choice matrix is shown. Complete the choice matrix by selecting the value equivalent to each function output. 

Consider the functions shown.

f(x) = -3(2^x)

g(x) = -3 + 2x

h(x) = 2(3^x)

j(x) = -3 – 2x

Answer:

the maximum height is 2 meters

The expected value of x is 1.80, the variance is 0.72, and the standard deviation is 0.85.

Calculate the expected value, variance, and standard deviation of the random variable x as follows. Round all answers to two decimal places, and keep in mind that x is the number of red marbles that Suzan has in her hand after selecting three marbles from a bag containing three red marbles and two green ones.

Expected Value: Since there are 3 red marbles and 2 green marbles in the bag, the probability of drawing a red marble is: P(R) = 3/5The probability of drawing a green marble is P(G) = 2/5Therefore, the expected value of the random variable X is: E(X) = μ = np = 3/5 * 3 = 1.80

Variance can be calculated using the following formula: Var(X) = npq, where p is the probability of success and q is the probability of failure of the event. In this scenario, the probability of drawing a red marble is P(R) = 3/5, and the probability of drawing a green marble is P(G) = 2/5.

Therefore, Var(X) = npq Var(X) = (3/5)*(2/5)*3Var(X) = 1.80 * 0.4Var(X) = 0.72Standard Deviation: The square root of the variance is equal to the standard deviation. Hence, the formula for standard deviation is: S.D. = √Var(X)S.D. = √0.72S.D. = 0.85

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To determine the degree of the Maclaurin polynomial required for the error in the approximation of the function f(x) = -x+1 at the indicated value of x to be less than 0.001, we can use the formula: N ≥ ln(error)/ln(absolute value of x) + 1.

For our given function, the error is 0.001, and the value of x is 0.2. Plugging these values into the formula, we get: N ≥ ln(0.001)/ln(0.2) + 1, which is equivalent to N ≥ 6.64 + 1 = 7.64. Therefore, we need the degree of the Maclaurin polynomial to be 7.64 in order for the error in the approximation of the function at the indicated value of x to be less than 0.001.

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Answer:

We see that each fraction is in simplest form, and they add up to 1, so this confirms that 168 is the highest number of similar bouquets that Fatima can make without having any flowers left over.

Step-by-step explanation:

Yeah, I guess what that person said ^^ ??

A hexagon with two lines

hope helped you please make me brainalist and keep smiling dude

I hope you are form India

Answer:

A) k = 0.037

B) 186°F

Step-by-step explanation:

List initial (T₀) and air (Tₐ) temperature

[tex]T_0=280^\circ\\T_a=67^\circ\\[/tex]

Part A

[tex]T=T_a+(T_0-T_a)e^{-kt}\\193^\circ=67^\circ+(208^\circ-67^\circ)e^{-k(3)}\\193=67+141e^{-3k}\\126=141e^{-3k}\\\frac{126}{141}=e^{-3k}\\\ln(\frac{126}{141})=-3k\\-\frac{1}{3}\ln(\frac{126}{141})=k\\k\approx0.037[/tex]

Part B

[tex]T=T_a+(T_0-T_a)e^{-kt}\\T=67+(208-67)e^{-0.037(4.5)}\\T\approx186^\circ\text{F}[/tex]

To compute the 90% confidence interval for the population proportion, large a sample should you draw to ensure that the sample proportion does not deviate from the population proportion by more than 0.05, 271 is the minimum sample

A confidence interval is a range of values where an unknown population parameter lies. The level of confidence is the likelihood of the interval containing the parameter.

The formula to calculate the sample size required to produce a specific margin of error with a known level of confidence for the estimation of a population proportion is given below: 95% confidence interval for population proportion using a sample size formula

[tex]\[n=\frac{z^{2}p(1-p)}{E^{2}}\][/tex]

Where

[tex]\[z\][/tex] is the z-score The formula is modified to calculate the sample size required to produce a specific margin of error with a known level of confidence as follows:

[tex]\[n=\frac{z^{2}}{4E^{2}}\][/tex]

Note: For this problem, the sample size needs to be large enough to ensure that the sample proportion does not deviate from the population proportion by more than 0.05.

