Identify the equation of the translated graph in general form x^2-y^2=8 for T(4,3)
Answers
Answer:
B
Step-by-step explanation:
A transformation of T(a,b) in the equation would give this form:
[tex](x-a)^2+(y-b)^2=8[/tex]
So, T(4,3) means translation of 4 units in x and 3 units in y. Thus, we can write:
[tex](x-4)^2+(y-3)^2=8[/tex]
Expanding and rearranging, we get:
[tex](x-4)^2-(y-3)^2-8=0\\x^2-8y+16-y^2+6y-9-8=0\\x^2-y^2-8x+6y-1=0[/tex]
Answer choice B is right.
Answer:
B
x^2-y^2-8x+6y-1=0
Related Questions
Determine the coordinates of the corners of the rectangle to compute the area of the rectangle using the distance formula (round to the nearest integer).
Answers
Answer:
The area of rectangle is [tex]72\ units^{2}[/tex]
Step-by-step explanation:
see the attached figure with letters to better understand the problem
Let
[tex]A(3.10),B(12,1),C(16,5),D(7,14)[/tex]
we know that
The area of rectangle is equal to
[tex]A=(AB)(BC)[/tex]
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
Find the distance AB
we have
[tex]A(3.10),B(12,1)[/tex]
substitute in the formula
[tex]AB=\sqrt{(1-10)^{2}+(12-3)^{2}}[/tex]
[tex]AB=\sqrt{(-9)^{2}+(9)^{2}}[/tex]
[tex]AB=\sqrt{162}\ units[/tex]
Find the distance BC
we have
[tex]B(12,1),C(16,5[/tex]
substitute in the formula
[tex]BC=\sqrt{(5-1)^{2}+(16-12)^{2}}[/tex]
[tex]BC=\sqrt{(4)^{2}+(4)^{2}}[/tex]
[tex]BC=\sqrt{32}\ units[/tex]
Find the area of rectangle
[tex]A=(\sqrt{162})*(\sqrt{32})=72\ units^{2}[/tex]
Answer:
d is the answer
Step-by-step explanation:
Triangle T was dilated to form triangle T'. Which ratio is the correct scale factor?
Please answer fast and correctly
Answers
Answer:
5/9
Step-by-step explanation:
The scale factor by which T was dilated is ...
(side of T')/(corresponding side of T)
= 20/36 = 10/18 = 5/9 . . . (reduced form)
Answer:
C) the answer is 5/9 or C
Step-by-step explanation:
i got it roght on the edgen quiz.
In a game, if you roll a 6 on a 6-sided number cube, you lose a turn.
(a) What is the probability that you roll a 6? Explain your reasoning.
(b) What is the probability that you either roll a 6 or do not roll a 6? Explain your reasoning.
(c) What is the probability that you don’t roll a 6? Explain your reasoning.
Answers
a) There are 6 sides, one of them having 6 on it. Therefore, the chances is 1/6.
b) Rolling a six or not rolling a six is guaranteed, because there is no other option. The probability is 1.
c) There are 6 sides, five of them not having a 6. So, the probability is 5/6.
Determine whether the value is a discrete random variable, continuous random variable, or not a random variable. a. The amount of snowfall in December in City A b. The number of bald eagles in a country c. The gender of college students d. The number of statistics students now reading a book e. The number of people with blood type A in a random sample of 18 people f. The number of points scored during a basketball game
Answers
Answer:
a) a continuous random variable; b) a discrete random variable; c) not a random variable; d) a discrete random variable; e) a discrete random variable; f) a discrete random variable
Step-by-step explanation:
A continuous random variable is one that can take multiple values between whole number values; for instance, fractions and decimals. Snowfall is a continuous random variable.
A discrete random variable is one that can only take whole number values. The number of bald eagles, the number of students reading a book, the number of people with blood type A, and the number of points scored in a basketball game are discrete random variables.
Gender of students is not a numerical value; this is not a random variable.
