Answer:
The area of a circle is pi multiplied by the radius squared (A = π r²)
The radius (r) is the distance from the center of the circle, to the edge of the circle.
Example:
if you have a circle with radius 2, the area would be:
r = 2
A = π (2)²
A = π(4)
A = 4π
Answer:
Area can be calculated by the formula = [tex]\pi r^{2}[/tex]
Step-by-step explanation:
We can calculate the area of a circle with the formula,
Area of Circle = [tex]\pi r^{2}[/tex]
Where r replicates the radius of the circle
There are 10 brown, 10 black, 10 green, and 10 gold marbles in bag. A student pulled a marble, recorded the color, and placed the marble back in the bag. The table below lists the frequency of each color pulled during the experiment after 40 trials.
Outcome Frequency
Brown 13
Black 9
Green 7
Gold 11
Compare the theoretical probability and experimental probability of pulling a gold marble from the bag.
The theoretical probability, P(gold), is 25%, and the experimental probability is 27.5%.
The theoretical probability, P(gold), is 50%, and the experimental probability is 11.5%.
The theoretical probability, P(gold), is 25%, and the experimental probability is 25%.
The theoretical probability, P(gold), is 50%, and the experimental probability is 13.0%.
The theoretical probability is 25%, and the experimental probability is 27.5%.
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. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty.If two events A and B occur on a single performance of an experiment, this is called the intersection or joint probability of A and B, denoted as P(A ∩ B).Given is that There are 10 brown, 10 black, 10 green and 10 gold marbles in bag. A student pulled a marble, recorded the color, and placed the marble back in the bag. The table below lists the frequency of each color pulled during the experiment after 40 trials.
Thee given table is -
Outcome Frequency
Brown 13
Black 9
Green 7
Gold 11
The probability of pulling out a gold ball will be -
P{gold} = 11/40 = 0.275 = 0.275 x 100 = 27.5%
P{gold} = 27.5%
Therefore, the theoretical probability is 25%, and the experimental probability is 27.5%.
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I know each x_i (i = 1, 2, ..., n) is a random variable based on the sample size n obtained. Therefore, [tex]\frac{}{X}[/tex] is a random variable since it would be a different (random) value for each new sample size of n collected. How would I further elaborate on this explanation to answer the question in the screenshot?
The sample mean can be classified as a random variable because it is calculated from the sample which is built as random.
How to obtain the mean of a data-set?The mean of a data-set is obtained as the sum of all observations in the data-set divided by the number of observations.
Hence the sample mean is obtained as the sum of all observations of the sample divided by the sample size.
As the observations of the sample are taken at random, the sum of these observations will be a random variable, and so will the sample mean.
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Find the equation of the line containing the point
P(1, 2)
and parallel to the graph of
5x + y = −2.
Answer:
y = -5x + 7
Step-by-step explanation:
Parallel lines on a graph have the same slopes/gradients.
m1=m2
First you want to rewrite the equation of the graph given. So put the 5x to the other side and you will have:
y = -5x -2
This means that the equation that we need must have the gradient -5 (bc it is m in y=mx+c)
The equation will be y = -5x + c
However we must still find c aka the y intercept.
Sub the point we are given (1,2) into the equation
We will have:
2 = -5(1) + c
2 = -5 + c
7 = c
Now that we know c, we know what the equation of the line is. Just sub it in (without 1 and 2)
y = -5x + 7
State if the two triangles are congruent. If they are, state how
you know.
Explanation:
ASA = angle side angle
The marked side is between the marked angles.
The markings on the angles tell us which angles pair up to be congruent. The tickmark on the sides tell us the sides are congruent.
AAS is similar to ASA, but with AAS the marked side isn't between the marked angles.
We cannot use SAS since we don't know anything about another pair of sides.
(Show your work please) Rewrite in simplest rational exponent form square root of x times the fourth root of x. Show each step of your process.Rewrite in simplest rational exponent form square root x times 4 square root x
By applying the exponential properties, it can be concluded that the simplest rational exponent is [tex]x^{\frac{3}{4} }[/tex]
Exponential is a repeated multiplication method with the same number, which is notated in the form aⁿ, where a is called the base and n is the exponent or power.
