It is often useful to find the constant term of a polynomial in order to find its roots.
Roots of polynomials are the solutions for any given polynomial for which we need to find the value of the unknown variable. If we know the roots, we can evaluate the value of polynomial to zero.
The polynomials are the expression written in the form of:
[tex]$$a_n x^n+a_{n-1} x^{n-1}+\ldots . .+a_1 x+a_0$$[/tex]
The formula for the root of linear polynomial such as ax+b is x=-b / a
The general form of a quadratic polynomial is[tex]$a x^2+b x+c$[/tex] and if we equate this expression to zero, we get a quadratic equation, i.e. [tex]$a x^2+b x+c=0$[/tex]
The roots of quadratic equation, whose degree is two, such[tex]$ a x^2+b x+c=0$[/tex] are evaluated using the formula; [tex]$x=\left[-b \pm \sqrt{ }\left(b^2-4 a c\right)\right] / 2 a$[/tex]The formulas for higher degree polynomials are a bit complicated.
Hence, it is often useful to find the constant term of a polynomial in order to find its roots.
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consider a normal distribution with a mean of 10 and standard deviation of 25. what’s the z score for the value of 35?
A normal distribution with a mean of 10 and standard deviation of 25, the z score for the value of 35 is 1.
A mean = 10
Standard Deviation = 25
We have to determine the z score for the value of 35. So X = 35.
The relationship between a value and a set of values' mean is described by the statistical measurement known as the Z-score. Standard deviations from the mean are used to measure Z-score. A Z-score of 0 indicates that the data point's value is equal to the mean score.
The formula is:
Z = (X - mean)/Standard Deviation
Now putting the values
Z = (35 - 10)/25
Z = 25/25
Z = 1
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Which of the following is a solution to the inequality below?
-C+2> 1
C = -4
c=2
C = 9
C = 7
The solution of inequality would be, C = -4, C = 2
What is solution to the inequality?
An inequality is a relationship characterized by a non-equal comparison of two numbers or mathematical expressions.
A number is a solution to an inequality in x if it can be used to replace x with a true statement. Thus, while 8 is not a solution for example 1, 4, it is. The collection of all solutions makes up the inequality solution set.
The solution to the inequality -C + 2 > 1 is C < 1.
So, the answer is:
C = -4
C = 2
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How do you convert 1500 Meter (m) to Mile US (mil)?
Utilize the following formula to convert metres to miles: m/1,609.344=mi (meters divided by 1,609.344 equals miles).
Is the 1500m the equivalent to the mile?Since 1896, the Summer Olympics have featured the event, and since 1983, the World Championships in Athletics have included it. It is equivalent to 15 to 16 miles or 1.5 kilometres.To convert a mile's worth into metres, all you have to do is multiply it by 1609.344. That simple, indeed.The statutory mile, which has a length of 5,280 feet, is one example of a mile (1.609 km). Its original unit of measurement was the mille passus, or "thousand paces," which was equivalent to 5,000 Roman feet.For instance, if it's 11 a.m. Eastern Daylight Saving Time in Washington, D.C., it means it's 1500 hours in Zulu time/UTC. See the legend in the following paragraph.To learn more about metres refer to:
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A 19,000 car has been reduced inpri by 4%. what is the new price of the car
The new price of the car after the 4% reduction is $18,240
What is the new price of the car?Percentage is simply number or ratio expressed as a fraction of 100.
Given that,
Initial price of the car = $19,000Percentage of reduction = 4%New price of the car = ?To determine the new price of the car after reduction;
New price = Initial price × ( 100% - 4% )
New price = Initial price × ( 96% )
Note that 96% is the same as 96/100
New price = $19,000 × 96/100
New price = $19,000 × 0.96
Multiply $19,000 and 0.96
New price = $18,240
Therefore, the new price is $18,240.
