There are 1240 students in the school.
What is Proportionalities (Ratios)?
It is possible to represent absolute connections using ratios or proportions, independent of the variables' actual raw values. For instance, if your business always produces widgets packaged in bundles of 20 widgets each, you will always have a 20 widgets to 1 bundle ratio regardless of how many bundles you produce. Accordingly, if you produce 100 bundles per day, you will have produced 2000 widgets in a single day. The proportion of widgets to bundles is constant and does not change. As long as the other ratio factor quantity is known or can be known, the ratio or proportion can then be used as a conversion factor to calculate the number of an unknown quantity of one ratio factor.
In our problem, we know that there are 11 boys : 9 girls in the school. We also know that there are 124 more boys than girls.
If we let x equal the number of girls in the school, the number of boys will then be x+124. We know the ratio of boys to girls and produce a conversion factor to determine the number of girls present in the school:
( number of boys)[tex]$\left(\frac{\text { girls }}{\text { boys }}\right)=$[/tex] number of girls
[tex](x+124)\left(\frac{9}{11}\right)=x[/tex]
Note that since we are looking to find the number of girls, it appears in the numerator of the conversion factor and boys in the denominator. If we were looking for the number of boys, we would flip the conversion factor to have the number of boys in the numerator and girls in the denominator.
Now let's simplify the equation and solve for x :
[tex]\begin{aligned}(x+124)\left(\frac{9}{11}\right) & =x \\\frac{9 x+1116}{11} & =x \\9 x+1116 & =11 x \\1116 & =11 x-9 x \\1116 & =2 x \\\frac{1116}{2} & =x=558\end{aligned}[/tex]
If we have 558 girls, the number of boys is then:
x+124=558+124=682boys
Adding the number of boys and girls together, we will have the total number of students in the school: 558+682=1240 students
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16 miles out of 40 miles
The 16 miles out of 40 miles. Then the percentage will be 40%.
What is the percentage?The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
The 16 miles out of 40 miles. Then the percentage is calculated as,
P = (16 / 40) x 100
P = 0.40 x 100
P = 40%
The 16 miles out of 40 miles. Then the percentage will be 40%.
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The missing part of the question is given below.
Determine the percentage.
What is the equation in STANDARD FORM of the line that passes through the points (-4, 47) and (2, -16)?
A) y = -10.5x + 5
B) 2x + 21y = 105
C) 2x -21y = 979
D) 21x + 2y = 10
:)
The equation of the straight line is 2y + 21x = 10. The correct option is (D).
How to represent a straight line on a graph?To represent a straight line on a graph consider two points namely x and y intercepts of the line. To find x-intercept put y = 0 and for y-intercept put x = 0. Then draw a line passing through these two points.
The given points are (-4, 47) and (2, -16) respectively.
The equation of the straight line passing through them can be written as,
(y - 47)/(x - (-4)) = (-16 - 47)/(2 - (-4))
=> (y - 47)/(x + 4) = -63/6
=> (y - 47)/(x + 4) = -21/2
=> 2(y - 47) = -21(x + 4)
=> 2y - 94 = -21x - 84
=> 2y + 21x = -84 + 94
=> 2y + 21x = 10
Hence, the standard form of the straight line passing through given points is 2y + 21x = 10.
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Adelyn is planning to sell popcorn to raise money for a fundraiser.
She will need to rent a popcorn popper and will also need to purchase popcorn kernels, oil, salt, and bags.
She has at most $90 to spend on the fundraiser.
The rental of the popcorn popper costs $50.
The cost of popcorn kernels, oil, salt, and bags is $0.25 per serving.
Which inequality could be used to find out how many servings of popcorn that Adelyn will be able to make?
Answer: 50 + 0.25 is less than 90
Step-by-step explanation:
The charge in dollars for cab rides in one city is modeled by f(c) = 4 + 2.5m, when m is the number of miles traveled. What is the charge for a 4-mile ride?
Please help with ixl
Answer:
<AFC
Step-by-step explanation:
Vertical angles are pairs of opposite angles that are created by two intersecting lines. As an example, the other pair of vertical angles are <CFD and <AFE.
if the equation x^2 + 16x + c = 0 has only one real solution, the value of c must equal
If the equation x² + 16x + c = 0 has only one real solution, the value of c is equal to 64.
Discriminant:The quadratic formula includes the discriminant, which comes after the square root. The discriminant of a quadratic equation is important because it indicates the quantity and kind of solutions.
