what is 7x=14 show your work

A searchlight is shaped like a paraboloid of revolution. if the light source is located 2 feet from the base along the axis of symmetry and the opening is 5 feet across, 2.5 feet deep should the searchlight be.

As per the given information,

A searchlight is shaped like a paraboloid of revolution. If the light source is located 2 feet from the base along the axis of symmetry and the opening is 5 feet across.

Here we have to Find: How deep should the searchlight be.

First of all, we need to find the equation of the paraboloid of revolution.

Let's assume that the axis of the paraboloid is along the y-axis and the vertex is at the origin (0, 0, 0).

So, the equation of the paraboloid is given by:

y² = 4ax

Where, a = 2 feet (distance of light source from vertex)

So, the equation of the paraboloid is:

y² = 8x ..... (1)

The opening of the paraboloid is given to be 5 feet across.

We know that the diameter of a circle is equal to twice the radius. Hence, the radius of the opening is 2.5 feet.

The vertex is the point (0, 0, 0). We need to find the depth of the searchlight. The depth is nothing but the perpendicular distance from the vertex to the plane of the opening. The plane of the opening is given by the equation x = -2.5 (since the opening is along the yz-plane)

The equation of the plane is given by x = -2.5

Now, we need to find the coordinates of the point where the paraboloid intersects the plane of the opening.

We can substitute x = -2.5 in equation (1) to get:

y² = -20

Squaring both sides, we get:

y = ±√(-20)

Since y can only be positive (since we are considering the upper half of the paraboloid),

y = √(-20) = i√20 = 2√5 i

So, the point where the paraboloid intersects the plane of the opening is (-2.5, 2√5 i, 0)

The depth is nothing but the perpendicular distance from the vertex (0, 0, 0) to the point (-2.5, 2√5 i, 0). Hence, the depth is given by:√((-2.5 - 0)² + (2√5 i - 0)² + (0 - 0)²)= √(6.25 + 20 - 0) = √26.25 = 2.5 feet

Hence, the depth of the searchlight should be 2.5 feet.

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A human organism developing in the uterus from the ninth week until birth is called a(n) fetus.

A fetus is the term used to describe a human organism that is developing in the uterus from the ninth week of gestation until birth. During this time, the fetus undergoes significant growth and development, as all of the major organs and body systems are formed and begin to function.

The ninth week of gestation is considered a significant milestone in fetal development, as most of the critical stages of organogenesis have been completed by this time. From this point onward, the fetus primarily grows and matures in preparation for life outside of the womb.

During the remaining weeks of gestation, the fetus undergoes a number of important developmental processes, including continued brain development, growth of the nervous system, and development of the lungs and other vital organs. At the same time, the fetus also gains weight and size, and begins to develop a layer of fat that will help to regulate body temperature after birth.

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The algebraic expression for the particle's velocity vₓ at a later time t is v(t) = ct²/2m +v₀ₓ.

Given that,

c = speed of light

t = time

v₀ₓ = initial velocity of particle

m = mass of particle

Velocity and acceleration are related through time. Acceleration is the rate of change of velocity, which is represented graphically as the slope of the velocity vs. time line. Velocity can be represented as the area underneath an acceleration vs. time line.

Newton's second law declares that an object having mass m will accelerate due to a net force (F) will accelerate at a rate of:

α = F/m

Therefore, the function that describes the acceleration at any point in time of the particle is:

α(t)=ct/m

The velocity function is the integral of the acceleration function, so we get:

v(t)= ∫ct/m dt

= ct²/2m +C

where the constant C is the initial velocity of the particle at time t=0. Therefore, the velocity function representing the velocity at any point in time is:

v(t) = ct²/2m +v₀ₓ

Therefore, the algebraic expression for the particle's velocity vₓ at a later time t is v(t) = ct²/2m +v₀ₓ.

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The median of a normal distribution with a mean of $\mu$ and standard deviation of $\sigma$ is simply equal to the mean $\mu$. Therefore, for a normal distribution with a mean of 61 and a standard deviation of 14, the median is also 61.

