From the given information, the value of x in the given table is 42.5.
To find the value of x, we can use the formula for the arithmetic mean (average) of a set of numbers:
Arithmetic mean = (sum of all numbers) / (number of numbers)
Given that the average score on the test is 62, we can use this information to find the sum of all the scores.
Given that number of students is 1,2,3 and 4 with scores of 40,55,70 respectively, we can use this information to find the sum of all the scores.
Sum of all scores = (1 * 40) + (2 * 55) + (3 * 70) + (4 * x)
Now we can substitute the given average score and the number of students into the equation and solve for x.
62 = (1 * 40) + (2 * 55) + (3 * 70) + (4 * x) / 10
620 = 40 + 110 + 210 + 4x
4x = 170
x = 42.5
So, the value of x is 42.5
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The complete question is -
ten students wrote a test, and the distribution of scores is shown in the frequency table. if the average (arithmetic mean) score is 62, what is the value of x?
Score - 40, 55, 70, x
Number of students - 1, 2, 3, 4
Find the range of the following functions.
i) [tex]\frac{x}{2+x^{2} }[/tex]
100 points for correct answers
i need it ASAP, thank u ^_^
Answer:
Step-by-step explanation:
y = x/(2+x²)
2y + yx² = x
yx² - x + 2y = 0
(1±√(1-8y²))/2y
Now, 1 - 8y² ≥ 0
8y²≤1
y² ≤ 1/8
y ∈ (-1/2√2, 1/2√2)
Thanks
A solid box with height 20cm, width 80cm and length 10cm needs to be painted.
The paint costs £0.04 per cm2.
How much will it cost to paint the outside of the box?
The amount it would cost to paint the outside of the box is £208
Calculating the cost to paint a boxFrom the question, we are to determine calculate how much it would cost to paint the outside of the box
To do this, we will calculate the surface area of the box
The surface area of a box is given by
S.A = 2(lw + lh + wh)
Where S.A is the surface area
l is the length
w is the width
and h is the height
From the given information,
l = 10 cm
w = 80 cm
h = 20 cm
Thus,
S.A = 2(10×80 + 10×20 + 80×20)
S.A = 2(800 + 200 + 1600)
S.A = 2(2600)
S.A = 5200 cm²
Also, from the given information
The paint costs £0.04 per cm2
Thus,
The cost is £0.04 × 5200
= £208
Hence, the cost is £208
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Math work………………………………………………………………………………………………………..
The equation of the line that passes through (3, 19) and (9, 25) will be y = x + 16.
What is the equation of a line passing through two points?Let the equation of the line pass through (x₁, y₁) and (x₂, y₂).
Then the equation of the line is given as,
[tex]\rm (y - y_2) = \left (\dfrac{y_2 - y_1}{x_2 - x_1} \right ) (x - x_2)[/tex]
The points are given below.
(3, 19) and (9, 25)
The equation of the line that passes through (3, 19) and (9, 25) will be given as,
(y - 25) = [(25 - 19) / (9 - 3)](x - 9)
y - 25 = (6/6)(x - 9)
y - 25 = x - 9
y = x - 9 + 25
y = x + 16
The equation of the line that passes through (3, 19) and (9, 25) will be y = x + 16.
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when a deck of 52 cards is well shuffled, what is the probability that the four kings are all next to each other and the four queens are all next to each other?
The probability of four Kings and four Queens being all next to each other in a well shuffled deck of 52 cards is approximately 0.00000000024 or 0.000000002%.
The probability of four Kings being all next to each other in a well shuffled deck of 52 cards is:
(1/51) * (1/50) * (1/49) * (1/48)
= 0.000000000077 or 0.00000077%
The probability of four Queens being all next to each other in a well shuffled deck of 52 cards is:
(1/51) * (1/50) * (1/49) * (1/48)
= 0.000000000077 or 0.00000077%
The probability of four Kings and four Queens being all next to each other in a well shuffled deck of 52 cards is:
0.000000000077 * 0.000000000077
= 0.00000000024 or 0.000000002%
The probability of four Kings and four Queens being all next to each other in a well shuffled deck of 52 cards is very small, approximately 0.00000000024 or 0.000000002%. This is because there are many other combinations of cards that can occur in a shuffled deck.
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Select the correct answer from each drop-down menu.
Ahmed is a school student of age 15. To support his expenses, Ahmed works in his free time. The place where he works requires him to stay at work
until 9 p.m. What exemption is considered here so that Ahmed's employer does not break any law?
FLSA lets children between 14 and 16 years of age work until 9 p.m. (April 1/June 1/March 1) between
and(StPatricks day/Memorial day/Labor day)
Answer: labour day
Step-by-step explanation:
the breaking strength of a rivet has a mean value of 10,000 psi and a standard deviation of 500 psi. what is the probability that the sample mean breaking strength for a random sample of 40 rivets is between 9950 and 10,250?
So, on solving the provided question, we can say that the probability will be P( -1.26 <Z<2.53) => P( Z < 2.53)
What is probability?Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a complete set of equally likely possibilities that result in a certain occurrence compared to the total number of outcomes.
the probability will be
mean = 10,000
standard deviation = 500
for point a -
n = 40
u = 10,000
P( 9,900 < x < 10,200)
P( -1.26 <Z<2.53)
P( Z < 2.53)
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Work out the area of a rectangle with base,
b
= 26mm and perimeter,
P
= 68mm.
Please help me
Answer:
208 mm
Step-by-step explanation:
A = Area. P = Perimeter. B = base.
Let's say H = Height
P = 2B + 2H
Now we already know the perimeter is 68 mm, so P = 68:
68 = 2B + 2H
In addition, we know that the base is 26 mm, so B = 26:
68 = 2(26) + 2H
68 = 52 + 2H
16 = 2H ==> subtract 52 on both sides
H = 8 ==> the height of the rectangle is 8 mm
A = B * H
A = 26 * 8 ==> plugin B=26 and H=8 into the Area formula
A = 208 ==> simplified
Hence, the area is 208 mm.
What is m<3? Please help
Angle m∠3 is 79degree
What is linear pair?
Linear pair of angles are produced when two lines intersect each other at a point. The sum of angles of the linear pair is always 180 degrees.
Given;
m∠1= (x+70)
m∠2= (5x+54)
Here, m1=m2
substituting the values of m1 and m2
x+70=5x+54
70+54=5x-x
124=4x
x=31 substituting in m2
m2=101
Now, m2+m3=180 (linear pair of angles)
101+m3=180
m3=79degree
So, the measure of angle m3 will be 79degree.
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Is there time t, for 5 < t < 10,at which the rate of change of the volume of water in the tub changes from positive to negative? Give reason for your answer
It is impossible to say if the rate of change of the volume changes from positive to negative at a specific time.
It is not possible to determine if there is a time t, for 5 < t < 10, at which the rate of change of the volume of water in the tub changes from positive to negative without any more information. The rate of change of the volume of water in the tub is the derivative of the function representing the volume of water in the tub with respect to time. The information provided does not specify the function or the rate of change of the volume of water in the tub so it is impossible to say if the rate of change of the volume changes from positive to negative at a specific time.
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The function y = 3p^3 – 8p^2 + 4p represents the population size of mackerel y based on the number of pounds of plastic p found in the ocean.
Find the zeros of the function and explain their meaning within the context of the situation.
*PLS ANSWER QUICKLY* the zeros of the function are {0,2/3,2} I know the zeros are the pounds but explain further pls. tank u
The zeros of the polynomial y = 3p³ - 8p² + 4p are calculated to be 0, 2/3, and 2.
What are Zeros or Root of FunctionThe zeros of a function, sometimes referred to as the roots or solutions, are the values of the independent variable (x) for which the function equals zero. In other words, these are the x-coordinates of the points where the graph of the function crosses the x-axis. You can get the zeros of a function by setting its value to zero and then figuring out what value(s) of x the equation needs.
For example, if the function is f(x), you would set f(x) to 0 and then find x:
For example, if the function is f(x), you would set f(x) to 0 and then find x:
f(x) = x² + 2x - 3 = 0
This equation can be written as (x-3)(x+1) = 0.
Inferring from the x-values that x - 3 = 3 or x + 1 = -1, x² + 2x - 3 = -1, 3
As a result, the zeros of the function f(x) = x² + 2x - 3 are -1 and 3.
In the issue at hand, y = 3p³ - 8p² + 4p
y = p(3p - 2)(p - 2) (p - 2)
Taking the zeros,
0 = p(3p - 2)(p - 2)
p = 0,
3p - 2 = 0,
p = 2 / 3,
p - 2 = 0, p = 2
The zeros of the polynomial or roots are (0, 2/3, and 2).
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a teacher has two large containers filled with blue, red, and green beads. he wants his students to estimate the difference in the proportion of red beads in each container. each student shakes the first container, randomly selects 50 beads, counts the number of red beads, and returns the beads to the container. the student repeats this process for the second container. one student sampled 13 red beads from the first container and 16 red beads from the second container. assuming the conditions for inference are met, what is the 95% confidence interval for the difference in proportions of red beads in each container?
Answer: Assuming the conditions for inference are met, we can use the difference in proportions of red beads in the two samples to estimate the difference in proportions of red beads in the population. The 95% confidence interval for the difference in proportions of red beads in the two containers is calculated as follows:
Difference in sample proportions = p1 - p2 = (13/50) - (16/50) = -0.03
Standard error of the difference in sample proportions = sqrt{(p1*(1-p1)/n1) + (p2*(1-p2)/n2)} = sqrt{(13/50)(37/50)/50 + (16/50)(34/50)/50} = 0.079
Margin of error = z* * standard error of the difference in sample proportions = 1.96 * 0.079 = 0.155
95% Confidence interval for the difference in proportions of red beads in the two containers = (difference in sample proportions - margin of error, difference in sample proportions + margin of error) = (-0.03 - 0.155, -0.03 + 0.155) = (-0.185, 0.125)
So, we can be 95% confident that the difference in the proportion of red beads in the two containers is between -0.185 and 0.125.
Step-by-step explanation:
a rotcaf is the number that results from adding a number and the greatest factor of the number that is less than the number. for example, the rotcaf of 9 is 9 3, or 12. what is the sum of the rotcafs of all the even numbers between 1 and 25?
234 is the sum of the rotcaf of all the even numbers between 1 and 25.To solve this question use the concept of series.
What is rotcaf?A rotcaf is the sum of the largest factors of the number that is smaller than the number and the number that is obtained by adding two numbers, the rotcaf of 9, for instance, is 9, 3, or 12.
Here given that,
even numbers between 1 and 25 which is: 2,4,6,8,10,12,14,16,18,20,22,24
for finding rotcaf:
(2 + 1) , (4 + 2), (6 + 3), (8 + 4),.....(24 + 12)
Here two series are present:
(1, 3, 5, 7,......23) and (2,4,6,8,......24)
Now, sum of the series is:
= [12 /2 {2+24}] + [12/2 {1 + 12}
= 156 + 78
= 234
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calculate the percentage of data points that fall within one standard deviation of the mean (55,54, 66,38,53,56,57,66,45,65)
Answer:
70% of the data points
Step-by-step explanation:
To calculate the percentage of data points that fall within one standard deviation of the mean, you can follow these steps:
Calculate the mean of the data set: (55+54+66+38+53+56+57+66+45+65)/10 = 55
Calculate the standard deviation of the data set: √ (((55-55) ²+(54-55) ²+(66-55) ²+(38-55) ²+(53-55) ²+(56-55) ²+(57-55) ²+(66-55) ²+(65-55)²)/9) = 7.8
Determine the range for data points within one standard deviation of the mean: Mean ± 1 * standard deviation = 55 ± 1 * 7.8 = [47.2, 62.8]
Count the number of data points that fall within this range: 55, 54, 53, 56, 57, 45, and 65 fall within this range.
Calculate the percentage of data points that fall within this range: (7/10) * 100 = 70%
Therefore, 70% of the data points in the given data set fall within one standard deviation of the mean.
Beth’s father asked her to buy party favors for her little brother’s birthday party. Party hats cost $1.60 each, balloons cost $.75 each, and noisemakers cost $.89 each. If each of the nine children receives one of each of the favors, find a reasonable estimate of the total cost of the party favors by rounding each amount to the nearest dollar.
Beth’s father asked her to buy party favors for her little brother’s birthday party. Party hats cost $1.60 each, balloons cost $.75 each, and noisemakers cost $.89 each. If each of the nine children receives one of each of the favors, find a reasonable estimate of the total cost of the party favors by rounding each amount to the nearest dollar.
Answer:
29$
Step-by-step explanation:
1.60+0.75+0.89=3.24 - dollars per one kid
3.24 * 9 = 29.16 - dollars total
round 29.16 to the nearest dollar - 29$
What is the slope of the line that passes through (8, 3) and (10, 3)?
explan how you got the answer
Answer:
[tex]m = \frac{y2 - y1}{x2 - x1} where \: m \: is \: slope[/tex]
(8,3)=(x1,y1)
(10,3)=(x2, y2)
Now,
[tex]m = \frac{3 - 3}{10 - 8} \\ = 0[/tex]
a nursery employee wishes to plant $2$ identical golden delicious apple trees and $5$ identical bartlett pear trees in one row. how many distinct arrangements are possible?
Using simple mathematical operations, we know that we can have 10 different arrangements to plant 2 apple trees and 5 pear trees in a row.
What are mathematical operations?An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value.
The operation's arity is determined by the number of operands.
A rule that specifies the right procedure to follow while evaluating a mathematical equation is known as the order of operations.
Parentheses, Exponents, Multiplication, and Division (from Left to Right),
Addition, and Subtraction are the steps that we can remember in that order using PEMDAS (from left to right).
So, we know that:
Golden delicious apple trees: 2
Bartlett pear tree: 5
Different arrangements that can be made are as follows:
2 * 5
10
Therefore, using simple mathematical operations, we know that we can have 10 different arrangements to plant 2 apple trees and 5 pear trees in a row.
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(will give brainly if possible)
What is the area of the image of the rectangle under this transformation?
Answer:
3600 square units
Step-by-step explanation:
From inspection of the given diagram, the area of the rectangle is:
[tex]\implies \sf Area=9 \cdot 4 = 36\; units \; squared[/tex]
Given matrix:
[tex]\left[\begin{array}{rr}5&10\\-8&4\end{array}\right][/tex]
To find the area scale factor, find the absolute value of the matrix determinant:
[tex]\implies \left| \:5 \cdot 4 - 10 \cdot (-8) \right|=\left|20+80\right|=100[/tex]
Therefore, the area of the image of the rectangle under the given matrix transformation is:
[tex]\implies \sf Area=36 \cdot 100=3600\;square\;units[/tex]
tan40*cot50-sec40*csc50
I know the answer is -1, but I'm not sure how to get it.
[tex]\tan 40^{\circ} \cot 50^{\circ}-\sec 40^{\circ} \csc 50^{\circ}\\\\=\tan 40^{\circ} \tan 40^{\circ}-\sec 40^{\circ} \sec 40^{\circ}\\\\=\tan^2 40^{\circ}-\sec^2 40^{\circ}\\\\=-1[/tex]
subtract the polynomial multiple questions 100points+brainleist
1) (-x^{2} -5x-3)-(-7x^{2} -8x-8)
2) (-2x^{3}+x) -(7x-3-7x^{3})
3) (3x^{3} +3x^{2} +9)-(5x^{3} -7x^{2} +6x-9)
4) (5x^{3} +5x^{2} +5)-(6x^{3} -6x^{2} +8x-5)
5) (5x^{3} +3x^{2} +5) - (7x^{3} -9x^{2} +8x-5)
The polynomials are subtracted to give;
1. 6x²- 5x⁻³ - 8x⁻⁸
2. 5x³+ x - 7x⁻³
3. -2x³ + 10x² -6x + 18
4. 11x³ + 11x² + 8x + 10
5. -2x³ + 12x² - 8x + 10
What are algebraic expressions?These are expressions that are composed of terms, coefficients, factors, variables and constants.