Some properties of exponent:
[tex]a^{x}[/tex] x [tex]a^{y}[/tex] = [tex]a^{x+y}[/tex]
[tex]a^{x}[/tex] : [tex]a^{y}[/tex] = [tex]a^{x-y}[/tex]
[tex](a^{x}) ^{y}[/tex] = [tex]a^{xy}[/tex]
[tex](\frac{a}{b} )^{x}[/tex] = [tex]\frac{a^{x} }{b^{x} }[/tex]
a⁰ = 1
a⁻ˣ = 1 / aˣ
In mathematics, a radical is described as [tex]\sqrt[n]{x}[/tex], where n is a positive integer ≥ 1 and x is a real number. Then n is called the index of the radical, x is the radicand, and the symbol √ is the radical.
The radical can be written as a rational exponent as follows:
[tex]\sqrt[n]{x} = x^{\frac{1}{n} }[/tex] or [tex]\sqrt[n]{x^{m} } = x^{\frac{m}{n} }[/tex]
From the problem, we can denote the expression as follows:
square root of x = √x
the fourth root of x = ⁴√x
The product of the two expressions will be:
(√x) x (⁴√x) = [tex]x^{\frac{1}{2}}[/tex] x [tex]x^{\frac{1}{4} }[/tex]
= [tex]x^{\frac{3}{4} }[/tex]
Thus the simplest rational exponent is [tex]x^{\frac{3}{4} }[/tex]
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Which of the following are square properties? Choose ALL that apply.
Diagonals are congruent.
Exactly one pair of parallel sides.
Four right angles.
Diagonals are perpendicular.
NO LINKS!!!!
Please help me with #4
Answer:
C) To know whether 2 triangles are similar, it is enough to know the measure of 2 angles in each triangle.
Step-by-step explanation:
Two triangles are said to be similar if:
corresponding angles are the same size, andcorresponding sides are in the same ratio.As there are three interior angles in a triangle, and the sum of the interior angles is always 180°, we need to know the measure of at least 2 angles in each triangle to determine if they are similar. The known angles don't have to be corresponding angles, as we can calculate the third angle and then compare all three angles to determine if the triangles are similar.
With regards to the sides of a triangle, it is not enough to know the measure of 2 sides to determine if they are similar. We would need to know at least one interior angle in this case.
Resolve the vector combinations below:
a. 45 m S and 35 m S
b. 15 m N and 60 m S
c. 5 m S, 10 m E, and 7m W
a. 45 m S and 35 m S: This vector combination resolves to 10 m S.
b. 15 m N and 60 m S: This vector combination resolves to 45 m S.
c. 5 m S, 10 m E, and 7m W: This vector combination resolves to 8 m E.
What is the vector?Vectors can be added, subtracted, and multiplied by scalars (numbers) to create new vectors. In physics, vectors are used to represent quantities such as velocity, force, and acceleration.
They can also be used in other fields such as engineering, computer graphics, and economics. Vectors can be represented in different ways, such as in Cartesian coordinates (x, y, z) or polar coordinates (magnitude, angle).
a. The vector combination of 45 m S and 35 m S is 10 m S. This is because the vectors are pointing in the same direction (south) and the magnitude of the resultant vector is the sum of the magnitudes of the individual vectors.
b. The vector combination of 15 m N and 60 m S is 45 m S. This is because the vectors are pointing in opposite directions (north and south) and the magnitude of the resultant vector is the difference of the magnitudes of the individual vectors.
c. The vector combination of 5 m S, 10 m E, and 7 m W is 8 m E. This is because the vectors are pointing in different directions (south, east, and west) and the magnitude of the resultant vector is found using the Pythagorean theorem.
The east and west vectors can be viewed as the legs of a right triangle, with the resultant vector being the hypotenuse. The magnitude of the resultant vector is the square root of the sum of the squares of the individual vectors.
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A and B are the parallel. Find the missing angles.
125
55
35
Answer:
Step-by-step explanation:
According to an article on The Guardian website, a British woman born in 2003 has probability 0.27 of living at least 100 years. Five high school friends all happen to be females born in 2003.Assuming that the survival of each one is independent of the others, what is the probability that at least one of them lives to be 100 years old?
The probability that at least one of the five female high school friends born in 2003 lives to be 100 years old is 0.054 or 5.4%.
