The value of y when x = -2, 0,2 is 1/49, 7, 49.
Simplification is an algebraic expression is when we utilize a range of approaches to make algebraic expressions more efficient and compact - in their simplest form - without changing the value of the original expression.
Given function y =\(7^{x}\)
We have to determine the y values when x = -2, 0, 2
Now substitute the x values in the given function
If x = -2 then
Y = 7(-2)
Y = 1/49
If x = 0 then
Y = 7(0)
Y = 1
If x = 2 then
Y = 7(2)
Y = 49
Therefore the value of y when x = -2, 0 ,2 is 1/49, 7 , 49
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x² + 5x + 6
Factor each polynomial.
pls help me with this:((((
А
The population of a city increased by 140 people last year. Which situation, when combined with that increase in population, results in a zero overall change in population?
The population of the city increases by 140 during the next year.
The population of the city decreases by 140 during the next year.
The population of the city stays constant during the next year.
D The population of the city decreases by 10 people per month during the next year.
B
С
Step-by-step explanation:
..
Answer:
D
Step-by-step explanation:
\(x+\frac{2}{x} = 3\)
solve for x
must be 2 variables that equal to x
Please put the steps.
Answer:
x=2, x=1
Step-by-step explanation:
Multiply both sides by x, so you get (x^2)+2=3x, which comes from \(xx+\frac{2}{x}x=3x\)
Solve for (x^2)+2=3x
(x^2)-3x+2=0
(x-2)(x-1)=0, use box method or FOIL if needed
x=2,x=1
ly| ≤3
Are the lines on graph at 3 and -3 also part of the answer?
Answer:
Yes, the lines on the graph at 3 and -3 a part of the solution,
Step-by-step explanation:
The inequality \(|y| \leq 3\) contains all the values of \(y\) 3 units from the origin including the values 3 and -3.
Thus, the lines on the graph y =-3 and y = 3 are the part of the solution.
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Which statements can be used to compare the
characteristics of the functions? Select two options.
Of(x) has an all negative domain.
g(x) has the greatest maximum value.
All three functions share the same range.
Oh(x) has a range of all negative numbers.
All three functions share the same domain.
The two statements that can be used to compare the characteristics of the functions are: 1. Of(x) has an all negative domain. 2. Oh(x) has a range of all negative numbers.
The correct answer to the given question is option A and C.
Among the given options, the two statements that can be used to compare the characteristics of the functions are:
1. Of(x) has an all negative domain.
2. Oh(x) has a range of all negative numbers.
Let's analyze each statement and its implications:
1. Of(x) has an all negative domain: This statement indicates that the function Of(x) only takes on negative values for its input (x). It means that all the values in the domain of Of(x) are negative numbers.
2. Oh(x) has a range of all negative numbers: This statement refers to the output (range) of the function Oh(x) and states that all the values it produces are negative numbers.
By comparing these statements, we can infer that Oh(x) and Of(x) both involve negative numbers in their characteristics.
Specifically, Of(x) has an all negative domain, while Oh(x) has a range consisting of all negative numbers.
However, it's important to note that the remaining statements about the functions sharing the same range or domain are not necessarily true based on the information provided.
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Provide a detailed distinction between the two training
methodologies that may be utilised in the organisation, as well as
the popular methods for each.
In an organization, two popular training methodologies that can be utilized are on-the-job training and off-the-job training.
Let's examine each methodology along with their popular methods:
1. On-the-Job Training:
On-the-job training refers to the process of acquiring knowledge and skills while performing tasks and responsibilities directly related to one's job. It takes place within the actual work environment and provides hands-on experience. Some popular methods of on-the-job training include:
a. Job Shadowing: This method involves a new employee observing and working closely with an experienced employee, learning from their day-to-day activities and tasks.
b. Mentoring: In this method, a more experienced employee (mentor) guides and supports a less experienced employee (mentee) by providing advice, feedback, and sharing their expertise.
c. Coaching: Similar to mentoring, coaching involves a more experienced employee providing guidance and support to enhance the skills and performance of the employee being coached.
d. Apprenticeships: This method combines on-the-job training with classroom instruction. It allows individuals to learn a trade or skill through practical experience while working alongside skilled professionals.
