As a result, the angle formed by Luis's backpack and the ground is roughly 53 degrees (rounded to the nearest degree).
what is function ?A function in mathematics is a relationship between a set of potential outputs and a number of potential inputs, with the feature that each input is associated to only one possible output. It is a principle or set of guidelines that allots a different output value towards each input value. Equations, graphs, and tables are frequently used to depict functions in order to explain how the output changes as the input does. They are employed to express relationships between various quantities, such as the length of time it takes for an automobile to drive a certain distance or the height of an object in relation to its weight. The concept of a function is crucial to many departments of science and math, and it is widely applied in areas like engineering,
given
We can use trigonometry to determine the angle that Luis's backpack creates with the ground.
Consider the backpack's handle to represent the hypotenuse of a right triangle, with the vertical leg being Luis's hand's distance from the ground (3 feet) and the horizontal leg being the backpack's height (3.5 feet).
The angle can be determined using the inverse tangent function (tan-1):
53.13 degrees at tan-1(3.5/3)
As a result, the angle formed by Luis's backpack and the ground is roughly 53 degrees (rounded to the nearest degree).
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A bee flies for 4.0 min at 32.5 in/min find the bees distance in ft
The distance that the bees cover in feet is 10.84 feet.
The speed at which the bees travel is given in the unit inches per min but the required solution is in feet so we need to convert the unit from in/min to ft/min using the unit conversion method.
We know that
1 inch=1/12feet.
so 32 inches/min=32.5 *(1/12) feet/min.
which is roughly equal to 2.71 feet/min (rounded to two decimal places).
Now by using the speed, distance, and time formula which is:
distance=speed*time
we can calculate the distance covered by bees at the given speed and time.
Substituting the values in the equation.
distance=2.71 feet/minute * 4.0 minutes.
=10.84 feet
Therefore, the bee's distance in feet will be 10.84 feet (rounded off to 2 digits).
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Which polynomial does the model represent? The model shows 1 black square block, 2 white thin blocks, 1 black thin block, 1 white small square block, 3 black small blocks
The polynomial represented by the model is [tex]]x^2 - x + 2[/tex]
Based on the provided model, the polynomial represented is:
1 black square block: x^2
2 white thin blocks: -2x
1 black thin block: x
1 white small square block: -1
3 black small blocks: +3
The polynomial that the model represents is:
[tex]x^2 - 2x + x - 1 + 3[/tex]
Combining like terms, we get:
[tex]x^2 - x + 2[/tex]
So, the polynomial represented by the model is [tex]x^2 - x + 2[/tex].
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find the area of each polygon below b=6 h=9 ft h =10cm b = 8 h=8m b=9m
Question One:
Zahir bought a house 15 years ago, and it is now valued $548 900.00.
Determine the initial value of the home when Zahir purchased it, if it's value
has grown at a rate of 4.8% compounded annually. (2 marks)
Question Two:
Kiran purchases a sofa for $1791.99 (taxes already included). The
department store offers her a promotion of 0% interest with no payments
for one year. If Kiran does not pay the amount in full within one year,
interest will be charged from the date of purchase at an annual rate of
27.93%, compounded monthly.
a) If Kiran does not make any payments, what will the department store bill
her one year after the date of purchase? Show your work. (2 marks)
b) Describe a different compounding period such that the overall cost of the
sofa is lower than if the annual interest rate were compounded monthly. Use
an example to help your explanation. (2 mark)
A. Kiran will be billed approximately $2,284.33 one year after the date of purchase if she does not make any payments.
B. In this case, the overall cost of the sofa would be approximately $2,284.08
How to solve the problemsTo find the initial value of the home when Zahir purchased it, we can use the compound interest formula:
Future Value = Initial Value * (1 + (interest rate))^years
Let Initial Value be P. We are given the Future Value as $548,900, the interest rate as 4.8%, and the number of years as 15.
