Answer:
0.0082 = 0.82% probability that a randomly selected person will wait more than 42 seconds.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean wait time of 30 seconds and a population standard deviation of 5 seconds.
This means that [tex]\mu = 30, \sigma = 5[/tex]
What is the probability that a randomly selected person will wait more than 42 seconds?
This is 1 subtracted by the pvalue of Z when X = 42. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{42 - 30}{5}[/tex]
[tex]Z = 2.4[/tex]
[tex]Z = 2.4[/tex] has a pvalue of 0.9918
1 - 0.9918 = 0.0082
0.0082 = 0.82% probability that a randomly selected person will wait more than 42 seconds.
a bag of sweets contains only two different flavours-strawberry and orange
the probability that a sweet is strawberry flavour is 0.8
what is the probability that a sweet is orange flavour
Answer:
0.2
Step-by-step explanation:
hope this helps you. have a good day
find the slope of the function: y²+x²y+x²=1 at the point (-1,2)
If cos 0 = 3/radical 22 and angle 0 is in Quadrant I, what is the exact value of tan 20 in
simplest radical form?
Answer:
[tex] \tan2\theta =-\dfrac{3\sqrt{13}}{2} [/tex]Step-by-step explanation:
To find:-
The value of [tex]\tan2\theta[/tex] .Answer:-
We are here given that the value of,
[tex]\longrightarrow \cos\theta=\dfrac{3}{\sqrt{22}} \\[/tex]
And we know that cosine is the ratio of base and hypotenuse. Therefore,
[tex]\longrightarrow \cos\theta =\dfrac{b}{h} \\[/tex]
So we can also say that,
[tex]\longrightarrow \cos\theta = \dfrac{b}{h}=\dfrac{3}{\sqrt{22}}\\[/tex]
Let us take the given ratio to be 3x:√22x . Now we may find out the value of perpendicular using Pythagoras theorem . The Pythagoras theorem is ,
Pythagoras theorem:-
In a right angled triangle the sum of squares of perpendicular and base is equal to the square of hypotenuse.Mathematically,
[tex]\longrightarrow \boxed{ \boldsymbol{p^2+b^2=h^2}} \\[/tex]
where the symbols have their usual meaning.
On substituting the respective values, we have;
[tex]\longrightarrow p^2+(3x)^2=(\sqrt{22}x)^2 \\[/tex]
[tex]\longrightarrow p^2 = 22x^2-9x^2\\[/tex]
[tex]\longrightarrow p^2=13x^2 \\[/tex]
[tex]\longrightarrow \boldsymbol{ p = \sqrt{13}x} \\[/tex]
Now again , we know that, tangent is defined as the ratio of perpendicular and base. Therefore,
[tex]\longrightarrow \tan\theta = \dfrac{p}{b} \\[/tex]
[tex]\longrightarrow \tan\theta = \dfrac{\sqrt{13}x}{3x}\\[/tex]
[tex]\longrightarrow \boldsymbol{ \tan\theta = \dfrac{\sqrt{13}}{3}}\\[/tex]
Now we may use a identity which is ,
[tex]\longrightarrow\boxed{ \boldsymbol{ \tan (2x)= \dfrac{2\tan x}{1-\tan^2 x}}}\\[/tex]
On substituting the respective values, we have;
[tex]\longrightarrow \tan2\theta = \dfrac{ 2\tan\theta}{1- \tan^2\theta}\\[/tex]
[tex]\longrightarrow \tan2\theta = \dfrac{2\bigg(\dfrac{\sqrt{13}}{3}\bigg)}{1-\bigg(\dfrac{\sqrt{13}}{3}\bigg)^2 } \\[/tex]
[tex]\longrightarrow \tan2\theta = \dfrac{\dfrac{2\sqrt{13}}{3}}{1-\dfrac{13}{9}} \\[/tex]
[tex]\longrightarrow \tan2\theta = \dfrac{\dfrac{2\sqrt{13}}{3}}{\dfrac{9-13}{9}} \\[/tex]
[tex]\longrightarrow \tan2\theta = \dfrac{\dfrac{2\sqrt{13}}{3}}{\dfrac{-4}{9}} \\[/tex]
[tex]\longrightarrow \tan2\theta = -\dfrac{2\sqrt{13}\cdot 9}{3\cdot 4 } \\[/tex]
[tex]\longrightarrow \boxed{\boldsymbol{ \tan2\theta = -\dfrac{3\sqrt{13}}{2}}} \\[/tex]
This is the required answer .
