The value of the exponential equation is A = ( 8/7 ) x ^ -15/2
What are the laws of exponents?When you raise a quotient to a power you raise both the numerator and the denominator to the power. When you raise a number to a zero power you'll always get 1. Negative exponents are the reciprocals of the positive exponents.
The different Laws of exponents are:
mᵃ×mᵇ = mᵃ⁺ᵇ
mᵃ / mᵇ = mᵃ⁻ᵇ
( mᵃ )ᵇ = mᵃᵇ
mᵃ / nᵃ = ( m / n )ᵃ
m⁰ = 1
m⁻ᵃ = ( 1 / mᵃ )
Given data ,
Let the exponential equation be represented as A
Now , the value of A is
A = 8 / ( 7√x¹⁵ ) be equation (1)
On simplifying the equation , we get
The value of √x¹⁵ = x ^ 15/2
Now , the equation will be
A = ( 8/7 ) x ^ -15/2
Hence , the exponential equation is A = ( 8/7 ) x ^ -15/2
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What is the conversion of 80 oz to gallons?
After conversion of 80 ounces into gallon we get 0.625 gallons.
A fluid ounce is the U.S. popular units system.
Ounces and fluid ounces are two unlike units.
1 fluid ounce is equal to the 1.04 oz weight.
US fluid ounce contain 29.6 milliliters and British fluid ounce contain 28.4 milliliters.
Ounce expressed by notation oz.
To convert ounces (oz) to gallons,
We know that
One gallon = 128 fluid ounces.
We want to convert 80 ounces to gallons,
we can use the following formula:
80 oz ÷ 128 oz/gal = 0.625 gallons
Hence,
We get 80 ounces is equal to 0.625 gallons.
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What is 500 Meters in Miles?
To convert meters into miles, divied the meter value by 1609.34. Multiply when we want to convert miles into meter.
500 meters is equal to the 0.31 miles.
The symbol for meter is m.
There are 1,609.344 meters in a mile.
The word "metre" is how this unit is spelled internationally.
Both the US Customary Units and the Imperial System recognise the mile as a unit of length or distance.
The symbol for mile is mi.
There are 0.00062137 miles in a meter.
500 meters is approximately 0.31 miles.
To convert meters to miles,
You can use the following conversion:
1 mile = 1609.34 meters
Therefore,
To convert 500 meters to miles,
You can divide 500 by 1609.34:
500 meters (1609.3) meters/mile ≈ 0.31 miles
500 metres is equivalent to 0.31 miles.
Thus, rounding to two decimal places,
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Transcribed image text: From a population of size 500, a random sample of 50 items is selected. The mode of the sample a. can be larger, smaller or equal to the mode of the population. b. must be equal to the mode of population, if the sample is truly random. c. must be equal to the mean of the population, if the sample is truly random. d. must be 500.
The mode of the sample can be larger, smaller, or equal to the mode of the population.
The correct answer is A.
The mode is the most frequent value in a dataset. In a random sample, the mode can differ from the mode of the population because random sampling is subject to sampling variability. In other words, each random sample is likely to have different sample statistics than the population parameters. Therefore, it is possible for the mode of the sample to be larger, smaller, or equal to the mode of the population.
However, as the sample size increases, the mode of the sample becomes more likely to approach the mode of the population. This is because larger samples provide more information about the population and therefore reduce the impact of sampling variability.
Option B is incorrect because even if the sample is truly random, it is still subject to sampling variability, which means that the mode of the sample may not be equal to the mode of the population.
Option C is also incorrect because the mean of the population is a different statistic than the mode, and it is not necessarily related to the mode of the sample.
Option D is clearly incorrect, as the mode of a sample cannot be equal to the population size.
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Given square PQRS, determine the missing information.
P
R
4 cm
1
S
X =
y=
Ox= 4y = 4
Ox + 4y = 2 sqrt(2)
x = 4y = 4 sqrt(2)
x = 4y - 8 sqrt(2)
The missing information in the square is option(b) x = 4y = 4 √(2) and y = 4.
Given square PQRS, the task is to determine the missing information. A square is a quadrilateral with four equal sides and four equal angles.
The coordinates of the vertices of a square are (x,y), (x+4,y), (x+4,y+4) and (x,y+4).
The missing information, x and y, can be found by solving the equations that represent the sides of the square. We can start by solving for x.
The equation for the side PQ is x + 4y = 2 √(2). Solving this equation for x gives x = 4y - 8 √(2).
Similarly, the equation for the side RS is x + 4y = 4 √(2). Solving this equation for x gives x = 4y = 4 √(2).
Therefore, the missing information is x = 4y = 4 √(2) and y = 4.
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Round 0.002391 to 2 significant figures
To round 0.002391 to 2 significant figures, we need to look at the digits after the first two significant digits (which are 2 and 3 in this case).
The digit in the third decimal place is 2, which is less than 5. Therefore, we leave the second significant digit (3) as it is, and we drop all the digits after that.
So, rounding 0.002391 to 2 significant figures, we get:
0.0024
Boats from all along the Atlantic coast were moored at a busy marina one summer day. Of the 16 boats at the marina, 8 were from Maine.
What is the probability that a randomly selected boat will be from Maine?
I NEED HELP ASAP
The solution is, the probability of picking a boat from Virginia is 3/8
What is probability?Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.
here, we have,
The formula of probability is often given as
P = no. of favorable event/ no. of total outcome
In this case, our variables are
no. of favorable event=6
no. of total outcome =16
Let's proceed to input our values and solve
P = 6/16
= 3/8
From the calculation above the probability of picking a boat from Virginia is 3/8
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what is the mean absolute error?
Answer:
Step-by-step explanation: Mean Absolute Error is a model evaluation metric used with regression models. The mean absolute error of a model with respect to a test set is the mean of the absolute values of the individual prediction errors over all instances in the test set.
The scale of a district map is 1/10,000. Find the distance on the mal, in centimeters, for each of the following actual distances.
A) 800m B) 5km
Please help!!
In your own words, explain what the main differences are between earned and unearned income
Earned income refers to the money an individual earns from working for an employer, running a business or providing a service. It is considered compensation for the labor or services provided by the individual. Examples of earned income include salaries, wages, bonuses, commissions, and tips.
Unearned income, on the other hand, is income that is not directly earned through labor or services provided. Instead, it comes from investments, government benefits, or other sources of passive income. Examples of unearned income include interest income, dividends, rental income, capital gains, and social security benefits.
One of the main differences between earned and unearned income is how they are taxed. Earned income is generally subject to payroll taxes, which includes Social Security and Medicare taxes, while unearned income is generally taxed at a different rate than earned income. Another difference is that earned income is more closely tied to an individual's skills, effort, and work output, while unearned income is often influenced by factors such as market conditions, investment decisions, and government policies.
HELP ASAP, WILL GIVE BRIANLIEST, 100 POINTS,
A donut shop wanted to determine the best price to sell its donuts. The manager of the shop gathered data from several donut shops in the city for the total cost, y, for different amounts of donuts, x. He created the following scatter plot with a line of fit.
scatter plot titled donut pricing with the x axis labeled number of donuts and the y axis labeled total cost in dollars, with points at 1 comma 1, 2 comma 2 and a half, 5 comma 5, 6 comma 5 and a half, 3 comma 2, 7 comma 7, 4 comma 4, 8 comma 5 and a half, 12 comma 10, 10 comma 9, 9 comma 9, and 8 comma 7, with a line passing through the coordinates 3 comma 3 and 8 comma 7
Find the slope of the line of fit and explain its meaning for the real-world situation.
The slope is 3 over 5, which means when 0 donuts are sold, it is predicted that the shop will earn $0.60.
The slope is 4 over 5, which means when 0 donuts are sold, it is predicted that the shop will earn $0.80.
