Ben will receive £390
How to calculate the fraction that will be received ?
Alex and Ben share £520
They share this money in the ratio 1:3
The fraction of this amount that Ben will receive can be calculated as follows
1 + 3
= 4x
4x= 520
x= 520/4
x= 130
Ben Fraction= 130 × 3
= 390
Hence Ben's fraction of the money is £390
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Which of the following expressions is equivalent to 32x − 3?
the quantity 9 to the power of x end quantity over 27
the quantity 6 to the power of x end quantity over 9
the quantity 2 to the power of x end quantity over 3
the quantity 1 to the power of x end quantity over 9
The expressions which is equivalent to the given expression; 3^(2x -3) is; the quantity 9 to the power of x end quantity over 27.
Option (A) is correct.
It is required to choose the expressions.
What are the laws of indices ?Index laws are the rules for simplifying expressions involving powers of the same base number. Index (indices) is the exponent which is raised to a number.
Given:
It follows from the task content that the equivalent expression as in the task content can be determined by the laws of Indices.
Now, according to laws of indices;
[tex]3^{2x} =( 3^{2}) ^{x}[/tex]
Thus, we now have;
[tex]= (3^{2} )^{x} )/3^{3} \\= (9^{x} )/3^{3} \\= (9^{x} )/27[/tex]
Therefore, the expressions which is equivalent to the given expression; 3^(2x -3) is; the quantity 9 to the power of x end quantity over 27.
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The value of a mobile sets of same models in two shapes A and B are given below.
Shop A- Marked price=Rs 25,000, Discount=10%, VAT=13%
Shop B- Marked price=Rs 24,000, Discount=8%, VAT=13%
Which shop is more expensive and by what percent?Find it
Shop A is more expensive by 1.8 % percentage .
The price displayed on the product label is called the display price or list price. This is the price at which the product will be sold. If discount is offered, M.P. > SP If no discount is offered, M.P. < SP. Discounting is the process of determining the present value of future payments or cash flows to be received. Value Added Tax (VAT) is a consumption tax on goods and services that add value at every stage of the supply chain, from initial production to the point of sale. The amount of VAT paid by the user is based on the cost of the product minus the material costs of the product already taxed in previous stages which is given by [tex]S.P=M.P\times\frac{100-D}{100}[/tex] ....(1)It is given that shop A has Marked price =Rs 25,000, Discount=10%, Putting above values in equation (1) we get
[tex]S.P=25000\times\frac{100-10}{100} \\\\S.P=25000\times\frac{90}{100} \\\\\S.P=22500[/tex]
Rate of VAT 13% is given by
[tex]=\frac{13}{100} \times 22500\\\\=2925[/tex]
The amount to be payed for buying mobile set is [tex]=22500+2925=25425[/tex]
It is given that shop B has Marked price =Rs 24,000, Discount=8%, Putting above values in equation (1) we get
[tex]S.P=24000\times\frac{100-8}{100} \\\\S.P=24000 \times\frac{92}{100} \\\\S.P=22080[/tex]
Rate of VAT 13% [tex]=13\% \ 22080[/tex]
[tex]=\frac{13}{100} \times 22080\\\\=2870.4[/tex]
The amount to be payed for buying mobile set is[tex]=22080+2870.4=24950.4[/tex]
As the amount of shop A is more than shop B so , shop A is more expensive
Percentage [tex]= \frac{25425-24950.4}{25425}\times100[/tex]
[tex]= \frac{474.6}{25425}\times100\\\\=0.01866\times100\\\\=1.8\%[/tex]
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Use the equality to find ratio of a:b
2a:9b
I dont understand the question, although it seems very easy in nature
To use the equality to find ratio of a:b, the ratio of a:b is 9 : 2
How to use the equality to find ratio of a:b?The ratio expression is given as
2a : 9b
In order to to use the equality to find ratio of a:b, we make use of the following representations
mx : ny => m : n = y : x
Using the above as a guide, we have
2a : 9b => a : b = 9 : 2
Rewrite as
a : b = 9 : 2
Hence, to use the equality to find ratio of a:b, the ratio of a:b is 9 : 2
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solve the inequality |2x|<6
-3 < x < 3
Step-by-step explanation:Isolate the variable by dividing each side by factors that don't contain the variable.
