Using the normal distribution, it is found that the median of the MCAT scores was of 500.9.
Normal Probability Distribution
In a normal distribution 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]
It 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, which is the percentile of X.The median is also the 50th percentile, hence, in the normal distribution, it is equals to the mean.In this problem, the mean score was 500.9, hence the median score was also of 500.9.
You can learn more about the normal distribution at https://brainly.com/question/24663213
Someone pls help me
[tex]\huge\boxed{\boxed{Hello!}}[/tex]
How to Find the Area of a Rectangle:
A=LW, where L stands for Length and W stands for Width.
In this case, L is 4 cm more than the width, and the width is 10 cm.
Thus, the length is 14 cm.
Multiply 14 by 10:
A=140 cm²
[tex]\huge\boxed{\boxed{\pmb{Answer:{\boxed{\sf{A=140cm^{2} }}}}}}[/tex]
Hope it helps!
Enjoy your day!
Please feel free to ask if you have any doubts.
✷[tex]\mathfrak{MistySparkles}[/tex]✷
Write the number.
18 ones
9 tens
2 hundreds
Answer:
308
Step-by-step explanation:
I had 2000 dollars but a frog take 1000? how much do i have
Answer:
1000 dollars
Step-by-step explanation:
2000-1000 = 1000
Solve the following systems of equations by substitution method.
1) y = -2 and 4x - 3y = 18
IF YOU WANT TO ANSWER MORE: HERE IS THE REST PART OF THE QUESTION—
2) y = 6x - 11 and 2x + 3y = 7
3) x = -3y - 5 and 4x - 5y = -3
4) x = 5y - 7 and -2x - 3y = -12
5) 5x - 3y - 8 = 0 and 2x - 3y - 6 = 0
6) x - 3y - 11 = 0 and 5x + y - 7 = 0
7) 2x - 3y = -1 and y = x - 1
8) -4x + y = 6 and -5x - y = 21
Answer:
1) x = 3 and y = -2
2) x = 2 and y = 1
3) x = -2 and y = -1
4) x = 3 and y = 2
5) x = 2
6) x = 2 and y = -3
7) x = 4 and y = 3
8) x = -3 and y = -6
Step-by-step explanation:
1. Answer :
y = -2
4x - 3y = 18 ----(1)
Substitute y = -2 in (1).
4x - 3(-2) = 18
4x + 6 = 18
Subtract 6 from both sides.
4x = 12
Divide both sides by 4.
x = 3
So,
x = 3 and y = -2
2. Answer :
y = 6x - 11 ----(1)
2x + 3y = 7 ----(2)
Substitute y = 6x - 11 in (2).
2x + 3(6x - 11) = 7
2x + 18x - 33 = 7
20x - 33 = 7
Add 33 to both sides.
20x = 40
Divide both sides by 20.
x = 2
Substitute x = 2 in (1).
y = 6(2) - 11
= 12 - 11
= 1
So,
x = 2 and y = 1
3. Answer :
x = -3y - 5 ----(1)
4x - 5y = -3 ----(2)
Substitute x = -3y + 5 in (2).
4(-3y - 5) - 5y = -3
-12y - 20 - 5y = -3
-17y - 20 = -3
Add 20 to both sides.
17y = -17
Divide both sides by 17.
y = -1
Substitute y = -1 in (1).
x = -3(-1) - 5
= 3 - 5
= -2
So,
x = -2 and y = -1
4. Answer :
x = 5y - 7 ----(1)
-2x - 3y = -12 ----(2)
Substitute x = 5y - 7 in (2).
-2(5y - 7) - 3y = -12
-10y + 14 - 3y = -12
-13y + 14 = -12
Subtract 14 from both sides.
-13y = -26
Divide both sides by -13.
y = 2
Substitute y = 2 in (1).
x = 5(2) - 7
= 10 - 7
= 3
So,
x = 3 and y = 2
5. Answer :
5x + 3y - 8 = 0 ----(1)
2x - 3y - 6 = 0 ----(2)
Solve for 3y in (1).
5x + 3y - 8 = 0
Subtract 5x from both sides.