This is because the normal distribution is a symmetric distribution, with the mean, median, and mode all located at the same point on the horizontal axis. The mean represents the center of the distribution and is also the balance point for the distribution, so half of the observations will be less than the mean and half will be greater than the mean.

Therefore, for a normal distribution with a given mean and standard deviation, we can use the mean as an estimate of the median. In this case, the mean is exactly equal to the median, so the median is 61.

It is worth noting that this property of normal distributions only holds for normal distributions, and not necessarily for other types of distributions. For example, in a skewed distribution, the mean and median may be quite different from each other.

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The inequality that represents the graph is Oys-3x+2. This inequality states that the y-value is greater than or equal to -3x+2.

Graph is a data structure that consists of nodes (also called vertices) and edges. Nodes represent entities such as people, places or objects, while edges represent the relationship between the nodes. Graphs are used to represent many different types of real-world relationships, such as social networks, transportation networks and communication networks. Graphs can also be used to solve complex problems in computer science, operations research and mathematics. Graphs provide an efficient way to store and manipulate data and can be used to represent both directed and undirected relationships.

This inequality can be interpreted as the solution set of all points that have a y-value that is at least -3x+2.

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Answer:The equation of a line that passes through a point is an algebraic equation. It can also be referred to as the Slope-Intercept Equation.The equation of the line that passes through the point (4, 4) and has a slope of 0 is written as: y = 4 The equation of the line through a point (x1, y1) can be represented by the algebraic equation:y = mx + cwhere:m = slopec = y - interceptFrom the question,(x1, y1) = (4, 4)m = slope = 0Substituting these values into the algebraic equation,4 = (0 x 4) + c Hence, y = 4The equation of the line that passes through the point (4, 4) and has a slope of zero is y = 4

Answer:

y=4

Step-by-step explanation:

If a line has a slope of 0, then it is a horizontal line, and all points on the line have the same y-coordinate. We are given that the line passes through the point (4, 4). Therefore, the equation of the line in slope-intercept form is:

y = b

where b is the y-coordinate of the point through which the line passes. In this case, b = 4, so the equation of the line is:

y = 4

Therefore, the equation of the line in slope-intercept form is y = 4.

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The correct answer to the question, "Which of the following is equivalent to the probability of getting less than 50% democrats in a random sample of size 100?" is: B. P( z < 50 — 55/ √55(45)/100).

To find the probability, we first calculate the z-score using the formula:

z = (x - μ) / σ

where x is the value (50%), μ is the mean (55%), and σ is the standard deviation.

The standard deviation can be calculated as:

σ = √(np(1-p))

where n is the sample size (100) and p is the proportion of democrats (0.55).

Now, plug in the values into the z-score formula:

z = (50 - 55) / √(100 * 0.55 * 0.45)

The probability is then found as P(z < z-score), which is represented by the option B.

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Answer:

Step-by-step explanation:

$105.20

The area of the circle with circumference 19cm is 6.42cm²( nearest hundredth).

Area of a circle is the region occupied by the circle in a two-dimensional plane. It can be determined easily using a formula, A = πr2. Where r is the radius.

The circumference of a circle is given as ;

C = 2πr

C = 9cm

therefore, 9 = 2× 3.14 × r

9 = 6.28r

r = 9/6.28

r = 1.43 cm

Area of circle = πr²

= 3.14 × 1.43²

= 6.42cm²( nearest hundredth)

therefore the area of the circle is 6.42cm²

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Tom will pay a total of $13,424.20 in interest over the term of the loan.

The formula to calculate the monthly payment for an amortized loan is given by:  `P = r(PV) / [1 - (1 + r)^(-n)]`Where P is the monthly payment, r is the interest rate per month, PV is the present value of the loan, and n is the number of payments or the total number of months.

Substituting the given values, we get:P = 0.0052083333 × 44,000 / [1 - (1 + 0.0052083333)^(-7×12)]P = 632.32Therefore, Tom's monthly payment is $632.32 (rounded to the nearest cent).b. Since Tom pays the monthly payment each month for the full term, his total amount to repay the loan is equal to the present value of the loan.

Therefore, the total amount to repay the loan is $44,000 (rounded to the nearest cent).c. The total amount of interest paid over the term of the loan can be calculated as the difference between the total amount repaid and the principal amount of the loan.

Therefore, the total interest paid is: Total interest paid = Total amount repaid - Principal amount of the loan Total interest paid = $57,424.20 - $44,000Total interest paid = $13,424.20

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The student question is about calculating the statistics and probabilities for two different sample sizes of adolescent girls who are developmentally delayed, reaching their adult height.

For the sample size of 29 girls, the estimated standard error is 1.6337, and the statistic is 1.10. For the larger sample size of 91 girls, the new estimated standard error is 0.9222, and the new statistic is 1.95. As the sample size increases, the statistic becomes smaller.

Using the Distributions tool to determine the probability of getting the statistic or something more extreme for each sample size, you can find the probabilities (p) for each case. For the sample size of[tex]29 (n=29),[/tex] you will obtain a specific probability (p).

Similarly, for the sample size of[tex]91 (n=91)[/tex], you will get another probability (p). The distribution will change with larger sample sizes (n).

To observe the distribution changes, you can use the Degrees of Freedom slider in the tool and move it from the smallest value to the largest value. This will help you see how the shape of the distribution changes as the sample size increases.

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The slice for apple will have an angle of 60 degrees, the slice for banana will have an angle of 90 degrees, the slice for guava will have an angle of 30 degrees, and the slice for grapes will have an angle of 180 degrees.

A pie chart is a circular statistical graphic, which is divided into slices to illustrate numerical proportion. In a pie chart, the arc length of each slice is proportional to the quantity it represents. Pie charts are commonly used in business, media, and other fields to represent percentages, ratios, and proportions. They are useful for quickly understanding the relative sizes of different categories or groups in a dataset.

Here,

To create a pie chart from the given data, we first need to calculate the angle of each slice of the pie chart. To do this, we use the following formula:

Angle for a slice = (Frequency of the category ÷ Total frequency) × 360°

Using the given data, we can calculate the angle of each slice as follows:

Angle for apple = (12 ÷ 72) × 360° = 60°

Angle for banana = (18 ÷ 72) × 360° = 90°

Angle for guava = (6 ÷ 72) × 360° = 30°

Angle for grapes = (36 ÷ 72) × 360° = 180°

Now, we can draw a circle and divide it into 12 parts (each representing 30 degrees). Then, we can draw the slices of the pie chart using the angles we calculated above.

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Answer: there are 12 fruit centers and 15 caramel centers

Step-by-step explanation:

Step-by-step explanation:

calculate the tax on an item, we need to multiply the price by the tax rate as a decimal.

For the sneakers:

Tax on sneakers = 0.08 * $129.99 = $10.40

For the boots:

Tax on boots = 0.08 * $89.99 = $7.20

The difference between the tax on the sneakers and the tax on the boots is:

$10.40 - $7.20 = $3.20

Therefore, the correct answer is (A) The tax on the sneakers is $3.20 more than the tax on the boots

Answer: A. The tax on the sneakers is $3.20 more than the tax on the boots.

The middle 50% of the distribution for X, or the IQR, lies between 87 acres and 261 acres.

A measurement of the dispersion or variability of a dataset is the interquartile range (IQR). The 75th and 25th percentiles of the data, or the difference between the upper and lower quartiles, are used to define it. The range of the middle 50% of the data is represented by it, in other words.

The IQR is a reliable indicator of the spread of the data that, in comparison to the range or standard deviation, is less susceptible to outliers or extreme values. For this reason, it is valuable in statistics. It is frequently employed as a measure of variability when the data contains extreme values or when the distribution is not normal.

Given that, mean = 174 and standard deviation = 58 acres.

Using the quartile values we have:

Q1 = mean - (1.5 * standard deviation)

Q1 = 174 - (1.5 * 58) = 87 acres

Q3 = mean + (1.5 * standard deviation)

Q3 = 174 + (1.5 * 58) = 261 acres

Hence, the middle 50% of the distribution for X, or the IQR, lies between 87 acres and 261 acres.

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The complete question is:

Answer:

The cost per T-shirt $5.

By reducing −16/5 ⋅ (−15/56) in lowest term, the answer is 6/7.

To perform the indicated operation and reduce the result to lowest terms, we need to multiply the two fractions:

(-16/5) x (-15/56) = (16 x 15) / (5 x 56)

(when we multiply two negative numbers, the result is positive)

= 240 / 280

Now we can simplify this fraction by dividing both the numerator and the denominator by their greatest common factor, which is 40:

240 / 280 = (240 ÷ 40) / (280 ÷ 40) = 6/7

Therefore, -16/5 ⋅ (-15/56) = 6/7 in lowest terms.

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Answer:

The number cube has 6 equally likely outcomes, so the probability of rolling a 1 or a 6 on any given roll is 2/6 = 1/3.

If Kenya rolls the number cube 90 times, we can use the expected value formula to find the expected number of times that a 1 or a 6 will land face up:

Expected number of 1's or 6's = (number of rolls) x (probability of rolling a 1 or a 6)

Expected number of 1's or 6's = 90 x (1/3)

Expected number of 1's or 6's = 30

Therefore, a reasonable prediction for the number of times that a 1 or a 6 will land face up is 30.

Therefore, the probability that [tex]X + Y < 2900 is 0.98.[/tex]

P[tex](X + Y < 2900) = 0.98.[/tex]
To calculate the probability, we need to use the joint probability density function of X and Y, given as f(xy) = 6 × 10^(-6) exp(-0.001x-0002y) for x < y.

We can then use the integral equation to solve this equation:

[tex]P(X + Y < 2900) = ∫02900∫x2900-x 6×10-6exp(-0.001x - 0.0002y)dydx[/tex]
The integral yields:

P(X + Y < 2900) = 0.98.

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The study described in the question is a randomized crossover trial, where each participant serves as their own control by receiving both treatments  in a randomized order

In a matched pairs experiment, each subject is paired with another subject who is similar in some relevant characteristic, and one subject receives the treatment while the other serves as a control. The two subjects in each pair are matched on this characteristic to reduce the effect of confounding variables.

In contrast, a randomized crossover trial is a type of experiment in which each participant receives both treatments (in this case, canned soup and fresh soup) in a randomized order, with a washout period between the treatments to minimize carryover effects. In this study, the participants were randomly assigned to either start with canned soup or fresh soup and then switched to the other treatment after a two-day break. Each participant thus serves as their own control, and the difference in outcome between the two treatments is compared within each individual.

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The given question is incomplete, the complete question is:

Bisphenol A in Your Soup Cans Bisphenol A (BPA) is in the lining of most canned goods, and recent studies have shown a positive association between BPA exposure and behavior and health problems. How much does canned soup consumption increase urinary BPA concentration? That was the question addressed in a recent study1 in which consumption of canned soup over five days was associated with a more than 1000 % increase in urinary BPA. In the study, 75 participants ate either canned soup or fresh soup for lunch for five days. On the fifth day, urinary BPA levels were measured. After a two-day break, the participants switched groups and repeated the process. The difference in BPA levels between the two treatments was measured for each participant. The study reports that a 95 % confidence interval for the difference in means (canned minus fresh) is 19.6 to 25.5 ?g/L. 1Carwile, J., Ye, X., Zhou, X., Calafat, A., and Michels, K., ‘‘Canned Soup Consumption and Urinary Bisphenol A: A Randomized Crossover Trial,” Journal of the American Medical Association, 2011; 306(20): 2218–2220.Is this a randomized comparative experiment or a matched pairs experiment?

By looking at the box plot, we can determine that the IQR is 40 pounds.

The interquartile range (IQR) of the players' weights is the difference between the upper quartile (Q3) and the lower quartile (Q1). The upper quartile is the value that 75% of the players' weights are below, and the lower quartile is the value that 25% of the players' weights are below.

Calculating the IQR requires the following steps:

In this case, the interquartile range of the players' weights is the difference between the upper quartile (Q3) and the lower quartile (Q1). By looking at the box plot, we can determine that the IQR is 40 pounds.

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The 4 in the hundredths place has a smaller value than the 4 in the tens place.

In the decimal number system, each digit to the left of the decimal point represents a power of 10, starting with 10^0 = 1 for the rightmost digit. Each digit to the right of the decimal point represents a negative power of 10, with the place value decreasing as you move farther to the right.

In the number 240.149, the 4 in the tens place represents 4 x 10 = 40. The 4 in the hundredth place represents 4/100 or 0.04, which is smaller than 40. Therefore, the 4 in the tens place has a greater value than the 4 in the hundredths place.

Hence, the value of a digit in a decimal number depends on its position relative to the decimal point. Digits to the left of the decimal point represent whole numbers, while digits to the right of the decimal point represent fractions or parts of a whole.


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The calculated total mass of Caroline in kg by the calculation below is 41,393.415 kilograms

Caroline's mass is 41,390,000 grams.

To convert grams to kilograms, we need to divide by 1000:

41,390,000 grams / 1000 = 41,390 kilograms

Caroline's baby sister's mass is 3,415 grams.

To convert grams to kilograms, we also need to divide by 1000:

3,415 grams / 1000 = 3.415 kilograms

Therefore, their total mass in kilograms is:

41,390 kilograms + 3.415 kilograms = 41,393.415 kilograms

Hence, the total mass is 41,393.415 kilograms

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(a) The probability that there is exactly one car and exactly one bus during a cycle is 0.020.

(b) The probability that there is at most one car and at most one bus during a cycle is 0.105.

(c) The probability that there is exactly one car during a cycle is 0.100, and the probability that there is exactly one bus during a cycle is 0.200. The probability that there is exactly one car is also 0.050.

(a) To find the probability that there is exactly one car and exactly one bus during a cycle, we need to look at the cell in the table where x = 1 and y = 1. This cell has a probability of 0.020. Therefore, the probability that there is exactly one car and exactly one bus during a cycle is 0.020.

(b) To find the probability that there is at most one car and at most one bus during a cycle, we need to add up the probabilities of the cells where either x = 0 or x = 1, and either y = 0 or y = 1. These cells are

x = 0, y = 0: 0.025

x = 0, y = 1: 0.010

x = 1, y = 0: 0.050

x = 1, y = 1: 0.020

Adding up these probabilities, we get

0.025 + 0.010 + 0.050 + 0.020 = 0.105

Therefore, the probability that there is at most one car and at most one bus during a cycle is 0.105.

(c) To find the probability that there is exactly one car during a cycle, we need to add up the probabilities of the cells where x = 1. These cells are

x = 1, y = 0: 0.050

x = 1, y = 1: 0.020

x = 1, y = 2: 0.030

Adding up these probabilities, we get

0.050 + 0.020 + 0.030 = 0.100

Therefore, the probability that there is exactly one car during a cycle is 0.100.

To find the probability that there is exactly one bus during a cycle, we need to add up the probabilities of the cells where y = 1. These cells are

x = 0, y = 1: 0.010

x = 1, y = 1: 0.020

x = 2, y = 1: 0.050

x = 3, y = 1: 0.060

x = 4, y = 1: 0.040

x = 5, y = 1: 0.020

Adding up these probabilities, we get

0.010 + 0.020 + 0.050 + 0.060 + 0.040 + 0.020 = 0.200

Therefore, the probability that there is exactly one bus during a cycle is 0.200.

Finally, the probability that there is exactly one car can also be obtained by summing the probabilities of the cells in the first row of the table

0.025 + 0.010 + 0.015 = 0.050

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YES "The engineered ACE2 immunoglobulin counters murine lethal SARS-CoV-2 infection through direct neutralization and Fc-effector activities".

What is  Immunoglobulin?

An Immunoglobulin is a blood protein that recognizes foreign molecules and signals the immune system to neutralize them.

Murine lethal SARS-CoV-2 is a laboratory-made strain of SARS-CoV-2 that can infect and kill mice. It is often used in research to study the virus and test potential treatments.

ACE2 is a protein found on the surface of cells that the SARS-CoV-2 virus uses to enter and infect cells.

An engineered ACE2 immunoglobulin is an artificially created version of ACE2 that is designed to bind to the virus and neutralize it. This is achieved through direct neutralization, where the ACE2 immunoglobulin binds to the virus and prevents it from entering cells.

Additionally, the ACE2 immunoglobulin has Fc-effector activities, which means it can activate other parts of the immune system to help fight the infection.

In summary, the engineered ACE2 immunoglobulin counters murine lethal SARS-CoV-2 infection through direct neutralization and Fc-effector activities. It is an artificially created protein that binds to the virus and signals the immune system to neutralize it.

Complete Question:

Does the engineered ace2 immunoglobulin counters murine lethal sars-cov-2 infection through direct neutralization and fc-effector activities?

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An important advantage of experiments over observational studies is that experiments can control for lurking variables to have a stronger case for causation. Another advantage is that experiments can isolate the effects of a specific treatment.

What is an experiment?

An experiment is a scientific study that is designed to test a hypothesis or investigate a cause-and-effect relationship between variables. Experiments allow researchers to manipulate one variable (independent variable) and observe the effect on another variable (dependent variable) while controlling for other variables that may affect the outcome (lurking variables).

What are observational studies?

Observational studies are research designs that observe and collect data from participants without manipulating any variables. In observational studies, the researchers only observe and record what happens naturally without intervening in any way. Observational studies are used when experiments are not feasible or ethical.

What are the advantages of experiments over observational studies?

Experiments have several advantages over observational studies. Some of the advantages include:

Control over variables: Experiments allow researchers to control for variables that may affect the outcome by manipulating one variable (independent variable) and keeping all other variables constant. This helps researchers to establish a cause-and-effect relationship between variables.

Isolation of specific effects: Experiments can isolate the effects of a specific treatment by comparing outcomes between treatment groups and control groups. This helps researchers to determine the effectiveness of the treatment with a high degree of accuracy.

Similarity between treatment groups: Experiments can ensure that approximately the same number of subjects is assigned to each treatment group, thereby minimizing the effects of individual differences on the outcome. This increases the statistical power of the study and reduces the likelihood of obtaining spurious results.

Control of extraneous variables: Experiments can control for lurking variables (extraneous variables) that may affect the outcome by manipulating one variable (independent variable) and keeping all other variables constant. This helps researchers to establish a strong case for causation.

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The Critical value to be used to gain the 98 confidence interval for the population mean is2.508 and can be determined using the t- distribution table.

critical value is the value of a test statistic that defines the upper and lower bounds of the confidence interval or determines the position of statistical significance in a statistical test.

Given

The following way can be carried out to determine the critical value

Step 1-First determine the degrees of freedom using the following formula

degrees of freedom = n- 1

where n is the sample size.

Step 2- Replace" n" in the below formula.

degrees of freedom = 23- 1

= 22

Step 3- Now you can use the t- distribution table to determine the critical value to get a 98 confidence interval.

critical value = 2.508

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Yes, the study group can claim a normal distribution of the sample means.

This is because when a group takes random samples from a population that has a normal distribution, the means of those samples will also follow a normal distribution. The reason for this is due to the Central Limit Theorem, which states that when a large enough number of samples are taken from a population, the distribution of the sample means will become more and more normal.

Since the study group is taking 20 random samples of 15 from a population with a normal distribution, it can be assumed that the means of the sample will have a normal distribution.  Therefore, when the study group draws 20 random samples of 15 from a population that has a normal distribution, they can be certain that the sample means will also follow a normal distribution.

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Answer:

When rounding to 1 significant figure, we keep the first non-zero digit and drop all the remaining digits. In this case, the first non-zero digit is 2, so we keep that and drop all the remaining digits:

a) 276040 rounds to 3 x 10^5 (or 300000 in standard form).

So the rounded number to 1 significant figure is 3 x 10^5.