No matter what the number is, the answer when raised to the power of zero is always 1.
No matter what the number is, the answer when raised to the power of zero is always 1
7 to the power of zero is written as 7^0.
The answer is 1, since any number raised to the power of zero is equal to 1.
Any number raised to the power of zero is equal to 1. This is true regardless of the number. For example, 7 to the power of 0 is written as 7^0. The answer is 1. This can be seen from the equation 7^0 = 7 x 1 = 1. Similarly, 8^0 = 8 x 1 = 1, and 9^0 = 9 x 1 = 1. This concept can be applied to any number, positive, negative, whole, fractional, or decimal. No matter what the number is, the answer when raised to the power of zero is always 1.
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Lola says these two expressions have the same value.
Expression A
Expression B
Left-bracket (StartFraction a Over b EndFraction) Superscript negative 4 Baseline Right-bracket Superscript 0
Left-bracket (StartFraction a Over b EndFraction) Superscript 0 Baseline Right-bracket Superscript negative 4
Which explains whether Lola is correct?
Answer: Lola is incorrect. The two expressions have different values.
Expression A is (a/b)^(-4)^0 which is equal to 1, since any non-zero number raised to the power of 0 is 1.
Expression B is (a/b)^0^(-4) which is (a/b)^(-4) which is the reciprocal of (a/b)^4. They are different values.
In general, it's important to be careful with the order of operations when working with exponents and to be aware of the difference between a^b^c and (a^b)^c or a^(b*c) depending on the context.
Step-by-step explanation:
Which of the following is a monomiał (select all that apply)?
10xy
35x-3
-300.25
√xy
11
The first one 10xy is a monomiał, it is a product of one non-negative integer power of x and one non-negative integer power of y.
What do math monomials mean?
A monomial is a polynomial with a single term. A monomial is a type of algebraic expression that normally contains one term, though it can potentially include several variables and a higher degree. For example, 9x3yz is a single term when 9 is the coefficient, x, y, and z are the variables, and 3 is the degree of the monomial.
The second one 35x-3 is not a monomiał, it is a polynomial with one variable x and an exponent of 1 and a constant term -3.
The third one -300.25 is a monomial, it's a product of one non-negative integer power of -300.25
The fourth one √xy is not a monomial, it is a product of a square root and a variable y, which is not a non-negative integer power.
The last one 11 is a monomial, it's a product of one non-negative integer power of 11.
So the monomials are: 10xy, -300.25, 11
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A factory produces 1,600 calculators in one day.They took a sample of those calculators and found that 3% were defective. What is the expected number of defective calculators produced that day?
The expected number of defective calculators produced that day is 48.
What is the expected number of defective?When a product doesn't meet the quality objective or results in a non-compliant situation, it is considered to be faulty. Based on the total observed items as well as the defective products, you may determine the defective rate. To compute the defect rate on your own, use the following formula. Divide the total number of faulty items by the total number of observed products using the formula. To find the defect rate %, multiply the result by 100.
r = (p / o) × 100
r being the defect rate
P stands for defective goods, and O for all observed goods.
O = P*r = 1600 * 3% = 48
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a unit vector lies in the xy plane, at an angle of 155 degrees from the x axis, with a positive y component. what is the unit vector? (it helps to draw a diagram.)
The unit vector that lies in the xy plane at an angle of 155 degrees from the x axis with a positive y component is (0.4237, 0.9055).
A unit vector is a vector with a magnitude of 1. To find the unit vector that lies in the xy plane at an angle of 155 degrees from the x axis with a positive y component, we can use the formula for a two-dimensional vector in polar coordinates:
r = (cos(θ), sin(θ))
where r is the unit vector, θ is the angle in radians, and cos(θ) and sin(θ) are the x and y components, respectively.
First, we need to convert the angle from degrees to radians:
θ = 155° * (π / 180°) = 2.68 radians
Next, we can plug in the values into the formula:
r = (cos(2.68), sin(2.68)) = (0.4237, 0.9055)
So, the unit vector that lies in the xy plane at an angle of 155 degrees from the x axis with a positive y component is (0.4237, 0.9055).
