The thermal energy of the first rock is twice the Thermal energy of the second rock.
The thermal energy of an object is directly proportional to its mass. Therefore, if the first rock has twice the mass of the second rock, it will also have twice the thermal energy.
Thermal energy is a measure of the internal energy of an object, which includes the kinetic energy of its particles. In this case, since both rocks are made of the same material and are at the same temperature, we can assume that their particles have the same average kinetic energy per particle.
The thermal energy of an object can be calculated using the formula:
Thermal energy = Mass * Specific heat capacity * Change in temperature
Since the specific heat capacity and the change in temperature are the same for both rocks (as they are made of the same material and are at the same temperature), we can simplify the comparison of their thermal energies based on mass alone.
Let's denote the mass of the second rock as "m" (arbitrary unit). Since the first rock has twice the mass, its mass can be represented as "2m".
Therefore, the thermal energy of the first rock is:
Thermal energy of the first rock = (2m) * Specific heat capacity * Change in temperature
And the thermal energy of the second rock is:
Thermal energy of the second rock = m * Specific heat capacity * Change in temperature
Comparing the thermal energies:
Thermal energy of the first rock / Thermal energy of the second rock = (2m) * Specific heat capacity * Change in temperature / (m) * Specific heat capacity * Change in temperature
The specific heat capacity and the change in temperature cancel out, leaving us with:
Thermal energy of the first rock / Thermal energy of the second rock = 2m / m = 2
Therefore, the thermal energy of the first rock is twice the thermal energy of the second rock.
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Determine the amplitude of function
The amplitudes of functions are a) 8 and b) 6.
Given are the functions we need to determine the amplitude of function,
a) y = 8 Sin (x/2) + 3
b) y = 6 Cos x + 2
So,
To determine the amplitude of a trigonometric function, you can follow these steps:
For a sine function of the form y = A×sin(Bx + C) + D:
The amplitude is equal to the absolute value of the coefficient A.
For a cosine function of the form y = A×cos(Bx + C) + D:
The amplitude is equal to the absolute value of the coefficient A.
Let's apply these steps to the given functions:
a) y = 8×sin(x/2) + 3
The coefficient of sin in this function is 8, so the amplitude is |8| = 8.
Therefore, the amplitude of function a) is 8.
b) y = 6×cos(x) + 2
The coefficient of cos in this function is 6, so the amplitude is |6| = 6.
Therefore, the amplitude of function b) is 6.
Hence the amplitudes of functions are a) 8 and b) 6.
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Need this asap will give brainliest
Answer:
measure of angle 7 + measure of angle 8 = 180°.
TriangleTriangle WXY with vertices W(8,-8), X(5,-2), and Y(3,-4) is drawn inside a rectangle, What is the area, in square units, of triangle LMN?
The area of the triangle whose dimensions are given in a vertices form would be = 9
How to calculate the area of a triangle given above?To calculate the area of the triangle, the formula that should be used is the coordinate geometry formula: area = the absolute value of Ax(By - Cy) + Bx(Cy - Ay) + Cx(Ay - By) divided by 2
Where; W=A, X= B, Y = C
Ax= 8
By= -2
Cy= -4
BX= 5
Ay = -8
CX= 3
That is:
= 8(-2--4)+5(-4--8)+3(-8--2)/2
= 16+20-18/2
= 18/2
= 9
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The value of an automobile company's stock fell 5 points over the last month.
What integer represents the change in the stock's value?
The value of an automobile company's stock fell 5 points over the last month. The integer that represents the change in the stock's value is -5.
In the context of stock market performance, positive values typically indicate an increase in the stock's value, while negative values indicate a decrease. In this case, since the stock's value fell by 5 points, we assign a negative sign to represent the change.
By convention, negative numbers are used to represent decreases or losses, while positive numbers represent increases or gains. When the stock's value decreases, it is common to use negative integers to signify the change.
In this scenario, a decrease of 5 points is denoted by the negative sign (-) followed by the numerical value 5. Therefore, the integer -5 represents the change in the stock's value.