The formula for the Discriminant of a Quadratic Equation ax²+bx +c = 0 is given by
Discriminant Δ = b² - 4acHere we have
x² + 16x + c = 0 equation has only one real solution
Compare given equation with ax²+ bx + c = 0
=> a = 1, and b = 16
As we know when an equation has only one real solution
then its Discriminant will be equal to zero
=> b² - 4ac = 0
By the above values,
=> 16² - 4(1)c = 0
=> 256 - 4c = 0
=> 4c = 256
=> c = 256/4
=> c = 64
Therefore,
If the equation x² + 16x + c = 0 has only one real solution, the value of c is equal to 64.
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For the function: y = startroot x minus 7 endroot minus 1 the domain is : x ≥ the range is: y ≥
The domain the function is In interval notation [7, ∞). The range of the function is in the interval (-1, ∞).
What is function?A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). A "vertical line test" can be used when examining a graph to determine whether a relation is a function. The relation is not a function if any point on the graph can be used to draw a vertical line that crosses the relation twice.
Here,
y=√(x-7)-1
x-7≥0
x≥7
at x=7
y=√(7-7)-1
y=-1
The function's domain is represented by the interval notation [7, ∞). The function's range falls within the range [-1, ∞).
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amelia paid a weekly salary of $500 to sell jewelry at international Diamond Center in addition,she makes a total of 12% of commission off all of her sales. How much does Amelia make this week if she sells $22,540 worth of jewerly this week?
Answer:
Step-by-step explanation:
Jermaine plays classical guitar at a local restaurant in the evenings. If jermaine plays 23 songs per evening, how many songs does he play in 73 evenings?.
Answer:
1679 songs
Step-by-step explanation:
23
x73
----------------------------
69
+ 1610
-------------------------------
1679
what goes in the missing box
Answer:
10
Step-by-step explanation:
in the first one, 6 16 8, (6×8)/3=16
in the third one, 9 21 7, (9×7)/3=21
using the same comcept, 5 ? 6, (5×6)/3=10
so, ?=10
a sample of size 115 will be drawn from a population with mean 48 and standard deviation 12 . use the ti-83 plus/ti-84 plus calculator. (b) find the 25th percentile of x . round the answer to at least two decimal places. the 25th percentile is
Using the ti-83 plus/ti-84 plus calculator, the 25th percentile of x is equal to 47.25 with a mean of 48 and a standard deviation of 12, respectively.
what is mean ?A dataset's mean is calculated by dividing the sum of all values by the total number of values. The term "average" is frequently used to describe it because it is the most widely used central tendency metric.
calculation
a) µ = 48
σ = 12
n= 115
X = 45
Z =(X - µ )/(σ/√n) = (45-48)/(12/√115)= -2.68
P(X<45) = P(Z<-2.68) = 0.0037
b) µ = 48.00
σ = 12.00
n= 115.00
P(X ≤ x) = 0.2500
z value at 0.25= -0.674 (excel formula =NORMSINV(0.25))
z=(x-µ)/(σ/√n)
X=z * σ/√n +µ= -0.674*12/√115+48= 47.25
Using the ti-83 plus/ti-84 plus calculator, the 25th percentile of x is equal to 47.25 with a mean of 48 and a standard deviation of 12, respectively.
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2/3x- 12 for x=18
show work
Determine if the two triangles are necessarily congruent. If so, fill in a flowchart proof to prove that they are.
Help please
The given statements are:
angle A = angle O (note the single tickmarks)side AC = side OM (these sides share a similar tickmark)angle C = angle M (note the double tickmarks)We can then use the ASA congruence theorem to prove the triangles are congruent, aka they are mirror copies of one another.
Each "A" refers to facts (1) and (3) shown above. Fact (2) is the "S" of ASA.
ASA = angle side angle
Verizon charges $0.50 per minute plus a monthly base fee. In October, Noah used 200 minutes and his bill was $100
The monthly base fee of the situation is $0
How to determine the monthly base fee of the situationFrom the question, we have the following parameters that can be used in our computation:
Charges per minute = $0.50 per minute
Number of minutes = 200 minutes
Total charges = $100
The above parameters mean that
Total charges = Monthly Base fee + Charges per minute x Number of minute
Substitute the known values in the above equation, so, we have the following representation
Monthly base fee + 0.50 * 200 = 100
This gives
Monthly base fee + 100 = 100
Subtract 100 from both sides
Monthly base fee = 0
Hence, the monthly base fee is $0
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Pls help fast i need help right neow.