To summarize, the process for finding a unit vector in the xy plane at an angle from the x axis is:
Convert the angle from degrees to radians
Use the formula for a two-dimensional vector in polar coordinates: r = (cos(θ), sin(θ))
Plug in the values into the formula to find the unit vector
Note: Keep in mind that the angle of a unit vector is relative to the positive x axis, with positive angles going counterclockwise and negative angles going clockwise.
Therefore, The unit vector that lies in the xy plane at an angle of 155 degrees from the x axis with a positive y component is (0.4237, 0.9055).
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The unit vector that lies in the xy plane at an angle of 155 degrees from the x axis with a positive y component is (0.4237, 0.9055).
A unit vector is a vector with a magnitude of 1. To find the unit vector that lies in the xy plane at an angle of 155 degrees from the x axis with a positive y component, we can use the formula for a two-dimensional vector in polar coordinates:
r = (cos(θ), sin(θ))
where r is the unit vector, θ is the angle in radians, and cos(θ) and sin(θ) are the x and y components, respectively.
First, we need to convert the angle from degrees to radians:
θ = 155° * (π / 180°) = 2.68 radians
Next, we can plug in the values into the formula:
r = (cos(2.68), sin(2.68)) = (0.4237, 0.9055)
So, the unit vector that lies in the xy plane at an angle of 155 degrees from the x axis with a positive y component is (0.4237, 0.9055).
To summarize, the process for finding a unit vector in the xy plane at an angle from the x axis is:
Convert the angle from degrees to radians
Use the formula for a two-dimensional vector in polar coordinates: r = (cos(θ), sin(θ))
Plug in the values into the formula to find the unit vector
Note: Keep in mind that the angle of a unit vector is relative to the positive x axis, with positive angles going counterclockwise and negative angles going clockwise.
Therefore, The unit vector that lies in the xy plane at an angle of 155 degrees from the x axis with a positive y component is (0.4237, 0.9055).
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The term-to-term rule for a sequence is "subtract k " the 1st term of the sequence is 40 the 4th term of the sequence is 35.5
a. Find the 2nd and 3rd terms of the sequence.
The 2nd and 3rd terms of the sequence will be 38.5 and 37, respectively.
What is an arithmetic sequence?A series of integers called an arithmetic succession or arithmetic chain of events has a fixed difference between the terms.
Let a₁ be the first term and d be a common difference.
Then the nth term of the arithmetic sequence is given as,
aₙ = a₁ + (n - 1)d
The first term is 40 and the fourth term is 35.5. Then the common difference is given as,
35.5 = 40 + (4 - 1)d
- 4.5 = 3d
d = - 1.5
Then the second term is given as,
a₂ = a₁ + d
a₂ = 40 - 1.5
a₂ = 38.5
Then the third term is given as,
a₃ = a₂ + d
a₃ = 38.5 - 1.5
a₃ = 37
The 2nd and 3rd terms of the sequence will be 38.5 and 37, respectively.
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Can anyone please help me!!
Use the discriminant to determine the number of real solutions of the quadratic equation.
-4x^2 - 2x +1=0
Answer choices:
Zero
One
Two
SECOND Question:
Use the Quadratic Formula to solve the equation. (Enter your answers as a comma-separated list.)
24x^2 -30x +9=0
x=?
Number of real solutions of -4x²- 2x +1=0 is two
The value of x = 3/4 and 1/2
Quadratic Formula:A quadratic equation, or quadratics, is a polynomial equation with a maximum degree of two. It takes the following form: ax²+bx+c = 0.
The quadratic Formula is the formula that is used to find the roots or solution of a quadratic equation. For the standard quadratic equation, the ax²+bx+c = 0 quadratic formula is given by
x = [-b±√(b²-4ac)]/2aWhere, Discriminant, d = b²-4ac
8. Given equation -4x²- 2x +1=0
From the discriminant formula,
Discriminant, d = b² - 4ac
Compare given equation with ax²+ bx + c = 0
=> a = -4, b = -2 and c = 1
Discriminant, d = (-2)² - 4(-4)(1)
= 4 + 16 = 20
Since the discriminant is positive, the given equation will have two solutions.
9. 24x² - 30x + 9 = 0
Compare given equation with ax²+ bx + c = 0
=> a = 24, b = -30 and c = 9
From the quadratic formula x = [-b±√(b²-4ac)]/2a
x = [- (-30) ±√((-30)²- 4(24) (9)]/2(24)
x = [ 30 ±√900 - 864]/48
=> x = [ 30 + √900 - 864]/48 and x = [ 30 - √900 - 864]/48
=> x = [ 30 + √36]/48 and x = [ 30 - √36]/48
=> x = [ 30 + 6]/48 and x = [ 30 -6]/48
=> x = [ 36]/48 and x = [ 24]/48
=> x = 3/4 and x = 1/2
Therefore,
Number of real solutions of -4x²- 2x +1=0 is two
The value of x = 3/4 and 1/2
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For the given central angle, determine the distance traveled along the unit circle from the point (1, 0). -112 degrees a. 0. 98 units c. 0. 62 units clockwise b. 0. 62 units d. 1. 95 units clockwise
-112° = 1.95 units clockwise. This can be solved using the concept of central angle.
Correct option is: d
What is central angle?A circle's central angle is the angle formed by two of its radii. The circle's two places of intersection (Note: The opposite end of the radii meets at the circle's centre) together make up a section known as the arc Length.
A central angle is an angle whose legs (sides) are radii intersecting the circle at two different places, A and B, and whose apex (vertex) is the center O of a circle. The central angle is the angle created by the two radii of the circle. A 360° angle is completed by the circle. A circle's central angle has a value between 0 and 360°.
For the given central angle,
-112° = d 1.95 units clockwise
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SCOOBY+DOOO=BUSTED;
FIND THE VALUE OF B+U+S+T+E+D ?
The value of B+U+S+T+E+D is 20. B represents the number 2, U represents the number 3, S represents the number 19, T represents the number 20, E represents the number 5, and D represents the number 4. When these numbers are added together, they equal 20.
BUSTED is an acronym for 'Believing Uncovering Solving Troubles Everywhere Dynamicly'. It is a popular phrase used by the characters in the Scooby-Doo cartoons. It is a phrase used to express the moment when the mystery is solved and the bad guy is caught.
BUSTED is an important part of the Scooby-Doo cartoon series. It expresses the moment when the mystery is solved and the bad guy is caught. It is also a great way to encourage children to believe in themselves and to use their own detective skills to solve a mystery. The value of B+U+S+T+E+D is 20, and it is a fun way to teach kids math and problem solving skills.
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how can i solve this
a. The value of a is 5500. b. The value of r is 0.92. c. There are 2022 trees still alive till 1st October 2023.
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
a) The value of a is 5500.
b) To find the value of r, we can use the equation N = ar where N is the number of trees still alive t years after 1st October 2018. We know that N = 5060 on 1 October 2019, so we can substitute these values into the equation:
5060 = 5500 r
r = 5060/5500
r = 0.92
c) To find the predicted percentage decrease in trees still alive between 1 October 2018 and 1 October 2030, we can use the equation:
[tex]N = ar^t[/tex]
Here a = 5500, r = 0.92 and t = 12
We can now substitute the values, then we get
N = 5500 × (0.92)¹² ≈ 2021.67
N = 2022
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LaVelle buys a jumbo package of 84 candies to 12 make favor bags for her son's birthday party. If she wants to make bags, how many candies should she put in each bag?
Different varieties of field daisies have numbers of petals that follow a fibonacci sequence. Three varieties have 13, 21, and 34 petals. How many petals do the next two varieties of field daisy have?.
The next two varieties of field daisy have 55 and 89 petals.
We know that the Fibonacci Sequence is the series of numbers such that:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ...
Here, the next term of the sequence is found by adding up the two numbers before it.
For exa., the fourth term 2 is the sum of (1+1),
the fifth term 3 is the sum of (1+2)
In this question the numbers of petals of field daisies follow a Fibonacci sequence.
The three varieties have 13, 21, and 34 petals.
The next variety of field daisy would be the sum of 21 and 34
21 + 34 = 55
And the fifth variety of field daisy would be the sum of 34 and 55
34 + 55 = 89
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While Sergeant Rote is sleeping, the power goes out. When the do
power comes back on, his digital clock resets to 12:00, then runs as e
usual. When he awakes at 6:05, his alarm clock displays 3:17. What
time did the power come back on at Sergeant Rote's house?
To determine the time the power came back on, we need to determine how much time has passed since the power went out and the alarm clock reset where the power came back on at 17.79 hours or 17 hours and 47 minutes (17:47).
What is meant by power outage?First, we know that when Sergeant Rote wakes up at 6:05, the alarm clock displays 3:17.Next, we need to determine how much time has passed since the alarm clock reset to 12:00. We can do this by subtracting 3:17 from 12:00.To subtract 3:17 from 12:00, we need to convert the minutes (17) to hours and minutes (0.28 hours or 16.8 minutes).12:00 - 0.28 hours = 11.72 hoursWe can convert 11.72 hours back to minutes by multiplying it by 60 (11.72 x 60 = 702.4 minutes)So, we know that 702.4 minutes have passed since the alarm clock reset.Now that we know how much time has passed since the alarm clock reset, we can add that time to the time when Sergeant Rote wakes up (6:05) to determine the time the power came back on.To add 702.4 minutes to 6:05, we first need to convert 6:05 to minutes (365 minutes)365 minutes + 702.4 minutes = 1067.4 minutesTo convert 1067.4 minutes back to hours and minutes, we divide it by 60 (1067.4 / 60 = 17.79 hours)So the power came back on at 17.79 hours or 17 hours and 47 minutes (17:47)To learn more about power refer:
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10,5,5/2 find 6th term
Answer:
Hey there!
Arithmetic sequences are made up of terms that are added or subtracted, and geometric sequences are made up of terms that are multiplied or divided.
Given this info, we can see that we go from 10 to -5. Because we know that this is geometric, we see that we must divide by -2 in our sequence.
We can see that this is true because -5/-2=5/2.
Now, we could simply continue dividing by negative two to get our answer, which is -5/16.
You could easily do that with a calculator, but if you had to find a term that was farther from the first term, that would take forever to do with a calculator, so there is an equation that you can use and plug in your numbers to find the answer quickly.
, where is the number of term in the sequence (6 in this problem), a is the first term of the sequence (10), and r is the common ratio (-1/2).
I hope this helps!
Step-by-step explanation:
Is 0 a negative number?
How do you find the distance between two points in Class 11?
To calculate the distance between two places, we can apply the distance formula d=((x2 - x1)² + (y2 - y1)²).
What is the distance?The distance of an object is its overall motion, regardless of direction.
Distance is the amount of space that an object has covered, regardless of where it began or concluded.
By understanding how far an object is from us, we may calculate its actual size.
It is possible to calculate the area that an object takes up in the sky.
The actual size of an object can then be determined by taking into account its distance.
The further away something is, the smaller it appears.
The distance between two locations on a plane is the length of the line segment connecting them.
The formula d=((x2 - x1)2 + (y2 - y1)2) is frequently used to calculate the separation between two points.
Therefore, to calculate the distance between two places, we can apply the distance formula d=((x2 - x1)² + (y2 - y1)²).
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what is the value of x 5x+2=22
Answer:
[tex]\bf x=4[/tex]
Step-by-step explanation:
[tex]\bf 5x+2=22[/tex]
Subtract 2 from both sides:-
[tex]\bf 5x+2-2=22-2[/tex]
[tex]\sf 5x=20[/tex]
Divide both sides by 5:-
[tex]\bf \cfrac{5x}{5}=\cfrac{20}{5}[/tex]
[tex]\bf x=4[/tex]
Therefore, value of x is 4!
______________________
Hope this helps!
Have a great day!
Answer: X= 4
Step-by-step explanation:
Just minus 2 on both sides so you get 5x=20. divide by 5 and then you get 4.
24x^(4)y^(3)z^(4)-32x^(3)yz^(5)
Answer: 8x^3yz^4(3xy^2-4z)
Step-by-step explanation:
Factor out the greatest common factor: [tex]8[/tex]
8 x 3 = 24
8 x 4 = 32
Factor out the smallest powers from both sides: [tex]x^3 yz^4[/tex]
Leave the remaining x, y, and z values
[tex]8x^3yz^4(3xy^2-4z)[/tex]
2350000000 as standard form
Answer:2350 million
Step-by-step explanation:
hope this helps
Decide whether each table could represent a proportional relationship. If the relationship could be proportional, what oils the constant of proportionality?
a) Annie's Attic is giving away $5 off coupons.
Therefore , the solution of the question is given by the theorem of
constant proportionality comes out to be 1.5 .
Define constant proportionality.The proportion between any directly proportional quantities is the proportionality constant. If the growth and decline of two quantities occur at the same rates, they are directly proportional. When two quantities, y and x, are approximately equal to one another, the proportionality constant, k, is equal to their product, y/x.
Here,
Given :
=> original price : $15 ,$25,$35
=> sale price: $10,$20,$30
To find the proportional relationship :
=> 15/10 =1.5
=> 25/20 = 5/4 = 1.25
=> 35/30 = 7/6 = 1.16
Therefore , the solution of the given problem of constant proportionality comes out to be 1.5 .
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30% of 50_ is 15 this
Answer: Yes, answer is 15
Step-by-step explanation:
Another way to look at this is 50% of 30, or just 1/2 of 30.
the total volume of cubes n the container r is 8^7 cubic cm , the volume of each cube is 8^2 cubic cm ; how many cubes are in the container?
A 5^8
B 8^7 x 8^-2
C 8^-9
D 8^5
E 8^-7 x 8^-2
There are [tex]8^5\\[/tex] cubes in the Container.
What is Exponents and Power?Exponents and powers are ways used to represent very large numbers or very small numbers in a simplified manner.
For example, if we have to show 3 x 3 x 3 x 3 in a simple way, then we can write it as [tex]3^4[/tex], where 4 is the exponent and 3 is the base.
Given:
Volume of Container = [tex]8^7[/tex] cm³
Volume of Each cube = 8² cm³
So, the number of cubes in the container
= Volume of Container / Volume of Each cube
= [tex]8^7[/tex] cm³ / 8² cm³
Now, using Exponents property
[tex]a^m / a^n= a^{m-n[/tex]
Then, number of cubes in the container
= [tex]8^7[/tex] cm³ / 8² cm³
= [tex]8^{7-2[/tex]
= [tex]8^5\\[/tex]
Hence, the number of cubes are [tex]8^5\\[/tex].
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How to find roots of quadratic equation by factorisation method?
To find the roots of a quadratic equation by the factorization method, you can use the following steps:
Write the equation in standard form (ax^2 + bx + c = 0)
Factor the equation completely by setting it equal to zero and factoring out the greatest common factor.
Set each factor equal to zero and solve for the roots.
For example, to find the roots of the equation x^2 + 5x + 6 = 0, we can factor it as (x+3)(x+2) = 0.
To find the roots, we set each factor equal to zero and solve for x:
x + 3 = 0, x = -3
x + 2 = 0, x = -2
So the roots of the equation x^2 + 5x + 6 = 0 are -3 and -2.
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Write a recursive formula for an, the nth term of the sequence 19, 15,11,7
The formula of the arithmetic progression for the sequence 19, 15, 11, 7 is a(n) = 19 - 4 · (n - 1), whose recursive formula is a(n) = 19 - 4 · (n - 1), a₁ = 19.
How to determine the recursive formula of an arithmetic progressions
Arithmetic progressions are sets of values generated by an expression of the form:
a(n) = a₁ + r · (n - 1)
Where:
a₁ - Index of the first element of the sequence.r - Common difference.n - Index of the n-th element of the sequence.And the recursive formula is:
a(n) = r · a(n - 1)
Where a(n - 1) is the n-1 th term of the sequence.
First, determine the first element of the sequence:
a₁ = 19
Second, find the common difference:
r = a₂ - a₁
r = 15 - 19
r = - 4
Third, write the complete formula for the arithmetic progression:
a(n) = 19 - 4 · (n - 1)
Fourth, write the recursive formula:
a(n) = a(n - 1) - 4
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What is an equation of the line that passes through the points (- 4 7 and 2/8 )?
An equation of the line that passes through the points (- 4, 7) and (2, 8) is 6y = x + 31.
In the given question, we have to find an equation of the line that passes through the points (- 4, 7) and (2, 8).
The point-slope approach is typically used when two points that sit on a specific line are specified.
A line's equation is written as y - y(1) = m(x - x(1)), where y(1) is the Y-axis coordinate, m is the slope, and x(1) is the X-axis coordinate.