What is the probability?Probability refers to the chance, odds, or likelihood that an expected outcome occurs when there are many possible outcomes.
Probability is a fractional value, lying between one and zero when the expected event is not 100% certain or uncertain.
Probability is computed as the quotient or ratio that results from dividing the expected value by the total weight.
The chance of British women born in 2003 living at least 100 years according to The Guardian website = 0.27
The probability that at least one of five female high school friends born in 2003 lives to be 100 years old = 0.27 x 1/5
= 0.054
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Help me ASAP math question.
The value of x is 900 and value of y is 300.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
From the given information we form a system of linear equations.
1.4x+1.6y=1740..(1)
x-3y=0..(2)
x=3y
Plug in x =3y in the equation 1.
1.4(3y)+1.6y=1740
4.2y+1.6y=1740
5.8y=1740
Divide both sides by 5.8
y=300
x=3(300)=900
Hence, the value of x is 900 and value of y is 300.
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i forget joint frequency
The joint frequency of adults who voted for chocolate is given as follows:
0.1148.
How to calculate a joint frequency?A relative frequency is calculated as the division of the number of desired outcomes by the number of total outcomes.
A joint frequency is calculated considering a combination of two events.
In the context of this problem, we have that out of 122 people, there are 14 adults who voted for chocolate, hence the joint frequency of adults who voted for chocolate is obtained as follows:
14/122 = 0.1148.
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What is the greatest number that evenly divides the sum of any three consecutive whole numbers
The greatest number that evenly divides the sum of any three consecutive whole numbers is three.
What is an Integer?
This is referred to as a whole number that can be positive, negative, or zero and we should note that it doesn't a fractional number and examples include 0, 2, -3 etc.
The product of any three consecutive integers is always divisible by 3 and the addition of any 3 consecutive numbers together it will always equal a multiple of 3 which is therefore the reason why it was chosen as the correct choice.
An example is n+2 is an integer, 3(n+2) is divisible by 3 in this scenario hence 3 is the correct choice.
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-11x-14x-26=-25-25x-1
What kind of equation is it
Answer:
Linear equation with one variable
Step-by-step explanation:
Here, that one variable is x.
- 11x - 14x - 26 = - 25 - 25x - 1
- 25x - 26 = - 25x - 25 - 1
- 25x - 26 = - 25x - 26
Multiply - 1 on both sides,
25x + 26 = 25x + 26
This equation has infinite solutions.
Where value you substitute in place of x, you will the same answer on the both the sides.
The graph below shows a linear relationship between x and y. Assume that both the x-axis and the y-axis have the same scale. Determine the value of the constant rate of change of y with respect to x (This is a numerical value.) Write a formula that expresses change in y in terms of change in x. Suppose that y = 1.5 when x=1 Write a formula that expresses y in terms of x.
The value of the constant rate of change of y with respect to x is 20.
A formula that expresses change in y in terms of change in x is y = kx.
Suppose that y = 1.5 when x = 1, a formula that expresses y in terms of x is k = 1.5.
How to determine the value of the constant rate of change?In Geometry, the rate of change of any straight line simply refers to its gradient or slope and it can be calculated by using this mathematical expression;
Rate of change (slope), m = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Rate of change (slope), m = (y₂ - y₁)/(x₂ - x₁)
Assuming that both the x-axis and the y-axis have a scale of 1:20, the constant rate of change is given by:
Constant rate of change = 20/1 = 20.
When y = 1.5 and x = 1, a formula that expresses y in terms of x is given by:
y = kx
k = y/x
k = 1.5/1
k = 1.5.
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Which expression is equivalent to 250h² - 100h?
O 50h(5h - 2)
○ 50(5h - 2)
○ 50h (5h+2)
50(5h+2)
Answer:
50h(5h - 2)
Step-by-step explanation:
Open up all the parenthesis on each answer
only the first one is correct
Answer:
50h(5h-2)
Step-by-step explanation:
Solution given
250h² - 100h
50*5*h*h-50*2*h
taking common
50*h(5*h-2)
50h(5h-2)
here taking common and keeping remaining on bracket
50h(5h-2)
Which table shows a proportional relationship between X and Y?
K12
X and Y don't have a proportionate relationship.No, not all yx ratios are equal.
