Polynomials can be divided using long division method and
synthetic division method.
What is a polynomial?
Algebraic expressions which are made up of coefficients and variables are called polynomials.
For example x + 3, 3y² -10, r³, t³ + 4t³ - 80, etc.
Polynomials can be classified as monomials, binomials and trinomials based upon the number of terms present.
According to the given question:
There are two methods that can be employed while dividing two given polynomials:
1. Long Division Method
The long division method is the most frequent and general method for dividing polynomials by binomials or any other form of polynomials.
Steps:
Step 1: Divide the dividend’s first term by the divisor’s first term, and use it as the quotient’s first term.
Step 2: Multiply the divisor, then place the product beneath the dividend
Step 3: To make a new polynomial, subtract.
Step 4: Use the new polynomial obtained after subtraction to repeat the operation.
2. Synthetic Division Method
It is a technique for dividing a polynomial by a linear binomial using only the coefficient values. We write the polynomials in standard form from the greatest degree term to the lowest degree term in this manner.
Steps:
Step 1: Ensure that the divisor is in the form of x − k.
Step 2: Write the dividend coefficients on the right and k on the left to set up the division.
Step 3: Now, reduce the coefficient of the dividend’s highest degree term to zero.
Step 4: Multiply k by that leading coefficient and write the product below the second coefficient on the dividend’s left side.
Step 5: Multiply the numbers in the second column.
Step 6: Multiply k by the number obtained in step 5 and write the result in the next column to the right.
Step 7: Finally, we’ll write the final solution, which will be one degree below the dividend.
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Luis has 60 m of fencing to build a four-sided fence around a rectangular plot of land. The area of the land is 216 square meters. Solve for the dimensions (length and width) of the field. The dimensions are __ meters by __ meters .
The dimensions are 12 meter by 18 meter .
what is perimeter of rectangle ?perimeter of rectangle = 2(length + width)
length and width of the Luis plot by L and W, respectively.
We know that the perimeter, is 60 meters. So we can write:
2L + 2W = 60
Simplifying this equation, we can divide both sides by 2:
L + W = 30
now , area of the plot is 216 square meters:
L x W = 216
use substitution to solve for one of the variables. Let's solve for L in the first equation:
L = 30 - W
We can substitute this expression for L into the second equation:
(30 - W) x W = 216
[tex]W^2 - 30W + 216 = 0[/tex]
We can solve this quadratic equation using the quadratic formula:
W = [30 ± [tex]\sqrt{30^2 - 4 * 1 * 216}[/tex] / 2
Simplifying:
W = [30 ± 6] / 2
So W = 18 or W = 12.
If W = 18, then L = 30 - 18 = 12.
If W = 12, then L = 30 - 12 = 18.
Therefore, the dimensions are 18 meters by 12 meters or 12 meters by 18 meters.
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A tent pole that is 8 feet tall is secured to the ground with a piece of rope that is 17 feet long from the top of the tent pole to the ground. Determine the number of feet from the tent pole to the rope along the ground.
40 feet
30 feet
15 feet
9 feet
The distance between the tent pole to the rope along the ground is 15 feet.
What is a cone?
A cone is a three-dimensional geometric form with a flat base and a smooth tapering apex or vertex. A cone is made up of a collection of line segments, half-lines, or lines that connect the apex—the common point—to every point on a base that is in a plane other than the apex.
Given that length of the tent pole is 8 feet.
The angle between the tent pole and the ground is 90°.
Thus the tent pole, the rope and the ground form a right angle triangle.
According too Pythagorean theorem, the square of the hypotenuse is equal to the sum of the square of the legs.
Here the legs of the right angle triangle is the tent pole and the the distance the tent pole to the rope along the ground.
Assume that the distance the tent pole to the rope along the ground be x.
The length of the rope is 17 feet which is hypotenuse of the right angle triangle.
Therefore,
x² + 8² = 17²
x² + 64 = 289
x² = 225
x = 15
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Answer: 15 feet
Step-by-step explanation:
first we grab 17 feet a square it
17^2 = 289
then we square 8 feet
8^2 = 64
subtract
289-64= 225
what squared equals 225?
15 does
Write a quadratic function h whose only zero is 2.
h(x) =
Answer:
h(x) = (x-2)^2
Step-by-step explanation:
A simple random sample of n subjects is selected in such a way that every possible sample of the same size n has the same chance of being chosen. (A simple random sample is often called a random sample, but strictly speaking, a random sample has the weaker requirement that all members of the population have the same chance of being selected.) Determine whether each of the following is a simple random sample and a random sample. Complete parts a through c. .. a. In Major League Baseball, there are 30 teams, each with an active roster of 25 players. The names of the teams are printed on 30 separate index cards, the cards are shuffled, and one card is drawn. The sample consists of the 25 players on the active roster of the selected team. This sample a simple random sample. It v a random sample. b. For the same Major League Baseball population described in part (a), the 750 names of the players are printed on 750 separate index cards, and the cards are shuffled. Twenty-five different cards are selected from the top. The sample consists of the 25 selected players. This sample V a simple random sample. It v a random sample c. For the same Major League Baseball population described in part (a), a sample is constructed by selecting the 25 youngest players. This sample a simple random sample. It a random sample.
This sample a simple random sample. It v a random sample.
What is simple random sample?A selection of participants from a population is randomly chosen by the researcher using simple random sampling, a sort of probability sampling. The probability of getting chosen is the same for every person in the population.A simple random sample is a subset of people picked at random from a larger group, all with the same probability. It is the process of choosing a sample at random.Simple random sampling, systematic sampling, stratified sampling, and cluster sampling are the four main types of random (probability) sampling.This sample a simple random sample. It v a random sample.To learn more about simple random sample refer to:
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Seventeen less than the product of 3 and a number is -50. what is the answer?
The number from the expression is 22. 3
What is an algebraic expression?An algebraic expression can be defined as a mathematical expression that consists of variables, terms, constants, coefficients, and factors.
These expressions are also seen to be made up of mathematical or arithmetic operation, such as;
SubtractionAdditionMultiplicationDivisionBracketParentheses, etcSome examples of algebraic expressions;
2x + 6
3x + 8
From the information given;
Let the number be x
Then'
3x - 17 = - 50
collect like terms
3x = 67
Make 'x' the subject
x = 22. 3
Hence, the value is 22. 3
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9 more than the quantity of 6 less than a number n is 18
Answer: n = 15
Step-by-step explanation:
9 + n - 6 = 18
3 + n = 18
n = 15
Solve for <1. (Will mark as brainiest!)
Answer:
< 1 = 64°
Step-by-step explanation:
First at all the sum of 2 angles should be 180°
< 3 + 116° = 180°
< 3 = 180 - 116
< 3 = 64°
Then, the sum of intern angles of a triangle must sum 180°, so:
< 1 + 52° + < 3 = 180°
< 1 +52 + 64 = 180
< 1 = 180 - 64 -52
< 1 = 64°
PLEASE HELP god bless you /Barak Allah fic A sports team has 65 men and 35 women as members. A new activity has just begun and some new members have joined. Given that the number of men is now 60% of the total members, how many of the 50 new members were women?
The required number of new boys in a sports team is 62.
As mentioned in the question, A sports team has 65 men and 35 women as members. A new activity has just begun and some new members have joined.
What is the percentage?The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.
here,
Given that the number of men is now 60% of the total members, how many of the 50 new members were women is to be determined,
Percentage of women, in the team = 100 - 60 = 40%
40% of total members are women = 35 + 50
Total members = 85 / 40%
Total member = 212
Number of new member that are boys = 212 - 85 - 65 = 62 boys
Thus, the required number of new boys in a sports team is 62.
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G(x) = 4x - 5, find g(3)
Step-by-step explanation:
this is a college question ? and you don't know how to do that ?
think back to elementary and middle school. and you had to use that all the way through high school as a very, VERY basic skill.
Focus !
g(3) just means that x = 3, and we need to replace every occurrence of x by 3. and then we calculate the result.
g(3) = 4×3 - 5 = 12 - 5 = 7
that's all to it.
piecewise function.
Express the function graphed on the axes below as a
Please help me
The piecewise function is:
f(x) = x + 1 if x < 2
f(x) = -7x + 42 if x > 5
How to express the function graphed?On the graph we can see a piecewise function (piecewise means that it has different equations defined for different intervals in the domain).
On the left side, we can see a linear equation that comes from negative infinity and ends at x = 2 with an open circle (so the domain does not contain that value).
That line passes through (-1, 0) and (0, 1), then the slope is:
a = (1 - 0)/(0 -(-1)) = 1
And the y-intercept is y = 1, then the equation of the line is:
y = x + 1
The other line starts at x = 5 (again, open circle) and keeps going, it passes through the points (5, 7) and (6, 0)
The slope is:
a = (0 - 7)/(6 -5) = -7
Then the line is something like:
y = -7*x + b
To find b, we use the point (6, 0)
0 = -7*6 + b
7*6 = 42 = b
Then this line is:
y = -7x + 42
Concluding, the piecewise function is:
f(x) = x + 1 if x < 2
f(x) = -7x + 42 if x > 5
The complete question is : Help please!! Express the function graphed on the axes below as a piecewise function.
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30 POINTS. The county rummage sale arranges 250 tables in three groups. The group on the left has 75 tables. The group on the right has 80 tables. Write an equation to find the number of tables in the middle group. Then sovle your equation.
Answer: There are 95 tables in the middle group
Step-by-step explanation:
There are a total number of 250 tables.
There are three groups.
We know how many tables the left and right groups have
let x be the number of tables in the middle
75+80+x=250
155+x=250
x=95
27/22 as a decimal rounded to the nearest hundreth
The expression as a rounded decimal is 1.23
How to evaluate the expression as a rounded decimalFrom the question, we have the following parameters that can be used in our computation:
27/22
To start with, we evaluate the expression using a calculator
So, we have the following representation
27/22 = 1.22727272727
Next, we approximate to the nearest hundredth
So, we have the following representation
27/22 = 1.23
Hence, the approximated expression is 1.23
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brett needs 2/3 cups of yogurt for one smoothie. He wants to know how many smoothies he can make with 2 4/6 cups of yogurt. which division expression can be used to represent the situation
Answer:
4
Step-by-step explanation:
2 4/6 = 16/6Based on the given conditions, formulate:
16/6 ÷ 2/3
Divide a fraction by multiplying its reciprocal:
16/6 × 3/2
(16 × 3) ÷ (6 × 2)
48/12 = 4
Thus, Brett can make 4 smoothies with 2 4/6 cups of yogurt.
Test the claim about the difference between two population means
μ1
and
μ2
at the level of significance
α.
Assume the samples are random and independent, and the populations are normally distributed.Claim:
μ1=μ2;
α=0.01
Population statistics:
σ1=3.6,
σ2=1.4
Sample statistics:
x1=18,
n1=27,
x2=20,
n2=26
Determine the alternative hypothesis.
Ha:
μ1
▼
greater than>
greater than or equals≥
less than<
less than or equals≤
not equals≠
μ2
Determine the standardized test statistic.
z=nothing
(Round to two decimal places as needed.)
Determine the P-value.
P-value=nothing
(Round to three decimal places as needed.)
What is the proper decision?
A.Fail to reject
H0.
There is enough evidence at the
1%
level of significance to reject the claim.
B.Reject
H0.
There is enough evidence at the
1%
level of significance to reject the claim.
C.Fail to reject
H0.
There is not enough evidence at the
1%
level of significance to reject the claim.
D.Reject
H0.
There is not enough evidence at the
1%
level of significance to reject the claim
The correct answer is Option C. The proper decision, in this case, is "Fail to reject H0. There is not enough evidence at the 1% level of significance to reject the claim."
The alternative hypothesis, in this case, is "μ1 ≠ μ2", as the claim being tested is that the two population means are equal.
To calculate the standardized test statistic, we can use the following formula:
z = (x1 - x2) / sqrt(((σ1^2) / n1) + ((σ2^2) / n2))Substituting in the values given in the problem, we get:
z = (18 - 20) / sqrt(((3.6^2) / 27) + ((1.4^2) / 26))
z = (-2) / sqrt((12.96 / 27) + (1.96 / 26))
z = (-2) / sqrt(0.481 + 0.075)
z = (-2) / sqrt(0.556)
z = (-2) / 0.746
z = -2.67
To calculate the P-value, we can use the standard normal table to look up the probability of getting a value of -2.67 or lower if the null hypothesis were true. The P-value in this case would be the probability of getting a value equal to -2.67 or lower, plus the probability of getting a value equal to 2.67 or higher.
Using the standard normal table, we find that the probability of getting a value equal to -2.67 or lower is 0.0039, and the probability of getting a value equal to 2.67 or higher is 0.9961. Therefore, the P-value is 0.0039 + 0.9961 = 1.0000.
Since the P-value is equal to 1.0000, which is greater than the level of significance α = 0.01, we fail to reject the null hypothesis.
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Which equations have the same value of X as 5/6x + 2/3=-9? Select three options
The equations have the same value of x are,
A) 5x + 4 = -54
B) 6(5/6x + 2/3) = -9(6)
C) 5x = -58
What is equation?
The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal. Consider the equation
3x + 5 = 14, where 3x + 5 and 14 are two expressions that are separated by the symbol "equal."
Consider the given equation
5/6 x + 2/3 = -9
Subtract 2/3 from both sides,
5/6x + 2/3 - 2/3 = -9 - 2/3
5/6x = -29/3
[tex]x = -\frac{29}{3}*\frac{6}{5}\\ x = -11.6[/tex]
The value of x is -11.6.
Hence, the equations have the same value of x are,
A) 5x + 4 = -54
B) 6(5/6x + 2/3) = -9(6)
C) 5x = -58
After solving above these equations we get the same value of x which is -11.6.
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Complete question:
Which equations have the same value of x as 5/6x + 2/3 = -9? Select three options. 6(5/6x + 2/3) = -9
6(5/6x + 2/3) = -9(6)
5 x + 4 = -54 5 x + 4 = -9
5 x = -13
5 x = negative 58
Two angles are complementary. The measure of one angle is 17 degrees. What is the measure of the other angle?
The measure of the other angle is 73°.
What are complementary angles?
Complementary angles are those whose combined angle is exactly 90 degrees. 30 degrees and 60 degrees, for instance, are complimentary angles.
How do you find a complementary angle?
Two angles are said to be complimentary if their sum is 90 degrees. So, to find the complement of an angle, subtract it from 90.
Here, we have
Given
Two angles are complementary. If one measures 17 degrees.
Complementary angles are two angles that add up to exactly 90 °.
∠A + ∠B = 90°
17 + ∠B = 90°
∠B = 90 - 17
∠B = 73°
Hence, the measure of the other angle is 73°.
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Consider the polynomial g(x) = 4x³ - x² - 24x + 6
a. List all possible rational zeros of the polynomial. (Assume all numbers shown are both + and -).
O 1, 2, 4, 1/2, 1/3, 2/3, 4/3, 1/6
O 1, 2, 3, 4, 6, 1/2, 3/2, 1/3, 2/3, 4/3, 1/4, 3/4, 1/6
O 1, 2, 3, 4, 6, 1/2, 3/2, 1/4, 3/4
1, 2, 3, 6, 1/2, 3/2, 1/4, 3/4
b. List all actual zeros of the polynomial (rational, irrational, real, and complex).
Give exact answers, separated by commas as necessary.
Zeros:
a. The rational roots of the polynomial g(x) = 4x³ - x² - 24x + 6 is 1/4.
b. The rational and irrational roots of the polynomial g(x) = 4x³ - x² - 24x + 6 are 1/4 and ± √6.
What is a factor of a polynomial?We know that if x = a is one of the roots of a given polynomial x - a = 0 is a factor of the given polynomial.
