The driver was driving at a speed of about 14 mi/h at the time of the skid. option is C. 14 mi/h
Using the formula s = √(30fd), where f is the coefficient of friction (0.7) and d is the length of the skid marks in feet (9), we can estimate the speed at the time of the skid:
s = √(30 × 0.7 × 9)
s ≈ 14.53 mi/h
Rounding to the nearest mi/h, the driver was driving at approximately 15 mi/h at the time of the skid. However, none of the given options match this result. The closest option is C. 14 mi/h, so I would choose that as the best available answer.
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On the first swing, the length of the arc through which a pendulum swings is 50 inches. the length of each successive
swing is 80% of the preceding swing. determine whether this sequence is arithmetic or geometric. find the length of the
fourth swing
The length of the fourth swing is 25.6 inches. The sequence is arithmetic or geometric.
The length of the arc through which a pendulum swings is 50 inches. To determine whether the sequence is arithmetic or geometric, and to find the length of the fourth swing, we will analyze the given information.
The length of the first swing is 50 inches. Each successive swing is 80% of the preceding swing. This means that to find the length of the next swing, we multiply the length of the current swing by 80% (or 0.8).
Since we are multiplying by a constant factor (0.8) to find the next term in the sequence, this is a geometric sequence, not an arithmetic sequence.
Now, let's find the length of the fourth swing.
1st swing: 50 inches
2nd swing: 50 * 0.8 = 40 inches
3rd swing: 40 * 0.8 = 32 inches
4th swing: 32 * 0.8 = 25.6 inches
The length of the fourth swing is 25.6 inches.
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John earns $8. 50 per hour proofreading advertisements at a local newspaper. Write a function in function notation. Use d as your variable to represent days
The function notation is E(h) = 8.5h where h represents the number of hours worked so the domain is {0, 1, 2, 3, 4, 5} and the range is {0, 8.5, 17, 25.5, 34, 42.5}.
Let E(t) be John's earnings in dollars after working t hours, where t is in the domain 0 ≤ t ≤ 5. Then E(t) = 8.50t, since John earns $8.50 per hour proofreading ads.
The domain of the function is 0 ≤ t ≤ 5, since John works no more than 5 hours per day.
The range of the function is 0 ≤ E(t) ≤ 42.50 since John earns $8.50 per hour and works no more than 5 hours per day.
Therefore, the maximum earnings he can make in one day is 5 hours multiplied by $8.50 per hour, which equals $42.50.
The minimum earnings are $0, which would occur if John does not work at all.
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The question is -
John can earn $8.50 per hour proofreading adverse at a local newspaper. He works no more than 5 hours a day. Write a function in function notation and find a reasonable domain and range of his earnings.
-8
Find the distance, d, of AB.
A = (-7, -7) B = (-3,-1)
-6 -4
A
-2
B -2
-4
-6
-8
d = √x2-x1² + y2 - Y₁|²
d = [?]
Round to the nearest tenth.
Distance
Step-by-step explanation:
Using the distance formula:
d = √[(x2 - x1)² + (y2 - y1)²]
where A = (x1, y1) and B = (x2, y2), we can find the distance between points A and B as follows:
d = √[(-3 - (-7))² + (-1 - (-7))²]
d = √[4² + 6²]
d = √52
d ≈ 7.2
Therefore, the distance between points A and B is approximately 7.2 units, rounded to the nearest tenth.
Olympiads School Calculus Class 9 Test 1 -. Find the equation(s) of the tangent line(s) to the curve defined by x² + x²y2 + y = 1 when = -1. (4 marks) . Find the intervals of concavity and any point(s) of inflection for f(x) = x? In x. (4 marks)
The equation of the tangent line to the curve x² + x²y² + y = 1 at the point where x=-1 is (-dx/dy + 2)/(1 - √5)(x + 1). The interval of concavity for f(x) = xlnx is (0, ∞) and there are no points of inflection.