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Unit 4 Mid Unit Assessment - Grade 6
Avery made a large pot of soup and she plans to divide the soup equally into smaller containers. If
the pot contains 30 cups of soup, describe one way to interpret 302 = 3 in this context.
(on the next question, you will be asked for a second interpretation)
Interpretation 1
Interpretation 1: Avery can divide the 30 number of cups of soup into 3 equal containers, each containing 10 cups of soup.
Avery can interpret 302 = 3 by understanding that 30 is the total amount of soup to be divided, and 2 represents the number of equal parts she wants to divide the soup into. This means that Avery can divide the 30 cups of soup into 3 equal containers, each containing 10 cups of soup.
Interpretation 1: Avery can divide the 30 number of cups of soup into 3 equal containers, each containing 10 cups of soup.
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After school, Terrell skateboards directly from school to a skate park and then from the skate park to a movie theater. The skate park is 8 miles south of the school and the movie theater is 6 miles east of the skate park. What is the straight-line distance between the school and the movie theater?
The required straight-line distance between the school and the movie theater is 10 miles, as of the given condition.
What are Pythagorean triplets?In a right-angled triangle, its sides, such as hypotenuse, and perpendicular, and the base is Pythagorean triplets.
The straight-line distance between the school and the movie theater can be found using the Pythagorean theorem. If the skate park is 8 miles south of the school and the movie theater is 6 miles east of the skate park, then the distance between the school and the movie theater is given as,
= √8² + 6² =
= √64 + 36
= √100.
= 10 miles
Thus, the straight-line distance between the school and the movie theater is 10 miles.
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(a) must it be true that log f(n) = ⇥(log g(n))? prove or disprove.
No, it is not required to be accurate. The growth rates of the two functions can vary.
It's not necessary for log f(n) to equal log g(n). Depending on the equation's constants and the inputs to the two functions, the growth rates of the two functions may differ. For instance, log f(n) = 2 log n and log
g(n) = 3 log n,
which are not equal, if
f(n) = n2 and g(n) = n3.
In this instance, log f(n) is equal to (log n) and log g(n) to (log n3), indicating that the two functions grow at various rates. Likely not equal are log f(n) and log g(n) if
f(n) = n and g(n) = n2,
respectively. Log f(n) is defined as (log n) and log Therefore, the statement "log f(n) = (log g(n)" is not necessarily true.
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Find out the length of segment GF?
Answer:
8
Step-by-step explanation:
Since the two horizontal lines are parallel, we have that triangle CDG and triangle CEF are similar (corresponding points in that order). Therefore, using similarity, CD/CG = CE/CF. Therefore 3/4 = 9/(4+x).
So 12 = 4+x, and x = 8.
Sum of Rational Numbers
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1
Which expression is modeled by the number line?
The expression modeled by the number line: -10, -9, -8, -7, -6, -5, -4, -3, -2, -1 is the sum of the first ten negative integers. The expression can be written as $-1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 - 9 - 10$
What is rational number ?Any number that can be written as a ratio of two integers, the numerator and the denominator, is said to be rational.The denominator cannot be equal to zero, and the ratio must be reduced to its lowest terms. For example, the fraction 2/4 can be reduced to 1/2, so 1/2 is a rational number. Decimal representation of a rational number is either finite or repeating. Rational numbers include both positive and negative fractions, as well as integers. They can be added, subtracted, multiplied, and divided just like any other number. All rational numbers form a dense set on the number line, meaning that between any two rational numbers, there is always another rational number. The set of rational numbers is a subset of the set of real numbers, which also includes irrational numbers like √2 or π.It represents the sum of the first ten negative integers from -1 to -10.To learn more about rational number refer:
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Need the answer ASP
A bird flew 3/5 of a mile in one quarter of an hour. At this rate how far will the bird fly in 2 1/2
hours?
