Diana bought a piece of cloth 48 inches wide and 1 yard long. It cost $12. She cut off one-fourth and used itto make a tablecloth. From the remaining material, she used a piece that was 12 inches wide and 12 incheslong to make a scarf and a piece 1.5 feet by 2 feet to make the cover for a pillow. Her sister saw Diana'ssewing efforts and said she really liked the material. She wanted to buy what was left to do some sewingof her own. Diana was willing to sell the leftover material for the rate that she had paid for it. How muchshould she charge her sister?
Answer
The amount that Diana's sister would buy the remaining 720 square inches piece of cloth = $5
Step-by-step Explanation
We are told that Diana bought a piece of cloth that was 48 inches wide and 1 yard long for $12.
Then, she had different parts of the cloth taken to do different stuff until the remaining piece of the cloth was to be bought by her sister at the same rate that she bought the original full piece of cloth.
Before we proceed, we need to establish and find the initial rate of the cloth, that is, how much is 1 unit of area.
Area of a rectangular figure (the cloth) = Length × Breadth
Length of the cloth = 1 yard = 36 inches
Breadth of the cloth = 48 inches
Area of the cloth = 36 × 48 = 1728 square inches.
1728 square inches of the cloth = $12
1 square inch of the cloth = (12/1728) = (1/144) dollars
So, now, we can now find how much of the cloth is removed.
- She cut off one-fourth of the cloth to make a tablecloth.
One-fourth of the 1728 square inches piec of cloth = (1/4) × 1728 = 432 square inches
- She used a piece that was 12 inches wide and 12 inches long to make a scarf.
Area of the piece she used to make a scarf = 12 × 12 = 144 square inches
- She used a piece that was 1.5 feet by 2 feet to make a cover for a pillow.
To find the area of this piece, we need to convert the dimensions into inches.
1 feet = 12 inches
So,
1.5 feet = 18 inches
2 feet = 24 inches
Area of this piece of cloth = 18 × 24 = 432 square inches
So, her sister now wants to buy the remaining piece of cloth from Diana.
Originally, the piece of cloth was 1728 square inches.
The total area removed from the original piece of cloth sum up to
432 + 144 + 432 = 1008 square inches.
The remaining piece of cloth will now have an area calculated by subtracting the area of pieces removed from the original area of the piece of cloth.
The area of the remaining piece of cloth = 1728 - 1008 = 720 square inches
Recall that the Diana's sister wants to but the remaining piece of cloth at the rate that Diana bought the original piece of cloth.
We have calculated this rate at which Diana bough the original piece of clothing to be (1/144) dollars for 1 square inch. So, we can then use this rate to calculate the amount Diana's sister will pay for the remaining piece of cloth
Area of the remaining piece of cloth = 720 square inch
1 square inch costs (1/144) dollars.
Let the cost of 720 square inches be x.
1 square inch = (1/144) dollars
720 square inches = x dollars
We can from a mathematical relationship simply by cross multiplying
1 × x = 720 × (1/144)
x = 5 dollars.
Hence, the amount that Diana's sister would buy the remaining 720 square inches piece of cloth = $5
Hope this Helps!!!
For the guess and check method, we would still need to first find the cost of 1 square inch of material which we obtained to be (1/144) dollars per square inch of cloth.
We would also still need to calculate the total area removed from the cloth, which we calculated to be 1008 square inches.
But now, we will now use the cost of 1 square inch, to calculate the cost of the pieces that have been removed from the cloth.
1008 × (1/144) = 7 dollars.
We can now guess how many dollars will top up the 7 dollars so that it gives the original 12 dollars that the cloth was bought.
After a series of guess, we will end up to get that it is (7 + 5) that is equal to 12 dollars.
So, guess and check would give us 5 dollars too as the answer.
please I just need help with these two questions
Question 1:
Each of these options can be read as "8 to 15", except for 15:8. This is read as "fifteen to eight". Lets say in 8:15 you have 8 of a and 15 of b. In 15:8, however, you have 15 of a and 8 of b. These are not the same ratio.
Question 2:
The amount of people that can go down the slide in 1 minute is 6, because 18/3 = 6. So:
12/6 = 2
6ppl/1min (multiply both terms by 2)
12ppl/2min
It would take 12 people 2 minutes to go down the slide.
Determine the average rate of change of f(x) = 4x²+x+3 over the interval [-2, 2].
Answer: The average rate of change is 1.
Step-by-step explanation:
The average rate of change f(x) on the interval [a,b] is (f(b)−f(a))/(b−a)
a=−2 , b=2, f(x)=4X^2+x+3.
(f(b)-f(a))/(b-a)= (3+(2)+4(2)^2-(3+(-2)+4(-2)^2)) / (2-(-2)) = 1
Can someone please answer this question for me:
Answer:
16c²+ 32 cd +16d²
Step-by-step explanation:
area of rectangle is side²
(4c+4d)²
16c²+ 16cd+16cd+16d²
16c²+32cr+16d²
what is the scale factor that creates the copy triangle DEF
The required scale factor is;
[tex]\frac{DE}{AB}=\frac{1.34}{2}=0.67=\frac{67}{100}[/tex]So, the required scale factor is 0.67 or 67/100
solve for x.
0.4x-2.8/4=1.5
x=
Answer:
5.5
Step-by-step explanation:
0.4x = 2.2
x = 5.5
2. Perform the indicated operation. Express your answer in simplest form. Show any necessary work. Then answer the question. (a) -2.48/12.4 (b) -12.5/-0.025 (c) Imagine your friend uses long division to determine the quotients, and is confused by how quickly you were able to determine the correct answer without performing long division. Explain how you were able to determine the quotients without performing long division.
Part a
we have the expression
[tex]\frac{-2.48}{12.4}[/tex]Multiply the fraction by 100/100 to remove decimal numbers
[tex]\frac{-2.48}{12.4}\cdot\frac{100}{100}=-\frac{248}{1,240}[/tex]Simplify the fraction
[tex]-\frac{248}{1,240}=-\frac{1}{5}[/tex]Part b
we have the expression
[tex]\frac{-12.5}{-0.025}[/tex]Multiply the expression by 1,000/1,000 to remove decimal numbers
so
[tex]\frac{-12.5}{-0.025}\cdot\frac{1000}{1000}=\frac{12,500}{25}[/tex]Simplify
[tex]\frac{12,500}{25}=\frac{500}{1}=500[/tex]Part c
to determine the quotients without performing long division
step 1
Convert the decimal numbers of the quotient to integer numbers, multiplying the numerator and denominator by a fraction of the form 10/10, 100/100,1000/1000, etc
step 2
Simplify the fraction in the simplest form
One meter is about 3.3 ft. Use this information to determine
a) the equivalent of one square meter in square feet.
b) the equivalent of one cubic meter in cubic feet.
The equivalent of one square meter in square feet is ____ft^2
The equivalent of one square meter in square feet is 10.89 [tex]ft^{2}[/tex] and of one cubic meter in cubic feet is 35.937 [tex]ft^{2}[/tex].
One meter is about 3.3 ft. So, we can write
1 meter = 3.3 ft
Part : A
We know, 1 meter = 3.3 ft
On squaring both sides of this equation, we will get
[tex](1 meter )^{2}[/tex]= [tex](3.3 ft )^{2}[/tex]
1 [tex]meter^{2}[/tex] = 10.89 [tex]ft^{2}[/tex] equation 1
The equivalent of one square meter in square feet is 10.89 [tex]ft^{2}[/tex] .
Part : B
We know, 1 meter = 3.3 ft
On taking cube on both sides of this equation, we will get
[tex](1 meter )^{3}[/tex]= [tex](3.3 ft )^{3}[/tex]
1 [tex]meter^{3}[/tex] = 35.937 [tex]ft^{3}[/tex] equation 1
The equivalent of one cubic meter in cubic feet is 35.937 [tex]ft^{2}[/tex]
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Jonas wants to make a poster of a drawing he made. The original drawing is 8 inches wide, and he wants the poster to be 30 inches wide. What zoom button setting will he have to use on the library copier to create a poster of this size?
Answer:
He should use a 375% zoom to create a 30-inch wide poster.
Step-by-step explanation:
30/8 = 3.75, and 8*3.75=30. So 375%.
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Brinlyn increased the amount of water she drank per day from 32 oz to 40 oz. By what percentage did Brinlyn increase the amount of water she drank each day?
Responses
Answer:
25%
Step-by-step explanation:
(40-32 / 32) × 100% = 25%
2 dot plots. Both number lines go from 0 to 10. Plot 1 is titled fifth grade. There are 2 dots above 1, 3 above 2, 1 above 3, 4 above 4, 5 above 5, 5 above 6, 2 above 7, 2 above 8, 0 above 9, 0 above 10. Plot 2 is titled seventh grade. There are 2 dots above 0, 2 above 1, 3 above 2, 5 above 3, 5 above 4, 3 above 5, 3 above 6, 1 above 7, and 0 above 8, 9, and 10.
The dot plot shows the number of hours, to the nearest hour, that a sample of 5th- and 7th-grade students spend watching television each week. How do the medians compare?
The 5th-grade range is
.
The 7th-grade range is
.
The ratio of variation of 5th grade to 7th grade is
.
The range of the number of hours spent watching tv for the 5th grade is 6.
The range of the number of hours spent watching tv for the 7th grade is 7.
Th ratio of variation is 6/7.
What is the range?A dot plot is a graph used to represent a dataset using dots. A dot plot is made up of a number line and dots. The dots in the dot plot represent the frequency of the data.
Range is a measure used to measure the variation of a dataset. Range is the difference between the largest number in a data and the smallest number in the dataset.
Range = largest number - smallest number
Range of the 5th grade students = 8 - 1 = 6
Range of the 7th grade students = 7 - 0 = 7
Ratio of variation of 5th grade to 7th grade = range of 5th grade / range of 7th grade
6 / 7
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Mrs. M purchased milk for $3.50 per gallon. Which represents the number of gallons of milk, g, Mrs M can purchase if she plans to spend $10.50 on milk.all of the > and < have a line beneath them a. g>0 and g<3b. g>0 and g<14c. g> 0 and g< 7d. g>0 and 8<2
Let x be the number of gallons Mrs M can purchase;
Given information:
Price per gallon: $3.50
Mrs M. Total budget: $10.50
[tex]\begin{gathered} 3.50x\text{ }≤\text{ }10.50 \\ \end{gathered}[/tex]Solving for the number of gallons Mrs M can purchase:
[tex]\begin{gathered} x\leq\frac{10.50}{3.50} \\ \\ x\text{ }\operatorname{\leq}\text{ }3 \end{gathered}[/tex]ANSWER
a. g>0 and g<3
Can someone help me make a floor plan using the shapes on the scale factor sheet?
Answer:
k = 4
Explanation:
1) The triangles in example 1 are similar triangles but differs in size
We are to calculate the scale factor k
Using the formula
Scale factor k = size of the larger triangle/size of the smaller trinagle
Since they are similar triangles;
k = DF/AB
Given
DF = 48
AB = 12
Substitute the given values into the expression for k above to have;
k = 48/12
k = 4
Hence the scale factor from triangle ABC to DEF is 4
Find the value of sin G rounded to the nearest hundreth if necessary
sin G = 0.84
Explanation:
[tex]\begin{gathered} GF\text{ = }\sqrt[]{35} \\ FE\text{ = }\sqrt[]{86} \\ GE\text{ = 11} \end{gathered}[/tex]We will apply trigonometry ratio SOHCAHTOA:
sin G is sine ratio (SOH)
sin G = opposite/hypotenue
[tex]\begin{gathered} \text{Angle = G} \\ \text{opposite = side opposite the angle G = }\sqrt[]{86} \\ \text{hypotenuse = longest side = 11} \end{gathered}[/tex][tex]\begin{gathered} \sin \text{ G = }\frac{\sqrt[]{86}}{11} \\ \sin \text{ G = }\frac{9.2736185}{11} \\ \sin \text{ G = 0.8431} \\ \\ To\text{ the nearest hundredth, } \\ \sin \text{ G = 0.84} \end{gathered}[/tex]in ABC, The sum of measures of A and B is 90°. A is 30° less than twice B use this information to find the measure of each angle
Given:
The sum of measures of A and B is 90°
so, we have the following equation:
[tex]A+B=90\rightarrow(1)[/tex]And, A is 30° less than twice B
so, we have the following equation:
[tex]A=2B-30\rightarrow(2)[/tex]Solving the equations (1) and (2)
Substitute with A from equation (2) into equation (1)
[tex]\begin{gathered} 2B-30+B=90 \\ 3B=120 \\ B=\frac{120}{3}=40 \end{gathered}[/tex]Substitute with B into equation (2) to find A:
[tex]A=2\cdot40-30=50[/tex]So, the answer will be:
The measure of angle A = 50
The measure of angle B = 40
The measures of the angles of a triangle are shown in the figure below. Solve for x.
34°
46°
x°
The measures of the angle x in the triangle is 100 degrees
How to determine the measures of the angle?From the question, we have the following parameters that can be used in our computation:
Angles = 34, 46 and x
The sum of angles in a triangle add up to 180 degrees
This is represented as
Sum of angles = 180
Substitute the known values in the above equation
So, we have
34 + 46 + x = 180
Evaluate the like terms in the above equation
So, we have
80 + x = 180
Evaluate the like terms in the above equation
So, we have
x = 100
Hence, the value of x is 100
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Solve the quadratic equation X^2+5x+6using the completing the square method. Be sure to explain each step.
We must solve the following quadratic equation by completing squares:
[tex]x^2+5x+6=0.[/tex]1) First, we rewrite the equation in the following way:
[tex]x^2+2\cdot\frac{5}{2}\cdot x+6=0.[/tex]2) We sum to both sides of the equation (5/2)², get:
[tex]x^2+2\cdot\frac{5}{2}\cdot x+(\frac{5}{2})^2+6=(\frac{5}{2})^2.[/tex]3) Expressing the first term as a square, we have:
[tex](x+\frac{5}{2})^2+6=\frac{25}{4}.[/tex]4) Passing the +6 at the left as -6 at the right:
[tex]\begin{gathered} (x+\frac{5}{2})^2=\frac{25}{4}-6, \\ (x+\frac{5}{2})^2=\frac{25}{4}-\frac{24}{4}, \\ (x+\frac{5}{2})^2=\frac{1}{4}. \end{gathered}[/tex]5) By taking the square root on both sides, we get two solutions:
[tex]\begin{gathered} x+\frac{5}{2}=+\frac{1}{2}\rightarrow x=\frac{1}{2}-\frac{5}{2}=-\frac{4}{2}=-2, \\ x+\frac{5}{2}=-\frac{1}{2}\rightarrow x=-\frac{1}{2}-\frac{5}{2}=-\frac{6}{2}=-3. \end{gathered}[/tex]Answer1) Re-writing the equation:
[tex]x^2+2\cdot\frac{5}{2}\cdot x+6=0.[/tex]2) Summing (5/2)² on both sides:
[tex]x^2+2\cdot\frac{5}{2}\cdot x+(\frac{5}{2})^2+6=(\frac{5}{2})^2.[/tex]3) Expressing the first term as a square:
[tex](x+\frac{5}{2})^2+6=\frac{25}{4}.[/tex]4) Simplifying:
[tex]\begin{gathered} (x+\frac{5}{2})^2=\frac{25}{4}-6, \\ (x+\frac{5}{2})^2=\frac{25}{4}-\frac{24}{4}, \\ (x+\frac{5}{2})^2=\frac{1}{4}. \end{gathered}[/tex]5) Taking the square root:
[tex]\begin{gathered} x+\frac{5}{2}=+\frac{1}{2}\rightarrow x=\frac{1}{2}-\frac{5}{2}=-\frac{4}{2}=-2, \\ x+\frac{5}{2}=-\frac{1}{2}\rightarrow x=-\frac{1}{2}-\frac{5}{2}=-\frac{6}{2}=-3. \end{gathered}[/tex]In a survey of 3400 people asked about their ice cream preference, 1600 enjoyed chocolate, 1250 enjoyedvanilla, 1700 enjoyed mint, 700 enjoyed mint and chocolate, 500 enjoyed mint and a vanilla, 600 had achocolate and vanilla, and 200 enjoyed mint, chocolate, and vanilla.a. How many people enjoyed vanilla, but not chocolate or mint? b.How many people did not enjoy chocolate, vanilla, or mint?
Answer:
Step-by-step explanation:
To understand the situations we must do a Venn diagram:
The total of people asked is 3400. Then,
a) For People who enjoyed vanilla but not chocolate or mint, seeing the diagram of Venn, we can deduce the equations:
[tex]undefined[/tex]b) For people who did not enjoy chocolate, vanilla or mint:
[tex]undefined[/tex]I need help with this
In other terms, imaginary numbers are those that have no known value and are represented by the square root of negative numbers. Most of the time, it is expressed as real values multiplied by an arbitrary unit called "i."
Is it possible for a quadratic to have both real and imaginary roots?Answer and justification Therefore, a quadratic equation with rational coefficients cannot have both a real and an imaginary root.
How can you find complex roots using Descartes' Rule of Signs?
We may determine the total number of positive + negative real roots using the rule of signs. We may get the potential number of complex roots by deducting this total from the polynomial's degree.
An imaginary integer is referred to as an imaginary zero if it produces a zero output when plugged into a polynomial (or a complex zero).
Complex numbers are those that are expressed as a+b, where a and b are actual numbers and I is a fictitious number called a "iota." I has the value (-1).
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A tailor has 20 yards of shirt fabric. How many shirts can she
complete if each shirt requires 2% yards of fabric?
Answer:
2%/100% ×20=
Step-by-step explanation:
from this one of the zeros from the hundred would cancel the zero from 20 which will give you 2/10×2 and mind you percentage cancel percentage. from this 2 will cancel 10 leaving the answer 2 over 5
what is the quotient of (6.47 x 10^-15) / (3.36 x 10^-29)
i need this answer asap pleasee
Answer:
The equation of the line is y=3x+3
line m and n are parallel when x=
we have those angles must measure the same so
[tex]\begin{gathered} 4x-6=150 \\ 4x=156 \\ x=\frac{156}{4}=39 \end{gathered}[/tex]so x=39
Jay's family is moving to a new home they packed 22 boxes in 1 5/6 hours what is the average number of boxes they packed per hour Pls asap
A construction crew is lengthening a road. The road started with a length of 54 miles, and the crew is adding 3 miles to the road each day.
Let L represent the total length of the road (in miles), and let D represent the number of days the crew has worked. Write an equation relating L to D. Then use this equation to find the total length of the road after the crew has worked 37 days.
The equation for calculation of total length is L = 54 + 3D and the total length for 37 days 165 miles.
The equation will be formed as total length will be sum of first length travelled with the product of number of miles travelled each day and number of days. Representing this as the equation -
L = 54 + 3D
Now, keep the value of D in formula to find the total length.
L = 54 + 3×37
Performing multiplication on Right Hand Side of the equation
L = 54 + 111
Performing addition on Right Hand Side of the equation
L = 165 miles
Therefore, the equation is L = 54 + 3D and total length is 165 miles.
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A bicycle company is manufacturing a new bicycle and trying to decide on a price that will maximizing their profit. the graph below represents profit (P), in thousands of dollars,generated by the price of each bike (x), in hundreds of dollarsIf the company wants to make a maximum profit,what should the price of the bicycle be?
