Mr. Dunston spend is $35.
Given:
Mr. Dunston and Mr. Dolland spent $45 all together.
Mr. Dunston and Ms. Campbell spent $65 all together.
If Ms. Campbell spent 3 times as much as Mr. Dolland.
Let x , y , z be spend of dunston ,dolland and campbell.
x + y = 45
x + z = 65
z = 3*y
x + 3y = 65
on substracting x + y = 45 and x + 3y = 65 we get,
x + y - x - 3y = 45 - 65
-2y = -20
2y = 20
y = $10.
substitute y value,
x + 10 = 45
x = 45 - 10
x = $35
Therefore Mr.Dunston spend $35.
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Solve the absolute value equation (3x-6)=12.
O a
Ob
Oc
Od
x=6,x=2
▸
x=-6, x=-2
x=6₂x=-2
x=-6₂x=2
The solution of the absolute value equation |3x - 6| = 12 is x= 6 and x = -2
The absolute value equation is
|3x - 6| = 12
We can write the absolute value equation in two ways
3x - 6 = 12
-(3x - 6) = 12
We have to solve each equation
The first equation is 3x - 6 = 12
3x - 6 = 12
3x = 12+6
3x = 18
x = 18/3
x = 6
The second equation is -(3x - 6) = 12
Apply the distributive property
-3x + 6 = 12
-3x = 12 - 6
-3x = 6
x = 6/-3
x = -2
Hence, the solution of the absolute value equation |3x - 6| = 12 is x= 6 and x = -2
The complete question is:
Solve the absolute value equation |3x - 6| = 12 .
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Start Fraction w superscript 12 baseline over w superscript 18 baseline End Fraction
A. w30
B. w–30
C. w6
D. w–6
Answer:
answer should be d
Step-by-step explanation:
it's d because if u fraction 6 u will get d
find zeros f(x)=x^4-6x^3-21x^2=150x-100 given k=5
The zeros of the polynomial x⁴ - 6x³ - 21x² - 150x - 100 are 0.6511 and 8.262 respectively
Zeros of a PolynomialZeros of polynomial are the points where the polynomial equals zero on the whole. In simple words, we can say that zeros of polynomial are values of the variable such that the polynomial equals 0 at that point. Zeros of a polynomial are also referred to as the roots of the equation and are often designated as α, β, γ respectively.
The zeros of a polynomial f(x) are the values of x which satisfy the equation f(x) = 0. Here f(x) is a function of x, and the zeros of the polynomial are the values of x for which the f(x) value is equal to zero. The number of zeros of a polynomial depends on the degree of the equation f(x) = 0. All such domain values of the function, for which the range is equal to zero, are called the zeros of the polynomial.
To find the zeros of this polynomial function, we have to write the function appropriately.
x⁴ - 6x³ - 21x² = 150x - 100
x⁴ - 6x³ - 21x² - 150x - 100 = 0
The roots of this function is 0.6511 and 8.262 respectively
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. x^4 – 2x^3 – 7x^2 + 8x + 12 = 0
The Required Factors (x + 1) (x - 3 ) (x + 2) (x - 2).
Given equation.
x^4 - 2x^3 - 7x^2+8x+12 = 0
Factors : factor is a number that divides another number, leaving no remainder. In other words, if multiplying two whole numbers gives us a product, then the numbers we are multiplying are factors of the product because they are divisible by the product.
polynomial : an expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable
Now, factorize the polynomial of degree 4 as follows.
= (x + 1) (x - 3) (x^2 - 4)
Then, again factorize polynomial of degree 2.
Therefore (x + 1) (x - 3 ) (x + 2) (x - 2)
This is the required factors.
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Which choice is equivalent to the fraction below 2/√x - √x+2
The fraction is equivalent to the [tex]\sqrt{x+2}-\sqrt{x}[/tex].
The correct option is (C).
Given,
The fraction is given as:
[tex]\frac{2}{\sqrt{x} -\sqrt{x+2} }[/tex]
To find the above fraction which choice is equivalent to the fraction?
