what is the area of this figure

The probability of selecting 4 red marbles out of the bag is approximately 0.0303, or 3.03%.

To find the probability of selecting 4 red marbles out of a bag containing 6 red, 4 blue, and 2 white marbles, we first need to determine the total number of possible combinations of 4 marbles that can be selected from the bag. This can be calculated using the formula for combinations, which is:
[tex]nC_{r}=    \frac{n!}{r!(n-r)}[/tex]

where n is the total number of items in the set, and r is the number of items being chosen. In this case, we have:

n = 12 (6 red + 4 blue + 2 white)
r = 4 (the number of marbles being chosen)

So the total number of possible combinations is:

[tex]12C_{4}=    \frac{12!}{(4!8!)} = 495[/tex]

Next, we need to determine the number of combinations that contain 4 red marbles. Since there are 6 red marbles in the bag, the number of ways to choose 4 of them is:

[tex]6C_{4}=    \frac{6!}{(4!2!)} = 15[/tex]

Therefore, the probability of selecting 4 red marbles out of the bag is:

[tex]p( 4 red) = \frac{15}{495}=\frac{1}{33}[/tex]

So the probability of selecting 4 red marbles out of the bag is approximately 0.0303, or 3.03%.

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The point-biserial correlation is specifically designed for this type of analysis and is used to determine the degree of association between a binary variable and a continuous variable.

What is an algebraic expression?

An algebraic expression is a mathematical phrase that contains variables, constants, and mathematical operations. It may also include exponents and/or roots. Algebraic expressions are used to represent quantities and relationships between quantities in mathematical situations, often in the context of problem-solving.

The most appropriate type of correlation for the psychologist to use in this scenario would be a point-biserial correlation. This is because the psychologist wants to measure the relationship between a dichotomous variable (whether parents were divorced or not) and a continuous variable (relationship satisfaction scores).

The point-biserial correlation is specifically designed for this type of analysis and is used to determine the degree of association between a binary variable and a continuous variable.

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Step-by-step explanation:

There are TWO triangles with base = 10  height = 24

   area of a triangle = 1/2 b* h  = 1/2 (10)(24) = 120 cm^2

        TWO of them totals 240 cm^2

then there is also THREE sides

 10 x 20       +   26 x 20       +     24 x 20 = 1200 cm^2

Add the two triangles to this to get the total surface area = 1440 cm^2

The probability of answering between 70 and 80 questions, inclusive, is 0.0676

What is probability?

Probability is the study of the chances of occurrence of a result, which are obtained by the ratio between favorable cases and possible cases.

P(70 ≤ X ≤ 80) = P(X = 70) + P(X = 71) + ... + P(X = 80)

Using the binomial probability formula, we get:

[tex]P(X = k) = (n choose k) * p^k * (1-p)^{(n-k)}[/tex]

where (n choose k) is the binomial coefficient, which can be calculated as:

(n choose k) = n! / (k! * (n-k)!)

Using a calculator or software, we can find:

P(70 ≤ X ≤ 80) = 0.0676

Therefore, the probability of answering between 70 and 80 questions, inclusive, is 0.0676 (rounded to four decimal places).

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On solving the provided query we have The test statistic (-2.5594) falls in  equation the rejection zone since it is less than the threshold value (-2.009).

A mathematical equation is a formula that connects two claims and uses the equals symbol (=) to denote equivalence. An equation in algebra is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign places a space between the variables 3x + 5 and 14. The relationship between the two sentences that are written on each side of a letter may be understood using a mathematical formula. The symbol and the single variable are frequently the same. as in, 2x - 4 equals 2, for instance.

a. The average hourly wage is equal to $22 under the null hypothesis, whereas it is not $22 under the alternative hypothesis.

A = $22 is the null hypothesis (H0).

Additional Hypothesis (Ha): $22

b. The test statistic's value can be determined as follows:

t = sqrt(sample size) / (population standard deviation / hypothesised mean) / (sample mean - hypothesised mean)

t = (20.2106 - 22) / (6 / sqrt(50))

t = -2.5594

c. The critical value with 49 degrees of freedom and a 5% significance level is 2.009.

d. The test statistic (-2.5594) falls in the rejection zone since it is less than the threshold value (-2.009).

