A 95% confidence interval for the mean of 3243 dollars.
What is a confidence interval?In statistics, the confidence interval formula is used to express the degree of uncertainty surrounding a sample estimate of a population parameter. It is used to describe the degree of uncertainty surrounding a sampling technique.
Given random sample = 55
mean = $2900
standard deviation = $1300
Confidence Interval = m ± z(SD/√n)
n = Number of terms
m = Sample average
SD = Standard Deviation
z = Value corresponding to confidence interval in z table
value of z for 95% confidence interval is 1.96,
substitute the values in formula,
Confidence Interval = m ± z(SD/√n)
Confidence Interval = 2900 ± 1.96(1300/√55)
Confidence Interval = 2900 ± 343.581
Confidence Interval = 3243.581
Confidence Interval = 3243
Hence the mean is 3243 dollars.
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Mabel has a 15 year adjustable rate mortgage with a fixed rate for the first 4 years. In the 5th year, the Interest rate rises to 5. 8%. The
remaining balance at the end of the 4th years is $231,975. 40. What is the monthly payment in the 5th year? (4 points)
The monthly payment in the 5th year is $2,005.18
To calculate the monthly payment in the 5th year of the adjustable rate mortgage, you would need to know the remaining balance of the loan at the beginning of the 5th year, the interest rate for the 5th year, and the loan term (number of remaining payments) for the 5th year. With the given information, you can calculate the monthly payment using the following formula:
M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1]
Where:
M = monthly payment
P = remaining balance at the beginning of the 5th year
i = interest rate for the 5th year (expressed as a decimal)
n = loan term for the 5th year (number of remaining payments)
Given that the remaining balance at the end of the 4th year is $231,975.40, and the interest rate for the 5th year is 5.8%
i = 5.8% / 12 = 0.004833
n = (1512) - (412) = 108
M = 231975.40 [ 0.004833(1+ 0.004833)^108] / [(1 + 0.004833)^108 -1]
M = $2,005.18
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you drive 60 miles north, then 34 miles west, then 20 miles south. how far are you from where you started?
The minimum distance from the starting point is 52.5 miles
First you travels 60 miles north as shown in the image, then 34 miles west and 20 miles south. We can draw a straight line from the endpoint to the stating point.
We could construct a triangle as shown in the figure. From that we can see that AC is the minimum distance from the start. AC is the hypotenuse of the triangle we have drawn..
To calculate the hypotenuse, we can use the Pythagoras theorem.
Hypotenuse² = base²+alt²
AC² = BC²+ AB²
= 34²+40² = 2756
AC = √2756 = 52.497 = 52.5 miles
So the minimum distance is 52.5 miles.
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A hockey player ran a simulation twice to estimate the proportion of wins to expect using a new game strategy. Each time, the simulation ran a trial of 1,000 games. The first simulation returned 590 wins, and the second simulation returned 640 wins. Construct and interpret 95% confidence intervals for the outcomes of each simulation.
The confidence interval from the first simulation is (0.560, 0.620), and the confidence interval from the second simulation is (0.610, 0.670). For the first trial, we are 90% confident the true proportion of wins with the new game strategy is between 0.560 and 0.620. For the second trial, we are 90% confident the true proportion of wins with the new game strategy is between 0.610 and 0.670.
The confidence interval from the first simulation is (0.564, 0.616), and the confidence interval from the second simulation is (0.615, 0.665). For the first trial, we are 90% confident the true proportion of wins with the new game strategy is between 0.564 and 0.616. For the second trial, we are 90% confident the true proportion of wins with the new game strategy is between 0.615 and 0.665.
The confidence interval from the first simulation is (0.564, 0.616), and the confidence interval from the second simulation is (0.615, 0.665). For the first trial, we are 95% confident the true proportion of wins with the new game strategy is between 0.564 and 0.616. For the second trial, we are 95% confident the true proportion of wins with the new game strategy is between 0.615 and 0.665.
The confidence interval from the first simulation is (0.560, 0.620), and the confidence interval from the second simulation is (0.610, 0.670). For the first trial, we are 95% confident the true proportion of wins with the new game strategy is between 0.560 and 0.620. For the second trial, we are 95% confident the true proportion of wins with the new game strategy is between 0.610 and 0.670.
