The probability of each of the events of {at most three lines are in use}, {fewer than three lines are in use}, {at least three lines are in use, {between two and five lines, inclusive, are in use}, {between two and four lines, inclusive, are not in use} and {at least four lines are not in use} are 0.70, 0.45, 0.55, 0.80, 0.35 and 0.40 respectively.
The problem involves finding probabilities of different events for a mail-order company with six telephone lines. The probability mass function (pmf) is given, and we use it to calculate the probabilities of different events such as "at most three lines are in use" or "between two and five lines, inclusive, are in use".
To calculate these probabilities, we use basic probability formulas such as the addition rule, subtraction rule, and the complement rule.
P(X ≤ 3) = 0.10 + 0.15 + 0.20 + 0.25 = 0.70
P(X < 3) = 0.10 + 0.15 + 0.20 = 0.45
P(X ≥ 3) = 1 - P(X < 3) = 1 - (0.10 + 0.15 + 0.20) = 0.55
P(2 ≤ X ≤ 5) = P(X ≤ 5) - P(X < 2) = (0.10 + 0.15 + 0.20 + 0.25 + 0.20) - 0.10 = 0.80
P(2 ≤ X ≤ 4) = 0.20 + 0.25 + 0.20 = 0.65, so P(2 ≤ X ≤ 4)ᶜ = 1 - 0.65 = 0.35
P(X ≥ 4) = 0.20 + 0.05 + 0.05 = 0.30, so P(X ≤ 3) = 1 - P(X ≥ 4) = 0.70 - 0.30 = 0.40
These formulas are applied based on the given events to determine the probabilities.
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which of the following code segments assigns bonus correctly for all possible integer values of score ?
The code segment that assigns bonus correctly for all possible integer values of score is D, which uses nested if statements to implement the game's rules for assigning a value to bonus based on the value of score.
The code segment that assigns bonus correctly for all possible integer values of score is D:
IF(score < 50)
{
bonus ← Ø
}
ELSE
{
IF (score > 100)
{
bonus ← score (10)
}
ELSE
{
bonus ← score
}
}
This code segment correctly implements the rules for assigning a value to bonus based on the value of score. It first checks if score is less than 50, and if so, it assigns 0 to bonus. If score is greater than or equal to 50, it checks if score is greater than 100, and if so, it assigns 10 times score to bonus. Otherwise, it assigns score to bonus. This covers all possible integer values of score and ensures that bonus is assigned correctly according to the game's rules.
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Complete question is in the image attached below
Use a triple integral to find the volume of the solid bounded below by the cone z = vx2 + y2 and bounded above by the sphere x2 + y2 + z2 = 18. (0.0.V18) x?+y+z=18 cubic units The volume of the solid is (Type an exact answer.)
The volume of the solid is given by the equation V = 36π (√2 - 1) using the triple integral.
A three-dimensional object's volume in three-dimensional space may be determined using the triple integral. The three-variable function is represented by the triple integral. If in space is a closed region, the region's entire volume may be expressed as V = Ddv, which is equivalent to V = D d x d y d z.
Cone: z = [tex]\sqrt{x^2+y^2}[/tex]
sphere: x² + y² + z² = 18
Here, we will use cylindrical coordinates to evaluate volume:
x = rcosθ , y = rsinθ, z = z
so, z = [tex]\sqrt{r^2cos^2\theta+r^2sin^2\theta} =r[/tex]
z = [tex]\sqrt{18-(x^2+y^2)} =\sqrt{18-r^2}[/tex]
r = [tex]\sqrt{18-r^2}[/tex]
r = 3
Finding limits,
[tex]Volume = \int\limits^2_0 \int\limits^3_0\int\limits^a_r {rdzdrd\theta} \, \\\\= \int\limits^2_0 \int\limits^3_0rz \ drd\theta\\\\= \int\limits^2_0 \int\limits^3_0 r(\sqrt{18-r^2}-r ) \ drd\theta\\\\[/tex]
Now, we have
[tex]\int\limits^3_0 {r\sqrt{18-r^2} } \, dr = -(9-18\sqrt{2} ) = 18\sqrt{2} -9[/tex]
Now the integral becomes,
Volume = 2π [(18√2-9) - 9]
= 2π x 18√2 - 18
V = 36π (√2 - 1)
Therefore, the volume of the solid is given by V = 36π (√2 - 1).
