24 cars lacked power steering but did have air conditioning and an automatic gearbox.
According to the question,
No. of cars with Air conditioning = 88
No. of cars with Automatic transmission = 96
No. of cars with power steering = 76
All three = 4
None of these extras = 19
Only air conditioning = 23
Only automatic transmissions = 61
Only power steering = 28
Power steering and automatic transmission both = 11
The calculation for missing values:
11 - 4 = 7
96-61-4-7 = 24
88-24-4-23=37
It is obvious that 24 cars lacked power steering but did have air conditioning and an automatic gearbox.
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How do you draw a line segment equal to a given segment?
draw a line from the starting point of the segment to the endpoint using the same angle and length.
1. Place a ruler or straightedge on the given segment and draw a line along the length of the ruler.
2. Use a compass to create a line segment equal to the given segment. Set the compass to the length of the given segment, place the point of the compass on one end of the segment, and draw an arc to the other end of the segment.
3. Use a protractor to measure the angle and length of the given segment. Then, draw a line from the starting point of the segment to the endpoint using the same angle and length.
The answer explains three methods for drawing a line segment equal to a given segment: using a ruler or straightedge, using a compass, and using a protractor.
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It take Thorton 4 hour to edit a video for hi chool. If he ha already pent 2. 5 hour on thi video, what percent of the video i edited?
Using the concept of fraction, the percentage edited on the video is 62.5 percent.
What is Percentage
Percentage is a standard mathematical concept used to express a portion of a whole number in terms of a hundred. It is denoted by the symbol “%” and is often expressed as a fraction or a decimal. For example, 25% can be expressed as 0.25 or 1/4.
In this problem, Thorton has done a 2.5 hours work. The percentage he has edited can be calculated using fraction or ratio as;
percentage edited = (2.5 / 4) × 100
Percentage = 0.625 × 100
Percentage = 62.5 %
From the above, Thorton has edited 62,5 percent of the video for his school project.
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Can you solve Pythagorean theorem with only C?
The Pythagorean theorem can be solved using a C programme, therefore yes. The Pythagorean theorem states that the hypotenuse's square length of a right triangle equals the sum of the squares of its other two sides. The slope is the side that faces the right angle.
Therefore, given the lengths of the two shorter sides (a and b), the length of the hypotenuse can be calculated using the formula: c = sqrt(a^2 + b^2).
Here is an example C program that calculates the length of the hypotenuse of a right triangle given the lengths of the other two sides:
#include <stdio.h>
#include <math.h>
Above command is for library
int main() {
double a, b, c;
Above command to initiate the variable.
printf("enter the first side's length.: ");
scanf("%lf", &a);
To enter the value in program
printf("enter the second side's length.: ");
scanf("%lf", &b);
Enter the value and print the value
c = sqrt(a*a + b*b);
Arithmetic command
print("The hypotenuse's length is: %lf\n", c); return 0;}
Print the value and return the program value to zero.
This program prompts the user to enter the lengths of the two shorter sides of the triangle, calculates the hypotenuse length using the Pythagorean theorem, and then prints the result.
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Maisie walked for 4 hours at an average speed of
1.6 miles per hour (mph).
How many miles did Maisie walk?
If your answer is a decimal, give it to 1 d.p.
Answer: Maisie walked 6.4 miles.
Step-by-step explanation:
Since Maisie is walking at a constant pace of 1.6 miles per hour we can set up the following equation:
y = 1.6(x)
In this equation, Y is the number of miles Maisie walked in total and X is the number of hours she walked. All we have to do is plug in 4 hours as x and solve.
y = 1.6(4)
y = 6.4 miles.
What are 3 examples of perfect squares?
Three examples of perfect squares is 1) 9, as it is equal to 3 x 3.2) 16, as it is equal to 4 x 4.3) 25, as it is equal to 5 x 5.
What is perfect squares?Perfect squares are numbers that can be expressed as the product of two equal integers, such as 4, 9, and 16. These numbers can be written as the square of a single number, such as 2² = 4, 3² = 9, and 4² = 16. Perfect squares are also known as whole squares, and they provide an easy way to find the square root of a number.