To find the equation(s) of the tangent line(s) to the curve x² + x²y² + y = 1 at x = -1, we need to find the derivative of the curve with respect to x, i.e.,
2x + 2xy²(dx/dy) + dy/dx = 0
At x = -1, we get
-2 + 2y²(dy/dx) + dx/dy = 0
dy/dx = (-dx/dy + 2)/(2y²)
Now, substituting x = -1 in the curve, we get
1 - y + y² = 0
Solving for y, we get
y = (1 ± √5)/2
Substituting y = (1 + √5)/2 in the equation for dy/dx, we get
dy/dx = (-dx/dy + 2)/(2(1 + √5)/4) = (-dx/dy + 2)/(√5 + 1)
Therefore, the equation of the tangent line to the curve at x = -1, y = (1 + √5)/2 is
y - (1 + √5)/2 = (-dx/dy + 2)/(√5 + 1)(x + 1)
Similarly, substituting y = (1 - √5)/2 in the equation for dy/dx, we get
dy/dx = (-dx/dy + 2)/(1 - √5)
Therefore, the equation of the tangent line to the curve at x = -1, y = (1 - √5)/2 is
y - (1 - √5)/2 = (-dx/dy + 2)/(1 - √5)(x + 1)
To find the intervals of concavity and any point(s) of inflection for f(x) = xlnx, we need to find the second derivative of the function with respect to x, i.e.,
f''(x) = (d²/dx²)(xlnx) = d/dx(lnx + 1) = 1/x
Now, to find the intervals of concavity, we need to find the values of x for which f''(x) > 0 and f''(x) < 0. We have
f''(x) > 0 when x > 0, which means the function is concave up on (0, ∞).
f''(x) < 0 when x < 0, which means the function is concave down on (0, ∞).
To find any point(s) of inflection, we need to find the values of x for which f''(x) = 0. However, in this case, f''(x) is never equal to zero. Therefore, there are no points of inflection for the function f(x) = xlnx.
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Line x is parallel to line y. Line z intersect lines x and y. Determine whether each statement is Always True.
Line x is perpendicular to line y. Line z crosses lines x and y. Only statements 3 and 4 are true.
∠6 = ∠8 is not true because they both lie on the same plane and makes an angle of 180° and can never be true. ∠6 = ∠1 is also not true because ∠1 is clearly obtuse angle and ∠6 is clearly acute angle so they cannot be equal. Hence, statement a and b are false.
∠7 = ∠3 is always true because they are corresponding angles and corresponding angles are always equal. m∠2 + m∠4 = 180° is also true because they lie on same plane and have common vertex and hence, they are supplementary angles and make a sum of 180°. Hence, statement 3 and 4 is always true.
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There are four spaces each so you can put either parentasis or brakets
In the given function the domain is [-1, ∞]
Range is [-3, ∞]
The interval when function is positive [0, ∞]
The domain of a function is the set of values that we are allowed to plug into our function.
This set is the x values in a function such as f(x).
The range of a function is the set of values that the function assumes
In the given function the domain is [-1, ∞]
Range is [-3, ∞]
The interval when function is positive [0, ∞]
The interval when function is negative [-∞, -1]
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Write a function to model the volume of a rectangular prism if the length is 26cm and the sum of the width and height is 32cm. what is the maximum possible volume of the prism?
To model the volume of a rectangular prism with length 26cm and width w and height h such that the sum of the width and height is 32cm, we can use the following function:
V(w, h) = 26wh
subject to the constraint:
w + h = 32
We can solve for one of the variables in the constraint equation and substitute it into the volume equation, giving us:
w + h = 32 => h = 32 - w
V(w) = 26w(32 - w) = 832w - 26w^2
To find the maximum possible volume, we can take the derivative of this function with respect to w and set it equal to zero
dv/dw= 832 - 52w = 0
Solving for w, we get:
w = 16
Substituting this value back into the constraint equation, we get:
h = 32 - w = 16
Therefore, the maximum possible volume of the prism is:
V(16, 16) = 26(16)(16) = 6656 cubic cm
So the function to model the volume of the rectangular prism is V(w) = 832w - 26w^2, and the maximum possible volume is 6656 cubic cm when the width and height are both 16cm.
