Answer:
Step-by-step explanation:
floating point
3. Andre and Elena are saving money. Andre starts with $50 in his savings account and adds $5 per week. Elena starts with $5 in her savings account and adds $10 each week. a. After four weeks, who has more money in their savings account? Explain how you
In given word problem Andre has more money than Elena after four weeks.
What is word problem?
A math word problem is a question that is written as one or more sentences and asks students to use their mathematical understanding to solve an issue from "real world." In order to understand the word problem, they must be familiar with the terminology that goes along with the mathematical symbols that they are used to.
Here,
Initial investment of Andre= $50
She add $5 per week for next 4 weeks , then
=> 4×5 = $20
Then total savings of Andre = $50+$20=$70.
Now Initial investment of Elena = $5
She adds $10 for each 4 weeks then
=> 10×4=$40.
Now total savings of Elena = $40+$5=$45.
Here $70>$45.
Hence after 4 weeks Andre has more money than Elena.
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50 POINTS!
Argument A
A chemistry professor claims that preparing a description of reduction-oxidation chemical reactions requires balancing the component half-reactions for oxidation and reduction by adding molecules or electrons into the chemical equation. Based on the professor's expertise in chemistry, we should conclude that reduction-oxidation chemical equations should be balanced in this way.
Argument A is (strong/weak)
Argument A is strong based on the logic.
What is logic?We know that logic is the process whereby we can be able to decode if an argument is true or false when we look at the premises and the conclusion. It is normal that the premise of the argument should be able to give rise to the conclusion.
In this case, we must note that the professor is an authority figure in chemistry and what he says must be taken as trust worthy as shown in the deductive argument that led to this conclusion as shown above.
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find the value of the variable
Answer: 25
Step-by-step explanation:
The sum of all exterior angles = 360
Using this, we can get the equation
2x+20+x+40+3x+6x=360
12x+60=360
12x=300
Simplify, and you get
x = 25
One side of a right-angled triangle is f. The other two sides are 2 times bigger than f and 7 smaller than f. Write an expression for the perimeter of the triangle in its simplest form.
Answer:
4f-7
Step-by-step explanation:
You want the perimeter of a triangle whose side lengths are f, 2f, and f-7.
PerimeterThe perimeter is the sum of the side lengths:
P = f +2f +(f -7)
P = 4f -7
The perimeter of the triangle is 4f-7.
__
Additional comment
No such triangle can exist. The sum of the two shortest sides is f+(f-7) = 2f-7, which is not greater than the longest side, 2f. The triangle inequality is not satisfied.
What is an example of center of dilation?
As an example, if the centre of dilation were in the centre of a circle with radius 5 and was going through a scale factor 2 dilation, the radius would be 10.
The process of dilation involves growing an object's size without changing its shape. The size of the item may increase or decrease depending on the scale factor. Using dilation math, a square with side 5 units may be made wider to have side 15 units, but the shape of the square remains the same.
Enlargements that generate a bigger picture are called dilations. Reduction describes the dilatation that shrinks the picture. The starting figure is stretched or contracted during a dilatation. The scale factor (or ratio) and the centre of a dilatation are both described. Occasionally, the words "dilate" and words like "magnify," "disptend," "expand," "inflate," and "swell" are used interchangeably. All of these words suggest "expanding in size or volume," but the word "dilate" specifically refers to increased diameter.
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What is the slope of the relationship?
What is 3÷7/4 because I need this or I will get a bad grade for math
Answer:
[tex]\frac{12}{7}[/tex]
Step-by-step explanation:
[tex]3 /\frac{7}{4} = \frac{12}{7}[/tex]
Here is a trick to divide fractions
Take the 2nd fraction in this case [tex]\frac{7}{4}[/tex] and flip it [tex]\frac{4}{7}[/tex]
Change the division sign to a multiplication sign and multiply
[tex]\frac{3}{1} * \frac{4}{7} = \frac{12}{7}[/tex]
Drives Co. sells portable hard drives. They can sell 905 drives when the price is $66/drive, and they can sell 800 drives when the price is $87/drive. If x represents the number of drives sold, determine the following. a. Drive Co.'s revenue function: R(X) = b. The price per drive when revenue is maximized: $ c. The maximum profit made from the sale of these drives if Drive Co. incurs production costs of $179 per drive and has fixed costs of $250: $
a. Drive Co.'s revenue function R(X) = (-x^2/5)-247x.
b. The price per drive when revenue is maximized is $370.6.
c. The maximum profit made from the sale of these drives if Drive Co. incurs production costs of $179 per drive and has fixed costs of $250 is $6030.