What is a ratio?If the ratios of two or more numbers or variables are equal to one another, they are said to be in proportion.
The answer to the query is
8; 10, 12; 14, given x
y : 5, 7, 9, 11
Ratios between various x and y values are not comparable.
( 8 /5)
≠ (10 / 7)
≠ (12 /9)
≠(14 /11)
We get to the conclusion that x and y have no proportional relationship.
Hence, Option(1) is the correct answer.
X and Y don't have a proportionate relationship.No, not all yx ratios are equal.
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The sum of the measures of angle P and angle Q is 100⁰.
• The measure of angle P is (3x - 15)°.
• The measure of angle Q is 25°.
What is the value of x? (7.11C, SS, RC3)
Answer:
x = 30
Step-by-step explanation:
You are given an angle and the sum of that angle with another that is (3x-15)°, and you want the value of x.
EquationThe sum of the two angles is given as 100°.
P +Q = 100°
(3x -15)° +25° = 100° . . . . . . use the given values for angles and sum
3x = 90 . . . . . . . . . . . . divide by ° and subtract 10
x = 30 . . . . . . . . . divide by 3
The value of x is 30.
Factorise fully 20xy - 54
Plss answer
The factorisation of 20xy - 54 can be expressed as 2( 10xy - 27 ).
What is factorisation?The concept here is the factorisation . The breaking or decomposition of an entity (such as a number, a matrix, or a polynomial) into a product of another entity, or factors, whose multiplication results in the original number, matrix, etc., is known as factorization or factoring in mathematics.
A number or other mathematical object is factorized or factored when it is written as the product of numerous factors, typically smaller or simpler things of the same kind.
We were given, 20xy - 54, we can see that that factor of 2 is common for both 20xy and 54.
Then we can factorize as 2( 10xy - 27 ).
2( 10xy - 27 )
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which of the following tables best shows the expected values in the f2 generation for a chi-square goodness-of-fit test for a model of independent assortment?
The chi-square goodness-of-fit test requires a comparison of the observed values with their expected values in the f2 generation.
Option A. Observed Values | Expected Values; this is the best choice for this comparison.The chi-square goodness-of-fit testThe chi-square goodness-of-fit test is used to determine how well observed values fit a model of independent assortment. The test requires a comparison of the observed values with their expected values in the f2 generation.
Option A is the best choice for this comparison, as it provides a direct comparison of the observed and expected values. This comparison allows for an assessment of the goodness-of-fit of the model, as any differences between the observed and expected values can be attributed to the model's performance.
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Complete the table of ordered pairs for the linear equation y=3x-11
Solve for the solution to a system of equations using the following matrices and Cramer’s rule. Show your work.
A= [2 1] X= [5 1] Y= [2 5]
[1 3] [5 3] [1 5]
A cylindrical pottery vase has a diameter of 4.3 inches and a height of 11 inches. What is the surface area of the vase? Use the formula SA= B+ Ph, since the vase has a bottom but no top. Use 3.14 for TT and round to the nearest tenth of a square inch.
Answer: To find the surface area of the cylindrical vase, we can use the formula:
SA = B + Ph
Where B is the area of the base (the circular top of the vase), P is the perimeter of the circular top of the vase, and h is the height of the vase.
We know that the diameter of the vase is 4.3 inches and the height of the vase is 11 inches. To find the radius of the base, we can divide the diameter by 2:
r = 4.3 inches / 2 = 2.15 inches
The area of the base is given by πr², so:
B = πr² = π * 2.15² = 14.65 square inches
To find the perimeter of the circular top we can use 2πr:
P = 2πr = 2 * 3.14 * 2.15 = 13.64 inches
Now we can substitute these values into the formula:
SA = B + Ph = 14.65 + 13.64 * 11 = 260.04 square inches
Rounded to the nearest tenth, the surface area of the vase is 260.0 square inches.
Step-by-step explanation:
4. Is 3 in the domain of the function ? Why or why not?
The domain of the function f(x) = √(x - 5) is x ≥ 5, thus, x = 3 is not in the domain.
Is 3 on the domain of the function?Remember that for a function y = f(x), we define the domain as the set of the possible inputs.