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x+2y=6
-7x+3y=-8 (using substitution)
Answer:
point form - (2,2)
x=2 y=2
4. A person wants to buy a car from Toyota Company. If the price of car
including VAT is Birr 5,000,000 then,
a) What is the price of car before VAT?
b) What is the value of VAT?
Answer:
Step-by-step explanation:a) To find the price of the car before VAT, we need to first calculate the percentage of VAT included in the price:
VAT% = (VAT / Total Price) x 100
where VAT% is the percentage of VAT, VAT is the value of VAT, and Total Price is the price of the car including VAT.
From the given information, we have:
Total Price = Birr 5,000,000
VAT% = 15% (assuming a VAT rate of 15% in Ethiopia)
Therefore, we can solve for the value of the car before VAT as follows:
Total Price = Car Price + VAT
Birr 5,000,000 = Car Price + 0.15Car Price
Birr 5,000,000 = 1.15Car Price
Car Price = Birr 4,347,826.09
So the price of the car before VAT is Birr 4,347,826.09.
b) To find the value of VAT, we can use the same formula as above and solve for VAT:
Total Price = Car Price + VAT
Birr 5,000,000 = Birr 4,347,826.09 + VAT
VAT = Birr 652,173.91
Therefore, the value of VAT is Birr 652,173.91.
58 of a birthday cake was left over from a party. the next day, it is shared among 7 people. how big a piece of the original cake did each person get?
If 58% of the birthday cake was left over from the party, then 42% of the cake was consumed during the party. That's why, each person would get approximately 8.29% of the original cake as a leftover piece the next day.
Let's assume that the original cake was divided equally among the guests during the party.
So, if 42% of the cake was shared among the guests during the party, and there were 7 people in total, each person would have received 6% of the cake during the party.
Now, the leftover 58% of the cake is shared among the 7 people the next day. To find out how big a piece of the original cake each person gets, we need to divide 58% by 7:
58% / 7 = 8.29%
Therefore, each person would get approximately 8.29% of the original cake as a leftover piece the next day.
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Answer the following questions for the function f(x) = x Sqrt (x^2 + 4) defined on the interval - 5 ≤ x ≤ 5. f(x) is concave down on the interval x = to x =
f(x) is concave up on the interval x = to x = The inflection point for this function is at x = The minimum for this function occurs at x = The maximum for this function occurs at x =
The function f(x) = x Sqrt (x^2 + 4) is concave down on the entire interval. The inflection point is at x is equal to 0. There is no minimum or maximum in the interval.
To find the concavity, we need to find the second derivative
f(x) = x√(x^2+4)
f'(x) = √(x^2+4) + x^2/√(x^2+4)
f''(x) = -4x^3/(x^2+4)^(3/2)
The second derivative is negative for all x, which means the function is concave down on the entire interval.
To find the inflection point, we need to solve
f''(x) = 0
-4x^3/(x^2+4)^(3/2) = 0
This is true only when x = 0. Therefore, the inflection point is at x = 0.
To find the minimum and maximum, we need to find the critical points. The critical points are found by setting the first derivative equal to zero
f'(x) = √(x^2+4) + x^2/√(x^2+4) = 0
Multiplying both sides by √(x^2+4), we get
x^2+4 + x^2 = 0
2x^2 = -4
x^2 = -2
This equation has no real solutions, which means there are no critical points in the interval. Therefore, there is no minimum or maximum in the interval.
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5+x =n what must be true about any value of x if n is a negaitive number
Therefore , the solution of the given problem of equation comes out to be x must be less than -5 for any value of x that causes 5 + x = n to be a negative number.
What is an equation?In order to demonstrate consistency between two opposing statements, variable words are frequently used in sophisticated algorithms. Equations are academic phrases that are used to demonstrate the equality of different academic figures. Consider expression the details as y + 7 offers. In this case, elevating produces b + 7 when partnered with building y + 7.
Here,
If n is a negative number and 5 + x = n, then x must be less than -5.
This is due to the fact that n would be greater than or equal to 5, which is not a negative number, if x were greater than or equal to -5, which would lead 5 + x to be greater than or equal to 0.
However,
if x is less than -5, then 5 + x will be less than 0, and n will be a negative number because n will be less than 5.