Firstly we find the value of m using the formula
m = [tex]\frac{y(2)-y(1)}{x(2)-x(1)}[/tex]
From the given points x(1) = -4, y(1) = 7, x(2) = 2, y(2) = 8.
Now putting the value
m = [tex]\frac{8-7}{2-(-4)}[/tex]
Now solving
m = [tex]\frac{1}{2+4}[/tex]
m = [tex]\frac{1}{6}[/tex]
Now we finding the equation of line. We can use any one point in the given points.
Now taking the points (2, 8), x(1) = 2 and y(1) = 8
Now putting the value in equation y - y(1) = m(x - x(1)).
y - 2 = [tex]\frac{1}{6}[/tex](x - 8)
Multiply by 6 on both side, we get
6(y - 6) = x - 5
6y - 36 = x - 5
Add 36 on both side, we get
6y = x + 31
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The complete question is:
What is an equation of the line that passes through the points (- 4, 7) and (2, 8)?
in most cases, the product of a monomial and a binomial is a ___.
If we multiply monomial and binomial, then it is become polynomial.
Perfect Squares: The Square of a Difference Squaring a binomial every time results in a trinomial.
In other words, if we find the product of 6 and 3 by simply calculating 6 times 3 which equals 18.
A monomial is a statement of the form k⋅xⁿ, where k is a real number and n is a positive integer. It is essentially a polynomial with a single term.
When we are multiplying two monomials, we can rewrite the product as a single monomial using properties of multiplication and exponents.
A polynomial equation with two terms normally joined by a plus or minus sign is called a binomial.
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Determine the value of x in the figure.
The value of x in the figure is 5.
Find the value of x in the illustration.In the given figure, x represents the measure of the angle between the two lines.The sum of the measures of the angles in the triangle is 180 degrees.Therefore, by subtracting the sum of the other two angles from 180 degrees, we can determine the value of x.In the figure, the measure of angle ABC is 30 degrees and the measure of angle BCD is 120 degrees.Therefore, we can calculate the value of x by subtracting the sum of the other two angles from 180 degrees.180 - (30 + 120) = 50Therefore, the value of x is 50 degrees.The figure provided is a triangle with two angles labeled as x and 60 degrees respectively.The third angle is not labeled as it is known to be equal to 180 degrees minus the sum of the two other angles.Therefore, x must equal 120 degrees.To learn more about a two-dimensional triangle refer to:
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Circle C is centered at the origin. Is point (5, 5) on the circle?
Answer:
no, the origin is located at 0,0
answer pls loads of points available
Answer:
87
Step-by-step explanation:
it is 887
what is 84.95 - 2.15 × (3.91 - 1.91) to the power of 3
Answer:
67.75
Step-by-step explanation:
[tex]84.95 - 2.15 \cdot (3.91 - 1.91)^3[/tex]
[tex]3.91-1.91=2[/tex]
[tex]2^3=8[/tex]
[tex]2.15\cdot8=17.2[/tex]
[tex]84.95 -17.2=67.75[/tex]
So, the final answer is 67.75
The linear function
y
=
2
x
+
25
models the average cost of a haircut in a certain city, where
y
, is the average price of a haircut
x
years after 1985. Find the slope for the model. Then describe what this means in terms of the rate of change in the average cost of a haircut over time.
a)
m
=
2
b) The average cost of a haircut in this city increased (Enter: increased or decreased or not changed ) at a rate of per year after 1985.
Therefore , the solution of the given problem of function comes out to be $33 will be the price of haircut in 1997.
What is function?Mathematics is a science that investigates numbers, their variations, mathematics and the local tissues, shapes, and the both their actual and potential placements. Function describes the connection between a collection of inputs, each of which has an associated output. A function is an association domain of inputs that results in a single, distinctive output for each input. Each function is given a city or municipality or a scope, often known as a realm.
Here,
Given : c = 2y + 29
where c is the typical cost of the a haircut and
y is the number of years since 1995.
For the model, the slope is 2.
It implies that starting in 1995,
the average price of a haircut will rise by 2 each year.
=>1995 has y=0 and a cost of 29.
=> 1996's y=1 results in a cost of 29+2=31.
=>When y=2 in 1997, the price is 29+4 = 33, and so forth.
Therefore , the solution of the given problem of function comes out to be $33 will be the price of haircut in 1997.
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