 1/100th of the remaining segment each minute. For example, at the the end of first minute g1 is at 99,00,000. Where is g at the end of fouth minute (g4) ?
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A rectangle garden is enclosed by 60 meters of fencing. The table shows some possible values for the length and width if the yard. If the values for length and area are plotted, what would the graph look like?
1. The Complete table is shown below.
2. The graph likes like parabola whose equation is y= 50x - x².
What is Parabola?Any point on a parabola is at an equal distance from both the focus, a fixed point, and the directrix, a fixed straight line. A parabola is a U-shaped plane curve. The topic of conic sections includes parabola, and all of its principles are discussed here.
Given:
Length Width Area
10 40 400
20 30 600
25 25 625
35 15 525
40 10 400
So, x+ y= 50
y= 50- x
so, area of figure is
= x (50- x)
= 50x - x²
So, we get parabola which is opened downward.
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Where do you stand on the 8 values test?
The community developed the 8 Values Test to assess a person's political position in light of eight essential political tenets. I am standing at 5 in the 8 value test.
The "8 values test" is a political assessment tool that compares and contrasts eight political philosophies: capitalism vs. socialism, traditionalism vs. progressivism, nationalism vs. globalism, libertarianism vs. authoritarianism, democracy vs. elitism, pacifism vs. militarism, ecology vs. production, and decentralization vs. centralization.
The exam generates a political compass based on their responses and presents them on a graph.
The 8 Values Political Test is distributed under the terms of the MIT License.
The 8 Values Political Test is not interchangeable with the Political Compass Test, a registered trademark of Pace News Ltd, or the Political Coordinates Test, a creation of IDRlabs.
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Nolan works as a park ranger for Pine Ridge State Park, where he tracks the black bear population. He estimates that there are 140 black bears in the park today and that the population will increase by a factor of 1/5
each decade.
Write an exponential equation in the form y=a(b)x that can model the park's black bear population, y, in x decades.
Use whole numbers, decimals, or simplified fractions for the values of a and b.
To the nearest whole number, what is the park's predicted black bear population in 5 decades?
The black bear population at that national park in 25 years would be 2973 approx, according to the considered model.
How to evaluate a given mathematical expression with variables if values of the variables are known?
You can simply replace those variables with the value you know of them and then operate on those values to get a final value. This is the result of that expression at those values of the considered variables.
According to the model, the relationship between the elapsed time t, in years, since the beginning of the study, and the black bear population B(t) is:
B(t) = 2500 * 2^0.01t
Here, if we take t = 25 years elapsed, the value of B(t) comes out as:
B(25) = 2500 * 2^0.01*25
B(25) = 2973
Thus, the black bear population be at that national park in 25 years would be 2973 approx, according to the considered model.
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Answer:
B(25) = 2500 * 2^0.01*25
B(25) = 2973
Step-by-step explanation:
This scale drawing shows a reduction in a figure. What is the value of x?
Enter your answer as a decimal in the box
The second trapezoid has the corresponding sides labeled 4.9 cm and x cm, the value of x is 4.2 cm
Without knowing the scale factor, we can use the ratio of corresponding sides of the two trapezoids to set up an equation and solve for x.
The ratio of the lengths of the corresponding sides of the two trapezoids is: 14.7 cm / 12.6 cm = 4.9 cm / x
To solve for x, we can cross-multiply:
14.7 cm × x
= 12.6 cm × 4.9 cm
Dividing both sides by 14.7 cm, we get:
x = (12.6 cm × 4.9 cm) / 14.7 cm
Simplifying the right side, we get:
x = 4.2 cm
Therefore, the value of x is 4.2 cm.
A trapezoid is a quadrilateral with at least one pair of parallel sides. The parallel sides are called the bases of the trapezoid, and the non-parallel sides are called the legs. The height of a trapezoid is the perpendicular distance between the bases. The area of a trapezoid is given by the formula A = (b1 + b2) × h / 2, where b1 and b2 are the lengths of the bases and h is the height. Trapezoids are commonly found in geometric and architectural designs, and they have various applications in engineering and physics.
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Complete Question
This scale drawing shows a reduction in a figure. What is the value of x? Enter your answer as a decimal in the box. x = Two trapezoids of different sizes. The first trapezoid has a side labeled 14.7 cm and a side labeled 12.6 cm. The second trapezoid has the corresponding sides labeled 4.9 cm and x cm, respectively. Find x in trapezoid.
how many inches in 15 cm
Answer:
5.90551 inches
Step-by-step explanation:
1 inch = 2.54 cm1 cm = 0.393701 inTo solve for the number of inches, we can use this equation:
15 × 0.393701 = 5.90551
Therefore, for every 15 cm, it is equivalent to 5.90551 inches.
The manager of the marbles store wants to increase the precision of the estimate of the true mean dollar amount of all purchases made by customers at his store that day.
Which sample size will give the manager the greatest precision of the estimate of the true mean dollar amount of all purchases made by customers at his store that day?
A) 20
B) 30
C) 40
D) 50
the probability of getting a single pair in a poker hand of 5 cardsis approximately 0:42. find the approximate probability that out of 1000 pokerhands there will be at least 450 with a single pair.
The approximate probability that out of 1000 poker hands there will be at least 450 with a single pair is 0.035
How to find the approximate probability ?
This is a binomial distribution problem with n = 1000 and p = 0.42. Let X be the number of poker hands with a single pair out of 1000 poker hands.
To find the probability that there are at least 450 poker hands with a single pair, we need to calculate P(X ≥ 450).
Using the normal approximation to the binomial distribution, we have:
μ = np = 1000 × 0.42 = 420
σ = √(np(1-p)) = √(1000 × 0.42 × 0.58) ≈ 16.08
Using the continuity correction, we can approximate P(X ≥ 450) as P(Z ≥ (449.5 - 420)/16.08) where Z is the standard normal distribution.
P(Z ≥ (449.5 - 420)/16.08) = P(Z ≥ 1.814) ≈ 0.035
Therefore, the approximate probability that out of 1000 poker hands there will be at least 450 with a single pair is 0.035.
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Please help!! Don’t understand this
Answer:
Step-by-step explanation:
Try putting it in Y= in the calculator