3y - 8 = -5x
Add 8 to both sides.
3y = -5x + 8
Substitute 3y = -5x + 8 in (2).
2x - (-5x + 8) - 6 = 0
2x + 5x - 8 - 6 = 0
7x - 14 = 0
Add 14 to both sides.
7x = 14
Divide both sides by 7.
x = 2
6. Answer :
x - 3y - 11 = 0 ----(1)
5x + y - 7 = 0 ----(2)
Solve for x in (1).
x - 3y - 11 = 0
Subtract 3y and 11 to both sides.
x = 3y + 11 ----(3)
Substitute x = 3y + 11 in (2).
5(3y + 11) + y - 7 = 0
15y + 55 + y - 7 = 0
16y + 48 = 0
Subtract 48 from both sides.
16y = -48
Divide both sides by 16.
y = -3
Substitute y = -3 in (3).
x = 3(-3) + 11
= -9 + 11
= 2
So,
x = 2 and y = -3
7. Answer :
2x - 3y = -1 ----(1)
y = x - 1 ----(2)
Substitute y = x - 1 in (1).
2x - 3(x - 1) = -1
2x - 3x + 3 = -1
-x + 3 = -1
Subtract 3 from both sides.
-x = -4
Multiply both sides by -1.
x = 4
Substitute x = x in (3).
y = 4 - 1
= 3
So,
x = 4 and y = 3
8. Answer :
-4x + y = 6 ----(1)
-5x - y = 21 ----(2)
Solve for y in (1).
-4x + y = 6
Add 4x to both sides.
y = 4x + 6 ----(3)
Substitute y = 4x + 6 in (2).
-5x - (4x + 6) = 21
-5x - 4x - 6 = 21
-9x - 6 = 21
Add 6 to both sides.
-9x = 27
Divide both sides by -9.
x = -3
Substitute x = -3 in (3).
y = 4(-3) + 6
= -12 + 6
= -6
So,
x = -3 and y = -6
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Mathematics
Thank You!
Answered by: ms115
Answer:
See below for all answers and explanations
Step-by-step explanation:
Problem 1
4x - 3y = 18
4x - 3(-2) = 18 <-- Substituting y = -2
4x + 6 = 18
4x = 12
x = 3
Problem 2
2x + 3y = 7
2x + 3(6x-11) = 7 <-- Substituting y = 6x - 11
2x + 18x - 33 = 7
20x - 33 = 7
20x = 40
x = 2
y = 6x - 11 <-- Substituting x=2 to solve for y
y = 6(2) - 11
y = 12 - 11
y = 1
Problem 3
4x - 5y = -3
4(-3y-5) - 5y = -3 <-- Substituting x = -3y - 5
-12y - 20 - 5y = -3
-17y - 20 = -3
-17y = 17
y = -1
x = -3y - 5 <-- Substituting y = -1 to solve for x
x = -3(-1) - 5
x = 3 - 5
x = -2
Problem 4
-2x - 3y = -12
-2(5y-7) - 3y = -12 <-- Substituting x = 5y - 7
-10y + 14 - 3y = -12
-13y + 14 = -12
-13y = -26
y = 2
x = 5y - 7 <-- Substituting y=2 to solve for x
x = 5(2) - 7
x = 10 - 7
x = 3
Problem 5
5x - 3y - 8 = 2x - 3y - 6 <-- Setting equations equal to each other
5x - 8 = 2x - 6 <-- Eliminating y-variable to solve for x
3x - 8 = -6
3x = 2
x = 2/3
5x - 3y - 8 = 0 <-- Substituting x = 2/3 into first equation
5(2/3) - 3y - 8 = 0
10/3 - 3y - 8 = 0
10/3 - 3y - 24/3 = 0
-14/3 - 3y = 0
-3y = 14/3
y = -14/9
Problem 6
x - 3y - 11 = 0 <-- Solve for x
x - 3y = 11
x = 11 + 3y
5x + y - 7 = 0
5(11+3y) + y - 7 = 0 <-- Substituting x = 11 + 3y
55 + 15y + y - 7 = 0
55 + 16y - 7 = 0
48 + 16y = 0
16y = -48
y = -3
x = 11 + 3y <-- Substitute y=-3 into first equation to solve for x
x = 11 + 3(-3)
x = 11 - 9
x = 2
Problem 7
2x - 3y = - 1
2x - 3(x-1) = -1 <-- Substituting y = x - 1
