The value of the exponential equation is A = 5/3
What are the laws of exponents?When you raise a quotient to a power you raise both the numerator and the denominator to the power. When you raise a number to a zero power you'll always get 1. Negative exponents are the reciprocals of the positive exponents.
The different Laws of exponents are:
mᵃ×mᵇ = mᵃ⁺ᵇ
mᵃ / mᵇ = mᵃ⁻ᵇ
( mᵃ )ᵇ = mᵃᵇ
mᵃ / nᵃ = ( m / n )ᵃ
m⁰ = 1
m⁻ᵃ = ( 1 / mᵃ )
Given data ,
Let the exponential equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
A = [ 2²⁰¹⁴ + 2²⁰¹² ] / [ 2²⁰¹⁴ - 2²⁰¹² ] be equation (1)
On simplifying the equation , we get
Taking the common factor as 2²⁰¹² , we get
A = 2²⁰¹² [ 2² + 1 ] / 2²⁰¹² [ 2² - 1 ]
On further simplification , we get
A = ( 2² + 1 ) / ( 2² - 1 )
A = ( 4 + 1 ) / ( 4 - 1 )
A = 5/3
Therefore , the value of A is 5/3
Hence , the equation is A = 5/3
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area of a sector with 150° and 6ft
The area of the sector is evaluated to be equal to 15π ft². B) is the correct option.
How to evaluate for the area of the sector.The area of a sector is calculated by multiplying the fraction of the angle for the sector divided by 360° and πr², where r is the radius.
the angle of the sector = 150°
the radius = 6 ft
hence the area of the sector is calculated as follows:
(150°/360°) × π × 6 ft × 6 ft
we simplify by division and multiplication
5/12 × π × 6 ft × 6 ft
5/12 × π × 36 ft²
5π × 3 ft²
15π ft²
Therefore, the area of the sector is evaluated to be equal to 15π ft² square meters.
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Students in Ms. Clark’s class are measuring the lengths of insects. Students are told that 1 inch = 2.5 cm. Ms. Clark tells her students that the longest insect in the world is the Giant Stick Insect that can measure 2 feet long. How many cm long is a Giant Stick Insect that measures 2 feet long?
Answer:
here u go
Step-by-step explanation:
Sounds like you're very young but here I go!
since 1 inch = 2.5 cm
and 24 inches = 2 feet
multiply inches and cm by 24
answer is 60 cm
i hope it helped it may be wrong tho :(
Please help quickly!!! The triangles are similar. AC=___ units
Answer:
Step-by-step explanation:
EB/BC=15/12=5/4
ED/AC=X+5/Y=5/4
5y=4x+20
y=0.8x+4
Can someone help me ASAP!! I will give brainliest if possible. Due today!! PLEASE help me on part a and part b
Part A: What type of figure is shown above
Part B: Find the surface area of the figure
Part C: Show your work to support your answer in part B
Part A) The figure shows the prism.
Part B) the surface area of the figure is,
⇒ S.A = 270 in²
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
By figure,
The shape shows the rectangular prism.
We know that;
The surface area of prism is,
⇒ S.A = 2B + ph
Where, B is base area, p is perimeter and h is height of prism.
Here, The base area of the prism is,
B = 10 × 5 = 50 in²
The perimeter of the base of prism is,
p = 2 (5 + 10)
= 100 in
Height of prism = 1.7 in
Hence, We get;
The surface area of prism is,
⇒ S.A = 2B + ph
⇒ S.A = 2 × 50 + 100 × 1.7
⇒ S.A = 100 + 170
⇒ S.A = 270 in²
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Solve the system {-x+y=-3
3x+3y=9 check your solution by graphing
The solution of the equation is (3, 0).
How to solve equations with 2 variables?A specific point on the graph represents the solution of a linear equation in two variables, ax+by = c, where the total of these two values will equal c when the x-coordinate is multiplied by a and the y-coordinate by b. Basically, there are infinitely many solutions to a linear equation with two variables.
