Since obtuse angles are greater than 90 degrees and acute angles are less than 90 degrees, then obtuse angles have greater measures than acute angles.
Happy to help
Answer:
Step-by-step explanation:
obtuse angles >90
acute angles <90
In the sales comparison approach, using comparables that are five and 15 years old when appraising a subject that is 10 years old is an example of what?
Final answer:
In the sales comparison approach, using comparables of different ages requires adjustments for age or vintage to estimate the accurate value of the subject property considering physical and economic differences.
Explanation:
In the sales comparison approach, the use of comparables that vary significantly in age compared to the subject property is an example of adjusting for age or vintage. When appraising a subject property that is 10 years old, by using comparables that are five and 15 years old, an appraiser is attempting to account for differences in physical deterioration, functional obsolescence, and external obsolescence that may exist. A key part of this approach is applying adjustments to the comparables to reflect these differences, thereby arriving at a more accurate value for the subject property.
It is important to ensure that the base year used for comparison is consistent, and adjustments are made for any significant differences in market conditions or property features. The age adjustment is just one of many adjustments that might be made, including location, size, and condition. This process requires careful consideration and professional judgment to ensure that the end value is reflective of the current market.
I don’t understand how to do this
Step-by-step explanation:
θ is in quadrant IV, so:
sin θ < 0
cos θ > 0
tan θ = sin θ / cos θ < 0
csc θ = 1 / sin θ < 0
sec θ = 1 / cos θ > 0
Without doing any calculations, we can see only the third option fits (in the second option, sin θ / cos θ = -9/18, not -18/9. In the fourth option, csc θ and sec θ are switched).
Let's go ahead and calculate the values. There are several ways to solve this. One way is to use Pythagorean identities (ex., 1 + cot²θ = csc²θ). Another way is to simply draw a triangle in the fourth quadrant.
cot θ = 1 / tan θ, and tan θ = opposite / adjacent. So cot θ = adjacent / opposite. If we draw a triangle with angle θ, where the adjacent side is 9 and the opposite side is -18, then we can use Pythagorean theorem to find the hypotenuse:
c² = a² + b²
c² = (9)² + (-18)²
c = √405
Therefore:
sin θ = -18 / √405
cos θ = 9 / √405
csc θ = √405 / 18
sec θ = √405 / 9
tan θ = -18/9
The median is:
a. the second quartile
b. the 50th percentile
c. the observation with half of the data on either side of it
d. all of the above
The median is all of the above: the second quartile, the 50th percentile, and the observation with half of the data on either side. It represents the central point of a data set where 50% of the values are below and 50% are above it.
Explanation:The question asks to identify what the median represents in statistical terms. The median is:
a. the second quartile b. the 50th percentile c. the observation with half of the data on either side of it d. all of the aboveThe correct answer is d. all of the above. The median or second quartile (Q₂) is the value that divides the ordered dataset in half. It is also known as the 50th percentile since it implies that 50% of the data lies below this point and 50% lies above it. For example, in a dataset 1, 1, 2, 2, 4, 6, 6.8, 7.2, 8, 8.3, 9, 10, 10, 11.5, the median is 7, meaning that half of the values are smaller than 7 and half of the values are larger than 7.
Write y= -3/4 x-6 in standard form using integers.
Answer:
3x + 4y = -24.
Step-by-step explanation:
y= -3/4 x-6
Multiply through by 4:
4y = -3x - 24
3x + 4y = -24.
Your brother has $2000 saved fo a vacation. His airplane ticket is $637. Write and solve an inequality to find out how much he can spend for everything else.
The amount he can spend for everything else is less than or equal to 1363
The inequality is : [tex]s\leq 1363[/tex]
Solution:
Let "s" represent the brother's money to spend
Your brother has $2000 saved for a vacation
His airplane ticket is $637
Write an expression for the total money spent by adding "s" and the price of plane ticket $ 637
We can frame a inequality as:
[tex]s+637\leq 2000[/tex]
Here we have used "less than or equal to" symbol, because he can spent only up to 2000
Solve the inequality for "s"
[tex]s+637\leq 2000\\\\\text{Add -637 on both sides of inequality }\\\\s+637-637\leq 2000-637\\\\s\leq 1363[/tex]
Thus the amount he can spend for everything else is less than or equal to 1363
Find the coordinates of the x- and y-intercepts for an ellipse with the equation (x+1)^2/9 + (y-2)^2/8 = 1
Answer:
x-intercepts: -1±√4.5y-intercepts: 2±8/3Step-by-step explanation:
The x-intercepts are where y = 0.
(x +1)^2/9 +(0 -2)^2/8 = 1
(x +1)^2/9 +1/2 = 1 . . . . . simplify a bit
(x +1)^2 = 9/2 . . . . . . . . .subtract 1/2, multiply by 9; next: square root, add -1
x = -1 ±√4.5 . . . . . x-intercepts
__
The y-intercepts are where x=0.
(0+1)^2/9 +(y-2)^2/8 = 1
1/9 + (y -2)^2/8 = 1 . . . . . simplify a bit
(y -2)^2 = 64/9 . . . . . . . . subtract 1/9, multiply by 8,
y = 2 ±8/3 . . . . . . take the square root, add 2 . . . . y-intercepts
7. In a state lottery, a player must choose 8 of the numbers from 1 to 40. The lottery commission then performs an experiment that selects 8 of these 40 numbers. Assuming that the choice of the lottery commission is equally likely to be any of the 40 8 combinations, what is the probability that a player has (a) all 8 of the numbers selected by the lottery commission
Answer:a) P(8 of the players numbers are drawn)=1.3×10^-8
b) P(7 of the players number are drrawn)=3.33×10^-c) P(at least 6 of the players number were drawn)=1.84×10^-4
Step-by-step explanation:
Players has 8 combinations of numbers from 1-40. The outcome S contains all the combinations of 8 out of 40
a) P(8 of the players numbers are drawn)= 1/40/8= 1.3×10^-8
There are one in hundred million chances that the draw numbers are precisely the chosen ones.
b) Number of ways of drawing 78 selected numbers from 1-40=8×(40-7)
8×32
P(7 of the players number are drawn)=8×32/40 =3.33×10^-6.
There are approximately 300,000 chances that 7 of the players numbers are chosen
c) P(at least 6 players numbers are drawn)= 32/2×(8/6) ways to draw.
P(at least 6 players numbers are drawn)=P(all 8 chosen are drawn)+P(7 players numbers drawn)+P(6 chosen are drawn) = 1+ 8 x32/40/8 +[8\6 ×32/2]
P(at least 6 players numbers are drawn) = 1.84×10^-4.
There are approximately 5400chances that at least6 of the numbers drawn are chosen by the player.
The probability that a player has all 8 of the numbers selected by the lottery commission
Explanation:To find the probability that a player has all 8 numbers selected by the lottery commission, we need to determine the favorable outcome and the total possible outcomes. The favorable outcome is 1 because the player needs to match all 8 numbers. The total possible outcomes can be calculated using the combination formula. There are 40 numbers to choose from and the player must choose 8, so the total possible combinations is C(40,8). Therefore, the probability of a player matching all 8 numbers is:
P(all 8 numbers matched) = 1 / C(40,8)
There are 1200 elephants in a herd. Some have pink and green stripes, some are all pink and some are all blue. One third are pure pink. Is it true that 400 elephants are definitely blue?Why?
Answer: Yes.
The remaining 2/3 elephants left could be a mix of blue and green shared equally.
Step-by-step explanation:
Total number of elephants= 1200
Number of possible colours=3 (blue,green and pink)
Number of pink elephants =1/3 of 1200
Number of pink elephants =1/3×1200
Pink elephants are 400
The remaining fraction will b 1-1/3=2/3
Total number of elephants - number of pink elephants = remaining number of elephants => 1200-400=800
It is true that 400 elephants are definitely blue because the number of elephants remaining is twice 400
Given:
Total number of elephants = 1200
Colours available:
Blue
Pink
Pink & green
Pure Pink = 1/3 of 1200
= 1/3 × 1200
= 1200/3
Pure Pink = 400
Elephants remaining = Total number of elephants - Pure Pink
= 1200 - 400
= 800
Therefore, it is true that 400 elephants are definitely blue because the number of elephants remaining is twice 400
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. Patrick, by himself, can paint four rooms in 10 hours. If he hires April to help, they can do the same hob together in 6 hours. If he lets April work alone, how long will it take her to paint four rooms?
Answer: 15 hours
Step-by-step explanation:
Given : Patrick, by himself, can paint four rooms in 10 hours.
i..e Time taken by Patrick to paint the 4 walls = 10 hours.
Since rate of work = [tex]\dfrac{Work}{Time}[/tex]
We consider the entire job as 1.
Then, the rate of work done by Patrick = [tex]\dfrac{1}{10}[/tex]
If he hires April to help, they can do the same hob together in 6 hours.
i.e. the rate of work done by Patrick and April together = [tex]\dfrac{1}{6}[/tex]
Then, the rate of work done by April = rate of work done by Patrick and April together - rate of work done by Patrick
[tex]\dfrac{1}{t}=\dfrac{1}{6}-\dfrac{1}{10}\\\\\Rightarrow\ \dfrac{1}{t}=\dfrac{10-6}{60}=\dfrac{4}{60}\\\\\Rightarrow\ \dfrac{1}{t}=\dfrac{1}{15}\\\\\Rightarrow\ t=15[/tex]
Hence,it will take 15 hours April to paint four rooms .
A 16 inch candle is lit and burns at a constant rate of 1.1 inches per hour. Let t represent the never of hours that have elapsed since the candle was lit.
a) write an expression in terms of t that represents the number of incrhs that have burned from the candle since it was lit.
b) write an expression in terms of t that represents the remaining length of the candle (in inches).
Answer:
(a) Number of inches that have burned from the candle since it was lit is (1.1t) inches
(b) The remaining length of the candle is (16 - 1.1t) inches
Step-by-step explanation:
(a). Length of candle before it was lit = 16 inches
Constant rate at which at which candle burns = 1.1 inches per hour
Let t represent the number of hours that have elapsed since the candle was lit
In 1 hour, 1.1 inches of the candle burned
Therefore, in t hours, (1.1t) inches of the candle would have burned since the candle was lit
(b) Remaining length of candle = length of candle before it was lit - length of candle that have burned = 16 inches - 1.1t inches = (16 - 1.1t) inches
HELP!! 13 PTS!!!
Write a function of the form f(x) = a/x-h + k
With vertical asymptote is x=-2, horizontal asymptote is y=-5. The graph expands vertically by a factor of 2 and reflects across the x-axis.
Answer:
Step-by-step explanation:
VA= -2
HA= -5
F(x)= 2(x+5)/-(x+2)
Vicky drew a scale drawing of a city. She used the scale 1 inch : 2 yards. If the actual width of a neighborhood park is 62 yards, how wide is the park in drawing?
Answer:
The park is 31 inches wide in the drawing.
Step-by-step explanation:
Given:
Vicky drew a scale drawing of a city. She used the scale 1 inch : 2 yards.
The actual width of a neighborhood park is 62 yards.
Now, to find the width of park in drawing.
Let the width of park in drawing be [tex]x.[/tex]
The scale drawing of the city is 1 inch : 2 yards.
So, 1 inch is equivalent to 2 yards.
Thus, [tex]x[/tex] is equivalent to 62 yards.
Now, to get the width of park in drawing by using cross multiplication method:
[tex]\frac{1}{2} =\frac{x}{62}[/tex]
By cross multiplying we get:
[tex]62=2x[/tex]
Dividing both sides by 2 we get:
[tex]31=x[/tex]
[tex]x=31\ inches.[/tex]
Therefore, the park is 31 inches wide in the drawing.
Answer:
Answer:
31 inches
Step-by-step explanation:
62 yds divided by 2 equals 31 in
Step-by-step explanation:
A uranium mining town reported population declines of 3.2%, 5.2%, and 4.7% for the three successive five-year periods 1985–89, 1990–94, and 1995–99. If the population at the end of 1999 was 9,320:
Answer:
Step-by-step explanation:
Heres the complete question:
A uranium mining town reported population declines of 3.2%, 5.2%, and 4.7% for the three successive five-year periods 1985–89, 1990–94, and 1995–99. If the population at the end of 1999 was 9,320:
How many people lived in the town at the beginning of 1985? (Round your answer to the nearest whole number.)
solution:
Let the population of the town at the beginning of 1985 be P. Then, given that in the first five-year period the population declined by 3.2%, i.e., 0.032, the population of the town at the end of 1989 would be
(1 – 0.032)P = 0.968P.
Again, given that in the second five-year period the population declined by 5.2%, i.e., 0.052, the population of the town at the end of 1994 would be
(1 – 0.052)(0.968P) = 0.948 x 0.968P = 0.917664P.