2x - 3x + 3 = -1
-x + 3 = -1
-x = -4
x = 4
y = x - 1 <-- Substitute x=4 to solve for y
y = 4 - 1
y = 3
Problem 8
-4x + y = 6 <-- Solve for y in first equation
y = 6 + 4x
-5x - y = 21
-5x - (6+4x) = 21 <-- Substituting y = 6 + 4x
-5x - 6 - 4x = 21
-9x - 6 = 21
-9x = 27
x = -3
y = 6 + 4x <-- Substitute x = -3 to solve for y
y = 6 + 4(-3)
y = 6 - 12
y = -6
Surface area of rectangular prism
Answer:
the answer is 60
Step-by-step explanation:
you multiply what's on top 5*12=60
multi step problems with percents
Answer:
142.24$
Step-by-step explanation:
112 = 100% 9x112
/ 100100. = 10.08$
? = 9%
112 = 100% 18x112 /100 =. 20.16$
? = 18%
so.......
112$ + 20.16$ + 10.08$
= 142.24$
Solve the equation.
[tex]\sqrt{y^{2} -20y+100 }= y-10[/tex]
Notice that
y² - 20y + 100 = y² - 2•10y + 10² = (y - 10)²
Then
√(y² - 20y + 100) = y - 10
is equivalent to
√((y - 10)²) = y - 10
|y - 10| = y - 10
If y ≥ 10, then |y - 10| = y - 10, and
y - 10 = y - 10 ⇒ 0 = 0
so there are infinitely many solutions, y ≥ 10.
Otherwise, if y < 10, then |y - 10| = -(y - 10), and
-(y - 10) = y - 10 ⇒ 10 = -10
which is false, so there are no solutions in this case.
[tex]\\ \tt\hookrightarrow \sqrt{y^2-20y+100}=y-10[/tex]
[tex]\\ \tt\hookrightarrow y^2-20y+100=(y-10)^2[/tex]
[tex]\\ \tt\hookrightarrow y^2-20y+100=y^2-20y+100[/tex]
Both sides are equal
Hence
No solutionOver the last three evenings, Diane received a total of 105 phone calls at the call center. The third evening, she received 4 times as many calls as the second evening. The first evening, she received 9 fewer calls than the second evening. How many phone calls did she receive each evening?'
Answer:
Make an eqaution from here.
Let’s make evening 2 “x”
So the first evening has 9 less then the secon evening so…
x-9
Of course theres the second evening (x).
X-9+x
Then the third evening has 4 times as much as the second meeting so…
x-9+x+4x
And when solved, it has to equal 105.
So solve from here.
Combine like terms.
6x-9=105
Isolate
6x=114
x= 19
First evening is 9 less then 19, so 10.
The second evening was 19 calls.
The third evening was 4 times the second evening so, 19*4= 76
1st night = 10
2nd night= 19 calls
Thrid night= 76 calls
x^4 - 3x^2 - 10 = 0 using the u
Answer:
[tex]x ^ { 4 } - 3 x ^ { 2 } - 10 = 0\\Let, t = x^{2} \\\rightarrow \: t^{2}-3t-10=0 \\\\\\t=\frac{-\left(-3\right)(+/-)\sqrt{\left(-3\right)^{2}-4\times 1\left(-10\right)}}{2} \\t=\frac{3(+/-)7}{2} \\\\So,\\t = 5 \: and \: -2\\\\Then,\\x = \sqrt{5} \: and \: -\sqrt{5}[/tex]
Hope it helps ⚜
A flagpole is 45 feet tall. A rope is tied to the top of the flag pole and secured to the ground 10 feet from the base of the flagpole. Will a 35 foot piece of rope be long enough to secure the flagpole? Justify your answer.
