Therefore , the solution of the given problem of expression comes out to be its final simplification is 5ln4y - 2lnx.
What is an expression?There is a need for mathematical operations such addition, multiplication, multiplication, and division. When variable combined, they produce the following: A mathematical operator, some data, and an equation A statement of fact is composed of values, parameters, plus operations like additions, subtractions, multiplications, and divisions. It is possible to contrast and compare various sentences and words.
Here,
Given :
To expand the given expression :
=> ln [ (4y)⁵/ x² ]
=> ln [ (4y)⁵/ x² ]
=> ln(4y)⁵ - lnx²
=> 5ln4y - 2lnx
Thus,
its final simplification is : 5ln4y - 2lnx.
Therefore , the solution of the given problem of expression comes out to be its final simplification is 5ln4y - 2lnx.
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the mean, median, and mode are all measures of central tendency. the mean is usually the preferred measure of central tendency, but there are specific situations in which it is impossible to compute a mean or in which the mean is not particularly representative of the distribution. which of the following statements about the mean are true? check all that apply.
It is commonly referred to as the arithmetic average. It is easily influenced by extreme scores. It can be used for data that are measured on a nominal scale. There can be more than one.
Statements about the mean that are true-It is commonly referred to as the arithmetic average, it is easily influenced by extreme scores, there can be more than one.
It is also known as the arithmetic mean, arithmetic average, or simply average. The mean measure of central tendency is also known as these terms.
When there are even numbers of data points rather than odd numbers, there might be more than one median when the two middle numbers are divided by two.
When there are scores that are uncertain, it can be located: With uncertain scores, the median can be discovered.
The mode is a real number in the data that occurs more frequently than other values, hence it correlates to an actual score in the data.
There can be more than one: there are multiple modes (bimodal, trimodal, and multimodal) where two or more values appear the same number of times.
Hence, the statements that are true about means are -It is commonly referred to as the arithmetic average, it is easily influenced by extreme scores, there can be more than one.
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Which of the following is not a reason for testing if the population correlation coefficient is zero?
-To see if r and rho (rho. are equal)
-All of the options are correct.
-To determine if a significant X-Y relationship exists.
-To make inference from sample to population.
-To bring sample size into the analysis.
The correct option on this statistics topic is (c) To determine if a significant X-Y relationship exists.
What is statistics as a subject?Statistics is a science and perhaps also the art of learning from data. As a discipline, it deals with the collection, analysis, and interpretation of data, and the effective communication and presentation of data-based results.
What is correlation coefficient?In statistics correlation coefficient is a single number that represents the strength and direction of the relationship between variables.
Different types of correlation coefficients may be appropriate for your data, depending on the measurement level and distribution. Pearson's product-moment correlation coefficient (Pearson's r) is commonly used to assess the linear relationship between two quantitative variables.
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PLEASE HELP ME ITS DUE AT 12:30
A homeowner has decided to put new flooring down in two rooms of his house. The first room is 24 ft by 15 ft and the second room is 12 ft by 13 ft. Each package of
flooring material will cover 12 square feet of floor and costs $9.03. If he can only buy whole packages, how many packages will he need? How much will it cost him?
He will need
packages of flooring material.
It will cost $
The homeowner will need 43 packages of flooring material and it will cost him $388.29.
What is the arithmetic?
Arithmetic is a branch of mathematics that deals with the study of numbers, including their properties, operations, and calculations. It involves performing basic mathematical operations, such as addition, subtraction, multiplication, and division, on numbers to solve mathematical problems.
The first room requires 24 ft * 15 ft = 360 square feet of flooring.
The second room requires 12 ft * 13 ft = 156 square feet of flooring.
So, the total amount of flooring material required is 360 + 156 = 516 square feet.
The homeowner will need 516 square feet / 12 square feet per package = 43 packages of flooring material.
So, the cost will be 43 packages * $9.03 per package = $388.29.
Hence, The homeowner will need 43 packages of flooring material and it will cost him $388.29.
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Verify that the indicated family of functions is a solution of the given differential equation. dP/dt = P(1-P); P = ce^t / 1+ ce^t?
The value for differential equation is found as -
[tex]\frac{dP}{dt} =\frac{d}{dt} (\frac{c_1e^t}{1+c_1e^t})\\[/tex]
[tex]\frac{dP}{dt} - (\frac{c_1e^t}{(1+c_1e^t)} )(1-\frac{c_1e^t}{(1+c_1e^t)^2})\\ =(\frac{c_1e^t}{(1+c_1e^t)^2} )-(\frac{c_1e^t}{1+c_1e^t})(1-\frac{c_1e^t}{1+c_1e^t})=0[/tex]
What is differential equation?
Any equation with one or more terms and one or more derivatives of the dependent variable with respect to the independent variable is referred to as a differential equation.
The equation given is - [tex]P=\frac{c_1e^t}{1+c_1e^t}[/tex]
Take derivative with respect to t -
[tex]\frac{dP}{dt} =\frac{d}{dt} (\frac{c_1e^t}{1+c_1e^t})\\\frac{dP}{dt} =\frac{d}{dt}c_1 (\frac{e^t}{1+c_1e^t})[/tex]
By Quotient rule [tex]\frac{d}{dt} \frac{u}{v} =\frac{v\frac{du}{dt}- u\frac{dv}{dt}}{v^2}[/tex] -
[tex]\frac{dP}{dt} =c_1 (\frac{(1+c_1e^t)\frac{d}{dt}(e^t)-(e^t)\frac{d}{dt}(1+c_1e^t)}{(1+c_1e^t)} )\\\frac{dP}{dt} =c_1 (\frac{(1+c_1e^t)(e^t)-(e^t)(0+c_1e^t)}{(1+c_1e^t)} )[/tex]
([tex]\frac{d}{dx} e^t=e^t[/tex] and [tex]\frac{d}{dx} c_1=0[/tex] here [tex]c_1=[/tex]constant)
[tex]\frac{dP}{dt} =c_1e^t (\frac{(1+c_1e^t-c_1e^t)}{(1+c_1e^t)^2} )\\\frac{dP}{dt} = (\frac{(c_1e^t)}{(1+c_1e^t)^2} )[/tex]
Now, [tex]\frac{dP}{dt} =P(1-P)[/tex] -
[tex]\frac{dP}{dt} - (\frac{c_1e^t}{(1+c_1e^t)} )(1-\frac{c_1e^t}{(1+c_1e^t)^2})\\ =(\frac{c_1e^t}{(1+c_1e^t)^2} )-(\frac{c_1e^t}{1+c_1e^t})(1-\frac{c_1e^t}{1+c_1e^t})\\\frac{dP}{dt} =(\frac{c_1e^t}{(1+c_1e^t)} )(\frac{1}{1+c_1e^t}-1+\frac{c_1e^t}{1+c_1e^t})\\\frac{dP}{dt} =(\frac{c_1e^t}{(1+c_1e^t)} )(\frac{1-(1+c_1e^t)+c_1e^t}{1+c_1e^t})\\\frac{dP}{dt} =(\frac{c_1e^t}{(1+c_1e^t)} )(\frac{1-1-c_1e^t+c_1e^t}{1+c_1e^t})\\[/tex]
[tex]\frac{dP}{dt} =(\frac{c_1e^t}{(1+c_1e^t)} )(\frac{0}{1+c_1e^t})\\\frac{dP}{dt} =(\frac{c_1e^t}{(1+c_1e^t)} )(0)\\\frac{dP}{dt} =0[/tex]
Therefore, the value is [tex]\frac{dP}{dt} =0[/tex].
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Use Exercise 41 to show that if the first 10 positive integers are placed around a circle, in any order, there exist three integers in consecutive locations around the circle that have a sum greater than or equal to 17 .
With placing positive integers around the circle. Yes, there exist three integers in consecutive locations around the circle that have a sum greater than or equal to 17.
What exactly is a circle?
A circle is a kind of ellipse with zero eccentricity and two foci that are coincident. A circle is also known as the locus of points drawn at equal distances from the center. The radius of a circle is the distance from its center to its outside line. The diameter of a circle is the line that divides it into two equal sections and is equal to twice the radius.
The equation for a circle in the plane is:
(x-h)^²+ (y-k)² = r²
When the coordinate points are (x, y)
(h, k) is the coordinate of a circle's center.
where r is the circumference of a circle.
where circle area = πr²
Circle circumference=2πr
Now,
First 10 positive integers
that are 1,2,3,4,5,6,7,8,9,10
after putting these in circle 1 and 10 will be adjacent
and
To prove :-there exist three integers in consecutive locations around the circle that have a sum greater than or equal to 17 .
Now as sum of =5+6+7=18
6+7+8=21
7+8+9=24
Hence,
There exist three integers in consecutive locations around the circle that have a sum greater than or equal to 17.
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NO LINKS!!! URGENT HELP PLEASE!!!! NO MULTIPLE-CHOICE!!!!!!
1. Find the maximum area for a rectangle perimeter of 120 meters. Make your answer convincing by including these things:
a. Sketches of rectangles with a perimeter of 120 meters (Include rectangles that do not have the maximum area and the rectangle you think does have the maximum area.)
b. A table of lengths and areas for rectangles with a perimeter of 120 meters (Use increments of 5 meters for the lengths.)
c. A graph of the relationship between length and area.
Explain how each piece of evidence supports your answer.
The maximum area is 900 square meters
How to determine the maximum areaGiven that
Perimeter, P = 120
So, we have
P = 2(l + w) = 120
This gives
l + w = 60
Make l the subject
l = 60 - w
The area is
A = lw
So, we have
A =w(60 - w)
Expand
A = 60w - w^2
Differentiate and set to 0
60 - 2w = 0
So, we have
w = 30
Recall that
A =w(60 - w)
So, we have
A = 30(60 - 30)
Evaluate
A = 900
The sketch of the rectangleSee attachment
Table of lengths and areas of rectanglesThis is represented as follows
Length (l) | Width (w) | Area (A)
30 | 30 | 900
35 | 25 | 875
40 | 20 | 800
45 | 15 | 675
50 | 10 | 500
55 | 5 | 275
The graph of the relationshipSee attachment
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Answer:
900 m²
Step-by-step explanation:
The maximum possible area of a rectangle is when the width and length are equal, i.e. it is a square.
To find the side length of a square, divide its perimeter by 4. Therefore, the width and length of a rectangle with perimeter 120 m is:
[tex]\implies \sf \dfrac{120}{4}=30\;m[/tex]
The area of a square is the square of its side length, so the maximum area for a rectangle with perimeter of 120 m is:
[tex]\implies \sf Area=30^2=900\;m^2[/tex]
Part AThe formula for the perimeter of a rectangle is:
[tex]\boxed{\sf Perimeter=2(width+length)}[/tex]
Therefore, if the perimeter is 120 m:
[tex]\implies \sf 120=2(width+length)[/tex]
[tex]\implies \sf width+length=60[/tex]
So the width and length must sum to 60 m.
Sketch various rectangles where the sum of their width and length is 60 m. For example:
10 m × 50 m30 m × 30 m20 m × 40 mPart BThe formula for the area of a rectangle is:
[tex]\boxed{\sf Area=width \times length}[/tex]
A table with the width, length and areas (in increments of 5 m for the lengths) is as follows:
[tex]\begin{array}{c|c|c}\vphantom{\dfrac12} \sf width\;(m)&\sf length\;(m)& \sf area\;(m$^2$)\\\cline{1-3}\vphantom{\dfrac12}5&55&275\\\vphantom{\dfrac12}10&50&500\\\vphantom{\dfrac12}15&45&675\\\vphantom{\dfrac12}20&40&800\\\vphantom{\dfrac12}25&35&875\\\vphantom{\dfrac12}30&30&900\\\vphantom{\dfrac12}35&25&875\\\vphantom{\dfrac12}40&20&800\\\vphantom{\dfrac12}45&15&675\\\vphantom{\dfrac12}50&10&500\\\vphantom{\dfrac12}55&5&275\end{array}[/tex]
Part CLet x be the length of the rectangle (in meters).
Let y be the area of the rectangle (in meters squared).
From inspection of the values of area from the table from part (b), the function is quadratic, since the second differences between the y-values is constant. The maximum point (vertex) is (30, 900). Therefore, the graph is a parabola that opens downwards.
[tex]\boxed{\begin{minipage}{5.6 cm}\underline{Vertex form of a quadratic equation}\\\\$y=a(x-h)^2+k$\\\\where:\\ \phantom{ww}$\bullet$ $(h,k)$ is the vertex. \\ \phantom{ww}$\bullet$ $a$ is some constant.\\\end{minipage}}[/tex]
As the vertex is (30, 900) and the parabola opens downwards (so the value of "a" is negative):
[tex]\implies y=-a(x-30)^2+900[/tex]
To find the value of a, substitute one of the other points into the equation:
[tex]\implies -a(10-30)^2+900=500[/tex]
[tex]\implies -a(-20)^2=-400[/tex]
[tex]\implies -400a=-400[/tex]
[tex]\implies a=1[/tex]
Therefore, the equation of the parabola is:
[tex]y=-(x-30)^2+900\qquad \{x|\;0 < x < 60\}[/tex]
Note: If the measure of one side of the rectangle is 60 m, then the measure of the adjacent side will be 0 cm, which is impossible. Therefore, the domain of the function must be set to (0, 60).
ExplanationFrom inspection of the table, the maximum area of a rectangle that has a perimeter of 120 m is when its width and length are both 30 m.
From the graph of the relationship between length and area of a rectangle with a perimeter of 120 m, the maximum area is when the length is 30 m ⇒ max area = 900 m².
Therefore, the maximum area of the rectangle is 900 m².
2/3 x −1/5 x = x − 1
Answer:
Exact Form:
x=15/8
Decimal Form:
x=1.875
Mixed Number Form:
x=1 7/8
Step-by-step explanation:
(25-a)/7=3
Please help me with this question I know it seems easy but still.
Answer:
a= 4
Step-by-step explanation:
Rearrange terms
Multiply all terms by the same value to eliminate fraction denominators
Cancel multiplied terms that are in the denominator
Multiply the numbers
than subastraract form both by 25
Simplify the expression
Subtract the numbers
Subtract the numbers
You will find the solution
Perform the given operation. Round to 4 decimal places if needed.
6.3 ÷ 88.12
Answer:
13.9873
Step-by-step explanation:
This problem can be solved using long division, use the picture for reference below.
First, change the divisor 6.3 to a whole number by moving the decimal point 1 places to the right. Then move the decimal point in the dividend the same, 1 places to the right.
We then have the equations:
881.2 ÷ 63 = 13.9873
and therefore:
88.12 ÷ 6.3 = 13.9873
For more information about long division involving decimals, I recommend looking at this video here: https://youtu.be/x48CYVaD0xE
WILL GIVE 100 POINTS FOR THIS QUESTION PLEASE BE FAST
Answer:
1. real rational decimal
2. real rational integer
3. real rational root, whole number
4. real rational
5.
6.
7. imaginary number
Step-by-step explanation:
i think this is it I'm so sorry if its wrong
i cant figure out 5 and 6 so sorry
1. real rational decimal
2. real rational integer
3. real rational root, whole number
4. real rational
5. real irrational root
6. real ration root, whole number
7. imaginary number
use differentials to approximate the value of sqrt(99.4). what is the percent error oin this calculation
The percentage error by calculating by differentials to approximate value of sqrt(99.4) = 0.00045 percentage.
For percentage error Here first we have to find the value of sqrt(99.4) by normal calculation and second we will calculate it by differential method then we will find the percentage error .
To approximate sqrt(99.4) we will use formula for linear approximation as given below
f(x) = f(c) + f′(c)(x−c)
and we are dealing with square root so we have to find the f(x) ad here
f(x) = √x
and we will calculate f'(x) and here it is
f'(x) = 1/(2√x)
Here, x=99.4 and we choose c =100 because that’s the closest perfect square number to 99.4. so
f(c) = f(100) = √100 = 10
f'(c) = f'(100) =1/(2√100) = 1/20
f(x) =f(c) + f′(c)(x−c)
f(x) = f(99.4)=f(100)+f'(100)(99.4-100)
=10+1/20*(-0.6)
=9.97
Here we find the value by differential = 9.97
and by simple calculation the value is = 9.96995486
ans percentage error = (real value - differential value)/100
= (9.96995486-9.97)/100 = 0.00045 percentage
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HELP ASAP FAST!!!!!!!
The solution is, the value of x= 12.4.
What is Pythagorean theorem?Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, a2 + b2 = c2.
here, we have,
radius = 22
so, from the given diagram we get,
height of the right angle triangle = √22²-19.8²
=9.59
so, x = 22- 9.59
= 12.41
Hence, The solution is, the value of x= 12.4.
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Find a possible equation for the line that is perpendicular to the graph of 5x -3y=12 if the two lines intersect at x=30.
Please show your work
The equation of the line perpendicular to 5x - 3y = 12 is y = -3/5x + 64.
How to Find the Equation of Perpendicular Lines?Given that two lines are perpendicular, their slopes are negative reciprocals of each other.
The equation 5x - 3y = 12 can be rearranged to find the slope:
y = (5/3)x - 4
So the slope of the line is 5/3.
The slope of a line perpendicular to it would be the negative reciprocal of 5/3:
-3/5
Since both lines intersects at x = 30, find a point on both lines by substituting x = 30 into 5x - 3y = 12:
5(30) - 3y = 12
150 - 3y = 12
-3y = 12 - 150
-3y = -138
y = 46
Write the equation of the perpendicular line by substituting (a, b) = (30, 46) and m = -3/5 into y - b = m(x - a):
y - 46 = -3/5(x - 30)
Rewrite in Slope-intercept form:
y - 46 = -3/5x + 18
y = -3/5x + 18 + 46
y = -3/5x + 64
The equation is: y = -3/5x + 64
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3x^2 - 6x over x^2 + 2x - 8
Q1) Find unknown value of the following in lowest term
a) 16: 20 =
Step-by-step explanation:
college level question ???? what the ...
oh my.
16 : 20 = 16 / 20 = 16 ÷ 20
16/20 = 4/5 = 0.8
Amelia's investment of $9810 earns
interest at 2.7% per year
compounded quarterly over 13 years.
What is the amount of interest
earned?
Write your answer to the nearest cent.
Interest =
Answer:
Step-by-step explanation:
To calculate the amount of interest earned by Amelia's investment, we can use the formula for compound interest:
A = P * (1 + r/n)^(nt), where
A = amount after t years
P = principal amount ($9810)
r = annual interest rate (2.7%)
n = number of times the interest is compounded per year (quarterly, so n = 4)
t = number of years (13)
Plugging in the values, we get:
A = $9810 * (1 + (0.027/4))^(4 * 13)
A = $9810 * (1.00675)^52
A = $9810 * 1.8972436
A = $18561.61 (rounded to nearest cent)
Therefore, the interest earned by Amelia's investment is $18561.61 - $9810 = $8751.61.
How much stainless-steel containing 15% chromium and stainless-steel containing 18% chromium must be mixed to create 9.00 kg new stainless-steel with 17% chromium?
The solution to the system of equations is 6kg of 15 % chromium and 3kg of 18 % stainless steel
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the amount of chromium be x
Let the amount of stainless steel be y
The percentage of amount of chromium = 15 % of x
The percentage of amount of stainless steel = 18 % of y
Now , the amount of mixture = 9 kg
The percentage of amount of mixture = 17 %
So , the equation will be
x + y = 9 be equation (1)
0.15x + 0.18y = 0.17 ( 9 )
On simplifying the equation , we get
15x + 18y = 153
Divide by 3 on both sides of the equation , we get
5x + 6y = 51 be equation (2)
Multiply equation (1) by 5 , we get
5x + 5y = 45 be equation (3)
Subtracting equation (3) from equation (2) , we get
y = 6 kg
So , the value of x = 3 kg
Hence , the mixture contains 6kg of 15 % chromium and 3kg of 18 % stainless steel
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3. Find the area of the following shape. Make sure to indicate what shapes were used, by sketching on the image, listing formulas, and show work listed for each shape. (5 total points – 2 for accurate shapes, 2 for accurate work, 1 for total area answer)
the total area of the figure will be 53.13 unit square.
What is Area?The area is the entire amount of space occupied by a flat (2-D) surface or an object's form. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a form on paper is the area that it occupies.
Given a figure that we will transform into three parts A, B, and C as shown in the attached figure
Where A is a semicircle with a radius of 3 unit
b is a triangle with a height of 6 and a base of 3 units
and C is a rectangle with a length of 6 and a width of 5 units
From the general formulas of area,
area of semicircle = pi/2 radius * radius
Area of rectangle = length * width
Area of triangle = 1/2 height * base
in our case,
area of semicircle = pi/2 3* 3
Area of semicircle = 14. 13 unit square
Area of rectangle = 6* 5
Area of rectangle = 30 unit square
Area of triangle = 1/2 6* 3
Area of triangle = 9
Thus, the total area of the figure will be = 14. 13 + 30 +9
Therefore, the total area of the figure will be 53.13 unit square.
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Find JK. Round to the nearest tenth.
The value of the segment JK in the given triangle is 7.40 units.
What are trigonometric functions?Simply put, trigonometric functions—also referred to as circular functions—are the functions of a triangle's angle. This means that these trig functions provide the relationship between the angles and sides of a triangle. Sine, cosine, tangent, cotangent, secant, and cosecant are the fundamental trigonometric functions.
The trigonometric function cos is given as:
Cos A = adjacent side / hypotenuse
Using the function of cos:
Cos J = adjacent side / hypotenuse
Cos 22 = x / 8
0.927 (8) = x
x = 7.40
Hence, the value of the segment JK in the given triangle is 7.40 units.
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One hundred tickets, numbered 1,2,3,...,100, are sold to 100 different people for a drawing. Four different prizes are awarded, including a grand prize (a trip to Tahiti). A) How many ways are there to award the prizes? B) How many ways are there to award the prizes if the person holding ticket 47 wins the grand prize? C) How many ways are there to award the prizes if the person holding ticket 47 wins one of the prizes? D) How many ways are there to award the prizes if the person holding ticket 47 does not win a prize? E) How many ways are there to award the prizes if the people holding tickets 19 and 47 both win prizes? F) How many ways are there to award the prizes if the people holding tickets 19, 47, 73, and 97 all win prizes? G) How many ways are there to award the prizes if none of the people holding tickets 19, 47, 73, and 97 wins a prize? H) How many ways are there to award the prizes if the grand prize winner is a person holding ticket 18, 47, 73, or 977 I) How many ways are there to award the prizes if the people holding tickets 19 and 47 win prizes, but the people holding tickets 73 and 97 do not win prizes?
A) There are 100 * 99 * 98 * 97 ways to award the prizes, since there are 100 choices for the first prize, 99 choices for the second prize, 98 choices for the third prize, and 97 choices for the fourth prize..
What is the combinatorics?
Combinatorics is a branch of mathematics that deals with counting and arranging objects, such as numbers, sets, and permutations.
B) If the person holding ticket 47 wins the grand prize, there are 99 * 98 * 97 ways to award the remaining prizes, since there are 99 choices for the second prize, 98 choices for the third prize, and 97 choices for the fourth prize.
C) If the person holding ticket 47 wins one of the prizes, there are 100 * 99 * 98 * 97 ways to award the prizes.
D) If the person holding ticket 47 does not win a prize, there are 99 * 98 * 97 * 96 ways to award the prizes, since there are 99 choices for the first prize, 98 choices for the second prize, 97 choices for the third prize, and 96 choices for the fourth prize.
E) If the people holding tickets 19 and 47 both win prizes, there are 98 * 97 * 96 * 95 ways to award the remaining prizes, since there are 98 choices for the third prize, 97 choices for the fourth prize, 96 choices for the fifth prize, and 95 choices for the sixth prize.
F) If the people holding tickets 19, 47, 73, and 97 all win prizes, there are 96 * 95 * 94 * 93 ways to award the remaining prizes, since there are 96 choices for the fifth prize, 95 choices for the sixth prize, 94 choices for the seventh prize, and 93 choices for the eighth prize.
G) If none of the people holding tickets 19, 47, 73, and 97 wins a prize, there are 96 * 97 * 98 * 99 ways to award the prizes, since there are 96 choices for the first prize, 97 choices for the second prize, 98 choices for the third prize, and 99 choices for the fourth prize.
H) If the grand prize winner is a person holding ticket 18, 47, 73, or 97, there are 3 * 99 * 98 * 97 ways to award the remaining prizes, since there are 3 choices for the grand prize winner (18, 47, or 73), and 99 choices for the second prize, 98 choices for the third prize, and 97 choices for the fourth prize.
I) If the people holding tickets 19 and 47 win prizes, but the people holding tickets 73 and 97 do not win prizes, there are 98 * 97 * 96 * 95 ways to award the prizes, since there are 98 choices for the first prize, 97 choices for the second prize, 96 choices for the third prize, and 95 choices for the fourth prize.
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The points (14,8) and (28,16) form a proportional relationship. Find the slope of the line through the points. Then use the slope to graph the line.
The slope of the line through the points is 4/7 and the graph is given below.
What is Slope?Slope of a line is the ratio of the change in y coordinates to the change in the x coordinates of two points given.
Given that, the points (14,8) and (28,16) form a proportional relationship.
A proportional relationship will be of the form y = kx, where k is the slope or constant of proportionality.
We have two points (14,8) and (28,16).
Slope = (16 - 8) / (28 - 14) = 8/14 = 4/7
Equation of the line is y = 4/7 x
When x = 0, y = 0
When x = 7, y = 4/7 × 7 = 4
When x = 14, y = 4/7 × 14 = 8
When x = 21, y = 4/7 × 21 = 12
and so on.
So the points are (0, 0), (7, 4), (14, 8), (21, 12), (28, 16) and so on.
Hence the slope of the line is 4/7.
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i need help pleaseee i would appreciate it
here is the picture
The values of the compositions of the functions are.
f(g(5)) = 4g(f(1)) = 1f(f(4)) = 0g(g(3)) = 5How to evaluate the expressions?Here we have two graphs for functions f(x) and g(x), and we need to use these to find the values of some compositions.
First, we want to find the value of:
f(g(5))
Using the second graph we can see that g(5) = 0, then:
f(g(5)) = f(0)
and using the first graph we can see that f(0) = 4, then
f(g(5)) = 4.
The second expression is:
g(f(1))
And we cans ee that f(1) = 3, then:
g(f(1)) = g(3) = 1
So:
g(f(1)) = 1
And so on, for the next two we have:
f(f(4)) = f(2) = 0
g(g(3)) = g(1) = 5
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IS THIS RIGHTT ???
PLEASE HELP MEEEE
The coordinate of the quadrilateral DEFG after trnaslation, reflection and dilation is mention on the graph.
What is a transformation of a point?A spatial transformation is each mapping of feature space to itself and it maintains some spatial correlation between figures.
The vertices of the quadrilateral DEFG (Red) is given as,
D(2, 2), E(6, 2), F(8, 4), G(2, 4)
The vertices of the quadrilateral D'E'F'G' after translation (Green) is given as,
D'(2, -4), E'(6, -4), F'(8, -2), G'(2, -2)
The vertices of the quadrilateral D"E"F"G" after reflection (Purple) is given as,
D"(-2, -4), E"(-6, -4), F"(-8, -2), G"(-2, -4)
The vertices of the quadrilateral D'''E'''F'''G''' after reflection (Black) is given as,
D'''(-1, -2), E'''(-3, -2), F'''(-4, -1), G'''(-1, -2)
The coordinate of the quadrilateral DEFG after trnaslation, reflection and dilation is mention on the graph.
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hannah's school hosted a book donation. there are 150150150 students at her school, and they donated a total of bbb books! hannah donated 333 times as
The formula to calculate the number of books donated by Hannah would be: bbb/150150150 = 333.
Essentially, we are taking the total number of books that were donated, bbb, and dividing it by the total number of students at Hannah's school, 150150150. The result of this equation is 333, which represents the number of books Hannah donated. To calculate this number we would first divide bbb by 150150150. Then, we would multiply the result by 333 to get the total number of books Hannah donated. For example, if the total number of books donated was 300,000, the number of books Hannah donated would be 49,950. This can be calculated by dividing 300,000 by 150150150 and then multiplying the result by 333.
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Graphs of the functions f and g are given.
(a) Which is larger, f(0) or g(0)?
A. f(0) is larger.
B. g(0) is larger.
C. Neither is larger.
(b) Which is larger, f(3) or g(3)?
A. f(3) is larger.
B. g(3) is larger.
C. Neither is larger.
After analyzing, it can be concluded that the functions f and g are:
A. f(0) is larger than g(0).
B. f(3) is larger than g(3).
Two Functions is LargerTo determine which of the two functions is larger at any given point, one must compare the heights of the two functions at the same point on the x-axis. At point x=0, the height of the f(x) function is larger than the height of the g(x) function, so f(0) is larger than g(0).
Similarly, at point x=3, the height of the f(x) function is larger than the height of the g(x) function, so f(3) is larger than g(3).
To compare which of two functions is larger at any given point, we need to compare the heights of the two functions at the same point on the x-axis. For example, at x=0, the height of the f(x) function is larger than the height of the g(x) function, so f(0) is larger than g(0). The same comparison can be made at any other point on the x-axis.
For example, at x=3, the height of the f(x) function is larger than the height of the g(x) function, so f(3) is larger than g(3). This comparison can be done for any point on the x-axis, which will allow us to determine which of the two functions is larger at any given point.
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Use Heron's Area Formula to find the area of the triangle. (Round your answer to two decimal places.) a = 57 , b = 43 , c = 58
The Area of the given triangle is 1146.27 sq. units.
Heron's Formula:An important plane geometry theorem also referred to as Hero's formula.
By dividing the quadrilateral into two triangles along its diagonal, this formula is also used to determine the quadrilateral's surface area.
Given the semiperimeter and the lengths of the sides a, b, and c
[tex]p=\frac{a+b+c}{2}[/tex]
of a triangle, Heron's formula gives the area of the triangle as
[tex]A=\sqrt{p(p-a)(p-b)(p-c)}[/tex].
Now in the given question,
a = 57
b = 43
c = 58
Hence, the semi-perimeter,
[tex]p=\frac{a+b+c}{2}[/tex]
[tex]p=\frac{57+43+58}{2} =79[/tex]
Now we calculate the area,
[tex]A=\sqrt{p(p-a)(p-b)(p-c)} \\A=\sqrt{79(79-47)(79-43)(79-58)} \\A=\sqrt{79(22*36*21)} \\A=\sqrt{79*16632} \\A=\sqrt{1313928} \\A=1146.266[/tex]
Hence, the area of triangle is 1146.27 sq. units.
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Use interval notation to indicate all real numbers greater than or equal to −3 and less than 13.
Answer: [-3, 13)
A square bracket [] means it includes the number, and a round bracket () means that value is not included.
Suppose P(t) is the number of individuals infected by a disease t days after it was first detected. Interpret P'(50) = -200.
Answer: P'(50) = -200 means that the derivative of P(t) with respect to t, evaluated at t = 50, is equal to -200. The derivative of a function represents the rate of change of the function. In this case, P'(50) = -200 represents the rate of change of the number of individuals infected by the disease 50 days after it was first detected.
Since P'(50) = -200, this means that the number of individuals infected by the disease is decreasing at a rate of 200 individuals per day when t = 50. In other words, 200 individuals are recovering or being treated each day, so the total number of infected individuals is decreasing.
Step-by-step explanation:
uncle sonny believes that dilations will result in the congruence of corresponding lines m and line segments. what do you say?
Answer:
Yes, Uncle Sonny is correct.
Step-by-step explanation:
If two figures are related by a dilation, then corresponding lines or line segments in the figures will be congruent. In a dilation, the ratio of the lengths of corresponding lines or line segments remains constant, which means they will have the same length. Therefore, they are congruent.