Answer:
the answer is irrational
Evaluate a2 - 6 for a = 4 and b = 17
Answer:
The answer is -94 but where is b
Step-by-step explanation:
2(4)-6(17)=-94
It costs $2.37 to paint one square foot of wall. You need to paint a wall that measures 864.5 square feet. It will cost to paint that wall. (Round your answer to the nearest hundredth)
a $204.88
b $2,048.87
c $2,048.86
d. $2,848.87
Answer:
B- hope this helps:)
Step-by-step explanation:
The total cost to paint 864.5 square feet of wall is $2,048.87.
It is given that the cost to paint one square foot of wall is $2.37.
We are asked to find the total cost to paint 864.5 square feet of wall.
What are the different place values in a given number with a decimal point?If we have a number that has a decimal point then we have two parts.
The whole number part and the fractional part.
After the decimal point, we will count the place value as tenths, hundredths, thousandths, and so on.
You can also see the given figure below.
We know that,
One square foot = $2.37.
Remember that Feet is the plural form of the foot.
We can write,
864.5 square feet = 864.5 x one square foot
Because in 864.5 square feet we have 864.5 one square foot.
And since one square foot cost $2.37.
864.5 square feet will cost 864.5 x 2.37 dollars.
Now,
864.5 x 2.37 = $2048.865.
Rounding to the nearest hundredth.
6 is in the hundredth place so we will round 86 to 87 since the number in the thousandth place is greater than 4.
Thus the total cost to paint a wall of 864.5 square feet is $2,048.87.
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4. 10 Unit Test: Surface Area and Volume - Part 1
UNIT TEST:
Surface Area and Volume - Part 1
Which net represents this solid figure?
The shape represented by this solid figure attached is a triangular prism with two triangle base and three rectangular faces.
What is a solid figure?A solid figure is a three dimensional shape having length, width and height. Examples of solid figures are cylinders, cone, pyramid and prism.
The shape represented by this solid figure attached is a triangular prism with two triangle base and three rectangular faces.
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Jorge bought 5 avocadoes at the rate of 60 cents per avocado. He also purchased six Dr. Pepper
sodas at the rate of 70 cents per soda. Write two separate equations for each situation. Define
the variable. How much money did Jorge spend altogether
Answer: $7.20
Step-by-step explanation:
A=Total Avocadoes D=Total Dr. Pepper
5*0.6=A
6*0.7=D
A+D=
5*0.6+6*0.7=
3+4.2=$7.20
\(\frac{tan(\frac{-2π}{3}} {sin\frac{7π}{4}} -sec (-π)\\\)What is the exact value of the trigonometric expression? State your answer in simplified radical form
The exact value of the trigonometric expression \(\frac{tan-(2\pi/3) }{sin(7\pi /4)} - sec(-\pi )\) in the simplified radical form is √6 + 1.
\(\frac{tan-(2\pi/3) }{sin(7\pi /4)} - sec(-\pi )\)
We have the angle,
-2π/3 = -120° = (360 - 120)° = 240° = 60°
Put the value of -2π/3 in tan -2π/3, we get
tan -2π/3 = tan (60) = √3
7π/4 × 180/π = 7 × (180/4) = 7 × 45 = 315° = 45°
Put the value of 7π/4 in sin 7π/4, and we get
sin 7π/4 = sin (45°) = √2/2
sec (-π) = sec (π) = -1
Now, substitute all the values in the given equation,
= {√3/(√2/2)} - (-1)
= (2√3/√2) + 1
= (2√3 × √2/√2 × √2) +1
= (2√6/2) + 1
= √6 + 1
--The given question is incorrect, the correct question is
''What is the exact value of the trigonometric expression? \(\frac{tan-(2\pi/3) }{sin(7\pi /4)} - sec(-\pi )\) State your answer in simplified radical form."--
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What is the absolute value of -|-4| ?