Finally, given that in the third five-year period the population declined by 4.7%, i.e., 0.047, the population of the town at the end of 1999 would be
(1 – 0.047)(0.917664P) = 0.874533792P.
We are given, 0.874533792P = 9320 or
P = 9320/0.874533792 = 10657.11.
Thus, 10657 people lived in the town at the beginning of 1985
Final answer:
This is a mathematics question requiring the computation of past populations based on given percentage declines and the population at the end of 1999.
Explanation:
The question involves calculating the population of a uranium mining town at a prior date based on given percentage declines over successive five-year periods and the known population at the end of 1999. Since the population at the end of 1999 was 9,320, we work backward using the given percentage declines for each five-year period to estimate the population at the beginning of 1985. The calculation takes into account a 3.2% decline for 1985-89, a 5.2% decline for 1990-94, and a 4.7% decline for 1995-99. By applying these percentage changes in reverse, we can determine the population at the start of 1985.
Help! Will give brainliest.
Answer:
Step-by-step explanation:
[tex]g(x)=log_{2}( x+4) -1\\let g(x)=y\\y=log_{2}(x+4)-1 \\x+4=2^{y+1} \\when y=0\\x+4=2^1=2\\x=2-4=-2\\when x=0\\4=2^{y+1}=2^y*2^1=2*2^y\\2^y=\frac{4}{2}=2=2^1\\so~y=1\\x -intercept=-2\\y-intercept=1[/tex]4. it is a transformation of 4 units left and 1 unit down.
Determine whether the underlined value is a parameter or a statistic. A study of 6076 adults in public rest rooms found that 23% did not wash their hands before exiting. Is the value a parameter or a statistic?
A. The value is a parameter because the 6,076 adults in public rest rooms are a sample
B. The value is a parameter because the 6,076 adults in public rest rooms are a population.
C. The value is a statistic because the 6076 adults in public restrooms are a sample
D. The value is a statistic because the 6,076 adults in public rest rooms are a population
Answer:
C
Step-by-step explaination:
A statistic is a data obtained by sampling a population
A sample is a part of a population studied for the purpose of testing of an hypothesis
6076 is a statistical value because it represents a part (sample) of the whole population
The value of 23% is a statistic calculated from a sample of 6076 adults in public restrooms.
Explanation:In this question, the value of 23% represents the proportion of adults in public restrooms who did not wash their hands before exiting. Since this value is calculated from a sample of 6076 adults, it is considered a statistic. A statistic is a number that represents a property of a sample. On the other hand, a parameter is a numerical characteristic of the entire population. In this case, if we had data for all adults in public restrooms, the proportion would be a parameter.
Knowing that 9 is closer to 10 than to 1 and understanding that 2 plus 1 equals 3 demonstrates a basic understanding of
a. reversibility.
b. intelligence.
c. whole number skills.
d. seriation.
Answer: C: Whole number skills
Step-by-step explanation: The question involves simple understanding of whole numbers from counting 1 to 10, and also addition of these whole numbers, which makes its a basic understanding of whole number skills
Working together, Melissa and Jing can mow a lawn in 5 hours. It would take Melissa 8 hours to do the job alone. What is the value of r, the part of the lawn that Jing could complete in 1 hour?A. 0.075.
B. 0.125.
C. 0.375.
D. 0.625.
Answer:
The amount of work completed by Jing in 1 hour is 0.075 which is option A
Step-by-step explanation:
Melissa & Jing can complete the work in 5 hours
This means that the amount of work completed by Melissa & Jing working together in 1 hour is (1÷5) = 0.2
Melissa will do the job in 8 hours, which means that the amount of job completed by Melissa working alone in 1 hour is (1÷8) = 0.125
The amount of work completed by Jing when he works alone in 1 hour will be the difference of amount of work completed by both of them in 1 hour with the amount completed by only Melissa in 1 hour.
There Amount of work completed by Jing in an hour = 0.2 - 0.125 = 0.075
Answer: option A
Step-by-step explanation:
If the square root of p2 is an integer greater than 1, which of the following must be true? I. p2 has an odd number of positive factors II. p2 can be expressed as the product of an even number of positive prime factors III. p has an even number of positive factors?
Answer:
Option | and Option || is True
Step-by-step explanation:
Given:
If the square root of [tex]p^{2}[/tex] is an integer greater than 1,
Lets p = 2, 3, 4, 5, 6, 7..........
Solution:
Now we check all option for [tex]p^{2}[/tex]
Option |.
[tex]p^{2}[/tex] has an odd number of positive factors.
Let [tex]p=2[/tex]
The positive factor of [tex]2^{2}=4=1,2,4[/tex]
Number of factor is 3
Let [tex]p=3[/tex]
The positive factor of [tex]3^{2}=9=1,3,9[/tex]
Number of factor is 3
So, [tex]p^{2}[/tex] has an odd number of positive factors.
Therefore, 1st option is true.
Option ||.
[tex]p^{2}[/tex] can be expressed as the product of an even number of positive prime factors
Let [tex]p=2[/tex]
The positive factor of [tex]2^{2}=4=1,2,4[/tex]
[tex]4=2\times 2[/tex]
Let [tex]p=3[/tex]
The positive factor of [tex]3^{2}=9=1,3,9[/tex]
[tex]9=3\times 3[/tex]
So, it is expressed as the product of an even number of positive prime factors,
Therefore, 2nd option is true.
Option |||.
p has an even number of positive factors
Let [tex]p=2[/tex]
Positive factor of [tex]2=1,2[/tex]
Number of factor is 2.
Let [tex]p=4[/tex]
Positive factor of [tex]4=1,2,4[/tex]
Number of factor is 3 that is odd
So, p has also odd number of positive factor.
Therefore, it is false.
Therefore, Option | and Option || is True.
Option ||| is false.
Working his way through school, Joe works two part-time jobs for a total of 18 hours a week. Job A pays $5.70 per hour, and Job B pays $6.80 per hour. How many hours did he work at each job the week that he made $111.40?
Answer:
A = 14.2/1.1 hours
B = 5.091 hours
Step-by-step explanation:
Formulate 2 simultaneous equations
5.7A + 6.8B = 111.40..........(1)
A +B =18...............................(2)
Multiply each item in (2) by 5.7 to get
5.7A + 5.7B = 97.2............(3)
subtract (1) - (3) on each side
5.7A -5.7A + 6.8B - 5.7B = 111.40 -97.2
1.1B = 14.2
B = 14.2 /1.1
to get A use equation (2)
A = 18 - B
A = 18 - 14.2/1.1 = 5.091
Answer:in the week , he worked 10 hours at Job A and 8 hours at job B
Step-by-step explanation:
Let x represent the number hours that Joe worked at job A in a week.
Let y represent the number of hours that Joe worked at job B in a week.
Working his way through school, Joe works two part-time jobs for a total of 18 hours a week. This means that
x + y = 18
Job A pays $5.70 per hour, and Job B pays $6.80 per hour. He made a total of $111.4 working at each job during the week. It means that
5.7x + 6.8y = 111.4 - - - - - - - - - -1
Substituting x = 18 - y into equation 1, it becomes
5.7(18 - y) + 6.8y = 111.4
102.6 - 5.7y + 6.8y = 111.4
- 5.7y + 6.8y = 111.4 - 102.6
1.1y = 8.8
y = 8
x = 18 - y = 18 - 8
x = 10
Jane wants to pick out an outfit for the school dance she can choose from 3 pairs of pants 5shirts and 2 pairs of shoes how many differnt outfits does jane have to choose from
Answer:
30
Step-by-step explanation:
we multiply each number. There are 3 pairs of pants 5 shirts and 2 pairs of shoes, so we multiply 3x5x2 to get 30
The number of different outfits that Jane has to choose from is 30
What is the rule of product in combinatorics?If a work A can be done in p ways, and another work B can be done in q ways, then both A and B can be done in p×q ways.
Remember that this count doesn't differentiate between order of doing A first or B first then doing other work after the first work.
Thus, doing A then B is considered same as doing B then A
It is given that:
There are 3 pairs of pants, 5 shirts to choose from and 2 pairs of shoes to choose from.
One outfit would include one-one of these 3 things.
Pants can be chosen in 3 waysShirts can be chosen in 5 waysShoes can be chosen in 2 ways.Thus, they all together can be chosen in 3 × 5 × 2 = 30 ways.
So there are 30 different outfit that Jane has to choose from.
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A rectangular garden is 2 feet longer than it is wide. If the width is doubled, 50 extra feet of fencing will be needed to keep out the rabbits. What are the dimensions of the original garden?
Answer:
The dimensions of the original garden is [tex]27\times25\ ft[/tex].
Step-by-step explanation:
Let the width of the rectangular garden be 'x'.
Now given:
A rectangular garden is 2 feet longer than it is wide.
so we can say that;
Length of the rectangle = [tex](x+2) \ ft[/tex]
Now to fence the garden we need to find the perimeter of the garden.
Now Perimeter of the garden is equal to twice the sum of the length times width.
framing in equation form we get;
Perimeter of the rectangle = [tex]2(x+x+2)=2(2x+2)=4x+4[/tex]
Now given:
If the width is doubled, 50 extra feet of fencing will be needed
It means that Perimeter of the doubled width rectangle is equal to perimeter of original garden plus 50.
framing in equation form we get;
[tex]2(2x+x+2)=4x+4+50\\\\2(3x+2)=4x+50[/tex]
Now Applying distributive property we get;
[tex]2\times3x+2\times2=4x+54\\\\6x+4=4x+54[/tex]
Combining the like terms we get;
[tex]6x-4x=54-4\\\\2x=50[/tex]
Dividing both side by 2 we get;
[tex]\frac{2x}{2}=\frac{50}{2}\\\\x=25 \ ft[/tex]
Length of the rectangular garden = [tex]x+2=25+2=27\ ft[/tex]
Hence the dimensions of the original garden is [tex]27\times25\ ft[/tex].
Two dice are thrown. Let E be the event that the sum of the dice is
even, let F be the event that at least one of the dice lands on 6 and
let G be the event that the numbers on the two dice are equal. Find
P(E), P(F), P(G), P(EF), P(F G), P(EG).
Answer:
P(E) = 1/2P(F) = 11/32P(G) = 1/6P(EF) = 5/52P(FG) = 1/32P(EG) = 1/6Step-by-step explanation:
For the sum to be even, both dice can be odd, or both even. The probability of a dice being odd is 1/2 and the same is for it to be even. Since the result of the dices are independent, we have that
P(E) = (1/2)² + (1/2)² = 1/2
Out of the 36 possible outcomes for the dice (assuming that you can distinguish between first and second dice), there are 11 cases in which one dice is a 6 (if you fix 1 dice as 6, there are 6 possibilities for the other, but you are counting double 6 twice, so you substract one and you get 6+6-1 = 11). Since all configurations for the dices have equal probability, we get that
P(F) = 11/32
The probability for the second dice to be equal to the first one is 1/6 (it has to match the same number the first dice got). Hence
P(G) = 1/6
for EF, you need one six and the other dice even. For each dice fixed as 6 we have 3 possibilities for the other. Removing the repeated double six this gives us 5 possibilities out of 32 total ones, thus
P(EF) = 5/32
If one dice is 6 and both dices are equal, then we have double six, as a result there is only one combination possible out of 32, therefore
P(FG) = 1/32
If both dices are equal, in particular the sum will be even, this means that G= EG, and as a consecuence
P(EG) = P(G) = 1/6
The probabilities are P(E) = 1/2, P(F) = 11/36, P(G) = 1/6, P(EF) = 1/6, P(FG) = 1/12, and P(EG) = 1/4.
Explanation:To find the probabilities, we need to use the concept of counting outcomes.
P(E):There are 36 equally likely outcomes when two dice are thrown. Out of these, 18 outcomes result in an even sum. So, P(E) = 18/36 = 1/2.
P(F):There are 11 outcomes where at least one die lands on 6 out of the 36 total outcomes. So, P(F) = 11/36.
P(G):There are 6 outcomes where both dice show the same number, out of the 36 possible outcomes. So, P(G) = 6/36 = 1/6.
P(EF):There are 6 outcomes where at least one die shows 6 and the sum is even. So, P(EF) = 6/36 = 1/6.
P(FG):There are 3 outcomes where both dice show 6 and at least one of them shows 6. So, P(FG) = 3/36 = 1/12.
P(EG):Out of the 36 outcomes, 9 outcomes result in both dice being the same and the sum being even. So, P(EG) = 9/36 = 1/4.
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The length of a rectangle is 4 meters less than twice the width. If the area of the rectangle is 240 square meters, find the dimensions.How many meters is the length? How many meters is the width?
Step-by-step explanation:
Let L be the length and W be the width.
The length of a rectangle is 4 meters less than twice the width.
That is
L = 2W - 4
The area of the rectangle is 240 square meters
That is
L x W = 240
(2W - 4) x W = 240
2W² - 4W = 240
W² - 2W - 120 = 0
(W -12 ) (W+10) = 0
W = 12 m or W = -10 m
So width of rectangle is 12 meter
Length = 2 x 12 - 4 = 20 m
Length is 12 meter and width is 20 meter.
At the baseball game, Adam bought 3 hot dogs and 2 sodas for $11. Four innings later, he purchased 2 hot dogs and 3 sodas for $10.25. Wat was the cost of a soda
Answer: the cost of one Soda was $1.75
Step-by-step explanation:
Let x represent the cost of one hot dog.
Let y represent the cost of one Soda.
At the baseball game, Adam bought 3 hot dogs and 2 sodas for $11. It means that
3x + 2y = 11 - - - - - - - - - - 1
In a later time, he purchased 2 hot dogs and 3 sodas for $10.25. It means that
2x + 3y = 10.25 - - - - - - - - -2
Multiplying equation 1 by 2 and equation 2 by 3, it becomes
6x + 4y = 22
6x + 9y = 30.75
Subtracting, it becomes
- 5y = - 8.75
y = - 8.75/- 5
y = 1.75
Substituting y = 1.75 into equation 1, it becomes
3x + 2 × 1.75 = 11
3x + 3.5 = 11
3x = 11 - 3.5 = 7.5
x = 7.5/3 = 2.5
Consider a= ⟨−2,5,1⟩, b= ⟨−5,2,−5⟩ and c= ⟨−1,−5,4⟩. Find the angles between the following vectors: The angle between a and b is:
Answer:
[tex]cos^{-1}(\frac{\sqrt 5}{6})[/tex]
Step-by-step explanation:
We are given that
[tex]a=<-2,5,1>,b=<-5,2,-5>[/tex] and c=<-1,-5,4>
We have to find the angles between a and b .
[tex]\mid a\mid=\sqrt{(-2)^2+(5)^2+(1)^2}=\sqrt{30}[/tex]
[tex]\mid b\mid=\sqrt{(-5)^2+(2)^2+(5)^2}=3\sqrt{6}[/tex]
[tex]a\cdot b=<-2,5,1>\cdot <-5,2,-5>=10+10-5=15[/tex]
Angle between two vectors a and b is given by
[tex]cos\theta=\frac{a\cdot b}{\mid a\mid \mid b\mid }[/tex]
Using the formula
[tex]cos\theta=\frac{15}{\sqrt{30}\times 3\sqrt{6}}[/tex]
[tex]cos\theta=\frac{5}{6\sqrt{5}}[/tex]
[tex]cos\theta=\frac{5\times \sqrt 5}{6\times (\sqrt 5)^2}=\frac{\sqrt 5}{6}[/tex]
[tex]\theta=cos^{-1}(\frac{\sqrt 5}{6})[/tex]
Hence, the angle between a and b=[tex]cos^{-1}(\frac{\sqrt 5}{6})[/tex]
What is the sum of the infinite geometric series?
120 + 20+ 10/3 + 5/9+...
Answer:
for an infinite geometric series the formula for the sum of the infinite geometric series when the common ratio is less than one is given by
[tex]\frac{a_{1} }{1 - r}[/tex] = [tex]\frac{120}{1 - \frac{1}{6} } = \frac{120}{\frac{5}{6} } =[/tex] [tex]\frac{120 \times 6}{5}[/tex] = 144.
Step-by-step explanation:
i) from the given series we can see that the first term is [tex]a_{1 }[/tex] = 120.
ii) let the common ratio be r.
iii) the second term is 20 = 120 × r
therefore r = 20 ÷ 120 = [tex]\dfrac{1}{6}[/tex]
iv) the third term is [tex]\frac{10}{3}[/tex] = 20 × r
therefore r = [tex]\dfrac{10}{3}[/tex] ÷ 20 = [tex]\dfrac{1}{6}[/tex]
v) for an infinite geometric series the formula for the sum of the infinite geometric series when the common ratio is less than one is given by
[tex]\frac{a_{1} }{1 - r}[/tex] = [tex]\frac{120}{1 - \frac{1}{6} } = \frac{120}{\frac{5}{6} } =[/tex] [tex]\frac{120 \times 6}{5}[/tex] = 144.
Answer:
C. 144
Step-by-step explanation:
(c+5)^3 solve using binomial theorem
Answer:
c^3+15c^2+75c+125
Step-by-step explanation:
Determine if the statement is true or false, and justify your answer. Suppose A is a matrix with n rows and m columns. If n < m, then the columns of A span Rn.
Answer:
The question is incomplete as there are given options ;
Q:
Determine if the statement is true or false , and justify your answer . Suppose A is a matrix with n rows and m columns . If n < m, then the columns of A span R True, since there are more columns than rows. O False, since there are not enough columns to span R". True, since every column of A must be a nonzero column, False, since every column of A may be a zero column, True, since every column of A must be a non zero column, False, since every column of A may be a zero column
Step-by-step explanation:
Considering a matrix A with n-rows and m-columns,
given that n is less than m i.e the rows is less than the columns
then the columns of A span Rn? TRUE OR FALSE?
the matrix is of nxm as n is less than m, hence from linear transformation, T will span : Rm towards Rn
the concept of ranking of a matrix is applied here as ranking entails the number of linearly independent rows or columns vectors in a matrix, in this case
the order is n x m where n is less than m, as such the rank of the matrix is n
So, Rank of MATRIX A is n
To prove if the rows vectors are linearly independent or not since n is the rank of the matrix
In this case, m columns vector will be considered with respect to n which is the rank and which is also less than m from the conditions, as such there exist a linearly independent relationship between them which R may be spanned since we know that from ranking, reduction to echelon form comes into play by trying to reduce every element of the column A to zero.
Trying to reduce to echelon form implies all the element of column A may or may not zero.from the foregoing, the last option is the correct answer ; False, since every column of A may be a zero column
The statement 'If n < m, then the columns of A span R^n' is false because it implies a guarantee without considering the linear independence of the columns, which is necessary for them to span the space.
Explanation:Determining whether the statement 'If n < m, then the columns of A span Rn' is true or false involves understanding linear algebra concepts. For a matrix A with more columns than rows (m > n), it is possible that the columns of A could span Rn, since there are enough vectors to possibly cover the entire n-dimensional space. However, without more information about the vectors, such as whether they are linearly independent, we cannot definitively conclude that they span the space.
The statement assumes that because there are more columns than rows, the columns automatically span the space. This could be true if the columns are linearly independent and cover the space. However, it's possible for a matrix to have redundant vectors that do not contribute to spanning the space, even if m > n. Therefore, the statement as given is false because it suggests a guarantee without consideration of linear independence.
she has 6 cherry candies, 3 grape candies, and 3 lime candies. If Charlotte randomly pulls one piece of candy out of the bag, what is the probability that it will be cherry? Round to the nearest hundredth.
Answer: [tex]\dfrac{1}{2}[/tex]
Step-by-step explanation:
We know that probability for any event = [tex]\dfrac{\text{Number of favorable outcomes}}{\text{Total outcomes}}[/tex]
Given : Charlotte has 6 cherry candies, 3 grape candies, and 3 lime candies.
I..e Total pieces of candies she has = 6+3+3= 12
Now , If Charlotte randomly pulls one piece of candy out of the bag, what is the probability that it will be cherry is given by :-
[tex]\text{P(cherry)}=\dfrac{\text{Number of cherries}}{\text{Total candies}}\\\\=\dfrac{6}{12}\\\\=\dfrac{1}{2}[/tex]
Hence, the probability that it will be cherry is [tex]\dfrac{1}{2}[/tex] .
The probability that Charlotte will pull a cherry candy out of the bag is 0.50 or 50%.
To determine the probability that Charlotte will randomly pull a cherry candy from the bag, we need to use the basic probability formula:
Probability = (Number of favourable outcomes) / (Total number of possible outcomes)
Step-by-Step Solution
Count the number of cherry candies: Charlotte has 6 cherry candies.Count the total number of candies: She has a total of 6 (cherry) + 3 (grape) + 3 (lime) = 12 candies.Calculate the probability: The probability of drawing a cherry candy is 6 (favourable outcomes) / 12 (total outcomes) = 0.5.Round to the nearest hundredth: Since 0.5 is already a decimal to the nearest hundredth, the final probability is 0.50.Therefore, the probability that Charlotte will pull a cherry candy out of the bag is 0.50 (or 50%).
Using the graph, find the value of y when x = 7. (image down below)
a.
y = 7
c.
y = 2.71
b.
y = 6.1
d.
y = 4.42