Answer:
Step-by-step explanation:
Let the speed of cyclist be C and bus be B.
Using the concept of relative speed:-
For incoming bus,speed = B + C
For overtaking bus,speed = B - C
Now,distance travelled b/w 2 incoming bus = (B + C)*4
Now,distance travelled b/w 2 overtaking bus = (B - C)*12
so,
(B + C)*4 = (B - C)*12
or, B=2C
Hence,distance b/w two buses in same direction,d=4*(3/2)B=6 B
Therefore, time gap=d/B=6 minutes
Time interval between consecutive buses is 6 minutes, determined using relative speeds and given overtaking and meeting intervals.
To solve this problem, let's denote the following:
- [tex]\( v_c \)[/tex] is the speed of the cyclist.
- [tex]\( v_b \)[/tex] is the speed of the buses.
- [tex]\( t \)[/tex] is the time interval between consecutive buses.
Step-by-Step Solution:
1. Relative Speed in the Same Direction:
When a bus overtakes the cyclist, it means the bus is catching up to the cyclist from behind. The relative speed of the bus with respect to the cyclist is:
[tex]\[ v_b - v_c \][/tex]
According to the problem, a bus overtakes the cyclist every 12 minutes:
[tex]\[ v_b - v_c = \frac{d}{12} \][/tex]
where [tex]\( d \)[/tex] is the distance between consecutive buses.
2. Relative Speed in the Opposite Direction:
When the cyclist meets an oncoming bus, they are moving towards each other. The relative speed is:
[tex]\[ v_b + v_c \][/tex]
According to the problem, the cyclist meets an oncoming bus every 4 minutes:
[tex]\[ v_b + v_c = \frac{d}{4} \][/tex]
3. Setting Up Equations:
From the given information, we have two equations:
[tex]\[ v_b - v_c = \frac{d}{12} \][/tex]
[tex]\[ v_b + v_c = \frac{d}{4} \][/tex]
4. Solving for [tex]\( d \)[/tex] and [tex]\( t \)[/tex] :
Let's add these two equations to eliminate [tex]\( v_c \)[/tex]:
[tex]\[ (v_b - v_c) + (v_b + v_c) = \frac{d}{12} + \frac{d}{4} \][/tex]
[tex]\[ 2v_b = \frac{d}{12} + \frac{d}{4} \][/tex]
[tex]\[ 2v_b = \frac{d}{12} + \frac{3d}{12} \][/tex]
[tex]\[ 2v_b = \frac{4d}{12} \][/tex]
[tex]\[ 2v_b = \frac{d}{3} \][/tex]
Multiply both sides by 3:
[tex]\[ 6v_b = d \][/tex]
Now, substitute [tex]\( d = 6v_b \)[/tex] back into either equation, let's use [tex]\( v_b + v_c = \frac{d}{4} \)[/tex]:
[tex]\[ v_b + v_c = \frac{6v_b}{4} \][/tex]
[tex]\[ v_b + v_c = 1.5v_b \][/tex]
[tex]\[ v_c = 0.5v_b \][/tex]
5. Finding the Time Interval [tex]\( t \)[/tex]:
We already established that the distance between consecutive buses is [tex]\( d = 6v_b \)[/tex].
The time interval [tex]\( t \)[/tex] between consecutive buses can be found using the speed of the buses:
[tex]\[ t = \frac{d}{v_b} \][/tex]
[tex]\[ t = \frac{6v_b}{v_b} \][/tex]
[tex]\[ t = 6 \text{ minutes} \][/tex]
So, the time interval between consecutive buses is 6 minutes.
A department store has a policy of charging a 15% service change on all returned checks. If a check for $725 is returned, how much will the service charge be?
Answer:
Step-by-step explanation:
How many solutions does the system have?
x+y=3
5x+5y=15
A. Exactly one solution
B. No solutions
C. Infinity many solutions
The system has infinitely many solutions because both equations represent the same line in the coordinate plane. So C. Infinity many solutions will be the answer.
To determine the number of solutions for this system of equations, let's analyze it:
[tex]\[\left\{\begin{array}{l}x + y = 3 \\5x + 5y = 15\end{array}\right.\][/tex]
We can simplify the second equation by dividing both sides by 5:
[tex]\[x + y = 3\][/tex]
This equation is identical to the first equation in the system. So, the two equations represent the same line in the coordinate plane.
When two equations represent the same line, they have infinitely many solutions, because every point on the line satisfies both equations.
Therefore, the correct answer is:
(C) Infinitely many solutions
Complete Question:
I don’t know how to find the surface area?
Answer:
Step-by-step explanation:
its just writing teh answwer out and then solving
Answer:
The surface area of a prism is the sum of the areas of the 6 faces. That will be
the 2 squares and the other 4 rectangles.
S=2*(b*h)+4(B*H)
b and h are base and height of the squares and B and H of the Rectangles.
b=2
h=2
B=5
H=2
so
S=2*(2*2)+4(2*5)=8+40=48
-2/x^2-4 + x-1/x^2-2x
1. Identify the type of problem
2. Think of how to do this problem
3. Do the Work
4. Answer
Answer:
I need help with this too
Step-by-step explanation:
Dave owns 15 shares of ABC Mining stock. On Monday, the value of each share rose $2, but on Tuesday the value fell $5. What is the change in the value of Dave's shares?
Answer:
The change in the value of Dave's shares = $ 105
Step-by-step explanation:
Total number of shares = 15
Let initial value of a share = x
On Monday, the value of each share rose = $ 2
Now the value of each share = x + 2
Total value of 15 shares on Monday = 15 (x + 2) -------- (1)
On Tuesday the value of each share fell = $ 5
Now the value of each share = x - 5
Total value of 15 shares on Tuesday = 15 (x - 5) --------- (2)
The change in the value of Dave's shares = 15 (x + 2) - 15 (x - 5)
⇒ 15 x + 30 - 15 x + 75 = 105
⇒ Thus the change in the value of Dave's shares = $ 105
In research essays, brackets [ ] are used by writers to demonstrate when:__________.a. small changes have been made within exact quotations. b. outside resources have been cited. c. original sources have been paraphrased. d. parts of a quotation were already within quotation marks.
Answer:
A. small changes have been made within exact quotations.
Step-by-step explanation:
Brackets are pair of marks which enclose words or figures in order to separate them from the context. Thus, the use of brackets indicate that the quotation's exact punctuation has been adapted to the punctuation or grammar structure of the essay.
Genevieve wants to verify that 1/5 * (5x - 20) - 1/2 * (4x - 8) equivalent to -x which procedure can Genevieve to determine if the two expressions are equivalent?
Answer with Step-by-step explanation:
We are given that
LHS
[tex]\frac{1}{5}(5x-20)-\frac{1}{2}(4x-8)[/tex]
Using distribution property
[tex]a\cdot (b+c)=a\cdot b+a\cdot c[/tex]
[tex]\frac{1}{5}(5x)-\frac{1}{5}(20)-\frac{1}{2}(4x)+\frac{1}{2}(8)[/tex]
After multiplication we get
[tex]x-4-2x+4[/tex]
Combine like terms
[tex](x-2x)+(4-4)[/tex]
Then, we get
[tex]-x+0=-x[/tex]
Hence,verified.
Answer:D
Step-by-step explanation: I took the unit test
A fire engine starts pumping water at 9:20 am at the rate of 800 gallons per minute. Another fire engine, pumping at the rate of 1000 gallons per minute, starts at 9:30 am. At what time will the two engines have pumped the same number of gallon
Answer:
10:10 AM
Step-by-step explanation:
The first thing is to use an identical time variable for both cases, we will do it as follows:
Let t = number of minutes of pumping time of the first fire engine
Therefore, for the second fire truck it would be:
(t-10) = pumping time of the second fire engine, since it started 10 min after the first engine.
To find the value of t, we equalize the equations of the first engine and the second engine:
We know that the first one would be: 800 * t
And the second: 1000 * (t-10)
Thus
1000 * (t-10) = 800 * t
1000 * t - 10000 = 800t
1000 * t - 800 * t = 10000
200 * t = 10000
t = 10000/200
t = 50 minutes
In other words, 50 minutes after the first engine starts pumping, it equaled the second
To know the time they were matched it would be like this:
9:20 AM +: 50 = 10:10 AM
Therefore, at 10:10 AM both engines were matched.
To check the above we have to:
50 * 800 = 40000
40 * 1000 = 40000
Therefore, in that time, they were equalized.
Answer:
At 10:10 am
Step-by-step explanation:
Hi to answer this question we have to write a system of equations:
Fire engine 1: 800 mWhere m: pumping time of the engine
Fire engine 2: 1000 (m-10)Because it starts 10 minute later
So, putting together both equations:
800m = 1000(m-10)
800m = 1000m - 10000
10000 = 1000m-800m
10000= 200m
10000/200=m
50 =m (50 minutes after the first engine starts)
So, 9:20 am + 50 minutes : 10:10 am .
A smart-phone is thrown upwards from the top of a 448-foot building with an initial velocity of 48 feet per second. The height h of the smart-phone after t seconds is given by the quadratic equation h = − 16 t 2 + 48 t + 448 h=-16t2+48t+448. When will the smart-phone hit the ground?
Answer:
The smart-phone hit the ground when t = 7 s
Step-by-step explanation:
The height "h" is defined as:
h=16t^2 + 48t + 448
And, when the smart-phone hits the ground, h = 0 ft . Then,
16t^2 + 48t + 448 = 0
And this is a quadratic equation, and we can solve it using the formula for ax^2 + bx + c = 0, which is
x=[tex]\frac{-b±\sqrt{b^{2}-4ac } }{2a}[/tex]
So,
t = [tex]\frac{-48±\sqrt{48^{2} -4(-16)(448)} }{2(16)}[/tex]
t = [tex]\frac{-48±\sqrt{2304+28672} }{-32}[/tex]
And, we have two responses,
t_1 = [tex]\frac{-48+\sqrt{30976} }{-32}[/tex] and t_2 = [tex]\frac{-48-\sqrt{30976} }{-32}[/tex]
t_1 = - 4 s and t_2 = 7 s
As we know, the time is a quantity that cannot have a negative value, so, we take the result 2.
Final answer:
The smart-phone will hit the ground after approximately 3 seconds.
Explanation:
To find when the smart-phone will hit the ground, we need to determine the value of t that makes h equal to zero in the quadratic equation h = -16t^2 + 48t + 448. This equation represents the height h of the smart-phone after t seconds. To solve the equation, we can use the quadratic formula t = (-b ± sqrt(b^2 - 4ac)) / (2a). Plugging in the values a = -16, b = 48, and c = 448, we can solve for t. The positive value of t will give us the time it takes for the smart-phone to hit the ground.
Step-by-step solution:
Substitute the values a = -16, b = 48, and c = 448 into the quadratic formula: t = (-48 ± sqrt(48^2 - 4*(-16)*448)) / (2*(-16))
Simplify the expression inside the square root: t = (-48 ± sqrt(2304 + 28672)) / (-32)
Simplify further: t = (-48 ± sqrt(30976)) / (-32)
Calculate the square root of 30976: t = (-48 ± 176) / (-32)
Determine the values of t: t = (-48 + 176) / (-32) = 3 or t = (-48 - 176) / (-32) = -5
Choose the positive value t = 3 since we are interested in the time it takes for the smart-phone to hit the ground
Therefore, the smart-phone will hit the ground after approximately 3 seconds.
3 freshmen and 2 sophomores from a sorority will attend a conference. If the sorority has 12 freshmen and 9 sophomores, in how many different ways can the conference attendees be selected?
Answer:
7920
Step-by-step explanation:
12C3 × 9C2
= 220×36
= 7920
The number of different ways the conference attendees be selected is 7920 ways
What are Combinations?
