Answer:
The answer to your question is letter B
Step-by-step explanation:
Data
12v³ - 32v² + 6v - 16
- Factor the first 2 terms by common factor
12v³ - 32v² = 4v² (3v - 8)
- Factor the last two terms by common factor
6v - 16 = 2(3v - 8)
- Write the previous results
4v²(3v - 8) + 2(3v - 8)
- Factor again by common factor
(3v - 8) (4v² + 2)
- Factor by common term
2(3v - 8)(2v² + 1)
Students in a statistics class were divided into two groups at random. Students in one group were given a set of words to memorize in a room with music playing. Students in the other group were given the same list of words to memorize but in a quiet room. Students in the quiet room were able to remember more words, on average. Is this an observational study or an experiment
Answer:
An experiment
Step-by-step explanation:
An observational study is a study in which the researchers collect data related to what is visible or heard. In this type of study the researchers do not have any control on the variables used for the research work .The researcher do not bring any changes in the behavior of the variables that is they are accepted the way they are.
An experiment is a method used in which the researchers pick up a sample from a group and test them to get a proof or knowledge about something.
Both Observational study as well as an experiment are used in statistics social sciences and psychology etc.
Thus the case given here is an experiment because there is no alterations done with the variables.
The scenario given is an experiment because it deliberately manipulates conditions (music or no music) to test its effect on students' ability to memorize words. By comparing outcomes, this study seeks to establish a causal relationship.
Explanation:The study described in the student's question is an experiment because it involves a deliberate manipulation of conditions to test a hypothesis. The manipulation in this case is the presence or absence of music while memorizing words. Since there are two groups and each group is subjected to different conditions (one with music and one without), this defines a controlled experiment. Experiments involve comparing the outcomes of different treatments, in this case, music or silence, which enables researchers to make causal inferences about the effect of the independent variable (music) on the dependent variable (ability to remember words).
Now, looking at the studies referenced, the effects of music on different cognitive tasks, like memorization and reading comprehension, have been explored in various ways. While some experiments, like the one comparing the memorization of words with and without music, show that silence may be more conducive for memorization, other studies have found positive effects of music on tasks such as reading comprehension or overall task behavior.
Factor the expression. 35g^2 – 2gh – 24h^2
(7g + 6)(5g + 4h2)
(7g + 6h)(5g – 4h)
(7g – 6h)(5g + 4h)
(7g – 6)(5g + 4)
Option C: [tex](7 g-6 h)(5 g+4 h)[/tex] is the correct answer.
Explanation:
The given expression is [tex]35 g^{2}-2 g h-24 h^{2}[/tex]
We need to determine the factor of the expression.
Now, let us break the given expression into two groups.
Hence, we get,
[tex]35 g^{2}+28 g h-30 g h-24 h^{2}[/tex]
Simplifying, we get,
[tex]\left(35 g^{2}+28 g h\right)+\left(-30 g h-24 h^{2}\right)[/tex]
Let us factor out 7g from the term [tex]\left(35 g^{2}+28 g h\right)[/tex]
Hence, we have,
[tex]7 g(5 g+4 h)+\left(-30 g h-24 h^{2}\right)[/tex]
Similarly, let us factor out -6h from the term [tex]\left(-30 g h-24 h^{2}\right)[/tex]
Thus, we have,
[tex]7 g(5 g+4 h)-6 h(5 g+4 h)[/tex]
Now, we shall factor out the term [tex]5g+4h[/tex] , we get,
[tex](7 g-6 h)(5 g+4 h)[/tex]
Thus, the factorization of the given expression is [tex](7 g-6 h)(5 g+4 h)[/tex]
Therefore, Option C is the correct answer.
Answer:
Option C is the correct answer.
Step-by-step explanation:
A population of butterflies grows in such a way that each generation is simply 1.5 times the previous generation. There were 350 butterflies in the first generation, how many will there be by the 19th generation?
Answer:
517,262
Step-by-step explanation:
A population of butterflies grow in such a way that each generation is simply 1.5 times the previous generation. There were 350 butterflies in the first generation, how many will there be by the 19th generation?
----------------
Ans: (1.5)^18 * 350 = 517,262
Answer: there will be 517262 butterflies by the 19th generation.
Step-by-step explanation:
The population of butterflies grows in such a way that each generation is simply 1.5 times the previous generation. This means that the population is increasing in geometric progression. We would apply the formula for determining the nth term of a geometric progression which is expressed as
Tn = ar^(n - 1)
Where
a represents the first term of the sequence.
r represents the common ratio.
n represents the number of terms.
From the information given,
a = 350
r = 1.5
n = 19
Therefore, the 19th term or generation, T19 would be
T19 = 350 × 1.5^(19 - 1)
T19 = 350 × 1.5^18
T19 = 517262
What kind of graph would be best to show the results of a group of students who were asked about their favorite kind of pizza. Explain your answer.
Answer:
A bar graph, because if you want to compare categories, you would want to categorize the results you get from a survey. If you were to use any other chart or graph, you would have to base it off of QUANTITATIVE data. Since this is QUALITATIVE data, it wouldn't make any sense to use any other chart or graph.
A bar graph is the best way to display categorical data such as the favorite kind of pizza.
What is the bar graph?A bar graph (also known as a bar chart) is a graphical representation of data that uses bars of different sizes. It is an excellent way of displaying relative sizes.
As per the question, a bar graph is the best way to display categorical data such as the favorite kind of pizza.
Each category (i.e., pepperoni, cheese, vegetarian, etc.) can be represented by a bar, with the height of the bar indicating the number or percentage of students who chose that category.
This allows for an easy visual comparison of the popularity of each kind of pizza.
Also, labels can be added to the x-axis and y-axis to provide additional information and context to the graph.
Therefore, a bar graph is an exact and effective way to present the data from the survey on students' favorite kinds of pizza.
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Find the solution of y = 6x + 1 for x =5
Answer:
31
Step-by-step explanation:
Y = 6x+1
When x is 5
y = 6(5)+1 = 30 +1 =31
At the zoo there are two different tours. One leaves every 30 minutes and one leaves every 45 minutes. If they both leave at 8:00am, at what time will they be the same again
The two zoo tours start at 8:00 am, one leaves every 30 minutes and the other every 45 minutes. The next time they will coincide, or leave at the same time, is at 9:30 am.
Explanation:The tours in the zoo that are mentioned in your question represent two different intervals, 30 minutes and 45 minutes. To figure out when these tours will coincide again, we actually need to find a common multiple of the two intervals. The smallest common multiple of 30 and 45 minutes is 90 minutes or 1 hour and 30 minutes.
So, if both tours start at 8:00 am, they will sync again 90 minutes later, which is 9:30 am. Therefore, the two tours will depart together again at 9:30 am.
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Out of 3000 light bulbs that were tested, 126 were defective. find the prbability of defective and non defective
Answer:
P(defective) = 126/3000 = 0.042
P(not defective) = 1 - P(defective)
= 1 - 0.042 = 0.958
The number of students absent over two different days at Valley View Middle School can be represented as the sum 42 + 15. Which of these are equivalent representations of this sum? Choose all that are correct. Your answer: 5(8 + 2) + 5(3) (3 x 14) + (3 x 5) (3 x 39) + (3 x 5) 3(39 + 12) 3(14 x 5) 3(14 + 5)
Answer:
e) , f)
Step-by-step explanation:
42+15= 57
If the available options are:
a) 5(8+2)+5(3)=(5x10)+15=50+15=65
b) (3 x 14) + (3 x 5)= 42+15=57
c) (3 x 39) + (3 x 5)=117+15=132
d) 3(39 + 12)=3x51=153
e) 3(14 x 5)=3x70=210
f) 3(14 + 5)=3x19=57
Answer:
Step-by-step explanation:
The areas of two circles are in a ratio of 169:121. What is the ratio of their radii?
Answer:
[tex]1 \frac{48}{121} [/tex]
Step-by-step explanation:
divide 169/121 and that equals the answer above
Answer:
13 : 11
Step-by-step explanation:
If the ratio of radii = a : b, then
ratio of areas = a² : b²
Given
ratio of areas = 169 : 121, then
ratio of radii = [tex]\sqrt{169}[/tex] : [tex]\sqrt{121}[/tex] = 13 : 11
Megan invested in ten bonds of total face value of $1.000, issued by Zen Corporation. The bonds paid 10 percer semiannual (5% every 6 months) interest till the maturity date, which of the following is the value of interest earned in the first installment on a single bond? A) $50 B) $100 C) $500 D) $90 E) $75
Answer:
$50 is the value of interest earned in the first installment on a single bond
Step-by-step explanation:
Applying Interest earned in the first installment on a single bond ;
= PRT/100
P = $1.000
R = 5%
T = 1
Plugging the values in the equation ;
Interest = 1000 x 5 x 1 /100
= $50, hence option A is the correct one.
Sonny pick a number of boxes x with 22 cans in each box the total number of cans pads with 660 which equation and solution represent the total number of boxes Sony packed
Answer:
Equation= X = 660÷22, Number of boxes is 30
Step-by-step explanation:
Since each box contains 22 cans, hence 22x is equivalent to 660 cans.
Equation = 22X = 660
Number of boxes X = 660÷22 = 30
Answer:
Step-by-step explanation:
Given:
Number of cans in a box, N = 22 cans
Total number of cans, Tc = 660 cans
Let the Number of boxes be x.
Therefore,
Tc = N × x
B.
660 = 22 × x
x = 660/22
= 30 boxes.
After taking 5 quizzes, your average is 76 out of 100. What must your average score be on the next five quizzes to increase your average to 81?
A. 78
B. 87
C. 83
D. 86
Answer:
Option D
86
Step-by-step explanation:
When your expectation is average of 81 for a total of 10 questions, your total score is 10*81=810
Currently, for 5 questions with an average of 76, your total score is 5*76=380
Difference between total expected score and current score is 810-380=430
Average of difference with 5 questions is 430/5= 86
An employee compiled sales data for a company once each month. The scatter plot below shows the sales (in multiples of $1000) for the company over time (in months). The equation represents the linear model for this data. y = 0.94x + 12.5 According to the model, how much do the company's sales increase per month? $9400 $940 $1250 $12,500 $5000
Answer:
Option B) $940
Step-by-step explanation:
We are given the following in the question:
[tex]y = 0.94x + 12.5[/tex]
The equation represents the company sales in thousand dollars and x is time in months.
Comparing to general form of linear equation.
[tex]y = mx + c[/tex]
Comparing, we get,
Slope, m = 0.94
y-intercept, c = 12.5
Interpretation:
Thus, the slope tells us the increase in sales of company with one unit increase in x that is it tells the increase in company's sale per month.
[tex]0.94\times 1000 = 940[/tex]
$940 is the increase in company's sale per month.
Option B) $940
Answer:
B 940
Step-by-step explanation:
simplify by dividing
3/5 ÷ -4/9
1. -27/20
2. 27/20
3. -12/45
4. 12/45
Answer:
The answer to your question is -27/20
Step-by-step explanation:
Divide 3/5 ÷ - 4/9
Process
1.- Just multiply the numerator of the first fraction by the denominator of the second fraction.
3 x - 9 = -27
2.- Multiply the denominator of the first fraction by the numerator of the second fraction.
5 x 4 = 20
3.- Join both results
-27/20
PLLLLLZ HELP I HAVE A DEADLINE Write a recursive formula for finding the nth term of each arithmetic sequence. 15.75, 14.25, 12.75, …
a1 = 15.75, an = an – 1 + 1.5
a1 = 12.75, an = an – 1 – 1.5
a1 = 11.25, an = an – 1 + 1.5
a1 = 15.75, an = an – 1 – 1.5
Answer: D. a1=15.75,an = an -1 -1.5
Step-by-step explanation:
Sorry about the no explanation, but the answer is correct.
The correct recursive formula for the arithmetic sequence 15.75, 14.25, 12.75, … is a1 = 15.75, an = an-1 - 1.5. This means the first term is 15.75 and each following term is 1.5 less than the previous term.
Explanation:The question asks for a recursive formula for the arithmetic sequence provided. An arithmetic sequence is a sequence of numbers wherein the difference between any two consecutive terms is constant. In this case, the common difference (d) is -1.5, because each term decreases by 1.5 from the previous term. Every term in the sequence follows the pattern of the first term, plus the common difference (d) multiplied by (n-1), where n is the term number.
To write a recursive formula for the sequence, we express the nth term (an) as the sum of the (n-1)th term and the common difference. Thus, the recursive formula for the sequence is: a1 = 15.75, an = an-1 - 1.5. This tells us that the first term a1 equals 15.75, and any term an (after the first term) is 1.5 less than the term before it(an - 1).
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Karen started walking at 1 mile per hour. After she walked 2.5 miles, her friend Ned started walking along the same route at a piece of 1 mile per hour. If they continue to walk at the same rate, will Ned ever catch up to Karen? Explain.
Answer: No, Ned will never catch up to Karen.
Step-by-step explanation:
Karen started walking at 1 mile per hour.
Time = distance/speed
If she walks 2.5 miles, it means that the time she spent walking is
2.5/1 = 2.5 hours.
After she walked 2.5 miles, her friend Ned started walking along the same route at a speed of 1 mile per hour. Since Ned is walking at 1 mile per hour which is even slower than Karen's speed, it means that for every 1 mile that Ned walks, Karen walks 2.5 miles. Therefore, if
they continue to walk at the same rate, Ned will never catch up to Karen.
Sebastian gathered data by surveying his neighbors comparing how much time they spend on the internet to how much mail they receive in a week. Explain the steps Sebastian should take in order to analyze the data.
Step-by-step explanation:
1. The first is a tabulation of the data, in an organized, clear and concise way for each event.
2. After tabulation, for a better understanding of the data, statistical data, such as the mean, median, and standard deviation of each event, should be collected.
3. Finally, graph the data obtained to see the trend of both cases and thus have a very precise way to make the comparison of both events
A shade of paint is made by evenly mixing m gallons of white paint, costing $12 a gallon, with n gallons of blue paint, costing $30. What is the cost, in dollars per gallon, of the resulting mixture?
Answer:
The cost of mixture is
[tex]\dfrac{12m + 30n}{m+n}\text{ dollars per gallon}[/tex]
Step-by-step explanation:
We are given the following in the question:
Cost of white per gallon = $12 a gallon
Amount of white paint in the mixture = m gallons
Total cost of white paint =
[tex]12\times m = 12m\$[/tex]
Cost of blue per gallon = $30 a gallon
Amount of blue paint in the mixture = n gallons
Total cost of blue paint =
[tex]30\times n = 30n\$[/tex]
Total cost of mixture =
Total cost of white paint + Total cost of blue paint
[tex](12m + 30n)\text{ dollars}[/tex]
Total amount of mixture =
Amount of white paint in the mixture + Amount of blue paint in the mixture
[tex]=(m+n)\text{ gallons}[/tex]
Cost of mixture per gallon =
[tex]=\dfrac{\text{Total cost}}{\text{Total amount}}\\\\=\dfrac{12m + 30n}{m+n}\text{ dollars per gallon}[/tex]
is the required cost of mixture.
Some students in Springfield make a parade float with a letter S on it draw lines divide the shape into rectangles then find how many square feet the letter is
To find the square footage of the letter S on the parade float, the students can divide it into rectangles and calculate the area of each rectangle.
Explanation:The students can divide the shape of the letter S on the parade float into rectangles and then calculate the area of each rectangle to determine the total area of the letter. To do this, they can measure the length and width of each rectangle and multiply them together to find the area. Once they have the area of each rectangle, they can add them all together to get the total square footage of the letter S on the float.
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Michaela has eight dollars to buy tickets at the school fair each ticket cost one dollar and 50 Cent what inequality Best represents how many tickets she can buy
Answer: the inequality that bests represents how many tickets she can buy is 1.5x ≤ 8
Step-by-step explanation:
Let x represent the number if tickets that she wants to buy at the school fair.
Each ticket cost one dollar and 50 Cent. This means that the total cost of x tickets would be
1.5 × x = $1.5x
Michaela has eight dollars to buy tickets at the school fair. Therefore, the inequality that bests represents how many tickets she can buy is
1.5x ≤ 8
Tina bake some cookies 1/2 of her cookies with peanut butter 1/2 of the peanut butter cookies also have chocolate chips what fraction of the cookies were peanut butter and have chocolate chips
Answer: 1/4
Step-by-step explanation:
so if 1/2 of 1/2 of cookies are with choclate chips therefore saying 1/2 cookies is the same as 2/4 cookies and since half of the cookies are with choclate chips so there are 1/4 cookies with choclate chips nd are peanut butter please mark brainliest.
Answer:1/4
Step-by-step explanation: Half of the cookies baked were peanut butter cookies. 1/2 of the peanut butter cookies have chocolate chips. 1/2 divided by 1/2 is 1/4. 1/4 of the total cookies baked are peanut butter chocolate chip cookies.
The population of United States is about 3×10(to the power of 8). The population of Kazakhstan is about 1.5×10(to the power of 7). How many times greater is the population of United States then Kazakhstan?
Answer:
The answer to your question is 20 times
Step-by-step explanation:
Data
United States' population = 3 x 10⁸
Kazakhstan's population = 1.5 x 10⁷
Process
1.- To solve this problem, just divide the United States' population by Kazakhstan's population.
3 x 10⁸ / 1.5 x 10⁷ = 20
2.- Conclusion
The population of the United States is 20 times greater than Kazakhstan's population.
Choose which statements are true about Pi. Check all that apply. Piis a whole number. Piis double the radius. Piis approximately 3.14. Pirepresents the ratio of the circumference to the diameter. Piis approximately StartFraction 22 over 7 EndFraction
Answer:
Answer in explanation
Step-by-step explanation:
In this question, we would be examining the validity of some statements on the number π(pi)
π Is a whole number?
This is wrong, π is a fraction of 22 to 7 parts I.e 22/7
π Is double the radius?
This is wrong. It is the diameter that is double the radius
π Is approximately 3.14?
This is correct to an extent. The actual value in decimal is around 3.142857142857143 which makes the 3.14 somehow correct
π represents the ratio of the circumference of the circle to the diameter?
This is correct.
Mathematically, circumference C = π * diameter D
Hence C/D = π
π Is approximately 22/7?
This is correct. This is the ratio used for π
Answer:
• Pi is approximately 3.14.
• Pi represents the ratio of the circumference to the diameter
• Pi is approximately 22/7
Step-by-step explanation:
From the options given:
A. Pi is a whole number:
Pi is equivalent to 3.141592654. Therefore, pi is not a whole number.
B. Pi is double the radius
Pi is not double the radius of a circle. Pi is a constant.
C. Pi is approximately 3.14.
In some cases, pi can be approximated as 3.14 instead of 3.141592654.
D. Pi represents the ratio of the circumference to the diameter.
Circumference of a circle, C = 2 × pi × radius
= 2 × pi × D/2 = pi × Diameter
Pi = circumference/Diameter
E. Pi is approximately 22/7
22/7 = 3.142857143
This is also a correct approximation.
A store purchased a DVD for $12.00 and sold it to a customer for 50% more than the purchase price.The customer was charged a 7% tax when the DVD was sold.What is the customer's total cost for the DVD?
Answer:
The customer's total cost for the DVD is $19.26
Step-by-step explanation:
Store buy the dvd for $12.00.
The store price is $12.00+50% more
The store price= $12.00 *(1+0.5)= $18.00
Final price (tax added)= $18.00 + 7%
Final price= $18.00 * (1 + 0.07)= $19.26
Answer:
The total cost of the DVD for the consumer was 19.26 $
Step-by-step explanation:
The sales price for the DVD was the price paid by the store plus 50%. To discover this value we will transform the percentage in a real number, by dividing it by 100, like following:
50/100 = 0.5
We then multiply this value by the price paid by the store (12) to find out how much is 50% of that. Then we add this value to the price paid by the store and we obtain the price of the DVD before taxes. So we do as following:
Price before taxes = price paid by the store + (price paid by the store)*0.5
Price before taxes = 12 + 12*0.5 = 18 $
On top of that there was 7% of tax for the consumer. We must repeat the same steps as before but using 7 instead of 50. So we have:
Final price = Price before taxes + (Price before taxes)*(7/100)
Final price = 18 + 18*0.07 = 19.26 $
The total cost of the DVD for the consumer was 19.26 $
solve for x
A. 36
B. 30
C. 10
D. 20
Answer:
The answer to your question is the letter B. x = 30
Step-by-step explanation:
Data
Find x
Process
To solve this problem use proportions. Compare the small triangle and the large triangle.
1) For the small triangle
x/ (24 - 4) = x/20
2) For the large triangle
(x + 6) / 24
3.- Equal both expressions
x/20 = (x + 6)/24
-Solve for x
24x = 20(x + 6)
-Expand
24x = 20x + 120
-Simplify like terms
24x - 20x = 120
4x = 120
-Result
x = 120/4
x = 30
Find a. If necessary, round your answer to the nearest hundredth.
Sorry the picture was upside down. :(
Answer:
The answer to your question is a = 4.81
Step-by-step explanation:
Process
1.- The angle B and 43° are supplementary
B + 43° = 180°
B = 180 - 43
B = 137°
2.- Calculate angle C
The sum of the internal angles in a triangle equals 180°
A + B + C = 180°
29 + 137 + C = 180
- Solve for C
C = 180 - 29 - 137
C = 14°
3.- Use the law of signs to find a
a / sin A = c / sin C
a / sin 29 = 2.4 / sin 14
- Solve for a
a = 2.4 sin 29 / sin 14
- Simplification
a = 2.4 (0.485) / 0.242
- Result
a = 4.809
Glenna wants to rent a car for a trip to key west for one weekshe calls two car rental companies to get prices. mr kotters rentals rents a cadillac escalade for $99 for one week plus $0.11per mile over 100 miles. barbarino's rentals has the same vehicle for $75 per week and $0.15 per mile over 150 miles. if its 432 miles to key west, which company has the better deal? How many miles would Glenna drive before she would be spending the same amount at either company?
Barbarino's Rentals offers the better deal for a 432-mile trip at $117.30 compared to Mr. Kotters Rentals at $135.52. To spend the same amount at either company, Glenna would have to drive 600 additional miles over the free miles provided by the rentals.
To determine which car rental company offers the better deal for Glenna's trip to Key West, we need to calculate the total cost from both companies for a 432-mile trip. Let's start with Mr. Kotters Rentals. The cost for one week is a flat $99, plus $0.11 per mile for each mile over 100.
Therefore, Glenna would pay for 332 extra miles at a rate of $0.11 per mile. This calculation is (432 miles - 100 miles) * $0.11/mile = 332 * $0.11 = $36.52 in additional mileage charges. The total cost from Mr. Kotters Rentals would be $99 + $36.52 = $135.52.
Next, we calculate the cost with Barbarino's Rentals. They charge $75 for the week plus $0.15 per mile over 150 miles. The calculation for mileage is (432 miles - 150 miles) * $0.15/mile = 282 * $0.15 = $42.30. The total cost from Barbarino's Rentals would come out to $75 + $42.30 = $117.30.
Comparing the two totals, Barbarino's Rentals is the better deal at $117.30 compared to Mr. Kotters Rentals, which would cost $135.52.
Now, to find out how many miles Glenna would have to drive for the costs to be the same at either company, we set up the equation:
99 + 0.11x = 75 + 0.15x, where x represents the additional miles driven over the respective free miles. Solving this equation:
0.04x = 24
x = 600 miles
So, Glenna would need to drive 600 additional miles for the total costs from both rental companies to be equal.
Select the best possible first step to solving the system by first eliminating the x variable.
3x + 5y = 1
2x + 4y = −4
Multiply the first equation by 2, and multiply the second equation by 3.
Multiply the first equation by −2, and multiply the second equation by 3.
Multiply the first equation by −2, and multiply the second equation by −3.
None of the above
Answer:
Option C is Correct
Step-by-step explanation:
Given System is
3x + 5y = 1
2x + 4y = −4
Multiply the first equation by −2, and multiply the second equation by 3
we get
-6x-10y = -2 ----------(i)
6x+12y = -12 ---------(ii)
then we add both equations we get
2y = -14
y = -7
now put y = -7 in euation one we get
-6x-10(-7) =14
-6x+70=14
subtracting 70 from both sides we get
-6x=-56
dividing (-6) both sides we get
x=56/6 or x =28/3
so here is our solution
(x,y)=(28/3 , -7)
answer.
LOGARITHMS, CONIC SECTIONS, SEQUENCES
Evaluating an exponential function with base e that models a real...
The number of milligrams D (n) of a drug in a patient's bloodstream h hours after the drug is injected is modeled by the following function.
D(h) =40e-0.5h
Find the initial amount injected and the amount in the bloodstream after 7 hours.
Round your answers to the nearest hundredth as necessary.
Initial amount:
milligrams
Amount after 7 hours:
milligrams
X
5
?
Explanation
Check
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Answer:
(a) 40 milligrams
(b) 1.21 milligrams
Step-by-step explanation:
Exponential Function
It's commonly used to model real situations in life, like this one proposed in the question where the number of milligrams of a drug D(h) in a patient's bloodstream h hours after the drug is injected is modeled by the following function.
[tex]D(h) =40e^{-0.5h}[/tex]
(a) The initial amount injected to the patient can be found when h=0
[tex]D(0) =40e^{-0.5(0)}=40e^{0}=40[/tex]
Initial amount: 40 milligrams
(b) Let's plug h=7
D(7) =40e^{-0.5(7)}=40e^{-3.5}=1.21
The amount in the bloodstream after 7 hours is 1.21 milligrams
) One year, professional sports players salaries averaged $1.5 million with a standard deviation of $0.9 million. Suppose a sample of 400 major league players was taken. Find the approximate probability that the average salary of the 400 players exceeded $1.1 million.
Answer:
Probability that the average salary of the 400 players exceeded $1.1 million is 0.99999.
Step-by-step explanation:
We are given that one year, professional sports players salaries averaged $1.5 million with a standard deviation of $0.9 million.
Suppose a sample of 400 major league players was taken.
Let [tex]\bar X[/tex] = sample average salary
The z-score probability distribution for sample mean is given by;
Z = [tex]\frac{ \bar X -\mu}{{\frac{\sigma}{\sqrt{n} } }} }[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = mean salary = $1.5 million
[tex]\sigma[/tex] = standard deviation = $0.9 million
n = sample of players = 400
The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.
So, probability that the average salary of the 400 players exceeded $1.1 million is given by = P([tex]\bar X[/tex] > $1.1 million)
P([tex]\bar X[/tex] > $1.1 million) = P( [tex]\frac{ \bar X -\mu}{{\frac{\sigma}{\sqrt{n} } }} }[/tex] > [tex]\frac{ 1.1-1.5}{{\frac{0.9}{\sqrt{400} } }} }[/tex] ) = P(Z > -8.89) = P(Z < 8.89)
Now, in the z table the maximum value of which probability area is given is for critical value of x = 4.40 as 0.99999. So, we can assume that the above probability also has an area of 0.99999 or nearly close to 1.
Therefore, probability that the average salary of the 400 players exceeded $1.1 million is 0.99999.
The approximate probability that the average salary of the 400 players exceeded $1.1 million will be "1".
ProbabilityAccording to the question,
Standard deviation, σ = 0.9
Mean, μ = 1.5
Let,
The salaries for professional sports player be "x".
Now,
The probability will be:
= P ([tex]\bar x[/tex] > 1.1)
= P ([tex]\frac{\bar x - \mu}{\frac{\sigma}{\sqrt{n} } }[/tex] > [tex]\frac{1.1 - \mu}{\frac{\sigma}{\sqrt{n} } }[/tex])
By substituting the values,
= P (Z > [tex]\frac{1.1 -1.5}{\frac{0.9}{\sqrt{400} } }[/tex])
= P (Z > -8.89)
By using the table,
= 1
Thus the above answer is correct.
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