548,900 = P * (1 + 0.048)^15
Now, we'll solve for P:
P = 548,900 / (1 + 0.048)^15
P ≈ 305,113.48
a. Future Value = Initial Value * (1 + (interest rate / number of periods))^(years * number of periods)
Initial Value = $1,791.99
Interest Rate = 27.93% (0.2793)
Number of periods = 12 (monthly)
Years = 1
Future Value = 1,791.99 * (1 + (0.2793 / 12))^(1 * 12)
Future Value ≈ 2284.33
Kiran will be billed approximately $2,284.33 one year after the date of purchase if she does not make any payments.
b. interest were compounded annually:
Future Value = Initial Value * (1 + interest rate)^years
Future Value = 1,791.99 * (1 + 0.2793)^1
Future Value ≈ 2284.08
In this case, the overall cost of the sofa would be approximately $2,284.08, which is slightly lower than if the interest were compounded monthly ($2,284.33).
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60 juniors and sophomores were asked whether or not they will attend the prom this year. The data from the survey is shown in the table. Find P(will attend the prom|sophomore).
Attend the prom Will not attend the prom Total
Sophomores 10 17 27
Juniors 24 9 33
Total 34 26 60
The probability of a sophomore attending the prom, given that they were selected from the group of sophomores, is:
P(will attend the prom|sophomore) = (number of sophomores attending the prom) / (total number of sophomores)
From the table, we see that the number of sophomores attending the prom is 10, and the total number of sophomores is 54 (10 + 17 + 27). Therefore:
P(will attend the prom|sophomore) = 10 / 54
Simplifying the fraction, we get:
P(will attend the prom|sophomore) = 5 / 27
So the probability of a sophomore attending the prom is 5/27 (18.519%).
Use cylindrical coordinates to evaluate the triple integral ∫∫∫√(x^2 + y^2) dV where E is the solid bounded by the
circular paraboloid z = 9 - (x^2 + y^2) and the xy-plane.
The value of the triple integral ∫∫∫[tex]E \sqrt{(x^2 + y^2)} dV[/tex] over the solid bounded by the circular paraboloid [tex]z = 9 - (x^2 + y^2)[/tex] and the xy-plane is 486π/5.
To evaluate the triple integral ∫∫∫[tex]E \sqrt{(x^2 + y^2)} dV[/tex], where E is the solid bounded by the circular paraboloid [tex]z = 9 - (x^2 + y^2)[/tex] and the xy-plane, we can use cylindrical coordinates. In cylindrical coordinates, the equation of the paraboloid becomes:
[tex]z = 9 - (r^2)[/tex]
The limits of integration are:
0 ≤ r ≤ 3 (since the paraboloid intersects the xy-plane at z = 0 when r = 3)
0 ≤ θ ≤ 2π
0 ≤ z ≤ 9 - (r^2)
The triple integral becomes:
∫∫∫[tex]E √(x^2 + y^2) dV = ∫0^3 ∫0^2π ∫0^(9-r^2) r√(r^2) dz dθ dr[/tex]
Simplifying, we get:
∫∫∫[tex]E √(x^2 + y^2) dV = ∫0^3 ∫0^2π ∫0^(9-r^2) r^2 dz dθ dr[/tex]
Evaluating the innermost integral, we get:
∫[tex]0^(9-r^2) r^2 dz = (9-r^2)r^2[/tex]
Substituting this back into the triple integral, we get:
∫∫∫[tex]E √(x^2 + y^2) dV = ∫0^3 ∫0^2π (9-r^2)r^2 dθ dr[/tex]
Evaluating the remaining integrals, we get:
∫∫∫[tex]E √(x^2 + y^2) dV = ∫0^3 (9r^2 - r^4) dθ[/tex]
= 2π [243/5]
= 486π/5
Therefore, the value of the triple integral ∫∫∫[tex]E \sqrt{(x^2 + y^2)} dV[/tex] dV over the solid bounded by the circular paraboloid [tex]z = 9 - (x^2 + y^2)[/tex] and the xy-plane is 486π/5.