Answer:
60 miles
Step-by-step explanation:
We know
3/5 = 0.6
one-quarter of an hour = 15 minutes
So, we know
0.6 mile in 15 minutes
2 1/2 hours = 150 minutes
0.6 times 10 = 60 miles
So, the bird flies 60 miles in 2 1/2 hours.
does the confidence interval provide convincing evidence that the two population proportions are equal? explain your answer. yes. because the interval is based upon two independent random samples, there is convincing evidence that the two population proportions are equal. no. even though 0 (no difference) is a plausible value for the difference there are many other plausible values in the interval that would suggest that the two proportions are not equal. no. because the interval contains 0, there is not convincing evidence that the two population proportions are equal. yes. because the interval contains 0, there is convincing evidence that the two population proportions are equal. no. because the conditions are not met, the interval cannot provide evidence that the two population proportions are equal.
No the confidence interval does not provide convincing evidence that the two population proportions are equal.
No. Because the interval contains 0, there is not convincing evidence that the two population proportions are equal. A confidence interval provides a range of plausible values for a population parameter based on a sample. If the interval contains 0, it means that there is some overlap between the two population proportions and that the difference between them is not statistically significant. However, this does not necessarily mean that the two population proportions are equal, only that there is not enough evidence to reject the null hypothesis of equality. Further analysis or additional data may be required to determine if the two population proportions are truly equal.
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No the confidence interval does not provide convincing evidence that the two population proportions are equal.
No. Because the interval contains 0, there is not convincing evidence that the two population proportions are equal. A confidence interval provides a range of plausible values for a population parameter based on a sample. If the interval contains 0, it means that there is some overlap between the two population proportions and that the difference between them is not statistically significant. However, this does not necessarily mean that the two population proportions are equal, only that there is not enough evidence to reject the null hypothesis of equality. Further analysis or additional data may be required to determine if the two population proportions are truly equal.
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Triangle ABC is graphed on a coordinate plane, as shown.
The coordinates of the pre-image are A(2,2) B(4,4) and C(-4,2). If the triangle was dilated by a scale factor of 2 with a center of dilation at the origin what are the coordinates of the vertices of ΔA′B′C′?
The new vertices of ΔA'B'C' are A'(4, 4), B'(8, 8), and C'(-8, 4)
What is center of dilation?
A dilation's center is a fixed point in the plane around which all points expand or shrink. Under a dilation (k 1), the sole invariant (not changing) point is the center, which might be within, outside, or on a figure.
The center of dilation is the origin, so to find the new coordinates of each vertex, we need to multiply the original coordinates by the scale factor of 2.
A(2, 2) becomes A'(2 * 2, 2 * 2) = A'(4, 4)
B(4, 4) becomes B'(4 * 2, 4 * 2) = B'(8, 8)
C(-4, 2) becomes C'(-4 * 2, 2 * 2) = C'(-8, 4)
So, The new vertices of ΔA'B'C' are A'(4, 4), B'(8, 8), and C'(-8, 4).
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I need help with this math equation. It is Comparing Functions.
1. B has the greater rate of change.
2. A has the greater rate of change.
3. B has the greater rate of change.
How to obtain the rate of change?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
The slope m represents the rate of change of the output variable relative to the input variable.The intercept b represents the initial value assumed by the output variable.For the rate of change, we must look at the slope of each function.
From the graph or from a table, the slope is given dividing the change in y by the change in x.
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If the dot indicates the center of the circle, which equation must be true?
The true equation is m∠A + m∠B = 180°
What is an angle?
An angle is a shape created by two rays that share a terminus and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. Dihedral angles are these.
Here, we have
Given: the dot indicates the center of the circle.
we have to find which equation is true.
"The angle formed by a diameter at the circumference is always a right angle (that is 90 degrees).
We concluded that the true equation is m∠A + m∠B = 180°
Hence, the true equation is m∠A + m∠B = 180°
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Determine whether the following relation repreent y
a a function of x
5x3y=15
The given equation does not represent y as a function of x.
A relation is a function if for every unique x value, there exists only one unique y value. The equation 5x³y = 15 does not define a unique value for y for a given value of x, and therefore does not represent y as a function of x.
Function Of X, Y OutputThe equation 5x³y = 15 does not represent y as a function of x. A function must have exactly one output value for each input value, but this equation doesn't have the unique output restriction.
The equation 5x³y = 15 represents a 3-dimensional surface in the x-y-z plane, where z = 5x³y. It does not define y as a function of x, because for a given x there can be multiple values of y that satisfy the equation. To define y as a function of x, additional information, such as an equation that relates y and x in a one-to-one manner, is needed.
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Let the vector pace P2 have the inner product
⟨p,q⟩=∫4−4p(x)q(x)dx
Find the following for p=2x, q=5x2. Solution
(i) ⟨p,q⟩=
(ii) d(p,q)=
(iii) ∥p∥=
(iv) ∥q∥=
Let the vector pace P2 have the inner product the following for p=2x, q=5x2 for ∫4−4p(x)q(x)dx are
⟨p, q⟩= ∫4−40x³ dxd(p, q)= - 120x²∥p∥= 2x∥q∥= 5x²1) For ⟨p,q⟩=∫4−4p(x)q(x)dx we can put the value of the p=2x, q=5x² so
⟨p, q⟩= ∫4− 4(2x)(5x²) dx
= ∫4−40x³ dx
2) For d(p,q)= 4−40x³dx ............( after derivating)
= 0 - 120 x²
= -120x²
3) ∥p∥ = ||2x|| = 2||x|| ( ||x|| > 0)
given that p is not any number which will be not affected by any sign of the x and will remain positive.
4) ∥q∥ = ||5x²|| = 5||x²|| (||x² > 0)
given that q is not any number which will be not affected by any sign of the x² and will remain positive.
In mathematics, objects called vectors have both magnitude and direction. The vector's magnitude determines its length. It is shown as a line with an arrow, with the length of the line indicating the vector's magnitude and the direction of the arrow indicating its direction. Other names for it include Euclidean vector, Geometric vector, Spatial vector, and simply "vector."
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Solve and Graph −3x+8<15
x>-7/3 is the solution of the inequality −3x+8<15.
What is Inequality?a relationship between two expressions or values that are not equal to each other is called 'inequality.
The given inequality is −3x+8<15
Minus three times of x plus eight less than fifteen.
Subtract 8 from both the sides
-3x<7
Divide both sides by 3
-x<7/3
x>-7/3
Hence, x>-7/3 is the solution of the inequality −3x+8<15.
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If each 2 cm on the scale drawing equals 4 feet, what are the actual dimensions of the room? (5 points) a Length = 16 feet, width = 12 feet b Length = 10 feet, width = 8 feet c Length = 32 feet, width = 24 feet d Length = 14 feet, width = 12 feet
The correct option is C. Length = 24 feet, width = 18 feet
How to find the Length of a room?To measure a rectangular room, use a tape measure, pencil and paper to record the length and width of the room. Then multiply these numbers to get the total area of the room.
The calculation is as follows:
Since 2cm = 6 feet
So,
The length is = 4(6) = 24 feet
And, the width be = 3(6) = 18 feet
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A scale drawing of Julie's living room is shown below:
A rectangle is shown. The length of the rectangle is labeled as length equal to 8 cm, and the width is labeled as width equal to 6 cm.
If each 2 cm on the scale drawing equals 4 feet, what are the actual dimensions of the room?
A)Length = 16 feet, width = 12 feet
B)Length = 10 feet, width = 8 feet
C)Length = 32 feet, width = 24 feet
D)Length = 14 feet, width = 12 feet
Add or Subtract the following equation
The solution for the given expression [tex]\frac{x^{2} + y^{2} }{x^{3} + y^{3} } - \frac{1}{x + y}[/tex] will be [tex]\frac{xy}{x^{3} + y^{3} }[/tex].
What is an expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
Given an expression [tex]\frac{x^{2} + y^{2} }{x^{3} + y^{3} } - \frac{1}{x + y}[/tex]
We will solve this equation using the simplification methods,
Since,
a³ + b³ = (a +b)(a² +b² - ab)
From this formula;
=> [tex]\frac{x^{2} + y^{2} }{x^{3} + y^{3} } - \frac{1}{x + y}[/tex]
=> [tex]\frac{x^{2} + y^{2} }{(x + y)(x^{2} + y^{2} - xy) } - \frac{1}{x + y}[/tex]
taking 1/(x +y) common,
=> 1/(x +y) { (x² + y²)/(x² +y² - xy) - 1}
=> 1/(x +y) { xy/(x² +y² - xy)}
=> xy/(x³ +y³)
Therefore, [tex]\frac{xy}{x^{3} + y^{3} }[/tex] will be the simplified form of the given Equation.
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What point on the line 3x – y = 4 is closest to the point A(–2, 3)?
The closest point on the line 3x - y = 4 to the point A(-2, 3) is (4, 3).
The point on the line closest to point A can be found by finding the line that is perpendicular to the line 3x - y = 4 and passes through A, then finding the point of intersection between the two lines.
To find the perpendicular line, we can use the slope-point form of a line, which is y - y1 = m(x - x1), where m is the slope of the line and (x1, y1) is a point on the line. The slope of a line perpendicular to the line 3x - y = 4 is the negative reciprocal of the slope of the line, which is undefined since the line 3x - y = 4 is a vertical line. Hence, the perpendicular line is a horizontal line with slope 0, and it passes through the point A(-2, 3). So, the equation of the line is y = 3.
The point of intersection of the two lines is the point closest to A. Solving the equations 3x - y = 4 and y = 3, we get the intersection point (x, y) = (4, 3).
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Anu brought an air cooler, its water tank is in the shape of a cuboid and can take 40 liters of water. Its dimensions are 50 cm x 20 cm. What will be the height of the water tank? (1000 cubic cm = 1 liter).
The height of the water tank of the air cooler brought by Anu is 40 cm.
What is the meaning of Height?Height is the vertical measurement of an object. If the measurement is not made vertically, the measurement is termed the length or width. Volume is a measure of how much space an object can occupy. Volume is used to determine the density of an object.
given,
Length = 50 cm
Width = 20 cm
Maximum tank volume = 40 liters = 40,000 cm3
Tank height?
Steps,
Tank volume = length x width x height
40,000 = 50 x 20 x height
40,000 = 1000 x height
Tank height = 40,000 : 1000
Tank height = 40 cm
So, the height of the air conditioning tank that can hold 40 liters of water is 40 cm.
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Solve the following initial value problem:
dy/dt=t^2+1, t ≥ 0, y = 6 when t=0
The solution of the initial value problem is [tex]y = (t^3/3 + t^2 + t + 6)e^{(t^3/3 + t)}[/tex]
A differential equation is a mathematical equation that relates a function and its derivatives to some independent variables.
In this case, the differential equation is given by:
dy/dt = t² + 1, t ≥ 0
with the initial value y = 6 when t = 0.
To solve this initial value problem, we can use the method of integrating factor.
We can find the integrating factor for this differential equation by using the formula:
[tex]= > e^{\intP(t)dt,[/tex]
where P(t) = t² + 1
So,
[tex]= > e^{\int P(t)dt} = e^{t^3/3 + t}[/tex]
By the product rule, we have:
[tex]= > d/dt(e^{t^3/3 + t)y} = d/dt(e^{t^3/3 + t)(t^2 + 1)})[/tex]
We can evaluate the integral on the right side using standard integration techniques, and we get:
[tex]= > e^{t^3/3 + t}y = e^{(t^3/3 + t)(t^3/3 + t^2 + t + C)[/tex]
Finally, we can isolate y by dividing both sides of the equation by e^(t^3/3 + t):
[tex]= > y = (t^3/3 + t^2 + t + 6)e^{(t^3/3 + t)}[/tex]
To find the value of C, we can use the initial value y = 6 when t = 0:
6 = Ce⁰
So, C = 6.
