Answer:
x=1, y=7
Step-by-step explanation:
-5x+2y=9
y=7x
Since you know what y is relative to x, you can plug it into the formula to find your answer.
-5x+2(7x)=9
14x-5x=9
x=1
y=7
Hope this helps!
A researcher wishes to estimate, with 99% confidence, the population proportion of adults who think the president of their country can control the price of gasoline. Her estimate must be accurate within 2% of the true proportion. a) No preliminary estimate is available. Find the minimum sample size needed. b) Find the minimum sample size needed, using a prior study that found that 38% of the respondents said they think their president can control the price of gasoline. c) Compare the results from parts (a) and (b). (a) What is the minimum sample size needed assuming that no prior information is available?
To determine the minimum sample size needed to estimate the population proportion, and the minimum sample size needed, assuming no prior information is available, is approximately 6636.
Explanation:To determine the minimum sample size needed to estimate the population proportion, we can use this formula: [tex]n = (Z^2 * p * (1-p)) / E^2.[/tex]
Where:
n is the minimum sample sizeZ is the z-value corresponding to the desired confidence level (in this case, 99% confidence corresponds to Z = 2.58)p is the estimated proportion (0.5 is typically used when there is no preliminary estimate available)E is the margin of error (0.02 in this case)By plugging in the values into the formula, we get:
[tex]n = (2.58^2 * 0.5 * (1-0.5)) / 0.02^2[/tex]
= 6635.44
Similarly, a prior study found that 38% of the respondents think the president can control the price of gasoline, which is 9448.7 The sample size needed when using the prior estimate (9449) is larger than when assuming no prior information (6636). This is because having a prior estimate reduces the uncertainty, which allows for a smaller sample size to achieve the same level of confidence and margin of error.
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Final answer:
The minimum sample size needed for estimating the population proportion depends on the desired confidence level, margin of error, and estimated proportion. The formula used is n = (Z^2 * p * (1-p)) / E^2, and without prior estimate, p is taken as 0.5, whereas using a prior study, the actual estimate from the study is used.
Explanation:
To calculate the minimum sample size needed to estimate the population proportion with certain confidence and precision, we use the following formula for sample size calculation:
n = (Z^2 * p * (1-p)) / E^2
Where:
n is the sample size
Z is the Z-score corresponding to the desired confidence level
p is the estimated proportion of the population (p-hat)
E is the margin of error
(a) Without preliminary estimate: Assuming that no prior information is available, we use p = 0.5 for the most conservative sample size estimate. For a 99% confidence level, the Z-score is approximately 2.576. With a margin of error E of 0.02, the formula becomes:
n = (2.576^2 * 0.5 * (1-0.5)) / 0.02^2
(b) Using a prior study: If a prior study found p = 0.38, the calculation uses this value. The formula with Z = 2.576 and E = 0.02 becomes:
n = (2.576^2 * 0.38 * (1-0.38)) / 0.02^2
(c) Comparing results: Using p = 0.5 in (a) will result in a larger sample size than using p = 0.38 in (b) because the variance (p * (1-p)) is maximized when p = 0.5.
Which statement best describes a physical change?
O Changes can occur to certain chemical properties of the substance, but the overall shape of the substance will remain the
same.
O Changes can occur to certain physical properties of the substance, but the overall shape of the substance will remain the
same.
Changes can occur to physical properties of a substance, but the chemical composition of the substance remains the
same.
Changes can occur to chemical properties of a substance, but the chemical composition of the substance remains the
same.
A teacher bought 15 boxes of markers. Each box contained 8 markers. Estimate how many markers she bought by rounding the number of markers in a box to the nearest ten.
Answer: She bought about 150 markers.
Step-by-step explanation:
Given : A teacher bought 15 boxes of markers.
i.e. Total boxes of markers = 15
Each box contained 8 markers.
That is , the estimated number of markers in each box = 10 [∵ 8≈10 [Round to the nearest tens]]
Now , the total number of markers in all 15 boxes of markers = (15) x (10)
= 150
Hence, she bought about 150 markers.
Una piscina portátil ha tardado en llenarse seis horas utilizando cuatro grifos iguales. ¿Cuántos grifos, iguales a
los anteriores, serían necesarios para llenarla en 3 horas?
