Log x is calculated by taking the logarithm of x, usually with base 10, which is written as log10(x). This is done by using a calculator or a computer program.
1. Choose a base for your logarithm, usually base 10.
2. Type in the equation log10(x) into the calculator or computer program.
3. Enter the number x into the equation in place of the variable.
4. Hit the “enter” or “calculate” button to find the logarithm of x.
Log x is calculated by taking the logarithm of x, usually with base 10, which is written as log10(x). This is done by using a calculator or a computer program.
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Carlos has a box of coins that he uses when playing poker
with friends. The box currently contains 45 coins,
consisting of pennies, dimes, and quarters. The number of
pennies is equal to the number of dimes, and the total
value is $4.23. How many of each denomination of coin does he have?
On solving the provided question, we can say that by equation, we have number of pennies = 19, number of dimes = 19,number of quarters = 45 - 2 × 19 = 45 - 38 = 7
What is equation?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.
The total number of coins in the box is 45 . The coins consist of pennies, dimes and quarters.
The number of pennies is equal to the number of dimes. The remaining number is the quarters. Therefore,
number of pennies = a
number of dimes = a
number of dimes = 45 - 2a
1 dime = 0.1 dollars
1 penny = 0.01 dollars
1 quarters = 0.25 dollars
The equation for total cost
[tex]3.84 = a(0.01) + a(0.1) + 0.25(45 - 2a)\\3.84 = 0.01a + 0.1a + 11.25 - 0.5 a\\3.84 = -0.39 a + 11.25\\3.84 - 11.25 = -0.39 a\\-7.41 = -0.39 a\\a = -7.41/-0.39\\a = 19[/tex]
number of pennies is 19
number of dimes is 19
number of quarters is 45 - 2 × 19 = 45 - 38 = 7
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Which statement is true?
O The graph of a vertical line IS a function.
O Every function is a relation.
O Every relation is a function.
O A horizontal line is NOT a function
Answer:
Every function is a relation.
Step-by-step explanation:
All functions are relations, therefore, the 2nd option is correct.
Cheers!
Examine the expression below, then answer the questions by circling the correct answers. 2x + 3y + 4 a. The term 2x could be read as: ● the sum of 2 and x. ● the product of 2 and x. ● the quotient of 2 and x.
Answer:
(b) the product of 2 and x
Step-by-step explanation:
You want to know how to read the term 2x.
ProductIn algebra, a product is often indicated by writing expressions next to each other without any sort of multiplication symbol. The term ...
2x
indicates the product of 2 and x.
__
Additional comment
The sum looks like 2+x.
The quotient looks like 2/x.
Which statements are correct? Check all that apply.
Answer:
[tex]\frac{1}{2}QP=UT, \overline{SU} \parallel \overline{RP}[/tex]
Step-by-step explanation:
Use the triangle midsegment theorem.
If f(x) = 3x – 12, what is f(2)?
A. 6
Β. -6
Ο C. 18
Ο D. - 18
The value of the function for x = 2 is -6.
What is a function?A function is defined as a relation between a set of inputs having one output each, a function is a relationship between inputs where each input is related to exactly one output.
Given that, a function f(x) = 3x – 12, we need to find f(2).
To find f(2) we will put x = 2 in the function,
f(x) = 3x-12
f(2) = 3(2) -12
f(2) = 6-12
f(2) = -6
Hence, the value of the function for x = 2 is -6.
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a ball is dropped from the top of a 88.51 meter tall tower. how long will it take to hit the ground? round your answer to 2 decimal places.
The ball takes 4.25 seconds to hit the ground.
The time it takes for a ball to fall from a given height can be calculated using the equation:
t = $\sqrt{\frac{2d}{g}}$
where t is the time (in seconds), d is the distance fallen (88.51 meters), and g is the acceleration due to gravity (approximately 9.8 m/s^2 on the surface of Earth).
Plugging in the given values, we have:
t = $\sqrt{\frac{2*88.51}{9.8}}$ = $\sqrt{18.089}$ = 4.25 seconds
To round the answer to 2 decimal places, we get 4.25 seconds
It's important to note that this equation assumes that there is no air resistance, and it's only valid for objects falling in a vacuum.
