The system of linear inequalities to model the situation is 10x + 20y ≤ 100 and y > 2x
How to create a system of linear inequalities to model the situationFrom the question, we have the following parameters that can be used in our computation:
Each finished schedule = $10Each meeting = $20Amount to make = Not more than $100You must make more than twice as many schedules as meetingsUsing the following representations:
x = the number of schedules madey = the number of meetings completedWe have the following system of inequalities from the given statements
10x + 20y ≤ 100
y > 2x
Hence, the system of inequalities is 10x + 20y ≤ 100 and y > 2x
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Juan had $3. 50. Julian had 2 1/2 time a much a juan how much money did julian have
We know that Julian has $8.75 using mathematical operations.
What are mathematical operations?A mathematical "operation" is the process of calculating a value utilizing operands and a math operator.
The supplied operands or integers must adhere to a set of predefined rules that are connected to the symbol of the math operator.
The five basic operations in mathematics are addition, subtraction, multiplication, division, and modular forms.
So, we know that:
Juan has $3.50.
Julian has 2½ times Juan.
So, the money Julian has is:
First, calculate 2½:
2½
4+1/2
5/2
2.5 times
The money Julian has is:
3.50 * 2.5
$8.75
Therefore, we know that Julian has $8.75 using mathematical operations.
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The flasks are in the shape of cones.
The smaller flask has a base radius of
8
cm and a vertical height of
20
cm.
The larger flask has a base radius of
14
cm.
The larger flask is now partly filled with liquid up to a vertical height of
15
cm.
Calculate the volume of liquid in the flask.
Give your answer in terms of π
The volume of the liquid in the conical flask is 980 π cm³
What is a Cone?
A cone is a three-dimensional shape in geometry that narrows smoothly from a flat base (usually circular base) to a point(which forms an axis to the centre of base) called the apex or vertex.
The volume of a cone is given by the equation
Volume of Cone = ( 1/3 ) πr²h
where r is the radius of the cone
h is the height of the cone
Given data ,
Let the two cones be A and B
Now , the smaller cone be A
The larger cone be B
The radius of the smaller cone is r = 8 cm
The height of the smaller cone is h = 20 cm
Now , the volume of the smaller cone V = ( 1/3 ) πr²h
Substituting the values in the equation , we get
Volume of cone A = ( 1/3 ) πr²h
Volume of cone A = ( 1/3 ) π x 8 x 8 x 20
Volume of cone A = 426.67 π cm³
Now ,
The larger flask is filled with height H = 20 cm
The radius of the larger cone is R = 14 cm
The height of the larger cone is H = 15 cm
Now , the volume of the smaller cone V = ( 1/3 ) πR²H
Substituting the values in the equation , we get
Volume of cone B = ( 1/3 ) πR²H
Volume of cone B = ( 1/3 ) π x 14 x 14 x 15
Volume of cone B = 980 π cm³
Therefore , the volume of the larger cone B is 980 π cm³
Hence , The volume of the liquid in the conical flask is 980 π cm³
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Charmaine wanted to study how the area of a rectangle changes with the length if its width is fixed. She computed the areas of several rectangles that have the same width and different lengths. She then plotted the results and connected them with a line, as shown below. The graph shows the area (incm^2 ) versus the length (in cm).
Find the range and domain of the functions
The Range of the length of a rectangle having fixed width and area increasing linearly is = {y ∈ R : c ≠ 0 or y ≠ 0}, and Domain = All real numbers,
What is a rectangle?An enclosed 2-D shape called a rectangle has four sides, four corners, and four right angles (90°). A rectangle has equal and parallel, opposite sides. Since a rectangle is a two-dimensional form, it has two dimensions: length and width. The rectangle's longer side is its length, while its shorter side is its breadth.
Given:
The width of the rectangle is fixed, and the length is changing.
The line is formed when connected through the graph.
The area of the rectangle = [tex]length\times width[/tex]
So when the width is fixed, the area would increase linearly and directly proportional to length.
Calculate the range of function y = cx,
y = area as shown in the graph, x is the length, and width is constant c.
Range = {y ∈ R : c ≠ 0 or y ≠ 0}
Calculate the domain,
It can be any real number, as the area can't be negative.
Domain = All real numbers.
Therefore, Range = {y ∈ R : c ≠ 0 or y ≠ 0}, and Domain = All real numbers.
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Population The expression n 25 gives the population (in thousands) of an animal after 5 years, where n is the starting population in thousands. Find the populatio
5 years if the starting population is 3,000
The population after 5 years if the starting population is 3000 is 75,000.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
The population after 5 years.
= n x 25
Where n is the starting population in thousands.
The expression can be considered as.
= nx²
Where x is the number of years.
Now,
n = 3000
The population after 5 years.
= 3000 x 25
= 75,000
Thus,
The population is 75,000.
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Karen was trying to factor 6x^2+106x 2 +106, x, squared, plus, 10. She found that the greatest common factor of these terms was 222 and made an area model:.
The width of area model is 2x units
What is area ?Area is the entire amount of space occupied by the shape of an object or a flat (2-D) surface.
According to the given information :
The given expression is [tex]6x^{2}+106x[/tex]
We need to find the width of area model , so The above expression represents the area of rectangle A
By making the factors of the above expression
A = [tex]6x^{2}+106x[/tex]
= [tex]2x( 3x + 53 )[/tex]
Area of rectangle is defined as
A = l × b
where l is length and b is width
In the above expression
b = 2x
l = 3x + 53
So , The width of area model is 2x units
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Graph the line that has a slope of -7/6 and includes the point (0, 1)
Answer: (6,-6),(0,1) plot these 2 points
Step-by-step explanation:
a basketball player has made 66% of his foul shots during the season. assuming the shots are independent, find the probability that in tonight's game he misses for the first time on his 6th attempt?
The probability that in tonight's game he misses for the first time on his 6th attempt = 0.2244
What is Probability?
A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.
The Probability that the basketball player made a foul shot = 0.66 or 60%
Then the probability of good shot is = 1-0.66
= 0.34
probability that in tonight's game he misses for the first time on his 6th attempt = (1-p) 5(p)
= ( 1- 0.34)⁵ (0.34)
= 0.2244
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Need help with part A
Answer: 0.4
Step-by-step explanation:
The question is asking for the probability to own a dog.
40% own a dog.
If you add all of the percentages you get 100%
40/100
=0.4
The probability is 0.4 times to randomly select a resident that only owns a dog.
Directions: simply ugly each expression by combining like terms
10x-16x
Answer: -6x
Step-by-step explanation:
Just subtract the coefficients:
The coefficient of 10x is 10
The coefficient of 16x is 16
now do ten minus 16 (TIP: if you don't really like negative numbers, then an easy way of subtracting 10-16 is 16-10=6, then add the negative sign to 6; -6)
10 - 16 = -6
Now put the x back: -6 = -6x
The correct answer is -6x
I NEED HELP 87 POINTS + BRAINLIEST
a) The Volume of space that is not occupied is; 13.80 in³
b) The length, are and volume have distinct final units.
c) The Volume of the composite shape is the sum of the Volume of Cone, Volume of Cylinder and Volume of Hemisphere
How to find the volume of a composite object?a) Tennis ball is usually considered to be a sphere. The formula for volume of sphere is;
V = ⁴/₃πr³
where r is radius.
Since diameter = 2.6 inches, then radius; r = 2.6/2 = 1.3 inches
Thus;
Volume of each tennis ball;
V = ⁴/₃π(1.3)³
For the three tennis balls;
V₃ = 3(⁴/₃π(1.3)³)
V₃ = 8.788π
Volume of the cylindrical container = πr²h
h is height = 3(2.6) = 7.8 inches
V_cyl = π(1.3² * 7.8)
V_cyl = 13.182π
Volume of space not occupied = 13.182π - 8.788π
Volume of space not occupied = 13.80 in³
b) For length, the unit will be singular
For Area, the unit will be squared
For Volume, the unit will be cubed
c) There are three objects that make up the composite object namely; Cone, Cylinder, hemisphere. Thus;
Volume of composite shape = Volume of Cone + Volume of Cylinder + Volume of Hemisphere
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She used a graphing tool to display the data in a scatter plot, with x representing the number of ice cubes and y representing the milliliters of juice. Then
she used the graphing tool to find the equation of the line of best fit:
y = -29 202x + 293.5.
Based on the line of best fit, approximately how many milliliters of juice will be in a glass with 7 ice cubes?
A. 10
B. 89
C. 118
D. 208
89.086 milliliters of juice will be in a glass with 7 ice cubes.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
Equation of line: y = -29 202x + 293.5.
So, for 7 ice cubes i.e., x= 7
The amount of juice is
y= -29.202 (7)+ 293.5
y= -204.414+ 293.5
y= 89.086
Hence, the juice is 89.086 milliliters
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Which of the following will be perpendicular to the line y = -1/4x + 10? Select all that apply. Please explain your answer choices.
a. y = 4x + 2
b. y = 1/4x - 9
c. y = -4x + 10
d. y = 4x - 5
Perpendicular lines have slopes that are opposite signs and reciprocals.
Since the line y = -1/4x + 10 has a slope of -1/4, the slope of the perpendicular line will be + 4/1 or 4. So any line with a slope of 4 will be perpendicular to y = -1/4x + 10.
This means A and D will be your answers.
The half-life of Radium-223 is 11.43 years. What is the annual decay rate? Express the result to four decimal places.
Express the annual decay rate as a percentage to two decimal places.
%
Answer:
Below
Step-by-step explanation:
e^(-kt) = 1/2 when t = 11.43
so k = .060642797
e^ (- .060642797 * 1) = .9411 <==== is left after one year
which means the decay in one year is
1 - .9411 = .05884 = 5.88% per year
I need some serious help
Answer: y=7x-23
Step-by-step explanation:
y-y1=m(x-x1)
Plug them in:
-2-12=m(-2-5)
-14=m(-7)
m=7
y=7x+b
Plug in a coordinate:
12=7(5)+b
12=35+b
-23=b
y=7x-23
Help please will mark brainiest!
Answer:
A = 12cm^2 B = 18cm^2 C = 54cm^2
Step-by-step explanation:
area = side 1 x side 2
PLEASE I NEED HELP!!!!
Step-by-step explanation:
as you wrote correctly, proportional relationships are in the form
y = mx
that means the line has to go through the origin (0, 0). otherwise it is in the form
y = mx + b
which is still linear but not proportional.
1a.
the rate of change is between 2 points A and B
(Yb - Ya)/(b - a)
in our case e.g. (4, 5.52) and (8, 11.04)
(11.04 - 5.52)/(8 - 4) = 5.52 / 4 = 1.38
when we use other points we get the same result. we see e.g. that when we double x (pounds), then also y (cost) is doubled.
the rate of change is 1.38.
this is also called the slope of the line.
b.
as mentioned in a., when we multiply x by a factor, then y is multiplied by the same factor. it also means that the function contains (0, 0) : for 0 pounds we pay $0.
c.
y = 1.38x
2a.
the slope is (as it is the same as the rate of change) the ratio of (y coordinate change / x coordinate change) when going from one point on the line to another.
we try to find points with integer coordinates to do that.
I see e.g. (3, 4) and (6, 8).
x changes by +3 (from 3 to 6).
y changes by +4 (from 4 to 8).
so, the slope is +4/+3 = 4/3.
b.
the simplest indicator is that the line goes through the origin (0, 0), which it does.
c.
y = (4/3)x
i have no idea how to do this pls help
Answer:
2
Step-by-step explanation:
How many 1/4 cups fit in a 1/2 cup?
This is a division problem.
We need to divide 1/2 by 1/4.
1/2 ÷ 1/4 =
= 1/2 × 4/1
= 4/2
= 2
Answer: 2
Write your answer in interval notation.
3x + 4 < - 17 OR 2x + 2 > - 4
Answer:
x < 3 or x ≥ 11
Step-by-step explanation:
(-∞, 3) or [11, ∞)
Step-by-step explanation:
subtract 4 from each side
2x < 6 . or . 3x ≥ 33
x < 3 or x ≥ 11
make sure you have an OPEN DOT at 3 pointing to negative infinity and a CLOSED DOT at 11 pointing to positive infinity.
Both question A and B please
The coordinates of P and Q are
P (-1/2, 3/2) Q (-4, -3/2)PQ have equal slope with BC so they are parallel
How to find the coordinates of P and QThe coordinates of P and Q is found using the midpoint formula
The formula is of the form
X= (x₂ + x₁)/2
Y = (y₂ + y₁)/2
solving for P (X, Y) Using points A(2, -1), B(-3, 4)
(X, Y) = ((2 + -3)/2, (-1 + 4)/2)
= (-1/2, 3/2)
solving for Q (X, Y) points A(2, -1), C(-5,-7)
(X, Y) = ((2 + -5)/2, (-1 + -7)/2)
= (-3/2, -4)
Parallel lines have equal slopes
Using BC = (4 - -7) / (-3 - -5) = 11/2
Using PQ = (-4 - 3/2) / (-3/2 - -1/2) = (-11/2) / (-1) = 11/2
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Find the y-intercept of the line y=1/3x–1.
Write your answer as an integer or as a simplified proper or improper fraction, not as an ordered pair.
Answer:
-1
Step-by-step explanation:
This line is already in slope, intercept form of y = mx + b <===='b' is the y-axis intercept = -1
The dimensions of this polygon are shown in feet (ft).
10ft/3ft/4ft/8ft
What is the area, in square feet, of the polygon?
The required area of the polygons is given as 100 ft², 9 ft², 16 ft², and 64 ft².
Given that,
The dimensions of this polygon are shown in feet (ft). 10ft/3ft/4 ft/8 ft. The area, in square feet, of the polygon is to be determined.
A polygon is defined as a geometric shape that is composed of 3 or more sides these sides are equal in length, and an equal measure of angle at the vertex,
Examples of polygons, equilateral triangles, squares, pentagons etc
Here,
Assumed that all the polygons are square,
The area of the square is given as (side)².
1,
Side = 10 ft
Area of the square = [10 ft]² = 100 ft²
Similarly,
For side 3 areas is 9 ft²,
For side 4 areas is 16 ft²,
For side 8 areas is 64 ft²,
Thus, the required area of the polygons is given as 100 ft², 9 ft², 16 ft², and 64 ft².
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PLEASE HELP! What can you conclude about the triangles? *Hint: What is congruent and how can you prove it?
The triangle's conclusion is that the two triangles are equal because they are congruent.
What are Congruent triangles?If each of the three corresponding sides and each of the three corresponding angles in two triangles equals one another, then the two triangles are said to be congruent.The two triangles generated in the illustration are triangles GHJ and GKM.To substantiate the triangle GHJ = GKMAngle JGH=Angle KGM ( opposite angles)angle K equals angle H (alternating angles)Angle H = thus Angle JWe can say that the triangles are congruent because the three angles of each triangle are equal.To Learn more About triangle's conclusion refer To:
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Use properties to rewrite the given equation. Which equations have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p? Select two options.
The equations that have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p are 2.3p – 10.1 = 6.49p – 4 and 230p – 1010 = 650p – 400 – p
How to determine the equations with the same solution?The equation is given as
2.3p – 10.1 = 6.5p – 4 – 0.01p
Evaluate the like terms on the right-hand side
So, we have the following representation
2.3p – 10.1 = 6.49p – 4
The above equation is an equivalent equation of the given equation
Multiply through the equation by 100
So, we have:
100(2.3p – 10.1 = 6.5p – 4 – 0.01p)
Evaluate
230p – 1010 = 650p – 400 – p
The above equation is also an equivalent equation of the given equation
Hence, the equations with the same solution are represented above
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12 ( 3/4 - 2x) Ue the ditributive property to remove the parenthee. Simplify your anwer a much a poible
Answer:
9 - 24x
Step-by-step explanation:
When using the distributive property, the number outside the parentheses (12) is "distributed" to each of the values inside the parentheses. In other words, 12 will be multiplied by 3/4 and 2x:
12(3/4 - 2x)
12(3/4) - 12(2x) <----- so now we successfully got rid of the parenthesis. Next, simplify
12(3/4) = 9
12(2x) = 24x
9 - 24x <----this is the final answer since it can't be simplified further
What is the slope of a line that is perpendicular to y=4/5x+15 and passes through point (-3,4)?
Answer:
Below
Step-by-step explanation:
The slope of the given line , m = 4/5
perpendicular slope is - 1/m = - 5/4
..
gujhtuvvvfgvbbhtdxccgyujjgttggg
Answer:
do you need help with anything if not hello
Step-by-step explanation:
When Karen went to bed, there were 234 birds on the lake. When she woke up in the morning, there were 751 birds on the lake. How many birds landed on the lake overnight?
please help
Answer:
517 birds
Step-by-step explanation:
Subtract 234 from 751, to find how many birds landed on the lake overnight.
GCF of 10 y 5 + 30 y 3 − 15 y
Answer:
5 y (2 y^4 + 6 y^2 - 3)
Step-by-step explanation:
The given input is 10y^5+30y^3-15y
10y^5+30y^3-15y has factors i.e 5 y (2 y^4 + 6 y^2 - 3)
By verifying each polynomial factor we get the GCF i.e common factor of the polynomial is 5 y (2 y^4 + 6 y^2 - 3) and simplified as 10 y^5 + 30 y^3 - 15 y
if your school uses Desmos pls respond
50 points
Answer:
I use desmos!
Step-by-step explanation:
Question is in picture
The length of line segment LB is equal by definition of bisector to 6 feet.
How to determine the missing length of a geometric system of two right triangles
In this question we find a geometric system with two right triangles generated by bisector AL, that is, a side that divides line segment CL into two segments of equal length. Then, the length of line segment LB is equal to:
CL = LB
Where CL and LB are measured in feet.
If we know that CL = 6 ft, then the length of line segment LB is 6 feet.
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