The probability that the drill bit will fail before 10 hours of usage is approximately 0.8.
The Weibull distribution is given by the cumulative distribution function (CDF) as follows:
F(t) = 1 - e^(-(t/B)^a)
Where F(t) is the probability of failure before time t, a is the shape parameter, B is the scale parameter, and e is the base of the natural logarithm.
In this case, a = 2 and B = 50. We want to find the probability that the drill bit will fail before 10 hours, so we will use t = 10:
F(10) = 1 - e^(-(10/50)^2)
Step-by-step calculation:
1. Calculate (10/50)^2: (0.2)^2 = 0.04
2. Calculate -(0.04): -0.04
3. Calculate e^(-0.04): 0.9607894391523232
4. Calculate 1 - 0.9607894391523232: 0.03921056084767683
The probability that the drill bit will fail before 10 hours of usage is approximately 0.8 (option d). Note that the calculated probability (0.0392) is much lower than the options given. However, the closest option to the calculated value is 0.8.
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Find the slope of the line. (Use/ for fraction, if needed)
(2,-3) (8,-2)
The slope of the line that contains points (2, -3) and (8, -2) is equal to 1/6.
How to calculate the slope of a line?In Mathematics, the slope of any straight line can be determined by using this mathematical equation;
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Based on the information provided, we can logically deduce the following data points on the line:
Points on x-axis = (2, 8).Points on y-axis = (-3, -2).Substituting the given data points into the slope formula, we have the following;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (-2 - (-3))/(8 - 2)
Slope (m) = 1/6
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Ryan invests $7,171 in a savings account with a fixed annual interest rate of 7% compounded 12 times per year. How long will it take for the account balance to reach $11,688.69?
Round your answer to the nearest whole year.
It will take 7 years for the account balance to reach $11,688.69.
To find how long will it take for the account balance to reach $11,688.69
we will use the compound interest formula that is
[tex]$ \text A = \text P(1 + \frac{\text r}{\text n})^{\text {nt}}[/tex]
where,
A = final amount
P = initial principal balance
r = interest rate
n = number of times interest applied per time period
t = number of time periods elapsed
Given that, P = $7,171
A = $11,688.69
r = 7%
n = 12
t = to find
Substitute the details in the formula and we get
[tex]$11688.69 = 7171(1 + \frac{0.07}{12})^{12t}[/tex]
[tex]$ \text t=\frac{\log _{\frac{1207}{1200}}\left(\frac{1168869}{717100}\right)}{12}[/tex]
t = 7.000003 = 7 years
Thus, It will take 7 years for the account balance to reach $11,688.69.
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Answer:
7 years-----------------------------
Use compound interest equation:
A = P(1 + r/n)^(nt), where A - future amount, P- investment, r - interest rate, n- number of compounds, t - time in yearsSubstitute the given to find the value of t:
11688.69 = 7171(1 + 0.07/12)^(12t)1.0058333333^(12t) = 11688.69 /71711.0058333333^(12t) = 1.62999442198ln 1.0058333333^(12t) = ln 1.6299944219812t = ln 1.62999442198 / ln 1.005833333312t = 84 (rounded)t = 7May someone explain this to me in step-by-step? I'd greatly appreciate it!
Thank you.
Answer:
x = 9
Step-by-step explanation:
x = the missing side
24/8 = x/3
8(x) = 24(3)
8x = 72
x = 9
====================================================
Explanation:
The slanted left-most sides of the figures are 24 and 8, when moving from left to right.
Let's reverse the direction and move from right to left. The jump from 8 to 24 is "times 3", which is the scale factor when moving from the smaller figure to the larger figure.
The smaller figure has 3 up top. Apply the "times 3" scale factor to get 3*3 = 9 as the top side length of the larger figure.
In other words, every side of the smaller figure is tripled to get the larger figure.
----------------
Here's another way to solve.
24/8 = x/3
24*3 = 8*x .... cross multiplying
72 = 8x
8x = 72
x = 72/8
x = 9 is the final answer.
solve the systems. 3r=1-s and 7s=4-6r
The left side of the equations is equal to the right side for the values (3/14,5/14).
What is a system of equations?
A system of equations is a set of two or more equations that contain multiple variables. The goal is to find the values of the variables that make all the equations in the system true at the same time. There are different methods to solve a system of equations, such as substitution, elimination, and graphing.
