the amount in Jason's savings will exceed the cost of a new television approximately 7.22 years from now.
a. The exponential growth equation to represent the price y of a new HD television t years from now is:
y = $2500[tex](1 + 0.04)^t[/tex]
where t is the number of years from now.
b. To predict when a new HD television will cost $3000, we can set y = $3000 and solve for t:
$3000 = $2500[tex](1 + 0.04)^t[/tex]
1.2 = [tex]1.04^t[/tex]
ln(1.2) = t ln(1.04)
t = ln(1.2) / ln(1.04)
t ≈ 3.97
Therefore, a new HD television will cost $3000 approximately 4 years from now.
c. To determine when the amount in Jason's savings will exceed the cost of a new television, we can use the formula for continuous compound interest:
A = [tex]Pe^(rt)[/tex]
where A is the amount in savings after t years, P is the principal amount, e is the mathematical constant approximately equal to 2.71828, r is the annual interest rate expressed as a decimal, and t is the time in years.
In this case, P = $2200, r = 0.047 (since the annual interest rate is 4.7%), and we want to find the time t when A = $2500. Plugging these values into the formula, we get:
$2500 = $2200[tex]e^(0.047t)1.13636 = e^(0.047t)[/tex]
ln(1.13636) = 0.047t
t = ln(1.13636) / 0.047
t ≈ 7.22
Therefore, the amount in Jason's savings will exceed the cost of a new television approximately 7.22 years from now.
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The angle measurements in the diagram are represented by the following expressions.
\qquad \blueD{\angle A=7x + 24^\circ}∠A=7x+24
∘
start color #11accd, angle, A, equals, 7, x, plus, 24, degrees, end color #11accd \qquad \greenD{\angle B=3x + 92^\circ}∠B=3x+92
∘
start color #1fab54, angle, B, equals, 3, x, plus, 92, degrees, end color #1fab54
Solve for xxx and then find the measure of \blueD{\angle A}∠Astart color #11accd, angle, A, end color #11accd:
\blueD{\angle A} =
The measure of the angles is 143°
Lines and anglesFrom the given diagram, the given measures are alternate exterior angles and they are equal.
Given the following parameters
∠A =7x + 24
∠B = 3x + 92
Equate
7x + 24 = 3x + 92
7x - 3x = 92 - 24
4x = 68
x = 17
Determine the measure of the angles
∠A = ∠B = 7x + 24
∠A = ∠B = 7(17) + 24
∠A = ∠B = 143 degrees
Hence the measure of the angles is 143°
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Based on historical data, it takes students an average of 48 minutes with a standard deviation of 15 ninutes to complete the Unit 5 test. What is the probability that your class of 20 students will have a mean Completion time greater than 60 minutes on the Unit test?
The probability that your class of 20 students will have a mean completion time greater than 60 minutes on the unit test is very low.
What is probability ?
Probability cam be defined as ratio of number of favorable outcomes, total number of outcomes
We can solve this problem by using the central limit theorem. According to the theorem, if we have a large enough sample size, the distribution of sample means will be approximately normal, regardless of the underlying distribution of the population.
The mean of the sample means will be equal to the population mean, and the standard deviation of the sample means (also known as the standard error) will be equal to the population standard deviation divided by the square root of the sample size.
In this case, we have a sample size of 20, which is not very large, but we can still use the central limit theorem as an approximation. The population mean is 48 minutes, and the population standard deviation is 15 minutes. The standard error of the sample mean is:
SE = σ / sqrt(n) = 15 / sqrt(20) = 3.354
To find the probability that the mean completion time for the sample is greater than 60 minutes, we need to standardize the sample mean using the formula:
z = (x - μ) / SE
where x is the sample mean, μ is the population mean, and SE is the standard error of the sample mean.
Plugging in the values, we get:
z = (60 - 48) / 3.354 = 3.57
We can now look up the probability of getting a z-score greater than 3.57 in a standard normal distribution table (or use a calculator). The probability turns out to be very small, approximately 0.0002 or 0.02%.
Therefore, the probability that your class of 20 students will have a mean completion time greater than 60 minutes on the unit test is very low.
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Ella's buys a computer for $785. Her local tax rate is 7%. How much does Ella pay for the computer, including tax?
Answer:
$839.95
Step-by-step explanation:
To get the amount of tax Ella would have to pay for, multiply the price of the computer by the tax rate
785 x .07 = 54.95
Then add the computer price and tax to get how much she paid for in total
785 +54.95= $839.95
Zoey needs to create a linear graph. Her graph will show the time on the x-axis and temperature (in °F) on the y-axis. Which set of data should Zoey use?
A the hourly temperature of a lake for six monthsthe hourly temperature of a lake for six months
B the temperature of an oven every minute until it reaches 350°the temperature of an oven every minute until it reaches 350°
C the average daily temperature of a town for a yearthe average daily temperature of a town for a year
D the temperature of a water sample increasing 2° every hour
The set of data that Zoey should use for the linear graph is given as follows:
D the temperature of a water sample increasing 2° every hour.
How to obtain the set of data for the graph?The graph represents a linear function, meaning that the rate of change of the output variable relative to the input variable must be constant.
The input and output variables of the graph are given as follows:
Input variable -> Time.Output variable -> Temperature.As the rate of change must be constant, the correct option is given by option d, which has a rate of change of 2º every hour. For the other options, the rate of change is not constant.
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7. A ball is dropped from a height of 80 cm. After each bounce it rebounds to 70% of its previous
maximum height.
c Find the total vertical distance travelled by the ball before it stops bouncing
d State one limitation with the model.
Through the given statement we can say that the vertical distance travelled by the ball is 84 m.
One limitation of this model is that it assumes that the ball rebounds to the same percentage of its previous maximum height after every bounce.
What is the vertical distance formula?The formula for vertical distance from the earth is y = - 1 2 g t 2 y = - frac 1 2 g t 2 y=-21gt2, where g is the acceleration of gravity and h is an elevation.
So :
C) the required total vertical distance that the given dropped ball travels until its bouncing stops:
= (12 m) + 2*(12 m)*(3/4)*[1 + 3/4 + (3/4)^2 + (3/4)^∞] [the factor 2 is for equal distance being covered up and down after each bounce of the ball]
= (12 m) + (24 m)*(3/4)*
(sum of an infinite GP series whose 1st term is 1 and common ratio is 3/4)
= (12 m) + (24 m)*(3/4)*[1/(1 - 3/4)]
= (12 m) + (24 m)*(3/4)*4
= (12 m) + (72m) = 84 m
D) This model's assumption that the ball will always bounce back to a certain proportion of its maximum height is one of its limitations. In fact, the rebound height can differ from one bounce to the next due to factors like air resistance, the ball's elasticity, and the surface it bounces on.
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1 of 431 of 43 Items
17:04
Skip to resourcesFeature
Find a Point on a Segment
Question 1
Find the point on PQ that divides the line segment directed from P to Q into the ratio of 1 : 3?
Responses
A (112
, 3)( 11 2 , 3)
B (52
, 5)( 5 2 , 5)
C (52
, 3)( 5 2 , 3)
D (112
, 5)( 11 2 , 5)
Question 2
Find the point on PQ that divides the line segment directed from P to Q into the ratio of 3 : 1?
Responses
A (112
, 3)( 11 2 , 3)
B (52
, 5)( 5 2 , 5)
C (52
, 3)( 5 2 , 3)
D (112
, 5)
The points on line segment in Question 1 is C (52, 3)( 5 2 , 3) and the answer to Question 2 is A (112, 3)( 11 2 , 3).
What is a line segment?
A line segment is a straight line that is bounded by two distinct endpoints. It is the shortest distance between two points and is usually represented by an arrow. Line segments are an essential part of geometry, as they form the basis for many shapes, such as triangles and rectangles.
A line segment can be divided into two parts in a given ratio if the difference of the coordinates of the end points of the line segment is divided in the same ratio.
For Question 1, the ratio of the line segment is 1:3. To find the point on the line segment, we will divide the difference of the coordinates of the end points of the line segment into the ratio 1:3. The coordinates of the end points of the line segment PQ are (10,2) and (14,6). The difference of the coordinates of the end points of the line segment PQ is (14-10, 6-2) = (4,4). The difference of the coordinates (4,4) is divided into the ratio 1:3. After dividing the difference of the coordinates into the ratio 1:3, we get the coordinates of the point on the line segment PQ as (52,3).
For Question 2, the ratio of the line segment is 3:1. To find the point on the line segment, we will divide the difference of the coordinates of the end points of the line segment into the ratio 3:1. The coordinates of the end points of the line segment PQ are (10,2) and (14,6). The difference of the coordinates of the end points of the line segment PQ is (14-10, 6-2) = (4,4). The difference of the coordinates (4,4) is divided into the ratio 3:1. After dividing the difference of the coordinates into the ratio 3:1, we get the coordinates of the point on the line segment PQ as (112,3).
In conclusion, the point on the line segment PQ that divides the line segment into the ratio of 1:3 is C (52, 3)( 5 2 , 3) and the point on the line segment PQ that divides the line segment into the ratio of 3:1 is A (112, 3)( 11 2 , 3).
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Find an equation for the graph.
Answer:
y=4sin(1/2πx)
Step-by-step explanation:
A = 4
Period for y=sin(x) is 2pi
Since the graph shows the period is 4. Then b must be 1/2pi
cara buys a crystal vase priced at 855 if the sales tax 10% how much tax will cara pay
Answer: 85.5
Step-by-step explanation: divide 855 by ten or move the decimal to the left one place for every zero
The variance will reach a maximum in a binomial distribution when
Answer:
Third choice
π = 1/2 and 1 - π = 1/2
Step-by-step explanation:
Formula for binomial distribution is
[tex]P(x) = \dfrac{n!}{x!(n-x)!} \pi^x (1-\pi)^{n-x}[/tex]
where
x is the number of successes
n = number of trials
π = probability of success on a single trial
The variance of the binomial distribution is
[tex]\sigma^2 = n \cdot \pi(1-\pi)[/tex]
The maximum variance occurs when
[tex]\pi = (1- \pi) = 1/2[/tex]
Hence the correct choice is the third choice
π = 1/2 and 1- π = 1/2
The sum of two numbers is 8. The larger number is 23 more than twice the smaller.
Answer:
-5 and 13.
Step-by-step explanation:
We will kick off by calling the first unknown x.
To get the expression for the larger number:
'23 more than twice the smaller number'
twice the smaller number (x) = 2x.
Thus, the bigger number = 2x+23.
We were told that the sum of these two = 8
Therefore,
x+2x+23=8
=> 3x+23=8
3x=-15
x = -5 (smaller number).
The larger number is 2x+23
= 2(-5) + 23
= 13.
Hope this helps! :)
What is the (backwards y looking thing) (∠FNL)
According to the given information, measure of angle FNL is given by 234 - 13x.
What is angle ?
In geometry, an angle is a figure formed by two rays, or line segments, that share a common endpoint, called the vertex of the angle. The two rays are called the sides or legs of the angle.
line FN || line EM || line DL,
line FD and line NL intersects line FN,line EM and line DL at pts F,E,D and N,M,L respectively
FE = ED ,NM = ML
angle FNL = (9x-40)deg
angle FDL = (4x-14)deg
Since line FN is parallel to line EM, we have:
angle FNM = angle FEL (corresponding angles)
Since line FN is parallel to line DL, we have:
angle FNL = angle FLD (alternate interior angles)
Similarly, since line FD intersects line FN and line EM at points F and E, we have:
angle FEL + angle FED = 180 degrees (linear pair)
Since FE = ED, we have:
angle FEL = angle FED (opposite angles of a parallelogram are equal)
Combining the above equations, we get:
angle FNL = angle FLD = angle FED = 180 - angle FEL
Also, since NM = ML, we have:
angle NML = angle MLM
Now, applying the angle sum property in triangle FNL, we get:
angle FNL + angle FLD + angle FEL = 180 degrees
Substituting the given values, we get:
(9x-40) + (4x-14) + (180 - angle FEL) = 180
Simplifying, we get:
13x - 54 + 180 - angle FEL = 180
13x - angle FEL = 54
Solving for angle FEL, we get:
angle FEL = 13x - 54
Substituting this value in the equation we derived earlier, we get:
angle FNL = angle FLD = angle FED = 180 - angle FEL
= 180 - (13x - 54)
= 234 - 13x
Therefore, measure of angle FNL is given by 234 - 13x
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HELP ILL MARK BRAINLIEST (the first answer choice i am not sure if right)
Answer: is mature enough to vote
Step-by-step explanation: the second drop box is asking about the opposing claim, which is the one that the professor gives.
Answer:
the last option, " is mature enough to vote".
Step-by-step explanation:
Professor Steinberg believes that 16 old can vote as their brains are mature enough to make informed decisions like voting.
Juli is going to launch a model rocket in her back yard. When she launches the rocket, the function h(t)=−16t2+76t model the height, h, in feet of the rocket above the ground as a function of time, t, measured in seconds. When will the rocket hit the ground? When will the rocket be 70 feet above the ground?
the rocket will be 70 feet above the ground after 1.25 seconds and again after 3.5 seconds.
Define factorizationFactorization, also known as factoring, is the process of expressing a mathematical object (such as a number, polynomial, or matrix) as a product of simpler objects.
To determine when the rocket hits the ground, we need to find the value of t when the height, h, is equal to 0. We can set h(t) = 0 and solve for t:
-16t²+ 76t = 0
-16t(t - 4.75) = 0
So either -16t = 0 or t - 4.75 = 0. The first equation has no solutions, so we solve the second equation:
t - 4.75 = 0
t = 4.75
Therefore, the rocket will hit the ground after 4.75 seconds.
To determine when the rocket is 70 feet above the ground, we need to find the value of t when h(t) = 70. We can set h(t) = 70 and solve for t:
-16t² + 76t = 70
-16t²+ 76t - 70 = 0
We can simplify this equation by dividing each term by -2:
8t² - 38t + 35 = 0
We can factor this equation:
(4t - 5)(2t - 7) = 0
So either 4t - 5 = 0 or 2t - 7 = 0. Solving these equations gives:
4t - 5 = 0
t = 1.25
2t - 7 = 0
t = 3.5
Therefore, the rocket will be 70 feet above the ground after 1.25 seconds and again after 3.5 seconds.
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A hot air balloon is at an altitude of 113.2 meters. The balloon's altitude decreases by 10.8 meters every minute. Which equation can you use to find the number of minutes m until the balloon is 70 meters?
Answer: 113.2 - 10.8x=70
Step-by-step explanation:
The speed limit is 50miles per hour. Kyle driving to a baseball game that starts in 2 hours. Kyle is 130 miles away from the baseball field. If Kyle drives at the speed limit, will he arrive in time
Answer:
To determine whether Kyle will arrive in time for the baseball game, we need to calculate how long it will take him to travel the 130 miles to the baseball field.
Using the formula:
distance = rate × time
We can rearrange the formula to solve for time:
time = distance / rate
Plugging in the given values, we get:
time = 130 miles / 50 miles per hour
time = 2.6 hours
This means that it will take Kyle 2.6 hours to travel the 130 miles to the baseball field at the speed limit of 50 miles per hour.
Since Kyle has 2 hours to get to the baseball game, he will not arrive in time if he drives at the speed limit. He would need to drive faster than the speed limit to make it to the game on time. However, it's important to note that speeding is illegal and dangerous, so Kyle should not exceed the speed limit. He may need to consider leaving earlier or finding alternative transportation to ensure that he arrives at the baseball game on time.
Step-by-step explanation:
may you please help me with this
Answer:
C). 8/9n - 1 1/3
Step-by-step explanation:
Answer:
[tex]\frac{8}{9} n - 1\frac{1}{3}[/tex]
Step-by-step explanation:
Using the distributive property [tex]\frac{4}{9}[/tex] times 2 equals [tex]\frac{8}{9}[/tex] and [tex]\frac{4}{9}[/tex] times 3 equals [tex]\frac{4}{3}[/tex] which simplifies to [tex]1\frac{1}{3}[/tex]
Which graph shows the solution to the system of linear equations? y= 2x y=X- 2
(-2, -4)
Step-by-step explanation:Systems of equations are sets of two or more equations that share the same variables.
Graphing
To graph a system of equations, simply graph each line individually. Both of the equations given are linear. Attached is a graph of both equations. As you can see the graphs intersect at (-2, -4).
Solutions to Systems of Equations
The solution to a system of linear equations is the coordinate point that the lines intersect. This is the point where the x and y-values make both equations true. To check the answer, plug the values into the equations. If both remain true, the answer is correct.
First, y = 2x
-4 = 2(-2)-4 = -4This is true. Next, y = x - 2
-4 = -2 - 2-4 = -4This is also true; thus the answer is (-2, -4).
I will mark you brainiest!
What is the area of the polygon shown?
A) 22 cm2
B) 38 cm2
C) 44 cm2
D) 50 cm2
Therefore, the area of the polygon is 22 cm². The correct answer is A) 22 cm².
Provide an area example.Another option is to plot the shape on a grid and count the squares: The rectangle's surface area is 15. Example: If each square is one meter in size, the area is 15 m2 (15 square meters).
To find the area of the polygon, we need to use the formula:
Area = (1/2) x Base x Height
We are given that the base of the polygon is 11 cm and the height is 4 cm. Therefore, we can substitute these values in the formula to get:
Area = (1/2) x 11 cm x 4 cm
Area = 22 cm²
Therefore, the area of the polygon is 22 cm². The correct answer is A) 22 cm².
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I NEED THIS EXTREMELY FAST
Answer:
4[tex]\frac{3}{8}[/tex]
Step-by-step explanation:
Answer:
4 3/8
Step-by-step explanation:
4*8=32 35-32=3
Brittany's W-2 reported total Medicare withholding based on wages of as $117,676. She contributed
$72.07 biweekly to her FSA and 10% of each paycheck to her retirement plan. She received a 1099 from
her bank for interest and dividends of $2,404 and a 1099 form in the amount of $4,600 from an employer
for whom she did some consulting work. What is Brittany's adjusted gross income?
Answer:
Step-by-step explanation
I:
Graph the equation shown below by transforming the given graph of the parent
function.
The answer of the question based on graph function is given below, graph is a reflection of the parent function y = x² about the x-axis, horizontally compressed by a factor of 2, and vertically shifted downward by 4 units.
What is Graph?A graph is visual representation of data or functions. It is way to display information in visual format, usually with use of coordinates and shapes.
The given equation is:
y = (-1/4 x)² - 4
To transform the graph of the parent function y = x², we can apply the following transformations:
Horizontal compression by a factor of 2: This will compress the graph horizontally, making it wider and shorter. The coefficient -1/4 in front of the x² indicates this compression.
Reflection across the x-axis: This will flip the graph of y = x² upside down. The negative sign after the x² in the equation indicates this reflection.
Vertical shift downward by 4 units: This will shift the entire graph downward by 4 units. The constant -4 at the end of the equation indicates this shift.
Using these transformations, we can graph the equation as follows:
Start with the graph of the parent function y = x²:
Apply the horizontal compression by a factor of 2 by multiplying the equation by -1/4:
y = (-1/4 x)²
Apply the reflection across the x-axis by negating the equation:
y = -(1/4 x)²
Apply the vertical shift downward by 4 units by subtracting 4 from the equation:
y = -(1/4 x)² - 4
The resulting graph is a reflection of the parent function y = x² about the x-axis, horizontally compressed by a factor of 2, and vertically shifted downward by 4 units.
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Solve for x.
Enter your answer in the box.
According the Question the value οf x will be 6.
What is circumference οf a circle?The measurement οf the circle's bοundaries is called as the circumference οr perimeter οf the circle. whereas the circumference οf a circle determines the space it οccupies. The circumference οf a circle is its length when it is οpened up and drawn as a straight line. Units like cm οr unit m are typically used tο measure it.
The circle's radius is cοnsidered while calculating the circumference οf the circle using the fοrmula. As a result, in οrder tο calculate the circle's perimeter, we must knοw the radius οr diameter value.
The side οf the circle JH . JG = JK . JM
JM = 7*16/8 = 14
X = 14-8 =6
Hene the value οf x will be 6.
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From 2014-2015 to 2024-2025, the number of students enrolled in an associate degree program is projected to increase by 21.5%. If the enrollment in associate degree programs in 2014-2015 is 6,500,000 , find the increase and the projected number of students in an associate degree program in 2024-2025.
By solving the increase in percentage, the projected number of students in an associate degree program in 2024-2025 is approximately 7,897,500.
What is an increase in percentage?
An increase in percentage is a measure of the change in a quantity expressed as a percentage of the initial value. It is calculated by subtracting the initial value from the final value, dividing the result by the initial value, and then multiplying the quotient by 100 to express the result as a percentage. The formula for calculating the percentage increase is:
percentage increase = (final value - initial value) / initial value * 100
To find the increase in the number of students enrolled in an associate degree program from 2014-2015 to 2024-2025, we can first calculate the amount of increase as a percentage of the initial enrollment:
Increase = 21.5% * 6,500,000 = 1,397,500
Therefore, the increase in the number of students is approximately 1,397,500.
To find the projected number of students in an associate degree program in 2024-2025, we can add the increase to the initial enrollment:
Projected enrollment = 6,500,000 + 1,397,500 = 7,897,500
Therefore, the projected number of students in an associate degree program in 2024-2025 is approximately 7,897,500.
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hii
what's the best way to recreate the incident as it happened and to picture
hii
what's the best way to recreate the incident as it happened and to picture
Use the graph of the function to answer the following question.
Which of the following statements about the function is TRUE?
A.The function has a maximum value of 0.
B.As x approaches ∞, the function approaches ∞.
C.The function is always decreasing.
D.The function is positive on the interval (- 1, 1).
The function is positive on the interval (-1, 1)," is the only answer that is accurate. Due to the fact that the function accepts positive values for x between -1 and 0, accepts 0 at x = 0, and then accepts positive values.
A function on an interval is what exactly?When a function is specified at each point along an interval without any gaps, leaps, or interruptions, the interval is said to be continuous for that function.
When we examine the function's graph, we can observe that:
Because the function accepts negative values for x > 1 and positive values for x -1, it does not have a maximum value of 0.
The function does not approach as x approaches. Instead, as x rises, the function alternates between positive and negative values.
There are times when the function increases. Rather, it is rising on the interval (1, ) and falling on the intervals (-, 1). At x = -1, it has a local minimum, while at x = 1, it has a local maximum.
Due to the fact that it accepts negative values for x between -1 and 0, the function is not positive on the range (-1, 1).
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4.
49%
6x
7xº
83°
33°
Please help me!
Erick wants to buy a new mountain bike that costs $250.
He has already saved $120 and plans to save $20 each week
from the money he earns for mowing lawns. He thinks he
will have saved enough money after seven weeks.
A. Complete the table. Then graph the data.
Time (weeks)
0
1
2
3
Money Saved ($)
120
___
___
___
B. How can you tell that the relationship is a linear function from th
table? How can you tell from the graph?
The values that complete the table would be: $140, $160, $180, $200, $220, $240, $260. This is a linear relationship because the data on the graph would show an ascending line with a constant slope.
How to complete the table?To complete the table we must take into account the information, in this case Erick saves $20 per week, so we would have to add $20 to his initial budget of $120 and add $20 each week. Based on this information, the data that completes this table would be:
$140, $160, $180, $200, $220, $240, $260.What would a graph look like with this data?The graph with this data would be a linear expression, so the line would go up from $120 to $260 constantly, with a difference of $20 each week.
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If anybody sees this can they help me out
The trees in a forest are being cut down at a monthly rate of 3.2%. This situation can be modeled by an exponentia function. The forest contained 5,500 trees when cutting began. Which function can be used to find the number of trees in the forest at the end of m months?
A) t(m) -5,500(0.032)m
B) t(m) - 5,500(1.968)m
C) t(m) -5,500(1.032)m
D) t(m) -5,500(0.968)m
Answer:
B
Step-by-step explanation:
The function that models the situation is an exponential decay function of the form:
t(m) = a(1 - r)^m
where:
t(m) is the number of trees after m months
a is the initial number of trees (5,500 in this case)
r is the monthly rate of decrease (3.2% or 0.032 as a decimal)
Substituting the values given in the options, we get:
A) t(m) = 5,500(0.032)^m
B) t(m) = 5,500(1-0.032)^m = 5,500(0.968)^m
C) t(m) = 5,500(1.032)^m
D) t(m) = 5,500(1-0.968)^m = 5,500(0.032)^m
Option B is the correct answer as it correctly models the situation with exponential decay with a starting value of 5,500 trees and a monthly rate of decrease of 3.2%.
Answer: The formula for exponential decay is given by:
t(m) = a(1-r)^m
where
a = initial value
r = decay rate
Here, the initial value is 5,500 and the monthly decay rate is 3.2% or 0.032. So the function that can be used to find the number of trees in the forest at the end of m months is:
t(m) = 5,500(1 - 0.032)^m
t(m) = 5,500(0.968)^m
Therefore, the answer is (D) t(m) = 5,500(0.968)^m.
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Help with the question
In this case, the population is children from 6 to 18 years old who had nonlethal scorpion sting; on the other hand, the sample is the 245 children selected.
How to identify the population and the sample?In a research study, the population is considered as the group of individuals being studied. However, as this number is often high, researchers often select a small random percentage that should be representative of the population, which is known as the sample.
Based on this, the population can be children from 6 to 18 years old who had nonlethal scorpion sting, while the sample are those children selected (245) to carry out the research study.
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Some researchers claim there is an association between taking vitamins and gaining weight. They took a random sample of people living in Boston, Massachusetts, and recorded whether they took vitamins and whether they gained weight. The results are shown in the following two-way table:
A student reading the results stated that more than half of the study participants are taking vitamins. Determine if the student is correct.
A) Yes, because 23.5% take one vitamin and 48.2% take more than one vitamin, which is a total of 71.7% taking vitamins.
B)Yes, because 27.4% take one vitamin and 49.5% take more than one vitamin, which is a total of 76.9% taking vitamins.
C) No, because 11.4% take one vitamin and 23.5% take more than one vitamin, which is a total of 34.9% taking vitamins.
D) No, because 16% take one vitamin and 26% take more than one vitamin, which is a total of 42% taking vitamins.
Option D is correct as 16% and 26% results in a percentage of 42%, in line with percentages in the "At least one vitamin" row of the table of random sample.
In random sample:
The student is incorrect. To determine the proportion of participants taking vitamins, we need to add up the percentages in the "At least one vitamin" row of the table. Adding 23.5% and 48.2%, we get a total of 71.7%, which is not more than half. Therefore, option A is incorrect.
Option B is also incorrect, as adding 27.4% and 49.5% gives a total of 76.9%, which is more than half but does not match the percentages in the table.
Option C is incorrect, as adding 11.4% and 23.5% gives a total of 34.9%, which is lower than the percentages in the table.
Option D is correct, as adding 16% and 26% gives a total of 42%, which matches the percentages in the "At least one vitamin" row of the table. Therefore, the correct answer is D.
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