Answer:
I call this a simple solution because it does not involve probability distributions. It just requires simple knowledge of probability, that’s it!
The question says any 15-minute interval, so one hour can be thought of as four 15-minute intervals.
Now, the question asks the probability of seeing at least one shooting star in those four 15-minute intervals.
Such a probability is the same as the complement of the probability of not seeing any shooting star in those four 15-minute intervals.
All of those four 15-minute intervals are independent of each other. So, their combined probability is the product of the individual probabilities.
The individual probability of not seeing any shooting star in an interval of 15 minutes is 1 - 0.2 = 0.8.
So, the combined probability of not seeing any of the shooting stars in the four intervals is: 0.8 * 0.8 * 0.8 * 0.8 = 0.8⁴ = 0.4096
Now, the complement of its probability is 1 - 0.4096 = 0.5904
So, that is the answer or the probability of seeing at least one shooting star in an interval of an hour.
Step-by-step explanation:
Why?
Before diving into the Poisson process, let me explain why such a demonstration is helpful even if the problem can be solved simply.
The problems we encounter in the real-life can’t be solved by mere simple probability formulas. That is the reason more complex concepts are developed in mathematics. They help model real-life scenarios. When the scenarios are not exactly the same as the mathematical model, we do some assumptions and approximate the scenarios with mathematical models. Then, we do the modeling.
Mathematical modeling requires prior practice. To visualize the mathematical models and naturalize ourselves to such (abstract) models, good practice with the problems always helps. So, even if these problems can be solved easily using simpler methods, such problems provide us a good opportunity to practice mathematics and modeling.
Assumptions
At first, let’s see if the assumptions of the Poisson process hold here. The number of events can be counted. The occurrences of the events are independent of each other. The average rate at which the events occur can be calculated and let’s assume two events can not occur exactly at the same instant in time.
So, all the assumptions of the Poisson process hold here. That gives us the green light to move forward.
Mathematical Work
Let’s assume the rate of λ per minute. Then, the rate corresponds to 15λ per quarter.
Now, the formula for the probability distribution is:
P(X = x) = μ^x * e^-μ / x!
Before we go further, let’s understand the mathematical statement. The mathematical statement expresses the probability of seeing x events in a time period. μ is the average number of events seen in the time period. The time period can be a minute, an hour, or even a day. It can be any time period.
At first, let’s see the first statement — In any 15-minute interval, there is a 20% probability that you will see at least one shooting star.
Here, the interval is of 15 minutes. So, the average number of events in the interval is 15λ. The probability of seeing 0 events (i.e X = 0) is:
P(X = 0) = μ⁰ * e^-(15λ) / 0! = 1 / e^(15λ) — — (1)
(1) is equal to 80% as the probability of at least one event happening is 20%.
So, 1 / e^(15λ) = 0.8
or, e^(15λ) = 1.25
or, 15λ = ln(1.25) = 0.2231
=> λ = 0.0149 / min
So, the average number of events (shooting stars) is 0.0149 per minute.
Now, the average number of events in an hour is:
0.0149 * 60 = 0.8926 / hour
So, the Poisson distribution expression becomes:
P(X = x) = 0.8926^x * e^-0.8926 / x! — — (2)
Here, the time period is an hour.
Now, let’s find the probability of not having even a single event in an hour:
P(X = 0) = 0.8926⁰ * e^-0.8926 / 0! = 0.4096
So, the probability of having at least one event is the complement of the above probability.
So, P(X≥1) = 1 - P(X=0) = 1 - 0.4096 = 0.5904
Step-by-step explanation:
A total of 5000 tickets were sold for a raffle. the prizes are $1000, $500, $200, and $100. what price should be charged so there is a 60% profit per ticket?
Answer: $0.576
Step-by-step explanation:
The total amount in prizes is $1800.
For there to be 60% profit, the total cost of the tickets need to be [tex]1800(1.6)=\$ 2880[/tex].
Thus, each ticket must sell for [tex]\frac{2880}{5000}=\$ 0.576[/tex]
$0.576 should be charged so there is a 60% profit per ticket.
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
The prizes are $1000, $500, $200, and $100.
So, total prize = 1000+ 500+ 200+ 100 = $1800.
The, the price of ticket to break
= 1800 / 5000
= $0.36
Now, the price for 60% ticket = 0.36 (1 + 0.6)
= 0.36 x 1.6
= $0.576
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Aiden ipens a savings account with a deposit of 4500. The account pays 3% simple interest.3. If Aiden does not make any more deposits or withdrawals, how much will he have in the account at the end of two years?A 4527B 4635C 4680D 4774E 4905
Answer: $4, 770
Aiden deposit $4500 into her account with an interest rate of 3%
Time = 2 years
Using the Simple Interest
[tex]\begin{gathered} I\text{ = }\frac{P\text{ x R x T}}{100} \\ P\text{ = \$4500} \\ R\text{ = 3\%} \\ T\text{ = 2} \\ I\text{ = }\frac{4500\text{ x 3 x 2}}{100} \\ I\text{ = }\frac{4500\text{ x 6}}{100} \\ I\text{ = }\frac{27000}{100} \\ I\text{ = \$270} \\ \text{The total amount in her account is } \\ \text{Balance = Principal + Interest} \\ \text{Balance = \$4500 + \$270} \\ \text{Balance = \$4, 770} \end{gathered}[/tex]In ΔTUV, t = 82 inches, v = 86 inches and ∠V=41°. Find all possible values of ∠T, to the nearest degree.
The value of ∠T is 38.722° as the definition of angle is "An angle is created by joining two line segments at one point, or we can say that an angle is the combination of two line segments at a common endpoint".
What is angle?An angle is created by joining two line segments at one point, or we can say that an angle is the combination of two line segments at a common endpoint. When two straight lines or rays intersect at a single endpoint, an angle is created. The vertex of an angle is the location where two points come together. The Latin word "angulus," which means "corner," is where the word "angle" originates. Based on measurement, there are different kinds of angles in geometry. The names of fundamental angles include acute, obtuse, right, straight, reflex, and full rotation. A geometrical shape called an angle is created by joining two rays at their termini. In most cases, an angle is expressed in degrees.
Here,
Side t = 82
Side u = 128.98238
Side v = 86
Angle ∠T = 38.722°
Angle ∠U = 100.278°
Angle ∠V = 41°
∠T = sin⁻¹(t·sin(V)/v)
=38.722°
Since the definition of an angle is "An angle is created by joining two line segments at one point, or we can say that an angle is the combination of two line segments at a common endpoint," the value of ∠T is 38.722°.
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dominic is making meatballs. he uses 3/4 cup of breadcrumbs for every 1 1/4 pounds of ground beef. how many cups of bradecrumbs does he need when he uses 1 3/4 pounds of ground beef?
The number of cups of breadcrumbs he will need when he uses 3/4 pounds of ground beef would be = 1¹/20 cup.
What are breadcrumbs?Breadcrumbs is a type of food product that is produced from crumbling of dried bread which is used making dishes such as meatballs.
The number of cups of breadcrumbs for 1¼ of meat ball = ¾ cup
Therefore the number of cups of breadcrumbs for 1¾ = X cup.
That is ; 1¼ = ¾ cup
1¾ = X cup
Make X cup the subject of formula;
X cup = 1 ¾ × ¾ ÷ 1¼
X cup = 21/16 ÷ 5/4
X cup = 21/16 × 4/5
X cup = 21/20
X cup = 1 ¹/20 cup
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how do you find 18.84 20.91 19.5 on a number line 14-22
In order to find the given numbers on a number line thats moves between 14 and 22, we shall illustrate with a number line.
The number line illustrated above shows the numbers arranged in order from 14 to 22.
The numbers indicated in the question are printed in blue.
The position of the numbers are also indicated with a black "stroke" in relation to the position of the numbers 14 to 22.
(c) In the diagram below:ARga nainP.50°B65%DNot drawn to scale(i) Calculate the angle BDC (ii) Calculate angle ABD (iii) Find angle BAD(iv) What type of triangle is triangle ABD ?CS
Given: Parallel lines PQ and RS. Triangle ABD and BDC are such that
[tex]\begin{gathered} BD=CD \\ m\angle ABR=50\degree \\ m\angle ADB=65\degree \end{gathered}[/tex]Required: To determine the triangle ABD type and calculate the angle BDC, ABD, and angle BAD.
Explanation: Since line PQ is parallel to line RS,
[tex]\angle ADB=\angle DBC=65\degree[/tex]Now since BD=CD, triangle BCD is an isosceles triangle. Hence,
[tex]\angle DBC=\angle DCB=65\degree[/tex]Now, in triangle BCD, we have
[tex]\begin{gathered} \angle B+\angle C+\angle D=180\degree\text{ \lparen Angle sum property\rparen} \\ 65\degree+65\degree+\angle D=180\degree \\ \angle D=50\degree \end{gathered}[/tex]Now RS is a straight line. Hence at point B, we have
[tex]\begin{gathered} 50\degree+\angle ABD+\angle DBC=180\degree\text{ \lparen Linear pair\rparen} \\ \angle ABD=65\degree \end{gathered}[/tex]Finally, in triangle ABD, we have
[tex]\begin{gathered} \angle A+\angle B+\angle D=180\degree \\ \angle A+65\degree+65\degree=180\degree \\ \angle A=50\degree \end{gathered}[/tex]Now since in triangle ABD, we have
[tex]\angle ABD=\angle ADB[/tex]The triangle ABD is isosceles.
Final Answer:
[tex]\begin{gathered} \angle BDC=50\degree \\ \angle ABD=65\degree \\ \angle BAD=50\degree \end{gathered}[/tex]The triangle ABD is isosceles.
4. Jill wants to buy $70,000 worth of insurance for her new house. If therate is $8.00 per $1000 of value, what will her insurance premium be?a. $590b. $560C. $530
Let's calculate the insurance premium Jill will have to pay for her insurance of her new home:
Insurance premium = 70,000 / 1,000 * 8
Insurance premium = 70 * 8
Now you can calculate easily the payment Jill will have to afford.
It is 6 miles in a kayak to the Fish Islands from my house. The trip to the island takes 2 hourstraveling against the current and 1¼ hours for the return trip (with the current). How fast can Ipaddle the Kayak if there was no current? The answer can be rounded to the nearest tenth.Solve Algebraically using linear systems
It is given that the distance is 6 miles and the time is 2 hours upstream and one and a quarter hour downstream.
The time downstream is given by:
[tex]1\frac{1}{4}=\frac{4+1}{4}=\frac{5}{4}\text{ hours}[/tex]Since the distance is constant, it follows:
[tex]\begin{gathered} \text{ Speed=}\frac{\text{ Distance}}{\text{ Time}} \\ \text{ Distance=SpeedxTime} \end{gathered}[/tex]So the distance is constant hence:
[tex]\text{ Distance upstream=Distance Downstream}[/tex]Let the speed of kayak be x and speed of current be y so the speed downstream is x+y and speed upstream is x-y so it follows:
[tex]\begin{gathered} \frac{5}{4}(x+y)=2(x-y) \\ 4\times\frac{5}{4}(x+y)=4\times2(x-y) \\ 5x+5y=8(x-y) \\ 5x+5y=8x-8y \\ 5y+8y=8x-5x \\ 13y=3x \\ x=\frac{13}{3}y \end{gathered}[/tex]Use the individual equation to find x and y as follows:
[tex]\begin{gathered} 6=2(x-y) \\ 6=2(\frac{13}{3}y-y) \\ 3=\frac{13-3}{3}y \\ \frac{9}{10}=y \end{gathered}[/tex]Hence the speed of the water current is 9/10 miles per hour.
The speed of the kayak is given by:
[tex]\begin{gathered} x=\frac{13}{3}y \\ x=\frac{13}{3}\times\frac{9}{10} \\ x=\frac{39}{10}=3.9\text{ miles per hour} \end{gathered}[/tex]Hence the speed of the kayak without the water current is 3.9 miles per hour.
The time required without water current is:
[tex]\begin{gathered} \text{Time}=\frac{Dis\tan ce}{Speed} \\ t=\frac{6}{3.9}\approx1.5\text{ hours} \end{gathered}[/tex]Hence it will take approximately 1.5 hours without the current.
Please help me solve question 6 on my algebra homework
We have the following equation:
[tex]y-5=2(x-2)[/tex]First, we leave the equation in the slope-intercept form.
[tex]\begin{gathered} y=2x-4+5 \\ y=2x+1 \end{gathered}[/tex]First, we leave the equation in the slope-intercept form.
Domain
The domain of a function is the set of the existence of itself, that is, the values for which the function is defined.
In this case, the solution is:
[tex]-\inftyIn interval notation[tex](-\infty,\infty)[/tex]Range
The range of the function is the set of all the values that the function takes in the existing interval of the domain.
In this case, the solution is:
[tex]-\inftyIn interval notation[tex](-\infty,\infty)[/tex]Zero
The zeros of a function are the points where the graph cuts the x-axis.
To find this, we equate the function to zero.
[tex]\begin{gathered} 2x+1=0 \\ x=-\frac{1}{2}=-0.5 \end{gathered}[/tex]In this case, the zero is in -0.5.
Y-intercept
To find the y-axis intercept, we solve the equation when x=0.
[tex]\begin{gathered} y=2\cdot0+1 \\ y=1 \end{gathered}[/tex]In conclusion, the y-axis intercept is in the coordinate (0,1)
Slope
Looking at the equation of the form y = mx+b we can easily tell what the slope is, remembering that "k" is the slope of the function.
[tex]\begin{gathered} y=2x+1 \\ k=2 \end{gathered}[/tex]In conclusion, the slope is k=2
Type of slope
There are four different types of slopes: negative, zero, positive and undefined.
In this case, the slope is positive, because the angle of the slope is greater than zero and less than 90 degrees.
In conclusion, the slope is positive
f(3)
We will solve the function when x=3
[tex]\begin{gathered} f(3)=2x+1 \\ f(3)=2\cdot3+1 \\ f(3)=6+1 \\ f(3)=7 \end{gathered}[/tex]Value of x, where f(x)=7
We must equal the function to 7 and clear "x".
[tex]\begin{gathered} 2x+1=7 \\ x=\frac{7-1}{2} \\ x=\frac{6}{2} \\ x=3 \end{gathered}[/tex]In conclusion, the value of "x" is x=3
-2. The sum of two cubes can be factored by using the formula o’ + b3 (a + b)(c? ab + b?).(a) Verify the formula by multiplying the right side of the equation.(b) Factor the expression 8x2 + 27.(C) One of the factors of q? - bºis a - b. Find a quadratic factor of q? - bº. Show your work.(d) Factor the expression x - 1.
Given that the sum of two cubes can be factored by using the formula
[tex]a^3+b^3=(a+b)(a^2-ab+b^2)[/tex]a) To verify the formula by multiplying the right side equation
[tex]\begin{gathered} (a+b)(a^2-ab+b^2) \\ =a(a^2-ab+b^2)+b(a^2-ab+b^2) \\ =a^3-a^2b+ab^2+a^2b-ab^2+b^3 \\ \text{Collect like terms} \\ =a^3-a^2b+a^2b+ab^2-ab^2+b^3 \\ \text{Simplify} \\ =a^3+b^3 \end{gathered}[/tex]Hence,
[tex](a+b)(a^2-ab+b^2)=a^3+b^3[/tex]b) To factor
[tex]8x^3+27[/tex]Using the sum of two cubes formula, i.e
[tex]a^3+b^3=(a+b)(a^2-ab+b^2)[/tex]Factorizing the expression gives
[tex]\begin{gathered} (2x)^3+(3)^3=(2x+3)((2x)^2-(2x)(3)+(3)^2)_{} \\ (2x)^3+(3)^3=(2x+3)(4x^2-6x+9) \end{gathered}[/tex]Hence, the answer is
[tex](2x+3)(4x^2-6x+9)[/tex]c) Given that one of the factors of a³ - b³ is a- b, the quadratic factor of a³ - b³ can be deduced by applying the differences of cubes formula below
[tex]a^3-b^3=(a-b)(a^2+ab+b^2)^{}_{}[/tex]Expanding the right side equations
[tex]\begin{gathered} (a-b)(a^2+ab+b^2)^{}_{}=a(a^2+ab+b^2)-b(a^2+ab+b^2) \\ =a^3+a^2b+ab^2-a^2b-ab^2-b^3 \\ \text{Collect like terms} \\ =a^3+a^2b-a^2b+ab^2-ab^2-b^3 \\ \text{Simplify} \\ =a^3-b^3 \end{gathered}[/tex]Hence, the quadratic factor is
[tex]a^3-b^3=(a-b)(a^2+ab+b^2)[/tex]d) To factor the expression
[tex]x^3-1[/tex]By applying the differences of cubes formula
[tex]a^3-b^3=(a-b)(a^2+ab+b^2)[/tex]Factorizing the expression gives
[tex]\begin{gathered} (x)^3-(1)^3=(x-1)(x^2+(x)(1)+1^2)^{}_{} \\ x^3-1^3=(x-1)(x^2+x+1) \end{gathered}[/tex]Hence, the answer is
[tex](x-1)(x^2+x+1)[/tex]
Christian and Lea are in charge of planning the school prom. They will spend $250 on decorations. Dinner will cost $12 per person (p) that attends theprom. Which equation represents the total cost (t) of the prom for any number of students attending?p = 250t + 12p = 12 + 250t=12p - 250t = 250p + 12
If one object costs $x then p objects will cost $px.
Given data:
It is given that they spend $250 on decorations and $12 per person for dinner.
Now the cost $250 is fixed.
Now, if cost od dinner for one person is $12.
So the cost of dinner for p persons will be $12p
Therefore, total cost 't' will be
[tex]t=12p+250[/tex]find the length of arc FH. Round to the nearest hundredth.(Degrees)
Given the circle G
As shown, m∠FGH = 36
And the radius of the circle = r = FG = 10 units
we will find the length of the arc FH using the formula:
[tex]\text{Arc}=\theta\cdot r[/tex]The given angle measured in degree, we will convert it to radian
So,
[tex]\theta=36\cdot\frac{\pi}{180}=\frac{\pi}{5}[/tex]So, the length of the arc =
[tex]\frac{\pi}{5}\cdot10=2\pi\approx6.283185[/tex]Round to the nearest hundredth.
So, the answer will be the length of the arc FH = 6.28
4+(6x2²)-9 use pemdas
Given:
[tex]4+(6\times2^2)-9[/tex]Required:
To solve the given expression.
Explanation:
Consider
[tex]\begin{gathered} =4+(6\times2^2)-9 \\ \\ =4+(6\times4)-9 \\ \\ =4+24-9 \\ \\ =28-9 \\ \\ =19 \end{gathered}[/tex]Final Answer:
[tex]4+(6\times2^2)-9=19[/tex]A vase can be modeled using x squared over 6 and twenty five hundredths minus quantity y minus 4 end quantity squared over 56 and 77 hundredths equals 1 and the x-axis, for 0 ≤ y ≤ 20, where the measurements are in inches. Using the graph, what is the distance across the base of the vase, and how does it relate to the hyperbola? Round the answer to the hundredths place.
We are given that a vase is modeled by the following hyperbola:
[tex]\frac{x^{2}}{6.25}-\frac{\left(y-4\right)^{2}}{56.77}=1[/tex]we are asked to determine the distance across the base. To do that we will first look at the graph of the equation:
Therefore, the base of the vase is the distance between the x-intercepts of the graph. To determine the x-intercepts we will set y = 0 in the equation. We get:
[tex]\frac{x^2}{6.25}-\frac{(0-4)^2}{56.77}=1[/tex]Solving the operation on the parenthesis we get:
[tex]\frac{x^2}{6.25}-\frac{16}{56.77}=1[/tex]Now we solve the fraction:
[tex]\frac{x^2}{6.25}-0.28=1[/tex]Now we add 0.28 to both sides:
[tex]\begin{gathered} \frac{x^2}{6.25}=1+0.25 \\ \\ \frac{x^2}{6.25}=1.25 \end{gathered}[/tex]Now we will multiply 6.25:
[tex]\begin{gathered} x^2=1.25(6.25) \\ x^2=7.81 \end{gathered}[/tex]Taking square root to both sides:
[tex]\begin{gathered} x=\sqrt[]{7.81} \\ x=\pm2.8 \end{gathered}[/tex]Therefore, the x-intercepts are -2.8 and 2.8.
Now we need to determine the distance between these two points. We will use the distance between two points in a line:
[tex]d=\lvert x_2-x_1\rvert[/tex]Substituting the points we get:
[tex]d=\lvert2.8-(-2.8)\rvert=\lvert2.8+2.8\rvert=5.6[/tex]Therefore, the distance is 5.6 inches and is related to the hyperbola in the sense that it is the distance between the x-intercepts.
I need help with geometry. I am supposed to solve for x in this diagram and assume lines marked with interior arrowheads are parallel :)
ANSWER:
40°
STEP-BY-STEP EXPLANATION:
We can make the following equality thanks to the properties of these angles:
[tex]\begin{gathered} 3x=120 \\ \text{ solving for x} \\ x=\frac{120}{3} \\ x=40\text{\degree} \end{gathered}[/tex]The value of x is 40°
simplify (6r+5)(r-8)
To solve, first open the parenthesis
6r(r-8) + 5(r-8)
6r² - 48r + 5r - 40
Re-arrange
6r² + 5r -48r-40
6r² -43r - 40
I don't understand how to add and subtract Intregers
Explanation
First of, you should know that integers are whole numbers.
There are positive integers (positive whole numbers, that is, normal whole numbers greater than 0, for example, 7, 98, 14 etc.) and there are negative integers (negative whole numbers, that is, whole numbers less than 0, for example, -3, -37, -101 etc.)
So, the first tip about adding and subtracting these numbers is to look at them in monetary terms.
Always look at positive numbers like money you have in your pockets (cash at hand).
And look at negative numbers like money you're owing someone.
So, we can then go through the different types of addition and subtraction of integers now.
- Addition of two positive numbers
** 2 + 2
You can interprete this simple addition as having $2 and another $2 is given to you, this means you've got $4 now.
2 + 2 = 4
** 17 + 7
You can interprete this simple addition as having $17 and another $7 is given to you, this means you've got $24 now.
17 + 7 = 24
- Subtraction of two positive integers
** 7 - 3
Look at this like having $7, then -3 means $3 is taken away from it, then you've got only $4 left.
7 - 3 = 4
** -15 + 10
This means you're owing $15, and you've got only $10, after paying the $10, there's still a debt of $5 left. So,
-15 + 10 = -5
Before the next two further types of adding/subtracting integers, weneed to also note the following
(+) × (+) = (+)
(+) × (-) = (-)
(-) × (+) = (-)
(-) × (-) = (+)
These helps us to simplify these additions and subtractions that involve a mix of positve numbers and negative numbers or just strictly working with negative numbers.
Addition of two negative numbers
** -5 + (-3)
Normally, with the former approach, this just means a debt of $5 is added to a debt of $3, these come together to give a bigger debt of $8.
But we can simplify the given equation further because we know that
(+) × (-) = (-), So,
-5 + (-3) = -5 - 3 (The plus sign before the -3 and the minus sign in the bracket multiply to give a negative/minus sign).
So,
-5 + (-3) = -5 -3 = -8
** -7 + (-4)
-7 + (-4) = -7 - 4 = -11
Subtraction of two negative integers
** -5 - (-5)
Recall that
(-) × (-) = (+), So,
-5 - (-5) = -5 + 5
Which then translates to owing $
All of the following are equivalent exceptO (4)(y)O 4+ y04.1O 4 yASK FOR HELPUNT QUESTION
Identify the key features for the following equation: y=4sin(x)−5What kind of cyclic model is the equation?
