Using a system of equations, it is found that there are 204 boys at the school.
What is a system of equations?A system of equations is when multiple variables are related, and equations are built to find the values of each variable, according to the relations given in the problem.
For this problem, the variables are given as follows, considering the situation described:
Variable x: number of boys in the school.Variable y: number of girls in the school.Variable z: number of male teachers in the school.Variable w: number of female teachers in the school.The average of the number of boys, girls, male teachers, and female teachers is 117, hence:
(x + y + z + w)/4 = 117
x + y + z + w = 468.
The average of the number of boys, girls, and male teachers is 151, hence:
(x + y + z)/3 = 151
x + y + z = 453.
Then:
x + y + z + w = 468.
453 + w = 468
w = 15.
There are 6 fewer male teachers than there are female teachers, hence:
z = w - 6 = 15 - 6 = 9.
So:
x + y + z = 453.
x + y = 444.
The number of female teachers is 1/16 the number of girls, hence:
y = 16w = 16 x 15 = 240.x = 444 - y = 444 - 240 = 204.There are 204 boys at the school.
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a fishing boat accidentally spills 15 barrels of diesel oil into the ocean. each barrel contains 42 gallons. if the oil film on the ocean is 2.5×102nm thick, how many square meters will the oil slick cover?
The square meters of the area the oil slick will cover is 9.6 × 10⁶ m².
What is meant by volume?Volume is defined as the amount of three-dimensional space enclosed by a closed surface.
The liter (L) is the metric system's base volume unit, with several extended volume units also available. There are also many metric volume units based on the a cubic length dimension, including such cubic meters or cubic centimeters. Gallons and ounces are examples of imperial volume units.Now, as per the given question;
First, we determine the entire volume of oil in gallons by multiplying the volume per barrel even by total number of barrels:
15×42 gal = 630 gal
This volume must be converted to square meters:
V = 630 gal × (0.00379 m³/ gal
V = 2.4 m³
The thickness (height) of a oil film in meters is required:
h = 250 nm × (m/10⁻⁹nm)
h = 2.5 × 10⁻⁷m
The surface area of a oil film is calculated by dividing the oil volume by height of the oil film.
A = V/h
A = 2.4 m³/2.5 × 10⁻⁷m
A = 9.6 × 10⁶ m²
Therefore, the area of the oil slick cover is found to be 9.6 × 10⁶ m².
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Anna took a taxi from her house to the airport. the taxi company charged a pick-up fee of $3 plus $2.25 per mile. the total fare was $48, not including the tip. how many miles was the taxi ride?
Answer:
20
Step-by-step explanation:
The total fare, f, is:
f = 2.25x + 3
We want to solve for x. the number of miles. This is fairly simple if we know f.
48 = 2.25x + 3
48 - 3 = 2.25x + 3 - 3
45 = 2.25x
45/2.25 = 2.25x/2.25
20 = x
Using graph paper, solve the following inequality. Then click on the graph until the correct one is displayed.
y ≥ |x - 1|
Using translation concepts, the first graph is the correct one.
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
For this problem, the function y = |x - 1| is a shift right of 1 unit of the function y = |x|. For the inequality, all the values above the line, including the line, are marked.
The graph of |x - 1| is triangular positive, with vertex at x = 1, hence the first graph is the correct one.
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I don't understand, help would be appreciated.
Answer:
Ok so "X" will ALWAYS be the first number in a ordered pair so in this case 3 WILL be the "X" value 5 will be the "Y" value. "X" is the Horizontal line on the graph you will always start with "X" so you will go over 3 times and up 5 I'm making this complicated but pretty much all you need to know is that "X" is 3
Note: I hope you have a good day and I hoped this helped! :))
What must be added to x² - 2xa to make it a perfect square?
Answer:
we need to add [tex]a^{2}[/tex] to make it a perfect square.
Step-by-step explanation:
since we know
[tex]a^{2}+b^{2}-2ab=(a-b)^{2}[/tex]
then after compairing it with x² - 2xa
we have;
missing term as [tex]a^{2}[/tex]
hence we need to add [tex]a^{2}[/tex] to make it a perfect square.
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Cylinder A has radius 3 cm and
height 10 cm
Cylinder B has radius 6 cm and
height 8 cm
10 cm
Cylinder A
8 cm
Cylinder B
6 cm
Cylinder A is half full of water.
Work out the volume of water in
Cylinder A.
Give your answer in terms of Pie
The volume of the water filled in the cylinder A is 141.77 cm³.