i give brainliest
Answer:
So the answer would be no, because the length of the rope is needs to be 46 and 35 is not long enough
Step-by-step explanation:
A flagpole, rope and the length of secure point from the flagpole are forming the right triangle, where the rope is a hypotenuse. Let a = 45 and b = 10ft. Use Pythagorean Formula to find length of the rope c
a² + b² = c²
Since we are going to solve for c, we set up the equation like this:
c² = 45² + 10² (Substitute into formula)
c² = 2,025 + 100 (Add)
c² = 2,125 (Simplify)
√c² = √2,125 (Take the square root from both sides)
c = 46.09772228646444 (Round to the nearest whole number)
c = 46
So the answer would be no, since the length of the rope needs to be 46ft long and a 35 foot piece of rope is not long enough.
Ms Bonilla is saving for a vacation she currently has 150 in her savings account and plans to add $25 to the account each week .
Enter a function, S(w) that describes the total amount in her savings account as a function of weeks , w
Answer and Step-by-step explanation:
Alright, so when creating any type of math problem, it is important to identify the parts of the problem and where they go. First, we need to start by putting the problem together. We will use one of the most common forms of equations of math, also known as the linear equation of y=mx+b.
So we have: S(w)=__x + __. S(w) is also equal to f(x), which is also equal to y. So: y= __x + __.
Let's start filling this equation in. So, because it says that she will add 25 dollars each week, The problem is addition. Also, the 25 dollars each week will represent the mx in this situation. Here's why:
The x in this can stand for the amount of week she added this 25 dollars to her account. So:
y= 25x + __.
Now, we can add the 150 to the problem because that is what she started with for this one-time deal. So now we have:
y= 25x + 150.
You can now where everything is represented, but we are not done. Let's change y and x back into S(w) and w like the question asks us to have. So:
S(w)= 25w + 150.
If you want to solve this question, just replace the number of weeks in place of all w's in the equation, like this: S(2)= 25(2) + 150.
I hope that this helps.
A school cafeteria surveys the students to see if there is demand for more
gluten-free meal choices. The results are in the table.
Total
Eat gluten-free Not Interested in
food gluten-free food
Buy lunch
20
50
70
Pack lunch
SO
20
70
Total
20
20
740
The school decides to offer more gluten free options. Which of these reasons
is supported by the survey data?
O A. Of the students who buy lunch, the yobability a student is
interested in gluten free food is greater than the probability a
student isnt interested in gluten free food
OB of the students who pack lunch the probability a student is
Interested in gluten-free food is greater than the probability a
student is interested in gluten free food
O c The probability that a student is interested in gluten free food is
greater than the probability that he or she is not interested in
gluten free food
The probability that a student buys lunch is greater than the
probability that he or she packs lunch
Answer:
B. Of the students who pack lunch, the probability a student is interested in gluten free food is greater than the possibility a student isn’t
Step-by-step explanation:
a figure is dilated by a factor of six
If a figure is dilated by a factor of 6, the perimeter of the figure will change by a factor of 6.
Step-by-step explanation:
The objects that have the same shape are known as similar figures. Since they are similar in shape it doesn't necessary for those objects to have the same size.
Dilation is the process that enlarges or shrinks the size of an object to its similar figure without changing its size. The Dilation is based on a factor that makes the object to enlarge or shrink.
Since its size has changed so as the perimeter will be changed for both of the figures. The perimeter of an object remains same as the scale factor used to dilate the object.
Consider a square with its side as 2 cm initially and dilated with factor 3.
Perimeter of the square = 4 a. where a is the side.
Then the perimeter of the square will be 8 cm initially.
After dilation the side of the square will be changed as 6.
Then the perimeter will change as 24 cm.
Thus the perimeter of the square initially has increased 3 times after dilation.
helpppppppppppppppppppppppppp
Answer:
6, 12, 24, 48, 96.
All the terms are multiples of 6.
Step-by-step explanation:
The given rule is to multiply by 2.
To find the next 4 numbers, we need to multiply 6, and the products that we've obtained after.
First number:
[tex]6 \times 2 = 12[/tex]
12 is our first number.