The graph shows the profit (measured in thousands of dollars) on the y-axis and the price per bike (measured in hundreds of dollars) on the x-axis, the parabola describes the relationship between both variables.
As you can see the parabola opens downwards, which means that the maximum value of the relationship is determined by the vertex of the curve.
The coordinates of the vertex indicate the value of the bikes (x-coordinate) that allows the company to make the maximum profit (y-coordinate)
Looking at the graph the coordinates for the vertex are, approximately, (6, 160)
x-coordinate: 6 hundreds of dollars
y-coordinate 160 thousands of dollars
The maximum profit will be $160,000, and they will reach it when the bicycles cost $600
Indigo Depot is having a clearance sale of their spring items. All clearance items are marked an additional 35 % off the sale price. A dress that originally cost $120 beforeany discount is on sale for 20 % off. What is the final price? Round your answer to the nearest cent, if necessary.
From the information provided, The original price had a discount of 35% slash during he clearance.
This means the clearance sales price would be;
[tex]\begin{gathered} \text{Clearance price}=120-(120\times0.35) \\ \text{Clearance sales}=120-42 \\ \text{Clearance sales}=78 \end{gathered}[/tex]This means a dress that "originally" cost $120 now sells for $78 during the clearance sales.
The dress is now on sale for 20% off.
Therefore, the final price would be;
[tex]\begin{gathered} \text{ Final price}=78-(78\times0.20) \\ \text{Final price}=78-15.60 \\ \text{ Final price}=62.40 \end{gathered}[/tex]ANSWER:
The final price is $62.40
15 points please help. Math. Marginal profit function
65.03x + 74757 is Marginal profit function .
What is profit?
The financial gain a business has when revenue exceeds costs and expenses is repeatedly alluded to as profit. One cup of lemonade, for instance, costs a child at a lemonade stand one quarter. She then charges $2 for the drink. She made $1.75 in profit just on cup of lemonade.Profit is the term used to describe the monetary gain experienced when the revenue from a commercial activity outpaces the costs, costs, and taxes incurred to support the activity in question.P(x) = 143 - 0.03x
C(x) = 75000 + 65x
C(x) - P(x) = 75000 + 65x - ( 143 - 0.03x)
= 75000 + 65x - 143 + 0.03x
= 65.03x + 74757
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savings 50,000 in 30 years with a saving compounded monthly at an interest rate of 6%. How much would I need to deposit a month?
The amount that needs to be deposited to have a saving of $50,000 in 30 years at the given interest rate is $8,302.10.
How is the principal investment required?The compound interest formula is expressed as;
P = A / (1 + r/n)^nt
Where P is principal, A is amount accrued, r is interest rate is compound period and t is time elapsed.
Given the data in the question;
Accrued amount A = $50,000Interest rate r = 6%Compounded monthly n = 12Elapsed time t = 30 yearsPrincipal P = ?First, convert rate from percent to decimal.
Rate r = 6%
Rate r = 6/100
Rate r = 0.06 per year
To determine the principal, plug the given values into the formula above and solve or P
P = A / (1 + r/n)^nt
P = $50,000 / (1 + 0.06/12)^( 12 × 30 )
P = $50,000 / (1 + 0.05)³⁶⁰
P = $50,000 / (1.05)³⁶⁰
P = $8,302.10
Therefore, the principal investment is $8,302.10.
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2y + 6 = y — 7. What is the value of y?
y=-13
Step-by-step explanation:
2y+6=y-7
2y+6-6=y-7-6
2y=y-13
2y-y=y-13-y
y=-13
The value after solving the given expression will be equal to -13.
What is an expression?Mathematical actions are called expressions if they have at least two terms that are related by an operator and include either numbers, variables, or both. Adding, subtraction, multiplying, and division are all reflection coefficient operations. A mathematical operation such as reduction, addition, multiplication, or division is used to integrate terms into an expression.
As per the given expression in the question is,
2y + 6 = y - 7
Rearrange the equation,
2y - y = -7 - 6
y = -13
Therefore, the obtained value for y will be -13.
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