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FOR 15 POINTS!! Select one of the Theorems from section 2.2 and do the following:
1. Explain why you chose to explore that theorem.
2. Write down the formal definition of the theorem.
3. Explain the theorem in your own words.
4. Find or create an example with new numbers and explain how/why it works.
Here are the 4 Theorems you can choose from:
1. Angle Sum Theorem
2. Third Angle Theorem
3 Exterior Angle Theorem
4. Corollary of Exterior Angle Theorem
In response to the stated question, we may state that We know that these two angles are complimentary since their total is 90 degrees.
what are angles?An angle is a form in Euclidean geometry that is composed of a pair of rays, known as such angle's sides, that meet at a center point known as the angle's vertex. Two rays may merge to generate an angle in the plane in which they are located. An angle is formed when two planes collide. They are known as dihedral angles. In plane geometry, an angle is a potential arrangement of two rays or lines whose share a termination. The English term "angle" is derived from the Latin word "angulus," which means "horn." The apex is the point in which the two rays, often known as the angle's sides, converge.
Angle Sum Theorem formal definition:
The total of the three interior angles of a triangle is always equal to 180 degrees.
The Angle Sum Theorem states:
According to the Angle Sum Theorem, the sum of a triangle's internal angles is always equal to 180 degrees. In other terms, using new numbers:
Consider a triangle having three angles of 70 degrees, 60 degrees, and 50 degrees. The Angle Sum Theorem states that the sum of these angles should be 180 degrees.
[tex]70 + 60 + 50 = 180\\90 + x + y = 180\sx + y = 90[/tex]
We know that these two angles are complimentary since their total is 90 degrees.
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two random vectors follow the same distribution does this mean every marginalized variables have to follow the same distribution
Yes. they can in fact, more than two independent variables can have the same distribution. Two random vectors follow the same distribution, which means that each marginalized variable must follow the same distribution.
In probability theory and statistics, the marginal distribution of a subset of a set of random variables is the probability distribution of the variables contained in that subset. It gives the probability of different values of variables in the subset without reference to the values of other variables. This contrasts with conditional distributions, which give probabilities based on the values of other variables.
The marginal variables are the variables of the subset of variables which are retained. These concepts are "marginal" because they can be found by adding the values of the rows or columns of a table and writing the sum in the blank space of the table.
The distribution of the marginal variable (marginal distribution) is obtained by marginalizing the distribution of the suppressed variable (that is, focusing on the sum in the margin), and the suppressed variable is called marginalized.
Complete Question:
If two random variables have the same PDF/PMF, then does this mean they have the same distribution?
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Brendan buys items at a cost of $23 each and sells them at $56 each.
His profit per item is
What is the equation of the line that is parallel to the
given line and passes through the point (-3, 2)?
V(o, 3)
O 3x - 4y = -17
(-3,2
O 3x - 4y = -20
4x + 3y = -2
4x + 3y = -6
The equation of the line that is parallel to the given line and passes through the point (-3, 2) is 3x - 4y = -17.
What is the formula for a parallel line equation?If the line's equation is axe + by + c = 0 and the coordinates are (x1, y1).
To find the equation of a line parallel to a given line, we must first understand that parallel lines have the same slope. As a result, we must first determine the slope of the given line.
3x - 4y = -17 is the given line. To determine its slope, solve for y and write the equation in slope-intercept form:
-3x - 4y = -3x - 17 y = (3/4)x + (17/4)
This line has a 3/4 slope.
Now we want to find the equation of a parallel line that passes through the point (-3, 2). Because the new line is parallel to the given line, it has a slope of 3/4.
We can write the equation of the new line using the point-slope form of the equation of a line as:
y - y1 = m(x - x1)
where m represents the slope and (x1, y1) represents the given point (-3, 2).
When m = 3/4, x1 = -3, and y1 = 2, we get:
y - 2 = (3/4)(x - (-3))
y - 2 = (3/4)(x + 3)
Divide both sides by 4 to get rid of the fraction.
4y - 8 = 3x + 9
3x - 4y = -17
As a result, the equation of the parallel line that passes through the point (-3, 2) is 3x - 4y = -17.
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Which of the following random variables can be approximated to discrete distribution and continuous distribution? a. b. C. d. The wages of academician and non-academician workers in UPSI. The time taken to submit online quiz answer's document. The prices of SAMSUM mobile phones displayed at a phone shop The number of pumps at Shell petrol stations in Perak. [2 marks] 10% chance of contamination by a particular
10% chance of contamination by a particular: It's not clear what random variable is being referred to here, but if it's the probability of contamination.
What is Distribution?In general terms, a distribution refers to the way something is divided or spread out. In the context of statistics and probability theory, a distribution is a mathematical function that describes the likelihood of different possible outcomes or values that a variable can take.
There are various types of distributions, but some of the most commonly used ones include:
Normal distribution: also known as the Gaussian distribution, it is a continuous probability distribution that is symmetrical around the mean, with most of the data falling within one standard deviation of the mean.
Binomial distribution: this is a discrete probability distribution that describes the likelihood of a certain number of successes in a fixed number of trials.
