The circumcenter is where three perpendicular bisectors intersect and the incenter is where the three angle bisectors intersect.
What is circumcenter?The circumscribed circle or circumcircle of a polygon in geometry is a circle that passes through each of the polygon's vertices. This circle's circumcenter and circumradius are its centre and radius, respectively.
Construct angle bisectors of each angle of the triangle and their intersection point gives the incenter.
To find Circumcenter:
Construct perpendicular bisectors of all sides of the triangle and their intersection point gives the circumcenter.
Circumcenter Theorem: It states that the vertices of a triangle are equidistant from the circumcenter.
Incenter Theorem: It states that the incenter is equidistant from the sides of the triangle.
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On Monday, a museum had 500 visitors. On Tuesday, it had 900 visitors. Estimate the percent change in the number of visitors to the museum. Use pencil and paper. Estimate how many people would have to visit the museum on Wednesday to have the same estimated percent change between Tuesday and Wednesday as between Monday and Tuesday. Explain your answer.
The percentage increase regarding the change in visitor is 80%.
How to calculate the percentage?From the information, the museum had 500 visitors and on Tuesday, it had 900 visitors.
It should be noted that the increase in numbers will be:
= 900 - 500
= 400
The percentage increase will be:
= Increase / initial value × 100
= 400/500 × 100
= 0.8 × 100
= 80%
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A scientist records 61 more shooting stars in the fall than in the spring. there are 15 shooting stars in the spring. how many shooting stars are in the fall?
The probability that shooting stars are there in the fall is 0.5904.
The probability of not seeing any falling star in that time period of 15 minutes is 1 - 0.2 = 0.8.
In this way, the combined probability of not seeing any of the falling stars in the four-time period is: 0.8 * 0.8 * 0.8 * 0.8 = 0.8⁴ = 0.4096
= 1 - 0.4096 = 0.5904
=P(X = x) = μˣ * e^-μ / x!
Here, the span is of 15 minutes. In this way, the typical number of events in the span is 15λ. The probability of witnessing 0 occasions (i.e X = 0) is:
P(X = 0) = μ⁰ * e^-(15λ) / 0! = 1 / e^(15λ) — — (1)
(1) is equal to 80% as the probability of at least one event happening is 20%.
So, 1 / e^(15λ) = 0.8
or, e^(15λ) = 1.25
or, 15λ = ln(1.25) = 0.2231
= λ = 0.0149 / min
In this way, the typical number of occasions (falling stars) is 0.0149 per minute.
Presently, the typical number of occasions in an hour is:
0.0149 * 60 = 0.8926 / hour
So, the Poisson distribution expression becomes:
P(X = x) = 0.8926ˣ * e^-0.8926 / x! — — (2)
Here, the time span is 60 minutes.
Presently, we should find the probability of not having even a solitary occasion in 60 minutes:
P(X = 0) = 0.8926⁰ * e^-0.8926 / 0! = 0.4096
So, the probability of having at least one event is the complement of the above probability.
So, P(X≥1) = 1 - P(X=0) = 1 - 0.4096 = 0.5904
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Type the correct answer in the box. If necessary, use / for the fraction bar.
Both pyramids in the figure have the same base area as the prism. The ratio of the combined volume of the pyramids to the volume of the pris
expressed as a fraction in simplest form, is
The ratio of the combined volume of these pyramids to the volume of the prism as a fraction is equal to 1/3.
How to calculate the volume of a pyramid?
The volume of a pyramid can be calculated by using this formula:
Volume = 1/3 × b × h
Where:
h is the height.
b is the base area.
Volume of this prism = 1/2 × b × hHere, both pyramids have the same base area as the prism, their volume is given by:
Volume of a pyramid = (1/3 × b × h) + (1/3 × b × h)
Volume of a pyramid = 2/3 × b × h
Also, the volume of this prism = 1/2 × b × h
Thus, the ratio is given by:
Ratio = (2/3 × b × h)/(1/2 × b × h)
Ratio = 2/3 × 1/2
Ratio = 1/3.
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Solve the equation given a domain of {-3}.
3x - 2y = 5
The solution to the equations is y = -7
How to solve the equations using the domain of the replacement sets?From the question, we have the equation to be given as
3x - 2y = 5
The above equation is a linear equation
The domain or the replacement set is given as
{-3}
Rewrite properly as
Domain = {-3}
or
x = -3
So, we replace the variables using the elements in the replacement set
When x = -3, we have
3 x -3 - 2y = 5
Evaluate the products
This gives
-9 - 2y = 5
Add 9 to both sides
-2y = 14
Divide both sides by -2
y = -7
So, we have
x = -3 and y = -7
Hence, the solution to the equation is y = -7
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What is the size of an angle called a revolution
Answer:
Step-by-step explanation:
The size of the angle of one whole revolution is 360 degrees. A revolution describes the angle of a circular surrounding sector as it rotates! This means one full revolution is 360 degrees. And half of a revolution is 180 degrees!