The 95% confidence intervals, along with their interpretations, are described by the following option:
The confidence interval from the first simulation is (0.560, 0.620), and the confidence interval from the second simulation is (0.610, 0.670). For the first trial, we are 95% confident the true proportion of wins with the new game strategy is between 0.560 and 0.620. For the second trial, we are 95% confident the true proportion of wins with the new game strategy is between 0.610 and 0.670.
What is a confidence interval of proportions?A confidence interval of proportions has the bounds given by the rule presented as follows:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which the variables used to calculated these bounds are listed as follows:
[tex]\pi[/tex] is the sample proportion, which is also the estimate of the parameter.z is the critical value.n is the sample size.
The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
For the first simulation, the parameters are given as follows:
[tex]n = 1000, \pi = \frac{590}{1000} = 0.59[/tex]
Hence the lower bound of the interval is of:
[tex]0.59 - 1.96\sqrt{\frac{0.59(0.41)}{1000}} = 0.56[/tex]
The upper bound is of:
[tex]0.59 + 1.96\sqrt{\frac{0.59(0.41)}{1000}} = 62[/tex]
For the second simulation, the parameters are given as follows:
[tex]n = 1000, \pi = \frac{640}{1000} = 0.64[/tex]
Hence the lower bound of the interval is of:
[tex]0.64 - 1.96\sqrt{\frac{0.64(0.36)}{1000}} = 0.61[/tex]
The upper bound is of:
[tex]0.64 + 1.96\sqrt{\frac{0.64(0.36)}{1000}} = 0.67[/tex]
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Write a formula representing the following function. Use the lower case letter k as the proportionality constant. The number of animal species, N, of a certain body length, L, is inversely proportional to the square of L.?
The formula that can be used to represent this function is N*L^2 = k
The number of animal species, N, is inversely proportional to the square of the body length, L. Therefore, the formula representing the function would be:
N = k/L^2
Where k is the proportionality constant. It represents the relationship between N and L^2, and it is a constant value.
The above formula can also be written as
N*L^2 = k
It means that the product of N and L^2 is constant.
It can be derived by assuming that there is some proportionality constant k such that N=k/L^2 and then testing this relationship against data on animal species and body lengths.
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Which of the methods is a direct method for solving simultaneous algebraic equations Mcq?
Cramer’s rule is the direct method for solving simultaneous algebraic equations.
Algebraic EquationBecause polynomials are included on both sides of the equal sign, algebraic equations are sometimes referred to as polynomial equations. Variables, coefficients, constants, and algebraic operations like addition, subtraction, multiplication, division, and exponentiation are all components of an algebraic equation.
Cramer’s ruleOne of the key techniques for solving a system of equations is Cramer's rule. In this approach, determinants of matrices are used to compute the values of the system's variables. Cramer's rule is frequently referred to as the determinant technique as a result.
Complete Question is given belowWhich of the methods is a direct method for solving simultaneous algebraic equations?
a) Jacobi’s method
b) Relaxation method
c) Cramer’s rule
d) Gauss seidel method
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On the first day, a tourist hiked 9 miles to the east from the camp. On the second day, the tourist hiked a few miles to the north. On the third day, the tourist returned to camp by straight way. If the tourist hiked a total of 90 miles, how many miles did the tourist hike on the third day?
On the third day of the camp miles hiked by the tourist as per given data is equal to 41 miles .
As given in the question,
On the first day,
Miles hiked by tourist is 9 miles to the east from camp.
Let x miles be hiked by tourist on the second day to the north.
let h miles be hiked by tourist on third day
Total distance travelled = 90 miles
It represent the right angled triangle
'h' represents the hypotenuse.
By Pythagoras theorem,
h² = x² + 9² ___(1)
x + h + 9 = 90
h = 81 - x __(2)
Substitute the value h from (2) in (1) we get,
( 81 - x )² = x² + 9²
⇒ 6561 - 162x + x² = x² + 9²
⇒ 162x = 6480
⇒ x = 40
⇒ h = 41 miles
Therefore, on the third day of the camp miles hiked by tourist is equal to 41 miles.
