Integrate the function y = f(x) between x = 2.0 to x = 2.8, using Simpson's 1/3 rule with 6 strips. Assume a = 1.2, b = -0.587 = - y = a/x +b*Sqrt(x)

Answers

Answer 1

the integral of the function y = f(x) between x = 2.0 and x = 2.8, using Simpson's 1/3 rule with 6 strips, is approximately 0.3790.

To integrate the function y = f(x) using Simpson's 1/3 rule, we'll follow these steps:

Step 1: Determine the interval and number of strips.

Step 2: Calculate the width of each strip.

Step 3: Evaluate the function at the interval points.

Step 4: Apply Simpson's 1/3 rule to compute the integral.

Given: y = a/x + b√(x) with a = 1.2 and b = -0.587

Interval: x = 2.0 to x = 2.8

Number of strips: 6

Step 1: Determine the interval and number of strips.

The interval is from x = 2.0 to x = 2.8.

We have 6 strips.

Step 2: Calculate the width of each strip.

The width, h, of each strip is given by:

h = (b - a) / n

  = (2.8 - 2.0) / 6

  = 0.1333

Step 3: Evaluate the function at the interval points.

We need to evaluate the function f(x) = a/x + b√(x) at the interval points.

Let's calculate the values:

f(2.0) = 1.2/2.0 - 0.587√(2.0)

      = 0.6 - 0.587 * 1.414

      = 0.6 - 0.8287

      = -0.2287

f(2.1333) = 1.2/2.1333 - 0.587√(2.1333)

         = 0.5624

f(2.2666) = 1.2/2.2666 - 0.587√(2.2666)

         = 0.5332

f(2.3999) = 1.2/2.3999 - 0.587√(2.3999)

         = 0.5128

f(2.5332) = 1.2/2.5332 - 0.587√(2.5332)

         = 0.4963

f(2.6665) = 1.2/2.6665 - 0.587√(2.6665)

         = 0.4826

f(2.8) = 1.2/2.8 - 0.587√(2.8)

      = 0.4714

Step 4: Apply Simpson's 1/3 rule to compute the integral.

Now, we'll apply the Simpson's 1/3 rule using the evaluated function values:

Integral = (h/3) * [f(x₀) + 4 * (Σ f(xi)) + 2 * (Σ f(xj)) + f(xₙ)]

Where:

h = width of each strip

f(x⁰) = f(2.0)

Σ f(xi) = f(2.1333) + f(2.3999) + f(2.6665)

Σ f(xj) = f(2.2666) + f(2.5332)

f(xₙ) = f(2.8)

Let's calculate the integral:

Integral = (0.1333/3) * [(-0.2287) + 4 * (0.5624 + 0.5128 + 0.4826) + 2 * (0.5332 + 0.4963) + 0.4714]

        = (0.1333/3) * [(-0.2287) + 4 * (1.5578) + 2 * (1.0295) + 0.4714]

        = (0.1333/3) * [(-0.2287) + 6.2312 + 2.0590 + 0.4714]

        = (0.1333/3) * [8.5329]

        = 0.1333 * 2.8443

        = 0.3790

Therefore, the integral of the function y = f(x) between x = 2.0 and x = 2.8, using Simpson's 1/3 rule with 6 strips, is approximately 0.3790.

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Related Questions

What does it mean for a sample to have a standar deviation of zero? describe the scores in such a sample

Answers

Given that sample standard deviation is zero. This indicates that the variance of sample is also zero as square of sample standard deviation is sample Variance. Variance is average of the squared deviations from mean. As shown in below formula

Since Variance = 0 , we substitute in formula and we get the sum of squares of deviations of all data points from mean should be zero. This is only possible if and only if all the data points in the data distribution are same as mean of the data distribution. In the case the variance and standard deviation will be zero.

Variance = Summation n to i = 1 \(\frac{(X_{1-X} )^2}{n-1}\)

        0 = Summation n to i = 1\(\frac{(X_{1-X} )^2}{n-1}\)

                Summation n to i \({(X_{1-X} )^2\) = 0

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the area of a square whose all sides are 3cm is​

Answers

Step-by-step explanation:

Hey there!

The sides of a square; 3cm.