At the beginning of a chemistry experiment, the volume of liquid in a container was 3 milliliters. During the experiment, the volume dropped to
2.1 milliliters. Find the percent of decrease.
Answer:
30%
Step-by-step explanation:
To calculate the percent of change, you find the amount of change and divide that my the original amount
[tex]\frac{3-2.1}{3}[/tex] = [tex]\frac{.9}{3}[/tex] = .3 As a percent, this would be 30%
Find the value of r so that the line passing through (-3, r) and (7,-6)
has a slope of 2 2/5
r =
The value of r is -10 for line with slope 2/5 .
What is slope?
A line's slope, often known as its gradient, is a numerical representation of the line's steepness and direction.
Main Body:
We know that the slope of line in two point form is
(y₂-y₁)/(x₂-x₁) = m where m = slope
given points are (-3,r) and (7,-6) m= 2/5
(-6-r)/(7+3)= 2/5
(-6-r)/10 =2/5
therefore value of r= -10
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correct answer gets brainliest!
Answer:
arc RP = 136°
Step-by-step explanation:
the inscribed angle PQR is half the measure of its intercepted arc, then
arc PR = 2 × ∠ PQR = 2 × 68° = 136°
For triangle XYZ, m∠X = (5g + 18)° and the exterior angle to ∠X measures (8g + 32)°. Find the measure of ∠X and its exterior angle. Interior angle = 68°; exterior angle = 112° Interior angle = 112°; exterior angle = 68° Interior angle = 73°; exterior angle = 105° Interior angle = 105°; exterior angle = 73°
The interior angle and the exterior angle of triangle XYZ is 68° and 112° respectively.
What is a triangle?
A triangle is a plane shape that has three sides.
Recall that, the sum of a interior angle and an exterior angle of a triangle is 180°.
Using the formula,
a+b = 180°............ Equation 1Where:
a = interior angle b = exterior angle.From the question,
Given:
a = m∠X = (5g + 18)° b = ∠X = (8g + 32)°Substitute these values into equation 1
(5g + 18)+ (8g + 32) = 180Solve for g
13g + 50 = 18013g = 130g = 130/13g = 10Hence, interior angle of X = (5×10)+18 = 50+18 = 68° and exterior angle of X = (8×10)+32 = 80+32 = 112°
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Answer: I belive the answer is A
Step-by-step explanation: i could be wrong
Last Spring, several of the Mt. Hood Community College (MHCC) jazz groups held a joint concert. Tickets sold for $8.00 to the general public and for $5.50 for students and staff. Ticket sales brought in $2,582.50. If 390 people attended the concert, how many were MHCC students and staff, and how many were general public? Using the variable p for the general public, and s for students/staff, write a system of equations to determine the breakdown of attendees.
The number of general public and students are 175 and 215 respectively.
How to calculate the value?Based on the information given:
Let p = general public
Let s = students/staff
390 people attended the concert. This will be:
p + s = 390 .... i
Tickets sold for $8.00 to the general public and for $5.50 for students and staff. Ticket sales brought in $2,582.50. This will be:
8p + 5.5s = 2582.5 .... ii
From equation i
p = 390 - s
8p + 5.5s = 2582.5 .... ii
8(390 - s) + 5.5s = 2582.5
3120 - 8s + 5.5s = 2582.5
Collect like terms
- 8s + 5.5s = 2582.5 - 3120
-2.5s = - 537.5
Divide
s = 537.5 / 2.5
s = 215
Students = 215
Note that p + s = 390
p + 215 = 390
P = 390 - 215
P = 175
Public = 175
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Approximately how many feet tall is the streetlight
Answer:
H = 30 ft
Step-by-step explanation:
Since the triangle is 90 degrees and we have to find out how tall the streetlight is we have to subtract 90 and 40 degrees. Which we get 50 degrees, after we subtract 20 from the 50 degrees. So we get 30 ft or 30 degrees.
a system is tested for faults once per hour. if there is no fault, none will be detected. if there is a fault, the probability is 0.78 that it will be detected. the tests are independent of one another. given that a fault has gone undetected for 2 hours, what is the probability that it will be detected in the next hour? round the answer to two decimal places. numeric response
The probability that it will be detected in the next hour is 0.04.
For a system, a fault test each hour is a Bernoulli with success defined as detecting a fault.
The probability of success is 0.78
Let 'x' denote the number of tests conducted up to and including the test that detected a fault.
Then x* - Geometry (0.78).
The probability mass function of the random variable x is;
P(x) = { P( 1 - P )ˣ⁻¹ x = 1,2, . . .
{ 0 otherwise
The Probability that a fault will be detected on the third hour, given that it has gone undetected during the first two hours is;
P(X = 3 / x = 2) = P(X = 3 and x > 2) / P(x > 2)
= P( x = 3 ) / 1- P(x ≤ 2)
= P( x = 3 ) / 1-P(x = 1) - P(x = 2)
= P(3) / 1-P(1) - P(2)
= (0.78)(0.2)² / 1 - (0·78)(0.2) - (0.78)(0.2)
= (0.78)(0.04) / 1 - (0.78)(0.2) - (0.78)(0.2)
= 0.0312 / 1 - 0.156 - 0.156
= 0.0312 / 0.688
= 0.04
The probability that it will be detected in the next hour is 0.04
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An investor invested a total of $2,900 in two mutual funds. One fund eamed a 7% profit while the other eamed a 3% profit. If the investor's total profit was $143, how much was invested in each mutual fund?
Answer:
one is 203
two is 87
Step-by-step explanation:
The temperature at the end of the day was 87 degrees. The temperature had decreased twice during the day, once by 9 degrees and another time by 7 degrees.
Which expression shows what the temperature was at the start of the day?
71+9+771+9+7
87−9−7
87+9+7
87+9−7
The temperature at the end of the day was 87 degrees. The temperature had decreased twice during the day, once by 9 degrees and another time by 7 degrees.
Which expression shows what the temperature was at the start of the day?
71+9+771+9+7
87−9−7
87+9+7
87+9−7
Find the perimeter of a rug that measures 2 yards by 11/12 yards
Answer:
5 5/6 yards
Step-by-step explanation:
You want the perimeter of a rug that is 2 yards by 11/12 yards.
PerimeterThe formula for the perimeter of a rectangle is ...
P = 2(L+W)
Using the given values, we find the perimeter to be ...
P = 2(2 yd + 11/12 yd) = 4 22/12 yd = 5 5/6 yd
The perimeter of the rug is 5 5/6 yards.
At the beginning of the game, April had a core of −150 point. April played for another 20 minute, and her final core wa −35
The expression that represents the change in April's score from the start to the end of the game is 355 - 150 = 205.
April played a game. The score at the beginning of the game was 150 points. After twenty minutes, her score was 355 points. We have to determine the change in her score from the beginning of the game to the end of the game.
Let the change in the score be represented by the variable "C". The change in her score is calculated below. The change in the score is the difference between the final and the initial score of April.
C = 355 - 150
C = 205
Hence, the change in her score from the beginning of the game to the end of the game is 205 points.
The complete question is given below.
At the beginning of the game, April had a score of 150 points. April played for another 20 minutes, and her final score was 355. Write and then evaluate a subtraction expression to determine the change of her score from the beginning of the game to the end of the game.
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What is the equation of the line in slope-intercept form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answer:
See below
Step-by-step explanation:
Find slope using two convenient integer coordinates
(-1,4) and (1, -8) are convenient
slope = (y1-y2) / (x1-x2) = (4 - -8) / ( -1 -1) = 12/-2 = -6
the y-axis intercept is -2 ( by looking at the graph)
y = -6x -2 Done.
Which expression shows the distance you would drive from the library to the grocery store along this road?
The expression that shows the distance you would drive from the library to the grocery store along this road is; |-5|+|7|
How to solve Absolute Value Inequalities?
An absolute value inequality is defined as an expression that has absolute functions as well as inequality signs. For example, the expression |x + 5| > 1 is an absolute value inequality that contains a greater than symbol.
Now, from the inequality line graph attached, we see that the point of the library is at -5 on the line graph.
Similarly, we also see that the point of the grocery store which i will liken to the maths class is at the point 7.
Thus, the distance between both points when we take absolute values into consideration is; |-5|+|7|
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If one factor of -24x^4y^5+16x^2y^3 is -8x^2y^3 what is the other factor
The polynomial is, -24x⁴y⁵+16x²y³. One of the factor is (-8x²y³),So other factor is 3x²y²-2 by the factorization method.
What is polynomial?Sums of terms of the form kxn, where k is any number and n is a positive integer, make up polynomials. For instance, the polynomial 3x+2x-5. a description of polynomials. The terms degree, standard form, monomial, binomial, and trinomial are all covered in this video. An expression that consists of variables, constants, and exponents and is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable).
Here,
The polynomial is,
=-24x⁴y⁵+16x²y³
One of the factor is (-8x²y³)
=-8x²y³*(3x²y²-2)
So other factor is 3x²y²-2.
One of the factor is (-8x²y³),So other factor is 3x²y²-2 by the factorization method for the The polynomial -24x⁴y⁵+16x²y³.