Determine the distance between each pair of points. Then determine the coordinates of the midpoint M of the segment joining the pair of points.
W(-12,8,10) and Z(-4,1,-2)
The midpoint is at ( -8 , 9/2 , 4)
In the given statement is
To find the midpoint of the line segment joining the pair of points
W(-12,8,10) and Z(-4,1,-2)
Midpoint:
The coordinates of the midpoint of a line segment are the average of the coordinates of the end points.
m = (A +B)/2
If we are given three points and we wish to find the midpoint of those points, we need to use the midpoint formula m =([tex]\frac{x_{1} +x_{2} }{2} , \frac{y_{1} +y_{2} }{2} , \frac{z_{1} +z_{2} }{2}[/tex] )
where:
(x1 , y1 ,z1) are the coordinates of the first point:
(x2 , y2 , z2) are the coordinates of the second point:
Now, We are given the three points W(-12,8,10) and Z(-4,1,-2)
Solving for the midpoint , we have,
m = ([tex]\frac{-12+(-4)}{2} , \frac{8+1}{2} ,\frac{10+(-2)}{2}[/tex])
m =( [tex](\frac{-16}{2} ) ,\frac{9}{2} , \frac{8}{2}[/tex])
m = ( -8 , 9/2 , 4)
Therefore, the midpoint is at ( -8 , 9/2 , 4)
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Francisco wants to build a cube-shaped storage container that holds 8 cubic feet of water for some goldfish he recently purchased. Using the formula,V=s3, whereVrepresents the volume of the container andsrepresents its side length, find the length of one side of the container.
Length of Side of cube - shaped storage container is 2 units .
Given : Volume of container = 8 cubic units .
To find : the length of one side of the container .
Formula for volume of cube : Volume of cube = [tex]x^{3}[/tex] .
According to ques .
[tex]x^{3}[/tex] = 8
Solving cubic equation ,
finding cube root of 8 and hence finding value of x .
[tex]\sqrt[3]{8}[/tex] = x
x = 2
2 * 2 * 2 = 8 .
Hence , length of each side of cube - shaped storage container = 2 units .
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An astronomical unit is the mean distance from the center of Earth to the
center of the sun. One astronomical unit is about 9.3 × 10 miles. Pluto
is about 40 astronomical units from the sun. What is the approximate
distance that Pluto is from the sun?
A. 3.72 × 10 miles
B. 4.30 × 10 miles
C. 3.72 × 10 miles
D. 4.30 × 10 miles
The approximate distance that Pluto is from the sun will be 3.72 × 10⁹ miles. Then the correct option is A.
What is conversion?Conversion means to convert the same thing into different units.
PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.
The average distance between the centers of the Earth and the Sun is measured in astronomical units.
We know that One astronomical unit is about 9.3 × 10⁷ miles.
Pluto is about 40 astronomical units from the sun. Then the approximate distance that Pluto is from the sun will be
⇒ 40 × 9.3 × 10⁷
⇒ 372 × 10⁷
⇒ 3.72 × 10⁹ miles
The approximate distance that Pluto is from the sun will be 3.72 × 10⁹ miles. Then the correct option is A.
Your question was incomplete, but the complete question was given below.
An astronomical unit is the mean distance from the center of Earth to the center of the sun. One astronomical unit is about 9.3 × 10⁷ miles. Pluto is about 40 astronomical units from the sun. What is the approximate distance that Pluto is from the sun?
A. 3.72 × 10⁹ miles
B. 4.30 × 10⁹ miles
C. 3.72 × 10⁷ miles
D. 4.30 × 10⁷ miles
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Find the measure of angle b.
Answer:
B= 67
Step-by-step explanation:
Being vertically opposite angle
Find value of x.
3x + 6 - 6 = 248
Answer:
x=82.7
Step-by-step explanation:
3x+6-6=248
3x=248
x=82.7
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Here we go ~
[tex]\qquad \sf \dashrightarrow \: 3x + 6 - 6 = 248[/tex]
[tex]\qquad \sf \dashrightarrow \: 3x = 248[/tex]
[tex]\qquad \sf \dashrightarrow \: x = \dfrac{248}{3} [/tex]
The approximate value will be :
[tex]\qquad \sf \dashrightarrow \: x \approx82.67[/tex]
What is the geometric mean of 8 and 22 in simplest form?
A. 4 √11
B. 15
C. 16√11
D. 176
The geometric mean of 8 and 22 in simplest form is 4√11. The answer is letter A.
Geometric mean, like arithmetic mean, is a kind of average and a measure of central tendency.
To solve for the geometric mean, we multiply the numbers together and then take a square root (for two numbers), cube root (for three numbers) etc. In other words, geometric mean is the nth root of the product of n values.
The formula for the geometric mean is given by:
GM = n√x1 x2 . . . xn
Solving for the geometric mean between 18 and 1.5 using the formula:
GM = n√x1 x2 . . . xn
where n = 2, x1 = 8, and x2 = 22
GM = √(8)(22)
GM = √176
GM = 4√11
Hence, the geometric mean of 8 and 22 is A. 4 √11.
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please help im slow when it comes to math
A specific atom has 10 protons and 10 neutrons. what is the atom's mass number? 0 0 10 10 20 20 100
The total number of protons and neutrons in an atom exists directed as the mass number. The atomic mass number of an atom with 10p and 10 n exists 20.
Which atom has 10 protons and 10 neutrons?The total number of protons and neutrons in an atom's nucleus is known as the mass number. Protons plus neutrons equal mass number.
The neon atom has 10 protons and 10 neutrons with the atomic number 10. It has 10 protons and neutrons inside of its nucleus, along with ten electrons outside, due to its atomic weight of 20.179.
Ne is an inert, colorless noble gas that is also the second-lightest of the noble gases. Due to its distinctive reddish glow, it is frequently utilized in lamps and signs.
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For each rational function, find any points of discontinuity.
y=2 / x+1
In rational functions, the discontinuities are caused by the denominator terms. Since the denominator of a fraction is non-zero, any term that is multiplied by the denominator is also non-zero.
If x = -1 then x+1 is 0.
So, the discontinuities are shown as x = -1
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Jane is a sales executive earning a salary of Ksh. 20,000 and a commission of 8% for the sales in exces of Ksh 100,000. If in January 2010 she earned a total of Ksh.48, 000 in salaries and commissions.
a) Determine the amount of sales she made that month
b) If the total sales in the month of February and march increased by 18% and then dropped by 25% respectively, calculate:
i) janes commission in February
ii) Her total earnings in march
Answer:
a
Step-by-step explanation:
Determine the amount of sales she made that month
a. The total amount of sales is Ksh 450,000
b. Her commission in february is Ksh 34,480
Total earning is Ksh 43,860
How to solve for the valuesa) Jane's total earnings in January were Ksh 48,000, and her base salary is Ksh 20,000. This means that she earned an additional Ksh 28,000 in commissions.
Since her commission rate is 8% for sales in excess of Ksh 100,000, we can calculate the amount of sales she made in January by first calculating the sales over which she got a commission.
Ksh 28,000 is 8% of the sales over Ksh 100,000. So we can set up the following equation and solve for the sales:
0.08 * sales = 28,000
Solving for sales:
sales = 28,000 / 0.08 = Ksh 350,000
Since she only earns a commission on sales in excess of Ksh 100,000, the total amount of sales she made in January would be:
Ksh 100,000 (no commission threshold) + Ksh 350,000 (sales over the threshold) = Ksh 450,000
b) i) If her total sales in February increased by 18%, her sales in February were:
1.18 * Ksh 450,000 = Ksh 531,000
But remember, she only gets a commission on sales over Ksh 100,000. So the sales that will earn a commission in February are:
Ksh 531,000 - Ksh 100,000 = Ksh 431,000
Her commission in February is 8% of this amount:
0.08 * Ksh 431,000 = Ksh 34,480
ii) If her sales in March then dropped by 25%, her sales in March were:
0.75 * Ksh 531,000 = Ksh 398,250
The sales that will earn a commission in March are:
Ksh 398,250 - Ksh 100,000 = Ksh 298,250
Her commission in March is 8% of this amount:
0.08 * Ksh 298,250 = Ksh 23,860
So, her total earnings in March (her base salary plus her commission) would be:
Ksh 20,000 + Ksh 23,860 = Ksh 43,860
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a. In the function y=a x²+b x+c, c represents the y -intercept. Find the value of the y -intercept in the function y=a(x-h)²+k .
Answer:
ah²+k
Step-by-step explanation:
The y-intercept is when x=0.