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a) The length of the median BE = √(10)

b) The length of the altitude BH = √(5)

c) The size of the angle ABC = 135.0°

d) The area of the triangle A = √(50)

e) The perimeter of the triangle = √(10) + √60

To solve this problem, we can begin by finding the coordinates of the vertices of the triangle by solving the system of equations formed by the given lines.

AB: 2x + 6y + 2 = 0

BC: 3x + 2y – 10 = 0

CA: 5x – 2y + 10 = 0

Solving for x and y, we get:

A(-2,2), B(-1,-1), C(2,-3)

a) To find the length of the median BE, we first need to find the midpoint of AC. Using the midpoint formula, we get D(0,-0.5). Then, we can use the distance formula to find the length of BE:

BE = √(((-1-2)² + (-1-3)²)/4) = √(10)

b) To find the length of the altitude BH, we need to find the equation of the line perpendicular to AB that passes through B. The slope of AB is -1/3, so the slope of the perpendicular line is 3. Using the point-slope form of the equation, we get:

y + 1 = 3(x + 1)

Solving for the point where this line intersects BC, we get H(-3,-8). Then, we can use the distance formula to find the length of BH:

BH = √(((-3-1)² + (-8-1)²)/10) = √(5)

c) To find the size of the angle ABC, we can use the dot product formula:

cos(ABC) = (AB dot BC) / (|AB| * |BC|)

We can find AB and BC using the distance formula, and then use the dot product formula to find cos(ABC), and then take the inverse cosine to find the angle ABC:

AB = √((-1-2)² + (-1-2)²) = √(10)

BC = √((-1-2)² + (-1-3)²) = √(15)

cos(ABC) = (-7/√150) / (√10 * √15) = -7/10

ABC = cos^-1(-7/10) = 135.0°

d) To find the area of the triangle, we can use the formula A = 1/2 * base * height, where the base can be any side of the triangle, and the height is the length of the altitude drawn to that side. Let's use AB as the base, and BH as the height:

A = 1/2 * √(10) * √(5) = √(50)

e) To find the perimeter of the triangle, we simply add up the lengths of all three sides:

AB + BC + CA = √(10) + √(15) + 2√10 = √(10) + √60

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The value of k for which P(Z ≤ k) = 0.258 is k = 0.65.

To find the value of k for which P(Z ≤ k) = 0.258, we need to use a standard normal distribution table or a calculator that can compute the inverse of the standard normal cumulative distribution function.

Using a standard normal distribution table, we can find the closest probability value to 0.258, which is 0.2580. Then, we look for the corresponding z-score in the table, which is approximately 0.65. Therefore, the value of k for which P(Z ≤ k) = 0.258 is k = 0.65.

Alternatively, we can use a calculator that can compute the inverse of the standard normal cumulative distribution function, such as the NORMSINV function in Excel or the invNorm function in a graphing calculator. Using this method, we can input the probability value of 0.258 and the calculator will return the corresponding z-score, which is approximately 0.65.

It's important to note that the value of k represents the cutoff point below which the cumulative probability is 0.258. In other words, P(Z ≤ k) = 0.258 means that there is a 25.8% probability that a random observation from a standard normal distribution is less than or equal to k. The remaining probability of 1 - 0.258 = 0.742 is the area to the right of k, which represents the probability that a random observation is greater than k.

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V(X) = 10.00

Explanation: A fair 6-sided dice are rolled a number of times, and let X is the number of sixes. The mean value of X is given as 2. To calculate the variance V(X), we'll use the formula for the variance of a binomial distribution:

V(X) = np(1-p),

where n is the number of trials and p is the probability of success (rolling a six).
Since the mean value of X is 2, we can write it as np = 2. The probability of rolling a six on a fair 6-sided dice is p = 1/6. We can solve for n using the mean value:

n(1/6) = 2
n = 12

Now that we know n, we can calculate the variance:

V(X) = np(1-p) = 12(1/6)(1 - 1/6) = 12(1/6)(5/6) = 10

So, the variance V(X) is 10.00 (rounded to 2 decimal places).

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Answer:

Step-by-step explanation:

The probability that a senior citizen takes either blood pressure-lowering or cholesterol-lowering medication is :

(e) 0.90

To find the probability that a senior citizen takes either blood pressure-lowering or cholesterol-lowering medication, you can use the following formula:

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

where:
P(A ∪ B) is the probability of taking either blood pressure-lowering (A) or cholesterol-lowering (B) medication,
P(A) is the probability of taking blood pressure-lowering medication,
P(B) is the probability of taking cholesterol-lowering medication, and
P(A ∩ B) is the probability of taking both medications.

From the survey, we have the following probabilities:
P(A) = 0.52 (52% take blood pressure-lowering medication)
P(B) = 0.43 (43% take cholesterol-lowering medication)
P(A ∩ B) = 0.05 (5% take both medications)

Now, substitute the values into the formula:

P(A ∪ B) = 0.52 + 0.43 - 0.05
P(A ∪ B) = 0.90

Therefore, the probability that a senior citizen takes either blood pressure-lowering or cholesterol-lowering medication is 0.90, or 90%.

The correct answer is:

(e.) 0.90.

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Given matrix A, to find matrix exponential e^(At) use Taylor series, but it's complex. Neither computing the series nor numerical methods directly provide the correct e^(At) due to infinite series, so none of the given options are correct.

The given matrix A is:

A = [ 3  0 ]
      [ 2  3 ]

To find the matrix exponential e^(At), we can use the Taylor series expansion:

e^(At) = I + At + (At)^2 / 2! + (At)^3 / 3! + ...

where I is the identity matrix and t is a scalar. However, calculating the matrix exponential using the Taylor series can be quite complex. In this case, you can either attempt to compute the series up to a certain order or use a numerical method to approximate the matrix exponential.

Unfortunately, none of the given options directly provides the correct e^(At) as the matrix exponential involves an infinite series of terms. So, the correct answer is:

e. None of the responses

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It is not necessary to know the number of successes to determine the mean of a binomial distribution. So the given statement is false.

The mean of a binomial distribution can be determined without knowing the number of successes involved in the problem. The mean of a binomial distribution is given by the product of the number of trials (n) and the probability of success on a single trial (p), denoted as np. This is a fixed value that represents the expected number of successes in a binomial distribution. The number of successes involved in the problem is not necessary to calculate the mean of a binomial distribution.

Therefore, it is not necessary to know the number of successes to determine the mean of a binomial distribution.

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a) Sample size is A. 637.

b) The sample size would decrease.

a) To determine the sample size needed to estimate the mean surgical wait time with a margin of error of 0.8 days and a 98% confidence level, we can use the formula:

n = [tex](\frac{zs}{E})^{2}[/tex]

where:

z = the z-score corresponding to the desired confidence level, which is 2.33 for a 98% confidence level

s = the population standard deviation, which is 10.3 days

E = the desired margin of error, which is 0.8 days

Substituting the values into the formula, we get:

n = [tex](\frac{2.33*10.3}{0.8} )^{2}[/tex] ≈ 637

Therefore, the sample size needed is 637, which corresponds to option A.

b) If the level of confidence was decreased to 95%, the sample size required would decrease. This is because a lower confidence level requires a smaller margin of error, which means we can achieve it with a smaller sample size. However, the exact sample size required would depend on the new desired margin of error and the updated level of confidence.

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Answer:

The probability of rolling an odd number or a two on a six-sided die is 1/2 + 1/6 = 2/3. This means that if you roll a six-sided die 300 times, you can expect to roll an odd number or a two approximately 200 times

Step-by-step explanation:

Answer: 400 TIMES

Step-by-step explanation:

1/6 +1/2

4/6

2/3

The volume of the parallelepiped with edges AB, AC, and AD is 10 cubic units.

The volume of the parallelepiped is given by the scalar triple product of the three vectors, which is defined as follows

V = | AB ⋅ (AC × AD) |

where AB is the vector from A to B, AC is the vector from A to C, and AD is the vector from A to D, and × denotes the cross product.

First, we need to calculate the cross product of AC and AD

AC × AD = (−3 − (−4), 4 − 1, (−2)⋅2 − (−4)⋅1) = (1, 3, −4)

Then, we can calculate the dot product of AB and the cross product of AC and AD

AB ⋅ (AC × AD) = (4 − 2, −5 + 3, 1 − 4) ⋅ (1, 3, −4) = (2, −2, −3) ⋅ (1, 3, −4) = 4 + (−6) + 12 = 10

Finally, we take the absolute value of the result to get the volume of the parallelepiped

V = |10| = 10  cubic units

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The height of the trapezoid needs to be 30/11 units in order for the trapezoid to have area 30.

To find the height of the trapezoid, we can use the formula for the area of a trapezoid, which is:

A = (1/2)h(b1 + b2)

where A is the area of the trapezoid, h is the height, b1 and b2 are the lengths of the parallel bases.

We know that the lengths of the parallel bases are 8 and 14, and we want the area to be 30. Substituting these values into the formula, we get:

30 = (1/2)h(8 + 14)

Simplifying the right-hand side, we get:

30 = 11h

Dividing both sides by 11, we get:

h = 30/11

Therefore, the height of the trapezoid needs to be 30/11 units in order for the trapezoid to have area 30.

To see why this works, we can visualize the trapezoid as a rectangle with a smaller right triangle on top. The height of the rectangle is equal to the height of the trapezoid, and the width is equal to the average of the lengths of the bases, which is (8+14)/2 = 11. The area of the rectangle is therefore 11h, and the area of the triangle on top is (1/2)bh, where b is the difference between the lengths of the bases, which is 14-8 = 6. The total area of the trapezoid is the sum of the area of the rectangle and the area of the triangle, which is:

A = 11h + (1/2)(6)(h) = 11.5h

Setting this equal to 30 and solving for h, we get the same result as before:

11.5h = 30

h = 30/11

Therefore, the height of the trapezoid needs to be 30/11 units in order for the trapezoid to have area 30.

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The value of c is 0.63 such that  P ( z ≤ c) = 0.7357 where Z follows standard normal distribution using z- score table.

The values that range from 0 to 1 in a z-table are referred to as the probabilities of various z-scores. To calculate the z- score with given probability we need to identify the row and the column the probability belongs to in the z- score table as they indicate the z- score.

Z is said to follow standard normal distribution.

Using a z- score table we can observe that probability 0.7357 lies in the column 0.03 and the row 0.6.

Therefore, summing up the row and column value of the probability we get the z- score.

That is, z- score = 0.03 + 0.6 = 0.63

Thus P ( z ≤ c) = 0.7357 can be written as,

P ( z ≤ 0.63) = 0.7357

Therefore, c = 0.63 (rounded up to two decimal places)

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The given question is incomplete, the complete question is

"Let Z be a standard normal random variable. Determine the value of c such that P(Z ≤ c) = 0.7357.

Carry your intermediate computations to at least four decimal places. Round your answer to at least two decimal places."

The correct order in greatest to least is A) 5, π, [tex]\sqrt{2}[/tex], 0.76, -2, 1/2.

Ordering the numbers from greatest to least: 5, π, √2, 0.76, -2, ½

To order the numbers from greatest to least we need to check all the numbers given and then we specify the smallest and largest value corresponding to the given numbers. Also ordering can be done in ascending order from least to greatest value which is increasing order.

If we want to specify the descending order for the given numbers the order of ascending will be totally reversed. Then we will get the numbers from greatest to the least in order which means decreasing order.

Therefore, the answer is (A) 5, π, [tex]\sqrt{2}[/tex], 0.76, -2, 1/2.

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The percentage of scores that are between 42 and 58 on this standardized test is calculated to be 95.44%

To find the percent of scores between 42 and 58, we need to first calculate the z-scores for each of these values using the formula:
z = (score - mean) / standard deviation
For a score of 42:
z = (42 - 50) / 4 = -2
For a score of 58:
z = (58 - 50) / 4 = 2
Next, we can use a z-table to find the area under the normal distribution curve between these two z-scores. Since the table gives us the area to the left of a z-score, we need to subtract the area to the left of -2 from the area to the left of 2:
area between -2 and 2 = area to the left of 2 - area to the left of -2
= 0.9772 - 0.0228
= 0.9544
So approximately 95.44% of scores are between 42 and 58 on this standardized test.

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The general solution to the non-homogeneous equation is

[tex](c_1 + 3) e^{t/2} + c_2 e^{-t/2}[/tex]

We have,

To solve the differential equation 4y" - y = 8e^{t/2}/2 + e^{t/2}, we first need to find the complementary solution by solving the homogeneous equation 4y" - y = 0.

The characteristic equation is 4r² - 1 = 0, which has roots r = ±1/2. Therefore, the complementary solution is:

y_c(t) = c_1 e^{t/2} + c_2 e^({-t/2}

where c_1 and c_2 are constants determined by the initial or boundary conditions.

Next, we need to find a particular solution to the non-homogeneous equation. Since the right-hand side contains e^{t/2}, we try a particular solution of the form:

y_p(t) = A e^{t/2}

where A is a constant to be determined.

Taking the first and second derivatives of y_p(t), we get:

y_p'(t) = A/2 e^{t/2}

y_p''(t) = A/4 e^{t/2}

Substituting these into the original differential equation, we get:

4(A/4 e^{t/2}) - A e^{t/2} = 8e^{t/2}/2 + e^{t/2}

Simplifying, we get:

A = 3

Therefore,

The particular solution is:

y_p(t) = 3 e^{t/2}

The general solution to the non-homogeneous equation is then:

y(t) = y_c(t) + y_p(t)

= c_1 e^{t/2} + c_2 e^{-t/2} + 3 e^{t/2}

= (c_1 + 3) e^{t/2} + c_2 e^{-t/2}

where c_1 and c_2 are constants determined by the initial or boundary conditions.

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The probability that the random variable X has a value greater than 5.3 is 0.47 or 47%.

Since X is uniformly distributed between 0 and 10 with a density of 0.1, we know that the probability density function (PDF) is:

f(x) = 0.1,  0 < x < 10

To find the probability that X is greater than 5.3, we need to integrate the PDF from 5.3 to 10:

P(X > 5.3) = ∫[5.3,10] f(x) dx

          = ∫[5.3,10] 0.1 dx

          = 0.1 * ∫[5.3,10] dx

          = 0.1 * [x]_[5.3,10]

          = 0.1 * (10 - 5.3)

          = 0.47

Therefore, the probability that the random variable X has a value greater than 5.3 is 0.47 or 47%.

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V can be generated by fewer vectors (from S2) than the number of linearly independent vectors (in S1), which is not possible as every vector in V can be expressed as a linear combination of vectors in S2. True, S1 cannot contain more vectors than S2.

Suppose that V is a finite-dimensional vector space, S1 is a linearly independent subset of V, and S2 is a subset of V that generates V.

If S2 generates V, it means that every vector in V can be expressed as a linear combination of vectors in S2. In other words, the span of S2 is equal to V.

On the other hand, S1 is linearly independent, which means that no vector in S1 can be expressed as a linear combination of other vectors in S1.

Now, if S1 contains more vectors than S2, it means that the number of linearly independent vectors in S1 is greater than the number of vectors that generate V in S2.

But this would imply that V can be generated by fewer vectors (from S2) than the number of linearly independent vectors (in S1), which is not possible as every vector in V can be expressed as a linear combination of vectors in S2.

Therefore, S1 cannot contain more vectors than S2.

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The integral test can be used to determine the convergence or divergence of a series of positive terms. To apply the test, you must first find an integral that is equivalent to the series. If the integral converges, then the series also converges.

If the integral diverges, then the series also diverges. Specifically, if the integral is finite (i.e. converges), then the series converges. If the integral is infinite (i.e. diverges), then the series diverges. Keep in mind that the integral test only applies to series with positive terms.
Hi! To determine if a series converges or diverges using the integral test, you need to consider these terms: improper integral, continuous function, positive, and decreasing function.

If the function f(x) is continuous, positive, and decreasing on the interval [1, ∞), you can use the integral test. Evaluate the improper integral ∫f(x)dx from 1 to ∞. If the integral converges, the series also converges. If the integral diverges, the series diverges as well.

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Answer:

C!

Step-by-step explanation:

i took this test!

<3

Answer:

c.3

Step-by-step explanation

if h =3 then it would be 3 x (4-3)

4-3=1

3x1=3

so there for 3x(4-3)=3

parantheses

exponents

multiplication

division

addition

subtraction

1. You can write the sample space for flipping a coin twice as HH, HT, TH, TT, where H stands for heads and T for tails.

2) The probability of flipping 2 heads can be calculated by multiplying the probabilities of getting a head on the first flip and the second flip:

P(2H) = P(H) x P(H) = 0.65 x 0.65 = 0.4225

Consequently, the likelihood of flipping two heads is 0.4225, rounded to four decimal place

3) We can use the following calculation to determine the likelihood of flipping exactly one head:

P(1H) = P(HT or TH) = P(HT) + P(TH)

P(HT) = P(H) x P(T) = 0.65 x 0.35 = 0.2275

P(TH) = P(T) x P(H) = 0.35 x 0.65 = 0.2275

P(1H) = 0.2275 + 0.2275 = 0.455

Consequently, the likelihood of flipping two heads is 0.4225, rounded to four decimal places.

