Answer:
Probability that at least three would be yellow = 0.556 .
Step-by-step explanation:
We are given that In Europe, 53% of flowers of the reward less orchid, Dactylorhiza sambucina are yellow.
The Binomial distribution probability is given by;
P(X = r) = [tex]\binom{n}{r}p^{r}(1-p)^{n-r}[/tex] for x = 0,1,2,3,.......
Here, n = number of trials which is 5 in our case
r = no. of success which is at least 3 in our case
p = probability of success which is probability of yellow flower of
0.53 in our case
So, P(X >= 3) = P(X = 3) + P(X = 4) + P(X = 5)
= [tex]\binom{5}{3}0.53^{3}(1-0.53)^{5-3} + \binom{5}{4}0.53^{4}(1-0.53)^{5-4} + \binom{5}{5}0.53^{5}(1-0.53)^{5-5}[/tex]
= [tex]10*0.53^{3}(0.47)^{2} + 5*0.53^{4}(0.47)^{1} + 1*0.53^{5}(0.47)^{0}[/tex]
= 0.556
Therefore, the probability that at least three would be yellow is 0.556 .
Two welders worked a total of 46 h on a project. One welder made $34/h, while the other made $39/h. If the gross earnings of the two welders was $1,669 for the job, how many hours did each welder work?
Answer:
x = 25 Total worked hours by welder winning 34 $ /h
y = 21 Total worked hours by welder winning 39 $ /h
Step-by-step explanation:
Let call
"x" numbers of hours worked by welder winning 34 $/h
"y" numbers of hours worked by welder winning 39 $/h
Then according to problem statement
x + y = 46 ⇒ y = 46 - x
1669 = 34*x + 39*y ⇒
We got a two equation system, solving
1669 = 34*x + 39* ( 46 - x ) ⇒ 1669 = 34*x + 1794 - 39*x
1669 - 1794 = - 5*x ⇒ -125 = - 5*x
x = 125/5 ⇒ x = 25
And as y = 46 - x y = 46 - 25 ⇒ y = 21
Very urgent... I need it right now.. please help me with explanation!
Answer:
a) Water height, H(g) = 8g^2 + 3g -4 - [9g^2 -2g -5] = 8g^2 + 3g -4 -9g^2 + 2g +5 = -g^2 +5g +1
b) g = 1
H(g) = -(1)^2 + 5(1) + 1 = -1 + 5 + 1 = 5
g=2
H(g) = -(2)^2 + 5(2) + 1 = -4 + 10 + 1 = 7
g=3
H(g) = -(3)^2 + 5(3) + 1 = -9 +15 +1 = 5
c) Greatest height
Find the vertex of the parabole
The vertex is at the mid point between the two roots.
To find the roots you can use the quadratic equation
The result is g = 5/2 + [√29]/2 and g = 5/2 - [√29]/2
The middle poin is 5/2 = 2.5
Now find H(2.5) = -(2.5)^2 + 5(2.5) + 1 = 7.5 ≈ 7.3
hope this helps
Assume that different groups of couples use a particular method of gender selection and each couple gives birth to one baby. This method is designed to increase the likelihood that each baby will be a girl, but assume that the method has no effect, so the probability of a girl is 0.5. Assume that the groups consist of 42 couples. Complete parts (a) through (c) below.
a. Find the mean and the standard deviation for the numbers of girls in groups of 48 births.
b. Use the range rule of thumb to find the values separating results that are significantly low or significantly high.
c. Is the result of 42 girls a result that is significantly high? What does it suggest about the effectiveness of the method?
Answer:
a) [tex]\mu = 24,\sigma = 3.46[/tex]
b) Significantly low:
[tex]x < 17.08[/tex]
Significantly high:
[tex]x > 30.92[/tex]
c) 42 girls are significantly high.
Step-by-step explanation:
We are given the following in the question:
[tex]p = 0.5[/tex]
a) mean and the standard deviation for the numbers of girls in groups of 48 births
[tex]\mu = np = 48(0.5) = 24\\\sigma = \sqrt{np(1-p)} = \sqrt{48(0.5)(1-0.5)} = 3.46[/tex]
b) Range rule of thumb
Significantly low: According to this rule the observations lying below two standard deviation of mean is considered significantly low.
