Answer:
The circumcenter of a triangle is the point where the three perpendicular bisectors of the sides of the triangle intersect.
Step-by-step explanation:
The process of calculation of circumcenter has been given below.
What is circumcenter of a triangle?
Circumcenter of a triangle is the point of intersection of the perpendicular bisectors of every sides of the triangle.
Let the coordinate of A, B, C [tex]\Delta[/tex] ABC be ([tex]x_1, y_1[/tex]), [tex](x_2, y_2)[/tex] and [tex](x_3, y_3)[/tex] respectively and let the coordinate of circumcenter of [tex]\Delta ABC[/tex] is (x, y)
We need to find the length of AB, BC and AC
The length will be obtained in terms of x and y
On solving the equations, we will obtain the value of x and y
The value of x and y is the required coordinate of the circumcenter.
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What is tan 30°?
1
60°
90°
√3
2
30°
OA. √2
B. √3
O C. √√3
OD. √3
2
O E 1
OF.
F. 7/3
The value of the given trigonometric function tan30° is equal to ( 1/ √3).
As given in the question,
In the given right angled triangle,
Let us consider triangle be ABC,
Measure of angle A = 30°
Measure of angle B = 90°
Measure of angle C = 60°
Side length BC = 1
Side length AB = √3
Now in triangle ABC,
Value of trigonometric function tan30° is given by:
tan 30° = (opposite side) / ( adjacent side)
⇒tan 30° = BC / AB
⇒tan 30° = 1 / √3
Therefore, the value of the given trigonometric function tan30° is equal to ( 1/ √3 ).
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secx - 2=0
(a) x= pi/3
Step-by-step explanation:
secx - 2=0
secx= 2
x= π/3
that's it
The x-values that satisfy the equation Sec(x) - 2 = 0 are x = π/3 and x = 5π/3.
To verify the given equation, we need to find the value(s) of x that satisfy the equation Sec(x) - 2 = 0.
Sec(x) represents the secant function, which is the reciprocal of the cosine function.
The equation can be rewritten as follows:
Sec(x) = 2
To find the solutions, we can take the reciprocal of both sides:
1 / Cos(x) = 2
Next, we can invert the equation to get the cosine function alone:
Cos(x) = 1/2
The cosine function has a value of 1/2 at two specific angles in the interval [0, 2π]: π/3 and 5π/3.
These angles correspond to the inverse cosine function (arccos), so we have:
x = arccos(1/2) = π/3 or x = arccos(1/2) + 2π = 5π/3
Therefore, the x-values that satisfy the equation Sec(x) - 2 = 0 are x = π/3 and x = 5π/3.
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Given that is a standard normal random variable, compute the following probabilities. Round your answers to 4 decimal places.
a.
b.
c.
d.
e.
f.
The probabilities, using the normal distribution, are given as follows:
a. P(0 < x < 0.5) = 0.1915.
b. P(-1.42 < x < 0) = 0.4222.
c. P(x > 0.46) = 0.3228.
d. P(x > -0.5) = 0.6915.
e. P(x < 2.05) = 0.9798.
f. P(x < -0.70) = 0.2420.
Normal Probability DistributionThe z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.For a standard normal random variable, the mean and the standard deviation are given as follows:
[tex]\mu = 0, \sigma = 1[/tex]
Hence each value of x is it's own z-score.
For item a, the probability is the p-value of Z = 0.5 subtracted by the p-value of Z = 0, hence:
P(0 < x < 0.5) = 0.6915 - 0.5 = 0.1915.
For item b, the probability is the p-value of Z = 0 subtracted by the p-value of Z = -1.42, hence:
P(-1.42 < x < 0) = 0.5 - 0.0778 = 0.4222.
For item c, the probability is one subtracted by the p-value of Z = 0.46, hence:
P(x > 0.46) = 1 - 0.6772 = 0.3228.
For item d, the probability is one subtracted by the p-value of Z = -0.5, hence:
P(x > -0.5) = 1 - 0.3085 = 0.6915.
For item e, the probability is the p-value of Z = 2.05, hence:
P(x < 2.05) = 0.9798.
For item f, the probability is the p-value of Z = -0.70, hence:
P(x < -0.70) = 0.2420.
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Each student in Mr. Jones's class has two standard number cubes. Each student records the number of rolls it takes until he or she rolls doubles. The results are shown on the dot plot. Based on the results, what is the probability of needing exactly 6 rolls to get doubles?
Answer:1/5
Step-by-step explanation:
it correct
Answer:
Step-by-step explanation:
Second part to the answer is 3/20
The shoe sizes of a group of middle school girls are shown.
5.5 6 7 8.5 6.5
6.5 8 7.5 8 5
If a shoe size of 9.5 is added to the data, how does the median change?
Answer: 7
Step-by-step explanation:
Median is the middle number of a data set.
You need to first start off with listing the shoe sizes in numerical order:
5, 5.5, 6, 6.5, 6.5, 7, 7.5, 8, 8, 8.5, 9.5
You have a total of 11 numbers in the set, so you can choose the sixth number in the set, which is 7.
So, 7 is the median number.
The median of current data is 6.5 while by adding 9.5 to the data group the median changes to 6.75.
What are the mode and median?Mode is the highest frequency number while the median is the middle value of a data set after writing in either an increasing or decreasing manner.
For example;
Set { 1,2,2,3,4,5,6} here mode is 2 and median is 3.
As per the given data,
5.5, 6, 7, 8.5 6.5,6.5, 8, 7.5, 8 5
Write the above data in increasing order,
5,5.5,6,6.5,6.5,7,7.5,8,8.5
The median is the middle value thus, 6.5 will be the median.
Now let's add 9.5 to the data group,
5,5.5,6,6.5,6.5,7,7.5,8,8.5,9.5
Now we have two middle values 6.5 and 7
Median = (6.5 + 7)/2 = 6.75
Hence "The median of current data is 6.5 while by adding 9.5 to the data group the median changes to 6.75".
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A triangular region of a community college parking lot was measured. The measure of the first angle of this triangle is double the measure of the second angle. The measure of the third angle is 117° greater than double the measure of the first angle. What are the measurements of all three angles?
The value of the first angle is 18
The value of the second angle is 9
The value of the third angle is 153
What is a triangle?It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
We have,
Let the second angle be = x ____(1)
The measure of the first angle of this triangle is double the measure of the second angle.
This means,
First angle = 2x _____(1)
The measure of the third angle is 117° greater than double the measure of the first angle.
This means,
Third angle = 117 + 2(2x) = 117 + 4x _____(3)
From (1) (2) and (3) we get,
x + 2x + 117 + 4x = 180
7x + 117 = 180
7x = 180 - 117
7x = 63
x = 9
The value of first angle is 2x = 2 x 9 = 18
The value of the second angle is x = 9
The value of third angle is 117 + 4x = 117 + 4 x 9 = 117 + 36 = 153
Thus,
The value of the first angle is 18
The value of the second angle is 9
The value of the third angle is 153
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Mac and Tosh are resting on top of the water near the end of the pool when Mac creates a surface wave. The wave travels the length of the pool and back in 25 seconds. The pool is 25 meters long. Determine the speed of the wave.
The speed of the wave is 2 m/s.
Given,
Time taken by wave to travel back and forth=25 seconds
Length of the pool = 25 meters
As given, the wave travels the length of pool and returns back then,
distance covered by wave is twice the length of pool i.e. [tex]2*25=50[/tex] meters
To find speed of the wave, use formula
[tex]Speed=\frac{Distance covered }{time taken}\\\\Speed=\frac{50}{25} \\\\Speed=2 m/s[/tex]
Thus, the speed of the wave is 2 meter/sec.
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An electrician requires 250 energy saving light bulbs. He comes across four suppliers of these light bulbs.
ELECTRA sells the light bulbs at R 123.00 each, with a R 350.00 delivery fee. ZZZ LIGHTING sells the light bulbs at R
140.00 with a 13% discount on the final amount, but with a
R 260.00 delivery fee. SPARX sells the light bulbs at R 255.00 each with a buy one, get one free offer and no delivery fee.
Finally, BRIGHTEX sells the light bulbs at R 190.00 each
with a third off the final amount, and a delivery fee of R 100.00. Which supplier offers the best deal for the electrician?
Supplier which gives the best deal of selling light bulbs for the electrician is ZZZ LIGHTING with the total selling amount of
$ 30676.2.
As given in the question,
Different suppliers sells energy saving light bulbs with different deals,
Number of bulbs required by an electrician = 250
Different deals of selling amount are as follow:
1. ELECTRA :
123 (250) + 350
=$31100
2. ZZZ LIGHTING :
140(250) + 260
= $35260
13% discount on final amount
= 13% of 35260
= 4583.8
Total amount to pay = 35260 - 4583.8
= $30676.2
3. SPARX :
Offer of Buy one get one and no delivery fee
Total amount to be pay for 125 light bulbs.
255 (125)
= $31875
4. BRIGHTEX :
190(250) + 100
= $47600
With a third off on the final amount
(1/3) of 47600
= $15866.666..
