Answer:
Money saved = $18
Step-by-step explanation:
Firstly, the term discount equals the difference between the price paid for and it's par value. Discount is a kind of reduction or deduction in the cost price of a product.
Given
Cost of an Item = 60$
Discount % = 30% on cost
Hence, Discount in $ = 60$*30%
= 18$
Actual Cost = 60$ - 18$ = 42$
Therefore, Savings = Discount
= 18$
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A paint mix uses red and white paintin a ratio of 1:12.
a) How much white paint will be needed to mix with 1.4
litres of red paint ?
b) Ifatotalof15.5litresofpaintismixed,calculate
the amount of white paint and the amount of red paint used. Give your answers to the nearest 0.1 litre.
Answer:
(a).16.8 litres
(b).red-1.2 litres
white-14.3 litres
A rug is in the shape of a square. It measures 18 feet on each side. What is its perimeter?
Answer:
72ft²
Step-by-step explanation:
a square has 4 equal sides, when each one is 18ft, the total perimeter will be 18×4=72ft²
Hii!
_____________________________________________________
[tex]\stackrel\star{\rightsquigarrow\circ\boldsymbol{\underbrace{Answer}\circ\leftharpoonup}}[/tex]
Perimeter of the rug = 72 ft
[tex]\stackrel\star{\rightsquigarrow\circ\boldsymbol{\underbrace{Explanation}\circ\leftharpoonup}}}[/tex]
[tex]\bullet[/tex] Let's work out the perimeter
[tex]\twoheadrightarrow\sf P=4a[/tex] a=length of one side
[tex]\bullet[/tex] Stick in the values
[tex]\twoheadrightarrow\sf P=4\cdot18[/tex]
[tex]\bullet[/tex] Multiply
[tex]\twoheadrightarrow\sf P=72ft[/tex]
--
Hope that this helped! Best wishes.
[tex]\stackrel\star{\textsl{Reach far. Aim high. Dream big.}}[/tex]
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Please help with this certain math problem
Answer: For this real-valued function;
[tex]fog = 2\sqrt{x-1} + 1\\ Domain = [1, )[/tex]
Step-by-step explanation:
COMPOSITE FUNCTIONIf f and g are functions, then the composite function or composition, of g and f is defined by
[tex]( f o g ) (x) = f(g(x))[/tex]
Given the functions [tex]f(x)=2x+1[/tex] , [tex]g(x)=\sqrt{x-1}[/tex],
Now composition for this;
[tex]fog = f(g(x))f(g(x)) = f(\sqrt{x-1} )[/tex]
[tex]f(\sqrt{x-1})[/tex]means we are to interchange variable x in [tex]f(x)[/tex] with the function [tex]\sqrt{x-1}[/tex]
[tex]f(\sqrt{x-1}) = 2(\sqrt{x-1})+1f(\sqrt{x+1}) = 2(\sqrt{x-1})+1fog = 2(\sqrt{x-1})+1[/tex]
The function inside the square root, x-1, must be more significant than or equal to zero (x-10), for the function to exist on any real-valued function.
[tex]if, x-1 \geq 0\\x\geq 0+1\\x \geq 1[/tex]
As a result, the range of the variable x must only include values that are larger than or equal to 1.
Hence, Domain = [1, )
DOMAIN = The domain of [tex]fog[/tex] is the set of all numbers [tex]x[/tex] in the domain of [tex]g[/tex] such that [tex]g(x)[/tex] is in the domain of [tex]f[/tex].Learn more about Composition and Domain here; https://brainly.com/question/6390405
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how to evaluate 16/81 1/2
An expression is defined as a set of numbers, variables, and mathematical operations. The value of (16/81)^(1/2) is 4/9.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The value of the given expression (16/81)^(1/2) can be calculated as shown below,
[tex](\dfrac{16}{81})^{\frac12}\\\\=\sqrt{\dfrac{16}{81}}\\\\= \dfrac49[/tex]
Hence, the value of (16/81)^(1/2) is 4/9.
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Answer:
★The square root of 16/81 = 4/9.
(-3,-2) (x,6) m=-8/5 solve for x
Answer:
-8
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
-8/5=(6-(-2))/(x-(-3))
-8/5=(6+2)/(x+3)
-8/5=8/(x+3)
5=-(x+3)
5=-x-3
-x=5+3
-x=8
x=-8
35. Use the Change of Base Formula to evaluate logs 92. Then convert logs 92 to a logarithm in base 3. Round to the n
2.810; log3 55.2
2.810; log3 21.903
1.964, log3 55.2
4.522; log3 21.903
What is the range of the function represented by the following graph?
