Answer:
Step-by-step explanation:
smaller
larger
bigger
larger
You want to be able to withdraw $20,000 each year for 20 years. Your account earns 9% interest.
a) How much do you need in your account at the beginning?
b) How much total money will you pull out of the account?
c) How much of that money is interest?
a) The amount of money in the account at the beginning is $222,222.222.
b) The total amount of money withdrawn from the account is $400,000.
c) The amount of interest earned is $177,777.778.
It is given that we want to be able to withdraw $20,000 per year for 20 years. The account earns 9% interest annually. Let the total amount of money withdrawn in the twenty years be represented by the variable "A".
A = $20,000*20 = $400,000
Let the amount of money in the account at the beginning be represented by the variable "P".
A = P*R*T
400,000 = P*0.09*20
400,000 = P*1.8
P = 222,222.222
The interest earned is the difference between the initial and the final amount in the bank. Let the interest earned be represented by the variable "I".
I = A - P = $400,000 - $222,222.222 = $177,777.778
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-
Which graph represents the function f(x) = |x] – 4?
Graph for the modulus function is as follows.
What is modulus function?
A modulus function is a function that determines a number or variable's absolute value.
Main body:
Given that,
Which graph represents the function f(x) = 4⌈x⌉?
Now,
to represent the graph of Y = IxI-4 .
So,
Taking x = 0, we get
Y = IxI -4
Y = I0I -4
Y = -4
Taking x = 1, we get
Y = IxI - 4
Y = I1I -4
Y = -3
Taking x = 2, we get
Y = IxI - 4
Y = I2I - 4
Y = -2.
Taking x = -1, we get
Y = IxI - 4
Y = I-1I - 4
Y = 1 -4
Y = -3
Taking x = -2, we get
Y = IxI - 4
Y = I-2I - 4
Y = -2
Hence the graph for the function is as follows.
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Consider the equation and the following ordered pairs: (1,y) and (x,−3).
6x+3y=15
Step 1 of 2 : Compute the missing x and y values so that each ordered pair will satisfy the given equation.
Answer
Keyboard Shortcuts
Complete the table below.
x y
row 11 Answer
row 2 Answer
−3
Answer:
(1,3)
(4,-3)
Step-by-step explanation:
To find y, replace x with 1 in the equation and solve for y
6x + 3y = 15
6(1) + 3y = 15
6 + 3y = 15 Subtract 6 from both sides
3y = 9 Divide both sides by 3
y = 3
(1,3)
To find x, replace y with -3 in the equation and solve for x
6x + 3y = 15
6x + 3(-3) = 15
6x - 9 = 15 Add 9 to both sides
6x = 24 Divide both sides by 6
x = 4
(4, -3)
Which function represents the graph of f (x) = -3 |x| after it is translated 5 units down?
The function that represents the graph f(x) = -3|x| is f(x) = -3|x| - 5
How to find the function of the graph ?
To ascertain whether a graph accurately depicts a function, use the vertical line test. The graph is a function if a vertical line drawn across it is moved and hits it only once at any given time. If there are multiple points where the vertical line intersects the graph, the graph is not a function.
As it is already given in the question that the function
f(x) = -3|x|
We will use transformation rules to solve the given question
f(x)→f(x-a) ⇒ Graph shifted to right by a units
f(x)→f(x+a) ⇒ Graph shifted to left by a units
f(x)→f(x) - a ⇒ Graph shifted downwards by a units
f(x)→f(x) + a ⇒ Graph shifted upwards by a units
When it is translated 5 units down
Then we subtract 5 outside of the given function
∴ f(x) = -3 |x| - 5
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Which phrase represents the algebraic expression for n – 4?
A. The quotient of a number and four.
B. Four less than a number.
C. Four minus a number.
D. Four more than a number
The phrase that represents the algebraic expression n - 4 is option b four less than a number.
Given,
The algebraic expression; n - 4
We have to find the phrase that represents the given algebraic expression.
Algebraic expression;
In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.). Terms comprise expressions.
An algebraic expression can be categorized into different categories depending on how many terms it contains: polynomial, quadrinomial, trinomial, monomial, and binomial.