The slope is 3 over 5, which means for each additional donut sold, the shop is predicted to earn $0.60.
The slope is 4 over 5, which means for each additional donut sold, the shop is predicted to earn $0.80.
Answer:
The slope of the line of fit and its meaning for the real-world situation include the following: C. The slope is 3/5, which means for each additional donut sold, the shop is predicted to earn $0.60.
What is the point-slope form?
Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
Where:
m represents the slope.
x and y are the points.
Based on the information provided, we can logically deduce the following data points on the line:
Points on x-axis = (7, 12).
Points on y-axis = (5, 8).
At data point (7, 12), a linear equation of this line in slope-intercept can be calculated by using the point-slope form form as follows:
y - 12 = (8 - 5)/(12 - 7)(x - 7)
y - 12 = 3/5(x - 7)
y = 3x/5 - 4.2 + 12
y = 3x/5 + 7.80
Mark as BRIANLIEST pls
how to convert millimolar to molar
One of the molar concentration units is the millimolar. The symbol or abbreviation mM stands for millimolar. 1 millimolar equals 1 mol/meter³ in terms of measurement units. In terms of molar, 1 millimolar is equivalent to 0 point 001 molar.
The term "molar concentration" (also known as "molarity," "amount concentration," or "substance concentration") refers to the amount of a substance per unit volume of solution and is used to describe the concentration of a chemical species, specifically a solute, in a solution.
The number of moles per liter, denoted by the unit symbol mol/L or mol/dm3 in SI units, is the most widely used unit for molarity in chemistry. One mol/L of a solution is referred to as one molar, or 1 M.
Because most solutions' volumes only slightly vary with temperature due to thermal expansion, the use of molar concentration in thermodynamics is frequently inconvenient. Typically, temperature correction factors are introduced to solve this issue, or a concentration measure that is not temperature dependent, like molality, is used.
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How to convert 95 confidence z score?
The z-score associated with a 95% confidence level is approximately 1.96.
The z-score associated with a 95% confidence level is the value of the standard normal distribution that corresponds to an area of 0.95 to the left of the z-score.
Using a standard normal distribution table or calculator, we can find that the z-score associated with a 95% confidence level is approximately 1.96.
Therefore, if we want to calculate the z-score for a 95% confidence level, we can use the formula
z = invNorm(1 - α/2)
where α is the significance level (α = 0.05 for a 95% confidence level), and inv Norm is the inverse normal cumulative distribution function. Using this formula, we can calculate the z-score as:
z = inv Norm(1 - 0.05/2)
= inv Norm(0.975) ≈ 1.96
Therefore, the z-score is 1.96
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Philippa is making jam. She needs to buy mini jam jars which come in packs of 12, lids which come in packs of 16 and labels which come in packs of 36. She doesn't want to have any items left over. Find the smallest number of packs of each item she can buy
Philippa can buy 12 packs of mini jam jars, 9 packs of lids, and 4 packs of labels without having any items left over.
To find the smallest number of packs of each item Philippa can buy without having any items left over, we need to find the least common multiple (LCM) of 12, 16, and 36. The LCM is the smallest number that is a multiple of all three numbers.
We can find the LCM by listing the multiples of each number and finding the smallest number that appears in all three lists:
Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144...
Multiples of 16: 16, 32, 48, 64, 80, 96, 112, 128, 144...
Multiples of 36: 36, 72, 108, 144...
The smallest number that appears in all three lists is 144. Therefore, the LCM of 12, 16, and 36 is 144.
To find the smallest number of packs of each item Philippa can buy, we need to divide the LCM by the number of items in each pack:
Packs of mini jam jars: 144 ÷ 12 = 12
Packs of lids: 144 ÷ 16 = 9
Packs of labels: 144 ÷ 36 = 4
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What is 30 Meters in Feet?
Around 98.4 feet are equal to 30 metres.
The common formula 1 metre (m) = 3.28 feet (ft) will be used to convert measurements from metres to feet. Here, the conversion value is 3.28. To convert 10 metres to feet, for instance, multiply 10 by 3.28, which is 32.8 ft. Therefore, 10 meters = 32.8 feet.
Converting from metres to feet: 3.28084 metres are nearly equal to one metre. Add 3.28084 feet to the given metre value to convert it to feet. Add 3.28084 feet to the given metre value to convert it to feet. For instance, the conversion of 5 metres to feet is as follows: We are aware that the conversion factor for 5 metres to feet is 3.28084.
30 m * 3.280839895 ft/m =98.4251968504 ft
So, 30 metres is roughly equivalent to 98.4 ft.
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The mean and the median are closely related concepts. The median is the numerical value separating the higher half of your data from the lower half. You can find the median by arranging all of the observations from lowest value to highest value and picking the middle value​ (assuming you have an odd number of​ observations). Although the mean and median are closely​ related, the difference between the mean and the median is sometimes of interest.
Suppose Country A has five families. Their incomes are $9000, $21,000, $29,000, $39,000, and $50,000.
Country A's median income is _______, and its mean income is ______.
Suppose country B also has five familities. Their incomes are $9000, 21000, 29000, 39000, and 151000.
Country B's median income is _____ and its mean income is ____.
Country _____ has a greater income inequality
Based on your answers to this​ question, would you expect the ratio of the mean income in the United States to the median income has risen or​ fallen? Explain.
A.
​Fallen, because means change less with standard deviation.
B.
​Risen, because means change more with extreme values.
C.
​Risen, because means increase but medians decrease with income.
D.
​Risen, because medians increase with variance but means do not.
Mean of country A is $29600 and median $29000. Mean of country B is $49800 and median is $29000. Country B has greater income inequality. So option B is the correct answer.
Mean of incomes in country A = (9000+ 21000+ 29000 + 39000+ 50000)/5 = $29600
Median income of country A = (5+1)/2 th term = 3rd term = $29000
Mean to median ratio = 29600/ 26000= 1.02
Mean income of country B = ( 9000+ 21000+ 29000+ 39000+ 151000)/5 = $ 49800
Median income = (n+1)/2 th term = (5+1)/2 = 3rd term = 29000
Mean to median ratio of country B = 49800/29000 = 1.71
Since mean and median are closer to each other, standard deviation is less. The mean to median ratio is greater for country B. So country B has greater income inequality.
If the income inequality has been increasing, then the mean-median ratio will increase, due to the extreme values, mean will increase. So option B is the correct answer.
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If there were two runners running a race, one along the inside and one along the outside, how far apart they start so the race is fair?
Answer:
I would believe inside of a race track is smaller than the outside. They are staggered so the runners all run the same distance.
Step-by-step explanation:
Rhett read of his book over the weekend. On Monday, he read 31 more
pages. If he has read 214 pages so far, the equation below can be used to
find p, the total number of
pages in the book.
p+31 = 214
How many total pages are in Rhett's book?
The total number of pages in Rhett's book is 183 pages.
What is the solution to the equation?A solution to an equation is a number that can be substituted for the variable to provide a valid number statement.
To find the total number of pages in Rhett's book, we need to solve for p in the equation:
p + 31 = 214
First, we can isolate p on one side of the equation by subtracting 31 from both sides:
p + 31 - 31 = 214 - 31
Simplifying:
p = 183
Therefore, the total number of pages in Rhett's book is 183 pages.
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Given l∥m∥n, find the value of x?
Answer:
x = 69
Step-by-step explanation:
[tex]x + 111 = 180[/tex]
[tex]x = 180 - 111[/tex]
[tex]x = 69[/tex]
Answer:
69°
Step-by-step explanation:
What is an angle?An angle is a measure of a turn, measured in degrees or °. Angles are made up of two rays, making the sides of the angle.
What types of angles are there?There are right angles (exactly 90 degrees), acute angles (less than 90 degrees), obtuse angles (more than 90 degrees), and reflex angles (more than 180 degrees).
We can see that if there is a straight line, the angles must add up to 180°. To solve for the value of x, we can use this equation:
180 - 111 = 69Therefore, the measure of angle x = 69°
What is the measure of arc e b c? 40° 90° 140° 220°
The measure of the arc is option (c) 140°
In geometry, an arc is a curved line that is a part of a circle's circumference. The measure of an arc can be calculated using the angle of the arc, which is measured in degrees.
In the case of EBC, the measure of the arc is 140°. This is because we can use the Angle-Side-Angle (ASA) congruence theorem, which states that two triangles are congruent if and only if two angles and the included side are equal.
In the case of EBC, we know that angle A equals 40° and angle C equals 90° so the only variable left is the measure of the arc, which is equal to 140°.
Therefore, the measure of EBC is 140°. This can be verified by drawing the triangle and measuring the arc with a protractor.
Therefore, option (c) is the right one.
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Complete Question:
What is the measure of arc EBC when the values of Angle a nd c are 90 and 40 degree respectively.
a) 40°
b) 90°
c) 140°
d) 220°
Many people enjoy cross-country and downhill skiing for recreation and for exercise. For others, skiing is a competitive sport. In ski races, fractions of a second can make the difference between winning and finishing second. Describe how the skier’s velocity changes during the race
The skier's velocity changes during the race due to the force of gravity, making turns on the course, and the conditions of the snow and terrain.
The skier's velocity changes during the race in several ways. Firstly, the skier starts at a slower velocity and gradually accelerates as they move down the slope. This is due to the force of gravity pulling them downwards, which increases their speed.
Secondly, the skier's velocity changes as they make turns on the course. When making a turn, the skier's velocity decreases as they have to slow down in order to make the turn. Once they have completed the turn, their velocity increases again as they accelerate down the slope.
Lastly, the skier's velocity also changes due to the conditions of the snow and the terrain. For example, if the snow is packed and icy, the skier's velocity will be faster than if the snow is soft and powdery. Similarly, if the terrain is steep, the skier's velocity will be faster than if the terrain is flat.
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Ms. Wallace needs 45 juice boxes for a class trip. The juice boxes come in packages of 12. If Ms. Wallace already has 5 juice boxes, which equation would you use to find how many packages (p) she should buy?
The equation that is used to find the number of packages is 12x + 5 = 45.
Linear equation:
The mathematical statement that is used to find an unknown quantity is known as the Linear equation. In this, we use variables like 'x, y, z... to represent the unknown quantity or unknown number.
[ In the given problem we use variable 'x' to represent the number of packages. ]
Here we have
Ms. Wallace needs 45 juice boxes for a class trip.
The juice boxes come in packages of 12
Let Ms. Wallace needs to buy 'x' number of packages
Number of juice boxes in 'x' packs = 12x
Given that Ms. Wallace already has 5 juice boxes,
=> 12x + 5 = 45
Therefore,
The equation that is used to find the number of packages is 12x + 5 = 45.
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A high school principal asks a physical education teacher and football coach to obtain a sample of 20 student each to compare times in physical activity each week. the physical education teacher randomly selects 20 students from her classes and the football coach randomly selects 20 students from football teams. Do you expect the comparison to be fair.
No, the comparison is not expected to be fair. The two groups being compared are not selected randomly from the same population
Describe Population?A population is a group of organisms of the same species that live in the same geographic area and are capable of interbreeding. The term "population" can refer to a group of animals, plants, bacteria, or any other type of living organism.
Populations can vary in size from just a few individuals to millions or even billions. The size of a population can be influenced by a number of factors, including birth rates, death rates, immigration, and emigration.
Populations also have characteristics that define their genetic makeup, such as the frequency of particular alleles or genes. This genetic diversity can influence the ability of a population to adapt to changes in its environment or to recover from disturbances, such as disease outbreaks or natural disasters.
Understanding population dynamics is important for fields such as ecology, conservation biology, and public health, as it can help us to better manage and protect populations of organisms, including our own.
No, the comparison is not expected to be fair. The two groups being compared are not selected randomly from the same population, as the physical education teacher's sample only includes students from her classes, while the football coach's sample only includes students from the football team. This could lead to potential biases and differences between the groups that may not accurately reflect the general population of students at the high school. To ensure a fair comparison, both samples should be selected randomly from the same population.
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how to convert microliters to milliliters
Using the formula 1 millilitre = 10⁻³ microliters, we can convert millilitres to microliters.
The volume unit is milliliters (mL). One microliter (uL) is likewise a volume unit, although it is a smaller unit.
We already know that Milli equals 10⁻³.
As a result, we may write the relationship using the unit conversion idea.
One microliter equals 10⁻³ milliliters.
For example, if we have 2 microliters, it is equal to 2 x 10⁻³ milliliters.
Thus, we now have a standard formula that we can use to calculate the time in microliters to milliliters and milliliters to microliters.
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Please help , I do not understand this at all
The frequency of the sine function is given as follows:
F = 0.5/π Hz.
How to obtain the frequency of a sine function?The standard definition of the sine function is given as follows:
y = Asin(B(x - C)) + D.
For which the parameters are given as follows:
A: amplitude.B: the period is 2π/B.C: phase shift.D: vertical shift.For the function y = sin(x), we have that B = 1, hence the period is given as follows:
P = 2π/B
P = 2π.
The frequency is one divided by the period, hence:
F = 1/P
F = 1/2π
F = 0.5/π Hz.
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Answer:
[tex]F=\dfrac{1}{2\pi}\; \sf Hz[/tex]
Step-by-step explanation:
The frequency of a sinusoidal wave refers to the rate at which the wave completes one full cycle, typically measured in Hertz (Hz), where 1 Hz signifies one complete oscillation of the wave in one second.
The period of a sinusoidal wave is the amount of time it takes for the wave to complete one complete oscillation.
The frequency (F) of a sinusoidal wave can be determined from its period (P) using the formula:
[tex]\boxed{F=\dfrac{1}{P}}[/tex]
The sine function y = sin(x) completes one full cycle over the interval [0, 2π]. Therefore, its period is P = 2π.
To calculate the frequency (F), substitute P = 2π into the frequency formula:
[tex]F=\dfrac{1}{P}=\dfrac{1}{2\pi}\; \sf Hz[/tex]
suponga que usted se mueve sobre una pista rectilinea y se dezplaza a partir de un punto fijo 12 metro hacia la derecha avanza en la misma dirección 5 metro y luego se regresa en sentido contraria 18 metros la distancia entre el punto fijo y usted es
You are 1 meter behind the fixed point.
What is distance in kinematics?The total path length covered by the moving body is called distance covered.
Given is that you move on a rectilinear track and move from a fixed point 12 meters to the right, advance in the same direction 5 meters and then return in the opposite direction 18 meters.
Total displacement = 12 + 5 - 18 = - 1
So, you are 1 meter behind the fixed point.
Therefore, you are 1 meter behind the fixed point.
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{Question in english -
Suppose you move on a rectilinear track and move from a fixed point 12 meters to the right, advance in the same direction 5 meters and then return in the opposite direction 18 meters, the distance between the fixed point and you is}
Darrel receives a weekly salary of $289. In addition, $13 is paid for every item sold in excess of 100 items. How much will Darrel earn for the week if he sold 122 items?
Daren will earn $286 for the week if he sold 122 items.
What is mean by Multiplication?Multiplication means to add number to itself a particular number of times. Multiply will be viewed as a process of repeated addition.
Given that;
Darrel receives a weekly salary of $289.
And, In addition, $13 is paid for every item sold in excess of 100 items.
Hence, The cost to earn for the week if he sold 122 items is,
⇒ (122 - 100) × $13
⇒ 22 × $13
⇒ $286
Thus, Daren will earn $286 for the week if he sold 122 items.
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Let v = (- 5,8) Calculate the magnitude of - v
The magnitude of -v is [tex]\sqrt{(89)}[/tex]
Describe magnitude ?In physics and mathematics, magnitude refers to the size or quantity of a physical or mathematical property. It can be represented by a scalar value or a vector with a scalar magnitude.
In the case of scalar magnitude, it represents a property's absolute value, which is always positive. For example, the magnitude of a force, velocity, or acceleration represents its absolute value without any direction.
In contrast, vector magnitude represents the length or size of a vector, including both its magnitude and direction. It can be calculated using the Pythagorean theorem, where the magnitude of a vector V with components (Vx, Vy, Vz) is:
[tex]|V| = sqrt(Vx^2 + Vy^2 + Vz^2)[/tex]
The magnitude of a vector is always positive and can be used to determine the distance between two points in space.
Overall, magnitude is an essential concept in many fields, including physics, mathematics, engineering, and computer science, and it plays a crucial role in understanding various physical and mathematical phenomena.
The magnitude of a vector is its length, which is calculated using the Pythagorean theorem. For a vector v = (a, b), the magnitude is given by:
[tex]|v| = sqrt(a^2 + b^2)[/tex]
The negative of a vector simply reverses its direction, but not its magnitude. Therefore, the magnitude of -v is the same as the magnitude of v.
Using this information, we can calculate the magnitude of -v as follows:
[tex]|-v| = |-( -5, 8)| = |(5, -8)|\\\|-v|\ = \sqrt{(5^2 + (-8)^2)} = \sqrt{(25 + 64) }= \sqrt{(89)}Therefore, the magnitude of -v is \sqrt{(89)}[/tex]
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jessica is bisecting a segment. first, she places the compass on one endpoint and opens it to a width larger than half of the segment. what is her next step? brainly
The next step would be to draw an arc with the compass centered at the endpoint.
This arc should intersect the segment at two points.
We have,
After Jessica places the compass on one endpoint of the segment and opens it to a width larger than half of the segment, her next step would be to draw an arc with the compass centered at the endpoint.
The concept used in Jessica's next step is the compass-and-straightedge construction method.
By opening the compass wider than half of the segment and drawing an arc with the compass centered at one endpoint, she creates two points of intersection between the arc and the segment.
These points will divide the segment into two equal halves, allowing her to bisect the segment.
Thus,
The next step would be to draw an arc with the compass centered at the endpoint.
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Which of the following equations represents a linear function?
A. y = x/12
B. y = 1/2x^2
C. y= 3x
D. y = 2 (2 + 3)
Answer: Option A,C and D represents a linear equation
Step-by-step explanation:
In linear function the variable has the power raised to one.
In equation ,y=x/12 ,y=3x and y=2(2+3) all the variables has the power of 1
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A commercial jet and a private airplane fly from Denver to Phoenix. It takes the commercial jet 2. 7 hours for the flight, and it takes the private airplane 4 hours. The speed of the commercial jet is 103 miles per hour faster than the speed of the private airplane. Round your answer to one decimal place if necessary
the speed of the private airplane is approximately 214.3 miles per hour. Rounding to one decimal place is not necessary but if you round it the answer will be 214 miles.
Let's call the speed of the private airplane "s". According to the problem, the speed of the commercial jet is 103 miles per hour faster than the speed of the private airplane. So, the speed of the commercial jet is:
s + 103
We know that the distance from Denver to Phoenix is the same for both planes. Let's call this distance "d".
Using the formula distance = rate x time, we can set up two equations:
For the private airplane:
d = s × 4
For the commercial jet:
d = (s + 103) × 2.7
Since both equations represent the same distance, we can set them equal to each other and solve for s:
s × 4 = (s + 103) × 2.7
4s = 2.7s + 278.1
1.3s = 278.1
s = 278.1 / 1.3
s = 214.3
Therefore, the speed of the private airplane is approximately 214.3 miles per hour.
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