Factors such as scene size, complexity, evidence type, available resources, and time constraints determine the appropriate crime scene search pattern.
Determining the appropriate crime scene search pattern requires careful consideration of various factors to ensure a systematic and thorough search. While I cannot provide a calculation for this question since it involves subjective decision-making, I can provide a detailed explanation of the factors that should be taken into account when selecting a search pattern.
1. Size and nature of the crime scene: Consider the overall size and layout of the crime scene. Is it a small confined space or a large outdoor area? The size will influence the choice of search pattern. For smaller scenes, a line or grid search may be more suitable, while larger scenes may require a quadrant or zone search.
2. Type of evidence and scene complexity: Evaluate the type of evidence that may be present and the complexity of the scene. Are there specific areas or items of interest that require a focused search? Does the scene have multiple levels or rooms? A spiral search may be effective for scenes with a well-defined center, while a quadrant search allows for targeted searches in specific areas.
3. Number of investigators available: Assess the number of investigators available for the search. Different search patterns require different levels of manpower. For example, a grid search may require more personnel compared to a line search. Consider the available resources and allocate personnel accordingly.
4. Time constraints and urgency: Consider the urgency of the search and any time constraints. If there is a need for a rapid search, a line or spiral search may be more efficient. However, if time permits, a more detailed and thorough search, such as a grid or quadrant search, can be implemented.
5. Expert opinion and experience: Seek input from experienced crime scene investigators or forensic experts who can provide valuable insights and recommendations based on their expertise and prior experiences.
Ultimately, the choice of search pattern should be based on a careful assessment of these factors, combined with the investigator's professional judgment and experience. The goal is to conduct a methodical and comprehensive search to ensure all relevant evidence is discovered and properly documented.
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The question probable may be:
What factors should be considered when determining the appropriate crime scene search pattern to use?
What is the meaning of "∀X, Y ∈ A(X ⊂ Y ⇐ ⇒ f(X) ⊂ f(Y ))"?
Which inequality represents the situation described below?
The distance, d, is less than 200 miles.
A. d ≥ 200
B. d > 200
C. d ≤ 200
D. d < 200
Hello!
The distance, d, is less than 200 miles.
B. d > 200
GEOMETRY 100 POINTS
Find the value of x
Step-by-step explanation:
Since it's five (5) sided it is a pentagon.
First find the sum of the interior angle of a Pentagon .
S = ( n -2 ) × 180°
n represent the number of sides
S = ( 5 -2 ) × 180°
S = 3×180°
S = 540°
5x+2+ 10x-3 +7x-11 +8x-19 + 13x -31 = 540°
43x - 62 = 540°
43x = 540° + 62
43x = 602°
x = 14°
Answer : 14°
Select the correct answer from each drop-down menu.
What is the distance and midpoint between points D and E on the number line?
D
-4 -3
distance = A. 6.2 B. 0.6 C. 4.2 D. 2.6
midpoint = A. 0.1 B. 0.6 C. 1.2 D. 0.3
well, if we take a peek at the number line above, from one integer to the next there are 5 slots or divisions, meaning each division is 1/5.
what's the distance of DE?
well, D is at -1 plus 4 slots, that means -1 and we move it further by 4/5, that makes it -1⅘.
now E is at 2 plus 2 slots more, so that means 2 and we move it further by 2/5 or 2⅖.
to get the distance we simply get their difference, not much to it.
[tex]\stackrel{mixed}{1\frac{4}{5}}\implies \cfrac{1\cdot 5+4}{5}\implies \stackrel{improper}{\cfrac{9}{5}}~\hfill \stackrel{mixed}{2\frac{2}{5}} \implies \cfrac{2\cdot 5+2}{5} \implies \stackrel{improper}{\cfrac{12}{5}} \\\\[-0.35em] ~\dotfill\\\\ |DE|\implies \left| -\cfrac{9}{5}-\cfrac{12}{5} \right|\implies \left| -\cfrac{21}{5} \right|\implies \cfrac{21}{5}\implies \text{\LARGE 4.2}[/tex]
how about the midpoint of DE?
well, we can move from the left over to the midpoint or we can move from the right, let's move from the right, so hmmm let's take half of 21/5 and subtract it from E, that's where the midpoint is.