Perfect squares are numbers that are the result of multiplying a number by itself. For instance, 4 is a perfect square because it is equal to 2 x 2.
Similarly, 9 is a perfect square because it is equal to 3 x 3. Perfect squares can be easily identified by their square root, which is the number that can be multiplied by itself to produce the perfect square.
For example, the square root of 16 is 4, since 4 x 4 = 16.
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What is the solution of the pair of equations y 0 and y =- 3?
The solution of the pair of equations y = 0 and y = -3 is y = -3/2.
The given pair of equations is:
y = 0
y = -3
We can solve this pair of equations using elimination. To do this, we first add the two equations together, which gives us:
y + y = 0 + (-3)
2y = -3
We then divide both sides by 2 to get the solution for y:
2y/2 = -3/2
y = -3/2
Therefore, the solution of the pair of equations y = 0 and y = -3 is y = -3/2.
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⎩ ⎪ ⎪ ⎨ ⎪ ⎪ ⎧ a(1)=20 a(n)=a(n−1)−17 third term
The third term of the arithmetic sequence will be negative 14.
What is an arithmetic sequence?A series of integers called an arithmetic succession or arithmetic chain of events has a fixed difference between the terms.
Let a₁ be the first term and d be a common difference.
Then the nth term of the arithmetic sequence is given as,
aₙ = a₁ + (n - 1)d
The first term is 20 and the common difference is calculated as,
aₙ = aₙ₋₁ - 17
aₙ - aₙ₋₁ = - 17
d = - 17
Then the third term is calculated as,
a₃ = 20 + (3 - 1) (-17)
a₃ = 20 + 2 (-17)
a₃ = 20 - 34
a₃ = - 14
The third term of the arithmetic sequence will be negative 14.
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The probability that a student chosen at random from a class has ginger hair is 5/14.
The probability that they have blonde hair is 9/28.
What is the probability that a student chosen from the class at random has either ginger or blonde hair?
Give your answer as a fraction in its simplest form.
Answer: The probability of a random student to have either ginger or blonde hair is 19/28.
Step-by-step explanation: Before anything is done, let's look and see what information the problem gives us and what we need to find out. We know that there's a 5/14 chance for a student to be ginger, and a 9/28 chance for them to be blonde. We need to find out the combined chance, as we want to know what the chances are for a student to have either hair color.
In order to do this, all we need to find is the sum of both fractions. Because the fractions have different denominators, we need to change one of them to match the other. 14 multiplied by 2 is equal to 28.
If we multiply both the numerator and denominator of 5/14 by 2, we get 10/28. Now, all we have to do is add that to 9/28. When we do that, we get 19/28.
19/28 cannot be simplified, so it is our final answer. Hope this helps!
Is 10 12 15 a right triangle?
No, 10, 12, and 15 are not the lengths of the sides of a right triangle.
A right triangle is a triangle with one 90 degree angle. The other two angles must be acute angles (less than 90 degrees).
The Pythagorean Theorem is a formula used to determine if three given side lengths can form a right triangle. The Pythagorean Theorem states that the sum of the squares of the two shorter sides of a right triangle is equal to the square of the longest side, also known as the hypotenuse.
In this case, the side lengths of the triangle are 10, 12, and 15. Therefore, the Pythagorean Theorem can be written as:
10^2 + 12^2 = 15^2
100 + 144 = 225
244 ≠ 225
Therefore, 10, 12, and 15 are not the side lengths of a right triangle.
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Consider each of the following word problems.
Write a word sentence to represent what you are going to do with the numerical values.
Include the proper brackets, exponents and operation signs.
Substitute the words with an appropriate variable.
Solve each problem in good form.
1. The school library had a used book sale. Paperbacks were 25 cents each and hardcover books
were $1.25 each. There were 54 paperbacks and 163 hardcover books sold. How much money did
the library raise?
2. Tamara has to go on a business trip. Including taxes, her round trip airfare is $398.60 and her
room costs $115.70 per night. The cab fare from the airport to the hotel is $40.00. If Tamara
stays for two nights, how much does the trip cost, excluding the cost of food?
