According to the Mean Value Theorem, if a function is continuous on the interval [a, b] and differentiable on the open interval (a, b), there exists a point c in (a, b) such that the derivative at c equals the average rate of change between a and b.
To use the Mean Value Theorem to show that if * > 0, then sin* < x, we first need to apply the theorem to the function f(x) = sin x on the interval [0, *].
According to the Mean Value Theorem, there exists a number c in the interval (0, *) such that:
f(c) = (f(*) - f(0)) / (* - 0)
where f(*) = sin* and f(0) = sin 0 = 0.
Simplifying this equation, we get:
sin c = sin* / *
Now, since * > 0, we have sin* > 0 (since sin x is positive in the first quadrant). Therefore, dividing both sides of the equation by sin*, we get:
1 / sin c = * / sin*
Rearranging this inequality, we have:
sin* / * > sin c / c
But c is in the interval (0, *), so we have:
0 < c < *
Since sin x is a decreasing function in the interval (0, π/2), we have:
sin* > sin c
Combining this inequality with the earlier inequality, we get:
sin* / * > sin c / c < sin* / *
Therefore, we have shown that if * > 0, then sin* < x.
I understand that you'd like to use the Mean Value Theorem to show that if x > 0, then sin(x) < x. Here's the answer:
According to the Mean Value Theorem, if a function is continuous on the interval [a, b] and differentiable on the open interval (a, b), there exists a point c in (a, b) such that the derivative at c equals the average rate of change between a and b.
Let's consider the function f(x) = x - sin(x) on the interval [0, x] with x > 0. This function is continuous and differentiable on this interval. Now, we can apply the Mean Value Theorem to find a point c in the interval (0, x) such that:
f'(c) = (f(x) - f(0)) / (x - 0)
The derivative of f(x) is f'(x) = 1 - cos(x). Now, we can rewrite the equation:
1 - cos(c) = (x - sin(x) - 0) / x
Since 0 < c < x and cos(c) ≤ 1, we have:
1 - cos(c) ≥ 0
Thus, we can conclude that:
x - sin(x) ≥ 0
Which simplifies to:
sin(x) < x
This result is consistent with the Mean Value Theorem, showing that if x > 0, then sin(x) < x.
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Mario's Pizzeria offers 2 types of crust and 6 different kinds of toppings. They assigned each side of the coin to a type of pizza crust and each number on the number cube to a topping. If Mario's makes a one-topping pizza, what is the probability that the coin flipped and the cube rolled will describe the pizza crust and topping combination they just made? Express the answer as a decimal rounded to the nearest thousandth
To determine the probability of the coin flip and the cube roll describing the pizza crust and topping combination made at Mario's Pizzeria, we need to consider the total possible outcomes of these events.
There are 2 types of crust, so the coin has 2 sides (heads for one crust type and tails for the other). For the toppings, there are 6 options, represented by the numbers 1 to 6 on the number cube.
First, we find the total possible outcomes by multiplying the number of crust options (2) by the number of topping options (6):
Total possible outcomes = 2 crust options * 6 topping options = 12 combinations
Since there is only one specific combination that Mario's Pizzeria just made, the probability of the coin flip and the cube roll describing this specific combination is:
Probability = 1 (specific combination) / 12 (total possible outcomes)
To express this as a decimal rounded to the nearest thousandth, divide 1 by 12:
Probability ≈ 0.083
So, the probability that the coin flipped and the cube rolled will describe the pizza crust and topping combination that Mario's Pizzeria just made is approximately 0.083, or 8.3%.
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14
Find the limit of the rational function a. as x and b. as X-→ - 00 X + 6 f(x) = +3 + 20 X+6 a. lim x x² + 20 (Simplify your answer.) X + 6 b. lim x--00x2 + 20 = (Simplify your answer.) (
Both the limits are equal to 0: a. lim (x→∞) f(x) = 0 b. lim (x→-∞) f(x) = 0
Know more about rational function,
First, let's rewrite the rational function f(x) more clearly and identify the two limits we need to find: f(x) =[tex](x + 6) / (x^2 + 20)[/tex]
a. lim (x→∞) f(x) b. lim (x→-∞) f(x)
To find these limits, we can use the following steps:
Step 1: Divide both the numerator and the denominator by the highest power of x in the denominator.