In reality, air resistance becomes significant as the speed of the falling object increases, and it will cause the object to fall more slowly than this equation predicts.
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when is a linear relationship is graphed the slope is value used to describe the ___ of a line
When a linear relationship is graphed, the slope is a value used to describe the rate of change of the line.
What is a slope?In Mathematics, a slope is sometimes referred to as gradient or rate of change and it is typically used to describe both the direction, ratio, and steepness of the function of a straight line based on its coordinates or points.
How to calculate the rate of change (slope)?Mathematically, the rate of change is also referred to as slope or gradient 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)
In this context, we can reasonably infer and logically deduce that the slope is a numerical value which is used for describing the rate of change of a line when a linear relationship is graphed.
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Complete Question:
When a linear relationship is graphed, the slope is a value used to describe the ____ of the line.
How do you determine SAS similarity?
SAS similarity is typically determined by measuring the angle between two molecules.
This can be done using a number of tools, such as the SAS Molecular Comparison Tool, or the Shape Analysis System. These tools measure the similarity of molecules by determining the angle between the two molecules and comparing the angles to a reference angle. The reference angle is determined by taking the average of angles between all angles of the reference molecule. The more similar the angles are, the more similar the molecules.
SAS similarity is typically measured by calculating the angle between two molecules using tools such as the SAS Molecular Comparison Tool or the Shape Analysis System. This angle is then compared to a reference angle to determine the similarity of the molecules.
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k + 4 over 5 = 1 over 3 over 5 what is k
The value of k for the expression is -11/3.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
(k + 4)/5 = (1/3)/5
This means,
k + 4 = 1/3
Subtract 4 on both sides.
k = 1/3 - 4
k = -11/3
Thus,
The value of k is -11/3.
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The solution is, k=4.
What is Subtraction?Subtraction is the process of taking away a number from another. It is a primary arithmetic operation that is denoted by a subtraction symbol (-) and is the method of calculating the difference between two numbers.
here, we have,
k + 4 over 5 = 1 over 3 over 5
i.e. (k+4)/5=1 3/5
k+4=1.6*5
k=8-4
k=4
Hence, The solution is, k=4.
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Please help fast in a hurry
Answer:
The answer is 15.71
Step-by-step explanation:
All you have to do is multiply Pie or 3.14 with 5 from the sphere. 3.14 x 5 = 15.7. If you use the Pie symbol when multiplying you'll get this answer -> 15.70796327. But I recommend using the pie symbol and just rounding it off. When rounding 15.70796327 to the hundredth place, do you know the saying 5 & up moves up and 4 & below stays??? Will it's the same thing here. 7 in 15.707 will move the 0 to a 1 instead of a 0.
if x is a poisson distributed random variable with a mean of 3, and y is another poisson distributed random variable with a mean of 2, and the two are independent, what is the variance of the sum x y?
The variance of the sum Z = X + Y is 5.
What is Variance?
A set of numerical data's spread or dispersion is measured by the term "variance." It describes the deviation of a data set's values from its mean (average). The variance indicates how evenly distributed the data is; conversely, the variance indicates how closely the data is grouped around the mean.
If X is a Poisson-distributed random variable with mean X = 3 and Y is a second Poisson-distributed random variable with mean Y = 2, and X and Y are independent, then the variance of the sum Z = X + Y is given by:
Var(Z) = Var(X) + Var(Y) = μX + μY = 3 + 2 = 5.
So, the variance of the sum Z = X + Y is 5.
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If y is a second Poisson distributed random variable with a mean of 2, and both x and y are independent Poisson distributed random variables, then the variance of the sum Z = X + Y is 5.
What is Variance?
A set of numerical data's spread or dispersion is measured by the term "variance." It describes the deviation of a data set's values from its mean (average). The variance indicates how evenly distributed the data is; conversely, the variance indicates how closely the data is grouped around the mean.
If X is a Poisson-distributed random variable with mean X = 3 and Y is a second Poisson-distributed random variable with mean Y = 2, and X and Y are independent, then the variance of the sum Z = X + Y is given by:
Var(Z) = Var(X) + Var(Y) = μX + μY = 3 + 2 = 5.