Here, we are required to determine whether the value a list of data sets are, discrete random variable, continuous random variable, or not a random variable.
Options B, D, E and F are examples of discrete random variable values.Option A is an example of a continuous random variable value.Option C is an example of a non-random variable value.First, it is important to know the characteristics of each type of value as follows;
A discrete random variable is one which usually (although not necessarily) are counts. The statement above means they may take on only a countable number of distinct values such as 0,1,2,3, and on. Put simply, they can take only a finite number of distinct values. Distinct in this case means whole number values. Examples are as follows;The number of bald eagles in a countryThe number of statistics students now reading a bookThe number of people with blood type A in a random sample of 18 peopleThe number of points scored during a basketball game
2. A continuous random variable is one which has an infinite number of possible values. This means that the value of a continuous variable is usually associated with fractions of whole numbers, i.e continuous random variables are used majorly for measurements such as length, height and so on. An example from the question above is;
The amount of snowfall in December in City3. A non-random variable is one whose values are definite. An example from above is;
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One diagonal of a cube has length 12. Compute the surface area of the cube.
Answers
Answer:
The surface area of the cube is [tex]288\ units^{2}[/tex]
Step-by-step explanation:
we know that
The length of a diagonal of a cube is equal to
[tex]D=b\sqrt{3}[/tex]
where
b is the length side of a cube
In this problem we have
[tex]D=12\ units[/tex]
so
[tex]12=b\sqrt{3}[/tex]
solve for b
[tex]b=\frac{12}{\sqrt{3}}\ units[/tex]
Simplify
[tex]b=4\sqrt{3}\ units[/tex]
Find the surface area of the cube
The surface area of the cube is equal to
[tex]SA=6b^{2}[/tex]
substitute the value of b
[tex]SA=6(4\sqrt{3})^{2}=288\ units^{2}[/tex]
What basic trigonometric identity would you use to verify that cot x sin x =cos x
Answers
[tex] \cot(x) \sin(x) = \frac{ \cos(x) }{ \sin(x) } \sin(x) = \cos(x) \\ \Rightarrow b. \cot(x) = \frac{ \cos(x) }{ \sin(x) } [/tex]
Answer:
B
Step-by-step explanation:
URGENT HELP PLZ MATH!
Find the measure of angle B.
Question 5 options:
30°
60°
90°
120°
Answers
➷ Angles in a triangle total to 108 degrees
180 - (45 + 15) = 120
Angle B is 120 degrees.
✽➶ Hope This Helps You!
➶ Good Luck (:
➶ Have A Great Day ^-^
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Answer:
The correct option is D.
Step-by-step explanation:
From the given figure it is clear that the measure of angle A is 45° and the measure of angle C is 15°.
According to the angle sum property of triangles, the sum of interior angles of a triangle is 180°. It means in triangle ABC,
[tex]\angle A+\angle B+\angle C=180^{\circ}[/tex]
[tex]45^{\circ}+\angle B+15^{\circ}=180^{\circ}[/tex]
[tex]\angle B+60^{\circ}=180^{\circ}[/tex]
[tex]\angle B=180^{\circ}-60^{\circ}[/tex]
[tex]\angle B=120^{\circ}[/tex]
The measure of angle B is 120°. Therefore the correct option is D.
A store marks up merchandise 40% for profit. If an item costs the store $15, what is the selling price?
Answers
Answer:
The selling price is $21
Step-by-step explanation:
What is the markup
Take the original price and multiply by the markup percent
markup = 15*40%
= 15*.4
= 6
The new price is the original price plus the markup
new price = 15+6
new price = 21
The selling price is $21
a mailing container for posters is made from 87.4 square inches of cardboard the container is in the shape of a triangular prism the base of the prism is an equilateral triangle with 2- inch side lengths and a height of 1.7 inches what is the length of the container
Answers
Answer:
The length of the container is [tex]14\ in[/tex]
Step-by-step explanation:
we know that
The surface area of a triangular prism (a mailing container) is equal to
[tex]SA=2B+PL[/tex]
where
B is the area of the triangular base
P is the perimeter of the triangular base
L is the length of the container
step 1
Find the area of the base B
[tex]B=\frac{1}{2}(2)(1.7)=1.7\ in^{2}[/tex]
step 2
Find the perimeter of the base P
[tex]P=3(2)=6\ in[/tex]
step 3
Find the length L of the container
we have
[tex]SA=87.4\ in^{2}[/tex]
[tex]B=1.7\ in^{2}[/tex]
[tex]P=6\ in[/tex]
substitute and solve for L
[tex]87.4=2(1.7)+(6)L[/tex]
[tex]L=[87.4-2(1.7)]/(6)[/tex]
[tex]L=14\ in[/tex]
PLEASE HELP! WILL MARK THE BRAINLIEST ANSWER!
x ÷ 5 = 1/10
Answers
X=1/2
Explanation
Multiple both sides times 5
Then the 5 just cancels out on the left side and you’re left with 1/2
The probability of a type ii error is represented by the greek symbol, β.
a. True
b. False
Answers
The answer to your question is a. TRUE
Final answer:
The statement that the probability of a Type II error is represented by the Greek symbol β is true. The β symbol denotes the likelihood of failing to reject a false null hypothesis, while the power of a test (1-β) indicates the probability of accurately detecting a false null hypothesis.
Explanation:
The question is asking whether the statement 'The probability of a type ii error is represented by the greek symbol, β' is true or false. The correct answer is a. True. In statistics, a Type II error, which occurs when a false null hypothesis is not rejected, is indeed represented by the Greek letter β (beta). Therefore, the probability of committing a Type II error is denoted as β (beta). Conversely, a Type I error, symbolized by α (alpha), happens when the null hypothesis is incorrectly rejected. It is important to minimize both α and β as they represent the probabilities of these two types of errors. While α is often set by the researcher (commonly at 0.05), β is affected by factors such as effect size, sample size, and the chosen significance level α.
The power of a statistical test, defined as 1 - β, is the probability of correctly rejecting a false null hypothesis. A high statistical power is desirable as it indicates a lower chance of committing a Type II error. Estimating or calculating β directly can be complex, but understanding its role is crucial for interpreting the results of hypothesis testing.
Box 1 contains 1000 lightbulbs of which 10% are defective. Box 2 contains 2000 lightbulbs of which 5% are defective. (a) Suppose a box is given to you at random and you randomly select a lightbulb from the box. If that lightbulb is defective, what is the probability you chose Box 1? (b) Suppose now that a box is given to you at random and you randomly select two light- bulbs from the box. If both lightbulbs are defective, what is the probability that you chose from Box 1? 4 Solve the Rainbow
Answers
Answer:
a) There is a 66.7% chance that you were given box 1
b) There is a 80% chance that you were given box 1
Step-by-step explanation:
To find this, we need to note that there is a 1/10 chance of getting a defective bulb with box 1 and a 1/20 chance in box 2.
a) To find the answer to this, find the probability of getting a defective bulb for each box. Since there is only one bulb pulled in this example, we just use the base numbers given.
Box 1 = 1/10
Box 2 = 1/2
From this we can see that Box 1 is twice as likely that you get a defective bulb. As a result, the percentage chance would be 2/3 or 66.7%
b) For this answer, we need to square each of the probabilities in order to get the probability of getting a defective one twice.
Box 1 = 1/10^2 = 1/100
Box 2 = 1/20^2 = 1/400
As a result, Box 1 is four times more likely. This means that it would be a 4/5 chance and have a probability of 80%
The solution involves using conditional probability and Bayes' theorem to find the chance of picking a defective lightbulb from a specific box. In part (b), the problem is slightly more complex, assuming the lightbulbs are selected independently.
Explanation:This problem involves conditional probability. We're given two scenarios (a box is selected randomly, a lightbulb picked is defective, and two lightbulbs chosen are wrong). Let's use the following symbols: B1 (Box 1), B2 (Box 2), D (faulty lightbulb).