Therefore, the solution to the initial value problem is:
[tex]y = (t^3/3 + t^2 + t + 6)e^{(t^3/3 + t)}[/tex]
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A regular pentagon is centere about the orgin and has a vertex at (0, 4). Which transformation maps the pentagon to itself?.
A clockwise rotation of 144° about the origin will map the pentagon onto itself. Option(c) is the correct answer.
The number of sides (n) of the pentagon is:
n =5
The pentagon will not be plotted onto itself when reflected across the x-axis because the pentagon has 5 sides (an odd number of sides).
To draw the pentagon onto itself, the pentagon has to be rotated.
The angle of rotation is:
θ [tex]= \frac{360}{n}[/tex]
θ [tex]=\frac{360}{5} = 72[/tex]
Other possible angles of rotation must be multiple of 72. i.e.
θ= 72, 144, 216, 288...
Hence, a clockwise rotation of 144° about the origin will map the pentagon onto itself.
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The complete question is:
A regular pentagon is centered about the origin and has a vertex at (0, 4). Which transformation maps the pentagon to itself?
a. A reflection across line m
b. A reflection across the x-axis
c) A clockwise rotation of 144 degrees about the origin
What statement describes a key feature of function G if g x equals x - 7
a. Y-intercept at 0, negative 7
b. Range of y < -7
c. Domain of x > -7
d. Horizontal asymptotic of y=-7
The statement that describes a key feature of function g if [tex]g(x)=e^x-7[/tex] is Horizontal asymptote of y= -7.
What is a horizontal asymptote?A horizontal line that is not a part of a function's graph but is essential because it directs the graph's x values is known as a horizontal asymptote.
A horizontal line that a function's graph appears to coincide with but does not actually do so is said to be its horizontal asymptote.
A line that is asymptotically sloped, vertical, or both has the equation x = a, y = a, or y = ax + b
In this instance, the declaration that enumerates the primary property of the function g if g(x) = [tex]e^x[/tex] - 7 is that the horizontal asymptote of y = -7.
This can be seen from the equation given.
Therefore option (d) is correct
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need help fast Select the correct answer.
Consider the function f(x) = 7x and the function g(x), which is given below.
G(X) = 1/3 x F(X) = 1/3 x 7^X
How will the graph of g(x) differ from the graph of f(x)?
A.
The graph of g(x) is the graph of f(x) vertically compressed by a factor of three.
B.
The graph of g(x) is the graph of f(x) vertically stretched by a factor of three.
C.
The graph of g(x) is the graph of f(x) vertically compressed by a factor of 1/3.
D.
The graph of g(x) is the graph of f(x) vertically stretched by a factor of 1/3.
The correct statement regarding the transformation and the difference of functions f(x) and g(x) is given as follows:
A.
The graph of g(x) is the graph of f(x) vertically compressed by a factor of three.
How to describe the transformation?The parent function for this problem is given as follows:
f(x) = 7^x.
The transformed function for this problem is given as follows:
g(x) = f(x)/3 = (1/3) x 7^x.
The only transformation is a multiplication by the constant 1/3. As the constant has an absolute value less than 1, the graph of g(x) is a vertical compression of the graph of f(x) by a factor of 3.
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How To Convert 36.5 °C to °F?
The 36.5 °C when converted to Fahrenheit it is equal to 97.7 °F.
