Equation of the circle. Please help.

Step-by-step explanation:

The elevator has an acceleration and deceleration of magnitude 1.0 m/s^2, so it takes (5 m/s) / (1 m/s^2) = 5 seconds to reach its maximum speed of 5 m/s.

To come to a stop from this maximum speed, it will also take 5 seconds.

The time it takes for the elevator to travel the entire distance of 200 m is given by:

t = 5 s + 5 s + d / v

where d is the distance traveled at constant speed and v is the constant speed.

We know that the total time is equal to t = 10 s + d / 5 m/s.

Thus, d = (10 s - 5 s) * 5 m/s = 25 m.

So the elevator spends 5 seconds accelerating, 5 seconds decelerating, and 10 - 5 = 5 seconds at constant speed.

Answer:

25% off

Step-by-step explanation:

Answer It’s Save 20$, cause if u buy Something More then 88$ U could 20% off which the new price will be 68$ (to make sure Take 88 from 20 Which will prob be 68) but 68$ would be the new price if Lacey Picked the “Save $20 one purchased Of $75 or more”

Step-by-step explanation hope this helps

Answer:

\(\text{C. }a_n=-8+(n-1)5\)

Step-by-step explanation:

The explicit formula for an arithmetic sequence is given by \(a_n=a_1+(n-1)d\), where \(a_n\) is the \(n\)th, \(a_1\) is the first them of the sequence, and \(d\) is the common difference.

In the given sequence -8, -3, 2, 7, we can see that we're adding 5 to each term. Therefore, the common different is positive five (+5). We can also identify the first term is -8. Therefore, we have:

Thus, the explicit formula for this sequence is:

\(\boxed{a_n=-8+(n-1)5}\)

On solving the provided question, we cans ay that the percentage of people that vote in favour is required by the random variable supplied in b, making that option the best one.

A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. It is frequently denoted using the percent symbol "%," though.

We estimate the parameter based on the sample values when the parameter is unknown. A point estimate is used to estimate the unknown parameter and is a function of sample values. Additionally, we are aware that statistic refers to the function of sample values. If a confidence interval is described as having a lower endpoint equal to the point estimate minus the margin of error, then

The proportion is used to calculate the percentage of people who possess a given quality. Since the random variables in letters a, c, and d are numerical, the confidence interval for the mean will be applied to them.

Additionally, the percentage of people that vote in favour is required by the random variable supplied in b, making that option the best one.

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Answer:

130-85=45

45/7.5=6

Step-by-step explanation:

so she would have 6 days to rent the jet ski if she wanted to spend all of her money on that.

ABC is the intermediate, and A is the catalyst in this reaction mechanism.

In the given mechanism, an intermediate is a species that is formed in one step but is then consumed in a subsequent step.

In this mechanism, the species ABC is an intermediate because it is formed in step 1 but is then consumed in step 2.

This means that it does not appear in the overall equation for the reaction, as it is not a reactant or product.
On the other hand, a catalyst is a species that speeds up the rate of a reaction without being consumed itself.

In this mechanism, there is no catalyst because none of the species involved speeds up the reaction without being consumed itself.

All the species are either reactants or products or intermediates.
Overall,

The mechanism shows a reaction between A, B, and C, which involves two steps. In the first step, A reacts with BC to form the intermediate ABC.

In the second step, BC reacts with ABC to form A, B2, and C2.

The overall equation for the reaction shows that two moles of BC react to form one mole each of B2 and C2.

This mechanism represents a complex reaction that occurs in multiple steps, and it is important to understand the role of intermediates in these steps to better understand the reaction as a whole.

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In this mechanism, ABC is an intermediate because it is formed in the first step and consumed in the second step. BC is a catalyst because it is not consumed or formed in the overall reaction but it facilitates the reaction by participating in both steps. ABC is the intermediate and A is the catalyst in this reaction mechanism.

Let's analyze the given reaction mechanism to identify the intermediate and the catalyst.

Step 1: A + BC → ABC
Step 2: BC + ABC → A + B2 + C2
Overall: 2BC → B2 + C2

1. Identify the intermediate:
An intermediate is a species that is produced in one step and consumed in another. In this mechanism, ABC is formed in step 1 and consumed in step 2. Therefore, ABC is the intermediate.

2. Identify the catalyst:
A catalyst is a species that is consumed in one step and regenerated in another step without being consumed in the overall reaction. In this mechanism, A is consumed in step 1 and regenerated in step 2. Since A does not appear in the overall reaction, it is the catalyst.

In conclusion, ABC is the intermediate and A is the catalyst in this reaction mechanism.

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Answer:

100

Step-by-step explanation:

The relationship between the ratios is multiplying by 10.

Have a splendiferous day!

Hope this helps!

Answer:

I think its c bc (PEMDAS) shoes multiplication comes first

Answer:

I also think it's. C

Parentheses

Exponents

Multiplication

Division

Addition

Subtraction

In this scenario, the lead investigator intends to test the null hypothesis H0: σ = 60 against the alternative hypothesis H1: σ ≠ 60, using a significance level of 0.07. However, the investigator has made an error in defining the critical region for rejecting the null hypothesis.

1. (a) To find y σ, we need to determine the critical values that define the region where H0 will be rejected. Since the investigator intends to reject H0 if y falls in the region (60σ, yσ) or (60+ yσ), we can calculate the value of y using the formula: y = (critical value - 60) / σ

Given that σ = 8 and the significance level is 0.07, we need to find the critical values from the standard normal distribution corresponding to a cumulative probability of 0.035 on both tails. The critical values can be obtained using a statistical table or software, and they are approximately ±2.17. Plugging in these values, we can calculate y: y = (2.17 * 8) ≈ 17.36. Therefore, y σ is approximately 17.36.

2. (b) The power of a statistical test measures the probability of correctly rejecting the null hypothesis when the alternative hypothesis is true. In this case, we need to calculate the power of the test when σ = 62. To find the power, we first need to determine the critical region using the incorrect definition provided by the investigator. The critical region is defined as (60σ, yσ) or (60+ yσ). Plugging in σ = 62 and y = 17.36 into these expressions, we get (60 * 62, 60 + 17.36 * 62) or (60 * 62, 60 + 17.36 * 62). This simplifies to (3720, 1745.32) or (3720, 4745.32).

3. Next, we calculate the probability that a random sample from a normal distribution with σ = 62 falls within the critical region. This probability can be obtained by finding the area under the normal distribution curve between the two critical values.

4. Using statistical software or tables, we find the probabilities corresponding to the critical values of 3720 and 4745.32 in a normal distribution with a mean of 60 and standard deviation of 62. Let's denote this probability as P(reject | σ = 62). This probability represents the power of the test when σ = 62.

5. (c) In order to evaluate the power of the test when σ = 62 with the correct definition of the critical region, we need to redefine the critical region. The correct critical region for rejecting the null hypothesis H0: σ = 60 against the alternative hypothesis H1: σ ≠ 60 would be determined by the appropriate critical values based on the desired significance level.

6. Since the significance level is not specified in the question, we cannot determine the exact critical values. However, by using the correct critical region, we can calculate the power of the test for a given σ = 62 using the same method explained in part (b).

7. In summary, the lead investigator incorrectly defined the critical region for the hypothesis test. The value of y σ was calculated to be approximately 17.36. The power of the test when σ = 62 using the incorrect critical region definition was determined by calculating the probability of falling within the defined region, while the power using the correct critical region definition cannot be determined without knowing the specific significance level.

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Answer: y=10(3)^x

Step-by-step explanation:

if you graph it it's the only one that has the matching table values to the one shown in the question.

Answer:

t = 4

Step-by-step explanation:

1. 2*t = 2t

2. 2*1 = 2

3. 2t+2 = 10

4. 10-2 = 8

5. 2t = 8

6. 8/2 = 4

7. t = 4

Answer:

t = 4

Step-by-step explanation:

2(t + 1) = 10

2t + 2 = 10

2t = 10 - 2

2t = 8

t = 8 ÷ 2

t = 4

-TheUnknownScientist

Answer:

x = 8

Step-by-step explanation:

Since C is the centroid, then

CP = \(\frac{1}{3}\) JP , that is

2x + 4 = \(\frac{1}{3}\) (8x - 4) ( multiply through by 4 to clear the fraction )

6x + 12 = 8x - 4 ( subtract 8x from both sides )

- 2x + 12 = - 4 ( subtract 12 from both sides )

- 2x = - 16 ( divide both sides by - 2 )

x = 8

The correct statement is: 'A one-variable data table has input values that are listed either down a column (column-oriented) or across a row (row-oriented). '

The correct answer is an option (a)

We know that a one-variable data table contain its input values either in a single column (column-oriented), or across a row (row-oriented).

And any formula in this data table must refer to only one input cell.

Whereas we se a two-variable data table to see how different values of two variables in one formula will change the formula results.

Custom data tables are used for: Building data-driven services that can easily be updated without modifying it and storing the results.

And the pre-formatted data tables stored as building blocks in galleries that can be accessed any time and be reused any number of times you want.

Therefore, the correct answer is an option (a)

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The complete question is:

A ________ data table has input values that are listed either as column-oriented or roworiented.

A) one-variable

B) two-variable

C) custom

D) pre-formatted

Answer:

7.) 0.7

8.) 1

9.) 4.24

Step-by-step explanation:

Answer:

4.24

Step-by-step explanation:

Answer:

Step 2 has error and step 4 has error.

Step-by-step explanation:

Here we can see that elimination method is  applied to solve the  system  of equations  for which -2 is multiplied both sides of equation first

-2(x+2y)=-2(10 which is correct

but in step 2

left side is -2x-4y and the right side is -10 which has to be -20 which makes this step wrong and this is the error made by student.

in Step 4 also ,value of the y has to be 5 but student plugged y =1 which is also error by student.

Correct solution is

   -2x-4y= -20

     2x+ 5y= 15

on adding ,we get

y = -5

plugging y =5 in equation x+2y= 10 ,we get x+2(-5) =10 ,we get x = 20

therefore (20,-5) is the  solution

Answer:

step 2

Step-by-step explanation:

Given that 9 F(X) Dx = 37 0 and 9 f(x) dx = 37, and 9 g(x) dx = 16, we have to find 9 [4f(x) + 6g(x)] dx.Now, 9[4f(x) + 6g(x)] dx = 4[9 f(x) dx] + 6[9 g(x) dx]using the linear property of the definite integral= 4(37) + 6(16) = 148 + 96 = 244Therefore, 9[4f(x) + 6g(x)] dx = 244. The integral limits are from 0 to integral.gif.

The given content is a set of equations involving integrals. The first equation states that the definite integral of function F(x) with limits from 0 to 9 is equal to 37. Similarly, the second equation states that the definite integral of function f(x) with limits from 0 to 9 is also equal to 37. The third equation involves the definite integral of another function g(x) with limits from 0 to 9, which is equal to 16.

The problem requires finding the definite integral of the expression [4f(x) + 6g(x)] with limits from 0 to 9. This can be done by taking the integral of 4f(x) and 6g(x) separately and then adding them up. Using the linearity property of integrals, the integral of [4f(x) + 6g(x)] can be written as 4 times the integral of f(x) plus 6 times the integral of g(x).

Substituting the values given in the third equation, we can calculate the value of the integral [4f(x) + 6g(x)] with limits from 0 to 9.

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9[4f(x) + 6g(x)] dx = 4[9 f(x) dx] + 6[9 g(x) dx] using the linear property of the definite integral= 4(37) + 6(16) = 148 + 96 = 244. The integral limits are from 0 to integral.

Given that 9 F(X) Dx = 37 0 and 9 f(x) dx = 37, and 9 g(x) dx = 16, we have to find 9 [4f(x) + 6g(x)] dx.

Now, 9[4f(x) + 6g(x)] dx = 4[9 f(x) dx] + 6[9 g(x) dx] using the linear property of the definite integral= 4(37) + 6(16) = 148 + 96 = 244.

The given content is a set of equations involving integrals. The first equation states that the definite integral of function F(x) with limits from 0 to 9 is equal to 37.

Similarly, the second equation states that the definite integral of function f(x) with limits from 0 to 9 is also equal to 37.

The third equation involves the definite integral of another function g(x) with limits from 0 to 9, which is equal to 16.

The problem requires finding the definite integral of the expression [4f(x) + 6g(x)] with limits from 0 to 9. This can be done by taking the integral of 4f(x) and 6g(x) separately and then adding them up.

Using the linearity property of integrals, the integral of [4f(x) + 6g(x)] can be written as 4 times the integral of f(x) plus 6 times the integral of g(x).

Substituting the values given in the third equation, we can calculate the value of the integral [4f(x) + 6g(x)] with limits from 0 to 9.

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Answer:

113.1 cm³

Step-by-step explanation:

diameter = 2 X radius

Volume of sphere = (4/3) X π X r ³

= (4/3) π (3)³

= 36π

= 113.1 cm³ to nearest tenth

The number formed by the digits 16, 06, and 68 is 160668, which is determined by concatenating them in the given order.

To determine the number formed by the given digits, we concatenate them in the given order. Starting with the first digit, we have 16. The next digit is 06, and finally, we have 68. By combining these three digits in order, we get the number 160668.

