The value of the variables are a = 1 and b = -1
How to solve the equationGiven that the equations are;
a - 3 = 2b
4a + 5b- 8 = 0
Using the substitution method, we have;
Make 'a' the subject of formula from equation (1)
a = 2b + 3
Now, substitute the value of the variable in the second equation
4(2b + 3) + 5b - 8 = 0
expand the bracket, we have;
8b + 12 + 5b - 8 = 0
collect the like terms, we get;
8b + 5b = 0 - 5
add or subtract the values
5b = -5
b = -1
Substitute the value of b as =-1
a = 2(-1) +3
expand the bracket
a = -2 + 3
a = 1
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how does 12 - 4.6 make 7.6
Molly has a rectangular piece of cardboard. If the length of the cardboard can be modeled by 3x - 1 and the width of the cardboard can be modeled by 2x + 5, which polynomial models the area of her piece of cardboard? *
The polynomial that models the area of Molly's cardboard is 6x^2 + 13x - 5.
How can the area of Molly's cardboard be modeled with a polynomial?
First, we were given that the length of the cardboard can be modeled by 3x - 1 and the width can be modeled by 2x + 5. To find the area, we use the formula:
Area = length x width
So, we substitute the expressions for the length and width:
Area = (3x - 1) x (2x + 5)
Next, we use the distributive property of multiplication to expand the expression:
Area =[tex]6x^2 + 15x - 2x - 5[/tex]
Simplifying, we get:
Area = [tex]6x^2 + 13x - 5[/tex]
Therefore, the polynomial that models the area of Molly's piece of cardboard is [tex]6x^2 + 13x - 5.[/tex]
This polynomial gives us a way to calculate the area of the cardboard for any value of x. For example, if we know that the length of the cardboard is 5 units, we can substitute x = 2 into the polynomial to find the area:
Area =[tex]6x^2 + 13x - 5[/tex]
Area =[tex]6(2)^2 + 13(2) - 5[/tex]
Area = 24 + 26 - 5
Area = 45
So, the area of the cardboard when x = 2 (and the length is 3x - 1 = 5) is 45 square units.
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A park is to be designed as a circle. A straight walkway will intersect the fence of the
park twice, requiring gates at each location. The city planner draws the circular park
and the walkway on a coordinate plane, with the equation
x² + y² - 4x = 9 for the circular park and the equation y = 2x modeling the
walkway. Write an ordered pair that represents the location of the gates in the third
quadrant.
o find the coordinates of the gates in the third quadrant, we need to find the points where the circle and the line intersect in the third quadrant.
Substituting y = 2x into x² + y² - 4x = 9, we get:
x² + (2x)² - 4x = 9
5x² - 4x - 9 = 0
Using the quadratic formula, we find:
x = (-(-4) ± √((-4)² - 4(5)(-9))) / (2(5))
x = (4 ± √136) / 10
We can discard the positive root since it is in the first quadrant. The negative root corresponds to the x-coordinate of the point of intersection in the third quadrant:
x = (4 - √136) / 10 ≈ -0.433
Substituting this value into y = 2x, we get:
y = 2(-0.433) ≈ -0.866
Therefore, the ordered pair that represents the location of the gates in the third quadrant is (-0.433, -0.866).
Fully simplify 3(w+11)/6w
The simplified form of the expression 3(w+11) / 6w is w + 11 / 2w .
How to simplify an expression?Simplifying expressions mean rewriting the same algebraic expression with no like terms and in a compact manner.
In other words, we have to expand any brackets, next multiply or divide any terms and use the laws of indices if necessary, then collect like terms by adding or subtracting and finally rewrite the expression.
Therefore, let's simplify the expression:
3(w+11) / 6w
Hence, let's divide both the numerator and denominator by 3
Therefore,
3(w+11) / 6w = w + 11 / 2w
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Box and whisker plots
Answer: Box and whisker plots are plots on number lines with a box and two lines off the edges, called whiskers. The box has a line at the upper quartile(1), one at the lower quartile(2), and one in the center of the box at the median(3). The two lines go to the ends of the data, one at the minimum(4) and one at the maximum(5).
