The total number of students who went to the conference was 240 students
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
The total number of schools = 5 schools
Let the schools be A , B , C , D , E
One of the schools sent boys and girls
The number of boys A = 16 boys
The ratio of boys to girls is = 1 : 2
So , the number of girls = 2 x number of boys
The number of girls A = 2 x 16
= 32 girls
Now , the equation will be
The number of students sent to conference by school A = 16 + 32
The number of students sent to conference by school A = 48 students
Now , the equation will be
All the schools sent the same number of students
So , The total number of students = Total number of students in A x 5
The total number of students = 48 x 5
= 240 students
Therefore , the total number of students is 240 students
Hence , The total number of students who went to the conference was 240 students
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The slope intercept form of a linear equation is y=mx+b,where x and y are coordianates of an ordered pair, m is the slope of the line, and b is where the Crosse...
Answer:
The equivalent equation solved for x is x = (y-b)/m
Step-by-step explanation:
Here is the complete question:
The slope-intercept form of a linear equation is y = mx + b, where x and y are coordinates of an ordered pair, m is the slope of the line, and b is where the line crosses the y-axis.
Which is an equivalent equation solved for x?
x = y-bmx = y-b over m
x= my + b
m=y−bxm is equal to the fraction with numerator y minus b and denominator x
x=y−bm
Step-by-step explanation:
To determine the equivalent equation solved for x, we will make x the subject of the formula.
From the given equation,
y = mx + b
To make x the subject of the equation,
First, add -b to both sides of the equation, so that we get
y +(-b) = mx +b +(-b)
Then, we will get
y-b = mx +b -b
y-b = mx
Finally, to make x the subject of the equation, we will divide both sides by the coefficient of x ( that is, m)
(y-b) / m = mx / m
Then,
(y-b)/m = x
∴ x = (y-b)/m
Hence, the equivalent equation solved for x is x = (y-b)/m.
The first option is correct
x = (y-b)/m = y-b over m
[Sin A + Sin 3A + Sin 5A + Sin 7A]÷
[Cos A + Cos 3A + Cos 5A + Cos 7A]
=Tan 4A
Do the following rewrites:
sin(x) = sin(4x - 3x) = sin(4x) cos(3x) - cos(4x) sin(3x)
sin(7x) = sin(4x + 3x) = sin(4x) cos(3x) + cos(4x) sin(3x)
sin(3x) = sin(4x - x) = sin(4x) cos(x) - cos(4x) sin(x)
sin(5x) = sin(4x + x) = sin(4x) cos(x) + cos(4x) sin(x)
cos(x) = cos(4x - 3x) = cos(4x) cos(3x) + sin(4x) sin(3x)
cos(7x) = cos(4x + 3x) = cos(4x) cos(3x) - sin(4x) sin(3x)
cos(3x) = cos(4x - x) = cos(4x) cos(x) + sin(4x) sin(x)
cos(5x) = cos(4x + x) = cos(4x) cos(x) - sin(4x) sin(x)
So in the numerator, we have
sin(x) + sin(3x) + sin(5x) + sin(7x)
= 2 sin(4x) cos(3x) + 2 sin(4x) cos(x)
= 2 sin(4x) (cos(3x) + cos(x))
In the denominator,
cos(x) + cos(3x) + cos(5x) + cos(7x)
= 2 cos(4x) cos(3x) + 2 cos(4x) cos(x)
= 2 cos(4x) (cos(3x) + cos(x))
So we have
(sin(x) + sin(3x) + sin(5x) + sin(7x)) / (cos(x) + cos(3x) + cos(5x) + cos(7x))
= (2 sin(4x) (cos(3x) + cos(x))) / (2 cos(4x) (cos(3x) + cos(x)))
= sin(4x) / cos(4x)
= tan(4x)
QED
There were 306 students in the cafeteria. After some went outside, there were 249 students left in the cafeteria. How many students went outside? Write an equation and solve the problem?
Answer:
The equation to solve the problem is
306 = 249 + x
x = 306 - 249
Hence:
57 students went outside
Step-by-step explanation:
Let the number of students outside be represented by x
Hence:
Number of students in the cafeteria = Number of students inside - Number of students who went outside
We are told:
There were 306 students in the cafeteria. After some went outside, there were 249 students left in the cafeteria.
The equation to solve the problem is given as:
306 = 249 + x
x = 306 - 249
Hence:
x = 57
57 students went outside
two supplementary angles differ by 34. find the angles..
Answer:
107°
73°
Step-by-step explanation:
Let the two supplementary angles be x° and y°.
x + y = 180....(1)
Since, supplementary angles differ by 34.
Therefore,
x - y = 34....(2)
Adding equations (1) & (2)
x + y = 180
x - y = 34
_________
2x = 214
x = 214/2
x = 107°
Plug x = 107 in equation (1)
107 + y = 180
y = 180- 107
y = 73°
here to you!!!!!!!! now prove it
Answer:
teenagers who watch TV =2
teenagers wearing glasses =5
hence probability =2/5=0.4
now you prove how ur answer is 0.5
Susan buys a movie ticket for $12.50 and 3 buckets of popcorn that cost $14.20 each with her
$100. Which statement is true?
Answer: the answer is NO
Step-by-step explanation:
Khan academy
What are the greatest common factors between 18
and 21?
Answer:
1, 2, 3, 6, 9, 18. Factors of 21: 1, 3, 7. The highest number that both sets contain is 3, so the GCF will be 3.
Step-by-step explanation:
CAN YALL HELP ME-
which type of transformation is described by (x y) (x+2 y+3)
Answer:
Reflection. Hope this helps you :)
Water flows through a pipe at a rate of 2 fluid ounces per second. Express this rate of flow in quarts per minute.
Answer:
3.90625 quarts per minute.
Step-by-step explanation:
we want to convert from ounces to quarts
and also from seconds to minutes
1 ounces is equal to 0.03125qtz
2 ounces will be x
cross multiply
x=0.0625 quarts
i minutes is equal to 60 sec
x minute is equal to 1 sec
cross multiply
x= 1/60
x=0.016 minute
rate of flow in quarts per minute.
=0.0625/0.016
=3.90625 quarts per minute.
pls help will mark brainliest
Answer:x=0,5
Step-by-step explanation:
6x -1/2=1
6x-1=1.2
6x-1=2
6x=2+1
6x=3
x=3/6
x=0,5
Anything helps thank you
Answer:
It's been a while since I've done stuff like that but I think the y intercept is the flat fee and the slope is the amount added.
Answer:
Ich habe keine Ahnung, aber danke für die Punkte!
Step-by-step explanation:
HELP ME ASAP 10 POINTS WILL BE GIVIN
Answer:
h = A/b
Step-by-step explanation:
A = bh Divide b from both sides of the equation
A/b = bh/b On the right side, the b in the numberator and denominator cancel out.
h = A/b
Last year, your store's total revenue was $272,000. The store's total discounts were $3,505 and returns totaled $1,459.
What were your store's net sales?
a) $209,844
b) $254.984
c) $267.036
d) $289,890
Answer: 267,306
Step-by-step explanation:
the grace your family is driving from Sacramento California to Key West Florida and 5 days they had travel 2045 miles at this rate, how long will it take them to travel from Sacramento to key west.
Step-by-step explanation:
it will take them 104 hours.
Try it
CO
Arrange the tiles on both boards to find the value of x.
What x value solves the equation?
3x - 5 = 1
.
X=
Board sum: 3x + (-5) = 1
Board was restored to starting
point.
Reset
A skydiver falls 288.52 feet in four seconds.
The skydiver fall feet per second.
Answer:
72.13
Step-by-step explanation:
72.13
4|288.52
28
08
8
Alexa brought 20 chocolate cookies and sugar cookies to the fall party in the ratio of 2:3. How many chocolate cookies does she have?
Answer:
8 chocolate cookies
Step-by-step explanation:
2+3 = 5
20/5=4
4x2
8
As a plane takes off it ascends at a 20 degree angle of elevation. If the plane has been traveling at an average rate of 290 ft/s and continues to ascend at the same angle, then how high is the plane after 10 seconds (the plane has traveled 2900ft).
Given :
As a plane takes off it ascends at a 20 degree angle of elevation.
If the plane has been travelling at an average rate of 290 ft/s and continues to ascend at the same angle.
To Find :
How high is the plane after 10 seconds.
Solution :
Distance travelled by plane, D = 2900 ft.
Angle of elevation, Ф = 20°.
Height gained is given by :
[tex]H = Dsin\ \phi[/tex]
H = 2900 × sin 20°
H = 991.86 ft.
Therefore, height of plane after 10 seconds is 991.86 ft.
Hence, this is the required solution.
whats the slope intercept form for the points [5,2] and [0,-1]
Answer:
[tex]\displaystyle y=\frac{3}{5}x-1[/tex]
Step-by-step explanation:
The Equation of a Line
The equation of the line in slope-intercept form is:
[tex]y=mx+b[/tex]
Where m is the slope and b the y-intercept.
The equation of a line passing through points (x1,y1) and (x2,y2) can be found as follows:
[tex]\displaystyle y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
We are given the points (5,2) and (0,-1), thus:
[tex]\displaystyle y-2=\frac{-1-2}{0-5}(x-5)[/tex]
Operating:
[tex]\displaystyle y-2=\frac{-3}{-5}(x-5)[/tex]
[tex]\displaystyle y-2=\frac{3}{5}(x-5)[/tex]
To find the slope-intercept form, we continue to simplify the expression:
Removing the parentheses:
[tex]\displaystyle y-2=\frac{3}{5}x-\frac{3}{5}\cdot 5[/tex]
[tex]\displaystyle y-2=\frac{3}{5}x-3[/tex]
Adding 2:
[tex]\displaystyle y=\frac{3}{5}x-3+2[/tex]
[tex]\mathbf{\displaystyle y=\frac{3}{5}x-1}[/tex]
Which number line represents the solutions to 1-2x] = 4?
+ +
+
-10 -8 -6 -4 -2 0 2 4
+ +
8 10
6
+
-10 -8 -6 -4 -2 0 2 4 6
+
8
10
+
+
-10 -8 -6 -4 -2 0 2 4 6 8
=>
10
A+
+ + + + + +
-10 -8 -6 -4 -2 0 2 4 6 8 10
Answer:
The answer is -2 and 2.
Step-by-step explanation:
You have to solve the modulus :
[tex] | - 2x| = 4 [/tex]
[tex] - 2x = ±4[/tex]
[tex] - 2x = 4[/tex]
[tex]x = - 2[/tex]
[tex] - 2x = - 4[/tex]
[tex]x = 2[/tex]
carmela walked 3 miles in 3/4 hours Hari walked 2 miles in 1/2 did they walk the same speed?
Answer:Yes
Step-by-step explanation:
Carmela:3/4/3=1/4 per mile
Hari:1/2/2=1/4 per mile
HEY CAN ANYONE PLS ANSWER DIS MATH QUESTION!!!!!!!
Answer:
Up to 10
Step-by-step explanation:
Cost of fish = $3.99Limit of money = $40Number of fish = xInequality:
3.99x ≤ 40x ≤ 40/3.99x ≤ 10.02Find the slope of the line that passes through (10,9) and (5,11)
Answer:
the answer is -2/5
Step-by-step explanation:
Help please photo is above
Answer:
y = 5
x = 10
Step-by-step explanation:
-4(2y) + 11y
-8y + 11y = 15
3y = 15
/ 3 /3
y = 5
x = 10
A sixth-grade science club needs $180 to pay for the tickets to a science museum. All tickets cost the same amount. What could \large 180\div15 mean in this context? Describe two interpretations of the expression. Then, find the quotient and explain what it means in each interpretation. Your answer:
Answer:
Two interpretations:
1. Ticket price for each student
2. Number of students
Quotient = 12
Step-by-step explanation:
Given that:
Total money to be paid for the tickets to the science museum = $180
To find:
Two interpretations, what does the expression [tex]\large 180\div15[/tex] represent ?
Solution:
The expression [tex]\large 180\div15[/tex] has two terms:
1st is 180, which is the amount of money to be paid for the tickets to the science museum.
As price of all the tickets is same, 15 might be one of the two things:
1. Total Number of candidates:
If 15 is the total number of candidates, then the expression [tex]\large 180\div15[/tex] represents the price of each ticket.
2. Price of each ticket:
If 15 is the price of each ticket, then the expression [tex]\large 180\div15[/tex] represents the Total number of candidates.
Now, let us find the quotient:
[tex]\large 180\div15=\bold{12}[/tex]
uh .. help i guess? :)
Answer:
90°
45°
45°
90°
Step-by-step explanation:
this is a square all the sides and angles are equal .
all angles being 90°.
and all diagonals of a square are also 90°
How to find a missing angle
Answer:
by solving it's angle it's easy
Find -0.2(4.75). Show your work
Answer:
4/95
Step-by-step explanation:
convert -4.75 into the fraction 19/4 and -0.2 into -2/10 then multiply across and simplify
How can 12 x 50 help you find 12 x 49?
Answer:
It can help by solving out 12x50 because it is easier to solve without a calculator
Step-by-step explanation
Answer:
12x50=600
12x49=588
600-12=588!
Step-by-step explanation:
28% of US adults say they are more likely to make purchases during a sales tax holiday. You randomly select 10 adults. Find the probability that the number of adults who say they are more likely to make purchases during a sales tax holiday is (a) exactly two, (b) more than two, and (c) between two and five, inclusive.
Answer:
a
[tex]P(X = 2) = 0.2547[/tex]
b
[tex]P(X > 2) = 0.5623 [/tex]
c
[tex]P(2 \le X \le 5 ) = 0.7817 [/tex]
Step-by-step explanation:
From the question we are told that
The proportion of US adults who say that they are likely to make purchase during a sale tax holiday is
[tex]p = 0.28[/tex]
The sample size is n = 10
Generally the distribution of US adults who say that they are likely to make purchase during a sale tax holiday, follows a binomial distribution
i.e
[tex]X \~ \ \ \ B(n , p)[/tex]
and the probability distribution function for binomial distribution is
[tex]P(X = x) = ^{n}C_x * p^x * (1- p)^{n-x}[/tex]
Here C stands for combination hence we are going to be making use of the combination function in our calculators
Generally the probability number of adult is exactly 2 is mathematically represented as
[tex]P(X = 2) = ^{10}C_2 * (0.28)^2 * (1- 0.28)^{10-2}[/tex]
=> [tex]P(X = 2) = 45 * 0.0784 * 0.0722[/tex]
=> [tex]P(X = 2) = 0.2547[/tex]
Generally the probability number of adult is more than 2 is mathematically represented as
[tex]P(X > 2) = 1- [P(X \le 2) ][/tex]
[tex]P(X > 2) = 1- [[P(X = 0)] +[P(X = 1) ] + [P(X = 2)] ][/tex]
=> [tex]P(X > 2) = 1- [^{10}C_0 * (0.28)^0 * (1- 0.28)^{10-0}] +[^{10}C_1 * (0.28)^1 * (1- 0.28)^{10-1}] + [^{10}C_2 * 0.28^2 * (1- 0.28)^{10-2}] ][/tex]
=> [tex]P(X > 2) = 1- [0.0374 + 0.1456 + 0.2547 [/tex]
=> [tex]P(X > 2) = 0.5623 [/tex]
Generally the probability number of adult is between two and five, inclusive is mathematically represented as
[tex]P(2 \le X \le 5 ) = [P(X = 2 ) + P(X = 3 ) +P(X = 4) + P(X= 5 )] [/tex]
=> [tex]P(2 \le X \le 5 ) = [[^{10}C_32 * 0.28^2 * (1- 0.28)^{10-2}] + [^{10}C_3* 0.28^3 * (1- 0.28)^{10-3}] +[^{10}C_4 * 0.28^4 * (1- 0.82)^{10-4}] + [^{10}C_5 * 0.28^5 * (1- 0.28)^{10-5}]] [/tex]
=> [tex]P(2 \le X \le 5 ) = [[0.2547] + [120* 0.02195 * 0.1003] +[210 * 0.00615 * 0.1393] + [252 * 0.0017 * 0.1935]] [/tex]
=> [tex]P(2 \le X \le 5 ) = [[0.2547] + [0.2642] +[0.1799] + [0.0829] [/tex]
=> [tex]P(2 \le X \le 5 ) = 0.7817 [/tex]