The net of a cylinder is a 2-dimensional representation of a 3-dimensional cylinder that has been "unwrapped" and laid flat. The net consists of two circles (representing the top and bottom of the cylinder) and a rectangle (representing the side of the cylinder).
The length of the base of the rectangle in the net of a cylinder represents the circumference of the cylinder, which is the distance around the circular base of the cylinder. The circumference of a circle is calculated using the formula C = 2πr, where C is the circumference, π is a mathematical constant approximately equal to 3.14, and r is the radius of the circle.
In the net of a cylinder, the base of the rectangle is the same as the circumference of the circles because it is equal to the distance around the circular base of the cylinder. The width of the rectangle represents the height of the cylinder, which is the same as the distance between the top and bottom circles.
Answer:
Therefore, the length of the base of a rectangle in the net of a cylinder is the same as the circumference of the circles because it represents the distance around the circular base of the cylinder.
Simplify the expression. 4+5/3^2−2^
2
The simplified expression is 25/9, of the given expression. 4 + (5/3)² − 2².
What is the exponentiation?
An exponential function is a mathematical function of the following form: f (x) = ax. where x is variable, and a is a constant called the base of the function. The most commonly encountered exponential-function base is the transcendental number e, which is equal to approximately
To simplify the expression, we need to follow the order of operations, which is:
Evaluate any expressions inside parentheses or brackets.
Exponents (ie, powers and square roots, etc.)
Multiplication and Division (from left to right)
Addition and Subtraction (from left to right)
Using this order, we can simplify the expression as follows:
4 + (5/3)² - 2²
= 4 + (25/9) - 4 ..........5/3 squared is 25/9 and 2 squared is 4
= (36/9) + (25/9) - (36/9) ..........rewrite 4 as 36/9 to have a common denominator of 9
= 25/9
Therefore, the simplified expression is 25/9.
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Explain why the discriminant affects the type of roots for a quadratic equation
Answer:
See below
Step-by-step explanation:
The roots aka solutions to a quadratic equation in standard form:
[tex]ax^2 + bx + c = 0[/tex]
are given by
[tex]x = \dfrac{ -b \pm \sqrt{b^2 - 4ac}}{ 2a }[/tex]
The term under the square root sign, [tex]b^2 - 4ac[/tex] is called the discriminant
The type and number of roots are determined by the sign of the discriminant
When [tex]b^2 - 4ac = 0[/tex] there is one real root.
When [tex]b^2 - 4ac > 0[/tex] there are two real roots.
When [tex]b^2 - 4ac < 0[/tex] there are two complex(imaginary) roots.
- Over the course of 24 hours, the tides on Earth complete one full cycle from low tide to high tide and back down again. On one particular beach, the tide drops to 2 feet below sea level for low tide and reaches 4 feet above sea level for high tide. Write a possible trigonometric function that would model the tide situation for
this beach.
The cosine function that would model the tide situation for this beach is given as follows:
y = -3cos(πx/12) + 1.
How to define the cosine function?The function is at it's minimum value at the origin, hence it is a reflected cosine function, defined as follows:
y = -Acos(Bx) + C.
The parameters are given as follows:
A: amplitude.B: the period is 2π/B.C is the vertical shift.The minimum value is of -2, while the maximum value is of 4, for a difference of 6, hence the amplitude of the function is given as follows:
2A = 6
A = 6/2
A = 3.
With no vertical shift, the function should oscillate between -A = -3 and A = 3, but it oscillates between -2 and 4, hence the vertical shift is given as follows:
C = 1.
The period is of 24 hours, hence the coefficient B is given as follows:
2π/B = 24
24B = 2π
B = π/12.
Hence the function is defined as follows:
y = -3cos(πx/12) + 1.
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The mean and standard deviation of a population are 200 and 20, respectively. Sample size is 25. What is the mean of the sampling distribution?.
The mean of the sampling distribution is 200, and the standard deviation of the sampling distribution is 4.
The sampling distribution is a theoretical distribution that represents the behavior of sample means from all possible samples of a given size that can be drawn from a population.
However, the standard deviation of the sampling distribution is not the same as the standard deviation of the population.
Mathematically, we can represent the mean of the sampling distribution as follows:
μ(x) = μ = 200
Where μ(x) represents the mean of the sampling distribution and μ represents the mean of the population.