4 2 3 1 5
|-----[___|____]-----------|
₀__₁__₂__₃__₄__₅__₆__₇__₈
I hope this helps.
1) A politician is about to give a campaign speech and is holding a 'stack of ten cue cards, of which the first 3 are the most important. Just before the speech, she drops all of the cards and picks them up in a random order. What is the probability that cards #1, #2, and #3 are still in order on the top of the stack? A) 0. 139% B) 3. 333% C) 0. 794% D) 0. 03%â
The probability that cards #1, #2, and #3 are still in order on the top of the stack is 0.03%. Therefore, the correct option is D.
To find the probability, we need to calculate the number of ways in which the first 3 cards can remain in order on the top of the stack, and divide it by the total number of ways the cards can be arranged.
The number of ways in which the first 3 cards can remain in order is 3! (3 factorial), because there are 3 cards and they can be arranged in 3! = 6 ways.
The total number of ways the cards can be arranged is 10!, because there are 10 cards and they can be arranged in 10! = 3,628,800 ways.
So, the probability is:
3! / 10! = 6 / 3,628,800 = 0.000166 = 0.0166%
We can convert it to a percentage by multiplying by 100:
0.0166 x 100 = 1.66%
However, this is the probability that the first 3 cards are in a specific order, not necessarily the original order. Since the question asks for the probability that the original order is maintained, we need to divide the probability by 3!, which gives:
0.0166 / 3! = 0.000277 = 0.0277%
This is closest to answer choice D) 0.03%.
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A student drilled a hole into a six-sided die and filled it with a lead weight, then proceeded to roll the die 200 times here are the observed frequencies 27 31 42 40 28 and 32 use a 0. 05 significance level to test the claim that the outcomes are not equally likely find the test statistic x^2 and critical value for the goodness-of-fit needed to test the claim
To test the claim that the outcomes of rolling the modified die are not equally likely, we can use a chi-square goodness-of-fit test. We will use a significance level of 0.05.
The null hypothesis is that the outcomes are equally likely. The alternative hypothesis is that the outcomes are not equally likely.
First, we need to calculate the expected frequencies assuming that the outcomes are equally likely.
Since the die has six sides, each outcome has a probability of 1/6. Therefore, the expected frequency for each outcome is 200/6 = 33.33.
To calculate the test statistic [tex]x^2[/tex], we can use the formula:
[tex]x^2 = Σ (observed frequency - expected frequency)^2 / expected frequency[/tex]
where Σ is the sum over all outcomes.
Using the observed and expected frequencies given in the problem, we get:
[tex]x^2 = (27 - 33.33)^2 / 33.33 + (31 - 33.33)^2 / 33.33 + (42 - 33.33)^2 / 33.33 + (40 - 33.33)^2 / 33.33 + (28 - 33.33)^2 / 33.33 + (32 - 33.33)^2 / 33.33[/tex]
[tex]x^2 = 3.02[/tex]
The degrees of freedom for this test is 6 - 1 = 5 (since there are 6 sides on the die).
Using a chi-square distribution table (or calculator), we can find the critical value for a significance level of 0.05 and 5 degrees of freedom to be 11.070.
Since the test statistic x^2 = 3.02 is less than the critical value of 11.070, we fail to reject the null hypothesis.
Therefore, we do not have enough evidence to conclude that the outcomes of rolling the modified die are not equally likely.
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Geometry question I need help with:
We denote triangle ABC, angle A measures 90°, angle B measures 30° and angle C measures 60°.