They are also composed of mathematical or arithmetic operations such as;
ParenthesesDivisionAdditionMultiplicationSubtractionBracket, etcPolynomials are algebraic expression with non-negative integer exponentiation of variables.
From the information given, we have the expressions;
1.{ (-x²) - 5x⁻³} - ( -7x² - 8x⁻⁸)
collect like terms
-x² + 7x² - 5x⁻³ - 8x⁻⁸
Add like terms
6x²- 5x⁻³ - 8x⁻⁸
2. (-2x³ + x) - ( 7x⁻³ - 7x³)
collect like terms
-2x³ + 7x³ + x - 7x⁻³
add like terms
5x³+ x - 7x⁻³
3. (3x³ + 3x² + 9) - (5x³ -7x² +6x - 9)
collect like terms
3x³- 5x³ + 3x² + 7x² -6x + 9 + 9
-2x³ + 10x² -6x + 18
4.5x³ + 5x² + 5 - (-6x³ - 6x² + 8x - 5)
collect like terms
5x³ + 6x³ + 5x² + 6x² + 8x + 5 + 5
11x³ + 11x² + 8x + 10
5. 5x³ + 3x² + 5 - (7x³ - 9x² + 8x - 5)
collect like terms
5x³ - 7x³ + 3x² + 9x² - 8x + 5 + 5
-2x³ + 12x² - 8x + 10
Hence, polynomials are also described as algebraic expressions
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What is called absolute?
The exact value of a number is often what is meant when the word absolute is used in mathematics.
The absolute value of a number is often what is meant when the word absolute is used in mathematics. For mathematicians, knowing the absolute value is essential. To display a number's absolute value, vertical bars are placed on either side of the number. The absolute value on a number line denotes separation from zero.
The absolute value of a negative number is a positive number. The absolute value of one positive number is equal to that of another positive number. No matter what its sign, a number's absolute value is always its non-negative value. For instance, 5 is also the absolute value of 5, as is the absolute value of -5.
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A shirt is on sale for 12% off. If the original price was $28, what is the sale price? $ Ontorn is having a store wide sale on all merchandise. All items
Answer:
price is now $24.64
and it was $3.36 off
Step-by-step explanation:
Solve for n.
n - 26 = -13
n =
Answer:
n = 13
Step-by-step explanation:
n - 26 = - 13 ( isolate n by adding 26 to both sides )
n = - 13 + 26
n = 13
categorical data . a. are always nonnumeric b. indicate either how much or how many c. are always numeric
Categorical data can be either numeric or nonnumeric. Numeric data includes values such as integers, decimals, and percentages. Nonnumeric data includes values such as text, dates, and names.
Categorical data is a type of data that can be either numeric or nonnumeric. Numeric data includes values such as integers, decimals, and percentages, while nonnumeric data includes values such as text, dates, and names. Categorical data is often used to indicate either how much or how many of something there is. For example, a survey might ask respondents to choose between several options, such as “none,” “some,” and “many,” which are all nonnumeric values, but can still provide useful information about how much of something a respondent has. In addition, categorical data can also be numeric, such as when data is collected on the number of hours a respondent works each week. Categorical data is useful for understanding the characteristics of a population in a more qualitative way.
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Please help ASAP and send me the solutions!! I really need it for homework. Thank you!!
To make x the subject of the expression, we have; x = 16y^2 - 5.
What is the Subject of formula?Subject of formula is a topic in mathematics which involves expressing an alphabet in terms of other alphabets in the given expression. From the given question, to make x the subject implies expressing x in terms of other variables in the given expression.
So that, [tex]\frac{\sqrt{x + 5} }{4}[/tex] = y
square both sides of the expression to have;
(x + 5)/ 16 = y^2x + 5
= 16y^2x = 16y^2 - 5
Therefore to express x as a subject of formula for the given expression, we have;
x = 16y^2 - 5
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four cards are chosen from a deck of 52 cards with replacement. a deck contains 13 cards each of spades, hearts, diamonds, and clubs. what is the prob
Answer:
Hi Hannah!
there's a little tiny mistake in your question
what's the probability of getting what heart spade etc
you didn't specify it
sorry for bothering but this is my favorite questions
a student surveyed 100 students and determined the number of students who take statistics or calculus among seniors and juniors. here are the results. a 3-column table with 2 rows. column 1 has entries senior, junior. column 2 is labeled statistics with entries 15, 18. column 3 is labeled calculus with entries 35, 32. the columns are titled type of class and the rows are titled class. let a be the event that the student takes statistics and b be the event that the student is a senior. what is p(ac or b)? 0.18 0.68 0.82 0.97
The probability of a senior student taking statistics or calculus is 0.82. This is calculated by adding the probability of a senior student taking statistics (0.15) and a senior student taking calculus (0.35).
p(a or b) = p(a) + p(b) - p(a and b)
p(a) = 15/100 = 0.15
p(b) = 35/100 = 0.35
p(a and b) = 15/100 = 0.15
p(a or b) = 0.15 + 0.35 - 0.15 = 0.82
The probability of a senior student taking either statistics or calculus is 0.82. This is calculated by adding the probability of a senior student taking statistics (0.15) and a senior student taking calculus (0.35) and subtracting the probability of a senior student taking both statistics and calculus (0.15). The probability of a senior student taking statistics is calculated by dividing the number of seniors taking statistics by the total number of students surveyed (15/100 = 0.15). The probability of a senior student taking calculus is calculated by dividing the number of seniors taking calculus by the total number of students surveyed (35/100 = 0.35). The probability of a senior student taking both statistics and calculus is calculated by dividing the number of seniors taking both statistics and calculus by the total number of students surveyed (15/100 = 0.15). Therefore, the probability of a senior student taking either statistics or calculus is 0.82.
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I WILL MARK BRAINLIEST! HELPPP
Answer:
The scatter plot provided shows a relationship between the independent variable (x) and the dependent variable (y) that appears to be non-linear. The data points seem to be scattered around the graph. The best fit line would be a polynomial equation, the degree of the equation depends on the shape of the data points. It is not possible to give an exact equation of the line of best fit without knowing the data points.
(a) It is not possible to give an approximate equation of the line of best fit without knowing the data points or a more detailed information of the graph.
(b) Without a clear equation to predict values, it is not possible to predict the value of y for x = 10.
three candidates are running for the office of grand satrapy of vorania. the third- and second-place candidates received and votes, respectively. there were no ties. if the winner received of the total votes, what is the smallest possible value of ?
The smallest possible value is 44%.
A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100.
Given that,
If only three persons are running for the office and the third-place candidate received 28 votes and the second-place candidate received 98 votes, the winner could have received only 99 votes.
In this case, the total number of votes cast would be 28 + 98 + 99 = 225 votes.
The percentage for the winning candidate would be: 99 / 225 = 44%
Therefore, the smallest possible value of x is 44%.
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I WILL MARK BRAINLIEST PLS HELP
Answer:
Commission Pay = $2,288
Gross Pay = 4,878
Step-by-step explanation:
Amount of Commission: To calculate the amount of commission earned, multiply the sales by the commission rate. In this case, $57,200 x 4% = $2,288.
Gross Pay: To calculate the gross pay, add the salary to the commission earned. In this case, $2,590 + $2,288 = $4,878.
What are the 4 solutions?
The four solutions in math include algebraic solutions, geometric solutions, numerical solutions, and analytical solutions.
1. Algebraic solutions involve solving equations with variables and operations such as addition, subtraction, multiplication, and division.
2. Geometric solutions involve visualizing shapes and solving problems related to angles, lines, and shapes.
3. Numerical solutions involve using numbers and operations such as addition, subtraction, multiplication, and division to solve problems.
4. Analytical solutions involve using logic and reasoning to solve problems. This may involve using diagrams, graphs, and other visual tools to help solve a problem.
The four solutions in math include algebraic solutions, geometric solutions, numerical solutions, and analytical solutions. Algebraic solutions involve solving equations with variables and operations, geometric solutions involve visualizing shapes and solving problems related to angles, lines, and shapes, numerical solutions involve using numbers and operations to solve problems, and analytical solutions involve using logic and reasoning to solve problems with the help of diagrams, graphs, and other visual tools.
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