To confirm if x - a = 0 is a factor of a polynomial we replace f(x) with f(a) and if the remainder is zero then it is confirmed that x - a = 0 is a factor.
Given, A cubic polynomial function g(x) = 4x³ - x² - 24x + 6.
Therefore,
g(x) = 4x(x² - 6) - 1(x² - 6).
g(x) = (4x - 1)(x² - 6).
g(x) = (4x - 1)(x + √6)(x - √6).
Hence, x = 1/4, ± √6.
So, The roots of the polynomial are 1/4 and ± √6.
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Please help me with my question step by step
give brainliest.help
The required, team 3, tower garden donation shows the proportional relationship between weeks and donation,
What is proportionality?Proportionality is described as the relationship between two or more sets of values, and whether these values are directly proportional or inversely proportionate to one other.
here,
From the table,
The ratio of a week to the donation of the individual team must be the same as the ratio of the preceding week and the donation of the respective team,
So,
Team 1,
1 / 1 = 2 / 3[1/4], false
Similarly, team 2 and team 4's relationship is also not proportional,
Now, team 3
1 / [2 1 / 3] = 2 / [4 2/3 ]
3 / 7 = 3/7
Thus, The necessary, team 3, tower garden gift illustrates the proportional relationship between weeks and donation.
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Can someone help me with this? I’m confused
Answer:
Option 4
Step-by-step explanation:
The domain of this function is the possible values of n that are suitable for this function. Since n represents a number of vehicles, the domain of n should be a whole number (since you cannot have a negative number of vehicles or half of a vehicle).
hope this helps :)
Using three mixed numbers as side lengths draw an equilateral triangle with a perimeter of 8 and 1/4 feet.
The side of the equilateral triangle is 2 ³/4 feet, having perimeter 8 ¹/₄ feet.
What is an equilateral triangle?If all three of a triangle's sides are the same length, the triangle is said to be equilateral. Congruent sides refer to sides that have the same length, and they characterize an equilateral triangle.
Given that,
The perimeter of equilateral triangle = 8 ¹/₄ feet.
Simplify the rational term.
8 ¹/₄ = (32 + 1) / 4 = 33 /4.
Let each side of an equilateral triangle is a feet.
The perimeter of the equilateral triangle = 3a
Since, 3a = 33/4
a = 11/4
a = 2 ³/4
The required side of the equilateral triangle is 2 ³/4.
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NO LINKS!! Find the specified term of the geometric sequence.
a6: a1 = 3, a2= 18, a3= 108, . . .
a6=
Answer:
23328
Step-by-step explanation:
since it is a geometrics sequence we will use the formula
[tex] {ar}^{n - 1} [/tex]
The first term(a) = 3
The second term = ar = 18
divide the first term and second term to find the common ratio
[tex] \frac{t2}{t1} = \frac{ar}{a} = \frac{18}{3} [/tex]
r = 6
Now lets find the sixth term
[tex]t6 = {ar}^{6 - 1} [/tex]
[tex]t6 = {ar}^{5} [/tex]
by substituting for the values
[tex]t6 = 3 \times {6}^{5} [/tex]
= 3 × 7776
= 23328
i hope this helped
Answer:
[tex]a_{6} = 23,328[/tex]
Step-by-step explanation:
⭐ Geometric Progression formula: [tex]a_{n} = a_1(b)^{n-1}[/tex]
[tex]a_{1}[/tex] is the first term of the geometric progression[tex]b[/tex] is the common ratio (the number each term gets multiplied by)[tex]a_{n}[/tex] is the notation for which term you are finding, where n is the term numberWe are given that [tex]a_{1}[/tex] = 3. Now, we need to find b.
b is the quotient of [tex]\frac{a__3}{a__2}[/tex].
[tex]\frac{a_3}{a_2}\\ \\\frac{108}{18}\\= 6[/tex][tex]b[/tex] = 6Let's substitute the first term and common ratio into the formula.
[tex]a_n = 3(6)^{n-1}[/tex]
The problem wants us to solve for the 6th term, so we have to substitute 6 for n and solve.