We apply the cosine of 30 degrees, becuase m(∡A) = 90° and find the hypotenuse of triangle ABC:
cos = (adjacent side) / (hypotenuse)
⇔ cos B = AB/BC ⇔
⇔ cos 30° = 8√3/v ⇔
⇔ √3/2 = 8√3/v ⇔
⇔ √3 • v = 2 • 8√3 ⇔
⇔ v√3 = 16√3 ⇔
⇔ v = 16√3 ÷ √3 ⇔
⇔ v = 16 millimeters
Hope that helps! Good luck! :)
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Pregunta 2: En una restaurante para 94 personas hay 19 mesas en las se pueden
sentar 4,5 o 6 personas. Si sabemos que en el total de mesas con 4 ó 5 sillas se
pueden acomodar 64 personas, ¿Cuántas mesas tienen 4 sillas?
There are 9 tables with 4 chairs in the restaurant.
Let's establish the variables:
Let x be the number of tables with 4 chairs
Let y be the number of tables with 5 chairs
Let z be the number of tables with 6 chairs
We know that there are a total of 19 tables, therefore:
x + y + z = 19 (equation 1)
We also know that the total number of people that can be accommodated in tables with 4 or 5 chairs is 64, therefore:
4x + 5y = 64 (equation 2)
We want to find the value of x, so we need to eliminate y from the equations above. We can do this by multiplying equation 2 by 4, and then subtracting it from equation 1:
x + y + z - 16x - 20y = 19 - 256
Simplifying:
-15x - 19y = -237
Dividing both sides by -19:
x = 9
Therefore, there are 9 tables with 4 chairs.
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Translated Question: Clear the selection Question 2: In a restaurant for 94 people there are 19 tables that can seat 4.5 or 6 people. If we know that the total number of tables with 4 or 5 chairs can accommodate 64 people, how many tables have 4 chairs?
As a reward for Musa's diligence and agreement, his father decided to distribute a sum of money amounting to 5,800 dinars to him and his brothers, the one with the highest average taking the largest amount, while that the one with the third rank gets an amount that is half of what the one with the first rank takes. Translate this situation as an equation with an unknown X, where X is the amount that the first rank takes. Solve the resulting equation , Solve an exact value . Gives exclusively between two consecutive natural numbers Each of the three sums
The amount that the first rank takes is 1934 dinars, and the amounts that the second and third ranks take are 967 dinars and 483.5 dinars (rounded to 484 dinars), respectively.
Let's assume that there are three brothers, including Musa. Let X be the amount of money that the brother with the highest average takes, and let Y be the amount of money that the brother with the third rank takes.
According to the given conditions, we can write the following equations:
X + Y + (5800 - X - Y) = 5800 (The total amount of money distributed should be equal to 5800 dinars)X > Y (The brother with the highest average should take the largest amount)X is an integer valueLet's simplify equation 1:
X + Y = 2900
Also, we know that:
X = (2Y + X)/2
(The amount that the third rank takes is half of what the first rank takes)
Simplifying this equation:
2X = 2Y + X
X = 2Y
Substituting this value of X in equation X + Y = 2900:
3Y = 2900
Y = 2900/3
Y ≈ 966.67
As the amount given must be a whole number between two consecutive natural numbers, we can round Y to the nearest natural number:
Y = 967
Then, X = 2Y = 2*967 = 1934
Therefore, the amount that the first rank takes is 1934 dinars, and the amounts that the second and third ranks take are 967 dinars and 483.5 dinars (rounded to 484 dinars), respectively.
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Look at the map and choose the correct option with the country indicated on the map.
Map of Central and South America. The country south to Brazil and with the Atlantic Ocean to its east is highlighted.
El Salvador
Uruguay
Costa Rica
Venezuela
The description concerns Uruguay, option B, since it is the only country among the answer choices that is located in South America to the South of Brazil.
Which countries are in South America?South America is a continent located in the western hemisphere of the Earth. It is situated south of North America, east of the Pacific Ocean, and west of the Atlantic Ocean. The continent is home to 12 independent countries and 3 dependent territories, with a total population of approximately 422 million people.
The largest country in South America is Brazil, followed by Argentina, Peru, and Colombia. The continent is characterized by diverse topography, including the Andes mountain range, the Amazon rainforest, the Atacama Desert, and the Patagonian plains. The region is also known for its rich cultural heritage, including pre-Columbian civilizations such as the Incas and the Mayas, as well as colonial influences from Spain and Portugal. Today, South America is a rapidly developing region with a diverse economy, including agriculture, mining, and manufacturing industries.
Uruguay is also a part of South America. It is located South of Brazil and, as a matter of fact, during colonization, it was a part of Brazil. We can conclude option B is the right answer.
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3. Take f(x, y) = › Y. Show that this function is differentiable at (0, 0) (you can only use the definition of differentiability). Is this function differentiable
at all points in R^2?
This function is not differentiable at all points in [tex]R^2[/tex]. To see this, consider the points on the x-axis, where y = 0. At these points, the function is not differentiable because it has a sharp corner.
To show that the function f(x, y) = |y| is differentiable at (0, 0), we need to show that there exists a linear transformation L such that:
[tex]lim (h,k) - > (0,0) [f(0+h,0+k) - f(0,0) - L(h,k)] / \sqrt{(h^2 + k^2)} = 0[/tex]
where f(0,0) = 0 since |0| = 0.
We have:
f(0+h,0+k) - f(0,0) = |k|
Now we need to find L(h,k), which is a linear transformation of (h,k) that approximates f(0+h,0+k) - f(0,0) near (0,0). We can take:
L(h,k) = 0
Since L is a constant function, it is a linear transformation. Also, we have:
f(0+h,0+k) - f(0,0) - L(h,k) = |k|
So we have:
[tex]lim (h,k) - > (0,0) [f(0+h,0+k) - f(0,0) - L(h,k)] / \sqrt{(h^2 + k^2) } = lim (h,k) - > (0,0) |k| / \sqrt{(h^2 + k^2)}[/tex]
Using the squeeze theorem, we can show that this limit is equal to 0, since[tex]|k| < = \sqrt{(h^2 + k^2)}[/tex] for all (h,k) and[tex]lim (h,k) - > (0,0)\sqrt{ (h^2 + k^2) } = 0.[/tex]
Therefore, f(x, y) = |y| is differentiable at (0,0).
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At the beginning of the summer, the water level in an underground well was -3 feet. During the hot summer months, the water level fell 4 feet. The expression -3 -4 gives the water level in feet at the end of the summer.
What was the water level at the end of the summer?
Answer:
-7 feet
Step-by-step explanation:
-3-4 = -7, so it is -7 feet
Need help please answer
A triangular prism has a net as shown below.
4m
5m
5m
3m
What is the surface area of this triangular prism?
20 points if you help me out!
Answer: 72 m²
Step-by-step explanation:
HELP MARKING BRAINLEIST IF CORRECT
Answer:
Since it is a right triangle, we can apply pythagores theorem.
Answer: a = 8.7 miles
Step-by-step explanation:
a^2 = c^2 - b^2
a^2 = 10^2 - 5^2
a^2 = 100 - 25
a^2 = 75
a ≈ 8.7
Therefore, the length of the missing leg is approximately 8.7 miles.
Mr. Ali has 15. 8 litres of juice. He fills equal numbers of 400 ml and 1 litre juice bottles to sell. If Mr. Ali has 3200 ml of juice left,how many equal numbers of juice bottles did he fill?
Mr. Ali filled 6 of the 400 ml juice bottles and 8 of the 1 liter juice bottles.
First, convert 15.8 liters to milliliters:
15.8 L = 15,800 mL
Let x be the number of 400 ml juice bottles filled, and let y be the number of 1 liter juice bottles filled.
The total amount of juice filled can be represented as:
400 ml/bottle * x + 1000 ml/bottle * y = 15,800 ml
Simplifying, we get:
4x + 10y = 158
We also know that there are 3200 ml of juice left:
400 ml/bottle * (x - 3200/400) + 1000 ml/bottle * y = 0
Simplifying, we get:
x + 2.5y = 28
We now have two equations with two variables. Solving for x and y, we get:
x = 6
y = 8
Therefore, Mr. Ali filled 6 of the 400 ml juice bottles and 8 of the 1 liter juice bottles.
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What is the probability of randomly selecting a quarter from a bag that has 5 dimes, 6 quarters, 2 nickels, and 3 pennies? 1/8 3/16 3/8 5/16
The probability of randomly selecting a quarter from the bag is 5/16
How to find the probability?Assuming that all the coins have the same probability of being randomly drawn, the probability of getting a quarter is equal to the quotient between the total number of quarters and the total number of coins in the bag.
There are 6 quarters, and the total number of coins is 16, then the probability of randomly selecting a quarter is:
P = 5/16
The correct option is the last one.
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There are 160 customers at Harris Teeter. 48 of them are children.What percent of the customers at Harris Teeter are adults?
PLEASE I NEED EXPLANATION
The percent of the customers at Harris Teeter that are adults is 70%
Calculating the percentage of the customers that are adultsFrom the question, we have the following parameters that can be used in our computation:
Customers = 160
Children = 48
using the above as a guide, we have the following:
Adults = Customers - Children
substitute the known values in the above equation, so, we have the following representation
Adults = 160 - 48
So, we have
Adults = 112
Next, we have
Percentage = 112/160 * 100%
Evaluate
Percentage = 70%
Hence, the percentage is 70%
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If θ is an angle in standard position and its terminal side passes through the point (-9,5), find the exact value of sec θ secθ in simplest radical form.
The exact value of secθ secθ in simplest radical form is 106/81.
How to calculate the valueThe length of the hypotenuse is the distance from the origin to the point (-9, 5):
√((-9)^2 + 5^2) = √(81 + 25) = √106
cosθ = adjacent/hypotenuse = -9/√106
Therefore, secθ = 1/cosθ = -√106/9.
In order to find the value of secθ secθ, we simply multiply secθ by itself:
secθ secθ = (-√106/9) * (-√106/9) = 106/81
The exact value of secθ secθ is 106/81.
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Eva invests $6700 in a new savings account which earns 5.8% annual interest, compounded daily. what will be the value of her investment after 3 years? round to the nearest cent.
Answer:
$7973.26
Step-by-step explanation:
PV = $6700
i = 5.8% ÷ 365
n = 3 years · 365
Compound formula
FV = PV (1 + i)^n
FV = 6700 (1 + 5.8% ÷ 365)^(3 · 365)
FV = $7973.26 (rounded to the nearest cent)
Answer:
The value of Eva's investment after 3 years will be approximately $8,108.46. Rounded to the nearest cent, this is $8,108.45.
Step-by-step explanation:
We can use the formula for compound interest:
A = P(1 + r/n)^(nt)where:
A = the final amountP = the principal (starting amount)r = the annual interest rate (as a decimal)n = the number of times the interest is compounded per yeart = the time (in years)In this case, we have:
P = $6700r = 0.058 (since the interest rate is 5.8%)n = 365 (since the interest is compounded daily)t = 3Plugging these values into the formula, we get:
A = 6700(1 + 0.058/365)^(365*3)A ≈ $8,108.46Therefore, the value of Eva's investment after 3 years will be approximately $8,108.46. Rounded to the nearest cent, this is $8,108.45.
Patty and Carol leave their homes in different cities and drive toward each other on the same highway.
• They start driving at the same time.
• The distance between the cities where they live is 300 miles.
• Patty drives an average of 70 miles per hour.
. Carol drives an average of 50 miles per hour.
Enter an equation that can be used to find the number of hours, t, it takes until Patty and Carol are at the same
location.
The equation to find the number of hours, t, until Patty and Carol are at the same location is: 70t + 50t = 300.
1. Patty and Carol start driving at the same time, towards each other on the same highway.
2. The distance between their cities is 300 miles.
3. Patty drives at an average speed of 70 mph, so in t hours she covers 70t miles.
4. Carol drives at an average speed of 50 mph, so in t hours she covers 50t miles.
5. As they drive towards each other, the sum of the distances they cover should equal the total distance between their cities.
6. Therefore, combining the distances covered by Patty and Carol, we get: 70t (Patty's distance) + 50t (Carol's distance) = 300 (total distance).