Area = l^2

\(area = {3}^{2} \)

\(a = 9\)

Therefore, the area is 9cm^2.

Hope it helps...

a+sign before the blank (Example: −300 ). If you answer is zero, enter " 0 ". (b) Discuss the value of the portfolio with and without the European put options. The lower the stock price, the 3 beneficial the put options. The options are worth nothing at a stock price of $ 3. There is a benefit from the put options to the overall portfolio for stock prices of $

Answers

The sign before the blank is "+" (Example: +300). (b) The value of the portfolio with European put options increases as the stock price decreases, providing a protective benefit to the overall portfolio.

The sign before the blank is "+" (Example: +300).

(b) The value of the portfolio with European put options increases as the stock price decreases. The put options provide a protective benefit to the portfolio, as they allow the holder to sell the stock at a predetermined price (strike price).

When the stock price is below the strike price, the put options become valuable as they enable the investor to sell the stock at a higher price than the market value. However, if the stock price is above the strike price, the put options have no value and do not contribute to the portfolio's overall worth.

Therefore, the benefit of the put options is realized when the stock price is below the strike price, and it diminishes as the stock price rises above the strike price.

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HELP MEEEE PLEASE IM CONFUSED

HELP MEEEE PLEASE IM CONFUSED

Answers

Horizontal data is not numerical

Define graph

A graph is a visual representation of data or information that displays the relationship between different variables or data sets. It is a diagram that uses lines, bars, dots, or other symbols to represent data points or values and displays how they are related to each other. Graphs are commonly used in mathematics, science, economics, and many other fields to represent data in a more accessible and easily understandable way.

In the given graph

The comparison is done between Number of stores and Franchise.

Number of stores is placed in y axis

Franchise is placed in y axis

For comparison, no data is given of Franchise as it showing the non numerical.

hence, Horizontal data is not numerical.

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Solve the equation 2(h+3.5) = -11.

Answers

Answer:-9

Step-by-step explanation:

Which of the following will cause a logical error if you are attempting to compare x to 5?
Answers:
a. if (x >= 5)
b. if (x = 5)
c. if (x == 5)
d. if (x <= 5)

Answers

Logical Error: In computer programming language, a logic error is a bug or in a program or code that causes it to operate incorrectly, but not to terminate abnormally (or crash).

A logic error developed unintended or undesired output or other behavior, although it may not immediately be recognized as such.

For example, assigning a value to the wrong variable may cause a many of unexpected program errors.

These errors can be programmer mistakes or sometimes machine less memory to load the code.

if(x>=5) {

// program

}

else if(x==5) {

//program

}

else(x<=5) {

//program

}

they all do not give any error.

x=5 gave an error because it is value assigning to 5.

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Helen has been sick and only able to work on a part time basis what type of disability may she be eligible for? What percentage should she expect the insurance policy to pay

Answers

The percentage of the amount which should be expected to be paid from the insurance policy based on the part time work Helen has been doing is:

Two-thirds of their average weekly wage

Based on the given question, we can see that partial disability benefit is the theme in play here as Helen has been sick and been working on a part time basis which helps her to be eligible for partial disability benefit.

Under this type of disability benefit, Helen is entitled to get about two-thirds of her average weekly wage because she is working part time because of her disability which is her sickness.

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You are driving on the freway and notice your speedometer says to. The car in front of you appears to be coming towards you at speed
4
1

to. and the car behind you appears to be gaining on you at the same speed
4
1

to. What speed would someone standing on the ground say each car is moving? (b) Suppose a certain type of fish always swim the same speed. You watch the fish swim a certain part of a river with length L. You notice that it takes a time
6
1

t
0

for the fish to swim downstream but only
3
1

t
0

to swim upstream. How fast is current of the river moving? (c) You now want to swim straight across the same river. If you swim (in still water) with a speed of
10
3L

, what direction should you swim in? (d) How long does it take to get across if the river has a width of
3
1

L. Problem 7 Relative (a) You are driving on the freeway and notice your speedometer says t
0

. The car in front of you appears to be coming towards you at speed
4
1

t
0

, and the car behind you appears to be gaining on you at the same speed
4
1

t
0

. What speed would someone standing on the ground say each car is moving? (b) Suppose a certain type of fish always swim the same speed. You watch the fish swim a certain part of a river with length L. You notice that it takes a time
6
1

t
0

for the fish to swim downstream but only
3
1

t
0

to swim upstream. How fast is current of the river moving? (c) You now want to swim straight across the same river. If you swim (in still water) with a speed of
f
a


3L

, what direction should you swim in? (d) How long does it take to get across if the river has a width of
3
1

L.