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Fins the degree of polynomial 3x^4-0x^3+0x^5
The degree of polynomial 3x^4-0x^3+0x^5 is 4
How to determine the degree of a polynomial?Degree of a polynomial is the highest power that its terms pertain (for multi-variables, the power of term is addition of power of variables in that term).
Therefore, inx^3+3x+5, the degree of the polynomial is 3 as the highest power in its terms is 3. (power and exponent are same thing);
Given in the question;
Polynomial= 3x^4-0x^3+0x^5
The highest degree from observation is of 3x that is equal to 4
Hence, the correct degree will be 4
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Two parallel lines are intersected by a transversal,
forming consecutive interior angles A and B, where
m
What is the value of x?
The value of x is 55 degrees.
What is the supplementary angle?If two lines are parallel and intersected by a transversal, then the consecutive interior angles formed are supplementary, meaning they add up to 180 degrees.
Since we know that m∠A + m∠B = 180 and we know that m∠A = x, we can use this information to find the value of x.
m∠A + m∠B = 180
x + (x+70) = 180
x + x + 70 = 180
2x = 110
x = 55
Therefore, the value of x is 55 degrees.
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A neighborhood was given a vacant lot in the shape of a rectangle on which to build a park. The neighborhood is considering how to split up the area. Which statements about the formulas for finding areas are true? Check all that apply.
Answer:
area : lxb,..,.................
Answer:
Step-by-step explanation:
These are the statements I think is true:
The parallelogram and rectangle formulas are both the same.
In the trapezoid formula, the bases are added.
Explanation:
I’ll just give you the formulas..
Area for trapezoid:
(a + b) ÷ 2 x h
a & b are the bases, h is for height.
Area for rectangle:
Length x width
Area for parallelogram:
Base x height
(Choose the height that is perpendicular to the base)
Also, I would liek you to know I did not understand the other few choices because ai think they have wrong grammar. But I really tried my best for now.
HOPE THIS HELPS!
Find the length of the third side. If necessary, round to the nearest tenth.
The length of the third side in the right angled triangle is 12 units
What is an equation?An equation shows the relationship between numbers and variables in an expression.
Pythagoras theorem shows the relationship between the sides of a right angled triangle. It is given by:
hypotenuse² = opposite² + adjacent²
From the diagram, let x represent the missing side, hence:
15² = 9² + x²
x² = 144
x = 12 units
The missing side is 12 units
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november 16, 2001, was a friday. if each of the years 2004, 2008, and 2012 had 366 days, and the remaining years from 2001 through 2014 had 365 days, what day of the week was november 16, 2014 ?
Sunday is the week was November 16, 2014
We see that there is a 13-year span from November 16, 2001, to November 6, 2014. If each year were 365 days, the total number of days in this 13-year span would be 365 x 13 = 4,745 days.
However, since 3 of the years during this span, each has 1 extra day, the actual number of days in this span is 4,745 + 3 = 4,748 days.
Since 4,748/7 = 678 R2, we know that there were 678 weeks and 2 days from Friday, November 16, 2001, until November 16, 2014. The remainder of 2 tells us that November 16, 2014, was 2 days after Friday, so it was Sunday.
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PLEASE HELP, needed ASAP. THANK YOU!!!
Question A
a. Perpendicular Lines Theorem
b. Exterior Intersection Theorem
c. Radius Tangent Theorem
d. Tangent Radius Theorem
Question B
a. The tangent line (or segment, or ray) is perpendicular to the radius of the circle at the point of tangency.
b. If two chords intersect inside a circle, the products of the measures of the segments of the chords are equal.
c. If two secants, a secant and a tangent, or two tangents intersect in the exterior of a circle, then the measure of the angle formed is one half the difference of the measures of the intercepted arcs.
d. If a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.
Question C
- What is the measure of ∠PRS
At the point of tangency, the tangent line (or segment, or ray) is perpendicular to the circle's radius.
What is meant by tangent line?In geometry, the straight line that "just touches" the curve at a particular position is known as the tangent line to a plane curve at that location. According to Leibniz, it is the path connecting two points on a curve that are infinitely close to one another.