Here we have the square root function:
f(x) = √(x - 5)
Remember that the argument of a square root needs to be zero or larger, then the domain of the given function is:
x - 5 ≥ 0
Solving for x:
x ≥ 5
The domain is the set of values equal to or larger than 5, thus, the value 3 is not in the domain.
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Multiply Both Equations to Eliminate a Variable
5.x - 3y = 6
2x + 5y = -10
The value of x and y obtained when multiplying equations to eliminate variable is y = -62/40 and x = -18/16.
What is elimination method?The elimination approach involves taking one variable out of the system of linear equations by utilizing addition or subtraction together with multiplication or division of the variable coefficients.
The given equations are:
5x - 3y = 6, and
2x + 5y = -10
Isolate the value of x in the following equation:
5x - 3y = 6
5x = 6 + 3y
x = (6 + 3y)/5
Substitute the value of x as follows:
2x + 5y = -10
(2) (6 + 3y)/5 + 5y = -10
12 + 15y + 25y = -50
40y = -50 -12
40y = -62
y = -62/40
Substitute the value of y to find the value of x:
2x + 5(-62/40) = -10
16x - 62 = -80
16x = -80 + 62
16x = -18
x = -18/16
Hence, the value of x and y obtained when multiplying equations to eliminate variable is y = -62/40 and x = -18/16.
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Does the equation below define a linear function?
y = -x³ - 11
Explain how you got your answer.
The equation does not define a linear function
How to determine the type of the functionFrom the question, we have the following parameters that can be used in our computation:
y = -x³ - 11
As a general rule, a linear equation is any equation that has a degree of 1
The given equation above has a degree of 3
Hence, it is not a linear equation
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question 1(multiple choice worth 1 points) (06.11 mc) identify the improper integral(s): the integral from 2 to 5 of dx over quantity x squared minus 1 the integral from 1 to infinity of quantity x minus 1 dx the integral from negative 2 to 3 of dx over quantity x plus 1 i and ii ii and iii i only iii only
The improper integrals are i and ii.
Improper integral
An improper integral is the limit of a definite integral in mathematical analysis when either one endpoint of the interval of integration approaches a limit, such as a real number, positive or negative infinity, or, in rare cases, when both endpoints approach limits.
According to the question
The first integral, the integral from 2 to 5 of dx over amount x squared minus 1, is incorrect because the denominator x2-1 becomes 0 at x=1, meaning the integrand expands to infinity at these places and the integral is not convergent across the range [2,5]. Since the interval of integration extends from 1 to infinity and the function is not limited, the second integral, the integral from 1 to infinity of amount x minus 1 dx, is incorrect. The integrals I and ii are both incorrect. The third integral, which is a standard integral and is the integral from negative 2 to 3 of dx over amount x + 1, is convergent.
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Find the domain of F(x)=8/x
Since divisions by zero is ill-defined, the domain for F(x)=8/x includes any real integers other than x=0. F(xdomain )'s is therefore (-infinity, 0) U (0, +infinity).
The definition of domainDescribe domain. The term "domain," which is unique to the internet, can apply to both the structure of the internet and the organization of a company's network resources. A domain is typically a sphere of information or a governing region.
What characteristics define a domain?A function's domain is the set of all potential inputs. For instance, the domain of f(x)=x2 and g(x)=1/x are all real integers with the exception of x=0.
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2/ ((s+1)(s+2) (0.5s+1)) inverse laplace
s3+5s2+8s+4
Step-by-step explanation:
Answer:
(1-e^(-2t))*u(t) - (1-e^(-t))*u(t)
Where u(t) is the step function
Step-by-step explanation:
use partial fraction decomposition. This involves expressing the rational function as the sum of simpler fractions, each with a pole at a different point in the complex plane. Once we have done this, we can use the formula for the inverse Laplace transform of a simple pole to find the inverse Laplace transform of the original function.
I need to know the 10th term?
to find a given term, substitute the corresponding value of n into the ninth term formula. For example, if the ninth term is 3n + 2, the 10th term of the sequence can be found by substituting n = 10 into the ninth term. 3 x 10 + 2 = 32 and so, the tenth term of the sequence is 32.
To find the nth term of an arithmetic sequence, use the following formula:
[tex]an = a + (n - 1)d[/tex]
an(nth term) = a(first term) + (n(term you are looking for) - 1) * d(common difference)