How do you describe a cylinder?A cylinder is a 3 solid that contains two parallel bases connected at a fixed distance by a curved surface.
These bases are typically circular in shape (such as a circle), with the center of a two bases connected by a line segment known as the axis.A cylinder does have two flat ends shaped like circles. A curved face which resembles a tube connects these two faces. A flat net for just a cylinder resembles a rectangle with such a circle connected at each end.The formula for the volume of the cylinder is;
Volume = πr²h
Where, π = 3.14,
radius r = 3 cm.
height h = 10 cm.
Put the values and obtain the volume.
Volume = (3.14)(3)²(10)
Volume = 282.74 cm³.
As, the cylinder is half filled with water;
Water volume = 282.74/2 cm³
Water volume = 141.77 cm³
Thus, the volume of water filled in cylinder A is 141.77 cm³.
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The correct question is-
Cylinder A has radius 3 cm and height 10 cm. Cylinder A is half full of water.
Work out the volume of water in Cylinder A.
16^((3)/(8))* 16^((1)/(8))
Which expression is equivalent to 9(15)?
9(10+5)
9 left parentheses 10 plus 5 right parentheses
9(10+50)
9 left parentheses 10 plus 50 right parentheses
9(1+5)
9 left parentheses 1 plus 5 right parentheses
9(1+50)
Answer:
9(10+5)
Step-by-step explanation:
because 10+5 is fifteen so then when you as them together you get the same expression as before
Answer:
9(10+5)
Step-by-step explanation:
because 10+5=15 and it's 9(15)
a² + b²
______
a-b
if a = 3 and b = 4
Please help!
Answer:
Step-by-step explanation:
3^2+4^ / 3-4 = -25
6 minus a number minus 11
Answer:
In equation form it should be: (6-x) -11
Step-by-step explanation:
BOOM!!! Your Welcome
The data set represents the heights, in centimeters, of ten model bridges made for
an engineering competition.
13
14
14
16
16
16
16
18
19
What is the MAD?
According to the given information the mean(MAD) of the data is = 16.
What is the mean mathematical term?The mean is the average of a set of variables in mathematics and statistics. The mean can be calculated in a variety of ways, such as the simple arithmetic mean (add the numbers and divide the sum by the number of observations), geometric mean, and harmonic mean.
According to the given data:(13 ,14 ,14, 16, 16, 16, 16, 18, 18, 19)
adding the numbers together.
(13 + 14 + 14 + 16 + 16 + 16 + 16 + 18 + 18 + 19)
= 160.
Then divide it by the amount of numbers. Which is ten.
160 divided by 10 = 16.
—MAD—
Subtract each value from the mean.
(|13-16| + |14-16| + |14-16| + |16-16| + |16-16| +|16-16| + |16-16| + |18-16| + |18-16| + |19-16|)
Negative numbers are unimportant; everything should be positive.
(3 + 2 + 2 + 0 + 0 + 0 + 0 + 2 + 2 + 3)
= 16.
16 divided by 16 (amount of numbers).
MAD = 1
–IQR—
Separate both sides in half.
(|13 14 14 16 16| ,|16 16 18 18 19|)
Take the middle value of each group.
Group1.
|13 14 (14) 16 16|
This one is 14.
Group 2:
|16 16 (18) 18 19|
This one is 18.
Subtract (number from group 2) 18 from (number from group 1) 14.
18 - 14 = 4
IQR = 4.
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f(x)= [[x]] is the "greatest integer" function. The range of f(x) = x-[[x]] is:
A pilot flew a jet from City A to City B, a distance of 2000 mi. On the return trip, the average speed was 20% faster than the outbound speed. The round-trip took 9 h 10 min. What was the speed from City A to City B?
A pilot flew a jet from City A to City B, a distance of 2000 mi. On the return trip, the average speed was 20% faster than the outbound speed. The round-trip took 9 h 10 min. What was the speed from City A to City B?
A bee flies at 20 feet per second directly to a flowerbed from its hive. The bee stays at the flowerbed for 17 minutes, and then flies directly back to the hive at 12 feet per second. It is away from the hive for a total of 19
minutes.
In linear equation, the distance of the flowerbed from the hive is 2250 feet.
What in mathematics is a linear equation?
There are only one or two variables in a linear equation. No variable can be multiplied by a number larger than one or used as the denominator of a fraction in a linear equation. All of the points fall on the same line when you identify the values that together make a linear equation true and plot those values on a coordinate grid.Let , the distance of the flowerbed from the hive is feet.