So, the variance of the sum Z = X + Y is 5.
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What is the number of solutions to an independent system with two equations and two unknowns?
If a system is independent, the linear equations will only cross once, leading to a single solution for the system. There are an endless number of solutions to a system if it is dependent because the linear equations cross at every point on the lines.
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
What makes an equation linear?
When a linear equation is graphed, it always produces a straight line since each term in the equation has an exponent of 1. This is the basis for the term "linear equation" being used to describe it.
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If it takes the Bower family 5 days to travel 2,400
miles. How many miles can they travel in 8 days?
Answer: The answer is 3,840 miles
Step-by-step explanation:
2,400 ÷ 5 = 480
480 x 8 = 3840
Hope this helps ^^
Given a polynomial f(x), if (x - 1) is a factor, what else must be true? 01-1
The factor (x - 1) exists. Therefore, the polynomial must be equal to zero for x = 1. f(1) = 0 is true as a result.
What is polynomial function?A polynomial function is a function that only employs non-negative integer powers or only positive integer exponents of a variable in an equation such as the quadratic equation, cubic equation, etc. For instance, the exponent of the polynomial 2x+5 is 1.f(x) = anxn + anxn+1 +... + a2x2 + a1x + a0 is the formula for a polynomial. The greatest power of x in an expression is the polynomial's degree. Polynomials of degree 0, 1, 2, 3, and 4 are constant (non-zero) polynomials, linear polynomials, quadratics, cubics, and quartics, respectively.No square roots of the variables, no fractional or negative powers on the variables, and no variables in the denominators of any fractions are allowed in an expression to qualify as a polynomial term.To learn more about polynomial function, refer to:
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Please can someone do this urgently
Answer:
13 miles
Step-by-step explanation:
i had that about 2 days ago
to see if the batch of screws has a significantly different mean length from 3 inches, what would the value of the z-test statistic be?
Using the z-score formula, it can be concluded that the z-score is 10.
In statistics, the z-score indicates how far the standard deviation is from the mean.
When we talk about z-score, there are at least two correlated formulas that should be considered:
z = (x - μ) / s and s = σ / √n
where:
x = measured value
μ = mean
s = standard deviation of the sample
σ = standard deviation of the population
We are given the following information about the problem:
Sample number (n) = 100
The mean length (μ) = 2.9 inches
The population standard deviation (σ ) = 0.1 inches
Value to be measured (x) = 3 inches
To find the z-score, first, we find the standard deviation of the sample (s):
s = σ / √n
= 0.1 / √100
= 0.1 / 10
= 0.01
Then we can input the value of s into the z-score formula:
z = (x - μ) / s
= (3 - 2.9) / 0.01
= 0.1 / 0.01
= 10
Thus, it can be concluded that the z-score is 10.
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Is there a connection between a student's dominant hand and their
size
(8 points)
Children of left-handed parents are more likely to be left-handed than are children of right-handed parents.
What is dominant?Dominant refers to the relationship between two versions of a gene. Individuals receive two versions of each gene, known as alleles, from each parent. If the alleles of a gene are different, one allele will be expressed; it is the dominant gene. The effect of the other allele, called recessive, is masked.Dominant refers to a relationship between two versions of a gene. If one is dominant, the other one must be not dominant. In that case, we call it recessive. A dominant gene, or a dominant version of a gene, is a particular variant of a gene, which for a variety of reasons, expresses itself more strongly all by itself than any other version of the gene which the person is carrying, and, in this case, the recessive. Now, it usually refers to inheritance patterns frequently used in conjunction with a Punnett square where, if an individual has two versions of a gene, and one is observed to frequently be transferred from one generation to another, then it is called dominant.To learn more about dominant refer to:
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The graph represents function 1, and the equation represents function 2. Function number 2 is (y = 2x + 7)
The rate of change of the function 2 is 2 more than the rate of change of the function 1.