2. Off-the-Job Training:
Off-the-job training refers to the process of learning and acquiring skills outside of the regular work environment. It usually takes place in a separate training facility or classroom setting. Some popular methods of off-the-job training include:
a. Workshops and Seminars: These are interactive sessions where participants learn new skills, gain knowledge, and exchange ideas on specific topics facilitated by subject-matter experts.
b. Conferences and Conventions: These events bring together professionals from a particular industry or field to attend presentations, panel discussions, and networking opportunities to learn about new trends and developments.
c. E-Learning and Online Courses: With advancements in technology, online platforms offer various courses and training programs that individuals can access remotely at their own pace and convenience.
d. Simulations and Role-Playing: These methods involve creating artificial scenarios or situations that closely resemble real work situations, allowing participants to practice and develop skills in a controlled environment.
e. Case Studies and Group Discussions: Participants analyze real-life scenarios and engage in group discussions to understand problem-solving techniques, decision-making processes, and best practices.
It's important to note that the selection of the training methodology and methods depends on the specific needs, goals, and resources of the organization, as well as the desired learning outcomes for the employees. A combination of both on-the-job and off-the-job training can often be beneficial for comprehensive skill development and knowledge acquisition.
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in the recent year 18.2% of all registered doctors were females. If there were 57,000 females registered doctors that year what was the total number of registred doctors
round your answer to the nearest whole number.
Out of a journey of 300km;the firt part of ditance 85km i covered at a peed of 51km/h, the econd part of 90km at a peed of 135km/h and the remaining ditance at a peed of 75km/h. Find:
(1) the ditance covered at a peed of 75km/h. (2) the total time taken. (3) the average peed for the whole journey
125 km are traveled when traveling at a pace of 75 km/h.
The entire travel time to complete 300 km is 1.14 hours, with an average travel speed of 263.15 km/hr.
Given that,
The first 85 kilometers are traveled at a 51 km/hr pace.
A pace of 135 km/hr is used to cover the second 90 km stretch.
75 km/hr is used to cover the remaining distance.
Journey distance is 300 kilometers.
Distance traveled at 75 km/hr is equal to 300 - (85 + 90) = 125 kilometers.
The total time required was 300/261 miles per hour, or 1.14 hours.
The distance traveled divided by the time required equals 300/1.14, or 263.15 kilometers per hour, as the average speed for the whole trip.
Thus, 125 km are traveled when traveling at a pace of 75 km/h.
The entire travel time to complete 300 km is 1.14 hours, with an average travel speed of 263.15 km/hr.
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PLEASE HELP FAST pleaaaaaaaaaaaaaaaaaaaaaaase
Answer:
i think the answer is C. 1.5w^2 + 7.5w + 9
Jordan has $20 to spend at Walgreens. All of the snacks at Walgreens cost $1.25 each. How much
money will Jordan have left if he buys 6 snacks?
$11.25
$11.75
$12.50
$12.25
Answer:
$12.50
Step-by-step explanation:
1.25 * 6 = 7.5
20-7.5 = 12.5
determine whether the sequence converges or diverges. if it converges, find the limit. (if the sequence diverges, enter diverges.) an = e−1/√n
The sequence converges to 1 found using the limit test.
To determine whether the sequence converges or diverges, we have to use the limit test. If the sequence is convergent, we have to find its limit as well.
A sequence is convergent if and only if its limit exists and is finite. It's divergent if it doesn't converge. It's not important whether the limit is positive, negative, or zero. A sequence that increases without bound or decreases without bound diverges.Let's move on to the solution.
To check whether the given sequence converges or diverges, we'll use the limit test.
If an > 0 for n > N, then lim an = 0 → the sequence converges to zero.
If an > 0 for n > N and lim an = L > 0 → the sequence converges to L.
If an > 0 for n > N and liman = ∞ → the sequence diverges to infinity.
If an < 0 for n > N and liman = - ∞ → the sequence diverges to negative infinity.
If an and bn > 0 for n > N, and liman/bn = C > 0 → the sequence converges to C.
an = e−1/√n
Here, n > 0. Also, e is a constant value, so we can rewrite the formula as;
an = e * e^(-1/√n)
Since e is a positive constant, we can ignore it for the limit test.
Now, let's find the limit using the limit test;
\(lim_an = lim e^(-1/√n)\)as n approaches infinity
This can be simplified as;
\(liman = lim 1/e^(1/√n)\) as n approaches infinity
Since e is a positive constant, it will remain as it is, and we'll work with the other half;
lim 1/e^(1/√n) as n approaches infinity
We can write
e^(1/√n) as \(e^(1/n^(1/2))\), which means;
\(lim 1/e^(1/√n) = lim 1/e^(1/n^(1/2))\) as n approaches infinity
Since the power of n in the exponent is increasing as n approaches infinity, the denominator will become too large, resulting in an exponent of zero, which gives 1.e.g.,
1/√1 = 1,
1/√2 = 0.7,
1/√3 = 0.6,
1/√4 = 0.5,
1/√5 = 0.45, ...
Therefore, as n approaches infinity, 1/n^(1/2) approaches zero, and the denominator becomes infinite, causing the fraction to approach zero.
lim_an = lim 1/e^(1/n^(1/2)) as n approaches infinity= 1/1= 1
Therefore, the sequence converges to 1.
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PLEASE HELP IM GONNA FAIL I NEED HELP NOT JUST AN ANSWER
14b x 13 + 12 = ?
I don't know how to begin! Will mark brainliest!
Answer: 2(7bx^13+6)
Step-by-step explanation:
Factor 2 out of 14bx13
14bx13 + 12 = 2 • (7bx13 + 6)
Answer:
182b +12
Step-by-step explanation:
14b × 13 +12
(14×13)b +12
182b +12
A state highway patrol official wishes to estimate the percentage/proportion of drivers that exceed the speed limit traveling a certain road.
A. How large a sample is needed in order to be 95% confident that the sample proportion will not differ from the true proportion by more than 3 %? Note that you have no previous estimate for p.
B. Repeat part (A) assuming previous studies found that the sample percentage of drivers on this road who exceeded the speed limit was 65%
A) Approx. 1067 is the required sample size to ensure 95% confidence that the sample proportion will not differ from the true proportion by more than 3%.
B) When the previous estimate is 65%, approx. 971 is the sample size needed to achieve 95% confidence that the sample proportion will not differ by more than 3% from the true proportion.
How to calculate the sample size needed for estimating the proportion?To determine the sample size needed for estimating the proportion of drivers exceeding the speed limit, we can use the formula for sample size calculation for proportions:
n = (Z² * p * (1 - p)) / E²
where:
n = the sample size.
Z = the Z-value associated with the confidence level of 95%.
p = the estimated proportion or previous estimate.
E = the maximum allowable error, which is 3% or 0.03.
We calculate as follows:
A. No previous estimate for p is available:
Here, we will assume p = 0.5 (maximum variance) since we don't have any prior information about the proportion. So, adding the values into the formula:
n = (Z² * p * (1 - p)) / E²
n = ((1.96)² * 0.5 * (1 - 0.5)) / 0.03²
n= (3.842 * 0.5 * (0.5))/0.03²
n = (1.9208*0.5)/0.0009
n ≈ 1067.11
Thus, to be 95% confident that the sample proportion will not differ from the true proportion by more than 3%, a sample size of approximately 1067 is required.
B. Supposing previous studies found that the sample percentage of drivers who exceeded the speed limit is 65%:
Here, we have a previous estimate of p = 0.65:
Putting the values into the formula:
n = (Z²* p * (1 - p)) / E²
n = ((1.96)² * 0.65 * (1 - 0.65)) / 0.03²
n= (3.842 * 0.65 *(0.35))/0.0009
n ≈ 971
Hence, with the previous estimate of 65%, a sample size of approximately 971 is necessary to be 95% confident that the sample proportion will not differ from the true proportion by more than 3%.