The bee flies 20 feet per second directly to a flowerbed from its hive and flies directly back to the hive at 12 feet per second.
time = distance / speed
So, the time taken by the bee to reach the flowerbed x/20 seconds and the time taken to fly back to the hive = x/12 seconds.
The bee stays at the flowerbed for 15 minutes or (15×60)seconds or 900 seconds and it is away from the hive for a total of 20 minutes or (20×60)seconds or 1200 seconds.
So, the equation will be
x/20 + x/12 + 900 = 1200
3x + 5x / 60 = 300
8x = 300 * 60
x = 2250
Thus, the distance of the flowerbed from the hive is 2250 feet.
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WILL MARK BRAINLIST !!
Find the value of xº from the given figure applying the activity.
Answer:
total inner angle of quadrilateral is 360 so
66 is remaining angle.
Please mark me as brainlist answer.
You has promised. Don't broke promise that you will give brainlist answer.
Answer:
The sum of the interior angle of a quadrilateral is given by the formula
(n-2)×180°
n represent the number of sides
(4-2)×180°
2×180°
=360°
then equate the angle to 360°
Find the midpoint of the given line segment with the given endpoints
(-3, 8) and (2, -4)
The midpoint of the given line segment with the given endpoints
(-3, 8) and (2, -4) is (-0.5, 2)
Midpoint of coordinatesThe formula for calculating the midpoint of coordinate is expressed as;
M(x, y) = (x₁+x₂/2, y₁+y₋/2 )
Given the coordinate points( -3, 8) and (2, -4)
Substitute
M(x, y) = (-3+2/2, 8-4/2)
M(x, y)= (-1/2, 4/2)
M(x, y) =(-0.5, 2)
Hence the midpoint of the given line segment with the given endpoints
(-3, 8) and (2, -4) is (-0.5, 2)
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Please Help fast
What does The function decrease by as well
Answer:
Step-by-step explanation:
the given graph is montonous so no decreasing or increasing
please mark me
Answer:
the graph decreases from -infinity to -3 and 3 to positive infinity and increase from -3 to +3
Step-by-step explanation:
Regression is a statistical technique developed by blaise pascal.
a. false.
b. true.
Blaise Pascal invented the statistical method known as regression. False. The author learned through the reading that adding a bathroom increases home prices more than adding a bedroom does.
What does a statistical regression mean?
A statistical method called regression links a dependent variable to one or more independent (explanatory) variables. A regression model can demonstrate whether changes in one or more of the explanatory variables are related to changes in the dependent variable.What does regression mean?
Regress, from which the word "regression" is derived, means "to go back" in Latin (to something). Regression is the method that, in this way, enables "going back" from muddled, challenging-to-interpret data to a clearer and more understandable meaningful model.Learn more about regression
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HURRY!! A church group set off from their church at 9:00AM for the beach. The group had to change a tire at 9:31AM. The group noted that the trip took them 63 minutes to finish. What time did the church group arrive at the beach?
answer:
10:03 am
explanation:
9:00 am + 1 hour (60 min) + 3 min = 10:03 am.
-7,5 + 4,2 =?
-0,9 * 2,7 =?
Answer:
-7.5+4.2=-3.3
-0.9*2.7=-2.43
Answer:
7.5 + 4.2 = 11.7
0.9 * 2.7 = 2.43
Step-by-step explanation:
Solve the following inequality. -2x < 10
Step-by-step explanation:
-2x<10
decide both side by -2
when ever we divide by negative number the sign will change. so this < sign will change to >
x>-5
Hey there!
-2x < 10
DIVIDE -2 to BOTH SIDES
-2x/-2 < 10/-2
SIMPLIFY IT!
x < 10/-2
x > 10/-2
x > -5
Therefore, your answer should be:
x > -5
Good luck on your assignment & enjoy your day’
~Amphitrite1040:)
there are 126 students.
2/9 of them are taking geometry. 3/7
of the students taking
geometry are male.
how many female students are taking geometry?
Out of 126, 2/9 of them are taking geometry , 3/7 of the students are males ,number of female students taking geometry are 16.
As given in the question,
Total number of students = 126
Number of Students taking geometry = (2/9) × 126
= 28
Number of male students taking geometry= (3/7) × 28
= 12
Number of female students taking geometry= 28 - 12
= 16
Therefore, out of 126, 2/9 are taking geometry , 3/7 are males ,number of female students taking geometry are 16.
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The value of an item (X) is greater than or equal to $5. Which represents this statement?
The value of an item is greater than or equal to 5. This statement is represented by the inequality [tex]x\geq 5[/tex] .
