Final answer:
The trigonometric functions and their inverse functions are related to each other because they undo each other's actions. Inverse trigonometric functions give the angle whose trigonometric ratio is a given value. The domains and ranges of inverse trigonometric functions are restricted to ensure that they are well-defined.
Explanation:
The trigonometric functions and their inverse functions are related to each other because they undo the actions of the other function. Let's take the sine function as an example. The sine function takes an angle as input and gives the ratio of the opposite side to the hypotenuse as output. Its inverse function, arcsine, takes a ratio as input and gives the angle whose sine is that ratio as output.
These comparisons make sense in the light of the definition of the inverse of a function because an inverse function undoes the action of the original function. In the case of trigonometric functions, they represent a ratio between the sides of a right-angled triangle, and their inverses give the corresponding angle.
The domains and ranges of the inverse trigonometric functions make sense in relation to their parent functions because they are restricted to a specific range to ensure that the inverse function is well-defined. For example, the domain of arcsine function is [-1, 1] because the output of sine function is always between -1 and 1. By restricting the domain, we can ensure that the inverse function is a one-to-one mapping and has a well-defined output for each input.
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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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
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
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.
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.
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
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
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.
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).
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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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.
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 $
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.
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
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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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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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:
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]
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.
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:
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
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
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 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
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.
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.
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:
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.
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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]