40 gallons
[tex]\frac{525}{25} \times 40=840[/tex] miles
Gas Mileage
[tex]\frac{525}{25}=21[/tex] miles per gallon
compute, using integration, the area of a circle of radius r centered at the origin by considering this as the area of a region bounded by two curves.
The area of the circle of radius r centered at the origin is π[tex]a^{2}[/tex]
Since the circle is symmetrical in relation to the x and y axes, we can calculate the area of a quarter of a circle and multiply it by 4 to get the entire circle's area.
The equation y y = + mn [a 2 - x 2] must be solved.
Y = [a 2 - x 2] = a [1 - x 2 / a 2] is the equation for the upper semicircle (y positive).
Using integrals, we can calculate the area of the circle's top right quarter as shown below.
(1 / 4) Circle's area is equal to 0a a [1 - x 2 / a 2]. dx
Let's replace x/a with sin t to make sin t equal to x/a, dx equal to a cos t dt, and the area is given by
The formula for area of a circle is (1 / 4) Area of circle = 0/2 a 2 (1 - sin2 t) cos t dt
Now that t can range from 0 to /2, we utilize the trigonometric identity [1 - sin2 t] = cos t, which equals (1 / 4) Circle area equals 0/2 a 2 cos2 t dt.
To linearize the integrand, use the trigonometric equation cos2 t = (cos 2t + 1) / 2;
(1 / 4) Circle's area is equal to 0/2 a (cos 2t + 1) / 2 dt.
the integral (1 / 4) be evaluated. Circle's area is equal to (1/2) a2 [(1/2) sin 2t + t]. 0π/2\s= (1/4) π a 2
The circle's entire area is calculated by multiplying by 4.
Area of a circle is equal to 4 * (1/4) a 2 a 2. additional references on integrals and calculus applications.
Area of circle = 4 * (1/4) π a 2 = π a 2 More references on integrals and their applications in calculus.
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4(w − 971) = –384
w =
Stuck
Step-by-step explanation:
you can ask questions for clarification
boiling an egg physcal or chemcal
Answer:
it's a chemical change.
Step-by-step explanation:
a raw egg is converted into a hard boiled one by chemical changes happening inside it. Its also an irreversible change
Solve the inequality 3(x-2) + 12x + 2(x+2).
O A. x≤4
Co B. x2-5
C. no solution
OD. all real numbers
The inequality x > 0 , x all real numbers .
What do you mean by inequality?
The phenomena of unequal and/or unjust allocation of resources and opportunities among members of a certain society is referred to as inequality. Different persons and contexts may interpret the word "inequality" differently.The most notable instances of social inequality include those related to health care, social class, gender inequality, and wealth disparity.= 3(x-2) + 12x + 2(x+2)
= 3x - 6 + 12x + 2x + 4
= 12x + 2x + 3x -6 + 4
= 17x - 2
17x - 2 = 0
x = 2/17
x > 0 , x all real numbers ..
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Belinda wants to invest $1,000. The table below shows the value of her investment under two different options for three different years:
Number of years 1 2 3
Option 1 (amount in dollars) 1100 1210 1331
Option 2 (amount in dollars) 1100 1200 1300
Part A: What type of function, linear or exponential, can be used to describe the value of the investment after a fixed number of years using option 1 and option 2? Explain your answer. (2 points)
Part B: Write one function for each option to describe the value of the investment f(n), in dollars, after n years. (4 points)
Part C: Belinda wants to invest in an option that would help to increase her investment value by the greatest amount in 20 years. Will there be any significant difference in the value of Belinda's investment after 20 years if she uses option 2 over option 1? Explain your answer, and show the investment value after 20 years for each option. (4 points)
A) The type of function that can be used to describe the value of the investment after a fixed number of years using option 1 and option 2 are respectively; Linear Function and Exponential function.
B) One function for each option to describe the value of the investment f(n), in dollars, after n years.;
Option 1; f(n) = n + 100
Option 2; f(n) = n + 100x
C) The amount from option 1 after 20 years would be 3000 and the amount from option 2 after 20 years would be 4900
How to solve Linear functions?A) For option 1, the linear function can be used to describe the value of the investment after a fixed number of years. This reason is that, in option one, the amount increases by a fixed amount every year.
For option 2, the exponential function can be used to describe the value of the investment after a fixed number of years. The reason is that, in option 2, the amount increase is higher than the previous year.
B) For option 1, the function is;
f(n) = n + 100
For option 2, the function is;
f(n) = n + 100x
C) After 20 years, the amount from option 1 would be 3000 and the amount from option 2 would be 4900. Thus, there is a difference of 1900.
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Dion received a paycheck for $800.00 and he wants to invest it in a savings account. A savings account at bank A earns 8% interest compounded monthly and a savings account at bank B earns 9% simple interest. If Dion plans to deposit the $800.00 and leave it in the account for 2 years, at which bank would he earn more interest? A. bank B B. The interest earned cannot be calculated from the given information. C. bank A D. The interest earned at both banks will be the same.
Answer:
A. Bank B
Step-by-step explanation:
First the formulae necessary to calculate compound and simple interest
P = principal = amount deposited
r = interest rate as a decimal (i% interest => r = i/100)
t = number of years
n = number of times compounded
[tex]\text{Compound Interest }= P\left(1 + \dfrac{r}{n}\right)^{nt} - P[/tex]
In this case, we have P = 800
r = 8/100 = 0.08
n = 12 since the interest is compounded monthly
t = 2 years
So compound interest
[tex]CI = 800\left(1 + \dfrac{0.08}{12}\right)^{12 \times 2} - 800\\\\CI = 800(1.00667)^{24} - 800\\\\\\CI = 938.31 - 800\\\\CI = $138.31[/tex]
For Bank B, the interest is calculated at 9% annually and the interest is given by the formula
SI = P x r x t
SI = 800 x 0.09 x 2 (r = 9%/100 = 0.09)
SI = $144.00
So depositing in bank B is preferred
Doug dives from a platform that is 5 meters above water. dive takes 1.8 meters below the surface of the water. How far does 's dive take ?
Doug dives a total distance of 6.8 meters from the platform to the bottom of the sea.
What is a numerical expression?A numerical expression is algebraic information stated in the form of numbers and variables that are unknown. Information can is used to generate numerical expressions.
We have been given that a Doug dives from a platform that is 5 meters above the water.
His dive takes him 1.8 meters below the surface of the water.
To determine the total distance Doug dived, add the height of the platform above water and the distance he dived below water.
= (5 + 1.8) meters.
= 6.8 meters.
Thus, Doug dives a total distance of 6.8 meters from the platform to the bottom of the sea.
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How many gallons of water will be in the
fish tank after 3 minutes? Explain your
reasoning (HURRY I NEED THIS ANSWER STEP BY STEP )
As a result, 4.8 litres of water will be in the fish tank after three minutes if the water release rate is 1.6 gallons per minute.
What is the concept of Linear system?A linear system is a mathematical representation of a system in systems theory that relies on the application of a linear operator. Compared to nonlinear systems, linear systems often have significantly simpler traits and properties. Linear systems are widely used in automatic control theory, signal processing, and telecommunications as a mathematical abstraction or idealization.
for 0.5 minutes , 0.8 gallons of water is required
To convert to gallons per minute, multiply by 2.
1.6 gallons per minute (0.8 x 2)
Gallons per minute multiplied by three minutes
3.0 minutes = 4.8 liters (1.6 x 3)
Therefore, 4.8 litres of water will be in the fish tank after 3 minutes if per minute water released is 1.6 gallons
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The complete question is:
How many gallons of water will be in the fish tank after 3 minutes? 0.5 mins = 0.8 gallons
A cyclist leaves New York traveling at an average speed of 9 miles per hour. 4 hours later, a car leaves Bay Shore, on the same route, traveling at an average speed of 21 miles per hour. How many hours after the car leaves New York will the car catch up to the cyclist?
