Lamp that can be bought with $12 is 21
What is an example of a unitary method?
A single or distinct unit is referred to by the word unitary. Therefore, the goal of this strategy is to establish values in reference to a single unit. The unitary technique, for instance, can be used to calculate how many kilometers a car will go on one litre of gas if it travels 44 km on two litres of fuel.
How is the unitary method divided?
This can be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees. In order to determine the value of one unit, we essentially divide the total value of a set of items by the number of units. The unitary approach is this.
Given that
Kwai bought 15 lamp for $8.25
$8.25 = 15 lamp
$1 = 15/8.25
$12 = (15/8.25)*12 = 21 approx.
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(1 point) if you have 140 meters of fencing and want to enclose a rectangular area up against a long, straight wall, what is the largest area you can enclose?
The largest area that can be enclose in straight wall is 2450 m².
What is meant by the largest area?Having to maximize or decrease a geometric figure's measurements, area, or volume is a special example of a geometry word problem.Let 'x' be the length of rectangle.
Let 'y' be the width rectangle.
Perimeter = 140 meters
2x + y = 140
y = 140 - 2x
Area = xy
Put the value of y in area.
Area = x(-2x + 140)
Area = -2x² + 140x
Differentiating the area with respect to x.
dA/dx = -4x + 140
Put dA/dx = 0 to get the critical point.
-4x + 140 = 0
x = 140/4
x = 35
Largest area at x = 35.
y = 140 - 2x
y = 140 - 2×35
y = 70
Area = xy
Area = 70×35
Area = 2450 m²
Thus, the largest area that can be enclose in straight wall is 2450 m².
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Alana meauring hi dining room table to make a tablecloth the table i zero. 45 m longer than it i wide if it i 1. 06 m wide how long i it?
The length of the table is 1.51 meters.
Allan is measuring his dining room table to make a tablecloth. The table is 0.45 meter longer than it is wide. The width of the table is 1.06 meter. We need to find out the length of the table.
Let the length of the table be represented by the variable "L". In the context of a mathematical problem or experiment, a variable is a quantity that may vary. The length of the table is the sum of the width of the table and the difference between the two quantities.
L = 1.06 + 0.45
L = 1.51
Hence, the length of the table is 1.51 meters.
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The Clark's updated their living room by purchasing a new chair for $162.98. They paid 9% sales tax on their purchase. If
the Clark's paid $180.98 total, determine if they paid the correct amount.
Please help
Graph -8+x=4y-16
Answer:
Step-by-step explanation:
I am going to transform this equation into slope-intercept form, as it is usually easier to graph it that way.
Given:
-8 + x = 4y - 16
Add 16 to both sides of the equation:
-8 + x + 16 = 4y
Divide both sides of the equation by 4:
-2 + [tex]\frac{1}{4}[/tex]x + 4 = y
Reflexive property and combine like terms:
y = [tex]\frac{1}{4}[/tex]x + 2
Now, we will graph. The 2 is our y-intercept and the [tex]\frac{1}{4}[/tex] is our slope, graphed as "rise over run." This means we will rise one unit up and run four units right.
See attached.
a gardener has 1040 feet of fencing to fence in a rectangular garden. one side of the garden is bordered by a river and so it does not need any fencing. garden bordered by a river what dimensions would guarantee that the garden has the greatest possible area?
The dimensions 520 by 360 feet would guarantee that the garden has the greatest possible area .
Let length be l and width be b of garden .
According to question ,
l + 2b = 1040
Area of garden = l * b
Substituting value of l in formula for area ,
Area = ( 1040 - 2b ) * b = 1040b - 2[tex]b^{2}[/tex]
Taking derivative of Area wrt. b and putting it equal to 0 ,
1040 - 4b = 0
b = 1040 / 4
b = 260 feet
Therefore , l = 1040 - 520 = 520 feet .
Maximum Area = 260 * 520 = 135200 [tex]feet^{2}[/tex] .
Hence , the dimensions 520 by 360 feet would guarantee that the garden has the greatest possible area .
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Kyra ha a rock collection. When he put her rock into 2 equal pille , there are no rock left over. When he put her rock into 3 equal pile , there are till no rock left over. When he put her rock into 4 equal pile , there are till no rock left over. How many rock could Kira have ?
By applying the lowest common multiple approach, Kyra may have acquired up to 12 rocks.
What does common factor mean?
A common factor is a whole number that is a factor of at least two other numbers. The highest common factor is the largest factor that will divide into two or more numbers (HCF). The phrase "lowest common multiple" refers to the smallest multiple that two or more numbers have in common (LCM).
The least common multiple of 2, 3, and 4 can be used to determine how much rock Kyra has.
Several of:
2 = 2, 4, 6, 8, 10, 12, 14, 16, 18, 20
3 = 3, 6, 9, 12, 15, 18, 21
4 = 4, 8, 12, 16, 20
The smallest number that 2, 3, and 4 have in common is 12. There are therefore 12 rock piles in Kyra's possession.
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if x varies inversly as the square root of y varies and x=1 when y=4, find;
relationship between x and y
the value of x when y =9
the value of y when x=12
Answer:
x = 2/√y or y = 4/x²x = 2/3y = 1/36Step-by-step explanation:
When x varies inversely as the square root of y, and x=1 when y=4, you want to find ...
the relationship between x and ythe value of x when y =9the value of y when x=12.Inverse variationThe given relation can be written using a constant of proportionality as ...
x = k/√y . . . . x varies as the inverse of the square root of y
The value of k can be found from the given values for x and y:
1 = k/√4 = k/2
2 = k . . . . . . . . . multiply by 2
RelationshipThe relationship between x and y can be written as ...
x = 2/√y
Solving for y, it can also be written as ...
y = 4/x²
For y = 9The value of x is ...
x = 2/√9
x = 2/3
For x=12The value of y is ...
y = 4/12² = 4/144
y = 1/36
Choose ALL answers that describe the quadrilateral UVWX if UV = 31,
VW = 67, WX = 45, XU = 56, m/U = 146°, m/V = 54°, m/W = 95°,
and m/X = 65°.
Parallelogram
□ Quadrilateral
Rectangle
Rhombus
Square
Trapezoid
The correct option ; Quadrilateral, has the given information describing quadrilateral UVWX.
What is meant by the term Quadrilateral? A polygon comprising four sides, 4 angles, and 4 vertices is called a quadrilateral.There are some aspects that all quadrilaterals share. These attributes are:There have been four of them.There have been four of them.360° is the summation of all interior angles.There have been two diagonals in them.For the given values in the question;
In the quadrilateral UVWX
Sides are;UV = 31,VW = 67, WX = 45, XU = 56, Angles are-m/U = 146°, m/V = 54°, m/W = 95°,and m/X = 65°.As, none of the sides are equal to other and none of the angles are equal to the other.
Thus, the this information shows the values are given for quadrilateral.
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Help please, I can’t think of what this is plus time is running out
The measure of width of given figure is 2 units. Therefore, option B is the correct answer.
From the given figure, the length is 9 units and the width is 1 unit.
What is a length?Length is defined as the measurement or extent of something from end to end. In other words, it is the larger of the two or the highest of three dimensions of geometrical shapes or objects. For example, a rectangle has its dimensions as length and breadth.
From the figure, the width is 1+1=2 units
The measure of width of given figure is 2 units. Therefore, option B is the correct answer.
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what is the difference between independent samples and related samples when dealing with two samples
The difference between an independent sample and a dependent sample is that the dependent sample for one set of items is paired measurement while measurements made on two samples are termed an independent sample.
In statistics, while considering two samples and conducting a hypothesis test, one should be aware of which type of test should be conducted based on samples whether they are dependent or independent. If the value of another sample is affected by any one sample then the samples are dependent. If no information can be deduced from the other sample using one sample then the samples are independent.
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A = LW is the formula for the area of a rectangle.
Solve the formula for W.
Darryl’s portfolio includes 66 shares of Essentia Inc., 95 shares of SFT Legal, and 180 shares of Grath Oil. If Essentia Inc. pays a yearly dividend of $1.79 per share, SFT Legal pays $2.62 per share, and Grath Oil pays $1.18 per share, how much does Darryl receive in dividends every year?
Darryl receive $579.44 in dividends every year .
In the question ,
it is given that
Darryl's portfolio
number of shares of Essentia Inc. = 66
dividend received from each share in a year = $1.79 per share
So , amount of dividend received from Essentia Inc. = 66 × 1.79
= $118.14
number of shares of SFT Legal = 95
dividend received from each share in a year = $2.62 per share
So , amount of dividend received from SFT Legal = 95 × 2.62
= $248.9
number of shares of Grath Oil = 180
dividend received from each share in a year = $1.18 per share
So , amount of dividend received from Essentia Inc. = 180 × 1.18
= $212.4
So , total dividend Darryl receives = $118.14 + $248.9 + $212.4
= $579.44
Therefore , amount of dividend received by Darryl each year is $579.44 .
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Write the coordinates of the vertices after a rotation 270° counterclockwise around the origin.
T=
U=
V=
W=
The coordinates of the vertices after a rotation 270° counterclockwise around the origin is
T' = (-8, -4)
U' = (-8, -6)
V' = (-3, -9)
W' = (-3, -7)
The coordinates of T = (4, -8)
The coordinates of U = (6, -8)
The coordinates of V = (9, -3)
The coordinates of W = (7, -3)
The rule of rotating 270 degree clockwise around the origin is
P(x, y) = P'(y, -x)
The coordinates of T' = (-8, -4)
The coordinates of U' = (-8, -6)
The coordinates of V' = (-3, -9)
The coordinates of W' = (-3, -7)
Hence, The coordinates of the vertices after a rotation 270° counterclockwise around the origin is
T' = (-8, -4)
U' = (-8, -6)
V' = (-3, -9)
W' = (-3, -7)
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the number of defectives in 10 different samples of 50 observations each is the following: 5, 1, 1, 2, 3, 3, 1, 4, 2, 3. what is the estimate of the population proportion of defectives?
The estimate of the population proportion of defectives is 0.05.
Given that,
There are 10 different samples of 50 observations, that is, total of 500 observations.
To find : The estimate of the population proportion of defectives
And total number of defectives from 500 observations is (5+1+1+2+3+3+1+4+2+3) = 25
Thus, the point estimate for the population proportion defectives will be,
=25/500=0.05
or just obtain the individual proportion of each sample and then take their average to obtain the same result.
Thus, the point estimate for the population proportion defectives will be 0.05
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Which of these strategies would eliminate a variable in the system of equations?
The strategy which would eliminate a variable in the system of equations is to multiply the top equation by 6 ,multiply the bottom equation by -5 then add the equation and is denoted as option B.
What is Equation?This is a mathematical term which is made up of two expressions and is connected by an equal sign.
In the example given below:
8x + 5y = -7
-7x + 6y = -4
We can multiply the top by 6 and the bottom by -5 which will result in:
48x + 30y = -42
35x - 30y = 20
They are then added to each other to give:
48x + 35x + 30y - 30y = -42 + 20
83x = - 22
x = -22/83
From this we can notice that the variable y was eliminated which is why option B is the correct choice.
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a farmer wants to make a rectangular field with a total area of 2000 square meters. it is surrounded by a fence. it is divided into 4 equal areas by fences. what is the shortest total length of fence this can be done with?
The shortest total length of fence this can be done with will be 440 m as the total area is 2000 m².
What is perimeter?The length of a shape's outline is its perimeter. You must add the lengths of all four sides of a rectangle or square to determine its perimeter. In this instance, x represents the rectangle's length and y its width. The distance around an object is called the perimeter. For instance, the yard of your home is fenced in. The fence's length serves as the perimeter. Your fence is 200 feet long if the yard is 50 feet by 50 feet.
Here,
The area=2000 m²
xy=2000
x=2000/y
p=4x+2y
p=4*(2000/y)+2y
=8000/y+2y
p'=-8000/y²+2
-8000/y²+2=0
2y²-8000=0
y²-4000=
y²=4000
y= 20 m
p=8000/20+2*20
p=400+40=440 m
Given that the total area is 2000 m², the shortest total length of fence that can be used is 440 m.
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the equation 32divided ? =8 she says the value of ? is 4 does ella answer make sense ?
Ella answer makes sense because the value of ? is 4
How to determine the value of ? in the equation make sense?
Given: the equation 32 divided ? =8 she says the value of ? is 4
32 / ? = 8
Let x represent ? in the equation, thus:
32 / x = 8 cross multiply
8x = 32
x = 32/8
x = 4
Since x = 4. This implies ? = 4
Also, the value that divides 32 to give is 4
Since the value of ? is 4. Therefore, Ella's answer makes sense
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Pls Help Me With this
1. 2.1 x 5.12 =____ 2.12.3 x 1.6 =
Estimate______ Estimate____
3. 6.5 x 3.1 =____ 4. 51.3 x 2.7 = ____
Estimate_____ Estimate______
The corresponding estimate for numbers in 1,2,3 and 4 are 10, 24, 21 and 153
How to estimate numbers?
Estimation and approximation is the process of using rounded values when presenting numerical data and making rough calculations.
The digits 1,2,3 and are rounded down and digits 5,6,7,8 and 9 are rounded up
1. 2.1 x 5.12 = 2 x 5 = 10
Explanation: The number after the digit 2 in 2.1 is 1, we will round down 2.1 to 2. Also, the number after the digit 5 in 5.12 is 1, we will round down 5.12 to 5
2. 12.3 x 1.6 = 12 x 2 = 24
Explanation: The number after the digit 12 in 12.3 is 3, we will round down 12.3 to 12. Also, the number after the digit 1 in 1.6 is 6, we will round up 1.6 to 2
3. 6.5 x 3.1 = 7 x 3 = 21
Explanation: The number after the digit 6 in 6.5 is 5, we will round up 6.5 to 7. Also, the number after the digit 3 in 3.1 is 1, we will round down 3.1 to 3
4. 51.3 x 2.7 = 51 x 3 = 153
Explanation: The number after the digit 51 in 51.3 is 3, we will round down 51.3 to 51. Also, the number after the digit 2 in 2.7 is 7, we will round up 2.7 to 3
Therefore, the estimate for 1,2,3 and 4 are 10, 24, 21 and 153 respectively
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What is an equation of the line that passes through the points (-4, -3) and (8, 6)?
Answer: [tex]y=\frac{3}{4} x[/tex]
Step-by-step explanation:
We will create a point-slope equation to solve.
First, we need to find the slope.
[tex]\displaystyle \frac{y_2-y_1}{x_2-x_1}= \frac{6--3}{8--4} =\frac{9}{12} =\frac{3}{4}[/tex]
Next, we will create our point-slope equation.
[tex]\displaystyle y-y_1=m(x-x_1)[/tex]
[tex]\displaystyle y--3=\frac{3}{4} (x--4)[/tex]
[tex]\displaystyle y+3=\frac{3}{4} (x+4)[/tex]
[tex]\displaystyle y=\frac{3}{4} x+3 -3[/tex]
[tex]\displaystyle y=\frac{3}{4} x[/tex]
Pls pls pls help it has to be turned in today!
Using the compound amount formula, the amount after 40 years is 2000(107/100)^40.
In the given question,
Esther got a summer job and decided to set aside $2000 to prepare for retirement without making monthly contribution.
She invests in the US stock market through as index fund that averages a 7% return compounded annually over this 40 year period.
We have to find the total balance in the account after 40 years.
We have to find total balance compounded annually.
The formula of the compound amount is
A = P(1+r/100)^n
where A = Amount
P = Principal Amount
r = interest rate
n = time
From the question we know that
P = $2000, r = 7%, n = 40
Now putting the value in formula
A = 2000(1+7/100)^40
Simplifying
A = 2000(1×100/100+7/100)^40
A = 2000(100/100+7/100)^40
A = 2000((100+7)/100)^40
A = 2000(107/100)^40
You can find the amount after simplifying the amount.
Hence, the amount after 40 years is 2000(107/100)^40.
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if y=10 when x=50 find y when x=125 ANSWER WITH COMPLETE SOLUTION PLEASE
[tex]{\sf{ \frac{10}{50} = \frac{y}{125} \\ →50y = 10 \times 125 \\→ y = 25}}[/tex]
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select all equations that are equivalent to (5x+6)/2=3-(4x+12)
The equivalent equation of the equation, [tex]\frac{5x+6}{2}=3-(4x+12)[/tex] is 5x + 6 = -18 - 8x
How to find equivalent equation?Two equations are said to be equivalent when they have the same solution set.
Equivalent equations are algebraic equations that have identical solutions or roots.
Therefore, let's find the equivalent equation of the equation.
[tex]\frac{5x+6}{2}=3-(4x+12)[/tex]
Let's open the bracket on the right side
[tex]\frac{5x+6}{2}=3-(4x+12)[/tex]
[tex]\frac{5x+6}{2}=3 - 4x - 12[/tex]
[tex]\frac{5x+6}{2}=(-9-4x)[/tex]
cross multiply
5x + 6 = 2(-9 - 4x)
5x + 6 = -18 - 8x
5x + 8x = -18 - 6
13x = - 24
divide both sides by 13
x = - 24 / 13
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How can a negative number be written in scientific notation?
PLS AWNSER
For example, what is ‒0.0026 written in scientific notation?
Does any part of the process change because the number being converted is negative?
Answer:
-2.6 x 10-3
Step-by-step explanation:
if you enter the equation into a calculator it will do it for you. If you want to do it with a calculator heres how to. You would move the decimal to the first whole number for example in this case 2. How many places is that? 3. Whenever a decimal point moves to the right the spot is negative. You would then write it 2.6 with 10 (exponent -3)
Answer:
Step-by-step explanation:
To rewrite in scientific notation means to add an exponent such as e-3 in this case or [tex]10^{x}[/tex] where x is the exponent.
you would convert -0.0026 to -2.6e-3 or [tex]-2.6*10^{-3}[/tex]
The basic way of converting to scientific notation is to move your number a certain amount of decimal places until there is one number left before the decimal mark. Then the amount of values moved turns into you're exponent. A negative exponent means your are going towards a smaller number. Make sure to keep the current sign of the number
aaron collects 54 rocks at the beach. he wants to give an equal number of rocks to 6 of his friends. how many rocks did each of aaron's friends get? if r represents the number of rocks each friend will get, which equation could be used to solve the problem?
Each of Aaron's pals receives nine (9) rocks in total.
The question states that,
Aaron collects a total of 54 rocks at the beach.
He wants to give an equal number of rocks to six (6) of his friends.
It is given that let 'r' be the number of rocks each of his friends gets.
The required equation is;
Rock's Aaron's friends get,
→ 6*r = 54
r = 54/6
r = 9
The total number of rocks each of Aaron's friends get is 9.
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P and q started a business. the profits earned are divided in the ratio of their capital, 2:3. if p invested capital of $40,000, what was the capital invested by q?
The capital invested by q is $60,000 when p invested capital of $40,000.
According to the question,
We have the following information:
The ratio of the profits earned by by p and q is 2:3.
Amount invested by p = $40,000
Now, let's take the amount invested by p to be $2x and the amount invested by q to be $3x.
So, we have the following expression:
2x = 40000
x = 40000/2
x = $20000
Now, putting the value of x in 3x in order to find the amount invested by q:
3*20,000
$60,000
Hence, the amount invested by q is $60,000 when p invested capital of $40,000.
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The Question: An employer provides two payment options for employees.
Option A: Receive $200 the first week. Receive an additional $50 for each of the following weeks.
Option B: Receive $200 the first week. Receive an additional 10% for each of the following weeks.
My Answer: Option A; 200, 250, 300, 350, 400, 450. Option B; 200, 220, 242, 266.2, 292.82, 322.1
Am I correct?
Answer:
Your first option is correct but your second is wrong
Step-by-step explanation:
In option b-
when an employee receives 10% additional for each of the following weeks:
10% of 200= 10/100 x200= 20
it means he will get $20 in extra in every week
so it will be- 220,240,260
The slope of a ramp leading from the door to the ground is 5/3. the first point has a height of 27 inches; the second point has a height of 12 inches. what is the horizontal distance,x, in inches that is between these two markers?
x=12in
Slope of ramp= SecФ =5/3
Let the height of first point be H1
Let the height of second point be H2
Then, H1=27in (Provided in the question)
H2=12in (Provided in the question)
The base of the right angled triangle then = H1-H2
Let the perpendicular be denoted as p
Let the base be denoted as b
Let the hypotenuse be denoted as h
then, b=H1-H2
b=27-12
b=15
The Formula of SecФ=1/CosФ
Since, CosФ= Base/Hypotenuse
SecФ=/Hypotenuse/Base
SecФ= h/b
SecФ= 5/3 (Provided in the question)
then,
5/3=15/b
cross multiplying
5b=15x3
b=15x3/5
cancelling out 15 by 5
b=3x3
b=9
From Pythagoras theorem
[tex]h^{2}[/tex]=[tex]p^{2}[/tex]+ [tex]b^{2}[/tex]
putting values in the equation above:
[tex]15^{2}[/tex]=[tex]p^{2}[/tex] +[tex]9^{2}[/tex]
15x15=[tex]p^{2}[/tex]+81
225-81=[tex]p^{2}[/tex]
[tex]\sqrt{225-81}[/tex]=p
[tex]\sqrt{144}[/tex]=p
12=p
Since slope of ramp is equivalent to angle of depression
thus, p=x
x=12in
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Rewrite the following equation in slope-intercept form.
y − 8 = 2(x + 6)
You have a $250 card to use at a sporting goods store. Each pair of sneakers is worth $80 and a pair of sacks costs an inequality that represents the possible numbers of x pairs of socks you can buy when you buy 2 pairs of sneake
The inequality that represents the the possible numbers of x pairs of socks you can buy when you buy 2 pairs of sneakers, using a system of equations, is of:
y ≤ 7.
What is a system of equations?A system of equations is a set of equations involving multiple variables that are related, and then operations are made to solve these equations and identify the numeric value of each variable in the context of the problem from which the system was built.
For this problem, the variables are given as follows:
Variable x: number of pairs of sneakers bought.Variable y: number of pairs of socks bought.You have a $250 card to use at a sporting goods store. Each pair of sneakers is worth $80 and a pair of socks costs $12, hence the inequality regarding the total spending is:
80x + 12y ≤ 250.
When two pairs of sneakers are bought, we have that:
x = 2.
Hence the inequality regarding how many pairs of socks can be bought is:
80(2) + 12y ≤ 250.
160 + 12y ≤ 250.
12y ≤ 90
y ≤ 90/12
y ≤ 7. (rounded down, as you can buy 7 pairs of socks but not 8).
Missing InformationThe cost of a pair of socks is of $12.
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A cycle Wheel does 1645 full turns in 7 minutes
work out the number of full turns per minute
The number of full turns per minute is 235.
Given that, a cycle Wheel does 1645 full turns in 7 minutes.
What is the unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Here,
The number of full turns per minute = Number of full turns/Number of minutes
= 1645/7
= 235 full turns per minute
Therefore, the number of full turns per minute is 235.
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