A tangent line is a simple straight line that only touches a function once. (See atop.) The instantaneous rate of change of the function at that specific position is shown by the tangent line. The derivative of the function at a location on the function is equal to the slope of the tangent line at that point (See below.)
Therefore, the correct answer is option a. The tangent line (or segment, or ray) is perpendicular to the radius of the circle at the point of tangency.
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What is the equation for the parabola?
The equation of parabola is f(x) = y= ax² + bx + c
Here we have to find the equation of the parabola.
In order to find the equation of parabola, here we need to know what is meant by parabola.
The term parabola in math is defined as a conic section produced by the intersection of a right circular cone and a plane parallel to an element of the cone.
Through the definition, we have found the standard form of parabola equation is expressed as,
=> f(x) = y= ax² + bx + c
Here we have know that the orientation of the parabola graph is determined using the “a” value.
While the value of a is greater than 0 (a>0) then the parabola graph is oriented towards the upward direction.
Whereas the value of a is less than 0 (a<0) then the parabola graph opens downwards.
And the axis of symmetry from the standard form of the parabola equation is given as x= -b/2a.
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PLEASE HELP I NEED ANSWER AND STEPS TO THIS QUESTION
The triangle ABC is equal to DEF because they possess the same sides.
What are congruent angles about?If all three sides and all three angles of two triangles are equal, then two triangles are said to be congruent.
The triangles are congruent if two sides and the included angle of one triangle match the corresponding sides and angle of another triangle.
Side-Side-Side, or SSS, is a type of triangle congruence rule that states that two triangles are congruent if their three sides are equal to their respective three sides of another triangle.
In this case, triangle ABC is equal to triangle DEF.
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Given the equation 10x−y=15. Find the value of x for which the pair of numbers (x; 3) would be a solution to this equation. Write a complete solution.
The complete solution to this problem is: x = 1.8, y = 3.
What do you mean by equation?Equations can be used to represent relationships between variables and to solve problems. They are written using an equal sign (=) and can include numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division.
For example, the equation 2x + 3 = 7 is an equation that states that the expression on the left side (2x + 3) is equal to the expression on the right side (7). The goal is to find the value of the variable x that satisfies the equation. In this case, x = 2 is a solution to the equation.
To find the value of x for which the pair of numbers (x; 3) would be a solution to the equation 10x - y = 15, we need to substitute the value of y with 3 and solve for x. So, we have:
10x - 3 = 15
Next, we can add 3 to both sides to isolate x:
10x = 18
Finally, we can divide both sides by 10 to find x:
x = 1.8
So, for the pair of numbers (x; 3) to be a solution to the equation 10x - y = 15, x must be equal to 1.8.
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math again... help..??
Answer: 20
Step-by-step explanation:
5x - 7 + 3x + 27 = 180
8x = 180 - 20
8x = 160
x = 20
Answer:
x = 20°
Step-by-step explanation:
5x - 7 + 3x + 27 = 180° (Linear pair)
8x + 20° = 180°
8x = 160°
x = 20°
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What is the perimeter of the following kite?
The perimeter of the following kite is 32.
What do a kite's area and perimeter measure?Perimeter is the total of the sides, whereas area is half the product of the diagonals. Remember that a kite is a quadrilateral with distinct adjacent congruent sides and that a rhombus is a quadrilateral with four congruent sides.
How big is a quadrilateral kite's perimeter?The sides of each pair can be added to determine the kite's perimeter. Kite is another name for a quadrilateral with two sides that are equally long on either side. Therefore, a kite's perimeter is equal to 2(a+b), or twice the length of its two sides.
parameter = 2(a+b)
P = 2[(3+3) + (6+4)]
P = 2(6 + 10)
P = 32.
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deb had 2 3/4 pounds of blueberries. deb let her friend clarence eat 1/4 of the blueberries. how many pounds of blueberries did clarence eat?
Deb had 2 3/4 pounds of blueberries. Deb let her friend clarence eat 1/4 of the blueberries. Clarence ate 0.6875 pounds of blueberries.