What is a slope?In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction
If a line passes through two points (x₁ ,y₁) and (x₂, y₂) ,
then the equation of line is
y - y₁ = (y₂- y₁) / (x₂ - x₁) x (x - x₁)
To find the slope;
m = (y₂- y₁) / (x₂ - x₁)
Given:
The graph of the function 1 is given in the attached image.
And the equation represents function 2.
Function 2,
y = 2x + 7
And we know the slope intercept form,
y = mx + b,
where m is the slope and b is the y-intercept.
So, the rate of change of the function 2 is 2.
And the function 1 passes through two points (0, 3) and (4, 3).
Then the rate of change of the function,
= 3 - 3/ 4
= 0
That means, the rate of change of the function 2 is 2 more than the rate of change of the function 1.
Therefore, the difference between the rate of change of the both the function is 2.
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The complete question:
The graph represents function 1, and the equation represents function 2: A coordinate plane graph is shown. A horizontal line is graphed passing through the y-axis at y = 6. Function 2 y = 2x + 7 How much more is the rate of change of function 2 than the rate of change of function 1? (4 points) a 1 b 2 c 3 d 4
2. What's the y-intercept of the
function y = -2(2)* + 2?
A. (0,-2)
B. (2,0)
C. (0,0)
D. (0,2)
The y-intercept of the given function is 0 i.e (0, 0).
Intercepts of a line:The term "intercept" refers to the location where a line or curve crosses a graph's axis. The x-intercept is the point at which the x-axis is crossed. The y-intercept is the point at which the y-axis is crossed.
We can find intercepts of a line by simply taking any one of the coordinates as 0, for example, take x = 0 to calculate the y-intercept and take y = 0 to calculate the x-intercept.
Here we have
y = -2(2)ˣ + 2
To find the y-intercept take x = 0
=> y = -2(2)⁰ + 2
=> y = -2(1) + 2
=> y = -2 + 2
=> y = 0
Therefore,
The y-intercept of the given function is 0 i.e (0, 0).
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What is the condition for real and equal roots?
The condition for real and equal roots is that the discriminant (D) of the quadratic equation must be equal to zero.
What is equal roots?Equal roots, also known as the "imaginary roots" of a quadratic equation, are solutions to a quadratic equation that cannot be expressed as real numbers. They take the form of a complex number, typically in the form of a + bi, where a and b are real numbers and i is the imaginary unit. Equal roots occur when the discriminant of a quadratic equation is negative, meaning that the equation has no real solution.
The discriminant is the mathematical expression found under the square root symbol in the quadratic formula. If the discriminant is equal to zero, then the roots of the equation will be equal (and real). This means that the two solutions to the equation will be the same value.
In algebraic terms, the condition for real and equal roots is expressed as follows:
If ax^2 + bx + c = 0, then D = b^2 - 4ac = 0.
When the discriminant is equal to zero, then the solutions to the equation will be of the form x = -b/2a, where a, b, and c are the coefficients of the equation.
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can anyone help please?
The simplest form of the given expression is:
(9² + 19)/(10² - 5³) = -4
How to solve the expression?Here we want to solve the following expression:
(9² + 19)/(10² - 5³)
We can replace the values:
9² = 81
10² = 100
5³ = 125
Reaplacing that we will get:
(9² + 19)/(10² - 5³) = (81 + 19)/(100- 125)
= 100/-25
= - (100/25) = -4
That is the simplest form of the expression.
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What is true when a system of equations has no solutions?
When a system of equations has no solutions, it is referred to as an inconsistent system.
What is equation?An equation is a mathematical statement that two expressions are equal. It consists of two expressions, one on each side of an equal sign. Equations are used to solve problems in mathematics, chemistry, physics, engineering, and other sciences. They can also be used to define relationships between different variables or constants. Equations are an important tool for understanding the world around us.
This means that there is no solution that can satisfy all of the equations at the same time. This can happen when the equations are contradictory, or when one equation is an exact multiple of the other equation. In some cases, a system of equations may have infinitely many solutions, meaning that there are an infinite number of solutions that satisfy the equations. However, in the case of an inconsistent system, no solutions exist.
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What is the graph of a system of linear equations in two variables which has exactly one solution?