Therefore, x must be less than -5 for any value of x that causes 5 + x = n to be a negative number.
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Which of the following is equivalent to [tex]\sqrt{x} 12qr^{2}[/tex]
The calculated value of the expression that is equivalent to √(x¹²qr²) is x⁶r√q
Calculating the expression that is equivalent to √(x¹²qr²)From the question, we have the following parameters that can be used in our computation:
√x12qr²
Express properly
So, we have
√(x¹²qr²)
Evaluating the expression in the brackets using the law of indices
So, we have
√(x¹²qr²) = x⁶r√(q)
Next, we open the brackets
This gives
√(x¹²qr²) = x⁶r√q
Hence, the expression that is equivalent to √(x¹²qr²) is x⁶r√q
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How do I find the answer to this problem The period of y = sin3 is _____
The period of the function y = sin(3x) is (2π/3).
I assume you meant to write "y = sin(3x)".
The period of the function y = sin(3x) can be found using the formula:
period = 2π / b
where "b" is the coefficient of x in the function.
In this case, b = 3, so:
period = 2π / 3
Therefore, the period of the function y = sin(3x) is (2π/3).
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Mollie drew mol and ted drew ted. they measured a few parts of their triangles
and found that ml = td, ol = ed, and l = d. what postulate can mollie and ted
use to justify why their triangles must be congruenta
Mollie and Ted can use the Side-Side-Side (SSS) postulate to justify why their triangles must be congruent.
According to the given information, the two triangles share three corresponding sides of equal length: ML = TD, OL = ED, and L = D.
The SSS postulate states that if three corresponding sides of two triangles are congruent, then the triangles are congruent. Therefore, because Mollie's triangle and Ted's triangle share three corresponding sides of equal length, they are congruent by the SSS postulate.
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PLEASE HELP (40 POINTS)
The coordinates of the points N and L are N = (-2d, 0) and L = (-4f, g)
Calculating the coordinates of N and LFrom the question, we have the following parameters that can be used in our computation:
M = (-2d - 4f, g)
O = (0, 0)
ON = 2d
Given that
ON = 2d
Then it means that
N = (-2d, 0)
For the point L, we have
LO = MN
Where
LO = √[(x - 0)² + (y - 0)²] i.e. the distance formula
LO = √[x² + y²]
Next, we have
MN = √[(-2d - 4f + 2d)² + (g - 0)²] i.e. the distance formula
MN = √[(-4f)² + g²]
So, we have
LO = MN
√[x² + y²] = √[(-4f)² + g²]
By comparison, we have
x = -4f and y = g
This means that the coordinates of point L = (-4f, g)
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50 PONTS ASAP Triangle LMN has vertices at L(−1, 4), M(−1, 0), and N(−3, 4) Determine the vertices of image L′M′N′ if the preimage is rotated 90° clockwise about the origin.
L′(4, 1), M′(0, 1), N′(4, 3)
L′(−1, −4), M′(−1, 0), N′(−3, −4)
L′(−4, −1), M′(0, −1), N′(−4, −3)
L′(1, −4), M′(1, 0), N′(3, −4)
The coordinates of the resulting triangle are L'(4, 1), M'(0, 1), and N'(4, 3)
What are the coordinates of the resulting triangle?From the question, we have the following parameters that can be used in our computation:
Triangle LMN has vertices at L(−1, 4), M(−1, 0), and N(−3, 4
This means that
L(−1, 4), M(−1, 0), and N(−3, 4Rotation rule = 90° clockwise around the origin.The rotation rule of 90° clockwise around the origin is
(x,y) becomes (y,-x)
So, we have
Image = (y, -x)
Substitute the known values in the above equation, so, we have the following representation
L'(4, 1), M'(0, 1), and N'(4, 3)
Hence, the coordinates of the resulting points, are L'(4, 1), M'(0, 1), and N'(4, 3)
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Out of 300 people sampled, 33 received flu vaccinations this year. Based on this, construct a 95% confidence interval for the true population proportion of people who received flu vaccinations this year. Give your answers as decimals, to three places < p <
A 95% confidence interval for the true population proportion of people who received flu vaccinations this year is 0.067 < p < 0.133.
