Answer:
[tex]H=-(t-3)^2+13[/tex]
Step-by-step explanation:
The path covered by the volleyball will be a downward parabola with the vertex being the highest point of the ball.
A general form of a downward parabola is given as:
[tex]y=-a(x-h)^2+k[/tex]
Where [tex](h,k)[/tex] is the vertex of the parabola and 'a' is a constant.
Now, let 'h' be the vertical height and 't' be the time taken.
So, the equation would be of the form:
[tex]H=-a(t-h)^2+k[/tex]
Now, as per question:
h = 2 seconds, k = 13 feet.
[tex]H=-a(t-3)^2+13[/tex]
Now, taking a = 1. So, the formula that can be used is:
[tex]H=-(t-3)^2+13[/tex]
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.
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].
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]
Which system is represented by the graph?
Answer:
The answer to your question is the first option
Step-by-step explanation:
Process
1.- Identify the y-intercepts of the lines
blue line y-intercept = -1
brown line y-intercept = -2
With this information, we can discard the last option because those lines don't have those y-intercepts.
2.- We observe in the graphs that the lines are increasing so the slopes are positive. From this information, we can discard the second option.
3.- Calculate the slopes of the lines of options 1 and 3
Blue line Points (0, -1) (1, 2)
m = [tex]\frac{2 + 1}{1 - 0} = \frac{3}{1} = 3[/tex]
Brown line Points (0, -2) (1, 1)
m = [tex]\frac{1 + 2}{1 - 0} = 3[/tex]
As the slopes are 3, we conclude that the answer is the first option.
Find a counterexample to show that the following conjecture is false.
The quotient of any two integers is always less than 1.
Answer:
4/2 = 2 > 1
Step-by-step explanation:
The quotient of any two integers of the same sign and the dividend having the larger magnitude will be greater than 1:
-88/-11 = 8 > 1
4/2 = 2 > 1
Hence the conjecture is false.
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.
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.
Fortuna worked 39.5 hours this week at $8.18 an hour.
What was her gross pay?
$327.20
$323.90
$323.11
$319.02
Answer:
c
Step-by-step explanation:
because 39.5 hours makes 8.18
Fortuna's gross pay is $323.11
What is unit rate?A unit rate means a rate for one of something. We write this as a ratio with a denominator of one. For example, if you ran 70 yards in 10 seconds, you ran on average 7 yards in 1 second. Both of the ratios, 70 yards in 10 seconds and 7 yards in 1 second, are rates, but the 7 yards in 1 second is a unit rate.
Given that, Fortuna worked 39.5 hours this week at $8.18 an hour.
Since, she is being paid $8.18 for 1 hour, that mean her unit rate is $8.18
To find total rate we will multiply her unit rate with total hours she worked.
Therefore,
The total pay = 39.5 × 8.18 = $323.11
Hence, Fortuna's gross pay is $323.11
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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)
A mini-golf course is determining the par score for each of its holes. The dot plot shows the number of strokes required to place a ball in the ninth hole for a sample of 31 players. A number line going from 1 to 9. 2 dots are above 1. 3 dots are above 2. 4 dots are above 3. 5 dots are above 4. 5 dots are above 5. 3 dots are above 6. 2 dots are above 7. 0 dots are above 8. 1 dot is above 9. Which measure of center is best to use to determine the expected number of strokes required for the ninth hole? a. The mean is the best choice because the data is nearly symmetrical. b. The median is the best choice because data is clustered. c. The mean is the best choice because the data is skewed to the right. d. The median is the best choice because the data is skewed to the left.
Answer:
A
Step-by-step explanation:
The mean is a good measure of central tendency because it takes into account all of the data compared to other. One of the instance where the mean is not good measure is when there are outliers ( extreme values) in the data in this case the median is better. In the scenario in the question the data set is nearly symmetrical therefore the mean is best central tendency measure to use
Answer:
Option A - The mean is the best choice because the data is nearly symmetrical.
Step-by-step explanation:
Given : A mini-golf course is determining the par score for each of its holes. The dot plot shows the number of strokes required to place a ball in the ninth hole for a sample of 25 players.
To find : Which measure of center is best to use to determine the expected number of strokes required for the ninth hole?
Solution :
To determine the expected number of strokes required for the ninth hole the best measure of center is the mean of the data as the data is nearly symmetrical about the center point 4 and 5.
We can also find the mean of the data,
Mean is defined as the sum of observation divided by number of observation.
i.e, Sum of observation is
Referring the dot plot of ninth hole strokes
Total number of observation n= 25
Therefore, Option A is correct.
The mean is the best choice because the data is nearly symmetrical.
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:
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:
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
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.
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.
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
(c+5)^3 solve using binomial theorem
Answer:
c^3+15c^2+75c+125
Step-by-step explanation:
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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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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The value of a baseball card in dollars has been found to be 0.15y + 0.35, where y is the number of years since it was released. By how much is the baseball card's value increasing per year?
Answer:
The value of the baseball increase $0.15
Step-by-step explanation:
we have
The expression above represent a linear equation in slope intercept form
where
The slope or unit rate is equal to
The y-intercept is equal to ----> original value of a baseball card
therefore
The value of the baseball increase $0.15 per year
Final answer:
The value of the baseball card is increasing by $0.15 per year. For the bat and ball problem, the ball costs $0.05 and the bat costs $1.05.
Explanation:
To find out how much the baseball card's value is increasing per year, we look at the formula given for the value of the baseball card: 0.15y + 0.35. In this formula, y represents the number of years since the card was released. The coefficient of y is 0.15, which indicates the yearly increase in the value of the card.
Therefore, the value of the baseball card is increasing by $0.15 per year.
Now let's look at the classic bat and ball problem. The total cost of the bat and the ball is $1.10, and the bat costs $1.00 more than the ball. If we denote the cost of the ball as x, then the cost of the bat is x + $1.00. Setting up the equation x + (x + $1.00) = $1.10, we combine like terms to get 2x + $1.00 = $1.10. Solving for x, we subtract $1.00 from both sides to get 2x = $0.10. Dividing both sides by 2 yields x = $0.05. So, the ball costs $0.05, and the bat costs $1.05.
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%).
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.
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)
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
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
. 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 .
Ken drives a taxi cab and receives $100 a day plus $0.50 for every mile he drives. He is saving up for a new television that costs about $2500. If Ken drives an average of 400 miles per day, how many days will he have to drive to save enough money to buy the television? In a inequality statment
Answer:
i got 8.33 so I would say about 9. Im not sure about inequality statements but I know that's about how many days since he makes 300 per day, and you divide that by 2500
Step-by-step explanation:
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.
Learn more about Probability here:https://brainly.com/question/22962752
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