3. Paula repairs swimming pools and earns $14.50/h for the first 35 h she works in a week. For
hours over 35 h, she earns 1.5 times as much. If she works 48 hours in a week, how much does she
earn?
4. Will and Liam collect baseball cards. Will has 26 cards and Liam has 19. They decided to combine
their cards. Because they shared, their father decided that he would triple the number of cards
that they had. After that, their friend Nestor thought that he would add his cards to their bunch.
Nestor didn’t know how many cards he had but he knew that he could lay them out in rows and that
they would make a square with one side of his square having 8 cards. How many cards did the boys
have altogether?
The amount and numbers are 1. $217.25, 2. $710, 3. $790.25 and 4. 167.
What is Multiplication?Multiplication of two numbers is defined as the addition of one of the number repeatedly until the times of the other number
1. Cost of a paperback = 25 cents = $0.25
Cost of a hardcover book = $1.25
There were 54 paperbacks and 163 hardcover books sold.
Money library raised = (0.25 × 54) + (1.25 × 163) = $217.25
2. Cost for round trip airfare = $398.60
Cost of room per night = $115.70
Cost of room for two nights = 2 × $115.70 = $231.40
Cab fare from airport to hotel = $40.00
Total fare from airport to hotel and the return = 2 × $40.00 = $80.00
Total cost = $398.60 + $231.40 + $80.00 = $710
3. Total working hour of Paula = 48 hours
Earning for first 35 hours = $14.50/h × 35
= $507.50
Remaining hours = 48 - 35 = 13 hours
Earning for next 13 hours = ($14.50/h × 1.5) × 13
= $282.75
Total earnings = $507.50 + $282.75 = $790.25
4. Number of cards Will has = 26
Number of cards Liam has = 19
When they combine, total cards = 26 + 19 = 45
When father also shared, total number of cards = 3 × 45 = 135
Number of cards Nestor has = 4 × 8 = 32
Total number of cards = 135 + 32 = 167
Hence all the questions are cleared using multiplication as one of the basic operations.
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What are the domain and range of the logarithmic function?
The domain of a logarithm function is (0, ∞). The range of the logarithm function is all real numbers.
What is a function?
A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
The given function is f(x) = log x.
When the value of x is less than or equal to 0, then the value of log x is undefined.
The possible value of x where f(x) exists is the domain of a function.
In the given function the value of x must be greater than zero.
The domain of the function is (0,∞).
log (0.1) = -1
log (0.023) = -1.638
The value of log x can be any real number.
The possible value of the logarithm function is any real number. Thus the range of the function is (-∞, ∞).
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Review the graph of complex number z. On a coordinate plane, the y-axis is labeled imaginary and the x-axis is labeled real. Point z is at (negative 7, negative 6). What is the conjugate of z?
The conjugate is -7+6i. The correct option is third.
What is conjugate?When two binomials have the same terms but different arithmetic operators in the center of these related words, they are said to be conjugate. For instance, the conjugate of p + q is p - q.
Given:
On a coordinate plane,
the y-axis is labeled imaginary and the x-axis is labeled real.
Point z is at (negative 7, negative 6).
Z(-7, -6)
So, the equation,
-7-6i
So, the conjugate of the equation is,
-7+6i
Therefore, -7+6i is the conjugate of the points.
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A heavy rainstorm damages this year's crop of peanuts. The price of peanut butter increases. What will happen to the demand of jelly?
Answer the 3 questions below related to this scenario.
Complete sentences are not required. Please number each answer.
1. Will there be an increase or decrease?
2. Which way will the graph shift?
3. What is the determinant?
On solving the provided question, we got to know that - to plot the graph, required equation is 3x +y -8 = 0
What is an expression?a collection of numbers, symbols, and operators (like + and ) that represent a value. Examples - 2 + 3 is a formula and there is also the statement 3 x/2. The equals symbol does not appear in expressions. Actually, none of these = ≠ < > ≤ ≥
We frequently have to understand a written phrase in order to write an expression. For instance, the notation x + 6 can be used to represent the phrase "6 added to some number," where x stands for the unknown value. To plot the graph,we need to find the equation first.
and to find the equation -
(y - y1) = m( x - x1)
y1 = -4
x1 = -2
y = 3
x = -5)
equation -
(-3)(x-1) = y-5
-3x + 3 = y-5
3x - 3 = 5-y
3x +y -8 = 0
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3. 2 Roulette wheel: The game of roulette involves spinning a wheel with 38 slots: 18 red, 18 black, and 2
green. A ball is spun onto the wheel and will eventually land in a slot, where each slot has an equal chance
of capturing the ball.
a) You watch a roulette wheel spin 9 consecutive times and the ball lands on a red slot each time. What is
the probability that the ball will land on a red slot on the next spin?
(please round to four decimal places)
b) You watch a roulette wheel spin 320 consecutive times and the ball lands on a red slot each time. What
is the probability that the ball will land on a red slot on the next spin?
x (please
round to four decimal places)
The probabilities for the game of roulette that involves spinning a wheel with 38 slots, for a and b, are 0.4737, or 18/38, or 47.37%.
The following are the rationales:
(a) The probability of the ball landing on a red slot on any given spin is 18/38, or 0.4737, or 47.37%. This probability does not change based on the outcome of previous spins, as each spin is independent of the others and the probability of landing on a red slot is always the same. So, the probability of the ball landing on a red slot on the next spin is also 18/38, or 0.4737, or 47.37%.(b) The probability of the ball landing on a red slot on any given spin is 18/38, or 0.4737, or 47.37%. This probability does not change based on the outcome of previous spins, as each spin is independent of the others and the probability of landing on a red slot is always the same. So, even though the ball has landed on a red slot 300 consecutive times, the probability of the ball landing on a red slot on the next spin is still 18/38, or 0.4737, or 47.37%Learn more about probability here: brainly.com/question/25839839
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HELP!!!
Marta bakes 3 types of cake: chocolate, fruit, and sponge. The recipe for each cake includes flour and sugar and she uses 3.3kg of flour and 3.1kg of sugar in total.
Each chocolate cake uses 225 g of flour and 300g of sugar
Each fruit cake uses 320g of flour and 250g of sugar
Each sponge cake uses 400 g of flour and 325g of sugar
Marta sells chocolate cakes for $12, fruit cakes for $10, and sponge cakes for $8 and makes a total of $114
How many of each cake does she make?
(Answer in the back of the book: 4 chocolate, 5 fruit, 2 sponge cakes)
The three equations for this problem are:
The total amount of flour used: 3.3kg = (225g/cake) * (number of chocolate cakes) + (320g/cake) * (number of fruit cakes) + (400g/cake) * (number of sponge cakes)The total amount of sugar used: 3.1kg = (300g/cake) * (number of chocolate cakes) + (250g/cake) * (number of fruit cakes) + (325g/cake) * (number of sponge cakes)The total revenue from sales: $114 = ($12/cake) * (number of chocolate cakes) + ($10/cake) * (number of fruit cakes) + ($8/cake) * (number of sponge cakes)Let's call the number of chocolate cakes x, the number of fruit cakes y, and the number of sponge cakes z
so the
first equation can be written as 3.31000 = (225x) + (320y) + (400z)second 3.11000 = (300x) + (250y) + (325z)and third one 114 = (12x) + (10y) + (8*z)let's use the third equation to get the value of x,y and z:
x = (114 - 10y - 8z) / 12y = (114 - 12x - 8z) / 10z = (114 - 12x - 10y) / 8If you get the values and substitute, then the answer would be:
4 chocolate cakes, 5 fruit cakes, 2 sponge cakes
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The sales tax in one town is 8%.So, the total cost of an item can be written as c=0.08cents .what is the total cost of an that sells for $12 ?its due tmrr asap
Answer: 12.96
Step-by-step explanation: you should multiply 12 * 0.08 = 0.96
then just add 0.96 + 12 = 12.96
please answer this
i really need it
i will give u a crown
Answer:
i am not to sure but if i am corroct it IS polynomial
Step-by-step explanation:
hope this helps
GIVEN: An exterior stud wall with brick veneer is 11 ft tall and 40 ft long. 25 % of the area of the wall is windows (glass, frame and sash). FIND: Total weight of the wall and the average dead load in lb/ft of the length of the wall (per foot of wall length) that the wall exerts on the floor.