Using a Z-score Table, the z-value that corresponds to 90% confidence interval is 1.645.

[tex]n=\frac{z^{2}}{4E^{2}}\ = \frac{1.645^{2}}{4(0.05)^{2}} = \frac{2.706225}{0.0100} = 270.6[/tex]

(rounded up to the next highest integer)Therefore, 271 is the minimum sample size required to compute a 90% confidence interval for the population proportion.

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The density function of the continuous random variable X, the total number of hours, in units of 100 hours, that a family runs a vacuum cleaner over a period of one year, is given in Exercise 3.7 on page 92 as f(x) = {x, 0 < x < 1, 2 - x, 1 ≤ x ≤ 2, 0, elsewhere.

To find the average number of hours per year that families run their vacuum cleaners, we must calculate the expected value of X. This is done by integrating the density function of X over the given range:

E(X) = ∫0,2 x * f(x) dx
      = ∫0,1 x2 dx + ∫1,2 (2-x) x dx
      = (1/3) + (-2 + 4 - 2/3)
      = 8/3

Therefore, the average number of hours per year that families run their vacuum cleaners is 8/3, or approximately 2.67 hours.

To find the proportion of individuals who can be expected to respond to a certain mail-order solicitation if X has the density function, we must calculate the cumulative density function of X. This is done by integrating the density function of X over the given range:

F(X) = ∫0,x f(x) dx
      = ∫0,x x dx + ∫x,2 (2-x) dx
      = (1/2)x2 + 2x - 2

Therefore, the proportion of individuals who can be expected to respond to a certain mail-order solicitation if X has the density function is (1/2)x2 + 2x - 2.

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Answer: 1. Here is a sketch of the overlapping triangles ΔEBT and ΔELH:

         H

        /|

       / |

      /  |

     /   |

    / θ  |

   /____|L

       E

       |

       |

       |

       |

       T

       |

       |

       |

       |

       B

2. ΔEBT~ΔELH because they have the same shape (both are right triangles with angle θ in common) and their corresponding sides are proportional. Specifically, angle θ is shared by both triangles, angle EBT is a right angle, and angle ELH is a right angle. Therefore, by the Angle-Angle Similarity Theorem, the two triangles are similar. Corresponding sides are proportional because EB/EL = BT/LH (by definition of similar triangles).

3. We are given that BT (the length of the thumb) is about 2 inches. We are also told that the distance from the eye to the landmark (EL) is unknown, but that the distance from the eye to the thumb (EB) is 10 inches (estimated by the person). We are given that LH (the height of the landmark) is 604 feet, or 604*12=7248 inches (since there are 12 inches in a foot). Therefore, we can label the diagram as follows:

         7248

        /|

       / |

      /  | EL

     /   |

    / θ  |

   /____|L

       E

       |10

       |

       |

       |

       T

       | 2

       |

       |

       |

       |

       B

4. To solve for EL, we use the fact that the triangles are similar: EB/EL = BT/LH. Substituting in the known values, we get:

10/EL = 2/7248

5. Multiplying both sides by EL and dividing both sides by 2, we get:

EL = 7248*5 = 36240 inches

Therefore, the distance from the eye to the landmark is 36240/12 = 3020 feet (rounded to the nearest foot).

Step-by-step explanation:

The total volume of the sample is 0.0067 m³ and the density of the sample is 2753.73 kg/m³.

An ore sample weighs 18.5 N in air. When the sample is suspended by a light cord and totally immersed in water, the tension in the cord is 11.8 N. When the ore sample is immersed in water, the tension in the cord is given as 11.8 N.

Thus, the buoyancy force experienced by the ore sample is given by the difference between the weight of the sample in the air and the tension in the cord.