*
1 point
Captionless Image
A. all real numbers greater than 4
B. all real numbers less than - 1
C. all real numbers greater than - 6
D. all real numbers less than - 4
Answer:
C the prove is right there on the graph
Answer:
C
Step-by-step explanation:
The graph clearly shows that all the numbers are greater than -6
for the function f(x)=5(x+2) find f (2)
Answer:
20
Step-by-step explanation:
To calculate f(2), just replace x in the equation of f(x) with 2:
[tex]f(x) = 5(x + 2)\\\\f(2) = 5(2+2)\\\\f(2) = 5(4)\\\\f(2) = 20[/tex]
If an investor invests $24,000 into two bonds, one that pays 4% in simple interest, and the other paying 2% simple
interest, and the investor earns $700 annual interest, how much was invested in each account?
Round your answers to the nearest dollar.
2% bond: $
4% bond: $
Answers:
2% bond: $11000
4% bond: $13000
========================================================
Explanation:
x = amount invested in the 4% bond
y = amount invested in the 2% bond
Amounts are in dollars
The two amounts add to $24,000 so
x+y = 24000
y = -x+24000 is one equation to set up
0.04x = interest earned from the 4% bond
0.02y = interest earned from the 2% bond
0.04x+0.02y = total interest earned = $700
0.04x+0.02y = 700 is another equation to set up
------------
The system of equations is
[tex]\begin{cases}y = -x+24000\\0.04x+0.02y = 700\end{cases}[/tex]
Apply substitution. Solve for x.
0.04x+0.02y = 700
0.04x+0.02(-x+24000) = 700
0.04x-0.02x+480 = 700
0.02x= 700-480
0.02x= 220
x= 220/(0.02)
x = 11000
Use this to find y
y = -x+24000
y = -11000+24000
y = 13000
Solve for x in the triangle. Round your answer to the nearest tenth.
14
x
68
X
Answer:
x=15.1
Step-by-step explanation:
Side definitionsIn a right triangle, the side across from the right angle is always the hypotenuse.
The other two sides are termed "legs".
Once one of the other two angles is chosen as the angle to work from, then the two legs can be defined as the "opposite" and the "adjacent"
The leg touching the angle is the "adjacent" leg (or adjacent side), and the leg across from the angle is the "opposite" leg (or opposite side).
Trigonometric function definitions[tex]\sin(\theta)=\dfrac{\text{opposite side}}{\text{hypotenuse}}[/tex]
[tex]\cos(\theta)=\dfrac{\text{adjacent side}}{\text{hypotenuse}}[/tex]
[tex]\tan(\theta)=\dfrac{\text{opposite side}}{\text{adjacent side}}[/tex]
In this situation, the given angle is in the bottom right. A value is given for the side opposite the given angle, and the requested value is on the hypotenuse.
So, the two sides of interest are the "opposite" and the "hypotenuse". The trigonometric function that relates these two sides is the sine function.
Calculating x[tex]\sin(\theta)=\dfrac{\text{opposite side}}{\text{hypotenuse}}[/tex]
[tex]\sin(68^o)=\dfrac{(14)}{(x)}[/tex]
Evaluating the sine function in a calculator (in degree mode):
[tex]0.9271838546...=\dfrac{14}{x}[/tex]
Multiply both sides by x:
[tex](0.9271838546...)x=\left (\dfrac{14}{x} \right)x[/tex]
[tex](0.9271838546...)x=14[/tex]
Divide both sides by the decimal number:
[tex]\left (\dfrac{(0.9271838546...)x}{0.9271838546...} \right)=\dfrac{14}{0.9271838546...}[/tex]
[tex]x=15.0994864...[/tex]
Rounded to the nearest tenth, x=15.1
A farmer has 324 feet of fencing to make three identical adjacent rectangular pens, as shown in the picture. What dimensions of each pen will maximize the total enclosed area?
The dimensions of each pen that will maximize the total enclosed area would be as; Length 81 feet; Width 81 feet.