(a) The probability of a lightbulb being defective, given it came from Box 1 (P(D|B1)), is 0.10. The total likelihood of a lightbulb being inferior (P(D)) can be worked out from the total of defective lightbulbs divided by the total number of lightbulbs. The probability we're after, according to Bayes' theorem, is P(B1|D) = [P(D|B1)*P(B1)] / P(D).
(b) This question is more complex but can be solved similarly. Assuming the lightbulbs are selected independently, the probability of picking two defective lights from a given box is simply the square of picking one defective lightbulb from that box. Thus, we calculate P(2D|B1) = [P(D|B1)]^2 = (0.10)^2 = 0.01 (or 1%). Then, we use Bayes' theorem in part (a) to find P(B1|2D).
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What is the domain of f(x) =3 square x?
Answers
Answer:
Set of all real numbers
Step-by-step explanation:
Given in the question the equation:
f(x) = ∛(x)
The domain of a cube root function is the set of all real numbers.
The interval notation (-∞ , ∞)
Cube Root of negative numbers exists:
Negative numbers can't have real number square roots, but negative numbers can have real number cube roots because when you are multiplying an odd number of negative numbers, the result is negative.
Example
(-2)³ = (-2)(-2)(-2) = -8
If a solid consists of three lateral faces and a base that are congruent isosceles triangles, what type of solid is it?. A. octahedron . B. triangular pyramid . C. right triangular pyramid . D. regular rectangular prism .
Answers
Answer:
B. triangular pyramid.
Step-by-step explanation:
-Octahedron has eight faces that are equilateral triangles, six vertices and twelve edges.
-Triangular pyramid has four triangular faces that have congruent isosceles triangles in which one of them is considered the base.
-Right triangular pyramid has a triangle base, three faces and six edges and the line that is located between the centre of the base and the vertex is perpendicular to the base.
-Regular rectangular prism has twelve sides, 8 vertices and six rectangular faces.
According to this, the answer is triangular pyramid.
The radius of a sphere is 6 units. Which expression represents the volume of the sphere in cubic units.
[tex] \frac{3}{4} \pi(6) {}^{2} \\ \\ \frac{4}{3} \pi(6) {}^{3} \\ \\ \frac{3}{4} \pi(12) {}^{2} \\ \\ \frac{4}{3} \pi(12) {}^{3} [/tex]
Answers
The volume of the sphere is
[tex]V= \frac{4}{3} \pi \: {(6)}^{3} [/tex]
EXPLANATION
The volume of a sphere is calculated using the formula;
[tex]V= \frac{4}{3} \pi \: {r}^{3} [/tex]
The given sphere has radius 6 units.
We substitute r=6 into the given formula to obtain;
[tex]V= \frac{4}{3} \pi \: {(6)}^{3} [/tex]
Based on the options provided, we do not have to simplify further.
The second choice is correct.
How do you know if a system or equations has one solution, no solution, or infinitely many solutions
Answers
Step-by-step explanation:
We transform the system of equations to the form:
[tex]\left\{\begin{array}{ccc}ax+by=c\\dx+ey=f\end{array}\right[/tex]
Where a & b and d & e are relatively prime number.
1.If a ≠ d or b ≠ e then the system of equations has one solution.
Example:
[tex]\left\{\begin{array}{ccc}2x-3y=-4\\3x+3y=9\end{array}\right[/tex]
Add both sides of equations:
[tex]5x=5[/tex] divide both sides by 5
[tex]x=1[/tex]
Substitute it to the second equation:
[tex]3(1)+3y=9[/tex]
[tex]3+3y=9[/tex] subtract 3 from both sides
[tex]3y=6[/tex] divide both sides by 3
[tex]y=2[/tex]
[tex]\boxed{x=1,\ y=2\to(1,\ 2)}[/tex]
2.If a = d and b = e and c = f then the system of equations has infinitely many solutions.
Example:
[tex]\left\{\begin{array}{ccc}2x+3y=5\\2x+3y=5\end{array}\right[/tex]
Change the signs in the second equation. Next add both sides of equations:
[tex]\underline{+\left\{\begin{array}{ccc}2x+3y=5\\-2x-3y=-5\end{array}\right}\\.\qquad0=0\qquad\bold{TRUE}[/tex]
[tex]\boxed{x\in\mathbb{R},\ y=\dfrac{5-2x}{3}}[/tex]
3.If a = d and b = e and c ≠ f then the system of equations has no solution.
Example:
[tex]\left\{\begin{array}{ccc}3x+2y=6\\3x+2y=1\end{array}\right[/tex]
Change the signs in the second equation. Next add both sides of equations:
[tex]\underline{+\left\{\begin{array}{ccc}3x+2y=6\\-3x-2y=-1\end{array}\right}\\.\qquad0=5\qquad\bold{FALSE}[/tex]
A bakery can make 30 donuts every 15 minutes. What is the unit rate at which the bakery makes donuts?
Answers
Answer:
Your answer is 2/1. 2 donuts every minute.
Step-by-step explanation: The rate you are given is 30 donuts every 30 minutes. This equals 30/15.
To make a unit rate, you must make the fraction have a ratio of x/1. You can simply do this by dividing and/or simplifying the equation 30/15.
The unit rate at which the bakery makes donuts is 2 donuts per minute. This is determined by dividing the total number of donuts (30) by the total time in minutes (15).
Explanation:The question is asking for the unit rate at which the bakery makes donuts. A unit rate is a ratio that compares the quantity of one thing to 1 of something else. In this case, we want to find how many donuts the bakery makes in 1 minute. Given that the bakery can make 30 donuts every 15 minutes, we divide 30 (donuts) by 15 (minutes) to find the unit rate. So, 30 donuts ÷ 15 minutes = 2 donuts per minute. Therefore, the unit rate at which the bakery makes donuts is 2 donuts per minute.
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Find the missing measurement. Round your answer to the nearest tenth.
Answers
Answer:
[tex]7.30\ mi[/tex]
Step-by-step explanation:
Let
b-----> the base of the missing measurement of the parallelogram
we know that
The area of the parallelogram is equal to
[tex]A=bh[/tex]
we have
[tex]A=27\ mi^{2}[/tex]
so
[tex]27=bh[/tex] ------> equation A
In this problem
[tex]h=3.7\ mi[/tex]
substitute the value in the equation A and solve for b
[tex]27=b(3.7)[/tex]
[tex]b=27/3.7=7.30\ mi[/tex]
Chris Nazarro had total travel expenses of $872. His transportation cost was $136. The hotel cost was $210 and business materials cost $500. If his lunch cost 30% of his dinner, how much was dinner to the nearest cent?
Answers
Answer:
[tex]\$20[/tex]
Step-by-step explanation:
Let
x-----> the cost of his lunch
y----> the cost of his dinner
we know that
[tex]x+y=872-136-210-500[/tex]
[tex]x+y=26[/tex] -----> equation A
[tex]x=0.3y[/tex] ---> equation B
substitute equation B in equation A
[tex]0.3y+y=26[/tex]
[tex]1.3y=26[/tex]
[tex]y=\$20[/tex] -----> the cost of the dinner
(1CQ) Determine whether the series -8/5+32/25-128/125+... is convergent or divergent.
Answers
Answer:
The series is convergent answer ⇒ (a)
Step-by-step explanation:
* The series is -8/5 + 32/25 + -128/125 + ........
- It is a geometric series with:
- first term a = -8/5 and common ratio r = 32/25 ÷ -8/5 = -4/5
* The difference between the convergent and divergent
in the geometric series is :
- If the geometric series is given by sum = a + a r + a r² + a r³ + ...
* Where a is the first term and r is the common ratio
* If |r| < 1 then the following geometric series converges to a / (1 - r).
- Where a/1 - r is the sum to infinity
* The proof is:
∵ S = a(1 - r^n)/(1 - r) ⇒ when IrI < 1 and n very large number
∴ r^n approach to zero
∴ S = a(1 - 0)/(1 - r) = a/(1 - r)
∴ S∞ = a/1 - r
* If |r| ≥ 1 then the above geometric series diverges
∵ r = -4/5
∴ IrI = 4/5
∴ IrI < 1
∴ The series is convergent
The ratio of successive terms leads to a limit of 4/5, which is less than 1. Hence, the series is convergent.
Convergence or Divergence of a Series
To determine whether the series -8/5+32/25-128/125+... is convergent or divergent, we observe the series' structure and apply the ratio test. For a series ∑a_n, the ratio test considers the limit L = lim (n→∞) |a_(n+1) / a_n|.
Let's compute this for our series:
[tex]a_n = (-1)^{(n+1)} * 8 * (4/5)^{(n-1)}[/tex]
Compute [tex]a_(n+1): a_(n+1) = (-1)^{(n+2)} * 8 * (4/5)^n[/tex]
Calculate |a_(n+1) / a_n| = [tex]|(-1)^{(n+2)} * 8 * (4/5)^n / (-1)^{(n+1)} * 8 * (4/5)^{(n-1)}| = |(4/5)|[/tex]
The limit L = |(4/5)| = 4/5 which is less than 1.
Since L < 1, by the ratio test, the series -8/5+32/25-128/125+... is convergent.
Solve for x in the given interval.
sec θ = -4.0545, for 0≤θ≤2π
Answers
Answer:
The answer is Ф = 1.82 or 4.46 ⇒ answer (c)
Step-by-step explanation:
* The domain of the function is 0 ≤ Ф ≤ 2π
- Lets revise the ASTC rule to solve the problem
# In the 1st quadrant all trigonometry functions are +ve
# In the 2nd quadrant sinФ and cscФ only are +ve
# In the 3nd quadrant tanФ and cotФ only are +ve
# In the 4th quadrant cosФ and secФ only are +ve
* Lets solve the problem
∵ secФ = -4.0545 ⇒ negative value
∴ Angle Ф is in the 2nd or 3rd quadrant
- In the 2nd quadrant Ф = π - α ⇒ (1)
- In the 3rd quadrant Ф = π + α ⇒ (2)
where α is an acute angle
* Now use the calculator to find α with radiant mode
- Let secα = 4.0545
∴ cosα = 1/4.0545
∴ α = cos^-1(1/4.0545) = 1.321585
* Substitute the value of α in (1) and (2)
∴ Ф = π - 1.321585 = 1.82
∴ Ф = π + 1.321585 = 4.46
* The answer is Ф = 1.82 or 4.46
A sheet of postage stamps 3 stamps wide by 4 stamps long covers 9 square inches. Given the same size stamps, how many square inches would be covered by a sheet 6 stamps by 10 stamps?
Answers
Answer: 45 in²
Step-by-step explanation:
3 stamps by 4 stamps = 12 stamps
9 in / 12 stamps = 0.75 in/stamp
6 stamps by 10 stamps = 60 stamps
60 stamps * 0.75 in/stamp = 45 in²
A fish tank is 3/4 full. 2/3 of the water leak out. After the water leaks out, 10 gallons are left in the tank. How many gallons of water does the tank hold when full?
Answers
Capacity of the fish tank is 40 gallons
ABCD is a trapezoid. Find the value of x and y.
Answers
A = x = 110 degrees
B = 117 degrees
C = y = 63 degrees
D = 70 degrees
In a trapezoid, the two angles on the same side of the parallel lines are supplementary, meaning their measures add up to 180 degrees.
So, for angle A and angle D:
A + D = 180
x + 70 = 180
x = 180 - 70
x = 110
For angle B and angle C:
B + C = 180
117 + y = 180
y = 180 - 117
y = 63
Therefore, in the trapezoid ABCD:
A = x = 110 degrees
B = 117 degrees
C = y = 63 degrees
D = 70 degrees
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Let f(x)=x2+17x+72 .