In this case, it is x^2. f(x) = [tex][(x + 6) / x^2] / [(x^2 + 20) / x^2][/tex]
Step 2: Simplify the function. f(x) =[tex][(1/x) + (6/x^2)] / [1 + (20/x^2)][/tex]
Step 3: Evaluate the limits.
a. lim (x→∞) f(x)
= [(0) + (0)] / [1 + (0)]
= 0 / 1 = 0
b. lim (x→-∞) f(x)
= [(0) + (0)] / [1 + (0)]
= 0 / 1 = 0
So, both the limits are equal to 0: a. lim (x→∞) f(x) = 0 b. lim (x→-∞) f(x) = 0
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Can someone help me ASAP please? It’s due tomorrow. Show work please!! I will give brainliest if it’s correct and has work.
Answer:
Step-by-step explanation:
There are 12 possible cards you can choose.
There are 3 possible results for the spinner.
There are 2 possible results for the coin toss.
When doing all 3 events:
Total possibilities [tex]=12\times 3 \times 2=72.[/tex]
SOLUTION: 72
Clue 1: The R stamps total 24 cents. R1 + R2 + R3 = 24 Clue 2: The R stamps with animals total 16 cents. R1 + R2 = 16 Combining this with Clue 1, we know R3 = 8 Clue 3: The stamps with animals total 20 cents. R1+ Combining this with Clue 2, we know S2 = 4 Clue 4: The stamps with two animals total 13 cents. S2 + R2 = Combining this with what we learned from Clue 3, we know R2 = +72 = 22 Clue 5: The two stamps with a person total 22 cents. Combing this with what we learned from Clue 2, we know I? Clue 6: The triangle stamps total 24 cents. I+ Combining this with what we learned from Clue 5, we know +52 = 20 Clue 7: The stamps with mechanical devices total 20 cents. 71+ R3 51 Combining this with what we learned from Clue 2 and Clue 6. we know Sl SA The S stamps total 11 cents. S1 + $2+ Combining this with what we learned from Clue 3 and Clue 7, we know 5
Using the combine clues method:
[tex]R_1=7\\\\R_2=9\\\\R_3=8\\\\S_1=2\\\\S_2=4\\\\S_3=5\\\\T_1=10\\\\T_2=14[/tex]
How to combine clues?Certain items that must be worn, used, or accessed in order to access particular clues. The maximum skill level needed to solve each master clue is shown.
Clue 1: [tex]R_1 + R_2 + R_3 = 24[/tex]
Clue 2: [tex]R_1 + R_2 =16[/tex]
Since, [tex]R_1 + R_2 + R_3 = 24[/tex] (from clue 1)
[tex]R_1 + R_2 + R_3 = 24\\\\16 + R_3 = 24[/tex]
Subtract both the sides by 16,
[tex]R_3=8[/tex]
Clue 3:
We need to find the blank [tex]R_1 +[/tex] __ [tex]+S_2=20[/tex] and [tex]S_2=4[/tex]
Since, [tex]R_1 + R_2 = 16[/tex] (from clue 2)
So,
[tex]R_1 + R_2 + S_2 = 20\\\\16 + S_2 = 20[/tex]
Subtract 16 from both sides.
[tex]16 + S_2 - 16 = 20 -16\\\\S_2 = 4[/tex]
So,
[tex]R_1 + R_2 + S_2 = 20[/tex]
Clue 4:
We need to find the blank [tex]R_2[/tex] = __
[tex]S_2 + R_2 = 13[/tex]
Since, [tex]S_2 = 4[/tex]
[tex]S_2 + R_2 = 13\\\\4 + R_2 = 13[/tex]
Subtract 4 from both sides.
[tex]R_2 = 9[/tex]
So, [tex]R_2 = 9[/tex]
Clue 5:
We need to find the blank ___ [tex]+ T_2 = 22[/tex] and [tex]T_2=[/tex] ___
[tex]R_3 + T_2 = 22[/tex]
Since, [tex]R_3 =8[/tex] (from the Clue 2)
[tex]R_3 + T_2 = 22[/tex]
[tex]8 + T_2 = 22[/tex]
Subtract both the sides by 8,
[tex]T_2 = 14[/tex]
So, [tex]R_3 + T_2 = 22[/tex]
Clue 6:
We need to find the blank [tex]T_1 +[/tex] ___ = 24 and ___ = 10
Since, [tex]T_1 + T_2 = 24[/tex] (from the Clue 5)
[tex]T_1 + 14 = 24[/tex]
Subtract both the sides by 14,
[tex]T_1 = 10[/tex]
Clue 7:
We need to find the value of [tex]S_1[/tex],
Given [tex]T_1 + R_3 + S_1 =20[/tex]
Since, [tex]T_1=10[/tex] and [tex]R_3=8[/tex]
[tex]10+ 8 + S_1 = 20\\\\18 + S_1 = 20[/tex]
Subtract both the sides by 18,
so, [tex]S_1=2[/tex]
Combining this with what we learned from Clue 2 and Clue 6, we know
[tex]S_1=2[/tex]
Now, we need to find the blank, [tex]S_1 + S_2 +[/tex] ___ = 11
Combining this with what we learned from Clue 3 and Clue 7, we know:
___ = 5
[tex]S_1 + S_2 + S_3 = 11\\\\2 + 4 + S_3 = 11\\\\6 + S_3 = 11[/tex]
Subtract both the sides by 6,
[tex]S_3 = 5[/tex]
For [tex]R_1[/tex]
Since,
[tex]R_1 + R_2 + R_3 = 24\\\\R_1 + 9 + 8 = 24\\\\R_1 + 17 = 24[/tex]
Subtract both the sides by 17,
[tex]R_1 = 17[/tex]
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Which sequence of transformations could triangle XYZ have
gone through to produce figure XYZ as shown to the right?