[tex]y=a(0-h)^2+k=ah^2+k[/tex]
urgent please help thank you!
The difference between the numbers will be:
1. -11.
2. 43
3. -/15
How to illustrate the information?The difference between the numbers will be:
1. (-5) - 6
= -5 - 6
= -11
2. 35 -(-8)
= 35 + 8
= 43
3. 2/5 - 3/5.
= -1/5
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Simplify the expression.
(1/3) (b + 12) - (1/4) (b+12)
The simplification of the given expression (1/3)(b + 12) - (1/4)(b + 12) is (b + 12)/12.
According to the given question.
We have an expression
(1/3)(b + 12) - (1/4)(b + 12)
As we know that, simplification of an expression means to write an equivalent expression which contains no similar terms.
Therefore, the simplification of the given expression (1/3)(b + 12) - (1/4)(b + 12) is given by
(1/3)(b + 12) - (1/4)(b + 12)
= (b + 12)[(1/3) -(1/4)] (taking (b + 12) common from each expression)
= (b + 12)[ (4-3)/12 ]
= (b + 12)[1/12]
= (b + 12)/12
Hence,the simplification of the given expression (1/3)(b + 12) - (1/4)(b + 12) is (b + 12)/12.
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Simplify 2(5n-4) pls helppp
Answer:
The answer is 10n-8
Step-by-step explanation:
Hope this helps!!
If b = the number blue bikes, which algebraic expression represents the phrase below?
The sum of the number of blue bikes and the 9 red bikes.
A.B divided by 9
B. B times 9
C. B minus 9
D. B plus 9
The expression that represents the sum of the number of blue bikes and the 9 red bikes is B + 9. Option D
What are algebraic expressions?Algebraic expressions are expressions that consists of terms, variables, coefficients, and constants.
They are also made up of arithmetic operations such as division, addition, multiplication, subtraction, etc
From the information given, we have that;
B is the number of blue bikes
And there are 9 red bikes
The expression for the sum of blue and red bikes is written as;
B + 9
Thus, the expression that represents the sum of the number of blue bikes and the 9 red bikes is B + 9. Option D
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Solve the inequality.
7(x − 3) > −7
Answer: x>2
Step-by-step explanation:
Answer:
Step-by-step explanation:
The constant of proportionality in an equation can never be 0. True or false?
Answer:
True
Step-by-step explanation:
WILL CHOOSE BRAINLIEST!!! The car dealership owner is trying to arrange 8 cars in a line for customers to see. In how many ways can the owner arrange the cars?
Answer:
8!
Step-by-step explanation:
8!=8*7*6*5*4*3*2*1
determine the two roots for perfect square 81 show your work
answer:
9
explanation:
9*9=81
81 sqrt= 9
Convert the decimal number 431 to binary in two ways: (a) convert directly to binary; (b) convert first to hexadecimal and then from hexadecimal to binary. which method is faster?
The conversion of decimal number directly to binary number will be faster.
What is a conversion of the number system?The number conversion deals with the operation to change the base of the number.
Binary number - It contains only 2 numbers that are 1 and 0.
Decimal number - It contains 10 numbers that are from 0 to 9.
Hexadecimal number - It contains 16 numbers that are from 0 to F.
Convert the decimal number 431 to binary will be
431 / 2 = 215 with 1 remainder
215 / 2 = 107 with 1 remainder
107 / 2 = 53 with 1 remainder
53 / 2 = 26 with 1 remainder
26 / 2 = 13 with 0 remainder
13 / 2 = 6 with 1 remainder
6 / 2 = 3 with 0 remainder
3 / 2 = 1 with 1 remainder
1 / 2 = 0 with 1 remainder
The decimal number 431 to binary number will be 110101111.
Convert first to hexadecimal and then from hexadecimal to binary. Then we have
(431)₁₀ = (1AF)₁₆ = (110101111)₂
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A figure with 4 sets of parallel sides is graphed on a grid. The figure is then rotated 90 degrees clockwise. How many pairs of parallel sides does the figure have after the
rotation?
1. 0
2. 1
3. 2
4. 4
The figure have 4 pairs of parallel sides after the 90 degree rotation.
What is 90° rotation of an object ?
For every point in the plane (x, y), a 90° rotation can be described by the transformation P(x, y) → P'(-y, x). We can achieve this same transformation by performing two reflections.
It is given that figure has 4 sets parallel sides is graphed on a grid and is then rotated 90 degrees clockwise.
The figures with 4 sets parallel sides are : square, rectangle, rhombus
Let us consider square as our figured graphed in grid :
Now, Transformation involves moving a shape from one position to another, 90 degrees clockwise transformation that carries the square onto itself that is after rotation there will be 4 pairs of parallel sides.
Therefore, the figure have 4 pairs of parallel sides after the 90 degree rotation.
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23. Find the missing dimensions in the dimension
strings below.
The dimension of the string is A=13'1".
The dimension of the string is A=19'5",B=1'9" and C=25'5".
1. Given that two strings
In the 1st line given 3'3",5'6",8'9" and 1'4".
In the 2nd line given A and 5'9"
Feet is nothing but there is usually a focus on measuring in feet when working with lumber, pipe, or shingles.
Feet are either denoted with the letter "ft" or an apostrophe (').
Inches are nothing but one foot is twelve inches long. The sign for feet and inches is the same.
A single apostrophe (') is used for feet. A double apostrophe (") is used for inches.
Now, We will add the 1st line given dimension.
That is 3'3"+5'6"+8'9"+1'4"=18'10".
Now the 2nd line will be
A+5'9"=18'10"
A=18'10"-5'9"
A=13'1"
Therefore, the dimension of the string is A=13'1".
2.Given that three strings
In the 1st line given 75'8".
In the 2nd line given A and 56'3".
In the 3rd line given 17'8",B,30'10" and C.
Now, We will add the 2st line given dimensions.
That is A+56'3"=75'8"
A=75'8"-56'3"
A=19'5"
Now the 3nd line will be
B+17'8"=19'5"
B=19'5"-17'8"
B=1'9"
And
30'10"+C=56'3"
C=56'3"-30'10"
C=25'5"
Therefore, the dimension of the string is A=19'5",B=1'9" and C=25'5".
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Simplify by combining like terms.
-5 a-4 a+b
By combining the like terms, the simplified form of the expression -5a-4a+b is -9a+b
Given,
The algebraic expression = -5a-4a+b
Combine the like terms
-5a-4a+b=(-5-4)a+b
=-9a+b
simplified form is -9a+b
Hence, By combining the like terms, the simplified form of the expression -5a-4a+b is -9a+b
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Please help with the question below 5 points each but beware if you use my points for no reason I'll report you.
Lauren covered the box below with paper, with no overlaps. The paper costs $1.50 per square foot. How much will it cost to cover the box?
rectangular prism measurements
base: 7ft
height: 9ft
width: 2ft
By finding the surface area of the box, we can see that the cost to cover the box is $285
How much will cost to cover the box?We assume that we need to cover the 6 faces of the box, then we need to find the total surface area.
The surface area is given as:
S = 2( B*H + H*W + B*W)
Where:
B = base = 7ftH = height = 9ftW = width = 2ftThen the surface area is:
S = 2*(7ft*9ft + 7ft*2ft + 9ft*2ft) = 190ft^2
Now we know that the paper costs $1.50 per square foot, then the cost to cover the box is:
cost = 190*$1.50 = $285
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Help me I just want someone to solve this problem and provide a step by step explanation on how you solved it:
a(2x + 3 )=9x + 15 + x
It has to be an a=
The equation solved in terms of a is 10x + 15/ 2x + 13
What is the subject of formula?The subject of a formula is defined as the variable that is expressed in terms of the other variables in an equation or given expression.
It is also described as the variable that is being worked out in a given equation.
Given the equation;
a(2x + 3) = 9x + 15 + x
collect like terms
a(2x + 3) = 10x + 15
To make 'a' the subject, divide both sides by the coefficient of a which is (2x + 3)
a = 10x + 15/ 2x + 13
Thus, the equation solved in terms of a is 10x + 15/ 2x + 13
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Melanie got a new employer-paid job through the Jones recruitment Agency. The job pays $52,400 per year, and the agency fee is equal to 25% of 1 month’s pay. How much must Melanie’s employer pay the agency?
Answer:
Melanie's employer must pay the agency a sum of $1,091.67
Step-by-step explanation:
job = $52,400
agency fee = 25% of 1 month's pay
52,400 / 12 = $4,366.67
.25 x $4,366.67 = $1,091.67
