The result of the function is h = 1 is equal to -2
Evaluating linear equationsLinear equations are equations that has a leading degree of 1.
Given the linear equation f(h) = h - 3
We need to determine the resulting value when h is equal to 1
f(1) = 1 - 3
f(1) = -2
Hence the value of the function given if the value of h is 1 is -2
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airlines sometimes overbook flights. suppose that for a plane with 50 seats, 55 passengers have tickets. define the random variable y as the number of ticketed passengers who actually show up for the flight. the probability mass function of y appears in the accompanying table. y 45 46 47 48 49 50 51 52 53 54 55 p(y) 0.05 0.10 0.13 0.14 0.25 0.16 0.06 0.05 0.03 0.02 0.01 (a) what is the probability that the flight will accommodate all ticketed passengers who show up? (b) what is the probability that not all ticketed passengers who show up can be accommodated? (c) if you are the first person on the standby list (which means you will be the first one to get on the plane if there are any seats available after all ticketed passengers have been accommodated), what is the probability that you will be able to take the flight? what is this probability if you are the third person on the standby list?
a) Probability that the flight will accommodate all ticketed passengers who show up is 0.16
b) Probability that not all ticketed passengers who show up can be accommodated is 0.67
c) The probability that you will be able to take the flight is 96%
Probability is a powerful tool to understand the likelihood of different outcomes in various situations, including overbooking of flights
In this scenario, the random variable y represents the number of ticketed passengers who actually show up for the flight, out of a total of 55 ticketed passengers for a plane with only 50 seats. The probability mass function of y provides the probabilities for each possible outcome.
(a) The probability that the flight will accommodate all ticketed passengers who show up is the probability of y being equal to 50, which is 0.16.
(b) The probability that not all ticketed passengers who show up can be accommodated is the sum of the probabilities of y being greater than 50, which is
=> 0.05 + 0.10 + 0.13 + 0.14 + 0.25 = 0.67.
(c) If you are the first person on the standby list, the probability of being able to take the flight is the probability of y being less than or equal to 50, which is 0.89. This means that there is an 89% chance that you will get on the plane. If you are the third person on the standby list, the probability is the probability of y being less than or equal to 52 (since two people need to cancel or not show up for you to get on), which is 0.96. This means that there is a 96% chance that you will get on the plane.
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Listed below in order are prices in dollars for a Big Mac hamburger in the , , , , , , , , , , , and . Such data are used to compare currency exchange rates and the costs of goods in different countries. Find the range, variance, and standard deviation for the given sample data. What do the measures of variation tell us about the prices of a Big Mac in different countries?
Based on the information, we can infer that the range is an adequate indicator to affirm that the price difference of the Big Mac in different countries is minimal.
How to find the range?To find the range of the given data we must perform the following procedure:
We must find the highest and lowest data, in this case the highest and lowest data are 6.8 and 1.98 respectively. So, to find the range we must find the difference between these two data:
6.8 - 1.89 = 4.91
How to find the variance?To find the variance we must apply the following formula:
S² = 1 / 11 - 1 ( 205.59 - (44.67)²/11)
S² = 2.42
How to find the standard deviation?To find the standard deviation we must apply the following formula:
S = [tex]\sqrt[n]{variance}[/tex]
S = [tex]\sqrt{2.42}[/tex]
S = 1.56
What do measures of variation tell us about the prices of a Big Mac in different countries?Based on the above data, we can infer that the range is an indicator that the difference in the Big Mac price in different countries is minimal.
Note: This question is incomplete. Here is the complete information:
Attached image
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consider the two matricesA = | 1 2 4 | and D = | -5 -6 -2 || 4 2 4 | | 1 -2 1 || 3 4 3 | | 3 4 3 |observe that D is obtained from A using two elementary row operations. find a matrix E such that EA = D (hint: E is the product of the two elementary matrices corresponding to the two row operations).
The value of the matrix E is such that EA = D (E is the product of the two elementary matrices corresponding to the two-row operations) will be:
Matrix E = | 0 1 0 |
| 1 0 0 |
We can find the elementary matrices corresponding to the two-row operations and multiply them together to obtain the matrix E.
First-row operation: Add -4 times the first row to the second row.
This is equivalent to multiplying A on the left by the elementary matrix:
| 1 0 0 |
|-4 1 0 |
| 0 0 1 |
Call this matrix E1.
E1A =
| 1 2 4 | | 1 0 0 | | 1 2 4 |
|-4 -6 -12| * | -4 1 0 | = |-5 -6 -2 |
| 3 4 3 | | 0 0 1 | | 3 4 3 |
Next row operation: Swap the first and third rows.
This is equivalent to multiplying E1A on the left by the elementary matrix:
| 0 0 1 |
| 0 1 0 |
| 1 0 0 |
Call this matrix E2.
E2E1A =
| 3 4 3 | | 0 0 1 | | -5 -6 -2 |
|-4 -6 -12| *| 0 1 0 | = | -4 -2 4 |
| 1 2 4 | | 1 0 0 | | 1 2 4 |
Therefore, the matrix E that satisfies EA = D is given by:
E = E2E1 = | 0 0 1 | | 1 0 0 |
E = | 0 0 1 |
EA = D
| 0 1 0 | * |-4 1 0 | = | 0 1 0 |
| 1 0 0 | | 0 0 1 | | 1 0 0 |
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caitlin took both the sat and the act college entrance exams. her scores on both exams are shown in the table, as well as the national mean scores and standard deviations. exam caitlin's exam score national mean exam score national standard deviation sat 1850 1500 250 act 28 20.8 4.8 she wants to know on which test she performed better. find the z-scores for her result on each exam. provide your answer below: sat z-score: ____
act z-score: ____
On the SAT her z-score was 1.4 and on the ACT her z-score was 1.5 Thus, due to the higher z-score, she performed better on the ACT.
The amount of standard deviations by which the value of a raw score differs from or differs above the mean value of what is observed or measured is known as the z score or standard score in the z test. The z-score calculates how far an X-score deviates from the mean by standard deviations. Calculating the ACT scores utilizing the Z- score -
Z = X - u/a
Calculating the SAT score -
Where X = 1850, u = 1500 and a = 250
Z = 1850 - 1500/250
= 350/250
= 1.4
Similarly,
Calculating the ACT score -
Where X = 28, u = 20.8 and a = 4.8
Z = 28 - 20.8/4.8
= 7.2/4.8
= 1.5
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1. Which of the following is not a variable cost?
A. wages paid to labor
B. seeds and fertilizers for paddy farmers
C. rent on land
D. electricity bills
2. The average total cost of producing computers in a factory is RM500 at the current
output level of 100 units per week. If fixed cost equals RM10,000
A. average fixed cost equals RM10,000.
B. total cost equals RM60,000 per week.
C. variable cost equals RM50,000 per week.
D. average variable cost equals RM400.
3. Which of these statements is false?
A. There are no fixed costs in the long run.
B. Total costs are equal to total fixed costs plus total variable costs.
C. In the short run, all inputs are fixed inputs.
D. A fixed cost is a cost that does not change as output changes.
4. Economies of scale occurs if the firm's:
A. long run average cost curve is horizontal.
B. average cost increases as the firm expands its production.
C. long run average cost decreases as the firm increases its output.
D. long run average cost curve is upward-sloping.
5. If total costs are RM200 for one unit of output and RM310 for two units, what is the marginal cost of the
second unit?
A. RM100
B. RM110
C. RM200
D. RM210
6. In the production of refrigerators, the item which represents variable costs is:
A. the tax on the company's property.
B. the salary of the night watchman.
C. the cost of fuel and electric power.
D. The insurance premium for the premises.
7. The average total cost of producing computers in a factory is RM250 at the current
output level of 100 units per week. If fixed costs equal RM5,000
A. average fixed cost equals RM50.
B. total cost equals RM40,000 per week.
C. variable cost equals RM10,000 per week.
D. average variable cost equals RM400.
9. The marginal cost of a good is
A. the addition to total cost of producing one more unit of output.
B. decreasing when average total cost is decreasing.
C. the difference between average total cost and average fixed cost.
D. always equal to average variable cost when the firm is maximizing profit.
Answer:
ur mom jk its
c
Step-by-step explanation:
Attachment is below:
The numbers that are solutions to the inequality k > -5 are given as follows:
A. -4.
F. -4.99.
G. -0.5.
What are the inequality symbols?The four inequality symbols, along with their meaning, are presented as follows:
> x: greater than x.< x: less than x.≥ x: at least x.≤ at most x.The inequality for this problem is given as follows:
k > -5.
Meaning that the solutions are all the numbers that are greater than -5.
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Give the correct notation for the quantity described and give its value.
Mean number of cell phone calls made or received per day by cell phone users. In a survey of
1917 cell phone users, the mean was 13.10 phone calls a day.¹
The notation for this sample is denoted by [tex]\overline{x}[/tex].
What is the difference between the sample and the population?The entire group about whom you want to make conclusions is referred to as a population.
The particular group from which you will gather data is known as a sample. The sample size is always smaller than the population as a whole.
Given, In a survey of 1917 cell phone users, the mean was 13.10 phone calls a day.
This a sample so the notation for the mean is [tex]\overline{x}[/tex].
If it is for population then the notation of mean would have been [tex]\mu[/tex].
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fill in the blank. surveys suggest that about 7 percent of people in the united states experience a___during a given year. please choose the correct answer from the following choices, and then select the submit answer button. answer choices
Surveys suggest that about 7 percent of people in the united states experience a depression during a given year.
The United States experienced a depression during the 1930s, which lasted from 1929 to 1939. This was one of the longest and deepest economic downturns in U.S. history. The Great Depression caused widespread unemployment, poverty, and hardship throughout the country.
The stock market crash of 1929 and the subsequent bank failures caused a sharp decline in industrial and agricultural production, as well as a dramatic drop in consumer spending. As a result, millions of Americans were left without jobs, and many lost their homes and other possessions.
The government responded to the crisis with a series of programs and initiatives, such as the New Deal, to stimulate the economy and provide relief for those most affected. These programs helped to create jobs and provide economic stability, but the Great Depression would not end until the U.S. entered World War II in 1941.
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Choose which point is a solution to the equation below. Y= 3x + 5
There are infinitely many possible solutions to the equation y = 3x + 5.
What is a linear equation?Equations whose variables have a power of one are called linear equations. One example with one variable is where ax+b = 0, where a and b are real values and x is the variable.
Given:
An equation,
y = 3x + 5.
The equation has an independent variable x and a dependent variable y.
And the x is a free variable.
So, the y varies as per the value of x.
There are infinite possible solutions to the equation.
Therefore, there are infinite possible solutions to the equation.
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Use Kruskal's algorithm to find a minimum spanning tree for the following graph. Indicate the order in which edges are added to form the tree. (Enter your answer as a comma-separated list of sets.)
A graph with 8 vertices and 12 edges is shown.
One edge with weight 12 connects vertex v0 and vertex v1.
One edge with weight 4 connects vertex v0 and vertex v5.
One edge with weight 20 connects vertex v1 and vertex v2.
One edge with weight 5 connects vertex v1 and vertex v3.
One edge with weight 7 connects vertex v1 and vertex v4.
One edge with weight 19 connects vertex v2 and vertex v7.
One edge with weight 2 connects vertex v3 and vertex v4.
One edge with weight 18 connects vertex v3 and vertex v7.
The minimum spanning tree for the above graph 1 is present above in graph figure 2. The order in which edges are added to form the tree is equals to {V₃, V₄ }, { V₀, V₅}, { V₁, V₃}, {V₅, V₆}, { V₄, V₅}, {V₆, V₇}, {V₂, V₇ }.
We have , a diagram present above in figure. This graph has 8 vertices and 12 edges. Also
The edge with weight 12 connects vertex V₀ and vertex V₁.Similarly, edages are connected to each other with different weights as shown in graph. Kruskal's algorithm is a greedy algorithm in graph theory of discrete mathematics that used to determine the minimum spanning tree for a connected weighted graph and adds increasing weight at each. In this case a graph present we determine the shortest spinning tree. Kruskal's algorithm stated that always select a minimum cost edge that should not result in a cycle. The order is which edges are added is
{V₃, V₄ }, { V₀, V₅}, { V₁, V₃}, {V₅, V₆}, { V₄, V₅}, {V₆, V₇}, {V₂, V₇ }.
Hence, the required graph is present above.
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Complete question:
Use Kruskal's algorithm to find a minimum panning tree for the above graph. Indicate the order in which edges are added to form the tree. (Enter your answer as a comma-separated list of sets.)
A graph with 8 vertices and 12 edges is shown.
One edge with weight 12 connects vertex v0 and vertex v1.
One edge with weight 4 connects vertex v0 and vertex v5.
One edge with weight 20 connects vertex v1 and vertex v2.
One edge with weight 5 connects vertex v1 and vertex v3.
One edge with weight 7 connects vertex v1 and vertex v4.
One edge with weight 19 connects vertex v2 and vertex v7.
One edge with weight 2 connects vertex v3 and vertex v4.
One edge with weight 18 connects vertex v3 and vertex v7.
Divide Using Synthetic Division
The result of the synthetic division is the final row. In this case, the result is -3, 5, -15, 18.
What is polynomial?A polynomial is an expression consisting of variable and coefficient and are used to model real world situation it is an equation of degree greater than one where the exponents of the variables can be any non-negative integer for example the polynomial equation x 2 + 3x + 2 represent a parable of windcraft polynomial are used in name variety of field such as mathematics and physics.
The process of synthetic division is used to divide polynomials of the form ax^n + bx^n-1 + ... + c, where a is the coefficient of the highest power of the variable x.
To divide -3 into the polynomial 1 8 9 -18 0, the following steps should be taken:
Step 1: Line up the divisor, -3, to the left of the polynomial, as shown below:
-3 | 1 8 9 -18 0
Step 2: Bring down the first coefficient in the polynomial, which is 1, and place it directly below the -3.
-3 | 1 8 9 -18 0
-3
Step 3: Multiply the -3 by the first coefficient and place the result in the next row, directly below the 8.
-3 | 1 8 9 -18 0
-3
-3
Step 4: Add the result to the 8, and place the new result in the next row.
-3 | 1 8 9 -18 0
-3
-3
5
Step 5: Repeat steps 3 and 4 for each coefficient in the polynomial.
-3 | 1 8 9 -18 0
-3
-3
5
-15
-15
18
Step 6: The result of the synthetic division is the final row. In this case, the result is -3, 5, -15, 18.
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Complete questions as follows-
Divide Using Synthetic Division
-3|1 8 9 -18 0
A forest ranger is watching the progress of a forest fire spreading towards her from the top of a 3334-foot mesa. In 6 minutes,
the angle of depression to the leading edge of the fire changes from 10.5° to 12.3°.
1) How many feet does the fire advance during the 6 minutes that the ranger is observing it?
2) At what speed (in MILES PER HOUR) is the fire spreading towards the ranger?
The speed of the fire is 3.214 miles per hour (rounded to three decimal places)
What do you mean by speed?It is defined as the distance traveled by an object per unit of time, typically in meters per second (m/s) or kilometers per hour (km/h).
Speed can be calculated by dividing the distance traveled by the time taken to cover that distance. It is a scalar quantity, meaning it only has magnitude and no direction.
Let's call the horizontal distance the fire advanced during the 6 minutes "d." We can use the tangent function to find d:
tan(12.3°) = (3334 - h) / d
tan(10.5°) = (3334 - h) / d
Solving for d in each equation, we get:
d = (3334 - h) / tan(12.3°)
d = (3334 - h) / tan(10.5°)
Since the time interval is the same for both observations, the fire advanced a distance equal to the difference between the two distances:
d = [(3334 - h) / tan(12.3°)] - [(3334 - h) / tan(10.5°)]
Plugging in the values and simplifying:
d = 1698.5 feet (rounded to the nearest tenth)
To find the speed at which the fire is spreading towards the ranger, we need to convert the distance from feet to miles, and the time from minutes to hours:
d = 1698.5 feet / 5280 feet per mile = 0.3214 miles
t = 6 minutes / 60 minutes per hour = 0.1 hours
The speed of the fire is then:
s = d / t = 0.3214 miles / 0.1 hours = 3.214 miles per hour (rounded to three decimal places)
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If c > 0, s^2+ t^2 = 6, and st = c+5, what is (s+t)^2 in terms of c ?
Answer: We can start by expanding the square on the left-hand side of the equation:
(s + t)^2 = s^2 + 2st + t^2
We know that s^2 + t^2 = 6, so we can substitute that into the equation:
(s + t)^2 = 6 + 2st
We also know that st = c + 5, so we can substitute that into the equation:
(s + t)^2 = 6 + 2(c + 5)
Simplifying the right-hand side:
(s + t)^2 = 6 + 2c + 10
So, in terms of c, (s + t)^2 = 6 + 2c + 10.
Step-by-step explanation:
Write this ratio as a fraction in simplest form without any units.
54 ounces to 3 pounds
Answer: 8/9
Step-by-step explanation: 3 x 16 = 48 ounces
48 / 54 = 8/9
The perimeter of a pentagon is 41.5 cm. write and solve and equation to detrmine the length of each side of the pentagon?
A pentagon has a 41.5 cm circumference, and its sides are each 8.3 cm long.
When you already know the value of one side, calculating the perimeter of a pentagon is made much simpler. The five sides of each pentagon are equal. If the length of one side is given to you.
Since a pentagon has five sides, we will abbreviate each side's length as "s". The lengths of all five sides add up to the perimeter of the pentagon, allowing us to formulate the following equation:
5s = 41.5
We must put "s" on one side of the equation alone in order to solve for it. Divide both sides by 5 to do this: s = 8.3
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Determine the coordinates of the point on the unit circle corresponding to the given central angle. If
necessary, round your results to the nearest hundredth.
202⁰
a. (-0.93,-0.37)
b. (-0.37, -0.93)
56:2
c.
(1, -0.37)
d. (-0.93, 0)
Answer:
a. (-0.93,-0.37)
Step-by-step explanation:
The unit circle is a circle with a radius of 1 that is centered at the origin (0, 0) of a coordinate plane. To find the coordinates of a point on the unit circle corresponding to a given central angle, we can use the relationship between the angle and the coordinates of the point.
For a central angle of 202 degrees, the point on the unit circle would be found by using the formula:
x = cos(202°)
y = sin(202°)
Rounding the results to the nearest hundredth, we have:
x = -0.927
y = -0.3746
So the coordinates of the point on the unit circle corresponding to the central angle of 202 degrees are (-0.93, -0.37).
Answer:
a. (-0.93, -0.37)
Step-by-step explanation:
A unit circle has its center at (0, 0) and a radius of 1.
The coordinates on the unit circle (x, y) are equivalent to (cos θ, sin θ), where θ is the angle (measured anticlockwise from the positive x-axis).
Therefore, given θ = 202°, the coordinates of the corresponding point on the unit circle are:
x = cos 202° = -0.93 (nearest hundredth)y = sin 202° = -0.37 (nearest hundredth)Therefore, the point on the unit circle is (-0.93, -0.37).
4 friends share 2 granola bars each friend gets _____ of the granola bar
Answer:
1/2 (half)
Step-by-step explanation:
4f over 2g then 1f over x
2/4 to get 1/2
each friend gets half (1/2)
Why do communist countries use authoritarian methods to maintain their economic and political system
Answer:
Communist countries use authoritarian governments because it requires the absolute obedience to authority figures. Communism is an extreme form of socialism because there is no private ownership or political freedom.
Step-by-step explanation:
When a new charter school opened in 2000, there were 540 students enrolled. write a formula for the equation n , representing the number of students attending this charter school t years after 2000, assuming that the student population:Increases by 11% per year N(t)=Decreases 23 students per year N(t)=Decreases 8.9% per year. N(t)=Increases 81 students per year . N(t)=Remains constant (does not change). N(t)=Increases 6.4% per year. N(t)=
a) Increased by 44 students per year= N(t) = 240 + 44t
b) Decreased by 32 students per year=N(t) = 240 - 32t
c) Increased by 40 students every 2 years=N(t) = 240 - 32t
d) Decreased by 24 students every 4 years=N(t) = 240 - 32t
e) Remained constant= N(t) = 240
f) Increased by 5 students every semester (twice in a year)=N(t) =240+10t
The original population of students in the year 2000 is 240.
[tex]N_0=240[/tex]
Let the number of years = t
a) If the population increased by 44 students every year, the population, after t years, would have increased by 44t
Therefore,
[tex]N(t)=N_0+44t[/tex]
N(t) = 240 + 44t
b) If the population decreased by 32 students per year, the population, after t years, would have decreased by 32t
Therefore, [tex]N(t)=N_0-32t[/tex]
N(t) = 240 - 32t
c) If the population Increased by 40 students every 2 years and increase is uniform per year, the population will increase by 40/2 = 20 students in 1 year. So in t years, the population would increase by 20 t.
Therefore,
[tex]N(t)=N_0+20t\\\\N(t)=240+20t[/tex]
d) Decreased by 24 students every 4 years
In 1 year, it decreases by 24/4 = 6 students
In t years, it decreases by 6t students
[tex]N(t)=N_0-6t\\\\N(t)=240-6t[/tex]
e) Remained constant
N(t)=N0
N(t)=240.
f) If the population increases by 5 students twice in a year
In 1 year, it increases by 5*2 = 10 students
In t years, it increases by 10t students
[tex]N(t)=N_0+10t\\\\N(t)=240+10t[/tex].
The Complete Question:-
When a new charter school opened in 2000, there were 240 students enrolled. Write a formula for the function N ( t ), representing the number of students attending this charter school t year after 2000, assuming that the student population:
a) Increased by 44 students per year
b) Decreased by 32 students per year
c) Increased by 40 students every 2 years
d) Decreased by 24 students every 4 years
e) Remained constant
f) Increased by 5 students every semester (twice in a year)
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In the 1970's, my parents bought a house for $20,000 and now the
same home is worth $400,000. What is the percent of change?
Answer:
Step-by-step explanation:
h = 100 * 400000 - 20000 / 20000 = 38000000/ 20000 = 1900/1 = 1900%
The integers from 1 to n, inclusive, are placed in order and equally spaced on a circle. At the ends of a diameter are the numbers 7 and 23 as shown in the figure. What is the value of n?
The required value of n is the integer "32" as shown in the given figure.
What are integers?integer, positive or negative whole-valued number, or 0. The integers are formed from a collection of counting numbers such as 1, 2, 3,...
Here,
According to the question,
Let the number of integers between 7 and 23, inclusive, be x (note that x is not necessarily equal to n). Then the number of integers between 1 and 7, inclusive, and the number of integers between 23 and n, inclusive, must also be x, because the integers are equally spaced on the circle.
n = 2(x) ....(i)
Since from above definition
x = 23 - 7
x = 16
Substitute the value of x = 16 in equation (i),
n = 2(16)
n = 32
Therefore, the value of n is "32".
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find the prime factorization of the following number. 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 35, 40, 56, 70, 80, 112, 140, 280 and 560write any repeated factors using exponents. 560
Prime Factorization is finding which prime numbers multiply together to make the original number.
Prime factorization of the following numbers is
1 = 1
2 = 2 × 1
4 = 2² × 1
5 = 5 × 1
7 = 7 × 1
8 = 2³ × 1
10 = 2 × 5
14 = 2 × 7
16 = 2⁴
20 = 2² × 5
28 = 2² × 7
35 = 5 × 7
40 = 2² × 5
56 = 2³ × 7
70 = 2 × 5× 7
80 = 2⁴ × 5
112 = 2⁴ × 7
140 = 2² × 5 × 7
280 = 2³ × 5 × 7
560 = 2⁴ × 5 × 7
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How many solutions does this equation have? -16 + n + 14n = -16 + 15n
Answer:
Infinitely many solutions
Step-by-step explanation:
Given the equation:
[tex]\displaystyle{-16+n+14n=-16+15n}[/tex]
Which can be simplified (for left side) to:
[tex]\displaystyle{-16+15n=-16+15n}[/tex]
Both sides are same, meaning that there are infinitely many solutions since no matter which n-values you substitute in, you'll end up getting true equation.
please help this is due bye 6:00
5+ – 6f–9+8f–8f
The simplified expression for the expression (5 – 6f–9+8f–8f) is (-4 - 6f).
How to apply operation on Expression?The rules that specify the order in which we should solve an expression involving many operations are known as the order of operations. PEMDAS stands for Parentheses, Exponents, Multiplication, Division, and Addition and Subtraction (from left to right).
Given:
5 – 6f–9+8f–8f
Solving the Expression
= 5 – 6f–9+8f–8f
= 5 - 9 -6f + 8f - 8f
= -4 + f(-6 +8 -8)
= -4 + f(-6)
= -4 - 6f
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Find a vector equation with parameter t for the line through the point (4,0,-3) and parallel to the vector 2i - 4j + 6k
Answer r(t)=
The vectorial equation of the line that passes through (4, 0, - 3) and is parallel to the vector <2, - 4, 6> is equal to (x, y, z) = (4, 0, - 3) + t · (2, - 4, 6).
How to derive the vectorial equation of a line
According to linear algebra, three-dimension lines can be derived from the knowledge of a point and a vector slope, whose formula is introduced below:
(x, y, z) = P(x, y, z) + t · M(x, y, z)
Where:
P(x, y, z) - Point on the linet - ParameterM(x, y, z) - Vector slopeTwo lines are parallel when they have the same vector slope. If we know that P(x, y, z) = (4, 0, - 3) and M(x, y, z) = (2, - 4, 6), then the vectorial equation of the line is:
(x, y, z) = (4, 0, - 3) + t · (2, - 4, 6)
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Which equation shows the same relationship as 1/2=3x1/6
Answer:
1 /2
Step-by-step explanation:
3×1 = 3
So it is 3 /6 = 1/2
3/6 ÷2 = 1/2
find a vector equation of the tangent line to the parametrized curve r(t) = 9t, t , t2 when t = 1. (your instructors prefer angle bracket notation < > for vectors.)
The vector equation of the tangent line is <9t+9, t+2, t^2>.
To find the tangent line to the curve at t=1, we need to find the derivative of r(t) and evaluate it at t=1.
r(t) = 9t <1> + 1 <2> + t^2 <3>
Taking the derivative of r(t) with respect to t, we get:
r'(t) = 9 <1> + 1 <0> + 2t <3>
Evaluating r'(1), we get:
r'(1) = 9 <1> + 1 <0> + 2(1) <3> = 9 <1> + 2 <3>
So the vector equation of the tangent line at t=1 is:
r(1) + tr'(1) = <9,1,1> + t<9,2,0>
Simplifying, we get:
<9t+9, t+2, t^2>
So the vector equation of the tangent line is <9t+9, t+2, t^2>.
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Connect and Reflect: Evaluate your work by answering these questions: How did this activity help you understand the US involvement in World War I? Did it change what you learned in any way? What would you like to know more about?
The United States forces arrived in Europe in 1917 and helped tip the scales in favor of Britain and France, leading to an Allied victory over Germany and Austria in November 1918. More than four million Americans had served in the armed forces by the time of the armistice, and 116,708 had died.
What led to US involvement in World War I despite maintaining neutrality?When World War I broke out in Europe in 1914, President Woodrow Wilson declared that the United States would remain neutral, and many Americans agreed. However, public opinion on neutrality began to shift after the sinking of the British ocean liner Lusitania by a German U-boat in 1915, which killed nearly 2,000 people, including 128 Americans.
Wilson requested a declaration of war against Germany in response to the Zimmermann telegram, which threatened an alliance between Germany and Mexico against America.
The United States of America officially entered World War I on April 6, 1917. Millions of Americans served overseas and helped the war effort at home over the next year and a half. Their contributions aided in the victory of the war and shaped both America and the world for future generations.
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A scientist places a cell in a Petri dish. At the end of 1 hour, the cell divides so
that there are 2 cells in the Petri dish. At the end of 2 hours, those cells divide so
there are 4 cells in the Petri dish. The cells continue to divide this way every hour.
Use the expression 2 to the 10th power to find the number of cells in the Petri dish after 10 hours.
Show your work.
According to a 2017 survey conducted by the technology market research firm The Radicati Group, U.S. office workers receive an average of 121 e-mails per day (Entrepreneur magazine website). Assume the number of e-mails received per hour follows a Poisson distribution and that the average number of e-mails received per hour is five.
a. What is the probability of receiving no e-mails during an hour (to 4 decimals)?
b. What is the probability of receiving at least three e-mails during an hour (to 4 decimals)? For this question, if calculating the probability manually make sure to carry at least 4 decimal digits in your calculations.
c. What is the expected number of e-mails received during 15 minutes (to 2 decimals)?
d. What is the probability that no e-mails are received during 15 minutes (to 4 decimals)?
The probability of receiving no e-mails during an hour is approximately 0.0067, or 0.67%. The probability of receiving at least three e-mails during an hour is approximately 0.8754, or 87.54%. The expected number of e-mails received during 15 minutes is 1.25. The probability of receiving no e-mails during 15 minutes is approximately 0.7788, or 77.88%
We know that the average number of e-mails received per hour is 5. Therefore, the parameter λ of the Poisson distribution is also 5, since the Poisson distribution's mean and variance are both equal to λ.
The probability of receiving no e-mails during an hour (or during any other fixed time interval of length t) can be calculated using the Poisson distribution as follows:
P(X = 0) = e^(-λ) * λ^0 / 0! = e^(-5) * 5^0 / 0! ≈ 0.0067
Therefore, the probability of receiving no e-mails during an hour is approximately 0.0067, or 0.67%.
The probability of receiving at least three e-mails during an hour can be calculated as follows:
P(X ≥ 3) = 1 - P(X < 3) = 1 - (P(X = 0) + P(X = 1) + P(X = 2))
We already know the value of P(X = 0) from part (a), so we just need to calculate P(X = 1) and P(X = 2) using the Poisson distribution:
P(X = 1) = e^(-5) * 5^1 / 1! ≈ 0.0337
P(X = 2) = e^(-5) * 5^2 / 2! ≈ 0.0842
Substituting these values into the equation above, we get:
P(X ≥ 3) = 1 - (0.0067 + 0.0337 + 0.0842) ≈ 0.8754
Therefore, the probability of receiving at least three e-mails during an hour is approximately 0.8754, or 87.54%.
Since the expected number of e-mails received per hour is 5, the expected number of e-mails received during 15 minutes (i.e., a quarter of an hour) is:
E(X) = λ * t = 5 * (1/4) = 1.25
Therefore, the expected number of e-mails received during 15 minutes is 1.25.
The probability of receiving no e-mails during 15 minutes can be calculated using the Poisson distribution with λ = 1.25 and t = 1/4:
P(X = 0) = e^(-λt) * (λt)^0 / 0! = e^(-1.25/4) * (1.25/4)^0 / 0! ≈ 0.7788
Therefore, the probability of receiving no e-mails during 15 minutes is approximately 0.7788, or 77.88%.
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