i believe the answer is independant.
if i'm wrong, please tell me so i can fix my mistake =)
Final answer:
The probability of a spinner, with equal chances of landing on any of its six regions, landing on Region 1 first and then on Region 3 in a second spin is 1/36, reflecting independent events.
Explanation:
The question concerns the concept of dependent probability, which involves calculating the likelihood of a sequence of events where the outcome of one event affects the outcome of another.
Since the spinner has an equal chance of landing on each of its six numbered regions, the probability of the first spin landing in region one is 1/6.
However, the second spin is independent of the first, making the probability of landing in region three also 1/6. Since these are independent events, the combined probability of both events happening in sequence is the product of their probabilities, which is 1/6 x 1/6 = 1/36.
REWARD 50 POINTS
After stepping into a room with unusual lighting, Erick's pupil has a radius of 4 millimeters. What is the pupil's area?
Answer:
50.24 mm²
Step-by-step explanation:
Area = pi × r²
3.14 × 4²
50.24 mm²
Subtract: (6x – 3) - (11x – 8)
Answer:
-5x+5
Step-by-step explanation:
(6x-3)-(11x-8)=
6x-11x-3+8=
-5x+5
The subtraction of (6x -3) - (11x - 8) is 5(x - 1)
The subtraction method of algebraic terms takes a process whereby you first open the brackets, followed by rearranging variables with common-like terms.
Given that:
(6x -3) - (11x - 8)
Open brackets
= 6x - 3 - 11x + 8
Collecting like terms by rearrangement
= 6x - 11x - 3 + 8
= -5x + 5
Multiply through by (-)
= 5x - 5
Factorize out (5)
= 5(x - 1)
Therefore, we can conclude that the subtraction of (6x -3) - (11x - 8) is 5(x - 1)
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Assume that 0
a. 16/63
b. -16/63
c. 63/16
d. -63/16
please help
What is the GCF for 84 and 90
Answer:
The GCF for 84 and 90 is 6.
Step-by-step explanation:
The factors of 84 are: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
The factors of 90 are: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
Then the greatest common factor is 6.
Answer:
GCF=6
Step-by-step explanation:
In order to find the GCF of 84 and 90 you must find the prime factors of each term.
what is the value of f(x)=6
Answer:
f(x)=6
Step-by-step explanation:
By Substitution
f(x or coefficient of x)
=6 since X doesn't exist in question above
Final answer:
The value of f(x) is 6, indicating a constant function where the output is the same irrespective of the input. For constant functions, the total differential is zero as there is no change in the function value with varying x.
Explanation:
The question is asking for the value of f(x) when f(x) is equal to 6. This is a type of question that involves understanding how functions work. In this particular case, the question seems to be abstract, suggesting that f(x) = 6 for all x, indicating a constant function. A constant function is one where the output value is the same no matter what the input value is.
Considering this, without additional context or a specific function definition besides f(x) = 6, we presume that the student is being asked to recognize this as a constant function. Therefore, the value of f(x) is always 6, regardless of the value of x.
However, if we are considering a function that changes with respect to x, the total differential would be involved to find infinitesimal changes in f(x) as x changes. For a constant function like this one, the differential would be zero since the function's value does not change as x changes.
You need to put your reindeer, Bloopin, Balthazar, Bloopin, Prancer, and Quentin, in a single-file line to pull your sleigh. However, Prancer and Balthazar are best friends, so you have to put them next to each other, or they won't fly. How many ways can you arrange your reindeer?
Answer:
120 ways
Step-by-step explanation:
Describe fully the single transformation that maps triangle P onto triangle Q.
Answer: 3
P's coordinates are:
Y X
1, 4
1, 2
2, 2
Once we multiply it by 3 it's equal to Q's coordinates.
Y X
3, 12
3, 6
6, 6
Therefore, P was enlarged 3 times more.
The point P was enlarged by a factor of 3 in both the x and y directions to obtain point Q.
From the graph, the coordinates of point P are given as:
P:
(1, 4)
(1, 2)
(2, 2)
From the given coordinates, we can observe that the x-coordinates of Q are three times larger than the x-coordinates of P, and the y-coordinates of Q are also three times larger than the y-coordinates of P.
After multiplying each coordinate of P by 3, we obtain the coordinates of point Q:
Q:
(3, 12)
(3, 6)
(6, 6)
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50 POINTS ANSWER FAST!!!!!!!!!!!
Answer:
d) 1/3
Step-by-step explanation:
fish = 3 + 2 + 1 = 6
bluegill = 2
p = 2/6 = 1/3
Answer:
1/3
Step-by-step explanation:
The total number of fish that were caught
3 trout + 2 bluegill + 1 bass = 6
P (bluegill) = number of bluegill/ total
=2/6
= 1/3
Write the equation in slope-intercept form.
- 4x + 2y = -8
Answer:
y=2x-4
Step-by-step explanation:
Slope intercept form is:
y=mx+b
We need to isolate y to be able to write the equation in slope intercept form
-4x+2y=-8
Add 4x to both sides
-4x+4x +2y= -8+4x
2y= 4x-8
Divide both sides by 2
2y/2=4x/2-8/2
y=2x-4
Now it is in y=mx+b or slope intercept form.
Given f (x )equals 5 x plus 9 and g (x )equals 3 x squared, first find f plus g, f minus g, fg, and StartFraction f Over g EndFraction . Then determine the domain for each function.
Answer with Step-by-step explanation:
We are given that
[tex]f(x)=5x+9[/tex]
[tex]g(x)=3x^2[/tex]
f(x) is linear function
Domain of f(x)=R
g(x) is a quadratic function
Domain of g(x)=R
[tex](f+g)(x)=f(x)+g(x)=5x+9+3x^2[/tex]
Domain of (f+g)=R
(f-g)(x)=f(x)-g(x)=[tex]5x+9-3x^2[/tex]
Domain of (f-g)=R
[tex]fg(x)=f(g(x))=f(3x^2)=5(3x^2)+9=15x^2+9[/tex]
Domain of fg=R
[tex]\frac{f}{g}=\frac{5x+9}{3x^2}[/tex]
The function is not defined where g(x)=0
[tex]3x^2=0[/tex]
[tex]x=0[/tex]
Domain of f/g=R-{0}
Laura retired from her job recently, and she has saved about $414,731.00 over the course of her career. She plans to withdraw $2,224.00 each month to pay for living expenses. After a certain amount of time, the balance in Laura's account is $381,371.00. How many months have passed since Laura retired
Approximately 140 months have passed since Laura retired.
Explanation:To find the number of months that have passed since Laura retired, we need to calculate the total number of months Laura's retirement savings can cover her living expenses, and then subtract that from the balance in her account.
First, we calculate the number of months Laura's retirement savings can cover her living expenses by dividing her total savings by the monthly withdrawal amount: $414,731.00 ÷ $2,224.00 = 186.41 months.
Then, we subtract the number of months from the balance in Laura's account to find the number of months that have passed since Laura retired: 186.41 - X = $381,371.00, where X is the number of months. So, X = 186.41 - $381,371.00 = 140.41.
Therefore, approximately 140 months have passed since Laura retired.
Find the surface area of the figure, Please hurry and give an accurate answer
Given:
The base of the triangle = 5 mm
The other side of the of the triangle = 9 mm
The 3rd side of the triangle = 9 mm
The height of the triangle = 7 mm
The height of the prism = 12 mm
To find the surface area of the the prism.
Formula:
The surface area of a triangular prism is
[tex]SA = bh+(s_{1} +s_{2} +s_{3})H[/tex]
Where,
h be the height of the triangle
H be the side of the prism
b be the base of the triangle
[tex]s_{1} ,s_{2} ,s_{3}[/tex] are the sides of the triangle.
Now,
Putting, b=5, H= 12, h=7, [tex]s_{1} =5,s_{2} =9,s_{3} =9[/tex] we get,
[tex]SA = (5)(7)+(5+9+9)(12)[/tex]
or, [tex]SA = 35+276[/tex]
or, [tex]SA = 311[/tex] sq mm
Hence,
The surface area of the triangular prism is 311 sq mm.
Find the volume of a cylinder that has a radius of 7 and a height of 16. Leave your answer in terms of
π.a0
Step-by-step explanation:
volume =π r*2 h
sub r=7, h =16,
volume = 49(16)π
=784π
A research firm conducted a survey of 49 randomly selected Americans to determine the mean amount spent on coffee during a week. The sample mean was $20 per week. The population distribution is normal with a standard deviation of $5. What is the point estimate of the population mean? Using the 95% level of confidence, determine the confidence interval for μ.
The point estimate of the population mean is $20 per week. The 95% confidence interval, using a z-score of 1.96, ranges from $18.20 to $21.80.
Explanation:The subject of this question deals with the statistical concept of confidence intervals. The point estimate of the population mean is simply the sample mean, which is $20 per week. To calculate the confidence interval for the population mean (μ), we first need to understand that for a 95% level of confidence, the z-score (standard score) is 1.96. This is derived from statistical tables or a z-distribution.
The confidence interval is then calculated with the formula:
(sample mean - (z-score * (standard deviation/√sample size)), sample mean + (z-score * (standard deviation/√sample size))
Substituting the known values in, the 95% confidence interval for μ is ($18.20, $21.80).
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The point estimate of the population mean is the sample mean of $20 per week. Using the given standard deviation and applying the formula for a 95% confidence interval, we determine the confidence interval for the population mean to be ($18.6, $21.4).
The point estimate of the population mean ( μ) is the sample mean which is $20 per week. To calculate the confidence interval, we can use the formula for a 95% confidence interval when the population standard deviation ( σ) is known:
CI = Y ± Z*( σ/ √n)
Given that σ = $5, n = 49, Z for a 95% confidence level is approximately 1.96. Plugging these values into the formula, we get the confidence interval:
CI = 20 ± 1.96*(5/√49)
CI = 20 ± 1.96*(5/7)
CI = 20 ± 1.96*(0.714)
CI = 20 ± 1.4
CI = (18.6, 21.4)
Therefore, the 95% confidence interval for the population mean ( μ) is ($18.6, $21.4).
What is the total number of outcomes when choosing water, milk, juice,
or tea; with or without ice: served in a glass or plastic cup? *
The total possible outcomes of a serving would be 16.
Step-by-step explanation:
Given that,
The total number of beverages = b = 4 ( water, milk, juice,
or tea)
Ice options = i = 2 (with or without ice)
Serving options = s = 2 (glass or plastic cup)
We have to find the total possible outcome x, that can be calculated using
x = b x i x s
Putting the values in the equation, we get
x = 4 x 2 x 2
x = 16
Hence, the total possible outcomes of a serving would be 16.
For the school fair, 3 English teachers, 8 math teachers, 5 science teachers, and 4 social studies teachers volunteered for the dunking booth. One of the teachers will be chosen at random for the dunking booth. Is it likely that a math teacher will be chosen for the dunking booth? Explain your answer.
Answer:
The likelihood that a math teacher is selected is 2 out of 5 possible cases or 40% chance.
Step-by-step explanation:
Please kindly check the attached files for explanation
Final answer:
It is likely that a math teacher will be chosen for the dunking booth since the probability is 8 out of 20 or 40%, which is close to a 50% chance.
Explanation:
To determine if it is likely that a math teacher will be chosen for the dunking booth, we need to look at the probability of selecting a math teacher from the total group of teachers. The total number of teachers is the sum of the English, math, science, and social studies teachers, which is 3 + 8 + 5 + 4 = 20. Since there are 8 math teachers, the probability of selecting a math teacher is 8 out of 20, or 40%.
This probability can be further simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 4, giving us 2 out of 5, or 40%. This indicates that there is a likelihood of 2 in 5 that a math teacher will be chosen, which can be considered likely since it is close to a 50% chance.
Please help me with the Square Root problems, Part 3. Please Show and Check the work.
[tex]9. \sqrt{x+12} +\sqrt{x} = 6\\\\10. 2\sqrt{x} = 1 - \sqrt{4x-1} \\\\11. 2x = \sqrt{4x-1} \\\\12. \sqrt{4x-1} = 2 - 2x[/tex]
Answers and Step-by-step explanations:
9. Subtract root x from both sides: [tex]\sqrt{x+12} =6-\sqrt{x}[/tex]
Square both sides: x + 12 = 36 - 12[tex]\sqrt{x}[/tex] + x
Subtract x and 36 from both sides: -24 = -12[tex]\sqrt{x}[/tex]
Divide both sides by -12: 2 = [tex]\sqrt{x}[/tex]
Square both sides again: x = 4
10. Switch the places of the two root expressions: [tex]\sqrt{4x-1} =1-2\sqrt{x}[/tex]
Square both sides: 4x - 1 = 1 - 4[tex]\sqrt{x}[/tex] + 4x
Subtract 4x and 1 from both sides: -2 = -4[tex]\sqrt{x}[/tex]
Divide by -4 from both sides: 1/2 = [tex]\sqrt{x}[/tex]
Square both sides again: x = 1/4
11. Square both sides: 4x^2 = 4x - 1
Move all the terms to one side: 4x^2 - 4x + 1 = 0
Factorize: (2x - 1)(2x - 1) = 0 ⇒ x = 1/2
12. Square both sides: 4x - 1 = 4 - 8x + 4x^2
Move all the terms to one side: 4x^2 - 12x + 5 = 0
(2x - 5)(2x - 1) = 0 ⇒ x = 5/2 or x = 1/2
Hope this helps!
Answer:
9. x = 4
10. x = ¼
11. x = ½
12. x = ½
Step-by-step explanation:
9. sqrt(x + 12) = 6 - sqrt(x)
Square both sides
x + 12 = 36 - 12sqrt(x) + x
12sqrt(x) = 24
sqrt(x) = 2
x = 4
10. 2sqrt(x) = 1 - sqrt(4x - 1)
Square both sides
4x = 1 - 2sqrt(4x - 1) + 4x - 1
-2sqrt(4x - 1) = 0
sqrt(4x - 1) = 0
4x - 1 = 0
x = ¼
11. 2x = sqrt(4x - 1)
4x² = 4x - 1
4x² - 4x + 1 = 0
4x² - 2x - 2x + 1 = 0
2x(2x - 1) - (2x - 1) = 0
(2x - 1)(2x - 1) = 0
x = ½
12. sqrt(4x - 1) = 2 - 2x
4x - 1 = (2 - 2x)²
4x - 1 = 4 - 8x + 4x²
4x² - 12x + 5 = 0
4x² - 2x - 10x + 5 = 0
2x(2x - 1) - 5(2x + 1) = 0
(2x - 1)(2x - 5) = 0
x = ½ , 5/2
x = 2.5 is rejected because it doesn't satisfy the equation
* when solving equations involving radicals, make sure to verify your answers by plugging in the values in the initial equation
6 11 of students at a school are girls. If there are 4741 students at the school, how many are boys?
Answer:
2155 or 5/11
Step-by-step explanation:
(5/11)4741=5×431=2155 boys
Solve the following inequality for n. Write your answer in simplest form.
4 + 3(10n+6) ≤ - 3 - 10
Answer:
the answer to this is -7/6
Do you know the answers?
Answer:
In the picture above
Step-by-step explanation:
I hope that it's a clear solution and explanation.
Goodluck.
A few years ago, a total of 26812681 thousand people lived in the metropolitan areas of Las Vegas, Nevada, and Sacramento, California. Sacramento had 277277 thousand more residents than Las Vegas. What was the population of each metropolitan area?
Answer:
The population of Lasvegas = 1202000.
Population of Sacramento = 1479000
Step-by-step explanation:
Let the population of each be
Las Vegas Nevada = L
and
Sacramento, California = S
Initially L + S = 2681 000 people
Sacramento had 277 thousand more residents than Las Vegas
This mean that:
L = Population of Las Vegas
L+ 277,000 = population of Sacramento
2,681,000=L+(L+277,000)
2,681,000=2L + 277,000
2,681,000-277,000=2L
2,404,000=2L
2,404,000/2=L
1,202,000=L
The population of Lasvegas = 1202000.
1,202,000+277,000=1,479,000
Population of Sacramento = 1479000
Check base on the question.
2,681,000=1,202,000+1,479,000
2,681,000=2,681,000
Final answer:
To solve the problem, we used algebra to define variables for the population of Las Vegas and Sacramento, set up an equation based on the given information, and solved for the populations of both metropolitan areas.
Explanation:
The question involves solving a basic algebra problem to find the population of Las Vegas and Sacramento metropolitan areas when given the total combined population and the difference in populations between the two areas.
Let x represent the population of Las Vegas. Then, Sacramento's population would be x + 277277 thousand.
Solving the equation x + (x + 277277) = 26812681 will give us the populations of both areas.
Combine like terms to get 2x + 277277 = 26812681.
Subtract 277277 from both sides to get 2x = 26535404.
Divide both sides by 2 to find the population of Las Vegas, x = 13267702 thousand.
To find Sacramento's population, add 277277 to Las Vegas' population to get 13544979 thousand.
Therefore, the population of the Las Vegas metropolitan area was 13267702 thousand, and Sacramento's metropolitan area had a population of 13544979 thousand.
plzzz help 4^2 × 5^2 -30
Answer:
370
Step-by-step explanation:
4^2 = 16
5^2 = 25
25 x 16 = 400
400 - 30 = 370
Your welcome! :D
Which expression represents the approximate area of the circle in square inches?a.9.42 times 3 b.9.42 times 3 squared c.9.42 times 6 d.9.42 times 6 squared
Answer: The answer is B
Step-by-step explanation:
Answer:
A. 9.42
Step-by-step explanation:
scientific notation for 1,424,600,000?
Answer: 1,424,600,000 = 1.4246 × 10^9
Step-by-step explanation: ten to the power of 9 =1000000000
1000000000 x 1.4246 = 1 ,424,600,000
A man drove his car 396 miles on Monday and 476 miles on Tuesday. How many miles did he drive altogether?
Jenny has a gift box shaped like a triangular prism. Each side of the base is 12 cm. The triangular base has a height of 10.4 cm. The prism is 68 cm tall. Find the amount of the gift wrap needed to cover the box
The total surface area will be 1360.2 square centimeters.
To find the amount of gift wrap needed to cover Jenny's gift box shaped like a triangular prism, we first need to calculate the surface area of the prism.
The box has two triangular bases and three rectangular sides.
Therefore,
Calculate the total surface area of the triangular prism: 2(base area) + (base perimeter * prism height)
Substitute the values:
= 2(1/2 * base side * base height) + (base side * 3base side + prism height)
Solve to find the total surface area:
= 2(1/2 * 12 cm * 10.4 cm) + (12 cm * 3 * 12 cm + 68 cm)
= 1360.2
After calculations, the total surface area will be 1360.2 square centimeters.
The amount of gift wrap needed to cover the box is 4,958.4 cm² or approximately 4.96 square meters.
To find the amount of gift wrap needed to cover a triangular prism, we need to calculate the total surface area of the prism.
Given information:
- Each side of the base is 12 cm.
- The triangular base has a height of 10.4 cm.
- The prism is 68 cm tall.
Calculate the area of the triangular base.
Area of a triangle = (1/2) × base × height
Area of the triangular base = (1/2) × 12 cm × 10.4 cm
Area of the triangular base = 62.4 cm²
Calculate the perimeter of the triangular base.
Perimeter of a triangle = sum of all sides
Perimeter of the triangular base = 12 cm + 12 cm + 12 cm = 36 cm
Calculate the area of the rectangular faces.
Area of a rectangle = length × width
Area of each rectangular face = 36 cm × 68 cm = 2,448 cm²
Total area of the rectangular faces = 2 × 2,448 cm² = 4,896 cm²
Calculate the total surface area of the triangular prism.
Total surface area = Area of the triangular base + Area of the rectangular faces
Total surface area = 62.4 cm² + 4,896 cm²
Total surface area = 4,958.4 cm²
Therefore, the amount of gift wrap needed to cover the box is 4,958.4 cm² or approximately 4.96 square meters.
Solve by elimination 4x-8y=8 -5x-y=-21
Use the formula for continuously compounded interest, A = Pert, to find the annual interest rate for an $8000 investment that earns $410.17 in one year.
a. 7%
b. 6%
c. 5%
d. 4%
Answer:
c 5%
Step-by-step explanation:
8000 + 410.7 = 8000 e^(r)
e^r = 1.05127125
r lne = ln1.05127125
r = 0.05006316309 × 100
5%
Answer:
C 5%
Step-by-step explanation:
I hope this is what you need
In 2017, the entire fleet of light‑duty vehicles sold in the United States by each manufacturer must emit an average of no more than 86 milligrams per mile (mg/mi) of nitrogen oxides (NOX) and nonmethane organic gas (NMOG) over the useful life ( 150,000 miles of driving) of the vehicle. NOX + NMOG emissions over the useful life for one car model vary Normally with mean 80 mg/mi and standard deviation 4 mg/mi. (a) What is the probability that a single car of this model emits more than 86 mg/mi of NOX + NMOG? (Enter your answer rounded to four decimal places.)
Answer:
probability that a single car of this model emits more than 86 mg/mi of NOX + NMOG = 0.8668
Step-by-step explanation:
mean, μ = 80 mg/mi
Standard deviation, [tex]\sigma = 4 mg/mi[/tex]
probability that a single car of this model emits more than 86 mg/mi of NOX + NMOG
[tex]P(X > x ) = P(z > \frac{x - \mu}{\sigma})[/tex]
[tex]P(X > x ) =1 - P(z < \frac{x - \mu}{\sigma})[/tex]
[tex]P(X > 86 ) =1 - P(z < \frac{86 - 80}{4})[/tex]
P(X > 86) = 1 - P(z < 1.5)
From the standard normal table, P(z < 1.5) = 0.9332
P(X > 86) = 1 - 0.9332
P(X > 86) = 0.0668
Find the 39th term of the arithmetic sequence
–66, - 68, – 70, ..
Answer:
Preview
Enter a mathematical expression (more..)
a boln. Video
Answer:
-142
Step-by-step explanation:
You seem to have an arithmetic sequence with first term -66 and common difference (-68-(-66)) = -2. The general term of such a sequence is given by ...
an = a1 +d(n -1) . . . . . for first term a1 and common difference d
We want to evaluate this equation for a1 = -66, d = -2, n = 39:
a39 = -66 -2(39 -1) = -66 -76 = -142
The 39th term is -142.