[tex]x = \mu - 2\sigma\\x = 24 - 2(3.46) = 17.08[/tex]
Significantly high: According to this rule the observations lying above two standard deviation of mean is considered significantly high.
[tex]x = \mu + 2\sigma\\x = 24 + 2(3.46) = 30.92[/tex]
c) Significance of 42 girls
[tex]42 > \mu + 2\sigma[/tex]
Since 42 is greater than 30.92, 42 girls are significantly high. Thus, the method is not significant.
For every positive 2-digit number, x, with tens digit t and units digit u, let y be the 2-digit number formed by reversing the digits of x. Which of the followingexpressions is equivalent to x − y ?a) 9(t − u) b) 9(u − t) c) 9t − u d) 9u − t e) 0
Answer:
a) 9(t - u)
Step-by-step explanation:
x = 10t + u
y = 10u + t
x - y = 10t + u - 10u - t
= 9t - 9u
= 9(t - u)
Ms.Perkins needs to order art supplies for the entire school.She would like to get at least 8,000 piece construction paper has 495 pieces , about how many pack will she need!
To find out how many packs of construction paper Ms. Perkins will need, divide the total number of pieces needed by the number of pieces in each pack. Using long division, we find that she will need at least 16 packs of construction paper.
Explanation:To find out how many packs of construction paper Ms. Perkins will need, we can divide the total number of pieces she needs (8,000) by the number of pieces in each pack (495). This will give us the number of packs required.
Using long division, we divide 8,000 by 495:
First, we divide 8,000 by 495 to get 16 with a remainder of 40.We then bring down the next digit, 0, making the new dividend 400.We divide 400 by 495, getting 0 with a remainder of 400.Finally, we bring down the 0, making the new dividend 4000. We divide 4000 by 495, getting 8 with a remainder of 40.Since the remainder is less than 495, we stop here. Therefore, Ms. Perkins will need at least 16 packs of construction paper.
Match each function formula with the corresponding transformation of the parent function y = –x 2 – 1. 1. y = –x2 – 1 Translated right by 1 unit 2. y = –(x – 1)2 – 1 Reflected across the x-axis 3. y = x2 + 1 Translated down by 1 unit 4. y = –x2 Reflected across the y-axis 5. y = –(x + 1)2 – 1 Translated left by 1 unit 6. y = –x2 – 2 Translated up by 1 unit
Answer:
1. f₁(x)=-x²+2x-2
2. f₂(x)=-x²+6x-10
3. f₃(x)=-x²-2
4. f₄(x)=-x²+10x-26
5. f₅(x)=-x²-2x-2
6. f₆(x)=-x²
Step-by-step explanation:
1. we have that f(x) is translated right by 1 unit , also
according to the graph f(x) has a vertex P(0,-1) then P₁ ( 1,-1) to f₁(x) therefore y-y₁ = -(x-x₁)² ⇒ y-y₁ = -(x-x₁)² ⇒ y+1 = -(x-1)² ⇒ y=-(x²-2x+1)-1 =-x²+2x-2
2. f(x) is reflected across the x-axis 3, same as in 1., P₂(3,-1) to f₂(x)
y+1 = -(x-3)² ⇒ y=-(x²-6x+9)-1 =-x²+6x-10
3. f(x) is translated down by 1 unit, P₃(0,-2) to f₃(x)
y+2 = -(x)² ⇒ y=-x²-2
4. f(x) is reflected across the y-axis 5, P₄(5,-1) to f₄(x)
y+1 = -(x-5)² ⇒ y=-(x²-10x+25)-1 =-x²+10x-26
5. f(x) is translated left by 1, P₅(-1,-1) to f₅(x)
y+1 = -(x+1)² ⇒ y=-(x²+2x+1)-1 =-x²-2x-2
6. f(x) is translated up by 1 unit, P₆(0,0) to f₆(x)
y+0 = -(x+0)² ⇒ y=-x²
Oliver read for 450 minutes this month. His goal is to read for 10% more minutes next month. If Oliver meets his goal,how many minutes will he read in all during the two months
Answer:
Oliver read in two months = 945 minutes
Step-by-step explanation:
Oliver read in this month = 450 minutes
Goal for the next month = 10 % more than this month = [tex]\frac{110}{100}[/tex] × 450
⇒ Oliver read in next month = 495 minute
⇒ Oliver total read in two months = 450 + 495 = 945 minutes
Thus Oliver read in two months = 945 minutes
Answer:
Oliver will read 945 minutes in 2 months.
