Answer:
b
Step-by-step explanation:
Two brothers, Michael and Alan, were in a bowling league that met once a
week. From past experiences, it is known that both brothers' scores are
approximately normally distributed where Michael has a mean score of 150
with a standard deviation of 30, and Alan has a mean score of 165 with a
standard deviation of 15. Assuming that their scores are independent, which
of the following values is closest to the probability that Michael will have a
greater core than Alan in a single game?
0.16
0.28
0.31
0.33
0.37
Answer:
The correct option is;
0.28
Step-by-step explanation:
The given parameters are;
The mean score for Michael, [tex]\bar x _1[/tex] = 150
The standard deviation, σ₁ = 30
The mean score for Alan, [tex]\bar x _2[/tex] = 165
The standard deviation, σ₂ = 15
Taking n₁ = n₂ = 1
[tex]z=\dfrac{(\bar{x}_{1}-\bar{x}_{2})-(\mu_{1}-\mu _{2} )}{\sqrt{\dfrac{\sigma_{1}^{2} }{n_{1}}-\dfrac{\sigma _{2}^{2}}{n_{2}}}}[/tex]
Taking μ₁ - μ₂ = 0
[tex]z=\dfrac{(150-165)}{\sqrt{\dfrac{30^{2} }{1}-\dfrac{15^{2}}{1}}} \approx -0.577[/tex]
The p-value for a z-score of -0.577 from the z-table is 0.28434
Therefore, the probability that Michael, with mean score, [tex]\bar x _1[/tex] = 150 will have a greater score than Alan, with a mean score of [tex]\bar x _2[/tex] = 165 is 0.28434 ≈ 0.28
Therefore, the correct option is 0.28
What is the value of x in the equation below?
29.46=13.82+4x
Answer:
x=3.91
Step-by-step explanation:
29.46=13.82+4x
13.82+4x=29.46
subtract 13.82 from both sides
4x=15.64
divide by 4
x=3.91
16x – 20y
20y = 60
Slope intercept form
Answer:
16x=60
X=15/4
Step-by-step explanation:
The role that an organism plays within the area it lives is known as its
Question 5 options:
A.Nest
B.Habitat
C.Home
D.Niche
I will report you if you try to steal my points
Answer:
D
Step-by-step explanation:
Ecology definition of niche
I really need help plz
Answer:
I think answer is A
Step-by-step explanation:
Cause you notice time is the x and distance (meters) is the y. So 1 minute = 200 meters.
convert 18 1/10 into a decimal.
Answer:
the answer is 18.1 1/10 is the same thing as .1
Tickets for a family of 6 to go skiing cost $48. whats the unit price ?
Here's a graph of a linear function.
Write the
equation that describes that function.
Express it in slope-intercept form.
Answer:
y = 1/2x + 3Step-by-step explanation:
As per graph, using the points (-6, 0) and (0, 3) we determine that:
the y-intercept is 3 and the slope is m = (3-0)/(0 - (-6)) = /3/6 = 1/2So the equation is:
y = mx + by = 1/2x + 3how do you find the perpendicular distance between a line segment and a point? (photo attached) i’m stuck
Answer:
Exact Distance = [tex]\frac{4\sqrt{10}}{5}[/tex]
Approximate Distance = 2.529822
============================================
Explanation:
This process is quite involved if you don't know the shortcut formula. I'll go over the long method first, and then show the shortcut in the next section.
First we'll need the equation of the line through points O and M. Use of the slope formula will show line OM has slope -1/3, which you are correct in stating.
Then use point slope form to determine the equation of line OM is y = (-1/3)x+11/3. This converts to the standard form x+3y = 11.
For anything in the form Ax+By = C, the equation perpendicular to this is of the form Bx-Ay = D. The A,B coefficients swap, and one item is negated. This helps form the negative reciprocal slope needed for the perpendicular line.
Compare x+3y = 11 to Ax+By = C. We see that A = 1 and B = 3.
So Bx-Ay = D turns into 3x-y = D. Then plug in the coordinates of H(-3,2) and compute to get
3x-y = 3(-3)-2 = -9-2 = -11. So D = -11
The equation 3x-y = D turns into 3x-y = -11 which is the equation of the line through point H and this line is perpendicular to line OM.