What is the surface area? 4 mm 10 mm 5mm square millimeters
Answer:
200
Step-by-step explanation:
Length*Width*Hight= 4*10*5=200
hope this helps
Answer: I am pretty sure it is 200
Step-by-step explanation:
I may be wrong sorry if it is have a good day :)
what is value of x in 96-3x=6
Answer:
X= 30
Step-by-step explanation:
96-3x=6
first move all terms not containg x to the right side of the Equation
Subtract 96 from both sides of the equation.
-3x = 6 - 96
subtract 96 from 6 and u will get
-3x= -90
Then u will have to divide each term by -3 and simplify which will get u
-3x/-3 when u divide from that u should get -90/-3
Then divide x by 1 and itll equal
x= -90/-3
Then divide -90 by -3 and you will get
x= 30
I hope this is good
What is the value of y?
Answer:
-1
Step-by-step explanation:
I know I just fill in -1 with x but I’m stuck with 2 different answers and this is an exam sooooo I don’t wanna risk it. Can someone please tell me the answer?
Answer:
g(-1) = 4
Step-by-step explanation:
Given:
g(x) = [tex] \frac{3x^2 - 2x + 7}{2x + 5} [/tex]
To find g(-1), substitute x = -1
Thus:
g(-1) = [tex] \frac{3(-1)^2 - 2(-1) + 7}{2(-1) + 5} [/tex]
g(-1) = [tex] \frac{3 + 2 + 7}{-2 + 5} [/tex]
= [tex] \frac{3 + 2 + 7}{-2 + 5} [/tex]
= [tex] \frac{12}{3} [/tex]
g(-1) = 4
A restaurant can seat 100 diners. Four of
the tables can each seat 6 people. The
rest of the tables can each seat 4 people.
How many tables does the restaurant
have in all?
100 people
6x4= 24
100-24= 76
76÷4= 19
19+4=23
lmk if I'm wrong
A researcher for a travel company is looking into the prices people are willing to pay for airplane tickets. The company has communicated that the overall population mean is $265 with a standard deviation of $40.93. The researcher has a sample of 130 ticket purchases from one location. By the central limit theorem, which interval can the researcher be 95% certain that the sample mean will fall within?
A.
$261.41 and $268.59
B.
$257.82 and $272.18
C.
$264.37 and $265.63
D.
$254.23 and $275.77
Answer:
I believe answer B.
Can someone help me solve for x please it’s urgent
Answer:
37.5
Step-by-step explanation:
16/46 = 20/(20+x)
or, 16(20+x) = 46×20
or, 320 + 16x = 920
or, 16x = 600
or, x = 600/16
x = 37.5
If you only have a
1
6
cup measuring cup and a recipe calls for
12
5
6
cups of flour, how many 1/6 cups would you need to use?
Answer:
I don't know rusuejwkdktosogo r
30 points for this A special truck cleans the surface of the ice rink shown. The figure is composed of a square and two semicircles.
85 ft
85 Ft
If the truck cleans the entire surface, how many square feet of ice will the truck clean?
Use 3.14 for . Round your answer to the nearest tenth.
The truck will clean about
square feet of ice
Answer:
12897 square feet
Step-by-step explanation:
So first find the area of the square:
85 * 85 = 7225
Then, the two semi circles together is a full circle. Use the circle area formula,
A = πr^2
The radius (r) would be half the diameter of the circle. The diameter of the circle would be 85. So half of that is 42.5. The radius is 42.5
Now:
A = π(42.5)^2
A = 3.14(42.5)^2
A = 3.14(1806.25)
A = 5671.625
Lastly, add the two areas up for the square and circle:
7225 + 5671.625 = 12896.625
Round to nearest tenth: 12897
3. Find the equation of a line that passes through the x-intercept of the line 3x+ 6y = 8 and is perpendicular to the line 2x - 5y = 10.
Answer:
y = -5/2x + 20/3
Step-by-step explanation:
x-int of 3x + 6y = 8
sub 0 for y
3x + 6(0) = 8
3x = 8
x = 8/3 or 2.667
line perpendicular to 2x - 5y = 10
put into y = mx + b form
2x - 5y - 10 = 0
5y = 2x - 10
y = 2/5 x - 2
find negative reciprocal of the slope 2/5 x (for the perpendicular line)
-5/2 x
find the y-int (b)
m = -5/2 x
must pass through (8/3,0)
y = mx + b
0 = -5/2(8/3) + b
0 = -40/6 + b
b = 20/3
therefor the equation of the line is y = -5/2x + 20/3
Admission prices at a football game were $5 for adults and $ 2 for children.
The total value of the tickets sold was $2520, and 654 tickets were sold. How many adult
tickets and how many child tickets were sold?
Show all six steps.
Answer:
404 adult tickets were sold, and 250 child tickets.
Step-by-step explanation:
This question can be solved by a system of equations.
I am going to say that
x is the number of adult tickets sold.
y is the number of child tickets sold.
654 tickets were sold.
This means that
[tex]x + y = 654[/tex]
[tex]y = 654 - x[/tex]
Admission prices at a football game were $5 for adults and $ 2 for children. The total value of the tickets sold was $2520.
This means that
[tex]5x + 2y = 2520[/tex]
Since [tex]y = 654 - x[/tex]
[tex]5x + 2(654 - x) = 2520[/tex]
[tex]5x + 1308 - 2x = 2520[/tex]
[tex]3x = 1212[/tex]
[tex]x = \frac{1212}{3}[/tex]
[tex]x = 404[/tex]
[tex]y = 654 - x = 654 - 404 = 250[/tex]
404 adult tickets were sold, and 250 child tickets.
2. The numbers from 101 to 150 are written as, 101102103104105.146147148149150.
What will be the remainder when this total number is divided by 3?
Answer:
We know that a number is divisible by 3 if the sum of its digits is a multiple of 3.
if the sum is a multiple of 3 + 1 (like 3*n + 1) the remainder is 1
if the sum is a multiple of 3 + 2 (like 3*n + 2) the remainder is 2.
Then we need to find the sum of all the single digits in the number:
101102103104...149150
the sum of all the single digits is:
( 1 + 1) + (1 + 2) + (1 + 3) + ... + (1 + 4 + 9) + ( 1 + 5)
The method i used is:
(from 101 to 110)
first we sum the hundreds digit 10 times, and then we add the unit digits for each case, this is:
1*10 + (1 + 2+ 3 + 4+ 5+ 6+ 7+ 8 + 9 + 1) = 10 + 46
From (111 to 119)
first we add the sum of the hundreds and tens digits 10 times, and then the units:
2*9 + ( 1 + 2+ 3 + 4+ 5+ 6+ 7+ 8 + 9 )
now if we also add the number 120 (so we have the range 111 to 120)
the sum becomes:
2*9 + ( 1 + 2+ 3 + 4+ 5+ 6+ 7+ 8 + 9 ) + 1 + 2
2*10 + (1 + 2+ 3 + 4+ 5+ 6+ 7+ 8 + 9 + 1 ) = 20 + 46
You already can see the pattern here.
in the range from (121 to 130) we will have the sum equal to 30 + 46
in the range from (131 to 140) we will have the sum equal to 40 + 46
in the range from (141 to 150) we will have the sum equal to 50 + 46
Then the total sum is:
(10 + 20 + 30 + 40 + 50) + 5*46 = 380
We know that 380 is multiple of 3 (because 3 + 8+ 0 = 12)
Then the remainder is 0.
8) Do these ratios form a proportion?
20 pedestrians : 5 years
7 pedestrians : 1 year
Please provide explanation.
Answer:
Since the division of the number of pedestrians by the number of years yields different values for each ratio, these ratios do not form a proportion.
Step-by-step explanation:
They will form a proportion if the division of the number of pedestrians by the number of years yields the same results.
20 pedestrians : 5 years
20/5 = 4 pedestrians per year.
7 pedestrians : 1 year
7/1 = 7 pedestrians per year.
Since the division of the number of pedestrians by the number of years yields different values for each ratio, these ratios do not form a proportion.
