The y-intercept of f(x + 4) + 8 is given as follows:
10.
What is a translation?A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.
The four translation rules for functions are defined as follows:
Translation left a units: f(x + a).Translation right a units: f(x - a).Translation up a units: f(x) + a.Translation down a units: f(x) - a.The parent function for this problem is given as follows:
[tex]f(x) = \log_2{x}[/tex]
The translated function is then given as follows:
[tex]g(x) = \log_2{x + 4} + 8[/tex]
The y-intercept of the function is the numeric value at x = 0, hence:
[tex]g(0) = \log_2{0 + 4} + 8[/tex]
g(0) = 2 + 8 = 10.
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ہے
8. A randomized controlled trial was designed to compare the effectiveness of splinting versus
surgery in the treatment of carpal tunnel syndrome. Results are given in the table. The results
are based on evaluations made one year after the treatment. Using a 0.01 significance level,
find the test statistic and critical value needed to test the claim that the success is independent
of the type of treatment.
Splint treatment
Surgery treatment
Successful
Treatment
60
67
Otest statistic = 0.848, critical value = 6.635
statistic 9 750 critical value = 6.635
Unsuccessful
Treatment
23
6
The test statistic and critical value needed to test the claim that the success is independent of the type of treatment are 9.750 and critical value is 6.635.
How to calculate the valueThe expected value for each cell is calculated as follows:
E = row total * column total / grand total
The grand total is 150.
The row totals are 83 and 67.
The column totals are 86 and 64.
The expected values are as follows:
Successful: 60 * 86 / 150 = 36.4
Unsuccessful: 60 * 64 / 150 = 29.6
Surgery treatment
Successful: 67 * 86 / 150 = 49.6
Unsuccessful: 67 * 64 / 150 = 27.4
The test statistic is calculated as 9.750
The critical value is calculated as follows:
α = 0.01
df = (r-1)(c-1) = (2-1)(2-1) = 1
x²(α, df) = 6.635
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The function f(x)=√x is shown on the graph.
4
3+
2+
--5-4-3-2-1₁
-2+
-3+
4
1 2 3 4
Which statement is correct?
O The range of the graph is all real numbers less than
or equal to 0.
O The domain of the graph is all real numbers less
than or equal to 0.
O The domain and range of the graph are the same.
O The range of the graph is all real numbers.
Answer:
The domain and range of the graph are the same
Step-by-step explanation:
The domain and range of the graph are both [tex][0,\infty)[/tex] because you cannot take the square root of a negative number to produce a real result, and you cannot square a real number to get a negative number.
Graph shows two triangles plotted on a coordinate plane. One triangle is at A (minus 4, 4), B (minus 8, 2), and C (minus 6, minus 6). Another triangle is at A prime (4, minus 2), B prime (2, 2), and C prime (6, 0). A sequence of transformations maps ∆ABC to ∆A′B′C′. The sequence of transformations that maps ∆ABC onto ∆A′B′C′ is a followed by a .
The sequence of transformations that maps triangle ABC onto triangle A'B'C' is a translation by (+8, -6) followed by a reflection across the y-axis.
To determine the sequence of transformations that maps triangle ABC onto triangle A'B'C', let's analyze the given coordinate points.
Triangle ABC:
A (-4, 4)
B (-8, 2)
C (-6, -6)
Triangle A'B'C':
A' (4, -2)
B' (2, 2)
C' (6, 0)
By comparing the corresponding vertices, we can identify the transformations:
Translation:
To transform A to A', we can observe that A' is obtained by moving 8 units to the right and 6 units downwards from A. Therefore, the first transformation is a translation by (+8, -6).
Reflection:
Next, we notice that B' is the reflection of B across the y-axis. Thus, the second transformation is a reflection about the y-axis.
Therefore, the sequence of transformations that maps triangle ABC onto triangle A'B'C' is a translation by (+8, -6) followed by a reflection across the y-axis.
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In a math class with 19students , a test was given the same day that an assignment was due.There we’re 10 students who passed the test and 14stdents who completed the assignments
In a math class with 19 students, on a day when a test and an assignment were given, there were 10 students who passed the test and 14 students who completed the assignment.
In a math class with 19 students, a test and an assignment were given on the same day.
Out of the 19 students, 10 of them passed the test and 14 students completed the assignment.
This information allows us to analyze the performance and completion rate of the students in the class.
Firstly, we can determine that there are at least 10 students who demonstrated a satisfactory level of understanding and knowledge in the subject matter, as they successfully passed the test.