[tex]\angle R \cong \angle STV[/tex]: Alternate interior angles theorem
[tex]\angle TSV \cong \angle U[/tex]: Alternate interior angles theorem
[tex]\angle R \cong \angle TSV[/tex]: Transitive property of congruence
[tex]\angle R \cong \angle U[/tex]: Transitive property of congruence
help pls
Write the equation of the line in slope-intercept form that is perpendicular to
y = -x – 18 and passes through (-6, 11).
Hence, the slope which is perpendicular to the line to [tex]y = -x - 18[/tex] and passes through [tex](-6, 11)[/tex] is [tex]y=x+17[/tex].
What is the equation?
The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.
Here given that,
The line in slope-intercept form that is perpendicular to [tex]y = -x - 18[/tex] and passes through [tex](-6, 11)[/tex].
As we know the slope of line is
[tex]y=mx+c[/tex]
where [tex]m[/tex] is the slope and [tex]c[/tex] is the y intercept.
Given points are [tex](-6,11)[/tex].
If we want to describe the perpendicular line to the original line then the slope of line is
[tex]m_2=-\frac{1}{m_1}[/tex]
In our given slope of line
[tex]y = -x -18[/tex]
where [tex]m_1=-1[/tex]
So,
[tex]m_2=-\frac{1}{m_1}\\\\m_2=-\frac{1}{-1}\\\\m_2=1[/tex]
Now for the slope of second line we use the point slope from the construct equation then,
[tex]y-y_1=m_2(x-x_1)\\\\y-11=1(x-(-6))\\\\y-11=x+6\\\\y=x+6+11\\\\y=x+17[/tex]
Hence, the slope which is perpendicular to the line to [tex]y = -x - 18[/tex] and passes through [tex](-6, 11)[/tex] is [tex]y=x+17[/tex].
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what is the rate of change of the surface area of the prism at that instant (in square kilometers per minute)?
The surface area, A, is changing at a rate of 288 km/min decreasing.
Given,
Base length, l = 6 km
Height, h = 10 km
dl/dt = -9 km/min
dh/dt = 12 km/min
Surface area of a prism, A = 2 × (lw + lh + wh)
For a square prism,
Length, l = width, w = 6km
A = 2 × (l² + lh + lh)
= 2(l²) + 4lh
A = 2(l²) + 4 lh
= 2 × (l² + 2lh)
dA/dt = 2 × (2I × dI/dt + 0 × dh/dt + 2 × 2h × dl/dt + 2l × dh/dt)
dA/dt = 2 × (2l × dl/dt + 0 + 2 × 2h × dl/dt + 2l × dh/dt)
= 2 × (2(6) × (-9) + 2(10) × (-9) + 2(6) × (12))
= 2 × (- 108 + -180 + 144)
= 2 × -144
= -288 km/min
The rate of change of the surface area, A is decreasing by 288 km/min.
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Question is incomplete. Completed question is given below;
The length s(t)s(t)s, (, t, )of the side of the base of a square prism is decreasing at a rate of 9 kilometers per minute and the height h(t)h(t)h, (, t, )of the prism is increasing at a rate of 12 kilometers per minute. At a certain instant t_0t 0 t, start subscript, 0, end subscript, the base's side is 6 kilometers and the height is 10 kilometers. What is the rate of change of the surface area A(t)A(t)A, (, t, )of the prism at that instant?
Neha drives a car that gets 25 miles per gallon when she is driving in the city and 40 miles per
gallon when she is driving on the highway. Her car's fuel tank will hold 15 gallons of gas. What
equation can we write to represent all the combinations of city miles and highway miles she can
drive on one tank of gas?
1. Record an equation that is a prediction.
Answer:
C/25 + H/40 = 15
Step-by-step explanation:
Let's call C the number of city miles, and H the number of highway miles.
The total gas used is therefore:
C/25 + H/40
The fuel tank holds 15 gallons, so:
C/25 + H/40 = 15
Pls answer it quickly
The two-column method can be used to prove that the triangles ΔACD and ΔBCD are congruent is presented as follows;
Statements [tex]{}[/tex] Reasons
1. AC ≅ BC [tex]{}[/tex] 1 Given
2 D is the midpoint of AB [tex]{}[/tex] 2 Given
3. CD ≅ CD [tex]{}[/tex] 3 Reflexive property → CD = CD
4 ∠ACD ≅ ∠BCD [tex]{}[/tex] 4 Median line of an isosceles triangle bisects the vertex angle
5 ΔACD ≅ ΔBCD [tex]{}[/tex] 5. SAS congruency postulate
What is the two-column method used to prove statements in geometry?The two-column method consists of two columns, including a statement column and a reasons column, in which each statement made is provided with an accompanying reason.