[tex]\stackrel{ E }{\cfrac{12}{5}}~~ - ~~\stackrel{ \textit{half of DE} }{\left( \cfrac{21}{5}\cdot \cfrac{1}{2} \right)}\implies \cfrac{12}{5}-\cfrac{21}{10}\implies \cfrac{(2)12~~ - ~~(1)21}{\underset{\textit{using this LCD}}{10}} \\\\\\ \cfrac{24-21}{10}\implies \cfrac{3}{10}\implies \text{\LARGE 0.3}[/tex]
Shamin Jewelers sells diamond necklaces for $442 less 10%. Jewelers offers the same necklace for $527 less 34%, 14% What additional rate of discount must offer to meet the competitor's price
Answer:
The selling price of the diamond necklace at Shamin Jewelers after 10% discount is:
$442 * 0.9 = $397.80
The selling price of the same necklace at the competitor's store after 34% and 14% discount is:
$527 * 0.66 * 0.86 = $247.08
So, Shamin Jewelers needs to offer an additional discount to meet the competitor's price:
$397.80 - $247.08 = $150.72
To calculate the additional rate of discount, we divide the difference by the original selling price at Shamin Jewelers and multiply by 100:
($150.72 / $442) * 100 = 34.11%
Therefore, Shamin Jewelers must offer an additional 34.11% discount to meet the competitor's price.
Step-by-step explanation:
PLEASE HELP AS SOON AS POSSIBLE
A) The slope between the points (0, -4) and (2, -1) is 1.5.
b) the slope between the points (0, -4) and (4, -1) is 0.75.
c) The slope of 0.75 indicates that for every 1 unit increase in x, there is a 0.75 unit increase in y.
Part A: To calculate the slope between two points, we use the formula:
slope = (change in y) / (change in x)
Let's choose the points (0, -4) and (2, -1).
Change in y = -1 - (-4) = 3
Change in x = 2 - 0 = 2
slope = 3 / 2 = 1.5
Therefore, the slope between the points (0, -4) and (2, -1) is 1.5.
Part B: Let's choose different points from the table, such as (0, -4) and (4, -1).
Change in y = -1 - (-4) = 3
Change in x = 4 - 0 = 4
slope = 3 / 4 = 0.75
Thus, the slope between the points (0, -4) and (4, -1) is 0.75.
Part C: The slopes from parts A and B provide information about the relationship between the points.
In part A, where the slope was calculated as 1.5, we can see that as the x-values increase by 2 units, the y-values increase by 3 units. This suggests a positive relationship between the points, meaning that as x increases, y also increases. The slope of 1.5 indicates that for every 1 unit increase in x, there is a 1.5 unit increase in y.
In part B, where the slope was calculated as 0.75, we observe a similar positive relationship between the points. As the x-values increase by 4 units, the y-values increase by 3 units. The slope of 0.75 indicates that for every 1 unit increase in x, there is a 0.75 unit increase in y.
Overall, the positive slopes in both parts A and B suggest that the points on the table exhibit a positive linear relationship. This means that as x increases, y also increases, and the rate of change is consistent based on the slope.
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What is mPN⌢
68°
136°
34°
92°
Answer:
arc PN = 136°
Step-by-step explanation:
the inscribed angle PLN is half the measure of its intercepted arc PN
then PN is twice the inscribed angle PLN , that is
PN = 2 × 68° = 136°
math math math math math math math
The measure of the angle m∠DAX on the straight line CX is equal to 140°
The sum of angles on a straight lineAngles that are on a straight line involves the sum of angles that can be arranged together so that they form a straight line. Angles on a straight line when added together sum up to 180°.
Given that AW bisects the angle m∠CAD and angle m∠CAW is equal to 20°, then;
m∠CAD = 2 × 20°
m∠CAD = 40°
m∠DAX + m∠CAD = 180° {sum of angles on a straight line}
m∠DAX + 40° = 180°
m∠DAX = 180° - 40° {subtract 40° from both sides}
m∠DAX = 140°
Therefore, the measure of the angle m∠DAX on the straight line CX is equal to 140°
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Answer: The measure of the angle m∠DAX on the straight line CX is equal to 140°
Step-by-step explanation: the gut below beat me to it
Explain your answer to the question in the picture with steps please, thank you.
Part (a)
Answer: Constant of proportionality = 5/8
Reason:
The general template equation is y = kx where k is the constant of proportionality. It is the slope of the line.
The direct proportion line must pass through the origin. In other words, the y intercept must be zero.
=====================================
Part (b)
Answer: Not Proportional
Reason:
The y intercept isn't zero.
Plug x = 0 into the equation to find y = 1 is the y intercept. This graph does not pass through the origin.
GEOMETRY 100 POINTS CHALLENGE
Answer:
x = 6
∠D = 127
Step-by-step explanation:
In a parallelogram, opposite angles are equal and adjacent angles add to 180
⇒ ∠A = ∠C and ∠C + ∠D = 180
∠A = ∠C
⇒ 13x - 25 = 9x - 1
⇒ 13x - 9x = 25 - 1
⇒ 4x = 24
⇒ x = 24/4
⇒ x = 6
∠C = 9x - 1
= 9(6) - 1
= 54 - 1
= 53
∠C + ∠D = 180
⇒ ∠D = 180 - ∠C
= 180 - 53
= 127
For the equation y = 3x + 4, find the value of y if x = 2.
Answer:
y=10
Step-by-step explanation:
y=3x+4
substitute for x
y=3(2)+4
y=6+4
y=10
GEOMETRY 100 POINTS CHALLENGE
Answer:
x = 10
Step-by-step explanation:
The diagonals of a rectangle are equal in length and bisect each other
⇒ JL = KM and
JN = LN = KN =MN
ΔJMN is an isosceles triangle since JN = MN
This means that the angles opposite to equal sides are equal
⇒ ∠JMN = ∠MJN
⇒ 7x - 2 = 3x + 38
⇒ 7x - 3x = 38 + 2
⇒ 4x = 40
⇒ x = 10
Pre calculus
Help me
Answer:
[tex]\displaystyle \frac{75}{2}[/tex] or [tex]37.5[/tex]
Step-by-step explanation:
We can answer this problem geometrically:
[tex]\displaystyle \int^6_{-4}f(x)\,dx=\int^1_{-4}f(x)\,dx+\int^3_1f(x)\,dx+\int^6_3f(x)\,dx\\\\\int^6_{-4}f(x)\,dx=(5*5)+\frac{1}{2}(2*5)+\frac{1}{2}(3*5)\\\\\int^6_{-4}f(x)\,dx=25+5+7.5\\\\\int^6_{-4}f(x)\,dx=37.5=\frac{75}{2}[/tex]
Notice that we found the area of the rectangular region between -4 and 1, and then the two triangular areas from 1 to 3 and 3 to 6. We then found the sum of these areas to get the total area under the curve of f(x) from -4 to 6.
Answer:
[tex]\dfrac{75}{2}[/tex]
Step-by-step explanation:
The value of a definite integral represents the area between the x-axis and the graph of the function you’re integrating between two limits.
[tex]\boxed{\begin{minipage}{8.5 cm}\underline{De\:\!finite integration}\\\\$\displaystyle \int^b_a f(x)\:\:\text{d}x$\\\\\\where $a$ is the lower limit and $b$ is the upper limit.\\\end{minipage}}[/tex]
The given definite integral is:
[tex]\displaystyle \int^6_{-4} f(x)\; \;\text{d}x[/tex]
This means we need to find the area between the x-axis and the function between the limits x = -4 and x = 6.
Notice that the function touches the x-axis at x = 3.
Therefore, we can separate the integral into two areas and add them together:
[tex]\displaystyle \int^6_{-4} f(x)\; \;\text{d}x=\int^3_{-4} f(x)\; \;\text{d}x+\int^6_{3} f(x)\; \;\text{d}x[/tex]
The area between the x-axis and the function between the limits x = -4 and x = 3 is a trapezoid with bases of 5 and 7 units, and a height of 5 units.
The area between the x-axis and the function between the limits x = 3 and x = 6 is a triangle with base of 3 units and height of 5 units.
Using the formulas for the area of a trapezoid and the area of a triangle, the definite integral can be calculated as follows:
[tex]\begin{aligned}\displaystyle \int^6_{-4} f(x)\; \;\text{d}x & =\int^3_{-4} f(x)\; \;\text{d}x+\int^6_{3} f(x)\; \;\text{d}x\\\\& =\dfrac{1}{2}(5+7)(5)+\dfrac{1}{2}(3)(5)\\\\& =30+\dfrac{15}{2}\\\\& =\dfrac{75}{2}\end{aligned}[/tex]
There are two numbers that have a sum of 47. Three times the lesser
number is equal to 9 more than the greater number. What are the
numbers?
Answer:
The numbers are 14 and 33---------------
Let the numbers be s and l.
We are given that:
Sum of the two is 47 and 3 times the lesser number is equal to 9 more than the greater number.Set up equations:
s + l = 473s = l + 9Eliminate l:
l = 47 - s and l = 3s - 9Solve for s:
47 - s = 3s - 93s + s = 47 + 94s = 56s = 14Find l:
l = 47 - 14l = 33100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
Step-by-step explanation:
4.a) A car consumes a gallon of petrol for every 30 km drive. The driver of the car set out on a journey of 420 km with 10 gallons of petrol in the fuel tank. i) How many more gallons of petrol will be needed to complete the journey? ii)find the cost of the petrol for the journey of 420km if a gallon of petrol cost GH¢5.50
i) 4 more gallons of petrol will be needed to complete the journey.
ii) The cost of the petrol for the 420 km journey is GH¢55.00.
i) To determine the number of gallons of petrol needed to complete the journey, we can calculate the total distance that can be covered with the available petrol and then subtract it from the total distance of the journey.
Given that the car consumes 1 gallon of petrol for every 30 km, we can calculate the distance that can be covered with 10 gallons of petrol by multiplying 10 (gallons) by 30 (km/gallon):
Distance covered with 10 gallons = 10 * 30 = 300 km
To find the remaining distance that needs to be covered, we subtract the distance covered with the available petrol from the total distance of the journey:
Remaining distance = Total distance - Distance covered with available petrol
Remaining distance = 420 km - 300 km = 120 km
Since the car consumes 1 gallon of petrol for every 30 km, we can determine the additional gallons of petrol needed by dividing the remaining distance by 30:
Additional gallons needed = Remaining distance / 30 = 120 km / 30 km/gallon = 4 gallons
Therefore, the driver will need 4 more gallons of petrol to complete the journey.
ii) To calculate the cost of the petrol for the journey of 420 km, we need to multiply the total number of gallons used for the journey by the cost per gallon.
Given that a gallon of petrol costs GH¢5.50, and the total number of gallons used for the journey is 10 (given in the problem), we can calculate the cost using the formula:
Cost of petrol = Total gallons used * Cost per gallon
Cost of petrol = 10 gallons * GH¢5.50/gallon = GH¢55.00
Therefore, the cost of the petrol for the journey of 420 km is GH¢55.00.
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Complete the frequency table for the following set of data. You may optionally click a number to shade it out.
The complete frequency table is
Interval Tally Frequency
0 - 1 ||||| 5
2 - 3 0
4 - 5 |||| 4
6 - 7 |||||||| 8
8 - 9 |||||| 6
Completing the frequency table of the set of dataFrom the question, we have the following parameters that can be used in our computation:
The set of data
The tally is used to calculate the frequencies of the readings using marks
So, we have
Interval Tally Frequency
0 - 1 ||||| 5
2 - 3 0
4 - 5 |||| 4
6 - 7 |||||||| 8
8 - 9 |||||| 6
The above represents the complete frequency table
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Pre calculus homework help
Answer:
[tex]f'(\frac{1}{3\sqrt{e}})=\frac{1}{2}[/tex]
Step-by-step explanation:
Find f'(x) using Product Rule
[tex]f(x)=x\ln(3x)\\f'(x)=\ln(3x)+3x(\frac{1}{3x})\\f'(x)=\ln(3x)+1\\\\f'(\frac{1}{3\sqrt{e}})=\ln(3\cdot\frac{1}{3\sqrt{e}})+1\\\\f'(\frac{1}{3\sqrt{e}})=\ln(\frac{1}{\sqrt{e}})+1\\\\f'(\frac{1}{3\sqrt{e}})=\ln(e^{-\frac{1}{2}})+1\\\\f'(\frac{1}{3\sqrt{e}})=-\frac{1}{2}\ln(e)+1\\\\f'(\frac{1}{3\sqrt{e}})=-\frac{1}{2}+1\\\\f'(\frac{1}{3\sqrt{e}})=\frac{1}{2}[/tex]
Answer:
[tex]f'\left(\dfrac{1}{3\sqrt{e}}\right)=\dfrac{1}{2}[/tex]
Step-by-step explanation:
Given function:
[tex]f(x)=x\ln(3x)[/tex]
To find f'(x), differentiate the given function using the product rule.
[tex]\boxed{\begin{minipage}{5.5 cm}\underline{Product Rule for Differentiation}\\\\If $y=uv$ then:\\\\$\dfrac{\text{d}y}{\text{d}x}=u\dfrac{\text{d}v}{\text{d}x}+v\dfrac{\text{d}u}{\text{d}x}$\\\end{minipage}}[/tex]
[tex]\textsf{Let\;$u=x^2}[/tex][tex]\textsf{Let\;$u=x$}\implies \dfrac{\text{d}u}{\text{d}x}=1[/tex]
[tex]\textsf{Let\;$v=\ln(3x)$}\implies \dfrac{\text{d}v}{\text{d}x}=\dfrac{1}{3x}\cdot 3=\dfrac{1}{x}[/tex]
Input the values into the product rule to differentiate the function:
[tex]\begin{aligned}\dfrac{\text{d}y}{\text{d}x}&=u\dfrac{\text{d}v}{\text{d}x}+v\dfrac{\text{d}u}{\text{d}x}\\\\&=x \cdot \dfrac{1}{x}+\ln(3x) \cdot 1\\\\&=1+\ln(3x)\end{aligned}[/tex]
To find the value of f'(1/(3√e)), substitute x = 1/(3√e) into the differentiated function:
[tex]\begin{aligned}f'\left(\dfrac{1}{3\sqrt{e}}\right)&=1+\ln\left(3\left(\dfrac{1}{3\sqrt{e}}\right)\right)\\\\&=1+\ln\left(\dfrac{1}{\sqrt{e}}\right)\\\\&=1+\ln e^{-\frac{1}{2}}\\\\&=1-\dfrac{1}{2}\ln e\\\\&=1-\dfrac{1}{2}(1)\\\\&=1-\dfrac{1}{2}\\\\&=\dfrac{1}{2}\end{aligned}[/tex]
[tex]\hrulefill[/tex]
Differentiation rules used:
[tex]\boxed{\begin{minipage}{4 cm}\underline{Differentiating $ax$}\\\\If $y=ax$, then $\dfrac{\text{d}y}{\text{d}x}=a$\\\end{minipage}}[/tex]
[tex]\boxed{\begin{minipage}{6 cm}\underline{Differentiating $\ln(f(x))$}\\\\If $y=\ln(f(x))$, then $\dfrac{\text{d}y}{\text{d}x}=\dfrac{1}{f(x)}\cdot f'(x)$\\\end{minipage}}[/tex]
Expand the function.
f(x) = (3x-4)4
81x4 − 432x³ + [? ]x²
+
-
X +
PLS HELP
The expansion of the function [tex](3x - 4)^4[/tex] simplifies to [tex]81x^4 - 432x^3 + 864x^2 - 768x + 256.[/tex]
To expand the function [tex]f(x) = (3x - 4)^4[/tex], we can use the binomial theorem. According to the binomial theorem, for any real numbers a and b and a positive integer n, the expansion of [tex](a + b)^n[/tex] can be written as:
[tex](a + b)^n = C(n, 0)a^n b^0 + C(n, 1)a^{(n-1)} b^1 + C(n, 2)a^{(n-2)} b^2 + ... + C(n, n-1)a^1 b^{(n-1)} + C(n, n)a^0 b^n[/tex]
where C(n, k) represents the binomial coefficient, which is given by C(n, k) = n! / (k!(n-k)!).
Applying this formula to our function [tex]f(x) = (3x - 4)^4[/tex], we have:
[tex]f(x) = C(4, 0)(3x)^4 (-4)^0 + C(4, 1)(3x)^3 (-4)^1 + C(4, 2)(3x)^2 (-4)^2 + C(4, 3)(3x)^1 (-4)^3 + C(4, 4)(3x)^0 (-4)^4[/tex]
Simplifying each term, we get:
[tex]f(x) = 81x^4 + (-432x^3) + 864x^2 + (-768x) + 256[/tex]
Therefore, the expanded form of the function [tex]f(x) = (3x - 4)^4[/tex] is [tex]81x^4 - 432x^3 + 864x^2 - 768x + 256[/tex].
Note that the coefficient of [tex]x^3[/tex] is -432, the coefficient of [tex]x^2[/tex] is 864, the coefficient of x is -768, and the constant term is 256.
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Note the complete question is
1. sin(2x - 30°) = cos(x - 10°)
2. 4sinx . cosx - 3sin^2x = 0
please help with this, i have an exam tomorrow and i don’t know how to do this
Answer:
1) x = 43.33
2) x = tan⁻¹(4/3) = 53.13
Step-by-step explanation:
1) Formula: cos(A) = sin(90 - A)
sin(2x - 30) = cos(x - 10)
⇒ sin(2x - 30) = sin(90 - (x - 10))
⇒ sin(2x - 30) = sin(90 - x + 10)
⇒ sin(2x - 30) = sin(100 - x)
⇒ 2x - 30 = 100 - x
⇒ 3x = 130
⇒ x = 130/3
x = 43.33
2) 4sinx . cosx - 3sin²x = 0
⇒ 4sinx . cosx = 3sin²x
⇒ 4cosx = 3sinx
⇒ [tex]\frac{4}{3} =\frac{sinx}{cosx}[/tex]
⇒ [tex]tan x = \frac{4}{3}[/tex]
⇒ x = tan⁻¹(4/3)
⇒ x = 53.13
Answer:
[tex]\textsf{1)} \quad x \approx 43.33^{\circ}[/tex]
[tex]\textsf{2)} \quad \boxed{\begin{aligned}x &= \pi n \;\text{radians}\\x&=0.93+\pi n\; \text{radians}\end{aligned}}\quad \boxed{\begin{aligned}x &= 180^{\circ}n\\x&=53.13^{\circ}+180^{\circ} n\; \end{aligned}}[/tex]
Step-by-step explanation:
Question 1Given trigonometric equation:
[tex]\sin(2x - 30^{\circ}) = \cos(x - 10^{\circ})[/tex]
To solve the given trigonometric equation, we can use the following trigonometric identity:
[tex]\boxed{\begin{minipage}{4 cm}\underline{Trigonometric identity} \\\\$\cos (\theta)=\sin(90^{\circ}-\theta)$\\\end{minipage}}[/tex]
Apply the trigonometric identity to the right side of the equation:
[tex]\begin{aligned}\sin(2x - 30^{\circ}) &= \cos(x - 10^{\circ})\\\\&= \sin(90^{\circ}-(x - 10^{\circ}))\\\\&= \sin(90^{\circ}-x +10^{\circ})\\\\&= \sin(100^{\circ}-x)\end{aligned}[/tex]
Since the sine function is equal, we can equate the angles:
[tex]2x - 30^{\circ}=100^{\circ}-x[/tex]
Now simplify and solve for x:
[tex]\begin{aligned}2x - 30^{\circ}&=100^{\circ}-x\\\\2x - 30^{\circ}+x&=100^{\circ}-x+x\\\\3x - 30^{\circ}&=100^{\circ}\\\\3x - 30^{\circ}+30^{\circ}&=100^{\circ}+30^{\circ}\\\\3x&=130^{\circ}\\\\\dfrac{3x}{3}&=\dfrac{130^{\circ}}{3}\\\\x&=\left(\dfrac{130}{3}\right)^{\circ}\\\\x&\approx 43.3^{\circ}\; \sf (nearest\;tenth)\end{aligned}[/tex]
Therefore, the solution to the equation sin(2x - 30°) = cos(x - 10°) is approximately x = 43.33°.
[tex]\hrulefill[/tex]
Question 2Given trigonometric equation:
[tex]4 \sin x \cos x-3\sin^2x=0[/tex]
Factor out the common term sin(x):
[tex]\sin x(4 \cos x-3\sin x)=0[/tex]
According to the zero product property, one of the factors must be equal to zero for the equation to hold.
Set each factor equal to zero and solve for x.
Factor 1
[tex]\sin x=0[/tex]
According to the unit circle, sin(x) = 0 when x = 0 and x = π.
As the sine function is periodic with a period of 2π, the solutions to sin(x) = 0 are:
[tex]x=0+2\pi n, \;\;x=\pi + 2\pi n[/tex]
Therefore, x is any multiple of π, where n is an integer:
[tex]\boxed{x = \pi n}[/tex]
Factor 2
[tex]\begin{aligned}4\cos x - 3 \sin x & = 0\\\\4 \cos x & = 3 \sin x\\\\\dfrac{4}{3}&=\dfrac{\sin x}{\cos x}\\\\\dfrac{4}{3}&=\tan x\\\\\implies x&=\arctan\left(\dfrac{4}{3}\right)\\\\x&=0.92729...\end{aligned}[/tex]
As the tangent function is periodic with a period of π, the solutions are:
[tex]\boxed{x=0.92729...+\pi n}[/tex]
where n is an integer.
Therefore, the solutions to the equation 4sin(x)cos(x) - 3sin²(x) = 0 are:
[tex]\boxed{\begin{aligned}x &= \pi n \;\text{radians}\\x&=0.93+\pi n\; \text{radians}\end{aligned}}[/tex] [tex]\boxed{\begin{aligned}x &= 180^{\circ}n\\x&=53.13^{\circ}+180^{\circ} n\; \end{aligned}}[/tex]
(where n is an integer)
A survey of 100 high school students provided this frequency table on how students get to school. What is the probability that a randomly selected student is a junior who takes the bus?
The probability of selecting a junior who takes the bus is P (Junior who takes the bus) = 12/200 = 0.06Hence, the probability that a randomly selected student is a junior who takes the bus is 0.06 or 6/100.
The given frequency table on how students get to school among the high school students is represented in the below table:Transportation Walk Bike BusDriveTotalGrade 9 11 10 14 15 50Grade 10 10 7 13 20 50Grade 11 8 6 12 24 50Grade 12 5 8 8 29 50 Total 34 31 47 88 200Given data from the above frequency table, we are interested in finding the probability of a randomly selected student being a junior who takes the bus.SolutionWe know that the total number of students is 200, and the total number of junior students is 50. Hence the probability of selecting a junior is P (Junior) = 50/200 = 0.25Similarly, the number of students who take the bus is 47 and the number of junior students who take the bus is 12.
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A couple decides that Sophia will drive the first 3/5 of a trip and Toby the last 2/5.the entire trip is 500 miles long how far will Sophia drive
Sophia will drive a distance of 300 miles.
To find out how far Sophia will drive, we need to calculate 3/5 of the total trip distance of 500 miles.
1: Calculate the distance driven by Sophia
To find the distance driven by Sophia, we need to multiply the total trip distance by the fraction representing the portion she will drive. Sophia will drive the first 3/5 of the trip.
Distance driven by Sophia = (3/5) * 500 miles
2: Simplify the fraction
To calculate the distance, we simplify the fraction 3/5.
Distance driven by Sophia = (3/5) * 500 miles
= (3 * 500) / 5 miles
= 1500 / 5 miles
= 300 miles
Therefore, Sophia will drive a distance of 300 miles.
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Select the correct answer.
Which graph represents the solutions to this equation?
x2 + 8x = -20
(as a graph pls!)
Answer:
Step-by-step explanation:
Find the area of the shape
Hello!
area
= 2*25 + (20 - 2)*(25-8)
= 50cm² + 306cm²
= 356cm²
GEOMETRY 100 POINTS
Find the length of BC
Answer:
x = 16
Step-by-step explanation:
Opposite sides are equal in a parallelogram
AD = BC
5x - 12 = 3x + 20
5x - 3x = 20 + 12
2x = 32
x = 32/2
x = 16
Solve by Factoring:
2x^2 - x - 3 = 0
Answer:
x = 3/2 or x = -1
Step-by-step explanation:
2x² - x - 3 = 0
2*(-3) = -6
Factors of -6:
(-1, 6), (1, -6), (-2, 3), (2, -3)
We need to find a pair that adds up to the co-eff of x which is (-1)
Factors :(2,-3)
2 - 3 = -1
so, 2x² - x - 3 = 0 can be written as:
2x² + 2x - 3x - 3 = 0
⇒ 2x(x + 1) -3(x + 1) = 0
⇒ (2x - 3)(x + 1) = 0
⇒ 2x - 3 = 0 or
x + 1 = 0
⇒ 2x = 3 or x = -1
⇒ x = 3/2 or x = -1
The x and y intercepts for the linear equation x – 2y = -8 is
Answer:
x- intercept = - 8 , y- intercept = 4
Step-by-step explanation:
to find the x- intercept let y = 0 in the equation and solve for x
x - 2(0) = - 8
x - 0 = - 8
x = - 8 ← y- intercept
to find the y- intercept let x = 0 in the equation and solve for y
0 - 2y = - 8
- 2y = - 8 ( divide both sides by - 2 )
y = 4 ← y- intercept
Find the population variance and standard deviation 8,11,15,17,19
The population variance of the data set is 16, and the population standard deviation is 4. These measures give an indication of how spread out the numbers are from the mean.
To find the population variance and standard deviation of a set of numbers, you can follow these steps:
Step 1: Find the mean (average) of the data set. In this case, the data set is 8, 11, 15, 17, and 19. The mean is calculated by summing up all the numbers and dividing by the total count. In this case, the mean is (8 + 11 + 15 + 17 + 19) / 5 = 14.
Step 2: Subtract the mean from each number and square the result. For example, subtracting 14 from 8 gives (-6)^2 = 36.
Step 3: Repeat Step 2 for each number in the data set. The squared differences for the given data set are 36, 9, 1, 9, and 25.
Step 4: Find the sum of all the squared differences. In this case, the sum is 36 + 9 + 1 + 9 + 25 = 80.
Step 5: Divide the sum of squared differences by the total count of numbers to calculate the population variance. The population variance is 80 / 5 = 16.
Step 6: Take the square root of the population variance to find the population standard deviation. The population standard deviation is √16 = 4.
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If P=(-4,-1), find: R y-axis (P)
Answer:
p which is the y axis is -1
explain your answer in steps to the question in the picture.
The calculated ratio of the flowers are
Daises : Roses = 7 : 5Flower : Daises = 12 : 5How to determine the ratio of flowersFrom the question, we have the following parameters that can be used in our computation:
Roses = 5
Flowers = 12
This means that
Daises = 12 - 5
Evaluate
Daises = 7
Next, we have the ratio to be
Daises : Roses = 7 : 5
Also, we have
Flower : Daises = 12 : 5
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