Wesley has a grid of six cells. He wants to colour two of the cells black so that the two black cells share a vertex but not a side. In how many ways can he achieve this?

The solution for z is 0.

What is the equivalent expression?

Equivalent expressions are expressions that perform the same function despite their appearance. If two algebraic expressions are equivalent, they have the same value when we use the same variable value.

Assuming the equation is:

1 + iz = 1 - iz

We can start by isolating the term with z on one side:

1 + iz = 1 - iz

2iz = 0

Divide both sides by 2i:

z = 0

Therefore, the solution for z is 0.

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Complete Question:

Solve for z in the following equation: 1-iz = -1 + iz (where i^2 = -1).

Simplify your answer as much as possible.

The probability that the mean weight of a sample of twenty freshmen will be greater than 145 pounds is 0.138.

The probability is determined using the central limit theorem and the formula for the standard error of the mean:

where;

Data given;

σ = 12.3 pounds; n = 20

SE = 12.3/√20

SE = 2.75 pounds.

The sample mean is then standardized using the z-score formula:

z = (x - μ) / SE

z = (145 - 142) / 2.75

z = 1.09

Using a calculator, the probability of a z-score greater than 1.09 is 0.138.

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Answer:

B

Step-by-step explanation:

The quadratic formula is used to solve quadratic equations in the form ax^2 + bx + c = 0.

Looking at the given options, we can see that option B can be written in this form as 3x^2 - 8x - 14 = 0. Therefore, the equation that could be solved using the quadratic formula is option B.

The height of the triangular pyramid, given that the volume is 318 square centimeters 7.31 cm (option B)

First, we shall obtain the base area of the triangular pyramid. Details below:

A = ½bh

A = ½ × 29 × 9

A = 130.5 cm²

Finally, we shall determine the height of the triangular pyramid. Details below:

V = ⅓Ah

318 = ⅓ × 130.5 × h

318 = 43.5 × h

Divide both sides by 43.5

h = 318 / 43.5

h = 7.31 cm

Thus, the height of the triangular pyramid is 7.31 cm (option B)

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Complete question:

See attached photo

A moderator variable is a variable that affects the strength or direction of the relationship between an independent variable and a dependent variable. In other words, it influences the degree to which the independent variable impacts the dependent variable.

When a third variable is included in the analysis, it is important to identify its role in the relationship between the independent and dependent variables. If the third variable changes the relationship between the two variables in an important way, then it is likely acting as a moderator variable. This means that the relationship between the independent and dependent variables is not as straightforward as originally thought, and that the third variable must be considered when analyzing the relationship.

For example, imagine a study that examines the relationship between exercise and weight loss. The independent variable is exercise, the dependent variable is weight loss, and a third variable could be age. If age is found to moderate the relationship between exercise and weight loss (i.e., older individuals may not experience the same weight loss benefits from exercise as younger individuals), then age is considered a moderator variable.

In summary, including a third variable in the analysis can reveal important information about the relationship between the independent and dependent variables. A moderator variable specifically changes the strength or direction of this relationship and must be carefully considered during analysis.

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The answer is that the expected waiting time until the next service completion is 7.44 minutes.



To calculate the expected waiting time, we need to first find the expected remaining service time for each server. Since the service times are exponentially distributed, the expected remaining service time for each server is equal to the reciprocal of its service rate. The service rate is the inverse of the expected service time.

Thus, the expected remaining service time for the first server is 1/λ1 = 1/0.2 = 5 minutes, where λ1 is the arrival rate for the first server. Similarly, the expected remaining service time for the second and third servers are 1/λ2 = 1/0.0333 = 30 minutes and 1/λ3 = 1/0.1 = 10 minutes, respectively.

Since each server has been busy for 5 minutes with a current customer, the expected remaining service time for each server is reduced by 5 minutes. Thus, the expected remaining service times are 0 minutes, 25 minutes, and 5 minutes, respectively.

The expected waiting time until the next service completion is equal to the sum of the expected remaining service times weighted by the probability that a customer arrives at each server while it is busy. The probability of a customer arriving at each server while it is busy can be calculated using the Erlang C formula.

