The car overtakes the cyclist at a distance of 72 miles from the starting point.
,Speed is the ratio of distance travelled to time taken. It is given by:
Speed = distance / time
Let the car overtake the cyclist at distance d and time t.
For the car:
48 = d / t
d = 48t
For the cyclist:
16 = d / (t + 3)
d = 16t + 48
48t = 16t + 48
32t = 48
t = 1.5 hours
d = 48(1.5) = 72 miles
The car overtakes the cyclist at a distance of 72 miles from the starting point.
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a certain pharmaceutical company know that, on average 4% of a certain type of pill has an ingredient that is below the minimum strength and thus unacceptable. what is the probability that fewer that 5 in a sample of 20 pills will be acceptable?
Using the binomial distribution, it is found that there is a 0% probability that fewer that 5 in a sample of 20 pills will be acceptable.
For each pill, there are only two possible outcomes, either it is acceptable, or it is not. The probability of a pill being acceptable is independent of any other pill, which means that the binomial distribution is used to solve this question.
Binomial probability distribution
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes. n is the number of trials. p is the probability of a success on a single trial.In this problem:
The sample has 20 pills, hence [tex]n = 20[/tex].100 - 4 = 96% are acceptable, hence [tex]p = 0.96[/tex]The probability that fewer that 5 in a sample of 20 pills will be acceptable is:
[tex]P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{20,0}.(0.96)^{0}.(0.04)^{20} = 0[/tex]
[tex]P(X = 1) = C_{20,1}.(0.96)^{1}.(0.04)^{19} = 0[/tex]
[tex]P(X = 2) = C_{20,2}.(0.96)^{2}.(0.04)^{18} = 0[/tex]
[tex]P(X = 3) = C_{20,3}.(0.96)^{3}.(0.04)^{17} = 0[/tex]
[tex]P(X = 4) = C_{20,4}.(0.96)^{4}.(0.04)^{16} = 0[/tex]
0% probability that fewer that 5 in a sample of 20 pills will be acceptable.
A similar problem is given at https://brainly.com/question/24863377
wren is going to add an ordered pair to the table that will cause the table to no longer be a function. Which could be the ordered pair?
X Y
-3 7
-1 5
0 3
2 6
_ _
Answer:
(0,-2)
Step-by-step explanation:
20 POINTS!! PLEASE HELP DUE NOWWW!
Gia started to solve the equation 3(x − 10) − 5x = 2x − 26 below. They want to move the variables to the left side of the equation for their next step.
Fill in Line 4 and give the property.
Line 1: 3(x − 10) − 5x = 2x − 26 Original Problem
Line 2: 3x − 30 − 5x = 2x − 26 Distributive Property
Line 3: -2x − 30 = 2x − 26 Collect Like Terms
Line 4: _______________ _______________
Answer:
-4x - 30 = -26 Inverse property of addition
Step-by-step explanation:
To move the variable to the left you would subtract the 2x from both sides and you'll be left with -4x - 30 = -26. Adding the negative of a number from the same number (ex. 30 + (-30)) is called inverse property of addition. which we did here but with 2x.
There are 4 circles and 16 squares. What is the simplest ratio of circles to the total of shapes
Answer:
Not including circles in total shapes: 1 circle to every 4 squares or 1:4
Including circles in total shapes: 1 circle to every 5 shapes or 1:5
Step-by-step explanation:
16 ÷ 4 = 4
20 ÷ 4 = 5
Answer: 1:5
Step-by-step explanation:
(6y^3) - 42y= -4y^3
please helpp
Answer:
i have no clue
Step-by-step explanation:
i said this bc apparently i have to help someone to get help and i just wanna finish this math homework lol
evaluate:
16÷(2+12)2
A. 2 14/25
B. 4 1/4
C. 6 2/5
D. 8 1/4
The result of the given expression in simplest form is [tex]\frac{4}{7}[/tex].
The given parameters:
16÷(2+12)2
The given expression can be evaluated in the following order as shown below;
add the numbers in the bracket;
2 + 12 = 14
multiply the numbers in the bracket by 2;
14 x 2 = 28
divide the 16 by your result after the multiplication;
[tex]= \frac{16}{28} \\\\[/tex]
divide the numerator and denominator by their common factor which is 4;
[tex]\frac{16}{(2+ 12) 2} = \frac{16}{28} = \frac{4}{7}[/tex]
Thus, the result of the given expression in simplest form is [tex]\frac{4}{7}[/tex].
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Patrick gets an allowance of $30 per week. If he babysits his brother, his parents give him an additional $5 per hour for every hour he babysits. Which equation can Patrick use to find y, the amount of money he will have after a week in which x hours of babysitting is done?
y = 30 + 5x
y = 35x
y = 30x + 5
y = 30x
26.52 x 90.7 step by step
[tex]Hiya![/tex]
Sokka is here to help!!
Here's a explanation!
[tex]26.52[/tex] × [tex]90.7 = 2405.364[/tex]
[tex]OR:[/tex]
Here's a paper I wrote of your answer.
Sorry, if my picture is blurry.
Hopefully, this helps you!!
[tex]Sokka[/tex]
mark has a board that is 12 feet long he cuts the board into 8 peices that are the same lenght. how long is each peice
Answer: So, all you have to do is divide in this situation. He starts with a board that is 12 feet long, keep that in mind. If he cuts that into 8 pieces it's like he is dividing. So 12 divided by eight or 12/8 would be 1.5. Your answer is that each piece would be 1.5ft long.
Write a story that could represent this math problem 4 x 10/15 =
Mathew decided to have a picnic with his 4 friends. They were each assigned to bring 10 different foods. The food were to be brought in 15 bags total. How much food are there in each bag in total?
Anita plans to give her husband 3 shirts for his birthday. She narrows the search to 3 shirts from a selection of 17 shirts at Dillon's Store or 3 from a selection of 20 shirts at The Men's Shop. In how many ways can she select the shirts
Using the combination formula, it is found that she can select the shirts in 775,200 ways.
The order in which the shirt are chosen is not important, hence, the combination formula is used to solve this question.
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:
3 shirts from a set of 17.Then, 3 shirts from a set of 20.They are independent, hence, to find the total, we multiply both combinations.[tex]T = C_{17,3} \times C_{20,3} = \frac{17!}{3!14!} \times \frac{20!}{3!17!} = 680 \times 1140 = 775200[/tex]
She can select the shirts in 775,200 ways.
To learn more about the combination formula, you can check https://brainly.com/question/25821700
Solve 3x3-6. Graph the solution.
A)
B)
C)
D)
PLEASE HELLPPPPPP IDONTKNOWTHISSS
Solve this system of equations using the Substitution method. Don't forget to write your final answer as a coordinate point. You must show all your work.
3x + y = -2
y = 2x + 3
= 3x+y=-2
= Linear equations with two variables have multiple infinite solutions.
= Assuming x=0
then y=-2
= Assuming x=1
then y=-2-3
= y=-5
= Assuming x=2
then y=-2-6
= y=-8
Writing them as coordinate points -
(0,-2),(1,-5),(2,-8)...and so on.
__________________________.
= y=2x+3
Assuming x=0
then y=3
Assuming x=1
then y=2+3
= y=5
Assuming x=2
then y=4+3
= y=7
Writing them as coordinate points -
(0,3),(1,5),(2,7)...and so on.
Answer:
Point Form:
( − 1 , 1 )
Equation Form:
x = − 1 , y = 1
Step-by-step explanation: there you go
Luis and Erin are playing a game. They each start with 0 points. At the end of the game, Luis has 250 points, and Erin has -250
Which statement about the game is true?
A. Erin and Luis have a total of 500 points.
B. Erin has lost 250 points.
C. Luis has 250 more points than Erin.
D. Erin and Luis have an equal number of points.
Answer:
B
Step-by-step explanation:
- The line AB has equation 5x – 2y = 7. The point A has coordinates (1, -1) and the point B has coordinates (3,k). (a) (i) Find the value of k. (ii) Find the gradient of AB. (b) Find an equation for the line through A which is perpendicular to AB. (c) The point C has coordinates (-6, -2). Show that AC has length pV2, stating the value of p.
Step-by-step explanation:
For finding k we'll have to plug in the x-value of the coordinate (3,k) into the equation, and solve for the y:
5(3) - 2y = 7
15 - 2y = 7
2y = 8
y = 4 => k =4
2) I assume the gradient is the slope of the line. If so, just isolate the y in the original equation and see what's the coefficient of the x:
-2y = -5x + 7
y = (5/2)x + 7/2 => the gradient is 5/2
3) the condition of perpendicularity is expressed by the following relation:
a * a' = -1
Where a is the slope of the first line and a' of the second line. We need to find a' that will be:
-1/a = -1/(5/2) = -2/5
The perpendicular line will be:
y = (-2/5)x + b
We need to find b, and we know that this line passes through A (1,-1):
-1 = (-2/5)*1 + b
b = -1+(2/5) = -3/5
The equation will be:
y = (-2/5)x - 3/5.
4) I don't know what that symbol means (pV2).
Describe the functions plz and thank u<3also 50pts
Answer:
See belowStep-by-step explanation:
Given function:
y = 1/2|x + 3| + 2This is a transformation of the absolute value function y = |x|.
The transformations are:
1. Dilation by a scale factor of 1/22. Translation left by 3 units3. Translation up by 2 pointsThe locator point is the vertex: (-3, 2)
Domain is any value: x = (- ∞, + ∞)
Range is anything not less than 2: y ≥ 2 or y = [2, + ∞)
See the graph attached
Use long division to solve 38 divided by 4
If you know how to set up the format for long division, the answer is 9.5 because 4 goes into 3 zero times, and you don't necessarily need to write down the zero on top since it equals nothing in a whole number. then, 4 goes into 38 nine times. (yes 38 because you didn't do anything with the 3 so you just make it 38) 4 × 9 = 36. it doesn't exactly make 38, so you take away 36 from 38 and you are left with a remainder of 2. then to get no remainder, add a zero to the end of 38. so it would look something like 4/380 so you take down the zero next to the 2 so it makes 20, 4 × 5 = 20 and you are left with a remainder of 0 and the answer: 9.5 ( P.S.: added the decimal because it wasn't exactly equal when doing 4 × 9 so we had to add a zero)
help please
No links
Answer:
62-0.75x8
Step-by-step explanation
$6=discount
8 tickets
Total=62.00
0.75 multiplied by 8= 6
62-6=56
56 is before the discount
Equation would be 62-0.75x8
f(x)=5x+4, g(x) square root of x find the domain of gof
Multiply and write in standard form:
(2x + 1)(5x - 2)
Show all work for full credit.
Answer:
10x^2+x-2
Step-by-step explanation:
(2x+1)(5x-2)
10x^2+5x-4x-2
10x^2+x-2
The following stock prices reflect the closing price for the past five days. Find the 3 day SMA
(Simple Moving Average) for days 2-4.
$44.25, $44, $41.75, $40, $39.75
Answer:
solution
Step-by-step explanation: total=209.75
2. Which expression is equivalent to 3ly-6)?
A. 3y - 6
B. 2y - 18+y
c. 5y + 18-2y
D.2y-18-5y
Answer:
pyfoydoye9ye9ye9ts8ts9teo5e
Mr. Henry planted 15 mango trees in his garden this morning. That is 25% of
the trees he is going to plant. How many mango trees is he going to plant in
all
The camp cook needed 2172 ounces of juice each day each carton of juice contains 64 ounces the Cook estimated that he needed 30 cartons of juice each day which expression proves that his estimate is incorrect
Answer: 384
Step-by-step explanation:
which expression has the same value as tan (-45degrees)?
Answer: B
Step-by-step explanation:
Trust
What is the prime factorization of 32?
A. 32 = 2 x 4x4
B. 32 = 2x2x2x2x2
C. 32 = 2x2x2x2
D. 32 = 2 * 2 * 2 * 4
Answer:
2nd option
Step-by-step explanation:
Repeatedly divide by 2 until the value 1 is reached
32 ÷ 2 = 16
16 ÷ 2 = 8
8 ÷ 2 = 4
4 ÷ 2 = 2
2 ÷ 2 = 1 ← finish here
Then
32 = 2 × 2 × 2 × 2 × 2
How do I multiply minted numbers? Please explain step by step to get marked as brainliest
Answer:
Step-by-step explanation:
Solve for x: one over four (4x + 15) = 24
A: 45
B: 207/4
C: 81/4
D: 9
Answer:
[tex]C. x = \frac{81}{4} = 20.25[/tex]
Step-by-step explanation:
[tex]\frac{1}{4}\left(4x+15\right)=24[/tex]
[tex]\mathrm{Multiply\:both\:sides\:by\:}4[/tex]
[tex]4\cdot \frac{1}{4}\left(4x+15\right)=24\cdot \:4[/tex]
[tex]\mathrm{Simplify}[/tex]
[tex]4x+15=96[/tex]
[tex]\mathrm{Subtract\:}15\mathrm{\:from\:both\:sides}[/tex]
[tex]4x+15-15=96-15[/tex]
[tex]\mathrm{Simplify}[/tex]
[tex]4x=81[/tex]
[tex]\mathrm{Divide\:both\:sides\:by\:}4[/tex]
[tex]\frac{4x}{4}=\frac{81}{4}[/tex]
[tex]Simplify[/tex]
[tex]x=\frac{81}{4}[/tex]
It is for my final, please help!
Answer:
The answer will be the third one.
Step-by-step explanation:
Hope it helps
Please help………………………
Answer:
= 180
y = 34
is the answer