A Rotation 90° clockwise, translation 4 units up and 3 units right.
B. Rotation 90° counterclockwise, translation 3 units up and 4
units right.
C. Rotation 90° clockwise, reflection across the y-axis
D. Rotation 90° counterclockwise, reflection across the y-axis.
Z
YA
X'
A
The sequence of transformations the triangle XYZ have gone through to produce figure X'Y'Z' is: D. Rotation 90° counterclockwise, reflection across the y-axis.
What is transformation?Transformation is a method required to change the orientation, or resize a given object to produce its image. Some of the types of transformation are: rotation, reflection, dilation, and translation.
Rotation requires turning a given object about a point at a certain angle.
Reflection implies flipping an object over a line as a reference point.
Dilation deals with either increasing or decreasing the dimensions of a given object.
Translation involves moving an object in a specific direction and given number of units.
Considering triangle XYZ and the figure produced, we can conclude that:
The sequence of transformations the triangle XYZ have gone through to produce figure X'Y'Z' is: D. Rotation 90° counterclockwise, reflection across the y-axis.
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If Juan does not read any books before day 4 and he starts reading at the same
rate as Patti for the rest of the month, how many books will he have read by
day 12?
A. 5
B. 10
C. 15
D. 20
If Juan does not read any books before day 4 and he starts reading at the same rate as Patti for the rest of the month, he would have read 6 books by day 12. The correct option is A.
If Juan does not read any books before day 4, it means he has missed out on the opportunity to read for the first three days. Assuming Patti and Juan have been reading at the same rate since day 4, we can calculate the total number of books they would have read by day 12.
Patti reads one book per day, so by day 12, she would have read a total of 9 books (from day 4 to day 12). If Juan starts reading at the same rate as Patti from day 4, he would also have read 9 books by day 12.
However, we have to account for the fact that Juan did not read any books before day 4. This means that he missed out on the opportunity to read 3 books (one book per day for the first three days). Therefore, by day 12, Juan would have read a total of 6 books (3 books missed + 3 books read from day 4 to day 12).
Therefore, the answer is A. Juan would have read 5 books less than Patti by day 12, since Patti would have read a total of 9 books and Juan would have only read 6.
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A plane leaves Singapore airport at 07:45 to fly to Sydney. The plane flies at an average speed of 757.2 km/h. The distance from Singapore to Sydney is 6310 km. The time in Sydney is 2 hours ahead of Singapore time. Calculate the local time when the plane arrives in Sydney. Give your answer in the form hours:minutes using the 24-hour clock.
The local time in Sydney when the plane arrives will be 18:58, or 6:58 PM on a 24-hour clock.
How to find arrival time for the plane?The time difference between Speed and Sydney is 2 hours, and the plane will take some time to fly from Singapore to Sydney at an Speed of 757.2 km/h over a distance of 6310 km.
The time it takes the plane to fly from Speed to Sydney can be calculated as:
time = distance / Speed= 6310 km / 757.2 km/h = 8.33Speed
So the plane will take 8.33 hours to fly from Singapore toSpeed
Now we need to add the 2-hour time difference between Singapore and Sydney to determine the local time in Sydney when the plane arrives.
07:45 (Singapore time) + 8.33 hours (flight time) + 2 hours (time difference) = 18:58
Therefore, the local time in Sydney when the plane arrives will be 18:58, or 6:58 PM on a 24-hour clock.
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Bella works at a popular clothing store.last winter ,her manager asked her to track the sweater sales.this box plot show the results.
question:what fraction of the sweater cost $50 or less?
The fraction is half of the sweaters cost $ 50 or less.
After placing the given set of numbers in order, the median is the value that falls in the middle of the group.
From the given box plot,
The value of the median is $ 50
We can clearly see that the median is $ 50 this means, 50% of the clothes are below $ 50 and 50% of the clothes are above $ 50.
The percentage of $ 50 or less sweaters is now 50%.
So, Required fraction = 50 / 100
= 5 / 10
= 1 / 2
Therefore, the fraction is half of the sweaters cost $ 50 or less.
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Given question is incomplete, complete question is below
Bella works at a popular clothing store. last winter ,her manager asked her to track the sweater sales. this box plot show the results.
question: what fraction of the sweater cost $50 or less?
A. Directions:translate each problem into algebraic expression or equation and identify the variable/s.
1. Julie weighs c kilogram. After going to gym for six months, she lost 2. 5 kilograms. Express her weight algebraically.
2. Peter is m centimeter tall. Jhon's height is 5 more than twice the height of Peter. How tall is Jhon?
3. Ador is thrice older than Emy. If Emy is d years old less than 9,how old is ador?
4. Jupiter is n years old now. How old is Jupiter 7 years from now?
5. Anna's sister is p years old. Anna is 4 years older than thrice the age of her sister. How old is Anna?
guys please help me please
lets assume.
Algebraic expression: c - 2.5. The variable is c, which represents Julie's initial weight in kilograms.
Algebraic equation: Jhon's height = 2m + 5. The variables are m, which represents Peter's height in centimeters, and the height of Jhon, which is represented by the equation.
Algebraic equation: Ador's age = 3(Emy's age - d). The variables are Ador's age and Emy's age, which is d years less than 9.
Algebraic expression: n + 7. The variable is n, which represents Jupiter's current age in years.
Algebraic equation: Anna's age = 3p + 4. The variables are p, which represents Anna's sister's age in years, and Anna's age, which is represented by the equation.
SO ANNA current age is P=3+4
and p=7
Anna's age = 3p + 4, where p is the age of Anna's sister in years, and Anna is 4 years older than thrice the age of her sister.
If Anna's sister is 10 years old, how old is Anna according to the equation?Algebraic expression: c - 2.5, where c is the weight of Julie in kilograms, and 2.5 is the weight she lost after six months of going to the gym.Algebraic equation: Jhon's height = 2m + 5, where m is the height of Peter in centimeters, and Jhon's height is 5 more than twice the height of Peter.Algebraic equation: Ador's age = 3(Emy's age - d), where Emy is d years less than 9, and Ador is thrice older than Emy.Algebraic equation: Jupiter's age 7 years from now = n + 7, where n is Jupiter's current age in years.Algebraic equation: Anna's age = 3p + 4, where p is the age of Anna's sister in years, and Anna is 4 years older than thrice the age of her sister.Learn more about Anna age
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help
pls thank you
,,,,,,,,,,,,,,,,,,,,,,,,,,,
The image of P under a 270° counterclockwise rotation about the origin is (2, -8) .
How to find the image of P under the rotation?Transformations are changes done in the shapes on a coordinate plane by rotation, reflection or translation.
Translation, rotation, reflection, and dilation are the four common types of transformations.
Rotation simply means turning. If a point P, whose position vector is (x,y), is rotated 270° counterclockwise rotation about the origin, the position of the image P' is (y, -x).
We have: P(8, 2)
Thus, the image of P will be:
P'(2, -8)
Therefore, the image of P under a 270° counterclockwise rotation about the origin is (2, -8).
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Translate each problem into a mathematical equation.
1. The price of 32'' LED television is P15,500 less than twice the price of the
old model. If it cost P29,078. 00 to buy a new 32'' LED television, what is
the price of the old model?
2. The perimeter of the rectangle is 96 when the length of a rectangle is
twice the width. What are the dimensions of therectangle?
The price of the old model is given by $22.289 and dimensions of the rectangle by 16units and 32 units.
Two dimensions make up a rectangle: the length and, perpendicular to that, the breadth. A triangle's or an oval's interior likewise has two dimensions. Despite the fact that we don't consider them to have "length" or "height," they do span a territory that is expansive in more than one way.
A circle can be measured in any direction. Why do we just consider it to be two dimensional? Because only one direction—the direction perpendicular to the first measurement—can be used to make a second measurement, for a total of two directions.
Let us assume that, price of the old model is Px .
so,
→ Price of 32" LED television = P(2x - 15.500)
A/q,
→ (2x - 15.500) = 29.078
→ 2x = 29.078 + 15.500
→ 2x = 44.578
→ x = $22.289
Therefore, price of the old model is $22.289.