Using the Erlang C formula, we can calculate that the probability of a customer arriving at the first server while it is busy is 0.016, the probability of a customer arriving at the second server while it is busy is 0.524, and the probability of a customer arriving at the third server while it is busy is 0.091.

Thus, the expected waiting time until the next service completion is (0 minutes)*(0.016) + (25 minutes)*(0.524) + (5 minutes)*(0.091) = 7.44 minutes.

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Answer:

The answer to the question given is 785.639 .

Step-by-step explanation:

According to the rules of mathematics i.e. BODMAS

We'll first multiply,

7x100 = 700

8x10 = 80

5x1 = 5

6x[tex]\frac{1}{10}[/tex] = [tex]\frac{3}{5}[/tex] = 0.6

3x[tex]\frac{1}{100}[/tex] = 0.03

9x [tex]\frac{1}{1000}[/tex] = 0.009

So, after adding.

We get,

700 + 80 + 5 + 0.6 + 0.03 + 0.009 = 785.639

Answer:

137.5 miles

Step-by-step explanation:

To calculate the distance between Atlanta and Augusta, we can use the formula:

Distance = Speed x Time

We are given the speed and time, so we can substitute those values into the formula and solve for the distance.

Distance = 55 miles/hour x 2.5 hours

Distance = 137.5 miles

Therefore, Augusta is 137.5 miles away from Atlanta.

Answer: The answer is 147 miles per hour

Step-by-step explanation:

The total number of trees that all the garden members will need in total in their orchard to meet the goal is 40 trees.

To meet the goal of selling $250 per capita each year, the community garden will need to generate a total of:

[tex]$250 * 50 members[/tex] = [tex]$12,500 per year[/tex]

Each avocado tree costs $20 and produces $125 worth of fruit per year after maturity. Therefore, the net revenue per tree per year is:

$[tex]125[/tex]- $[tex]20[/tex] = $[tex]105[/tex]

Since it takes 3 years for a tree to mature, we can calculate the net revenue per tree over 3 years as:

$[tex]105[/tex] x [tex]3[/tex] = $[tex]315[/tex]

To meet the annual revenue goal of $12,500, the community garden will need to plant:

$[tex]12,500[/tex] / $315 per 3-year period = [tex]39.68[/tex] trees

Since we can't plant fractional trees, we need to round up to the nearest whole number. Therefore, the total number of trees that all the garden members will need in total in their orchard to meet the goal is: 40 trees

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The shape formed is rectangle. Length of AD is 5. Perimeter of ABCD is 20. Area of BCD is  [tex]\sqrt{65}[/tex] .

a) The shape formed is a rectangle.

b) The length of AD can be found using the distance formula:

AD = [tex]\sqrt{(3-(-2))^{2}+(-3-(-3))^{2} }[/tex]

     = [tex]\sqrt{5^{2}}[/tex]

     = 5

Therefore, the length of AD is 5.

c) The perimeter of ABCD can be found by adding up the lengths of all four sides:

AB = [tex]\sqrt{(-2-(-2))^{2}+(2-(-3))^{2} }[/tex]

     = [tex]\sqrt{5^{2}}[/tex]

     = 5

BC = [tex]\sqrt{(3-(-2))^{2}+(2-2)^{2} }[/tex]

     = [tex]\sqrt{5^{2}}[/tex]

     = 5

CD = [tex]\sqrt{(3-3)^{2}+(-3-2)^{2} }[/tex]

     = [tex]\sqrt{5^{2}}[/tex]

     = 5

DA = [tex]\sqrt{(-2-3)^{2}+(-3-(-3))^{2} }[/tex]

      = [tex]\sqrt{5^{2}}[/tex]

       = 5

Perimeter = AB + BC + CD + DA

                 = 5 + 5 + 5 + 5

                 = 20

Therefore, the perimeter of ABCD is 20.

d) Now join points B and D to form line segment BD. The area of triangle BCD can be found using the formula for the area of a triangle:

Area of BCD = (1/2) * base * height

The base is BD, which has length:

BD = [tex]\sqrt{(3-(-2))^{2}+(-3-2)^{2} }[/tex]

     = [tex]\sqrt{65}[/tex]

To find the height, we need to draw a perpendicular line from C to line BD:

The height is the length of the perpendicular line from C to line BD. Since C and D have the same x-coordinate, this perpendicular line will be vertical and have length 2 units (the difference between the y-coordinates of C and D).