Para llenar la piscina en 3 horas, serían necesarios 8 grifos. Se aplica la regla de tres inversa: si aumentamos los grifos, disminuirá el tiempo requerido.
Explanation:Esta pregunta se resuelve aplicando la regla de tres inversa. Si cuatro grifos tardan seis horas en llenar la piscina, para llenarla en la mitad de tiempo (3 horas), serán necesarios el doble de grifos.
La regla de tres inversa señala que si aumentamos la cantidad de grifos, disminuirá el tiempo requerido para llenar la piscina y viceversa. En este caso, como queremos reducir el tiempo a la mitad, necesitaremos el doble de grifos. Entonces, necesitaremos 4 * 2 = 8 grifos para llenar la piscina en 3 horas.
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The measures of two angles have a a sum of 180°. The measures if the angles are in a ratio of 5:1. Determine the measures of both angles by setting up and solving an equation.
Answer:
one angle is 150 degrees and the other is 30 degrees.
Step-by-step explanation:
please kindly check the attached file for explanation.
Answer:
I think, one angle is 150 and the other 30.
Step-by-step explanation:
First, you can make a table of 3 columns: Angle 1, Angle 2 and Total
Then, you will work with the ratio 5:1 and say
Angle 1 Angle 2 Total
5 1 6
Then you do a little algebra process like this:
6a=180
6 x a /6= 180 / 2
a=30
6a=180
6 x a / 6=180/2 This means 6 times a divided by 6= 180 divided by 2. We insolate the variable, and we cross out the two six
a=30 And our answer is 30.
You can choose any variable. In this case I did with the variable a since we are talking about angles.
Returning to the table, the thing we need to do is this:
Angle 1 Angle 2 Total
5 1 6
150 30 180
We need to multiply 5x30 and 1x30
Then we add 150 plus 30 is 180.
So one angle is 150 and the other 30.
Hope this helps.
Compared with the rest of Europe, northern Italy had many
churches.
cities.
farms.
forests.
Step-by-step explanation:
compared with the rest of Europe northern Italy had many cities
When compared with the rest of Europe, one will notice that Northern Italy has a lot of cities.
The Northern part of Italy is much more developed than the South and is so developed that it has one of the highest rates of developments in all of Europe.
This is due to the high density of cities located there such as:
Milan Genoa Turin Venice etcThere are about 23 cities in Northern Italy alone which leads us to conclude that in Europe, Northern Italy has one of the highest number of cities.
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Charlene and Gary want to make perfume. In order to get the right balance of ingredients for their tastes they bought 3 ounces of rose oil at $4.03 per ounce, 2 ounces of ginger essence for $3.42 per ounce, and 4 ounces of black currant essence for $3.92 per ounce. Determine the cost per ounce of the perfume. The cost per ounce of the perfume is $ (Round to the nearest cent.)
Answer:
$3.85 per ounce
Step-by-step explanation:
If we assume that all of the purchased ingredients are used in a mixture, their total cost is ...
3(4.03) +2(3.42) +4(3.92) = 34.61
The total quantity of mix is ...
3 + 2 + 4 = 9 . . . ounces
Then the cost per ounce is ...
$34.61/(9 oz) ≈ $3.85 /oz
The cost per ounce of the perfume that Charlene and Gary made is $3.85. This is calculated by adding the total cost of each ingredient and dividing by the total quantity of all ingredients.
Explanation:To find the cost per ounce of the perfume that Charlene and Gary wish to make, you need to determine the total cost of all the ingredients first, then divide by the total quantity of the perfume produced.
First, calculate the total cost of each ingredient:
Rose oil: 3 ounces * $4.03/ounce = $12.09Ginger essence: 2 ounces * $3.42/ounce = $6.84Black currant essence: 4 ounces * $3.92/ounce = $15.68Total cost is thus $12.09 + $6.84 + $15.68 = $34.61.
The total quantity of the perfume is 3 ounces (rose oil) + 2 ounces (ginger essence) + 4 ounces (black currant essence) = 9 ounces.
Therefore, the cost per ounce of the perfume is $34.61 / 9 ounces = $3.85 per ounce (rounded to the nearest cent).
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If you erased 1/4 of the shaded part below. How much of the original figure will be shaded?
Answer:1/2
Step-by-step explanation: i dont really have a explanation but its right
Step-by-step explanation:
uhhh link an image please?
Two thirds of a number is negative Twenty
The unknown number was found from the equation to be -30.
EquationAn equation is an expression used to show the relationship between two or more variables and numbers.
Let x represent the unknown number. Two thirds of a number is negative Twenty, hence:
(2/3)x = -20
Multiply both sides of the equation by 3/2, hence:
(2/3)x * 3/2 = -20 * 3/2
x = -30
The unknown number was found from the equation to be -30.
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Select the correct answer.
Which sequence of transformations proves that shape I is similar to shape II?
Answer:
c
Step-by-step explanation:
im not explaining im taking the test
Subtract 6 from me. Then multiply by 2. If you subtract 49 and then divide by 4, you get 8. What number am I?
Answer:
46.5
Step-by-step explanation:
Four circles, each with a radius of 2 inches, are removed
from a square. What is the remaining area of the square?
Exact answer = 64 - 16pi
Approximate answer = 13.7345175425633
Units for the area are in square inches.
==============================================================
Work Shown:
The radius of each circle is 2 inches. Double this value to get the diameter to be 4 inches.
Two circles along the top have their diameters combine to 8 inches total, which is the side length of the square.
The area of the entire square, before we subtract off the circles, is 8^2 = 64 square inches.
Let A = 64
The area of one circle is pi*r^2 = pi*2^2 = 4pi square inches. Four circles combine to an area of 4*4pi = 16pi square inches.
Let B = 16pi
Subtract A and B to get the area of the shaded region, which is the leftover area after subtracting off the four circles
A-B = 64-16pi
To get the approximate answer, use a calculator
64-16pi = 13.7345175425633
Which sequence below represents an exponential sequence? A) {2, 6, 10, 14, 18,...} B) {3, 5, 9, 16, 24,...} C) {4, 8, 24, 96,....} D) {256, 64, 16, 4,....}
Answer:d
Step-by-step explanation:
Clearly from observation option D is the exponential sequence
256,64,16,4 is decreasing exponential function
[tex]\Rightarrow \frac{256}{64}=\frac{4^4}{4^3}=4[/tex]
[tex]\Rightarrow \frac{64}{16}=4[/tex]
for other option they simply follow an AP
2,6,10,14,18
common difference d=4
A storage tank will have a circular base of radius r and a height of r. The tank can be either cylindrical or hemispherical (half a sphere). Complete parts (a) through (e) below. a. Write and simplify an expression for the ratio of the volume of the hemispherical tank to its surface area (including the base). For a sphere, Vequals four thirds pi r cubed and SAequals 4 pi r squared . What is the volume of the hemispherical tank (including the base)? Vequals nothing (Simplify your answer. Type an exact answer in terms of pi .)
Answer:
Volume: [tex]\frac{2}{3}\pi r^3[/tex]
Ratio: [tex]\frac{2}{9}r[/tex]
Step-by-step explanation:
First of all, we need to find the volume of the hemispherical tank.
The volume of a sphere is given by:
[tex]V=\frac{4}{3}\pi r^3[/tex]
where
r is the radius of the sphere
V is the volume
Here, we have a hemispherical tank: a hemisphere is exactly a sphere cut in a half, so its volume is half that of the sphere:
[tex]V'=\frac{V}{2}=\frac{\frac{4}{3}\pi r^3}{2}=\frac{2}{3}\pi r^3[/tex]
Now we want to find the ratio between the volume of the hemisphere and its surface area.
The surface area of a sphere is
[tex]A=4 \pi r^2[/tex]
For a hemisphere, the area of the curved part of the surface is therefore half of this value, so [tex]2\pi r^2[/tex]. Moreover, we have to add the surface of the base, which is [tex]\pi r^2[/tex]. So the total surface area of the hemispherical tank is
[tex]A'=2\pi r^2 + \pi r^2 = 3 \pi r^2[/tex]
Therefore, the ratio betwen the volume and the surface area of the hemisphere is
[tex]\frac{V'}{A'}=\frac{\frac{2}{3}\pi r^3}{3\pi r^2}=\frac{2}{9}r[/tex]
Goes through every edge exactly one; starts and stops at different places. a Hamiltonian Path b Hamiltonian Circuit c Euler Path d Euler Circuit
Answer:
D. Euler Circuit.
Step-by-step explanation:
An Euler Circuit goes through every edge exactly once; starts and stops at the same vertex.