We can also calculate the standard error of the mean using the following formula:
σ(x) = σ / √(n)
Where σ(x) represents the standard deviation of the sampling distribution, σ represents the standard deviation of the population, and sqrt(n) represents the square root of the sample size.
Plugging in the values given in the problem, we get:
σ(x) = 20 / √(25) = 4
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Solve for the roots in simplest form using the quadratic formula: 4x^2+21=-20x
The roots of the quadratic equation 4x^2 + 21 = -20x in simplest form are x = -1/2 and x = -7/2.
What is quadratic formula ?
The quadratic formula is a standard formula used to solve quadratic equations of the form ax^2 + bx + c = 0, where a, b, and c are constants and x is the variable. It is derived using the method of completing the square and provides a simple way to find the roots (or solutions) of the quadratic equation.
The quadratic formula is:
x = (-b ± √(b^2 - 4ac)) / 2a
Steps to be followed:
To solve the quadratic equation 4x^2 + 21 = -20x using the quadratic formula, we first need to rearrange the equation in standard quadratic form, which is ax^2 + bx + c = 0. In this case, we have:
4x^2 + 20x + 21 = 0
So, we can identify a = 4, b = 20, and c = 21. Now we can substitute these values into the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a
Plugging in the values of a, b, and c, we get:
x = (-20 ± √(20^2 - 4(4)(21))) / 2(4)
Simplifying the expression under the square root, we get:
x = (-20 ± √(400 - 336)) / 8
x = (-20 ± √64) / 8
x = (-20 ± 8) / 8
This gives us two possible solutions:
x = (-20 + 8) / 8 = -1/2
x = (-20 - 8) / 8 = -7/2
Therefore, the roots of the quadratic equation 4x^2 + 21 = -20x in simplest form are x = -1/2 and x = -7/2.
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Feb 17 A zoo feeds its monkeys a mixture of fruits and biscuits. The diagram shows the ratio of fruit n mass to biscuit mass. Ratios with tape diagrams The table shows the mass, in grams, of fruit and biscuits that the zoo fed two of the monkeys. Monkey A Fruit mass Based on the ratio, complete the missing values in the table. B Biscuit mass Fruit mass (g) Biscuit mass (g) 28 45
help fast
Answer:
Fruit mass = 63.2 g
Biscuit mass = 94.8 g
Step-by-step explanation:
Since the ratio of fruit mass to biscuit mass is 2:3, the fraction of fruit mass to the total of fruit and biscuit mass is 2/5 and the fraction of biscuit mass to the total of fruit and biscuit mass is 3/5.
For Monkey A, the total of fruit and biscuit mass is 73 g, which means that the fraction of fruit mass is 2/5 × 73 g = 29.2 g and the fraction of biscuit mass is 3/5 × 73 g = 43.8 g. Therefore, the values for fruit mass and biscuit mass are:
Fruit mass = 29.2 g
Biscuit mass = 43.8 g
For Monkey B, the total of fruit and biscuit mass is 73 + 85 = 158 g, which means that the fraction of fruit mass is 2/5 × 158 g = 63.2 g and the fraction of biscuit mass is 3/5 × 158 g = 94.8 g. Therefore, the values for fruit mass and biscuit mass are:
Fruit mass = 63.2 g
Biscuit mass = 94.8 g
A ring-shaped region is shown below. Its inner radius is 11 m. The width of the ring is 3 m. 11 m Find the area of the shaded region. Use 3.14 for л. Do not round your answer.
The area of the shaded region is 235.5 m².
What is the area of the shaded region?To find the area of the shaded region, we need to subtract the area of the inner circle from the area of the outer circle.
The outer radius of the ring can be found by adding the width of the ring to the inner radius:
Outer radius = inner radius + width
= 11 m + 3 m
= 14 m
The area of a circle is given by the formula:
Area = π × (radius)²
Therefore, the area of the inner circle is:
Area of inner circle = π × (11 m)²
= 121π m²
And the area of the outer circle is:
Area of outer circle = π × (14 m)²
= 196π m²
To find the area of the shaded region, we need to subtract the area of the inner circle from the area of the outer circle:
Area of shaded region = Area of outer circle - Area of inner circle
= 196π m² - 121π m²
= 75π m²
= 75 x 3.14
= 235.5 m²
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If p - r = 11 and q - r = -5, what is the value of p - q? -16 -6 6 16
The value of the expression P-q will be 16. The correct option is C.
What is an expression?In mathematics, expression is defined as the relationship of numbers, variables, and functions using mathematical signs such as addition, subtraction, multiplication, and division.
To find the value of p - q, we need to eliminate r from the two equations given to us.
We can do this by solving for r in one of the equations and then substituting that expression into the other equation.
Let's solve for r in the equation p - r = 11:
r = p - 11
Now we can substitute this expression for r into the equation q - r = -5:
q - (p - 11) = -5
Simplifying this equation by distributing the negative sign, we get:
q - p + 11 = -5
Subtracting 11 from both sides, we get:
q - p = -16
Therefore, p - q = -(q - p) = -(-16) = 16.
So the answer is 16.
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A water bottle has 20 ounces in it. After you drink x ounces of water, there are 8 ounces left. Which equation represents this situation?.
Answer:
Step-by-step explanation
The bottle had 20 ounces that before and 8 ounces after
8+x=20
20-x=8
20-8=x
20-8=12
Please help find the radius, circumference, and area
CAN SOMEONE HELP PLEASE?✨
Answer:
[tex]\sf{The\;Marginal\;Revenue\;} $MR(8) = \boxed{288} \;dollars per unit$}[/tex]
Step-by-step explanation:
What is Marginal Revenue?
Marginal Revenue is the revenue that is gained from the sale of an additional unit. It is the revenue that a company can generate for each additional unit sold
Given the equation for revenue function
[tex]R(q) = -7q^2+400q[/tex]
the Marginal Revenue [tex]MR(q)[/tex] is the first derivative of this function wrt [tex]q[/tex]
[tex]MR(q) = \dfrac{d}{dq}\left(R(q)\right)\\= \dfrac{d}{dq}(-7q^2 + 400q)\\\\= \dfrac{d}{dq}(-7q^2) + \dfrac{d}{dq}(400q)\\\\= -14q + 400\\\\[/tex]
For [tex]q = 8,[/tex] this works out to:
[tex]MR(8) = -14(8) + 400\\\\= -112 + 400\\\\= 288[/tex]
And that is the answer
Step-by-step explanation:
is given above in the pdf
What is the volume of this figure?
Answer: 186 cubic in
Step-by-step explanation:
Part of Thor's job at a nonprofit organization, Rag Na Care, is to simply answer the phone to collect donations. The data collected shows a weak
negative linear relationship between the number of hours he worked each week, , and the amount of donations in dollars, y, that the organization
collected each week
a. What does it mean for the relationship between the variables when the correlation is weak in this context?
Part of Thor's job at a nonprofit organization, Rag Na Care, is to simply answer the phone to collect donations. The datis collected shows a weak negative linear relationship between the number of hours he worked each week, z. and the amount of donations in dollars, g, that the organization collected each week
b What does it mean for the relationship between the variables when the correlation is negative in this context?
Part of Thor's job at a nonprofit organization, Ray Na Care, is to simply answer the phone to collect donations. The data collected shows a weak negative reasonship between the number of hours he worked each week and the amount of donations in dollars that the organization
codected each week Ther's boss, Nick Fury sees the data and tete hem, "We certainly tend to bring in a less money when you're working here! This graph saves you're the cause of this decrease in donations!
What wrong with the Thor's bom claim? Explain your reasoning "Tell me why"
a. Thor works more hours each week, the quantity of donations the organization raises each week declines, but the link is not very strong.
What is negative correlation?When two variables are correlated negatively, the other variable's value falls as the value of the first variable rises.
The correlation coefficent, which expresses correlation on a scale from +1 to -1, is used. Numbers less than 0 indicate a negative connection. An increase in one variable confidently foretells a drop in the other when there is a perfect negative correlation, with a coefficient of -1. Non-zero coefficients between +1 and -1 are used to show lower degrees of connection. 0 means there is no propensity for the variables to change simultaneously, either positively or negatively.
a. A weak negative linear relationship between hours worked and donations collected in this context means that as Thor works more hours each week, the quantity of donations the organization raises each week declines, but the link is not very strong.
b. When we say there is a weak correlation between two variables, we are referring to their level of relationship. The negative correlation in this instance indicates that there is a propensity for the amount of donations collected to decline as the time spent working increases, but the relationship is not very strong, indicating that there is a lot of variability in the data and making firm predictions or conclusions based on this correlation alone is challenging.
c. Tom's boss's claim is wrong as the negative correlation or the decline in donation is a mere coincidence and does not have a relation to Thor's work.
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The point P(4, 28) lies on the curve y = x² + x + 8. If Q is the point (x,x² + x + 8), find the
slope of the secant line PQ for the following values of x.
For x = 4.1:
Slope of PQ =5.1
For x = 4.01:
Slope of PQ =6.01
For x = 3.9:
Slope of PQ =15.1
For x = 3.99:
Slope of PQ =105.99
From the results above, we can guess that the slope of the tangent line to the curve at P is approximately 6.
Step by step explanationTo find the slope of the secant line PQ, we need to first find the coordinates of point Q in terms of x:
Q = (x, x² + x + 8)
Then, the slope of the secant line PQ is given by:
(yQ - yP) / (xQ - xP)
where yP = 28 and xP = 4, and yQ and xQ depend on the value of x.
For x = 4.1:
Q = (4.1, 4.1² + 4.1 + 8) = (4.1, 28.51)
Slope of PQ = (28.51 - 28) / (4.1 - 4)
= 0.51 / 0.1
= 5.1
For x = 4.01:
Q = (4.01, 4.01² + 4.01 + 8) = (4.01, 28.0601)
Slope of PQ = (28.0601 - 28) / (4.01 - 4)
= 0.0601 / 0.01
= 6.01
For x = 3.9:
Q = (3.9, 3.9² + 3.9 + 8) = (3.9, 26.49)
Slope of PQ = (26.49 - 28) / (3.9 - 4)
= -1.51 / -0.1
= 15.1
For x = 3.99:
Q = (3.99, 3.99² + 3.99 + 8) = (3.99, 26.9401)
Slope of PQ = (26.9401 - 28) / (3.99 - 4)
= -1.0599 / -0.01
= 105.99
As x approaches 4 from both sides, the x-coordinate of Q approaches 4, and the slope of PQ approaches the slope of the tangent line to the curve at P(4,28). From the results above, we can guess that the slope of the tangent line to the curve at P is approximately 6.
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Triangle UVW is similar to triangle XYZ. Find the measure of side XY. Figures are not drawn to scale.
The triangle XYZ has a scale factor of 2.53 and hence side length XY is
7.6 units.
What is a scale factor?The scale factor defines a variable in a ratio of two different measurements.
Sometimes drawings of large models are represented in a scale factor of a smaller unit.
Given, The side WV, of the triangle UVX is 6 and the corresponding side XZ of triangle 15.2.
So, The scale factor is 15.2/6 = 2.53.
Therefore, The side length XY = 3×2.53 = 7.6.
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7/17.5 cm=12/x what is x
We receive the ratio as follows:
7/17.5 = 12/x
We can cross-multiply and solve for x to determine x:
7x = 17.5 × 12
7x = 210
x = 210/7
x = 30
Hence, x has a value of 30 cm.
What are measurements?Measuring is a method that involves comparing an object's characteristics to a reference value to ascertain its attributes. The primary metric for expressing any quantity of items, things, and occurrences is measurement.
Measuring MethodsIn a number of branches of mathematics, we work with several fundamental categories of measurement variables. As follows:
Time Length Weight Volume TemperatureThe fundamental idea in the study of science and mathematics is measurement. The qualities of an object or event can be quantified so that we can compare them to those of other objects or occurrences. When discussing the division of a quantity, measurement is the word that is used the most frequently. Also, in that, it requires a specific number of items to complete a specific task. We frequently encounter many measurements kinds for length, weight, times, etc. in our daily lives.
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In Hillsdale, the library is due south of the courthouse and due west of the community
swimming pool. If the distance between the library and the courthouse is 15 miles and the
distance between the courthouse and the city pool is 25 miles, how far is the library from the
community pool?
The library is 20 miles from the community pool as calculated after performing mathematical operations.
What are mathematical operations?The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.
Given, In Hillsdale, the library is due south of the courthouse and due west of the community swimming pool.
Also given,
The distance between the library and the courthouse is 15 miles.
The distance between the courthouse and the city pool is 25 miles,
Using the Pythagorean theorem, we have:
x = 25² - 15²
x² = 625 - 225
x = 400
Taking the square root of both sides, we get:
x = 20
Therefore, the library is 20 miles from the community pool
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1.Find the equation of the lines given the two points. 2. a) (-8, 3) and (-6, 0) b) (5, 4.5) and (5, -1)
The equation of the lines with the points (-8, 3) and (-6, 0) is y = -3x/2 + 9.
The equation of the lines with the points (5, 4.5) and (5, -1) is y = 4.5.
How to determine an equation of this line?In Mathematics, 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.At data point (-8, 3), a linear equation in standard form for this line can be calculated by using the point-slope form as follows:
y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
y - 3 = (0 - 3)/(-6 + 8)(x + 8)
y - 3 = -3x/2 - 12
y = -3x/2 + 9
For points (5, 4.5) and (5, -1), we have:
At data point (5, 4.5), a linear equation in standard form for this line can be calculated by using the point-slope form as follows:
y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
y - 4.5 = (-1 - 4.5)/(-5 - 5)(x - 5)
y - 4.5 = 0
y = 4.5
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1/2 x^2 +. 1 =0
solve each equation by graphing related function
Answer:
Step-by-step explanation:
A writer and a publisher go to lunch. The publisher pays for the whole bill and tells the writer to pay her back once they return to the office. If the writer orders a $5 sandwich and a $3 coffee for his lunch, which number line represents the scenario correctly?
Answer:
Step-by-step explanation:
ITS GOING LEFT AND RIGHT HOPE THIS HELPS IF NOT TEXT ME PLSS .
From a deck of regular playing cards, one card is chosen at
random. Find the probability the card is a diamond or a face card.
The probability the card is a diamond or a face card is [tex]\frac{11}{26}[/tex].
What are examples and probability?Probability refers to the likelihood that any random occurrence will occur. This expression refers to estimating the probability that any specific event will take place. For example, when we throw a coin into the air. Possibility: P(A) = f / N, determines the likelihood that an event will occur. Although probability and ratios are linked, the former dictates the latter. The probability of an occurrence must be known before determining its probability.
When we find the probability, we obtain:
There are 52 cards in a standard deck of cards.As there are four suits, there are 12 face cards, which we identify as the Kings, Queens, and Jacks. There are 13 diamonds total, 3 of which are face cards that have previously been counted. There are thus 10 diamonds without faces.
Out of the 52 cards in the deck, 10 diamonds plus 12 face cards equal 22.
P= [tex]\frac{22}{52}[/tex]= [tex]\frac{11}{26}[/tex].
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Fowler Co. provides the following summary of its total budgeted production costs at three production levels: Volume in Units 1,000 1,500 2,000 Cost A $1,420 $2,130 $2,840 Cost B 1,550 2,200 2,900 Cost C 1,000 1,000 1,000 Cost D 1,630 2,445 3,260 The cost behavior of each of the Costs A through D, respectively, is A. Semivariable, variable, fixed, and variable. B. Variable, semivariable, fixed, and semivariable. C. Variable, fixed, fixed, and variable. D. Variable, semivariable, fixed, and variable.
On solving the provided question we can say that Variable, semi-variable, fixed, and variable is the right answer, hence it is (D).
What is a Variable?A variable is something that may be changed in the setting of a math concept or experiment. Variables are often represented by a single symbol. The characters x, y, and z are often used generic symbols for variables. Variables are characteristics that can be examined and have a large range of values.
A semi-variable cost (Mixed)
Cost A's overall cost rises as manufacturing volume grows, but the per-unit cost stays the same. This implies that there are two types of costs: fixed and variable.
B: Variable Cost
The manufacturing volume directly correlates with the overall cost of Cost B. This suggests that the price is purely arbitrary.
Price C: Fixed
Regardless of the volume of output, the overall cost of Cost C is constant. This suggests that the price is set in its entirety.
D: Variable Cost
The manufacturing volume directly correlates with the overall cost of Cost D. This suggests that the price is purely arbitrary.
Variable, semivariable, fixed, and variable is the right answer, hence it is (D).
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if anyone can help me with this question thank you
The vertical function of the ball can be modelled using the equation h(t) = 16t^2 + 75t + 4, where h(t) is the height of the ball at time t, 16 is the acceleration due to gravity, 75 is the initial velocity of the ball, and 4 is the initial height of the ball.