[tex]a_6 = 3(6)^{6-1}\\a_6 = 3(6)^5\\a_6 = 3(7,776)\\a_6 = 23,328[/tex]
Which pairs of rectangles are similar polygons? Select Similar or Not Similar for each pair of rectangles. Similar Not Similar A and B Similar – A and B Not Similar – A and B B and C Similar – B and C Not Similar – B and C A and C Similar – A and C Not Similar – A and C Three rectangles labeled A, B, and C. The length of rectangle A is labeled as 100 centimeters and the width is labeled as 80 centimeters. The length of rectangle B is labeled as 120 centimeters and the width is labeled as 100 centimeters. The length of rectangle C is labeled as 90 centimeters and the width is labeled as 72 centimeters.
A polygon is a plane shape with a minimum of three straight sides. Thus the appropriate answer are:
i. A and B Not Similar
ii. B and C Not Similar
iii. A and C Not Similar
Polygons are majorly plane shapes which have straight sides. They are named with respect to the number of their sides, and the minimum sides is three. Some common examples are: trigon (3 sides), octagon (8 sides), hexagon (6 sides), pentagon (5 sides) , etc.
Two or more shapes are said to be similar if and only if they have some common properties with respect to their sides or internal angles.
Considering the ratios of the sides of the given polygons, it can be deduced that:
i. A and B Not Similar
ii. B and C Not Similar
iii. A and C Not Similar
Thus none of the polygons are similar.
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Kate and Miley are selling girl scout cookies Kate sold 27 boxes in 45 minutes Miley sold 12 boxes in 30 minutes at the same rates how many total boxes will the girls have sold in one hour?
Kate and Miley sold 60 boxes of cookies in one hour.
What is ratio?Ratio basically compares quantities, that means it show value of one quantity with respect to other quantity.
If a and b are two values, their ratio will be a:b.
Given that,
Cookies sold by Kate in 45 minutes = 27 boxes.
Also,
Cookies sold by Miley in 30 minutes = 12 boxes.
To find the total boxes of cookies sold by girls in one hour,
Use ratio method,
Cookies sold by Kate in 3/4 hours = 27 boxes,
Cookies sold by Kate in 1 hour = 27 x (4/3) = 36
Cookies sold by Miley in 1/2 hours = 12 boxes,
Cookies sold by Miley in 1 hour = 12 x 2 = 24 boxes
Total cookies sold by Kate in Miley in one hour = 36 + 24 = 60
There are 60 boxes of cookies sold by the girls in one hour.
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A stage manager is trying to seat important guests in the front row of a theater. The row has seven seats, and she would like a diplomat in the first seat, a singer in the second seat, and a movie director in the third seat. After this, the remaining diplomats, singers, and movie directors will be seated in the last four seats, in no particular order. If there are 3 diplomats, 2 singers, and 2 directors attending the show, how many different front row plans are possible?
Answer: 12 row plans
The first seat has 2 possible options, the 2 directors. The second seat has another 2 options. With each director comes 2 options for the second seat, so 2 x 2=4 possible options for the 1st and 2nd seats. The third seat has 3 options. That means for each combination of the 1st and 2nd seat, there are 3 possible options. 4x3=12 combinations.
Step-by-step explanation:
Ester writes 6 x 7 = 42 to find
the number of students seated
at tables. Describe what each
factor represents.
Answer:
6 rows to 7 steal in each rows
The display summarizes grades on a World History exam.
A vertical box plot is titled world history exams, with a minimum of 54, a maximum of 94, a lower quartile of 70, a median of 83, and an upper quartile of 88.
Which of the following describes the data set?
The data is univariate and categorical.
The data is univariate and numerical.
The data is bivariate and categorical.
The data is bivariate and numerical.
The option that best describes the data is The data is band numerical
What is univariate data?This kind of data just has one variable. Since there is only one variable that varies, univariate data analysis is the most straightforward type of analysis.
In this case the one variable is World History scores exam
What are numerical data?Data that is expressed as numbers rather than in any linguistic or descriptive form is referred to as numerical data.