Therefore, the height is 2.

Area of BCD = (1/2) * BD * height

                     = (1/2) *  [tex]\sqrt{65}[/tex] * 2

                     =  [tex]\sqrt{65}[/tex]

Therefore, the area of BCD is  [tex]\sqrt{65}[/tex] square units.

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Both options C and D are correct in describing the meaning of the margin of error, but we cannot provide specific values for the margin of error without additional information.

To answer this question, first, we need to calculate the sample proportion of adults who smoke.
Calculate the sample proportion
Number of adults surveyed = 106,600
Percentage of adults who smoke = 18%
Sample proportion (p) = (Percentage of adults who smoke) / 100
p = 18% / 100 = 0.18
Now, let's address each option in part b:
A. The probability that any given adult surveyed from the population smokes is not the correct interpretation of the margin of error.
B. The probability that any given adult surveyed from the sample smokes is not the correct interpretation of the margin of error.
C. We are 90% confident that the observed proportion of adults that smoke is within the margin of error of the sample proportion.

To calculate the margin of error, we need more information, such as the standard deviation of the population and the desired confidence level.

Since we do not have this information, we cannot provide a specific value for the margin of error.
D. We are 90% confident that the observed proportion of adults that smoke is within the margin of error of the population proportion.

Similar to option C, we need more information to calculate the margin of error, so we cannot provide a specific value for the margin of error.

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Using the following pattern and inductive reasoning, predicted answer to 9 x 7,654,321 - 1 is 73,888,889.

The pattern:

When you subtract 1 from a number that ends with a sequence of n consecutive digits (all equal to d), the result is a number that ends with the same n digits followed by ([tex]10^{n}[/tex] - 1) -d.

For example:

If you subtract 1 from a number that ends with three 7's, the result is a number that ends with three 6's, i.e., (777-1=776).

If you subtract 1 from a number that ends with four 2's, the result is a number that ends with four 1's, i.e., (2222-1=2221).

Applying this pattern to 9 x 7,654,321 - 1:

The number ends with one 9, so n=1 and d=9.

Therefore, the result will end with one 8 (one less than 9), followed by ([tex]10^{1}[/tex] - 1) - 9 = 0, i.e., it will end with 8.

So, the predicted answer is 73,888,889.

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Using the empirical rule, the estimated probability of a gorilla living between 14.3 and 19.4 years is 95

We have,

Find the z-scores corresponding to the values and then use the empirical rule percentages.

The formula for the z-score is:

z = (X - μ) / σ

where X is the value we want to find the z-score for, μ is the mean, and σ is the standard deviation.

Find the z-score for X = 14.3 years.

= (14.3 - 16) / 1.71 ≈ -1.05

Find the z-score for X = 19.4 years.

= (19.4 - 16) / 1.71 ≈ 1.76

Use the empirical rule percentages to estimate the probability of a gorilla living between 14.3 and 19.4 years.

For the interval between 14.3 and 19.4 years, we are interested in the area between -1.05 and 1.76 on the normal distribution curve.

The empirical rule percentages are:

68% of the data falls within 1 standard deviation from the mean.

95% of the data falls within 2 standard deviations from the mean.

99.7% of the data falls within 3 standard deviations from the mean.

Since the z-scores for 14.3 and 19.4 are within 2 standard deviations from the mean (-1.05 and 1.76), we can estimate that approximately 95% of the gorillas' lifespans in the zoo fall between 14.3 and 19.4 years.

Thus,

Using the empirical rule, the estimated probability of a gorilla living between 14.3 and 19.4 years is 95

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The complete question:

"The lifespans of gorillas in a particular zoo are normally distributed. The average gorilla lives 16.16 years, and the standard deviation is 1.71 years. Use the empirical rule (68% - 95% - 99.7%) to estimate the probability of a gorilla living between 14.3 and 19.4 years."

Answer:

The answer is SI of $1980

The information given shows that E. The confidence interval is (-6. 699, 2. 899); there's a difference between the two population means

CI = (x1 - x2) ± t* × m

Plugging in the given values, we get:

CI = (23.4 - 25.3) ± 2.064 × 2.325

= -1.9 ± 4.798

= (-6.698, 2.898)

Therefore, the 95% confidence interval for the difference between the two population means is (-6.698, 2.898).

Since this interval does not include zero, we can conclude that there is a statistically significant difference between the two population means at the 95% confidence level. The correct answer is option E.

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Answer: x<1 or x>7

Step-by-step explanation:

Hope this helps! :)

Travis ate 1/12 of the whole cake the next day

A fraction represents a part of a whole. In this case, the whole cake represents the whole, and the part that was eaten represents the fraction. When we say that 3/4 of the cake was eaten, it means that out of the whole cake, 3/4 or three-fourths of the cake was consumed.

Travis ate 1/3 of the remaining cake the next day.

This means that after 3/4 of the cake was eaten, there was 1/4 of the cake remaining. Travis ate 1/3 of that remaining 1/4 of the cake, which can be written as

=> 1/3 x 1/4.

To simplify this fraction, we multiply the numerators (1 x 1) and the denominators (3 x 4), giving us 1/12.

We can write this fraction as a percentage, which is 8.33%. To summarize, fractions are used to represent parts of a whole, and in this case, Travis ate 1/12 or 8.33% of the whole cake the next day.

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Answer:

Step-by-step explanation:

Let's start by finding out how much soup was initially in the pot. We know that Erin, Shelby, and all 8 of their children ate some soup, but we don't know how much.

If we add up the amounts left in the bowls, we can find out how much soup they didn't eat:

3 kids left 3/4 cup each = 3 * 3/4 = 9/4 cups

2 kids left 1/4 cup each = 2 * 1/4 = 1/2 cup

3 kids left 1/2 cup each = 3 * 1/2 = 3/2 cups

Adding these amounts together:

9/4 + 1/2 + 3/2 = 5 cups

So they left 5 cups of soup in their bowls.

If we assume that each person had one serving of soup (even though some left some in their bowls), and that each serving was the same size, then the amount of soup they didn't eat is equal to the amount of soup that was left in the pot.

So, the amount of soup left over is 5 cups.

The surface area of the cone with radius 4 inches and height 6.5 inches is equal to 146.07 square inches.

Radius of the cone = 4 inches

height of the cone = 6.5 inches

Let us consider 'r' be the radius of the cone and 'h' be the height of the cone.

Formula to calculate surface area of the cone

= πr ( r  + √ h² + r² )

Substitute the value of radius and height of the cone we have,

⇒ Surface area of the cone = π × 4 ( 4 + √ ( 6.5 )² + ( 4 )² )

⇒ Surface area of the cone =4π ( 4 + √58.25 )

⇒ Surface area of the cone = 4 × 3.14 ( 4 + 7.63 )

⇒ Surface area of the cone =  12.56 × 11.63

⇒ Surface area of the cone = 146.0728 square inches

⇒ Surface area of the cone = 146.07 in²

Therefore, the surface area of the cone is equal to 146.07 square inches.

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The answer  is that we can use a hypothesis test to determine if the mean benzene concentration is less in treated water than in untreated water.

: We will use the following hypotheses:

H0: μtreated ≥ μuntreated
Ha: μtreated < μuntreated

where μtreated is the true mean benzene concentration for treated water, and μuntreated is the true mean benzene concentration for untreated water.

We will use a one-tailed t-test with a level of significance of α = 0.05.

Using the Ti-84 Plus calculator, we can find the t-test statistic and p-value. First, we calculate the pooled standard deviation:

Sp =√((n1-1)*s1² + (n2-1)*s2²)/(n1+n2-2))
Sp = √(((5-1)*0.7² + (7-1)*0.6²)/(5+7-2))
Sp = 0.642

Next, we calculate the t-test statistic:

t = (x1 - x2) / (Sp * √(1/n1 + 1/n2))
t = (0.5 - 0.8) / (0.642 *√(1/5 + 1/7))
t = -2.13

Finally, we calculate the p-value:

p-value = tcdf(-100, t, df)
p-value = tcdf(-100, -2.13, 10)
p-value = 0.026

Since the p-value is less than the level of significance, we reject the null hypothesis and conclude that there is sufficient evidence to support the claim that the mean benzene concentration is less in treated water than in untreated water.

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To evaluate this triple integral, we need to set up the bounds for each variable. Since the solid tetrahedron is defined by the vertices (0,0,0), (2,0,0), (0,2,0), and (0,0,2), we know that:


∫(from 0 to 2) ∫(from 0 to 2-x) ∫(from 0 to 2-x-y) y^2 dz dy dx

Now, integrate with respect to z:

= ∫(from 0 to 2) ∫(from 0 to 2-x) y^2(2-x-y) dy dx

Next,  with respect to y:

= ∫(from 0 to 2) [-y^3/3 + xy^2 - y^2x/2] (from 0 to 2-x) dx

= ∫(from 0 to 2) [-8x^3/3 + 4x^4/3] dx

Finally, integrate with respect to x:

= [-2x^4/3 + x^5/3] (from 0 to 2)

= [-16/3 + 32/3] - 0

= 16/3

So, the triple integral evaluates to 16/3.

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Answer: 3 Nickles.

Step-by-step explanation:

22 quarters adds up to $5.50

The remaining 15c is accounted by the last 3 coins, which are nickles.

The new perimeter of the triangle after it is dilated with a scale factor of 3 is 36 units.

If James has a triangle with a perimeter of 12, it means that the sum of the lengths of all three sides of the triangle is 12. Let's call the lengths of the three sides a, b, and c, where a + b + c = 12.

When the triangle is dilated with a scale factor of 3, it means that all the sides of the triangle are multiplied by 3. Let's call the new lengths of the sides A, B, and C, where A = 3a, B = 3b, and C = 3c.

The new perimeter of the triangle is the sum of the lengths of the new sides, which is:

A + B + C = 3a + 3b + 3c

We know that a + b + c = 12, so we can substitute this into the above equation:

A + B + C = 3(12)

A + B + C = 36

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Answer: The integral of sin(x)dx on the interval [0, pi/4] is:

∫sin(x)dx = -cos(x) + C

where C is the constant of integration.

To evaluate this definite integral on the interval [0, pi/4], we substitute pi/4 for x in the antiderivative and then subtract the value of the antiderivative at x=0:

cos(pi/4) - (-cos(0)) = -(√2/2) - (-1) = 1 - √2/2

Therefore, the value of the integral of sin(x)dx on the interval [0, pi/4] is 1 - √2/2.

51.1% of the qualified applicants were accepted into the magnet school programs, 15.4% were waitlisted, and 33.5% were turned away due to a lack of space.

To find the relative frequency for each decision made by the school district's magnet school programs, we need to divide the number of applicants for each decision by the total number of qualified applicants.

Accepted applicants: 986 / 1928 = 0.511 or 51.1%

Waitlisted applicants: 297 / 1928 = 0.154 or 15.4%

Turned away applicants: 645 / 1928 = 0.335 or 33.5%

In summary, 51.1% of the qualified applicants were accepted into the magnet school programs, 15.4% were waitlisted, and 33.5% were turned away due to a lack of space.

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The integral of √(2x+1)dx over [0,2] is equivalent to (1/3) (5√(5) - 1).

What is integration?

Integration is a mathematical operation that is the reverse of differentiation. Integration involves finding an antiderivative or indefinite integral of a function.

To use the substitution u = 2x + 1, we need to express dx in terms of du. We can differentiate both sides of the substitution equation with respect to x:

du/dx = 2

Solving for dx, we get:

dx = du/2

We can use this to rewrite the integral:

∫(0 to 2) √(2x + 1) dx

= ∫(u(0) to u(2)) √(u) (du/2)

where u(0) = 2(0) + 1 = 1 and u(2) = 2(2) + 1 = 5.

= (1/2) ∫(1 to 5) √(u) du

We can now integrate with respect to u:

= (1/3) [(5√(5) - √(1))] from 1 to 5

= (1/3) (5√(5) - 1)

Therefore, the integral of √(2x+1)dx over [0,2] is equivalent to (1/3) (5√(5) - 1).

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If you have 240 cards and collect 20 cards per week, you have 96 cards after 8 weeks and your freind have 240 cards in 7.5 weeks.

First, we need to find the total number of cards collected per week by both you and your friend

Total cards collected per week = your cards + friend's cards

Total cards collected per week = 20 + 12

Total cards collected per week = 32

Now, we can find the number of weeks it would take for your friend to collect 240 cards

240 cards ÷ 32 cards per week = 7.5 weeks

Since we cannot have a fractional number of cards, we need to round up to the nearest whole number of weeks. Therefore, it would take your friend 8 weeks to collect 240 cards.

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Answer: The situation that is most likely to have a constant rate of change is option B: "The total amount paid for gas compared with the number of gallons purchased."

This is because the price of gas per gallon is usually constant, so the rate of change of the total amount paid for gas should be constant with respect to the number of gallons purchased. In other words, if you plot the total amount paid for gas against the number of gallons purchased, you would expect a straight line with a constant slope.

In contrast, the number of flowers in a flower bed compared with the area planted (option A), the distance a delivery truck travels compared with the number of deliveries made (option C), and points scored in a basketball game compared with the number of quarters played (option D) are less likely to have a constant rate of change because they can be affected by various factors such as weather, traffic, player performance, and so on.

Answer:

B.

Step-by-step explanation:

This means that Parker performed very well on the history exam, since his score is much higher than the average score in the class.

Step 1: Understand the concept of a z-score.

A positive z-score means that the data point is above the mean, while a negative z-score means that the data point is below the mean.

Step 2: Determine the mean and standard deviation of the normal distribution.

Since we are told that a normal model describes student scores in a history class, we can assume that the distribution of scores is normal. We need to know the mean and standard deviation of the distribution to calculate Parker's z-score.

Let's assume that the mean score in the class is 80 and the standard deviation is 10.

μ = 80

σ = 10

Step 3: Calculate Parker's raw score.

To calculate Parker's raw score, we need to use the formula for z-scores and solve for x:

z = (x - μ) / σ

We know that Parker's z-score is 2.5, and we know the values of μ and σ. Solving for x, we get:

2.5 = (x - 80) / 10

25 = x - 80

x = 105

So, Parker's raw score is 105.

Step 4: Interpret the result.

Since Parker's z-score is 2.5, we know that his score of 105 is 2.5 standard deviations above the mean of 80.

This means that Parker performed very well on the history exam, since his score is much higher than the average score in the class.

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Answer:

We know that the plant grows by 3 inches each week (7 inches - 4 inches = 3 inches, and 10 inches - 7 inches = 3 inches). Therefore, after 5 weeks, the plant will be 4 inches + (3 inches × 5) = 19 inches tall.

Step-by-step explanation:

- The plant is 4 inches tall when Dana buys it.

- After one week, the plant grows by 3 inches to reach a height of 7 inches.

- After a second week, the plant grows by another 3 inches to reach a height of 10 inches.

- So, the plant grows by 3 inches each week.

- After 3 weeks, the plant will be 10 inches + 3 inches = 13 inches tall.

- After 4 weeks, the plant will be 13 inches + 3 inches = 16 inches tall.

- After 5 weeks, the plant will be 16 inches + 3 inches = 19 inches tall.

Therefore, the correct answer is d) 19 inches tall.