The reasons in the prove for the congruency of the triangles, ΔACD and ΔBCD are as follows;
Reflexive property
The reflexive property of equality indicates that the value of a number or measure is equal to itself, therefore, the length of the segment CD is the same as the length of the segment CD.
Median of an isosceles triangle
In an isosceles triangle, two sides are congruent. The median segment drawn from the altitude of an isosceles triangle forms two congruent segment at the base, such that the two triangles formed by the median line are congruent, by Side-Side-Side, SSS congruency postulate, therefore, the angles formed at the vertex of the triangle by the median segment are also congruent
SAS congruency postulate
The Side-Angle-Side congruency postulate states that two triangles are congruent if two sides and the included angle of one triangle are congruent to two sides and the included angle of the other triangle.
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Find the equation of the line that passes through (4,4) and is parallel to y = 3 x + 4.
The line's equation that is parallel to the given line is= 3x - 8
What is Equation?A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation. as in 3x + 5 Equals 15, for instance.
Equations come in a variety of forms, including linear, quadratic, cubic, etc.
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. We have LHS = RHS (left hand side = right hand side) in every mathematical equation.
To determine the value of an unknown variable that represents an unknown quantity, equations can be solved. The statement is not an equation if there is no "equal to" symbol in it.
According to our question-
The line's equation in the form of the slope intercept is,
y = mx + c
m is the line's slope, and c is its y-intercept.
line equation provided that,
Therefore, the line's slope is
Finding the equation of the line that crosses (4,4) and runs parallel to the provided lines is necessary.
Because all parallel lines have the same slope.
Equation for the necessary line is,
Replace point (4,4) in the line above.
In order for the line equation to become,
3x - 8
Hence, The line's equation that is parallel to the given line is= 3x - 8
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for the trapezoid below,solve for x. X= blank
Answer:
180-125 = x
x= 55 ( allied angle)
write an equation of the line that passes through (7,10) and is perpendicular to the line y=-1/5x-9
An equation of the line that passes through (7,10) and is perpendicular to the given line is y=5x-25.
Given that, the line that passes through (7,10) and is perpendicular to the line y=-1/5x-9.
What is slope of a line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
Here, slope of a line y=-1/5x-9 is m=-1/5.
The slope of a line perpendicular to given line is m1=-1/m2
So, slope =5
Substitute m=5 and (x, y)=(7, 10) in y=mx+c, we get
10=5(7)+c
⇒c=-25
Substitute m=5 and c=-25 in y=mx+c, we get
y=5x-25
Hence, an equation of the line that passes through (7,10) and is perpendicular to the given line is y=5x-25.
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Is 4,6,8 a right triangle
Answer: It is an obtuse triangle.
Answer: No
Step-by-step explanation:
To know if a triangle is a right triangle, we can use Pythagorean Theorem to test.
Pythagorean Theorem: [tex]a^2+b^2=c^2[/tex]
[tex]4^2+6^2=8^2[/tex] [exponents]
[tex]16+36=64[/tex] [add]
[tex]52\neq 64[/tex]
Therefore, this is not a right triangle.
A boat travel 42 mile uptream in 3 hour looking for a lot diver. It then travel downtream 70 mile in 2 hour. Write a ytem to repreent the ituation. Then find the peed of the boat and the peed of the current. Ue b for boat and c for current
The speed of boat is 14 miles per hour and the speed of current 35 mile per hour
Speed:
The general formula to calculate the speed is written as
Speed = Distance/Time
Given,
A boat travel 42 mile uptream in 3 hour looking for a lot diver. It then travel downstream 70 mile in 2 hour.
Here we need to find the speed of boat and the speed of current.
While we looking into the given question, we have identified the following values,
Distance = 42 mile
time = 3 hour
Then the speed is calculated as,
=> speed = 42/3
=> speed = 14 miles per hour
Similarly, for the current is
distance = 70 miles
time = 2 hour
Then the speed is calculated as,
=> speed = 70/2 = 35 miles per hour.
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One angle measures 27°, and another angle measures (8d − 9)°. If the angles are complementary, what is the value of d?
d = 72
d = 21
d = 3
d = 9
Answer:
d = 9°
Step-by-step explanation:
When the sum of two angles is equal to 90 degrees, they are called complementary angles.
soln
27° + (8d – 9)° = 90°
27° + 8d – 9° = 90°
27°–9° + 8d = 90°
18° + 8d = 90°
8d = 90° – 18°
8d = 72°
divide both sides by (8)
d = 9°
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At the beginning of an experiment, a scientist has 176 grams of radioactive goo. After 135 minutes, her sample has decayed to 11 grams. What is the half-life of the goo in minutes? Find a formula for G ( t ) , the amount of goo remaining at time t . G ( t ) = How many grams of goo will remain after 32 minutes?
Answer:
The amount of goo remaining after 32 minutes is approximately 54.7 grams.
Step-by-step explanation:
The half-life of a substance is the amount of time it takes for half of the substance to decay. To find the half-life of the goo in the experiment, we need to solve the equation G ( t ) = G ( 0 ) / 2 for t , where G ( 0 ) is the initial amount of goo and G ( t ) is the amount of goo remaining after time t .In this case, G ( 0 ) = 176 grams and G ( 135 minutes ) = 11 grams, so we can write the equation as follows:11 grams = 176 grams / 2Solving for t , we get:t = 135 minutes * ( 1 / 2 ) = 67.5 minutesThis is the half-life of the goo in the experiment.To find the amount of goo remaining after time t , we can use the equation G ( t ) = G ( 0 ) * ( 1 / 2 ) ^ ( t / t1/2 ) , where G ( 0 ) is the initial amount of goo, t is the time at which we want to find the amount of goo remaining, and t1/2 is the half-life of the goo.In this case, G ( 0 ) = 176 grams, t = 32 minutes, and t1/2 = 67.5 minutes, so we can plug these values into the equation to find the amount of goo remaining after 32 minutes:G ( 32 minutes ) = 176 grams * ( 1 / 2 ) ^ ( 32 minutes / 67.5 minutes )This equation tells us that the amount of goo remaining after 32 minutes is approximately 54.7 grams.
How do you solve this
Answer:
(f+g), (f-g), (f·g), domain is [-3, 3]f/g, domain is [-3, 3)Step-by-step explanation:
Given f(x) = √(3+x) and g(x) = √(3-x), you want the domains of various combinations of f and g.
DomainsThe domain of each of these functions is the interval on which it is defined. The domain of the square root function is all argument values greater than or equal to zero.
Domain of fThe argument of the square root will be non-negative when ...
3 +x ≥ 0
x ≥ -3 . . . . . . subtract 3
-3 ≤ x . . . . . . written using left-pointing arrow
Domain of gThe argument of the square root will be non-negative when ...
3 -x ≥ 0
3 ≥ x . . . . . add x
x ≤ 3 . . . . . written using left-pointing arrow
Intersection of domainsAny combination of functions f and g will only be defined on the domain where both f and g are defined. That is, the domain will be the intersection of the domains of f and g:
(-3 ≤ x) ∩ (x ≤ 3) = -3 ≤ x ≤ 3
Domain of f+gThe domain of f+g is the intersection of the domains of f and g.
[-3, 3]
Domain of f-gThe domain of f-g is the intersection of the domains of f and g.
[-3, 3]
Domain of f·gThe domain of f ·g is the intersection of the domains of f and g.
[-3, 3]
Domain of f/gThe domain of f/g is the intersection of the domains of f and g, excluding the value of x that makes g(x) = 0. That value is x=3.
[-3, 3)
__
Additional comment
The graphs of the combinations of functions are attached. You notice the graph of f/g tends to infinity as x → 3. It is undefined at x=3.
Why do you need to state restrictions on the variable when dividing rational expressions?.
It is important to state the restrictions before simplifying rational expressions because the simplified expression may be defined for restrictions of the original.
What is rational expressions?
The ratio of two polynomials is a rational expression. F can be expressed in the form p/q, where p and q are polynomials, if f is a rational expression.
Fractional terms are seen in rational expressions. We include constraints because with some x values, the equation may become undefined. Undefined inquiries are hypothetical or ideal. The seven expressions for undefined words are (∞-∞),∞^∞, N/0, 0⁰, 1^∞, ∞/∞ and 0×∞ respectively. N/0 is the most typical constraint on rational expressions. Any number divided by 0 is therefore undefined. For instance, if you substitute 0 for x in the case of the function f(x) = 6/x2, the outcome is 6/0, which is undefined. If you graphed this function, you would see a break at x=0.
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Write the equation of the line passing through the points (10,3) and (-2,-3).
The equation of the line is
Answer:
[tex]y=\frac{1}{2} x-2[/tex]
If x=6 what is 4x
??????????????
Answer:
24
Step-by-step explanation:
6*4=24