To find out how many pounds of blueberries Clarence ate, we need to first convert the 2 3/4 pounds to a decimal. We can do this by dividing the numerator (3) by the denominator (4) and adding the result to the whole number (2).
2 3/4 pounds = 2 + (3/4) = 2 + 0.75 = 2.75 pounds
Now we know that Deb had 2.75 pounds of blueberries. To find out how many pounds of blueberries Clarence ate, we need to multiply this amount by the fraction of blueberries he ate (1/4).
2.75 pounds x 1/4 = 0.6875 pounds
So Clarence ate 0.6875 pounds of blueberries.
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raj inteded to run a certain distance on saturday he ran an entire distance and then half of the way back to the starting point what percentage did he run on saturday did he actully run on saturday?
The percentage he run on Saturday is 150%
How to determine the distance Raj run on Saturday?A word problem is a mathematical exercise where significant background information on the problem is presented in ordinary language rather than in mathematical notation
Let the d represent the entire distance Raj run on Saturday.
If he ran an entire distance and then half of the way back to the starting point. We can write:
Percentage ran on Saturday = (d + 1/2(d))/(d) × 100%
Percentage ran on Saturday = 1.5d/d × 100%
Percentage ran on Saturday = 1.5 × 100%
Percentage ran on Saturday = 150%
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Mr. White is renting a large truck for one week and a few additional days d. He does not have to pay a per mile fee. Evaluate the expression 295+90d to find how much he will pay for a 10-day rental.
Answer:
I believe the answer is 1195 dollars
Step-by-step explanation:
Hannah needs to buy apples and on box of cereal at the grocery store. At Giant Eagle, a box of cereal costs $2.89 and apples cost $1.29 per pound. At Shop & Save, the apples are $1.05 per pound and a box of
cereal is $3.37. How many pounds of apples can Hannah buy for the cost for her purchase to be the same from both stores?
a. Choose a variable and explain what it represents
b. Write and solve the equation
c. Explain your answer using a complete sentence.
There are 2 pounds of apples Hannah buy for the cost for her purchase to be the same from both stores.
What is an expression?A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation. It is possible to multiply, divide, add, or subtract in math. An expression that includes variables, constants, and algebraic operations is known as an algebraic expression in mathematics (addition, subtraction, etc.). Terms combine to form expressions. The addition, subtraction, multiplication, and division mathematical operations are used to create mathematical expressions. For instance, "4 added to 2" will be expressed as 2+4 in mathematics.Given that;
At Giant Eagle, a box of cereal costs $2.89 and apples cost $1.29 per pound.
And, At Shop & Save, the apples are $1.05 per pound and a box of
cereal is $3.37.
Now,
Let number of pounds of apples can Hannah buy for the cost for her purchase to be the same from both stores = x
So, We can formulate;
For, At Giant Eagle, a box of cereal costs $2.89 and apples cost $1.29 per pound.
The total cost is,
⇒ $2.89 + $1.29x
And, For Shop & Save, the apples are $1.05 per pound and a box of
cereal is $3.37.
Total cost is,
⇒ $3.37 + $1.05x
Now, We can equate both the equation to find the number of pounds of apple to buy.
⇒ $3.37 + $1.05x = $2.89 + $1.29x
⇒ 3.37 + 1.05x = 2.89 + 1.29x
⇒ 3.37 - 2.89 = 1.29x - 1.05x
⇒ 0.48 = 0.24x
⇒ x = 0.48 / 0.24
⇒ x = 2
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The difference of c and 6 is greater than or equal to -26
A phrase, "the difference of c and 6 is greater than or equal to -26" as an expression, is c - 6 ≥ -26.
What is an expression?A term is a single mathematical phrase. It might consist of only one variable-a letter-one number-positive or negative-or several variables multiplied but never added or subtracted. A number is placed in front of some nouns that have variables. The number used before a sentence is called a coefficient.
Given:
A phrase: The difference of c and 6 is greater than or equal to -26.
The difference of c and 6 can be expressed as,
c - 6.
And c - 6 is greater than or equal to -26 can be expressed as,
c - 6 ≥ -26.
The expression is c - 6 ≥ -26.
Therefore, the phrase can be expressed as c - 6 ≥ -26.
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4. What is the solution to 4(q + 56.5) = 30q- 112?
To find the solution to the equation 4(q + 56.5) = 30q - 112, we can start by isolating the variable on one side of the equation.
First, we'll distribute the 4 on the left side:
4q + 4(56.5) = 30q - 112
4q + 226 = 30q - 112
Now we'll subtract 4q from both sides:
226 = 26q - 112
Next, we'll add 112 to both sides:
338 = 26q
Finally, we'll divide both sides by 26 to find the value of q:
q = 13
So the solution to the equation 4(q + 56.5) = 30q - 112 is q = 13.
Answer:
q=13
Step-by-step explanation:
Eight less than five times a number is two less than three times the number into an equation
Please I need this
When 16 is subtracted from half of the number r, the result is at most 18.
Write this as an inequality and solve to find the possible values of r.
X = 68 is the possible values of r.
How to get the perfect solution?Based on the given conditions,
X÷2-16 18
Rearrange variables to the left side of the
Equation: x/2=18+16
Calculate the sum or difference:
X/2=34
Divide both sides of the equation by the
Coefficient of variable X=34 × 2
Calculate the product or quotient: x=68
An inequality can be represented in four ways: equation notation, set notation, interval notation, and solution graph. Many basic inequalities may be handled by adding, removing, multiplying, or dividing both sides until the variable is all that remains. However, these factors will alter the direction of the inequality: Using a negative number to multiply or divide both sides. Swapping the left and right sides.
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Is Y =- 3 represent a line parallel to x-axis?
Yes.The equation y = -3 represents a line that is parallel to the x-axis.
In a two-dimensional coordinate system, the x-axis is the horizontal axis and the y-axis is the vertical axis. A line parallel to the x-axis will have a constant y-value, and a line parallel to the y-axis will have a constant x-value.
In this case, the equation y = -3 represents a line that has a constant y-value of -3. This means that for every point on the line, the y-coordinate will be -3 and the x-coordinate can take any value. This line is parallel to the x-axis as it does not change in its x-coordinate, so it does not have a slope and it's equation is a horizontal line.
Note, a line parallel to the x-axis is also called a horizontal line, and a line parallel to the y-axis is also called a vertical line.
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Please help thank you
Answer: M=3
Step-by-step explanation: because for every 3 pencils there is 1 student.
Is 3x³ a polynomial?
Yes, 3x^3 is a polynomial. It is a third-degree polynomial, which is a monomial.
A polynomial is a mathematical expression that can be written as the sum or difference of one or more terms, where each term is a constant multiplied by one or more variables raised to a non-negative integer power.
A monomial is a polynomial with only one term. It is of the form ax^n, where a is a constant and n is a non-negative integer. In this case, the constant is 3 and the variable is x raised to the power of 3.
The degree of a polynomial is the highest power of the variable in the polynomial.
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Hot milk is poured into a cold ceramic bowl. Which of the following most likely happens?
Answer:
When hot milk is poured into a cold ceramic bowl, heat moves from the milk to the bowl.
What is the remainder when x⁴ x³ 2x² X 1 is divided by x 1?
The remainder is 2 when x⁴ + x³ - 2x² + x + 1 is divided by x - 1.
The given polynomial is x⁴ + x³ - 2x² + x + 1.
The given divisor is x - 1
First we choose a term to multiply with the first term of the divisor such that we get the first term of the polynomial.
(x)(x^3) = x^4
Thus, we multiply the divisor (x - 1) by x^3 which gives x^4 - x^2.
Now we subtract this from the polynomial which gives 2x^3 - 2x^2 + x + 1.
Next we multiply the divisor by 2x^2 which gives 2x^3 - 2x^2. Again we subtract the same from the remaining polynomial 2x^3 - 2x^2 + x + 1 and get x + 1.
Repeating the same we multiply the divisor by 1 which gives x - 1. Subtracting the same from the remaining polynomial x + 1 we get the remainder 2.
Thus, the quotient is x^3 + 2x^2 + 1.
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