This indicates that approximately 52.63% (10 out of 19) of the students achieved a passing grade on the test.
Furthermore, we know that 14 students completed the assignment.
This implies that these students fulfilled the requirements and submitted the necessary work within the given timeframe.
Consequently, we can deduce that approximately 73.68% (14 out of 19) of the students in the class completed the assignment.
It's worth noting that there may be overlap between the students who passed the test and those who completed the assignment, as well as students who did both.
However, without additional information, we cannot determine the exact number of students who passed the test, completed the assignment, or did both.
This data provides insight into the performance and diligence of the students in the math class, indicating the proportions of students who met the criteria for passing the test and completing the assignment.
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Ethan and Calvin meet daily in the elevator. One morning they found that if they multiply their current ages, they get 238. If they did the same after four years, this product would be 378. Determine the sum of the current ages of Ethan and Calvin.
The sum of Ethan and Calvin's current ages is approximately 45.65.
Let's assume Ethan's current age is represented by 'E', and Calvin's current age is represented by 'C'.
From the given information, we can establish the following equations:
The product of their current ages is 238:
E × C = 238
The product of their ages after four years is 378:
(E + 4) × (C + 4) = 378
We can solve this system of equations to determine the values of E and C, and then calculate their sum.
From equation 1, we can express E in terms of C:
E = 238 / C
Substituting this value of E into equation 2:
(238 / C + 4) × (C + 4) = 378
Expanding and simplifying the equation:
(238 + 4C) × (C + 4) = 378
[tex]238C + 952 + 4C^2 + 16C - 378 = 0\\4C^2 + 254C + 574 = 0[/tex]
Now, we can solve this quadratic equation for C using the quadratic formula:
C = (-b ± √(b^2 - 4ac)) / (2a)
Plugging in the values:
a = 4, b = 254, c = 574
C = (-254 ± √([tex]254^2[/tex]- 4 × 4 × 574)) / (2× 4)
After solving, we find two possible values for C: C ≈ -73.85 and C ≈ -39.65
Since age cannot be negative, we discard the negative value. Thus, C ≈ 39.65.
Plugging this value of C back into equation 1:
E × 39.65 = 238
E ≈ 238 / 39.65
E ≈ 6
Therefore, Ethan's current age (E) is approximately 6 and Calvin's current age (C) is approximately 39.65.
The sum of their current ages is:
6 + 39.65 ≈ 45.65
Hence, the sum of Ethan and Calvin's current ages is approximately 45.65.
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Find the area please answer asap need help
Answer:
5.85
Step-by-step explanation:
Jonah's swimming pool is 21 meters by 20 meters. He swam from one corner of the pool to the opposite corner. How far did Jonah swim?
Jonah swam a distance of 29 meters from one corner of the pool to the opposite corner.
To determine how far Jonah swam from one corner of the pool to the opposite corner, we can use the Pythagorean theorem. According to the theorem, in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the two sides of the right-angled triangle are the length and width of the swimming pool, which are 21 meters and 20 meters respectively. The distance Jonah swam represents the hypotenuse of the triangle.
Using the Pythagorean theorem:
[tex]Hypotenuse^2 = Length^2 + Width^2[/tex]
[tex]Hypotenuse^2[/tex] =[tex]21^2 + 20^2[/tex]
[tex]Hypotenuse^2[/tex]= 441 + 400
[tex]Hypotenuse^2[/tex]= 841
Taking the square root of both sides, we find:
Hypotenuse =[tex]\sqrt{841[/tex]
Hypotenuse = 29
Jonah swam a distance of 29 meters from one corner of the pool to the opposite corner.
According to the Pythagorean theorem, in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
The two sides of the right-angled triangle are the length and width of the swimming pool, which are 21 meters and 20 meters respectively. The distance Jonah swam represents the hypotenuse of the triangle.
Using the Pythagorean theorem:
[tex]Hypotenuse^2 = Length^2 + Width^2\\Hypotenuse^2 = 21^2 + 20^2\\Hypotenuse^2 = 441 + 400\\Hypotenuse^2 = 841[/tex]
Taking the square root of both sides, we find:
Hypotenuse = [tex]\sqrt841[/tex]
Hypotenuse = 29
Jonah swam a distance of 29 meters from one corner of the pool to the opposite corner.
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Find the volume of the cylinder. Round your answer to the nearest hundredth, if necessary.
Answer:
The volume is 423.33 cubic millimeters.
Step-by-step explanation:
The formula for volume of a cylinder is given by:
V = πr^2h, where
V is the volume in cubic units,r is the radius of the circle,and h is the height (distance between the two circles in a cylinder).Step 1: Find radius, r, of the cylinder:
The diagram shows us the diameter, d, of the circle is 7 mm. Since the diameter is twice the radius, r, we can find r by dividing the diameter by 2:
r = d / 2
r = 7 / 2
r = 3.5 mm
Thus, the radius of the cylinder is 3.5 mm.
Step 2: Plug in values and round to the nearest hundredth to find the volume, V, of the cylinder:
Now we can plug in 3.5 for r and 11 for h to find V, the volume of the cylinder. We can round at the end.
V = π(3.5)^2(11)
V = π(12.25)(11)
V = 134.75π
V = 423.3296101
V = 423.33 mm^2
Thus, the volume of the cylinder is 423.33 cubic millimeters.
What is the area of the rectangle above?
OA. 96 square units
OB. 20 square units
OC. 104 square units
OD. 40 square units
The area of the rectangle with a length of 12 units and a width of 8 units is 96 sqaure units.
How to determine the area of a rectangle?A rectangle is a 2-dimensional shape with parallel opposite sides equal to each other and four angles are right angles.
The area of a rectangle is expressed as;
Area = length × breadth
From the image:
Length of the rectangle = 12 units
Breadth of the rectangle = 8 units
Area of the rectangle = ?
Plug the given values into the above formula and solve for the area:
Area = length × breadth
Area = 12 units × 8 units
Area = 96 sqaure units
Therefore, the measure of the area is 96 sqaure units.
Option A) 96 sqaure units is the correct answer.
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i need the whole problem done plus the steps to it please, im stressed and its due soon
Total Surface Area of the Triangular prism = 30 ft².
Here, we have,
The triangular prism is attached.
The triangular prism shown has 2 triangular faces and 3 lateral faces.
here, we have,
Base of the triangle =2 ft
Height of the Triangle =3 ft
Area of one Triangular Face is:
A = 1/2 * 2 * 3 = 3 ft²
The dimensions of the lateral rectangles are:
2 ft by 3 ft
3 ft by height 3 ft
3 ft by height 3 ft
Therefore, total surface area of the triangular prism
=2(Area of one Triangular Face)+Area of 3 rectangular faces
= 2 *3 + ( 2*3 + 3*3 + 3*3)
= 6 + 24
= 30 ft²
Total Surface Area of the Triangular prism = 30 ft².
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Anna wants to determine the height of a right rectangular prism. The prism has a volume of 380 cm³ and a base whose area is 50 cm². She lets h represent the height of the prism.
What equation can she write to solve the problem?
The height of the right rectangular prism is 7.6 cm.
To determine the height of the right rectangular prism, we can use the formula for the volume of a prism:
Volume = Base Area * Height
Given that the volume is 380 cm³ and the base area is 50 cm², we can write the equation as:
380 = 50 * h
Now, let's solve for h by dividing both sides of the equation by 50:
h = 380 / 50
Simplifying the expression:
h = 7.6 cm
Therefore, the height of the right rectangular prism is 7.6 cm.
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How mant times does 9 go into 18
Answer:
2 times, with a remainder of 0.
Step-by-step explanation:
If you had 2 friends and you had to divide 18 between both you would get 9. each with no left over
Which is the radian measure for 30° and its associated coordinate point on the unit circle?
7 pie/6
Pie over 6
Answer:
57
Step-by-step explanation:
this is the boybfiend
The radius of a circular play ground is 77m. Calculate the distance covered by a runner is 5 complete rounds around the ground. ( ans2420) how ?
Step-by-step explanation:
To solve this problem, we need to find the circumference of the circular playground and then multiply it by the number of rounds the runner completes.
The circumference of a circle can be calculated using the formula:
Circumference = 2 * π * radius
Given that the radius of the playground is 77m, we can substitute this value into the formula to find the circumference:
Circumference = 2 * π * 77
Now, we need to calculate the distance covered by the runner in 5 complete rounds. Since one round is equal to the circumference, the distance covered in 5 rounds would be:
Distance = 5 * Circumference
Substituting the value of the circumference, we have:
Distance = 5 * (2 * π * 77)
To simplify, we can use an approximation of π as 3.14:
Distance ≈ 5 * (2 * 3.14 * 77)
Calculating further:
Distance ≈ 5 * (6.28 * 77)
Distance ≈ 5 * 483.56
Distance ≈ 2417.8
Therefore, the distance covered by the runner in 5 complete rounds around the circular playground is approximately 2417.8 meters, which can be rounded to 2420 meters (as given in the answer).
Hope this helps!
Answer:
2420
Step-by-step explanation:
Circumference = 2πr
One complete round will be equal to the circumference = 2πr
Five rounds will be five times the circumference
= 5*2πr
= 10πr
[tex]= 10 *\frac{22}{7}*77 \\\\= 10* 22* 11\\\\= 2420[/tex]
A student was given the following diagram and asked to prove that AX= XC.
What would be the reason for the fourth step in the proof?
Given: AB- BC and ZABX 2CBX
Prove: AX XC
Statements
1. AB BC and ZABXZCBX
2. BX BX
3. AABXACBX
4. AXEXC
B
X
Reasons
Given
Reflexive Property of Equality
SAS Triangle Congruence Theorem
A. Definition of perpendicular bisector
B. Substitution property of equality
C. Corresponding parts of congruent triangles are congruent
(CPCTC)
D. Definition of midpoint
K
The reason for the fourth step to prove the congruence of [tex]\overline{AX}[/tex] and [tex]\overline{XC}[/tex], based on the congruence of the triangles ΔABX and ΔCBX is the option C.
C. Corresponding parts of congruent triangles are congruent (CPCTC)
What are congruent triangles?Congruent triangles are triangles that have the same shape and size.
The completed two column table to prove the congruence of the segment [tex]\overline{AX}[/tex] and [tex]\overline{XC}[/tex] can be presented as follows;
Statement [tex]{}[/tex] Reasons
1. [tex]\overline{AB}[/tex] ≅ [tex]\overline{BC}[/tex] and ∠ABX ≅ ∠CBX [tex]{}[/tex] Given
2. [tex]\overline{BX}[/tex] ≅ [tex]\ovderline{BX}[/tex] [tex]{}[/tex] Reflexive property of Equality
3. ΔABX ≅ ΔCBX [tex]{}[/tex] SAS Triangle Congruence Theorem
4. [tex]\overline{AX}[/tex] ≅ [tex]\overline{XC}[/tex] [tex]{}[/tex] CPCTC
The reason for the fourth step can be presented as follows;
CPCTC is an acronym for corresponding parts of congruent triangles are congruent. The triangles ΔABX and ΔCBX are congruent, therefore, CPCTC indicates that the segments [tex]\overline{AX}[/tex] and [tex]\overline{XC}[/tex] which are corresponding parts are therefore congruent.
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find the surface area
The Surface Area of Cone is 706.5 cm².
We have dimension of Cone
height = 12 cm
Radius = 9 cm
Now, l = √9² + 12² = √81 + 144 = 25 cm
So, the Surface Area of Cone
= πrl
= 3.14 x 9 x 25
= 706.5 cm²
Thus, the Surface Area of Cone is 706.5 cm².
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PLEASE SOLVE THIS FAST!!!!
A surveyor wants to determine the width of a river. She surveys the area and finds the following measures below.
She uses a pair of similar triangles, to help her find the answer.
A surveyor wants to determine the width of a river is 43.34 m.
From given figure, angle ACB = angle ECD (Vertically opposite angles are equal)
Angle BAC = Angle EDC = 90
So, triangle ABC and triangle ECD are similar.
AB/DE = AC/CD
AB/18.6 = 79.6/34.2
AB/18.6 = 2.33
AB = 2.33×18.6
AB = 43.34 m
Therefore, a surveyor wants to determine the width of a river is 43.34 m.
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80% of the sixth graders have lunch during fourth period if 120 sixth graders had lunch fourth periods how many total six graders are there?
Answer: there is a total of 150 sixth graders
explanation :
0.8x = 120
120 / 0.8 = 150
6th graders at lunch = 150
100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
Answer:
[tex](x - 3)^2 + (y + 2)^2 = 16[/tex]
Step-by-step explanation:
The equation of a circle with a center at (h, k) and radius r is given by:
[tex](x - h)^2 + (y - k)^2 = r^2[/tex]
We are given that the points G(5,-2) and H(1, −2) lie on the circle. We can use the distance formula to find the distance between these two points.
[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]
[tex]d = \sqrt{(5 - 1)^2 + ((-2) - (-2))^2} = \sqrt{16} = 4[/tex]
Therefore, the radius of the circle is 4.
We can now find the center of the circle by taking the average of the x-coordinates and y-coordinates of the points G and H.
[tex](h, k) = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right) = \left(\frac{5 + 1}{2}, \frac{-2 - 2}{2}\right) = (3, -2)[/tex]
Therefore, the equation of the circle is:
[tex](x - 3)^2 + (y + 2)^2 = 4^2[/tex]
Simplifying the equation, we get:
[tex]\bold{(x - 3)^2 + (y + 2)^2 = 16}[/tex] is a required equation.
total population = 8,000,000
civilian labor force = 4,000,000
number of unemployed individuals who are actively seeking jobs = 400,000
number of unemployed individuals who are not seeking work 100,000.
This information indicates that country y's unemployment rate equals.
The given information indicates that country y's unemployment rate equals 10 %.
How to find the unemployment ?The formula to calculate the unemployment rate is:
Unemployment Rate = ( Number of Unemployed Individuals / Civilian Labor Force ) × 100
In this case, the number of unemployed individuals actively seeking jobs is 400,000, and the civilian labor force is 4,000,000.
Unemployment Rate = ( 400, 000 / 4, 000, 000) × 100
Simplifying the calculation :
= 0. 1 x 100
= 10 %
In conclusion, the unemployment rate in Country Y is 10%.
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Beth and Kelly spent the same total amount of money for dog sitting while on vacation. Beth took her dog, Pockets, to Rover Sleepover and was charged $24.50 per day and a fee of $90.50 for food and cleaning. Kelly took her dog, Monty, to Pet Palace and was charged $32 per day and a $45.50 cleaning fee.
How many days were Beth and Kelly on vacation?
Beth and Kelly were on vacation for 6 days. both spent same amount of money for dog sitting while on vacation.
Let's assume the number of days Beth and Kelly were on vacation is represented by 'd.'
For Beth:
Total cost for dog sitting = (Cost per day * Number of days) + Cleaning and food fee
24.50d + 90.50
For Kelly:
Total cost for dog sitting = (Cost per day * Number of days) + Cleaning fee
32d + 45.50
Since both Beth and Kelly spent the same amount, we can set their total costs equal to each other and solve for 'd':
24.50d + 90.50 = 32d + 45.50
Rearranging the equation:
24.50d - 32d = 45.50 - 90.50
-7.50d = -45
Dividing both sides by -7.50:
d = -45 / -7.50
d = 6
Therefore, both Beth and Kelly were on vacation for 6 days.
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Which expression is equivalent to 3 x 5 x 5 x5 x 5 x 5 x5 ?
Answer:
3(5)^6
Step-by-step explanation:
There is 6, 5's in the expression meaning our answer has to be 3(5)^6.
:)
Answer:
the answer for the question given above is equal to 46875
find the surface area
The surface area of the triangular prism is 193.05 cm².
We have,
The figure is a triangular prism.
Now,
There are 4 triangular surfaces.
Each surface area is the same except the base surface.
So,
3 surface area.
= 3 x (1/2 x 9 x 11.3)
= 3 x 50.85
= 152.55 cm²
And,
Base surface area.
= 1/2 x 9 x 9
= 40.5 cm²
Now,
The surface area of the triangular prism.
= 152.55 + 40.5
= 193.05 cm²
Thus,
The surface area of the triangular prism is 193.05 cm².
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Select all of the words for which the probability of selecting the letter A at random is 13
Responses
CAB
CAB
ANT
ANT
BANK
BANK
ALPINE
ALPINE
ABOARD
ABOARD
ABRASIONS
ABRASIONS
BASEBOARDS
The words for which the probability of selecting the letter A at random is 1/3 are:
a) CAB
b) ANT
c) ABOARD
Given data ,
Let the probability of selecting the letter A at random be P ( A ) = 1/3
Now , the number of letters in the words CAB are = 3
The number of A's in the word CAB = 1
So , the probability is P ( A ) = 1/3
Now , Now , the number of letters in the words ANT are = 3
The number of A's in the word ANT = 1
So , the probability is P ( A ) = 1/3
And , Now , the number of letters in the words ABROAD are = 6
The number of A's in the word ABROAD = 2
So , the probability is P ( A ) = 2/6 = 1/3
Hence , the probability is solved
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the following number of people attended last 10 screenings of a movie. mean median or mode
We can see here that the measure that should be used to summarize the data is: A. Mean.
What is mean?The mean, which is used to indicate the average value of a group of values in statistics, is a measure of central tendency. It is determined by adding up all of the dataset's values and then dividing the total by the number of values.
Mean = (Sum of all values) / (Total number of values)
The mean is widely used in statistics to summarize and describe the average value of a dataset. It is a useful measure for understanding the central tendency of a set of values.
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The complete question is:
The following number of people attended last 10 screenings of a movie.
196, 197, 198, 199, 202, 203, 204, 205, 206, 208
Which measure should be used to summarize the data?
A. Mean
B. Median
C. Mode
Find the area of a trapezoid with bases of 16 feet and 10 feet and a height of 3 feet. 39 ft2 78 ft2 240 ft2 480 ft2
Answer: 39 ft2
Step-by-step explanation:
The area of the trapezoid is 39 square feet.
To find the area of a trapezoid, you can use the formula:
Area = (1/2) × (base1 + base2) × height
Given that the bases of the trapezoid are 16 feet and 10 feet, and the height is 3 feet, we can substitute these values into the formula:
Area = (1/2) × (16 + 10) × 3
Area = (1/2) × 26 × 3
Area = (1/2) × 78
Area = 39 ft^2
Therefore, the area of the trapezoid is 39 square feet.
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______
36 | 8,325
is it
203 R17 or 231 R9 or 231 R11 or 234 R1
The quotient is 231, and the remainder is 9 or 231 R9.
To perform long division to find the quotient and remainder of 8,325 divided by 36, you would proceed as follows:
______
36 | 8,325
- 7,200 (36 x 200)1,125
1,080 (36 x 30)45
and, 36 (36 x 1)
9
The quotient is 231, and the remainder is 9.
Therefore, the correct answer is 231 R9.
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find the missing side. round to the nearest tenth
The required angle is 24.5°.
Given is a right triangle with perpendicular side 16 and the base = 35 we need to find an acute angle in it,
To find the acute angle in a right triangle given the lengths of the perpendicular side and the base, you can use the tangent function.
The tangent of an angle is defined as the ratio of the length of the perpendicular side to the length of the base side.
In this case, the perpendicular side is 16 and the base is 35.
Let's denote the acute angle as θ.
Using the tangent function, we can set up the equation:
tan(θ) = perpendicular side / base
tan(θ) = 16 / 35
To find the value of θ, we can take the inverse tangent of both sides:
θ = tan⁻¹(16 / 35)
θ = 24.5°
Hence the required angle is 24.5°.
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7. For the three-part question that follows, provide your answer to each part in the given workspace. Identify each part with a coordinating re
A, Part B, and Part C.
in.
Part A: Determine the value of the diameter of the circle shown above.
Part B: Determine the value of the radius of the circle shown above.
Part C: Explain your reasoning for Part A and Part B of this problem.
- AA- A
B
U Font Family
FE E
C
1
D
1+
4
Answer:
A: The diameter is 6in.
B: The radius is 3in.
C: The diameter is given to us in the problem. A line is drawn out that strikes through the center point. of the circle, and it is labeled 6in in the middle, so we can deduce that it is the diameter. The radius of a circle is 1/2 the length of the diameter, so 6/2 = 3in. If the 6in was on either side of the line, then that would be labeling the radius.
Triangle FGH is inscribed in circle O, the length of radius OH is 6, and maFGH-20. What is the area of the sector formed by angle FOH, in terms of pi 1) 2k 2) 3/2 (3) 4
PLEASE HELP ME, NO FAKE ANSWERS (sorry that it's blurry)
Triangle FGH is inscribed in circle O, the length of radius OH is 6, and ma FGH-20. The area of the sector formed by angle FOH, in terms of pi is 6π. Hence, it is neither of the options.
Given that triangle FGH is inscribed in circle O, the length of radius OH is 6, and m∠FGH = 20.
We have to find the area of the sector formed by angle FOH, in terms of pi.
Using the central angle, we know that the measure of ∠FOH is twice that of ∠FGH, which is 40°.
Therefore, the measure of the central angle FOH is 2 * 40 = 80°.
The area of the sector formed by angle FOH, in terms of pi is given by, A = r²θ/2 where A = Area of the sector, r = radius of the circle and θ = central angle in radians.
To calculate the value of A in terms of pi, we have to convert the central angle from degrees to radians.
1 radian = 180°/π radians
Therefore, 80° = 80° * (π/180°) = 4π/9 radians.
Now we can plug in the given values of r and θ to find the area of the sector.
A = (6)² * (4π/9) / 2 = 18π/3 = 6π
Thus, the area of the sector formed by angle FOH, in terms of pi is 6π.
Hence, option 1) 2k is incorrect. Option 2) 3/2 (3) is incorrect. Option 3) 4 is incorrect. Answer: 6π.
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