To solve the system of equations given, we can use the substitution method:
1-s = 3r
7s = 4 - 6r
We can start by solving the first equation for one of the variables.
1-s = 3r
s = 1 - 3r
Now we can substitute this expression of s into the second equation
7(1 - 3r) = 4 - 6r
7 - 21r = 4 - 6r
-14r = -3
r = 3/14
Now we can substitute this value of r into either equation to find the value of s
s = 1 - 3r
s = 1 - 3(3/14)
s = 1 - 9/14
s = 5/14
So, the solution of the system of equations is (r,s) = (3/14,5/14)
We can check by substituting the solution into the original equations.
3r = 1 - s = 1 - 5/14 = 9/14
7s = 4 - 6r = 4 - 6(3/14) = 4 - 18/14 = -14/14 = -1
The solution is correct, since the left side of the equations is equal to the right side for the values (3/14,5/14)
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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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Functions!!!
Pls help my teacher didn’t do her job and teach
Answer:
1=yes
2=no
3=no
4=no
5=yes
6=yes(im not sure on this last one)
Step-by-step explanation:
If no vertical line can intersect the curve more than once, the graph does represent a function.
Answer:
Graph 1= It's a function
Graph 2= No
Graph 3= No
Graph 4= No
Graph 5= Yes
Graph 6= Yes
Step-by-step explanation:
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]
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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When a company runs all 50 of its machines, it takes 72 hours to finish a job. If the company only runs 30 of its machines, it takes 120 hours to finish the same job. An equation for the inverse variation between the number of machines, x, the company runs and the time, y, in hours, it takes to finish the job is y=k/x . What is the value of K?
Answer: 3600
Step-by-step explanation: If y = k/x is the formula, solving for k gives xy = k, so 72(50) = 3600; or 30(120) = 3600.
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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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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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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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 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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What is the slope of the relationship?
What is the average rate of change of
g
gg over the interval
−
8
≤
x
≤
−
2
−8≤x≤−2minus, 8, is less than or equal to, x, is less than or equal to, minus, 2?
The average rate of change of g over the interval −8 ≤ t ≤ 2 is equal to -0.5 or -1/2.
How to determine the average rate of change?In Mathematics, the average rate of change of f(x) on a closed interval [a, b] is given by this mathematical expression:
Average rate of change = [f(b) - f(a)]/(b - a)
Next, we would determine the average rate of change of the function g(t) over the interval [-8, 2]:
a = -8; g(a) = 1
b = 2; g(b) = -4
Substituting the given parameters into the average rate of change formula, we have the following;
Average rate of change = (-4 - 1)/(2 - (-8))
Average rate of change = -5/10
Average rate of change = -0.5 or -1/2.
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Complete Question:
What is the average rate of change of g over the interval −8 ≤ t ≤ 2?
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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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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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?
Which customer has the smallest total bill, including tax and tip?
Customer #2 has the smallest total bill, including tax and tip.
How to know the customer with lowest bill?From the information, three business associates are at their favorite local café for lunch. They have finished their meals and just received their bills. Each bill is labeled at the top as Customer #1, Customer #2, or Customer #3.
For customer #1:
(1.06(12.95))(1.15) = 15.79;
The tip is 0.15(1.06(12.95)) = 2.06.
For customer #2:
1.06x = 11.65; x = 10.99; 20%
The tip = 0.2(10.99) = 2.20;
total = 11.65+2.20 = 13.85.
For customer #3:
1.06(11.50) + 0.18(11.50) = 14.26;
The tip is (0.18)(11.50) = 2.07.
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Three business associates are at their favorite local café for lunch. They have finished their meals and just received their bills. Each bill is labeled at the top as Customer #1, Customer #2, or Customer #3. Note: Sales tax is 6%, and tips are rounded to the nearest $0.25. Customer #1: The bill, before sales tax has been added, is $12.95. This customer plans to leave a 15% tip, calculated after the tax has been added. Customer #2: The bill, after sales tax has been added, is $11.65. This customer plans to leave a 20% tip, calculated before the tax was added. Customer #3: The bill, before sales tax has been added, is $11.50. This customer plans to leave an 18% tip, calculated before the tax is added.
1. Which customer has the smallest total bill, including tax and tip?
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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The shortest route from London to Bristol is 120 miles.
A lorry is expected to take 2 hours to travel this route.
The lorry actually travels by a different route which increases the distance by 20%, but it still arrives in 2 hours.
By how many more mph than the expected speed does the lorry travel?
Answer:
12 mph
Step-by-step explanation:
First we're going to start by finding the difference in miles from the first route to the second route.
The first route is 120 miles and the second is 20% more than the first. To find the difference you should first multiply the 120 by 20%.
120*0.2=24
You then need to add the additional 24 miles to the original 120 to find the distance of the second route.
120+24=144
After we will begin to find the mph expected speed for both routes.
The first route was 120 miles and it was expected to take 2 hours to get there. This means you need to divide 120 by 2 to find out how many miles they were traveling within one hour.
120/2=60
So the expected mph for the first route would be 60.
We want to repeat the same thing for the second route.
144/2=72
The mph for the second route was 72.
Now you need to find out how much faster the mph was for the second route than the first by subtracting the first from the second.
72-60=12
The second route was 12 mph faster than the first.
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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Can y’all help me with this?
I just need to know what to do when it’s negative cause I’ve been doing positive the whole time..
Answer:
1/5
Step-by-step explanation:
When raised to the negative power, the numerator is inversed,
2^(-1) = 1/2
10^-1 = 1/10
2^-2 = 1/2^2 or 1/4
4^(-1/2) = 1/(4^(1/2)) = 1/2
25^(-1/2) = 1/25^(1/2) = 1/5
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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Grouping symbols, Exponents, Multiply & Divide, Add & Subtract (GEMDAS). it is called by ____
Grouping symbols, Exponents, Multiply & Divide, Add & Subtract (GEMDAS). It is called by GEMS.
An effective acronym for teaching pupils the hierarchy of operations is PEMDAS.
The PEMDAS rule explains to pupils how to solve multi-step arithmetic problems and in what sequence to complete the operations to arrive at the right solution.
Groupings, Exponents, Multiplication or Division, Subtraction or Addition is referred to as GEMS. All grouping symbols, including parentheses, brackets, and braces, are referred to as groupings. The acronym GEMS has been adopted to take the role of PEMDAS. These can be used in place of one another.
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What is the slope of y =- 3x 10?
Answer:
The Slope would be 3
For which value the given polynomial x³ 3x² 4x 12 is zero *?
When x = 4, the given polynomial is equal to zero.
The given polynomial is x³ 3x² 4x 12.
To find the value of x for which the polynomial is equal to zero, we need to solve the equation
x³ 3x² 4x 12 = 0
This can be done by factoring the polynomial, which gives us
(x – 4)(x² + 3x + 3) = 0
The value of x for which the polynomial is equal to zero is x = 4.
To prove this, we can substitute x = 4 in the original equation and verify.
x³ 3x² 4x 12 = 0
(4)³ 3(4)² 4(4) 12 = 0
64 + 48 + 16 + 12 = 0
130 = 0
This shows that when x = 4, the given polynomial is equal to zero.
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Select the correct answer from each drop-down menu. 4 rows with circles and triangles, left to right. Row 1, circle, triangle, 2 circles, triangle. Row 2, triangle, circle, 2 triangles, circle, triangle. Row 3, circle, 2 triangles, circle, triangle. Row 4, triangle, 2 circles, 2 triangles. The ratio of the number of circles to the number of triangles in simplest form is . The number of circles that need to be added to make the ratio 1 : 1 is .
The ratio of the number of circles to the number of triangles in simplest form is 3:4. The number of circles that need to be added to make the ratio 1 : 1 is 3.
How to determine the ratio in simplest form?First of all, we would have to determine the total number of circles and the number of triangles based on the information provided in the chart (see attachment) as follows;
Total number of circles, C = 9 circles.
Total number of triangles, T = 12 triangles.
Therefore, the ratio of the number of circles to the number of triangles is given by
C:T = 9:12
Dividing both sides of the ratio by 3, we have the following ratio in simplest form:
C:T = 3:4
In order to make the ratio 1:1, the number of circles that need to be added can be calculated as follows;
9 + x:12=1:1
(9 + x)/12 = 1/1
9 + x = 12
x = 12 - 9
x = 3 circles.
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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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