At this point, we have this system of equations
x+3y = 11
3x-y = -11
Solve that system however you wish. Substitution may be the best choice. Doing so leads to the intersection point (-2.2, 4.4)
The last step is to apply the distance formula between the points H(-3,2) and the intersection point (-2.2, 4.4)
The distance you should get is [tex]\frac{4\sqrt{10}}{5} \approx 2.529822[/tex]
I'm skipping steps because listing everything out would take up way too much space in my opinion.
--------------------------------------------------------
The first section goes over a fairly lengthy process of finding the perpendicular distance. Luckily, there's a shortcut.
Consider an equation of the form Ax+By=C, aka standard form. Now consider a point P located at (m,n) that is not on the line Ax+By = C. We can find the distance from P to the line using this formula below
[tex]d = \frac{|Am+Bn-C|}{\sqrt{A^2+B^2}}[/tex]
In this case, A = 1, B = 3 and C = 11 found back in the previous section. So you'll still need to calculate the equation of line OM.
Also, we'll use (m,n) = (-3,2) which are the coordinates of point H
From here it's a fairly straightforward computation
[tex]d = \frac{|Am+Bn-C|}{\sqrt{A^2+B^2}}\\\\d = \frac{|1*(-3)+3*2-11|}{\sqrt{(1)^2+(3)^2}}\\\\d = \frac{|-8|}{\sqrt{1+9}}\\\\d = \frac{8}{\sqrt{10}}\\\\[/tex]
Optionally we can rationalize the denominator like so
[tex]d = \frac{8}{\sqrt{10}}\\\\d = \frac{8\sqrt{10}}{\sqrt{10}\sqrt{10}}\\\\d = \frac{8\sqrt{10}}{\sqrt{10*10}}\\\\d = \frac{8\sqrt{10}}{\sqrt{100}}\\\\d = \frac{8\sqrt{10}}{10}\\\\d = \frac{2*4\sqrt{10}}{2*5}\\\\d = \frac{4\sqrt{10}}{5}\\\\d \approx 2.529822\\\\[/tex]
There are different ways to write down the answer, but they all represent the same number.
Which of the following expressions are undefined? CHOOSE ALL THAT APPLY
A. 6/0
B. 5/0
C. 6/5-5
Answer:
6/0, 5/0, 6/5-5
Step-by-step explanation:
You cannot divide a number by 0:
6/0 is dividing by 05/0 is dividing by 06/5-5=6/0 which is dividing by 0
Select all of the fractions that are equivalent to -2/3
o 2/-3
o -3/-2
o -2/-3
o - 2/3
o -3/2
o -2/2
Please helppp
Answer:
Step-by-step explanation:
⇒o 2/-3 Doesn't matter where the minus is as long as there an odd numbere of them.
o -3/-2
o -2/-3
⇒o - 2/3 This is given. Is it really listed.
o -3/2
o -2/2
There really are only 2 of them. 3/2 in any form is not equal to 2/3.
-2/2 = - 1 not -2/3
-2/-3 There are an even number of - signs. The answer is 2/3
Richardo had saved $80 from his summer job to buy video games. He
bought 4 games and the cashier gave him $16.40 in change. If each
game cost the same amount, how much was each game?
Leave off the dollar sign in your answer.
Answer:
$15.90
Step-by-step explanation:
80 - 16.40 = 63.60
63.60÷4 =15.9
15.9 = $15.90
Algebra 1 easy. Will give brainlest PLZ ASAP!
Answer:
2, -2
Step-by-step explanation:
just test each one
Mr. Mills is 5 feet and 11 inches tall. How many inches tall is he?
Answer:
71
Step-by-step explanation:
There are 12 inches in a foot:
12 inches x 5 feet = 60
60 + 11 inches = 71 inches total
Answer:
71 inches
Step-by-step explanation:
12 inches in a foot
12*5
60+11
71 inches
Hope this hopes. Have a great day. May it be filled with joy and happiness.
please help 15 points i will give u
If I would drop two eggs off of a building (one being at a higher position than the other) which one would drop faster and why?
Answer: Simple Answer.
The simplest way to obtain the minimal floor is to throw an egg from the first floor, then from the second and so on. This way when the egg is finally broken then we will know that this is the floor. This is a reliable algorithm, but in the worst-case scenario it would take 100 throws.
The important thing to notice is that it is the only reliable algorithm when you have only one egg. So you need to start using this algorithm when you break the first egg.
Step-by-step explanation: Intuitive answer.
This way, our first egg should be used to split the 100 floors range into smaller ranges as efficiently as possible. Thus, an intuitive and popular answer is to throw the first egg from 1/n-th of the floors to check. For instance 1/3. Then the algorithm will look like the following:
Throw the egg from 33rd floor. If it breaks, then we check the first 32 floors using the second egg.
Otherwise, we throw the egg from 33 + (67 * 1/3) = 55th floor. If it breaks, then we check floors 34 to 55 using the second egg.
…
Worst case scenario for 1/3 is max(33, 24, …) = 33. This way we might find a perfect n that optimizes the number of throws using some dynamic programming. This is a valuable solution that presents programming thinking, but it is not an optimal solution.
The optimal solution is when all arguments of this max function are equal. How do we achieve it? Looking from the end, the last D(n) is going to be 1, because we will finally get to the point where there is only the single floor for the first egg. Therefore D(n-1) should be equal to 2 because it has one less throw of the first egg.
We see then that the first egg should be thrown finally from the 99th floor, previously from 99–2=97, previously from 97–3=94, 90, 85, 79, 72, 64, 55, 45, 34, 22 and the 9th floor. This is an optimal solution! This way, we need 14 throws in the worst case scenario (the smallest difference is 13, but we had to make one extra throw on the 9th floor).
Simple equation to find the answer is following:
Where f is number of floors. This can be simplified to: min n*n+ divided by 2 greater than f
That is equal to: n=ceil 8f + 1 - 1, divided by 2
Review: Angle Bisectors
A
Directions: Label the diagram with the
proper congruence markings and known
measurements.
Answer:
m∠AOC = 15°m∠BOC = 15°Step-by-step explanation:
Given the angle ∠AOB
It is stated that CO is the angle bisector of ∠AOB.
Given that ∠AOB = 30°
As we know that the angle bisector bisects the angle into two equal angles.
Thus, the angle bisector CO bisects the angle ∠AOB into two equal angles, which are:
m∠AOCm∠BOCas
∠AOB = 30°
Thus, the two formed angles i.e m∠AOC and m∠BOC by the angle bisector would be half of the angle bisector as the angle bisector bisects the angle ∠AOB into two equal angles.
Therefore,
m∠AOC = 15°m∠BOC = 15°If the sales tax rate is 5%, how much tax will you pay on a $35 sweatshirt? * 5 points
$36.75
$1.75
$35.75
$2.25
Answer:
$36.75
Step-by-step explanation:
You do 5% of 35 which equals 1.75 that’s your sales tax.
then add 1.75+35.00= 36.75
Which expression represents each mathematical phrase?
Drag the answer into the box to match each phrase.
(1) the product of 7 and a number
(2) the sum of 7 and a number
(3) 7 less than a number
(4) 7 more than twice a number
(a) 2+x+7
(b) 7+x
(c) 2x+7
(d) x-7
(e) 7x
(f) 7-x
Answer:
(1) = (e) 7x. (2) = (b) 7+x. (3) = (d) x-7. (4) = (c) 2x+7
i need this question answered by 2:30 its for 20 points pls help
Answer:
46800
Step-by-step explanation:
10x15x24x13=46800
Find the value of x.
Answer:
x=102
Step-by-step explanation:
Can anyone help me please??? Almost done Thank you!!
Answer:
you might’ve already answered this but it’s 65
Step-by-step explanation:
the two sides in a triangle have to be congruent so if one angle is 65, the other has to be 65 too :)
Answer:
65
Step-by-step explanation:
the given triangle is an isoceles triangle and opposite angles of opposite equal sides of isosceles triangle are equal
A family has a hybrid car that gets 40 miles per gallon (mpg) and a pickup truck that gets 17 mpg. They drive at least 500 miles per week using both vehicles but don't want to use more than 20 gallons of gas. Make a recommendation for using each vehicle. Part A Write an expression that represents the total amount of gasoline used. Then write an inequality to show the maximum amount of gasoline that the family wants to use. Define the variables and list any constraints on the variables.