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Detailly write notes on the following topics in railway:
a) Station layout (5 pages)
b) high speed train
The layout of a railway station will vary depending on the size and complexity of the station. High-speed trains offer a number of advantages over conventional trains, but they also have some disadvantages.
Station Layout
A railway station is a facility where passengers can board and disembark trains. Stations typically have a number of different areas, including:
Platforms: Platforms are the areas where trains stop to allow passengers to board and disembark. Platforms are typically made of concrete or asphalt and are located alongside the tracks.
Trainman Blog
Waiting areas waiting areas are areas where passengers can wait for their train. Waiting areas are typically located inside the station building and may have seating, restrooms, and vending machines.
IRCTC Help
Ticketing areas are where passengers can purchase tickets for their train journey. Ticketing areas are typically located inside the station building and may have staffed counters or self-service ticket machines.
Times of India
Baggage claim areas are where passengers can collect their luggage after disembarking from a train. Baggage claim areas are typically located inside the station building and may have conveyor belts or carousels where luggage is delivered.
The Logical Indian
Station buildings are structures that house the various facilities and services found at a railway station. Station buildings may be large or small, depending on the size of the station.
Swarajya
Trackside areas are the areas alongside the tracks where trains operate. Trackside areas may have a number of different features, such as signals, switches, and level crossings.
Railway trackside areaOpens in a new window
Mumbai Mirror
The layout of a railway station will vary depending on the size and complexity of the station.
High Speed Train
A high-speed train is a train that travels at speeds of over 200 kilometers per hour (124 miles per hour). High-speed trains are typically used for long-distance travel, as they can cover large distances quickly and efficiently.
There are a number of different types of high-speed trains, each with its own design and specifications. However, all high-speed trains have a number of common features, including:
Lightweight construction are typically made of lightweight materials, such as aluminum and composites. This helps to reduce the weight of the train and improve its fuel efficiency.
Aerodynamic design high-speed trains are designed to be as aerodynamic as possible. This helps to reduce drag and improve the train's top speed.
Advanced braking systems high-speed trains need to be able to stop quickly and safely. This is why they typically have advanced braking systems, such as disc brakes and anti-lock braking systems.
High-tech signaling systems high-speed trains need to be able to operate safely at high speeds. This is why they typically have high-tech signaling systems that allow them to communicate with each other and with the railway infrastructure.
High-speed trains have a number of advantages over conventional trains, including:
Faster travel times high-speed trains can travel at speeds that are twice or even three times faster than conventional trains. This can significantly reduce travel times for long-distance journeys.
Reduced environmental impact high-speed trains are typically more fuel-efficient than conventional trains. This means that they have a lower environmental impact.
Improved safety high-speed trains are typically equipped with advanced safety features that can help to prevent accidents.
However, high-speed trains also have a number of disadvantages, including:
High cost high-speed trains are typically more expensive to build and operate than conventional trains.
Limited availability high-speed trains are not available in all countries or on all routes.
Demand for high-speed rail there is a high demand for high-speed rail in some countries, but not in others. This can make it difficult to justify the high cost of building and operating high-speed trains.
Overall, high-speed trains offer a number of advantages over conventional trains, but they also have some disadvantages. The decision of whether or not to invest in high-speed rail is a complex one that needs to be made on a case-by-case basis.
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Aayan took a test and got 5/7 of the questions correct. If he got 65 questions correct, how many questions were there in the test?
Our answer of 91 questions is correct. Aayan took a test with a total of 91 questions.
To solve this problem, we can set up a proportion based on the information given and use algebra to find the total number of questions on the test.
Let's denote the total number of questions on the test as 'x'. We know that Aayan got 5/7 of the questions correct, which means he got 5/7 of the total number of questions correct.
We can set up the proportion:
(5/7) = 65/x
To solve for 'x', we can cross-multiply:
5x = 7 * 65
5x = 455
Next, we divide both sides of the equation by 5 to isolate 'x':
x = 455/5
x = 91
Therefore, there were 91 questions in the test.
To verify our answer, we can check if Aayan getting 65 questions correct is indeed 5/7 of the total number of questions.
65 is indeed 5/7 of 91:
(5/7) * 91 = 65
Therefore, our answer of 91 questions is correct. Aayan took a test with a total of 91 questions.
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The mode of evolution responsible for the production of recombinant influenza viruses composed of a genome derived from two different influenza variants is called _____.
The mode of evolution responsible for the production of recombinant influenza viruses composed of a genome derived from two different influenza variants is called reassortment.
Reassortment occurs when two or more different strains of influenza viruses infect the same host, such as a human or an animal, and exchange genetic material. This process leads to the creation of a new virus with a genome that consists of segments from different parental strains.
In the case of influenza viruses, their genomes are segmented, meaning they consist of multiple RNA segments. Each segment carries specific genetic information necessary for viral replication and assembly. During reassortment, segments from different parental viruses can mix and combine, resulting in the formation of a novel virus with a unique combination of genetic material.
Reassortment plays a significant role in the emergence of new influenza strains, including those with pandemic potential. It contributes to genetic diversity and can lead to the generation of viruses with altered antigenic properties, making them capable of evading preexisting immunity in the population.
Understanding the mechanisms of reassortment is crucial for the surveillance and monitoring of influenza viruses, as it helps in predicting and responding to the emergence of new strains and designing effective vaccines to combat them.
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In the figure below, there are three right trangles. Complete the following.
A
C
D
B
(a) Write a similiarity statement relating the three right triangles.
ACDA~A~A
(b) Complete each proportion.
BD
BC
BC
DA
DC
=
0
BD
X
5
Part (a)
Let one of the angles be \(\theta\). After solving for all of the other angles using the triangle sum theorem, we see that \(\triangle CDA \sim \triangle BDC \sim \triangle BCA\).
Part (b)
\(\frac{BD}{BC}=\frac{BC}{CA}, \frac{DA}{DC}=\frac{DC}{DB}\)
Give the values of a,b and c needed to write the equations Standard form
2/3(x+5)-1
The general form of the equation 2/3(x - 4)(x + 5) = 1 is 2x^2 + 2x - 43 = 0
and the coefficients of general form a = 2, b= 2 and c = -43
To find the general form of the given equation, we need to simplify and expand the equation.
First, we can simplify the left-hand side of the equation by multiplying 2/3 into the brackets
2/3(x - 4)(x + 5) = (2/3)(x^2 + x - 20)
Next, we can multiply both sides of the equation by 3 to eliminate the fraction
2(x^2 + x - 20) = 3
Expanding the left-hand side, we get
2x^2 + 2x - 40 = 3
Simplifying further, we get
2x^2 + 2x - 43 = 0
So, the coefficients of the general form of the equation are
a = 2
b = 2
c = -43
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The given question is incomplete, the complete question is:
Give the values of a, b, and c needed to write the equation's general form. 2/3(x - 4)(x + 5) = 1
The coordinates of the midpoint of gh are m(-13/2,-6) and the coordinates of one endpoint are g(-4,1). what is the other endpoint?
Applying the midpoint formula, the coordinates of the other endpoint are: (-9, -13).
How to Apply the Midpoint Formula?The midpoint formula, which can be used in determining the coordinates of the midpoint between two endpoints is usually expressed as: M[(x1 + x2)/2, (y1 + y2)/2].
Given the following coordinates:
Midpoint of GH --> m(-13/2,-6) = (x, y)
One endpoint ---> G(-4, 1) = (x1, y1)
The other endpoint ---> (x2, y2)
Plug in the values into the formula used in calculating the midpoint:
m(-13/2,-6) = [(-4 + x2)/2, (1 + y2)/2]
Solve for x2
-13/2 = (-4 + x2)/2
-13/2 × 2 = -4 + x2
-13 = -4 + x2
-13 + 4 = x2
-9 = x2
x2 = -9
Solve for y2
-6 = (1 + y2)/2
2(-6) = 1 + y2
-12 = 1 + y2
-12 - 1 = y2
-13 = y2
y2 = -13
Thus, using the midpoint formula, the coordinates of the other endpoint are: (-9, -13).