To construct a 95% confidence interval for the true population proportion of people who received flu vaccinations, we can use the formula:
CI = p ± z√((p(1-p))/n)
where:
CI is the confidence interval
p is the sample proportion (33/300 = 0.11)
z is the z-score associated with a 95% confidence level, which is approximately 1.96
n is the sample size (300)
Substituting the values, we get:
CI = 0.11 ± 1.96√((0.11(1-0.11))/300)
CI = 0.11 ± 0.043
CI = (0.067, 0.133)
Therefore, the 95% confidence interval for the true population proportion of people who received flu vaccinations is 0.067 < p < 0.133.
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You can use indirect measurement to estimate the height of a building. First, measure your distance from the base of the building and the distance from the ground to a point on the building that you are looking at. Maintaining the same angle of sight, move back until the top of the building is in your line of sight. Answer both A and B
The building is perfectly vertical and the observer is at a consistent height above the ground.
A) Explain how the method of indirect measurement can be used to estimate the height of a building?The method of indirect measurement can be used to estimate the height of a building by using similar triangles and the principles of proportionality. First, the distance from the base of the building to the observer and the distance from the ground to a known point on the building are measured. By maintaining the same angle of sight, the observer can move back until the top of the building is in their line of sight. At this point, a second pair of measurements is taken: the distance from the new location to the base of the building and the height of the visible portion of the building from the ground. By using the principles of proportionality between similar triangles, the height of the entire building can be estimated.
Specifically, the ratio of the height of the known point on the building to the distance from the observer to that point can be set equal to the ratio of the height of the entire building to the distance from the observer to the base of the building. This proportion can be solved algebraically to find the estimated height of the entire building.
B) What are some potential sources of error or inaccuracy in this method of estimation?
There are several potential sources of error or inaccuracy in this method of estimation. One major source of error is the assumption that the two triangles being compared are similar. If the angle of sight is not maintained exactly or if the ground is not perfectly level, the triangles may not be similar and the estimated height may be incorrect.
Additionally, the accuracy of the estimated height depends on the accuracy of the distance measurements. If the distances are not measured precisely, the estimated height will be proportionally less accurate.
Finally, this method assumes that the building is perfectly vertical and that the observer is at a consistent height above the ground. If the building is not perfectly vertical or the observer's height above the ground changes, this can also affect the accuracy of the estimated height.
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Find the measure of the question marked arc (view photo )
The arc angle indicated with ? is derived as 230° using the angle between intersecting tangents.
What is an angle between intersecting tangentsThe angle between two tangent lines which intersect at a point is 180 degrees minus the measure of the arc between the two points of tangency.
angle G = 180° - arc angle HF
arc angle HF = 180° - 50°
arc angle HF = 130°
so the arc angle indicated with ? is;
? = 360° - 130°
? = 230°
Therefore, using the angle between the intersecting tangents, the arc angle indicated with ? is 230°.
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Question 4 < > Evaluate ſtan® z sec"" zdz +C
To evaluate ſtan® z sec"" zdz +C, we can use integration by substitution. Let u = sec z, then du/dz = sec z tan z dz.
Using the identity 1 + tan^2 z = sec^2 z, we can rewrite the integral as:
∫ tan z (1 + tan^2 z) du
Simplifying this expression, we get:
∫ u^3 du
Integrating u^3 with respect to u, we get:
(u^4 / 4) + C
Substituting back u = sec z, we get:
(sec^4 z / 4) + C
Therefore, the solution to the integral ſtan® z sec"" zdz +C is (sec^4 z / 4) + C.
It seems like you are looking for the evaluation of an integral involving trigonometric functions. Your integral appears to be:
∫tan^n(z) * sec^m(z) dz + C
To solve this integral, we need the values of n and m. Please provide these values, and I'll be glad to assist you further in evaluating the integral.
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8 Real / Modelling An advertising company uses a graph of this
equation to work out the cost of making an advert:
y=10+0.5x
where x is the number of words and y is the total cost of the bill in
pounds.
a)Where does the line intercept the y-axis?
b)How much is the bill when there are no words in the advert?
c)What is the gradient of the line?
d)How much does each word cost?