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
Let the Dimension of each pen
Length = x
Width = y
Area = xy
Perimeter equation
2(x + y) = 324
x + y = 162
Substituting the perimeter equation
Area = x(162 - x)
Area = -x^2 + 162x
If the zeros of the quadratic are 0 and 162, then the median will be at where the maximum area occurs.
162/ 2
= 81
Hence, The dimensions of each pen that will maximize the total enclosed area would be as; Length 81 feet; Width 81 feet.
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What is the proper ordering (from least to greatest) of the
following numbers?
1.0.32
2.0.32%
3.3.2%
4. 3299
Answer:
.0032 .032 .32 3299
Step-by-step explanation:
0.32% =.0032
3.2% = .032
.32
3299
Find f(g(x)) and g(f(x)).
f(x)=x²-2 and g(x)=√x+1
Answer:
1. x - 1
2. [tex]\sqrt{x^2-1}[/tex]
Step-by-step explanation:
[tex]f(g(x)) = \sqrt{x+1}^2 - 2\\ = x + 1 - 2\\= x - 1[/tex]
[tex]g(f(x)) =\sqrt{x^2-2+1}\\ = \sqrt{x^2-1}[/tex]
Simplify that a chemical is mxing two acid solutions one of 45% concentration and the other of 55% cencetration which of the following concentration could not be obtained
47 49 53 59
The concentration could not be 59.
What is concentration?
The concentration of a solution is a measure of the amount of solute that has been dissolved in a given amount of solvent or solution.
Given:
solutions one of 45% concentration
other of 55% concentration.
The concentration should lie between 45 % to 55 %.
This is because it is not possible to get a mixture concentration which is lower than the lower concentrated acid or higher than the higher concentration acid.
Hence, Mixture concentration must be between 45% and 55%.
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what is the 10th term for sequence 4; 8; 13; 19; 26
Answer:
40
Step-by-step explanation:
The scale on a map shows that 200 miles is represented by 5 inches on a map. Which proportion can be used to find the distance on the map, x, that represents 50 miles? StartFraction 5 over 200 EndFraction = StartFraction x over 50 EndFraction StartFraction 200 over 5 EndFraction = StartFraction x over 50 EndFraction StartFraction 50 over 200 EndFraction = StartFraction 5 over x EndFraction StartFraction 5 over 50 EndFraction = StartFraction x over 200 EndFraction
The proportion can be used to find the distance on the map (x) that represents 50 miles will be x/50 = 5 / 200. Then the correct option is A.
What are ratio and proportion?A ratio is a collection of ordered integers a and b represented as a/b, with b never equaling zero. A proportionate expression is one in which two items are equal.
The scale on a map shows that 200 miles is represented by 5 inches on a map.
Then the proportion can be used to find the distance on the map (x) that represents 50 miles will be
x/50 = 5 / 200
Then the correct option is A.
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find the value of x y and z?
Answer:
Step-by-step explanation:
What is the product?
2 3
5 9 -1 -7
11 5 -3
10 15 20
45 -5 -35
55
10
4 2
55
7
14
25 -15
45 -1 -7
315
+7 9
CO
8
9
4 1-2
Answer:
A.
Step-by-step explanation:
Hello, this is what we call matrix. multiplication matrix to be precised.
so it is;
5×2=10
5×3=15
5×4=20
5×9=45
5×-1= -5.
5×-7= -35
5×11=55
5×5=25
5×-3= -15.
i hope you understand. That is matrix for you but it has different categories
2x+3y=9 -2x+2y=6 The y cordinate
Answer:
y = 3
Step-by-step explanation:
2x + 3y = 9
-2x + 2y = 6
We have to add these two equations which gives us 5y = 15. Now, if you divide by 5 on both sides you get y = 3.
look at the picture
A variable is normally distributed with mean 6 and standard 2 deviation .
a. Find the percentage of all possible values of the variable that lie between 5 and 9.
b. Find the percentage of all possible values of the variable that exceed 1.
c. Find the percentage of all possible values of the variable that are less than 4.
The normal distribution is also known as the Gaussian distribution. The percentage of all possible values of the variable that are less than 4 is 15.87%.
What is a normal distribution?
The normal distribution, also known as the Gaussian distribution, is a symmetric probability distribution about the mean, indicating that data near the mean occur more frequently than data distant from the mean. The normal distribution will show as a bell curve on a graph.
A.) The percentage of all possible values of the variable that lie between 5 and 9.