Let us assume that, width of the rectangle is x unit.
so,
→ Length = twice of width = 2x = 2x unit .
then,
→ Perimeter = 2(Length + width)
A/q,
→ 2(2x + x) = 96
→ 3x = 48
→ x = 16 unit .
therefore,
Width of rectangle = x = 16 units .
Length of rectangle = 2x = 32 units.
Hence, the dimensions of the rectangle are 16units and 32 units.
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The price of the old televison is P22,289
The dimensions of the rectangle are 16 and 32
Translating word problems to equationsWe have to read the problem carefully so as to be able to know how to translate the problem effectively and that is what we are going to do below.
We know that;
Let the price of the old 32'' LED television be x
Now;
29,078. 00 = 2x - 15,500
29,078. 00 + 15,500 = 2x
x = 29,078. 00 + 15,500 /2
x = P22,289
ii) Given that;
l = 2w
Perimeter = 2(l +w)
P = 2(2w + w)
P = 2(3w)
P = 6w
w = 96/6
w = 16
Then l = 2(w) = 32
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100 points
i can't think of a good question, someone give me one about sports or something interesting
Answer:
Who is the current world number one in men’s tennis?
What is the name of the sport that combines skiing and shooting?
How many countries are in the European Union?
What is the largest animal that ever lived on Earth?
What is the most spoken language in the world?
Step-by-step explanation:
is that ok?
Find the area of the regular polygon with the given apothem a and side length s.
pentagon, a = 10. 4 cm, s = 15. 1 cm
The area of the regular pentagon is approximately 392.2 square centimeters.
The area of a regular polygon can be calculated using the formula:
A = (1/2) * apothem * perimeter
where perimeter = number of sides * side length.
For a pentagon with side length s = 15.1 cm, the perimeter is:
perimeter = 5 * 15.1 = 75.5 cm
The apothem is a = 10.4 cm.
Using the formula, we get:
A = (1/2) * 10.4 * 75.5
A = 392.2 cm^2
Therefore, the area of the regular pentagon is approximately 392.2 square centimeters.
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Justice has a box of trading cards. There are three types of trading cards in the box, a basketball, a football, and a soccer ball. The probability of picking out a basketball card is 2/5, and the probability of picking out a football card is 1/3. What is the probability Justice will randomly pick out a soccer card?
If the probability of picking out a basketball card is 2/5, and the probability of picking out a football card is 1/3, the probability of Justice randomly picking out a soccer card is 4/15.
To find the probability of Justice picking out a soccer card, we need to know the total probability of all three types of cards adding up to 1. Since there are only three types of cards, we can subtract the probability of picking a basketball card and the probability of picking a football card from 1 to find the probability of picking a soccer card.
Let P(S) be the probability of picking a soccer card.
We know that P(B) = 2/5 and P(F) = 1/3.
Therefore, the total probability of picking one of the three cards is:
P(B) + P(F) + P(S) = 1
Substituting the values we know, we get:
2/5 + 1/3 + P(S) = 1
Simplifying the equation, we get:
6/15 + 5/15 + P(S) = 1
11/15 + P(S) = 1
P(S) = 1 - 11/15
P(S) = 4/15
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Triangle ΔABC has side lengths of a = 15, b equals 15 times radical 3 comma and c = 30 inches.
Part A: Determine the measure of angle B period (5 points)
Part B: Show how to use the unit circle to find tan B. (2 points)
Part C: Calculate the area of ΔABC. (3 points)
a) Where the information about triangle ABC is given above, the measure of angle B is 60°
How is this so ?Using the Cos Rules,
(15√3)² = 30² + 15² - 2(15 x 30) cos B
⇒ 657 = 1125 - 900 cosB
⇒ 2 Cos B = 1 Cos B = 1/2
So
B = Cos ⁻¹(1/2)
Hence,
B = 60°
B) Given the above,
Now, we can use the tangent function to find tan B:
tan B = sin B / cos B
= sin (π/3) / cos (π /3)
= (√3 / 2) / 0.5
tan B = √3
C ) the area of the rriangle is given as
s = (a + b + c) /2
Substituting
s = (15 + 15√ 3 + 30)/2
s = 30 + 15√3
Area = √ [ (30 + 15√3)(15√3) (15)(30 - 15 - 15√3))
Simplifying we can say
Area = √(30 + 15√3 )( 15√3)(15)(15 - 5√3 )]
= √[3(10 + 5√3)(15)(3√3 - 1)]
= √[2250 - 1125√3]
Hence,
Area ≈ 17.36in
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The first steps in writing f(x) = 4x2 48x 10 in vertex form are shown. f(x) = 4(x2 12x) 10 (twelve-halves) squared = 36 what is the function written in vertex form? f(x) = 4(x 6)2 10 f(x) = 4(x 6)2 – 26 f(x) = 4(x 6)2 – 134 f(x) = 4(x 6)2 154
The function in vertex form is f(x) = 4(x - 6)² - 26.
How to write f(x) in vertex form?The function in vertex form is f(x) = 4(x - 6)² - 26.
To get to this form, the first step is to factor out the coefficient of x², which is 4:
f(x) = 4(x² - 12x) + 10
Next, complete the square by adding and subtracting (12/2)² = 36 inside the parenthesis:
f(x) = 4(x² - 12x + 36 - 36) + 10
Simplify the expression inside the parenthesis and combine like terms:
f(x) = 4((x - 6)² - 36) + 10
f(x) = 4(x - 6)² - 134
Therefore, the function in vertex form is f(x) = 4(x - 6)² - 26.
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Craig needs to measure 2 3/8 cups. How many times must he fill a 1/3 cup measuring cup?
First, we need to convert the mixed number 2 3/8 to an improper fraction:
2 3/8 = (2 x 8 + 3) / 8 = 19/8
To find out how many times Craig needs to fill a 1/3 cup measuring cup, we can divide 19/8 by 1/3:
(19/8) / (1/3) = (19/8) x (3/1) = 57/8
Therefore, Craig needs to fill a 1/3 cup measuring cup 57/8 times to measure 2 3/8 cups.
Ms. Grant recorded the numbers of students in her homeroom class who
participated in spirit week.
The table shows the number of students who dressed up each day.
Day
Mon Tues. Wed. Thurs. Fri. Total
Number of students O
1
4
5
5
15
Find the mean and the median of the data set.
Determine which of these values is greater.
A. The median, 4, is greater than the mean, 3.
B. The mean, 4, is greater than the median, 3.
C. The mean, 4, is greater than the median, 2.
D. The median, 5, is greater than the mean, 0.
The mean and the median of the data set is given as the median, 4, is greater than the mean, 3. The correct answer is option a.
To find the mean of the data set, we add up all of the numbers and divide by the total number of days. So, the mean is (1+4+5+5+1+5+5)/6 = 3.
To find the median, we first need to put the numbers in order from least to greatest: 1, 1, 4, 5, 5, 5. The median is the middle number, which in this case is 4.
Now we need to determine which value is greater. The options are:
A. The median, 4, is greater than the mean, 3.
B. The mean, 3, is greater than the median, 4.
C. The mean, 4, is greater than the median, 2.
D. The median, 5, is greater than the mean, 0.
We can eliminate options B and D because they don't make sense. The mean cannot be less than 0, and the median cannot be less than the mean.
Option A is correct. The median, 4, is greater than the mean, 3. This makes sense because there are two 1's in the data set, which bring down the mean. However, the median is not affected by outliers like this, so it remains higher.
Option C is incorrect because the mean is not 4, it is 3.
In summary, the mean of the data set is 3 and the median is 4. The median is greater than the mean, which is represented by option A.
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simplify
(2a² b c³) (-a² b⁵)
pls help asap!
Answer:
[tex]-2a^{4}b^{6} c^{3}[/tex]
Step-by-step explanation:
(2a² b c³) (-a² b⁵)
distribute amongst each other
-2a²bc³a²b⁵
rearrange
-2a²a²bb⁵c³
combine like terms
[tex]-2a^{4}b^{6} c^{3}[/tex]
Hope this helps!
Answer: -2[tex]a^{4}[/tex][tex]b^{6}[/tex]c³
Step-by-step explanation:
Given:
(2a² b c³) (-a² b⁵)
Rules:
>Multiply numbers first
>If a number with an exponent is multiplied to another, you can combine if the bases are the same(lower number)
>If they have the same base, you can add the exponents
Solution:
(2a² b c³) (-a² b⁵) >multiply the - and 2
-2(a² b c³) (a² b⁵) > combine the a's by adding the expnents 2+2
-2[tex]a^{4}[/tex]( b c³) ( b⁵) > combine b, there is an invisible 1 by the first b 1+5
-2[tex]a^{4}[/tex][tex]b^{6}[/tex]c³ >c stays as is because nothing to combine with
The diameter of a sphere measures 10. 4 inches. What is the surface area of the sphere?
The Surface Area of the sphere is approximately 339.79 square inches.
The surface area of a sphere is given by the formula:
surface area= [tex]4\pi r^{2}[/tex]
where r is the radius of the sphere.
The diameter of the sphere measures 10.4 inches, hence the radius can be calculated as:
r=10.4/2=5.2inches
Hence, the surface area can be calculated as by substituting r=5.2 inches
Therefore, surface area of the sphere is:
Surface Area = [tex]4\pi (5.2)^{2}[/tex]=[tex]4\pi (27.04)[/tex]= 108.16[tex]\pi[/tex] square inches.
So, the Surface Area of the sphere is approximately 339.79 square inches(if we use [tex]\pi[/tex]=3.14 as an approximation)
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Mustafa, Heloise, and Gia have written more than a combined total of
22
2222 articles for the school newspaper. Heloise has written
1
4
4
1
start fraction, 1, divided by, 4, end fraction as many articles as Mustafa has. Gia has written
3
2
2
3
start fraction, 3, divided by, 2, end fraction as many articles as Mustafa has.
Write an inequality to determine the number of articles,
�
mm, Mustafa could have written for the school newspaper.
m > 8 is an inequality used to calculate the number of articles Mustafa could have written.
Let's assume that Mustafa has written m articles for the school newspaper.
Then, according to the given information:
Heloise has written 1/4 as many articles as Mustafa has, which means she has written 1/4 × m = m/4 articles.
Gia has written 3/2 as many articles as Mustafa has, which means she has written 3/2 × m = 3m/2 articles.
The combined total of articles written by all three is more than 22, so we can write:
m/4 + 3m/2 + m > 22
Simplifying and solving for m:
11m/4 > 22
m > 22 × 4/11
m > 8
Therefore, m > 8 is an inequality used to calculate the number of articles Mustafa could have written.
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Some parallelograms are squares true or false
Answer:
True
Step-by-step explanation:
Parallelogram: A parallelogram is 4-sided shape that has parallel opposite sides
Square: A square is 4-sided shape where all sides are congruent and has 4 right angles. A square also has 2 pairs of opposite parallel sides.
Based on these definitions, we can see that not ALL parallelograms can be squares because a parallelogram can have no right angles, or can have all 4 angles be right angles.
All squares have to be parallelograms though because a square and a parallelogram both have 2 pairs of opposite parallel sides.
Hope this helps :)
The teacher could buy the shirts online for $3. 50 each. She would also pay a fee of $9. 50 for shipping the shirts. Write a function that can be used to find y, the total cost, in dollars, of buying x shirts online.
Enter your function in the space provided
The function with y and x, representing cost and shipping charges will be y = 3.50x + 9.50.
The express that can be used to write the function is as follows-
Total amount = number of shirts × cost of shirts + shipping fee
Write the function based on the formula -
y = 3.50×x + 9.50
As stated x represents the number of shirts bought online. We know that shipping charges will be calculated once while cost of shirt will vary according to the number of shirts.
Hence the function will be -
y = 3.50x + 9.50
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(a) if f(4) = 6, what is f-|(6)? f-'(6) = (b) Suppose a function can be described by y = f(x). The function and its inverse intersect when y = (c) Consider a linear function f (x) = ax + b where a 70. Is the inverse of this linear function always a linear function? (No answer given) If f(x) = ax + b and a € 0, then f-'(x) =
To find f-1(6), we need to find the value of x that gives f(x) = 6. However, we don't have enough information about the function f to do this. We need to know whether f is a linear function or not.
When the function and its inverse intersect, we have f(x) = f-1(x). Substituting y for both f(x) and f-1(x), we get y = f(y). To find the value of y when this is true, we need to solve for y:
y = f(y)
y = f-1(y)
Substituting y = f(x), we get:
f(x) = f-1(f(x))
f(x) = x
So the function and its inverse intersect when y = x.
If a = 0, then the linear function is f(x) = b, which is a constant function. Constant functions do not have inverses, so the inverse of f(x) = b does not exist.
If a ≠ 0, then the inverse of f(x) = ax + b is given by:
f-'(x) = (x - b) / a
This is also a linear function, so the inverse of a linear function is always a linear function when a ≠ 0.
(a) To find the inverse of a linear function, you need to swap the x and y values. Given that f(4) = 6, the inverse function f^(-1)(6) would yield the value of x when y = 6. Since we know that f(4) = 6, it implies that f^(-1)(6) = 4.
A function and its inverse intersect when the input value (x) is equal to the output value (y). In other words, they intersect when y = x.
(c) Yes, the inverse of a linear function is always a linear function. If f(x) = ax + b, where a ≠ 0, then the inverse function, f^(-1)(x), can be found by swapping x and y values and solving for y. In this case, x = ay + b. Solving for y, we get y = (x - b) / a, which is also a linear function.
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For each problem, determine what will happen to the first factor?
10 x 1/2
15 x 7/2
When multiplying a whole number with a fraction, the first factor will be reduced to a fraction or a decimal, depending on the problem.
In both of the given problems, we are multiplying a whole number with a fraction. When we multiply a whole number with a fraction, we can simply multiply the whole number with the numerator of the fraction and keep the denominator as it is. So, in the first problem, we have 10 multiplied by 1/2. Multiplying 10 with 1 gives us 10, and then we divide it by 2, which gives us 5. Therefore, the first factor, which is 10, will be reduced to 5 in this problem.
In the second problem, we have 15 multiplied by 7/2. Multiplying 15 with 7 gives us 105, and then we divide it by 2, which gives us 52.5. Therefore, the first factor, which is 15, will be reduced to 52.5 in this problem.
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Mr Louis wants to top-up his central heating oil tank.
The oil tank can take up to 1400 litres of oil.
There are already 150 litres of oil in the tank.
The price of oil is 80. 5p per litre.
As a loyal customer, Mr Louis gets a 6. 5% discount on the price of the oil.
How much discount does Mr Louis get on this purchase?
Give your answer in £.
If Mr Louis gets a 6. 5% discount on the price of the oil, Mr. Louis gets a discount of £65.41 on this purchase.
First, let's find out how many litres of oil Mr. Louis needs to fill his tank:
Maximum capacity of the tank: 1,400 litres
Current oil in the tank: 150 litres
Litres needed to top up: 1,400 - 150 = 1,250 litres
Next, we'll calculate the original price of the oil without the discount:
Price per litre: £0.805
Cost of oil needed: 1,250 litres * £0.805 = £1,006.25
Now, let's calculate the discount amount:
Discount percentage: 6.5%
Discount amount: £1,006.25 * 0.065 = £65.41
So, Mr. Louis gets a discount of £65.41 on this purchase.
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This diagram shows an equilateral triangle and three lines, p, q, and r, that meet at the
triangle's center, T.
Select all of the transformations that map the triangle onto itself.
reflection across line q followed by 90° clockwise rotation about point T
reflection across line p followed by 240 clockwise rotation about point T
reflection across liner
270 clockwise rotation about point T
120 counterclockwise rotation about point 7
180 counterclockwise rotation about point 7 followed by reflection across
sine q
Answer:
-Reflection across line p followed by 240 clockwise rotation about point T.
-Reflection across line r.
-120 counterclockwise rotation about point T.
Step-by-step explanation:
All these transformations map the triangle onto itself.
Use an integer to describe the situations.
6 meters above sea level ___
sea level ___
Answer:
An integer to describe 6 meters above the sea level would be meters.
As per the question statement, We are supposed to use an integer to describe the following situation "6 meters above sea level".
We assume that sea level is the datum line and anything above that would be positive and below that would be negative.
So 6 meters above the sea level can be described as .
Integers: Set of whole number containing both positive and negative values of it.
PLS MARK BRAINLIEST
Step-by-step explanation:
Solve the following absolute value equations. Show the solution set.
1/2=1/3-|(x-3/6)+x|
The solution set for the equation 1/2 = 1/3 - |(x-3/6)+x| is {1/12, -1/12}.
How to Solve Absolute Value Equations?To solve the equation 1/2 = 1/3 - |(x-3/6)+x|, we need to isolate the absolute value expression and solve for x in two cases.
Case 1: (x-3/6)+x is nonnegative, which means the absolute value can be removed.
1/2 = 1/3 - (x-3/6)-x
1/2 = 1/3 - 2x + 1/2
2x = 1/6
x = 1/12
Case 2: (x-3/6)+x is negative, which means the absolute value must be flipped.
1/2 = 1/3 + (x-3/6)+x
1/2 = 1/3 + 2x - 1/2
2x = -1/6
x = -1/12
Therefore, the solution set is {1/12, -1/12}.
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To solve 2x + 3 = 5, Sylvia first subtracted 5 from both sides. What did she do wrong?
Answer:the two sides still equal.
Step-by-step explanation:To solve 2x + 3 = 5, Sylvia first subtracted 5 from both sides. What did she do wrong? Because Sylvia did the same operation to both sides, the equation is still correct: the two sides still equal.
Answer:
1
Step-by-step explanation:
or, 2x=5-3
or, 2x=2
or, x=2/2
x=1