Step-by-step explanation:
Given:
Number of minutes read this month = 450 mins
Percent of minutes to read next month = 10%
We need to find the number of minutes he read in two months.
Solution:
First we will find the number of minutes he read in next month.
number of minutes he read in next month is equal to Number of minutes read this month plus Percent of minutes to read next month multiplied by Number of minutes read this month.
framing in equation form we get;
number of minutes he read in next month = [tex]450+\frac{10}{100}\times 450 =450+45 =495\ mins[/tex]
Now number of minutes he read in two months is equal to sum of Number of minutes read this month and number of minutes he read in next month.
framing in equation form we get;
number of minutes he read in two months = [tex]450+495 = 945\ mins[/tex]
Hence Oliver will read 945 minutes in 2 months.
Constructing arithmetic sequences Learn Recursive formulas for arithmetic sequences(Opens a modal)Recursive formulas for arithmetic sequences(Opens a modal)Explicit formulas for arithmetic sequences(Opens a modal)Explicit formulas for arithmetic sequences(Opens a modal)Arithmetic sequence problem(Opens a modal)Converting recursive
An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. The recursive formula for an arithmetic sequence is an = a1 + (n-1)d, and the explicit formula is an = a1 + (n-1)d.
Explanation:An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. The recursive formula for an arithmetic sequence is given by: an = a1 + (n-1)d, where an is the nth term, a1 is the first term, n is the position of the term, and d is the common difference. The explicit formula for an arithmetic sequence is given by: an = a1 + (n-1)d. The explicit formula allows you to directly find any term in the sequence without having to find the previous terms.
A TRAFFIC LIGHT IS RED FOR 38 SECONDS YELLOW FOR 10 SECONDS AND GREEN FOR ONE MINUTE AND TWELVE SEONDS. IN A CONSTANTLY REPEATING CYCLE, WHAT IS THE PROBABILITY THAT AT THE MOMENT A PASSING PEDESTRIAN GLANCES AT IT, THE LIGHT WILL BE GREEN
A ball slides up a frictionless ramp. It is then rolled without slipping and with the same initial velocity up another frictionless ramp (with the same slope angle). In which case does it reach a greater height, and why
Answer:
Rolling case achieves greater height than sliding case
Step-by-step explanation:
For sliding ball:
- When balls slides up the ramp the kinetic energy is converted to gravitational potential energy.
- We have frictionless ramp, hence no loss due to friction.So the entire kinetic energy is converted into potential energy.
- The ball slides it only has translational kinetic energy as follows:
ΔK.E = ΔP.E
0.5*m*v^2 = m*g*h
h = 0.5v^2 / g
For rolling ball:
- Its the same as the previous case but only difference is that there are two forms of kinetic energy translational and rotational. Thus the energy balance is:
ΔK.E = ΔP.E
0.5*m*v^2 + 0.5*I*w^2 = m*g*h
- Where I: moment of inertia of spherical ball = 2/5 *m*r^2
w: Angular speed = v / r
0.5*m*v^2 + 0.2*m*v^2 = m*g*h
0.7v^2 = g*h
h = 0.7v^2 / g
- From both results we see that 0.7v^2/g for rolling case is greater than 0.5v^2/g sliding case.
A ball will reach a greater height when it slides up a frictionless ramp and is then rolled without slipping up another frictionless ramp with the same slope angle.
