Answer:
Yes, the approximate length of one side is a prime number less than 25.
The approximate dimensions of the room are 19 ft by 18 ft.
Step-by-step explanation:
Assuming the dining room is rectangular in shape
Approximate area of the dining room = 342 ft^2
The area of a rectangle is calculated by multiplying the length of the rectangle by the width.
Assuming the approximate length is a prime number less than 25
The closest prime number to 25 is 19
Approximate length = 19 ft
Approximate width = approximate area ÷ approximate length = 342 ft^2 ÷ 19 ft = 18 ft
Approximate dimensions of the room = 19 ft by 18 ft
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.
Which of the following subsets of P2P2 are subspaces of P2P2? A. {p(t) | p′(t){p(t) | p′(t) is constant }} B. {p(t) | p(−t)=p(t){p(t) | p(−t)=p(t) for all t}t} C. {p(t) | p′(6)=p(7)}{p(t) | p′(6)=p(7)} D. {p(t) | ∫10p(t)dt=0}{p(t) | ∫01p(t)dt=0} E. {p(t) | p′(t)+2p(t)+8=0}{p(t) | p′(t)+2p(t)+8=0} F. {p(t) | p(5)=6}{p(t) | p(5)=6}
Subset B, D, E, and F are subspaces of P2.
Explanation:In order for a subset to be a subspace of P2, it must satisfy three conditions: it must be closed under addition, closed under scalar multiplication, and contain the zero vector. Let's analyze each subset to determine if it is a subspace:
A. {p(t) | p′(t) is constant}: This subset is closed under addition and scalar multiplication, so it satisfies the first two conditions. However, it does not contain the zero vector, so it is not a subspace.B. {p(t) | p(−t)=p(t) for all t}: This subset is closed under addition and scalar multiplication, and it contains the zero vector. Therefore, it satisfies all three conditions and is a subspace.C. {p(t) | p′(6)=p(7)}: This subset is not closed under addition and scalar multiplication, so it is not a subspace.D. {p(t) | ∫10p(t)dt=0}: This subset is closed under addition and scalar multiplication, and it contains the zero vector. Therefore, it satisfies all three conditions and is a subspace.E. {p(t) | p′(t)+2p(t)+8=0}: This subset is closed under addition and scalar multiplication, and it contains the zero vector. Therefore, it satisfies all three conditions and is a subspace.F. {p(t) | p(5)=6}: This subset is closed under addition and scalar multiplication, and it contains the zero vector. Therefore, it satisfies all three conditions and is a subspace.Learn more about subspaces of P2 here:https://brainly.com/question/32735601
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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.
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.
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
What does The Bureau of Consumer Protection do for consumers?
Answer:
The Bureau of Consumer Protection stops unfair and fraudulent business practices and taking appropriate actions against them.
Step-by-step explanation:
The Bureau of Consumer Protection is a body who looks into safeguarding the financial interests of the consumers. It stops unfair and fraudulent business practices by taking necessary and appropriate actions against them. They take necessary reaction as of suing the person or business involved. The Bureau of Consumer Protection also develops rules and regulations to maintain a fair marketplace. They also educate consumers about their responsibilities and rights.
Answer:
The Bureau of Consumer Protection stops unfair and fraudulent business practices and taking appropriate actions against them. The Bureau of Consumer Protection is a body who looks into safeguarding the financial interests of the consumers. It stops unfair and fraudulent business practices by taking necessary and appropriate actions against them. They take necessary reaction as of suing the person or business involved. The Bureau of Consumer Protection also develops rules and regulations to maintain a fair marketplace. They also educate consumers about their responsibilities and rights.
Step-by-step explanation:
e d g e
find the point of intersection of lines given
y=2x+1
y=-x+11
Answer:
(10, 21)
Step-by-step explanation:
To get the point of intersection of the lines given ( it means we need to find at what value of x will correspond to the value of y)
y = 2x+1
y = x+11
insert equation i in equation ii
2x+1=x+11
2x-x = 11-1
x = 10
y = 2x+1 = 2(10)+1 = 20+1 = 21
(x,y) = (10, 21)
Answer: (10/3, 23/3)
Step-by-step explanation:
To determine the point of intersection of the two lines, we would solve both equations simultaneously. The given system of linear equations is expressed as
y = 2x + 1- - - - - - - - - - - - -1
y = - x + 11 - - - - - - - - - - - -2
We would eliminate y by
Subtracting equation 2 from equation 1, it becomes
0 = 3x - 10
Adding 10 to the left hand side and the right hand of the equation, it becomes
3x - 10 + 10 = 0 + 10
3x = 10
Dividing the left hand side and the right hand side of the equation by 3, it becomes
3x/3 = 10/3
x = 10/3
Substituting
x = 10/3 into equation 1, it becomes
y = 2 × 10/3 + 1
y = 20/3 + 1
y = 23/3
Jackson flipped a coin ten time. He flipped heads 4 times and tails 6 times. What is the experimental probability that Jackson will flip heads on his next flip ?