Now, According to the question:
Simplify or expand
[tex]\frac{2}{\sqrt{x} -\sqrt{x+2} }[/tex]
Rationalize the denominator:
[tex]\frac{2(\sqrt{x} -\sqrt{x+2} )}{(\sqrt{x} -\sqrt{x+2})(\sqrt{x} -\sqrt{x+2} ) }[/tex]
Expand the expression:
[tex]\frac{2(\sqrt{x} +\sqrt{x+2} )}{(\sqrt{x})^2-(\sqrt{x+2} )^2 }[/tex]
[tex]\frac{2(\sqrt{x} +\sqrt{x+2} )}{x-(x+2)}[/tex]
[tex]\frac{2(\sqrt{x} +\sqrt{x+2} )}{-2}[/tex]
Determine the sign and cross out the common factor:
[tex]\sqrt{x+2}-\sqrt{x}[/tex]
Hence, The fraction is equivalent to the [tex]\sqrt{x+2}-\sqrt{x}[/tex].
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Select all of the numbers that are correctly written in scientific notation.
A. 42 times 10 superscript 5 baseline
B. 1.1 times 10 superscript 4 baseline
C. 7.0 times 20 superscript 4 baseline
D. 6.01 times 10 superscript negative 4 baseline
E. 18 point 0 time 10 cubed
The numbers that are correctly written in scientific notation are:
B) 1.1 x 10⁴D) 6.01 x 10⁻⁴.What is scientific notation?Scientific notation is a shorthand (approximate) manner of writing long or short numbers using decimal forms raised to 10 power a baseline.
The rules for correctly writing a scientific notation include the following:
The base should always be 10. The exponent must be a non-zero integer (either positive, like option B, or negative, like option D). The absolute value of the coefficient is greater than or equal to 1 but should be less than 10.Coefficients can be positive or negative numbers including whole and decimal numbers.Thus, the scientific notation rules are correctly satisfied by Options B and D, unlike Options A, C, and E.
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Answer Options:A) 42 x 10⁵
B) 1.1 x 10⁴
C) 7.0 x 20⁴
D) 6.01 x 10⁻⁴
E) 18.0 x 10³
Can a normal approximation be used for a sampling distribution of sample means from a population with μ=52 and σ=9, when n=49?
Answer: Yes
Step-by-step explanation:It can because math works like that.
Desmond made a scale drawing of a house. The garage is 4 centimeters wide in the drawing. The actual garage is 5 meters wide. What is the scale factor of the drawing?
Simplify your answer and write it as a fraction.
The scale factor of the drawing that Desmond is illustrating is is 1/125.
What is a scale factor?A scale factor is the ratio between rte scale of a particular object and the new object.
In this case, Desmond made a scale drawing of a house, the garage is 4 centimeters wide in the drawing and the actual garage is 5 meters wide.
100 centimeters = 1 meters
5 meters = 500 centimeters
Therefore, the scale will be:
= 4 / 500
= 1 / 125
= 1:125
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Please help me with these thank you
The value of (2/3) ÷ (1/4) is 8/3 and the value of 7 ÷ (2/3) is 21/2.
This is a question from the division of fractions.
We know the property of fractions is given by:-
(m/n) ÷ (a/b) = (m/n)*(b/a) = mb/na
Hence, we can write,
(2/3) ÷ (1/4) = (2/3) * (4/1) = 2*4/3*1 = 8/3
7 ÷ (2/3) = (7/1)*(3/2) = 7*3/ 1*2 = 21/2
Fractions
A fraction represents a part of a whole or, more generally, any number of equal parts. Numerators and denominators are also used in fractions that are not common, including compound fractions, complex fractions, and mixed numerals.
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Use Structure A shoe store buys packs of socks wholesale for $5 each and marks them up by 40%. The store decides to discount the packs of socks by 40%. Is the discounted price $5?
Multiple choice question.
cross out
A)
yes; The packs of socks are marked up to $7 and then discounted to $5.
cross out
B)
yes; The packs of socks are marked up to $9 and then discounted to $5.
cross out
C)
no; The packs of socks are marked up to $7 and then discounted to $4.20.
cross out
D)
no; The packs of socks are marked up to $5.20 and then discounted to $4.99.
The correct option regarding the price is C. no; The packs of socks are marked up to $7 and then discounted to $4.20.
How to calculate the price?In this situation, a shoe store buys packs of socks wholesale for $5 each and marks them up by 40%. The price will be:
= Original price + Markup
= 5 + (40% × 5)
= 5 + 2
= $7
Then, the store decides to discount the packs of socks by 40%. This will give a price of:
= 7 - (40% × 7)
= 7 - 2.8
= $4.2
The price isn't discounted to $5.
In conclusion, the correct option is C.
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What Is a factor?
Hi
A factor is a number that divides another number, leaving no remainder
Calculate capital if assets are £451,100, liabilities are £20,500, income is £351,200 and expenses are £270,600.
The capital is £430,600.
Define capital.
The money that a company has on hand to support both its current operations and potential expansion is known as capital. One source of funding for it is the earnings from its operations. When calculating a company's capital worth, all of the company's physical assets and financial assets would be included (minus its liabilities).
The capital account—also referred to as the capital and financial account—records the net flow of investment transactions into an economy and is used in macroeconomics and international finance.
Solution Explained:
Given, Assets = £451,100 and liabilities = £20,500
Capital = Assets - Liabilities
= 451100 - 20500
= £430,600
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-3x + 6 = 4 - 6x
I kept getting 1.5 But it's not correct. ???
Answer:
-2/3 or -0.6666
Step-by-step explanation:
-3x + 6 = 4 -6x
Let's move the x to one side
-3x +6x=4-6
Combine like terms
3x = -2
Divide both sides by 3
-2/3=x
or -0.666666
Degree 5; zeros: 7, -i, 3+i; let a represent the leading coefficient
Therefore the required polynomial is [tex]f(x) = a(x^5+13x^4+53x^3+83x^2+52x+70)[/tex]
What is an leading coefficient?
The numbers placed in front of the variable with the biggest exponent are known as leading coefficients. They can be whole numbers, fractions, or decimals, as well as positive, negative, real, or imaginary, just like conventional coefficients.
According to fundamental theorem of algebra , if a + bi be a zero of a polynomial with real coefficients then a-bi is also a zero
Now given that f(x) be a polynomial with degree 5 and with zeros -7,-i,-3+i
and f(x) be a polynomial with real coefficients.
therefore by fundamental theorem of algebra
+i and -3-i are also zeros of f(x)
so zeros of f(x) are 7, -i, -3 + i, i, -3 -i
Degree is 5, so there is at most 5 zeros therefore the required polynomial will be
f(x) = a(x + 7)(x + i )(x - i)(x +3- i)(x +3 +i)
= a[(x +7)(x² + 1)(x² +6x + 10)]
[tex]= a\left[x^5+ 13x^4 + 53x^3 +83x^2 + 52x + 70]\right[/tex]
[tex]f(x) = a(x^5+13x^4+53x^3+83x^2+52x+70)[/tex]
Therefore the required polynomial is [tex]f(x) = a(x^5+13x^4+53x^3+83x^2+52x+70)[/tex]
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Evaluate the expression when m = -3.
2
m² -7m+6
Answer:
36
Step-by-step explanation:
substitute m = - 3 into the expression
m² - 7m + 6
= (- 3)² - 7(- 3) + 6
= 9 + 21 + 6
= 36
accounts recivable of 88000 and accounts payable of 39000 and has revenues of 121000 and expenses of 83000 what is the companies net income
The required net income of the companies is given as 49,000.
Given that,
Accounts receivable of 88000 and accounts payable of 39000 and have revenues of 121000 and expenses of 83000 what is the company's net income is to be determined.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
Here,
Total income = 88000 + 121000 = 209000
Total outflow = 39000 + 83000 = 122000
Net income = 209000 - 122000 = 49000
Thus, the required net income of the companies is given as 49,000.
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On a map of Texas, the cities of Midland, Lubbock, and Odessa form a triangle.
Midland is
20 miles from Odessa, and Lubbock is 113 miles from Midland. What is the farthest,
in miles,
Odessa could possibly be from Lubbock?
If Midland is 20 miles from Odessa, and Lubbock is 113 miles from Midland. Then 111.22 miles is Odessa from Lubbock.
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
Given,
The cities of Midland, Lubbock, and Odessa form a triangle.
The distance between Midland and Odessa is 20 miles.
The distance between Lubock and Odessa is unknown, we need to find this.
This can be find by using Pythagorean theorem
Odessa from Lubbock=20²+x²
113²=20²+x²
12769=400+x²
12369=x²
x=111.22
Hence, 111.22 miles, Odessa could possibly be from Lubbock.
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Graph the polygon with the given vertices and its image after a reflection in the line y=x.
A(2, -1), B(-1, 2), C(2, 3), D(4,2)
In the given picture the polygon ABCD is the formed polygon (in red color) and the reflection of the polygon is A'B'C'D' (in green color).
Graphing the polygon and reflection in a graph:
A polygon is a 2 - dimensional shape, that is formed by three or more straight edges. To graph, a polygon, plot the given points on the plane and connect the vertices using straight lines, without crossing any lines.
Reflecting image in the line y = xTo reflect the image in the line y = x, switch the values of x to y and y to x. After switching the points, join the formed points and draw the reflected image.
Here we have
A(2, -1), B(-1, 2), C(2, 3), D(4,2)
After switching the values of x to y and y to x the resultant points are
A'(-1, 2), B'(2, -1), C'(3, 2), D'(2,4)
In the given picture the polygon ABCD is the formed polygon (in red color) and the reflection of the polygon is A'B'C'D' (in green color).
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0°F; drops 15° new temperature
SOMEONE HELP ME.
A blueprint for a building includes a rectangular room that measures 3 inches long and 5.5 inches wide. The scale for the blueprint says that 1 inch on the blueprint is equivalent to 10 feet in the actual building. What are the dimensions of this rectangular room in the actual building.
The dimension of the rectangular room in the actual building are 55 feet by 30 feet.
How to find the dimension of the rectangular room in the actual building?Scale is used to represent the relationship between a measurement on a model and the corresponding measurement on the actual object.
A blueprint for a building includes a rectangular room that measures 3 inches long and 5.5 inches wide. The scale for the blueprint says that 1 inch on the blueprint is equivalent to 10 feet in the actual building.
The dimensions of this rectangular room in the actual building can be found as follows:
let's find the length of the actual room
1 inches = 10 feet
3 inches = ?
cross multiply
length = 30 ft
Let's find the width of the room
1 inches = 10 feet
5.5 inches = ?
cross multiply
width = 55 ft
Therefore, the width and length of the room are 55 feet and 30 ft respectively.
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A sample of 39 customers was taken at a local computer store. The customers were asked the prices of the computers they had bought. The data are
summarized in the following table.
Number of computers Price (in dollars)
13 - 2300
11 - 1800
15 - 2150
Find the mean price for this sample. Round your answer to the nearest dollar.
The mean is xbar = Σxf/Σf = 64,950/43 = 1510.47
What is mean?A group of two or more numbers is simply averaged mathematically to get the term "mean." There are several ways to calculate the mean for a given collection of numbers, including as the arithmetic mean approach, which utilizes the sum of the series' values, and the geometric mean method, which uses the average of a group of products. However, the majority of the time, the results from all of the main approaches to calculating a simple average are roughly the same.acc to our question-
Mean price = total amount spent on computers / number of computers= (6*900 +18*800+14*2600+5*1750)/(6+18+14+5) =64,950/43 = 1510.47x f fx900 6 5400800 18 144002600 14 364001750 5 875043 64950xbar = Σxf/Σf = 64,950/43 = 1510.47hence,The mean is xbar = Σxf/Σf = 64,950/43 = 1510.47
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A system consists of three identical components. In order for the system to perform as intended, all of the components must perform. Each has the same probability of performance. If the system is to have a .92 probability of performing, what is the minimum probability of performing needed by each of the individual components? Round your answer to three decimal places.
If each has the same probability of performance. If the system is to have a .92 probability of performing, The minimum probability of performing needed by each of the individual components is: 0.97126.
How to determine the probability:Given data:
Number of identical component = 3
Probability of performing = .92
Now let determine the probability
Probability = 0.92 ^(1/3)
Probability = 0.92^0.3333
Probability =.9726
Therefore the probability is .9726.
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Your office window is a 45 feet high. Looking out your window, you find that the top of a statue lines up exactly with the bottom of a building that is b = 600 horizontal feet
from your office. You know that the statue is c= 125 feet from the building. How tall is the statue? (See the figure below. Round your answer to two decimal places.)
The height of the statue that exactly with the bottom of a building is approximately 9.3926 feet tall.
height of the office window , a = 45 feet
the bottom of a building that is horizontal from the office, b = 600 feet
let x represent the angle
tan(x) = a/b
tan(x) = 45/600
x = tan⁻¹(0.75)
x = 4.28 degree
the height of the statue, h = ?
the statue is from the building, c = 125 feet
tan(45/600) = h/125
h = tan(0.075) x 125
h = 9.3926 feet
The height of the statue that exactly with the bottom of a building is approximately 9.3926 feet tall.
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the side length of a square is √8 find the area.
is the number rational or irrational?
The area of a square with a side length √8 represents a rational number, which is equal to 8 square units.
Is the number behind the area of the square a rational number?
Rational numbers are real numbers of the form m / n, where m and n are integers, where n ≠ 0. The rest of real numbers are irrational (i.e. π, √5, ∛7, e) Besides, the area of the square is determined by the following formula:
A = l²
Where l is the side length of the square.
First, substitute the side length of the square in the area formula:
A = (√8)²
Second, use algebraic properties to simplify the expression and find the corresponding result:
A = ([tex]8^{\frac{1}{2} }[/tex])²
A = 8
This number represents a rational number as 8 is equivalent to the rational number 8 / 1.
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1. Draw a picture, write and solve an equation to find Mary's weight, w, when she was 10 years old.
The Weight of Mary is 80. Students who are having trouble solving a problem can use the "draw a picture" method to create a visual representation of the issue.
"Draw a picture" method ?Students who are having trouble solving a problem can use the "draw a picture" method to create a visual representation of the issue.
the justifications.
Inquiry 1.
Formula: w = 10 8 pound
Answer: x = 80 lb
Inquiry 2:
Formula: d = 108 lb - 8 pound
d = 72 lb
Explanation:
First of all
When Mary was born, she weighed 8 pounds.
Statement 2: Mary weight 10 times as much when she was 10 years old.
w = 10 8 pounds, or 80 pounds.
Description of the illustration:
She was born weighing 8 pounds, which is represented by each cell. The 10 cells indicate that the number 8 lbs. has been repeated 10 times.
Next, the sum of the multiplication is shortened:
8 + 8 + 8 + 8 + 8 + 8 + 8 + 8 + 8 + 8 = 10 × 8 = 80.
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Lightest weight
750g
0.7kg
7.5kg
705g
7.05kg
Answer:
.7 kg
Step-by-step explanation:
1. Convert answers in grams into kilograms
1000g = 1 kg
750g = .75kg
705g = .705 kg
2. Find smallest number of kg
= .7 kg
Given: AB=BC AC < bisector of
Considering the given figure we have that
< BAC = < CAD definition of angle bisection
< BAC = < BCA base angles of isosceles triangle
What is angle bisection?This refers to when angles are being shared or divided into two equal parts.
In the given problem, line AC is the bisector of < BAC. creating wo equal angles in the process. hence
< BAC = < CAD definition of angle bisection
Triangle BAC is an isosceles triangle, since the sides BA and BC are equal. the angles are also equal therefore
< BAC = < BCA base angles of isosceles triangle
Line AC is also a transversal line, connecting the two parallel lines BC and AD. This creates opportunity for alternate angle theorem
< BCA = < CAD alternate internal angle theorem
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simplify this expression-12÷3×(-8+(-4)²-6)+2
Answer: -6
Step-by-step explanation:
Question content area top
Part 1
Find an equation for the line with the given properties. Express your answer using either the general form or the slope-intercept form of the equation of a line.
Perpendicular to the line y=
1
2x−2; containing the point (−3,6)
The equation of the line in slope-intercept form is y = -x/12 + 23/4
How to find the equation of the line?Given that: the line is perpendicular to the line y= 12x−2 and it contains the (−3,6).
The equation of line is an algebraic form of representing the set of points, which together form a line in a coordinate system
The slope-intercept form of a straight line is:
y = mx + c,
where m is the slope and c is the y-intercept
When the two lines are perpendicular, the product of their slope is -1 i.e.
m₁ x m₂ = -1
where m₁ and m₂ represent the slope of the lines
Let the slope of the given line be m₁ and the slope of the unknown line be m₂
Line1(given):
y = 12x−2 and m₁ x m₂ = 12
m₁ x m₂ = -1
12 x m₂ = -1
m₂= -1/12
Line 2(unknown) with the point (−3,6):
y = mx + c
6 = -1/12 (-3) + c
6 = 1/4 + c
c = 6 -1/4 = 23/4
y = -x/12 + 23/4
Therefore, the slope-intercept form of the equation of the line is y = -x/12 + 23/4
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How will the mode be affected if the outlier is removed from the data set below? 58, 60, 53, 54, 60, 35, 58, 60
will the mode decrease?
will the mode not change?
is there not enough information?
will the mode increase?
The mode will not change.
Given data,
58,60,53,54,60,35,58,60
Outlier is the value in a set of data that much higher or lower than other values in data.
from given data, outlier is 35.
Mode is the value in a set of data that occurs more frequently in set of data.
from given data, 60 occurs more frequently.
Hence, 60 is the mode of data.
If outlier is removed from the data set then it will not affect the mode of the data
Thus, the mode will not change.
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