Answer:
- 4
Step-by-step explanation:
the absolute value function always give a positive result , that is
| - a | = | a | = a
then
- | - 4 | = - | 4 | = - 4
WILL GIVE 100 POINTS AFTER YOU ANSWER
What is the mean of this data set: 17, 13, 18, 20, 17, 15, 12
16
20
17
19
Mean of a data = Sum of all observations ÷ Total number of observations
Mean of this data will be :
Sum of all observarions = 17 + 13 + 18 + 20 + 17 + 15 + 12 = 112
Total number of observations = 7
Mean = 112 ÷ 7
Mean = 16
Therefore the mean of this data set = 16
help meeeeeeeeeeee pleaseee rnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
1. The cheese production for 2006 is 7.76 billion.
2. The cheese produced in 2014 is 9.84 billion.
What is a function?It should be noted that a function is simply used to show the relationship between the variables that are given.
In this situation, there's a 3% growth per year and the function for the cheese production is modelled as:
y = 7.1(1.03)^x
y = cheese production
x = number of years after 2003.
1. Therefore, since 2006 is 3 years after 2003, this will be
y = 7.1(1.03)^x
y = 7.1(1.03)³
y = 7.1 × 1.093
y = 7.76 billion
The production is 7.76 billion.
2. The production in 2014 will be;
y = 7.1(1.03)^x
y = 7.1(1.03)^11
y = 7.1 × 1.385
y = 9.84 billion
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A rectangle with perimeter 18 cm has a length that is 3 cm more than twice its width. Find the dimensions of the rectangle. SOLVE EACH APPLICATION USING ALGEBRA. TYPE THE EQUATION OR INEQUALITY AND PLEASE SHOW WORK.
Answer:
Length = 7 cm
Width = 2 cm
Step-by-step explanation:
Perimeter of rectangle = 18 cm
Let length of rectangle = \(l\) cm
Let width of rectangle = \(w\) cm
As per given statement, length is 3 cm more than the twice of its width:
Writing equation:
\(l = 2\times w +3 ....... (1)\)
Formula for perimeter of a rectangle is given as:
\(P = 2 \times (Length + Width)\)
OR
\(P = 2 \times (l + w)\)
Putting values of P as given and \(l\) by using equation (1):
\(18 = 2 \times (2w +3 + w)\\\Rightarrow \dfrac{18}2 = 3w +3 \\\Rightarrow 9 = 3w +3\\\Rightarrow 3w = 9 -3\\\Rightarrow w = \dfrac{6}{3}\\\Rightarrow w = 2\ cm\)
Putting value of \(w\) in equation (1):
\(l = 2\times 2 +3 \\\Rightarrow l = 4+3\\\Rightarrow l = 7\ cm\)
So, the dimensions are:
Length = 7 cm
Width = 2 cm
1. According to the podcast, why and how is chicken the reason American trucks dominate the truck market in the United States? Briefly explain. 2. Name two reasons a party (e.g., a politician or an industry association) may want to impose a tariff? 3. Who are they usually trying to protect? Who would be hurt by a tariff on automobiles? Explain. 4. Describe how competition encourages innovation? In your answer to this question, include a discussion on why American trucks "basically stayed the same over the years. 5. Describe ways foreign companies tried to get around American-imposed tariffs on automobiles. 6. Do you think the methods you described in your previous answer are efficient for an economy? Why or why not? 7. Lastly, how can a tariff be used as a bargaining chip? In your opinion, is that a good reason to impose tariffs - why or why not?
1. Chicken became the key product that drove the creation of the Interstate Highway System, which led to the dominance of American trucks in the US truck market.
2. A party may want to impose a tariff to protect domestic industries from foreign competition or to generate revenue for the government.
3. A party is usually trying to protect domestic industries, but a tariff on automobiles would hurt both domestic consumers who would pay higher prices and foreign producers who would face reduced demand.
4. Competition encourages innovation by providing incentives for companies to improve their products and services to stay ahead of their rivals; American trucks stayed the same because they faced little competition due to protectionist policies.
5. Foreign companies tried to get around American-imposed tariffs on automobiles by establishing factories in the US, forming joint ventures with American companies, or exporting through third countries.
6. The methods used to get around tariffs can be efficient in the short term, but they may not be sustainable or desirable in the long term as they can lead to trade imbalances and undermine the competitiveness of domestic industries.
7. Tariffs can be used as a bargaining chip to negotiate better trade deals, but they should be imposed judiciously and only as a last resort to avoid damaging the economy and harming consumers.
1. In the podcast, chicken is cited as the reason why American trucks dominate the truck market in the United States.
This is because in the 1960s, the government imposed regulations on the trucking industry that limited the amount of weight a truck could carry.
To get around these regulations, the industry started using smaller trucks to transport goods, which were often not strong enough to handle the weight.
However, they found that if they put chicken on the back of the trucks, the weight of the cargo would distribute more evenly and the smaller trucks could handle the load.
This led to the development of the modern pickup truck, which is now a staple of the American automobile market.
2. Parties may want to impose tariffs for various reasons, such as to protect domestic industries and jobs from foreign competition, to raise revenue for the government, or to level the playing field in international trade.
Two specific reasons for imposing tariffs could be to protect national security interests or to address unfair trade practices by other countries.
3. Tariffs are usually imposed to protect domestic industries and jobs, and the parties that are being protected are typically the producers of the goods or services in question.
However, tariffs can also harm consumers who may have to pay higher prices for imported goods or may have fewer choices in the marketplace. For example, if a tariff is imposed on automobiles, domestic car manufacturers may benefit, but consumers may have to pay more for cars, and foreign automakers may lose market share.
4. Competition encourages innovation by creating incentives for companies to improve their products or services to gain a competitive advantage.
In the case of American trucks, the lack of competition may have contributed to their lack of innovation over the years. Since they dominated the market, there was little pressure to improve or innovate, and as a result, they have largely stayed the same.
However, the rise of foreign competition in recent years has led American truck manufacturers to invest more in innovation to stay competitive.
5. Foreign companies have tried to get around American-imposed tariffs on automobiles in various ways, such as by moving production to countries not subject to the tariffs, by exporting parts and assembling them in the United States, or by lobbying the government for exemptions or tariff reductions.
6. The methods used by foreign companies to get around tariffs may not be efficient for the economy as a whole because they can lead to higher costs and inefficiencies in the supply chain.
However, they may be necessary for individual companies to remain competitive in the short term.
Ultimately, a more efficient solution would be to address the root causes of the trade imbalances that lead to tariffs in the first place.
7. A tariff can be used as a bargaining chip by threatening to impose tariffs on imports from a country unless they make concessions in trade negotiations.
While this can be an effective strategy in certain situations, it can also lead to a trade war and harm both economies.
In general, tariffs should be used sparingly and as a last resort, and efforts should be made to address underlying trade issues through diplomacy and negotiation.
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what kind of function can be used to model the amount of air pollution in this city over the next several years, assuming no other significant changes
By using the concept of depreciation, it can be concluded that-
The function that could be used to model the amount of air pollution in this city over the next several years, assuming no other significant changes is an exponential function.
What is growth?
Growth is the exponential increase in the value of an asset or article or population at a certain rate over a certain period of time
EPA calculated that the air pollution should decrease by approximately 8% each year
The function that could be used to model the amount of air pollution in this city over the next several years, assuming no other significant changes is an exponential function.
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Complete Question
One function of the Environmental Protection Agency (EPA) is to reduce air pollution. After implementing several pollution reduction programs in a certain city, EPA calculated that the air pollution should decrease by approximately 8% each year. What kind of function could be used to model the amount of air pollution in this city over the next several years, assuming no other significant changes?
divide the sum of 65 12 and 8 3 by their difference
4x²=9/16 Solve the equation and show your work.
3x = -21
{please put the answer in step by step bc i never understood this :( }
Answer:
x= -7
Step-by-step explanation:
Assuming your asking for the value of x, the answer is -7. Something I never understood about the school's way of teaching is that the equal sign is just a sign. It means that whats on one side of it is always the same as on the other side. 3=3, 9740=9740, it's just a fact. You can do anything to the numbers... As long as you do it to both sides of the = so that they stay the same. therefore if im told 6=6, i can divide both side by 3 and get 2=2. Its still a true statement, 2 does equal 2. If you try to only divide one side of the equal sign, it doesnt work. By only dividing the right side by three, you would get 6=2, and that just isnt true. Doing the same thing to your equation(3x=-21) I can divide BOTH sides by 3.
3x(/3)=-21(/3)
**x times 3, divided by three =x
**-21/3 =-7
x=-7
Fifty metal spheres, each with a radius of 2 cm, are melted. The melted solution is poured into a box. What is the volume of all the melted solution. Round your answer
to the nearest tenth of a centimeter.
1675.5 cm3
837.8 cm
418.9 cm
33.5 cm
Help me please
Answer:
The first option is correct 1675.5 cm^3Step-by-step explanation:
Step one:
we are given the radius as
r=2cm, and the number of spheres is 50 in numbers
let us find the volume of one sphere and multiply the area by 50 to get the volume of the 50 spheres
Step two:
\(volume=4/3 \pi r^3\)
\(volume=4/3*3.142 *2^3\\\\volume=100.5/3\\\\volume=33.5\)
The volume of one sphere is 33.5in^3
Hence the volume of the 50 spheres will be
=33.5*50
=1675.7cm^3 approx.
Volume of the melted solution will be 1675.5 cm³.
Radius of each metal sphere = 2 cm
Expression for the volume of the sphere is given by,
Volume = \(\frac{4}{3}\pi r^{3}\)
Here, r = radius of the sphere
By substituting the value of radius in the expression,
Volume = \(\frac{4}{3}\pi (2)^3\)
= 33.51 cm³
Volume of the melted solution = Volume of 50 spheres
Volume of 50 spheres = 50 × (33.51)
= 1675.5 cm³
Therefore, Volume of the melted solution will be 1675.5 cm³.
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I NEED AN ANSWER ASAP PLEASE
Step-by-step explanation:
the correct answer is option a 6a-7
Find the values of x and y. The diagram is not to scale.
A. x = 68, y = 75
B. x = 75, y = 68
C. x = 40, y = 68
D. x = 75, y = 70
Answer:
B
Step-by-step explanation:
The top vertex of the triangle on the right = 40° ( alternate angles )
The sum of the 3 angles in a triangle = 180° , then
y - 2 + 74 + 40 = 180 , that is
y + 112 = 180 ( subtract 112 from both sides )
y = 68 , so
y - 2 = 68 - 2 = 66
The 3 angles lying on the straight line sum to 180°
x - 1 + 40 + 66 = 180 , that is
x + 105 = 180 ( subtract 105 from both sides )
x = 75
Which number should be added to
both sides of this quadratic equation
to complete the square?
(-3/2)² + 1 = x² − 3x + (-3/2)²
Answer:
9/4
Step-by-step explanation:
You want to know the value required to complete the square in the equation 1 = x² -3x.
PictureYour picture shows the required value: (-3/2)² = 9/4.
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You paint four walls. Each wall is a rectangle with a length of 20 feet and a height of 12 feet. One gallon of paint covers about 320 square feet. How many gallons of paint do you need in order to cover the walls?
Answer:
3 gallons
Step-by-step explanation:
Each wall 12 x 20 = 240 feet squared
4 walls = 4 x 240 = 960 squared feet
960 divided into 320 = 3
1 gallon --------320
1 gallon------------320
1 gallon-----------320
3 gallons----------960
Paul bought a photo frame which measured 10 inches in length and 8 inches in width. Determine the diagonal length of the photo frame.
Answer: 12.4 inches
Step-by-step explanation:
\(c^{2}=a^{2} + b^{2} \\c^{2}=8^{2} + 10^{2}\\\sqrt{c^{2}=164\\\)
c=12.8, c=-12.8
It can not be -12.8 as there's no such thing as a negative length. Therefore the diagonal length of the photo frame is 12.8 inches
The level of pesticides found in the blubber of whales is a measure of pollution of the oceans by runoff from land. Suppose that the concentration of the insecticide dieldrin in all male minke whales is N(340 ng/g, 50 ng/g). The concentration is measured in nanograms per gram of blubber. If one whale is selected at random, what is the probability that the concentration of the insecticide dieldrin is greater than 356 ng/g? Round you answer to 3 decimal places.
The probability that the concentration of the insecticide dieldrin is greater than 356 ng/g is 0.3745 (approx).
Given that the concentration of the insecticide dieldrin in all male minke whales is N(340 ng/g, 50 ng/g).
Here, μ = 340 and σ = 50. The concentration is measured in nanograms per gram of blubber.
Now, we have to find the probability that the concentration of the insecticide dieldrin is greater than 356 ng/g.
To calculate the probability of P(X > 356), standardize the random variable X using the formula z = (X - μ) / σ.
Here, X = 356.
So, z = (X - μ) / σ= (356 - 340) / 50= 0.32
Now, the probability P(X > 356) is equivalent to P(Z > 0.32) using the standard normal distribution table.
To find this probability, we need to subtract the standard normal table value of 0.6255 from 1.
Note: N(μ, σ) represents a normal distribution with mean μ and standard deviation σ.
Therefore,
P(X > 356) = P(Z > 0.32) = 1 - 0.6255= 0.3745 (approx)
Hence, the probability that the concentration of the insecticide dieldrin is greater than 356 ng/g is 0.3745 (approx).
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Since it is not easy to determine how well a sampling plan discriminates between good and bad quality, you should always examine __________ before using a sampling plan.
The sampling plan's reliability or validity. Before using a sampling plan, it is crucial to examine its reliability or validity. This assessment helps determine how well the sampling plan can discriminate between good and bad quality.
Reliability refers to the consistency and stability of the sampling plan's results. A reliable sampling plan consistently produces similar outcomes when applied to the same population under similar conditions. If a sampling plan is unreliable, its results may vary widely, leading to inconsistent judgments about quality.
Validity, on the other hand, refers to the extent to which the sampling plan accurately measures or identifies the desired characteristics or qualities. A valid sampling plan provides a true representation of the quality being assessed and ensures that good quality is distinguished from bad quality effectively.
By examining the reliability and validity of a sampling plan, we can gain confidence in its ability to accurately discriminate between good and bad quality. This examination may involve conducting pilot tests, analyzing historical data, or seeking expert opinions to assess the plan's effectiveness and suitability for the specific context.
Without considering the reliability and validity of a sampling plan, there is a risk of making incorrect judgments or decisions based on flawed or biased sampling outcomes. Therefore, it is essential to evaluate these aspects before using a sampling plan to ensure the reliability and accuracy of the results obtained.
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Hash Codes (cont.) Polynomial accumulation:
■ We partition the bits of the key into a sequence of components of fixed length (e.g., 8, 16 or 32 bits) ao a₁ an-1 ***
■ We evaluate the polynomial p(z)= a + a₁z + a₂z² + ... + a₁-12-1 at a fixed value z, ignoring overflows Especially suitable for strings (e.g., the choice z = 33 gives at most 6 collisions on a set of 50,000 English words) a Polynomial p(z) can be evaluated in O(n) time using Horner's rule: .
The following polynomials are successively computed, each from the previous one in 0(1) time Po(z)=an-1 Pi(z)=an-i-1+zPi-1(z) (i=1,2,..., n-1) We have p(z) =Pn-1(z)
The given information explains the process of polynomial accumulation for generating hash codes. It involves partitioning the key into fixed-length components, evaluating a polynomial using Horner's rule, and successively computing polynomials based on previous ones.
The given information describes polynomial accumulation for generating hash codes. Here's a breakdown of the process:
Partitioning the key: The key, which could be a string or any other data, is divided into fixed-length components. These components can be, for example, 8, 16, or 32 bits each.
Polynomial evaluation: The polynomial p(z) = a + a₁z + a₂z² + ... + a₁-12-1 is evaluated at a fixed value of z. This means substituting the components of the key into the polynomial and calculating the result. This step ignores overflows.
Horner's rule: Horner's rule is used to efficiently evaluate the polynomial in O(n) time, where n is the number of components in the key. Horner's rule allows the polynomial to be evaluated as a series of multiplications and additions, reducing the computational complexity.
Successive computation: The polynomials Po(z), Pi(z) for i = 1, 2, ..., n-1 are successively computed from the previous polynomial in O(1) time. Each polynomial Pi(z) is obtained by multiplying the previous polynomial by z and adding the next component of the key.
Final polynomial: The final polynomial p(z) is obtained as Pn-1(z), which is the result of the last computation in the sequence.
This polynomial accumulation process helps generate hash codes by transforming the key components into a polynomial representation. The choice of z value can affect the number of collisions observed, and in the given example, z = 33 is suggested for strings to minimize collisions among a set of 50,000 English words.
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A rectangle has a length of 26 inches and a width of 14 inches. If 1 inch = 2.54 centimeters, find the area of the rectangle in centimeters. Round the answer to the nearest tenth.
560.4 cm2
56.4 cm2
2,348.4 cm2
924.6 cm2
PLS hurry and thank you
The area of the rectangle will be 2,348.3824 cm² as "A rectangle has a length of 26 inches and a width of 14 inches and 1 inch=2.54 cm".
What is area?The measurement that expresses the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a shape or planar lamina. Area is the total amount of space occupied by a flat (2-D) surface or an object's shape. On a piece of paper, draw a square using a pencil. It has two dimensions. The area of a shape on paper is the area that it occupies. Consider your square as being composed of smaller unit squares.
Here,
Length in inches=26
Width in inches=14
area in inches=26*14
=364 inch²
Now,
1 inch=2.54 cm
area in cm,
=364*2.54*2.54
=2,348.3824 cm²
Since "a rectangle has a length of 26 inches and a width of 14 inches and 1 inch=2.54 cm," the area of the rectangle will be 2,348.3824 cm².
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Tara has a bag with 3 white marbles, 2 black marbles, and 5 green marbles. She will draw two marbles from the bag one at a time without replacement. What is the probability that she will draw a black marble and then a green marble?
Answer: 1/nine.
Step-by-step explanation:To locate the probability of drawing a black marble after which a inexperienced marble, we need to keep in mind the range of approaches we can draw a black marble and then a inexperienced marble, and divide that with the aid of the whole range of methods we are able to draw marbles with out replacement.
The opportunity of drawing a black marble on the primary draw is two/10, because there are 2 black marbles out of a total of 10 marbles. Then, in view that we draw the second one marble with out alternative, there will be nine marbles left within the bag. If we drew a black marble on the first draw, there could be 1 black marble and five inexperienced marbles left in the bag. So the possibility of drawing a green marble on the second draw, for the reason that a black marble became drawn on the first draw, is five/nine.
The chance of drawing a black marble after which a inexperienced marble is the manufactured from the chance of drawing a black marble on the primary draw and the opportunity of drawing a inexperienced marble on the second draw, given that a black marble turned into drawn on the primary draw. So we multiply 2/10 by five/nine to get 1/nine.
Therefore, the chance of drawing a black marble after which a inexperienced marble is 1/nine.
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Find the slope of the tangent to the parametric curve at the indicated point. (Round your answer to two decimal places.) x = t^2 + 2t, y = 2^t − 2t The x y-coordinate plane is given. The curve starts at the point (48, 16), goes down and left becoming more steep, crosses the y-axis at the approximate point (0, 4.3), changes direction at the point (−1, 2.5), goes down and right becoming less steep, crosses the y-axis at the point (0, 1), crosses the x-axis at the point (3, 0), changes direction at the approximate point (5.2, −0.2), goes up and right becoming more steep, crosses the x-axis at the approximate point (7.9, 0), passes through the point (24, 8) marked with a dot and coordinates, and exits the window in the first quadrant.
at the point (24,8), we can find t = 2 and the slope of the tangent is 2.
How to solve the quadrant?
To find the slope of the tangent to the parametric curve, we need to first find the derivative of the y-coordinate with respect to the x-coordinate. This can be done using the chain rule of differentiation:
dy/dx = (dy/dt) / (dx/dt)
= (2t - 2) / (2t + 2)
At the point (48,16), we can find the value of t by solving the equations:
x = t² + 2t = 48
y = t² - 2t = 16
Solving these equations, we get t = 4 or -6. At t = 4, the point on the curve is (48,16), and at t = -6, the point is (-32,68). However, since the curve is going down and left at (48,16), we need to consider the slope of the tangent at the point where t = -6.
Substituting t = -6 into the derivative expression, we get:
dy/dx = (2(-6) - 2) / (2(-6) + 2) = -5/7
Therefore, the slope of the tangent to the parametric curve at the point (48,16) is -5/7.
Using similar methods, we can find the slopes of the tangents at the other key points on the curve. At the point (0,4.3), we can find t = -0.75 and the slope of the tangent is 0.2. At the point (-1,2.5), we can find t = -0.5 and the slope of the tangent is -1. At the point (0,1), we can find t = 0.5 and the slope of the tangent is -0.6. At the point (3,0), we can find t = -1 and the slope of the tangent is -1/3. At the point (5.2,-0.2), we can find t = 0.2 and the slope of the tangent is 3. At the point (7.9,0), we can find t = 1.3 and the slope of the tangent is 15/17. Finally, at the point (24,8), we can find t = 2 and the slope of the tangent is 2.
Therefore, the curve starts out with a steep negative slope, then levels off to a shallow negative slope, changes direction and becomes steep in the positive direction, levels off to a shallow positive slope, and then becomes steep in the positive direction again. The slope of the tangent at the point (24,8) is positive, indicating that the curve is still going up and to the right at that point.
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Suppose the function y= 1. 50x – 21. 50 represents the earnings of a basketball team from selling
cupcakes for $1. 50 each. The team spends $21. 50 on baking supplies to make 200 cupcakes
A) Identify which variable represents the domain
1. 50
B) Are there constraints on positive and negative values of the domain?
C) Determine which set of real numbers makes sense in this context.
200 and
D) Determine the domain of this situation,
A) The domain is x.
B) Domain can be positive but cannot be negative.
C) The set of real numbers makes sense in this context is non-negative integer.
D) The domain in this context can be 0, 1, 2, 3, and so on.
Given is a function y = 1.50x - 21.50 that represents the earnings of a basketball team from selling cupcakes for $1. 50 each.
We need to determine the answers asked related to this function,
A) In the function y = 1.50x - 21.50, the variable x represents the domain. It represents the number of cupcakes sold.
B) In this context, the domain (number of cupcakes sold) should be a positive value. Negative values do not make sense because you cannot sell a negative number of cupcakes.
C) In this context, it makes sense for the number of cupcakes sold (the domain) to be a non-negative integer. Selling fractional cupcakes or negative cupcakes would not be meaningful.
D) The domain of this situation would be the set of non-negative integers, meaning x can take on values of 0, 1, 2, 3, and so on.
Therefore, the answers are =
A) The domain is x.
B) Domain can be positive but cannot be negative.
C) The set of real numbers makes sense in this context is non-negative integer.
D) The domain in this context can be 0, 1, 2, 3, and so on.
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7. In a translation, the sides or angles of the preimage and
image have the same lengths and_____
Answer:
Step-by-step explanation:
same lenghts for sides, same measurements for angles and the orientation of the points is preserved
The following figure is a rhombus. Find the value of m. Then, use that value to find the measure of VW
Answer:
\(m=8\)The length of VW = 36 units.Step-by-step explanation:
We know that a rhombus is a quadrilateral with four sides. All four sides have the same length.
From the diagram, it is clear that
The length of VW= 6m-12The length of WX = 4m+4As all the four sides of the rhombus have equal length.
So we can observe
\(VW=WX\)
\(6m-12 = 4m+4\)
Add 12 to both sides
\(6m-12+12=4m+4+12\)
\(6m=4m+16\)
\(2m=16\)
Divide both sides by 2
\(\frac{2m}{2}=\frac{16}{2}\)
\(m=8\)
so
The length of VW= 6m-12
= 6(8)-12 ∵ \(m=8\)
= 48-12
= 36
Thereofore, the length of VW = 36 units.
Let X be normally distributed with mean μ = 2.5 and standard deviation σ = 2. a. Find P(X > 7.6). (Round "z" value to 2 decimal places and final answer to 4 decimal places.)
P(X > 7.6) b. Find P(7.4 ≤ X ≤ 10.6).
Given, X is normally distributed with mean μ = 2.5 and standard deviation σ = 2. To find the probability of P(X > 7.6), first we need to find the z value by using the formula,z = (x - μ) / σz = (7.6 - 2.5) / 2z = 2.55 The z value is 2.55. Using the standard normal table, we can find the probability of P(X > 7.6) = P(Z > 2.55) = 0.0055 (approx).
Hence, the answer for the given problem is:P(X > 7.6) = 0.0055.The value of z for the P(7.4 ≤ X ≤ 10.6) can be calculated as below,Lower value z = (7.4 - 2.5) / 2z = 2.45 Upper value z = (10.6 - 2.5) / 2z = 4.05 Using the standard normal table, we can find the probability of P(7.4 ≤ X ≤ 10.6) = P(2.45 ≤ Z ≤ 4.05) = P(Z ≤ 4.05) - P(Z ≤ 2.45) = 0.9995 - 0.9922 = 0.0073 (approx).Thus, the answer for the given problem is:P(7.4 ≤ X ≤ 10.6) = 0.0073.
Thus, the solution for the given problem is:P(X > 7.6) = 0.0055 and P(7.4 ≤ X ≤ 10.6) = 0.0073.
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