We can write radicals [tex]9^{\frac{3}{2}[/tex] as [tex](3^2)^{\frac{3}{2}[/tex] forms to help us communicate our answers.
What are surds and indices?We know there are two types of radicals one is surds when the number has been raised by such power that it is greater than zero and less than one,
The other type of radicals are indices where a number is raised to such power that is greater than one.
Suppose, We have a radical [tex]16^{\frac{1}{4}[/tex].
Now, We know 2⁴ = 16.
So, We can rewrite [tex]16^{\frac{1}{4}[/tex] as [tex](2^4)^{\frac{1}{4}[/tex] and multiply the exponents which
results to 1.
Again say we have [tex]9^{\frac{3}{2}[/tex] and we know 3² = 9, Se we can rewrite [tex]9^{\frac{3}{2}[/tex] as [tex](3^2)^{\frac{3}{2}[/tex] , and the exponent multiplies to 3 so it is now 3³ which is 27.
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I need a real answer with solution please help.
Answer:
A and D
Step-by-step explanation:
Given the function:
[tex]\displaystyle{f(x)=\sqrt{5-x^2}}[/tex]
In order to find the first-order derivative of square root function, we have to convert the form of surd to exponent form. Therefore:
[tex]\displaystyle{f(x)=\left(5-x^2\right)^{\frac{1}{2}}}[/tex]
Since the exponent is a constant and that the base is an expression with variable, we can apply the chain rule (power rule variation):
[tex]\displaystyle{f(x) = u^n \to f'(x) = nu^{n-1} \cdot \dfrac{du}{dx}}[/tex]
Therefore:
[tex]\displaystyle{f'(x)=\dfrac{1}{2}\left(5-x^2\right)^{\frac{1}{2}-1} \cdot \dfrac{d}{dx}\left(5-x^2\right)}\\\\\displaystyle{f'(x)=\dfrac{1}{2}\left(5-x^2\right)^{\frac{1}{2}-\frac{2}{2}} \cdot \dfrac{d}{dx}\left(5-x^2\right)}\\\\\displaystyle{f'(x)=\dfrac{1}{2}\left(5-x^2\right)^{-\frac{1}{2}} \cdot \dfrac{d}{dx}\left(5-x^2\right)}[/tex]
Deriving 5 - x²:
[tex]\displaystyle{\dfrac{d}{dx}\left(5-x^2\right) = 0 - 2x^{2-1}}\\\\\displaystyle{\dfrac{d}{dx}\left(5-x^2\right) = -2x}[/tex]
Thus:
[tex]\displaystyle{f'(x)=\dfrac{1}{2}\left(5-x^2\right)^{-\frac{1}{2}} \cdot (-2x)}\\\\\displaystyle{f'(x)=\dfrac{1}{2}(-2x)\left(5-x^2\right)^{-\frac{1}{2}} }\\\\\displaystyle{f'(x)=-x\left(5-x^2\right)^{-\frac{1}{2}} }[/tex]
You can also convert to the square root form of:
[tex]\displaystyle{f'(x)= \dfrac{-x}{\sqrt{5-x^2}}}[/tex]
Therefore, A and D are correct.
1. Find Sn for the arithmetic series where a1= 3 , an= 42 , n= 14
2. Find sn for the arithmetic series where a1= −20 , n= 25 , an= 148
3. Find sn for the arithmetic series where a1=5 , d=1/2 , n=13
The value of the sum of the series is are 315, 1600 and 104
How to determine the sum of the seriesIn an arithmetic series, the sum of the first "n" terms (Sn) is given by the formula:
Sn = n/2 * (a1 + an)
Where "a1" is the first term and "an" is the nth term.
For the first series, we have
In this series, a1= 3 , an= 42 , n= 14
Plugging these values into the formula, we get:
Sn = 14/2 * (3 + 42)
Sn = 315
For the second series, we have
In this series, a1= −20 , n= 25 , an= 148
Plugging these values into the formula, we get:
Sn = 25/2 * (-20 + 148)
Sn = 1600
For the third series, we have
In this series, a1=5 , d=1/2 , n=13
So, we have
an = a + (n - 1)d = 5 + 12 * 1/2 = 11
Plugging these values into the formula, we get:
Sn = 13/2 * (5 + 11)
Sn = 104
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There are 45
students in the University Travel Club. The following information and Venn diagram show how many students traveled to Germany, France, and Spain. How many students have been to Germany or Spain but not France?
20
members have visited Germany
20
have been to Spain
19
have visited France
10
have been to Germany and France
4
have only been to Germany
6
have only been to France
3
have been to only Spain and France
3
have been to all three countries
Some of the members have not been to any of the three
The number of students that have been to Germany or Spain but not France is given as follows:
18.
How to obtain the amounts?The amounts are obtained considering the Venn diagram in the problem.
For the 20 students that went to Spain, we have that:
x went only to Spain.3 have gone to Spain and France.3 have gone to Spain, Germany and France.6 have gone to Spain and Germany.Hence the value of x is obtained as follows:
x + 3 + 3 + 6 = 20
x + 12 = 20
x = 8.
The number of people who have gone to Spain or Germany but not France is given as follows:
6 + 4 + 10 = 18.
(or means at least one of Spain or Germany).
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Someone help quick please
Y=5+3x for x
For the equation Y=5+3x the solution for x is (y-5)/3=x.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given equation is Y=5+3x
y equal to five plus three times of x
In the given equation x and y are the variables.
We have to solve for variable x.
Subtract 5 from both the sides
y-5=3x
Divide both sides by 3
(y-5)/3=x
Hence, for the equation Y=5+3x the solution for x is (y-5)/3=x.
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Good morning,
My name is Mr. Shine (I was given that name because I have the most sparkly diamonds in the
midwest). I am forwarding you the bill for your client Mr. Spendalot who stopped by my store Ice
Box last evening. I have exactly $1,000,000 in inventory of the best diamond rings, necklaces,
cuban chains, grilles, and watches. Now, I must make a profit on this inventory, so I markup all
inventory by 150% before selling it to my loyal customers.
Your client bought a whopping 31% of my entire inventory. He said my special was just too good
to pass up and he just had to buy more more more. What’s that special you ask?
Discounted Special:
Spend 100k+ and get 10% off
Spend 250k+ and get 20% off
Spend 500k+ and get 30% off
Spend 750k+ and get 40% off
Spend 1 million+ and get 50% off
After giving him this discount, I of course had to charge him an 8.5% sales tax on his purchase.
Yes I know, we all hate taxes, but that’s just the cost of doing business. Now your client Mr.
Spendalot is a very kind man and he agreed to give me and my staff a tip of 15%, how
generous of him! He told me to send you the details and you, his accountant, will calculate the
total. If you get this total right, he said he’s giving you the brand new Lamborghini he purchased
at the dealership next door to my store. Must be nice, hopefully you are good at your job!
Good Luck,
Mr. Shine
Answer:
The task is to calculate the total amount spent by Mr. Spendalot. To do this, you need to calculate the amount of inventory purchased, apply the discount, calculate the sales tax, and add the tip. Here's one way to do it:
Calculate the amount of inventory purchased: 31% of $1,000,000 is 31/100 * $1,000,000 = $310,000
Determine the discount: Based on the purchase amount of $310,000, Mr. Spendalot qualifies for a discount of 10%. So, the discount is $310,000 * 10% = $31,000.
Calculate the sales tax: 8.5% of the purchase amount after discount is 8.5/100 * ($310,000 - $31,000) = $2,067.50
Add the tip: 15% of the purchase amount after discount and sales tax is 15/100 * ($310,000 - $31,000 + $2,067.50) = $52,101.13
Calculate the total: The total amount spent by Mr. Spendalot is ($310,000 - $31,000 + $2,067.50 + $52,101.13) = $393,168.63.
So, the total amount spent by Mr. Spendalot is $393,168.63.
Step-by-step explanation:
Determine the amount of purchase before discount: Mr. Spendalot bought 31% of Mr. Shine's inventory, which is $1,000,000. Therefore, his purchase before discount is 31% of $1,000,000, or $310,000.
Calculate the discount: Based on the information in the discount table, Mr. Spendalot's purchase qualifies for a 40% discount. Therefore, the discount amount is $310,000 * 40%, or $124,000.
Determine the amount of purchase after discount: After getting the 40% discount, Mr. Spendalot's purchase is $310,000 - $124,000, or $186,000.
Calculate the sales tax: Mr. Shine charged an 8.5% sales tax on Mr. Spendalot's purchase after discount. Therefore, the sales tax amount is $186,000 * 8.5%, or $15,791.
Determine the tip: Mr. Spendalot gave Mr. Shine and his staff a 15% tip on his purchase after discount and sales tax. Therefore, the tip amount is $186,000 + $15,791 * 15%, or $31,328.