How to convert Celsius to Fahrenheit?When measuring temperature, different units of measurement, such as Celsius and Fahrenheit, can be used. Celsius (°C) is a unit of measurement in the metric system, which is widely used in many countries worldwide, whereas Fahrenheit (°F) is a unit of measurement in the imperial system, which is primarily used in the United States.However, the conversion requires the following expression:Temperature in degrees Fahrenheit = [Temperature in degrees Celsius * 1.8] + 32As a result, we can use the expression to convert a 36.5 °C temperature to a Fahrenheit temperature;Temperature (degrees Fahrenheit) = (36.5 * 1.8) + 32°F temperature = 65.7 + 32= 97.7
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for what value of θ is | r | a maximum if r = sinθ and 0 < θ < π?
The value of θ for which | r | has maximum value if r = sinθ is θ = π/2.
Given r = sinθ and the range of θ is 0 < θ < π
If 0 < θ < π the range of sinθ is:
0 ≤ sinθ ≤ 1
So, in 0 < θ < π, the maximum value of sinθ is 1 and this value occurs at θ = π/2.
Now, we are asked to determine the value θ for which | r | is maximum and it is also given that r = sinθ and we have already found out that the maximum of sinθ in 0 < θ < π is 1.
Therefore, the maximum value of | r | is 1 and this value occurs at θ = π/2.
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Here are the ingredients to make strawberry trifle for 4 people
Kevin needs the following ingredients for the recipe for 3 people 90g strawberry jelly, 6 sponge fingers, 315 ml custard, and 135g tinned fruit.
How to find the amount of ingredients for three people?To find the amounts of each ingredient to make this recipe for three people we must carry out the following procedure:
1. We must make a rule of three to find the exact amounts of each ingredient as shown below:
4 - 120g strawberry jelly3 - ?3*120g/4=90g strawberry jelly.4 - 83 - ?3 * 8 / 4 = 6 sponge fingers4 - 420 ml custard3 - ?3*420ml/4=315ml custard.4 - 180g tinned fruit3 - ?3 * 180g / 4 = 135g tinned fruitAccording to the above, the following ingredients are needed for this recipe:
90g strawberry jelly.6 sponge fingers315 ml custard135g tinned fruitNote: This question is incomplete because there is some information missing. Here is the complete information:
120g strawberry jelly
8 sponge fingers
420ml custard
180 g tinned fruit
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Use properties to rewrite the given equation. Which equations have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p? Select two options.
The correct two expressions have the same solution are,
⇒ 230p - 1010 = 650p - 400 - p
⇒ 23p - 101 = 65p - 40 - 0.1p
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
The expression is,
⇒ 2.3p - 10.1 = 6.5p - 4 - 0.01p
Now, We can simplify as;
⇒ 2.3p - 10.1 = 6.5p - 4 - 0.01p
Multiply by 10 both side,
⇒ 23p - 101 = 65p - 40 - 0.1p
And, ⇒ 2.3p - 10.1 = 6.5p - 4 - 0.01p
Multiply by 100 both side,
⇒ 230p - 1010 = 650p - 400 - p
Thus, The correct two expressions have the same solution are,
⇒ 230p - 1010 = 650p - 400 - p
⇒ 23p - 101 = 65p - 40 - 0.1p
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The complete question is this;
Use properties to rewrite the given equation. Which equations have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p? Select two options. 2.3p – 10.1 = 6.4p – 4 2.3p – 10.1 = 6.49p – 4 230p – 1010 = 650p – 400 – p 23p – 101 = 65p – 40 – p 2.3p – 14.1 = 6.4p – 4
A number cube is tossed 60 times.
Outcome Frequency
1 12
2 13
3 11
4 6
5 10
6 8
Determine the experimental probability of landing on a number greater than 5.
The experimental probability of landing on a number greater than 5 is 2/15.
What is Probability?Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1.
Given A number cube is tossed 60 times,
Outcome Frequency
1 12
2 13
3 11
4 6
5 10
6 8
The number of times greater than 5 comes up = 8 (frequency of 6 is 8)
Probability of getting a number greater than 5
= (frequency of getting6) / (total number of trials)
⇒ probability of getting a number greater than 5 = 8 / 60 = 2/15
Hence probability is 2/15.
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