Answer:
The number of sections in Ancient history is 10, number of students in Medieval history is 22 and the number of students in Modern history is 13.
Step-by-step explanation:
[tex]x[/tex] = Number of sections in Ancient history
[tex]y[/tex] = Number of sections in Medieval history
[tex]z[/tex] = Number of sections in Modern history
The number of sections that are allowed is 45 so
[tex]x+y+z=45[/tex]
The number of students in each section is 4700 where 100 of them take ancient history 50 of them take medieval history and 200 take modern history so
[tex]100x+50y+200z=4700[/tex]
The number of professors is 58 where Ancient and Medieval History need only 1 professor per section and Modern History sections are taught by a team of 2 professors, so
[tex]x+y+2z=58[/tex]
Solving the first and last equations by subtracting them we get
[tex]-z=-13\\\Rightarrow z=13[/tex]
Substituting this value in the second equation and first equation we get
[tex]100x+50y+2600=4700\\\Rightarrow 100x+50y=2100\\\Rightarrow 2x+y=42[/tex]
[tex]x+y+13=45\\\Rightarrow x+y=32[/tex]
Solving these equations by subtracting them we get
[tex]x=10[/tex]
[tex]x+y=32\\\Rightarrow y=32-10=22[/tex]
So, [tex]x=10, y=22, z=13[/tex]
Hence, the number of sections in Ancient history is 10, number of students in Medieval history is 22 and the number of students in Modern history is 13.
Ingrid and Harish were trying to solve the equation:
22 - 3x = x + 1
Ingrid said, "First, I'll subtract x from both sides so I have a? - 4x = 1. Then I can solve by completing the
square. If I add 4 to each side, I can rewrite the equation as (x - 2)² = 5."
Harish said, “I'll isolate the xạ term by adding 3x to both sides of the equation. Then I'll solve by taking the
square root."
Whose solution strategy would work?
Answer:
Only Ingrid's equation is correct
Answer:
Only Ingrid’s solution works
3. In the same opera theater personal balcony sections with three rows of seating are being mapped as well. In
these sections there must be an odd number of seats in each row and each row must have two more seats
than the one before it. The last stipulation is that the front row must have one quarter the total seats in the
back 2 rows combined. How many seats will be in each row?
Answer:
Number of seats in first row = 2
Number of seats in 2nd row = 4
Number of seats in 3rd row = 6
Step-by-step explanation:
Let's say number of seats in first row is x.
Now we are told that each row must have two more seats
than the one before it.
Thus, the remaining 2 rows have;
(x + 2) and (x + 4) seats respectively.
We are told that that the front row must have one quarter the total seats in the
back 2 rows combined.
Thus;
x = ¼((x + 2) + (x + 4))
Multiply both sides by 4 to give;
4x = x + 2 + x + 4
4x = 2x + 4
4x - 2x = 4
2x = 4
x = 4/2
x = 2
Thus;
Number of seats in first row = x = 2
Number of seats in 2nd row = (x + 2) = 2 + 2 = 4
Number of seats in 3rd row = (x + 4) = 2 + 4 = 6
Answer:
3, 5, and 7
Explanation:
look at photo attached
determine the annual amount that an investor would earn on a rental property that pays $850.00 per month.
Answer:10,200
Step-by-step explanation:
How do I solve this equation? -6=b/18 and v-15-=-27
Answer:
-6 = b/18
-6×18=b
-108 = b ans.
and
v-15- = -27
v = -27 +15
v = -12 ans.
The data below represent commute times (in minutes) and scores on a well-being survey. Complete parts (a) through (d) below. Commute Time (minutes), x 5 15 30 35 50 84 105 Well-Being Index Score, y 69.1 67.8 66.2 65.9 64.6 62.6 60.2 (a) Find the least-squares regression line treating the commute time, x, as the explanatory variable and the index score, y, as the response variable. y=negative 0.083−0.083x+69.04069.040 (Round to three decimal places as needed.) (b) Interpret the slope and y-intercept, if appropriate. Interpret the slope. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. For an index score of zero, the commute time is predicted to be nothing minutes. (Round to three decimal places as needed.) B. For every unit increase in index score, the commute time falls by nothing, on average. (Round to three decimal places as needed.) C. For a commute time of zero minutes, the index score is predicted to be nothing. (Round to three decimal places as needed.) D. For every unit increase in commute time, the index score falls by nothing, on average. (Round to three decimal places as needed.) E. It is not appropriate to interpret the slope.
Answer:
(a) [tex]\hat y=69.04-0.083\cdot x[/tex]
(b) D. For every unit increase in commute time, the index score falls by 0.083, on average.
Step-by-step explanation:
(a)
Form the least-squares regression line using Excel as follows:
Go to Data → Data Analysis → Regression
A dialog box will open.
Select the X and Y variable.
Press Ok.
The regression output is attached below.
The least-squares regression line is:
[tex]\hat y=69.04-0.083\cdot x[/tex]
(b)
The slope of a regression line is the average rate of change in the dependent variable (y) with 1 unit change in the independent variable (x).