Given,
The equation of the function is:
[tex]y=4sinx-5[/tex]The standard equation of wave is,
[tex]y=Asin\text{ \lparen Bx+C\rparen+D}[/tex]Here, A is the amplitude
B is the period.
C is the phase shift.
D is vertical shift.
As the given function have the sine function so, the cyclic model of the wave is sine.
Amplitude = 4.
Midline = -5
Minimum = -9
Hence, the key feature of the cyclic model is identified.
I don't understand if this equation is a linear equation or not. Can you please help me?
we have the equation
[tex]\frac{x}{4}-\frac{y}{3}=1[/tex]To remove the fractions, multiply both sides by (4*3=12)
[tex]\begin{gathered} \frac{12x}{4}-\frac{12y}{3}=12 \\ 3x-4y=12 \\ 4y=3x-12 \\ y=\frac{3}{4}x-3 \end{gathered}[/tex]this is the equation of a line
that means
is a linear equation
find the area of the semicircle round to the nearest tenth use 3.14 for pi do not include units with your answer to 22.5 in
Semicrcle area = π•Diameter^2 / 8
. = 3.14 • (2 R)^2/8
. = 3.14• (45)^2/8
. = 3.14• 2025/8= 794.81
Then answer is
Area of semicircle = 795 square inches
The length of the rectangle below is 7 than it’s width. Given that the total distance around the rim of the shape is 46 units, what is the value of x?
drawing a sketch, giving an example, or providing a written description, please indicate themeaning of each of the following shapes.
For the given shapes, we will draw a sketch
a) A cone
the sketch of the cone will be as follows:
The cone has a circular base of radius = r, and a height of (h) and has a flat surface and curved surface as shown.
b) The diameter of the circle:
The diameter is a line segment (d) that connects two points lying on the circle through the center of the circle
c) The radius of the circle:
The radius of the circle (r) is a line segment that connects the center of the circle and any point lying on the circle
An equilateral triangle and an isosceles triangle share a common side. What is the measure of /_ABC?
The sum of all the angles in a triangle is equal to 180 degrees
For an equilateral triangle, all sides are equal
i.e 60 + 60 + 60= 180
For an isosceles triangle, two sides are equal
the first image is an isosceles triangle why the second image is an equilateral triangle
Which equation is an identity?O 3(x - 1) = x + 2(x + 1) + 1Ox-4(x + 1) = -3(x + 1) + 1O 2x + 3 = 1 (4x + 2) + 2(6x - 3) = 3(x + 1) – x-2
Identity equations are always true, no matter the values that the variables take.
We have to calculate for each one, and if the result gives a true statement, then the equation is an identity:
1) 3(x - 1) = x + 2(x + 1) + 1
[tex]\begin{gathered} 3\left(x-1\right)=x+2\left(x+1\right)+1 \\ 3x-3=x+2x+2+1 \\ 3x-3=3x+3 \\ 3x-3x=3+3 \\ 0=6 \end{gathered}[/tex]This is FALSE (for any value of x), so the equation is not an identity.
2) x-4(x + 1) = -3(x + 1) + 1
[tex]\begin{gathered} x-4\left(x+1\right)=-3\left(x+1\right)+1 \\ x-4x-4=-3x-3+1 \\ x(1-4+3)=-2+4 \\ 0=2 \end{gathered}[/tex]This is FALSE, so the equation is not an identity.
3) 2x + 3 = 1 (4x + 2) + 2
[tex]\begin{gathered} 2x+3=14x+2+2 \\ 3-2-2=14x-2x \\ -1=12x \\ x=\frac{-1}{12} \end{gathered}[/tex]This equation holds true only for x=-1/12, so it is not an identity.
4) (6x - 3) = 3(x + 1) – x-2
[tex]\begin{gathered} \left(6x-3\right)=3\left(x+1\right)-x-2 \\ 6x-3=3x+3-x-2 \\ 6x-3=2x+1 \\ 6x-2x=1+3 \\ 4x=4 \\ x=1 \end{gathered}[/tex]This equation holds true only for x=1, so it is not an identity.
Neither of the options is an identity.
Function A Function B Tell whether each function is linear or nonlinear. х y 4 0 1 3 5 24 8 2 3 13 0 1 2 3 4 5 Function A is a function. Function B is a function.
Function A is NOT LINEAR
Function B is LINEAR
The slope (change in y over change in x) does not follow a linear pattern in function A. That is the increase/decrease in the y coordinates is not at the same rate as that of the x coordinate. Whereas, for the other function, function B, the slope follows a linear pattern, that is the rate of change in y over the rate of change in x is the same rate, that is why function B has a straight line graph
Triangle ACD is dilated about the origin.10D'987-854DC92СA-5-4-3-2-102- 1-2Which is most likely the scale factor?0 1 / 3OOo
Step 1
Find the length of any two sides of both figures
[tex]\begin{gathered} In\text{ the original image} \\ AC=3\text{ units} \\ CD=2\text{ units} \\ In\text{ the dilated image} \\ A^{\prime}C^{\prime}=9\text{ units} \\ C^{\prime}D^{\prime}=6\text{ units} \end{gathered}[/tex]Step 2
Write the ratio that will be used to get the dilation factor.
[tex]\begin{gathered} \frac{C^{\prime}D^{\prime}}{CD}=\frac{A^{\prime}C^{\prime}}{AC} \\ \frac{6}{2}=\frac{9}{3} \\ 3=3 \\ \text{Therefore, the scale factor = 3} \end{gathered}[/tex]14. In your rectangular backyard, you knowthe width of the yard is three lessthan four times the length. If the perimeterof your yard is 24 yards, what isthe width?18 3/5yards3 yards9 yards15 yards
ANSWER:
3rd option: 9 yards
STEP-BY-STEP EXPLANATION:
Given that:
Length = L
Width = W = 4L - 3
The perimeter is the sum of all the sides, therefore:
[tex]\begin{gathered} p=L+L+W+W \\ \\ \text{ We replacing:} \\ \\ 24=L+L+4L-3+4L-3 \\ \\ \text{ We solve for L} \\ \\ 24+3+3=10L \\ \\ L=\frac{30}{10} \\ \\ L=3\text{ yd} \\ \\ \text{ Therefore:} \\ \\ W=4L-3=4(3)-3=9\text{ yd} \end{gathered}[/tex]So the correct answer is 3rd option: 9 yards
7)Which table of values BEST represents a model of exponential decay?х012.34-12a(x)1a.251017-1012.34b.b(x)97531- 1х-101234cfx)346101834c.х-101234d.dx)191954723115
Answer:
the one that represents a model of experimental decay is d.
Step-by-step explanation:
In mathematics, exponential decay describes the process of REDUCING an amount by a consistent percentage rate over a period of time, it is different from linear decay because in linear decay factor relies on a percentage of the original amount, there is a constant rate of decay.
Therefore,
As we can see on the graphs, the only table of values that represent DECAYS is options b and d. But, notice option B is a linear decay since it has a constant rate of decay.
So, the one that represents a model of experimental decay is d.
4. Angelo gave 3 of a bag of pretzels to Ben. Ben ate a portion (x) of the pretzels and then gave 4 of the remaining pretzels in the bag to Connor. The expression below represents Connor's portion of the bag of pretzels. 2/3 314 Which expression is equivalent to Connor's portion of the bag of pretzels?
we have Connor's portion of the pretzels
[tex]\frac{2}{3}\times(\frac{3}{4}-x)[/tex]then simply the expression
[tex]\begin{gathered} \frac{2}{3}\times\frac{3}{4}-\frac{2}{3}x \\ \frac{2\times3}{3\times4}-\frac{2}{3}x \\ \frac{6}{12}-\frac{2}{3}x \\ \frac{1}{2}-\frac{2}{3}x \end{gathered}[/tex]answer: C