According to the Euler's Theorem, A graph has an Euler path if there are two 2-degree vertices without odd degrees and all other vertices have even degrees.
Mathematically, it is given as;
V+F=2-E
where;
F is the number of faces
V the number of vertices
E the number of edges.
Final answer:
An Euler Path traverses every edge of a graph exactly once and can start and end at different vertices, fitting the student's question.
Explanation:
The student's question hints at two different types of paths in graph theory: the Euler Path and the Hamiltonian Path. An Euler Path goes through every edge exactly once and can start and stop at different vertices. This path doesn't have to cover all vertices, but it must include every edge.
Here's a breakdown of the terms:
Hamiltonian Path: A path that visits every vertex exactly once, but it may start and end at different vertices.
Hamiltonian Circuit: A path that visits every vertex exactly once and starts and ends at the same vertex (creating a cycle).
Euler Path: A path that uses every edge exactly once, but it may start and end at different vertices.
Euler Circuit: A path that uses every edge exactly once and starts and ends at the same vertex (creating a cycle).
On the other hand, a Hamiltonian Path also goes through every vertex exactly once, but it is not concerned with edges.
In this case, since the definition provided in the question states the requirement is about edges and not vertices, the correct answer is c. Euler Path.
10, 15, 22.5, 33.75.... what’s next?
.
Answer:
50.625
Step-by-step explanation:
1) 10/2=5
10+5= 15
2) 15/2 = 7.5
15+7.5 = 22.5
3) 22.5/2 = 11.25
22.5+11.25= 33.75
4) Answer: 33.75/2 = 16.875
33.75+16.875 = 50.625
Solve for m.
12.6 + 4m = 9.6 + 8m
m
=
Answer:
m = 3/4
Step-by-step explanation:
12.6 + 4m = 9.6 + 8m
4m - 8m = 9.6 - 12.6
- 4m = - 3
- m = - 3/4
m = 3/4
Write 144 as a product of primes.
Use index notation where appropriate
Answer:
144=2x2x2x2x3x3
Step-by-step explanation:
Answer:
[tex]2^4\cdot3^2[/tex]
Step-by-step explanation:
The first step is to break this down. 144=12^2 or 12*12. Now you can break down 12. 12=4*3=2*2*3. This means that 144=2*2*3*2*2*3=[tex]2^4\cdot3^2[/tex]. Hope this helps!
correct answer gets brainliest
Answer:
C
Step-by-step explanation:
Answer:
C. 24 degrees
Step-by-step explanation:
The 3 angles inside ∠ABE: ∠ABC,∠DBC and∠EBD must add to 126 degrees
∠ABC+∠DBC+∠EBD =126
We already know that ∠DBC is 30 degrees, and ∠EBD is 72 degrees, so we can substitute them in
∠ABC+30+72=126
Combine like terms
∠ABC+102=126
Subtract 102 from both sides
∠ABC=24
So, ∠ABC equals 24 degrees, and C is the correct choice
The perimeter of a rectangle is 35 cm. The rectangle s area in sq. cm) as a function of its length (in cm) is
graphed
What is the approximate average rate at which the area decreases, as the rectangle's length goes from 13 cm
to 16 cm?
Answer: 11 1/3
Dhdgdhdhd
To find the rate at which the area of the rectangle decreases as its length changes, use the formula for the area of a rectangle and evaluate the area at the two lengths. Then, calculate the average rate of decrease by taking the change in an area divided by the change in length.
Explanation:The problem involves understanding the properties of rectangles and how the changes in one dimension (length in this case) can affect another (area). Let's consider a rectangle with a perimeter of 35 cm. If 'L' is the length and 'W' is the width, the perimeter = 2*(L+W) which equals 35 cm.
Next, we figure out that W= 17.5 - L as we isolate W in the equation. The area of the rectangle is then given by A = L * W = L * (17.5 - L). If we plug in L = 13 cm and L = 16 cm, we get two area values. The decrease in area ΔA = A2 - A1.
Finally, the average rate of change, or the rate at which the area decreases, as the length goes from 13 cm to 16 cm is calculated by ΔA / ΔL.
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Javier solved this system of equations. y = 3x – 4, y = 3x – 4 6x – 8 = 6x – 8 –8 = –8 What can you conclude about the number of solutions to this system of equations? There is one solution, (–8, –8). There is one solution, (–8, 0). There is no solution. There are infinitely many solutions.
Answer:
there are infinite many solutions.
Step-by-step explanation:
i have taken this before
Answer:
D
Step-by-step explanation:
Joan has 2 dozen golf balls how many golf balls does she have
Anwer:12
Step-by-step explanation:
Answer:
24
Step-by-step explanation:
1 dozen= 12
12x2=24
A population is a group of a single species living in a certain area at a certain time. A community is all combination of all of the populations in an area
Answer:
The above definition of Population & Community of species is correct.
Step-by-step explanation:
Population is the group of organisms living together in same geographical area, at a point of time. Community is the group of all organisms living together in same geographical area, at a point of time.
Population is the smaller group of interbreeding individuals of same species, Community is a bigger group of different species sharing same geographical area.
Eg : Lions in a particular forest can be defined as 'population' ; & all the organisms in a particular forest can be defined as 'community'.
The radius of a cylindrical construction pipes is 2ft if the pipe is 24 ft long what is its volume
V= (3.14)x(2²)x(24)= 301.592 ft³
Answer:
96π ft^3 or 301.59 ft^3 to the nearest hundredth.
Step-by-step explanation:
Volume = π r^2 L (r = radius L = length).
= π * 2^2 * 24
= 96π ft^3.
The perimeter of a triangle is 24inches. The longest side is 4 more than the middle side , and the smallest side is half the length of middle side. What are the lengths?
Answer:
Step-by-step explanation:
the length of the smallest side is 4 inches.
the length of the middle side is 8 inches.
the length of the longest side is 12 inches.
Step-by-step explanation:
Let x represent the length of the middle side of the triangle.
The longest side is 4 more than the middle side. It means that the length of the middle side is x + 4.
The smallest side is half the length of middle side. It means that the length of the smallest side is
x/2
The formula for determining the perimeter of a triangle is
Perimeter = a + b + c
Where a, b and c are the lengths of each side of the triangle. The perimeter of the triangle is 24 inches. It means that
x + 4 + x + x/2 = 24
Multiplying both sides of the equation by 2, it becomes
2x + 8 + 2x + x = 48
5x = 48 - 8
5x = 40
x = 40/5
x = 8 inches
The length of the longest side is
8 + 4 = 12 inches
The length of the smallest side is
8/2 = 4 inches
The radioactive element carbon-14 has a half-life of 5750 years. The percentage of carbon-14 present in the remains of plants and animals can be used to determine age. How old is a skeleton that has lost 50% of its carbon-14?
Answer:
A skeleton that has lost 50% of its carbon-14 is 5750 years old.
Step-by-step explanation:
The halflife on an element is the amount it takes to decrease to half it's original amount, that is, when the amount is 50% of the initial amount.
How old is a skeleton that has lost 50% of its carbon-14?
If the skeleton lost 50% of its carbon-14 it has the other 50%, that is, it is in it's half-life.
The radioactive element carbon-14 has a half-life of 5750 years.
This means that a skeleton that has lost 50% of its carbon-14 is 5750 years old.
A skeleton that has lost 50% of its carbon-14 is 5,730 years old, which corresponds to one half-life of carbon-14 (C-14).
Explanation:The age of a skeleton that has lost 50% of its carbon-14 can be determined using carbon-14 dating. Since the half-life of carbon-14 (¹⁴C) is 5,730 years, if a skeleton has only 50% of the original carbon-14 remaining, it would mean that one half-life has passed. Therefore, the skeleton would be 5,730 years old. Carbon-14 dating measures the radioactive decay of ¹⁴C in formerly living matter to estimate its age. This method is effective for dating biological tissues up to about 50,000 to 60,000 years old.
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a statistics professor finds that when she schedules an office hour for student help, an average of 2.4 students arrive. find the probability that in a randomly selected office hour, the number of student arrivals is 2
Answer:
P=0.2613
Step-by-step explanation:
-Notice that this is a poison probability distribution problem.
-The Poisson probability function is expressed as:
[tex]P(X=x)=\frac{\lambda^x e^{-\lambda}}{x!}[/tex]
where:
x=0,1,2,3[tex]e[/tex] Euler's constant[tex]\lambda[/tex] =mean number of occurrences.Given that x= 2 and [tex]\lambda=2.4[/tex], the probability is calculated as:
[tex]P(X=2)=\frac{\lambda^xe^{-\lambda}}{x!}\\\\=\frac{2.4^2e^{-2.4}}{2!}\\\\\\=0.2613[/tex]
Hence, the probability that in a randomly selected office hour, the number of student arrivals is 2 is 0.2613
Final answer:
To find the probability that in a randomly selected office hour, the number of student arrivals is 2, we can use the Poisson distribution. The average number of student arrivals is 2.4.
Explanation:
To find the probability that in a randomly selected office hour, the number of student arrivals is 2, we can use the Poisson distribution. The average number of student arrivals is 2.4, so the parameter λ for the Poisson distribution is 2.4.
The probability of getting exactly 2 student arrivals can be calculated using the formula:
P(X=k) = (e^-λ * λ^k) / k!, where X is the random variable representing the number of student arrivals, k is the desired value (2 in this case), and λ is the average number of student arrivals per office hour.
Calculate e^-λ: e is the base of the natural logarithm and λ is 2.4. e^-2.4 ≈ 0.0908.
Calculate λ^k: 2.4^2 ≈ 5.76.
Calculate k!: 2! = 2.
Plug in the calculated values into the formula: P(X=2) = (0.0908 * 5.76) / 2 ≈ 0.2613.
So, the probability that in a randomly selected office hour, the number of student arrivals is 2 is approximately 0.2613 or 26.13%.
Suppose that 40% of a population has brown hair. You want to estimate the probability that it will take at least a sample of four to find one person with brown hair. You set up a random digit simulation where 0, 1, 2, 3 represents a person with brown hair and 4, 5, 6, 7, 8, 9 represents a person that does not have brown hair. Which would constitute a trial for this simulation?
Answer:
A
Step-by-step explanation:
A trail would consist of three random digits.
The problem asks for the probability that it will take at least a sample of four to find one person with brown hair. This implies that the first three people do not have brown hair. Therefore, a trial would consist of three random digits. A success is none of the three digits are 0, 1, 2, or 3. For example, 675 would be a success and a failure would be 792.
Answer:
A
Step-by-step explanation:
USA testprep said...
A trail would consist of three random digits.
The problem asks for the probability that it will take at least a sample of four to find one person with brown hair. This implies that the first three people do not have brown hair. Therefore, a trial would consist of three random digits. A success is none of the three digits are 0, 1, 2, or 3. For example, 675 would be a success and a failure would be 792.
The quality control team of a company checked 800 digital cameras for defects. The team found that 20 cameras had lens defects, 25 cameras had charging defects, and 6 cameras had both defects. What is the probability that a camera has a lens defect given that it has a charging defect?
Answer:
6/25
Step-by-step explanation:
Given two events A and B, the conditional probability of event A is the probability that event A occurs given that event B has occurred. It is calculated as
[tex]p(A|B)=\frac{p(A\cap B)}{p(B)}[/tex]
where
[tex]p(A\cap B)[/tex] is the probability that both A and B occur at the same time
[tex]p(B)[/tex] is the probability that B occurs
In this problem, we call:
A = the camera has a lens defect
B = the camera has a charging defect
Here we have:
a = 20 is the number of cameras with lens defects
b = 25 is the number of cameras with charging defects
c = 6 is the number of cameras having both defects
n = 800 is the total number of cameras
So we have:
[tex]p(A\cap B)=\frac{c}{n}=\frac{6}{800}[/tex] is the probability that the camera has both lens and charging defect
[tex]p(B)=\frac{b}{n}=\frac{25}{800}[/tex] is the probability that the camera has a charging defect
So the conditional probability is
[tex]p(A|B)=\frac{6/100}{25/100}=\frac{6}{25}[/tex]
If the parabola shifts 3 units to the left, which equation represents the translated parabola?
A) f(x)=x^2-8x-14
B) f(x)=x^2+9x+14
C) f(x)=x^2+4x-21
D) f(x)=x^2+5x-14