The number of ways of selecting r objects from n unlike objects is:
ⁿCₓ = n! / ( ( n - x )! x! )
Given data ,
The number of fresher men in sorority = 12 fresher men
The number of sophomores in sorority = 9 sophomores
In the conference ,
The number of fresher men from sorority =3 fresher men
The number of sophomores from sorority = 2 sophomores
To calculate the number of different ways the conference attendees be selected is by using combination
So , the combination will become
Selecting 3 fresher men from 12 and selecting 2 sophomores from 9
And , the equation for combination is
ⁿCₓ = n! / ( ( n - x )! x! )
The combination is ¹²C₃ x ⁹P₂
¹²C₃ x ⁹P₂ = 12! / ( 9! 3! ) x 9! / ( 7! 2! )
= ( 12 x 11 x 10 ) / ( 3 x 2 ) x ( 9 x 8 ) / 2
= 1320 / 6 x 72 / 2
= 220 x 36
= 7920 ways
Hence , the number of different ways the conference attendees be selected is 7920 ways
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A student wants to know how his IQ of 160 stacks up with the population. Using your knowledge of IQ scores (mean=100, SD=15), how many standard deviations is his IQ score above the mean?
The standard deviation is his IQ score above the mean is found by the Z score whose value is 4.
What is the standard deviation?It is defined as the measure of data disbursement, It gives an idea about how much is the data spread out.
[tex]\rm \sigma = \sqrt{\dfrac{ \sum (x_i-X)}{n}[/tex]
σ is the standard deviation
xi is each value from the data set
X is the mean of the data set
n is the number of observations in the data set.
It is given that,
Sample average, x = 160
mean, [tex]\mu[/tex] = 100
Standard deviation, [tex]\sigma =[/tex] 15
The Z-test value is found as,
[tex]\rm Z = \frac{x- \mu}{\sigma} \\\\ Z = \frac{160-100}{15} \\\\ Z = 4[/tex]
Thus, the standard deviation is his IQ score above the mean is found by the Z score whose value is 4.
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A student with an IQ score of 160 is 4 standard deviations above the mean IQ of 100 according to the given normal distribution, where one standard deviation equals 15 points.
To calculate how many standard deviations a score is above or below the mean, you can use the formula:
Z = (X - x) / SD
Where:
Z is the Z-score, which indicates the number of standard deviations a data point is from the mean.X is the data pointx is the mean of the distributionSD is the standard deviationApplying this to the student's IQ score:
Z = (160 - 100) / 15
Z = 60 / 15
Z = 4
Therefore, a student with an IQ score of 160 is 4 standard deviations above the mean IQ, which is considered exceptionally high.
Determine whether the following sampling is dependent or independent. Indicate whether the response variable is qualitative or quantitative. A researcher wishes to compare academic aptitudes of married lawyers and their spouses. She obtains a random sample of 517 such couples who take an academic aptitude test and determines each spouse's academic aptitude.
Answer:
a) Independent
b) Quantitative
Step-by-step explanation:
We are given the following in the question:
Sample size, n = 517
Sample:
Married lawyers and their spouses.
Response variable:
Comparison of academic aptitudes of married lawyers and their spouses.
a) The given sampling is an example of independent sampling.
This is an independent sample because an individual of sample does not effect any other individual of the sample.
b) The response variable is academic aptitude. Since it is a numeric measure, it is a quantitative variable.
It is a quantitative measure because the scores can be expressed in numerical.
Answer:
The sampling is independent and the response variable is quantitative.
Explanation:
Given a random sample of [tex]517[/tex] couples
The researcher wishes to compare academic aptitudes of married lawyers and their spouses. Then, she obtains a random sample of [tex]517[/tex] such couples who take an academic aptitude test and determines each spouse's academic aptitudeAn individual of the sample will not affect any other individual of the sample.Therefore, the sampling is independent.Here, the response variable is the aptitude test.The scores of the academic test are represented in numerical form.Thus, the response variable is quantitative.Learn more about Random sample, refer:
https://brainly.com/question/16786843Altogether there were 72 slices of pizza. Twice as many slices had pepperoni compared to the the slices with just cheese. How many slice had just cheese?
Answer:24
Step-by-step explanation:
By setting up an equation c + 2c = 72, where 'c' represents cheese slices and '2c' represents pepperoni slices, and solving for 'c', we find there were 24 slices of pizza with just cheese.
To solve the problem about the number of pizza slices with different toppings, we can set up an equation based on the information given.
If 'c' represents the number of slices with just cheese, then 2c would represent the number of slices with pepperoni, because there are twice as many pepperoni slices as there are cheese slices. Since the total number of slices is 72, we can form the following equation:
c + 2c = 72
Combining like terms (c + 2c), we get 3c = 72. To find the value of 'c', we divide both sides of the equation by 3:
3c / 3 = 72 / 3
c = 24
Therefore, there were 24 slices of pizza with just cheese.
What does the Principle of Superposition tell us about relative ages of the strata in the cross-sections you were looking at? Older rocks might be found on top of younger rocks-what could cause that? Why is an igneous intrusion younger than the rocks it’s found in?
Answer:
1. The Principle of superposition states that a strata of rock is younger than the one over which it is laid.
2. The intrusion of the younger rock by the principle of cross-cutting relationship
3. The intrusion igneous rock arrived after the rock it is found in had already been in place and is stable.
Step-by-step explanation:
In geology, the Principle of superposition states that, in its originally laid down state, a strata sequence consists of older rocks over which younger rocks are laid. That is, a stratum of rock is younger than the stratum upon which it rests.
The principle of cross cutting relationships in a geologic intrusion occurrence, the feature which intrudes or cut across another feature is always than the feature it cuts across.
The reason is that based on the geologic time frame, the rock 1 which ws cut across by rock 2 was already in the geologic zone in a more steady state than rock , therefore it is older than the cutting rock 2.
Twenty people get into an elevator in a hotel with seven floors, and all of them get off at some point. How many different possibilities exist for how the people could get off the elevator?
The number of different possibilities for how the people could get off the elevator can be calculated using the concept of permutations.
Explanation:To calculate the number of different possibilities for how the people could get off the elevator, we can use the concept of permutations.
Since each person can choose one of the seven floors to get off at, and there are twenty people, we need to find the number of permutations of 20 people taken 7 at a time. This can be calculated using the formula:
P(20, 7) = 20! / (20 - 7)!
where the exclamation mark (!) denotes factorial. Evaluating this expression gives us the total number of different possibilities for how the people could get off the elevator.
The number of different possibilities for how the people could get off the elevator can be calculated using the concept of permutations.
Explanation:To calculate the number of different possibilities for how the people could get off the elevator, we can use the concept of permutations.
Since each person can choose one of the seven floors to get off at, and there are twenty people, we need to find the number of permutations of 20 people taken 7 at a time. This can be calculated using the formula:
P(20, 7) = 20! / (20 - 7)!
where the exclamation mark (!) denotes factorial. Evaluating this expression gives us the total number of different possibilities for how the people could get off the elevator.
Which statement describes the system of equations? It has infinitely many solutions. It has no solution. It has one solution . It has one solution (8, 2).
A system of equations can have no solution, one unique solution, or infinitely many solutions. A single solution indicates that the equations intersect at a point, no solution suggests parallel lines, and infinitely many solutions mean the equations are the same line expressed differently.
Explanation:When discussing a system of equations, the possible solutions include having no solution, one unique solution, or infinitely many solutions. If a system has no solution, this typically means the equations represent parallel lines that never intersect. In contrast, if there is one solution, the equations represent two lines that intersect at a single point, such as the given solution (8, 2). The presence of infinitely many solutions indicates that the equations are the same line, represented in different forms, and thus they intersect at every point along the line.
To determine which of these scenarios applies to a particular system of equations, one should begin by determining the number of unknowns and the number of equations given. A single linear equation in two variables, such as those given in Practice Test 4 Solutions 12.1 Linear Equations, represents a line. A system composed of two linear equations can be solved using algebraic methods such as substitution or elimination.
If the system consists of the same equation expressed differently, such as y = 2x + 3 and 2y = 4x + 6, then they are essentially the same line, and the system would have infinitely many solutions.
Can someone please actually help me with this?
Images Below
Answer:
65
62
Step-by-step explanation:
In inscribed quadrilaterals, opposite angles are supplementary.
First problem:
x + 148 = 180
x = 32
2x + 1 = 65
Second problem:
x + 20 + 3x = 180
x = 40
180 − (2x + 38) = 62
Evaluate A ^ 2 for A = - 3 . -9 -6 6 9
Answer:
9
Step-by-step explanation:
We want to evaluate
[tex]A^2[/tex]
for A=-3.
This means, we need to substitute A=-2, into the given equation and simplify.
We substitute to get:
[tex] A^2 = {( - 3)}^{2} [/tex]
In this case the base is -3, so it multiplies itself twice.
[tex]A^2 = {( - 3)} \times - 3[/tex]
This gives us:
[tex]A^2 = 9[/tex]
Kim is a medical supplies salesperson. Each month she receives a 5% commission on all her sales of medical supplies up to $20,000 and 8.5% on her total sales over $20,000. Her total commission for May was $3,975. What were her sales for the month of May?
Answer: her sales for the month of May is $55000
Step-by-step explanation:
Let x represent her total sales for the month of May.
Each month she receives a 5% commission on all her sales of medical supplies up to $20,000. This means that for her first sales worth $20000, she earns a commission of
5/100 × 20000 = 1000
She also earns 8.5% on her total sales over $20,000. This means that for sales over $20000, she earns
8.5/100(x - 20000) = 0.085x - 1700
Her total commission for May was $3,975. The expression becomes
1000 + 0.085x - 1700 = 3975
0.085x = 3975 + 1700 - 1000
0.085x = 4675
x = 4675/0.085
x = 55000
Kim's total sales for the month of May were $55,000. The first $1,000 of her commission came from the 5% commission on her first $20,000 in sales. The remaining $2,975 of her commission came from the 8.5% commission on her additional $35,000 in sales.
Explanation:To find out Kim's sales for the month of May, let's first understand her commission structure. She earns a 5% commission on all her sales of medical supplies up to $20,000, and 8.5% on any of her total sales over $20,000. Her total commission for the month of May is given as $3,975.
If her sales were $20,000 or below, her commission would be 5% of that, which would be $1,000 at most. Her commision is definitely more than that, we can infer that her sales were more than $20,000.
To figure out her actual sales, we need to subtract $1,000 from her total commission of $3,975, which gives us $2,975. This amount is the commission she earned at the rate of 8.5% for sales over $20,000. To find out the sales corresponding to this commission, we should divide $2,975 by 8.5% (or 0.085). That gives us the sales amount over $20,000 as $35000.
Therefore, Kim's total sales for the month are the $20,000 she sold to make the first $1,000 of her commission, plus the additional $35,000. So Kim's total sales for the month of May were $55,000.
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A boeing-747 is flying from New York City to Los Angeles. It leaves La Guardia Airport in NYC at 9:20am with an expectred arrival time at LA of 1:38pm. However, when it reaches Springfield (Illinois) which is 920 miles away from NYC, the piolets are informed that there is a storm in their path which they must avoid. In order to do so they turn 38 degrees to the right. Eventually they cleared to turn back left and return to their original flight path. They rejoin the path when they reach the four corners which is still 650 miles from LA at which point the piolets make one last turn 52 degrees to the right in order to head directly to los angeles. They arrive without futer incidents. How many minutes was the flight delayed
Answer:
I do not know sorry
Step-by-step explanation:
Rewrite the radical expression as an expression with a rational exponent. the fourth root of seven to the fifth power
Answer:
[tex]\sqrt[4]{7^5}[/tex]
Step-by-step explanation:
I apologize, I do not know how to explain this.
Answer:
7⁵/₄
Step-by-step explanation:
⁴√7⁵
The fourth root is equivalent to the power 1/4.
= 7^(1/4 * 5)
= 7^(5/4).
Every cereal box has a gift inside, but you cannot tell from the outside what the gift is. The store manager assures you that 15 of the 50 boxes on the shelf have the secret decoder ring. The other 35 boxes on the shelf have a different gift inside. If you randomly select two boxes of cereal from the shelf to purchase, what is the probability that BOTH of them have the secret decoder ring?
Answer:
3/35
Step-by-step explanation:
(15/50)×(14/49)
= 3/35 or 0.0857
Answer:
3/35.
Step-by-step explanation:
Probability (the first one selected has the decoder ring) = 15/50 = 3/10.
Probability (the second one selected has the decoder ring) = 14/49 = 2/7.
Therefore the probability that both have the ring =
3/10 * 2/7
= 6/70
= 3/35.
Note: The probabilities are multiplied because the 2 events are independent.
A soft drink company holds a contest in which a prize may be revealed on the inside of the bottle cap. The probability that each bottle cap reveals a prize is 0.2 and winning is independent from one bottle to the next. What is the probability that a customer must open three or more bottles before winning a prize
Answer:
The probability that the customer must open 3 or more bottles before finding a prize is 0.64
Step-by-step explanation:
In order for a customer to have to open at least 3 bottles before winning a prize, then the first two bottles shouldnt have a price. The probability that a bottle doesnt have a price is 1-0.2 = 0.8. Since the bottles are independent from each other, then the probability that 2 bottles dont have a prize is 0.8² = 0.64. Therefore, the probability that the customer must open 3 or more bottles before finding a prize is 0.64
Answer:
We conclude that the probability that a customer must open three or more bottles before winning a prize is P=0.64.
Step-by-step explanation:
We know that the probability that each bottle cap reveals a prize is 0.2 and winning is independent from one bottle to the next.
Therefore, we get p=0.2 and q=1-p=1-0.2=0.8.
So we will calculate the probability that the buyer will not win the prize in the first and second bottles. We get:
[tex]P=0.8\cdot0.8=0.64[/tex]
We conclude that the probability that a customer must open three or more bottles before winning a prize is P=0.64.
Xavier and his children went into a grocery store and he bought $6 worth of apples and bananas. Each apple costs $0.75 and each banana costs $0.50. He bought a total of 11 apples and bananas altogether. Determine the number of apples, x,x, and the number of bananas, y,y, that Xavier bought.
Answer: Xavier bought 2 apples and 9 bananas.
Step-by-step explanation:
Let x represent the number of apples that Javier bought.
Let y represent the number of bananas that Javier bought.
At the store, he bought $6 worth of apples and bananas. Each apple costs $0.75 and each banana costs $0.50. This is expressed as
0.75x + 0.5y = 6 - - - - - - - - - - - - 1
He bought a total of 11 apples and bananas altogether. This means that
x + y = 11
Substituting x = 11 - y into equation 1, it becomes
0.75(11 - y) + 0.5y = 6
8.25 - 0.75y + 0.5y = 6
- 0.75y + 0.5y = 6 - 8.25
- 0.25y = - 2.25
y = - 2.25/ - 0.25
y = 9
x = 11 - y = 11 - 9
x = 2
Factor the expression.
6n3 + 8n2 + 3n + 4
A. (2n2 + 1)(3n + 4)
B. (2n2 – 1)(3n + 4)
Answer:
The answer to your question is letter A
Step-by-step explanation:
Data
Factor 6n³ + 8n² + 3 n + 4
- To factor this expression, factor the common terms of the first two factors
6n³ + 8n² = 2n²(3n + 4)
- Factor 1 in the second two terms 1(3n + 4)
- Factor all the expression by like terms 2n²(3n + 4) + 1(3n + 4)
(3n + 4)(2n² + 1)
#10 FIND X, Y, AND Z!
WILL GIVE BRANLIEST
Answer:
25/6
Step-by-step explanation:
Because the line in the middle is an angle bisector, 5*10 = 12*x.
This means that 50 =12x, so 25/6 = x
Write 3.45 as a reduced mixed number.
Answer:
3 [tex]\frac{9}{20}[/tex]
Step-by-step explanation:
3.45=3 45/100
reduce and divided by 5
3 45/100= 3 9/20
Answer:
Step-by-step explanation:
add me on fortnite
#7 HELP ! WILL GIVE BRANLIEST
Answer:
x = 8, y = 4√3, z = 8√3
Step-by-step explanation:
Assuming that y is the altitude of the triangle (perpendicular to the hypotenuse), the triangles are similar. So we can write proportions:
x / 4 = 16 / x
x² = 64
x = 8
4 / y = y / 12
y² = 48
y = 4√3
z / 12 = 16 / z
z² = 192
z = 8√3
Note: after finding one side, you can also use Pythagorean theorem to find the other two sides.
It is known that a certain function is an inverse proportion. Find the formula for this function if it is known that the function is equal to 12 when the independent variable is equal to 2.
Answer:
[tex]y=\frac{24}{x}[/tex]
Step-by-step explanation:
We have been given that a certain function is an inverse proportion. We are asked to find the formula for the function if it is known that the function is equal to 12 when the independent variable is equal to 2.
We know that two inversely proportional quantities are in form [tex]y=\frac{k}{x}[/tex], where y is inversely proportional to x and k is constant of variation.
Upon substituting [tex]y=12[/tex] and [tex]x=2[/tex] in above equation, we will get:
[tex]12=\frac{k}{2}[/tex]
Let us solve for constant of variation.
[tex]12\cdot 2=\frac{k}{2}\cdot 2[/tex]
[tex]24=k[/tex]
Now, we will substitute [tex]k=12[/tex] in inversely proportion equation as:
[tex]y=\frac{24}{x}[/tex]
Therefore, the formula for the given scenario would be [tex]y=\frac{24}{x}[/tex].
ixl geometry help pls !
[tex]\bf ~\hspace{5em} \textit{ratio relations of two similar shapes} \\\\ \begin{array}{ccccllll} &\stackrel{\stackrel{ratio}{of~the}}{Sides}&\stackrel{\stackrel{ratio}{of~the}}{Areas}&\stackrel{\stackrel{ratio}{of~the}}{Volumes}\\ \cline{2-4}&\\ \cfrac{\stackrel{similar}{shape}}{\stackrel{similar}{shape}}&\cfrac{s}{s}&\cfrac{s^2}{s^2}&\cfrac{s^3}{s^3} \end{array}~\hspace{6em} \cfrac{s}{s}=\cfrac{\sqrt{Area}}{\sqrt{Area}}=\cfrac{\sqrt[3]{Volume}}{\sqrt[3]{Volume}} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]
[tex]\bf \cfrac{small}{large}\qquad \qquad \stackrel{sides}{\cfrac{3}{7}} ~~ = ~~ \stackrel{areas}{\sqrt{\cfrac{A_1}{98}}}\implies \left( \cfrac{3}{7} \right)^2 = \cfrac{A_1}{98}\implies \cfrac{3^2}{7^2}= \cfrac{A_1}{98} \\\\\\ \cfrac{9}{49}= \cfrac{A_1}{98}\implies 882 = 49A_1\implies \cfrac{882}{49}=A_1\implies 18=A_1[/tex]
Answer:
The answer to your question is 18 in²
Step-by-step explanation:
Data
Big rectangle Small rectangle
Area = 98 in² Area = ?
Height = 7 in Height = 3 in
Process
1.- Calculate the base of the big rectangle
Area = base x height
solve for base
base = Area / height
substitution
base = 98 / 7
base = 14 ni
2.- Use proportions to find the base of the small rectangle
x / 3 = 14 / 7
Simplify
x = (14)(3) / 7
result
x = 6 in
3.- Calculate the area of the small rectangle
Area = 6 x 3
= 18 in²