What are the zeros of the function?
Enter your answers in the boxes.
Answers
Hence zeros of function are
,x=-9, x=-8
Value of x that makes function value 0.
How to solve?[tex]x^{2[/tex] +17x+72=0
[tex]x^{2}[/tex]+ 8x+9x+72=0
x(x+8)+9(x+8)=0
(x+9)(x+8)=0
x=-9,-8
Hence ,x=-9, x=-8
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Final answer:
The zeros of the function f(x) = x² + 17x + 72 are -9 and -8, found by factoring the quadratic equation.
Explanation:
To find the zeros of the function f(x) = x² + 17x + 72, we need to solve the equation for x when f(x) = 0. This can be done by factoring the quadratic equation if possible.
The quadratic factors as (x + 9)(x + 8) = 0. So the solutions to the equation x² + 17x + 72 = 0 are:
x = -9
x = -8
Therefore, the zeros of the function are -9 and -8.
60 points Need help Asap
Answers
Answer:
45 units ^2
Step-by-step explanation:
make sure to divide the triangle and sqaure up when finding the area of this polygon..
hope this helps!!
There are 10 rolls of film in a box and 3 are defective. two rolls are to be selected, one after the other. what is the probability of selecting a defective roll followed by another defective roll?
Answers
Answer:
1 / 15 = 0.06666666666....Step-by-step explanation:
Total Number of Rolls = 10
Number of Defective Rolls = 3
Probability = Number of Defective Rolls / Total Number of Rolls
Probability = 3 / 10
Now there is one less defective roll.
Total Number of Rolls = 10 - 1
Number of Defective Rolls = 3 - 1
Total Number of Rolls = 9
Number of Defective Rolls = 2
Probability = Number of Defective Rolls / Total Number of Rolls
Probability = 2 / 9
Multiply the two probabilities together to find the overall probability.
3 / 10 * 2 / 9
3 * 2 = 6
10 * 9 = 90
6 / 90
Simplify
6 / 90 = 3 / 45 = 1 / 15 = 0.06666666666....
To find the probability of selecting two defective rolls of film in a row from a box of 10 rolls where 3 are defective, you multiply the probability of each selection. The result is a 1/15 chance of selecting two defective rolls consecutively.
Explanation:The question deals with the concept of probability without replacement. In this scenario, we calculate the probability by considering each step independently. Initially, there are 10 rolls of film, and 3 are defective. The probability of selecting a defective roll first is 3 out of 10, or 3/10. Once a defective roll has been selected, there are now 9 rolls left with 2 being defective. The probability of selecting another defective roll is then 2 out of 9, or 2/9. To find the overall probability of both events happening in sequence ('and' probability), we multiply the probabilities of each step:
P(First defective and second defective) = P(First defective) * P(Second defective | First defective) = (3/10) * (2/9) = 6/90 = 1/15.
Therefore, the probability of selecting two defective rolls in a row is 1/15.
Emma's total bill for dinner was $20. The cost of her dessert was 30% of the total bill. What was the cost of her dessert?
Answers
Answer:
The answer is $6
Step-by-step explanation:
20 divided by 30% is 6! So it’s therefore 6$
Solve x^2-8x=20 by completing the square. Which is the solution set of the equation?
Answers
Step-by-step explanation:
x^2 - 8x = 20
1. Subtract 20 from both sides
x^2 - 8x - 20 = 20 - 20
2. Simplify
x^2 - 8x - 20 = 0
3. Factor the equation out by grouping
(x - 10)(x + 2) = 0
4. Change signs:
x = 10, x = -2
Hope This Helped!!
~Shane
Answer:{-2,10}
Step-by-step explanation:
trust
Consider the characteristics of the graph. Which statement DOES NOT describe the data set
Answers
Where are the statements ?
Answer: The data is skewed right.