A group of 20 friends are going to travel to a school reunion together, 7 of them can drive. They have a 7 seat car (1 driver and 6 passengers), a 5 seat car (1 driver and 4 passengers) and the remaining 8 will take a bus. How many ways can the friends travel (ignoring passenger seat positions within each vehicle)? Give an exact answer, do not round. Do not include commas or dots in your answer.
Using the combination formula, it is found that there are 99768240 ways in which they can travel.
The passenger seat positions are not important, which means that the order is not important, which is why the combination formula is used.
Combination formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this problem:
In the first car, 7 of the 20 friends are going to sit.In the second, 5 of the remaining 13 are going to sit.In the bus, the remaining 8.The, the number of ways is given by:
[tex]N = C_{20,7}C_{13,5}C_{8,8}[/tex]
[tex]N = \frac{20!}{7!13!} \times \frac{13!}{5!8!} \times \frac{8!}{0!8!} = 99768240[/tex]
There are 99768240 ways in which they can travel.
A similar problem is given at https://brainly.com/question/24437717
XIn is getting an estimate from a printer for flyers for the drama club. Xin orders color prints and negotiate a 10% discount on the print job for the drama club. If f represents the number of flyers XIn order, does 0.10(17.5+0.20f) represent the total cost of the print job? Why or why not?
Answer:
Yes.
Step-by-step explanation:
10% is 0.10 in decimal form. Therefore, once he pays the $17.80 setup fee and then 0.20f (or $0.20 per flyer), then we would multiply by 10% (Or 0.10).
In conclusion:
Yes. 0.10( 17.50 + 0.20f ) does represent the total cost of the print job.
Help me please!!! It’s due at 11:59
Answer:
18
Step-by-step explanation:
Let the required number be x.
Step 1write the expression for the difference of the number and 4.
=> x - 4
Step 2the question equates 5 times the difference with some other terms, so find the equation for 5 times the difference.
=> 5( x - 4)
Step 3The equation in Step 2 is said to be equal to "two less than four times the number".
Find the expression for four times the number
=> 4x
Step 4Find the expression for two less than 4x.
=> 4x - 2
Step 5Equate the terms that it says are equal:
=> 5(x - 4) = 4x - 2
distributing 5 within the parenthesis:
=> 5x - 20 = 4x - 2
taking like terms on one side:
=> 5x - 4x = 20 - 2
(the sign carried by the terms get inverted while changing their sides)=> x = 18
and x was the required number, so the answer Is 18.
Work out the volume of the frustrum please
Answer:
3744:\p=11756.16 m^2
Step-by-step explanation:
[tex] {12}^{2} \pi(18 + 9) - {4}^{2} \pi \times 9 = 3744\pi \: \: {m}^{2} [/tex]
write the equation of the line that is parallel to y=2x+1
Answer:
y = 2x, y = 2x+2, y=2x+100, y=2x-57, etc.
Step-by-step explanation:
Any line with the same slope will be parallel.
Help please if you can!!!!!!!!!!!!!!!
Answer:
559.41 miles/hour
Step-by-step explanation:
Just use a calculator
A manager started a meeting with his staff at 9:30.The meeting ended at 10:25.How long did the meeting last
How long the meeting last = End time - Starting time
= 10:25 - 9:30
= 9:85 - 9:30 [I converted 10:25 to make it easier to see the
subtraction. This is posibble because 1hr = 60mins]
= 55 mins
write the log equation as an exponential equation. you do not need to solve for x.
Answer:
[tex]5^{1/6} =2x[/tex]
Step-by-step explanation:
Log and exponential forms are inverses. Additionally, the information from one can be used to write in it another form. In a log equation, there are three parts. The formula is [tex]log_{b}(x)=y[/tex]. The formula for exponential equations is [tex]b^y=x[/tex]. This means to find this equation in exponential form write 5 as the base, 1/6 as the power, and 2x as the other side of the equation. This looks like, [tex]5^{1/6} =2x[/tex].