P(5<X<9) = P(X<9) - P(5<X)
= P(z<1.5) - P(-0.5<z)
= 0.9332 - 0.3085
= 0.6247
= 62.47%
B.) The percentage of all possible values of the variable that exceed 1.
P(X>1) = 1 - P(X<-2.5)
= 1-0.0062
= 0.9938
= 99.38%
C.) The percentage of all possible values of the variable that are less than 4.
P(X<4) = P(X <4)
= P(z<-1)
= 0.1587
= 15.87%
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Which of the following linear equations passes through points (-1,5) and (1,-5)?
Y=-5x
Y=5x+10
Y=-2x+3
Answer:
y = -5x
Step-by-step explanation:
gradient = delta y / delta x
gradient = -10 / 2
gradient = -5
y = mx + b
5 = -5(-1) + b
5 = 5 + b
b = 0
y = -5x
a + b = c
a + b + c =36
Given that a and b have the same value, work out the values of a,b and c
Answer:
a=9
b=9
c=18
Step-by-step explanation:
c(a+b)+a+b=36
2a+2b=36
a+b=18
c=18
Russell has been offered positions by two cable companies. The first company pays a salary of $17,000 plus a commission of $20 for each cable package sold. The second pays a salary of $14,300 plus a commission of $30 for each cable package sold. How many cable packages would need to be sold to make the total pay the same?
Russell has to sell 270 cable packages to make the total pay of both the companies as same.
Suppose that Russell sells x cable packages such that the total pay of both the companies is the same.
Then the revenue Russell would make at the first company is $17000+20x
And, the revenue Russell would make at the second company is
$14300+30x
Since, the above two values are equal
so, 17000+20x=14300+30x
⇒17000-14300=30x-20x
⇒10x=2700
⇒x=270
The above problems are called mathematical modelling.
Mathematical modelling is the process of locating such equations to explain actual occurrences.
These formulae are referred to as mathematical models together with the definitions given to the variables.
Therefore, Russell has to sell 270 cable packages to make the total pay of both the companies as same.
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D
4
3
2
1
-5 -4 -3 -2 -1 0
1
2
GO
-4
-5
A
1
2
3 4 5 Match the graph with its equation
This graph represents the equation y = -3
Solve for x : 2/5x -9 < 3/5x+3
X < 60
X > -60
-x < -60
-x < 60
Answer:
x>-60
Step-by-step explanation:
Combine multiplied terms into a single fraction
2/5x - 9 < 3/5x + 3
2x/5 - 9 < 3/5x + 3
Find common denominator
2x/5 - 9 < 3/5x + 3
2x/5 + 5(-9)/5 < 3/5x + 3
Combine fractions with the common denominator
2x + 5(-9)/5 < 3/5 + 3
I HOPE YOU GOT THE ANSWER JUST SIMPLIFY IT (2x + 5(-9)/5 < 3/5 + 3) AND YOU WILL GET THE ANSWER YOURSELF AS I HAVE GIVEN ABOVE PLS MARK ME AS THE BRAINLILEST IF YOU LIKE TO AND MY ANSWER HELPED YOU:)
Answer:
[tex]\boxed {x > -60}[/tex]
Step-by-step explanation:
2/5x - 9 < 3/5x + 3
-1/5x < 12
x > -12 x 5
x > -60
Need help with this geometry question
Answer: 10 inches
Step-by-step explanation:
Diagonals of a parallelogram bisect each other, so the top of the jack is 5(2)=10 inches off the ground.
Simplify -2ab^3 (5a-4a^2 + 6ab^2 - 4b). ?
Answer:
10a^2b^3−8a^3b^3+12a^2b^5−8ab^4
Step-by-step explanation:
5 hundreds minus 4 tens?*
Answer:
460
Step-by-step explanation:
4 tens is equivalent to 40, so 500-40 is = to 460.
Hope this helps! :D
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[tex]\large \bold {ANSWER}[/tex]
[tex]\large \boxed { \large \sf \green{460}}[/tex][tex]\large \bold {SOLUTION}[/tex]
5 hundreds is 5 multiplied by 100, so it equals 500. 4 tens is 4 times 10, so 40.
500 - 40 = 460So 5 hundreds minus 4 tens is 460.
What’s the vertex of this graph??
Answer:
(4, -3)
Step-by-step explanation:
A vertex is just a point where 2 lines going in different directions meet. so the answer is (4, -3)