Poisson distribution: another discrete probability distribution that describes the likelihood of a certain number of events occurring in a fixed interval of time or space.
Exponential distribution: a continuous probability distribution that describes the time between events occurring at a constant rate.
Distributions are essential in statistical analysis as they can help to understand and analyze data, make predictions, and draw conclusions about a population based on a sample of data.
Given by the question.
a. The wages of academician and non-academician workers in UPSI: This random variable can be approximated to a continuous distribution as wages can take on any numerical value within a range. However, it's worth noting that in practice, there may be discrete intervals or categories of wages, in which case a discrete distribution may be more appropriate.
b. The time taken to submit online quiz answer's document: This random variable can also be approximated to a continuous distribution as it can take on any numerical value within a range.
c. The prices of SAMSUNG mobile phones displayed at a phone shop: This random variable can be approximated to a continuous distribution as prices can take on any numerical value within a range.
d. The number of pumps at Shell petrol stations in Perak: This random variable can be approximated to a discrete distribution since the number of pumps can only take on integer values.
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a triangle has integer side lengths of 3,6, and x. for how many values of x will the triangle be acute?
The values of x representing side length for which triangle is acute is given by 4, 5, and 6 .
For a triangle to be acute,
Sum of the squares of the two shorter sides must be greater than the square of the longest side.
Mathematically,
a^2 + b^2 > c^2
where a, b, and c are the side lengths of the triangle,
With c being the longest side.
The sides are given as 3, 6, and x.
Without loss of generality,
Assume that 3 and 6 are the shorter sides,
3^2 + 6^2 > x^2
Simplifying this inequality, we get,
45 > x^2
Taking the square root of both sides, we get,
6.71 > x
Since x must be an integer, the possible values of x are 4, 5, and 6.
Triangle inequality is satisfied,
Sum of any two sides of a triangle must be greater than the third side.
3 + 6 > x
3 + x > 6
6 + x > 3
Inequalities are all satisfied for x = 4, 5, and 6.
Therefore, there are 3 possible values of x is 4, 5, and 6 for which the triangle is acute.
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The bells bought a $386,000 house. They made a down payment of $49,000 and took out a mortgage for the rest. Over the course of 15 years they made monthly payments of $2843.81 on their mortgage until it was paid off.
What was the total amount they ended up paying for the house (including the down payment and monthly payments)?
How much interest did they pay on the mortgage?
Answer:
Step-by-step explanation:
The total amount paid for the house is the sum of the down payment and the total amount paid for the mortgage.
The total amount paid for the mortgage can be calculated as follows:
Number of monthly payments = 15 years x 12 months/year = 180 months
Total amount paid for the mortgage = 180 x $2843.81 = $511,086.80
Therefore, the total amount paid for the house is:
$386,000 + $511,086.80 = $897,086.80
To calculate the amount of interest paid, we need to subtract the principal amount (the original amount borrowed) from the total amount paid for the mortgage.
Principal amount = Total amount borrowed - Down payment = $386,000 - $49,000 = $337,000
Total interest paid = Total amount paid for the mortgage - Principal amount = $511,086.80 - $337,000 = $174,086.80
Therefore, they paid a total of $897,086.80 for the house, and they paid $174,086.80 in interest on their mortgage.
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Given parallelogram RUST and m∠RUT = 43º, what other angle has the same measurement?
A) ∠RTS
B) ∠RUS
C) ∠STU
Answer:
(c) ∠STU
Step-by-step explanation:
Transversal UT between parallel sides RU and ST creates alternate interior angles RUT and STU. These are congruent.
∠STU has the same measure as ∠RUT
_____
The figure shown is a trapezoid, not a parallelogram.
A bookcase contains 2 statistics books and 5 biology books. If 2 books are chosen at random, the chance that both are statistics books isA 1 / 21B 10 / 21C 11D 21 / 11
If 2 books are chosen at random, then the probability that both are statistics books is (a) 1/21.
The number of statistics book in bookcase is = 2;
The number of biology books in bookcase is = 5;
So, the total number of books is = 7;
The Probability of choosing a statistics book on the first draw is 2/7, since there are 2 statistics books out of a total of 7 books.
After the first book is chosen, there will be 6 books left, including 1 statistics book out of a total of 6 books.
So, the probability of choosing another statistics book on the second draw is 1/6.
In order to find the probability of both events happening together (i.e. choosing 2 statistics books in a row), we multiply the probabilities of each event:
So, P(choosing 2 statistics books) = P(1st book is statistics) × P(2nd book is statistics given that the 1st book was statistics);
⇒ (2/7) × (1/6)
⇒ 1/21
Therefore, the required probability is (a) 1/21.