Here the slope value is -0.083. This value implies that with 1 minute change in the commute times the Well-Being Index Score falls by 0.083 units.
The intercept of a regression line is the average value of the dependent variable (y) when the independent variable (x) value is 0.
Here, the intercept value is 69.04. This value implies that for a person with commute time 0, their Well-Being Index Score is 69.04.
The correct option is:
D. For every unit increase in commute time, the index score falls by 0.083, on average.
Round 5,896,487 to the
nearest ten-thousand.
Answer:12
Step-by-step explanation:
u half to round it to the nerest hundreths and than multiplye it by 4
Answer: 5,900,000
Step-by-step explanation: 5,900,000 ~ 5,896,487 ( 800,000) Round it ~ = 5,900,000
What is answer in this question.
Answer:
A line segment congruent to PQ
What is the maximum of the numbers listed below?
5.2, 5.4, 4.9, 4.4, 5.1
Answer:
5.4
Step-by-step explanation:
5.2, 5.4, 4.9, 4.4, 5.1
4.4, 4.9, 5.1, 5.2, 5.4
5.4 is the maximum
Hope this helped!
I need some help understanding this
Answer:
????what is the question
6299 round to neaRest hundred
Answer:
6300
Step-by-step explanation:
plz give me a harder answer next time :)
question in the picture
Answer:
The answer is B
Step-by-step explanation:
Answer:
2 divided by 3
Step-by-step explanation:
Help me pls will give out points
[tex]y = ab^{x} [/tex]
[tex]y = 3 \times {4}^{x} [/tex]
"a" is the initial amount (3), and "b" is the growth factor (4).
To find "b" plug in the knowns into the exponential function equation and solve.
[tex]y = ab^{x} [/tex]
[tex]48 = 3 \times {b}^{2} [/tex]
[tex]16 = {b}^{2} [/tex]
[tex] \sqrt{16} = b[/tex]
[tex]b = 4[/tex]
Round 43.586 to the nearest tenth. Pleaseee help ASAP
Answer:
43.6
Step-by-step explanation:
I hope this helps you :)
Answer:
43.59
Step-by-step explanation:
43.59 because it is
Help please on number 2 math problem.
Answer:
Its's $3 for an adult ticket and $1 for a student ticket
Step-by-step explanation:
Kari wants to measure the height of a tree. She walks exactly 90 feet away from the base of the tree and looks up to the top of it. The angle from the ground to the top of the tree is 32 degrees. This particular tree grows at an angle of 85 degrees with respect to the ground rather than vertically. How tall is the tree to the nearest tenth of a foot? Enter a number answer only.
Answer:
this is a Sin(), Cos() and Tan() function problem. use the Mnemonic (new-monic) SOH CAH TOA (soo caw tow ah ) to remember which function sin() cos() or tan() to use.. :) these types of problems are pretty confusing, Use that Mnemonic to keep the functions in order
Step-by-step explanation:
since we know the distance to the tree.. and we know the angle and we have a formula TOA to figure out the one pieces of info we don't know ... use TOA that tells us our formula.. TOA(Ф)=Opp / Adj where Tan(Ф) is using Ф= to our angle of 32 degrees ( remember Ф can be in degrees or radians, its in degrees for this problem) Adj = the Adjacent side of the triangle from the known angle.. the 32 degree angle , Opp = the Opposite side of the triangle formed by the imaginary lines from Kari to the base of the tree and from Kari to the top of the tree.. and then the tree , from it's base to it's top... we know the angle and the Adj side of that triangle so we can figure out that last part of TOA by saying Tan(Ф)=Opp/ Adj .... or say Tan(32)= Opp / Adj ⇒ Tan(32)=Opp / 90 ⇒ Tan(32) *90 = Opp this will be the height from the ground to the top of the tree.. but.. the tree is at an angle , keep in mind... sooo Tan(32)*90=56.238 feet now take the new triangle that we know one side to... from the ground to the height of the tree.. in a vertical line from the ground to a point at 56.238 feet .. that is the Adj side of this new triangle.. the tree is on the Hypotenuse of this new trialge, which we want to find. we know the Adj side we know the angle to find the Hypotenuse use CAH , from our Mnemonic at the top, the Mnemonic is really important b/c keeping track of which part goes where in the triangles is pretty confusing. Cos(5)=Adj / Hyp ⇒ Cos(5)=56.238 / Hyp ⇒56.238 / Cos(5)= Hyp = 56.453 feet :) that's how tall that tree is , lets chop it down :P and blame it on George Washington :P The tree, to the nearest 10th of a foot, is 56.5 feet
WILL MARK BRAINLIEAT I NEED ANSWER NOWSelect the correct answer.
If the function 5x + y = 1 has the domain {-2, 1,6}, then what is the corresponding range?
O A.