I need help please there are three more questions after that and they are 7/10+2/5+3/4
NUMBER 2: 3/4+7/8+5/6 NUMBER 3: 3/5+7/8+3/10
Answer:
1. 19/21 which is closest to 1
2. 1 hour , 1 hour , 2 hours
3. 19/21
4. 11/15
5. second statement is correct ( should be
closer to 1/2)
6. 7/10+2/5+3/4= 37/20
7. 3/4 +7/8+5/6= 59/20
8. 3/5 + 7/8+3/10= 71/40
what has the same value as 0.45
Answer:
9/20 or 45%
Step-by-step explanation:
Step-by-step explanation:
WHY IT IS SAYING YO WRITE AT LEAST 20 CHARACTERS
OHH, IT IS ALREADY 20 CHARACTERS
Write an equation of a line that passes through the point T ( − 2, − 5 ) and is parallel to the line y = 5 x + 7 .
Answer:
y = 5x + 5
Step-by-step explanation:
the slope to be parallel y = 5x + 7 must still be 5. To make the line pass through T, the given point, you plug (-2, -5) into the y= mx + b formula. This becomes( -5 )= 5 (-2) + B, and you solve for b. In this equation, b = 5.
what is an equation of the line in the slope- intersepct is (0,3)
Answer:
using the formula x/a + y/b =1
a: slope intercept on the x axis
b:slope intersect on the y axis
x/0 + y/3 = 1 (since x/0 is undefined ,the slope doesn't exist and it is impossible for a slope to be linear)
Suppose the water level of a river is 34 feet. It recedes 1/2 foot a day. What is the equation you could use to calculate the water for a specific day?
[tex]Answer : 34-\dfrac{1}{2} n \ \ ; \ \ \rm where \ n \ is \ the \ number\ of \ days[/tex]
Answer:
f(x) = -1/2x + 34Step-by-step explanation:
This is a linear relationship.
Using the slope intercept form:
y = mx + bGiven:
The y-intercept is b = 34The slope is m = -1/2The equation is:
f(x) = -1/2x + 34, where x is the number of daysFind the slope and y-intercept for a line passing through the following two points, then create a slope intercept equation.
(5,3) and (4,5)
Slope=
Y-intercept=
Slope intercept equation=
Answer:
Slope = -2
Y-intercept = 13
y = -2x + 13
Step-by-step explanation:
(5-3)/(4-5) = 2/-1 = -2
3 = -2(5) + b
3 = -10 + b
b = 13
y = -2x + 13
What is 5x-7=-10x+8
subtract 5 from both sides -
5x - 7 = -10x + 8
-5 -5
-7 = -15x + 8
subtract 8 from both sides -
-7 = -15x + 8
-8 -8
-15 = -15x
now divide both sides by -15 -
-15/-15 = -15x/-15
The answer: x = 1
(x alone also equals 1)
hope this helps! :)
Dr. Reyes is examining whether exercise is linked to mood. She recruits a sample of college students and asks them to answer whether they exercised at least three times last week (yes or no) and to rate their mood in the last week (1: Not happy at all to 5: Very happy). Her results show that students who exercised in the last week also reported happier moods. Can Dr. Reyes make a causal inference from her study
The answer to whether Dr. Reyes can make a causal inference from the study is;
No, she can't make a casual inference from the study because she met only one of the three criteria's for causality.
To answer this question, we need to know the conditions for causality in statistics research because causality gives the relationships such that a change in one variable would have to result in a change in another variable.
Now, the three conditions are;
1) Covariation; This condition means that the causal variable must have to vary with with the variable it is assumed to cause in a systematic manner.
2) Temporal precedence; Thus condition simply means that cause must precede effect. In summary it denotes that the variable that has the causal effect must come before the effect that it is meant to cause.
3) Control for extraneous variables; This condition means that results of an experiment or research must not be due to factors outside of the experiment/research
Now, in our question, he fulfilled the covariation condition because the
result of the research is tied to the responses from the sample students.
However, she did not fulfill the temporal precedence because the cause of
their moods did not precede the effects in his research.
Also, she did not fulfill the condition of control of extraneous variables
because other factors outside of the research itself may have affected their
moods.
Read more at; https://brainly.com/question/10811163
ind all natural numbers n such that 1+3+5+7+...+(2n-1) sum is divisible by 4
Answer:
All even natural numbersStep-by-step explanation:
This is an AP with:
The first term = 1Number of terms = nCommon difference = 2Find the sum of the first n terms:
[tex]S_n= n(1+2n-1)/2=n^2[/tex]The sum is divisible by 4 if n is even number:
n = 2k ⇒ n² = 4k² ≡ 0 mod 4
WILL GIVE BRANLIEST TO RIGHT ANSWER
Answer:
4x + 28
3x - 30
24x + 30
14x - 7y
Step-by-step explanation:
Use M a t h w a y to solve
Can y’all help me with all of these
Please, help me in this!
222 inches times 45 inches equals how many ft ?
Answer:
9990 inches
Step-by-step explanation:
Answer:
9990 in²
Step-by-step explanation:
Simple multiplication: 222 × 45 = 9990
To check your work either divide 9990 with 45 OR 222
Increase the following amount by the percentage given
55 by 137%
Answer:
130.35
Step-by-step explanation:
https://percentages.calculators.ro/22-number-increased-with-percentage-of-its-value.php?number=55&percentage_increase=137&new_value=130.35
A team of explorers on an expedition was interrupted by bad weather on 20% of the days. If the weather was bad for 45 days, what was the total number of days the team was on its mission?
Answer:
a total of 9 days
Step-by-step explanation:
20% of 45 is 9
answer
=9days
step by step explanation
20% is always over 100,so you are to do 20 over a hundred of 45 days....since 45 can't divide 100 do 20
[tex] \times [/tex]
45 divide by one hundred and the final answer will be 9
*20 points* 7x + 24 = 2x - 6 How many solutions?
Answer:
x= -6
Step-by-step explanation:
so i'm thinking 1 solution.
(let me know if i'm wrong)
Answer:
infinitely many solutions.
Step-by-step explanation:
If solving an equation yields a statement that is true for a single value for the variable, like x = 3, then the equation has one solution. If solving an equation yields a statement that is always true, like 3 = 3, then the equation has
These triangles
are congruent
by the triangle
congruence
postulate [? ]
A. SAS
B. SSS
C. Neither, they are not congruent
Answer:
B-SAS
Step-by-step explanation:
Was right on acellus
Emiliano earned $50 in July. He earned $70 in August. What is the percent increase or decrease in Emiliano's monthly earnings? A. 40% increase O B. 29% increase C. 40% decrease D. 20% decrease
Answer:
the answer is 40% increase
Identify the initial condition and the rate of change
a = b − 21
In the given expression :
a = b - 21rate of change = 1
Initial condition = - 21
Answer:
Option BStep-by-step explanation:
Given relationship:
a = b - 21It could be shown as:
a = 1*b + (-21)The rate of change is 1 and the initial condition is -21.
Correct choice is B
Solve x please!!!!!!!
Answer:
X=7
Step-by-step explanation:
These are supplementary angles. So they measure to 180º. 180º-95º=85º. 85º-10= 84º. 84º÷12x= 7.
Answer:
12x+1°+95°=180° (int angles)
12x+96°=180°
12x=180°-96°
=84°
x=84÷12
=7
What is the equation of a line through point (-12,20) that is perpendicular to the line
with equation y=-6x + 4?
Find the slope of the perpendicular line
When two lines are perpendicular, the product of their slopes is -1. This means that the slopes are negative-reciprocals of each other.
⇒ if the slope of one of the lines = - 6
then the slope of the perpendicular line (m) = ¹/₆
Determine the equation
We can now use the point-slope form (y - y₁) = m(x - x₁)) to write the equation for this line:
⇒ y - 20 = ¹/₆ (x - (-12))
∴ y - 20 = ¹/₆ (x + 12)
We can also write the equation in the slope-intercept form (y=mx+c) like the equation in the question by making y the subject of the equation and expanding the bracket to simplify:
since y - 20 = ¹/₆ (x + 12)
y - 20 = ¹/₆x + 2
y = ¹/₆x + 22
∴ the slope-intercept equation of the perpendicular line is y = ¹/₆ x + 22.
To test my answer, I have included a Desmos Graph that I graphed using the information provided in the question and my answer.
Divide. Round to the nearest tenth
2.29 divided by 3.5
Answer:
yes
Step-by-step explanation:yes
2.29 divided by 3.5
= 0.6542857143
and
rounded to the nearest tenth
= 0.7
Hope this helped you- have a good day bro cya)