So,
n - 4
That is,
4 is less than from a number
Therefore,
The phrase that represents the algebraic expression n - 4 is option b four less than a number.
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Answer:
the answer is b
Step-by-step explanation:
One card is drawn from a well-shuffled deck of fifty-two cards (no jokers).
(a) Find the probability of drawing a card below a 6 (count an ace as high). (Enter your answer as a fraction.)
(b) Find the odds of drawing a card below a 6 (count an ace as high).
(c) Use the Law of Large Numbers to interpret both the probability and the odds of drawing a card below a 6 (count an ace as high).
(Refer to the picture attached for answer choices)
Probability of drawing a card below a 6 (count an ace as high) is 4/13
Total number of outcome : n(S) = 52
(a) In a deck number of card below a 6 (counting ace as high) is {5 , 4 , 3, 2}
so , n(E) = 4 × 4 = 16
The probability of drawing a card below a 6 (count an ace as high) = P(E)
[tex]P(E) =\frac{n(E)}{n(s)}[/tex] =16/52
P(E) = 4/13
(b) Probability of drawing a card below a 6 (count an ace as high) is 4/13
Hence , the odds of drawing a card below a 6 (count an ace as high). is 0.308
(c) we should expect to draw a card below a 6 about four times out of every 13 attempts .Also, we should expect to draw a card below or 6 four times for every nine times we draw a 6 or above is the law of large number to interpret both the probability and odds of drawing a card below 6
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The school play ran for 3 nights. 185 tickets were sold for the first night. 160 tickets were sold for the second night. 192 tickets were sold for the third night. The tickets cost $4 each. What information is NOT necessary to calculate the total amount of money raised from ticket sales?
A) 192 tickets were sold the for the third night.
B) The school play ran for 3 nights.
D) 185 tickets were sold for the first night.
C) The tickets cost $4 each.
Answer:B
Step-by-step explanation:
Becauee it already says the first night how many tickets were sold also on the second and the third night. And if someone read the equation they would have known that the play went in for three nights.
A combination lock uses 4 numbers, each of which can be 0 to 32. If there are no restrictions on the
numbers, how many possible combinations are available?
If there are no restrictions on the numbers then the possible number of combinations is 1,185,921.
What is a combination?
Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant. You can choose the components of combos in any order.
Here,
There are 4 numbers needed for the combination and one can pick between 0 and 32.
This means that there are 33 numbers that can be used for the lock including 0.
The number of possible combinations is:
= Number that can be used with no restrictions on the number combination lock limit
= 33 ⁴
= 1,185,921 combinations
Hence, If there are no restrictions on the numbers then the possible number of combinations is 1,185,921.
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ABCDEFGHIJ is a regular decagon. It rotates clockwise about its center to form the polygon A'B'C'D'E'F G'HIJ. Match each angle of rotation to the
point that A' (the image of A) coincides with after that rotation.
252°
108°
135°
180°
288°
324°
A0DO
D after three rotations: 3 × 36° = 108°
F after five rotations: 5 × 36° = 180°
H after seven rotations: 7 × 36° = 252°
I after eight rotations: 8 × 36° = 288°
Given,
In the question:
ABCDEFGHIJ is a regular decagon. It rotates clockwise about its center to form the polygon A'B'C'D'E'F G'HIJ.
To find the each angle of rotation to the point A' coincides with after that rotation.
Now, According to the question:
let's know about Decagon:
A decagon is a ten-sided polygon or 10-gon. The total sum of the interior angles of a simple decagon is 1440°. A self-intersecting regular decagon is known as a decagram.
Every regular polygon with n sides can be divided into n congruent triangles. The angle with vertex the center of the polygon will measure
360 : n degrees. We are given a regular decagon, therefore:
n = 10
α = 360 : n = 36°
We consider that, if the decagon is not rotated, A' coincides with A and the rotation is towards the next letter of the alphabet. This means that after one rotation of 36° A' will coincide with B, after two rotations A' will coincide with C and so on.