The car will catch up the cyclist 3 hours after it starts moving.
In how many hours the car will catch up the cyclist?The cyclist travels at 9 miles per hour, and travels for 4 hours before the car starts moving, so the equation for the position of the cyclist as a function of time, t, is:
C(t) = 9*4 + 9*t = 36 + 9*t
And the car moves at 21 miles per hour, then the position is:
P(t) = 21*t
The car will catch the cyclist when:
C(t) = P(t), this gives:
36 + 9*t = 21*t
36 = 21*t - 9*t = 12*t
36/12 = t
3 = t
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Please help me with this lesson on ixl! I don't understand.
Answer:
8/25
Step-by-step explanation:
change the 5/4 into a 4/5 and change the divide into a mulltiple while you do this
then multiply 2 x 5 = 8
5 x 5 = 25
let g be a translation 2 units up, followed by a reflection in the x-axis and vertical stretch by a factor of 4 of the graph of f(x)=x2
The equation the function after the transformation is g(x) = -4x² - 8
How to determine the transformation of the function?The equation of the function is given as
f(x) = x²
The sequence of transformations is given as follows:
Translate up by 2 unitsReflection across the x-axisVertically stretched by a factor of 4When the above transformations are combined, we have:
Translate up by 2 units: g(x) = f(x) + 2Reflection across the x-axis: g(x) = -(f(x) + 2)Vertically stretched by a factor of 4: g(x) = -4(f(x) + 2)So, we have
g(x) = -4(x² + 2)
Expand
g(x) = -4x² - 8
Hence, the function g(x) is g(x) = -4x² - 8
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Red letters and blue letters are used in a game. Some of the letters are X. All the other letters are Y. X Y X Y The ratio of the number of red letters to the number of blue letters is 2:5 The ratio of the number of red Xs to the number of red Ys is 1: 3 The ratio of the number of blue Xs to the number of blue Ys is 3:1 Work out what fraction of all the letters are Xs.
17/28 of all the letters are X's.
Please help me I keep getting the wrong answer :(
Answer:
Step-by-step explanation:
Problem 2:
Count the blocks.
You can find 1 1000 block
You can find 2 100 block
You can find 3 10 block
You can find 6 1 block.
Together it is 1236.
Problem 3:
Expanded notation is the number listed in groups of base 10. To solve, just put the number of blocks and the block number.
(1 x 1000)+(2 x 100)+(3 x 10) + (6 x 1)
Problem 4:
Find the number between the clues.
Since A is close to 100 and less than 100, you could put 75, which is close to 100 but not quite enough.
Since B is pretty close to a 100 but greater than 100, you could put 110.
Since C is in the middle of both 100 and 200, you could put 150 because it's in the middle of both numbers.
Since D is in between C which is 150 and 200, you could put 175 as that is half of both numbers.
Since E is close to 200 but bigger than D which is 175, you could put 180.
bro please
Which graph represents the inequality 2.5 is less than the product of −0.5 and a number?
number line with open circle on point 0.2 and arrow shaded to the left
number line with open circle on point negative 5 and arrow shaded to the left
number line with open circle on point negative 0.2 and arrow shaded to the right
number line with open circle on point negative 5 and arrow shaded to the right
A graph represents the inequality 2.5 is less than the product of −0.5 and a number is: D. number line with open circle on point negative 5 and arrow shaded to the right.
What is a number line?A number line can be defined as a type of graph with a graduated straight line which is composed of both positive and negative numbers that are placed at equal intervals along its length.
In order to solve this word problem, we would assign a variable to the number and then translate the word problem into an algebraic equation as follows: Let x represent the number.
Translating the word problem into an algebraic equation, we have;
2.5 < -0.5x
Next, we would solve the given inequality as follows:
2.5/0.5 < -0.5x/0.5
5 < -x
x > -5
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y=−2x+4y, equals, minus, 2, x, plus, 4
Complete the missing value in the solution to the equation.
The missing value in the solution to the equation y = -2x+4y is y.
According to the question,
We have the following information:
y = -2x+4y
y equals minus 2 x plus 4.
Now, look at the equation, we know that the solution of y is -2x+4y.
Now, the statement that is given is incomplete because we have 4 is multiplied by y.
(More to know: this equation can be further solved. We have y = -2x+4y. Now, we can move the same variables to one side. So, we have -3y = -2x. Now, the two negative signs when divided gives the positive result.)
Hence, the statement can be completed by y.
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Please help me asap!!!!! Worth 20 points
Answer:
Step-by-step explanation
Third, second, first.
The third has 5% chance that it will get the investor its money back, second having a 34% of the investor getting its money back, and the first having a 54% chance. Hope this was quick enough for you!
Oct 13, 5:31:26 PM
My Stu...
Tasks -...
Classw...
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Violet has a points card for a movie theater.
• She receives 45 rewards points just for signing up.
She earns 2.5 points for each visit to the movie theater.
. She needs 75 points for a free movie ticket.
DeltaMa...
Which equation or tape diagram could be used to represent the context if v
represents the number of visits Violet must make to earn a free movie ticket?
Equation that can be used to represent the number of visits Violet must make to earn a free movie ticket is:
2.5v+45=75
What is an equation?A formula that expresses the equality of two expressions, by connecting them with the equals sign '= 'is called an equation
Unknowns are the variables for which the equation is solved and unknown values that satisfy the equation are called solutions.
Firstly, multiply 2.5 by the number of visits (v) to calculate how many points Violet earned in total.
Now add 75 to the product of 2.5(v) because Violet started with 75 points.
To find out how many times Violet would require to visit the movie theater to get a free movie ticket:
Subtract 45 from 75, that leaves you with 30, and after dividing that by 2.5, the number of points per visit comes out to be 12
Violet would need to visit the theater 12 times to earn a free movie ticket.
To check if that's right, substitute the value of 'v' in the equation,
12*2.5 + 45 = 75
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Solve for X!
Please help
In the given triangle,
sides vx and vw are equal,
and ∠v = 40°
∠w = ∠x (Adjacent angles of the equal sides of a triangle are equal)
Also, ∠v + ∠w + ∠x = 180° (Angle sum property of a triangle)
⇒ 40° + ∠x + ∠x = 180°
⇒ 2∠x = 140°
⇒∠x = 70°
What are Isosceles Triangles?The term "isosceles triangle" refers to a triangle with two equal sides. The isosceles triangle has equal sides and equal measures for two of its three angles. This results in an uneven angle. Assume that if the measure of an unequal angle is given to us, we can quickly determine the other two angles using the angle sum property. The isosceles triangle can be characterized as acute, right, or obtuse depending on the angle formed by the two legs. The isosceles triangle can be sharp if the two angles across from the legs are equal and smaller than 90 degrees (acute angle).A right isosceles triangle has two equivalent sides, one of which serves as the triangle's base and the other as its perpendicular. The third uneven side is known as the hypotenuse. As a result, we may employ the well-known Pythagoras theorem, which states that the hypotenuse's square equals the sum of its base and perpendicular squares.
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Which postulate or theorem proves A MNQA PNQ?
AAS
ASA
HL
SAS
Answer: AAS
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Which two identify the same sequence
The correct answer is options A and E.
f(x) = 6x + 4
f(1) = 6(1) + 4 = 10
f(2) = 6(2) + 4 = 16
f(3) = 6(3) + 4 = 22
[tex]\begin{gathered} \text{When n=1,} \\ a_1=10 \\ a_{n+1}=a_{1+1}=a_2=a_1+6\text{ = 10+6=16} \\ _{}when\text{ n=2} \\ a_{n+1}=a_{2+1}=a_3=a_2+6=16+6=22 \end{gathered}[/tex]Clearly, options A and E are the same sequences.
Please help me asap
y=2x+2 y=-1/2x-3 what is the solution?
•(-2,1)
•(-2,-2)
•(-2,-1)
•(2,-2)
Answer: (-2, -2)
Step-by-step explanation:
Since both equations are set equal to y,
[tex]2x+2=-\frac{1}{2}x-3\\\\\frac{5}{2}x=-5\\\\x=-2\\\\\implies y=2(-2)+2=-2\\\\\therefore (x,y)=(-2, -2)[/tex]
Evaluate a + b for a = 2 and b = 3.
Answer: 5
Step-by-step explanation: Substitute the value of the variable into the expression and simplify
Write an equation in slope-intercept form given the table:
X 0 1 2 3
Y 3 6 9 12
Answer:
y = 3x + 3
Step-by-step explanation:
The slope is 3
change in y over the change in x. As the y increases by 3, the x increases by 1. [tex]\frac{3}{1}[/tex] = 3
Use any of the points from the table to write the equation in the slope intercept form
Let's use the first point (0,3) Any point would give us the same answer.
We will use the x from the point which is 0 and use the y from the point which is 3. We will also use the slope of 3. We will plug all of these into the equation and solve for b or the y-intercept.
y = mx + b
3 = 3(0) + b
3 = 0 + b
3 = b
y = 3x + 3
The distance between Dallas and Austin on a map is about 9 centimeters. The map uses a scale in which 1 centimeter represents 20 miles. What is the actual distance between Dallas and Austin in miles?
help please
The actual distance between Dallas and Austin in miles is 180 miles.
What is Unit conversion?Conversion of units means to convert between different units of measurement for the same quantity. Example of units are - m, cm, litre.
Given is the distance between Dallas and Austin on a map is about 9 centimeters. The map uses a scale in which 1 centimeter represents 20 miles.
The maps use scale in order to depict large distances with very small length measurements. As mentioned in the question - 1 cm represents 20 miles. This scale shrinks 20 miles of distance into 1 cm
Distance between Dallas and Austin on a map - 9 cm
On map - 1 cm = 20 miles
Therefore, 9 cm will be equivalent to (9 x 20) or 180 miles.
Hence, the actual distance between Dallas and Austin in miles is 180 miles.
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what is the slope of y=5x+7
Answer: 5
Step-by-step explanation: This equation appears in the Slope-Intercept form, which is Y=Mx+B. In which Y is the coordinate, M is the slope, X is the coordinate and B is the Y-Intercept, or where the line passes the Y-Axis.
Answer: the slope of this equation is 5
Step-by-step explanation: the term "5x" represents the slope of this equation.
slope-intercept form: y = mx + b
m = slope
b = y-intercept
Martha bought yards of fabric for $1.75 per yard. Which expressions could Martha use to find out how much her fabric will cost?
Answer:C = 1.75f
Step-by-step explanation:
C = Cost
F = Fabric in yards
Depending on the amount of fabric in yards she will buy that is the amount she spends.
Name the marked angle in 2 different ways.
Answer:
Acute angle
OLN angle
Step-by-step explanation:
The length of a piece of rope is 19.5 feet. Molly needs to cut the rope into pieces 2 feet long. How many pieces can she make?
Answer: 9
Step-by-step explanation:
1. To divide by 2 you need an even number, and the closest even number below 19.5 is 18.
2. 18 feet divided by 2 feet per piece of rope equals nine pieces of rope.
guys please help e with this one too
Answer:
C. t = 3/5
Step-by-step explanation:
[tex]10t + 4 - 2t = 2 - 2(t - 4)[/tex]
[tex]4 + 8t = 2 - 2t + 8[/tex]
[tex]4 + 8t = 10 - 2t[/tex]
[tex]4 + 10t = 10[/tex]
[tex]10t = 6[/tex]
[tex]t = .6 = \frac{3}{5} [/tex]
Ten minutes after jumping into the ocean, a
diver is 25 feet below the surface. After 30
minutes, the diver has descended 75 feet. How
fast was the diver descending?