Numerical data, also known as quantitative data, is gathered in number form and differs from all other sorts of number data because it can be calculated mathematically and statistically.
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Can someone answer this for me. I NEED HELPPP
Find the value of y if m∠3 =65° and m∠1 =(15y+5)°
Answer: 4 i think
Step-by-step explanation:
65=15y+5
65 - 5 = 15y +5 -5
60 = 15y
60/15 = 15y/15
4 = y
3/4x + 2/3y - 3/8x + 1/2y
[tex]\frac{3}{8} x+\frac{7}{6} y[/tex].
Step-by-step explanation:1. Write the expression.[tex]3/4x + 2/3y - 3/8x + 1/2y[/tex]
2. Operate with like terms.a) First, start by operating with the terms that contain the "x" variable.
[tex]3/4x- 3/8x\\ \\\frac{3}{4}x-\frac{3}{8}x\\ \\ \frac{3*2}{4*2}x-\frac{3}{8}x\\ \\\frac{6}{8}x-\frac{3}{8}x\\ \\x(\frac{6}{8} -\frac{3}{8} )\\ \\x(\frac{6-3}{8} )\\ \\x(\frac{3}{8} )\\ \\\frac{3}{8}x[/tex]
b) Start with terms containing "y".
[tex]2/3y+1/2y\\ \\\frac{2}{3}y +\frac{1}{2} y\\ \\\frac{2*2}{3*2}y +\frac{1*3}{2*3} y\\ \\\frac{4}{6}y +\frac{3}{6} y\\ \\y(\frac{4+3}{6})\\ \\y(\frac{7}{6})\\ \\\frac{7}{6} y[/tex]
3. Put the terms together.[tex]\frac{3}{8} x+\frac{7}{6} y[/tex].
CAN SOMEONE HELP WITH THIS QUESTION?✨
The time required to grow $5000 to $8300, if the rate of interest is 7.5 %, is 7 years.
What is interest?When the loan is given to you, then some amount is charged to you for the principal amount and that is called interest.
Given:
The principal amount, p = $5000,
The amount, A = $8300
The rate of interest, r = 7.5 %,
Calculate the time as shown below,
[tex]A = p(1 + r / 400)^{4n}[/tex]
8300 = 5000 (1 + 7.5 / 400)⁴ⁿ
8300 / 5000 = (1 + 0.01875)⁴ⁿ
1.66 = (1.0188)⁴ⁿ
1.66 = (1.077)ⁿ
(1.077)⁷ = (1.077)ⁿ
n = 7
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A 41-year old woman has $398,100.00 in an IRA account. Due to medical concerns of a family member, she decided to make no additional contributions to the account but expect it to grow at 8% compounded every 4 months. How much does she expect to have in the account when she retires at age 65?
She expects to have $2710591.78 when she retires at age 65 with the principal amount is 398100, the interest rate is 8%, time period is 24 and number of times interest applied is 3 by the concept of compound interest.
What is compound interest?Interest that is paid on the principal and interest at regular periods is known as compound interest. The interest is calculated for the new principal at regular intervals after the interest that has already accumulated has been combined with the existing principal amount. The initial principal plus the interest that has accrued thus far are added together to form the new principal.
Interest on the principal + periodic compound = compound interest.
According to the question the principal amount is 398100, the interest rate is 8%, time period is 24 and number of times interest applied is 3.
Here the interest is compounded every 4 months
So, the formula of compound interest is as follows:
A=p (1+ [tex]\frac{r}{n}[/tex]) ∧ (n× t)
Where P is the principal balance, r is the interest rate, n is the number of times interest is compounded per year and t is the number of years.
Here the interest is compounded every 4 months hence the value of n is 12/4 which is equal too 3.
Insert the values of p, n, t, r in above equation,
A=398100(1+[tex]\frac{8}{300}[/tex]) ∧ (3×24)
A=398100× (1.027) ∧ (72)
A=398100×6.809
A=2710591.78
She expects to have amount $2710591.78 when she retires at age 65.
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