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Find the slope of the line that passes through the pair of points.
(3, 1), (9, 1)
Answer:
gradient:
y2-y1/x2-x1
1-1/9-3
0/-6
= 0
what type of statistics is used to estimate how likely it is that a statistical result based on data from a random sample is representative of the population from which the sample sia sssumed to have been selecteed
We use Inferential Statistics is used to estimate how likely it is that a statistical result based on data from a random sample is representative of the population.
Given that;
What kind of statistics is used to gauge the likelihood that a statistical finding based on information from a random sample is representative of the population the sample is presumed to have been drawn from?
Inferential Statistics:
You attempt to conclude using inferential statistics that go beyond the immediate facts alone. For instance, we use inferential statistics to try to infer what the population would think from the sample data. Alternately, we utilize inferential statistics to assess the likelihood that an observed difference between groups in this study is a reliable one or one that may have occurred by chance. Descriptive statistics are used to simply describe what's happening in our data, while inferential statistics are used to conclude more general conditions from our data.
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Find the value of (2.4) · (1.3). Show your reasoning.
The evaluation of the expression (2.4) · (1.3) gives 3.12
How to evaluate the expression?From the question, we have the following expression that can be used in our computation:
(2.4) · (1.3)
Express as products
This gives
(2.4) * (1.3)
Remove the brackets
So, we have the following representation
2.4 * 1.3
Evaluate the product
3.12
Hence, the solution is 3.12
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Graph the image of rhombus ABCD after a rotation 270° counterclockwise around the origin.
After rotation, the coordinates of the vertex of the rhombus become:
A(-8,-6)B(-3,-6)C(0,-10)D(-5,-10)How to rotate an image 270°?We refer to the process of rotating an object about a fixed point or line as rotation. By rotating an object, we might be able to fit it into a specific location or even learn more relevant details about the current activity. When an object is rotated, it seems as though its shape has changed, but it hasn't.We know , when a point (x,y) rotates 270° counterclockwise about the origin, our point (x,y) becomes (y,-x)
From the graph the coordinates of the vertex of the rhombus are:
A(6,-8)B(6,-3)C(10,0)D(10,-5)Therefore after rotation, the coordinates of the vertex of the rhombus become:
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A triangle has sides with lengths of 8 miles, 12 miles, and 17 miles. Is it a right triangle?
What is the slope of a line that is perpendicular to y=4/5x+15 and passes through point (−3, 4)?
Answer:
Step-by-step explanation:
The slope of the line y = -5x-4 is -5 or -5/1 so the slope of the perpendicular line is +1/5 eg…
y = x/5 + c
To find c we substitute x=15, y=-2
-2 = 15/5 + c
-2 = 3 + c
C = -5
So the equation is
Y = x/5 - 5
g) In the figure alongside, AB is an electric pole. When an
electric wire falls, its one end touches the ground at P,
5 m away from the base of the pole. If the length of the wire
from the top of the pole to the ground is 13 m, complete
the following problems.
(i) Find the height of the pole.
(ii)If the other end of the wire touches the grand at Q, 9 m away from the
base to the opposite side of the pole, find the length of the falling wire.
Step by step solution
The height of the electric pole is 12 m
When an electric wire falls, its one end touches the ground at P, 5 m away from the base of the pole,
base = 5
length of the wire from the top of the pole to the ground is 13 m
Height of the plant can be calculated by pythagoras theorem
h² = p² + b²
13² = p² + 5²
p² = 169 - 25
p = √144
p = 12m
Therefore, the height of the electric pole is 12 m
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Solve for v in terms of u and w.
u= –vw
Solve for the value of e.
Answer: e=
(9e-8)
(4e+6)
Submit Answer
posse
Answer:
Step-by-step explanation:
Expand: 36e^2+12e-48=e
Subtract e from both sides 36e^2+11e-48=0
Using the quadratic formula, e=(-11+-sqrt7033)/72
The candy jar is only 1/4 full and all three brothers want an equal share. What fraction of the candy jar should each brother get?
Answer: 1/12
Step-by-step explanation: If the candy jar is only 1/4 full, and there's 3 brothers, they would each receive 1/3 of 1/4. THis would be 1/12 of the jar.
What is the least angle measure by which this figure can be
rotated so
that it maps onto itself?
45°
90°
180°
360°
90° is the least angle measure by which this figure can be rotated so that it maps onto itself.
The correct option is (B)
From the figure,
As the figure has two axis of symmetry, placing x and y axis such that the origin lies on its centroid.
Angle between x axis and y axis is 90°.
So rotating any degree which is a multiple of 90 i.e., 90°, 180°, 270°, 360°...… would yield the original figure.
Therefore, 90° is the least angle measure by which this figure can be rotated so that it maps onto itself.
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