The formula for the general term of the arithmetic sequence is:
a) an = -10 + (n-1) * 6 and first-term = -10
b) an = -10 + (n-1) * 6 and first-term = 6
c) an = 36 + (n-1) * (-5) and first-term = 36
What is an arithmetic sequence?An arithmetic sequence is a sequence of numbers in which each term (after the first) is obtained by adding a fixed number called the common difference, d, to the preceding term. The first term of an arithmetic sequence is denoted by 'a'. The general formula for an arithmetic sequence is:
a, a + d, a + 2d, a + 3d, ...
where 'a' is the first term, 'd' is a common difference, and each term after the first is obtained by adding 'd' to the preceding term.
According to the given informationa) To find the common difference, we subtract any term from the term that comes after it. For example, we can subtract -10 from -4, or 2 from 8, and we get:
-4 - (-10) = 6
8 - 2 = 6
Since both of these subtractions give us the same result, we know that the common difference is d = 6. To find the first term, we can use any term and subtract the product of the common difference and its position in the sequence minus 1. For example, we can use the second term -4 and its position 2 to get:
a = -4 - (2-1) * 6 = -10
Therefore, the formula for the general term of the sequence is:
an = -10 + (n-1) * 6
b) The common difference between consecutive terms is -2 because each term is 2 less than the term before it. To find the first term, we can use any term and add the product of the common difference and its position in the sequence minus 1. For example, we can use the second term 8 and its position 2 to get:
a = 8 + (2-1) * (-2) = 6
Therefore, the formula for the general term of the sequence is:
an = 6 + (n-1) * (-2)
c) The common difference between consecutive terms is -5 because each term is 5 less than the term before it. To find the first term, we can use any term and add the product of the common difference and its position in the sequence minus 1. For example, we can use the second term 31 and its position 2 to get:
a = 31 + (2-1) * 5 = 36
Therefore, the formula for the general term of the sequence is:
an = 36 + (n-1) * (-5)
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In order to study the cause and effect relationship between two variables, a researcher must perform what type of study ?
A. correlational
B. descriptive
C. experimental
D. meta-analysis
of study?
Answer: C. experimental study.
Experimental studies are used to establish cause-and-effect relationships between variables by manipulating one variable (independent variable) and observing the effect on another variable (dependent variable) while controlling for other potential factors. Correlational studies examine the relationship between two variables but do not establish causality, descriptive studies describe a phenomenon without manipulating variables, and meta-analysis is a statistical method that combines the results of multiple studies to provide an overall summary.
Step-by-step explanation:
When the function f(x) is divided by 3x + 1, the quotient is 3x² − 4x − 1
and the remainder is -10. Find the function f(x) and write the result in
standard form.
The function f(x) is f(x) = 9x³ - 7x² - 13x - 11 written in standard form.
What is the polynomial equation?
A polynomial equation is an equation in which the variable is raised to a power, and the coefficients are constants. A polynomial equation can have one or more terms, and the degree of the polynomial is determined by the highest power of the variable in the equation.
When f(x) is divided by 3x + 1, the quotient is 3x² - 4x - 1 and the remainder is -10. We can use polynomial long division to write f(x) in the form:
f(x) = (3x² - 4x - 1)(3x + 1) - 10
Multiplying out the right side gives:
f(x) = 9x³ - 7x² - 13x - 11
Therefore, the function f(x) is f(x) = 9x³ - 7x² - 13x - 11 written in standard form.
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What percent of U.S. vice presidents were at least 60 years old when they took office? Explain how you found your answer.
(Please help asap!!)
The percent of U.S. vice presidents were at least 60 years old when they took office is 26.5%
How to determine the percentage?It may interest you that US America has had about 49 vice presidents till date
Out of this 49 vice presidents,
13 of them were more than 60 years at the beginning of their office
This implies that 13/49 * 100 = 26.53%
In conclusion the percentage of US America vice presidents is 26.53%
for clarity, read the article below.
Americans over 60 hold many of the highest offices in the U.S. government. An analysis of the current 117th Congress revealed that it’s the oldest, on average, of any Congress in at least the past 20 years. The average age of U.S.
Presidents are also being elected at older ages than in the past; at 70, President Donald Trump was the oldest to take office, though his record was quickly surpassed by his successor, President Joe Biden, who took office at age 78.
As the average age of elected officials has risen, some have questioned whether we should restrict individuals over a certain age from holding office. In 2019, former President Jimmy Carter expressed concern over the age of the presidential candidates in the 2020 election, stating:
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group the data
1-5,6-10,11-15,16-20 to construct a tally chart and work out the frequency of each group
Based on this data, what is a reasonable estimate of the probability that Patsy sells fewer than 5 feathers next festival?
A reasonable estimate of the probability that Patsy sells fewer than 2 feathers at the next festival is about 0.2485.
How to estimate the probability of given data?
To estimate the probability that Patsy sells fewer than a certain number of feathers at the next festival, we need to use the given data to calculate the mean and standard deviation of the number of feathers she has sold in the past festivals.
The mean, denoted by μ, is calculated by adding up all the number of feathers sold and dividing by the total number of festivals. So,
μ = (3 + 6 + 1 + 4 + 2 + 3 + 7 + 2) / 8 = 3.375
The standard deviation, denoted by σ, is a measure of how spread out the data is. It is calculated by first finding the variance, which is the average of the squared differences between each data point and the mean, and then taking the square root of the variance. So,
Variance = ((3-3.375)² + (6-3.375)²+ (1-3.375)² + (4-3.375)² + (2-3.375)² + (3-3.375)² + (7-3.375)² + (2-3.375)²) / 8 = 4.0898
σ = √(4.0898) = 2.022
Now, to estimate the probability that Patsy sells fewer than a certain number of feathers at the next festival, we need to standardize the value by subtracting the mean and dividing by the standard deviation. So, let X be the number of feathers sold at the next festival, then,
Z = (X - μ) / σ
Let's say we want to estimate the probability that Patsy sells fewer than 2 feathers at the next festival. Then,
Z = (2 - 3.375) / 2.022 = -0.679
We can use a standard normal distribution table or calculator to find the probability that a standard normal random variable is less than -0.679, which is approximately 0.2485.
Therefore, a reasonable estimate of the probability that Patsy sells fewer than 2 feathers at the next festival is about 0.2485.
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Correct question is "The number of feathers Patsy 3, 6, 1, 4, 2, 3, 7, 2 Peacock sold at each of the festivals this year. Based on this data, what is a reasonable estimate of the probability that Patsy sells fewer than feathers next festival? "
a tank contains 60 kg of salt and 2000l of water. a solution of a concentration 0.015 kg of salt per liter enters a tank at the rate 9l/min. the solution is mixed and drains from the tank at the same rate. (a) what is the concentration of our solution in the tank initially? (b) find the amount of salt in the tank after 3.5 hours. (c) find the concentration of salt in the solution in the tank as time approaches infinity.
(a) The concentration of the solution in the tank will be changing over time.
(b) The amount of salt in the tank after 3.5 hours is 63.292 kg.
(c) When the inflow and outflow rates are equal, the amount of salt in the tank will remain constant.
(a) To find the concentration of the solution in the tank initially, we can use the formula:
concentration = mass of salt / volume of solution
The mass of salt in the tank initially is 60 kg, and the volume of solution is 2000 liters.
Therefore, the initial concentration is:
concentration = 60 kg / 2000 L
concentration = 0.03 kg/L
However, we know that a solution with a concentration of 0.015 kg/L is entering the tank at a rate of 9 L/min.
Therefore, the concentration of the solution in the tank will be changing over time.
(b) To find the amount of salt in the tank after 3.5 hours, we can use the formula:
amount of salt = initial amount of salt + (concentration of incoming solution - concentration of solution in tank) x rate x time
The initial amount of salt is 60 kg, and the concentration of the incoming solution is 0.015 kg/L.
We need to find the concentration of the solution in the tank after 3.5 hours.
The rate of flow is 9 L/min, so the total volume of solution that has entered the tank after 3.5 hours is:
volume of solution = rate x time
volume of solution = 9 L/min x 210 min
volume of solution = 1890 L
The total volume of solution in the tank after 3.5 hours is:
total volume = initial volume + volume of incoming solution - volume of drained solution
total volume = 2000 L + 9 L/min x 210 min - 9 L/min x 210 min
total volume = 2000 L
Therefore, the concentration of salt in the tank after 3.5 hours is:
amount of salt = 60 kg + (0.015 kg/L - concentration of solution in tank) x 9 L/min x 210 min
amount of salt - 60 kg = (0.015 kg/L - concentration of solution in tank) x 1890 L
concentration of solution in tank = 0.015 kg/L - (amount of salt - 60 kg) / 1890 L
Now we can substitute the concentration of the solution in the tank into the formula and solve for the amount of salt:
amount of salt = 60 kg + (0.015 kg/L - (0.015 kg/L - (amount of salt - 60 kg) / 1890 L)) x 9 L/min x 210 min
amount of salt = 63.292 kg
Therefore, the amount of salt in the tank after 3.5 hours is 63.292 kg.
(c) To find the concentration of salt in the solution in the tank as time approaches infinity, we need to find the concentration that the solution will reach when the inflow and outflow rates of solution are equal.
At this point, the amount of salt in the tank will remain constant.
Let's denote the concentration of salt in the solution in the tank as c.
We know that the volume of solution in the tank remains constant at 2000 L, and that the inflow and outflow rates are both 9 L/min. Therefore, the amount of salt that enters the tank per minute is 0.015 kg/L x 9 L/min = 0.135 kg/min, and the amount of salt that leaves the tank per minute is c x 9 L/min.
When the inflow and outflow rates are equal, the amount of salt in the tank will remain constant.
Therefore, we can set the rate of inflow equal to the rate of outflow and solve for c:
0.015 kg/L x 9.
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Choose the word that makes this sentence true.
A square is ____ a rectangle.
Answer: the same as or equal to
Step-by-step explanation: The shapes are the same one's just stretched
Answer:
A square is a special kind of a rectangle
Step-by-step explanation:
Every Square is a rectangle but not every rectangle is a square.
if a garden box is 4x by 3x and the area of the box in square feet is equal to four times the perimeter in feet what is the value for x that satisfies these requirements
The answer to this question is x = 6
At midnight, the temperature in a city was 5 degrees celsius. The temperature was dropping at a steady rate of 2 degress celsius per hour. Write an inequalty that represents t, the number of hours past midnight, when the temperature was coler than -4 degrees celsius
( 5 - 2t ) < - 4 is an inequalty that represents t, the number of hours past midnight, when the temperature was coler than -4 degrees celsius.
What is linear equation?
An algebraic equation with simply a constant and a first- order( direct) element, similar as y = mx b, where m is the pitch and b is the y- intercept, is known as a linear equation.
The below is sometimes appertained to as a" direct equation of two variables," where y and x are the variables. Equations whose variables have a power of one are called direct equations. One illustration with only one variable is where layoff b = 0, where a and b are real values and x is the variable.
The midnight temperature is 5 °C and the temperature is decreasing at the rate of 2°C per hour.
If t is the hours past midnight then after t hours the temperature will be ( 5 - 2t ).
Now, if this temperature is colder than - 4° C, then the inequality can be written as ( 5 - 2t ) < - 4.
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The inequality that represents t, the number of hours past midnight, when the temperature was cooler than -4 degrees celsius( 5 - 2t ) < - 4
What is inequality?
The term "inequality" is used in mathematics to describe a relationship between two expressions or values that is not equal to one another. Inequality results from a lack of balance. When two quantities are equal, we use the symbol '=', and when they are not equal, we use the symbol. If two values are not equal, the first value can be greater than (>) or less than (), or greater than equal to () or less than equal to ().
The midnight temperature is 5 °C and the temperature is decreasing at the rate of 2°C per hour.
If t is the hours past midnight then after t hours the temperature will be
=> ( 5 - 2t ).
Now, if this temperature is colder than - 4° C, then the inequality can be written as ( 5 - 2t ) < - 4.
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A tree in Abdul's backyard grows 0.9 meters each month.If the tree is 5.76 meters tall,for how many months has the tree been growing?
Answer:
the tree has been growing for about 6 months and 12 days
Step-by-step explanation:
5.76/0.9 = 6.4
a road perpendicular to a highway leads to a farmhouse located 1 1 mile away. an automobile traveling on the highway passes through this intersection at a speed of 45mph. 45 mph . how fast is the distance between the automobile and the farmhouse increasing when the automobile is 9 9 miles past the intersection of the highway and the road? the distance between the automobile and the farmhouse is increasing at a rate of miles per hour.
The distance traveling between them is increasing at a rate of miles per hour = 45 m/h.
The distance between the automobile and the farmhouse is increasing by 45 mph, since the automobile is traveling at this speed.
When the automobile is 9 miles past the intersection of the highway and the road, the distance between the automobile and the farmhouse is increasing at a rate of 45 mph, due to the automobile traveling at this speed.
When the automobile is 9 miles past the intersection of the highway and the road, the distance between the automobile and the farmhouse is increasing at a rate.
So,
The rate at which the distance between the automobile and the farmhouse is increasing when the automobile is 9 miles past the intersection is 45 mph.
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An aircraft (at Z) is spotted by two observers (at X and Y) who are L = 1850 feet apart. As the airplane
passes over the line joining them, each observer takes a sighting of the angle of elevation to the plane,
as indicated in the figure. If A=25°, and B=25°, how high is the airplane?
Answer: We can use trigonometry to solve this problem. Let's call the height of the airplane H, and let's call the distance from observer X to the airplane D. Then the distance from observer Y to the airplane is L - D.
From the point of view of observer X, we can write:
tan(A) = H / D
tan(25°) = H / D
From the point of view of observer Y, we can write:
tan(B) = H / (L - D)
tan(25°) = H / (L - D)
We now have two equations with two unknowns (H and D). We can solve for one of the unknowns in terms of the other, and then substitute that expression into the other equation to eliminate one of the unknowns.
Let's solve the first equation for D:
D = H / tan(25°)
Substituting this expression for D into the second equation, we get:
tan(25°) = H / (L - H / tan(25°))
Multiplying both sides by (L - H / tan(25°)), we get:
tan(25°) (L - H / tan(25°)) = H
Expanding the left-hand side, we get:
tan(25°) L - H = H tan^2(25°)
Adding H to both sides, we get:
tan(25°) L = H (1 + tan^2(25°))
Dividing both sides by (1 + tan^2(25°)), we get:
H = (tan(25°) L) / (1 + tan^2(25°))
Now we can substitute this expression for H into the equation D = H / tan(25°) to get:
D = ((tan(25°) L) / (1 + tan^2(25°))) / tan(25°)
Simplifying, we get:
D = L / (1 + tan^2(25°))
Now that we know the distance D, we can use the equation tan(A) = H / D to find H:
tan(25°) = H / D
H = D tan(25°)
Substituting D = L / (1 + tan^2(25°)), we get:
H = (L / (1 + tan^2(25°))) tan(25°)
Plugging in the given values L = 1850 feet and A = B = 25°, we get:
H = (1850 / (1 + tan^2(25°))) tan(25°)
H ≈ 697.3 feet
Therefore, the airplane is about 697.3 feet high.
Step-by-step explanation:
When you went to know the mass of a bowling ball what unit do you choose
Standard unit chose to measure the mass of a bowling ball is equal to kilogram .
The unit typically used to measure the mass of a bowling ball is the pound (lb) or the kilogram (kg).
It depends on the country as different countries have different standard unit for measuring mass.
In the United States, the weight of a bowling ball is often measured in pounds.
While in many other countries, the weight is measured in kilograms.
When measuring the mass of a bowling ball,
It is important to use a calibrated scale that is designed to handle the weight of the ball.
Some scales are specifically designed for weighing bowling balls.
And they may have a higher weight capacity than a typical bathroom scale.
It is also important to ensure that the scale is on a flat, stable surface to ensure an accurate measurement.
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CAN I PLEASE GET HELP!
The result of 10 trials expressed in percentage is 70%.
List out the 10 trials in table format.We can utilize the random number table to produce 10 random numbers between 0 and 1 to approximate Nestor's performance in the ten races. If a number is less than or equal to 0.79, it is considered a "medal," and if it is larger than 0.79, it is considered a "no medal." This approach can be repeated ten times to get a sense of the range of possible outcomes.
For ten trials, we get the following results using the random number table shown below:
To estimate the likelihood that Nestor will win at least six of the following ten races, we count how many trials resulted in six or more medals. Seven of the ten trials resulted in six or more medals. As a result, we estimate the likelihood to be 7/10, or 70%.
The likelihood is 70% when expressed as a percentage.
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how do i solve this question 4
A system of equations that model the situation are e = a - 12 and a + e = 100.
The number of tickets Alberto won is 56 tickets.
The number of tickets Elian won is 44 tickets.
How to determine the number of each type of tickets won?In order to write a system of linear equations to describe this situation, we would assign variables to the number of tickets Alberto won and number of tickets Elian won, and then translate the word problem into an algebraic equation as follows:
Let the variable a represent the number of tickets Alberto won.Let the variable e represent the number of tickets Elian won.Since Alberto won 12 tickets less than Elian, a linear equation that models this situation is given by:
e = a - 12 .....equation 1.
Additionally, when they put their tickets together they have exactly 100 tickets;
a + e = 100 .....equation 2.
By solving the system of linear equations simultaneously, we have:
a + a - 12 = 100
2a = 112
a = 112/2
a = 56 tickets.
For the number of tickets (e) Elian won, we have:
e = a - 12
e = 56 - 12
e = 44 tickets.
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3. A sporting goods store received an order of 64 baseball caps, of which 16 were green. If 1 (1 point)
of the 64 caps is selected at random, what is the probability it will not be green?
25%
75%
80%
50%
The answer is option (b) 75%.
What is Probability?
Probability is a measure of the likelihood that a particular event will occur. It is expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. The probability of an event can be determined by dividing the number of ways the event can occur by the total number of possible outcomes.
The probability of selecting a non-green cap is the number of non-green caps divided by the total number of caps:
P(non-green) = 48/64 = 3/4 = 0.75
Therefore, the probability that a randomly selected cap will not be green is 0.75 or 75%.
So the answer is option (b) 75%.
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isabel owns a mexican restaurant that serves aguas frescas, cold drinks often made with fresh fruit, isabel wants to know which flavor of agua fresca is the most popular with customers at her restaurant. which sampling method would provide the best representation of the consumer population at isabel's restaurant?
a. selecting every customer during one lunch hour
b. selecting every customer who responds to an online poll
c. selecting every 20th customer over the period of a month
d. selecting every 3rd customer who purchases agua fresca in one day
Option (c) selecting every 20th customer over the period of a month, known as systematic sampling, may be time-consuming and may not accurately capture the daily fluctuations in customer preferences.
What is quadratic equation?
it's a second-degree quadratic equation which is an algebraic equation in x.
The best sampling method for Isabel to determine the most popular flavor of aguas frescas would be (d) selecting every 3rd customer who purchases aguas frescas in one day. This method, known as systematic sampling, ensures that the sample is randomly selected, while also allowing Isabel to collect data over a short period of time.
Option (a) selecting every customer during one lunch hour, may not provide a good representation of the entire customer population as customers who visit the restaurant during lunch hour may differ from those who visit at other times.
Option (b) selecting every customer who responds to an online poll would also not provide a good representation of the entire customer population as not all customers may have access to or be willing to respond to an online poll.
Option (c) selecting every 20th customer over the period of a month, known as systematic sampling, may be time-consuming and may not accurately capture the daily fluctuations in customer preferences.
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im stuck on this need a bit of help
The author of the poem, "Heritage," is the Jamaican-American poet, Claude McKay. Based on the poem, it is clear that he is nostalgic for the fruits and landscapes of Jamaica.
How to explain the poemHere is an acrostic list of some of the things he might be nostalgic for:
J - Joyful memories of fruit-trees laden with bananas, cocoa, and alligator pears
A - Awe-inspiring mystical blue skies over the hills
M - Memories of dewy dawns
A - Alligator pears and avocados, also known as butter pears, grown in Jamaica
I - Images of low-singing rills, small streams or brooks
C - Crisp tangerines,
A - Appreciation for the highest prize at parish fairs, which celebrates the bountiful harvests of Jamaica
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4 out of 7 questions. PLEASE help me.
A tangent line is line GJ.
A secant line is line HF.
A chord is line GF.
What is the chord of a circle?In Mathematics and Geometry, the chord of a circle can be defined as a line segment that typically join any two (2) points on a circle. This ultimately implies that, a chord simply refers to the section of the line that is used for connecting two (2) separate points on a circle such as line GF.
What is a secant line?In Mathematics and Geometry, a secant line can be defined as a type of line that intersects the edge of a circle twice i.e it goes through the interior of the circle twice and intersects its boundary twice such as line HF.
In conclusion, a tangent line is a type of line that lies outside of a circle and intersects the edge of a circle exactly once i.e it touches the outside of the circle only once such as line GJ.
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can you give me a simple fast answer
The mapping that is a function will be B). X
How to explain the functionEvery function got a set of input values called " Domain " and a set of respective output values as " Range"
And function worked as Function( Input value ) = Output value
There are basic rules for function :
1. There always exist output value for every single input value.
2. Every input value should have one and only one output value
For W : Rule 2 is violated
Here, Input value 6 result to two output value 2 and 4
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A recent conference had 750 people in attendance. In one exhibit room of 70 people, there were 18 teachers and 52 principals. What prediction can you make about the number of principals in attendance at the conference?
There were about 193 principals in attendance.
There were about 260 principals in attendance.
There were about 557 principals in attendance.
There were about 680 principals in attendance.
Therefore , the solution of the given problem of unitary method comes out to be there were approximately 557 principals present.
What is an unitary method?To complete the assignment, use the iii . -and-true basic technique, the real variables, and any pertinent details gathered from basic and specialised questions. In response, customers might be given another opportunity to sample expression the products. If these changes don't take place, we will miss out on important gains in our knowledge of programmes.
Here,
Let's determine the principals' proportion to everyone else in the display room:
=> Number of principals divided by the total number of visitors to the display room =
=> 52/70 (number of principals / total number of visitors).
to determine the approximate number of principals present at the conference:
Estimated number of principals attending the conference = Principals as a percentage of all attendees in the exhibit hall * Total attendees =
=> (52 / 70) * 750
=> 557 principals are expected to have attended the meeting.
As a result, it is possible to forecast that there were approximately 557 principals present at the meeting,
which corresponds to the response option "There were approximately 557 principals present."
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Directions: find the value of the hypotenuse for each of the following right triangles.
1. a = 5, b = 8
2. a = 6, b = 7
3. a = 4, b = 9
4. a = 3, b = 12
5. a = 11, b = 10
6. a = 8, b = 7
7. a = 9, b = 4
8. a = 7, b = 11
9. a = 13, b = 15
10. a = 5, b = 6
By Pythagoras Hypotenuse for 1. 9.43 , 2. 9.22 , 3. 9.85 , 4. 12.37, 5. 14.87 , 6. 10.63
7. 9.85 , 8. 13.04 , 9. 19.85 , 10. 7.81
Theorem of Pythagoras defined?The Pythagorean theorem, commonly referred to as Pythagoras' theorem, is a key relationship in Euclidean geometry between a right triangle's three sides. It declares that the hypotenuse's square, which is the side that is opposite the right angle, is equal to the sum of the squares of the other two sides. In other words, if the hypotenuse is length c and the legs of a right triangle are lengths a and b, then a² + b² = c².
The Pythagorean theorem, which asserts that the square of the hypotenuse is equal to the sum of the squares of the other two sides, can be used to determine the hypotenuse of a right triangle.
This theorem allows us to calculate the hypotenuse value for each of the right triangles presented as follows:
1. a = 5, b = 8
c = √(a² + b²) = √(5² + 8²) = √(25 + 64) =√(89) ≈ 9.43
2. a = 6, b = 7
c = √(a² + b²) = √(6² + 7²) = √(36 + 49) = √(85) ≈ 9.22
3. a = 4, b = 9
c = √(a² + b²) = √(4² + 9²) = √16 + 81) = √(97) ≈ 9.85
4. a = 3, b = 12
c =√(a² + b²) = √(3² + 12²) = √(9 + 144) = √(153) ≈ 12.37
5. a = 11, b = 10
c = sqrt(a^2 + b^2) = sqrt(11^2 + 10^2) = sqrt(121 + 100) = sqrt(221) ≈ 14.87
6. a = 8, b = 7
c = √(a² + b²)= √(8² + 7²) = √(64 + 49) = √(113) ≈ 10.63
7. a = 9, b = 4
c =√(a² + b²)=√(9² + 4²) = √(81 + 16) = √(97) ≈ 9.85
8. a = 7, b = 11
c = √(a² + b²)= √(7² + 11²) = √(49 + 121) ≈√(170) ≈ 13.04
9. a=13,b=15
c=√(a² + b²)=√((13²)+(15²))=√((169)+(225))=√(394))≈19.85
10.a=5,b=6
c=√(a²+b²)=sqrt((5²)+(6²))=s√((25)+(36))=√(61))≈7.81
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Hi! Please help!
The line plots represent data collected on the travel times to school from two groups of 15 students. Labeled- Bus 47 Travel Times Numbers on the line plot are 0,2,4,6,8,10,12,14,16,18,20,22,24,26,28. One dot is above the number 4. One dot is above the number 6. Two dots are above the number 10. Two dots are above the number 12. One dot is above the number 14. Three dots above the number 16. Two dots above 18. Two dots above 22. One dot above 28.
Second bus- Bus 14 Travel Times
Same numbers as first line plot. Two dots above 8. One dot above 10. Four dots above 12. Two dots above 14. One dot above 16. Three dots above 18. One dot above 20. One dot above 28.
Compare the data and use the correct measure of center to determine which bud typically has the faster travel time. Round your answer to the nearest whole number, if necessary, and explain your answer.
Bus 47, with a median of 16
Bus 14, with a median of 14
Bus 47, with a mean of 16
Bus 14, with a mean of 14
Answer:
(A) Bus 47, with a median of 16.
Step-by-step explanation:
To determine which bus typically has the faster travel time, we need to compare the measures of center for each data set. Since the data sets are small and discrete, we can use either the median or the mean as a measure of center.
For Bus 47, the median is the middle value, which is 16.For Bus 14, the median is also the middle value, which is 14.
Comparing the medians, we can see that Bus 47 has a higher median, which suggests that it typically has a faster travel time than Bus 14.
Therefore, the answer is (A) Bus 47, with a median of 16.
the product of three distinct positive integers is 144. if the sum of the three integers is 26, what is the sum of their squares?
We can then check the sum of each set of three integers and see which one adds up to 26. We find that the set 2, 8, 16 has a sum of 26, so these are the three distinct integers that multiply to 144.Therefore, the sum of the squares of the three integers is 324.
To solve this problem, we can start by listing all the factors of 144 and looking for three distinct integers that multiply to 144. The factors of 144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, and 144. We can eliminate any factor that is not a positive integer or is repeated, leaving us with the following possibilities:
- 1, 2, 72
- 1, 3, 48
- 1, 4, 36
- 1, 6, 24
- 2, 3, 24
- 2, 4, 18
- 2, 8, 9
- 3, 4, 12
- 3, 6, 8
To find the sum of their squares, we simply square each integer and add them together:
2² + 8² + 16² = 4 + 64 + 256 = 324
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The sum of the squares of the three distinct positive integers is 589.
Let's denote the three distinct positive integers as a, b, and c. We know the following:
1. a * b * c = 144
2. a + b + c = 26
Our goal is to find the sum of their squares, i.e.,[tex]a^2 + b^2 + c^2.[/tex]
Find the prime factorization of 144. It is [tex]2^4 * 3^2[/tex]
We need to find three distinct factors of 144 that add up to 26.
By analyzing the factors, we find that the integers are 2, 3, and 24.
Calculate the sum of their squares:
[tex]a^2 + b^2 + c^2 = 2^2 + 3^2 + 24^2 = 4 + 9 + 576 = 589[/tex].
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1. A trapezoid is defined as a quadrilateral with only 2 parallel sides. An
isosceles trapezoid is defined as a trapezoid with the non-parallel sides being
congruent. Prove that the base angles on an isosceles trapezoid (
are congruent.
Answer:
A trapezoid is defined as a quadrilateral with only 2 parallel sides. An
isosceles trapezoid is defined as a trapezoid with the non-parallel sides being
congruent. Prove that the base angles on an isosceles trapezoid ( are congruent
PLEASE HELP AND EXPLAIN AND SHOW WORK ON HOW YOU GOT THE ANSWER I WILL MARK YOU BRAINLIEST
Answer:
No, this triangle is NOT a right angle.
Step-by-step explanation:
The known fact is that the largest number is our hypotenuse. The other two numbers can go on either side.
A square plus B square equal C square is our equation
Let's plug in the numbers: 15^2+5^2=16^2
Now we solve.
Once we solve our squares and add them together, we get 250=256. Since these two number are not equal to each other, this triangle is NOT a right angle
much love to you.
Plot points between and beyond each x-intercept and vertical asymptote. Find the value of the function at the given value of x.
f(x)= 2/ x^2+3x-10
the points we plotted are (-6, -1/2), (-4, 1/2), (0, -1/5), (3, 1/2), and (6, 1/5).
What is function?
a function is a relationship or expression involving one or more variables. It has a set of input and outputs.
To find the x-intercepts, we set the numerator of the function equal to zero:
[tex]2 / (x^2 + 3x - 10) = 0[/tex]
This is only true if the numerator is equal to zero, so:
2 = 0
This is not possible, so the function has no x-intercepts.
To find the vertical asymptotes, we look for values of x that make the denominator equal to zero:
[tex]x^2 + 3x - 10 = 0[/tex]
We can factor the quadratic as:
(x + 5)(x - 2) = 0
This means that the function has vertical asymptotes at x = -5 and x = 2.
Now, let's plot some points between and beyond each x-intercept and vertical asymptote:
When x = -6, f(x) = 2 / (-6)² + 3(-6) - 10 = -1/2
When x = -4, f(x) = 2 / (-4)² + 3(-4) - 10 = 1/2
When x = 0, f(x) = 2 / (0)² + 3(0) - 10 = -1/5
When x = 3, f(x) = 2 / (3)² + 3(3) - 10 = 1/2
When x = 4, f(x) = 2 / (4)² + 3(4) - 10 = -1/2
When x = 6, f(x) = 2 / (6)² + 3(6) - 10 = 1/5
Therefore, the points we plotted are (-6, -1/2), (-4, 1/2), (0, -1/5), (3, 1/2), and (6, 1/5).
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Make sure you click on the answer in the drop box that goes in the blank for each numbered blank.
BLANK #1 PLEASE ANSWER ALL THE BLANKS 100 points
1 - THEOREM, 2 - RIGHT, 3 - SUM, 4 - LEGS, 5 - SQUARE, 6 - A, 7 - B, 8 - C, 9 - HYPOTENUSE, 10 - 90-DEGREES
The full statement reads: The pythagoras theorem tells us how the side lengths of right triangles are related. In any right triangle the sum of the squares of the two legs should equal the square of the hypotenuse. The legs are called A and B and the hypotenuse is C. The hypotenuse is always the longest side of a right triangle and its across from the 90-degrees angle.
Some properties of right angled trianglesLet us assume the triangle is ABC, and the angle C is 90 degrees. let the length the side AB = c, the length of side AC = b, the length of side BC is a.
1. The sum of the two non 90 degree angles is equal to 90 degrees.
2. cos(B) = a/c , sin(B) = b/c
3. cos(A) = b/c, sin(A) = a/c
4 [tex]c^2 = a^2 + b^2[/tex]
5 the diameter of the circumcircle of this triangle is c.
6 tan(A) = a/b
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17. Kade has $40 in savings and wants to purchase a video game console that costs $250 plus
8.25% sales tax. Kade wants to wait until he has enough in savings to cover the purchase. If Kade
saves $50 each week, what is the minimum number of weeks Kade should wait before making his
purchase?
A. 3 weeks
B. 4 weeks
C. 5 weeks
D. 7 weeks
The minimum number of weeks Kade should wait before making his purchase is 5 weeks.
Given that, Kade has $40 as his saving, and he wants to buy a video game console that costs $250 plus 8.25% sales tax.
He saves $50 each week to buy the same, we need to find the number weeks in which he can buy the game,
Total cost of the game = 250 + 250 × 8.25%
= 250 + 250 × 0.0825
= 250 + 20.625
= 270.625
Hence, he needs to save = $270.625 - $40 = $230.625
Let the number of weeks be x,
∴ 50x = 230.625
x = 4.61 ≈ 5
Hence, the minimum number of weeks Kade should wait before making his purchase is 5 weeks.
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Triangle PQR has vertex coordinates at P(4, 0), Q(4, 3), R(5, 1). If the triangle is translated so that Q′(4, −5), determine the translation direction and number of units.
8 units down
8 units up
8 units to the right
8 units to the left
Answer:
To determine the translation direction and number of units, we need to find the vector that connects Q to Q', and then determine the magnitude and direction of that vector.
The vector that connects Q to Q' can be found by subtracting the coordinates of Q from the coordinates of Q':
Q' - Q = (4, -5) - (4, 3) = (0, -8)
This vector indicates a translation 8 units downwards, in the negative y direction. Therefore, the translation direction is downwards and the number of units is 8.
So the correct answer is: 8 units down.
Triangle PQR was translated 8 units down.
Explanation:In mathematics, particularly in the field of geometry, a translation refers to moving each point in a shape or a figure to a different position by sliding it to a certain direction for a fixed number of spaces. Each point is moved the same distance and in the same direction.
In the case of your Triangle PQR, the Q point moves from (4, 3) to the new coordinate Q'(4, -5). The x-coordinate in both points remains at 4. Hence, there's no left or right movement. But the y-coordinate changes from 3 to -5. This indicates a downward movement. The distance between 3 and -5 on the number line is 8 units. Therefore, the triangle was translated 8 units down.
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