Answer:
10/21
Step-by-step explanation:
Probability = Expected outcome/total outcome
If he randomly checks the IDs of 5 of the 9 students in the establishment, the total outcome will be expressed as:
9C5 = 9!/4!5!
9C5 = 9×8×7×6×5!/5!×24
9C5 = 9×8×7×6/24
9C5 = 126
Total outcome = 126
For the expected
First we know that 4out of 9 students are minor, and we want to know the probability that exactly 2 are minor, this can be done in 4C2 ways
4C2 = 4!/2!2!
4C2 = 4×3×2/4
4C2 = 6
Also since 4 out of 9 are minor, then 5 are not minor and if out of every 5, exactly two are minor, then 3 are not.
Those not minor can be expressed in 5C3 ways
5C3 = 5!/2!3!
5C3 = 5×4×3!/2×3!
5C3 = 20/2
5C3 = 10
Total expected outcome = 4C2 × 5C3
Total expected outcome= 6×10 = 60
Hence, the probability a server will refuse to serve alcoholic beverages to exactly 2 minors will be;
= 60/126
= 30/63
= 10/21
Hannah's restaurant bill had $20. She left a $3 tip. What percent of the bill did Hannah leave as a tip?
A.) 3%
B.) 12%
C.) 15%
D.) Not Here
Write an equation in the form of y=kx for the graph below. (k=y/x) K is in decimal
Form
Answer:
k = 3.5
Step-by-step explanation:
From the graph in the picture attached,
Relation between balloons height (y) is directly proportional to the time (x)
y ∝ x
y = kx
Where 'k' is a proportionality constant.
Now we substitute the point (8, 28) in the equation,
28 = k(8)
k = [tex]\frac{28}{8}[/tex]
k = 3.5
k ≈ 3.5
Therefore, value of constant 'k' is 3.5
A simple random sample of 11 observations is derived from a normally distributed population with a known standard deviation of 2.2 Compute the margin of error with 95% confidence Compute the margin of error with 90% confidence.
Answer: 7.1% and 6%.
Step-by-step explanation:
Given data:
Sample size (n) = 11
Standard deviation = 2.2
Margin of error confidence level 95% = 1.96
Margin of error confidence level of 90% = 1.65
Solution:
P = 2.2/11
= 0.2.
ME = z √p (1-p)/n
at 95% interval
ME = 1.96 * √ 0.2 ( 1 – 0.2 ) / 11
= 1.96 * 0.03636
= 0.071.
= 7.1%
At 90% interval
ME = 1.65 * √ 0.2 ( 1 – 0.2 ) / 11
= 1.65 * 0.03636
= 0.06.
= 6%
4. (10 points)A lighthouse is located on a small island 4 mi away from the nearest point P on a straight shoreline and its light makes ten revolutions per minute. How fast (in mi/min) is the beam of light moving along the shoreline when it is 4 mi from P
Answer:
The beam of the light is moving along the shoreline at the rate of [tex]\mathbf{ 160 \ \pi \ mi/min}[/tex]
Step-by-step explanation:
From the given information: Let say x is the distance between the lighthouse and the shoreline. Then, the tangent of trigonometry can be written as:
[tex]tan (\theta )=\dfrac{x}{4}[/tex]
In respect to time, the expression can be derived as:
[tex]sec^2 (\theta) \dfrac{d \theta}{dt} = \dfrac{1 }{4}\dfrac{dx}{dt}[/tex]
[tex]\dfrac{dx}{dt}=\dfrac{4}{cos ^2 (\theta) }\dfrac{d \theta}{dt}[/tex]
To estimate the value of [tex]\dfrac{dx}{dt}[/tex], we need to know cos²(θ) and D
where;
D = [tex]\sqrt{4^2+4^2}= \sqrt{32}\ mi[/tex]
[tex]cos (\theta) = \dfrac{4}{D}[/tex]
[tex]cos (\theta) = \dfrac{4}{\sqrt{32}}[/tex]
[tex]cos (\theta) = \dfrac{4}{\sqrt{16 \times 2}}[/tex]
[tex]cos (\theta) = \dfrac{4}{4 \sqrt{\ 2}}[/tex]
[tex]cos (\theta) = \dfrac{1}{ \sqrt{\ 2}}[/tex]
[tex]cos ^2 (\theta)= \dfrac{1}{2}[/tex]
Finally, we substitute the value of [tex]cos^2(\theta)[/tex] and [tex]\dfrac{d \theta}{dt}[/tex] in the expression derived earlier.
i.e.
[tex]\dfrac{dx}{dt} = \dfrac{4}{\dfrac{1}{2}}\times 10 \ rev/min[/tex]
where;
10 rev/min = (10 × 2π) rad/min = 20π rad/min
Then:
[tex]\dfrac{dx}{dt} = \dfrac{4}{\dfrac{1}{2}}\times 20 \ \pi[/tex]
[tex]\mathbf{\dfrac{dx}{dt} = 160 \ \pi \ mi/min}[/tex]
Calculate and express your answer in decimal form
Need help asap
(1.) 20.4
(2.) 150
(3) 8
(4.) 15
(01.02)
Given that f(x) = -x + 4 and g(x) = -2x - 3, solve for f(g(x)) when x = 2.(1 point)
please hurry
Solve for t: 5t - 4 = 11
Answer:
t=3
Step-by-step explanation:
5t-4=|11
+4 |+4
5t= | 15
÷5 | ÷5
t = 3
find the mean of the following : 158, 213, 107, 213, ,213, if needed round to the nearest tenth.
A 181
B 180.8
C 107
D 213
Answer:
the correct answer is 180.8. i saw that other ppl had this answer on brianly but had 0 star ratings even though they were correct.
Step-by-step explanation: i just took this test and trusted the person who ansered and got it wrong.
3x + 2y = 8 ( in y=mx+b form $
Answer:
y =-3/2x+4
Step-by-step explanation:
simple
A pair of shoes are on sale for 30 percent off the original price of 49.95 how many is the discount in dollars
Answer:
14.98
Step-by-step explanation:
I used a calculater
Determine whether the data shown is DISCRETE or CONTINUOUS.
Answer:
Option (b)
Step-by-step explanation:
From the graph attached in the figure,
Graph (a) is a scatter plot of a data set.
Data in this graph is not connected. In other words, a scatter plot represents a discrete function.
Similarly, in the graph (b) there is a straight line.
All points lying on this straight line are connected and follow the same rule.
Therefore, graph (b) represents a continuous function.
Therefore, Option (b) is the correct option.
PLEASE PLEASE PLEASE HELP!!!! A lot of points! Will mark brainliest and leave thanks on all of your answers if it's correct!
The LCM(12, 15, 20, k) = 420. What is the least possible value of k?
Answer:
add them all up and subtract 420 from 15+20+12!
Step-by-step explanation:
hope this helps
PLEASE HELP ME OUT ILL GIVE 15 POINTS PLUS BRAINLIST FOR CORRECT ANSWER ITS MULTIPLE CHOICE
Answer:
The first picture is a function. The second picture is not a function.
Step-by-step explanation:
The first one is a function because no x-values repeat. Different x-values can be paired with the same y-function.
The second one is not a function because it fails the horizontal line test. The line would touch in two spots, therefore failing the line test.
ALL SMART PEOPLE OR PEOPLE COME AND HELP ILL MARK BRAINLIEST AND ITS EXTRA PTS SO HURRY
Answer:
y=5/4x+-2, and y=-4/1x+3
Step-by-step explanation:
Find the volume of the solid lying under the plane z 2x 5y 1 and above the rectangle x, y 1 x 0 1, .
Answer:
The volume [tex]V = \frac{75}{2}[/tex] units
Step-by-step explanation:
From the question we are told that
The equation of the plane is [tex]z = 2x + 5y + 1[/tex]
The range of the rectangle on the x and y axis is [tex]\{ (x, y) | -1 \le x \le 0 , 1 \le y \le 4 \}[/tex]
Generally the volume is mathematically represented as
[tex]V = \int\limits^{4}_{1} \int\limits^0_{-1} {z} \, da[/tex]
Here stands for the area of the solid
So
[tex]V = \int\limits^{4}_{1} \int\limits^0_{-1} {(2x + 5y + 1 )} \, dxdy[/tex]
[tex]V = \int\limits^{4}_{1} [{(\frac{2x^2}{2} + 5xy + x )} ] | \left \ 0} \atop {-1}} \right. \, dy[/tex]
[tex]V = \int\limits^{4}_{1} [{(x^2 + 5xy + x )} ] | \left \ 0} \atop {-1}} \right. \, dy[/tex]
[tex]V = \int\limits^{4}_{1} [{((0)^2 + 5(0)y + (0) )} ] -[{((-1)^2 + 5(-1)y + (-1) )} ] \, dy[/tex]
[tex]V = \int\limits^{4}_{1} 5y \, dy[/tex]
[tex]V = 5 [ \frac{y^2}{2} ]|\left \ 4 } \atop { 1 }} \right. \, dy[/tex]
[tex]V = 5( [ \frac{4^2}{2} ] - [ \frac{1^2}{2} ] )[/tex]
[tex]V = \frac{75}{2}[/tex]
Tyler runs 4 laps around the track.Jorge runs 8 times as many laps as Tyler. How many laps does Jorge run? Which equation can help you answer the question? 8x4 = or 8Divided by 4
Answer:
Jorge ran 32 laps
Step-by-step explanation:
The equation is 8x4=32
Determina la magnitud del peso de una persona cuya masa es de 90kg
An arts academy requires there to be 4 teachers for every 88 students and 5 tutors for every 45 students. How many students does the academy have per teacher? Per tutor? How many tutors does the academy need if it has 108 students?
Answer:
18 students for each teacher and 10 for each tutor, and if the academy had 80 students it would have 8 tutors
Step-by-step explanation:
What is the range of the following set of
points (3.4), (7-2). (11-8))?
Answer:
The range of the following set of points is {4, -2, -8}
Step-by-step explanation:
The domain of a set of ordered pairs is the values of x-coordinates of all ordered pairsThe range of a set of ordered pairs is the values of y-coordinates of all ordered pairsEx: In the set of points {(1, 3), (-4, 5), (2, -5)} the domain is {1, -4, 2} and the range is {3, 5, -5}∵ The set of points is {(3, 4), (7, -2), (11, -8)}
∵ The range is the y-coordinates of these points
∵ The y-coordinates of the points are 4, -2, -8
∴ The range is {4, -2, -8}
∴ The range of the following set of points is {4, -2, -8}
7x+3(8x+7)? simplify or expand the expression
Answer:
31x+21
Step-by-step explanation:
7x+3(8x+7)
7x+24x+21
31x+21
Answer 31x + 21
Step-by-step explanation: can’t
What is the value of x?
Answer:
x = 8
Step-by-step explanation:
Step 1:
17x + 14 + 4x - 2 = 180 Sum of a line
Step 2:
21x + 12 = 180 Combine Like Terms
Step 3:
21x = 168 Subtract 12 on both sides
Step 4:
x = 168 ÷ 21 Divide
Answer:
x = 8
Hope This Helps :)
Step-by-step explanation:
4x - 2 + 17x + 14 = 180
21x + 12 = 180
Subtract 12 from both sides and you get :
21x = 168
Devide
[tex] \frac{21x}{21} = \frac{168}{21} \\ x = 8[/tex]
Madelyn has a mask collection. She keeps 399 of the masks on her wall, which is 95% of her entire collection. What is the total number of masks in Madelyn's collection?
Answer:
418
Step-by-step explanation:
Lebron James is 6 feet 9 inches tall. There are 2.54 centimeters in 1 inch. What is Lebron's height in
centimeters?
Answer:
205.74 cm
Step-by-step explanation:
An electronics store receives a shipment of 35 graphing calculators including 7 that are defective. Eight calculators are chosen at random to be sent to a local high school. 8. How many total selections can be m
Complete question :
An electronics store receives a shipment of 35 graphing calculators, including 7 that are defective. 8 of these calculators are selected for a local high school. (A) How many selections can be made? (B) How many of these selections will contain no defective calculators?
Answer:
23535820 ways
3108105 ways
Step-by-step explanation:
A.) How many selections can be made:
Number of ways of selecting 8 calculators from 35
35C8 :
Combination formula :
nCr = n! /(n-r)! r!
35C8 = 35! / (35-8)!8!
35C8 = 35! / 27! 8!
35C8 = (35*34*33*32*31*30*29*28) / (8*7*6*5*4*3*2*1)
35C8 = 948964262400 / 40320
= 23535820 ways
B.) number of non-defective calculators :
35 - 7 = 28
28C8 = n! /(n-r)! r!
28C8 = 28! / (28-8)!8!
28C8 = 28! / 20! 8!
28C8 = (28*27*26*25*24*23*22*21) / (8*7*6*5*4*3*2*1)
28C8 = 2506375872000 / 40320
= 3108105 ways
what are the partial products for 24x69
Solve the Systems of equations. HELP PLEASE
Answer:
Im pretty sure every hat and mask is 1 dollar
Yes ik im dumb but plz answer!!!!
Answer:
C. 125%
Step-by-step explanation:
Because an entire box of 100 is colored, we automatically know it is at least 100%. Which means both A and B are incorrect. There are two tens filled, so we have 120%. There is another 5 boxes are filled, so we have 125%, which is C.
I hope that this helps! :)
jina made $168 for 12 hours of work at the same rate, how many hours would she have to work to make $252
Solve (t - 3)² = 6. The arrow is at a height of 48 ft after approximately s and after s.
Answer:
t = 3.74165738677 or 3.74
Step-by-step explanation:
Step 1:
( t - 3 )² = 6 Equation
Step 2:
t² - 3² = 6 Open Parentheses
Step 3:
t² - 9 = 6 Exponents
Step 4:
t² = 14 Add 9 on both sides
Step 5:
t = [tex]\sqrt{14}[/tex] Find the square root of 14
Answer:
t = 3.74165738677 or 3.74 Round
Hope This Helps :)
Answer:
The arrow is at a height of 48 ft after approximately 0.55s and after 5.45s.
Step-by-step explanation:
took the assignment
Leyla earned $320 for doing chores around the house for
16 weeks. On average, how much did she earn per week?
Answer:2.00
Step-by-step explanation:
Answer:20
Step-by-step explanation: