The probability that both Rachel and Robert are in the picture is 3/16.
The terms probability and possibility are interchangeable. It is a mathematical branch concerned with the occurrence of a random event. The value is between 0 and 1. In mathematics, the probability was introduced to predict the likelihood of events occurring.
Given that
Rachel and Robert both begin at the same point
Rachel completes a lap every 90 seconds.
Robert completes a lap every 80 seconds.
The photographer captures 1/4th of the track, centered on the starting line.
As a result, the photo captures 1/8th of the track on either side of the starting line.
The photographer captures it between 10 and 11 minutes, or 600 and 660 seconds.
Let us calculate the time interval between 600 and 660 seconds during which Rachel and Robert will be running in the quarter-length region of the track centered on the starting line. Specifically, 1/8th of the track length on each side of the starting line.
Robert will complete 1/8th of a lap in 10 seconds. So, between 630 and 650 seconds, Robert will be in the area of the ground captured by the photographer.
Rachel finishes one lap in 90 seconds. As a result, Rachel will take the starting line at the 630th second (after 7 laps).
Rachel will complete 1/8th of a lap in 90/8 seconds. So, Rachel will be in the area of the ground captured by the photographer from (630 - 90/80) seconds to (630 + 90/80) seconds.
i.e., for a duration of 90/80 seconds out of the 60 seconds both of them are in the frame captured by the photographer.
Required probability = {time window in which both Rachel and Robert are in the favorable zone}/{time window in which the photographer captures the picture}
= {90/8}/60
= 3/16
Therefore the probability that both Rachel and Robert are in the picture is 3/16
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the augusta national golf club in augusta, georgia is an 18-hole course that consists of par-3 holes, par-4 holes, and par-5 holes. a golfer who shoots par has a total of 72 strokes for the entire course. there are two more par-4 holes than twice the number of par-5 holes, and the number of par-3 holes is equal to the number of par-5 holes. find the numbers of par-3, par-4, and par-5 holes on the course.
No. of par-3 holes be represented by = 5
No. of par-4 holes be represented by = 8
No. of par-5 holes are represented by = 5
Total number of courses in the club= 18 (given in the question)
Total shot taken by golfer=72 (given in the question)
Let par-3 holes be represented by t
Let par-4 holes be represented by f
Let par-5 holes be represented by v
forming equations:
f+2=2v
t=v
f + v + t = 18
f+2=2v
f=2v-2 -(i)
t=v -(ii)
f + t + v=18
putting values from (i) and (ii)
(2v-2) + v + v=18
2v-2+2v=18
4v=18+2
4v=20
v=20/4
v=5
Number of par-5 holes=5
from (i)
f=2v-2
putting value
f=2(5)-2
f=10-2
f=8
Number of par-4 holes=8
from (i)
t=v-
putting value
t=5
t=5
Number of par-3 holes=5
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g(x)= x^2-5 9x-17 (x+1)(x-5) g(7)=
The solution for g(7) in the piecewise function g(x) = (x + 1)(x - 5) is 16
How to determine the solution for the function?From the question, we have the equation that can be used in our computation to be a piecewise function
This piecewise function is represented as g(x)
Also from the question, we have the following function that we are to compute
g(7)
This means that the value of x is 7, and we calculate g(x) when x = 7
To do this, we make use of an equation in the piecewise function, where the domain occupies x = 7
This domain is x c (2, oo)
And the function is
g(x) = (x + 1)(x - 5)
Substitute the known values in the above equation, so, we have the following representation
g(7) = (x + 1)(x - 5)
So, we have the following equation
g(7) = (7 + 1)(7 - 5)
There is no constant to add or subtract to both sides of the equation
Also, there is no factor to multiply or divide from both sides of the equation
So, we have the following representation
g(7) = (7 + 1)(7 - 5)
Solving further, we have
g(7) = 16
Hence, the solution is 16
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What is the equation of the line that passes through the point (6,-5) and has a slope of -{1}{3}?
Answer:
y = - [tex]\frac{1}{3}[/tex] x - 3
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
here m = - [tex]\frac{1}{3}[/tex] , then
y = - [tex]\frac{1}{3}[/tex] x + c ← is the partial equation
to find c substitute (6, - 5 ) into the partial equation
- 5 = - 2 + c ⇒ c = - 5 + 2 = - 3
y = - [tex]\frac{1}{3}[/tex] x - 3 ← equation of line
I don’t know the answer to this can you please help me
Answer:
The answer is 24 I think
Step-by-step explanation:
just multipy the numbers
There are 15 circles and 6 squares. What is the simplest ratio of squares to total shapes?
Answer:
2/7Step-by-step explanation:
There are 15 circles and 6 squares.
Total shapes:
15 + 6 = 21Ratio of squares to total shapes:
6/21 = 2/7Answer:
the answer is 2:7
Step-by-step explanation:
6÷3 : 21÷3
=2:7
the rabbit population in a certain area is 200%of last years population. There are 700 rabbits this year how many were there last year
Answer:
the answer is 350
Step-by-step explanation:
if it increased by 200% that means it doubled
so when x is doubled we get 700
so: 2x=700
x=700/2
x=350
help meeeeeeeeeeeeeeeeeee pleaseeee rn rnnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeeeeeeeeeeeee pleaseeee rn rnnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
a variable t follows a uniform probability distribution where t is between 0 and 8 what is the probability that the random variable has a value greater than 5?
There is a 1/3 chance that random variable will have a value higher than 5.
Define the term random variable?A random variable is called with an unknown value or a function that gives values to each of the results of an experiment. Random variables are similarly defined by letters and fall into one of two categories: continuous variables, which can take on any value within a continuous range, or discrete variables, which have specified values.For the variable t, which follows uniform probability distribution.
0 ≤ t ≤ 8
Total variables = 9.
For the probability of value greater than 5 for the random variable.
P(t > 5) = P(t = 6) + P(t = 7) + P(t = 8)
P(t > 5) = 1/9 + 1/9 + 1/9
P(t > 5) = 3/9
P(t > 5) = 1/3
Thus, there is a 1/3 chance that random variable will have a value higher than 5.
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Lat week, Lia old 20 hand-engraved watch band, earning a total profit of $105. 0. She plan to make 50 engraved watch band to ell at the community art fair. If he ell all 50 watch band, how much profit can Lia expect to earn?
$
If Lisa sells 50 watch bands, she gets a profit of $262.50.
A unitary method is defined.
Mathematicians use the unitary method to solve problems by first determining the value of a single unit, or 1, (by dividing), and then determining the necessary value by multiplying the value of the single unit.
We must first ascertain the cost of one watch band.
To determine this, we simply divide $105 by 20, which equals $5.25.
We can divide $5.25 by 50 because she sells all 50 watchbands.
50 multiplied by $5.25 equals $262.50.
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nikolai and teresa are trying to decide which restaurant they should take their friend thomas to for his birthday. nikolai wants to take thomas to a vietnamese restaurant (which serves generous portions of inexpensive but delicious food), and teresa wants to take thomas to a french restaurant (which serves expensive and beautifully presented food). to resolve the issue, they decide to flip a coin. if nikolai wins the coin toss they will take thomas to the vietnamese restaurant and the next time a friend of theirs has a birthday they will take her or him to the french restaurant teresa likes. if teresa wins the coin toss, they will go to the french restaurant first and the vietnamese restaurant later. the conflict style they used is best described as:
The conflict style they used is Collaboration.
Given, that Nikolai wants to take Thomas to a Vietnamese Restaurant (which serves generous portions of inexpensive but delicious food), and Teresa wants to take Thomas to a French restaurant (which serves expensive and beautifully presented food)
To resolve the issue, they decide to flip a coin.
If Nikolai wins the coin toss they will take Thomas to the Vietnamese restaurant and the next time a friend of theirs has a birthday they will take her or him to the French restaurant Teresa likes and If Teresa wins the coin toss, they will go to the French restaurant first and the Vietnamese restaurant later.
Here, we can see that this is a win-win situation as both can go to their favorite restaurant.
So, the conflict style they used is Collaboration. As, Collaboration generates solutions that satisfy both the parties’ needs.
Hence, the conflict style they used is Collaboration.
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(car sales) of the cars sold during the month of july, 90 had air conditioning, 102 had automatic transmission, and 72 had power steering. 7 cars had all three of these extras. 22 cars had none of these extras. 25 cars had only air conditioning, 61 cars had only automatic transmissions, and 33 cars had only power steering. 11 cars had both automatic transmission and power steering. how many cars had exactly two of the given options?
There were 58 cars sold with exactly two of the given options.
1. There were 90 cars sold with air conditioning.
2. There were 102 cars sold with automatic transmission.
3. There were 72 cars sold with power steering.
4. There were 7 cars sold with all three options.
5. There were 22 cars sold with none of the options.
6. There were 25 cars sold with only air conditioning.
7. There were 61 cars sold with only automatic transmission.
8. There were 33 cars sold with only power steering.
9. There were 11 cars sold with both automatic transmission and power steering.
Let's just count the number of cars that have exactly two of the given options:
Air Conditioning & Automatic Transmission: 25
Air Conditioning & Power Steering: 22
Automatic Transmission & Power Steering: 11
So there are 25 + 22 + 11 = 58 cars that have exactly two of the given options.
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Use the following diagram for questions 1-3.
1. Find x.
2. Find y
3. Find z
Answer:
x= 40° y= 66° z=106° ....
The value of angles are x = 40° , y = 66°, z = 106°
Since there are two parallel lines and two intersecting lines forming a triangle we will use the properties of lines and triangles to find out the value of x,y,z. First of all y = 66° because of the vertical angle theorem, which means that adjacent angles formed by the intersection of two lines are supplementary or equal to 180° degrees. The third angle of the triangle formed is 74°. Using the sum of all angles of the triangle is equal to 180° we can find the third angle of triangle x which is equal to 40°. Now z can be found using the property sum of two opposite interior angles which will come out to be 106°. Hence by this, we can find all the angles.
I hope this answer helps.
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Solve for the value of v.
123°
(2v+1)°
Step-by-step explanation:
the angles between 2 intersecting lines must be the same on both sides of either line, they are just left-right mirrored.
so,
123 = 2v + 1
2v = 122
v = 61
A rectangle has width 2x + 0.6 and width x -0.4. The perimeter of the rectangle is
51.4 cm. What are the length and width of the rectangle?
Answer:notsure
Step-by-step explanation:
Pls help/ The y-intercept of f(x)=(1.6)x is ______________________ the y-intercept of the function in the graph:
The y-intercept of f(x) = (1.6)x is (a) less than the y-intercept of the function in the graph
How to complete the blank?The equation of the function is given as
f(x) = (1.6)x
To determine the y-intercept, we set x = 0
So, we have
f(0) = 1.6 * 0
Evaluate
f(0) = 0
For the graph, we have
When x = 0, the function has a value of 1
This means that
y-intercept is 1
0 is less than 1
Hence, the y-intercept of f(x) = (1.6)x is (a) less
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3n=1/9 Find the value of n.
PLEASE HELP
Answer: n=1/27=0.037
Step-by-step explanation:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation : 3*n-(1/9)=0
Simplify 1/9
3n - 1/9 = 0
Rewrite the whole as a fraction using 9 as the denominator :
3n 3n • 9
3n = —— = ——————
1 9
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole
Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator
2.2 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
3n • 9 - (1) 27n - 1
———————————— = ———————
9 9
End of step 2
27n - 1
——————— = 0
9
Start of step 3
When a fraction equals zero ...
Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.
Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.
Here's how:
27n-1
————— • 9 = 0 • 9
9
Now, on the left hand side, the 9 cancels out the denominator, while, on the right hand side, zero times anything is still zero.
The equation now takes the shape :
27n-1 = 0
Solving a Single Variable Equation:
3.2 Solve: 27n-1 = 0
Add 1 to both sides of the equation :
27n = 1
Divide both sides of the equation by 27:
n = 1/27 = 0.037
how many different three-letter strings can be formed from the letters a, b, c, d, e (repeats allowed) if the string must contain either all vowels or all consonants?
8 strings can be formed with all vowels from a, b, c, d, e and 27 strings can be formed with all consonants from a, b, c, d and e.
What is permutation and combination?
A permutation is an orderly arrangement of things or numbers.
Combinations are a means to choose items or numbers from a collection or set of items without worrying about the items' chronological order.
The amount of two-letter words that can be created using the letters in a word, like GREAT, is an illustration of permutations: ⁵P₂ = 5!/(5-2)!
How many different ways we may write the words utilizing the vowels in the word GREAT is an example of a combination: ⁵C₂ = 5!/[2! × (5-2)!]
Given, the letters that can be used to create the required three letter word in question: a, b, c, d, e.
Total number of letters that can be used = 5
Total number of vowels in the available letters to be used = 2 ('a' and 'e')
Total number of consonants in the available letters to be used = 3 ('b', 'c' and 'd')
Case 1: A three letter word having all vowels where letters can be repeated
Here, since two letters are to put in three empty positions, the total number of ways to form this word = 2³ = 2 × 2 × 2 = 8
Case 2: A three letter word having all consonants where letters can be repeated
Here, since three letters are to put in three empty positions, the total number of ways to form this word = 3³ = 3 × 3 × 3 = 27
Thus, 8 strings can be formed with all vowels from a, b, c, d, e and 27 strings can be formed with all consonants from a, b, c, d and e.
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Help please
74°
94°
100°
106°
Answer:
106
Step-by-step explanation:
180-74=106
You can find x by looking at the corresponding angle under it and we know a straight line is 180 degrees and the other side of the x is 74 degrees then we just subtract to find the x angle
Hopes this helps please mark brainliest
Describe the sampling distribution of p. Assume the size of the population is 30,000. n 700, p 0.388 Describe the shape of the sampling distribution of p. Choose the correct answer below. O A. The shape of the sampling distribution of p is not normal because n s0.05N and np(1-p)210. O B. The shape of the sampling distribution of p is approximately normal because ns0.05N and np(1-p) <10. C. The shape of the sampling distribution of pis not normal because n s05N and np(1-p)<10 O D. The shape of the samplingdistrbution of p is approximately normal because n s0.05N and np(1 -p)210 Determine the mean of the sampling distribution of p. Round to three decimal places as needed.) Determine the standard deviation of the sampling distribution of p. Round to three decimal places as needed.)
The correct option regarding the sampling distribution of p, considering the Central Limit Theorem, is given as follows:
D. The shape of the sampling distrbution of p is approximately normal because n <= 0.05N and np(1 -p) > 10.
The mean of the sampling distribution of p is of:
0.388.
The standard deviation of the sampling distribution of p is of:
0.0184.
What is defined by the Central Limit Theorem?The Central Limit Theorem defines the distribution of the sampling distribution of sample proportions of a proportion p in a sample of size n, in which:
The mean is [tex]\mu = p[/tex].The standard deviation is [tex]s = \sqrt{\frac{p(1 - p)}{n}}[/tex]The shape is approximately normal.As long as these two conditions are respected:
[tex]n \leq 0.05N[/tex][tex]np(1 - p) > 10[/tex]The values of the parameters in this context are given as follows:
N = 30000, n = 700, p = 0.388.
Hence the conditions are:
n/N = 700/30000 = 0.0233 < 0.05.np(1 - p) = 700 x 0.388 x 0.612 = 166 > 10.Then the shape is approximately normal and option D is correct.
The mean of the distribution is of:
[tex]\mu = p = 0.388[/tex]
The standard error of the distribution is of:
[tex]s = \sqrt{\frac{p(1 - p)}{n}} = \sqrt{\frac{0.388(0.612)}{700}} = 0.0184[/tex]
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I need help like asap !!!
only numbers and decimal points
Now we have to,
→ find the required value of b.
Formula we use,
→ (AC)² = (BC)² + (AB)²
Then the value of a will be,
→ (10.5)² = b² + (3)²
→ 110.25 = b² + 9
→ b² = 110.25 - 9
→ b = √101.25
→ [ b = 10.06 in ]
Hence, value of b is 10.06 in.
Solve this system of linear equations without graphing: {5x+4y=810x−4y=46[tex]Solve this system of linear equations without graphing: {5x+4y=810x−4y=46[/tex]
The solution of given system of linear equations is x = 3.6 and y = 2.5.
A "system" of equations is a collection of equations that you answer all at once. Ax + By + C = 0, where A and B are the coefficients and C is the constant, can be used to describe a linear equation. Non-linear equations are more difficult to comprehend than linear equations.
Solving the equations,
5x +4y = 8
10x − 4y = 46
Adding the above equations, we get
5x + 10x + 4y - 4y = 8 + 46
15x=54
Dividing by 15,
x = 3.6
Now, putting the value of x in second equation,
10(3.6) - 4y = 46
36 - 4y = 46
4y = -10
Dividing by 4, we get
y = -2.5
Therefore, the solution of given system of linear equations is x = 3.6 and y = 2.5.
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Jonshelle is developing a new bread recipe. The relationship between cups of water, w, and cups of flour, f, is a=2/5b. What is the scale factor of flour to
water?
Answer: the i8 49
Step-by-step explanation:98493
Which of the
following best describes the
slope of the line below?
• A. Positive
• B. Negative
• C. Zero
• D. Undefined
Answer:
negative
Step-by-step explanation:
Translate the sentence into an inequality. The sum of a number times 3 and 23 is greater than 25.
Translation of the given sentence with variable y into inequality is given by 3y + 23 > 25.
As given in the question,
Given sentence is :
Let the number be represented by y.
The sum of y times of 3 and 23 is greater than 25.
Translation of the given sentence into inequality is given by :
y times 3 is represented by 3y
Sum of y times 3 and 23 is given by 3y + 23
Sum is greater than 25
3y + 23 > 25
Simplify the inequality we get,
3y > 25 -23
⇒3y > 2
⇒y > 2/3
Therefore, translation of the given sentence with variable y into inequality is given by 3y + 23 > 25.
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Toss one dime.
The probability of getting heads
is 1. Predict how many times
you would get heads if you
flipped the dime 200 times.
[?] times
We can get heads for 200 times if we flipped the dime for 200 times.
What do you mean by Probability?
Probability is a mathematical measurement to measure the possibility of happening a particular incident or event mathematically.
Also, from the definition of probability, Probability is the ratio of the Number of Favorable event points to the number of total event points with respect to a particular event or incident.
[tex]Probability=\frac{Number of Favorable event Points}{Number of Total event Points}[/tex]
According to the given problem,
The probability of getting heads is 1.
Total number of flip of dime is 200
so, we can get heads from 200 flips [tex]=200*1=200 Times[/tex]
Hence, we get 200 heads from 200 flips of dime.
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if the interest for 5 years on Rs 3000 is Rs 525, find the interest on Rs 2200 for 6 years at the same rate of interest.
Using the formula of simple interest, the interest on Rs 2200 for 6 years at the same rate of interest is Rs 462.
In the given question,
The given principal amount = Rs 3000
The given time = 5 years
Interest amount = 525
Now finding the rate of interest.
As we know that the formula of simple interest.
I = P*R*T/100
525 = 3000*R*5/100
Multiply by 100 on both side we get
52500 = 15000*R
Divide by 15000 on both side
R = 52500/15000
R = 3.5
In the question we have to find the interest on Rs 2200 for 6 years at the same rate of interest.
To find the interest put the value in I = P*R*T/100
As given P=2200, R=3.5%, T=6 years
I = P*R*T/100
I = 2200*3.5*6/100
I = 462
Hence, the interest on Rs 2200 for 6 years at the same rate of interest is Rs 462.
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-7 + 5x = 5x + 9 help me pls
Answer:
solve for x 7 (5x+9)=- (x-9) 7(5x + 9) = −(x − 9) 7 ( 5 x + 9) = - ( x - 9) Simplify 7(5x+9) 7 ( 5 x + 9). Tap for more steps... 35x+63 = −(x−9) 35 x + 63 = - ( x - 9) Simplify −(x−9) - ( x - 9).
Step-by-step explanation:
Rewrite 0+0+7(5x+9)= -(x----9)
Apply the distributive property. 7 (5x) + 7.9= - (x-9)
Bacteria colonies can increase by 73% every 2 days. If you start with 55 bacteria microorganisms, how large would the colony be after 10 days?
Answer:
In order to complete the equation we need to use this method :
Future Amount = I(1+r)^t
I=Initial Amount
R=Growth rate
T=Time periods
Now that we know that....
Letsss seee:
You started with 55 so
Future Amount = 55(1+r)^t
The growth rate is 73% so we have to convert to decimal so
Future Amount=55(1+.73)^t
Time period is 73% every 2 days and you want to see how large the colony would be after 10 days so you do 10/2:
Future Amount=55(1+.73)^5
Future Amount therefore equals 852.301407 BUT You have to round to the nearest whole number Sooo
The Answer is 852.Step-by-step explanation:
Hope this helpss you Tony!
Answer:
How large would the colony be after 10 days?
852 is the answer.
Step-by-step explanation:
help me pleaseeeeeeeeeeeeeeeeee !!!!!!!!!!!!!!!!!!!!!!
Step-by-step explanation:
the flight path of a rocket or a thrown object is a parabola as described by the function.
h(t) = -16t² + 40t + 7
the negative sign of the prime coefficient (-16) tells us that the parabola opens downwards, and that the vertex as the extreme point of the parabola is a maximum.
we get the extreme point of a curve by finding the zero solution of the first derivative of the function.
and the extreme value itself by using that value in the original equation and calculate the result.
h'(t) = -32t + 40
0 = -32t + 40
32t = 40
t = 40/32 = 5/4 = 1.25 seconds
h(5/4) = -16×(5/4)² + 40×5/4 + 7 =
= -16×25/16 + 10×5 + 7 =
= -25 + 50 + 7 = 32 ft
the rocket will reach its maximum height of 32 ft after 1.25 seconds.
4. The drama club is printing t-shirts for its members. The printing company chargesa certain amount for each shirt plus a setup fee of $40. There are 21 students in the drama club.
a. If there are 21 students in the club and the t-shirt order costs a total of $187, how much does each t-shirt cost? Show your reasoning.
Answer:
$7
Step-by-step explanation:
You want the cost of a shirt when the cost of 21 shirts plus a $40 setup fee is $187.
CostThe total cost of the order is the sum of the setup fee and the extended cost of the shirts.
cost = (setup fee) + (number of shirts) × (cost per shirt)
187 = 40 + 21 × (cost per shirt)
Subtracting 40 gives ...
147 = 21(cost per shirt)
Dividing by 21, we have ...
7 = cost per shirt
Each T-shirt costs $7.