What is a function?
The characteristic that every input is associated to exactly one output defines a function as a relationship between a set of inputs and a set of allowable outputs.
Drive Co. sells portable 905 hard drives when the price is $66/drive and can sell 800 hard drives when the price is $87/drive.
Let p be the price of hard drive and x be the number of hard drives.
When x = 905, then p = 66.
So, (x1,p1) = (905,66)
Similarly, when x = 800, then p = 87.
So, (x2,p2) = (800,87)
So, the equation of line between x and p is given as -
p-p1=[(p2-p1)/(x2-x1)}(x-x1)
Plugging in the values -
p-66=[(87-66)/(800-905)](x-905)
p-66=(21/-105)(x-905)
-105p+6930=21x-19005
-105p-21x=-19005-6930
-105p-21x=-25935
p=(-21x/105)-247
p=(-x/5)-247
So, the price function p(x) = (-x/5)-247.
Now, derive the revenue function -
Revenue = Number of drives × price per drive
Revenue = x · p(x)
Revenue = x · (-x/5)-247
Revenue = (-x^2/5)-247x
Therefore, the revenue function R(x) = (-x^2/5)-247x.
For maximum revenue -
dR/dx = R'(x) = 0 and R''(x)<0
dR/dx = -2x/5-247 = 0
-2x/5 = 247
x = -1235/2
x = -617.5
Therefore, the number of drives at maximum revenue is 618 drives.
The price per drive is -
p(618) = {-618/5}-247
p(618) = -370.6
Therefore, the price per drive is $370.6.
Now, the profit S(x) = Revenue R(x) - Total Cost C(x)
C(x) = fixed cost + variable cost
Variable cost = number of drives × price per drive
C(x) = 250 + 179x
Substituting the values -
S(x) = [(-x^2/5)-247x] - [250+179x]
S(x) = (-x^2/5)-68x-250
In order to get maximum profit differentiate the equation and equate it to 0.
dS/dx = 0
dS/dx = -2x/5-68 = 0
-2x/5 = 68
x = 340/-2
x = -170
d^2S/dx^2 = -2/5<0
So, maximum profit will be at x = 170.
S max = S(170) = [(170)^2 /5] - 68 (170) - 250
= 5780 - 11560 - 250
= -6030
Therefore, the maximum profit earned is $6030.
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Lin has a summer reading assignment. After reading the first 30 pages of the book, she plans to read 40 pages each day until she finishes. Lin makes the graph shown here to track how many total pages she'll read over the next few days. After day 1, Lin reaches page 70, which matches the point (1,70) she made on her graph. After day 4, Lin reaches page 190, which does not match the point (4,160) she made on her graph. Lin is not sure what went wrong since she knows she followed her reading plan.Sketch a line showing Lin's original plan on the axes. Click on the graph and select edit to complete the graph. Once done, hit save and close to see your completed graph. What does the vertical intercept mean in this situation? How do the vertical intercepts of the two lines compare?
No. of pages read on day of planning are represented by vertical intercept.
The difference between vertical intercept of original plan and line drawn by Lin is 10 unit.
What is slope-intercept form of line?The slope intercept form equation for a straight line with a slope, 'm', and 'c' as the y-intercept can be given as:
y = mx + c.
Given,
No. of pages Lin read on day of planning = 30
No. of pages she plans to read everyday = 40
If total pages are y for x days then,
y = 40x + 30
which is the original plan of Lin.
comparing it with slope-intercept form of line
y = mx + c
slope m = 40
vertical intercept of original plan c = 30 unit
slope m represents the no. of pages read everyday.
vertical intercept represents the no. of pages read on day of planning.
vertical intercept c' of line drawn by Lin = 40 unit
Comparing intercept of original plan to line drawn by Lin
= |c - c'|
= |30 - 40|
= 10 unit
Hence, the vertical intercept represents the no. of pages read on day of planning.
There is 10 unit difference between vertical intercept of original plan and line drawn by Lin.
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solve................... 5(x+3)<60
x<9
5(x+3)<60
5(x+3)/5<60/5 .................... Dividing by 5 into both the sidesx+3< 12
x+3 - 3< 12-3 ......... Subtracting 3 from both sidesx<9
Which simply means x will always be less than 9 in this case.
These are the Simple inequation in one variable which can be simply solved by operating the same operations on both sides to get a simplified answer.
We follow the same algorithm even for equations where the left side and right sides are equal so we simply transfer the left digits to the right side simply by changing their operational signs like + will be -, * will be /.
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Lia i currently taking phyic a one of her elective in chool. Her grade at the end of the year i determined by the average of four exam, each worth 100 point. On her firt tet he got an 84, on her econd he got a 92, and on her third an 80. What mut he core on her fourth exam to get exactly 80% in the coure?
a. 60
b. 64
c. 84
d. 85
64 marks must he score on her fourth exam to get exactly 80% in the course.
From the question, we are informed that Lisa is currently taking physics as one of her electives in school and that her grade at the end of the year is determined by the average of four exams, each worth 100 points.
First test = 84,
Second test = 92
Third test = 80
Forth test = y
And,
The fourth test is denoted by y.
Since we are told that she must get exactly 80% in the course and she took 4 exams, that means her total score will be: = 80 × 4 = 320
Therefore,
⇒ 84 + 92 + 80 + y = 320
⇒ 256 + y = 320
⇒ y = 320 - 256
⇒ y = 64
The fourth exam's score is 64.
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consider a square based straight pyramid. suppose that the base is a square with sides 22 in long, and all other edges are 61 in long. find an approximate.value if the angle.found between the base and a triangular face
The approximate angle between the base and a triangular face is; 79.43°
How to use pythagorean theorem?The dimensions of the pyramid are;
Side Length; a = 22 inches
Edge length; b = 61 inches
Using Pythagoras theorem:
h = height of pyramid
h = √(b² - 1/2a²)
h = √(61² - 22²/2)
h = √(3479)
h = 58.98
Slant height :
L = √(58.983² + 22²/4)
L =√(3479 + 121)
L = 60
Sinα = h/L
α = sin⁻¹(58.983/60)
α = 79.43°
That is the approximate angle found.
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A farmer estimates that he has 9,000 bees producing honey on his farm. The farmer becomes concerned when he realizes the population of bees seems to be decreasing steadily at a rate of 5% per year. If the number of bees in the population after x years is represented by f(x), which statements about the situation are true? Check all that apply.
The correct options regarding given function are (b), (c) and (f).
What is a function?
An association between each element of a non-empty set A and at least one element of a different non-empty set B is called a function.
The set of values that we are permitted to enter into our function is known as the domain of a function.
A function's range is the collection of values it gives as outputs.
The options given are:
a)The function f(x) = 9,000([tex]1.05^{x}[/tex]) represents the situation.
b)The function f(x) = 9,000([tex]0.95^{x}[/tex]) represents the situation.
c)After 2 years, the farmer can estimate that there will be about 8,120 bees remaining.
d)After 4 years, the farmer can estimate that there will be about 1,800 bees remaining.
e)The domain values, in the context of the situation, are limited to whole numbers.
f)The range values, in the context of the situation, are limited to whole numbers.
Now given,
Number of bees initially = 9000
Rate of decay = 5%
f(x) = Number of bee population after x years
So, f(x) = 9000([tex]0.95^{x}[/tex])
After 2 years, number of bees is
f(2) = 9000(0.95²) = 8122.5 ≈ 8120
After 4 years, number of bees is
f(4) = 9000(0.95⁴) = 7330.56≈7330
The domain of the function is number of years(x) which can be whole as well as decimal numbers.
The range of the function is number of bees after x years, which should be a positive integer number. So whole numbers are the domain.
Therefore the correct options regarding given function are (b), (c) and (f).
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The slope of the line segment A-D is the same as the slope of the line segment A-F. What are the two line segments that make this proportion equal?
1. Which of the following would be in the solution set to the system of inequalities given below?
y>4x+7
8x-2y> 10
a No solution
b (-4,1)
c Both (-4,1) and (6,2) are solutions
d (6,2)
Option A will be the solution set of given linear inequalities.
What exactly are linear inequalities?
In mathematics, inequality denotes a mathematical expression in which neither side is equal. In Math, an inequality occurs when a connection produces a non-equal comparison between two expressions or two integers. The equal sign "=" in the phrase is substituted by any of the inequality symbols, such as greater than symbol (>), less than symbol (<), greater than or equal to symbol (≥), less than or equal to symbol (≤), or not equal to symbol ((≠). In mathematics, there are three types of inequalities: polynomial inequalities, rational inequalities, and absolute value inequalities.
Hence,
For given inequalities
y>4x+7
8x-2y>10
there will be no solution as the graph of these inequalities does not coincide anywhere.
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(-4,0) is the solution of the set to the system of inequalities
What is Inequality?
A relationship between two expressions or values that are not equal to each other is called 'inequality.
The given two inequalities are
y<-3x-6 and 4x-2y<-8
Let us check for (-4, 0)
0<-3(-4)-6
0<6
4x-2y<-8
4(-4)-2(0)<-8
-16<-8
So (-4, 0) is the solution of the inequalities.
Now let us check for (0, 2)
replace y value as 2 and x as 0.
2<-3(0)-6
2<-6
Which is not true.
Hence, (-4,0) is the solution of the set to the system of inequalities.
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Which of the following is a solution of equation 3x² 13x 14 0?
The solution of the given equation 3x² + 13x + 14 = 0 is given by :
option b . x = -2.
As given in the question,
Given equation is equal to :
3x² + 13x + 14 = 0
Solve the given equation by method of splitting middle term we get,
3x² + 13x + 14 = 0
⇒ 3x² + 6x + 7x + 14 = 0
⇒ 3x ( x + 2 ) + 7 ( x + 2 ) = 0
⇒ ( 3x + 7 ) ( x + 2 ) = 0
⇒ ( 3x + 7 ) = 0 or ( x + 2 ) = 0
⇒ x = -7/3 or x = -2
From the given options:
Option b . x = -2 is the solution of the equation 3x² + 13x + 14 = 0.
Therefore, the solution of the given equation 3x² + 13x + 14 = 0 is equal to : option b. x = -2.
The above question is incomplete, the complete question is:
Which of the following is one of the solution of equation 3x² + 13x + 14 = 0?
a. x = 2 b. x = -2 c. x = 3 d. x = -3
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9=24
(15. Jake and Adam are at the arcade. So far, Jake has spent a total of $4.00 by playing skee-ball 8
times and air hockey 4 times. Adam has spent a total of $6.50 by playing skee-ball 10 times and air
hockey 8 times.
a. How much does it cost to play skee-ball?
b. How much does it cost to play air hockey?
By linear equation, the cost of playing skee ball is $0.25 and that of air hockey is $0.50.
How are simultaneous linear equations solved?Elimination and substitution are the two most frequently used techniques for simultaneous linear equations. Some questions have a more obvious solution, frequently because it makes solving the equations easier, while others leave the method selection up to the individual.
Loss by Jake=$4
Loss by Adam=$6.50
let,
hockey played=y
skee-ball played=x
for Jake,
8x+4y=4
for Adam,
10x+8y=6.50
solving both equation simultaneously,
we will get
x=1.5/6=0.25
y=0.50
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PLS HELP FAST! Calculate the average rate of change on the interval
The average rate of change for the quadratic function in the graph is 1
What is average rate of change of quadratic function?The proportion of change along the y-axis to change along the x-axis represents the average rate of change between the two points.
Since the graph of a quadratic function is curved and lacks a constant rate of change between any two distinct locations, it is referred to as the average rate of change rather than the slope.
The average rate of change between points (2, 0) and (3, 1) is
= (0 - 1) / (2 - 3)
=-1 / -1
= 1
The average rate of change within the interval 1 to 3 is 1
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Write a function rule to represent the situation. the total cost C for p pounds of lithium each pound costs $3.89 Write a function rule using C and p as variables. enter your response here (Type an equation.)
Answer: C = P$3.89
Step-by-step explanation:
Which function is the result of translating y = x2 downward by 3 units and to the left by 4 units?.
The outcome of translating y = x^2 downward by 3 units and to the left by 4 units is y = (x+4)^2-3.
What exactly is Graph?A graph is a mathematical depiction of a network that describes the connection between lines and points.
We must determine which function results from translating y = x^2 downward by 3 units and to the left by 4 units.
A translation is a movement of the graph that is either horizontally or vertically parallel to the axis.
Replace x with x+4 y = (x+4)^2-3 to shift the graph four units to the left.
As a result, y = (x+4)^2-3 is the result of translating y = x^2 by 3 units downward and 4 units to the left.
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wbat is the y- intercept of this graph?
Answer:
Step-by-step explanation:
To find the y-intercept on a graph, you must look at where the line intercepts through the y-axis.
For this problem it would be 16
Greta has two pet lizards, Draco and Lizzy. For every 11 crickets Greta feeds Draco, she always feeds Lizzy 8 crickets. Last week, Greta fed Draco 77 crickets.
How many crickets did Greta feed Lizzy?
The answer is 56 crickets.
What is a ratio?The quantitative relation between two amounts shows the number of times one value contains or is contained within the other. for example-"the ratio of computers to students is now 2 to 1"
Given here: Greta has two pet lizards, Draco and Lizzy. For every 11 crickets Greta feeds Draco, she always feeds Lizzy 8 crickets. Thus the ratio is 11:8 Therefore if Draco got 77 crickets ten lizzy should get 8×7=56 crickets.
Hence, The answer is 56 crickets.
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What is the difference between X₁ and X₁?
A. X₁ is a random variable, and X₁ is a specific numerical value.
B. X₁ is a random variable, and x₁ is a specific numerical value.
C. There is no difference. They are both random variables.
D. There is no difference. They are both specific numerical values.
The difference between X₁ and X₁ is "X₁ is a random variable, and X₁ is a specific numerical value".
Any variable whose value is uncertain or any function that values each result of an experiment is referred to as a random variable. Random variables are frequently identified by letters and fall into one of two categories: discrete variables, which have definite values, or continuous variables, which can take on any value within a continuous range.
A parameter's estimated value in numbers, specifically. The sample mean is the most accurate estimate of the population mean. A range or interval of values used to gauge the parameter. The value of the parameter under consideration may or may not be included in this estimation.
So we can say the difference between X₁ and X₁ is "X₁ is a random variable, and X₁ is a specific numerical value".
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What is m/M?
Enter your answer in the box.
Answer: ∠M = 98°
Step-by-step explanation:
Given:∠M = (3x-16)°
∠N = x°
∠O = (x+6)°
Sum of all angles in a triangle is 180°
Therefore, 180° = ∠M +∠N +∠O, substitute the given values
180° = (3x-16)° + x° + (x+6)° (add/combine like terms)
180° = (3x+x+x)° + (-16+6)°
180° = (5x)° + (-10°)
180° + 10° = (5x)° ( divide both sides by 5)
190°/5 = (5x)°/5
38° = x°
IF ∠M = (3x-16)°, substitute x°=38°,
Therefore, ∠M = 3(38)-16
∠M = 114 - 16 = 98°
i need help with this
The trinomials in factor form are listed below:
Case A: (x + 2)²
Case B: (x - 3) · (x - 9)
Case C: (x - 7) · (x + 6)
Case D: (x - 9) · (x + 1)
How to factorize trinomials of the form x² + b · x + c
Herein we find four case of trinomials of the form x² + b · x + c that must be factorised, this can be done by using the following algebraic property:
x² - (r₁ + r₂) · x + r₁ · r₂ = (x - r₁) · (x - r₂)
Where r₁, r₂ are real roots of the quadratic equation.
Now we proceed to factorise each trinomial (quadratic equation), that is, their factor form:
Case A
x² + 4 · x + 4
x² + (2 + 2) · x + 2 · 2
(x + 2) · (x + 2)
(x + 2)²
Case B
x² - 12 · x + 27
x² - (3 + 9) · x + (- 3) · (- 9)
(x - 3) · (x - 9)
Case C
x² - x - 42
x² - (7 - 6) + (- 7) · 6
(x - 7) · (x + 6)
Case D
x² + 8 · x - 9
x² - (- 9 + 1) · x + (- 9) · 1
(x - 9) · (x + 1)
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What are the 5 types of inequality math?
The four ways to depict an inequality: solution graph, interval notation, set notation, and equation notation.
What is meant by inequality?In mathematics, an inequality displays the connection between two values in an unbalanced algebraic statement. One of the two variables on the two sides of the inequality may be greater than, greater than or equal to, less than, or less than or equal to another value, according to inequality signals.
There are four ways to depict an inequality: solution graph, interval notation, set notation, and equation notation.
A comparison of any two values, known as an inequality, demonstrates whether one value is less than, larger than, or equal to the value on the opposite side of the equation. A relationship in a real-world scenario can be demonstrated by writing an inequality.
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What is the slope of y =- 3x 10?
Answer:
The Slope would be 3
Can 8 7 and 15 form a triangle?
It is not possible to construct a triangle whose sides are 8 cm 7 cm and 15 cm because the sum of two sides(8 cm and 7 cm) are equal to third side(15 cm).
In the given question, we have to check that it is possible to construct a triangle whose sides are 8 cm 7 cm and 15 cm.
The sum of the two sides must always be greater than the third side in order to determine whether or not the given sides may form a triangle.
To check this we firstly add the 8 and 7
8 + 7 = 15
15 = 15
Now we add 8 and 15
8 + 15 > 7
23 > 7
Now we add 7 and 15
7 + 15 > 8
22 > 8
It is not possible to construct a triangle whose sides are 8 cm 7 cm and 15 cm because the sum of two sides(8 cm and 7 cm) are equal to third side(15 cm).
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An Isosceles triangle has two congruent sides. the first side is expressed by x+2 and the second side is expressed by 2x-25 what is the value of X
The value of x is 27
How to determine the value
From the information given, we have that the triangle is an isosceles triangle.
The properties of an isosceles triangle are;
It has two equal sidesTwo equal anglesIt has three edges and three verticesSum of internal angles is 180We have that;
First side = x + 2
Second side = 2x - 25
Equate the two sides, we get;
x+ 2 = 2x - 25
collect like terms
x - 2x = - 25 - 2
subtract like terms
-x= -27
make 'x' the subject
x = 27
Hence, the value is 27
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What are the 3 types of 3D models describe each?
Solid Modeling: This type of model involves the creation of a 3D object with a fixed boundary, usually a closed surface. Surface Modeling: This type of model involves the creation of a 3D surface using curves, patches, and surfaces. Wireframe Modeling: This type of model involves creating a 3D object with a wireframe of interconnected lines and points.
1. Solid Modeling: This type of model involves the creation of a 3D object with a fixed boundary, usually a closed surface. It is often used in industrial design and architecture. The model consists of a series of interconnected faces and edges which are used to create a solid object. This type of modeling is useful for creating realistic models of objects with complex shapes.
2. Surface Modeling: This type of model involves the creation of a 3D surface using curves, patches, and surfaces. The model is composed of a series of connected surfaces which can be used to create a smooth surface. This type of modeling is often used in animation and video game development.
3. Wireframe Modeling: This type of model involves creating a 3D object with a wireframe of interconnected lines and points. It is often used in engineering and CAD systems to create a 3D representation of a design. The model consists of a series of connected lines, points, and curves which can be used to create a model of an object. This type of modeling is useful for creating simple models of objects with basic shape
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