Determine the solution for the equation, 5w - 9= 44.

To prove the statement using mathematical induction, we need to follow two steps: the base case and the inductive step. By completing the base case and the inductive step, we can conclude that the statement is true for all positive integers n.

Base Case: Let n = 1.

The left-hand side of the equation is 4, and the right-hand side is -(4-1) = -3.

So, the equation holds true for n = 1.

Inductive Step: Assume that the equation holds true for some positive integer k.

That is, 4 + 4² + 4³ + ... +\(4^{k}\)  = -(4-1).

Now, we need to prove that the equation holds true for k+1.

Consider the sum 4 + 4² + 4³ + ... + \(4^{k}\) + \(4^{k+1}\).

Using the assumption, we can substitute -(4-1) for the sum up to k:

4 + 4² + 4³ + ... + \(4^{k}\)+ \(4^{k+1}\) = -(4-1) + \(4^{k+1}\).

Simplifying the right-hand side, we get:

-(4-1) + \(4^{k+1}\) = -3 +\(4^{k+1} \\\)  = \(4^{k+1}\) - 3.

Therefore, the equation holds true for k+1.

To prove the statement using mathematical induction, By completing the base case and the inductive step, we can conclude that the statement is true for all positive integers n.

To learn more about mathematical induction visit:

brainly.com/question/29503103

#SPJ11

The complete question is: <Use mathematical induction to prove the following statements. Show your work.

11. 4 + 4² +4³ +...+\(4^{k}\) = -( 4-1 ) >

Answer:

-1.3333333333333

Step-by-step explanation:

Answer:

8.1796

Step-by-step explanation:

2.86 x 2.86 = 8.1796

The risk of explosion in the process industry is 6.6594e-06 per year.

To calculate the risk of explosion, we need to consider the probability of a gas release, the probability of ignition, and the probability of fatal injury.

Step 1: Calculate the probability of an explosion.

The probability of a gas release per year is given as\(1.23 * 10^-^5\).

The probability of ignition is 0.54.

The probability of fatal injury is 0.32.

To calculate the risk of explosion, we multiply these probabilities:

Risk of explosion = Probability of gas release * Probability of ignition * Probability of fatal injury

Risk of explosion = 1.23 * \(10^-^5\) * 0.54 * 0.32

Risk of explosion = 6.6594 *\(10^-^6\) per year

Therefore, the risk of explosion in the process industry is approximately 6.6594 * 10^-6 per year.

Learn more about explosion  

brainly.com/question/16787654

#SPJ11

The equation modeling function g after the given transformations on the parent sine function is:

g of (x) = A x sine(C(x minus D))+k

where A is the vertical stretch factor, C is the reciprocal of the horizontal stretch factor, D is the horizontal shift, and k is the vertical shift.

Substituting the given values, we get:

g of (x) = 3*sine((1/1)(x+1))+(-4)

Simplifying further, we get:

g of (x) = 3*sine of (x+1)-4

Therefore, the equation modeling function g is g of (x) = 3*sine(x+1)-4 after the given transformations on the parent sine function.

Learn more about Functions:

https://brainly.com/question/25638609

#SPJ4

The value of f left parenthesis 3 right parenthesis is 45.

According to the statement

We have given that the F(x) = 5(x)^2

and we have to find the value when Sophia have a 3 right parenthesis.

So, Parenthesis are used in mathematical expressions to denote modifications to normal order of operations.

And now we have to find the value for 3 right parenthesis

And for this purpose we have to put the value X= 3 in the f(x) then

F(x) = 5(x)^2

F(3) = 5(3)^2

F(3) = 5*9

F(3) = 45.

here the value of 3 right parenthesis is 45.

So, The value of f left parenthesis 3 right parenthesis is 45.

Learn more about PARENTHESIS here https://brainly.com/question/1473593

#SPJ4

Answer: False

Step-by-step explanation:

Researchers typically report the adjusted R-squared value in addition to the regular R-squared value, not because they lack confidence in the actual R-squared, but because the adjusted R-squared provides additional information about the goodness of fit of a statistical model. The regular R-squared value measures the proportion of the variance in the dependent variable that is explained by the independent variables in the model. However, it can be biased and increase as more predictors are added to the model, even if the additional predictors do not contribute significantly to the prediction.

The adjusted R-squared, on the other hand, takes into account the number of predictors in the model and penalizes the addition of irrelevant predictors. It provides a more conservative measure of the goodness of fit by adjusting for the number of predictors and the sample size. Researchers often use the adjusted R-squared to evaluate and compare different models with varying numbers of predictors or to assess the overall explanatory power of a model while considering its complexity.

In summary, researchers report the adjusted R-squared value to address the limitations of the regular R-squared and to provide a more accurate assessment of the model's goodness of fit.

Answer:

187/2

Step-by-step explanation:

The formula for d in terms of t is d = 5t2.

The distance that a ball falls in t seconds when dropped vertically is given by the formula d = 0.5 gt2, where g is the acceleration due to gravity and is equal to 9.8 m/s2.

To find a formula for d in terms of t if D is directly proportional to the square of t, we can write:

d = kt2 where k is a constant.

To find the value of k, we use the given information that the ball falls 20 metres in 2 seconds.

Substituting this into the formula, we get:

20 = k(2)220

= 4kk

= 20/4k

= 5

Substituting this value of k into the formula, we get:

d = 5t2

Therefore, the formula for d in terms of t is d = 5t2.

This means that for any value of t, we can use this formula to find the distance that a ball falls when dropped vertically in t seconds. The formula gives us a quick and easy way to calculate the distance without having to use the more complex formula involving acceleration due to gravity.

Learn more about distance -

brainly.com/question/30395212

#SPJ11

If two random variables, Y1 and Y2, are independent, the condition that needs to be satisfied is that the joint probability distribution of Y1 and Y2 factors into the product of their individual probability distributions.

Mathematically, for independent random variables Y1 and Y2, the condition can be expressed as:

P(Y1 = y1, Y2 = y2) = P(Y1 = y1) * P(Y2 = y2)

This means that the probability of both events Y1 = y1 and Y2 = y2 occurring together is equal to the product of the probabilities of each event occurring individually.

In simpler terms, knowing the outcome or value of one random variable does not provide any information about the outcome or value of the other random variable if they are independent. They do not influence each other's probability distributions.

Learn more about  probability   from

https://brainly.com/question/30390037

#SPJ11

Answer:

2.5

Step-by-step explanation:

When graphing an exponential function, a T-chart is commonly used to determine the values. The correct answer is option A.

The T-chart employs positive real numbers since this is the most typical form of exponential function.

Exponential functions are utilized to represent processes that increase or decrease exponentially, as well as to model phenomena in many different disciplines, including science, economics, and engineering.

The exponential function can be represented by the following equation:

\(y=a^x\), where a is the base, x is the exponent, and y is the outcome.

When a is a positive number greater than one, the function is called exponential growth, while when a is a fraction between 0 and 1, the function is called exponential decay.

The T-chart is used to determine the values to use in the graph and connect the dots as required. Positive real numbers are used as the values in the T-chart in order to effectively graph the exponential function.

Therefore, the correct answer is option A.

For more questions on exponential function

https://brainly.com/question/30241796

#SPJ8

the equation of the normal plane to the curve at the point (0, 1, 3) is 2x + 6z - 18 = 0.

To find the equation of the normal plane, we first calculate the gradient vector of the curve at the given point. The gradient vector is obtained by taking the partial derivatives of the curve with respect to each variable: ∇r = (dx/dt, dy/dt, dz/dt) = (2cos(2t), 2sin(2t), 6).

At the point (0, 1, 3), the parameter t is 0. Therefore, the gradient vector at this point becomes ∇r = (2cos(0), 2sin(0), 6) = (2, 0, 6).

The normal vector of the plane is the same as the gradient vector, so the normal vector is (2, 0, 6). Since the normal vector represents the coefficients of x, y, and z in the equation of the plane, the equation of the normal plane becomes:

2(x - 0) + 0(y - 1) + 6(z - 3) = 0.

Simplifying the equation, we have:

2x + 6z - 18 = 0.

Learn more about gradient vector here:

https://brainly.com/question/29751488

#SPJ11

Answer:

im literally doing the same question , i hope someone helps us .  

Step-by-step explanation:

Answer:

G (0,5) i think

Step-by-step explanation:

Answer:

3/7

Step-by-step explanation:

The total is 7 blocks. There are three stars. Probability is PART/WHOLE.

3/7

The quotient of √x ³ / √5 x ² is √ ( x / 5 )

To find : the product of √x ³ / √5 x ²

By checking the power of roots for each term

The terms which are given are √x ³ and √5 x ²

Since both the numbers have the same root power they can be combined under the same square root for further operation

Dividing the terms

=> √ ( x ³ / 5 x ² )

=> √ ( x / 5 )

Therefore, we get the quotient of √x ³ / √5 x ² as √ ( x / 5 ).

Learn more about Roots here:

https://brainly.com/question/16932620?referrer=searchResults

#SPJ9

1. The men are playing Dominos in the game.

2. A sandwich with pork ham and cheese is the kind of Cuban food shown.

3. The man in the yellow shirt and white pants is shown Dancing.

4. The Cuban flag has one star.

Dominoes refers to a group of tile-based games with playing pieces that resemble dominoes. A line usually divides the two square ends of each rectangular domino tile. Either a blank space or a series of dots designate each end. Each tile in a set has a back that is either blank or has a similar design, making them all identical.

The playing pieces are what make up a domino set, sometimes referred to as a deck or pack. The typical European domino set consists of 28 tiles with spot counts ranging from zero to six in all possible combinations. Some other names for these tiles are pieces, bones, rocks, stones, men, cards, and simply dominoes.

To know more about word problems visit: brainly.com/question/2610134

#SPJ4

Answer:

(x+5)²+(y+5)² =4

Step-by-step explanation:

the standard equation is

(x-h)²+(y-k)²=r²

where (h, k) is the center in our case ( -5, -5) and r is the radius that in our case r=2, so substitute

(x+5)²+(y+5)²=2²

Answer:

\((x+5)^2+(y+5)^2=4\)

Step-by-step explanation:

Hi there!

Equation of a circle: \((x-h)^2+(y-k)^2=r^2\) where the circle is centered at (h,k) and r is the radius

1) Determine the center of the circle

On the graph, we can determine that the circle is centered at the point (-5,-5). Plug this into the equation:

\((x-(-5))^2+(y-(-5))^2=r^2\\(x+5)^2+(y+5)^2=r^2\)

2) Determine the value of r²

In the graph, we can see that the radius of the circle is equal to 2 units. Therefore, the value of r² is 4. Plug this back into the equation:

\((x+5)^2+(y+5)^2=4\)

I hope this helps!

To find the general solution of the differential equation 9y" + 48y' + 64y = 0, we can assume a solution of the form y = e^(rx), where r is a constant to be determined.

First, let's find the derivatives of y:

y' = re^(rx)

y" = r^2e^(rx)

Now, substitute these derivatives into the differential equation:

9(r^2e^(rx)) + 48(re^(rx)) + 64(e^(rx)) = 0

Factor out e^(rx):

e^(rx)(9r^2 + 48r + 64) = 0

Since e^(rx) is never zero, the equation becomes:

9r^2 + 48r + 64 = 0

Now, we can solve this quadratic equation for r. Factoring or using the quadratic formula, we find that r = -4/3.

Therefore, the general solution of the differential equation is:

y = C1e^(-4/3x) + C2xe^(-4/3x)

Here, C1 and C2 are constants of integration that can take any real values. This solution represents the family of functions that satisfy the given differential equation. The first term C1e^(-4/3x) represents the exponential decay component, while the second term C2xe^(-4/3x) represents a linearly increasing or decreasing component depending on the value of C2.

Learn more about integration here: brainly.com/question/32234560

#SPJ11

The driver B has the fastest typical race time.

It is required to find which driver's race times were the most variable.

A statement is a declarative sentence that is either true or false but not both. A statement is sometimes called a proposition. The key is that there must be no ambiguity. To be a statement, a sentence must be true or false, and it cannot be both.

Given:

From the options presented, driver B has the fastest typical race time because he recorded the smallest time taken to complete an individual race.

Also from the standard deviation given 3.96  seconds  for driver B, it shows that the individual time spread from the standard deviation is minimal and that the driver maintained a fairly consistent time of race throughout the racing period.

Therefore, the driver B has the fastest typical race time.

Learn more details about statement here:

https://brainly.com/question/2285414

#SPJ1

Answer:

9

Step-by-step explanation:

Exterior sides =  180 - 140 = 40

number of sides = 360 / 40 = 9 sides

If Liza takes 120 steps, then the number of steps taken by Pete will be 72.

A ratio is an ordered set of integers a and b expressed as a/b, with b never equaling 0. A percentage is a mathematical expression in which two things are equal.

Pete, Lulu, and Liza are walking in the Boston downtown. Each time Pete takes 4 steps, Lulu takes 3 steps. Each time Lulu takes 5 steps, Liza takes 4 steps.

Then the relation between is given as

4 Pete → 4 Lulu

5 Lulu → 4 Liza

Then we have

\(\rm \dfrac{5}{3} \times 4 \ Pete \rightarrow \dfrac{5}{3} \ Lulu \rightarrow 4 \ Liza\)

If Liza takes 120 steps, then the number of the step taken by Pete will be

\(\rm \dfrac{5}{3} \times 4 \ Pete \rightarrow 4 \times 120 \\\\Pete \rightarrow 72\)

More about the ratio and the proportion link is given below.

https://brainly.com/question/14335762

#SPJ1

Answer:

8a^2+a-7

Step-by-step explanation:

The correct answer is D. setne 23 47. Based on the provided information, I understand that you have a comparison function in C code and its corresponding assembly code. You are asked to fill in the blanks by selecting the appropriate instructions based on the given values of a and b and the status flags SF, OF, ZF, and CF. Let's go through the options:

A. setg 47 23: This option is incorrect because setg is used to set a byte to 1 if the Greater flag (ZF=0 and SF=OF) is set, but the given values of a and b are 47 and 23, respectively, so it does not satisfy the condition for setg to be set.

B. setl 23 47: This option is incorrect because setl is used to set a byte to 1 if the Less flag (SF≠OF) is set, but the given values of a and b are 23 and 47, respectively, so it does not satisfy the condition for setl to be set.

C. sete 23 23: This option is incorrect because sete is used to set a byte to 1 if the Zero flag (ZF=1) is set, but the given values of a and b are 23 and 23, respectively, so it does not satisfy the condition for sete to be set.

D. setne 23 47: This option is correct. setne is used to set a byte to 1 if the Zero flag (ZF=0) is not set, which means the values of a and b are not equal. In this case, the given values of a and b are 23 and 47, respectively, so they are not equal, and setne should be used.

Therefore, the correct answer is D. setne 23 47

To know more about byte visit-

brainly.com/question/32309440

#SPJ11

Answer:

Function                         Not a function      

not a Function                   function

pg 2

B- explanation is that 2 inputs dont have the same output 8-1, 8-1,4-1,3-1

pg 3

1. yes; -5 is not in the set

2. yes; 2 is not in the set

3. no; .75 is 3/4

4. no; -4 is already in the set

The given example of a high school student regarding video game playing is quantitative data collection.

Quantitative data can be measured or counted. The high school student in this example is compiling numerical information about how much time each member of their homeroom class spends playing video games.

The student can first add up the total number of hours each person spends playing video games each week in order to determine the average number of hours spent playing video games each week.

The student can then divide the total number of hours spent playing video games by the number of students in their homeroom class to determine the weekly average.

Learn more about quantitative data collection:

https://brainly.com/question/26533307

#SPJ4

Answer:

deededededededededede

Step-by-step explanation:

dedededededededede

Answer:

2(w-4)=9

Step-by-step explanation:

Twice the difference between a number and 4 means 2 will be multiplied to both w and 4. Then the equation is equal to 9.

Answer:

Step-by-step explanation:

If you mean 3x^3 - 42x^2 - 4x + 5 = 0 you can graph it manually or with technology

The roots are 14.09, 0.30 and -0.39 to nearest hundredth.