M = 3
....................
Answer:
m = 3
Step-by-step explanation:
10m = 10-5(m-7)
10m = -(5m-5×7)+10
10m = -(5m-35)+10
10m = -5m + 35 + 10
10m = -5m +45
15m = 45
15m/15 = 45/15
m = 3^2*5/3*5
m = 3^2-1
m = 3
Si una persona tiene que pagar $120 de impuestos sobre una renta de $1,500, ¿cuál es la tasa impositiva?
The tax rate is 8% if the person pay $120 in taxes.
What is the tax rate if the person pay $120 in taxes?A tax rate is a percentage at which an individual or corporation is taxed. The U.S. imposes a progressive tax in which the higher the individual's income, the higher the tax.
To get tax rate, we will divide the amount of taxes paid ($120) by the income ($1,500) and then multiply by 100.
Tax rate = (Taxes paid / Income) * 100
Tax rate = ($120 / $1,500) * 100
Tax rate ≈ 8%.
Translated question:
If a person has to pay $120 in taxes on an income of $1,500, what is the tax rate?Read more about tax rate
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The generic metal A forms an insoluble salt AB(s) and a complex AC5(aq). The equilibrium concentrations in a solution of AC5 were found to be [A] = 0. 100 M, [C] = 0. 0360 M, and [AC5] = 0. 100 M. Determine the formation constant, Kf, of AC5. The solubility of AB(s) in a 1. 000-M solution of C(aq) is found to be 0. 131 M. What is the Ksp of AB?
8x-4y=-96 in slope intercept form
Answer:
y=2x+24
Step-by-step explanation:
-4y=-8x-96
divide everything by -4
y= 2x +24
can someone please help me find the answer to the following?
1. Surface area:
We need to split trinagular prism into 5 different polygons. Then calculate the area for each of them, and finally add up the five results to find the total surface area.
We have 2 triangles and 3 rectangles.
Both triangles are equal, so, we only need to find the area for one of them:
- Triangle:
\(A_t\text{ = }\frac{b\cdot h}{2}\)We know h (h = 5 in), but we don't know b, and here is where the Pythagorean theorem comes in:
\(hypotenuse^2=side^2_1+side^2_2\)For our trinagle, we know the hypotenuse length (13 in) and one side length (5 in), so:
\(\begin{gathered} \text{missing}_{}\text{ side = }\sqrt[]{hypotenuse^2-side^2_1} \\ \text{missing}_{}\text{ side = }\sqrt[]{13^2-5^2} \\ \text{missing}_{}\text{ side = }\sqrt[]{169\text{ - 25}}\text{ = }\sqrt[]{144}\text{ = 12} \end{gathered}\)And so, going back to the triangle area, we have:
\(A_t\text{ = }\frac{b\cdot h}{2}\text{ = }\frac{12\cdot5}{2}=30in^2\)- "Front" rectangle area:
\(A_r\text{ = }length\cdot\text{ width = 13 }\cdot20=260in^2\)- "Right" rectangel area:
\(A_r\text{ = }length\cdot\text{ width = 20 }\cdot5=100in^2\)- "Left" rectangle area:
\(A_r\text{ = }length\cdot\text{ width = 20 }\cdot12=240in^2\text{ (12 comes from Pythagorean theorem result)}\)Finally, the surface area of the triangle prism is:
30 + 30 + 260 + 100 + 240 = 660 in^2
2. Volume
The volume is just the area of the base triangle times the height of the prism. So:
\(V=A_t\cdot\text{ h = 30 }\cdot20=600in^3\)What operation is the inverse of the one in the equation 9 = p/8 ?
A.subtraction
B.division
C.multiplication
D.addition
Multiplication operation is the inverse of the one in the given equation which is 9 = p/8.
What is an inverse?
The opposite of another operation is referred to as the "inverse" in mathematics. The operations that cancel out or are the opposite of one another are referred to as inverse operations. The work of a pair is reversed by an inverse operation.
We are given an equation as 9 = p/8.
In this equation, we can see that the operation used is division.
We know that inverse of division is multiplication.
Hence, multiplication operation is the inverse of the one in the given equation.
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please can someone help me
9514 1404 393
Answer:
BD < DC < BC < AC < AB
Step-by-step explanation:
The law of sines can be used to figure this. First we need to know the unmarked angles.
∠ABC = 180° -50° -67° = 63°
∠BCD = 180° -57° -72° = 51°
The law of sines tells us the ratio of side lengths is equal to the ratio of opposite angles. Since side BC is common to both triangles, we can let it have a measure of 1. Then the lengths we develop for the other sides represent their ratio to the length of BC.
AB/sin(C) = BC/sin(A) ⇒ AB = sin(C)/sin(A) = sin(67°)/sin(50°) ≈ 1.202
BD/sin(C) = BC/sin(D) ⇒ BD = sin(C)/sin(D) = sin(51°)/sin(72°) ≈ 0.817
AC/sin(B) = BC/sin(A) ⇒ AC = sin(B)/sin(A) = sin(63°)/sin(50°) ≈ 1.163
BC = 1 . . . . by definition above
DC/sin(B) = BC/sin(D) ⇒ DC = sin(B)/sin(D) = sin(57°)/sin(72°) ≈ 0.882
The relative lengths from least to greatest are ...
0.817 (BD), 0.882 (DC), 1.000 (BC), 1.163 (AC), 1.202 (AB)
Then the order of sides is ...
BD < DC < BC < AC < AB
__
The triangle solver results attached confirm these values. In the second attachment, node D is represented by node A.
_____
Additional comment
Angles B and C are ambiguous angle designators, as there is one such angle in each of the two triangles. We trust you can figure which one is meant by considering the angle measure and the other angle in the proportion. The law of sines only pertains to angles that are inside the same triangle.
Miranda has 180 beads for making helpers. She buys 240 more beads. She wants to store the beads in a case with 6 sections. how many beads should Miranda put in each section. HELP ASAP
Answer:
70 is the answer.
Step-by-step explanation:
180+240= 420
420 divided by 6 is 70
Find the measure of two complementary angles, ZA and ZB, if
mA=7x+4 and mZB=4x+9.
The measure of ∠A is 53.
The measure of ∠B is 37.
What is an expression?An expression contains one variable or more than one variable with addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
∠A and ∠B are complementary.
This means,
∠A + ∠B = 90
Now,
∠A = 7x + 4
∠B = 4x + 9
7x + 4 + 4x + 9 = 90
11x + 13 = 90
11x = 90 - 13
11x = 77
x = 7
Now,
∠A = 7x + 4 = 7 x 7 + 4 = 49 + 4 = 53
∠B = 4x + 9 = 4 x 7 + 9 = 28 + 9 = 37
Thus,
∠A = 53
∠B = 37
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Suppose we are given a set L of n line segments in the plane, where each segment has one endpoint on the line y = 0 and one endpoint on the line y = 1, and all 2n endpoints are distinct. Describe a polynomial-time algorithm to compute the largest subset of L in which every pair of segments intersects. Provide running time analysis and proof of correctness for your algorithm.
One possible algorithm to find the largest subset of line segments in the plane where each pair of segments intersects is to sort the segments based on their x-coordinate of the endpoint on the line y = 1.
Then, use a sweeping line from left to right to keep track of the segments that are intersecting the line y = 0. When the sweeping line reaches the right endpoint of a segment, it can be removed from the set of intersecting segments.
The set of intersecting segments at any given time represents a candidate subset of segments that intersect each other. The size of the largest subset can be updated as the sweeping line moves to the right.
The running time of this algorithm is O(nlogn), as the sorting step takes O(nlogn) time and the sweeping line takes O(n) time to process each segment.
The proof of correctness follows from the observation that the set of intersecting segments at any given time during the sweeping process is a candidate for the largest subset.
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Foundations of Algebra B
ous Activity
Week
Juan's Fundraising Progress
Total Sold in
Fruit Baskets
($)
Total Sold
in Pencils
($)
O
Juan is selling fruit baskets and pencils for his
fundraisers. He started his fundraising early and has 12
weeks to reach his goal of selling $300.00 worth of
goods to pay for his trip's cost.
If Juan uses the table shown to represent all of his
data, what interval for the weeks would you use in
column 1 so that all 12 weeks are represented?
Week labels:
English
1, 2, 3, 4
2, 4, 6, 8
3, 6, 9, 12
1, 3, 6, 10
Juan have to sell 4 fruit baskets to make enough money.
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.
Given that, Juan's Fundraising Progress Juan sold fruit baskets for $16.50 each and pencils for $1.50 each. His goal is to sell $300 worth of goods to pay for his trip's cost.
His goal is to sell $300, the pencil sold a total of $81, so the fruit basket will sell a total of 300-81=219
Las three week: 219-165 =$54
Fruit baskets for $16.50 per each
54/16.50 =3.27
So, he have to sell 4 fruit baskets to make enough money
Hence, Juan have to sell 4 fruit baskets to make enough money.
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"Your question is incomplete, probably the complete question/missing part is:"
Juan's Fundraising Progress Juan sold fruit baskets for $16.50 each and pencils for $1.50 each. His goal is to sell $300 worth of goods to pay for his trip's cost. How many fruit baskets will Juan need to sell the last three weeks to achieve his goal?
Five years ago, someone used her $40,000 saving to make a down payment for a townhouse in RTP. The house is a three-bedroom townhouse and sold for $200,000 when she bought it. After paying down payment, she financed the house by borrowing a 30-year mortgage. Mortgage interest rate is 4.25%. Right after closing, she rent out the house for $1,800 per month. In addition to mortgage payment and rent revenue, she listed the following information so as to figure out investment return: 1. HOA fee is $75 per month and due at end of each year 2. Property tax and insurance together are 3% of house value 3. She has to pay 10% of rent revenue for an agent who manages her renting regularly 4. Her personal income tax rate is 20%. While rent revenue is taxable, the mortgage interest is tax deductible. She has to make the mortgage amortization table to figure out how much interest she paid each year 5. In last five years, the market value of the house has increased by 4.8% per year 6. If she wants to sell the house today, the total transaction cost will be 5% of selling price Given the above information, please calculate the internal rate of return (IRR) of this investment in house
Can you show the math as far as formulas go?
Given the following information: Five years ago, someone used her $40,000 saving to make a down payment for a townhouse in RTP. The house is a three-bedroom townhouse and sold for $200,000 when she bought it. After paying down payment, she financed the house by borrowing a 30-year mortgage.
Mortgage interest rate is 4.25%. Right after closing, she rent out the house for $1,800 per month. In addition to mortgage payment and rent revenue, she listed the following information so as to figure out investment return: 1. HOA fee is $75 per month and due at end of each year 2. Property tax and insurance together are 3% of house value 3. She has to pay 10% of rent revenue for an agent who manages her renting regularly 4. Her personal income tax rate is 20%. While rent revenue is taxable, the mortgage interest is tax deductible. She has to make the mortgage amortization table to figure out how much interest she paid each year 5. In the last five years, the market value of the house has increased by 4.8% per year 6.
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20%
120°
y=[ ? ]°
Enter
Step-by-step explanation:
Solution,
here ,
20° + 120° + x = 180°
reason : The sum of interior angle of triangle is 180°.....
140°+ x = 180°
x = 180° - 140°
x = 40°
Now..
x + y = 180° ....
reason : Supplementary angle...
40° + y = 180°
y = 180° - 40°
y = 140°
\(...\)
Sophia earns 40 points every time she shops at a grocery store. She needs a total of 2,680 points to receive a free prize. So far, she has earned 1,280 points. How many more times will Sophia have to shop at the grocery store in order to earn the additional points she needs for a free prize? Let t represent the number of times Sophia visits the store. Which of the following equations best represents the solution to the above question?
The answer is B 1280+40t = 2680 it's on my test
how many degrees does the minute hand of a clock turn in 45 minutes
The clock minutes rotate 270 degrees in 45 minutes.
How to calculate the angular size of a clock's handsWhile rotating, the clock's hands are seen to move at a speed of six degrees per minute.
The number of degrees for a clock minute is solved by
60 minutes = 360 degrees
1 minute = ?
cross multiplying
60 * ? = 360
? = 360 / 60
? = 6
hence 1 minute is 6 degrees
The formula to use to get the calculation is multiplying the number of minutes by 6
Number of degrees in 45 minutes = 45 * 6
Number of degrees in 45 minutes = 270 degrees
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Can anyone help me with this?
8^5/8^3
Answer:
64
Step-by-step explanation:
do multiplication :)
can you find another way to solve this problem without using the original one.
The area of the isosceles trapezoid is 37.25 unit².
What is isοsceles trapezοid?An isοsceles trapezοid is a trapezοid with cοngruent base angles and cοngruent nοn-parallel sides. A trapezοid is a quadrilateral with οnly οne side parallel.
An isοsceles trapezοid can be defined as a trapezοid whοse nοn-parallel sides and base angles have the same measure. That is, if the twο οppοsite sides (bases) οf a trapezοid are parallel and the twο nοn-parallel sides are οf equal length, it is an isοsceles trapezοid. See the diagram belοw.
Area of trapezium = 1/2(h)(a + b)
where h = height
a = smaller base = 10
b = larger base = 15
Now to find height, we see a triangle at the end of trapezium, draw the imaginary altitude
Now, the base = 5/2 ⇒(15 - 10= 5)/2
= 2.5
Using trigonometry ratio
tan(θ) = Height/ Base
tan(40°) = Height/ 2.5
0.8391 = Height/ 2.5
Height = 2.5/ 0.8391
Height ≈ 2.98
Now, The area = 1/2(2.98)(10 + 15)
= 1/2(2.98)(10 + 15)
= 37.25 unit²
Thus, The area of the isosceles trapezoid is 37.25 unit².
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Question 2 Fill in the blanks to complete the sentence. A recipe for sparkling grape juice calls for 112 quarts of sparkling water and 34 quart of grape juice. a. How much sparkling water would you need to mix with 9 quarts of grape juice? 12 quarts b. How much grape juice would you need to mix with 154 quarts of sparkling water? Use decimal notation. 6 quarts c. How much of each ingredient would you need to make 100 quarts of punch? Round your answer to the nearest whole quart. sparkling water: quarts grape juice: quarts
Answer:
a) 18 quarts of sparkling water
b) 1.875 quarts of grape
Step-by-step explanation:
Question 2 Fill in the blanks to complete the sentence.
A recipe for sparkling grape juice calls for 1 1/2 quarts of sparkling water and 3/4 quart of grape juice.
a. How much sparkling water would you need to mix with 9 quarts of grape juice?
3/4 quarts of grape = 1 1/2 quarts sparkling water
9 quarts of grape = x
x = (9 × 1 1/2) ÷ 3/4
x = (9 × 3/2) × 4/3
x = 27/2 × 4/3
x = 18 quarts of sparking water
b. How much grape juice would you need to mix with 15/4 quarts of sparkling water?
1 1/2 quarts of sparkling water = 3/4 quarts of grape
1 5/4 quarts of sparkling water = x
x = (3/4 × 15/4 ) ÷ 1 1/2
x = (0.75 × 3.75 ) ÷ 1.5
x = 1.875 quarts of grape
c. How much of each ingredient would you need to make 100 quarts of punch?
Round your answer to the nearest whole quart. sparkling water: quarts grape juice: quarts
11w +99 < 33 algebra answer
Answer:
w < -6
Step-by-step explanation:
Step 1: Subtract 99 from both sides.
11w + 99 − 99 < 33 − 99
11w<−66
Step 2: Divide both sides by 11.
\(\frac{11w}{11} < \frac{-66}{11}\)
Answer:
w < -6
Based on the answers you obtained regarding the proportion of sales that occur on line compared to in-store, choose the correct conclusion that interprets the results within the context of the hypothesis test. Select the correct answer below:
O There is sufficient evidence that the proportion of sales that occur on their online retail store, instead of at their brick-and-mortar store, is more than 75%.
O There is NOT sufficient evidence that the proportion of sales that occur on their online retail store, instead of at their brick-and-mortar store, is more than 75%.
O There is sufficient evidence that the proportion of sales that occur on their online retail store, instead of at their brick-and-mortar store, is more than 5%.
O There is NOT sufficient evidence that the proportion of sales that occur on their online retail store, instead of at their brick-and-mortar store, is more than 5%.
The correct answer is "There is NOT sufficient evidence that the proportion of sales that occur on their online retail store, instead of at their brick-and-mortar store, is more than 75%."
To interpret the results of a hypothesis test, we need to consider the significance level and the p-value obtained from the test. If the p-value is less than or equal to the chosen significance level (commonly set at 0.05 or 0.01), we reject the null hypothesis. If the p-value is greater than the significance level, we fail to reject the null hypothesis.
In this case, the conclusion states that there is not sufficient evidence to support the claim that the proportion of sales occurring on the online retail store is more than 75%. This implies that the p-value obtained from the hypothesis test is greater than the chosen significance level, indicating that the observed data does not provide strong evidence to reject the null hypothesis.
Therefore, based on the hypothesis test results, we cannot conclude that the proportion of sales on the online retail store exceeds 75%. It is important to note that the alternative hypothesis may have been specific to a proportion greater than 75%, and the test did not provide enough evidence to support this claim.
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a person owns three suits, ten ties, and ten shirts. how many ways can they select a traveling wardrobe of two suits, four ties and six shirts?
There are a total of 3 x 10 x 10 = 300 possible combinations of suits, ties, and shirts that a person can select from. However, when selecting a traveling wardrobe, there are only 10 possible suit combinations, 10x10 = 100 possible tie combinations, and 10x10x10 = 1000 possible shirt combinations. This makes a total of 10 x 100 x 1000 = 100,000 possible selections of two suits, four ties and six shirts.
The sheer number of possible combinations indicates how important it is to choose wisely. The two suits should be complementary and appropriate to the occasion; the four ties can be chosen to match the suits, and the six shirts should be selected to mix and match with the ties and suits. Care should be taken to avoid repeating clothing items, and the person should also consider the climate and purpose of the trip in order to select the most suitable wardrobe.
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Mrs jaffa has 48 starbursts and 64 skittles. she wants to package them in a plastic bag so that each bag has an equal number of starbursts and an equal number of skittles. what is the greatest number of bags mrs.jaffe can put together with pieces of candy left over
Answer:
The answer is 7
Step-by-step explanation:
48 and 64 is 112, divided by 7 would be 16, so Mrs.Jaffa would use 7 bags in all. Hope this helps
Help me!
If x=⟨–3,6⟩ and y=⟨5,6⟩, find the sum x+y.
Why the heck did my answer get deleted??
ANYWAYS
the answer is (2, 12)
the explanation is that you would add the x value to the y value. for example (x, y) + (2x, 3y) would equal (3x, 4y) because you add the x and y values.
A project has an initial cost of $30 million.The project is expected to generate a cash flow of $2.85 million at the end of the first year.All the subsequent cash flows will grow at a constant growth rate of 3.85% forever in future.If the appropriate discount rate of the project is 11%,what is the profitability index of the project? a.1.917 b.1.328 c.1.387 d.1.114 ortcehov e. None of the above
Profitability index is 1.387. Thus, the correct option is (c) 1.387.
The formula for calculating the profitability index is:
P.I = PV of Future Cash Flows / Initial Investment
Where,
P.I is the profitability index
PV is the present value of future cash flows
The initial investment in the project is $30 million. The cash flow at the end of the first year is $2.85 million.
The present value of cash flows can be calculated using the formula:
PV = CF / (1 + r)ⁿ
Where,
PV is the present value of cash flows
CF is the cash flow in the given period
r is the discount rate
n is the number of periods
For the first-year cash flow, n = 1, CF = $2.85 million, and r = 11%.
Substituting the values, we get:
PV = 2.85 / (1 + 0.11)¹ = $2.56 million
To calculate the present value of all future cash flows, we can use the formula:
PV = CF / (r - g)
Where,
PV is the present value of cash flows
CF is the cash flow in the given period
r is the discount rate
g is the constant growth rate
For the subsequent years, CF = $2.85 million, r = 11%, and g = 3.85%.
Substituting the values, we get:
PV = 2.85 / (0.11 - 0.0385) = $39.90 million
The total present value of cash flows is the sum of the present value of the first-year cash flow and the present value of all future cash flows.
PV of future cash flows = $39.90 million + $2.56 million = $42.46 million
Profitability index (P.I) = PV of future cash flows / Initial investment
= 42.46 / 30
= 1.387
Therefore, the correct option is (c) 1.387.
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A survey is given to a random sample of some of the freshman students at a certain high school. Which statement about the results of the survey is true? O
O The responses can be used to make valid inferences about the entire freshman class at that school.
O The responses can be used to make valid inferences about the entire student body at that school.
O The responses can be used to represent freshman students at all high schools.
O The responses can be used to represent high school students at all high schools.
A survey is given to a random sample of some of the freshman students at a certain high school therefore the statement about the results of the survey which is true is that the responses can be used to make valid inferences about the entire freshman class at that school which is therefore denoted as option A.
What is a Survey?
This is referred to as a method of gathering information using relevant questions from a sample of people with the aim of understanding populations as a whole.
Since the survey was given to random freshman in that school, then it means that it is unbiased and will provide a valid information about them in that particular school.
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A sprinkler that sprays water in a circular area can spray up to a radius of 22ft what is the maximum area of lawn that can be watered by the sprinkler use 3.14 to approximate date for Pie enter your answer as a decimal rounded to the nearest tenth in the Box
[ ] ft^2
To find the maximum area of the lawn that can be watered by the sprinkler, we can use the formula for the area of a circle:
A = πr^2
Given that the radius of the sprinkler's spray is 22ft, we can substitute this value into the formula:
A = 3.14 * (22)^2
A ≈ 3.14 * 484
A ≈ 1519.76
Rounded to the nearest tenth, the maximum area of the lawn that can be watered by the sprinkler is approximately 1519.8 ft^2.\(\huge{\mathcal{\colorbox{black}{\textcolor{lime}{\textsf{I hope this helps !}}}}}\)
♥️ \(\large{\textcolor{red}{\underline{\texttt{SUMIT ROY (:}}}}\)
Find the product of 32 and 46. Now reverse the digits and find the product of 23 and 64. The products are the same!
Does this happen with any pair of two-digit numbers? Find two other pairs of two-digit numbers that have this property.
Is there a way to tell (without doing the arithmetic) if a given pair of two-digit numbers will have this property?
Let's calculate the products and check if they indeed have the same value:
Product of 32 and 46:
32 * 46 = 1,472
Reverse the digits of 23 and 64:
23 * 64 = 1,472
As you mentioned, the products are the same. This phenomenon is not unique to this particular pair of numbers. In fact, it occurs with any pair of two-digit numbers whose digits, when reversed, are the same as the product of the original numbers.
To find two other pairs of two-digit numbers that have this property, we can explore a few examples:
Product of 13 and 62:
13 * 62 = 806
Reversed digits: 31 * 26 = 806
Product of 17 and 83:
17 * 83 = 1,411
Reversed digits: 71 * 38 = 1,411
As for determining if a given pair of two-digit numbers will have this property without actually performing the multiplication, there is a simple rule. For any pair of two-digit numbers (AB and CD), if the sum of A and D equals the sum of B and C, then the products of the original and reversed digits will be the same.
For example, let's consider the pair 25 and 79:
A = 2, B = 5, C = 7, D = 9
The sum of A and D is 2 + 9 = 11, and the sum of B and C is 5 + 7 = 12. Since the sums are not equal (11 ≠ 12), we can determine that the products of the original and reversed digits will not be the same for this pair.
Therefore, by checking the sums of the digits in the two-digit numbers, we can determine whether they will have the property of the products being the same when digits are reversed.
The length of a rectangle is 11 less than 9 times the width. The
perimeter of the rectangle is 18 inches.
Answer:
Length = 7 Width = 2
Step-by-step explanation:
L = Length
W = Width
L=9w-11
2L+2W=18
2(9W-11) + 2W = 18
18W - 22 +2W = 18
20W -22 = 18
20W = 40
W = 2
L = 9(2)-11
L=18-11
L=7
The length and width of the rectangle is equals to 7inches and 2inches respectively.
What is rectangle?" Rectangle is defined as the quadrilateral whose opposite sides are congruent and parallel to each other , one of the interior angle is of measure 90°."
Formula used
Perimeter of the rectangle = 2 (length + width)
According to the question,
Given,
Perimeter of the rectangle = 18inches
'x' represents the width of the rectangle
As per the condition given,
Length of the rectangle = \(9x -11\)
Substitute the value in the formula we get,
\(2(9x -11 +x)=18\)
⇒\((10x-11)=\frac{18}{2}\)
⇒\(10x= 9+11\)
⇒\(x= 2inches\)
Length of the rectangle = \(9(2)-11\)
= \(18-11\)
= \(7inches\)
Hence, length and width of the rectangle is equals to 7inches and 2inches respectively.
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1.-Draw a box-and-whisker plot for the data set
12, 5, 22, 30, 7, 36, 14, 42, 15, 53, 25
The box-and-whisker plot of the data is given below.
What is box-and-whisker plot?
When we plot a graph for the box plot, we outline a box from the first quartile to the third quartile. A vertical line that goes through the box is the median. The whiskers (small lines) go from each quartile towards the minimum or maximum value.
Given data is
12,5,22,30,7,36,14,42,15,53,25
First we will arrange it in ascending order.
5,7,12,14,15,22,25,30,36,42,53
The maximum and minimum value are 5 and 53.
First quartile is 3 and third quartile is 9
median is 22 (middle term).
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Answer these two questions seperately PLEASE. The first question is what are solid solutions? and the second question is how are they formed in minerals? Please write in your own words and please reference your work by providing the url to the sources please. The first question should be around 125-150 words and the second question should be around 125-150 words. Thank
Solid solutions refer to a type of homogeneous mixture where two or more substances are combined at the atomic or molecular level to form a single, solid phase. These solutions are characterized by a uniform distribution of atoms or molecules throughout the material, resulting in a consistent composition and properties.
In solid solutions, the constituent substances can be elements or compounds that have similar crystal structures and atomic sizes. The atoms or molecules of the different components occupy the same lattice sites within the crystal structure, replacing or substituting for each other. This substitution can occur in varying proportions, leading to different compositions within the solid solution.
Solid solutions can be formed through several processes. One common method is through the gradual substitution of atoms or ions in the crystal lattice during the cooling or solidification of a melt or solution. This process is known as solid-state diffusion. Another way is by precipitation from a solution or vapor, where the atoms or molecules of the solute are incorporated into the growing crystal lattice of the host material.
Overall, solid solutions are essential in various fields of science and technology, including metallurgy, materials science, and geology, as they can significantly influence the properties and behavior of the resulting materials.
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Find the indicated one-sided limits, if they exist. (if an answer does not exist, enter dne.)
The limit doesn't exist.
What is a limit?
The value that a function (or sequence) approaches when the input (or index) gets closer to a particular value is known as a limit. Calculus and mathematical analysis are impossible without limits, which are also required to determine continuity, derivatives, and integrals.
In addition to being closely related to limit and direct limit in category theory, the idea of a limit of a sequence is further generalized to include the concept of a limit of a topological net.
A function's limit is typically expressed in formulas as
\(\lim_{x \to c } F(x) = L\)
It is typically used to assign values to specific functions at locations where none are defined while maintaining consistency with existing values.
\(F(x) = -x+8 ,x\leq 0\)
\(F(x) = 4x+9 , if x > 0\)
\(\lim_{x \to 0^{+} } F(x) = \lim_{n \to 0^{+} } (4x+9) = 9\)
\(\lim_{x \to 0^{-} } F(x) = \lim_{x \to 0^{-} } (-x+8) =8\)
\(\lim_{x \to 0^{+} } F(x) \neq \lim_{x \to 0^{-} } F(x)\)
So limit doesn't exist
For limit to exist
\(\lim_{x \to 0^{+} } F(x) = \lim_{x \to 0^{-} } F(x) = \lim_{x \to 0} f(x)\)
must be satisfied
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