Second Number:
[tex]12 \times 2 = 24[/tex]
24 is our second number.
Third Number:
[tex]24 \times 2 = 48[/tex]
48 is our third number.
Last Number:
[tex]48 \times 2 = 96[/tex]
96 is our last number.
All the terms are multiples of 6.
Proof:
*When you divide 12 by 6, 24 by 4, 48 by 8, 96 by 16, the quotient is 6.6 has multiples of 12, 24, 48, and 96.6 has multiples of 12, 24, 48, and 96.12, 24, 48, and 96 have a factor of 6.In 157.83, the 3 is at the tenths place value.
Select one:
True
False
Answer:
False
Step-by-step explanation:
Your answer is false because the 3 in 157.83 is in the hundereths place not the tenths place.
I hope it helps! Have a great day!
Lilac~
write as a polynomial. a(a+9b)^2
NEED HELP ASAP
Write an explicit formula for an, the nth term of the sequence 22, 20, 18,....
Answer:
I thino the awnser is 103.5
Step-by-step explanation:
Answer:
16,12,10,8
Step-by-step explanation:
a+(n-1)d
20-22=18-2=-2
Solve for n. Isolate it on the left side of the equation.
Attached is a picture of the equation.
Will mark Brainliest! :)
Answer: Brainlest would be much appreciated
(A= amount P=principal r= interest rate n= number of times interest is compounded per unit 't' nt=time)
n=4. I'm not sure tho!!
9th grade math (i think, or 8th grade)
Answer:
28.26
Step-by-step explanation:
a=3.14159...(pi)r^2
Based on the Diagram below
Answer:
BD=ALTITUDES
CD=MEDIANS
AD=ANGLE BISECTORS
There are 6 children that each want to eat half of a chocolate bar. If they buy a
package of 4 chocolate bars, how many will be left over after they've eaten?
Answer:There would be 1 chocolate bar left over
Step-by-step explanation: 2 people can eat 1 bar.
Answer:
1 chocolate bar
Step-by-step explanation:
Since they want to eat 1/2 a bar, 2 people can eat 1 bar. 6 total children / 2 that eat 1 bar = 3 chocolate bars eaten
4 original chocolate bars - 3 already eaten = 1 remaining chocolate bar
Help me please please please
Answer:
24 [tex]in^{3}[/tex]
Step-by-step explanation:
volume formula= l x w x h
Box A:
4 x 3 x 4 = 48
Box B: 48/2 = 24
What is the volume of this right rectangular prism?
A rectangular prism with a length of 6.1 centimeters, a width of 5.4 centimeters, and a height of 8 centimeters.
Enter your answer as a decimal to the nearest hundredths place in the box.
Benjamin threw a rock straight up from a cliff that was 60 ft above the water. If the height of the rock h, in feet, after t seconds is given by the equation h=-16t^2+68t+60, how long will it take for the rock to hit the water?
Answer:
5 sec
Step-by-step explanation:
Hit the water, means h = 0
Solve -16t^2 + 68t +60 =0
4t^2 - 17t - 15 = 0
(4t + 3)(t - 5) = 0
so t = 5 sec
Sum of two numbers 120 and difference is 60. Find two
numbers.
Answer: 30&90
Step-by-step explanation:
HELP me please i dont know the answer to this
Answer:
c
Step-by-step explanation:
helpp me pleass ..........
Answer:
Step-by-step explanation:
1 and 7 is Corresponding
2 and 8 is Alternate exterior
this is what I know but I am not sure
2P - 3 > P + 6
Thanks!
[tex]2p - 3 > p + 6 \\ 2p - p > 6 + 3 \\ p > 9[/tex]
Winter breaks starts in 3 4/7 weeks. Write the mixed number as a fraction greater than one.
Answer:
25/7
Step-by-step explanation:
mixed number to improper fraction greater than 1
-multiply the denominator by the whole number then add that number to the top number and put the original denominator under that number.
Pythagorean Theorem Study Guide answers
Answer:
the theorem states that the length of the hypotenuse when squared is equal to the addition of the adjacent and opposite when squared