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An artist is sculpting a spherical statue that has a diameter of 10 inches. if the clay to sculpt the statue weighs approximately 1.1 oz/in3 what is the weight of the statue to the nearest ounce?
The weight of the statue to the nearest ounce is 576 ounces.
The volume of a sphere can be calculated using the formula V = (4/3)πr^3, where r is the radius of the sphere. Since the diameter is given as 10 inches, the radius is half of that, or 5 inches.
Using the formula, we can find the volume of the sphere:
V = (4/3)πr^3
V = (4/3)π(5^3)
V = (4/3)π(125)
V = 523.6 cubic inches (rounded to one decimal place)
Since we know the weight of the clay per cubic inch, we can find the weight of the statue by multiplying the volume by the weight per cubic inch:
Weight = Volume × Weight per cubic inch
Weight = 523.6 in^3 × 1.1 oz/in^3
Weight = 575.96 oz (rounded to two decimal places)
Therefore, the weight of the statue is approximately 576 ounces or 36 pounds (rounded to the nearest pound).
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An amusement park has 2 drink stands and 18 other attractions. What is the probability that a randomly selected attraction at this amusement park will be a drink stand? Write your answer as a fraction or whole number.
Considering the definition of probability, the probability that a randomly selected attraction at this amusement park would be a drink stand is 1/10.
Definition of probabilityProbability establishes a relationship between the number of favorable events and the total number of possible events.
The probability of any event A is defined as the ratio between the number of favorable cases (number of cases in which event A may or may not occur) and the total number of possible cases:
P(A)= number of favorable cases÷ number of possible cases
Probability that a selected attraction is a drink standIn this case, you know:
Total number of drink stands= 2 (number of favorable cases)Total number of other attractions= 18Total number of attraccions = Total number of drink stands + Total number of other attractions= 20 (number of possible cases)Replacing in the definition of probability:
P(A)= 2÷ 20
Solving:
P(A)= 1/10
Finally, the probability in this case is 1/10.
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Which triangles are similar?
OA. Triangles B and C
OB. Triangles A, B, and C
C. Triangles A and C
OD. Triangles A and B
Answer:
C. Triangles A and C.
Step-by-step explanation:
In triangles A and C, the ratios of corresponding sides are equal, and the corresponding angles are congruent.
Using the change-base formula, which of the following is equivalent to the logarithmic expression below?
log7 18
The logarithmic expression log7 18 is equivalent to log 18 / log 7 using the change-base formula.
The change-base formula states that the logarithm of a number to a certain base can be converted to the logarithm of the same number to a different base by dividing the logarithm of the number to the first base by the logarithm of the number to the second base.
In this case, we want to convert log7 18 to a logarithm with base 10. Therefore, using the change-base formula, we can write:
log7 18 = log 18 / log 7
Using a calculator, we can evaluate the right-hand side of the equation to get:
log7 18 = 1.2553 / 0.8451
log7 18 = 1.4845 (rounded to four decimal places)
Therefore, the logarithmic expression log7 18 is equivalent to log 18 / log 7, which is approximately equal to 1.4845.
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Factor completely. If the polynomial is not factorable, write prime.
a^8 - a^2 B^6
The polynomial, a⁸ - a²·B⁶ in factored form is; a²·(a³ - B³)·(a³ + B³)
What is a polynomial?A polynomial consists of the differences or sums of terms that are the product of powers of the same variable.
The specified polynomial can be presented as follows;
a⁸ - a²·B⁶
The common factor in the terms of the polynomial is a², therefore, we get;
a⁸ - a²·B⁶ = a⁶ × a² - a²·B⁶
a⁶ × a² - a²·B⁶ = a²·(a⁶ - B⁶)
(a⁶ - B⁶) = (a³ - B³) × (a³ + B³)
The polynomial is therefore; a⁸ - a²·B⁶ = a²·(a³ - B³)·(a³ + B³)
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Estimate the area under the curve f(x)=1/x on [1,2] by using 4 approximating rectangles with a) left endpoints, b) right endpoints, then c) take the average.
our final estimate for the area under the curve f(x)=1/x on [1,2] using 4 approximating rectangles and taking the average of the left and right endpoints is 0.76.
To estimate the area under the curve f(x)=1/x on [1,2], we can use 4 approximating rectangles.
a) Using left endpoints, the width of each rectangle is (2-1)/4 = 0.25. The left endpoints of the rectangles are 1, 1.25, 1.5, and 1.75. The height of each rectangle is f(x) evaluated at the left endpoint.
So, the heights are f(1) = 1/1 = 1, f(1.25) = 1/1.25 = 0.8,
f(1.5)=1/1.5 = 0.67, and f(1.75) = 1/1.75 = 0.57.
The area of each rectangle is width times height, so the areas are
0.25*1 = 0.25, 0.25*0.8 = 0.2, 0.25*0.67 = 0.1675, and 0.25*0.57 = 0.1425.
Adding these areas together, we get an estimate of the total area under the curve as
0.25 + 0.2 + 0.1675 + 0.1425 = 0.76.
b) Using right endpoints, the width of each rectangle is the same as before. The right endpoints of the rectangles are
1.25, 1.5, 1.75, and 2.
The heights are f(x) evaluated at the right endpoint. So, the heights are
f(1.25) = 0.8, f(1.5) = 0.67, f(1.75) = 0.57, and f(2) = 0.5.
The areas of the rectangles are the same as before, so adding them up, we get an estimate of the total area as
0.2 + 0.1675 + 0.1425 + 0.25 = 0.76,
which is the same as before.
c) To get the average of the two estimates, we add them together and divide by 2:
(0.76+0.76) / 2 = 0.76.
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Let y = tan(5x + 5). Find the differential dy when x = 3 and dx = 0.4 Find the differential dy when x = 3 and dx = 0.8
When x = 3 and dx = 0.4, the differential dy is approximately 4.056, and when x = 3 and dx = 0.8, the differential dy is approximately 8.113.
Differential,
To find the differential dy, we use the formula:
dy = f'(x) * dx
where f'(x) is the derivative of the function y = tan(5x + 5) with respect to x.
Taking the derivative, we get: f'(x) = sec^2(5x + 5) * 5 Plugging in x = 3, we get: f'(3) = sec^2(20) * 5
Now we can find the differential dy for dx = 0.4 and dx = 0.8:
When dx = 0.4: dy = f'(3) * dx dy = sec^2(20) * 5 * 0.4 dy ≈ 4.056
When dx = 0.8: dy = f'(3) * dx dy = sec^2(20) * 5 * 0.8 dy ≈ 8.113
Therefore, when x = 3 and dx = 0.4, the differential dy is approximately 4.056, and when x = 3 and dx = 0.8, the differential dy is approximately 8.113.
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Ortion of
a student is randomly chosen from the group.
what is the probability that the student likes cola b and does not like cola a?
o 0.1
0.2
0.3
o 0.4
Out of the 100 students, 20 like only cola b. Therefore, the probability that a randomly chosen student likes only cola b and does not like cola a is 0.2 or 20%, which is the answer. The answer is option B.
The probability that the student likes cola b and does not like cola a can be calculated as follows
Let's start by finding the number of students who like only cola b. We know that 50 students like cola b in total, but 30 of those students also like cola a. Therefore, the number of students who like only cola b is
50 - 30 = 20
So, out of 100 students, 20 like only cola b. Therefore, the probability that a randomly chosen student likes only cola b is
P(likes only cola b) = 20/100 = 0.2
Therefore, the probability that the student likes cola b and does not like cola a is 0.2.
The answer is option B: 0.2.
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--The given question is incomplete, the complete question is given
" In a class of 100 students, 60 students likes cola a, 50 students likes cola b and 30 students likes both.
From class a student is randomly chosen from the group.
what is the probability that the student likes cola b and does not like cola a?
0.1
0.2
0.3
0.4 "--