The gradient in the given equation is 0.5.
The given linear equation is y=10+0.5x where x is the number of words and y is the total cost of the bill in pounds.
a) When x=0, we get y=10
So, at (0, 10) the line intercept the y-axis.
b) $10 is the bill when there are no words in the advert.
c) Compare y=0.5x+10 with y=mx+c, we get m=0.5
So, the gradient of the line is 0.5
d) From equation, we can see the cost of each word is $0.5.
Therefore, the gradient in the given equation is 0.5.
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Evaluate the definite integral
∫ (t^5 - 2t^2)/t^4 dt
To evaluate the definite integral of the given function, ∫ (t^5 - 2t^2)/t^4 dt, follow these steps:
1. Simplify the integrand: Divide each term by t^4.
(t^5/t^4) - (2t^2/t^4) = t - 2t^(-2)
2. Integrate each term with respect to t.
∫(t dt) - ∫(2t^(-2) dt) = (1/2)t^2 + 2∫(t^(-2) dt)
3. Apply the power rule to the remaining integral.
(1/2)t^2 + 2(∫t^(-2+1) dt) = (1/2)t^2 + 2(∫t^(-1) dt)
4. Integrate t^(-1) with respect to t.
(1/2)t^2 + 2(ln|t|)
Now, since we need to evaluate the definite integral, we should have the limits of integration. Let's assume the limits of integration are a and b. Then, apply the Fundamental Theorem of Calculus:
[(1/2)b^2 + 2(ln|b|)] - [(1/2)a^2 + 2(ln|a|)]
This expression gives the value of the definite integral for the given function within the limits a and b.
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A person was driving their car on an interstate highway
and a rock was kicked up and cracked their windshield
on the passenger side.
The driver wondered if the rock was equally likely to
strike any where on the windshield, what the probability
was that it would have cracked the windshield in his line
of site on the windshield. Determine this probability,
provided that the windshield is a rectangle with the
dimensions 28 inches by 54 inches and his line of site
through the windshield is a rectangle with the
dimensions 30 inches
by 24 inches.
a) 0. 373
b) 0. 139
c) 0. 423
d) 0. 476
There is about a 47.62% or 0.476 chance that the rock hit the windshield in the driver's line of sight. Option D.
To determine the probability that the rock hit the driver's line of sight on the windshield, we need to compare the area of the driver's line of sight rectangle to the total area of the windshield rectangle.
The area of the windshield rectangle is:
A1 = 28 in x 54 in = 1512 sq in
The area of the driver's line of sight rectangle is:
A2 = 30 in x 24 in = 720 sq in
Therefore, the probability that the rock hit the driver's line of sight on the windshield is:
[tex]P= \frac{A2}{A1}= \frac{720 \:sq in}{1512 \:sq in }[/tex] = 0.476 or 47.6%
So, there is about a 47.62% chance that the rock hit the windshield in the driver's line of sight.
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Determine whether the two figures are similar. If so, give the similarity ratio of the smaller figure to the larger figure. The figures are not drawn to scale.
*
Captionless Image
Yes; 3:5
Yes; 2:3
Yes; 2:5
No they are not similar
Determine whether the two figures are similar: D. No, the two figures are not similar.
What are the properties of quadrilaterals?In Geometry, two (2) quadrilaterals are similar when the ratio of their corresponding sides are equal in magnitude and their corresponding angles are congruent.
Additionally, two (2) geometric figures such as quadrilaterals are considered to be congruent only when their corresponding side lengths are congruent (proportional) and the magnitude of their angles are congruent;
Ratio = 12/8 = 10/6 = 10/6
Ratio = 3/2 ≠ 5/3 = 5/3
In conclusion, the two figures are not similar because the ratio of their corresponding sides is not proportional.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
PLS HLEP AND SHOW WORK I WILL MATK BRAINLYEST
Answer:
38. (A) True
39. (B) False
Step-by-step explanation:
The set of people working in the summer consists of both female an male since there is no determiner to show that the 80% of students are a specific gender. Therefore, the answer to the first question is True (A).
My expression for finding the probability of being female and working part time in summer only is:
[tex]\frac{84}{100} \\\\ \\ \\ \\[/tex][tex](\frac{1}{2} *\frac{80}{100})\\[/tex][tex]=\frac{42}{125}[/tex] which is also equal to 0.336. Therefore the second question is false.
Please forgive me if I'm wrong but I'm open to any correction or criticisms.
A regular size chocolate bar was 5 4/9 inches long. if the king size bar is 3 2/5 inches longer, what is the length of the king size bar?
please help me!!!!
Answer:
8 38/48
Step-by-step explanation:
HELP!!!
Find the Area of a Rectengle with the base of 3x+1 in and a height of 2x-3 in.
A.5x^2-2 in^2
B.6x^2+7x-2 in^2
C.10x-4 in
D.6x^2-7x-3 in^2
The area of a rectangle with base of 3x+1 in and a height of 2x-3 in is given as follows:
D. A = 6x² - 7x - 3 in².
How to obtain the area of a rectangle?The area of a rectangle of length l and width w is given by the multiplication of dimensions, as follows:
A = lw.
The dimensions for this problem are given as follows:
w = 3x + 1.l = 2x - 3.Hence the expression for the area of the rectangle is given as follows:
A = (3x + 1)(2x - 3)
A = 6x² - 9x + 2x - 3
A = 6x² - 7x - 3 in².
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using mad when do you see a moderate amount of overlap in these two graphs when the mad is $20
Lower Bound: 20 - 29.67 ≈ -9.67
Upper Bound: 20 + 29.67 ≈ 49.67.
How to solveThe conversion of MAD to the standard deviation for normal distributions can be obtained using the given relationship:
Standard Deviation (σ) = MAD / 0.6745
For both distributions, the MAD holds a value of $20, thus arriving at σ ≈ 29.67.
There are two normal distributions now defined by their parameters as follows:
Mean (µ1) = $100 and Standard Deviation (σ1) = 29.67
Mean (µ2) = $120 and Standard Deviation (σ2) = 29.67.
Since both distributions share an equivalent standard deviation, we can perform a comparison of means to determine the overlap between them.
4
Typically there is observed moderate overlapping within one standard deviation from the difference in means.
The calculation of the difference in means indicates µ2 - µ1 = 120 - 100 = 20. Taking one standard deviation (which equates to 29.67) into consideration with respect to the difference of the means leads us to this range:
Lower Bound: 20 - 29.67 ≈ -9.67
Upper Bound: 20 + 29.67 ≈ 49.67.
It's noteworthy that negative values would not make sense within this context leading us to assume that the approximate overlap range is situated between $0 and $50 resulting in these normal distributions manifesting a sensible amount of overlap therein.
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The Complete Question
When comparing two normal distribution graphs with a mean of $100 and $120 respectively, and both having a MAD of $20, at what range do you see a moderate amount of overlap between the two distributions?
if ab|| cd and m22 is increased by 20 degrees, how must m23 be changed to keep the segments parallel?
a. m23 would stay the same.
b. m23 would increase by 20 degrees.
c. m23 would decrease by 20 degrees.
d. the answer cannot be determined.
The correct answer is (b) m23 would increase by 20 degrees.
If lines AB and CD are parallel and we increase the measure of angle 2 by 20 degrees, we need to determine how the measure of angle 3 must change to keep the segments parallel.
Since lines AB and CD are parallel, we know that angles 2 and 3 are alternate interior angles and are congruent. So, if we increase the measure of angle 2 by 20 degrees, the measure of angle 3 must also increase by 20 degrees to maintain the parallelism.
We can prove this by using the converse of the Alternate Interior Angles Theorem, which states that if two lines are cut by a transversal so that a pair of alternate interior angles are congruent, then the lines are parallel.
Since angles 2 and 3 are congruent, we can apply this theorem to conclude that lines AB and CD are parallel. Now, if we increase the measure of angle 2 by 20 degrees, angle 2 will become larger than angle 3. Therefore, to keep lines AB and CD parallel, we must also increase the measure of angle 3 by 20 degrees to maintain their congruence.
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