P(at least n times) = 1 - (1 - p)^k, where p is the probability of the event happening and k is the number of trials.
The probability of an event happening at least n times out of k trials can be calculated using the formula P(at least n times) = 1 - (1 - p)^k. Here, p is the probability of the event happening, and k is the number of trials. The formula is based on the principle that the probability of an event happening at least n times is equal to one minus the probability of it happening less than n times. The probability of it happening less than n times is calculated by taking the probability of the event happening once, and then multiplying it by itself k times. This is because each trial is independent, and the probability of the event happening for each trial is the same. The result of this multiplication is then subtracted from one, which gives us the probability of it happening at least n times out of k trials
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There are 32 crates. Each crate holds 27 cans of soup. Which expressions that are NOT good ways to use compatible numbers to estimate the number of cans in the crates.a. 30 X 20b. 30 X 30c. 32 X 27d. 25 X 32e. 25 X 30
a)30*20 b)30*30 d)25*32 e)25*30 are NOT good ways to use compatible numbers to estimate the number of cans in the crates.
And the best expressions that is the good ways to use compatible numbers to estimate the number of cans in the crates is 32*27
As given in the question,
There are 32 crates. Each crate holds 27 cans of soup.
i.e. Number of total crates = 32
Number of can of soups in each crate = 27
The total number of cans of soup in every crates = 32*27
The total number of cans of soup in every crates = 864
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Let Z be a standard normal random variable and calculate the following probabilities, drawing pictures wherever appropriate. (Round your answers to four decimal places.)(a) P(0≤Z≤2.54)(b) P(0≤Z≤2)(c) P(−2.40≤Z≤0)(d) P(−2.40≤Z≤2.40)(e) P(Z≤1.36)(f) P(−1.25≤Z)(g) P(−1.40≤Z≤2.00)(h) P(1.36≤Z≤2.50)(i) P(1.40≤Z)(j) P(|Z|≤2.50)
(a) P(0≤Z≤2.54) represents the area under the standard normal curve between 0 and 2.54 on the x-axis. This can be found by using a standard normal table or calculator to find the area between 0 and 2.54, which is approximately 0.4966.
(b) P(0≤Z≤2) represents the area under the standard normal curve between 0 and 2 on the x-axis. This can be found by using a standard normal table or calculator to find the area between 0 and 2, which is approximately 0.4772.
(c) P(−2.40≤Z≤0) represents the area under the standard normal curve between −2.40 and 0 on the x-axis. This can be found by using a standard normal table or calculator to find the area between −2.40 and 0, which is approximately 0.3821.
(d) P(−2.40≤Z≤2.40) represents the area under the standard normal curve between −2.40 and 2.40 on the x-axis. This can be found by using a standard normal table or calculator to find the area between −2.40 and 2.40, which is approximately 0.7621.
(e) P(Z≤1.36) represents the area under the standard normal curve to the left of 1.36 on the x-axis. This can be found by using a standard normal table or calculator to find the area to the left of 1.36, which is approximately 0.9155.
(f) P(−1.25≤Z) represents the area under the standard normal curve to the right of −1.25 on the x-axis. This can be found by using a standard normal table or calculator to find the area to the right of −1.25, which is approximately 0.1151.
(g) P(−1.40≤Z≤2.00) represents the area under the standard normal curve between −1.40 and 2.00 on the x-axis. This can be found by using a standard normal table or calculator to find the area between −1.40 and 2.00, which is approximately 0.7170.
(h) P(1.36≤Z≤2.50) represents the area under the standard normal curve between 1.36 and 2.50 on the x-axis. This can be found by using a standard normal table or calculator to find the area between 1.36 and 2.50, which is approximately 0.0951.
(i) P(1.40≤Z) represents the area under the standard normal curve to the right of 1.40 on the x-axis. This can be found by using a standard normal table or calculator to find the area to the right of 1.40, which is approximately 0.0821.
(j) P(|Z|≤2.50) represents the area under the standard normal curve between −2.50 and 2.50 on the x-axis. This can be found by using a standard normal table or calculator to find the area between −2.50 and 2.50, which is approximately 0.5199.
In all cases, a standard normal table or calculator is used to find the area under the standard normal curve. The area represents the probability of the given event.