Explanation:A ball will reach a greater height when it slides up a frictionless ramp and is then rolled without slipping up another frictionless ramp with the same slope angle. This is because, when the ball slides up, it gains potential energy which is then converted to kinetic energy as it rolls up the second ramp. The ball will reach a greater height because it retains some of the initial energy it gained from sliding up the first ramp.
Learn more about Kinetic and Potential Energy here:https://brainly.com/question/11749818
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In a network of 40 computers, 5 hold a copy of a particular file. Suppose that 7 computers at random fail. Let F denote the number of computers that fail and have a copy of the file. A) What is E[F]?B) What is the range of F? C) What is the probability that F = 2?
Answer:
a. E(F)=0.875
b. 99.9976%
c. P(X=2)=0.1683
Step-by-step explanation:
a. We notice that this is a binomial distribution with the probability of success;
[tex]p=\frac{5}{40}=0.125[/tex]
#We are given the sample size, n=7. The Expected value is calculated as:
[tex]E(X)=np\\\\E(F)=np , n=7, p=0.125\\\\E(F)=7\times 0.125\\\\=0.875[/tex]
Hence the expectation, E(F)=0.875
b. To calculate the probability of the range of F, we need to calculate all possible outcomes of F in the given sample;
[tex]P(X\leq 5)=1-P(X=6)-P(X=7)\\\\=1-{7\choose 6}(0.125)^6(1-0.125)^1-{7\choose 7}(0.125)^7(1-0.125)^0\\\\=1-0.000023365-0.000000476\\\\=0.999976158\\\\=99.9976\%[/tex]
Hence, the range of F is 99.9976%
c. The probability that F=2 is calculated using the binomial distribution function as:
[tex]P(X=2)={7\choose 2}(0.125)^2(1-0.125)^5\\\\=0.1683[/tex]
Hence, the probability of F=2 is 0.1683
Using the hypergeometric distribution, it is found that:
a) E(F) = 0.875
b) The range is {0, 1, 2, 3, 4, 5}
c) 0.1741 = 17.41% probability that F = 2.
The computers are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.
Hypergeometric distribution:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes. N is the size of the population. n is the size of the sample. k is the total number of desired outcomes.In this problem:
There are 40 computers, hence [tex]N = 40[/tex].Of those computers, 7 fail, hence [tex]n = 7[/tex].5 of the computers hold a copy, hence [tex]k = 5[/tex].Item a:
The expected value of the hypergeometric distribution is:
[tex]E(F) = \frac{nk}{N}[/tex]
Hence:
[tex]E(F) = \frac{35}{40} = 0.875[/tex]
Item b:
The range is the possible values that F can assume, which is from 0 to k, hence 0 to 5.
Item c:
The probability is P(X = 2), applying the hypergeometric distribution.
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 2) = h(2,40,7,5) = \frac{C_{5,2}C_{35, 5}}{C_{40,7}} = 0.1741[/tex]
0.1741 = 17.41% probability that F = 2.
You can learn more about the hypergeometric distribution at https://brainly.com/question/25303388
Brandy set her watch 4 seconds behind and it falls behind another 1 second every day. How many days had it been since brandy last set her watch if the watch is 22 seconds behind?
Answer:
18 days
Step-by-step explanation:
Let x represent number of days.
We have been given that Brandy's watch falls 1 second every day. So Brandy's watch will fall [tex]1x[/tex] seconds behind in x days.
We are also told that Brandy set her watch 4 seconds behind, so Brady's watch will be behind by total [tex]x+4[/tex] seconds in x days.
Since Brady's watch is 22 seconds behind, so we will equate [tex]x+4[/tex] by 22 to solve for x as:
[tex]x+4=22[/tex]
[tex]x+4-4=22-4[/tex]
[tex]x=18[/tex]
Therefore, Brandy set her watch 18 days ago.
Answer:
Its been 19 days since brandy last set her watch as the watch is 22 seconds behind.
Step-by-step explanation:
We are given the following in the question:
Brandy set her watch 4 seconds behind and it falls behind another 1 second every day.
Thus, this forms an arithmetic progression.
4, 5, 6, 7, ...