Answers

a) The speed of the car in front of you appears to be coming towards you is 41t₀. The speed of the car behind you appears to be gaining on you at the same speed is 41t₀. Someone standing on the ground would say that the two cars are moving at t₀ + 41t₀ = 82t₀.

b) We know that the speed of the fish in still water is V, and the speed of the current is C. And the time the fish takes to swim downstream is 61t₀ and upstream is 31t₀. So:

Downstream: V + C = L / (61t₀)

Upstream: V - C = L / (31t₀)

Adding the two equations we get:

2V = (4L / 61t₀) → V = (2L / 61t₀)

Therefore, C = (L / 61t₀) which is the speed of the current.

c)In order to get across the river, you have to swim at a speed perpendicular to the current (so that you don't get drifted away) and with a speed of fa * 3L, as given. Therefore, the required angle can be found by:

f a3L = (V cos α)sin α

= (C cos α)sin αtan α

= (fa * 3L) / C

= 3fa * 61t₀ / Ld)

The width of the river is 31L. The time taken to get across can be found using the formula:

Time = (Distance) / (Speed)

Since the speed of the current is C, the effective speed (in still water) is fa * 3L, the distance to be crossed is 31L, and the time taken is:

Time = (31L) / (fa * 3L - C)  

= (31L) / (3fa * 61t₀ / L)

= (31L²) / (3fa * 61t₀)

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PLEASE ANSWER ASAP!!!!!!!Calculate the quotient below and give your answer in scientific notation.
0.00065
5 x 10-2
?

Answers

Answer:

Step-by-step explanation:

0.00065 ÷5*10^-2

0.00065 ÷ 0.05= 0.013

Please help me?! All you have to do is find the missing side

Please help me?! All you have to do is find the missing side

Answers

Answer:

see explanation

Step-by-step explanation:

To find the missing side, subtract the sum of the 2 given sides from the perimeter.

(11)

6x + 6y - (2x + y + x + 2y)

= 6x + 6y - (3x + 3y)

= 6x + 6y - 3x - 3y ← collect like terms

= 3x + 3y ← missing side

(12)

11x + 2y - (2x + 3y + 6x - 5y)

= 11x + 2y - (8x - 2y)

= 11x + 2y - 8x + 2y ← collect like terms

= 3x + 4y ← missing side

what is the critical value for 96 confidence interval for a sample size of 15

Answers

The critical t-value is approximately 1.753.

To find the critical value for a 96% confidence interval with a sample size of 15, we need to determine the t-value from the t-distribution table. The t-distribution table is a statistical tool used to determine the probability of a t-value given the degrees of freedom (df) and the desired level of significance (α).

In this case, we have a sample size of 15, which means our degrees of freedom are 14 (n - 1). Looking at a t-distribution table for 14 degrees of freedom and a 96% confidence interval.

This means that if we were to construct a confidence interval from a sample size of 15, the margin of error would be calculated by multiplying the critical t-value of 1.753 by the standard deviation of the sample and dividing by the square root of the sample size. The resulting interval would contain the population mean with 96% confidence.

It's essential to note that the critical value will change as the sample size and confidence level change. Therefore, it's crucial to use the correct table to find the corresponding critical values for a given dataset's sample size and confidence level.

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subscript indices must be either positive integers or logicals:T/F

Answers

Therefore,  subscript indices must be either positive integers or logical. True

Explanation: The statement "subscript indices must be either positive integers or logicals" is true. Subscript indices are used to identify elements in an array. A positive integer subscript identifies a particular element in an array, while a logical subscript identifies a subset of elements based on a logical condition. For example, if we have an array A, then A(1) would identify the first element of the array, while A(A > 0) would identify all elements in the array that are greater than zero. Subscript indices cannot be negative or non-integer values.

Therefore,  subscript indices must be either positive integers or logical. True

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Need 2 more. 50 points!

Please show work, Thanks! :)

Need 2 more. 50 points!Please show work, Thanks! :)
Need 2 more. 50 points!Please show work, Thanks! :)

Answers

Answer:

1) C

2) C

Step-by-step explanation:

Question 1)

We want a parabola that has the vertex (-8, -7) and also passes through the point (-7, -4).

So, we can use the vertex form. Remember that the vertex form is:

\(y=a(x-h)^2+k\)

Where a is our leading co-efficient and (h, k) is our vertex.

We know that our vertex is (-8, -7). So, substitute this into the equation:

\(y=a(x-(-8))^2+(-7)\)

Simplify:

\(y=a(x+8)^2-7\)

Now, we need to determine the value of our a. To do so, we can use the point the problem had given us. We know that the graph passes through (-7, -4).

So, when x is -7, y is -4. Substitute -7 for x and -4 for y:

\((-4)=a((-7)+8)^2-7\)

Solve for a. Add within the parentheses:

\(-4=a(1)^2-7\)

Square:

\(-4=a-7\)

Add 7 to both sides. Therefore, the value of a is:

\(a=3\)

So, our entire equation in vertex form is:

\(y=3(x+8)^2-7\)

Our answer is C.

Question 2)

We are given a graph and are asked to find the equation of the graph.

Again, let's use the vertex form. From the graph, we can see that the vertex is at (-2, 2). Let's substitute this into our vertex equation:

\(y=a(x-(-2))^2+2\)

Simplify:

\(y=a(x+2)^2+2\)

Again, we need to find the value of a.

Notice that the graph crosses the point (-1, 5).

So, let's substitute -1 for x and 5 for y. This yields:

\(5=a((-1)+2)^2+2\)

Solve for a. Add within the parentheses.

\(5=a(1)^2+2\)

Square:

\(5=a+2\)

Subtract 2 from both sides. So, the value of a is:

\(a=3\)

Therefore, our entire equation is:

\(y=3(x+2)^2-2\)

Our answer is C.

And we're done!

Which expression is equivalent to

Which expression is equivalent to

Answers

The equivalent result of the expression is 944077.02

What is exponential function examples?

As for its use, the exponential function can help in performing various calculations, for example: population growth, evolution of capital by compound interest, radioactive decay of chemical substances, development of bacteria in a colony, etc.

According to exponential law of indices. Given the exponential equation below;

\({(2.3)^5/(0.9)^4}^3\)

Simplify to have:

\({(2.3)^5/(0.9)^4}^3(64.36343/0.6561)^3\)

Simplifying further will give;

\((64.36343/0.6561)^3 = 98.1000304832^3\\(64.36343/0.6561)^3 = 944077.02\)

Hence the equivalent result of the expression is 944077.02

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what is the volume occupied by a mixture of 0.522 mol of N2 and 0.522 mol of O2 GASES AT .83 ATM AND 42.7C?

Answers

the volume occupied by the mixture of N2 and O2 gases at 0.83 atm and 42.7°C is approximately 41.62 liters.

To find the volume occupied by the mixture of gases, we can use the ideal gas law equation:

PV = nRT

Where:

P = pressure of the gases (in atm)

V = volume of the gases (in liters)

n = number of moles of gas

R = ideal gas constant (0.0821 L.atm/mol.K)

T = temperature of the gases (in Kelvin)

First, let's convert the temperature from Celsius to Kelvin:

T(K) = T(C) + 273.15

T(K) = 42.7 + 273.15

T(K) = 315.85 K

Now we can calculate the volume:

For N2:

n(N2) = 0.522 mol

P(N2) = 0.83 atm

T = 315.85 K

For O2:

n(O2) = 0.522 mol

P(O2) = 0.83 atm

T = 315.85 K

Using the ideal gas law for each gas:

V(N2) = (n(N2) * R * T) / P(N2)

V(O2) = (n(O2) * R * T) / P(O2)

Calculating the volumes:

V(N2) = (0.522 * 0.0821 * 315.85) / 0.83

V(N2) ≈ 20.81 L

V(O2) = (0.522 * 0.0821 * 315.85) / 0.83

V(O2) ≈ 20.81 L

Since the number of moles and pressure are the same for both gases, the volumes will also be the same.