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Yields of 10 strawberry plants in a uniformity trial are given by two researchers as
3
239, 176, 235, 217, 234, 216, 318, 190, 181, and 225. Using these data:
a. Write the null and alternate hypotheses given you want to determine if the mean of
the 10 strawberry plants differs from 205 g.
b. Conduct a t-test at the 95% level of confidence to test the null hypothesis in part a.
c. Test the same hypothesis in part a at the 95% level of confidence using a Confidence
Interval
The hypotheses are
Null hypothesis: The mean of the 10 strawberry plants is equal to 205g (μ=205).Alternate hypothesis: The mean of the 10 strawberry plants is not equal to 205g (μ≠205).We fail to reject the null hypothesis in (b) and (c)
The null and alternate hypothesesHere, we have
The mean of the 10 strawberry plants differs from 205
So, the hypotheses are
Null hypothesis: μ=205Alternate hypothesis: μ≠205)A t-test at the 95% level of confidenceWe start by calculating the mean and the sample standard deviation
Using an online calculator, we have
Mean = 223.1
Standard deviation = 40.4
Calculate the t-statistic
t-statistic = (223.1 - 205) / (40.4 / √10) = 1.42
The degrees of freedom for this test are 9 (n - 1).
Using a t-distribution table, the critical value for a one-tailed t-test with 9 degrees of freedom and a 95% level of confidence is 1.833.
Since the calculated t-statistic of 1.42 is less than the critical value of 1.833, we fail to reject the null hypothesis.
Test the same hypothesis at the 95% level of confidence:Calculate the standard error:
Standard Error = 40.4 / √10 = 12.78
Calculate the z-statistic:
z-statistic = (223.1 - 205) / 12.78 = 1.41
In this case, the z-statistic (1.41) is less than the critical value (1.960) from the standard normal distribution table, so we accept the null hypothesis.
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3. Solve these systems of equations without graphing. Show your work using formal algebra.
a. 2x + 3y = 7
2y = 12x 2
b. 2x 9y = 12
3x + 18y = 18
a. 2x + 3y = 7
2y = 12x - 2
To solve this system of equations, we can begin by isolating one of the variables. Let's first isolate y in the second equation:
2y = 12x - 2
y = 6x - 1
Now we can substitute this expression for y into the first equation:
2x + 3(6x - 1) = 7
2x + 18x - 3 = 7
20x = 10
x = 1/2
Now that we know the value of x, we can substitute it back into the equation y = 6x - 1 to find the value of y:
y = 6(1/2) - 1
y = 3/2 - 1
y = -1/2
So the solution to this system of equations is (x, y) = (1/2, -1/2).
b. 2x - 9y = 12
3x + 18y = 18
To solve this system of equations, we can begin by using the first equation to solve for one of the variables. Let's solve for x:
2x - 9y = 12
2x = 9y + 12
x = (9y + 12)/2
Now we can substitute this expression for x into the second equation:
3((9y + 12)/2) + 18y = 18
(27y + 36) + 18y = 18
45y = -18
y = -4/5
Now we can substitute this value of y back into the equation x = (9y + 12)/2 to find the value of x:
x = (9(-4/5) + 12)/2
x = (3 + 12)/2
x = 15/2
So the solution to this system of equations is (x, y) = (15/2, -4/5).
find the standard deviation for the distribution of the number of people you talk to before finding your first piece of gum.
The standard deviation in statistics is a measurement of how much a group of values can vary or be dispersed.
What is standard deviation?The standard deviation in statistics is a measurement of how much a group of values can vary or be dispersed. A low standard deviation suggests that values are often close to the set's mean, whereas a large standard deviation suggests that values are dispersed over a wider range. The term "standard deviation" (or "") refers to the degree of dispersion of the data from the mean. Data are grouped around the mean when the standard deviation is low, and are more dispersed when the standard deviation is high.How dispersed the data is is indicated by the standard deviation. It expresses the deviation of each observed value from the mean. Any distribution will have roughly 95% of values within 2 standard deviations of the mean.To learn more about standard deviation refer to:
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Note that triangle ABD from part A is a 30 - 60 - 90 triangle.
Drag the tiles to the correct box to show how the Pythagorean theorem can be used to find
We will examine the 30-60-90 triangle concept in this session and learn everything there is to know about it, including its formula, definition, sides, area, and the rules that apply to this triangle.
What is the triangle of 30-60-90?A 30-60-90 triangle is a special sort of right triangle that always has angles that are 30, 60, and 90 degrees.
The angles of the triangles ABC and PQK in this instance are 30°, 60°, and 90°, respectively.
The side opposing the 30° angle, AB = y, will always be smaller because 30° is the triangle's smallest angle.
The side opposing the 60° angle, BC = y 3 = y 3, will be of medium length because 60° is the triangle's mid-sized degree angle.
The hypotenuse AC = 2y will be the greatest side on the side across from the 90° angle because 90° is the largest angle.
Considering that the Pythagorean Theorem is given by:
a² =b² +c²AD² + 1² = 2²AD² = 3²To learn more about triangle refer to:
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Complete question -
let f be the function defined above, for what value of b is f continuous at x=2?
For f to be continuous at x=2, b must be equal to 6. That is, when b=6, there is no break in the function at x=2, and the function is continuous.
To determine the value of b for which f is continuous at x=2, we need to first find the limit of f(x) as x approaches 2 from the left and from the right. From the left, the limit is 4b-4. From the right, it is 2b+2. To make the function continuous at x=2, we need to make sure that the left- and right-hand limits are equal. Setting the two limits equal to each other, 4b-4 = 2b+2, and solving for b yields b=6. Therefore, for f to be continuous at x=2, b must be equal to 6.
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please help! Thank you
The unit rate of change in this situation is 0.25 mile per hour.
What is the unit rate of change in this situation?The unit rate of change in this situation is 0.25 mile per hour.This means that for every 1 hour the painting crew works, they will paint 0.25 mile of the road.This rate of change can be calculated by dividing the total distance painted (9.5 miles) by the total amount of time (hours) it took to paint it (38 hours). Therefore, 9.5 miles/38 hours = 0.25 mile/hour.This unit rate of change indicates that the painting crew is consistently painting 0.25 mile of the road per hour.This is important because it helps the crew accurately plan how long it will take to complete the 24-mile stretch of road, as well as how much paint they need to purchase and how much manpower is needed.To learn more about the unit rate of change refer to:
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3. Consider a large slice of air over a city to be a box 125 km x 125 km (L x W) that reaches up to an altitude of 1.5 km. Clean air is blowing into the box along one of its sides with a speed of 4 m/s. Suppose an air pollutant with a reaction rate of k = 0.23/hr is emitted into the box at a total mass loading rate of 10 kg/s. a. Find the steady state concentration if the air in the box is assumed to be perfectly mixed. b. If the wind speed suddenly drops to 1 m/s, estimate the concentration of this pollutant 3-hr later.
a. Steady state concentration = 10/0.23 = 43.48 kg/m^3
b. Concentration 3 hrs later = 10/0.23 * e^(-3*0.23/1) = 34.99 kg/m^3
a. The steady state concentration of the air pollutant can be found by the equation C = M/k, where C is the concentration, M is the mass loading rate, and k is the reaction rate. In this case, C = 10 kg/s/0.23/hr = 43.48 kg/m^3. b. To calculate the concentration of the pollutant 3 hours later, we can use the equation C = M/k * e^(-kt), where t is the time in hours. In this case, C = 10/0.23 * e^(-3*0.23/1) = 34.99 kg/m^3. This equation takes into account the decrease in wind speed and the decrease in reaction rate due to the decrease in concentration.
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1.4.3 Quiz: Draw a Diagram
Question 2 of 6
Read the problem below and find the solution. Draw a diagram on your own
paper to help solve it.
A group of 23 friends gets together to play a sport. First, people must be
divided into teams. Each team has to have exactly 4 players, and no one can
be on more than one team. How many teams can they make? (It is possible
that not everyone can be on a team.)
(Do not include units in your answer.)
Answer here
+
SUBMIT
There can be a maximum of 5 teams.Three persons will be excluded.
What is an expression?Mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented using mathematical symbols. They can also be used to denote the logical syntax's operation order and other properties.
Considering that 23 pals gather to play a sport together.The participants must first be divided into teams. There must be exactly 4 participants on each team, and no one may play for more than one team.
The number of teams will be determined using the formulas below:
Total teams = 23 / 4 = 20 / 4 = 5.
Three persons will be left.
Therefore, there can be a maximum of 5 teams.Three persons will be excluded.
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To find the number of teams that can be made with 23 friends, where each team has exactly 4 players, we can divide the total number of friends by the number of players per team.
Number of friends = 23
Number of players per team = 4
To find the number of teams, we divide the number of friends by the number of players per team:
23 / 4 = 5 remainder 3
Since we cannot have a team with 3 players, we can only form complete teams of 4 players. Therefore, the maximum number of teams that can be formed is 5.
Therefore, the answer is 5 teams.
H
The 3 points plotted below are on the graph of y=b².
Based only on these 3 points, plot the 3 corresponding points that must be on the graph of
y = log, z by clicking on the graph.
y
161
14+
12-
10+
8
6
4-
Click to add points
2+
●
6
8
10
12
14
16
The 3 corresponding points that must be on the graph are (1,0),(4,1),(16,2). for proper calculation please scroll down.
What is Function?A relation between a collection of inputs and outputs is known as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function.
Points on the graph are A(0,1), B(1,4),C(2,16).
Now, these are the points on the graph for the function
y=b^x
Since, we know that the funtion
y=[tex]log_{b}X[/tex]
is the inverse of
y=b^x
Therefore, the points are the reflection of the given point.
So, change the x coordinate with y and y with x to get the points for the function
y= [tex]log_{b}X[/tex]
The points will become,
(0, 1) ~ (1, 0)
(1, 4) ~ (4, 1)
(2, 16) ~ (16, 2)
Therefore, the 3 corresponding points that must be on the graph are (1, 0), (4, 1), (16, 2).
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In a class there are 42 students. the numbers of girls is 2times the numbers of boys. how many boys and girls are there in the class
x = No. of girls
y = no. of boys
2y + y = 42
3y = 42
y = 14
no. of girls = 2 × 14 = 28
no of boys = 14
Factor the trinomial by grouping. -
8x²2² +14x+3.
a. Find two numbers whose product is 8.3=24 and whose sum is 14.
b. Write 14x using the factors from part (a).
c. Factor by grouping.
a. The two numbers whose product is 24 and whose sum is 14 are 6 and 4
b. 14x = 6x + 8x
c. 8x²2² + 6x + 8x + 3
=8x²2² + (6x + 8x) + 3
=8x²2² + 14x + 3
The trinomial 8x²2² + 14x + 3 can be factored by grouping as (8x²2² + 14x) + 3
In a group of 30 pupils, 13 play the flute only. 1 plays the piano only. 4 play both instruments. A student is chosen at random. What is the probability the student plays neither instrument?
A student who is chosen at random has a 2/5 chance of playing neither instrument.
What is probability?Probability is a number that expresses the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.
Given, a group of 30 pupils, 13 play the flute only. 1 plays the piano only. 4 play both instruments
From the general formula of probability:
Probability = desired outcome / total outcomes
Total outcomes = 30
In our case desired outcome = is chosen student plays neither instrument
desired outcome = 30 - 13 -1 -4
desired outcome = 12
thus,
Probability = 12/30
probability = 2/5
Therefore, the probability of a randomly selected student playing neither instrument is 2/5.
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You buy a milkshake from a shoppe that only has chocolate, vanilla, and strawberry flavors. Find the probability that your milkshake consists of more than 3
flavors.
Step-by-step explanation:
soln on
n(s)=6
n(p)=3
therefore
probability =6/3
David draws a quadrilateral. Opposite sides are parallel. The shape has no right angles. All four sides are not the same length. What quadrilateral did David draw?
Since David drew a quadrilateral with opposite sides parallel, no right angles and all four sides are not the same length, the quadrilateral would be referred to as a scalene trapezoid.
What are the types of quadrilateral?In Geometry, there are different types of quadrilateral and these include the following:
ParallelogramSquaresRectangleRhombusTrapezoidWhat are properties of a scalene trapezoid?Generally speaking, some of the properties of a scalene trapezoid include the following:
The opposite sides of a scalene trapezoid are parallel. A scalene trapezoid has no right angles. All four sides of a scalene trapezoid are not the same length.In conclusion, we can reasonably infer and logically deduce that David drew a scalene trapezoid.
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NEED HELP ASAP!!! DUE TOMORROW
Answer:M<R corresponds to M<T, meaning M<R is 4x+1.
Step-by-step explanation:
the cost of chesse increased by 25%. how much is the new price of the cheese that originally cost $4.20. PLEASE HELP WILL GIVE BRAINLIST FOR SOLULTIONS
Answer:
$5.25
Step-by-step explanation:
Original cost of cheese = $4.20
An increase in price of 25% means the cost increase = 25% of $4.20
25% in decimal = 25/100 = 0.25 (or 1/4)
25% of $4.20 = 0.25 x $4.20 = $1.05
or, if you are more comfortable working with fractions
25% of $4.20 = 1/4 x $4.20 = $1.05
This is only the cost increase.
Add this increase to the original cost to get the new price:
New price = $4.20 + $1.05 =$5.25
convert the following numbers from the given base to the other three bases listed in the table: decimal binary octal hexadecimal 369.3125 ? ? ? ? 10111101.101 ? ? ? ? 326.5 ? ? ? ? f3c7.a
Decimal: 369.3125 Binary: 101111001.0101 Octal: 571.5 Hexadecimal: 171.A8. The number 369.3125 can be converted from decimal to binary, octal, and hexadecimal as follows: Binary: 101111001.0101, Octal: 571.5, Hexadecimal: 171.A8.
Decimal: 10111101.101 Binary: 10111101.101 Octal: 277.125 Hexadecimal: BD.1A
Decimal: 326.5 Binary: 10100010.1 Octal: 502.1 Hexadecimal: 142.8
Decimal: F3C7.A82 Binary: 1111001111100111.10101000010 Octal: 36367.5212 Hexadecimal: F3C7.A82
To convert a number from one base to another, we can use the following steps:
1. Identify the number and its base.
2. Convert the number to its equivalent in decimal form.
3. Convert the decimal form of the number to the desired base.
For example, to convert the number 369.3125 from decimal to binary, octal, and hexadecimal, we can follow these steps:
1. Identify the number and its base: 369.3125 is a decimal number.
2. Convert the number to its equivalent in decimal form: 369.3125 is already in decimal form, so we don't need to convert it.
3. Convert the decimal form of the number to the desired base:
Binary: 101111001.0101
Octal: 571.5
Hexadecimal: 171.A8
The number 369.3125 can be converted from decimal to binary, octal, and hexadecimal as follows: Binary: 101111001.0101, Octal: 571.5, Hexadecimal: 171.A8. Similarly, the number 10111101.101 can be converted to binary, octal, and hexadecimal as follows: Binary: 10111101.101, Octal: 277.125, Hexadecimal: BD.1A. Finally, the number 326.5 can be converted to binary, octal, and hexadecimal as follows: Binary: 10100010.1, Octal: 502.1, Hexadecimal: 142.8, and the number F3C7.A82 can be converted to binary, octal, and hexadecimal as follows: Binary: 1111001111100111.10101000010, Octal: 36367.5212, Hexadecimal: F3C7.A82.
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For the same particle as in question 1, write and evaluate an integral expression, in terms of sine and cosine, that gives the distance the particle travels from t = 1.5 to t = 2.75.
An integral expression, in terms of sine and cosine, that gives the distance the particle travels from t = 1.5 to t = 2.75 is 1.5→2.75 √{(-2sin(πt))²+(4cos(πt))²} dt.
We have been given two functions representing the displacement of the particle,
x(t)=2cos(πt)
y(t)=4sin(πt)
To find the velocity vector with the help of these functions, we have to differentiate them with respect to time
i.e,
dx(t)/dt=d{2cos(πt)}/dt=-2sin(πt)
dy(t)/dt=d{4sin(πt)}/dt=4cos(πt)
and finally, the velocity vector would be written as,
v(t)=-2sin(πt) i +4cos(πt) j
Now to get the distance for the given limits we have to integrate the magnitude of the given velocity
i.e, integrate 1.5→2.75 √{(-2sin(πt))²+(4cos(πt))²} dt
which would approximately result in a value of 3.69 units in length.
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2. If 9 men can do a piece of work in 6 days, how long will it take 12 men to do the same work?
Answer: 4.5 Days
Step-by-step explanation:
The work requires 9 men x 6 days or 54 man-days.
So 12 men will do the same work in 54 man-days/12 men
= 4.5 days.
I hope this is right sorry if its not
A school group is going on a trip to a museum. Admission is $10 per student. Eight students have guaranteed they will go, but additional students may be going. The total admission the group will have to pay can be represented by the expression 10(8 + x). The group leader simplifies this expression to 80 + x to calculate how much money they will need. Is this correct? If 6 additional students go, will they have enough money to cover the admission cost?
The value of the equation is y = 10 ( 8 + x ) = 80 + 10x , where y is the total cost of admission
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
The cost of admission per student is c = $ 10
Let the total cost of admission be represented as y
Now , the number of students = 8 students
The number of additional students = x
So , the total cost of admission y = 10 ( x + 8 )
On simplifying the equation , we get
The total cost of admission y = 10x + 80
Now , if 6 more students go , the equation will be
The total cost of admission y₁ = 10 ( x + 6 + 8 )
On simplifying the equation , we get
The total cost of admission y₁ = 10x + 140
Hence , the equation is y = 10x + 80
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Y=2x + 9; 6x -3y = 0 / 4x -2y = 3; 2x -4y -3 cual de la siguientes parejas de rectas no son paralelas?
Yes, 6x -3y = 0 and 2x -4y -3 are parallel. This is because they both have the same slope, -3/2. The slope of a line can be calculated from its equation, by dividing the coefficient of the x term by the coefficient of the y term.
How to solve the problem?Two lines are parallel if they have the same slope. The slope of a line is represented by the letter "m" in the equation y = mx + b.
In this case, Y=2x + 9 has a slope of 2 and 4x -2y = 3 has a slope of -1/2, these slopes are different, which means that these two lines are not parallel.
On the other hand, 6x -3y = 0 and 2x -4y -3 are parallel because they have the same slope, -3/2. The slope of a line is the amount of change in the y coordinate for each unit of change in the x coordinate.
Yes, 6x -3y = 0 and 2x -4y -3 are parallel. This is because they both have the same slope, -3/2. The slope of a line can be calculated from its equation, by dividing the coefficient of the x term by the coefficient of the y term.
In the case of 6x -3y = 0, the slope is -3/6 = -1/2. In the case of 2x -4y -3, the slope is -4/2 = -2. Since both lines have the same slope, they are parallel. This means that they never intersect and have the same direction.
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The numbers 840 and 8316, written as the products. of their prime factors, are 840= 2¹ × 3 × 5 × 7 and 8316= 22 x 3³ x 7 x 11. Hence, find
(i) the greatest whole number that will divide both 840 and 8316 exactly,
(ii) the smallest non-zero whole number that is divisible by both 840 and 8316.
Pls help asap
Answer:
1) 84
2) 83160
Step-by-step explanation:
Greatest common divisor and Least common multiple
840 = 2³ * 3 * 5 * 7
8316 = 2² * 3³ * 7 * 11
i) The greatest whole number that will divide both 840 and 8316 is the
Greatest common divisor. Find only the common factors.
Greatest common divisor = 2² * 3 * 7
= 84
84 is the greatest whole number that divides both 840 and 8316.
Answer: 84
ii) The smallest non-zero whole number that is divisible by 840 and 8316 is Least common multiple of 840 & 8316.
Least common multiple = 2³ * 3³ * 5 * 7 * 11
= 8 * 27 * 5 * 7 * 11
=83160
There are three children, three pets, and three favorite colors. the children are: angela, lisa, and susan. the pets are: a cat, a dog, and a fish. the colors are: blue, green, and red.
6 is the number of ways described when There are 3 children, 3 pets, and 3 favorite colors. We can represent the children, pets, and colors in a list and explained below .
Children:
1. Angela
2. Lisa
3. Susan
Pets:
1.Cat
2. Dog
3. Fish
Colors:
1.Blue
2.Green
3. Red
We can use the combination rule to find the number of ways to assign a child, a pet, and a color to each other. The combination rule states that if we have n items and want to choose k items at a time, the number of ways to do this is given by the formula:
n! / (k! (n-k)!)
Where n! denotes the factorial of n, meaning the product of all positive integers less than or equal to n.
In this case, we have 3 children, 3 pets, and 3 colors, and we want to assign one of each to each other. So we can use the formula to find the number of ways to do this:
3! / (1! (3-1)!) = 3! / (1! 2!) = 3 * 2 * 1 / (1 * 2) = 3
So there are 3 ways to assign a child, a pet, and a color to each other.
We can also use the permutation rule to find the number of ways to assign a child, a pet, and a color to each other. The permutation rule states that if we have n items and want to choose k items at a time and order matters, the number of ways to do this is given by the formula:
n! / (n-k)!
In this case, we have 3 children, 3 pets, and 3 colors, and we want to assign one of each to each other. So we can use the formula to find the number of ways to do this:
3! / (3-3)! = 3! / 0! = 3 * 2 * 1 / 1 = 6
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A train leaves New York for Boston, 200 miles away, at 5:00 P.M. and averages 75 mph. Another train leaves Boston for New York on an adjacent set of tracks at 4:00 P.M. and averages 65 mph. At
what time will the trains meet? (Round to the nearest minute.)
They have both travelled a total of 160 miles, they will now combine. They will get together at 5:46:40.
What time will the trains meet?50t = 40(t+1)
10t = 40
They are not travelling in the same way. They would cross paths in 4 hours if they were travelling in the same direction.
Before the NY train departs for Boston, a Boston train goes 40 miles.
After they have both travelled a total of 160 miles, they will now combine.
40x+50x=160
90x=160
x=16/9
1:46:40
After they have both travelled a total of 160 miles, they will now combine. They will get together at 5:46:40.
They will get together at 5:46:40.
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A rectangular garden has a walkway around it. The area of the garden is 2(5.5x +3.5). The combined area of the garden and the walkway is 3.5(8x + 6). Find the area of the walkway around the garden as the sum of two terms.
The area of the walkway around the garden is 17x+14.
What is area?Area is the amount of space occupied by a two-dimensional figure. In other words, it is the quantity that measures the number of unit squares that cover the surface of a closed figure. The standard unit of area is square units which is generally represented as square inches, square feet, etc.
Given that, the area of the garden is 2(5.5x +3.5). The combined area of the garden and the walkway is 3.5(8x + 6).
Area of a walkway = The combined area of the garden and the walkway - The area of the garden
= 3.5(8x+6)-2(5.5x +3.5)
= 28x+21-11x-7
= 17x+14
Therefore, the area of the walkway around the garden is 17x+14.
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Consider the linear system
x+y-y z=2
x+2y+ z=3
x+y+(k^2-5)z= k
where k is an arbitrary constant. For which value(s) of k does this system have a unique solution? For which value(s) of k does the system have infinitely many solutions? For which value(s) of k is the system inconsistent?
The system is inconsistent for k=0.
The system has a unique solution when k=1 and k=-3. To see this, we plug in these values of k into the system and solve the resulting three equations in three unknowns. For k=1, we have x=2, y=1, and z=0. For k=-3, we have x=3, y=2, and z=0.
The system has infinitely many solutions when k=5. In this case, we have x+y-5z=2, x+2y+z=3, and x+y+25z=5, which yields the solution x=2, y=1, and z=0/5. Since any non-zero value of z will also satisfy the system, the system has infinitely many solutions.
The system is inconsistent when k=0. In this case, we have x+y=2, x+2y+z=3, and x+y-z=0, which has no solution. Therefore, the system is inconsistent for k=0.
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The graph shows the relationship between time and the number of soda bottles a machine can make. Use the points (5,100) and (7,140) to find the number of soda bottles the machine can make each minute.
Based on the graph which shows the relationship between time and the number of soda bottles a machine can make, this machine can make 20 soda bottles each minute.
How to calculate the number of soda bottles?In Geometry, the rate of change of any straight line simply refers to the slope and it can be calculated by using this mathematical equation (expression);
Rate of change (slope), m = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Rate of change (slope), m = (y₂ - y₁)/(x₂ - x₁)
From the information provided in the graph above, we can logically deduce the following data points located on the line:
Points on the x-coordinate = (5, 7).Points on the y-coordinate = (100, 140).Substituting the given data points into the rate of change formula, we have the following;
Rate of change (slope), m = (y₂ - y₁)/(x₂ - x₁)
Rate of change (slope), m = (140 - 100)/(7 - 5)
Rate of change (slope), m = 40/2
Rate of change (slope), m = 20.
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Write the number in standard form.
-2+√-8
2
The standard form of the given number -2+√-8 is -2+2i
What is the imaginary number?
An imaginary number is a number that can be written in the form of a real number multiplied by the imaginary unit, denoted by the symbol "i". The imaginary unit, "i", is defined as the square root of -1, which is a number that when multiplied by itself results in -1.
The given number cannot be written in standard form, because √-8 is an imaginary number and cannot have a real value. The square root of a negative number is an imaginary number, and these numbers are denoted by the imaginary unit, i.
The imaginary unit is defined as the square root of -1.
The number -2+√-8 is equal to -2+i*2.
The standard form of a complex number is a+bi, where a and b are real numbers and i is the imaginary unit.
So, The standard form of the given number -2+√-8 is -2+2i
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