What does acceleration due to gravity mean?Acceleration due to gravity is the rate of change of velocity (speed) of an object in free fall due to the force of gravity. It is denoted by g and is equal to 9.80665 m/s2 at sea level. It is the force of gravity that causes objects to fall to the ground and accelerates them as they approach the ground. When an object is in free fall, it accelerates at a rate of 9.8 m/s2. This means that after one second, the object will be travelling at 9.8 m/s, after two seconds it will be travelling at 19.6 m/s, and so on. Without the force of gravity, objects would not accelerate in free fall.
The equation h(t) = 16t^2 + 75t + 4 models the vertical function of the ball by combining the effects of acceleration due to gravity (16), initial velocity (75), and initial height (4). The term 16t^2 represents the acceleration due to gravity, which causes the ball to accelerate in the vertical direction at a rate of 16 meters per second squared. The term 75t represents the initial velocity of the ball, which causes the ball to move in the vertical direction at a rate of 75 meters per second. Finally, the term 4 represents the initial height of the ball, which is 4 meters. By combining these three effects, the equation h(t) = 16t^2 + 75t + 4 accurately models the vertical function of the ball.
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Find the greatest common factor (GCF) of 14 and 12.
An airplane was preparing for landing. When it began its descent towards the airport, the plane's altitude was thirty four thousand feet. After descending at a steady rate for ten minutes, its altitude was twenty four thousand feet.
Define units for the amount of time that the plane descends and the plane's altitude. Enter a variable for the amount of time that the plane descends and use this variable to write an expression for the plane's altitude.
When will the plane be at an altitude of three thousand feet?
How long before the plane touches down on the runway?
Use the Worksheet to complete the problem. The column labels describe the quantity from the problem scenario that the column is about. The row labels describe the type of value that goes in the row: quantity descriptions, units of measure, algebraic expressions, or numeric values to answer a question.
Quantity Name
Time
Altitude
Unit
Given Value 1
Given Value 2
Slope
feet per minute
Intercept
feet
Expression
When will the plane be at an altitude of three thousand feet?
Question 1
How long before the plane touches down on the runway?
Question 2
The units for the amount of time that the plane descends are minutes, and the units for the plane's altitude are feet. Let's define a variable t for the amount of time that the plane descends. Then we can write an expression for the plane's altitude in terms of t as:
Altitude = 34,000 - (1,000 * t)
This expression represents the plane's initial altitude of 34,000 feet, minus the rate of descent (1,000 feet per minute) times the amount of time that the plane descends.
To find when the plane will be at an altitude of 3,000 feet, we can set the expression equal to 3,000 and solve for t:
3,000 = 34,000 - (1,000 * t)
31,000 = 1,000 * t
t = 31
So the plane will be at an altitude of 3,000 feet after 31 minutes of descent.
To find how long before the plane touches down on the runway, we can set the expression equal to 0 and solve for t:
0 = 34,000 - (1,000 * t)
34,000 = 1,000 * t
t = 34
So the plane will touch down on the runway after 34 minutes of descent.
Here is the completed worksheet:
Quantity Name | Time | Altitude
--- | --- | ---
Unit | minutes | feet
Given Value 1 | 10 | 34,000
Given Value 2 | | 24,000
Slope | | -1,000
Intercept | | 34,000
Expression | t | 34,000 - (1,000 * t)
Question 1 | 31 | 3,000
Question 2 | 34 | 0
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helphelphelphelp
i need help quick
whoever answers this first..
i will give them 100 points
Answer:
Decreased by 19%.
-------------------------------
Decrease by of x 10% can be shown as a product of x and:
100% - 10% = 90% = 0.9Same applies to the second decrease, then we get a final number:
x*0.9*0.9 = 0.81 xIt represent a one off decrease of:
1 - 0.81 = 0.19 = 19%Hence the answer is 19%.
Answer:
19%
Step-by-step explanation:
let's start from 100 and remove 10%100 - 100/10 = 90
let's take 10% off again90 - 90/10 = 91
find the difference between 100 and 81100 - 81 = 19%
for a better understanding look at the figure
Mrs. Smith has 310 pencils in her classroom. Each student gets 3³
pencils. How many students are in her class? Leave your answer in
exponent form.
A. 313
B. 330
C. 37
D. 39
The number of students in mrs. Smith's class in exponent form is 3⁷.
How many students are in Mrs. Smith class?Given that, Mrs. Smith has 3¹⁰ pencils in her classroom. Each student gets 3³ pencils.
Let the number of students in the class be represented by n.
Total number of pencils = 3¹⁰Number of pencils each student gets = 3³Number of students in the class = nTo get the number of students in the class, divide the total number of pencils by the number of pencils each student got.
n = Total number of pencils ÷ Number of pencils each student gets
n = 3¹⁰ ÷ 3³
Since they both have the same base, we subtract the exponents
n = 3¹⁰ ⁻ ³
n = 3⁷
Therefore, the number of students is 3⁷.
Option D) 3⁷ is the correct answer.
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During a drought, the cost of corn increases. Suddenly, gasoline costs $3.86 per gallon. A diesel truck uses 4 gallons to drive 60 miles. With the increased cost of gasoline, is it cheaper to drive the old truck or the diesel truck?
It is cheaper to drive the old truck, which costs $11.58 to drive 60 miles, compared to the diesel truck, which costs $15.44 to drive the same distance, given the current fuel prices.
Describe Algebraic Expression?An algebraic expression is a mathematical phrase that consists of variables, numbers, and mathematical operations such as addition, subtraction, multiplication, and division. It is a combination of constants, variables, and operators that represent a value or a relationship between values.
For example, "3x + 5" is an algebraic expression where "3" and "5" are constants, "x" is a variable, and "+" is an operator. The expression can be evaluated by substituting a value for "x" and performing the necessary operations.
Algebraic expressions can also be simplified by combining like terms and using the rules of arithmetic to simplify the expression. For instance, the expression "2x + 3x" can be simplified to "5x" by adding the coefficients of the like terms "x".
Algebraic expressions are used extensively in algebra to represent equations and relationships between variables. They are also used in a wide range of mathematical and scientific applications, including physics, engineering, and finance.
To compare the cost of driving the old truck to the diesel truck, we need to know the fuel efficiency of the old truck. Let's assume that the old truck uses gasoline and has a fuel efficiency of 20 miles per gallon.
To drive 60 miles, the old truck will use 60/20 = 3 gallons of gasoline.
At $3.86 per gallon, the cost of 3 gallons of gasoline is 3 * $3.86 = $11.58.
The diesel truck uses 4 gallons of diesel to drive 60 miles. The cost of diesel is not given in the problem, so we'll assume it's the same as the cost of gasoline, $3.86 per gallon.
At $3.86 per gallon, the cost of 4 gallons of diesel is 4 * $3.86 = $15.44.
Therefore, it is cheaper to drive the old truck, which costs $11.58 to drive 60 miles, compared to the diesel truck, which costs $15.44 to drive the same distance, given the current fuel prices.
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g bar graphs (aka. column charts) with error bars are used to show the comparison between two variables, not the relationship.truefalse
True. bar graphs (aka. column charts) with error bars are used to show the comparison between two variables, not the relationship.
What are error bars?A confidence intervals bar chart (shown as red lines)
In graphs, error bars are used to graphically show data variability and to denote error or uncertainty in reported measurements. They provide a basic indication of a measurement's accuracy or, alternatively, how far the true (error-free) value may deviate from the reported value. The standard deviation of uncertainty, the standard error, or a specific confidence range (such a 95% interval) are frequently represented as error bars. Due to the fact that these values are not the same, the measure chosen needs to be specified clearly in the graph or supporting text.
According to the definition the statement is true.
True. bar graphs (aka. column charts) with error bars are used to show the comparison between two variables, not the relationship.
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pls help asap pls i pay 54
The value of BC is 9cm.
What is a similar triangle?
If two triangles have the same shape or have the same shape as their mirror images, they are said to be comparable. One can be created from the other more precisely by evenly scaling, possibly with the inclusion of further translation, rotation, and reflection.
Here, we have
Given: BA = 6cm, AC = 8cm
BC =?
In a similar triangle, their side is also proportional.
BA/ED = AC/DF = BC/EF
BA/ED = BC/EF
6/18 = BC/27
18BC = 6×27
BC = 6×27/18
BC = 9cm
Hence, the value of BC is 9cm.
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