Buoyancy force experienced by the ore sample = Weight of the sample in the air - Tension in the cord

Buoyancy force experienced by the ore sample = (18.5 N) - (11.8 N)

Buoyancy force experienced by the ore sample = 6.7 N

Also, we know that the weight of the ore sample in air is equal to the weight of the ore sample when immersed in water.

Weight of the ore sample = Weight of the displaced water

Weight of the ore sample = Buoyancy force experienced by the ore sample

Weight of the ore sample = 6.7 N

The density of the ore sample

Density is given by the formula Density = Mass/Volume

Where Density is measured in kg/m³

Mass is measured in kg

Volume is measured in m³

Also, the density of water is given as 1000 kg/m³.

The density of the ore sample = Mass/Volume

Mass = Density x Volume

Volume of the ore sample can be obtained from volume of the displaced water.

Volume of the displaced water = Weight of the ore sample/Density of water

Volume of the displaced water = (6.7 N)/(1000 kg/m³)

Volume of the displaced water = 0.0067 m³

Density of the ore sample = (18.5 N)/(0.0067 m³)

Density of the ore sample = 2753.73 kg/m³

Therefore, 0.0067 m³ is the sample's total volume and 2753.73 kg/m³ is the density of the sample.

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The number 10 is 30% of the following number: 33.33.

In Mathematics, a percentage can be defined as any number that is expressed as a fraction of hundred (100). This ultimately implies that, a percentage indicates the hundredth parts of any given number.

In order to determine the whole number which 10 is 30%, we would apply the following mathematical expression (formula);

Quantity = percent × number

Substituting the given parameters into the percentage and quantity formula, we have the following;

10 = 30/100 × number

10 = 0.3  × number

Number = 10/0.3

Number = 33.33.

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A graph that matches the equation include the following: A. graph A.

In Mathematics and Geometry, the point-slope form of a straight line can be determined by using this mathematical equation:

y - y₁ = m(x - x₁)

Where:

Based on the information provided about the equation of this line, we can logically deduce the following parameters;

y + 6 = 3/4(x + 4)

y = 3x/4 + 3 - 6

y = 3x/4 - 3

Therefore, the slope, m is equal to 3/4 while the y-intercept is at point (0, 3).

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Answer:

12

Step-by-step explanation:

Given the ratio [tex]9:36[/tex], we can say that the ratio of driftwood is divided by 3 for the number of shells.

[tex]\frac{9}{3} =3\\\frac{36}{3}=12[/tex]

So, to fill the blank and create an equivalent ratio, you need to input 12.

Answer:

7.44

Step-by-step explanation:

?

(a) The possible choices are (1,3), (1,5), and (3,5), and the maximum of each pair is 3, 5, and 5, respectively.

(b) Since each pair has probability 1/3 of being chosen, the probability mass function for X is P(X=3) = 1/3 and P(X=5) = 2/3.

(c) The expectation of X is E(X) = 3(1/3) + 5(2/3) = 4.

(d) The variance of X can be calculated as Var(X) = E(X^2) - (E(X))^2 = (3^2)(1/3) + (5^2)(2/3) - 4^2 = 2/3.

(a) We can list all the possible choices of two integers from the set {1,3,5}: (1,3), (1,5), and (3,5). For each choice, we can determine the maximum of the two integers. These maximums are 3, 5, and 5, respectively.

(b) Since each pair has an equal probability of being chosen, the probability mass function for X can be calculated as the probability of getting 3 or 5. There is only one pair that results in X=3, which is (1,3). There are two pairs that result in X=5, which are (1,5) and (3,5). Thus, P(X=3) = 1/3 and P(X=5) = 2/3.

(c) To find the expectation of X, we multiply each possible value of X by its corresponding probability and sum the results. Thus, E(X) = 3(1/3) + 5(2/3) = 4.