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The given question is incomplete, the complete question is
A bookcase contains 2 statistics books and 5 biology books. If 2 books are chosen at random, the chance that both are statistics books is
(a) 1/21
(b) 10/21
(c) 11
(d) 21/11
A firm is a monopoly for the good it produces. Its average cost function is AC = 9+(3/10)q+30/q, where q is the quantity produced. The demand equation for its good is given by q = 40 - (4/3)p where p is the price.
(a) Find expressions, in terms of q, for the total revenue.
(b) What is the equation for the Total cost?
(c) Find the expression for profit. (d) Find the total output and revenue at the break even point.
(e) Find the profit when 20 units are produced.
(f) Find the profit when 7 units are produced.
(g) Find the output required to obtain a profit of RM100.
The answer of the given question is (a) TR = p(40 - (4/3)p), or TR = 40p - (4/3)p² , (b) TC = 9q + (3/10)q² + 30 , (c) π = 40p - (4/3)p² - 9q - (3/10)q² - 30 , (d) TR ≈ 342.67 , (e) the profit when 20 units are produced is approximately RM188.27 , (f) the profit when 7 units are produced is approximately -RM24.44, indicating a loss , (g) the output required to obtain a profit of RM100 is approximately 8.78 units.
What is Equation?An equation is mathematical statement that asserts yhe equality of two expressions. It typically consists of variables, constants, and mathematical operations like addition, subtraction, multiplication, and division, among others. Equations are often used to solve problems, to model real-world phenomena, and to describe mathematical relationships.
(a) The total revenue is given by TR = p x q. Substituting the demand equation q = 40 - (4/3)p, we get TR = p(40 - (4/3)p), or TR = 40p - (4/3)p².
(b) The total cost is given by TC = q x AC. Substituting the given average cost function, we get TC = 9q + (3/10)q² + 30.
(c) The profit is given by π = TR - TC. Substituting the expressions we found in parts (a) and (b), we get π = 40p - (4/3)p² - 9q - (3/10)q² - 30.
(d) At the break even point, the firm earns zero profit, so we set π = 0 and solve for q. Substituting the expression we found in part (a) for p, we get:
0 = 40p - (4/3)p² - 9q - (3/10)q² - 30
0 = 40(40/3 - (3/4)q) - (4/3)(40/3 - (3/4)q)² - 9q - (3/10)q² - 30
0 = 533.33 - 51.25q - 0.22q^2
Solving for q using the quadratic formula, we get:
q = (51.25 ± sqrt(51.25² - 4(-0.22)(533.33))) / 2(-0.22)
q ≈ 22.75 or q ≈ 206.58
We reject the solution q ≈ 206.58 because it is outside the relevant range of output, which is between 0 and 40. Therefore, the total output at the break even point is approximately 22.75 units. To find the total revenue at the break even point, we substitute q = 22.75 into the demand equation from part (a) and get:
p = (40/3) - (3/4)q
p ≈ 15.08
TR = p x q
TR ≈ 342.67
(e) To find the profit when 20 units are produced, we substitute q = 20 into the expression for profit we found in part (c) and get:
π = 40p - (4/3)p² - 9q - (3/10)q² - 30
π ≈ 188.27
Therefore, the profit when 20 units are produced is approximately RM188.27.
(f) To find the profit when 7 units are produced, we substitute q = 7 into the expression for profit we found in part (c) and get:
π = 40p - (4/3)p² - 9q - (3/10)q² - 30
π ≈ -24.44
Therefore, the profit when 7 units are produced is approximately -RM24.44, indicating a loss.
(g) To find the output required to obtain a profit of RM100, we set the profit equation equal to 100 and solve for q:
Profit = TR - TC
100 = pq - ACq
100 = (40-(4/3)p)*q - (9+(3/10)q+30/q)*q
100 = (40-(4/3)p - 9q - 3q²/10)
Multiplying by 10 and rearranging terms, we get a quadratic equation in q:
3q² + 91q - 310 = 0
Solving for q using the quadratic formula, we get:
q = (-91 ± sqrt(91² - 43(-310)))/(2*3)
q ≈ 8.78 or q ≈ -29.44
Since the quantity produced cannot be negative, the output required to obtain a profit of RM100 is approximately 8.78 units.
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describe the reflection of figure efgh
Step-by-step explanation:
Please provide the figure then it will be easy to answer
Find the value of the derivative (if it exists) at the given extremum. (If an answer does not exist, enter DNE.) f(x) = (x + 4)^2/3 f'(-4) = Find the critical numbers of the function. f(x) = x^6 - 6x^5
The critical numbers of f(x) = x^6 - 6x^5 are x = 0 and x = 5 at the given extremum.