An inequality is a mathematical relation which compares the values of two different entities.
The various symbols used in expressing inequalities are
a>b means a is greater than bb<a means b is less than a[tex]a\geq b[/tex] means a is greater than or equal to b[tex]a\leq b[/tex] means a is less than or equal to b.Linear inequalities in one variable are represented on the number line.
For example: a>100 represents all numbers greater than 100 along the number line
Linear inequalities in two variables are represented as a region in a cartesian plane.
For example: 2x+3y<6 represents a region below the straight line 2x+3y=6.
The given statement denotes that the value of the item is greater than or equal to 5.
Therefore the required inequality is : [tex]x\geq 5[/tex].
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If the parents of a family already have two boys, what is the probability that the next two offspring will both be girls?
The probability that the next two offspring will both be girls is 1/3.
To find P both children are girls
A: Event that both children are girls
A: {MM} and B: {MF, FM, MM} →→ P (A ∩∩ B) = {MM}
Probability that both are males, if we know one is a female =P(A/B)=P(A∩B)/P(B)
(P(A∩B)P(B))
Given S = {MM, MF, FM, FF}, we can see that: P (A) = 1414; P (B) = 3434; P (A ∩∩ B) = 1414
Therefore,
P(B/A)=P(A∩B)/P(A) = (1/4)/(3/4)=1/3.
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PLEASE HELP ME ASAP PLEASE.
Answer:
See below
Step-by-step explanation:
g (h(6)) :
h (6) = 3 ( 6^2) + 2 = 110
then g (110) = sqrt (110)
h (g(5))
g(5) = sqrt 5
then h( sqrt5) = 3 ( sqrt5)^2 + 2 = 17
An explanation needed, thx
The points (-4,2) and (4,2) are two vertices of a square. State all other order pairs that could be the other two vertices of the square.
15. If the endpoints of a diameter of a circle are (2, -1) and (4, 0), what is the y
coordinate of the center of the circle?
Y = -0.5
The center point of a straight line can be located using the midpoint formula. You may occasionally need to determine the difference between two specific numbers. For that, you find the average of the two numbers. In a similar way, we obtain the halfway number (or point) between two coordinates using the midpoint formula in coordinate geometry
Let the midpoint of (x₁ ,x₂ ) and (y₁ , y₂) is (x ,y)
x,y = ( x₁ + x₂)/2 , (y₁ +y₂)/2
Since radius is half of the diameter, we need to find the findthe midpoint of the diameter
Using midpoint formula,
y = (y₁ + y₂)/2
= (0 + (-1))/2
= -0.5
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Yasmin invests money in an account paying a simple interest of 3% per year. If no money will be added or removed from the investment, what should she multiply her current balance by to find her total balance in a year in one step?
hi
so the amount will be increased by 1 + 3/100 = 1.03
so multiply current balance by 1.03 and she will know balance in a year
is 90.790170 rational or irrational
Answer:
irrational number
Step-by-step explanation:
because it has no repeating pattern
The number x = 90.790170 is rational number as it is a finite decimal and can be represented as a fraction.
Given data:
Let the number be represented as x.
Now, the value of x = 90.790170
Rational numbers can be positive, negative, or zero, and they can be written in the form a/b, where a is the numerator and b is the denominator, with b not equal to zero.
The number 90.790170 is a rational number. A rational number is any number that can be expressed as a fraction of two integers, where the denominator is not zero.
Since 90.790170 is a finite decimal (it doesn't repeat or go on forever), it can be represented as a fraction of two integers.
Hence, 90.790170 is rational.
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Find the sum of the whole numbers from 1 to 680.
The sum of the whole numbers from 1 to 680 is 231540.
What is the sum of the whole numbers from 1 to 680?Arithmetic sequence is a list of numbers where each number is equal to the previous number, plus a constant called the common difference.
The formula for sum of first n numbers can be expressed as;
Sₙ = (n/2)( a₁ + aₙ )
Where n is the number of terms, a₁ is the first term and aₙ is the nth term.
Given that,
The numbers are whole numbers from 1 to 680
Number of terms n = 680First term a₁ = 1680th term a₆₈₀ = 680Sum S₆₈₀ = ?Plug the given values into the equation above.
Sₙ = (n/2)( a₁ + aₙ )
S₆₈₀ = (680/2)( 1 + 680 )
S₆₈₀ = 340( 681 )
S₆₈₀ = 231540
Therefore, the sum of the whole numbers from 1 to 680 is 231540.
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