The maximum error of the midpoint approximation is 0.55.
How to find the maximum error of the midpointTo estimate the maximum error, we can consider the worst-case scenario by assuming that the second derivative is at its maximum value throughout the interval [11, 31]. In this case, we can use the largest possible value for M.
To find the maximum error of the midpoint approximation, we need to determine the width of the interval and divide it by 2.
Width of the interval = upper bound - lower bound = 10.5 - 9.4 = 1.1
Maximum error (E) = (Width of the interval) / 2 = 1.1 / 2 = 0.55
Therefore, the maximum error of the midpoint approximation is 0.55.
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A charity run has prizes for the top finisher in each of 10 age categories. The
times of the prize-winners are shown. Which scatterplot accurately reflects these data?
Age 13 17 21 26 34 36 44 51 62 70
Time (minutes) 23 17 17 15 19 20 24 25 29 30
The scatter plot that accurately describes the data is given as follows:
Scatter plot A.
What is the scatter plot?The scatter plot is built inserting all the points of the table in a graph, which are in the following input-output format:
(Input, Output).
The input and output variables for this problem are given as follows:
Input variable: age.Output variable: time.Hence the points are given as follows:
(13, 23), (17, 17), (21, 17), ..., (70,30).
And all these points are marked on the scatter plot given by option A.
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can someone help me with this i need help to pass math
The angle that has been formed and is shown as x is shown as 52.1°.
What is the angle x?In a right triangle, the tangent of an angle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle. The tangent function is denoted as tan.
We can see that we need to find the tangent of the angle;
Tan x = 36/28
x = Tan-1(36/28)
x = 52.1°
Thus it is clear from the calculation that we have done above that the angle that is marked x is 52.1°.
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Help Due!!!! HELP ASAP!!!
The interval representing the range of the graphed function in this problem is given as follows:
a) (0, ∞).
How to define the domain and range of a function?The domain of a function is defined as the set containing all the values assumed by the independent variable x of the function, which are also all the input values assumed by the function.The range of a function is defined as the set containing all the values assumed by the dependent variable y of the function, which are also all the output values assumed by the function.From the image of the problem, the output y of the function is composed by the positive values, hence the interval representing the range is given as follows:
(0, ∞).
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I need help, I was trying to solve it but I got lost.
Answer: [tex]x\approx 6.2[/tex]
Step-by-step explanation:
Detailed explanation is attached below.
The graph of f(x) and table for g(x)= f(kx) are given.
A coordinate plane with a quadratic function labeled f of x that passes through the points negative 2 comma 4 and negative 1 comma one and vertex 0 comma 0 and 1 comma 1 and 2 comma 4
x g(x)
−8 4
−4 1
0 0
4 1
8 4
What is the value of k?
k = −4
k is equal to one fourth
k is equal to negative one fourth
k = 4
------------------------------
The quadratic functions f(x) and g(x) are described in the table.
x f(x) g(x)
−6 36 4
−5 25 1
−4 16 0
−3 9 1
−2 4 4
−1 1 9
0 0 16
1 1 25
2 4 36
In which direction and by how many units should f(x) be shifted to match g(x)?
Left by 4 units
Right by 4 units
Left by 8 units
Right by 8 units
------------------
Answer both questions for brainliest! (as long as correct)
For the first question, we can see that g(x) = f(kx). To find k, we can compare the x values of f(x) and g(x). We can see that when x = -8 for g(x), x = -2 for f(x). This means that k(-8) = -2. Solving for k gives us k = -2/-8 = 1/4. Therefore, k is equal to one fourth.
For the second question, we can see that g(x) is f(x) shifted to the right by 4 units. Therefore, f(x) should be shifted to the left by 4 units to match g(x). The answer is left by 4 units.
Received message. For the first question, we can see that g(x) = f(kx). To find k, we can compare the x values of f(x) and g(x). We can see that when x = -8 for g(x), x = -2 for f(x). This means that k(-8) = -2. Solving for k gives us k = -2/-8 = 1/4. Therefore, k is equal to one fourth. For the second question, we can see that g(x) is f(x) shifted to the right by 4 units. Therefore, f(x) should be shifted to the left by 4 units to match g(x). The answer is left by 4 units.
hopes thats help thank you
Can I have help finding the area
Step-by-step explanation:
One rectangle 10 x 6 = 60 cm^2
Two sqaures 2 * 4x4 = 32 cm^2 Total = 92 cm^2
Recipe for fruit punch orange juice 6 cups pineapple juice 3 cups cranberry juice one cup Felicia has 32 fluid ounces of pineapple juice does she have enough pineapple juice to make one recipe?
PART- A
A-Yes she has just enough pineapple juice.
B-yes she has more than enough pineapple juice.
C- No she needs 8 more fluid ounces of pineapple juice.
D- No she needs 16 more fluid ounces of pineapple juice.
PART B- Jared also wants to make fruit punch. He has 8 pints of each Orange juice, pineapple juice, and cranberry juice. Which of the following are true…
A- he doesn’t have enough of each type of juice to make 1 recipe.
B- He has enough of each type of juice to make 1 recipe.
C- he has enough of each type of juice to make 2 recipes.
D- he has enough of each type of juice to make 3 recipes.
The statement which is true is he has enough of each type of juice to make 1 recipe, the correct option is B.
We are given that;
Orange juice cup= 6
Pineapple juice cup=3
Now,
PART A: To answer this question, we need to convert the units of measurement to be consistent. The recipe uses cups as the unit of measurement, while Felicia has pineapple juice in fluid ounces. We can use the fact that 1 cup = 8 fluid ounces to convert Felicia’s amount of pineapple juice to cups:
32 fluid ounces = 32 / 8 cups = 4 cups
The recipe requires 3 cups of pineapple juice, so Felicia has more than enough pineapple juice. The correct answer is B.
PART B: we need to convert the units of measurement to be consistent. The recipe uses cups as the unit of measurement, while Jared has each type of juice in pints. We can use the fact that 1 pint = 2 cups to convert Jared’s amounts of juice to cups:
8 pints = 8 * 2 cups = 16 cups
Jared has 16 cups of each type of juice. The recipe requires 6 cups of orange juice, 3 cups of pineapple juice, and 1 cup of cranberry juice. This adds up to 10 cups of juice for one recipe. So, Jared has enough of each type of juice to make one recipe and have some left over. However, he does not have enough of each type of juice to make two recipes, since that would require 20 cups of juice in total. T
Therefore, by unitary method the answer will be He has enough of each type of juice to make 1 recipe.
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Which of these numbers is between 1/3
and 87/100
on a number line? the options are
11/100
3/5
92/10
3/10
3/5 is the fraction between the numbers 1/3 and 87/100
Measuring fractions using number lineA number line is a graphical representation of numbers that can be used to understand and visualize numerical relationships. It is a straight line that extends infinitely in both directions and is usually drawn horizontally.
Writing the fractions as percentage:
1/3 * 100 = 33.3%
87/100 = 87%
This shows that the required number must be between 33.3% and 87%
From the given options:
3/5 * 100 = 3 * 20
3/5 * 100 = 60%
Hence the value in between the numbers 1/3 and 87/100 is 3/5
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Teams in the National Football League in America are divided into two conferences: the AFC and the NFC. Some teams have animals as their mascots, and others do not. The following two-way table displays this data.
How many teams are in the NFC?
The total number of teams that are in the NFC from the given two way frequency table is: 16 teams
How to Interpret a two way frequency table?A two-way table is one way to display frequencies for two different categories collected from a single group of people. One category is represented by the rows and the other is represented by the columns.
Two-way frequency tables are also referred to as a visual representation of the possible relationships between two sets of categorical data
From the attached two way table, we see that:
Total number of animals = 15
Total number of non-animals = 17
Total Number of NFC = 16
Total number of AFC = 16
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Robbie grew 6 inches in eight months. What is his average growth rate per month?
100 Points! Algebra question. Describe the end behavior of the graph in the function. Photo attached. Thank you!
50 Points! Multiple choice algebra question. Photo attached. Thank you!
Answer:
We can start by finding the value of the expression inside the tangent function: tan(1/2 (0 + π/2)) = tan(π/4) = 1
Now we can substitute this value into the original equation and simplify:
y = -3 + tan(1/2 (0 + π/2))
y = -3 + 1
y = -2
The vertical shift of the graph is the constant term in the equation, which is -2. Since this value is negative, the graph is shifted downwards. Therefore, the correct answer is (A) 3 units down
What should be the third row in the following series of shapes
Answer:
The answer is number 2
Find the volume of the sphere use three
Answer: 2916 cubic feet
Step-by-step explanation:
V=(4/3)*3*(9^3)
V=(4/3)*3*729
V=2916
3. (x + 5)2 - y ; x = -2 and y = 1
4. 3x + 4y2 ; × =-3 and y = 5
if anyone could help me with these thank you so much
Answer:
Question 3: 5
Question 4: 91
Step-by-step explanation:
[tex](x+5)2-y[/tex]
[tex]x = -2[/tex]
[tex]y =1[/tex]
[tex](-2 + 5)2 - 1[/tex]
[tex](3)2-1[/tex]
[tex]6-1 = 5[/tex]
[tex]3x +4y^2[/tex]
[tex]x = -3[/tex]
[tex]y=5[/tex]
[tex]3(-3)+4(5)^2[/tex]
[tex]-9 + 100[/tex]
[tex]=91[/tex]
Makayla leans a 18 foot ladder aginst a wall so that it forms and angle of 64 degrees with the ground. what the horizontal distance between the base of the ladder and the wall
The horizontal distance between the base of the ladder and the wall is approximately 16.2 feet.
To answer the question, we need to use trigonometry. In this case, we can use the sine function, which relates the opposite side of a right triangle to its hypotenuse. In this case, the ladder is the hypotenuse, and the horizontal distance between the base of the ladder and the wall is the opposite side.
The angle formed by the ladder and the ground is the angle of interest.
Let x be the horizontal distance between the base of the ladder and the wall. Then, using the sine function, we have:
sin(64 degrees) = x/18
Multiplying both sides by 18, we get:
x = 18 sin(64 degrees) ≈ 16.2 feet
Therefore, the horizontal distance between the base of the ladder and the wall is approximately 16.2 feet.
It is important to note that when using trigonometry, we need to use the appropriate trigonometric function depending on the sides and angles we are given. In this case, we were given the hypotenuse and the angle opposite the horizontal distance, so we used the sine function.
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What is the mode of the data set below? 0, 4 , 3, 4, 0, 9, 1
The mode of the data is 0
What are the measures of central tendency?Central tendency is defined as the statistical measure identifying a single value as representative of an entire distribution.
It provides an accurate description of the entire data.
The three major measures of central tendency are given as;
ModeMeanMedianThe mode is defined as the measure of central tendency representing the most occurring number in a given data set
From the information given, we have;
0, 4 , 3, 4, 0, 9, 1
Then, the mode is 0
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Rewrite the following equation in exponential form. log2 (16) = 4 /5
Answer: 2^(4/5)=16
Step-by-step explanation:
log a (b)=c
this converts to:
a^c=b
so...
2^(4/5)=16
What is the area of the rectangle part of the shape below?
Answer:
The Answer is 80√3 or 138.56 to 2d.p
Step-by-step explanation:
sin 60=L/8
L=sin60×8
L=4√3
Area of rectangle =L×W
A=20×4√3
A=80√3=138.56 to 2d.p
You start driving west for 20 miles, turn left, and drive south for another 14 miles. At the end of driving, what is your straight line distance from your sta
rting point? Round to the nearest tenth of a mile.
The straight-line distance from your starting point at the end of driving is approximately 24.4 miles.
To find the straight-line distance from your starting point, we can use the Pythagorean states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
The distance you drove west and turned left forms two sides of a right triangle, and the straight-line distance from the starting point will be the hypotenuse.
Given:
Distance driven west = 20 miles
Distance driven south = 14 miles
Using the Pythagorean:
Hypotenuse² = (Distance driven west)² + (Distance driven south)²
Hypotenuse² = 20² + 14²
Hypotenuse² = 400 + 196
Hypotenuse² = 596
To find the length of the hypotenuse (straight-line distance), we take the square root of both sides:
Hypotenuse = √596
Hypotenuse ≈ 24.4 miles (rounded to the nearest tenth)
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Write a polynomial function in factored form that has roots at x=7, x=-10, and x=3. Each root should have a multiplicity of 1.
The polynomial function in factored form with roots x = 7, x = -10, and x = 3, each with a multiplicity of 1, is [tex]f(x) = x^3 - 76x + 210.[/tex]
To write a polynomial function in factored form with the given roots, we can use the factored form equation:
f(x) = (x - r1)(x - r2)(x - r3)...
Where r1, r2, r3 represent the roots of the polynomial.
Given the roots x = 7, x = -10, and x = 3, we can write the factored form equation as:
f(x) = (x - 7)(x + 10)(x - 3)
Expanding this equation will give us the polynomial function in factored form:
[tex]f(x) = (x - 7)(x + 10)(x - 3)[/tex]
[tex]= (x^2 - 7x + 10x - 70)(x - 3)[/tex]
[tex]= (x^2 + 3x - 70)(x - 3)[/tex]
[tex]= x^3 - 3x^2 + 3x^2 - 9x - 70x + 210[/tex]
[tex]= x^3 - 76x + 210[/tex]
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Teams in the National Football League in America are divided into two conferences: the AFC and the NFC. Some teams have animals as their mascots, and others do not. The following two-way table displays this data.
how many teams are in the NFC
The total number of teams that are in the NFC from the given two way frequency table is: 16 teams
How to Interpret a two way frequency table?A two-way table is one way to display frequencies for two different categories collected from a single group of people. One category is represented by the rows and the other is represented by the columns.
Two-way frequency tables are also referred to as a visual representation of the possible relationships between two sets of categorical data
From the attached two way table, we see that:
Total number of animals = 15
Total number of non-animals = 17
Total Number of NFC = 16
Total number of AFC = 16
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Log2x + log4x + log16 = 7
the solution to the equation log2x + log4x + log16 = 7 the logarithms using the properties of Logarithms is x ≈ 53.408.
To solve the equation log2x + log4x + log16 = 7, we can simplify the logarithms using the properties of logarithms.
First, we can use the property loga + logb = log(ab) to combine the logarithms:
log2x + log4x + log16 = log(2x * 4x * 16)
Next, we simplify the expression inside the logarithm:
log(2x * 4x * 16) = log(32x^3)
Now, our equation becomes:
log(32x^3) = 7
To eliminate the logarithm, we can rewrite the equation in exponential form:
32x^3 = 10^7
Simplifying further:
32x^3 = 10,000,000
Now, we can solve for x by dividing both sides of the equation by 32:
x^3 = 10,000,000 / 32
x^3 = 312,500
To find the value of x, we take the cube root of both sides:
x = ∛312,500
x ≈ 53.408
Therefore, the solution to the equation log2x + log4x + log16 = 7 is x ≈ 53.408.
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What type of angles are angle 1 and angle 8 ?
Answer:
Angles 1 and 8 are alternate exterior angles.
Describe the transformations from the parent y=1/x :
y=3/x+5 -3
The transformations to the parent function are given as follows:
Vertical stretch by a factor of 3.Translation left 5 units.Translation down 3 units.How to obtain the transformations?The parent function for this problem is given as follows:
y = 1/x.
The transformed function for this problem is given as follows:
y = 3/(x + 5) - 3.
Hence the transformations to the parent function are given as follows:
Vertical stretch by a factor of 3. -> multiplication by 3 in the numerator.Translation left 5 units, as x -> x + 5.Translation down 3 units, as y -> y - 3.More can be learned about transformations at https://brainly.com/question/28687396
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A coffee house blended 16 pounds of espresso flavored
coffee beans with 10 pounds of vanilla flavored coffee
beans. The 26 pound mixture cost $229. A second mixture
included 14 pounds of espresso flavored coffee beans and 11
pounds of vanilla flavored coffee beans. The 25 pound
mixture cost $219.50. Find the cost per pound of the
espresso and vanilla flavored coffee beans.
Answer:
Use systems of equations to solve.
Let x represent the cost per pound of the espresso coffee beans and
y represent the cost per pound of the vanilla coffee beans.
6x + 5y = 77.50
20x + 13y = 234.50, both of these are given.
Rewrite these equations so you can eliminate one of the variables;
60x + 50y = 775, Multiply both sides of the equation by 10
60x + 39y = 703.5, Multiply both sides of the equation by 3
Now Subtract equation 2 from equation 1,
11y = 71.5
y = 6.5
Solve for x,
6x + 5(6.50)= 77.50
x = 7.50
Therefore, the cost per pound of the espresso coffee beans is $7.50, and
the cost per pound of the vanilla coffee beans is $6.50.
Use the 68-95-99.7 rule to find the following quantities. Do not round any answers.
What portion of scores are between 59 and 91?
What portion of exam scores are less than 67?
What portion of exam scores are between 67 and 91?
The portion of scores that are between 59 and 91 is 98%.
The portion of exam scores that are less than 67 is 16%.
The portion of exam scores that are between 67 and 91 is 82%.
What is a normal distribution curve?A normal distribution curve is a type of probability distribution that is commonly used in statistics to represent a large set of data. It is also known as a bell curve. The curve is bell-shaped, symmetrical, and smooth.
Comparing the exam score diagram in the question, to a standard normal distribution curve, we will have the following;
The portion of scores that are between 59 and 91 is;
= 100% - (59 to 43 portion)
= 100% - 2%
= 98%
The portion of exam scores that are less than 67 is;
= (67 to 59) + (59 to 43)
= 14% + 2%
= 16%
The portion of exam scores that are between 67 and 91 is ;
= (67 to 75) + (75 to 83) + (83 to 91)
= 34% + 34% + 14%
= 82%
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Two coins are tossed simultaneously for 360 times.
The number of times '2. Talls' appeared was three times 'No Tall' appeared and number of times '1 tall* appeared is double the number of times 'No Tail' appeared. Find the probabilly of getting Two tails.
The probability of getting Two Tails is 0.1 or 10%.
Let's assume that '2. Tails' appeared x times.
According to the given information, 'No Tail' appeared 3x times, and '1 Tail' appeared 2 × 3x = 6x times.
The total number of tosses is 360. We can express this information in an equation:
x + 3x + 6x = 360
Simplifying the equation:
10x = 360
x = 36
Now we know that '2. Tails' appeared 36 times, 'No Tail' appeared 3x = 3 × 36 = 108 times, and '1 Tail' appeared 6x = 6 × 36 = 216 times.
To find the probability of getting Two Tails, we divide the number of times '2. Tails' appeared by the total number of tosses:
Probability of Two Tails = Number of times '2. Tails' appeared / Total number of tosses
= 36 / 360
= 0.1
Therefore, the probability of getting Two Tails is 0.1 or 10%.
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What are the values of the trigonometric ratios for this triangle?
sin θ =
cos θ =
tan θ =
4/3 3/5 4/5 5/3 5/4 3/4
Answer:
Sin θ = 3/5 cos θ = 4/5 tan θ= 3/4
8cm into kilometres
Answer:
[tex]\huge\boxed{\sf 0.00008\ km}[/tex]
Step-by-step explanation:
Statement:To convert cm to km, we need to divide by 100,000.Solution:= 8 cm
= 8 / 100,000 km
= 0.00008 km[tex]\rule[225]{225}{2}[/tex]
Answer:
0.00008
80 cm is 0.0008 so you know I just assumed