To find the derivative of f(x), we use the chain rule and power rule:
f(x) = (x + 4)^(2/3)
f'(x) = (2/3)(x + 4)^(-1/3)(1)
f'(-4) = (2/3)(-4 + 4)^(-1/3)(1) = DNE (the derivative does not exist at x = -4)
To find the critical numbers of f(x), we first find the derivative:
f(x) = x^6 - 6x^5
f'(x) = 6x^5 - 30x^4
Next, we set the derivative equal to zero and solve for x:
6x^5 - 30x^4 = 0
6x^4(x - 5) = 0
So the critical numbers of f(x) are x = 0 and x = 5.
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A wire is stretched from the ground to the top of an antenna tower. The wire is 35 feet long. The height of the tower is 7 ft greater than the distance d from the towers base to the end of the wire. Find the distance d and the height of the tower
The distance from the base of the tower to the end of the wire is approximately 16.41 feet, and the height of the tower is approximately 23.41 feet.
What is Distance?
Distance is a numerical measurement of how far apart objects or points are. It is a scalar quantity, which means it only has a magnitude (size) and not a direction.
Let h be the height of the tower, and let d be the distance from the base of the tower to the end of the wire.
We are told that h = d + 7, and we know that the wire is 35 feet long. We can use the Pythagorean theorem to relate d and h to the length of the wire:
[tex]d^2 + h^2 = 35^2[/tex]
Substituting h = d + 7, we get:
[tex]d^2 + (d + 7)^2 = 35^2[/tex]
Expanding the left-hand side, we get:
[tex]2d^2 + 14d - 696 = 0[/tex]
Dividing both sides by 2, we get:
[tex]d^2 + 7d - 348 = 0[/tex]
We can solve this quadratic equation using the quadratic formula:
[tex]d =\frac{ (-b \pm \sqrt{(b^2 - 4ac)}) }{2a}[/tex]
where a = 1, b = 7, and c = -348. Substituting these values, we get:
d ≈ 16.41 or d ≈ -21.41
Since d represents a distance, it must be positive, so we take d ≈ 16.41.
Finally, we can use h = d + 7 to find the height of the tower:
h ≈ 23.41
Therefore, the distance from the base of the tower to the end of the wire is approximately 16.41 feet, and the height of the tower is approximately 23.41 feet.
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what is the integral of e^{\cos\left(e^{\cos\left(e^{\cos\left(e^{\cos\left(x\right)}\right)}\right)}\right)}
The integral of [sin x / cos x] + [cos x / sin x] is (1/2) x ln |tan x| - (1/2) x ln |sec x| + C
The integral you have provided can be rewritten as:
∫ [sin x / cos x] + [cos x / sin x] dx
Using algebraic manipulation, we can simplify this expression to:
∫ (sin² x + cos² x) / (cos x x sin x) dx
Now, we can use the method of partial fractions to break down the integrand into simpler fractions. To do this, we first need to factor the denominator:
cos x x sin x = (1/2) x (sin 2x)
We can then express the integrand as:
(sin² x + cos² x) / [(1/2) x (sin 2x)]
Using the partial fractions technique, we can express the integrand as:
(sin² x + cos² x) / [(1/2) x (sin 2x)] = A / sin 2x + B / cos 2x
where A and B are constants that we need to determine. To solve for A and B, we can multiply both sides by sin 2x x cos 2x, which gives us:
sin² x + cos² x = A x cos 2x + B x sin 2x
We can then use the trigonometric identities sin² x + cos² x = 1 and cos 2x = 2 x cos² x - 1, and sin 2x = 2 x sin x x cos x, to simplify the equation to:
1 = (2A - B) x cos² x + (2B) x sin x x cos x - A
We now have two equations (for x = 0 and x = π/2) and two unknowns (A and B), which we can solve simultaneously to obtain:
A = 1/2 and B = -1/2
Using these values, we can express the integrand as:
(sin² x + cos² x) / [(1/2) x (sin 2x)] = (1/2) x [1 / sin 2x - 1 / cos 2x]
We can now integrate each term separately:
∫ [sin x / cos x] + [cos x / sin x] dx = ∫ [(1/2) x (1 / sin 2x - 1 / cos 2x)] dx = (1/2) x ln |tan x| - (1/2) x ln |sec x| + C
where C is the constant of integration. Therefore, the final answer to the given integral is:
∫ [sin x / cos x] + [cos x / sin x] dx = (1/2) x ln |tan x| - (1/2) x ln |sec x| + C
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Complete Question:
what is the integral of
[sin x / cos x] + [cos x / sin x]
to conduct a hypothesis test comparing variances of independent samples from two populations, the test statistic will have
To conduct a hypothesis test comparing variances of independent samples from two populations, the test statistic will have an F-distribution.
The F-distribution is a probability distribution that describes the ratio of two independent chi-squared distributions divided by their degrees of freedom. In this case, the numerator and denominator degrees of freedom are based on the sample sizes and variances of the two populations being compared.
The null hypothesis for the F-test is that the variances of the two populations are equal, and the alternative hypothesis is that they are not equal. The F-test allows us to determine if the difference in variances is statistically significant, and if we reject the null hypothesis, we can conclude that the variances are significantly different.
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If n is an integer and n > 1, then n! is the product of n and every other positive integer that is less than n. for example, 5! = 5 x 4 x 3 x 2 x 1a. Write 6! in standard factored formb. Write 20! in standard factored formc. Without computing the value of (20!)2, determine how many zeros are at the end of this number when it is written in decimal form. Justify your answer
a. 6! = 6 x 5 x 4 x 3 x 2 x 1 = 720. b. 20! = 20 x 19 x 18 x ... x 2 x 1. c. There are 16 zeros at the end of the decimal representation of (20!)2.
a. 6! = 6 x 5 x 4 x 3 x 2 x 1 = 720
b. 20! = 20 x 19 x 18 x ... x 2 x 1. To write this in factored form, we can identify the prime factors of each number and write the product using exponents. For example, 20 = 2² x 5, so we can write 20! as:
20! = (2² x 5) x 19 x (2 x 3²) x 17 x (2² x 7) x 13 x (2 x 2 x 3) x 11 x (2³) x (3) x (2) x 7 x (2) x 5 x (2) x 3 x 2 x 1
Simplifying, we get:
20! = 2¹⁸ x 3⁸ x 5⁴ x 7² x 11 x 13 x 17 x 19
c. The number of zeros at the end of (20!)² in decimal form is determined by the number of factors of 10, which is equivalent to the number of factors of 2 x 5. Since there are more factors of 2 than 5 in the prime factorization of (20!)², we only need to count the number of factors of 5. There are four factors of 5 in the prime factorization of 20!, which contribute four factors of 10 to the square. Therefore, (20!)²ends in 8 zeros when written in decimal form.
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ANYONE GOOD AT ALGEBRA 1?? ( y=mx+b )
PARALLEL, PERPENDICULAR, OR NEITHER?
Directions: Determine whether the lines given in each box are parallel,
perpendicular, or neither.
( y=mx+b )
1. y = 3x - 7
y = 3x + 1
2. y= -2/5x + 3
y= 2/5x + 8
3. y = -1/4x
y= 4x-5
4. 2x + 7y= 28
7x - 2y=4
5. y= -5x + 1
x - 5y = 30
6. 3x + 2y = 8
2x + 3y = -12
7. y= -4x - 1
8x + 2y = 14
8. x + y = 7
x - 7 = 9
9. y= 1/3x + 9
x - 3y =3
10. 4x + 9y = 18
y= 4x+9
11. 5x-10=20
y= -2x+6
12. -9x + 12y =24
y= 3/4x - 5
13. y= x-3
x-y = 8
14. 10x+8y= 16
5y=4x-15
15. y=5/3x + 7
6x-10y=10
16. x-2y=18
2x+y=6
17. x=4
x=-6
18. x=1
y=-8
Answer:
1.Neither
2.Perpendicular
3.Perpendicular
4.Neither
5.Perpendicular
6.Perpendicular
7.Neither
8.Neither
9.Perpendicular
10.Neither
11. Perpendicular
12.Perpendicular
13.Neither
14.Neither
15.Neither
16.Neither
17.Parallel
18.Neither
here are the answers in order from top to bottom
An instructor is administering a final examination. She tells her class that she with give an A grade to the 10% of the students who earns the highest marks. Past experience with the same examination has yielded grades that are normally distributed with a mean of 70 and a standard deviation of 10. If present class runs true to form, what numerical score would a student need to earn an A grade?
To earn an A grade, a student needs to score at least 82.8 , calculated using the inverse normal cumulative distribution function with a mean of 70, a standard deviation of 10, and a 10th percentile of 0.10.
Given that the grades are normally distributed with a mean of 70 and a standard deviation of 10.
We need to find the score which is at the 10th percentile of the distribution.
Using the standard normal distribution table, we can find the z-score that corresponds to the 10th percentile.
From the table, we can see that the z-score is approximately -1.28.
Using the formula for standardizing a normal distribution:
z = (x - μ) / σ
where z is the z-score, x is the raw score, μ is the mean, and σ is the standard deviation.
Substituting the given values, we have:
-1.28 = (x - 70) / 10
Solving for x, we get:
x = (-1.28 * 10) + 70
x = 82.8
Therefore, a student would need to earn a score of approximately 82.8 to receive an A grade.
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Need Help with Part C
Answer:
(a, b) -2
(c) -1, -1.5, -2, -2.5
Step-by-step explanation:
You want the average and instantaneous rates of change at various times in year 3, given the money in the bank after t years is 180+3t-t².
(a) ChangeThe amount at the beginning of year 3 is ...
180 +3t -t² = 180 +t(3 -t)
180 +2(3 -2) = 182 . . . . . . t=2
The amount at the end of year 3 is ...
180 +3(3 -3) = 180 . . . . . . t=3
The amount increased by 180 -182 = -2 thousand dollars.
(b) Rate of changeThis change occurred in one year, so the average rate of change is ...
change/years = -2/1 = -2 thousand dollars per year
(c) Instantaneous rate
The derivative of the amount function will give its instantaneous rate of change:
da/dt = 3 -2t
The values of t at the beginning of the quarters in year 3 are ...
t = 2: da/dt = 3 -2·2 = -1 thousand per year at start of 1st quarter
t = 2.25: da/dt = 3 -2(2.25) = -1.5 thousand per year at start of Q2
t = 2.50: da/dt = 3 -2(2.50) = -2 thousand per year at start of Q3
t = 2.75: da/dt = 3 -2(2.75) = -2.5 thousand per year at start of Q4
1. Eduardo runs 6 laps around the track at Lincoln Park School. Then he runs 3 miles to get home. How far will he run in all? Show your work.
So the solution equation is 6x + 3 and the total miles is equal to 6x + 3.
Where x represents the length of Lincoln Park School.
What is linear equation?A linear equation is an algebraic equation of the form y=mx+b. m is the slope and b is the y-intercept. The above is sometimes called a "linear equation in two variables" where y and x are variables.
What is the definition of mile?Mile is a unit of measurement that equals 1760 yards or approximately 1.6 kilometer's. It the mostly used in the continent of North America.
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Select which function f has an inverse g that satisfies g prime of 2 equals 1 over 6 period
f(x) = 2x3
f of x equals 1 over 8 times x cubed
f(x) = x3
1 over 3 times x cubed
The function that satisfies F Has An Inverse G That Satisfies G'(2) = 1/6 is f(x) = 2x³ (option a).
More precisely, if f(x) is a function, then its inverse function g(x) satisfies the following two conditions:
g(f(x)) = x for all x in the domain of f
f(g(x)) = x for all x in the domain of g
In other words, if we apply f(x) to an input value x, and then apply g(x) to the resulting output, we get back to the original input value.
Now, let's look at the given condition: G'(2) = 1/6. This means that the derivative of the inverse function at x=2 is 1/6. We can use this condition to eliminate some of the options.
f(x) = 2x³
If we take the derivative of f(x), we get: f'(x) = 6x²
To find the inverse function, we can solve for x in the equation y = 2x³:
x = [tex]y/2^{(1/3)}[/tex]
Now we can express the inverse function g(x) in terms of y:
g(y) = [tex]y/2^{(1/3)}[/tex]
To find the derivative of g(x), we use the chain rule:
g'(x) = f'(g(x))⁻¹
g'(2) = f'(g(2))⁻¹
g'(2) = f'([tex]1/2^{(1/3)}[/tex])⁻¹
g'(2) = 6([tex]1/2^{(1/3)}[/tex])²)⁻¹
g'(2) = 6/36 = 1/6
Since g'(2) = 1/6, option a) is the correct answer.
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Consider parallelogram ABCD below.
Use the information given in the figure to find m/BAC, m/B, and x.
Answer:
Since opposite angles in a parallelogram are congruent, we know that:
m∠DAB = m∠BCD = 67°
Since ∠BAC and ∠BCD are adjacent angles, we know that:
m∠BAC + m∠BCD = 180°
So we can solve for m∠BAC:
m∠BAC + 67° = 180°
m∠BAC = 113°
Since opposite angles in a parallelogram are congruent, we know that:
m∠BAD = m∠BC
So we can solve for m∠BC:
m∠BAD = 16
m∠BC = 16°
Finally, we can solve for x by using the fact that the interior angles of a quadrilateral sum to 360 degrees:
m∠DAB + m∠BAC + m∠BCD + m∠CDA = 360°
67° + 113° + m∠BCD + 90° = 360°
m∠BCD = 90°
So we can solve for x:
m∠4B - m∠BCD = 90° - 90° = 0
4x - 59° = 0
4x = 59°
x = 14.75°
Therefore, m/BAC = 113°, m/B = 16°, and x = 14.75°.
Question 6
One gallon of water weighs 8.34 lb. How much weight is added to a fire truck when its tank is filled
with 750 gal of water?
Question 7
1
Answer:
6255 lbs
Step-by-step explanation:
so the questions says 1 gallon of water = 8.34
So, 8.34 * 750 = 6255Lbs
Answer:
Step-by-step explanation:
1 x 8.34 = 8.34 lb (one gal multiplied by the weight of 8.34)
750 x 8.34 = 6255 lb (750 gal multiplied by the weight of 8.34)
6,255 pounds is added.
A particular fruits weights are normally distributed, with a mean of 408 grams and a standard deviation of 32 grams .
If you pick 16 fruits at random,then 20% of the time, their mean weight will be greater than how many grams.
The mean weight of 16 fruit picked at random, then their mean weight will be greater than 414.72 grams 20% of the time
What is the mean value of a dataset?The mean value of a set of data, is the sum of the values in the data, divided by the number of data in the dataset.
The population mean = 408 grams
The population standard deviation = 32 grams
The mean of 16 fruits such that the probability of the mean is larger than the value is 0.2, can be obtained as follows;
The standard error of the mean = The standard deviation/√(Sample size)
Therefore;
The standard error = 32/√(16) = 8
The mean that corresponds to a probability of 0.2, which is the 80th percentile of the normal distribution, can be found using the z-score of the 80th percentile, which is about 0.84
Therefore, we get;
z = (Sample mean - 408)/8 = 0.84
The sample mean = 8 × 0.84 + 408 = 414.72
The sample mean = 414.72 grams
Therefore;
The mean weight of the 16 fruit such that their weight is greater than the mean weight of the population 20% of the time is 414.72 grams.
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Solve for x, using a
tangent and a secant line.
64°
X
145°
x = [?]° Remember: a = b
c-b
2
Enter
Considering the secant-tangent theorem, the value of x is given as follows: x = 17º.
What is the secant-tangent theorem?The secant-tangent theorem states that when a tangent and a secant line intersect at a point outside a circle, the measure of the angle of intersection is given by half the difference between the arc length of the far arc by the arc length of the near arc.
Hence the equation is given as follows:
y = (far arc - near arc)/2.
The parameters for this problem are given as follows:
far arc = 145º.near arc = x.Angle = 64º.Hence the value of x is obtained as follows:
64 = (145 - x)/2
145 - x = 128
x = 17º.
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evaluate the triple integral. t 7x2 dv, where t is the solid tetrahedron with verticies (0, 0, 0), (1, 0, 0), (0, 1, 0), and (0, 0, 1)
The value of the triple integral is 7/180.
To evaluate the triple integral, we first need to set up the limits of integration. Since the solid tetrahedron T is defined by the four vertices (0, 0, 0), (1, 0, 0), (0, 1, 0), and (0, 0, 1), we can use these points to set up the limits of integration as follows:
For z, we integrate from the bottom of the solid (z = 0) to the top (z = 1 - x - y).
For y, we integrate from the left side of the solid (y = 0) to the right (y = 1 - x).
For x, we integrate from the back of the solid (x = 0) to the front (x = 1).
Therefore, the triple integral can be written as:
∫∫∫ t 7x^2 dv = ∫∫∫t 7x^2 dV
= ∫[0,1] ∫[0,1-x] ∫[0,1-x-y] 7x^2 dz dy dx
∫[0,1] ∫[0,1-x] ∫[0,1-x-y] 7x^2 dz dy dx
= ∫[0,1] ∫[0,1-x] 7x^2 (1 - x - y) dy dx
= ∫[0,1] [7x^2 (1 - x) (1/2 - x/3)] dx
= 7/180
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Below is the graph of a trigonometric function. It has a minimum point at
(1, 1.5) and an amplitude of 1.5. What is the midline equation of the function?
The midline equation of the function is y = 1.5.
What is amplitude of trigonometric functions?The gap between a trigonometric function's highest and least values is known as its amplitude. The difference between the greatest and minimum numbers is, in other words, divided by two. For instance, the amplitude is A in the equation y = A sin(Bx) + C. The amplitude, also known as the average value of the function across a period, denotes the "height" of the function above and below the midline. It gauges the magnitude or intensity of the oscillation of the function's representation of. The oscillation is more prominent and subtler depending on the amplitude, which ranges from higher to lower values.
Given that, the function has minimum point at (1, 1.5) and an amplitude of 1.5.
Using the definition of the amplitude the midline is the given amplitude.
Hence, the midline equation of the function is y = 1.5.
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Answer:
3
Step-by-step explanation:
Khan Academy
5. Mr. Sharma had a triangular plot of land having length of edges 40 m, 30.5m and 48.5 m 1,What is the perimeter of his plot? 2,If he constructed a circular pond of radius 7 m inside the plot, find the circumference of the pond. 3,If he built a cuboidal house on his plot with length 20 m., width 18 m. and height 25 m, what is the volume of his house? 4, If one of the rooms of his house is 10 m long, 6 m wide and 4 m high, calculate the surface area of the room.
Answer:
perimeter of plot=119m
circumference of pond=44m
volume of house=9000 m^3
surface area of room=248 m^2
Step-by-step explanation: