Triangle ABC in quadrant 4 and polygon A' B' C' in quadrant 3 should be rotated 90 degrees clockwise in both directions.
In geometry, a transformation is a process that changes the position, scale, or orientation of a shape. Common transformations include translations, rotations, reflections, and dilations.
Transformations known as rotations involve turning a shape around a central fixed point known as the centre of rotation. The amount of rotation in degrees is determined by the angle of rotation, which can be either clockwise or anticlockwise.
The position of A' in relation to A denotes a clockwise rotation.
A clockwise rotation is further indicated by the fact that B' is situated beneath B.
The fact that C' is positioned to the right of C suggests that the rotation is also clockwise.
Since all of the relevant vertices of polygon A' B' C' are turned clockwise in relation to triangle ABC,
Therefore, the right answer is a 90° clockwise rotation.
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F(x) = x squared + 2 and g(x) = x + 14
find the value of "a" if F(a) = g(a)
Answer:
Step-by-step explanation:
Find the probability of exactly four
successes in six trials of a binomial
experiment in which the probability of
success is 40%.
P = [? ]%
Round to the nearest tenth of a percent
The probability of exactly four successes in six trials of a binomial experiment is given by P ( A ) = 9.2 %
Given data ,
The formula for Binomial Distribution is given by
P ( x ) = [ n! / ( n - x )! x! ] pˣqⁿ⁻ˣ
In this case, we want to find P(X=4), the probability of exactly four successes in six trials
On simplifying , we get
n = 6
k = 4
p = 0.40
P(X=4) = C(6, 4) x 0.40⁴ * (1-0.40)⁽⁶⁻⁴⁾
P(X=4) = 15 x 0.40⁴ x 0.60²
P(X=4) ≈ 9.2 %
In a binomial experiment with six trials and a success rate of 40%, the probability of exactly four successes, rounded to the closest tenth of a percent, is roughly 9.2%.
Hence , the probability is 9.2 %
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Answer: 13.82%
Step-by-Step Explanation:
The arithmetic mean of the monthly salaries of two people is $4360. One person earns $3479 per month. What is the monthly salary of the other person?
If arithmetic mean of the monthly salaries of two people is $4360. One person earns $3479 per month then the monthly salary of the other person is $5241
The arithmetic mean of the monthly salaries of two people is $4360
One person earns $3479 per month
We have to find the monthly salary of the other person
Arithmetic mean = a+b/2
4360 = 3479+b/2
4360×2 = 3479+b
8720 = 3479+b
Subtract 3479 from both sides
8720-3479 =b
$5241 =b
Hence, $5241 is the monthly salary of the other person.
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which exspreshion is equivelent to -3(2x-8)+4x
a -2x-8
b -2x+24
c -10x-8
d -10x+24
-2x+24 is equivalent to expression -3(2x-8)+4x.
Option B is the correct answer.
We have,
First, simplify the expression inside the parentheses:
-3(2x-8) = -6x + 24
Then substitute this into the original expression:
-3(2x-8)+4x = -6x + 24 + 4x = -2x + 24
Therefore,
The equivalent expression is -2x+24.
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un college de 620 eleves compte 372eleves demi pensionnaires Quel est le pourcentage d'eleves demi pensionnaires de ce college?
merciiii d'avance
Answer: Percentage of half board students in college is 60%
Step-by-step explanation:
We know that percentage of desired quantity is:
n% = ( number of desired quantity / total number of quantity ) * 100
n% = ( n / N ) * 100 .......... (i)
where n% = percentage of desired quantity.
N = total number of quantity.
n = number of desired quantity.
Now, as per the question:
Half board students in college = 372
Total students in college = 620
percentage of Half board students in college = (372/620) * 100
n% = (372/620)*100
n% = 60%
Therefore, at 372 half board students in college , percentage of half board students in college is 60%.
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A parabolic archway is 25 meters high at the vertex. At a height of 23 meters, the width of the archway is 12 meters, as shown in the figure.
The width of the archway at ground level, given the height can be found to be 42.42 meters.
How to find the width ?To find the width of the parabolic archway at ground level, the formula is:
y = a ( x - h ) ² + k
The height given is 23 meters and the width is 12 meters so the value of a can be found to be :
23 = a ( 6 - 0 ) ² + 25
23 = a ( 6 ) ² + 25
-2 = 36 a
a = -1 /18
We can then find the width of the archway at ground level:
0 = ( -1 /18 )( x ²) + 25
x ² = 450
x = ± √ 450
The width of the archway at ground level is:
= 2 x √ 450
= 2 x 21. 21
= 42.42 meters
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Spring break homework due tonight!! Please help!!
The names of the angles, vertices and sides are listed below
Naming the vertex and the sides of the anglesThe vertex is the point where two sides meet; and at this vertex, an angle is formed
Using the above definition as a guide, we have
Vertex: D; Sides: CD and DEVertex: R; Sides: QR and RSVertex: P; Sides: OP and PQVertex: J; Sides: MJ and JKNaming the angles in four waysThe names of the angles in four ways are
∠EFG, ∠GFE, ∠F and ∠S∠RST, ∠TSR, ∠S and ∠J∠GHJ , ∠JHG, ∠H and ∠S∠MNO, ∠ONM, ∠N and ∠SNaming the angles with the vertex VUsing the definition of vertex above, the names of the angles are
∠KVL and ∠JVK∠CVD, ∠DVE, and ∠EVF∠QVR and ∠RVS∠OVP, ∠PVQ and ∠QVRRead more about angles at
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ANSWER PLS Sketch the graph of 2x^(2)-3x-9=y using your graphing calculator.
What are the x-intercepts of this graph?
a.-3, -3/2
b.-3, 3/2
c. 3, 3/23
d. 3, -3/2
The x-intercepts of the given quadratic function are: d: 3, -3/2
How to draw the graph of a quadratic function?The general form of expression of a quadratic function is:
y = ax² + bx + c
The formula to find the roots of quadratic functions is:
x = [-b ± √(b² - 4ac)]/2a
We are given the quadratic equation as:
y = 2x² - 3x - 9
Thus:
x = [-(-3) ± √((-3)² - 4(2 * -9))]/2(2)
x = (3 ± 9)/4
x = 3, -3/2
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use to potagreom thyreom to finmd 13 squared, 6, 7
Answer:
Step-by-step explanation:
On a certain hot summer's day, 574 people used the public swimming pool. The daily prices are $1.75 for children and $2.25 for adults. The receipts for admission totaled $1180.00. How many children and how many adults swam at the public pool that day?
Answer:
Let c be the number of children and a be the number of adults.
1.75c + 2.25a = 1,180->1.75c + 2.25a = 1,180
c + a = 574->1.75c + 1.75a = 1,004.5
-------------------------------
.5a = 175.5
a = 351, so c = 223
So there were 351 adults and 223 children that day.
Surface area of the composite solid
The area of the composite solid is 602.88m²
What are composite solids?A composite solid is a solid that is composed, or made up of, two or more solids.
The solid consist of two cones. one big and one small cone
Area of a cone can be expressed as;
A = πr² + πrl
A = πr(r+l)
For the Big cone
A = πr(r+l)
A = 3.14 × 8 ( 8+10)
A = 25.12 × 18
A = 452.16m²
Area of the small cone
A = 3.14 × 4( 4 + 8)
A = 12.56 × 12
A = 150.72m²
Therefore the area of the composite solid
= 452.16 + 150.72
= 602.88 m²
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A rectangle has a perimeter of 45 ft. The length and width are scaled by a factor of 1.5. What is the perimeter of the resulting rectangle?
Answer:
67.5
Step-by-step explanation:
The perimeter of the resulting rectangle is 67.5 ft
What is the perimeter of the resulting rectangle?
Given that
Perimeter = 45 ft
Scale factor = 1.5
So, we have
Resulting perimeter = 45 * 1.5
Evaluate
Resulting perimeter = 67.5
What is the area of this figure?
The area is the sum of the individual areas
The figure can be divided into two trapezoids
Using the above and the area formulas as a guide, we have the following:
Area = 1/2 * (3 + 5) * 2 + 1/2 * (3 + 7) * 4
Evaluate
Area = 28
Hence, the area is 28 sq units
answer this question.
Using the sine function with the given angle C and hypotenuse, we find that the length of the side x is approximately 16.23 units.
We can use the trigonometric ratios of the right triangle to find the length of the side x. Since we know the angle C and the hypotenuse, we can use the sine function, which relates the opposite side to the hypotenuse
sin(C) = opposite / hypotenuse
sin(37°) = x / 27
Multiplying both sides by 27, we get
x = 27 sin(37°)
Using a calculator, we find that
x ≈ 16.23
Therefore, the length of the side x is approximately 16.23 units.
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a bike lock has a 4 digit combination. each character can be any digit between 1-9. the only restriction is that all 4 characters cannot be the same (e.g. 1111, 2222, 3333... etc.). how many combinations are possible?
The possible combination is 6552.
For each of the 4 numbers in the combination, there are 9 digits to pick from, making the following total number of possibilities entirely possible:
9 x 9 x 9 x 9 = 6561
The number of possibilities with identical values for all four digits must be subtracted, nevertheless.
There is only one combination for each of the nine possible ways to select the digit that will occur four times (1, 2, 3, 4, 5, 6, 7, 8, or 9).
Therefore, the total number of possible combinations with the given restriction is:
6561 - 9 = 6552.