The total weight of the wall is 49,500 lb, and the average dead load per foot of wall length is 1237.5 lb/ft.
To find the total weight of the wall and the average dead load per foot of wall length, we need to calculate the total area of the wall and the area of the windows, then use that information to determine the weight of the remaining brick veneer.
First, we calculate the total area of the wall by multiplying the length and height:
40 ft * 11 ft = 440 ft²
Next, we calculate the area of the windows by multiplying the total area of the wall by 25% (the percentage of the wall that is windows):
440 ft² * 0.25 = 110 ft²
Now we can find the area of the brick veneer by subtracting the area of the windows from the total area of the wall:
440 ft² - 110 ft² = 330 ft²
To find the weight of the brick veneer, we can assume a weight of 150 lb/ft². We can calculate this by multiplying the area of the brick veneer by the weight per square foot:
330 ft² * 150 lb/ft² = 49,500 lb
Now to find the average dead load in lb/ft of the length of the wall, we divide the total weight of the wall by the total length of the wall:
49500 lb / 40 ft = 1237.5 lb/ft
So the total weight of the wall is 49,500 lb, and the average dead load per foot of wall length is 1237.5 lb/ft.
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HELP!
4(2x-3)=6x+2
I thought when I simplify it 22x=14 but its wrong
Answer:
the answer is 1
Step-by-step explanation:
4(2x-3)=6x+2
8x-12=6x+2
+6x +6x
14x-12 =2
+12 +12
14x=14
x=1 and don't worry we all make mistakes
(a) What is the probability that the proportion of voters in the sample of Region A who support the ballot measure is greater than 0.50
Using the normal distribution and the central limit theorem, it is found that there is a 0.0901 = 9.01% probability that the proportion of voters in the sample of Region A who support the ballot measure is greater than 0.50.
What is probability?Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one. Probability has been introduced in Maths to predict how likely events are to happen. The meaning of probability is basically the extent to which something is likely to happen. This is the basic probability theory, which is also used in the probability distribution, where you will learn the possibility of outcomes for a random experiment. To find the probability of a single event to occur, first, we should know the total number of possible outcomes.To learn more about distribution refer to:
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What is 200/51 equal to
Answer:
Approx 3.92
Step-by-step explanation:
Solve 3x^2 - 6x - 9?
Answer:
3(x+1)(x-3)
Step-by-step explanation:
Well, this isn't an equation, but we can factor it like this:
[tex]3x^2-6x-9=3(x^2-2x-3)=3(x+1)(x-3)[/tex]
Solve these for points I got a one in algebra so this would be helpful to my grade
The solution for each system of equations is given as follows:
1) x = -4, y = -8.
2) x = 5, y = -1.
3) x = -7, y = 2.
4) No solution.
5) x = 2, y = -6.
6) x = -3, y = 4.
How to solve the system of equations?The system of equations are solved using the elimination method, writing one variable as a function of another, replacing in the other equation, and then obtaining each variable.
For item 1, we eliminate x, as follows:
x = 12 + 2y.
Hence the solution for y is obtained as follows:
5(12 + 2y) + 3y = -44
60 + 10y + 3y = -44
13y = -104
y = -104/13
y = -8.
Then the solution for x is given as follows:
x = 12 + 2y = 12 + 2(-8) = -4.
For item 2, we have that:
y = 19 - 4x.
Hence:
7x - 2(19 - 4x) = 37
7x - 38 + 8x = 37
15x = 75
x = 5.
Hence the solution for y is of:
y = 19 - 4(5) = -1.
For item 3, we can simplify the second equation by two, hence:
-x + y = 9.
y = 9 + x.
Hence:
3x + 8(9 + x) = -5
3x + 72 + 8x = -5
11x = -77
x = -7.
Hence the solution for y is of:
y = 9 - 7 = 2.
For item 4, we have that:
x = 7 + 3y.
Hence:
2(7 + 3y) - 6y = 12
14 + 6y - 6y = 12
0y = -2. (no solution, division by zero).
For item 5, we have that:
y = -2 - 2x.
Hence:
5x + 3(-2 - 2x) = -8
5x - 6 - 6x = -8
-x = -2
x = 2.
Hence the solution for y is of:
y = -2 - 2(2)
y = -6.
For item 6, we simplify the second equation by two, hence:
2x + y = -2
y = -2 - 2x.
Replacing on the first equation, we have that:
2x + 5(-2 - 2x) = 14.
2x - 10 - 10x = 14
-8x = 24
8x = -24
x = -3.
Hence the solution for y is obtained as follows:
y = -2 - 2(-3)
y = -2 + 6
y = 4.
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For a loan of. 8,75,000 how much interet will be charged by the bank for 2
month if the rate i 4. 75% per year?
Total interest charged by bank in 2 months is 6793.83.
What is compound interest ?Compound interest is the interest paid on both principal and interest, compounded at regular intervals. At regular intervals, the interest so far accumulated is clubbed with the existing principal amount and then the interest is calculated for the new principal. The new principal is equal to the sum of the Initial principal, and the interest accumulated so far.
The interest that is obtained through the reinvestment of money is known as compound interest. The original principal investment grows substantially more quickly (sometimes referred to as exponentially) when interest is reinvested and allowed to compound over time.
Total loan amount = 875000
total time = 2 months
Rate = 4.75%
Total interest = 875000(1 + [tex]\frac{4.75}{100}[/tex])[tex]\)^{\frac{1}{6} }[/tex] - 875000 = 6793.83
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Find the product using any method. (Need some help!!)
Answer:
2n^2-8n-24
Step-by-step explanation:
Uhm i just did this one with one of my classmates like 2-3 months ago so it just came to mind.
Hope this helped tho! :)
The table shows data for 4 cyclists during one day of training.
Complete the table by finding the rate of speed for each cyclist. Use the formula r = d ÷ t.
Cyclist Distance (mi) Time (hr) Rate (mi per hr)
Alisha 40 4
Jose 30 2
Raul 40 4
Ruthie 80 5
Rate of speed of each cyclist is:
Alisha 10mi/hr
Jose 15mi/hr
Raul 10mi/hr
Ruthie 16mi/hr
Data given of each cyclist;
Formula used: [tex]r=\frac{d}{t}[/tex]
here,
r=rate of speed
d=distance
t=time
Alisha: Distance=40mi; Time=4hr
applying the formula
[tex]r=\frac{d}{t} \\r=\frac{40}{4} =10mi/hr[/tex]
Jose: Distance=30mi; Time=2hr
applying the formula
[tex]r=\frac{d}{t}\\ r=\frac{30}{2} =15mi/hr[/tex]
Raul: Distance=40mi; Time=4hr
applying the formula
[tex]r=\frac{d}{t} \\r=\frac{40}{4}=10mi/hr[/tex]
Ruthie: Distance=80mi; Time=5hr
applying the formula
[tex]r=\frac{d}{t} \\r=\frac{80}{5} =16mi/hr[/tex]
Alisha= 10mi/hr
Jose= 15mi/hr
Raul= 10mi/hr
Ruthie= 16mi/hr
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ind the Average Rate of Change of the table below for the interval 0 < x < 4
The average rate of change is equivalent to 2.
What is expression?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
Given is the table as shown below -
[x] : 0 1 2 3 4
[y] : -2 -3 1 3 6
The rate of change in the interval 0 < x < 4 is -
AROC = (6 + 2)/(4 - 0)
AROC = 8/4
AROC = 2
Therefore, the average rate of change is equivalent to 2.
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Which choice is equivalent to the quotient shown here for acceptable
values of x?
√12(x-1)+√√2(x-1)²
For acceptable x values of √12(x-1)+√√2(x-1)², the option is equivalent to the quotient given here (x-1) ² is [tex]$2 \sqrt{3} \sqrt{x-1}-\sqrt{2}(x-1)$\\[/tex] .
How do you find the quotient of a set?The equivalent of the quotient displayed above for allowable x values is
[tex]$\sqrt{1} \cdot 2(x-1)+\sqrt{\sqrt{2}}(x-1)^2$[/tex]
[tex]$2(x-1)+\sqrt[2 \cdot 2]{2}(x-1)^2$\\[/tex]
[tex]\$2(x-1)+\sqrt[4]{2}(x-1)^2$\\$(2 x-2)+\sqrt[4]{2}\left(x^2+2 x(-1)+(-1)^2\right)$\\$(2 x-2)+\sqrt[4]{2}\left(x^2-2 x+1\right)$\\$2 x-2+\sqrt[4]{2}\left(x^2-2 x+1\right)$\\$2 x+\sqrt[4]{2}\left(x^2-2 x+1\right)-2$\\$2 x+\left(\sqrt[4]{2} \cdot x^2-\sqrt[4]{2} \cdot 2 x+\sqrt[4]{2}\right)-2$\\$2 x+\left(\sqrt[4]{2} \cdot x^2-2 \cdot \sqrt[4]{2} \cdot x+\sqrt[4]{2}\right)-2$\\$2 x+\sqrt[4]{2} \cdot x^2-2 \cdot \sqrt[4]{2} \cdot x+\sqrt[4]{2}-2$[/tex]
[tex]$f(x)=\sqrt{12(x-1)}-\sqrt{2(x-1)^2}$[/tex]
[tex]$\frac{d}{d x}\left(\sqrt{12(x-1)}-\sqrt{2(x-1)^2}\right)$[/tex]
[tex]$\sqrt{12(x-1)}-\sqrt{2(x-1)^2}=2 \sqrt{3} \sqrt{x-1}-\sqrt{2}(x-1)$[/tex]
[tex]$\sqrt{12(x-1)}-\sqrt{2(x-1)^2}$[/tex]
[tex]$\sqrt{12(x-1)}=2 \sqrt{3} \sqrt{x-1}$[/tex]
[tex]$\sqrt{2(x-1)^2}=\sqrt{2}(x-1)$\\$=2 \sqrt{3} \sqrt{x-1}-\sqrt{2}(x-1)$\\[/tex]
Values that might result in a fraction's denominator being equal to zero are excluded. Finding these omitted values is crucial for resolving a rational statement because you cannot divide by 0.
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Given:
sin (C) 4/9
Find tan (C)
[tex]sin(C)=\cfrac{\stackrel{opposite}{4}}{\underset{hypotenuse}{9}}\qquad \textit{let's find the \underline{adjacent side}} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2 - b^2}=a \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ \sqrt{9^2 - 4^2}=a\implies \sqrt{65}=a \\\\[-0.35em] ~\dotfill[/tex]
[tex]tan(C)=\cfrac{\stackrel{opposite}{4}}{\underset{adjacent}{\sqrt{65}}}\implies tan(C)=\cfrac{4}{\sqrt{65}}\cdot \cfrac{\sqrt{65}}{\sqrt{65}}\implies tan(C)=\cfrac{4\sqrt{65}}{65}[/tex]
what can you say about the series ∑an in each of the following cases
a) lim |(an+1)/(an)∑|=1
n→[infinity] b) lim nth root(|(an)|=2/3
n→[infinity]
c) lim |(an+1)/(an)|=0.8
n→[infinity]
d) lim |(an+1)/(an)|=3/2
n→[infinity]
e) lim |(an+1)/(an)|=3
n→[infinity]
f) lim nth root(|(an)|=1/2
n→[infinity]
In each of the cases, the series ∑an is convergent. This means that the limit of the sequence of partial sums of the series is finite.
In case a, since the limit of the ratio of consecutive terms is 1, the series is convergent and its sum is equal to the limit of the sequence of partial sums of the series.In case b, since the limit of the nth root of the absolute value of the terms is 2/3, the series is convergent and its sum is equal to the limit of the sequence of partial sums.In case c, since the limit of the ratio of consecutive terms is 0.8, the series is convergent and its sum is equal to the limit of the sequence of partial sums.In case d, since the limit of the ratio of consecutive terms is 3/2, the series is convergent and its sum is equal to the limit of the sequence of partial sums.In case e, since the limit of the ratio of consecutive terms is 3, the series is convergent and its sum is equal to the limit of the sequence of partial sums.In case f, since the limit of the nth root of the absolute value of consecutive terms is 3/2, the series is convergent and its sum is equal to the limit.Learn more about Convergent here:
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