A' will coincide with D after three rotations: 3 × 36° = 108°
A' will coincide with F after five rotations: 5 × 36° = 180°
A' will coincide with H after seven rotations: 7 × 36° = 252°
A' will coincide with I after eight rotations: 8 × 36° = 288°
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Consider the composite function g(f(x)) =x√6.
If f(x) = 3x2, what is g(x)?
O g(x)=√2x
O g(x)=√x+3
O g(x)=√6x
O g(x)=√9-x
The value of g(x) is √2x.
What is a composite function?
A function whose values are obtained from two given functions by first applying one to an independent variable and then using the result to apply the second, and whose domain is made up of those independent variable values for which the first function's result falls within the second function's domain.
Here, we have
g(f(x)) =x√6.
f(x) = 3x²
By applying a composite function
g(f(x)) =√6x
g(3x²) = x√6
g(x) must be √(2x)
because if we substitute x = 3x² in this we get
= (√2(3x^2))
= √2√3√(x²)
= √6 x
Hence, the value of g(x) is √2x.
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Determine which integer will make the inequality 12 > 2x + 4 true.
Answer: Integers less than 4 will make the inequality true.
Step-by-step explanation:
1) subtract both sides by 4 to isolate 2x so we are now left with 8 > 2x.
2) divide both sides by 2 so we are left with just x, leaving us now with 4 > x.
Integers must be less than 4 because if you substitute x as 4, we have 12 > 12, which is not true. But, if we substitute x as 3, we are left with 12 > 10, which makes the inequality true.
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Line AD and line EG are parallel line, Transversal CH < ABC and EFH are same side exterior angles
What are same side exterior angles?The presence of two parallel lines and a transversal line leads to some important theorem used in geometry
Some of the theorems include
alternate interior anglesalternate exterior anglescorresponding angles same side exterior anglesThe exterior angles refers to angles above line AD and below line EG, which are the parallel lines. These angles according to the figure are 4 and they include
< ABC< CBD< EFH< GFHThe exterior angles to the left of the transversal line forms a pair of same side exterior, similarly, to the right of the transversal line forms another pair of same side exterior angles.
The question is asking of same side exterior angles to < ABC, which is to the left of the transversal line. The pair that are same side exterior angles to the left of the transversal line are
< ABC< EFHHence < EFH and < ABC are same side exterior angles
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Prove that
cos 2A/cos A-sin A
= cos A + sin A
The value of cos 2A/cos A-sin A = cos A + sin A is proved
cos 2A = 2cos²A - 1
= 2cos²A - (sin²A + cos²A)
= 2cos²A - sin²A - cos²A
= cos²A - sin²A
We need to prove that
cos 2A/cos A-sin A = cos A + sin A
L.H.S
cos 2A/cos A-sin A
= cos²A - sin²A/ cos A-sin A
= (cos A + sin A)(cos A-sin A)/ cos A-sin A
= cos A + sin A
R.H.S
LHS = RHS proved
Therefore, cos 2A/cos A-sin A = cos A + sin A is proved
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In 2016 the cdc estimated the mean weight of us women over the age of 20 years was 168.5 pounds with a standard deviation of 68 pounds. What is the expected mean for a sample of 150 women
The expected mean for a sample of 150 women is 168.5 pounds.
What is expected mean?Expected mean can be defined as the mean weight of a number . Based on the given data we were told that the mean weight of the us women was 168.5 pounds which implies that the expected mean is 168.5 pounds.
The formula for expected mean is :
E ( X ) = μ = ∑ x P ( x )
Where:
x = values of the random variable X
P(x) = Corresponding probability
∑ =Sum of all products xP(x)
μ = mean
Therefore the expected mean is 168.5 pounds.
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find the missing angle measures
a=b
b=(b+16)
c=(2b)
Answer:
a = 41°
b = 57°
c = 82°
Step-by-step explanation:
all angles in a triangle must add up to equal 180°
so 4b + 16 = 180180 - 16 = 4b164 = 4b164 / 4 = 41b = 41°therefore a = 41°, b = (41 + 16) --> 57°, and c = 2(41) = 82°Find the ratio of the volume of the triangular prism
to the volume of the cuboid.
Give your answer in its simplest form.
4 cm
20 cm
9 cm
cm
5 cm
6 cm
The ratio of the volume of the triangular prism to the volume of
the cuboid is 3: 20
What do you mean by prism?
A prism is a three-dimensional solid object with identical ends. It is a result of the elements of flat faces, identical bases, and equal cross-sections. The prism's faces are either parallelograms or rectangles without bases.The base of the triangular prime is a right triangle with legs 5 cm, 4 cm
∴ b = 5 cm and h = 4 cm
∵ Its height is 9 cm
∴ H = 9 cm
→ Substitute them in the rule of the prism above
∵ V = 1/2 * (5)(4) × 9
∴ V = 90 cm³
∵ The dimensions of the base of the cuboid are 6 cm and 5 cm
∴ L = 6 cm and W = 5 cm
∵ Its height is 20 cm
∴ H = 20 cm
→ Substitute them in the rule of the cuboid above
∵ V = 6 × 5 × 20
∴ V = 600 cm³
→ Find the ratio between them
∵ V: V = 90: 600
→ Divide each term of the ratio by 30 to simplify them
∴ V: V = 3: 20
∴ The ratio of the volume of the triangular prism to the volume of
the cuboid is 3: 20
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help please
what c=math ........
The value of c for the expression, -0.65(c-7) = 1.95, is 4.
According to the question,
We have the following expression:
-0.65(c-7) = 1.95
Now, 0.65 is in multiplication on the left hand side. So, it will be in the division on the right hand side. Note that the negative sign can also be moved to the right hand side.
c-7 = -1.95/0.65
c-7 = -3
Moving 7 from the left hand side will result in the change of the sign from minus to plus:
c = -3+7
c = 4
Hence, the value of c is 4 for the given expression.
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Find the rectangular equation for the plane curve defined by the parametric equation
x=t+4, y=t^2
-infinity < t < infinity
The rectangular equation for the plane curve defined by the parametric equation x = t + 4, y = t² is; y = x² - 8x + 16
What is the Rectangular Equation?We are given the parametric equations as;
x = t + 4
y = t²
Now, for us to convert parametric equations to a rectangular equation (cartesian equation) means that we are solving for t in terms of x and then plugging it back into the y equation. Therefore, we have;
x = t + 4
t = x - 4
Thus;
y = (x - 4)²
Expanding this gives;
y = x² -4x - 4x + 16
y = x² - 8x + 16
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16. Doug's family buys 7 postcards while on vacation. Each
postcard costs $0.25 including tax.
Part A
How can Doug use place-value blocks to
find the total cost of the postcards? What is
the total cost?
The total cost is $1.75
What is Place value?The foundation of our entire number system is place value. In this approach, the value of a digit in a number is determined by where it appears in the number. The digits in the numbers 42,316 and 61,432 are distinct from one another.Given that we've done it:
7 postcards were purchased by Doug's family.Each postcard costs $0.25 after tax.The total price is shown by:
7 x 0.25 = $1.75Now, let's display the following in a number line:
Put all the numbers with a difference of 0.25 on the number line, run it seven times, and the result will appear.There are 7 hops between each step of 0.25 duration to get to the needed answer.So, after seven hops, we arrive at 1.75, which is the correct response.
Hence, the total cost is $1.75
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Solve the following facts. (Round to the nearest hundredth.) A. Current ratio _______________ B. Acid test __________________ C. Average day's collection ___________ D. Asset turnover _____________ E. Profit margin on sales _____________ Current Assets $ 18,000 Accounts Receivable 3,000 Current Liabilities 16,000 Inventory 2,000 Net Sales 41,000 Total Assets 29,000 Net Income 6,000
The solutions to the financial ratio requirements based on the supplied facts are:
A. Current ratio is 1.125.
B. Acid test is 1.
C. Average days' collection is 26.7 days.
D. Asset turnover is 1.4x.
E. Profit margin on sales is 14.63%.
What are financial ratios?Financial ratios are ratios that show the relative magnitude of one financial account to another.
Financial ratios are used to compare or represent an entity's financial performance or position in relative terms.