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2. A cylindrical water tank has a diameter of 4.6 feet and a height of 10.0
feet. A cubic foot of water is about 7.5 gallons. About how many gallons
of water are in the tank if it is completely full?
A 1,100 gallons
B. 1,250 gallons
C. 1,725 gallons
D. 3,450 gallons
Answer: Dude, I think its B. but I wouldn't use this site, its not a good rabbit hole to go down.
Step-by-step explanation:
The holiday health club has reduced its annual membership by 10%. if jorge sanchez purchases a years membership and pays $270, what is the regular membership fee?
The regular membership fee of the Holiday Health Club is $300.
Let the regular membership fee be x. According to the problem, the club has reduced its annual membership by 10%, so the discounted membership fee is 0.9x. We know that Jorge Sanchez has purchased a year's membership for $270, which is the discounted membership fee. Therefore, we can set up an equation as follows:
0.9x = 270
Solving for x, we get:
x = 270/0.9
x = 300
Hence, the regular membership fee of the Holiday Health Club is $300.
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5. A salesman bought a computer from a manufacturer. The salesman then sold the computer for
$15 600 making a profit of 25%. Unfortunately, he suffered a 5% loss due to damages when
assembling
a. What was his actual profit earnings? (10 marks)
The salesman's actual profit earnings after suffering a 5% loss due to damages when assembling the computer is $14,820.
Let's first calculate the original cost price of the computer to the salesman. We know that the salesman sold the computer for $15,600 and made a profit of 25%, which means that the selling price is 125% of the cost price.
Let the cost price of the computer be x.
Selling price = 125% of cost price
$15,600 = 1.25x
Solving for x, we get:
x = $12,480
So, the salesman's cost price of the computer was $12,480.
Now, the salesman suffered a loss of 5% due to damages when assembling the computer.
Loss = 5% of cost price
Loss = 5% of $12,480
Loss = $624
So, the actual earnings of the salesman after the loss is: $15,600 - $624 = $14,820.
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Simplify and evaluate
Answer:
In simplified form: 1/27
Evaluated: 0.037
Step-by-step explanation:
To simplify and evaluate 81^(-3/4), we use the rule that (a^m)^n = a^(mn) and rewrite the expression as (3^4)^(-3/4). Then, we use the rule that a^(-n) = 1/(a^n) to get:
81^(-3/4) = (3^4)^(-3/4) = 3^(-3) = 1/(3^3) = 1/27
Therefore, 81^(-3/4) simplifies to 1/27 and evaluates to 0.037
Billy has $80 to spend. He spent $54.50 on Bruno Mars Tickets. If Stickers cost $1.34 each, what is the maximum number of Stickers he can buy? Define a variable then write and solve an inequality. Write your answer using a complete sentence.
Answer:
Billy can buy 19 or less than 19 stickers.
Step-by-step explanation:
Solving inequality:Let the unknown variable - number of stickers be 'x'.
Cost of one sticker = $1.34
Cost of 'x' stickers = 1.34 * x = 1.34x
Maximum amount that can be spent for buying stickers = 80 - 54.50
= $25.50
Inequality:
1.34x ≤ 25.50
Solving:
Divide both sides by 1.34,
[tex]\sf x \leq \dfrac{25.50}{1.34}[/tex]
x ≤ 19.03
x ≤ 19
Billy can buy 19 or less than 19 stickers.
A cylinder has volume 108 cm? What is the volume of a cone with the same
radius and height? Use 3. 14 for it and be sure to add units to your answer.
The volume of the cone with the same radius and height as the cylinder is 36 cm³.
To find the volume of a cone with the same radius and height as the cylinder, we first need to find the radius and height of the cylinder.
The formula for the volume of a cylinder is V = πr^2h, where r is the radius and h is the height.
We are given that the volume of the cylinder is 108 cm^3.
So, 108 = πr^2h
To solve for r and h, we need more information. However, we can use the fact that the cone has the same radius and height as the cylinder to our advantage.
The formula for the volume of a cone is V = (1/3)πr^2h.
Since the cone has the same radius and height as the cylinder, we can substitute the values of r and h from the cylinder into the cone formula.
V = (1/3)π( r^2 )(h)
V = (1/3)π( r^2 )(108/π)
V = (1/3)( r^2 )(108)
V = 36( r^2 )
Therefore, the volume of the cone with the same radius and height as the cylinder is 36 cm³
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Which expressions are equivalent to 2(2x + 4y + x − 2y)? (1 point)
Answer:
6x + 4y
Step-by-step explanation:
2(2x + 4y + x − 2y)
= 4x + 8y + 2x - 4y
= 6x + 4y
Find the error. A class must find the area of a sector of a circle determined by a ° arc. The radius of the circle is cm. What is the student's error?
The student's error could be in the wrong formula he used. The area of the sector is 245.043 sq.
How do we calculate?The formula for area of a sector is
A = (θ/360) * π * r^2
where:
θ is the central angle of the sector in degrees
r is the radius of the circle
In this case, the central angle θ is 45 degrees and the radius r is 25 cm. So the area of the sector should be:
A = (45/360) * π * (25)^2
A = (1/8) * π * 625
A = 78.125π ≈ 245.043 sq. cm
The student could have made an error during any step of the calculation.
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Ignacio chooses a plant at random that does not have a white bloom. What is the probability of the complement of the event? Express your answer as a fraction in simplest form
The probability of the complement of the event of Ignacio chooses a plant at random that does not have a white bloom is 0.7692.
The probability of an occurrence is a figure that represents how likely it is that the event will take place. In terms of percentage notation, it is stated as a number between 0 and 1, or between 0% and 100%. The higher the likelihood, the more probable it is that the event will take place.
Probability is a way to gauge how likely something is to happen. Several things are difficult to forecast with absolute confidence. With it, we can only make predictions about the likelihood of an event happening, or how likely it is.
The probability that Ignacio chooses the plant which have white bloom in it is,
P = number of white bloom / total number of flowers
P = 21 / 91
So the probability that the chosen flower is not white is,
1 - P = 1 - 21/91 = 70/91 = 0.7692.
Therefore, the probability of not choosing white is 0.7692.
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need help on this problem
Answer:
a. n < 14
b. n ≥ 14
Step-by-step explanation:
a.
We see the line to the left of 14, meaning it will be smaller than 14. So, the inequality is n < 14
b.
The line goes to the right of 14, meaning it will be bigger than 14. This has a close circle meaning there will be an equal sign. So, the inequality is n ≥ 14
Examples of geometric transformations can be found throughout the real world. Think about some places where you might use or se transformations. Give at least three examples for each type of transformation. Make use of the Internet, books, magazines, newspapers, and everyday life experiences to come up with your examples.
Geometric transformations can be found in everyday life, such as moving furniture (translation), opening a door (rotation), using mirrors (reflection), zooming in and out of maps (scaling), skewing images in Photoshop (shearing), and stretching a rubber band (stretching).
Here are some examples of different types of transformations and their applications:
Translation:
Moving furniture in a room
Moving a vehicle on a map
Shifting a picture on a wall
Rotation:
Swinging a pendulum
Turning a key in a lock
Opening a door
Reflection:
Mirrors reflecting images
Water reflections of a landscape
Reflective surfaces on cars and buildings
Scaling:
Enlarging or reducing a picture on a screen
Adjusting the size of a printout
Shearing:
Skewing an image in Photoshop
Tilting a picture frame on a wall
Slanting the roof of a building for better drainage
Stretching:
Stretching a rubber band
Stretching a balloon before inflating it
Stretching a canvas for painting
These are just a few examples of the many ways geometric transformations are used in our everyday lives. By understanding these concepts, we can appreciate the beauty and functionality of the world around us.
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√3x^3 BRAINLIEST IF CORRECT!!!!!1
Answer:
[tex] \sqrt{3 {x}^{3} } = x \sqrt{3x} [/tex]
We note that x>0 here.
Answer:
The answer is x√3x
Step-by-step explanation:
√3x³=x√3x
The guidance department has reported that of the senior class 2. 3% are members of key club 8. 6% are enrolled in AP physics and 1. 9% are in both
The percentage is 9.0% of the senior class are either members of the Key Club, enrolled in AP Physics, or both.
We need to find the percentage of seniors who are either members of the Key Club, enrolled in AP Physics, or both. We can use the formula:
Total percentage = Key Club percentage + AP Physics percentage - Both percentage
Step 1: Identify the given percentages
Key Club percentage = 2.3%
AP Physics percentage = 8.6%
Both percentage = 1.9%
Step 2: Apply the formula
Total percentage = 2.3% + 8.6% - 1.9%
Step 3: Calculate the result
Total percentage = 9.0%
So, 9.0% of the senior class are either members of the Key Club, enrolled in AP Physics, or both.
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An aircraft factory manufactures airplane engines. The unit cost C (the cost in dollars to make each airplane engine) depends on the number of engines made. If x engines are made, then the unit cost is given by the function =Cx+−0.5x2180x25,609. How many engines must be made to minimize the unit cost?
Do not round your answer.
The number of engines that must be made to minimize the unit cost are 180
How many engines must be made to minimize the unit cost?From the question, we have the following parameters that can be used in our computation:
C(x) = −0.5x² + 180x + 25,609.
Differentiate the above equation
So, we have the following representation
C'(x) = -x + 180
Set the equation to 0
So, we have the following representation
-x + 180 = 0
This gives
x = 180
Substitute x = 180 in the above equation, so, we have the following representation
C(180) = −0.5(180)² + 180(180) + 25,609
Evaluate
C(180) = 41809
Hence, the engines that must be made to minimize the unit cost are 180
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Jose reads his book at an average rate of
2. 5
2. 5 pages every four minutes. If Jose continues to read at exactly the same rate what method could be used to determine how long it would take him to read
20
20 pages?
To determine how long it would take Jose to read 20 pages at his average rate, you can use a proportion.
Let x be the time in minutes it would take Jose to read 20 pages.
Then, you can set up the following proportion:
2.5 pages / 4 minutes = 20 pages / x minutes
To solve for x, you can cross-multiply:
2.5 pages * x minutes = 4 minutes * 20 pages
2.5x = 80
Finally, divide both sides by 2.5 to isolate x:
x = 32
Therefore, it would take Jose 32 minutes to read 20 pages at his average rate.
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If a circle has a circumference of 40π and a chord of the circle is 24 units, then the chord is ____ units from the center of the circle
A circle with a circumference of 40π and a chord of the circle is 24 units, then the chord is 16 units from the center of the circle,
The circumference of a circle is given by the formula C = 2πr, where r is the radius of the circle. Here, we are given that the circumference is 40π. That is
40π = 2πr
Dividing both sides by 2π, we get:
r = 20
Now, we need to find the distance between the chord and the center of the circle. Let O be the center of the circle, and let AB be the chord. We know that the perpendicular bisector of a chord passes through the center of the circle. Let P be the midpoint of AB, and let OP = x.
By the Pythagorean Theorem,
x^2 + 12^2 = 20^2
Simplifying,
x^2 + 144 = 400
x^2 = 256
x = ±16
Since OP is a distance, it must be positive. Therefore, x = 16, and the chord is 16 units from the center of the circle.
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On a coordinate plane, 2 triangles are shown. Triangle D E F has points (6, 4), (5, 8) and (1, 2). Triangle R S U has points (negative 2, 4), (negative 3, 0), and (2, negative 2).
Triangle DEF is reflected over the y-axis, and then translated down 4 units and right 3 units. Which congruency statement describes the figures?
ΔDEF ≅ ΔSUR
ΔDEF ≅ ΔSRU
ΔDEF ≅ ΔRSU
ΔDEF ≅ ΔRUS
The congruency statement that describes the figures is:
ΔDEF ≅ ΔRSU
To answer your question, let's first find the image of triangle DEF after reflecting over the y-axis and then translating down 4 units and right 3 units.
1. Reflect ΔDEF over the y-axis:
D'(−6, 4), E'(−5, 8), F'(−1, 2)
2. Translate ΔD'E'F' down 4 units and right 3 units:
D''(−3, 0), E''(−2, 4), F''(2, −2)
Now, we have ΔD''E''F'' with points (−3, 0), (−2, 4), and (2, −2). Comparing this to ΔRSU with points (−2, 4), (−3, 0), and (2, −2), we can see that:
ΔD''E''F'' ≅ ΔRSU
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Answer:
ΔDEF ≅ ΔRSU
Step-by-step explanation:
The 8th grade class of City Middle School has decided to hold a raffle to raise money to fund a trophy cabinet as their legacy to the school. A local business leader with a condominium on St. Simons Island has donated a week’s vacation at his condominium to the winner—a prize worth $1200. The students plan to sell 2500 tickets for $1 each.
1) Suppose you buy 1 ticket. What is the probability that the ticket you buy is the winning ticket? (Assume that all 2500 tickets are sold. )
2) After thinking about the prize, you decide the prize is worth a bigger investment. So you buy 5 tickets. What is the probability that you have a winning ticket now?
3) Suppose 4 of your friends suggest that each of you buy 5 tickets, with the agreement that if any of the 25 tickets is selected, you’ll share the prize. What is the probability of having a winning ticket now?
4) At the last minute, another business leader offers 2 consolation prizes of a week-end at Hard Labor Creek State Park, worth around $400 each. Have your chances of holding a winning ticket changed? Explain your reasoning. Suppose that the same raffle is held every year. What would your average net winnings be, assuming that you and your 4 friends buy 5 $1 tickets each year?
1) If there are 2500 tickets sold, and you buy 1 ticket, then the probability of your ticket being the winning ticket is 1/2500 or 0.04%.
2) If you buy 5 tickets, then the probability of having a winning ticket is 5/2500 or 0.2%.
3) If you and your 4 friends each buy 5 tickets, then there will be a total of 25 tickets. The probability of having a winning ticket in this scenario is 5/25 or 20%.
4) The chances of holding a winning ticket have not changed. This is because the consolation prizes are separate from the main prize, and the probability of winning the main prize is still the same.
The addition of consolation prizes does not affect the probability of winning the main prize.
Assuming the same raffle is held every year and you and your 4 friends buy 5 tickets each year, the average net winnings would be calculated as follows:
Total cost of tickets = $1 x 5 x 5 = $25
Total prize money = $1200 + ($400 x 2) = $2000
Probability of winning = 5/2500 = 0.2%
Expected value of winning = $2000 x 0.2% = $4
Average net winnings = ($4 - $25)/year = -$21/year
This means that on average, you and your friends would lose $21 per year if you participate in the raffle every year.
However, it is important to note that this is just an average and there is a chance of winning a larger prize which would make the net winnings positive.
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Answer correctly and if you dont know it just dont say anything
the table of values represents a linear function g(x), where x is the number of days that have passed and g(x) is the balance in the bank account:
x g(x)
0 $600
3 $720
6 $840
part a: find and interpret the slope of the function. (3 points)
part b: write the equation of the line in point-slope, slope-intercept, and standard forms. (3 points)
part c: write the equation of the line using function notation. (2 points)
part d: what is the balance in the bank account after 7 days? (2 points)
Answer:
part a: The slope of the function represents the rate of change of the balance in the bank account per day. To find the slope, we can use the formula: slope = (change in y)/(change in x).
Using the values from the table, we have: slope = (720-600)/(3-0) = 120/3 = 40. Therefore, the slope of the function g(x) is 40.
part b: Using the point-slope form of the equation of a line, we can write: g(x) - 600 = 40(x-0). Simplifying, we get: g(x) = 40x + 600. This is the slope-intercept form of the equation, where the y-intercept is 600 and the slope is 40.
To write in standard form, we can rearrange the equation as: -40x + g(x) = 600.
part c: Using function notation, we can write the equation as: g(x) = 40x + 600.
part d: To find the balance in the bank account after 7 days, we can use the equation we found in part c and substitute x = 7: g(7) = 40(7) + 600 = 880. Therefore, the balance in the bank account after 7 days is $880.
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In ΔLMN, m = 2. 1 inches, n = 8. 2 inches and ∠L=85°. Find the length of l, to the nearest 10th of an inch
The length of l is approximately 6.1 inches to the nearest tenth of an inch.
To find the length of l, we can use the Law of Cosines which states that:
c^2 = a^2 + b^2 - 2ab*cos(C)
where c is the side opposite angle C, and a and b are the other two sides.
In this case, we want to find the length of l, which is opposite the given angle ∠L. So we can label l as side c, and label m and n as sides a and b, respectively. Then we can plug in the values we know and solve for l:
l^2 = m^2 + n^2 - 2mn*cos(L)
l^2 = (2.1)^2 + (8.2)^2 - 2(2.1)(8.2)*cos(85°)
l^2 = 4.41 + 67.24 - 34.212
l^2 = 37.438
l = sqrt(37.438)
l ≈ 6.118
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pls help
what is the volume
And total surface area
Only a small percentage of Americans owned cars before the 1940s. By 2017, there were nearly 250 million vehicles for 323 million people, significantly increasing the need for roadways. In 1960, the United States had about 16,000 km of interstate highways. Today, the interstate highway system includes 77,000 km of paved roadways. What percent increase does this represent?
A. 381 percent
B. 792 percent
C. 38 percent
D. 79 percent
The percent increase in the interstate highway system from 1960 to now is 381%.
option A.
What is the percent increase?The percent increase from 16,000 km to 77,000 km is difference between the old value and new value divided by the old value expressed in 100%.
percent increase = 100% x (new value - old value) / old value
percent increase = 100% x (77,000 - 16,000) / 16,000
percent increase = 100% x 61,000 / 16,000
percent increase = 381.25%
Thus, the percent increase in the interstate highway system from 1960 to now is approximately 381%, which is option A.
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Select the equivalent expression. \left(\dfrac{4^{3}}{5^{-2}}\right)^{5}=?( 5 −2 4 3 ) 5 =?
(its khan academy)
(4^3/5^-2)^5 = ?
The equivalent expression is $\left(\dfrac{4^{3}}{5^{-2}}\right)^{5} = 102400000000000000000$.
Find the simplified equivalent expression of the following?We can simplify the expression inside the parentheses first:
\begin{aligned} \frac{4^3}{5^{-2}} &= 4^3 \cdot 5^2 \ &= (2^2)^3 \cdot 5^2 \ &= 2^6 \cdot 5^2 \ &= 2^5 \cdot 2 \cdot 5^2 \ &= 2^5 \cdot 10^2 \ &= 3200 \end{aligned}
Now we can substitute this value into the original expression and simplify further:
\begin{aligned} \left(\frac{4^3}{5^{-2}}\right)^5 &= (3200)^5 \ &= (2^8 \cdot 5^2)^5 \ &= 2^{40} \cdot 5^{10} \ &= (2^4)^{10} \cdot 5^{10} \ &= 16^{10} \cdot 5^{10} \ &= (16 \cdot 5)^{10} \ &= 80^{10} \ &= 102400000000000000000 \end{aligned}
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15√2 = x√2please help me, how do i solve this? i'm in 9th grade and i completely forgot how to do this.
The equation 15√2 = x√2 can be solved, the value of x that satisfies the equation is 15.
To solve the equation 15√2 = x√2, you can divide both sides by √2 since the square root of 2 is a common factor on both sides of the equation. This gives:
15√2 / √2 = x√2 / √2
On the left side of the equation, the √2 and the denominator cancel out, leaving:
15
On the right side of the equation, the √2 and the denominator also cancel out, leaving:
x
So the solution to the equation is:
x = 15
Therefore, the value of x that satisfies the equation is 15.
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