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Jacob works three days per week for Mr Nkosi at his playschool for pre-school
children. Jacob is paid R200 per day. Mr Nkosi paid R624 to the UIF for one year
in advance, regarding his employee Jacob.
a) What is Jacob's gross salary per year?
b) What percentage is R624 of Jacob's gross salary per year?
c) Does Jacob have to contribute to the UIF? Give a reason for your answer.
The R200 Jacob is paid per day, working three days per week, and the amount Mr Nkosi paid to the UIF, evaluated using percentages indicates;
a) R31,200
b) 2%
c) Jacob does not have to contribute to the UIF
What is a percentage?A percentage is a representation of a ratio of numbers or proportion of a quantity expressed as a fraction of 100.
The number of days Jacob works per week for Mr Nkosi at his playschool for pre-school = Three days per week
The amount
The amount Jacob is paid per day = R200
Amount Mr Nkosi paid to the UIF for one year in advance regarding Jacob = R624
a) Jacob's gross salary in a year = 52 × 3 × R200 = R31,200
b) The percentage R624 is of Jacob's gross salary = (R624/R31,200) × 100 = 2%
c) The amount Mr Nkosi has to contribute to the UIF regarding Jacob in a year is two percent (2%) of Jacob's gross salary, therefore;
Jacob does not have to contribute to the UIF
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Do larger sample sizes increase the certainty of the statistical test? why or why not?
Yes, larger sample sizes do increase the certainty of a statistical test. This is because as the sample size increases, the sample becomes more representative of the population, leading to more accurate results.
larger sample sizes generally increase the certainty of the statistical test. This is because larger samples provide more information and reduce the likelihood of chance variations affecting the results. The estimated parameter becomes more stable and accurate with a larger sample size. Additionally, larger sample sizes allow for the detection of smaller effect sizes and greater statistical power. However, it is important to note that sample size alone does not guarantee the validity of the statistical test. Other factors such as sampling methods, data quality, and appropriate statistical analysis must also be considered.
Yes, larger sample sizes do increase the certainty of a statistical test. This is because as the sample size increases, the sample becomes more representative of the population, leading to more accurate results. Additionally, larger sample sizes decrease the margin of error and increase the statistical test's power, allowing for better detection of true differences or relationships in the population. Overall, larger sample sizes lead to more reliable and valid conclusions in statistical tests.
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The diameter of a circular cookie cake is 14 inches. How many square inches make up half of the cookie cake? Approximate using π = 3.14.
615.44 square inches
307.72 square inches
153.86 square inches
76.93 square inches
Answer:
Step-by-step explanation:
The area of a circle is given by the formula:
area = π x (radius)²
where the radius is half of the diameter. In this case, the radius of the cookie cake is:
radius = 14 / 2 = 7 inches
Using π = 3.14, the area of the entire cookie cake is:
area = 3.14 x 7² = 3.14 x 49 ≈ 153.86 square inches
To find half of the cookie cake, we need to divide this area by 2:
half area = 153.86 / 2 = 76.93 square inches
Rounding the answer to the nearest whole number, we get:
half area ≈ 77 square inches
Therefore, the answer is approximately 77 square inches. The closest option is D) 76.93 square inches.
A rectangle is drawn on a coordinate plane. Three vertices of the rectangle are points A(−4,3), B(2,3), and C(2,−1). Point D is the fourth vertex of the rectangle.
What is the distance from point C to point D?
Enter your answer in the box.
An item on sale costs 65% of the original price. The original price was $75 .
Use the ALEKS calculator to find the sale price.
Answer: 27 out of 65%
20POINTS!!!!Let f(x)=3/4x2−1. The function g(x) is a vertical stretch of f(x) by a factor of 8. What is the equation of g(x)?
Calculator allowed This is a new version of the question. Make sure you start new workings. Bookwork code: B10 4 Calculate the area of the shaded section of this shape 4 cm 6 cm 10% 11 cm 3 cm 1 8 cm Not drawn accurately
Step-by-step explanation:
Area of the large trapezoid :
height * average of bases
area = 8 * (6+11)/2 = 68 cm^2
MINUS the area of the parallelogram 4x3 =12 cm^2
68 - 12 = 56 cm^2 = shaded region
Solve for z.
A = x+y+z
Answer:
A- x - y = z
Step-by-step explanation:
A = x + y + z
- x
A - x = y + z
- y
A- x - y = z
Find the value of the variable(s).
Please help
14) The value of the variable x is 220° using the inscribed angle theorem.
15) The value of x and y are 134° and 75° respectively using the opposite angle property of quadrilateral.
Inscribed Angle Theorem states that the angle inscribed in a circle has a measure of half of the central angle which forms the same arc.
