The needed two values of x are: 59 and -12.
The difference between a sequence's maximum value and minimum value is referred to as the sequence's range.
A sequence's range is just a set that identifies the sequence. The set x1, x2, x3, and so forth is typically used to describe the range; it is also written as xn; n = 1, 2, 3,...
Given sequence of 8 numbers as: 28, 39, 21, x , 33, 38, 2, 45
Given range of above sequence: 57
Since the value x can assume any value, it have option to be minimum value in the sequence or maximum value in the sequence such that the range remains at 57.
Case 1: x as minimum value of given sequence:
If so, then the maximum value is 45. Then-
range = maximum value - minimum value
57 = 45 - x
x = -12
Case 2: x as maximum value of the given sequence:
If so, then the minimum value of the sequence is 2. Then-
range = maximum value - minimum value
57 = x - 2
x = 59
Thus, the needed two values of x are: 59 and -12.
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When a space shuttle returns from a mission, the last part of its descent to the ground
must be between 17 degrees and 19 degrees with the horizontal (ZZ). If the pilot of
space shuttle Pioneer plans to descend from 11,700 feet (UH) at an angle of 18
degrees (ZZ) from the runway, determine the horizontal distance from the landing site
(ZU) at which the pilot must begin the descent.
Use the diagram to determine the measure of the sought side.
Answer:
please see the followings,
11700 ÷ tan 18 = ZU
50 POINTS! Calculate the expression in the most efficient way possible. Show steps.
5^1125 * 0.2^1123
Answer:
25
Step-by-step explanation:
Given expression:
[tex]5^{1125} \times 0.2^{1123}[/tex]
Rewrite 0.2 as a fraction:
[tex]\implies 5^{1125} \times \left(\dfrac{1}{5}\right)^{1123}[/tex]
[tex]\textsf{Apply exponent rule} \quad \left(\dfrac{a}{b}\right)^c=\dfrac{a^c}{b^c}:[/tex]
[tex]\implies 5^{1125} \times \dfrac{1^{1123}}{5^{1123}}[/tex]
Simplify the numerator by applying the exponent rule a¹ = a:
[tex]\implies 5^{1125} \times \dfrac{1}{5^{1123}}[/tex]
[tex]\textsf{Apply the fraction rule} \quad a \times \dfrac{b}{c}=\dfrac{ab}{c}:[/tex]
[tex]\implies \dfrac{5^{1125} \times1}{5^{1123}}[/tex]
[tex]\implies \dfrac{5^{1125}}{5^{1123}}[/tex]
[tex]\textsf{Apply exponent rule} \quad \dfrac{a^b}{a^c}=a^{b-c}:[/tex]
[tex]\implies 5^{1125-1123}[/tex]
Simplify the exponent:
[tex]\implies 5^{2}[/tex]
Simplify:
[tex]\implies 5 \cdot 5[/tex]
[tex]\implies 25[/tex]
What is the sum of 3 sides?
The sum of the three sides of the triangle is 24.
The sum of three sides of a triangle is calculated using the formula S = a + b + c, where a, b, and c are the lengths of each side of the triangle.
To calculate the sum of three sides of a triangle, first measure the lengths of each side and assign a value for each side. For example, if the lengths of the sides are 6, 8, and 10 respectively, then the values for each side would be a = 6, b = 8, and c = 10.
Next, plug in the values of the sides into the formula S = a + b + c to calculate the sum:
S = 6 + 8 + 10
S = 24
Therefore, the sum of the three sides of the triangle is 24.
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Seth built a wooden step stool out of two rectangular prisms and two cubes. Before fastening the components together, he stained each component to give it its final color.
To completely stain the bottom rectangular prism, Seth had to cover
square inches of wood. For one of the cubes to be completely stained, he had to cover
square inches of wood. To completely stain the top rectangular prism, he had to cover
square inches of wood.