When concatenating the digits, the position of each digit is crucial. The placement of the digits determines the resulting number. In this case, the digits are arranged as 16, 06, and 68, and when they are concatenated, we obtain the number 160668. It's important to note that the leading zero in the digit 06 does not affect the value of the resulting number. When combining the digits, the leading zero is preserved as part of the number.

Therefore, the number formed by the digits 16, 06, and 68 is 160668.

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Answer:

★ For example, Graphing is one of the simplest ways to solve a system of linear equations, all you have to do is graph each equation as a line and find the points where the lines two intersect.

Step-by-step explanation:

Hope you have a great day :)

The Marginal Rate of Substitution (MRS) for each utility function is:

(a) MRS = xb/xa

(b) MRS = 3y/x

(c) MRS = xa/xb

(d) MRS = y/x

(e) MRS = 2

To locate the Marginal Rate of Substitution (MRS) for every software function, we want to calculate the partial derivatives with recognition to the variables concerned. Let's decide the MRS for each feature:

(a) u(xa, xb) = \(xa^(1/2) * xb^(1/2)\)

MRS = ∂u/∂xa / ∂u/∂xb

= (∂/∂xa \((xa^(1/2) * xb^(1/2))\)) / (∂/∂xb \((xa^(1/2) * xb^(1/2))\))

= \((1/2 * xa^(-1/2) * xb^(1/2)) / (1/2 * xa^(1/2) * xb^(-1/2))\)

= xb/xa

(b) u(x, y) = \(x^(3/4) * y^(1/4)\)

MRS = ∂u/∂x / ∂u/∂y

= (∂/∂x \((x^(3/4) * y^(1/4)))\) / (∂/∂y \((x^(3/4) * y^(1/4))\))

=\((3/4 * x^(-1/4) * y^(1/4)) / (1/4 * x^(3/4) * y^(-3/4))\)

= 3y/x

(c) u(xa, xb) = (1/2) * ln(xa) + (1/2) * ln(xb)

MRS = ∂u/∂xa / ∂u/∂xb

= (∂/∂xa [(1/2) * ln(xa) + (1/2) * ln(xb)]) / (∂/∂xb [(1/2) * ln(xa) + (1/2) * ln(xb)])

= (1/2) * (1/xa) / (1/2) * (1/xb)

= xa/xb

(d) u(x, y) = (4/3) * ln(x) + (4/1) * ln(y)

MRS = ∂u/∂x / ∂u/∂y

= (∂/∂x [(4/3) * ln(x) + (4/1) * ln(y)]) / (∂/∂y [(4/3) * ln(x) + (4/1) * ln(y)])

= (4/3) * (1/x) / (4/1) * (1/y)

= y/x

(e) u(xa, xb) = 2 * xa + xb

MRS = ∂u/∂xa / ∂u/∂xb

= (∂/∂xa (2 * xa + xb)) / (∂/∂xb (2 * xa + xb))

= 2 / 1

= 2

Therefore, the Marginal Rate of Substitution (MRS) for every utility characteristic is:

(a) MRS = xb/xa

(b) MRS = 3y/x

(c) MRS = xa/xb

(d) MRS = y/x

(e) MRS = 2

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(a) The MRS for this utility function is √(xb / xa).

(b) The MRS for this utility function is 3 *\((y / x)^(0.25).\)

(c) The MRS for this utility function is xb / xa.

(d) The MRS for this utility function is y / x.

(e) The MRS for this utility function is 2.

To find the Marginal Rate of Substitution (MRS) for each utility function, we need to calculate the ratio of the marginal utilities of the two goods.

The MRS represents the rate at which a consumer is willing to trade one good for another while maintaining the same level of utility.

(a) \(u(xa, xb) = xa^(1/2) * xb^(1/2)\)

To find the MRS, we calculate the partial derivatives of the utility function with respect to each good and take the ratio:

MRS = (d(u(xa, xb))/d(xa)) / (d(u(xa, xb))/d(xb))

= \((0.5 * xb^0.5 * xa^(-0.5)) / (0.5 * xa^0.5 * xb^(-0.5))\)

=\((xb^0.5) / (xa^0.5)\)

= √(xb / xa)

Therefore, the MRS for this utility function is √(xb / xa).

(b) u(x, y) = \(x^(3/4) * y^(1/4)\)

MRS = (d(u(x, y))/d(x)) / (d(u(x, y))/d(y))

= \((0.75 * x^(-0.25) * y^(0.25)) / (0.25 * x^(0.75) * y^(-0.75))\)

= \((3 * y^(0.25)) / (x^(0.25) * y^(-0.75))\)

= \(3 * (y / x)^(0.25)\)

Therefore, the MRS for this utility function is 3 * \((y / x)^(0.25).\)

(c) u(xa, xb) = (1/2) * ln(xa) + (1/2) * ln(xb)

MRS = (d(u(xa, xb))/d(xa)) / (d(u(xa, xb))/d(xb))

= [(1/2) * (1/xa)] / [(1/2) * (1/xb)]

= xb / xa

Therefore, the MRS for this utility function is xb / xa.

(d) u(x, y) = (4/3) * ln(x) + (4/1) * ln(y)

MRS = (d(u(x, y))/d(x)) / (d(u(x, y))/d(y))

= [(4/3) * (1/x)] / [(4/1) * (1/y)]

= y / x

Therefore, the MRS for this utility function is y / x.

(e) u(xa, xb) = 2 * xa + xb

MRS = (d(u(xa, xb))/d(xa)) / (d(u(xa, xb))/d(xb))

= 2 / 1

= 2

Therefore, the MRS for this utility function is 2.

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45

bc 2$ * 20 + 5= 45$

Answer:

45

Step-by-step explanation:

a) Marginal probability distributions for X and Y are: X 1 2 P(y) Y 0 0.30 0.10 1 0.40 0.20 P(x) 0.50 0.50 and b) Corr(X,Y) = -1.68 and c) Var(W) = -0.34

a) Marginal probability distributions for X and Y are: X 1 2 P(y) Y 0 0.30 0.10 1 0.40 0.20 P(x) 0.50 0.50

b) The covariance and correlation for X and Y are:

Cov(X,Y)= E(XY) - E(X)E(Y)

Cov(X,Y)= (1 * 0 + 2 * 0.3 + 1 * 0.1 + 2 * 0.2) - (1 * 0.5 + 2 * 0.5)(0 * 0.5 + 1 * 0.4 + 0 * 0.1 + 1 * 0.2)

Cov(X,Y)= (0 + 0.6 + 0.1 + 0.4) - (0.5 + 1) (0.4 + 0.2)

Cov(X,Y)= 0.12 - 0.9 * 0.6

Cov(X,Y)= 0.12 - 0.54

Cov(X,Y)= -0.42

Corr(X,Y)= Cov(X,Y)/σxσyσxσy

= √[∑(x-µx)²/n] × √[∑(y-µy)²/n]σxσy

= √[∑(x-µx)²/n] × √[∑(y-µy)²/n]σx

= √[∑(x-µx)²/n]

= √[(0.5 - 1.5)² + (0.5 - 0.5)² + (0.5 - 1.5)² + (0.5 - 1.5)²]/2σx

= 0.50σy

= √[∑(y-µy)²/n]

= √[(0 - 0.5)² + (1 - 0.5)²]/2σy

= 0.50

Corr(X,Y) = Cov(X,Y)/(0.50 * 0.50)

Corr(X,Y) = (-0.42)/0.25

Corr(X,Y) = -1.68

c) The mean and variance for the linear function W = X + Y are:

Hw = E(W)

Hw = E(X + Y)

Hw = E(X) + E(Y)

Hw = 1.5 + 0.5

Hw = 2

Var(W) = Var(X + Y)

Var(W) = Var(X) + Var(Y) + 2Cov(X,Y)

Var(W) = 0.25 + 0.25 - 2(0.42)

Var(W) = 0.50 - 0.84

Var(W) = -0.34

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L = lenght = 4w + 7

W = width

Perimeter = 2L + 2W

74 = 2 (4W + 7 ) + 2 W

74 = 8W + 14 + 2 W

74 = 10W + 14

74-14 = 10W

60 = 10W

60/10 = W

6 = W

L = 4W + 7

L= 4(6) +7

L= 24+7

L= 31

Answer:

Lenght = 31 inches

Width = 6 inches

Answer:

6

Step-by-step explanation:

Answer:

To compute the total cost based on the number of drinks and tacos, we can use the given prices of $2 for a drink and $5 for a taco. Let's assume the number of drinks is represented by "d" and the number of tacos is represented by "t". The **total cost** can be calculated as:

totalcost = (2 * d) + (5 * t)

For example, if we have 2 drinks and 3 tacos, the calculation would be:

totalcost = (2 * 2) + (5 * 3) = 4 + 15 = 19

So, with 2 drinks and 3 tacos, the total cost would be $19.

You can substitute the values of "d" and "t" with the desired quantities to calculate the total cost for different combinations of drinks and tacos.

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Answer:

The Moon has a gravitational pull 1/6 of that of Earth

Step-by-step explanation:

(What is your question?)

The probability of the first person having a birthday in any month is 1 (12/12). For the second person, to have a different birth month, the probability is 11/12. For the third person, it's 10/12, and so on. The smallest value of n for which the probability of at least two people sharing the same birth month is more than 0.5 is 5.

The probability that two people in a group of n people are born in the same month can be calculated using the formula:

1 - (12/12) * ((11/12)^(n-1))

This formula represents the probability of the first person being born in any of the 12 months (12/12), and the probability of the second person being born in a different month than the first (11/12). We raise this probability to the power of (n-1) because we are looking for the probability that none of the first n-1 people share a birth month, and then subtract this value from 1 to get the probability that at least two people share a birth month.

To find the smallest value of n for which this probability is more than .5, we can solve the equation:

1 - (12/12) * ((11/12)^(n-1)) > 0.5

Simplifying this equation gives:

(11/12)^(n-1) < 0.5/12

Taking the logarithm of both sides and solving for n gives:

n > log(0.5/12) / log(11/12) + 1

n > 17.43

Therefore, the smallest value of n for which the probability of at least two people sharing a birth month is more than .5 is n = 18.

To answer your question, we can use the concept of complementary probability. Instead of directly finding the probability of at least two people having the same birth month, we'll first find the probability of all people having different birth months and then subtract it from 1.

Let's consider n people. The probability of the first person having a birthday in any month is 1 (12/12). For the second person, to have a different birth month, the probability is 11/12. For the third person, it's 10/12, and so on.

So, the probability of all n people having different birth months is:
P(different) = (12/12) * (11/12) * (10/12) * ... * (12-n+1)/12

The probability of at least two people having the same birth month is:
P(at least two same) = 1 - P(different)

Now, we need to find the smallest value of n for which P(at least two same) > 0.5.

You can check different values of n starting from 1, but you will find that for n = 5:

P(different) ≈ 0.492
P(at least two same) ≈ 1 - 0.492 = 0.508

So, the smallest value of n for which the probability of at least two people sharing the same birth month is more than 0.5 is 5.

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Step-by-step explanation:

tan2x = sin2x/cos2x

we know that ,

Since, tan2x = 2sinx*cosx/cos²x- sin²x

Dividing by cos²x in numerator and denominator.

We get ,

The ladder will reach 15 feet length up the building.

1. The ladder is 20 feet long

2. The ladder is set up 5 feet from the base of the building

3. Subtract the 5 feet from the length of the ladder (20 feet)

4. The answer is 15 feet

The 20-foot ladder is set up 5 feet from the base of the building. To calculate how far up the building the ladder reaches, we need to subtract the 5 feet from the length of the ladder. The answer is 15 feet. This means the ladder will reach 15 feet up the building (5 feet from the base). This can also be visualized by imagining that the remaining 15 feet of the ladder is being used to reach up the building. The 5 feet of the ladder not used to reach up the building is used to support the ladder on the ground.

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Answer:

Step-by-step explanation:

Explanation:

Step one:

The original price of the video game= $28.5

Cash at hand= $22

Discount= 30%

Tax= 10%

1. Pat's strategy

Amount discounted

=30/100*28.5

=0.3*28.5

=$8.55

28.5-8.55

=$19.95

Amount of tax added

=10/100*28.5

=0.01*28.5

=2.85

=17.15+2.85

=$22.8

Hence going by Pat's strategy, the total amount to be paid is

=$22.8

2. Henri's strategy

=70/100*28.5

=0.70*28.5

=$19.95

110% of $28.5

=110/100*28.5

=1.1*28.5

=$31.35

the tax is

31.35-28.5

=$2.85

i. Hence by Henri's strategy, the sales price with tax is

=19.95+2.85

=$22.8

ii. Yes Pat's strategy will compute the correct total,

   30% of $28.5 is $8.55 which is the amount to be deducted as a discount

   10% of $28.5 is $2.85 which is the amount to be added as tax

    Hence the total amount to be paid is $22.8

iii  Yes Henri's strategy also gave the correct total

  70% of 28.5 is $19.95

  110% of 28.5 of tax is the same as adding 10% of 28.5 to 28.5

   = 31.35, substracting the original price we got the tax added

    which is $2.85

iv. No, they both don't have enough money to purchase the video game,

  because they only have $22and the game is to be sold for $22.8