First term, a = 4
Common difference, d = 1
The [tex]n^{th}[/tex] terms is 22. We have to find the value of n.
The [tex]n^{th}[/tex] terms of A.P is given by
[tex]a_n = a + (n-1)d[/tex]
Putting values, we get,
[tex]22 = 4 + (n-1)1\\18 = n-1\\n = 19[/tex]
Thus, its been 19 days since brandy last set her watch as the watch is 22 seconds behind.
In a certain game, a large container is filled with red, yellow, green, and blue beads worth, respectively, 7, 5, 3, and 2 points each. A number of beads are then removed from the container. If the product of the point values of the removed beads is 147,000, how many red beads were removed?
A) 5
B) 4
C) 3
D) 2
E) 0
Step-by-step explanation:
Below is an attachment containing the solution.
A bookcase has 4 shelves. The bottom shelf has 10 books. Each of the other shelves has 5 more books than the shelf below it. How many books are in the bookcase.
Answer:
70
Step-by-step explanation:
I need help I have no clue
Answer:
The answer to your question is x = 64; y = 20
Step-by-step explanation:
Angles 2x + 2 and 130° are vertical angles so they measure the same.
2x + 2 = 130
- Solve for x
2x = 130 - 2
2x = 128
x = 128/2
x = 64
Angles 3y - 10 and 50° are vertical angles, so they measure the same.
3y - 10 = 50
3y = 50 + 10
3y = 60
y = 60/3
y = 20
A ship departs from Port miami with 5678 tons of cargo the ship docks at the Bahamas and the uploads some cargo the crew also loads three times the quantity of cargo that was unloaded of the ship holds 8588 tons now how many tons of cargo did the ship unload at the bahamas
Answer: the ship unloaded 1455 tons of cargo at the bahamas.
Step-by-step explanation:
Let x represent number of tons of cargo that the ship unloaded at the bahamas.
The initial number of tons of cargo in the ship is 5678 tons. If it unloads x tons of cargo, the number of tons of cargo left would be
5678 - x
The crew also loads three times the quantity of cargo that was unloaded. This means that the number of tons of cargo that it loaded is 3x. The total number of tons of cargo in the ship would be
5678 - x + 3x
= 5678 + 2x
If the ship holds 8588 tons now, it means that
5678 + 2x = 8588
2x = 8588 - 5678
2x = 2910
x = 2910/2
x = 1455 tons of cargo
What is the value of X in the following parallelogram?
Answer: x = 35
Step-by-step explanation:
In a parallelogram, the opposite sides and the opposite angles are equal and parallel.
Also, the consecutive angles in a parallelogram are supplementary. This means that the sum of the consecutive angles is 180 degrees.
Angle (2x - 10) and angle (2x + 50) are consecutive angles. Therefore,
2x - 10 + 2x + 50 = 180
2x + 2x - 10 + 50 = 180
4x + 40 = 180
4x = 180 - 40 = 140
x = 140/4
x = 35
Please assist on these problems
Answer:
a) linear. Cost per minute is a constant.
b) f(x) = 40 -0.15x
d) f(100) = 25. The remaining value is $25 after using 100 minutes.
Step-by-step explanation:
a) Since the cost per minute is a constant, the remaining dollar value of the phone decreases by the same amount for each minute used. The cost as a function of minutes used is a linear function with a constant rate of change.
__
b) The value starts at $40 and decreases by $0.15 for each increment of x (minutes used). The function can be written as ...
f(x) = 40 -0.15x
__
d) Put 100 where x is in the function definition and do the arithmetic.
f(100) = 40 -0.15×100 = 40 -15
f(100) = 25
According to the variable and function definitions, x=100 means 100 minutes have been used; f(x) = 25 means the remaining value of the phone is 25 dollars.
f(100) = 25 means the phone's remaining value is $25 when 100 minutes have been used.
A company's revenue can be modeled by r=2t^2-23t+77, where r is the revenue (in millions of dollars) for the year that is t years since 2005. Predict when the revenue was or will be at 14 million
Answer:
t=2652
Step-by-step explanation:
The workers in a factory are organized into five-person teams. When conducting a work-environment survey, a researcher randomly selected 10 teams to obtain a total sample of 50 workers. The researcher used ____ sampling.
Answer:
cluster sampling
Step-by-step explanation:
ideal groups of objects are naturally chaos arranged in groups, and randomly selected. Unlike class sampling, with homogeneously arranged groups and only a few randomly selected objects from each group, in cluster sampling, each group is allocated in a chaotic and all objects in the group become part of the sample.
The measure of the seven angles in a nonagon measure 138, 154, 145, 132, 128, 147, and 130. If the two remaning angles are equal in measure, what is the measure of each angle
Answer:
The measure of each angle is 143 degrees.
Step-by-step explanation:
We are given the following in the question:
A nonagon in which measure of seven angles are:
138, 154, 145, 132, 128, 147, 130.
Angle sum property of a nonagon:
The sum of interior angles if a nonagon are 1260 degrees.Let the two equal angle of nonagon be x degrees. Thus, we can write:
[tex]138+154+ 145+132+ 128+ 147+ 130+2x = 1260\\\Rightarrow 974 + 2x = 1260\\\Rightarrow 2x = 1260 - 974\\\Rightarrow 2x = 286\\\Rightarrow x = 143[/tex]
Thus, the measure of two equal angles is 143 degrees.
Final answer:
Using the formula for the sum of interior angles of a polygon and subtracting the sum of the seven given angles from the total, we find that the remaining two equal angles in a nonagon each measure 111 degrees.
Explanation:
The measure of the seven angles in a nonagon are given as 138, 154, 145, 132, 128, 147, and 130 degrees. To find the measure of each of the remaining two equal angles, we first need to calculate the sum of the angles in a nonagon. Using the formula for the sum of interior angles (S = (n-2) × 180 degrees, where n is the number of sides), we find that a nonagon has interior angles that add up to 1260 degrees. We then sum the seven given angles and subtract this total from 1260 to find the total measure of the remaining two angles. Finally, we divide this result by 2 to get the measure of each of the two equal angles. This allows us to determine that the measure of each of the two equal angles in the nonagon is 111 degrees.
I need helpp please help me!!!
Answer:
SAS
Step-by-step explanation:
Nolini says that if the denominator is more than twice the numerator, the fraction can always be replaced with a 0. Is she correct? Give an example in your explanation.
Answer:
yes
Step-by-step explanation:
It depends on how accurate you want your answer to be, but basically yes, imagine we set our numerator to be x, and our denominator to be 2x, if we built our fraction we will get that:
[tex]\frac{x}{2x}=\frac{1}{2}[/tex]
If the denominator of a fraction is exactly twice the numerator, then the fraction will be simplified to 1/2 or 0.5.
Now, the greater the denominator is, the closer the fraction will get to zero.
Take for example I had an fraction like this:
[tex]\frac{3}{6}=0.5[/tex]
which approximates to 0. If we made the denominator bigger, let's say 7, we would get:
[tex]\frac{3}{7}=0.43[/tex]
notice the answer is closer to 0 this time, so it's valid to round it to zero. If we made the denominator greater, let's say 25, we would get:
[tex]\frac{3}{25}=0.12[/tex]
and so on. So it is true that if the denominator of a fraction is greater than twice the numerator, we can always replace the fraction with a 0 (depending on how accurate you want your answer to be).
If the denominator is more than twice the numerator, the number is therefore less than halve, 1/2 but cannot always be replaced with a 0.
An example;
Suppose we have a numerator, 2.
Then, we have a denominator which is more than twice the numerator; say 5
The resulting fraction is therefore;
2/5.The fraction 2/5 is definitely less than 1/2 but cannot always be replaced with a 0.
Read more on fractions:
https://brainly.com/question/17220365
Define a function called isSenior that takes a parameter containing an integer value and returns True if the parameter is greater than or equal to 65, and False otherwise.
Answer:
So if the parameter 's value is 7 or 803 or 141 the function returns true . But if the parameter 's value is -22 or -57, or 0, the function returns false .
My Code:
bool is Positive ( int x ) {
if ( x > 0 )
{
return true;
}
else {
return false ;
}
}
solve the following problems using 5-D process part 2
(Describe/Draw, Define, Do, Decide, and Declare)
a. The number of girls in the Spanish Club is four more than twice the number of boys. There are 61 students in the Spanish Club. Find the number of boys and the number of girls in the Spanish Club.
b. Carrie and John went bowling together. They each bowled one game. Carrie knocked down 12 more pins than John did. The sum of their bowling games was 230. What was Carrie's and John's bowling scores?
The two problems are almost identical: you have to set up a system, and then solve it.
In the first case, let [tex]g[/tex] and [tex]b[/tex] be, respectively, the number of girls and boys.
We know that [tex]g=2b+4[/tex] (the number of girls in the Spanish Club is four more than twice the number of boys). Also, we know that [tex]g+b=61[/tex] (there are 61 students in total).
So, we have the system
[tex]\begin{cases}g=2b+4\\g+b=61\end{cases}[/tex]
We can use the first equation to substitute in the second
[tex]g+b=61 \iff (2b+4)+b=61 \iff 3b+4=61 \iff 3b=57 \iff b=19[/tex]
And then solve for [tex]g[/tex]:
[tex]g=2b+4=2\cdot 19+4=38+4=42[/tex]
For the second problem, let [tex]c[/tex] and [tex]j[/tex] be the number of pins knocked down by, respectively, Carrie and John. Just like before, we have the system
[tex]\begin{cases}c=j+12\\c+j=230\end{cases}[/tex]
And you can solve it in the very same way we solved the previous one.
identify the type of function shown in the graph.
The type of Function shown in the graph
Step-by-step explanation:
1.The vertical line test can be used to determine whether a graph represents a function. A vertical line includes all points with a particular x value. The y value of a point where a vertical line intersects a graph represents an output for that input x value.
2.Different types of graphs depend on the type of function that is graphed. The eight most commonly used graphs are linear, power, quadratic, polynomial, rational, exponential, logarithmic, and sinusoidal. Each has a unique graph that is easy to visually differentiate from the rest.
3.we can represent a function using a graph. Graphs display many input-output pairs in a small space. The visual information they provide often makes relationships easier to understand. We typically construct graphs with the input values along the horizontal axis and the output values along the vertical axis.
Answer:
y= 1/2 csc (x)
Step-by-step explanation:
probably
The amount of time it takes for a student to complete a statistics quiz is uniformly distributed (or, given by a random variable that is uniformly distributed) between 32 and 64 minutes. One student is selected at random. Find the probability of the following events.
A. The student requires more than 59 minutes to complete the quiz.
Probability =
B. The student completes the quiz in a time between 37 and 43 minutes.
Probability =
C. The student completes the quiz in exactly 44.74 minutes.
Probability =
Answer:
(A) 0.15625
(B) 0.1875
(C) Can't be computed
Step-by-step explanation:
We are given that the amount of time it takes for a student to complete a statistics quiz is uniformly distributed between 32 and 64 minutes.
Let X = Amount of time taken by student to complete a statistics quiz
So, X ~ U(32 , 64)
The PDF of uniform distribution is given by;
f(X) = [tex]\frac{1}{b-a}[/tex] , a < X < b where a = 32 and b = 64
The CDF of Uniform distribution is P(X <= x) = [tex]\frac{x-a}{b-a}[/tex]
(A) Probability that student requires more than 59 minutes to complete the quiz = P(X > 59)
P(X > 59) = 1 - P(X <= 59) = 1 - [tex]\frac{x-a}{b-a}[/tex] = 1 - [tex]\frac{59-32}{64-32}[/tex] = [tex]1-\frac{27}{32}[/tex] = 0.15625
(B) Probability that student completes the quiz in a time between 37 and 43 minutes = P(37 <= X <= 43) = P(X <= 43) - P(X < 37)
P(X <= 43) = [tex]\frac{43-32}{64-32}[/tex] = [tex]\frac{11}{32}[/tex] = 0.34375
P(X < 37) = [tex]\frac{37-32}{64-32}[/tex] = [tex]\frac{5}{32}[/tex] = 0.15625
P(37 <= X <= 43) = 0.34375 - 0.15625 = 0.1875
(C) Probability that student complete the quiz in exactly 44.74 minutes
= P(X = 44.74)
The above probability can't be computed because this is a continuous distribution and it can't give point wise probability.
A rectangular prism 5 feet long by 5 feet high by 6 feet deep and wide 15 tons what was the volume of the average stone how much did it one cubic foot of the stone weigh
Answer:
One cubic foot of the stone weigh 10 tons.
Step-by-step explanation:
There is a mistake in the question, thus it is corrected:
A typical stone on the lowest level of the great pyramid in Egypt was a rectangular prism 5 feet long by 5 feet high by 6 feet deep and weighed 15 tons. What was the volume of the average stone and how much did it one cubic foot of the stone weigh?
Now, to find the volume of average stone and how much one cubic foot of stone weigh.
Dimension of rectangular prism:
Length = 5 feet.
Height = 5 feet.
Width = 6 feet.
Now, to get the volume of stone which was a rectangular prism we put formula:
[tex]Volume=length\times width\times height[/tex]
[tex]Volume=5\times 6\times 5[/tex]
[tex]Volume=150\ cubic\ feet.[/tex]
The volume of the average stone was = 150 cubic feet.
Weight of stone = 15 tons.
Now, to get one cubic foot of the stone weigh we divide the volume of the average stone by weight of stone:
The volume of the average stone ÷ weight of stone
[tex]150\div 15[/tex]
[tex]=10\ tons.[/tex]
Therefore, one cubic foot of the stone weigh 10 tons.
Two trains continuously travel between Washington D.C. and Baltimore which are 120 miles apart. The trains start simultaneously, with train A starting in Washington DC and train B starting in Baltimore, and travel at 30 and 90 mph respectively. If the station turnaround times are negligible, what is the distance between the point where the trains meet for the first time and the point where they meet for the second time?
Answer:
Step-by-step explanation:
Two train traveling in opposite direction
Distance apart the train is 120miles
Train A
Speed =30mph
Train B
90mph
What is common to the train is the same time, they will meet at the same time
Let assume they meet at distance x from from Washington
Then A has travelled x mile distance
Then, B has travelled 120-x mile distance
Time for train A to get to x,, = time for train B to get 120-x
Time=distance/speed
da/Sa=db/Sb
Let da be distance of train A
And db be distance of train B
Sa be speed of train A
Sb be speed of train B
Then,
da/Sa=db/Sb
x/30=120-x/90
Cross multiply
90x=3600-30x
90x+30x=3600
120x=3600
Then, x=3600/120
x=30miles
Then will meet at 30miles from Washington
Second part of the questions
Train B is faster than train A
Train B has already travelled 90miles while train B travels 30 miles
This shows that train A will not get to Baltimore before train B catch up
Then, let train A travel y distance
Then B will have to complete the 30 miles and then with another 30 miles that A has travel and then y
Total distance B travel will be
db=30+30+y
db=60+y
And da=y
Therefore,
da/Sa=db/Sb
y/30=60+y/60
Cross multiply
60y=1800+30y
60y-30y=1800
30y=1800
Then, y=1800/30
y=60miles
That means they will meet at 60miles from both Washington and Baltimore, or they are at mid points
a. Money market accounts
b. Single stocks
c. Bonds
d. Mutual funds
e. Fixed annuities
f. Real estate
For this assignment:
1. Put the investments in order by least risk to greatest risk. You can list by letter only (for example: a, b, c, d, e, f).
2. On a second line, order the investments by least return to greatest return. Again, you can list by letter only.
3. Review the sorted lists, and determine the one investment type you would select to start your investment portfolio. Provide a one-paragraph explanation of why you selected the investment along with your expected returns.
Answer:
Investments in order by least risk to greatest risk: A, C, E, D, F, B.
Step-by-step explanation: