Daljeet Kaur
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We have been given a trigonometric function `f(x)=cos(pi/2x)+1` . We are asked to find the amplitude, midline, and period of function to graph it. We know that the general form of a cosine is... 
Answered a Question in Math
We have been given a logarithmic equation. We are asked to solve for all values of x that satisfy the given equation. `(log_4(x^2)4)^3+(log_8(x^3)8)^3=(log_2(x^2)12)^3` First of all, we will... 
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We have been given that a 5 N force that acts along the direction vector (2, 3) moves an object from A(1, 3) to B(3,7). We are asked to find the work done if the given units are in meters. We can... 
Answered a Question in Math
In order to find limits for a function at any given value, we follow these steps. (1) The very first step is direct substitution. We can find some limits using direct substitution. ` ``... 
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We have been given a probability distribution function `f(x)=0.50e^(0.50x)` for `x>=0`. a) When we have a probability distribution function in the form `f(x)=lambda*e^(lambda*x)`, then the... 
Answered a Question in Math
We have been given the equation `y=x^2+7x5` . We are asked to write it in the form `y=(x+a)^2+b` and find the values of a and b. In order to convert the given equation into the required form, we... 
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This question contains three different questions. Let us solve them one by one. (1) `3y+6=5y8` In order to solve this equation, we will use opposite operations. Upon subtracting 5y and 6 from both... 
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To find the value of bacteria before 6 hours, we will use the double life formula. `f(t)=a*(2)^t`, where f(t) is the final value, a is the initial value, 2 is the growth factor, and t is the time... 
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Secant is a trigonometric ratio that relates the hypotenuse and adjacent side to a given angle in the right triangle. The ratio of a secant for the adjacent side and the hypotenuse is given by... 
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To find the mean absolute deviation, we can use the following formula: `(sum x_i  barx)/n` , where `sum` represents the sum, `x_i` is the data point of the data set, `barx` represents the mean... 
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Our number system is based on the concept of place value. In the number system, the value of a digit in any number is determined by its position in the number. The position of a digit in a number... 
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An inverse function is a function that reverses the action of a function. If we input some value of x (say a) in a function, it will give us the corresponding yvalue (b), while the inverse... 
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The vertex form of a parabola is given by `y=a(xh)^2+k` , where a represents the leading coefficient, and point (h, k) represents the vertex of the parabola. We can convert the standard equation... 
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Factoring is the process that undoes the distributive property. The distributive property states that `a(b+c)=axxb+axxc` . Here the left side is in factored form, and the right side is in expanded... 
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We can think of an equation like a weighing scale. We have an equal sign in an equation, which means that both sides of the equation are equal. In order to balance equations, we need to perform the... 
Answered a Question in Math
The hypotenuse is the longest side of a right triangle, and it is the side opposite to the right (or 90 degrees) angle. There are 3 ways to find the hypotenuse of a right triangle: When we know... 
Answered a Question in Math
The volume of a prism depends on the base of the prism. We can find the volume of a prism by multiplying its base area with the height of the prism. If a prism is rectangular with base length l and... 
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There are three main ways to write the equation of a line. The standard form of a line: `Ax+By=C` Point slope form: `(yy_0)=m(xx_0)`, where m is the slope of the line and `(x_0,y_0)` is a point... 
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A hexagon is twodimensional shape with 6 equal sides. The sum of all internal angles of a hexagon is equal to 720 degrees. To find the area of a regular hexagon with a side 'a', we can use the... 
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To find the midpoint of two given points, we can use the midpoint formula. Let us say that we have points `(x_1,y_1)` and `(x_2,y_2)`, then the midpoint of these points is given by the average of... 
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There are different shapes in geometry, and the volume formula for each geometric shape is different. Let us see the volume formulas for different geometric shapes one by one. The volume of a cube... 
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Median is a measure of the center of data. Median is the best measure of center when extreme outliers are involved, because it is less affected by outliers than mean. To find the median of a data... 
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An arithmetic sequence is also known as an arithmetic progression. When the difference between any two consecutive terms of a sequence remains the same, then the sequence is known as an arithmetic... 
Answered a Question in Math
We can find outliers of a data set using the IQR rule. The IQR rule or interquartile rule states that a data point is considered a lower outlier if it is less than the first quartileâ€”1.5*IQR. A... 
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The pvalue is used in the hypothesis test. It is the probability associated with test statistics. It is used to test a null hypothesis. The pvalue depends on the alternate hypothesis. Alternate... 
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Correlation tells us how two variables are associated or related to one another. There are three types of correlation: 1. Positive or negative correlation 2. Linear or nonlinear correlation 3.... 
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A proportion states that two ratios are equivalent. If we have two equivalent ratios as a : b = c : d, then we can set up a proportion like `a/b=c/d`. In order to solve proportions, we need to set... 
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In order to graph a parabola, we need some points on the parabola. For that, we can use different values of x in the given equation of a parabola and find their corresponding yvalue. We can also... 
Answered a Question in Math
The amplitude of a trigonometric function is the vertical distance from the midline to the maximum value (top) or minimum value (bottom). We can also find the amplitude of a function by dividing... 
Answered a Question in Math
In order to multiply exponents, we can use the product rule of exponents. The following are rules to multiply exponents: When the bases of exponents are the same: The product rule of exponents... 
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The product of slopes of two perpendicular lines is equal to 1. The slope of a line perpendicular to a given line is the negative reciprocal of the slope of the given line. Let us say that the... 
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The slopeintercept form of an equation takes the form y=mx+b, where m represents the slope of the line and b represents the yintercept. This is known as slopeintercept form, as we can directly... 
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The hypotenuse is the longest side of a right triangle. It is the side that is opposite to the right angle. To find the hypotenuse of a right triangle, we can use the Pythagorean theorem. We can... 
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Critical points of a function are the points where the first derivative of the function is equal to zero, or the derivative of the function does not exist. In order to find critical points of a... 
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To find the radius from the circle, we can use the circumference of the circle formula. The circumference of a circle is given by the formula `C=2pir`, where C represents the circumference of a... 
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An algebraic expression is an expression that contains variables and constants using operational symbols like plus, minus, division, and multiplication. To simplify expressions, we need to follow... 
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Slope of a line is the measure of the steepness and direction of the line. Slope of a line is equal to rise divided by run. Rise is the difference between two ycoordinates, and run is the... 
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To find sample standard deviation, we will use the following formula: `s=sqrt((sum (x_ibarx))^2/(N1))`, where s represents sample standard deviation, `barx` represents sample mean, and N... 
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A linear equation is an equation in form `Ax+b=c`. Some examples of linear equations are `5x3=0`, `x+5x=3x+9`, and `m3m=7`. In order to solve linear equations, we need to separate variables in... 
Answered a Question in Math
The slope of a line is the measure of the steepness and direction of the line. If the slope is negative, then the line will be pointing downwards. If the slope is positive, then the line will be... 
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An inflection point is a point where the graph of a function changes its concavity. To find inflection points of a function, we need to find the second derivative of the function and set it equal... 
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A rectangle is a special quadrilateral with four right angles. A rectangle has four sides. The opposite sides of a rectangle are equal in measure. Let us say we have a rectangle with length l and... 
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To simplify a radical of the nth root, we need to factor out perfect nth power expressions or numbers outside the radical. We know that a square root is the second root of a number or expression.... 
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To find a missing side of a triangle, we need to know the type of triangle. If a triangle is a right triangle, then we can find its missing side length using the Pythagorean theorem. The... 
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The rate of change is the rate at which one quantity changes with respect to another quantity. There are two types of rate of change: one is the average rate of change, and the other is the... 
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Probability is the measure of the likelihood that a certain event may occur or not. Probability is always between zero and 1. The probability of a certain event is 1. If today is Sunday, then... 
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The greatest common factor is also known as GCF. We can find the GCF for numbers as well as algebraic expressions. To find the greatest common factors of two or more numbers, we find prime factors... 
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A hypotenuse is a side opposite to the right angle or 90 degrees angle in a right triangle. The hypotenuse is the longest side in a right triangle. We can find the length of the hypotenuse of a... 
Answered a Question in Math
A rectangular prism is a 3dimensional shape in form of a cuboid. It has 6 faces. All faces of a rectangular prism are rectangles such that two opposite faces are congruent. To find the volume of a... 
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The tangent line is the line to a given curve at any given point that touches the curve exactly once at the given point. Let us say that we have a function f(x) and we need to find tangent line at...
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