Consistent independent systems are linear systems that have only one possible solution. When two lines are independent they are distinct and consistent when two lines intersect.
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
What makes an equation linear?
When a linear equation is graphed, it always produces a straight line since each term in the equation has an exponent of 1. This is the basis for the term "linear equation" being used to describe it.
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What is a segment whose endpoints are on the circle?
A chord is any segment with ends that are located on the circle. It should be emphasized that the diameter is the circle's longest chord, which runs through its center.
The chord of a circle is a section of a line that connects two points on its circumference. The chord is one of the several line segments that may be made in a circle whose ends are on the rim. To find the chord PQ, look at the circle below.
A chord that runs across the center of the circle is another way to think of the diameter. When a chord is drawn, it separates the circle into the major segment and the minor segment, which are referred to as the segments of the circle.
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Someone Please Help!! Geometry similar triangle proofs! Thx
As Q is the midpoint of the supplied NR, we may demonstrate that MRN = PQN by using SAS congruency.
what is triangle ?Due to its three sides and three vertices, a triangle is a polygon. One of the fundamental geometric forms, it. Triangle ABC is the designation given to a triangle with vertices A, B, and C. In Euclidean geometry, when the three points are not collinear, a distinct plane and triangle are found. As a polygon, a triangle has three sides and three corners. The places where the three sides converge are referred to as the triangle's corners. Combining three triangle angles yields a result of 180 degrees.
given
∠MRN and ∠PQN are right angles
statements
∠MRN = ∠PQN = 90° (given)
Q is the mid point of NR (given)
NQ = 1/2NR ( definition of mid point )
PQ = 1/2 MR (given MR = 2PQ)
ΔMRN ≈ ΔPQN SAS
As Q is the midpoint of the supplied NR, we may demonstrate that MRN = PQN by using SAS congruency.
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I don’t know how to do the problem
the graph of F(x), shown below, resembles the graph of G(x) = x², but it has been changed somewhat. Which of the following could be the equation of F(x)?
Answer:
D
Step-by-step explanation:
The graph of [tex]F(x)[/tex] passes through [tex](0,-2)[/tex].
Eliminate B and C.The graph of [tex]F(x)[/tex] opens downward.
Eliminate A.The function f(x) is f(x) = -x² - 2.
What is Function?In mathematics, a function is an expression, rule, or law that establishes the relationship between an independent variable and a dependent variable. In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
We have the function
G(x) = x²
As, the graph passes through (0, -2)
then, option B and C cannot be the function.
Now, the graph of f(x) opens downward then option A cannot be the function.
As, the graph moves 2 units downwards then the function f(x) is
f(x) = -x² - 2.
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A spinner with four equal sectors labeled "purple," "orange," and "green" is spun 45 times. What is the probability that the spinner will land on "purple" in fewer than 20% of the spins?
A. 0. 212
B. 0. 221
C. 0. 460
D. 0. 779
If the spinner with four equal sectors labeled as "purple," "orange," and "green" is spun 45 times , then the probability that spinner will land on purple in fewer than 20% of spins is (b)0.221 .
the total number of sectors is = 4 sectors ;
the probability that spinner will land on purple is = [tex]\frac{1}{4}[/tex] ;
the spinner is spun 45 times , that means ,
number of trials (n) is = 45 ;
the probability that spinner will land on "purple" in fewer than 20% of spins can be calculated as :
P(p<0.20) = [tex]P(Z < \frac{0.20-0.25}{\sqrt{\frac{0.25(1-0.25)}{45} } })[/tex]
Simplifying further ,
we get ;
= [tex]P(Z < \frac{-0.05}{\sqrt{\frac{0.25\times 0.75}{45} } })[/tex]
= [tex]P(Z < -0.77)[/tex] , from the z table ,
we get the value as 0.221 .
Therefore , the required probability is 0.221 .
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Which equation represents a line that is perpendicular to the line passing through (-4,7) and (1,3)?
Which of these angles is a central angle of the circle shown below?
Answer: ∠SPT (it is because P is the point marked as the center point in the circle, and SPT represents the center angle P)