{-9, 6, 31}
B. {9, -6, -31}
C. {-11, 4, 29}
D. {11, -4,-29}
Answer:
D, R: {11, -4, -29}
Step-by-step explanation:
According to the given set of domains, the corresponding range is found by substituting the x values into the equation and solving for y.
i.e {-2} -> 5x + y = 1, -10 + y = 1, y = 11
{1} -> 5x + y = 1, 5 + y = 1, y = -4
{6} -> 5x + y = 1, 30 + y = 1, y = -29
Answer:
The short answer is D
how many days are in 2 years + 18 months?
please help!!!!
Answer:
1277
Step-by-step explanation:
Answer:
1278.04
Step-by-step explanation:
Why? In 1 year there are approximately 365.24 days, but in 1 month there are approx 30.42 days.
So 365.24 × 2 = 730.48
And 30.42 × 18 = 547.56 (+
-----------------------
1278.04
PLS HELP ME! Write a rule (function) for the data in this table.
Answer:
y = x - 3
How I know I'm correct:if you plug in the numbers from the table, it checks out.
y = x - 3
0 = 3 - 3
0 = 0
y = x - 3
1 = 4 - 3
1 = 1
y = x - 3
2 = 5 - 3
2 = 2
and so on
Solve for x in the equation.
Answer:
The solution is [tex]\displaystyle x=1\pm \sqrt{47}[/tex]. Fourth option
Explanation:
Solve for x:
[tex]2x^2+3x-7=x^2+5x+39[/tex]
Move all the terms from the right to the left side of the equation, a zero in the right side:
[tex]2x^2+3x-7-x^2-5x-39=0[/tex]
Join all like terms:
[tex]x^2-2x-46=0[/tex]
The general form of the quadratic equation is:
[tex]ax^2+bx+c=0[/tex]
Solve the quadratic equation by using the formula:
[tex]\displaystyle x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
In our equation: a=1, b=-2, c=-46
Substituting into the formula:
[tex]\displaystyle x=\frac{-(-2)\pm \sqrt{(-2)^2-4(1)(-46)}}{2(1)}[/tex]
[tex]\displaystyle x=\frac{2\pm \sqrt{4+184}}{2}[/tex]
[tex]\displaystyle x=\frac{2\pm \sqrt{188}}{2}[/tex]
Since 188=4*47
[tex]\displaystyle x=\frac{2\pm \sqrt{4*47}}{2}[/tex]
Take the square root of 4:
[tex]\displaystyle x=\frac{2\pm 2\sqrt{47}}{2}[/tex]
Divide by 2:
[tex]\displaystyle x=1\pm \sqrt{47}[/tex]
First option: Incorrect. The answer does not match
Second option: Incorrect. The answer does not match
Third option: Incorrect. The answer does not match
Fourth option: Correct. The answer matches exactly this option
BRAINLIST AND 20 POINTS I REALLY NEED HELP ASAP (10 POINTS FOR EACH QUESTION)
Answer:
7 bottles
$10
Step-by-step explanation:
multiply
1/6×42= 7 bottles
5/9×18= $10
Solve. Write your answer without exponents.
3^0 x 3^4
Step-by-step explanation:
3^0 is 1 and 3^4 is 81
I think you can solve it now
Hope this helps <3
80 times what equals 44??
Answer:
0.55
Step-by-step explanation:
Answer:
0.55
Step-by-step explanation:
44 divided by 80
= 0.55
Wait i got a question is that little star suppose to be this × or this ÷
Answer:
You're really gonna sit there and just focus on your life all day ... And the section was tiny—it covered the same amount of ...
Step-by-step explanation:
make me as brain liest
if given f(x)=2x+5 what is f(x)=17
Answer:
39
Step-by-step explanation:
F(17)= 2(17)+5
2x17=34 +5=39
Please y’all Help me
Answer:
Upload a file please
Step-by-step explanation:
Write a linear equation that is parallel to the line 3x−2y=14 and passes through the point (−6,−11) in slope-intercept form.
#2.) Town B is 380 km do south of town A. Town C is 460 km due east of town B. What is the distance from town A to town C? Explain your reasoning. Be ute to round your answer appropriately.
D 1. Find (f + g)(x) if f(x) =
4x^2– 5x + 8 and g(x) = 2x^2 + x - 2.
1- (f+g)(x) = 2x^2 + 6x - 10
2- (f+g)(x) = 6x^2 + 4x - 6
3- (f +9)() = 6x^2 - 4x + 6
4- (f+g)(x) = 2x^2- 6x + 10
answer 2
Step-by-step explanation:
the second one
TJ is think of a number which he calls n he finds 1/3 of the number
Answer:
Step-by-step explanation:
Let the number TJ thinks of be n.
If he finds 1/3 of the number, the expression that models this situation is expressed as:
1/3 of n
= 1/3 * n
= n/3
hence the expression that models the scenario is n/3
Answer:
1/3n-5
Step-by-step explanation:
whats 225.286 rounded to the nearest ones? please help ASAP
Answer:
225
Step-by-step explanation:
Answer:
The answer is 225