Using this notation helps provide clarity and consistency in understanding the direction and magnitude of changes in stock prices. It allows investors, analysts, and market participants to communicate and interpret market movements accurately and effectively.
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.Mr. Kalada is three times as old as his son. After fifteen years, Mr. Kalada will be twice as old as his son's age at that time. Hence, Mr. Kalada's present age is
Answer:
Mr Kalada's present age is 45 years old
Step-by-step explanation:
Solve 5(2x – 3) = x – 15 + 9x for x. Question 7 options: A) Infinitely many solutions B) –18∕5 C) 0 D) –12∕5
Step-by-step explanation:
5(2x – 3) = x – 15 + 9x
10x - 15 = x - 15 + 9x
10x - 9x - x = -15 + 15
0 = 0
Answer = A) Infinity many solutions
A pair of equations is shown below:
y = 3x − 5
y = 6x − 8
Part A: Show all of your steps of how you will use substitution to determine the values for x and y. (4 points)
Part B: What is the solution, or ordered pair, for the two equations?
Part A: equate the expressions 6x - 8 = 3x - 5
collect the like terms 6x -3x = -5 + 8
Divide by the coefficient x = 1
Part B: The values are (1, -3)
How to determine the valuesTo determine the value of the variables, we need to consider the equations.
From the information given, we have the equations given as;
y = 3x − 5
y = 6x − 8
Now, equate the expressions, we get;
6x - 8 = 3x - 5
collect the like terms, we have;
6x - 3x = -5 + 8
add or subtract the like terms
3x = 3
Divide by the coefficient
x = 1
Substitute the value
y= 6(1) - 9
expand the bracket
y = 6 - 9 = -3
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MP4 Model with Math Write an
expression for the volume of the bar magnet.
0.5 in. N
2.25 in.
S
0.25 in.
The volume of the bar magnet with dimensions 0.5 in. (length), 2.25 in. (width), and 0.25 in. (thickness) is 0.28125 cubic inches.
The expression for the volume of a bar magnet can be calculated by multiplying its length, width, and thickness.
In this case, the dimensions provided are:
Length = 0.5 in.
Width = 2.25 in.
Thickness = 0.25 in.
To find the volume, we multiply these dimensions together:
Volume = Length × Width × Thickness
= 0.5 in. × 2.25 in. × 0.25 in.
Simplifying this expression, we get:
Volume = 0.28125 in³
Therefore, the volume of the bar magnet with dimensions 0.5 in. (length), 2.25 in. (width), and 0.25 in. (thickness) is 0.28125 cubic inches.
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Evaluate your data. Has there been an increase in the number of certain individuals of this
population of bacteria? Please explain how you think this might lead to the emergence of a
superbug over time, or the extinction of certain strains of this bacteria.
The increase in certain individuals leads to:
Selective pressure.Emergence of antibiotic-.Extinction .Genetic variations.Difficulty in treating infections.Competition for resources leading to disadvantage for other strains.An increase in certain individuals within a bacterial population can lead to:
Selective pressure favoring individuals with advantageous traitsEmergence of antibiotic-resistant strains or "superbugs"Extinction of less competitive strainsGenetic variations being passed on to future generationsDifficulty in treating infections caused by resistant bacteriaCompetition for resources leading to disadvantage for other strainsOutcome depends on selective pressure, genetic diversity, resource availability, and adaptability.Learn more about antibiotic-rich environments here:
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Which of the following is the appropriate notation when calculating conditional probabilities
The notation which is the most appropriate notation when calculating conditional probabilities is option B.
What is the notation for conditional probabilities?The appropriate notation for calculating conditional probabilities is often denoted using the vertical bar symbol "|". This symbol represents "given" or "conditional on."
In a mathematical expression, the conditional probability of event A given event B is written as P(A | B), where "P" stands for probability. This notation indicates that the probability of event A occurring is being calculated assuming that event B has already occurred.
Thus option B is correct.
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find the invoice total, the amount should be paid after cash discount, the total amount due including shipping and insurance.
The total invoice is $788.80, we find this by find the cost of each item.
To find the invoice total, we need to calculate the total cost of each item.
For the tablecloth:
Quantity: 16
Unit Price: $35.00
Total Cost = Quantity × Unit Price = 16 × $35.00 = $560.00
For the rings:
Quantity: 8
Unit Price: $6.50
Total Cost = Quantity × Unit Price = 8 × $6.50 = $52.00
For the cups (cases):
Quantity: 4 cases
Unit Price: $25.30
Total Cost = Quantity × Unit Price = 4 × $25.30 = $101.20
For the bowls:
Quantity: 12
Unit Price: $6.30
Total Cost = Quantity × Unit Price = 12 × $6.30 = $75.60
Now, let's calculate the invoice total by adding up the total costs of each item:
Invoice Total = $560.00 + $52.00 + $101.20 + $75.60
= $788.80
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PLEASE HELP!!! Solve 5sin(π/3x)=3 for the four smallest positive solutions
This one's a special case of a right angled triangle with sides (3, 4, and 5 units)
Back to the problem :[tex]\qquad\displaystyle \tt \dashrightarrow \: 5 \sin \bigg( \frac{ \pi}{3} x \bigg) = 3[/tex]
[tex]\qquad\displaystyle \tt \dashrightarrow \: \sin \bigg( \frac{ \pi}{3} x \bigg) = \frac{3}{5} [/tex]
Now, check the triangle, sin 37° = 3/5
therefore,
[tex]\qquad\displaystyle \tt \dashrightarrow \: \sin \bigg( \frac{ \pi}{3} x \bigg) = \sin(37 \degree) [/tex]
[ convert degrees on right side to radians ]
[tex]\qquad\displaystyle \tt \dashrightarrow \: \sin \bigg( \frac{ \pi}{3} x \bigg) = \sin \bigg(37 \degree \times \frac{ \pi}{180 \degree} \bigg ) [/tex]
There are three more possible values as :
[tex]\qquad\displaystyle \tt \dashrightarrow \: \sin( \theta) = \sin(\pi - \theta) [/tex]
[tex]\qquad\displaystyle \tt \dashrightarrow \: sin( \theta) = \sin \bigg( { 2\pi}{} + \theta \bigg) [/tex]
[tex]\qquad\displaystyle \tt \dashrightarrow \: sin( \theta) = \sin \bigg( \frac{ 3\pi}{} - \theta\bigg) [/tex]
Equating both, we get : First value :[tex]\qquad\displaystyle \tt \dashrightarrow \: \frac{ \pi}{3} x = 37 \times \frac{ \pi}{180} [/tex]
[tex]\qquad\displaystyle \tt \dashrightarrow \: x = 37 \times \frac{ \cancel \pi}{180} \times \frac{3}{ \cancel \pi} [/tex]
[tex]\qquad\displaystyle \tt \dashrightarrow \: x = \frac{37}{60} [/tex]
or in decimals :
[tex]\qquad\displaystyle \tt \dashrightarrow \: x = 0.616666... = 0.6167[/tex]
[ 6 repeats at third place after decimal, till four decimal places it would be 0.6167 after rounding off ]
similarly,
Second value :[tex]\qquad\displaystyle \tt \dashrightarrow \: \pi - \frac{ \pi}{3} x = 37 \times \frac{ \pi}{180} [/tex]
[tex]\qquad\displaystyle \tt \dashrightarrow \: \pi \bigg(1 - \frac{x}{3} \bigg ) = 37 \times \frac{ \pi}{180} [/tex]
[tex]\qquad\displaystyle \tt \dashrightarrow \: 1 - \frac{x}{3} = \frac{37}{180} [/tex]
[tex]\qquad\displaystyle \tt \dashrightarrow \: - \frac{x}{3} = 0.205 - 1[/tex]
[tex]\qquad\displaystyle \tt \dashrightarrow \: \frac{x}{3} = 0.795[/tex]
[tex]\qquad\displaystyle \tt \dashrightarrow \: x = 3 \times 0.795[/tex]
[tex]\qquad\displaystyle \tt \dashrightarrow \: x = 2.385[/tex]
Third value :[tex]\qquad\displaystyle \tt \dashrightarrow \: 2\pi + \frac{ \pi}{3} x = 37 \times \frac{ \pi}{180} [/tex]
[tex]\qquad\displaystyle \tt \dashrightarrow \: \pi \bigg(2 + \frac{x}{3} \bigg ) = 37 \times \frac{ \pi}{180} [/tex]
[tex]\qquad\displaystyle \tt \dashrightarrow \: 2 + \frac{x}{3} = \frac{37}{180} [/tex]
[tex]\qquad\displaystyle \tt \dashrightarrow \: \frac{x}{3} = 0.205 - 2[/tex]
[tex]\qquad\displaystyle \tt \dashrightarrow \: \frac{x}{3} = - 1.795[/tex]
[tex]\qquad\displaystyle \tt \dashrightarrow \: x = 3 \times -1 .795[/tex]
[tex]\qquad\displaystyle \tt \dashrightarrow \: x = -5.385[/tex]
Fourth value :[tex]\qquad\displaystyle \tt \dashrightarrow \: 3 \pi - \frac{ \pi}{3} x = 37 \times \frac{ \pi}{180} [/tex]
[tex]\qquad\displaystyle \tt \dashrightarrow \: \pi \bigg(3 - \frac{x}{3} \bigg ) = 37 \times \frac{ \pi}{180} [/tex]
[tex]\qquad\displaystyle \tt \dashrightarrow \: 3 - \frac{x}{3} = \frac{37}{180} [/tex]
[tex]\qquad\displaystyle \tt \dashrightarrow \: - \frac{x}{3} = 0.205 - 3[/tex]
[tex]\qquad\displaystyle \tt \dashrightarrow \: \frac{x}{3} = 2.795[/tex]
[tex]\qquad\displaystyle \tt \dashrightarrow \: x = 3 \times 2.795[/tex]
[tex]\qquad\displaystyle \tt \dashrightarrow \: x = 8.385[/tex]
" x can have infinite number of values here with the same result, here are the four values as you requested "
I hope it was helpful ~
In the figure below, S is the center of the circle. Suppose that JK = 20, LM = 3x + 2, SN = 12, and SP = 12. Find the
following.
Answer:
x = 6
JN = 10
Step-by-step explanation:
if the values of SN and SP are the same, so are the corresponding sides next to the right angles.
which means:
if SP = SN, then JK = LM.
Use the reverse version of the function for calculating LM (3x + 2).
-2 * 1/3
Now apply that function to 20.
(20-2)/3
= 18/3
= 6.
x = 6
Now JK is a chord.
and Radius SQ intersects JK at a perpendicular right angle (at point N).
So JN would be half the length of JK.
20/2 = 10.
JN = 10
Write a system of linear equations for the graph below. really need lots of help with this!
i also need the y's
Answer:
friend with this information you cannot know the answer you have to say everything says about that mathematical problem
50 Points! Multiple choice algebra question. Photo attached. Thank you!
Answer:
B). No two lines are parallel
Step-by-step explanation:
In spherical geometry, there are no parallel lines. This is because any two lines on a sphere will eventually intersect.
Can u help me please fill in the square
The equation of the circle is (x + 4)² + (y - 1)² = 81
Given is an equation of a circle we need to convert it in standard form,
x² + y² + 8x - 2y = 64,
To convert the equation of a circle to standard form, you need to complete the square for both the x and y variables.
The standard form of a circle equation is:
(x - h)² + (y - k)² = r²
where (h, k) represents the center of the circle, and r represents the radius.
Let's convert the given equation to standard form step by step:
x² + y² + 8x - 2y = 64
Rearrange the equation to group the x-terms and y-terms:
x² + 8x + y² - 2y = 64
Now, complete the square for the x-terms.
Take half of the coefficient of x (which is 8 in this case), square it, and add it to both sides of the equation:
x² + 8x + 16 + y² - 2y = 64 + 16
Simplify:
(x + 4)² + y² - 2y = 80
Complete the square for the y-terms.
Take half of the coefficient of y (which is -2 in this case), square it, and add it to both sides of the equation:
(x + 4)² + y² - 2y + 1 = 80 + 1
Simplify:
(x + 4)² + (y - 1)² = 81
Now, the equation is in standard form, with the center at (-4, 1) and a radius of √81 = 9.
Hence the equation of the circle is (x + 4)² + (y - 1)² = 81
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The manufacturer of a DVD player has found the revenue R (in dollars) is R(p) = -4p² + 1700p,
when the unit price is p dollars. What is the maximum revenue to the nearest whole dollar?
a. $722,500
c. $180,625
b. $1,445,000
d. $361,250
The maximum revenue, to the nearest whole dollar, is $180,625 (option c).
To find the maximum revenue, we need to determine the vertex of the quadratic function represented by the revenue equation.
The revenue equation is given as:
R(p) = -4p² + 1700p
The vertex of a quadratic function in the form of f(x) = ax² + bx + c can be found using the formula:
x = -b / (2a)
For the given revenue equation, a = -4 and b = 1700. Plugging these values into the formula, we have:
p = -1700 / (2 × -4)
p = -1700 / -8
p = 212.5
The maximum revenue occurs at p = 212.5.
To find the maximum revenue, we substitute this value back into the revenue equation:
R(p) = -4(212.5)² + 1700(212.5)
R(p) = -4(45256.25) + 361250
R(p) = -181025 + 361250
R(p) = 180625
Therefore, the maximum revenue, to the nearest whole dollar, is $180,625 (option c).
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Please help me
The stem-and-leaf plot shows the numbers of confirmed cases of a virus in 15 countries.
A stem and leaf plot. A vertical line separates each stem from its first leaf. The first row has a stem of 4 and leaves 1, 1, 3, 3, and 5. The second row has a stem of 5 and leaves 0, 2, 3, and 4. The third row has a stem of 6 and leaves 2, 3, 3, and 7. The fourth row has a stem of 7 and leaf 5. The fifth row has a stem of 8 and no leaves. The sixth row has a stem of 9 and leaf 7. The key shows 5 vertical bar 0 is equal to 50 cases.
How many of the countries have more than 60 confirmed cases
Answer:
There are 6 countries with more than 60 confirmed cases
Step-by-step explanation:
- Draw your stem and leaf plot
-There is a stem without a leaf (There are no values in this class)
-Count the values in the stem and leaf plot and ensure they are 15. Each value represents the number of confirmed case in a county.
There are six numbers greater than 60 which are 62,63,63,67,65 and 97
Hence, there are 6 countries which have more than 60 confirmed cases
The sum of two numbers is 28. The first number is 7 more than twice the second number. Let a represent the first number. Let b represent the second number. What is the second number? Use the table to guess and check. Two Numbers a b a + b = 28 Check a = 2 b + 7
Answer:
Let’s solve this problem step by step. Since a + b = 28 and a = 2b + 7, we can substitute the value of a in the first equation to get 2b + 7 + b = 28. Solving for b, we get 3b + 7 = 28, which means 3b = 21 and b = 7. So, the second number is 7.
answer pls
its about a sea level . i need the answr in 10 mina pls
The new height above sea level would be Option (C) 3980m.
New sea-level = Previously given sea level + 20m
Given,
Height above sea previously = 4000m
Increase in sea level = 20m
Now, since there has been a rise in sea level due to global warming the distance between the previous 4000m mark and the sea level would decrease. This shall now be less than 4000m. The distance/height would reduce by 20m. It can also be observed that the distances below the sea level would increase due to a rise in the sea level mark.
∴ New height above sea level = 4000m - 20m
= 3980m.
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2. Derek is saving money for the down payment on a used car. So far, he has saved $200. His parents have said tha
help him put aside money, they will pay him 6% interest each month on the money Derek has saved. How long
take Derek to save at least $1,000 for the down payment if the only additions to his savings account are his par
interest payments?
a) Fill the table in. Make sure you indicate the correct process for each.
Month
0
1
2
3
4
5
6
Process
Bak
Derek is saving money for the down payment on a used car. So far, he has saved $200. His parents have said they help him put aside money, they will pay him 6% interest each month on the money Derek has saved. It will take Derek approximately 28 months to save at least $1,000 for the down payment on the used car if the only additions to his savings account are his parents' interest payments.
Month Process
0 Derek saves $200 (initial savings)
1 Derek receives 6% interest on $200 (interest = $200 * 0.06 = $12), total savings = $200 + $12 = $212
2 Derek receives 6% interest on $212 (interest = $212 * 0.06 = $12.72), total savings = $212 + $12.72 = $224.72
3 Derek receives 6% interest on $224.72 (interest = $224.72 * 0.06 = $13.48), total savings = $224.72 + $13.48 = $238.20
4 Derek receives 6% interest on $238.20 (interest = $238.20 * 0.06 = $14.29), total savings = $238.20 + $14.29 = $252.49
5 Derek receives 6% interest on $252.49 (interest = $252.49 * 0.06 = $15.15), total savings = $252.49 + $15.15 = $267.64
6 Derek receives 6% interest on $267.64 (interest = $267.64 * 0.06 = $16.06), total savings = $267.64 + $16.06 = $283.70
It will take Derek approximately 28 months to save at least $1,000 for the down payment on the used car if the only additions to his savings account are his parents' interest payments.
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An artist made a cone of stainless steel, then sliced it into three pieces. what is the volume of the largest piece? PLEASE SHOW WORK AND EXPLAIN HOW YOU GOT YOUR ANSWER I WILL MARK YOU BRAINLIEST!!!
The volume of the largest piece is 10, 597. 5 cm³
How to determine the volumeThe largest part of the cone takes the shape of a cylinder.
Now, the formula for calculating the volume of a cylinder is expressed as;
V = πr²h
The parameters of the formula are enumerated as;
V is the volume of the cylinder.r is the radius of the cylinder.h is the height of the cylinder.Now, substitute the values, we get;
Diameter = 2 radius
Radius = 30/2
Radius = 15cm
Height = 15cm
Now, substitute the values, we get;
Volume = 3.14 × 15² ×15
Find the square value and substitute, we have;
Volume = 10, 597. 5 cm³
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Geometry
Show work and number
Using the trigonometric ratios:
(1). sinA = 5/13, cosA = 12/13 and tanA = 5/13. And by Pythagoras rule:
(2). x = √116
(3). x = 90
What is trigonometric ratios?The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.
The basic trigonometric ratios includes;
sine, cosine and tangent.
(1). sinA = 5/13 {opposite/hypotenuse}
cosA = 12/13 {adjacent/hypotenuse}
tanA = 5/13 {opposite/adjacent}
By Pythagoras rule
(2). x = √(4² + 10²)
x = √(16 + 100)
x = √116
(3). 106² = x² + 56²
x² = 106² - 56²
x = √(11236 - 3136)
x = √8100
x = 90
Therefore, using trigonometric ratios:
(1). sinA = 5/13, cosA = 12/13 and tanA = 5/13. And by Pythagoras rule;
(2). x = √116
(3). x = 90
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The Maths GCSE test scores of 240 students are shown in the histogram below.
The required median is 110- 120 and the upper quartile of the scores is 110-120.
Given that, the data from the histogram is
CI | f
80-90 | 5
90-100, | 3
100-110, | 4
110-120, | 4
120-130, | 3
130-140, | 3
140-150, | 2
150-160 | 2
To find the median and upper quartile of the given scores, make the cumulative frequency table.
The cumulative frequency table is given below.
CI | f | cf
80-90 | 5 | 5
90-100, | 3 | 8
100-110, | 4 | 12
110-120, | 4 | 16
120-130, | 3 | 19
130-140, | 3 | 22
140-150, | 2 | 24
150-160 | 2 | 26
N = 26.
The median is the N/2 th score when N is even.
Median = 13th score = 110-120 scores
To find the upper quartile, the product of (3/4 and N )th score gives the upper quartile.
Upper quartile = (3/4 x 26)th score.
Upper quartile = 19.5th score.
The upper quartile score range is 110 - 120.
Therefore,the required median is 110- 120 and the upper quartile of the scores is 110-120.
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Name two other positive angles of rotation that take A to B. Explain your reasoning
The two other positive angles of rotation that take A to B are 19π/6 and 31π/6.
How to explain the anglesThe unit circle is rotationally symmetric, meaning that any angle of rotation on the unit circle will take a point to another point on the unit circle with the same distance from the origin. This means that if we rotate point A by 7π/6 radians, we can also rotate it by 19π/6 or 31π/6 radians and end up at the same point B.
The point A has polar coordinates (1, 0). This means that it is located at a distance of 1 unit from the origin and has an angle of 0 radians with the positive x-axis.
The point B has polar coordinates (√3/2, 1/2). This means that it is located at a distance of √3/2 units from the origin and has an angle of 7π/6 radians with the positive x-axis.
If we rotate point A by 19π/6 radians, we get a point with polar coordinates (√3/2, -1/2). This point is located at the same distance from the origin as point B and has the same angle with the positive x-axis.
Therefore, the two other positive angles of rotation that take A to B are 19π/6 and 31π/6.
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Please actually help me I really need it
Area of shape 1:
Area of triangle = 1/2 × b × h
Area of triangle = 1/2 × 6 × 8
Area of triangle = 24 cm²
Area of shape 2:
Area of Semicircle = πr²/2
Radius of Semicircle = Diameter / 2
Radius of Semicircle = 3 cm
Then,
Area of semicircle = π(3)²
Area of semicircle = 9π cm²
Total Area = Area of semicircle + Area of triangle
Total Area = (24 + 9π) cm²
Total Area = 52.27 cm² .
Hence Total area of the figure combining triangle and semicircle is 52.27 cm².
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9. PUGS is a parallelogram. The equation of line PU is y = 4x-2. What is the slope of GS?
Does anyone know how to solve this?
Which of the following options represents the phrase "eight less than the quotient of 24 and 12"?
Hello!:
24/12 - 8
= 2 - 8
= -6
According to the synthetic division below, which of the following statements are true? -4/3 7 20
According to the synthetic division below, the true statements are as follows:
B. The number 4 is a root of F(x) = 3x2-13x+4.
D. (3x2 - 13x+4) - (x - 4) = (3x - 1)
F. (x-4) is a factor of 3x2.13x+ 4.
How to determine the true statementsSynthetic divisions are the manual ways of bypassing long divisions while performing the Euclidean dividion of polynomials. For the given expressions, we can determine the true statements in this way:
1. F(x) = 3x² - 13x +4.
(x-4) (3x-1)
So, x = 4 or 1/3
4 is an actual root of the function.
2. (3x² - 13x + 4) ÷ (x - 4) = (3x - 1)
3. 3x² - 13x + 4 = (x-4) (3x-1)
So, since all these expressions are true, they meet the requirements for the synthetic division.
Learn more about synthetic divisions here:
https://brainly.com/question/29638766
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Complete Question:
According to the synthetic division below, which of the following statements are true? Check all that apply. 4 4)3 -13 12 3 0 O A. The number -4 is a root of F(x) = 3x2.13x + 4. B. The number 4 is a root of F(x) = 3x2-13x+4. O C. (3x2 - 13x + 4) - (x + 4) = (3x - 1) D. (3x2 - 13x+4) - (x - 4) = (3x - 1) O E. (x + 4) is a factor of 3x2 - 13x + 4. IF (x-4) is a factor of 3x2.13x+ 4.