Current Ratio = Current Assets ÷ Current Liabilities
= $18,000 ÷ $16,000
= 1.125
Acid Test Ratio = (Current Assets - Inventory) ÷ Current Liabilities
= ($18,000 - 2,000) ÷ $16,000
= $16,000 ÷ $16,000
= 1
Average Days' Collection = Accounts Receivable ÷ Net Sales x 365 days
= $3,000 ÷ $41,000 x 365
= 26.7 days
Asset Turnover = Net Sales ÷ Total Assets
= $41,000 ÷ $29,000
= 1.4x
Profit Margin on Sales = Net Income ÷ Net Sales x 100
= $6,000 ÷ $41,000 x 100
= 14.63%
Current Assets = $18,000
Accounts Receivable = $3,000
Current Liabilities = $16,000
Inventory = $2,000
Net Sales = $41,000
Total Assets = $29,000
Net Income = $6,000
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Find all zeros of f(x) = x³ - 4x² - 5x + 14. Enter the zeros separated by commas. Enter exact values,
using radicals and/or fractions if necessary, not decimal approximations.
Question Help: Message instructor
Check Answer
Jump to Answer
Answer: x=-2, x=3+[tex]\sqrt{2}[/tex], 3-[tex]\sqrt{2}[/tex]
Step-by-step explanation:
f(x) = x³ - 4x² - 5x + 14
-2 | 1 -4 -5 14
-2 12 -14
1 -6 7 0
x³ - 4x² - 5x + 14 = (x+2)(x²-6x+7)
x²-6x+7=0
x²-6x+9-2=0
(x²-6x+9)-2=0
x²-6x+9=2
x²-3x-3x+9=2
x(x-3)-3(x-3)=2
(x-3)²=2
x-3=[tex]\sqrt{2}[/tex], -[tex]\sqrt{2}[/tex]
x=3+[tex]\sqrt{2}[/tex], 3-[tex]\sqrt{2}[/tex]
Hence, zeroes are x=-2, x=3+[tex]\sqrt{2}[/tex], 3-[tex]\sqrt{2}[/tex]
Step-by-step explanation:
our first "suspicion" for a factoring is an integer factor of the constant term : 14.
14 = 2 × 7 or -2 × -7
I started to try 2 or -2 and found that -2 is indeed a zero solution.
so, the first factors are
f(x) = (x + 2)(x² + ...)
let's divide (x³ - 4x² - 5x + 14) by (x + 2) to get the x² term.
x³ - 4x² - 5x + 14 ÷ x + 2 = x² - 6x + 7
- x³ + 2x²
--------------
0 -6x² - 5x
- -6x² - 12x
----------------
0 7x + 14
- 7x + 14
------------
0 0
f(x) = (x + 2)(x² - 6x + 7)
the zeros for x² - 6x + 7 we get from the general solution for a quadratic equation
ax² + bx + c = 0
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
x = (6 ± sqrt((-6)² - 4×1×7))/(2×1) =
= (6 ± sqrt(36 - 28))/2 = (6 ± sqrt(8))/2 =
= 3 ± sqrt(8/4) = 3 ± sqrt(2)
x1 = 3 + sqrt(2)
x2 = 3 - sqrt(2)
so, the zeros are
-2, 3 - sqrt(2), 3 + sqrt(2)
Sara volunteered to get hot dogs for her softball team. Of the 16 players on the team, 12 wanted ketchup, 7 wanted mustard, and 4 wanted both. How many players wanted: H. only ketchup? O. only mustard? W. neither ketchup nor mustard?
Answer:
H) 8, O) 3, W) 1------------------------------
GivenTotal players = 16,Wanted ketchup = 12,Wanted mustard = 7,Wanted ketchup and mustard = 4.Find the numbers of players who ...Wanted only ketchup = 12 - 4 = 8,Wanted only mustard = 7 - 4 = 3,Wanted neither ketchup nor mustard = 16 - (8 + 4 + 3) = 1FIND THE SLOPE OF YHE LINE
HURRYYY
The slope of given line is 43
The slope of the line is the rate of change of y with respect to xSlope of a line gives the steepness of line.