14) Using this theorem,
x° = Central angle formed with the 2 points given on the circle
Inscribed angle = 110°
x = 110 × 2 = 220°
15) Here a quadrilateral is inscribed inside the circle.
We know that, opposite angles are supplementary in a quadrilateral.
So, 46° + x° = 180°
x° = 180° - 46° = 134°
Similarly,
y° = 180° - 105° = 75°
Hence the values of x 220° in the first figure and the values of x and y are 134° and 75° respectively in the second figure.
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Susan rolled a die 744 times. Which of the following would be a good estimate of the number of times she rolled the number 3 on the die?
What is the surface area of this cone?
Use ≈ 3.14 and round your answer to the nearest hundredth.
10 in
10 in
square inches
The surface area of the cone is 628 in²
What is surface area of cone?A cone is a shape formed by using a set of line segments or the lines which connects a common point, called the apex or vertex.
The area occupied by a three-dimensional object by its outer surface is called the surface area.
The surface area of cone is expressed as;
SA = πr( r+l)
where l is the slant height and r is the radius
SA = 3.14 × 10( 10+ 10)
SA = 31.4 × 20
SA = 628 in².
Therefore the surface area of the cone is 628 in²
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Crystal cuts a piece of wood into the shape of a triangle. The height of the triangle is 5 inches, and the base of the triangle measures 8 inches. Crystal makes a scale drawing of the triangle. If the height of her scale drawing is 2 inches, what is the area of her scale drawing?
A. 1.6 square inches
B. 6.4 square inches
C. 3.2 square inches
D. 20 square inches
Answer:
20 square units
Step-by-step explanation:
Given
Height ( h ) = 5 inches
Base ( b ) = 8 inches
To find : Area of the triangle
This triangle is a right angled triangle.
Reason
The height is perpendicular ( ⊥ ) to the base.
Formula
Area of right angled triangle = bh/2
Area of this triangle
= (5 x 8)/2
= 40/2
= 20 square units
An observer stands 120 feet away from a church and measures the angles of elevation of the top and bottom of the steeple to be 24. 4 degrees and 18. 2 degrees respectively. What is the height of the steeple to the nearest foot
The height of the steeple is approximately 62 feet (rounded to the nearest foot).
How to solve for the heightLet x be the height of the steeple, and y be the height from the ground to the bottom of the steeple. The distance from the observer to the church is 120 feet.
Using the tangent function for angle A:
tan(A) = y / 120
tan(18.2) = y / 120
Solve for y:
y = 120 * tan(18.2) ≈ 40.76 feet
Using the tangent function for angle B:
tan(B) = (y + x) / 120
tan(24.4) = (40.76 + x) / 120
Solve for x:
x = 120 * tan(24.4) - 40.76 ≈ 61.92 feet
The height of the steeple is approximately 62 feet (rounded to the nearest foot).
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Write the number 2414six in base five
The base five representation of 2414₆ is 43234₅.
Base five representation is a way of representing numbers using only the digits 0, 1, 2, 3, and 4. This system is also known as quinary or pentimal.
To convert the number 2414₆ to base five, we need to first convert it to base 10 and then convert the result to base five.
To convert 2414₆ to base 10, we can use the formula
2 × 6³ + 4 × 6² + 1 × 6¹ + 4 × 6⁰ = 432 + 144 + 6 + 4 = 586₁₀
Now we can convert 586₁₀ to base five using the following steps
586 ÷ 5 = 117 remainder 1
117 ÷ 5 = 23 remainder 2
23 ÷ 5 = 4 remainder 3
4 ÷ 5 = 0 remainder 4
2414₆ = 43234₅.
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if f(x)= sqrtx, which equation describes the graphed function?
The equation of the function represented by the graph is y = -f(x + 3)
Describing the equation of the functionFrom the question, we have the following parameters that can be used in our computation:
f(x) = √x
The graph is first reflected across the y-axis
So, we have
f'(x) = -√x
Next, it is shifted to the right by 3 units
So we have
f''(x) = -√(x + 3)
This means that
y = -f(x + 3)
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Which equation satisfies the values in the table?
A.c=h+435
B.h=73.5h
C.h=c+435
D. h=73.5c
The correct equation which satisfies the values in the table is,
⇒ y = 0.5x + 3
We have to given that;
To find the correct equation of the table.
Now, Let two points on the table are,
⇒ (1, 3.5) and (2, 4)
Hence, Slope of the line is,
m = (y₂ - y₁) / (x₂ - x₁)
m = (4 - 3.5) / (2 - 1)
m = 0.5 / 1
m = 0.5
Thus, The equation of line with slope 0.5 is,
⇒ y - 3.5 = 0.5 (x - 1)
⇒ y - 3.5 = 0.5x - 0.5
⇒ y = 0.5x + 3
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