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You design a tree house using a coordinate plane in which the coordinates are measured in meters (m ).
The vertices of the rectangular floor are (0, 5), (4, 3), (4,13), and (8, 11).
Part A: What is the perimeter of the tree house floor?
__ m
Part B: What is the area of the tree house floor?
__ m²
Part A: The perimeter of the tree house floor is 32 m.
Part B: The area of the tree house floor is 40 m².
Tree House Area and PerimeterPart A: The perimeter of the rectangular floor can be found by adding up the lengths of all four sides.
The first side has a length of 4 m and extends along the x-axis from (0, 5) to (4, 5).The second side has a length of 10 m and extends along the y-axis from (4, 5) to (4, 15).The third side has a length of 8 m and extends along the x-axis from (4, 15) to (0, 13).The fourth side has a length of 10 m and extends along the y-axis from (0, 13) to (0, 5).So the perimeter is 4 + 10 + 8 + 10 = 32 m.Part B: The area of the rectangular floor can be found by multiplying the length by the width.
The length is 4 m and the width is 10 m, so the area is 4 * 10 = 40 m².This is about a tree house design using a coordinate plane in which the coordinates are measured in meters (m). The task is to calculate the perimeter and the area of the rectangular floor of the tree house, given the vertices of the floor. The perimeter is found by adding up the lengths of all four sides of the rectangular floor, and the area is found by multiplying the length by the width.
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please help: Can a triangle have side lengths with the given lengths? Explain. 8m, 10m, 19m
Answer:
no
Step-by-step explanation:
The sum of the lengths of any two sides of a triangle is always greater than the length of the third side.
8+10 is 18
which is less than 19
Plz help I’m being timed!!!!
Answer:
the answer is the third one. with 13 as the leading coefficient
Step-by-step explanation:
Which of the following is a Prime Number? 9, 5,4
Answer:
5
Step-by-step explanation:
9 = 1,3,9
5 = 1,5
4 = 1,2,4
PLZ QUICK!!
Which is the graph of y – 3 = (x + 6)?
A coordinate grid with a line passing through the points at (negative 3, 1), (0, negative 1), and (3, negative 3).
A coordinate grid with a line passing through the points at (negative 2, 1), (0, 0), and (4, negative 3).
A coordinate grid with a line passing through the points at (negative 3, 0), (0, negative 2), and (3, negative 4).
A coordinate grid with a line passing through the points at (negative 3, 3), (0, 1), and (3, negative 1).
Answer:
See attached graph
Step-by-step explanation:
The equation is y-3=(x + 6)
Write the equation in a slope intercept form, then graph the equation on a graph tool to see the points that line on the line.
Alternatively , using the coordinates in the answer choices given, input them in the equation of the graph and select the answer choice that has all its coordinates true to the equation.
y-3 = x+6 -----can be written as : y= x+9
Graph y= x+9 to see the graph and the points that are on the line as attached.
The line passes through points (-5, 4) and (-4, 5).
Hence, option E is correct.
Use the concept of drawing a graph defined as:
Drawing the curve that represents a function on a coordinate plane is known as graphing a function. Every point on the curve will satisfy the function equation if the curve (or graph) reflects the function.
The given equation of a line:
y – 3 = (x + 6)
To plot the graph:
Put x = 0 we get y = 9
put x = 1 we get y = 10
put x = 2 we get y = 11
put x = 2 we get y = 12
proceed similarly.
Now plot the curve by addressing these points.
Hence,
The line passes through points (-5, 4) and (-4, 5) which is option E.
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The complete question is:
Which is the graph of y – 3 = (x + 6)?
A. A coordinate grid with a line passing through the points at (negative 3, 1), (0, negative 1), and (3, negative 3).
B. A coordinate grid with a line passing through the points at (negative 2, 1), (0, 0), and (4, negative 3).
C. A coordinate grid with a line passing through the points at (negative 3, 0), (0, negative 2), and (3, negative 4).
D. A coordinate grid with a line passing through the points at (negative 3, 3), (0, 1), and (3, negative 1).
E. A coordinate grid with a line passing through the points at (negative4, 5)and (negative 5, 4).
each letter of the word probable is written on a separate card. the cards are placed face down and mixed up. what is the probability that randomly selected card has a consonant?
Thus, the probability that a randomly selected card has a consonant is 62.5%. This means that if you were to randomly select a card from the pile of cards, there is a 62.5% chance that the card would be a consonant.
The number of consonants in the word "probable" and the total number of cards. There are 5 consonants in "probable" (p, r, b, l, and b) and a total of 8 cards.
In the word "probable," there are 5 consonants (p, r, b, b, and l) and 3 vowels (o, a, and e). To calculate the probability of choosing a consonant, divide the number of consonants by the total number of letters:
Probability = (Number of consonants) / (Total number of letters)
The probability of selecting a consonant can be calculated by dividing the number of consonants by the total number of cards:
5 consonants / 8 cards = 0.625 or 62.5%
Therefore, the probability that a randomly selected card has a consonant is 62.5%. This means that if you were to randomly select a card from the pile of cards, there is a 62.5% chance that the card would be a consonant.
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In baseball, the lengths of the paths between consecutive bases are 90 feet, and the paths form right angles. The player on first base tries to steal second base. How far does the ball need to travel from home plate to second base to get the player out? round your answer to the nearest tenth.
Answer:
AC = 127,26 f distance from home plate to second base
Step-by-step explanation:
Let call A , B , C Home plate, first base and second base respectively
These three point form a right triangle with legs ( AB = BC = 90 feet)
we have an isosceles triangle with a right angle and two angles of 45⁰
So we need to compute distance AC (hypotenuse)
AC² = AB² + BC² ⇒ AC² = 2AB² ⇒ AC = AB √2
AC = 90 * 1,414
AC = 127,26 f
Choose the expression that uses the greatest common factor and the distributive property to rewrite 66 + 78.
The formula for finding (66 + 78) using the greatest common factor, GCF, and the distributive property is 6(11+13).
Define the term greatest common factor?The greatest common factor, which is the product of two or more numbers, is the largest number (GCF). A natural number is created by dividing them by the biggest number (factor). The greatest common factor is the one with the largest number among the common factors.For the stated question-
Evaluating the total of 66 + 78.
The GCF as well as the distributive property, however, are mentioned in the question as being employed in this assessment.
Because the GCF of 66 and 78 is 6, this means that.
Thus, we can infer that 6(11+13) is the necessary expression.
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Joe and Mary were both given exactly 61 lbs of clay to make a 3D solid. Joe made a perfect cube with side length of a and Mary made a perfect sphere of radius r. What is the ratio of a / r?
Considering the given information in the question, Joel and Mary were both given exactly 61 lbs of clay with which Joe made a perfect cube with side length of a and Mary made a perfect sphere of radius r. The ratio of a / r = ∛ ( ⁴/₃π).
Given that
Joel and Mary were both given exactly 61 lbs of clay to make a 3D solid.
Joe made a perfect cube with side length of a and Mary made a perfect sphere of radius r.
We need to determine the ratio of a / r.
So, let's find the volume of the solid made by Joe and Mary.
Volume of a cube = (side length)³= a³
Volume of a sphere = ⁴/₃πr³
Joe made a cube, so the volume of the clay he used is equal to the volume of the cube made by him.
Similarly, Mary made a sphere, so the volume of the clay she used is equal to the volume of the sphere made by her.
Given that, both of them got the same amount of clay to work with.
∴a³ = ⁴/₃πr³...[1]
To find the ratio of a/r, we can rewrite the equation [1] in terms of a and r, and solve for a/r.
∛a³ = ∛(⁴/₃πr³)
a = ³√(⁴/₃π) × r
∛ a³ = r × ∛ ⁴/₃π
a/r = ∛ (⁴/₃π)
Answer: a/r = ∛ ( ⁴/₃π).
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Kerry starts school at 8:30 AM today. If she gets out after her 5th class, according to the chart, what time will she leave school today?
Answer: 3:45
Step-by-step explanation: