Player B is the most consistent, with a range of 7.
The best measure of variability for this data would be the range, which is the difference between the maximum and minimum values.
For Player A: Range = 11 - 1 = 10
For Player B: Range = 8 - 1 = 7
Therefore, Player A has a higher range and thus more variability in their data. So, the correct answer is:
Player B is the most consistent, with a range of 7.
What is variability?
Variability refers to the degree of variation or diversity in a set of data or observations. It is a measure of how spread out the data points are from the central tendency, such as the mean or median.
What is range?
Range is a statistical measure that describes the difference between the maximum and minimum values in a dataset. It is calculated by subtracting the smallest value from the largest value.
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Answer:
(d) Player B is the most consistent, with an IQR of 2.5.
Step-by-step explanation:
Given these numbers of goals, you want to know which player is most consistent, and the best measure of that.
A: {1, 1, 2, 4, 4, 5, 5, 5, 11}B: {1, 1, 1, 2, 2, 3, 3, 4, 8}Variability measuresThe variability measures we're to consider here are range and IQR.
The range is the difference between the maximum and the minimum:
A: 11 -1 = 10B: 8 -1 = 7The smaller range indicates player B is more consistent.
The IQR is the difference between the upper and lower quartiles. In each of these 9-element data sets, those quartiles will be the average of elements 2 and 3, and the average of elements 7 and 8 when the data is in order.
A: ((5+5) -(1+2))/2 = 3.5B: ((3+4) -(1+1))/2 = 2.5The smaller IQR indicates player B is more consistent.
OutliersIn each case, the maximum data value is more than 1.5 times the IQR above the upper quartile value, so can be considered an outlier. The outlier has a direct effect on range, so range is not a good measure of variability.
Player B is the most consistent, with an IQR of 2.5, choice D.
__
Additional comment
If the outlier is excluded from each data set, the IQR for player A remains the same at 3.5. The IQR for player B drops to 2.0.
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i need help ASAP
Calculate the amount of interest on $2,000.00 for 4 years, compounding daily at 2.25 % APR.
From the Monthly Interest Table use $1.094171 in interest for each $1.00 invested
A $2,088.34
B $2188.34
C $2,288.34
D $2,388.34
Answer:
Step-by-step explanation:
First, we need to calculate the annual interest rate from the given APR.
APR = 2.25%
Daily interest rate = 2.25% / 365 = 0.00616438
Now, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the principal (initial amount)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = time in years
In this case, P = $2,000, r = 0.00616438, n = 365 (daily compounding), and t = 4.
A = 2000(1 + 0.00616438/365)^(365*4)
A = 2000(1.00616438)^1460
A = $2,388.34 (rounded to the nearest cent)
Therefore, the answer is option D) $2,388.34.
assuming the rest of your diet remains constant, how many days will it take you to lose 10 pounds? you must burn an extra 3500 calories to lose 1 pound of body weight. express your answer using two significant figures.
The number of days that it would take to lose 10 pounds, given the calories in the morning latte is 97 days.
How to find the number of days ?Determine the total number of calories you need to burn to lose 8 pounds:
Calories to burn = Pounds to lose × Calories per pound
Calories to burn = 8 × 3,500 = 28,000
Calculate the number of calories you save per day by giving up your morning latte:
Daily calorie savings = Calories in latte
Daily calorie savings = 290
Determine how many days it would take to burn the total number of calories needed to lose 8 pounds:
Days to lose weight = Calories to burn / Daily calorie savings
Days to lose weight = 28,000 / 290 = 97 days
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Full question is:
Assuming the rest of your diet remains constant, how many days will it take you to lose 8 pounds? You must burn an extra 3500 Calories to lose 1 pound of body weight. (your daily latte contains 290 Calories. You want to lose weight by giving up your morning latte and drinking water instead.)
Could someone help me? Please.
The solution of the system of equations is (2, 1).
How to solve the system of equations graphically?Here we have the system of equations:
y = 2x - 3
y = -x + 3
To solve the system of equations graphically, we need to graph both of these lines in the same coordinate axis and then find the point where the lines intersect.
That point will be the solution of the system.
On the image at the end you can see the graph of the system of equations, there we can see that the solution is (2, 1).
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15 - (p + 1) where p = 3 and 4 = 10 calculate
Answer:
11
Step-by-step explanation:
15 - (p + 1)
Let p=3
15 - (3 + 1)
Parentheses first
15 - (4)
11
Answer:
11
Step-by-step explanation:
Given that,
p = 3
So, to find the value of the expression you have to solve it by replacing p with 3.
15 - ( p + 1 )
15 - ( 3 + 1 )
15 - 4
11
If you add two positive numbers together, which of the following is true about the result?
Answer:
If you add two positive numbers together you will get a positive.
Step-by-step explanation:
Whic expression is not equivalent to 3x-(4-×)
The expression 3x-(4-x) is equivalent to 4x-4
The distributive property is a mathematical property that describes the relationship between multiplication and addition or subtraction. It states that when a number is multiplied by a sum or difference of two or more numbers, the result is the same as if we multiplied the number by each of the individual terms inside the parentheses and then added or subtracted the products.
To simplify the expression 3x-(4-x), we can distribute the negative sign to the second term inside the parentheses, which gives:
3x - (4 - x) = 3x - 4 + x
Now we can combine the like terms (3x and x) to get:
3x - 4 + x = 4x - 4
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The given question is incomplete, the complete question is:
Which expression is equivalent to 3x-(4-x)?
What is the value of letter D on the number line?
Answer:
What is the value of the letter D on the number line?
Three and twenty-five hundredthsStep-by-step explanation:
You're welcome
Jacqui wants to prove that figures abc and def are similar. Which series of transformations would prove that these two figures are similar
One figure should be rotated to match the other's alignment. Expand one figure till it is the same size as another.
what is transformations ?A figure or object in a coordinate plane can be transformed to create a new figure or object that has been relocated, flipped, or altered in some other way. Translations, rotations, and reflections are the three primary forms of transformations. Moving a figure horizontally or vertically without altering its size or shape is known as translation. Rotation entails angling a figure around a fixed point, often known as the rotational center.
given
The subsequent transformations must be used in order to demonstrate similarity between two figures:
Translation (moving the figures to the same spot) (moving the figures to the same position)
Rotation (rotation one figure to fit the other) (rotating one figure to match the other)
Dilation (resizing the figures such that they have the same shape, but maybe different sizes) (resizing the figures so that they have the same shape, but possibly different sizes)
Consequently, the following set of transformations should be used to demonstrate that the figures abc and def are similar.
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the adaptive-response-rate single exponential smoothing model is best applied to time series data that are multiple choice non stationary. stationary and non seasonal. seasonal. stationary and seasonal. seasonal and nonstationary.
The adaptive-response-rate single exponential smoothing model is best applied to time series data that are non stationary and seasonal which means option D is the right answer.
The adaptive response rate single exponential smoothing model is used to demonstrate the changes in the forecasting data and the fluctuation in data values with respect to time which are smoothened by a coefficient. The larger the coefficient, the greater the smoothing effect.
This kind of model is ineffective for stationary time series as it takes into account the smoothing of the information. Adaptive smoothing is computationally difficult. Exponential smoothing produces accurate forecasts. The forecast shows projected demand and actual demand.
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Which table represents the function y =1/3 x + 4?
Input x 0 -3 -6
Output y 4 3 2
Input x 6 9 12
Output y 6 9 12
Input x 0 3 6
Output y 4 6 8
Input x 3 6 9
Output y 5 7 9
The table that represents the function y =1/3 x + 4 is the second table. This can be seen by comparing the input and output values of the given tables.
What is function?A function defines the relationship between two variables, wherein one variable depends on the other. In other words, a function is a rule or mapping from one set of values, known as the domain, to another set of values, known as the range.
The table that represents the function y =1/3 x + 4 is the second table. This can be seen by comparing the input and output values of the given tables.
The second table's input values are (6, 9, 12) and the output values are (6, 9, 12). This is equal to the equation y = 1/3 x + 4, where 1/3 x + 4 = x.
The other tables do not represent the function y = 1/3 x + 4. For example, the first table has input values of (0, -3, -6) and output values of (4, 3, 2), which do not match the equation y = 1/3 x + 4.
The third table has input values of (0, 3, 6) and output values of (4, 6, 8), which also do not match the equation y = 1/3 x + 4.
Finally, the fourth table has input values of (3, 6, 9) and output values of (5, 7, 9). This does not match the equation y = 1/3 x + 4 either.
Therefore, the table that represents the function y =1/3 x + 4 is the second table.
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what moves beyond excel graphs and charts into sophisticated analysis techniques such as controls, instruments, maps, time-series graphs, and more?
Answer:
Data Visualization Tools
Step-by-step explanation:
if the number of samples were doubled, what would be the new confidence interval (keeping the same confidence level?)
If the number of samples is doubled, the new confidence interval would be 9.61, 10.39 or narrower (smaller) while keeping the same confidence level.
. When calculating the confidence interval, the standard error is used, along with the sample mean and the critical value from the distribution. If we have a larger sample size, we can be more confident in our estimate of the population parameter because the sample mean will more closely resemble the population mean. As a result, the confidence interval can be narrower, indicating a higher degree of precision. For Example:Suppose a sample of 50 was taken, and the mean weight of an object was 10 grams with a standard deviation of 2 grams.
At a 95 percent confidence level, the confidence interval for the mean weight would be 10 ± (1.96)(2/√50) = (9.15, 10.85)Now suppose that the sample size is doubled to 100. The standard error will be cut in half, i.e., 2/√100 = 0.2. As a result, the new confidence interval would be 10 ± (1.96)(0.2) = (9.61, 10.39). Notice that the new confidence interval is narrower, indicating a higher degree of precision while keeping the same confidence level.
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discuss in this part. example 8.1 we use the method of steepest descent to find the minimizer of f(xi,x2,xs)
Here, we will use the method of steepest descent to find the minimiser of the function f(x1, x2, x3). The steepest descent method is an iterative optimization algorithm used to find the local minimum of a function.
Step 1: Initialize the starting point (x1, x2, x3) and set the initial values.
Step 2: Compute the gradient of the function f(x1, x2, x3) with respect to each variable (x1, x2, x3). The gradient is a vector that points in the direction of the steepest increase of the function.
Step 3: Calculate the step size, which determines how far along the descent direction we move. This can be done using various techniques, such as line search or a constant step size.
Step 4: Update the current point by moving in the direction of the negative gradient (steepest descent direction) with the computed step size. The new point will be (x1_new, x2_new, x3_new).
Step 5: Check the convergence criteria. If the change in the function value or the variables is below a certain threshold, stop the iteration process. Otherwise, return to Step 2 with the updated point.
By following these steps, the method of steepest descent will help us find the minimizer of the function f(x1, x2, x3).
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At rolling hills middle school the ratio of the total number of students to the number of students with pets is 3 to 1 if there are 243 students at the school how many students have pets
If there are 243 students at the school, then there are 81 students at Rolling Hills Middle School who have pets.
If the ratio of the total number of students to the number of students with pets at Rolling Hills Middle School is 3 to 1, this means that for every 3 students at the school, there is 1 student with a pet.
Let's represent the total number of students at the school as "3x" (since the ratio is 3 to 1, we can use any multiple of 3 as a placeholder for the total number of students), and the number of students with pets as "x". Therefore, we can write the following equation:
3x : x = 3 : 1
To solve for x, we can cross-multiply:
3x * 1 = x * 3
3x = 3x
We can see that the equation is true for any value of x, which means that there are many possible solutions. However, since we know that the total number of students at the school is 243, we can use this information to solve for x:
3x = 243
x = 81
Therefore, there are 81 students at Rolling Hills Middle School who have pets.
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Consider the equation − 2(x + 2) = x − 3(x + 1) − 1. Is it always true, sometimes true, or never true?
Answer: Always true.
Step-by-step explanation: Use algebra. They end up being the same statements, which means x could be whatever and the equation would still be true.
A large bag contains the following marbles:
40 blue marbles
8 green marbles
16 yellow marbles
21 white marbles
Tyra selects a marble from the bag at random. Based on the information, which statement is true?
A.
The correct option for the large bag contains marbles:
A: The marble she selects is twice as likely to be yellow as it is to be green.B: She chooses a marble that has a higher probability of being blue than any other color put together.Explain about the multiple of the number?Multiples are the outcomes of multiplying a numeral by a specific number in mathematics. Examples of multiples of 5 include 10, 15, 20, 25, 30, and cetera.Multiply the integer even by whole number to discover its multiples. For instance, 15 is the third multiple of 5 since 5 3 = 15. The first five multiples of 4 include, for instance, 4, 8, 12, 16, and 20. The first multiple of 4 is 4 since 1 4 = 4.The given question:
marbles in the bag:
40 blue marbles
8 green marbles
16 yellow marbles
21 white marbles
One marble is selected by Tyra.
Then, the correct option are-
A: There is a two to one chance that the marble she chooses will be yellow rather than green.
16 yellow marbles = 2* 8 green marbles
B: Compared to all the other colors combined, the stone she chooses is more likely to be blue.
40 blue marbles have the highest number.
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The complete question is-
A large bag contains the following marbles: •
40 blue marbles
8 green marbles
16 yellow marbles
21 white marbles
Tyra selects a marble from the bag at random. Based on the information, which statement is true?
A The marble she selects is twice as likely to be yellow as it is to be green.
B.The marble she selects is more likely to be blue than all the other colors combined.
C. The marble she selects is equally likely to be yellow or white
D. The marble she selects is three times as likely to be white as it is to be green.
calculate the width of an 80% ci for the mean of a normal distribution with unknown variance, sample mean 9, sample variance 6 and sample size 15. use two decimal places.
With the given parameters, the width of the 80% CI for the normal distribution's mean is roughly 1.5.
The following formula can be used to determine the width of an 80% confidence interval (CI) for the mean of a normal distribution with unknown variance, the sample mean 9, sample variance 6, and sample size 15:
width = t * (s / √(n))
where s is the sample standard deviation (the square root of the sample variance), n is the sample size, and t is the value from the t-distribution with n-1 degrees of freedom for an 80% CI (from a t-table or calculator).
We must first determine the sample standard deviation:
s = √(6) ≈ 2.45
Then, we can find the worth of t from a t-table or mini-computer for a 80% CI with 14 levels of opportunity (15-1):
t = 1.339Lastly, these numbers can be used to calculate the 80% CI width:
width = 1.339 * (2.45 / √(15)) = 1.5With the given parameters, the width of the 80% CI for the normal distribution's mean is roughly 1.5.
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5. Challenge Problem
The largest pizza that is sold commercially is available
from Paul Revere's Pizza Company. The pizza has
a 4-foot diameter and costs about $100.00.
a. What is the circumference of the pizza?
b. If the pizza was sliced by cutting eight diameters
with a pizza cutter, how may slices would be created?
I'm a pizza with pizzaz!
c. Sliced according to B (above), what is the measurement
of the outside edge of each of the slices?
d. Sliced according to B (above) what is the cost per slice?
Each slice has an exterior edge that measurement roughly 0.6981 feet in length. Hence, the price per slice is around $11.11.
What does measurement and example mean?
Comparison of a parameter with a predetermined reference value is the process called measurement. For instance, when a measurement is represented as 10 kg, kg is the accepted unit of mass and 10 represents the physical quantity's size. Make correction suggestions.
The formula for calculating the arc length of the a sector, which is as follows, may be used to get the measurement of each slice's outer edge:
arc length is equal to (angle/360) x 2r.
when r is the pizza's radius, which is equal to its diameter. When we replace r with 2 feet & angle with 40 degrees, i get:
arc length is (40/360) x 2 x 2 feet, which is rounded to 0.6981 feet with 4 decimal places.
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solve for x, using a tangent and secant line
Check the picture below.
[tex]x^2=(8+2)(2)\implies x^2=20\implies x=\sqrt{20}\implies x\approx 4.5[/tex]
The value of x is 4.5 rounded to the nearest tenth.
What is Tangent and Secant of a Circle?Tangent of a circle is defined as the line which passes through exactly one point on the circle.
Secant of a circle is the line which passes through two points on the circle.
Secant-Tangent Rule states that if a tangent and a secant are drawn to a circle from the same point outside the circle, then the square of the length of the tangent segment is equal to the product of the lengths of secant and the segment of secant outside the circle.
Using the theorem, we can say here that,
(8 + 2) 2 = x²
x² = 10 × 2
x² = 20
x = √20
x = 4.472 ≈ 4.5
Hence the value of x is 4.5.
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help will be much appreciated
The average speed of the total journey is 75 kilometres per hour.
How to find average speed?Anil completes the 72 kilometres journey between Bristol and Cardiff for 48 minutes. He then drive 69 kilometres from Cardiff to Swansea at an average speed of 60 kilometres per hour.
Therefore, let's find Anil average speed for the total of his journey as follows:
speed of his first journey = distance / time
speed of his first journey = 72 / 48
speed of his first journey = 1.5 km/minutes = 90 km/hrs
Therefore,
average speed of the total journey = 90 + 60 / 2
average speed of the total journey = 150 / 2
average speed of the total journey = 75 kilometres per hour
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in a survey, 69% of americans said they own an answering machine. if 15 americans are selected at random, find the probability that exactly 7 own an answering machine. round your answer to three decimal places.
Rounding to three decimal places, the probability that exactly 7 Americans out of a sample of 15 own an answering machine is approximately 0.170.
To find the probability that exactly 7 of the 15 Americans selected at random own an answering machine, we can use the binomial distribution formula:
P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)
where P(X = k) is the probability of getting exactly k successes, n is the sample size, p is the probability of success, and (n choose k) is the binomial coefficient which represents the number of ways to choose k successes out of n trials.
In this case, n = 15, p = 0.69 (the proportion of Americans who own an answering machine), and k = 7. Thus, the probability of getting exactly 7 Americans who own an answering machine out of a sample of 15 is:
P(X = 7) = (15 choose 7) * 0.69^7 * (1 - 0.69)^(15 - 7)
Using a calculator or statistical software, we can evaluate this expression to find:
P(X = 7) ≈ 0.170
This means that if we were to repeat this survey many times with samples of size 15, we would expect approximately 17% of the samples to have exactly 7 Americans who own an answering machine.
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Question 5(Multiple Choice Worth 2 points)
(Surface Area of Cylinders MC)
Ice cream is packaged in cylindrical gallon tubs. A tub of ice cream has a total surface area of 232. 36 square inches. If the diameter of the tub is 8 inches, what is its height? Use π = 3. 14. 6. 75 inches
5. 25 inches
3. 375 inches
2. 625 inches
As per the surface area, the height of the cylindrical gallon tub of ice cream is approximately 2.625 inches. (option d).
In this problem, we have been given the diameter of the tub, which is 8 inches. The radius of the tub can be calculated by dividing the diameter by 2, which gives us a radius of 4 inches.
We have also been given the total surface area of the tub, which is 232.36 square inches. Using the formula for surface area, we can write:
232.36 = 2π(4)² + 2π(4)h
232.36 = 100.48 + 25.12πh
Subtracting 100.48 from both sides, we get:
131.88 = 25.12πh
Dividing both sides by 25.12π, we get:
h = 131.88 / (25.12π)
Using the value of π as 3.14, we can simplify this expression to:
h = 131.88 / 79.104
h ≈ 2.6256 inches
Hence the correct option is (d).
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The sum of two numbers is 18. Their difference is -8. Find the two numbers.
Part A
Write a system of equations that represents the situation.
x + y =
x-y =
Part B
Solve the system of equations. Express the coordinates as decimals if necessary.
The two numbers in the system of equation is 5 and 13.
What is system of equation?A group of multiple-variable equations that must all be solved concurrently make up a system of equations. Finding values for the variables that satisfy every equation in a system of equations is the objective. Each equation in the system reflects a connection between the variables. In order to find a singular solution or a group of solutions, systems of equations can be solved using a variety of methods, such as substitution or elimination. In many disciplines, including mathematics, physics, engineering, and economics, systems of equations can occur.
Let us suppose the two numbers as x and y.
x + y = 18
x - y = -8
The second equation can be written as:
x + 8 = y
Substitute the value of y in equation 1:
x + x + 8 = 18
2x = 10
x = 5
Substitute the value of x to get y:
x + y = 18
5 + y = 18
y = 13
Hence, the two numbers in the system of equation is 5 and 13.
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the fox population iun a certain region has an annual growth rate of 9% per year. in the year 2012 there were 23900 fox counted in the area. what is the fox population predicted in the year 2020
The population of foxes in the region in 2020 is predicted to be 40,174.
The population of foxes in the region in 2020 can be calculated using the formula [tex]P = P0 (1+r)^n[/tex], where P is the population at the end of n years, P0 is the initial population, and r is the annual growth rate. The fox population iun a certain region has an annual growth rate of 9% per year. in the year 2012 there were 23900 fox counted in the area.In this case, P0 = 23900 and r = 0.09. Since the starting year is 2012, the number of years since then is n = 8. Plugging these values into the formula, P = 23900 (1.09)^8 = 40,174. Therefore, the population of foxes in the region in 2020 is predicted to be 40,174.
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find the number of ways of arranging N people in a straight line if two particular people must always be separated
The number of ways to arrange N people with A and B separated is given by expression N! - 2*(N-1)! .
What exactly are expressions?
In mathematics, an expression is a combination of numbers, variables, operators, and functions that are grouped together in a meaningful way. Expressions can be as simple as a single number or variable, or they can be complex and include many different elements. They are used to represent mathematical relationships and operations, and can be evaluated or simplified using mathematical rules and techniques. Examples of expressions include:
3x + 7(2a - b) / (c + 1)sin(x) + cos(y)Now,
Let the two particular people be A and B.
If we place A in a spot, there are N-1 spots left for B to be placed. Once A and B are placed, there are (N-2)! ways to place the remaining people. Therefore, the number of ways to arrange N people with A and B separated is:
(N-1) * (N-2)!
Alternatively, we can find the total number of ways to arrange N people in a line (N!) and subtract the number of ways to arrange them with A and B together.
To find the number of ways to arrange N people with A and B together, we can treat A and B as a single entity, so there are (N-1)! ways to arrange the remaining people with AB together. However, A and B can be arranged in two ways (AB or BA), so we need to multiply (N-1)! by 2.
Therefore, the number of ways to arrange N people with A and B separated is:
N! - 2*(N-1)!
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if 10 friends are going to occupy 10 seats in shuttle on the way to the airport, how many different ways can they arrange themselves in the shuttle? provide your answer below:
If 10 friends are going to occupy 10 seats in a shuttle on the way to the airport, then they can arrange themselves in the shuttle in 10! or 3,628,800 ways.
Step-by-step explanation: There are 10 friends and 10 seats to be occupied in a shuttle.
Therefore, the number of ways to arrange the 10 friends in 10 seats is given by 10! (10 factorial), which is calculated as follows: 10! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1= 3,628,800
Therefore, 10 friends can arrange themselves in the shuttle in 3,628,800 ways.
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Select the correct answer.
A graph with a y-axis and an x-axis in positive and negative planes. A figure is formed M F G H I J K L is made by connecting points (-3,5), (8,5), (8,2), (3,2), (3,-5), (-8,-5), (-8,-2), and(-3,-2).
Eleanor is participating in a game show in which she has to complete a lap with seven different obstacles. The lap starts and ends at F. The obstacles are placed at points G, H, I, J, K, L, and M. What is the total length of the lap?
A.
52 units
B.
54 units
C.
56 units
D.
58 units
Thus, the total length of lap covered to get the seven different obstacles is found as: 52 units.
Define about the distance formula?the Pythagorean theorem is used to calculate the distance between two locations using the distance formula. The Pythagorean theorem can be rewritten as d = √((x2 - x1)²+(y2 - y1)²) to calculate the separation between any two locations.
Given data:
Points on y-axis and an x-axis are given,
M(-3,5), F(8,5), G(8,2), H(3,2), I(3,-5), J(-8,-5), K(-8,-2), and L(-3,-2).
Starting and ending point is F.
Points lies between the starting and ending are-
F ,G, H, I, J, K, L, M, F
Total length = sum of all length
d = √((x2 - x1)²+(y2 - y1)²)
FG = √((8 - 8)²+(2 - 5)²)
FG = √9
FG = 3
GH = √((8 - 3)²+(2 - 2)²)
GH = √25
GH = 5
HI = √((3 - 3)²+(2 + 5)²)
HI = √49
HI = 7
IJ = √((3 + 8)²+(-5 + 5)²)
IJ = √121
IJ = 11
JK = √((-8 + 8)²+(-2 - 5)²)
JK = √9
JK = 3
KL = √((-8 + 3)²+(-2 + 2)²)
KL = √25
KL = 5
LM = √((-3 + 3)²+(-2 - 5)²)
LM = √49
LM = 7
MF = √((8 + 3)²+(+5 - 5)²)
MF = √121
MF = 11
Total length = 3 + 5 + 7 + 11 + 3 + 5 + 7 + 11
Total length = 52 units
Thus, the total length of the lap covered to get the seven different obstacles is found as: 52 units.
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2x + y = -7
3x = 6 + 4y
x = ?
y = ?
2x + y = -7
y= -7-2x
put this value in 2nd equation
3x=6+4(-7-2x)
3x=6-28-8x
11x= -22
x= -2
y= -7-2(-2)
y= -7+4
y= -3
Can you help me with this?
The equation of the line that contains the point (-6, 5) and is parallel to x + 2y = 14 in slope-intercept form is y = (-1/2)x + 2.
What are parallel lines?Due to their similar slopes, parallel lines move in the x direction with the same rate of change. If we know the slope of a line, we can use that slope to determine the slope of any line that is parallel to it. The point-slope form of a line can be used to get the equation of a line that is parallel to a given line and passes through a specified point.
The given equation of the line is:
x + 2y = 14
Rewriting the equation in standard form we have:
y = (-1/2)x + 7
where, -1/2 is the slope of the line.
The slope of two parallel lines are equal. Thus the slope of new line is m = -1/2.
Now, using the point slope form:
y - y1 = m(x - x1)
Substitute the values:
y - 5 = (-1/2)(x - (-6))
y - 5 = (-1/2)x - 3
y = (-1/2)x + 2
Hence, the equation of the line that contains the point (-6, 5) and is parallel to x + 2y = 14 in slope-intercept form is y = (-1/2)x + 2.
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Kendrick bought a calculator priced at $71. Shipping and handling cost an additional 25% of the price. What was the total cost of the calculator, including shipping and handling?
Answer:
The answer to our problem is, $17.75
Step-by-step explanation:
First we need to find out what is 25% of 71
25% of 71 is 17.75. Or [tex]17\frac{3}{4}[/tex] We would need to stick to the term in decimals because of we are using money. Have you ever heard of a fraction in money my guess is no. So let’s stay with decimals. 17.75
How I got it:
25 percent * 71
= (25:100)* 71
= (25* 71):100
= 1775:100
= 17.75
Percentage solution with steps:
Step 1: Our output value is 71.Step 2: We represent the unknown value with x.Step 3: From step 1 above, 71 = 100%.Step 4: Similarly, x = 25%.Step 5: This results in a pair of simple equations:71 = 100% (1)
X = 25% (2)
Step 6: By dividing equation 1 by equation 2 and noting that both the RHS (right hand side) of bothequations have the same unit (%); we have
[tex]\frac{71}{x} = \frac{25}{100}[/tex]
X = 17.75
Thus the answer to your problem is, $17.75