Answer:
[tex]Z=x+y[/tex]
[tex]x+y<20[/tex]
Step-by-step explanation:
Let the gallons of fuel used in the hybrid per week car be [tex]x[/tex] and [tex]y[/tex] be the number of gallons used in the pickup truck per week.
Number of miles driven using both vehicles is at least 500 per week. The inequality that represents the number of miles driven is.
[tex]40x+17y\geq 500[/tex]
The expression of total amount of fuel used would be [tex]Z=x+y[/tex].
Now the sum of the fuels used in both the cars is more than 20 gallons per week. The inequality that represents the total amount of gasoline used is
[tex]x+y<20[/tex]
rationalise the denoninator of 1 ÷ 5 - square root of 2
Answer:
Square root2 /3
Step-by-step explanation:
1. Multiply both numerator and denominator by square root of 2.
2. Square root 2 times itself is just 2 that so denominator is 5-2
3. 1 times Square root 2 is just Square root 2. So numerator is Square root 2
4. 5-2=3 so final answer is Square root 2 over 3
a) An agent sold some carpets at the rate of Rs 4500 each and received Rs 9000 as commission
at 10%. Find the number of carpets he sold.
Answer:
A
Step-by-step explanation:
not sure gusto ko lang tumulong
In your sock drawer you have 4 blue socks, 5 grey socks, and 3 black socks. Half asleep one morning, you grab 2 socks at random and put them on. Find the probability that you end up wearing exactly 1 black sock.
3 out of 12
1 out of 4
yea hopefully correct
the question is "what is the rate of change of the average height in feet of the trees on the farm with respect to the number of years since the trees were planted"
please help!
Answer:
Rate Of Change= 7
Step-by-step explanation:
all you have to do is see the difference, imma make a table here first
x y
1 10
3 24
6 45
11 80
15 108
from 10 to 24 you add 14
from 1 to 3 you add 2
so y/x
14/ 2 = 7
check:
from 24 to 45 you add 21
from 3 to 6 you add 3
so y/x
21/3 = 7
From y/x your final answer will always be 7.
So the rate of change will be 7.
Hope this helped a little!
Simplify the expression:
10t - 40 + 3t + t
Answer:
Your correct answer is 14t - 40
Step-by-step explanation:
Combine like terms:
10t + 3t + t = 14t
Since there are no other integers, just tag on the -40:
14t - 40
**please mark brainliest!!
Diana worked on her science project for 513 hours. Gabe worked on his science project 114 times as long as Diana. Paula worked on her science project 34 as long as Diana. How long did Gabe and Paula work on their projects?
Answer:
Gabe worked for 6 2/3 hours and Paula worked for 4 hours.
Step-by-step explanation:
It is given that,
Diana worked on her science project for 5 1/3 hours.
Gabe worked on his science project 1 1/4 times as long as Diana.
Paula worked on her science project 3/4 as long as Diana.
Solution,
ATQ,
Gabe worked for :
[tex]5\dfrac{1}{3}\times 1\dfrac{1}{4}\\\\=\dfrac{16}{3}\times \dfrac{5}{4}\\\\=\dfrac{20}{3}\ h\\\\=6\dfrac{2}{3}\ h[/tex]
Pauls worked for :
[tex]\dfrac{3}{4}\times 5\dfrac{1}{3}\\\\=\dfrac{3}{4}\times \dfrac{16}{3}\\\\=4\ h[/tex]
Hence, Gabe worked for 6 2/3 hours and Paula worked for 4 hours.
drummer and a guitarist each wrote songs for their band. The guitarist wrote 8 fewer than
wice the number of songs that the drummer wrote. They wrote a total of 46 songs.
Vhich system of equations models this situation if the drummer wrote d songs and the
guitarist wrote g songs?
Answer:
g = 2d - 8
g + d = 46