Given:
-x+y=-3....................(1)
3x+3y=9...................(2)
Solving Equation (1) and (2) we get
3x + 3(-3 + x) = 9
3x - 9 + 3x= 9
6x = 18
x= 18/ 6
x= 3
and, y= -3+ x
y= -3 + 3
y= 0
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statistics are often calculated with varying amounts of input data. write a program that takes any number of non-negative integers as input, and outputs the max and average. a negative integer ends the input and is not included in the statistics. assume the input contains at least one non-negative integer.Output the average with two digits after the decimal point followed by a newline, which can be achieved as follows:
System.out.printf("%.2f\n", average);
Ex: When the input is:
15 20 0 3 -1
the output is:
20 9.50
The average with two digits after the decimal point followed by a newline is 7.4
An integer is a whole number, either positive or negative, that does not have any decimal points. Non-negative integers are those that are greater than or equal to zero.
To write such a program, we can use a loop to continuously read in integers from the user until a negative integer is entered. We then ignore the negative integer and calculate the maximum and average of the non-negative integers that were entered.
The maximum is simply the largest integer in the set. We can use a variable to keep track of the largest integer as we read in the input. At the end of the loop, the variable will hold the maximum value.
The average is the sum of all the integers divided by the total number of integers.
We add each non-negative integer to the sum and increment the count. At the end of the loop, we divide the sum by the count to get the average.
To output the average with two digits after the decimal point, we can use the printf method, which allows us to format our output. The format string "%.2f\n" specifies that we want to output a floating-point number with two decimal places followed by a newline character.
=> (15 + 20 + 0 + 3 - 1) / 5 = 7.4
In summary, a program that takes any number of non-negative integers as input, and outputs the max and average can be written using a loop, variables to keep track of the maximum, sum, and count, and the printf method to format the output. Understanding the basics of integers and how to perform calculations with them is essential for programming and statistical analysis.
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Watch help video
Use the distributive property to write an
Answer:
4(5s +9t - 6)
equivalent expression
Submit Answer
Answer:
20s + 36t - 24
Step-by-step explanation:
4(5s + 9t - 6)
20s + 36t - 24
We can go any further, so that is the answer.
The shape of a piece of land is a parallelogram whose adjacent sides are 12m and 17m and the corresponding diagonal is 25m. find the area of the land
Answer:
The area of the land can be found using the formula A = 1/2*D1*D2, where D1 and D2 are the diagonals of the parallelogram. In this case, the area is 1/2*25*12 = 150m^2.
Answer:
180m^2
Step-by-step explanation:
since you said that two sides measure 12 and 17 and the diagonal is 25 you can use herons formula to find the area of each individual triangle then multiply it by two
using heron's formula it gives us the answer of 90 m^2 for one triangle so we can multiply it by two to get the area of the whole shape and 90x2=180m^2
How many liters in 1 kg?
Tony spent a total of 140 minutes studying for his algebra test this total was 5 more than 3 minutes the amount of minutes he spent studying for his biology test how many minutes did Tony spend studying for his biology test
Proportionately, if Tony spent a total of 140 minutes studying for his algebra test, and this total was 5 more than 3 minutes the amount of minutes he spent studying for his biology test, the time Tony spent studying for his biology test was 132 minutes.
What is proportion?Proportion refers to the equation of two or more ratios.
Ratios show the relative size of a value compared to another.
Proportions are fractional values like ratios.
The total minutes Tony spent studying for his algebra test = 140
5 more than 3minutes = 8 minutes
140 > 132 by 8 minutes (140 - 8)
The time spent studying biology = 132
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what is 127kg to lbs
Answer:
279.987
Step-by-step explanation:
Answer:
279.987073 lbs
Step-by-step explanation:
1 kg = 2.20462262 lbs
2.20462262 * 127 = 279.987073
A quilter created the following shape to use in a block for a new quilt.
A six-sided figure with a large base of 13 inches. The side to the right of the base is 7 and one-half inches. The small side parallel to the base is 5.18 inches. There are two sides that form a point at a right angle. The smaller is 5 inches, and the larger is 6 inches.
What is the area of the shape for the quilt block?
sixty-three and three fourths in2
one hundred twelve and one half in2
one hundred twenty-seven and one half in2
225 in2
The area of the quilt block 112.5 square inches.
The correct option is B: one hundred twelve and one half in²
What is the area of the quilt block?The area of the quilt block = area of a rectangle + area of a triangle
Ares of rectangle = length * breadth
Area of rectangle = 7.5 inches * 13 inches
Area of rectangle = 97.5 square inches
Area of the triangle = base/2 * height
base = 5 inches
height = 6 inches
Area of triangle = 5/2 inches * 6 inches
Area of triangle = 15 square inches
The area of the quilt block = 15 square inches + 97.5 square inches
The area of the quilt block = 112.5 square inches
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Riley planted flowers in some of her garden. Then, she planted
vegetables in 2/8 of her garden. Now, 7/8 of Riley's garden is planted. What
fraction of Riley's garden is planted with flowers?
O2/8 of her garden
O 3/8 of her garden
4/8 of her garden
O 5/8 of her garden
Answer
Step-by-step explanation:
A survey found that 80% of
travel agents posses valid
passports. There are 2,460
travel agents at the
convention. Predict how
many hold valid passports.
Answer:
Step-by-step explanation:
There would be 1,968 people who hold valid passports.
Christa’s mother is 45. Her uncle’s are 35, 35, 30 and her aunt is 36.What is the mean of Christa’s mother, aunt, and uncle’s age
Answer: 36.2
Step-by-step explanation:
To find the mean, you add up all the values then divide by the number of values present. So, 45+35+35+30+36= 181. 181 divided by 5 is 36.2
Given the following segment lengths find a length of the segment
The length of the line segment AB is 11/2 mm.
What is a triangle?A triangle is a three-sided closed-plane figure formed by joining three noncolinear points.
Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.
We know a line segment parallel to one side of a triangle divides the other two sides in the same ratio.
Therefore, AC/AB = EC/ED.
22/AB = 44/11.
2/AB = 4/11.
4AB = 22.
AB = 11/2.
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Triangle ABC is similar to triangle FGH. Given the following angle measures, find the missing angle measures.
The measures of angles in similar triangles are ∠ F = 22°, ∠ G = 75° and ∠ H = 83°
What are similar triangles?Similar triangles have the same corresponding angle measures and proportional side lengths.
Given that, Triangle ABC is similar to triangle FGH, we need to find the measures of the angles,
The sum of interior angles of a triangle = 180°
Considering Δ ABC,
∠ A + ∠ B + ∠ C = 180°
∠ C = 180°-(22°+75°)
∠ C = 83°
Since, we know that the similar triangles have congruent corresponding angles,
Therefore,
∠ A = ∠ F, ∠ B = ∠ G and ∠ C = ∠ H
Therefore, the measures of angles in Δ FGH are ∠ F = 22°, ∠ G = 75° and ∠ H = 83°
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What is the missing value in the ratio
videos. weeks
? 1
18. 2
27. 3
54. 6
Answer:
9
Step-by-step explanation:
54÷6= 9
27÷3= 9
18÷2= 9
hence the answer is 9.
Malcolm trains on his kayak every weekend. He paddles upstream (against current) for 3 ½ hours and then returns downstream (with current) in 2hrs 6 minutes. If the river flows at 3km/ h, find:
* The paddling speed in still water
* The distance he paddles upstream.
If Malcolm trains on his kayak every weekend. The speed is 12km/h and the distance is 31.5km.
How to find the speed and distance?Let's call Malcolm's paddling speed in still water "v".
When paddling upstream, Malcolm is fighting the current, so his effective speed is v - 3 km/h. And when paddling downstream, his effective speed is v + 3 km/h.
The time it takes for him to paddle upstream= 3.5 hours
Distance he covers in this time = (v - 3) * 3.5.
The time it takes for him to paddle downstream = 2.1 hours
Distance he covers in this time = (v + 3) * 2.1.
Let set the sum of these two distances equal to each other and solve for v:
(v - 3) * 3.5 = (v + 3) * 2.1
Expanding both sides:
3.5v - 10.5 = 2.1v + 6.3
Subtracting 2.1v from both sides:
1.4v - 10.5 = 6.3
Adding 10.5 to both sides:
1.4v = 16.8
Dividing both sides by 1.4:
v = 12 km/h
So Malcolm's paddling speed in still water is 12 km/h. To find the distance he paddles upstream, we can use the formula (v - 3) * 3.5, which gives us:
(12 - 3) * 3.5 = 9 * 3.5 = 31.5 km
Therefore the distance Malcolm paddles upstream is 31.5 km.
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Lance bought 15 sets of 3 tennis balls. Some of the tennis balls, t, were lost during each of the 4 matches he played. Now, the are 37 tennis balls left. Which equation represents this situation?
its in the screenshot.
Answer:
1. 12 inches
2. 36 inches
Step-by-step explanation: Solve for side b using the Pythagorean therom since this is a right triangle.
[tex]a^2+b^2=c^2[/tex] - Where c is the largest side aka hypotenuse(if you are unsure, look at the side opposite to the right angle)
Substitute the given values to solve for the unknown side
[tex]9^2+b^2=15^2[/tex]
Expand
[tex]81+b^2=225[/tex]
Subtract 81 from both sides
[tex]b^2=144[/tex]
Which means
[tex]b=+-12[/tex]
but since its a triangle in the first quadrant and can only contain positive values, we disregard the negative solution. So b=12.
Lastly, for perimeter, just add all the side lengths together.
[tex]P=9+12+15[/tex]
Which means that the perimeter is 36 inches!
Jason packs a box full of styrofoam pieces how many square inches of styrofoam can the box fold ?
The number of styrofoam is 11.
What is a cube?
It is a polygon having six faces.
The volume of a cube is a side³
We have,
The area of the box = 44 square inches
Styrofoam is considered a square shape.
The side length of the styrofoam = 2 in
The area of the foam = 2² = 4 square inches
Now,
The number of styrofoam.
= 44 / 4
= 11
Thus,
11 styrofoam.
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Complete question:
Jason packs a box full of styrofoam pieces in a rectangular shape surface with an area of 44 square inches.
Each styrofoam is a square shape with a side length of 2 inches.
How many square inches of styrofoam can the box fold ?
I need help plssssssssssssss
Work Shown:
[tex]\tan(\text{angle}) = \frac{\text{opposite}}{\text{adjacent}}\\\\\tan(26) = \frac{x}{5.7}\\\\x = 5.7*\tan(26)\\\\x \approx 2.78007575482541\\\\x \approx 2.8\\\\[/tex]
Make sure your calculator is in degree mode.
Which is the value of the 3rd term in the expansion of (x+6)*6?
Answer:
540x⁴
Step-by-step explanation:
You want the 3rd term of the expansion of (x +6)⁶.
Binomial expansionThe k-th term of (a +b)^n is ...
C(n, k)a^(n-k)b^k
where terms are numbered 0 to n.
Third termThe third term of (x+6)⁶ is the above expression with k=2:
C(6, 2)a⁴b²
Where a=x and b=6, this is ...
15x⁴6² = 540x⁴
__
Additional comment
C(n, k) is the function that represents the number of combinations of n things taken k at a time:
C(n, k) = n!/(k!(n-k)!)
C(6, 2) = 6!/(2!·4!) = 6·5/(2·1) = 15
Three side lengths of 6,8 and 15 units will form a triangle
Answer:
The area would be 360 because 8 x 6 x 15 = 720 divided by 2 = 360
Translate the following phrase into an algebraic expression: "9 times 5 less than twice x"
What is the function graphed below?
y = | x - 1|
y = | x | - 1
y = | x + 1|
y = | x | + 1
The function represented by the graph is y = |x + 1|
How to determine the function of the graphThe complete question is added as an attachment
From the question, we have the following parameters that can be used in our computation:
The equation of the graph is an absolute value graph
An absolute value graph is represented as
y = |x|
The function is shifted left by 1 units
So, we have
y = |x + 1|
Hence, the function is y = |x + 1|
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Label the following on the coordinate plane below: quadrant I, II, III, and IV; the origin, the x‐axis, and
the y‐axis. Also, label the sign of the coordinate points found in each quadrant.
Answer:
Quadrant I is located on the top right of the graph (Positive x, Positive y)
Quadrant II is located on the top left of the graph (Negative x , Positive y)
Quadrant III is located on the bottom left of the graph (Negative x, Negative y)
Quadrant IIII is located on the bottom right of the graph (Positive x, Negative y)
The origin is at the center of the graph with (0,0) as its x and y components
Step-by-step explanation: ^^ Please give 5 star and thanks.
What is the best approximation for the perimeter of the pentagon ABCDE? A Pentagon ABCDE image on the graph with E intercepts at (0, 1), vertices A (4, 3), B (7, 3), C (8, 0), and D (2, minus 3) 25 units 22 units 17 units 54 units
The Perimeter of the pentagon ABCDE is 17 units.
What is Distance Formula?If two points in coordinates plane P(a, b) and Q(c, d) then the distance between these points are
PQ = √(c-a)² + (d-b)²
Given:
The coordinates of Pentagon are A (4, 3), B (7, 3), C (8, 0), and D (2, -3) and E(0, 1).
Using Distance formula
AB = √(7-4)² + (3-3)²
AB = √9
AB = 3
BC = √(8-7)² + (0-3)²
BC = √1 + 9
BC = √10
CD = √(2-8)² + (-3-0)²
CD = √36 + 9
CD = √45
CD = 3√5
DE = √(0-2)² + (-3-1)²
DE = √4 + 16
DE = √20
DE = 2√5
So, Perimeter of the pentagon ABCDE = AB+BC+CD+DE+EA
= 3 + √10 + 3√5 + 2√5
= 3 + √10 + 5√5
= 17.342 unit
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Answer: 22
Step-by-step explanation:
Just because it is right yk.
A great-uncle has decided to give you a gift of $1,000. Being a financially savvy uncle, before giving you the money, he offers you a choice of the following: You can take the $1,000 today. You can wait five years and be given $1,200 instead 1. How will you decide if the offer presented by your great uncle is to your advantage? 2. Research interest rates for a savings account, checking account, and money market account at different financial institutions. Note the compounding period for each. How much would $1,000 be worth in each account in five years? 3. What are some factors that cause the value of money today to be different from its value in the future?
1. To decide if the offer presented by your great uncle is to your advantage, you need to consider the time value of money. This means that money available today is worth more than the same amount of money available in the future, due to the potential for earning interest or returns on the money. In this case, you need to compare the value of $1,000 today with the value of $1,200 in five years. If you can earn a rate of return greater than 4% over the next five years, it would be better to take the $1,000 today and invest it to earn a higher return. However, if you cannot earn a return greater than 4%, it would be better to wait and take the $1,200 in five years.
2. Interest rates and compounding periods will vary depending on the financial institution and type of account. As an example, let's assume that you are considering a savings account, checking account, and money market account with the following interest rates and compounding periods:
Savings account: 2% interest rate compounded annuallyChecking account: 0.1% interest rate compounded monthlyMoney market account: 2.5% interest rate compounded quarterlyUsing a compound interest calculator, the future value of $1,000 in each account after five years would be:
Savings account: $1,104.08Checking account: $1,005.02Money market account: $1,130.473. The value of money today can be different from its value in the future due to inflation, changes in interest rates, economic growth, and changes in the supply and demand for goods and services. Inflation is one of the biggest factors that can affect the value of money over time. If the rate of inflation is high, the value of money will decrease over time, meaning that the same amount of money will buy fewer goods and services in the future. On the other hand, if the rate of inflation is low, the value of money will increase over time, meaning that the same amount of money will buy more goods and services in the future. Interest rates can also affect the value of money, as higher interest rates can make it more attractive to save money, while lower interest rates can make it more attractive to borrow money. Economic growth and changes in the supply and demand for goods and services can also affect the value of money, as these factors can affect the overall price level of goods and services in the economy.