Answer:
Step-by-step explanation:
Given that,
Outcomes Heads= 4heads and
Outcomes Tails= 6tails
Total outcome of events n=10
Probability of head in is first throw is, the is the outcome of head divide by the total possible outcomes
P(Head in first throw)=4/10
P(H)=2/5
P(H) = 0.4
P(H) =40%
Answer:
0.4
Step-by-step explanation:
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
Look at the figure. Complete the statement and justify your answer. line VT ≅ _____
line TX ; Reflexive Property of Congruence
line VX ; Reflexive Property of Congruence
line VX ; Converse of the Isosceles Triangle Theorem
line TX ; Converse of the Isosceles Triangle Theorem
Answer:
line VX ; Converse of the Isosceles Triangle Theorem
Explanation:
Since the angle marks on the base of the triangle is same, they measure the same.
The Converse of the Isosceles Triangle Theorem states: If two angles of a triangle are congruent, then sides opposite those angles are congruent.
So line VT ≅ VX
George is a fast worker. He can mop 34 ft2 in 1 minute. The court is shaped like a rectangle. It is 95 ft long by 50 ft wide. How many minutes will it take George to mop the gym floor?
a.) 4,750 minutes
b.) 2691.7 minutes
c.) 139.7 minutes
d.) 246.1 minutes
Answer:
C. 139.7 minutes
Step-by-step explanation:
To find the answer we have to find the area of the floor and then divide it by how many feet George can clean in a minute.
To find the area, multiply the length by the width.
95 * 50 = 4,750
The floor is 4,750 sq ft. Divide this number by 34 to figure out how many minutes it will take for him to clean the entire floor.
4,750/34 = 139.7
It will take George approximately 139.7 minutes to mop the floor.
To determine the time it will take George to mop a 95 ft by 50 ft gym floor at a rate of 34 ft^2 per minute, we calculate the floor's area (4,750 ft^2) and divide it by the rate, resulting in approximately 139.7 minutes.
To find out how many minutes it will take George to mop the gym floor, we first need to calculate the total area of the floor that he will mop. The floor is a rectangle with dimensions 95 ft by 50 ft. Multiplying these dimensions gives us the area of the rectangle:
Area = Length x Width
Area = 95 ft x 50 ft
Area = 4,750 ft^2
Now we know that George can mop 34 ft^2 per minute. To determine how many minutes it will take him, we divide the total area by the area he can mop per minute:
Time = Total Area / Area per Minute
Time = 4,750 ft^2 / 34 ft^2/min
Time = 139.7 minutes
Therefore, it will take George approximately 139.7 minutes to mop the gym floor, which corresponds to option (c).
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
Does the point (2√3, 2) lie on the circle that is centered at the origin and contains the point (0, -4)? Explain?
Answer:
The answer to your question is Yes, the point P lies on the circle
Step-by-step explanation:
Data
P (2[tex]\sqrt{3}[/tex], 2)
Center (0, 0)
Q (0, -4)
Process
1.- Find the radius of the circle
dCQ = [tex]\sqrt{(0-0)^{2}+ (-4 + 0)^{2}}[/tex]
dCQ = [tex]\sqrt{0^{2} + (-4)^{2}}[/tex]
dCQ = [tex]\sqrt{16}[/tex]
dCQ = 4
2.- Find the equation of the circle
(x - 0)² + (y - 0)² = 4²
-Simplification
x² + y² = 16
3.- Substitute P in the equation of the circle
(2[tex]\sqrt{3}[/tex])² + (2)² = 16
4(3) + 4 = 16
12 + 4 = 16
16 = 16
4.- Conclusion
The point (2[tex]\sqrt{3}[/tex], 2) lies on the circle because when we evaluate the equation of the circle with this point, we get the length of the radius.
Consider the following. (a) Explain why −0.41 cannot be the probability of some event. A probability must be between zero and one. A probability must be greater than one. A probability must be an integer.
Answer:
A probability must be between zero and one
Step-by-step explanation:
We are to explain why −0.41 cannot be the probability of some event.
Probability is the chance of occurring a particular event out of total possible events.
If total possible events are n, and number of favourable outcomes for any event A is x then probability is x/n.
Here note that both x and n cannot be negative.
also x cannot exceed n.
Probability can never exceed 1 and also can never be an integer except 0 or 1 as special cases.
So the probability can never be negative and cannot exceed 1.
So correct answer is
A probability must be between zero and one
Help please!!!!!
Simplify each expression
1) -8(v+4) 2) -9(-8+3x)
Answer:
88
Step-by-step explanation:
Answer:
1) -8(v+4) = -8v - 32
2) -9(-8+3x) = 72 - 27x
For the experiment described, write the indicated event in set notation.
A die is tossed twice with the tosses recorded as an ordered pair. Represent the following event as a subset of the sample space: The second toss shows a two.
a.{(1,2),(3,2),(5,2)}
b. {(1,2),(2,2),(4,2),(5,2),(6,2)}
c. {(3,2)}
d. {(1,2),(2,2),(3,2),(4,2),(5,2),(6,2)}
Answer:
d. {(1,2),(2,2),(3,2),(4,2),(5,2),(6,2)}
Step-by-step explanation:
First one can be any of the six outcomes
Final answer:
The event that the second toss shows a two is represented as a subset of the sample space and includes all possible outcomes of the first toss with a two as the second element, written as {(1,2), (2,2), (3,2), (4,2), (5,2), (6,2)} which is option d.
Explanation:
The question asks to represent a specific event from a probability experiment in set notation. The experiment involves tossing a die twice, and the event of interest is that the second toss results in a two. The sample space for two tosses of a six-sided die consists of all ordered pairs where the first element is the result of the first toss, and the second element is the result of the second toss. Since the die has six sides, the first element can be any number from 1 to 6, and the same applies to the second element.
The event that the second toss shows a two can be represented by the subset of the sample space where the second element of each ordered pair is a 2. Therefore, the correct set notation for this event would be {(1,2), (2,2), (3,2), (4,2), (5,2), (6,2)} which corresponds to option d. This subset includes all possible outcomes of the first toss combined with the fixed outcome of the second toss being a two.
A cellular phone company charges a $25 monthly fee and an additional $0.10 per minute. If m represents the number of minutes of phone usage, which equation can be used to determine the total monthly cost, c?
Answer:
c= 0.10m+ 25
Step-by-step explanation:
using the format y=mx+b
25 is your flat cost that they charge every month, and 0.10 is what they charge per minute.
m is the number of minutes so that is the unknown variable.
c is your total cost.
you take the flat cost per month (25 dollars) and add it to however many minutes multiplied by 0.10 (.10m)
The equation for determining the total phone bill given a monthly fee of $25 and a rate of $0.10 per minute is, c = 25 + 0.10m. Here, c represents the total monthly cost and m represents the number of minutes of phone usage.
Explanation:The subject of the question is linear algebra, and it requires forming an equation for a given scenario. In this case, the monthly cost of the cellular phone service is a function of the number of minutes of phone usage. The fixed monthly fee is $25, and there is an additional charge of $0.10 per minute.
So if m represents the number of minutes of phone usage, and c represents the total monthly cost, then the equation that can be used is: c = 25 + 0.10m
This is because for each minute used, an extra $0.10 is added to the total cost. If no minutes are used, the total cost is just the fixed $25. If 50 minutes are used, for example, the total cost is $25 + (0.10 * 50) = $30.
Learn more about Linear Algebra here:https://brainly.com/question/33704306
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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.
PLEAAAAAAASE HEEEEEELP!!!!
I WILL GIVE 20 POINTS!
Formulate the recursive formula for the following geometric sequence.
\(\left\{-16,\ 4,\ -1,...\right\}\)
The recursive formula for the geometric sequence is [tex]a_n=(-\frac{1}{4} )a_{n-1}[/tex]
Explanation:
The given sequence is [tex]\{-16,4,-1,........\}[/tex]
We need to determine the recursive formula for the given geometric sequence.
To determine the recursive formula, first we shall find the common difference.
Since, it is a geometric sequence, the common difference can be determined by
[tex]r=\frac{4}{-16} =-\frac{1}{4}[/tex]
[tex]r=-\frac{1}{4}[/tex]
Hence, the common difference of the given geometric sequence is [tex]r=-\frac{1}{4}[/tex]
The recursive equation for the geometric sequence can be determined using the formula,
[tex]a_n=r(a_{n-1})[/tex]
Substituting the value [tex]r=-\frac{1}{4}[/tex], we get,
[tex]a_n=(-\frac{1}{4} )a_{n-1}[/tex]
Thus, the recursive formula for the geometric sequence is [tex]a_n=(-\frac{1}{4} )a_{n-1}[/tex]
Dianna and Becky were playing on the same soccer team and took turns being goalie. They stoped 9 out of 10 shots made against them. If the other team scored 3 points, how many balls did Dianna and Becky stop from going into the net?
Answer:
27 balls
Step-by-step explanation:
If Dianna and Becky stopped 9 out of 10 shots made against them.
It means they allowed in 1 out of 10 shots made against them.
This is best solved using ratios
Proportion of Shots Stopped : Proportion of Shots allowed=9:1
If the other team scores 3 points, it means the number of shots allowed =3
Let x be the number of shots stopped
Number of Shots Stopped : Number of Shots allowed=x:3
Therefore:
9:1=x:3
[tex]\frac{9}{1}=\frac{x}{3}[/tex]
Cross multiplying
x=9 X 3 =27
Dianna and Becky stopped 27 balls from going into the net,
Pre-Calc Help:
Find the length of the major axis of the equation x² + 4y² = 4.
Answer choices:
4
8
Answer:
4
Step-by-step explanation:
Jaime can paddle her kayak at an average rate of 6 miles per hour in still water. After 2 hours of paddling north in a river, she traveled 8 miles. What is true about the direction of the current in the river? A It is moving in the same direction as the kayak because it sped Jaime up. B It is moving in the same direction as the kayak because it slowed Jaime down. C It is moving in a different direction as the kayak because it sped Jaime up. D It is moving in a different direction as the kayak because it slowed Jaime down.
Answer: D It is moving in a different direction as the kayak because it slowed Jaime down.
Step-by-step explanation:
Jaime can paddle her kayak at an average rate of 6 miles per hour in still water.
Distance = speed × time
After 2 hours of paddling north in a river, she traveled 8 miles. This distance covered was supposed to be
6 × 2 = 12 miles
Therefore, the following is true about the direction of the current in the river:
D It is moving in a different direction as the kayak because it slowed Jaime down.
Use the following information to complete parts I, II, and III. 1 hour=3600 seconds
1 year = 31556952 secondsI. Use scientific notation to estimate the number of hours in one year. II. Use scientific notation to calculate the exact number of hours in one year. III. In two or more complete sentences, compare your answers to parts I and II. In your comparison, discuss similarities and differences.
Answer:
I) 8.760 * 10 ³ hours
II) 8.76582 * 10 ³ hours
Step-by-step explanation:
1) No. of hours in one year:
24 hours* 365 days= 8760 hours
Scientific Notation= 8.760 * 10 ³ hours
2) 1 year = 31556952 seconds
1 hour=3600
1 year = 31556952 seconds/3600 = 8765. 82 hours
Scientific Notation= 8.76582 * 10 ³ hours
3) The exact numbers of hours using 365 days is 8760 which is written as 8.760* 10 ³ in scientific notation. But using the given data we get =8.76582 * 10 ³ hours
Comparing these answers the first one has only 3 significant figures
But the second answer has six significant figures if we round these we get 8.8 * 10 ³ hours which has two significant numbers
Aslo rounding the first gives 8.8 * 10 ³ hours which has two significant numbers and is the same as the other answer rounded
Which of the following is one of the cheapest routes to pass through each vertex once starting and ending with Vertex "A" and using the Nearest Neighbor Algorithm.
Group of answer choices
ABCDA, $960
ACDBA, $900
ACBDA, $960
None of the Above
Answer:
The answer is A
Step-by-step explanation:
The cheapest route should be c) ABCDA, $960
calculation of cheapest route:Starting at A: Options are B = 220, C = 240, D = 310
Now
Choose B since it has the smallest value.
Now
From B: Options are C = 200, D = 210
Choose C since it has the smallest value.
From C: There is only one option i.e. D = 230 here we cannot choose A since it was our beginning point.
From D: We touched all of the vertices due to this, return to the starting point, A = 310
So,
A → B → C → D → A --> 220 + 200 + 230 + 310 = 960
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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.
Jake scored 67 on the calculus midterm. If the final exam counts twice as much as the midterm exam, then for what range of scores on the final would Jake get an average between 81 and 92? Both tests have a maximum of 100 points.
Jake cannot achieve an average above 89 with the final exam alone.
The final exam counts twice as much as the midterm, so the weights are 2 for the final and 1 for the midterm. The average score A can be calculated using the formula:
[tex]\[ A = \frac{\text{weight of midterm} \times \text{midterm score} + \text{weight of final} \times \text{final score}}{\text{total weight}} \][/tex]
Given that Jake's midterm score is 67 and the weights are 1 for the midterm and 2 for the final, the total weight is 1 + 2 = 3 . We want Jake's average A to be between 81 and 92.
For the lower bound of the average (81), we have:
[tex]\[ 81 = \frac{1 \times 67 + 2 \times f}{3} \][/tex]
Solving for f :
[tex]\[ 81 \times 3 = 67 + 2f \] \[ 243 = 67 + 2f \] \[ 2f = 243 - 67 \] \[ 2f = 176 \] \[ f = \frac{176}{2} \] \[ f = 88 \][/tex]
So, the minimum score Jake needs on the final exam to achieve an average of at least 81 is 88.
For the upper bound of the average (92), we have:
[tex]\[ 92 = \frac{1 \times 67 + 2 \times f}{3} \][/tex]
Solving for f:
[tex]\[ 92 \times 3 = 67 + 2f \] \[ 276 = 67 + 2f \] \[ 2f = 276 - 67 \] \[ 2f = 209 \] \[ f = \frac{209}{2} \] \[ f = 104.5 \][/tex]
However, since the maximum score for the final exam is 100, the highest possible average Jake can achieve is 100 (since [tex]\( 67 + 2 \times 100 = 267 \)[/tex], and [tex]\( \frac{267}{3} = 89 \))[/tex].
In conclusion, Jake needs to score at least 88 on the final exam to achieve an average of at least 81, but he cannot achieve an average above 89 with the final exam alone. Thus, the range of scores on the final exam for Jake to get an average between 81 and 92 is from 88 to 100. However, the upper bound of Jake's average is actually 89, not 92, due to the maximum score constraint on the final exam.
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
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
Suppose that three compact discs are removed from their cases, and that after they have been played, they are put back into the three empty cases in a random manner. Determine the probability that at least one of the CD’s will be put back into the proper cases.
Answer:
The probability that at least one of the CD'S will be put back into the proper cases is 2/3
Step-by-step explanation:
The total amount of possibilities of putting back the CD's is equal to the total amount of ways of ordering a set of 3 elements, in other words, 3! = 6. In 4 of those 6 ways, at least one of the CD's is put back properly:
- All CD's are put back into the proper cases
- First disc is put back into its proper cases, Second disc is put back in third's position, and third disc is put back in second's position.
- Second Disc is put back correctly, and first and third not
- Thir disc is put back correctly and first and second got 'swapped'.
Thus, the probability that at least one of the CD'S will be put back into the proper cases is 4/6 = 2/3.
En un barco, 1/7 del número de tripulantes se encarga del mantenimiento de la maquinaria, 2/7 de la cocina, 3/7 de las recámaras y pasillos, y los 18 restantes son oficiales
Answer:
see the explanation
Step-by-step explanation:
The question in English is
On a ship, 1/7 of the crew members maintain the machinery, 2/7 the kitchen, 3/7 the bedrooms and corridors, and the remaining 18 are officers
Let
x ----> members that maintain the machinery
y ---->members that maintain the kitchen
z ----> members that maintain bedrooms and corridors
w ----> members that are officers
T ----> total number of members
we know that
The total sum of the fractions must be equal to 1
[tex]\frac{1}{7}+\frac{2}{7}+\frac{3}{7}+w=1[/tex]
[tex]w=1-\frac{6}{7}[/tex]
[tex]w=\frac{1}{7}[/tex]
Remember that
The number of officers is 18
so
[tex]18=\frac{1}{7}T[/tex]
Find out the total number of members
solve for T
[tex]T=18(7)=126\ members[/tex]
Find out the number of members that maintain the machinery
[tex]x=\frac{1}{7}T[/tex]
[tex]x=\frac{1}{7}(126)=18\ members[/tex]
Find out the number of members that maintain the kitchen
[tex]y=\frac{2}{7}T[/tex]
[tex]y=\frac{2}{7}(126)=36\ members[/tex]
Find out the number of members that maintain bedrooms and corridors
[tex]z=\frac{3}{7}T[/tex]
[tex]z=\frac{3}{7}(126)=54\ members[/tex]