4) You may calculate the likelihood of flipping at least one head by deducting the likelihood of flipping no heads from one:

P(at least 1H) = 1 - P(0H)

To find P(0H), we can use the formula:

P(0H) = P(TT) = P(T) x P(T) = 0.35 x 0.35 = 0.1225

So, P(at least 1H) = 1 - 0.1225 = 0.8775

Therefore, the probability of flipping at least 1 head is 0.8775, rounded to 4 decimal places.

5)  You may calculate the likelihood of receiving no heads by multiplying the chances of getting a tail on the first and second flips:

P(0H) = P(T) x P(T) = 0.35 x 0.35 = 0.1225

So, the probability of flipping no heads is 0.1225, rounded to 4 decimal places.

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The statement "If y1 and y2 are solutions to y''-6y²+5y=4x, then 2y1+3y2 is also a solution to the ODE" is false.

The given ODE is:

y'' - 6y² + 5y = 4x

Now, let y1 and y2 be two solutions of the above ODE. Then,

y1'' - 6y1² + 5y1 = 4x ... (1)

y2'' - 6y2² + 5y2 = 4x ... (2)

Now, we need to show whether 2y1 + 3y2 is also a solution of the ODE. So, let's find its second derivative:

(2y1 + 3y2)'' = 2y1'' + 3y2''

Substituting the values from equations (1) and (2), we get:

(2y1 + 3y2)'' = 2(6y1² - 5y1 + 4x) + 3(6y2² - 5y2 + 4x)

Simplifying, we get:

(2y1 + 3y2)'' = 12(y1² + y2²) - 10(2y1 + 3y2) + 10x

So, we can see that 2y1 + 3y2 is not a solution of the ODE, as it does not satisfy the ODE. Therefore, the statement "If y1 and y2 are solutions to y''-6y²+5y=4x, then 2y1+3y2 is also a solution to the ODE" is false.

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Answer:

18

Step-by-step explanation:

(1 1/2 ✖ 2 ✖ 3) ➗1/2

Answer: 18

Step-by-step explanation:

first find the volume 1.5x3x2=9

then you take 9 and divide it by 0.5

9/0.5 is 18

The value of p could be either 0.2846 or 0.7154.

To find the value of p, we need to use the formula for the probability of k successes in a multinomial distribution:

P(k1,k2,...,kn) = n!/(k1!k2!...kn!) * p1k1 * p2k2 * ... * pn^kn

where n is the number of trials, k1,k2,...,kn are the number of successes in each category, and p1,p2,...,pn are the probabilities of success in each category.

Since we are given that the probability of five successes out of ten trials is 0.2007, we can set k1=5, k2=0, ..., kn=0, and solve for p:

0.2007 = 10!/(5!0!...0!) * p5 * (1-p)5

0.2007 = 252 * p5 * (1-p)5

0.000795238 = p5 * (1-p)5

Taking the fifth root of both sides, we get:

0.5707 = p * (1-p)

Solving for p using the quadratic formula, we get:

p = 0.2846 or p = 0.7154

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The test statistic t0 for a sample with n = 20, x = 7.5, s = 1.9, and if H1: μ < 8.3 is calculated to be  -1.886.

To calculate the test statistic t0, we can use the following formula:

t0 = (x - μ) / (s / √n)

where x is the sample mean, μ is the hypothesized population mean (in this case, 8.3), s is the sample standard deviation, and n is the sample size.

Given the values provided:

x = 7.5 (sample mean)

μ = 8.3 (hypothesized population mean)

s = 1.9 (sample standard deviation)

n = 20 (sample size)

Plugging these values into the formula, we get:

t0 = (7.5 - 8.3) / (1.9 / √20)

t0 = -0.8 / (1.9 / √20)

t0 = -0.8 / (1.9 / 4.472) (rounded to three decimal places)

t0 = -0.8 / 0.424

t0 = -1.886 (rounded to three decimal places)

Therefore, the test statistic t0 is calculated to be -1.886.

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