(d) The variance of X can be calculated using the formula Var(X) = E(X^2) - (E(X))^2. We can calculate E(X^2) by multiplying each possible value of X squared by its corresponding probability and summing the results. Thus, E(X^2) = (3^2)(1/3) + (5^2)(2/3) = 16/3. Substituting E(X) = 4 and E(X^2) = 16/3 into the formula for variance gives Var(X) = 2/3.

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(a) Point estimate (mean difference): 2.2 tomatoes. (b) The standard deviation of differences: Approximately 3.47. (c) The test statistic: Approximately 1.38.

To perform a t-test for the population mean difference, follow these steps:

(a) Calculate the point estimate (mean difference): The point estimate is the mean difference between the yields of fertilizer A and fertilizer B.

Mean difference = (Sum of differences) / Number of pairs

Using the given data gives:

Mean difference = ((7-4) + (6-7) + (5-6) + (8-5) + (10-3)) / 5

Subtracting gives:

Mean difference = (3 - 1 - 1 + 3 + 7) / 5

Solving gives:

Mean difference = 11 / 5

Dividing gives:

Mean difference = 2.2

(b) Calculate the standard deviation of the differences:

To calculate the standard deviation of the differences, we need to calculate the squared differences, find their sum, divide by (n-1), and then take the square root.

Squared differences:[tex](3 - 2.2)^2, (-1 - 2.2)^2, (-1 - 2.2)^2, (3 - 2.2)^2, (7 - 2.2)^2[/tex]

Solving gives:

Sum of squared differences = (0.64 + 12.96 + 12.96 + 0.64 + 21.16)

Solving gives:

The sum of squared differences = 48.36

The standard deviation of the differences [tex]= \sqrt{48.36 / 4}[/tex]

Solving gives:

The standard deviation of the differences [tex]= \sqrt{2.09}[/tex]

Rounded to three decimal places

The standard deviation of the differences ≈ 3.47

c) Calculate the test statistic:

The test statistic (t) = (Point estimate - Null hypothesis value) / (Standard deviation /√(sample size))

Let's assume the null hypothesis is that there is no difference between the two fertilizers

(i.e., mean difference = 0).

[tex]t = (2.2 - 0) / (3.47 / \sqrt5)[/tex]

Substituting [tex]\sqrt 5 = 2.236[/tex]

t = 2.2 / (3.47 / 2.236)

Rounded to two decimal places

t ≈ 1.378

So, the test statistic is approximately 1.378.

The gardener can compare this test statistic to critical values from the t-distribution to determine whether the difference between the two fertilizers is statistically significant at a certain significance level. If the calculated test statistic is greater than the critical value, she ma

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The quantity of  water are needed to fill the tank to the top is 960 cubic inches

The total volume of the tank is given by multiplying its length, width, and height

Volume of tank = 24 inches × 10 inches × 12 inches = 2,880 cubic inches

The volume of water in the tank is given by multiplying the filled height with the base area of the tank:

Volume of water = 8 inches × 24 inches × 10 inches = 1,920 cubic inches

To find how many more cubic inches of water are needed to fill the tank to the top, we need to subtract the volume of water in the tank from the total volume of the tank:

Volume of air space = Volume of tank - Volume of water

= 2,880 cubic inches - 1,920 cubic inches

= 960 cubic inches

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The given question is incomplete, the complete question is:

Julio bought a fish tank shaped like a rectangular prism. The inside of the tank measures

24 inches in length, 10 inches in width, and 12 inches in height. The tank is filled with water to a height of 8 inches. How many more cubic inches of water are needed to fill the tank to the top?

Viola needs to jump a distance of 0.04 m on her next attempt to increase her mean to 3.82 m

On average, she has jumped 3.80 m so far. Therefore, the sum of distances jumped so far by her is:

3.80 m × the total number of jumps taken so far.

On the next jump, she reaches 3.99 m. Therefore, after the next jump, the total distance jumped so far by her will be 3.80 m × total number of jumps taken so far + 3.99 m. The new mean is 3.81 m.

Therefore, (3.80 m × total number of jumps taken so far + 3.99 m)/(total number of jumps taken so far + 1) = 3.81.

The above equation can be simplified as 3.80 m × total number of jumps taken so far + 3.99 m = 3.81 m × (total number of jumps taken so far + 1).

This simplifies to 3.80 m × total number of jumps taken so far + 3.99 m = 3.81 m × total number of jumps taken so far + 3.81 m. Now, we need to solve the above equation to find out the distance she needs to jump on her next attempt to increase her mean to 3.82 m.

3.80 m × total number of jumps taken so far + 3.99 m = 3.81 m × total number of jumps taken so far + 3.81 m.

0.01 m = 0.01 m × total number of jumps taken so far.

1 = total number of jumps taken so far. Now, she needs to jump a distance of (3.82 m × (total number of jumps taken so far + 1)) - (3.80 m × total number of jumps taken so far)

= (3.82 m × (1 + 1)) - (3.80 m × 1)

= 3.82 m × 2 - 3.80 m

= 0.04 m

Therefore, she needs to jump a distance of 0.04 m on her next attempt to increase her mean to 3.82 m.

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W satisfies all the three conditions of being a subspace of V. So, W is a subspace of V.

W is the set of all 3 x 2 matrices of the form [a,b; (a + b),0; 0,c]. It needs to be verified that W is a subspace of V, which has standard operations. Let us check whether W satisfies the three conditions to be a subspace of V or not:

Closure under addition: If X, Y are any two elements of W, then X + Y is also in

W.[a₁, b₁; (a₁ + b₁), 0; 0,c₁] + [a₂, b₂; (a₂ + b₂), 0; 0,c₂] = [a₁ + a₂, b₁ + b₂; (a₁ + b₁ + a₂ + b₂), 0; 0,c₁ + c₂]

The resulting matrix has the same form as W. So, W is closed under addition.

Closure under scalar multiplication: If X is any element of W and k is any scalar, then k

X is also in W.k[a, b; (a + b), 0; 0,c] = [ka, kb; k(a + b), 0; 0,kc]

This is of the same form as W. So, W is closed under scalar multiplication.

Contains zero vector: The zero vector is [0,0; 0,0; 0,0], which is of the same form as W. So, W contains the zero vector.

Therefore, W satisfies all the three conditions of being a subspace of V. So, W is a subspace of V.

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1/6 + 1/4= 10/24 (5/12 simplified)

2.50× 12= 30

This is the total sum of money shared.

7/12 is given to Farooq

7/12 of 30 is 17.5

answer= £17.5

Answer:

Step-by-step explanation:

Let h be the height of the trapezoid.

The area of a trapezoid is given by the formula:

Area = (1/2) × (sum of parallel sides) × (height)

In this case, we know that the area is 21 cm², one base length is 5 cm, and the other base length is 9 cm. So we can write:

21 = (1/2) × (5 + 9) × h

Simplifying this equation, we get:

21 = 7h

Dividing both sides by 7, we get:

h = 3

Therefore, the height of the trapezoid is 3 cm.

Answer:

Step-by-step explanation:

Area of Trapezium is 21 cm². Parallel sides are 5 cm and 9 cm .

Shorter parallel side is 5 cm and the Longer Side is 9 cm.

As we know that formula of area of Trapezium is,

Where,

On substituting the values of area and the two parallel sides in the above formula we will get the required Height.

Substituting the values,

21 = ½ (5 + 9)h

21 = ½ × 14 × h

21 = 7 × h

h = 21/7

h = 3 cm

Therefore, Height of the Trapezium will be 3 cm respectively.

The correct order of steps is 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12.

To find the inverse of 55 modulo 89 using the Euclidean algorithm, the steps are:
1. 89 = 1.55 +34
2. 55 = 1.34 +21
3. 34 = 1.21 + 13
4. 21 = 1.13 + 8
5. 13 = 1.8 +5
6. 8 = 1.5 +3
7. 5 = 1.3 +2
8. 3 = 1.2 +1
9. 2 = 1.2
10. The Bézout coefficient of 55 is 34, and it is an inverse of 55 modulo 89.
11. The Bézout coefficients of 55 and 89 are 34 and -21, respectively.
12. The gcd in terms of 55 and 89 is written as 1 = 34-21.89 = 34-21. (55-1.34) = 13.34-21.55 = 13. (21-1.13) - 3.13 = 5.21-8. 13 = 5. (8-1.5) - 1.5 = 2.8-3.5 = 2. (3-1.2) = 2.3-1.5 = 2. (2-1) = 3-1.2 = 3-1. (1-0) = 34-21.89
The correct order of steps is 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12.

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Therefore , the solution of the given problem of function comes out to be he function's average rate of change over the range 3 x 4 is 4.

There will be questions on design, mathematics, each subject, and both real expression and imagined locations on the midterm exam. a list of the relationships between different elements that cooperate to create the same result. A service is composed of numerous distinctive components that cooperate to create distinctive results for each input. Every mailbox also has a specific address, which may be an enclave, a neighborhood.

Here,

Calculate the difference between the function values at

=> x = 4 and x = 3, then split by the difference in x-values,

which is 4 - 3 = 1, to determine the average rate of change of the function over the range 3  x  4.

We can see from the table that f(4) = -5 and f(3) = -9. As a result, the following function numbers are different:

=> f(4) - f(3) = (-5) - (-9) = 4

=> 4 - 3 = 1 represents the x-value disparity.

Therefore, the function's average rate of change over the period 3 x 4 is:

Average rate of change is equal to

=> (f(4)-f(3))/(4-3) = 4/1 = 4.

Consequently, the function's average rate of change over the range 3 x 4 is 4.

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Answer: The value of x is 3.45%

Step-by-step explanation:

We can solve the problem by using the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = final amount

P = principal (initial investment)

r = annual interest rate (as a decimal)

n = number of times the interest is compounded per year

t = time in years

In the first year, Charlie gets 2% interest, compounded annually. So, using the formula, we have:

A1 = 4000(1 + 0.02/1)^(1*1)

A1 = 4080

After the first year, Charlie has £4080 in her account. For the next two years, she gets x% interest, compounded annually. Using the formula again, we have:

A2 = 4080(1 + x/100/1)^(1*2)

A2 = 4080(1 + x/100)^2

Finally, after three years, Charlie has £4228.20 in her account. So, we can set up an equation:

A1 * A2 = 4000 * (1 + 0.02) * 4228.20

Substituting the values of A1 and A2, we get:

4080(1 + x/100)^2 = 4366.4496

Dividing both sides by 4080, we get:

(1 + x/100)^2 = 1.0694

Taking the square root of both sides, we get:

1 + x/100 = 1.0345

Subtracting 1 from both sides and multiplying by 100, we get:

x = 3.45

Therefore, the value of x is 3.45%.

Answer:

Step-by-step explanation:

You need to find the volume if one shoe box by doing:

Length x Width x Height

Of the shoe box

Then multiply by 30 to get the volume for all the shoe boxes

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Answer:

C. The means of the data are different, but since they are more than twice the respective mean absolute deviations, the difference is not significant.

Step-by-step explanation:

As per the GDP, the percentage did the price level rise between 2016 and ​2019 is 27.5%

To calculate the percentage increase in production, we first need to find the nominal GDP for each year. Nominal GDP is the current dollar value of all goods and services produced within a country's borders during a specified period of time. We can use the GDP deflator and real GDP to calculate nominal GDP as follows:

Nominal GDP = Real GDP x GDP deflator

Using the information provided in the question, we can calculate the nominal GDP for each year as follows:

Nominal GDP in 2016 = Real GDP in 2016 x GDP deflator in 2016

Nominal GDP in 2019 = Real GDP in 2019 x GDP deflator in 2019

Once we have the nominal GDP for each year, we can calculate the percentage increase in production as follows:

Percentage increase in production = (Nominal GDP in 2019 - Nominal GDP in 2016) / Nominal GDP in 2016 x 100% = 27.5%

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a. Two levels of factor B were used in the experiment.

b. The degrees of freedom associated with interaction are 50.

c. The error mean square is 6.00. d. The mean square for factor A is 175.00.e. The experiment was conducted with three replicates.f. The interaction is significant. Factor A is significant. Factor B is not significant.g. An estimate of the standard deviation of the response variable is 2.449. h. If the experiment had been run in blocks (CRBD) there would have been 12 degrees of freedom for blocks.Solution:Factorial design: A factorial design is an experimental design that consists of two or more factors, each with two or more levels, and each subject is assigned to one and only one level of each factor. The objective of a factorial experiment is to analyze the effect of each factor on the response variable and to examine if there is any interaction between factors.a. Two levels of factor B were used in the experiment.b. Interaction degrees of freedom = AB = 50.c.

Mean square for error: MSE = 150/10 = 15.d. Mean square for factor A: MS(A) =[tex]SSA/dfA = 350/2 = 175.e.\\[/tex] Three replicates were conducted (from the error df = 10).f. Interaction is significant. Factor A is significant. Factor B is not significant.g. Estimate of the standard deviation of the response variable: sqrt(15/2) = 2.449.h. If the experiment had been conducted in a CRBD, there would have been 12 degrees of freedom for the block.

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The length and width of the rectangle is about 33cms and 9cms. This can be calculated with the help of the given area of the rectangle.

Let the original length and width of the rectangle be L and W respectively.

The given area of the rectangle is 297 square cm.

Area = L × B

297 = L × B

As per the question, the length is increased by 3 cm and the width is decreased by 1 cm.

Therefore, the new length and width are L + 3 and W - 1 respectively.

The new area is 3 square cm more than the original area.

So, (L + 3) × (W - 1) = 297 + 3

L×W -L +3W - 303 = 0

297 - L +3W - 303 = 0

-L + 3W - 6 = 0

-297/W + 3W = 6

-297 + 3W² = 6W

W² - 2W - 99 = 0

Using the quadratic formula, we get,

W = -2±[tex]\sqrt{ 2^2 - 4X1 X ( -99 ) ] ) / 2 X1 }[/tex]

[tex]W =\frac{-2±\sqrt{ (4+396)}}{2}[/tex]

[tex]W =\frac{-2±20}{2}[/tex]

Width can't be negative so, W = 9 cm

So, L  297/W

L = 297/9

L = 33cm

Therefore, the length and width of the rectangle are 33 cm and 9 cm respectively.

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a) Option A, A x2 statistic provides strong evidence in favor alternative hypothesis if its value is a large positive number.

b) Option B, The null hypothesis that sex and personal goals are not related vs. the alternative hypothesis that sex and personal goals are related.

c) Option B, The variables considered in a chi-squared test used to evaluate a contingency table B. are categorical.

(a) A x2 statistic provides strong evidence in favor of the alternative hypothesis if its value is a large positive number. The x2 statistic is used in hypothesis testing to determine whether there is a significant difference between observed and expected frequencies. A large positive value indicates that the observed frequencies are significantly different from the expected frequencies, which supports the alternative hypothesis.

(b) The hypotheses being tested in a chi-squared test on a contingency table are the null hypothesis that sex and personal goals are not related vs. the alternative hypothesis that sex and personal goals are related. This test determines whether there is a significant association between two categorical variables.

(c) The variables considered in a chi-squared test used to evaluate a contingency table are categorical. These variables cannot be averaged or assumed to be normally distributed. The chi-squared test is used to analyze the relationship between two or more categorical variables, where each variable has a discrete set of categories.

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