To find the total volume occupied by the mixture of gases, we can sum the individual volumes:

V(total) = V(N2) + V(O2)

V(total) = 20.81 + 20.81

V(total) ≈ 41.62 L

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(-1, 1) and (1, -1) is on the line.
The equation of the line in point slope form is:

Answers

Answer:

6

Step-by-step explanation:

What is the value of x?


A hexagon (6 sides)

133°
112°

120°
128°
100°


please help asap, no links

Answers

Answer:

X is 120° I hope this helps you

he life expectancy of a typical lightbulb is normally distributed with a mean of 1,975 hours and a standard deviation of 25 hours. What is the probability that a lightbulb will last between 1,950 and 2,050 hours

Answers

The probability that a lightbulb will last between 1,950 and 2,050 hours is 0.84, or 84%.

To solve this problem, we need to find the probability that the lifespan of a lightbulb will fall between 1,950 and 2,050 hours.

First, we need to standardize the distribution using the z-score formula:

z = (x - μ) / σ

where x is the value we are interested in, μ is the mean, and σ is the standard deviation.

For x = 1,950 hours:

z = (1,950 - 1,975) / 25 = -1

For x = 2,050 hours:

z = (2,050 - 1,975) / 25 = 3

Now, we need to find the area under the standard normal distribution curve between z = -1 and z = 3. We can use a standard normal distribution table or a calculator to find this area.

Using a standard normal distribution table, we find that the area to the left of z = -1 is 0.1587 and the area to the left of z = 3 is 0.9987. Therefore, the area between z = -1 and z = 3 is:

0.9987 - 0.1587 = 0.84

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Find the limit. (If the limit is infinite, enter ' [infinity] ' or

−[infinity] ', as appropriate. If the limit does not otherwise exist, enter DNE.) lim
x→[infinity]

(
8x+9
−3

)

Answers

Step-by-step explanation:

Take a picture and repost

This is for college Algebra please help me ​

This is for college Algebra please help me

Answers

Step-by-step explanation:

h o g   =   6 ( x^2 + x - 2)   + 1

             = 6x^2 + 6x -12 + 1

             = 6x^2 + 6x -11              put in -7 for 'x'

                  6 (-7^2) + 6 (-7) - 11

               = 241

* * * edited * * *

The sticker price is the price you must pay for the vehicle

True or False

Answers

it's true...........

Answer:

False

Step-by-step explanation:

Verified correct with test results.

Find the real numbers that satisfy the equation below. Express your answer in set-builder notation. |x| = x

Answers

Answer:

Explanation:

We were given that:

\(|x|=x\)

\(undefined\)

x=y+8 and x=5y+12
(x,y)

Answers

3 x + 2 y + z x + y + z   ,  x = 2  ,  y = 3  ,  z = 1 tan ( x )  ,  x = − π 3 x + 2 y + z  ,  x = 2  ,  y = 3  ,  z = 1

Pls help! I found a linear function, but I don't understand, what should I do with a and b

Pls help! I found a linear function, but I don't understand, what should I do with a and b

Answers

The cost of each desk is $42.

The initial cost to make these new school desks is $635.

What is a solution of linear function?

The terms "linear function" in mathematics apply to two different but related ideas: A polynomial function of degree zero or one that has a straight line as its graph is referred to as a linear function in calculus and related fields.

Assume that the cost of each desk be m.

The initial cost to make these new school desks be c.

Then the total cost will represent by the equation:

y = mx + c .....(i)

Putting x =21 and y = 1517 in the equation (i)

1517 = 21m + c ...(ii)

Putting x = 47 and y = 2609 in the equation (i)

2609 = 47m + c ...(iii)

Subtract equation (ii) from (iii)

47m + c =2609

21m + c = 1517

(-)     (-)     (-)

___________

26m = 1092

Divide both sides by 26

m = 42

Putting m = 42 in equation (ii)

1517 = 21 × 42 + c

1517 = 882 + c

c = 1517 - 882

c = 635

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What is the product of 3/6 and 5/12 in simplest radical form?

Answers

Answer:

5/24

Step-by-step explanation:

3/6 x 5/12 = 1/2 x 5/12 = 5/24

Find the product of 1/2 * 3 1/4 * 1 1/2.
Please help I'm not really good at these.

Answers

Answer:

2 7/16

Step-by-step explanation:

1/2*13/4=13/8

13/8*3/2=39/16

39/16=2 7/16

Hope this helped!! :)

Stay safe and have a wonderful day/night!!!!!

Brainliest?!?!

A car traveing 66 km/h slows down at a constant 0.47 m/s^2 just by 7leting up on the gas" Calculate the distance the cir coasts before t steps Express your answer to two significant figures and include the appropriate units. x incorrect; Try Again; One attempt remaining Part B Cakilate the time A takes to sop Express your answer to two significant figures and include the appropriate units Calculate the time it takes to stop. Express your answer to two significant figures and include the appropriate units. Part C Calculate the distance it travels during the first second. Express your answer to two significant figures and include the appropriate units. Calculate the distance it travels during the fifth second Express your answer to two significant figures and include the appropriate units.

Answers

a) The correct option for distance is B.

b) The correct option is C.

c) The correct option is D.

a) The formula to calculate the distance is given as: 

d = vit + 0.5at2

Here, v is the initial velocity, a is the acceleration, and t is the time taken.

Initially, the car is moving at a velocity of 66 km/h, which can be converted to meters per second using the conversion factor: 

1 km/h = 0.27777777778 m/s.

Therefore, the initial velocity of the car is: 

v = 66 km/h × 0.27777777778 m/s/km/h

= 18.33333 m/s

The car decelerates at a constant rate of 0.47 m/s2.

Therefore, a = -0.47 m/s2 (negative sign indicates deceleration)

The time it takes for the car to stop can be calculated using the formula: 

v = at + v0

where v0 is the initial velocity of the car, which is 18.33333 m/s.

Therefore, the time taken for the car to stop is: 

t = -v0 / a

= -18.33333 / (-0.47)

= 39.01596 seconds.

Rounding off the answer to two significant figures, the time taken for the car to stop is 39 seconds.

Hence, the correct option is B.

Calculate the distance it travels during the first second. Express your answer to two significant figures and include the appropriate units.

The distance traveled during the first second can be calculated using the formula: 

d = vit + 0.5at2

For the first second, the initial velocity is 18.33333 m/s, and the acceleration is -0.47 m/s2.

Therefore, the distance traveled in the first second is: 

d = 18.33333 × 1 + 0.5 × (-0.47) × 12 = 18.119915 meters.

Rounding off the answer to two significant figures, the distance traveled during the first second is 18 meters.

Hence, the correct option is C.

Calculate the distance it travels during the fifth second. Express your answer to two significant figures and include the appropriate units.

The distance traveled during the fifth second can be calculated as the difference between the distance traveled during the fifth second and the distance traveled during the fourth second. The distance traveled during the fourth second is given by: d4 = 18.33333 × 4 + 0.5 × (-0.47) × 42 = 68.95992 meters

The distance traveled during the fifth second is given by: d5 = 18.33333 × 5 + 0.5 × (-0.47) × 52 = 86.7999 meters

Therefore, the distance traveled during the fifth second is: d5 - d4 = 86.7999 - 68.95992 = 17.83998 meters.

Rounding off the answer to two significant figures, the distance traveled during the fifth second is 18 meters.

Hence, the correct option is D.

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I’m doing rlly old work and I don’t remember doing it but anybody wanna answer cs

Im doing rlly old work and I dont remember doing it but anybody wanna answer cs

Answers

Answer:

Its 2

Step-by-step explanation:

Because an exponent is usually the little number on the right sideof another number . It stands for how much times your going to multiply by

For example like your question 9 with a exponent of 2

It would be 9x9 which should be 81 .

Hope I helped -

Sleepy~

whats the answer to m(x)= -2x Find m(5)

Answers

Answer:tryna. Get points don't mind me

Step-by-step explanation:

the differce of a number and twenty four is equal to forty six​

Answers

Answer:

n - 24 = 46

Step-by-step explanation:

Answer:

It is 70 because when you add 24 and 46 it is 70

so when you subtract 24 from 70, you get 46

:)

Step-by-step explanation:

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