The formula of finding the slope of line with two given points is as follows,
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Thewith[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]TheThe[tex]Hdb\pi[/tex]TheThelinem=y2-yy2-y1/xw-xq
x2-x1
x2-x1
x2-x1
It can be seen from the given image thatthat the line moves 3unit in x direct and 4unit in y direction.So the slope will be
be m=43
Hence,the slope of the give line is 43
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Fin the measurement of the angle
A=
B=
C=
D=
E=
F=
G=
45°
Answer:
Step-by-step explanation:
A=60
B=75
C=45
D=60
E=75
F=45
G=90
Which one
tell us number of energy levels
A.protons
B.neutrons
C.periods
D,family/groups
Periods are the rows that span the periodic table. Families or groups are the columns that go from Page 2 up.
How many different energy levels are there?The maximal energy level of the electrons serves as a marker for the period (or row) in the periodic table that an atom belongs to (1 through 7). The table has 7 periods, hence there are 7 energy levels. The first period's atoms have electrons in the first energy level. The second period's atoms have electrons in two different energy states. The third period's atoms have electrons in three different energy levels. The fourth period's atoms have electrons in four different energy levels. Typically, the number of the period itself is the same as the number of energy levels in each period. The first period's atoms have electrons in the first energy level.
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I need help quick this assignment has to be turn in soon please and thanks
Answer:
Step-by-step explanation:
rearrange the perimeter forumula for a rectangle to find the width.
P=2w+ 2l
The width of the rectangle is given as w = p/2 - l which is derived from perimeter of rectangle
Perimeter of RectangleThe perimeter of a rectangle is the total distance covered by its boundaries or the sides. Since there are four sides of a rectangle, thus, the perimeter of the rectangle will be the sum of all four sides.
In this question, we simply need to make the width (w) the subject of formula.
The equation given is
p = 2w + 2l
p = perimeter of rectanglew = width l = lengthp = 2w + 2l
p = 2(w + l)
p / 2 = w + l
w = p/2 - l
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A metallurgist has one alloy containing 29% aluminum and another containing 51% aluminum. How many pounds of each alloy must he use to make 48 pounds of a third alloy containing 50% aluminum? (Round to two decimal places if necessary.)
The number of pounds of 29% alloy and 51% alloy required to make the third alloy containing 50% aluminum is 45.82 pounds and 2.18 pounds respectively.
The number of pounds of alloy that must be used.Let
x = pounds of 29% alloyy = pounds of 51% alloyx + y = 48
29x + 51y = 50*48
x + y = 48
29x + 51y = 2400
Solve simultaneously
From (1)
x = 48 - y
Substitute into (2)
29x + 51y = 2400
29(48 - y) + 51y = 2400
1392 - 29y + 51y = 2400
- 29y + 51y = 2400 - 1392
22y = 1008
divide both sides by 22y = 1008/22
y = 45.82 pounds
Substitute y = 45.82 pounds into (1)
x + y = 48
x + 45.82 = 48
x = 48 - 45.82
x = 2.18 pounds
So therefore, the number of pounds of 29% alloy and 51% alloy is 45.82 pounds and 2.18 pounds respectively.
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(MARKING BRAINLIEST) Sam works as a salesman and earns 5.5% commission on everything he sells if Sam sells a television for $1200 how much commission will he earn ?
Answer:
$66
Explanation:
Sam earns a 5.5% commission on everything he sells. He sells a television for $1200. What is 5.5% of $1200?
Convert 5.5% to decimal form: 0.055. Now, multiply 1200 by 0.055.
Sam will earn $66 because 5.5% of 1200 is 66.
If you double a number and then add 32,you get 2/9of the original number. What is the original number?
Answer:
- 18
Step-by-step explanation:
let the number be n then double the number is 2n and
2n + 32 = [tex]\frac{2}{9}[/tex] n
multiply through by 9 to clear the fraction
18n + 288 = 2n ( subtract 2n from both sides )
16n + 288 = 0 ( subtract 188 from both sides )
16n = - 288 ( divide both sides by 16 )
n = - 18
the original number is - 18