Once the stool was fastened together, he applied a coat of sealant to all exposed surfaces of the stool, including the bottom, to cover a total of
square inches.
To complete stain the bottom rectangular prism, he needs to cover 624 square inches.
What is surface area?A solid object's surface area is a measurement of the overall space that the object's surface takes up.
Given that:
Bottom rectangular prism:
Length = 22 in
Width = 8 in
Height = 6 in
The surface area of the rectangular prism is:
SA = 2( lh + wh + lw)
SA = 2((22)(6) + (8)(6) + (22)(6))
SA= 624 square inches.
To complete stain the bottom rectangular prism, he needs to cover 624 square inches.
Square:
Side = 4 in
The surface area of the cube is:
[tex]SA = 6a^2[/tex]
[tex]SA = 6 (4)^2\\\\SA= 96[/tex]square inches.
To completely stain two squares, he needs to cover 96 * 2 = 196 square inches.
Top rectangular prism:
Length = 18 in
Width = 5 in
Height = 2 in
The surface area of the rectangular prism is:
SA = 2( lh + wh + lw)
SA = 2((18)(2) + (5)(2) + (18)(5))
SA = 136 square inches
Hence to completely stain top rectangular prism, he needs to cover 136 square inches.
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An ice cream factory makes 310 quarts of ice cream in 10 hours how many quarts could be made in 48 hours what was the ate per day
The factory can make 744 quarts of ice cream per day.
To find out how many quarts of ice cream could be made in 48 hours, we can use the principle of proportionality. Since the factory makes 310 quarts of ice cream in 10 hours, we can set up a proportion:
310 quarts / 10 hours = x quarts / 48 hours
To solve for x, we can cross multiply:
310 quarts * 48 hours = 10 hours * x quarts
x = (310 quarts * 48 hours) / 10 hours = 1480 quarts
So the factory could make 1480 quarts of ice cream in 48 hours.
To find the rate per day, we need to divide the number of quarts made per hour by the number of hours in a day. Since there are 24 hours in a day, we can calculate the rate per day as:
rate per day = (310 quarts / 10 hours) * 24 hours = (31 quarts/hour) * 24 hours = 744 quarts/day
So the factory can make 744 quarts of ice cream per day.
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Kate loves to read. She wants to read all 70 books in her bookcase and has already finished 2. Write an equation to represent the time it will take for Kate to read all 70 books if she can read 3 books per month.
Answer:
simply do 70 divided by 12, then that divided by 3, in total it should take 1, 2, or 3 hours to read 3 books a month
Step-by-step explanation:
How do you solve 9x 7 =- 7?
The value of x is 0
Now, According to the question:
Let's know:
How to find the value of 'x'
Generally, the algebraic expression should be any one of the forms such as addition, subtraction, multiplication and division. To find the value of x, bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to find the result.
The given equation is:
9x - 7 = -7
To solve the value of 'x'
9x - 7 = -7
Add 7 on both sides:
9x - 7 + 7 = -7 + 7
9x = 0
x = 0/9
x = 0
Hence, The value of x = 0
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The complete question is this:
How do you solve 9x - 7 = -7
NEED HELP QUICKLY!
x=?
y=?
A hurricane blows onto the East Coast of the United States on September 16, 2017. The maximum sustained wind speed is 176 kilometers (109 miles) per hour and the sea level height is pushed 2.3 meters (7.5 feet) above normal. What category is this hurricane
This hurricane would be classified as a Category 2 hurricane on the Saffir-Simpson Hurricane Wind Scale.
What hurricane classification is this?This hurricane would be classified as a Category 3 hurricane. The Saffir-Simpson Hurricane Wind Scale is used to classify hurricanes based on their maximum sustained wind speeds.Category 3 hurricanes have wind speeds between 178 and 209 kilometers (111 and 130 miles) per hour.The maximum sustained wind speed of this hurricane is 176 kilometers (109 miles) per hour, which is below the threshold for Category 4 hurricanes, but still within the range of Category 3 hurricanes. The storm surge is also a major factor in the classification of hurricanes. Storm surges are caused by the winds of a hurricane pushing the water of the ocean up onto the coast.This hurricane has a storm surge of 2.3 meters (7.5 feet).The Saffir-Simpson Hurricane Wind Scale does not take into account the height of storm surges. Therefore, this hurricane would be classified as a Category 3 hurricane due to its maximum sustained wind speed of 176 kilometers (109 miles) per hour and the storm surge of 2.3 meters (7.5 feet).The Saffir-Simpson Hurricane Wind Scale is a useful tool for measuring the severity of a hurricane and can help to prepare people in its path.To learn more about the Saffir-Simpson Hurricane Wind Scale refer to:
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Problem 2
Use each of the numbers 4, 40, and 4000 once to make true statements.
The correct numbers to complete the statements given are 40, 400, and 4000.
What does this question require you to do?This question requires you to complete a statement with a given number (40, 400 or 4000) to make the statement true by dividing the number by 40.1. To find the correct order the numbers must be place using division, let's find out the results of each of these divisions:
40 / 40.1 = 0.997400 / 40.1 = 9.974000 / 40.1 = 99.7Based on the above, it can be concluded:
40 / 40.1 = is much less than 1400 / 40.1 = is close to 14000 / 40.1 = is much greater than 1Based on this, the complete statements are:
The value of 400 ÷40.01 is close to 1The value of 40 ÷40.01 is much less than 1.The value of 4000÷40.01 is much greater than 1.Note: This question is incomplete; here is the complete question:
Use each of the numbers 4, 40, and 4000 once to make true statements.The value of ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯÷40.01 is close to 1
The value of ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯÷40.01 is much less than 1.
The value of ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯÷40.01 is much greater than 1.
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A student constructs a regular square pyramid with a base that has sides of 13. 2 cm and a
slant height of 6 cm. Find the surface area of the pyramid. Find the surface are of the pyramid
The surface area of a regular square pyramid is 332.64 square cm
We know that the surface area of pyramid is nothing but the sum of the areas of its lateral faces and its base.
surface area of pyramid
= areas of lateral faces of pyramid + area of base of pyramid
We know that the formula for the lateral surface area of regular pyramid is:
A = ½ × P × l
where P is the perimeter of the base and l is slant height
Here, a base of regular square pyramid with has sides of 13. 2 cm
a = 13.2 cm and slant height of 6 cm i.e., l = 6 cm
Using the formula of area of square, the base area of pyramid would be,
B = (13.2)²
B = 174.24 sq.cm.
the perimeter of base is:
P = 4 × 13.2
P = 52.8 cm
So, using the above formula of lateral surface area of pyramid the lateral surface area would be
A1 = 1/2 × 52.8 × 6
A1 = 158.4 sq. cm.
So, the surface area of the pyramid is:
A = A1 + B
A = 158.4 + 174.24
A = 332.64 square cm
Therefore, the surface area of the pyramid = 332.64 square cm
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The areas of the squares adjacent to two sides of a right triangle are 29.2529.2529, point, 25 units^2 2 squared and 131313 units^2 2 squared. 13\text{ units}^213 units 2 29.25\text{ units}^229.25 units 2 xx Find the length, xxx, of the third side of the triangle.
Using the Pythagoras Theorem the third side c of the right-angled triangle is obtained as 6.5 units.
What is Pythagoras Theorem?
In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse. Due to its position opposite the 90° angle, the hypotenuse in this case is the longest side.
The data given is -
Assume a, b and c are sides of right-angled triangle.
Then, two adjacent sides of right-angled triangle are -
a^2=29.25 squared units
b^2=13 squared units
The unknown side c is taken to be x.
Find the length of c using Pythagoras Theorem -
c^2=a^2+b^2
where, c is the hypotenuse, a is the perpendicular and b is the base.
Plugging the values in the equation -
x^2=29.25+13
x=√(29.25+13)
x=√42.25
x=6.5
Therefore, the third side measures x=6.5 units.
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William spends a winter day recording the temperature once every three hours for science class. At 9 am, the temperature was -12.2°F. Between 9am and noon, the temperature rose 16.2°F. Between noon and 3pm, the temperature dropped 9.1°F. Between 3pm and 6pm, the temperature dropped 5°F. What was the temperature at 6pm?
If William spends a winter day recording the temperature once every three hours for science class. If the temperature dropped 9.1°F. Between 3pm and 6pm, the temperature dropped 5°F. The temperature at 6pm is: -11.1°F
How to find the temperature?Between 9am and noon, the temperature rose 16.2°F, so the temperature at noon will be:
Temperature at noon = -12.2 + 16.2
Temperature at noon = 3.0°F
Between noon and 3pm, the temperature dropped 9.1°F, so the temperature at 3pm will be:
Temperature at 3pm = 3.0 - 9.1
Temperature at 3pm = -6.1°F
Between 3pm and 6pm, the temperature dropped 5°F, so the temperature at 6pm was:
Temperature at 6pm =-6.1 - 5
Temperature at 6pm = -11.1°F
Therefore the temperature at 6pm is -11.1°F.
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A 64 acre coconut farm is arranged in an 8 by 8 array. Mika wants to know the average number of coconut palms on each acre of land. The number in each cell tells how many coconut palms grow on that particular acre
Therefore , the solution of the given problem of median comes out to be
A. 44.3.
Specify median.The value that exactly falls in the center of an ordered dataset is the median value. A central tendency measure or average is the difference between both the lowest and highest 50% of the data. The methods for calculating the median and mode vary according to whether you have had an odd or perhaps even number of data points.
Here,
To do the average you add all the numbers then divide by how ever many numbers there are. I remember this through a rhyme:
=> 48 + 38 + 47 + 48+ 43+ 34+ 64+ 54 + 53+ 67 = 443/10 =44.3
Hey fiddle fiddle the medians the middle
You add and divide for the mean
The mode is the one you so the most
And the range is the difference between them
Therefore , the solution of the given problem of median comes out to be
A. 44.3.
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The solution of the given problem of median comes out to be
option (A) 44.3.
What is median?
The value that exactly falls in the center of an ordered dataset is the median value. A central tendency measure or average is the difference between both the lowest and highest 50% of the data. The methods for calculating the median and mode vary according to whether you have had an odd or perhaps even number of data points.
Here,
To do the average you add all the numbers then divide by how ever many numbers there are. I remember this through a rhyme:
=> 34 + 51 + 43 + 35 + 52 + 35 + 62 + 38 + 34 + 59 = 443/10 =44.3
Hey fiddle fiddle the medians the middle
You add and divide for the mean
The mode is the one you so the most
And the range is the difference between them
Therefore , the solution of the given problem of median comes out to be
A. 44.3.
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The complete question is:
A 64‐acre coconut farm is arranged in an 8‐by‐8 array. Mika wants to know the average number of coconut palms on each acre. Each cell in the table represents an acre of land. The number in each cell tells how many coconut palms grow on that particular acre.
45 54 40 34 44 66 32 65 66 33 42 36 33 51 50 35 51 45 66 33 47 43 66 61 46 35 48 67 60 59 52 67 46 32 64 35 55 47 61 59 45 48 53 62 55 58 51 41 48 38 47 48 43 34 64 54 53 67 44 59 58 48 62 45
The numbers in green represent Mika's random sample of 10 acres. What is the average number of coconut palms on the randomly selected acres? Round your answer to the nearest tenth. The average number of coconut palms is
A. 44.3
B. 49.3
PLEASE HELP ME I REALLY NEED IT!!!!!!!!
Answer: for A it is: 3 and 4 represent the number values for X and Y.