A carpenter is creating two new templates for his designs. One template will be in the shape of a right triangle, where the longer leg is 4 inches more than six times the shorter leg. The second template will be in the shape of a rectangle, where the width is 5 inches more than the triangle’s shorter leg, and the length is 3 inches. The carpenter needs the areas of the two templates to be the same. Write a system of equations to represent this situation, where y is the area, and x is the length of the shorter leg of the triangle. Which statement describes the number and viability of the system’s solutions?
A. The system has two solutions, but only one is viable because the other results in negative side lengths.
B. The system has only one solution, and it is viable because it results in positive side lengths.
C. The system has only one solution, but it is not viable because it results in negative side lengths
. D. The system has two solutions, and both are viable because they result in positive side lengths.
Answer:
The system has two solutions, but only one is viable because the other results in negative side lengths.
Step-by-step explanation:
Took the plato test and passed it, I don't know what the purpose of the first answer is, but here is the correct answer.
Help me with this EdPuzzle pls.
Answer:
2 in^3
Step-by-step explanation:
First you find the volume of one cube by doing 1/2*1/2*1/2, after this you times this number by 16 to get the volume of the whole structure
What does p equal Help?
Answer:
your answer will be P=27
Step-by-step explanation:
hope it helps...
If ADC measures 35º, what does
Answer:
by inscribed angle rule do it.
Step-by-step explanation:
hope this help
Answer:
70°
Step-by-step explanation:
∠ADC is a inscribed angle. ∠ABC is a central angle. The inscribed angle's measurement will be 1/2 of the measurement of the central angle.
In this case, the inscribed angle ∠ADC is given to you with a measurement of 35°. To solve for ∠ABC, multiply 2 to the given value:
35 x 2 = 70
70° is your answer.
~
If n and k are positive integers and 8” = 2*, what is the value of n/k
Answer:
B) 1/3
Step-by-step explanation:
If n=1 and k=3, then 8^n=2^k is true. Therefore, n/k=1/3.
Express the shaded area as a fraction, a decimal, and a percent of the whole
Answer:
Fraction : 3/9
Decimal : 0.33333333 (the .3 continues)
Percent : 33.33333%
Step-by-step explanation:
Dividing 3 by 9 will give you a continous set of 3.
The distance around a circle is 69.08 feet. Determine the area of the circle.
Answer:
138.16
Step-by-step explanation:
Which is bigger: 4 quarts or 9 pints?
Answer:
9 pints
Step-by-step explanation:
4 quarts is equal to 8 pints.
a new desk cost (d) dollars. A bookshelf cost $114 less than the desk. A new lamp cost twice as much as the bookshelf
Answer: what are you looking for (d)? there isnt enough info
Step-by-step explanation:
When Sebastian left his house in the morning, his cell phone battery was partially
charged. Let B represent the charge remaining in Sebastian's battery, as a
percentage, t hours since Sebastian left his house. The table below has select values
showing the linear relationship between t and B. Determine how much battery life
Sebastian's phone would have 4 hours after leaving his house.
t
B
1
36
2.5
31.5
5
24
what is 2/5 * 2 3/4 equal to
Answer: the answer 11/10 1.1 sorry if its wrong
Step-by-step explanation: have a nice day buddy
happy easter
Hi please help me with these questions asap.
Step-by-step explanation:
A. r=42/2=21
B.
[tex] {21}^{2} \pi + 60 \times 42 = \\ = 441\pi + 2520[/tex]
C.
[tex]42\pi + 60 \times 2 = \\ = 42\pi + 120[/tex]
Mrs. Spina bought 4 boxes of 8 pork chops. She set aside 12 and separated the rest into packs of4 to freeze. How many packs of chops did Mrs. Spina freeze
Step-by-step explanation:
Number of pork chops Mrs Spina bought =
Number of boxes x number of pork chops per box
= 4x8
= 32
Number of Pork chops to freeze = 32 - 12 (set aside) = 20
Number of packs of pork chops to freeze = Number of pork chops to freeze / pork chops per pack
= 20/4
= 5 packs.
Select the correct answer.
If a six-sided die is rolled 30 times, how many times can you expect to get a 6?
OA 3
OB.
5
OC. 6
OD 10
PL HELP WILL MARK BRAINLY 10 POINTS
Answer:
5 times
Step-by-step explanation:
1/6·30=5
so your answer is b)5
Can i have a brainliest please or 10 points?