Calculate the total cost: Adding up the purchase after discount, sales tax, and tip, we get the total cost of $186,000 + $15,791 + $31,328, or $233,119.
Conclusion: Mr. Spendalot's total purchase cost is $233,119.
The task requires you to calculate the total amount spent by Mr. Spendalot at Mr. Shine's store Ice Box. Mr. Shine has an inventory worth $1,000,000 which he marks up by 150%. Mr. Spendalot bought 31% of this inventory, and was given a discount based on the amount he spent:
Spend 100k+ and get 10% off
Spend 250k+ and get 20% off
Spend 500k+ and get 30% off
Spend 750k+ and get 40% off
Spend 1 million+ and get 50% off
After the discount, Mr. Spendalot was charged 8.5% sales tax. He also left a 15% tip for Mr. Shine and his staff. Your goal is to calculate the total amount spent by Mr. Spendalot.
The nearest whole number of 7 and 3/8
Answer:
7
Step-by-step explanation:
A tugboat traveled -1.5 miles in 0.3 hours what was its velocity
Velocity of tugboat is -5 miles/hour .
What is velocity?The velocity of an object is the change in position (displacement) over a time interval. Velocity includes both speed and direction, thus velocity can be either positive or negative while speed can only be positive.
Given,
Displacement by tugboat = - 1.5 miles
Time taken in travelling = 0.3 hours
Velocity = Displacement/ Time
= - 1.5 / 0.3
= - 5 miles/hours
Hence, -5 miles/hour is Velocity of tugboat.
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if you invest $550 at a 4% interest rate will be the interest
Answer:
22
Step-by-step explanation:
550x4%=550x0.04=22
Answer:
$22
Step-by-step explanation:
550 x 4% = 550 x 0.04 = $22
If the terminal side of angle θ goes through the point (8/17,−15/17) on the unit circle, then what is cos(θ)?
The cosine of the angle θ is 8/17 whose terminal side passes through the given point
What are trigonometric functions?In mathematics, trigonometric functions are real functions that relate an angle of a right-angled triangle to ratios of two side lengths. The six trigonometric functions are Sine, Cosine, Tangent, Secant, Cosecant, and Cotangent
Given here: The terminal side goes through the point (8/17, -15/17)
Thus we have cosθ =8/17 and sin θ =-15/17
now tan θ =sinθ /cosθ
tanθ = -15/8
θ = -61.9275
Hence, cosθ =8/17
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Figure A is a scale image of Figure B, as shown.
1³/
Figure A
Figure B
The scale that maps Figure A onto Figure B is 1 : 71
Enter the value of z.
Therefore , the solution of the given problem of linear equation comes out to be x = 21.75.
A linear equation is precisely what?A linear regression curve is built on the equation y=mx+b. The y-intercept is m, and the slope is B. The previous sentence is sometimes referred as a "mathematical equation merging multiple variables," even if y or y are independent parts. The only variables in bivariate linear equations are two. There are no known solutions to application issues involving linear equations. Y=mx+b, also written as mx+b, is the expression for a straightforward system of equations.
Here,
Given :
From a mixed number, you must convert it to a decimal number. You can do this by following the instructions below:
In order to start, you must reduce the fraction's denominator by its numerator.
Step 2: You must now multiply the resulting quotient by the whole number component.
You therefore obtain:
=> 7 1/4 = 7 + 0.25 = 7.25
The scale picture that transforms "Figure a" into "Figure b" is then: 1: 71
The specified length of the appropriate side of "Shape a" must then be multiplied by in order to determine the value of "z."
The outcome is as follows:
=>x = (3)(7.25)
=> x = 21.75
Therefore , the solution of the given problem of linear equation comes out to be x = 21.75.
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The complete question is "Figure a is a scale image of figure b the scale that maps figure a onto figure b is 1:7 1/4 enter the value of x
Both figures are triangles
Figure a is smaller than figure b
Figure a to the right has a 3
Figure b to the right has a x"
ASSIGNMENT
1. Suppose the demand function for a product is given
by: Qa = 500 - 5P, compute the:
(a) quantity demanded at the unit price of Ghé 10
(b) price to sell 200 units
(c) price for zero demand
(d) quantity demanded at zero price
(e) the own-price elasticity of demand at the price for
which 200 units are sold.
The value of quantity demanded at unit price Gh¢10 is 450 units. b. The price to sell 200 units is Gh¢60. c. The price for 0 demand is Gh¢100. d. The quantity demanded at zero price is 500 units.
What is demand function?The link between the quantity demanded for a commodity (the dependent variable) and its price is represented by the demand function (independent variable).
a) At the price of Gh¢10 , then
Qd= 500 - 5P
Qd= 500 -5(10)
Qd= 500-50 = 450 units
The value of quantity demanded at unit price Gh¢10 is 450 units.
b) If there are 200 units,then
Qd= 500- 5P
200 = 500-5P
5P = 500-200
P= 300/5
P= Gh¢60
The price to sell 200 units is Gh¢60
c) if demand is zero, it mens Qd= 0
Qd= 500- 5P
0= 500-5P
5P= 500
P= Gh¢100
The price for 0 demand is Gh¢100.
d) If P= 0, then
Qd= 500-5P
Qd= 500-5(0)
Qd= 500 units
The quantity demanded at zero price is 500 units.
Hence, the value of quantity demanded at unit price Gh¢10 is 450 units. b. The price to sell 200 units is Gh¢60. c. The price for 0 demand is Gh¢100. d. The quantity demanded at zero price is 500 units.
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Evaluate the function find h (6) if h (x) = 2x + 1
Answer:
h(6) = 13
Step-by-step explanation:
Functions! One of my favorites to answer :)
h(x) = 2x + 1
So, now we plug in h(6). Remember that when we replace the x with the number, we replace it in the right side of the equation as well:
h(6) = 2(6) + 1
Now we multiply 2 * 6:
h(6) = 12 + 1
Now 12 + 1:
h(6) = 13, final answer.
Hope this helps :D
Answer: 13
Step-by-step explanation:
h(x) = 2(x) + 1
h(6) = 2(6) + 1 = 12 + 1 = 13
PLEASE HELP!! ILL GIVE BRAINLIEST!!!
The area enclosed by the track is 7,530.64 m².
What are the circumference and diameter of a circle?The circumference of a circle is the distance around the circle which is 2πr.
The diameter of a circle is the largest chord that passes through the center of a circle it is 2r.
We know, The area of a circle is πr² and the area of a rectangle is (length×width).
By observing the diagram the total area enclosed by the track is the
sum of the area of a rectangle having a length of 104m and a complete circle having a diameter(2r) of 52 m and the diameter is equal to the width of the rectangle.
Therefore, The area of the track is,
= (104×52) + π(26)².
= 5408 + 2,122.64 m².
= 7,530.64 m².
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Find the mean for the number of hours of sleep: 6 7 5 8 6 7 6 8
66
6.7
7
6.625
66.25
The mean of the numbers is 22.625
How to find the mean?The average of all the data in a set. The arithmetic mean is the simplest and most widely used measure of a mean, or average. It simply involves taking the sum of a group of numbers, then dividing that sum by the count of the numbers used in the series.
The mean or average of the set of the data is calculated thus
(6+7+5+8+6+7+6+8)/8
181/8 = 22.625
Therefore, the mean for the number of hours of sleep: 6 7 5 8 6 7 6 8 is 22.625
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What is the surface area of the right rectangular prism? 125 m 2 75 m 2 250 m 2 200 m 2
The surface area of a right rectangular prism is 250 m².
Option C is the correct answer.
What is a prism?A prism is a three-dimensional object.
There are triangular prism and rectangular prism.
We have,
From the figure,
Width = w = 5 m
Height = h = 5 m
Length = l = 10 m
The surface area of a right rectangular prism.
= 2 (lw + lh + wh)
= 2 (10 x 5 + 10 x 5 + 5 x 5)
= 2 (50 + 50 + 25)
= 2 (125)
= 2 x 125
= 250 m²
Thus,
250 m² is the surface area of a right rectangular prism.
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Answer:
250m 2
I hope this helps <3
evaluate the following 2x²+3x+4 if x=1
(x+y) (x+y) if x=2 and y=2
5x² +2x if x=2 and y=5
(x+y)³ if x=7 and y=3
The value of the expressions will be:
2x² + 3x + 4, when x=1 is equal to 9.
(x+y)², when x=2 and y=2 is equal to 16.
5x² + 2x, when x=2 is equal to 24.
(x+y)³, when x=7 and y=3 is equal to 1000.
How to calculate the expression2x² + 3x + 4, when x=1 is:
= 2(1)² + 3 + 4
= 2 + 3 + 4
= 9.
(x+y)², when x=2 and y=2 is equal to:
= (2 + 2)²
= 4²
= 16.
5x² + 2x, when x=2 is equal to:
= 5(2)² + 2(2)
= 20 + 4
= 24.
(x+y)³, when x=7 and y=3 is equal to:
= (7 + 3)³
= 10³
= 1000.
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the team to win 3 games wins the playoffs. what is the probability of a team winning a 5 game playoff if it has 50% chance of winning each game
Therefore , the solution of the given problem of probability comes out to be probability of winning a 3 game out of 5 is 0.5 .
What specifically does the probability method entail?Calculating the likelihood that a statement is true or that an event will take place is the focus of probability theory, a branch of mathematics. Any quantity between 0 and 1, whereby 1 frequently represents certainty range 1 and 0 normally denotes possibility, can be used to represent chance. A probability diagram illustrates the likelihood that a particular event will take place.
Here,
Given :
Since,
the probability to win a game is 50% .
So they have to win 3 games ,
and so , the probability to win the game is:
=> 1/2 * 1
=> 0.5
thus,
probability of winning a 3 game out of 5 :
=> 0.5
Therefore , the solution of the given problem of probability comes out to be probability of winning a 3 game out of 5 is 0.5 .
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(x⁵ - 7x⁴ + 3x² - 8) : (x² - 3x + 1)
Answer:
x³ - 4x² + 3x - 8. is the answer.
kirans mother gets a restuarant bill for 25$ she has a coupon for 15% off what is the amount after the discount is applied
The amount after the discount is applied would be $21.25.
What is the percentage?
The percentage is defined as a ratio expressed as a fraction of 100.
As per the question, the given data as:
Bill amount = 25$
Coupon for 15% off
The amount after the discount can be calculated as:
⇒ 25$ - 15% of 25$
15% is expressed as 15/100 in fractional form
⇒ 25 - (15/100)(25)
15/100 is expressed as 0.15 in decimal form
⇒ 25 - (0.15)(25)
⇒ 25 - 3.75
⇒ 21.25
Thus, the final amount would be $21.25.
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1 whole number 1/16 to decimal 50 points pls full solution
Answer:
Below
Step-by-step explanation:
1/16 is 1 ÷ 16 use calculator to find = .0625
Answer:
1.06
Step-by-step explanation:
Step 1: divide numerator (1) by the denominator (16):
1 ÷ 16 = 0.0625
Step 2: add this value to the integer part:
1 + 0.0625 = 1.0625. So,
1 1/16 = 1.0625
When throwing two fair six sided dice, what is the probability that the sum of the values on the two dice is 11?
Answer:
2/36
Step-by-step explanation:
there are a total of 36 possible rolls
and the only to ways to get an 11 on two fair six-sided dice is when it is (5,6) or (6,5)
It was an extremely cold day on the mountain. The temperature dropped 22 degrees to -13 Degrees F. What was the temperature before the drop?
If the temperature dropped 22 degrees to -13 Degrees F, the temperature before the drop was 9 Degrees F.
What is temperature drop?Temperature drop refers to a decrease in the temperature of a system or environment.
This decrease can be measured in units of temperature such as degrees Celsius or Fahrenheit, and it can occur due to a variety of reasons such as changes in atmospheric conditions, the loss of heat from a body or system, or other physical processes.
The initial temperature is calculated by
initial temperature = final temperature + temperature drop
initial temperature = -13 + 22
initial temperature = 9
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which direction does the graph of the equation shown below open v^2-4x+4y-4=0
The graph of the equation x^2 - 4x + 4y - 4 = 0 is a circle, so it doesn't have a direction of opening.
How to detemrine the directionFrom the question, we have the following parameters that can be used in our computation:
x^2 - 4x + 4y - 4 = 0
The equation x^2 - 4x + 4y - 4 = 0 is of a conic section
i.e. the equation of a circle
The equation of a circle does not have a particular direction it opens to
Hence, it is a closed shape
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Help I don’t get this question
well, we can simply find how much for each tulip in each store.
store left has them for £9.8 for 4, that means 9.8 / 4 = 2.45, so £2.45 for each tulip.
store right had them for £4.2 each, but they went down by 1/3, so hmm a whole is 3/3 so if we take away 1/3 from 3/3, 3/3 - 1/3 = 2/3, so the new discounted price is really 2/3 of £4.2, that's (2/3) * 4.2 = 2.8, so £2.8 each.
so store left has them cheaper, doesn't matter at a dozen or less or more.
how much is it at store left for 12? 12 * 2.45 = 29.4, or £29.4.
solve the following inequalities sketch a number line - (x + 5 +) greater than 2 (1 - x)
When graphed, a linear equation always produces a straight line since each element in the equation has an exponent of 1.
What are examples of linear equations?Ax+By=C is the usual form for two-variable linear equations. A standard form linear equation is, for instance, 2x+3y=5. When an equation is given in this format, finding both intercepts is rather simple (x and y).
What three types of linear equations are there?The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.
Given, 3x−2<2x+1
⇒3x−2x<1+2
⇒x<3 or x∈(−∞,3)
At x=3, the lines y=3x-2 and y=2x+1 will both intersect.
The dark line unmistakably depicts the 3x-2<2x+1 solution.
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How many gallons of a 34% sugar solution do we need to mix with 96 gallons of a 10% sugar solution so that the resulting mixture is an 18% sugar solution?
On solving the provided question, we can say that by percentage 9.6 gallons of a 34% sugar solution do we need to mix with 96 gallons of a 10% sugar solution
What is percentage?A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. It is frequently denoted using the percent symbol "%," though. The amount of percentages has no dimensions. With a denominator of 100, percentages are basically fractions. To show that a number is a percentage, place a percent symbol (%) next to it. For instance, if you correctly answer 75 out of 100 questions on a test (75/100), you receive a 75%. To compute percentages, divide the amount by the total and multiply the result by 100. The percentage is calculated using the formula (value/total) x 100%.
by percentage
mix with 96 gallons of a 10% sugar solution
the resulting mixture is an 18%
10/100 X 96 = 9.6
9.6 gallons of a 34% sugar solution do we need to mix with 96 gallons of a 10% sugar solution
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worth 60 points!! question 2)
Answer:
y = 4
Step-by-step explanation:
the equation of the midline is the average of the sum of the maximum and minimum values.
maximum value = 6
minimum value = 2
then
y = (6 + 2) ÷ 2 = 8 ÷ 2 = 4
y = 4 ← equation of midline
PLS HELP THIS IS DUE TODAY
1. PM:MQ and KM:ML (Given)
2. KM/MQ = PM/ML (Property of cross multiplication)
3. ∠ PMK = ∠ LMQ (vertical angles are congruent)
4. ΔPMK ~ ΔLMQ (SAS~)
What are similar triangles?Similar triangles are triangles that have the same shape, but their sizes may vary, if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.
Given,
PM:MQ and KM:ML
To prove
ΔPMK ~ ΔLMQ
By the figure,
PM:MQ = KM:ML (Given)
Cross multiplying
KM/MQ = PM/ML
∠ PMK = ∠ LMQ (vertical angles)
Using Side - Angle - Side theorem
ΔPMK ~ ΔLMQ
Hence,
1. PM:MQ = KM:ML , since its given
2. KM/MQ = PM/ML using cross multiplication
3. ∠ PMK = ∠ LMQ both are vertical angles
4. ΔPMK ~ ΔLMQ using side-angle-side theorem of similarity
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Adam sells pencils for $2.50 per dozen. The expression [Drop Down 1] represents the [Drop Down 2], where
a represents the number of dozen pencils sold.
The total revenue can be calculated as "2.50a" dollars.
What is the dozen?
A dozen is a grouping of twelve objects, shapes, or numbers. It is abbreviated as doz or dz. Dozen is one of the most primitive customary units of numbers. The number system with the base number 12 is called duodecimal or dozenal.
In this scenario, Adam is selling pencils in dozens and the price he charges for each dozen is $2.50.
To calculate the total revenue, we need to multiply the number of dozens sold (represented by "a") with the price per dozen ($2.50).
The expression "2.50a" represents this calculation, where "a" represents the number of dozens sold and "2.50" represents the price per dozen.
Hence, the total revenue can be calculated as "2.50a" dollars.
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Parker draws a circle with an area of
40 squared
. He challenges Lauren to draw a circle that has a radius
4 times bigger than the radius of his circle.
what is the estamaited area of laurens circle
The estimated area of Laurens's circle is 642 squared.
What is a circle?A circle is a two-dimensional figure with a radius and circumference of 2πr.
The area of a circle is πr².
We have,
Parker:
Area = 40 squared
This means,
πr² = 40
r² = 40/3.14
r² = 12.74
r = √12.74
r = 3.6
Laurens:
r = 4 x 3.6
r = 14.3
Area = πr²
Area = 3.14 x 14.3 x 14.3
Area = 642
Thus,
Laurens's circle area is 642 squared.
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