Step-by-step explanation:
Sorry, but you B and C you did not give enough information
A horizontal curve is being designed around a pond with a tangent length of 1200 ft and a central angle of 29.86 degrees. If the PI is at station 105 00, determine the station of PT
The station of PT is 12305.58 ft
The station of PT can be determined using the formula:
PT = PI + R * (central angle in radians)
To use this formula, we first need to convert the central angle from degrees to radians. We can do this by multiplying the central angle by (π/180)
Next, we need to determine the radius (R) of the curve. We can use the formula:
R = L / (central angle in radians)
Where L is the tangent length.
Finally, we can substitute the values into the formula for PT:
PT = 105 00 + (1200 / (29.86 * (π/180)))
PT = 105 00 + (1200 / (0.5236))
PT = 105 00 + 2295.58
PT = 12305.58
It's important to note that this calculation assumes that the degree of curvature is a circular curve and that the PI is at the tangent point of the curve.
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The angles of a triangle measure 88°, 53°, and 39º. Which of the following could NOT be the measure of an exterior angle of the triangle?
Answer:35° being the smallest interior angle of the triangle, the exterior angle attached to it is the largest. It measures 180° - 35° = 145°.p.
Step-by-step explanation:
13. Solve:* 3b⁴ x 6b² =
Answer:
18b^6
Step-by-step explanation:
3b⁴ x 6b²
Suppose $PABCD$ is a right square pyramid with apex $P$ and base $ABCD$. If $PBD$ is an equilateral triangle with side length 6, then what is the volume of $PABCD$
The volume of a right square pyramid PABCD is 50.91 cubic units
Let l be the side length of right squared pyramid and h be the height.
We know that the formula for the volume of the right squared pyramid.
V = a²h / 3
And the formula for the height of right squared pyramid.
h = (1/√2)a
Here, the side length (a) = 6 units
So, using above formula of height,
h = (1/√2) × 6
h = 6/√2
h = 3√2 units
Now using the formula for the volume of the right squared pyramid, the volume of pyramid PABCD would be,
V = (6² × 3√2) / 3
V = 6² × √2
V = 36√2
V = 50.91 cubic units
Therefore, the volume of PABCD is 50.91 cubic units
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028)
the cost to insure jewellery is a fixed amount plus a percentage of the value of the jewellery. it costs 32$ to insure 1000$ worth of jewellery or 44.5$ to insure 3500$ worth of jewellry.what is the fixed amount to insure jewellery?
i wrote jewellery so much it isnt a word anymore send help ( explanatio ) asap!
Answer:
The fixed cost to insure jewellery is $0.602.
Step-by-step explanation:
We can use the information provided to set up a system of two equations in two variables, and then use the system to solve for the fixed cost of insuring the jewellery. Let x be the fixed cost and y be the percentage of the value of the jewellery. Then we can write the following two equations:
1000x + 1000y = 32 (1) (cost equation for insuring $1000 worth of jewellery)
3500x + 3500y = 44.5 (2) (cost equation for insuring $3500 worth of jewellery)
We can use either of these equation to solve for the fixed cost(x), to do that we can first solve for y from either of the equation, and then substitute it in other equation.
From equation (1)
y = (32 - 1000x) / 1000
then substitute this in equation (2)
3500x + 3500((32-1000x) / 1000) = 44.5
3500x + 32 - 3500x =44.5 - (1000x)
-20x = -12.05
x = 0.602 $
So, the fixed cost to insure jewellery is $0.602.
That means you have to pay $0.602 as a fixed cost, in addition to 0.01(y) as a percentage of the value of jewellery to insure it.
True or False? A rectangle's area is found by adding the length of the sides and its perimeter is found by multiplying the base by the height.
Answer: The Answer is false!
Step-by-step explanation:
The area of a rectangle is found by multiplying the length by the width.
A straight line is shown on the coordinate grid below. a) What is the y-intercept of this line? b) What is the gradient of this line? Give each of your answers as an integer or as a fraction in its simplest form. Y 8- 7- 6- 5- 4- 3- 2- 1- ܝ ܚ ܚ ܢ ܗ ܘ ܙܢ ܣ -8-7-6-5 -4 -32 -1.0 -2+ -3. -4- -8- 12 4 X
Answer:
a. 4
b. -2
Step-by-step explanation:
coordinate: (2,0), (0,4)
gradient = 4 - 0 / 0 - 2
= -2
please convert 16/100 into a decimal
Answer:
0.16 btw thanks for the points
Answer: 0.16
Step-by-step explanation:
put 16 over 100 and divide it. Then you get your answer 0.16.
which system of inequalities is represented on this graph? NEED THIS ASAP picture below
A random sample of 432 voters revealed that 100 are in favor of a certain bond issue. A 95 percent confidence interval for the proportion of the population of voters who are in favor of the bond issue is
A 95 percent confidence interval for the proportion of the population of voters who are in favor of the bond issue is (0.2301, 0.2759).
How to find a confidence interval for a population proportion?A part of a population with a particular attribute, expressed as a fraction, decimal or percentage of the whole population. For a finite population, the population proportion is the number of members in the population with a particular attribute divided by the number of members in the population.A proportion is a part, share or number considered in comparative relation to a whole. It can be equal to 0, 1 or any value between 0 and 1. It can be expressed as a number or percentage. One example in official statistics would be the proportion of the Canadian population who lives in a given province.p′ = x / n where x represents the number of successes and n represents the sample size. The variable p′ is the sample proportion and serves as the point estimate for the true population proportion.A population proportion is a fraction of the population that has a certain characteristic. For example, let's say you had 1,000 people in the population and 237 of those people have blue eyes. The fraction of people who have blue eyes is 237 out of 1,000, or 237/1000.(0.2301, 0.2759).
This interval is calculated using the following formula:
(sample proportion - margin of error, sample proportion + margin of error)
Where the sample proportion is the number of favorable voters (100) divided by the sample size (432), and the margin of error is calculated using the standard error and a critical value from a normal distribution table.
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Complete the equation of the line who’s y intercept is (0,-1) and slope is 4
Y=4x-1
The equation of a line is:
Y=mx+c
We are told that the slope is 4 which is also gradient, meaning that M=4
Now we are left with:
Y=4x+c
There are two ways to get C:
1. We know that C represents the y-intercept so immediately we can conclude that C=-1
2. You can work it out by substituting the coordinate for the X and Y value:
-1=4(0)+c
-1=C
So in conclusion, the equation of the line is:
Y=4x-1
There are 3.5 loaves of bread, each weighing 1.5 lbs. Anton's family eats 2.5 loaves of bread. What is the total weight of the loaves of bread that are left?
The total weight of the loaves of bread remaining is 1.5 lbs
How to find the total weight of the loaves of bread leftFrom the problem it can be deduced that'
There are 3.5 loaves of bread
each weighing 1.5 lbs
Anton's family eats 2.5 loaves of bread
the total weight of the loaves of bread that are left = ?
The loaves of bread that are left
= 3.5 loaves - 2.5 loaves
= 1 loaf
Since 1 loaf weighs 1.5 lbs the weight of the left over bread is 1.5 lbs
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Using expanded forms, explain why the following problems with unlike bases do not follow the multiplication and division rules of exponents
Pls hurry and thank you!!!!
113.778=one hundred thirteen million seven hundred seventy-eight thousand, and 11,664=eleven thousand six hundred sixty-four is the enlarged form.
What do you meant by expanded form ?1.Comprehensive Notation Form:
[tex]$$\begin{aligned}& 11,664= \\& 10,000 \\& +1,000 \\& +600 \\& +\quad 60 \\& +4 \\&\end{aligned}$$[/tex]
Increased Factors Form:
[tex]$$\begin{aligned}& 11,664= \\& 1 \times 10,000 \\& +1 \times 1,000 \\& +6 \times 100 \\& +6 x \quad 10 \\& +4 \times \quad 1 \\&\end{aligned}$$[/tex]
Increased Exponential Form:
[tex]$$\begin{aligned}& 11,664= \\& 1 \times 10^4 \\& +1 \times 10^3 \\& +6 \times 10^2 \\& +6 \times 10^1 \\& +4 \times 10^0 \\&\end{aligned}$$[/tex]
Text Format:
11,664=eleven thousand six hundred sixty-four
2. Comprehensive Notation Form:
[tex]$$\begin{aligned}& 113.778= \\& 100 \\& +10 \\& +3 \\& +\quad 0.7 \\& +\quad 0.07 \\& +\quad 0.008 \\&\end{aligned}$$[/tex]
Comprehensive Notation Form:
[tex]$$\begin{aligned}& 113.778= \\& 1 \times 100 \\& +1 \times \quad 10 \\& +3 \times \quad 1 \\& +7 \times \quad 0.1 \\& +7 \times \quad 0.01 \\& +8 \times \quad 0.001 \\&\end{aligned}$$[/tex]
Increased Exponential Form:
[tex]$$\begin{aligned}& 113.778= \\& 1 \times 10^2 \\+ & 1 \times 10^1 \\+ & 3 \times 10^0 \\+ & 7 \times 10^{-1} \\+ & 7 \times 10^{-2} \\+ & 8 \times 10^{-3}\end{aligned}$$[/tex]
Text Form:
113.778=one hundred thirteen million seven hundred seventy-eight thousand,
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How do you solve composite functions examples?
The composite function is the result of first applying the function (x^2 - 1) to the input and then applying the function (5x + 2) to the result. The final result of the composite function is 5x^3 + 2x - 3.
Step 1: Apply (x^2 - 1) to the input:
(x^2 - 1) = x^2 - 1
Step 2: Apply (5x + 2) to the result:
(5x + 2)(x^2 - 1)
= 5x^3 - 5x + 2x - 2
Step 3: Simplify:
5x^3 - 5x + 2x - 2
= 5x^3 + 2x - 3
A composite function is the result of applying two or more functions in succession. The order of operations for a composite function is to first apply the first function, then apply the second function to the result of the first, and so on. In the example given, the composite function
f(x) = (5x + 2) ∘ (x^2 - 1)
is the result of first applying the function
(x^2 - 1)
to the input and then applying the function (5x + 2) to the result. The calculation can be broken down into three steps: Step 1 is to apply (x^2 - 1) to the input to get x^2 - 1, Step 2 is to apply (5x + 2) to the result to get 5x^3 - 5x + 2x - 2,
and Step 3 is to simplify the result to get the final answer of
5x^3 + 2x - 3.
To summarize, the composite function
f(x) = (5x + 2) ∘ (x^2 - 1)
is the result of first applying the function (x^2 - 1) to the input, and then applying the function (5x + 2) to the
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For the function below, write the differential.
f(x) = ln(1 + x^2)
dy = ( ) dx
Calculate dy for the given values of x and dx.
x = 2 and dx = 0.2
dy =
How accurate is dy in approximating Δy (i.e., what is their difference) to the nearest thousandth?
The dy for the given values of x and dx is dy = 0.5632, and their difference to the nearest thousandth is 0.0005.
The difference between dy and Δy can be determined by subtracting dy from Δy and taking the absolute value. In this case, dy approximates Δy to the nearest thousandth with a difference of 0.0005. This is a very small difference, indicating that dy is an accurate approximation for Δy.
The accuracy of dy can be attributed to the fact that the function f(x) = ln(1 + x^2) is a smooth function, meaning that the rate of change at a point (i.e., the derivative) is nearly constant. This allows dy to accurately approximate the change in y, Δy, over a small interval of x. Furthermore, the choice of dx = 0.2 is a small enough value that it does not significantly affect the accuracy of the approximation.
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