= $15867 (approximately)
Final payment = 47600 - 15867
= $31733
$31875 > $31733 > $31100 > $30676.2
Therefore, supplier which gives the best deal of selling light bulbs for the electrician is ZZZ LIGHTING with the total selling amount of
$ 30676.2.
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A water skier is towed 65 m to the south of the starting point, and then is turned 40° cast of south for another 35m. What is the skier’s displacement from the starting point?
Using cosine law,
d^2 = 65^2 + 35^2 - 2(65)(35)cos140
= 8935.5022
d = sqrt(8935.5022)
= 94.5 m
Angle = inverseCos(35sin40 / 94.5) = 76.23 degrees South of East
Help with another slope and intercept ?
Answer:
Slope = 1/3
Y-intercept = 0
Step-by-step explanation:
Hello!
Slope - Intercept Form: y = mx + b
m = slopeb = y-interceptThe slope is the coefficient before the x-variable. Which means that the slope would be 1/3.
The y-intercept is the constant term after the x-term. In this case, there is no term, so the y-intercept is 0.
Answer:
Slope: 1/3
y-intercept: 0
Step-by-step explanation:
y=mx+b
the coefficient (m) of x is always the slope, so therefore the slope is 1/3
the y-intercept (b) is not here in this equation, so the y-intercept is 0
Which is the line x = y?
A, B, C, or D?
Answer:
The correct answer is: C
1:
Give examples of two points that you could use to plot the graph of the function
f(x) = (3x³ + 2)/(x2-5).
The two points that could be used to plot the graph of the function (0, -0.4) and (-0.874, 0)
In this question, we have been given a function f(x) = (3x³ + 2)/(x^2-5).
We need to plot the graph of the function.
We find some coordinates of point on the graph of function.
For x = 0,
f(0) = (30³ + 2)/(0^2-5)
f(0) = 2/(-5)
f(0) = -0.4
For f(x) = 0,
0 = (3x³ + 2)/(x^2-5)
(3x³ + 2) = 0
3x³ = -2
x = -0.874
for x = 1,
f(1) = (3(1)³ + 2)/(1^2-5)
f(1) = 5/(1 - 5)
f(1) = 5/(-4)
f(1) = -1.25
The graph of function f(x) = (3x³ + 2)/(x2-5) is as shown below.
Therefore, the two points that could be used to plot the graph of the function (0, -0.4) and (-0.874, 0)
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NEED ASAP PLSSSS
The arc length of this circle is 9.42 inches. Determine the length of the radius.
Complete your work in the space provided.
The length of radius of the given circle is equivalent to 6
Calculating length of an arcA circle's arc is referred to as a portion or section of its circumference. A chord of a circle is a straight line that can be formed by joining the arc's two ends.
The formula for calculating the length of an arc is expressed as:
L = rФ
where
r is the radius of the circle
Ф is the angle subtended.
Given the following parameters
L = 9.42
Ф = π/2
Determine the radius
r = L/Ф
r = 9.42/(π/2)
r = 2(9.42)/(π
r = 6
This gives the length of the radius of the circle.
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How many subsets does the set S, seasons of the year, have? S={ Summer, Spring, Fall, Winter }.
The number of subsets that the set S , seasons of the year is 16 .
In the question ,
it is given that
the Set S have elements as the seasons of the year , that is
Set S [tex]=[/tex] { Summer , Spring , Fall , Winter }
So , the number of elements that are present in the set S = 4 ,
we know that the number of subsets of the set having n elements is = 2ⁿ .
So , the number of subsets of the set S having 4 elements is = 2⁴ = 16
Therefore , The number of subsets that the set S , seasons of the year is 16 .
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Find 18 and 90 using GCF prime factorization
3/1 divided by 3/4 in simplest form
Answer:
4
Step-by-step explanation:
3/1=3
hence 3/(3/4 )= 3 x4/3=4
Answer:
4
Step-by-step explanation:
keep switch flip
3/1 * 4/3 = 12/3 = 4
200% of x is b min. Find the amount
Answer:
The answer is 269 in.
hope this helps!
Sorry I’m late oops
Step-by-step explanation:
Which expression is equivalent to 5m - (2m - 8) + 12 + 6m?
A 9m + 4
B.9m + 20
C.13m + 4
D. 13m + 20
Answer:
b) 9m + 20
Step-by-step explanation:
Given expression,
→ 5m - (2m - 8) + 12 + 6m
Simplifying the expression,
→ 5m - (2m - 8) + 12 + 6m
→ 5m - 2m + 8 + 12 + 6m
→ (5m - 2m + 6m) + (8 + 12)
→ 9m + 20
Hence, answer is 9m + 20.
which expression includes a coefficient of 2?
A.
[tex]x {}^{2} - 5[/tex]
B. 4x + 2
C. 3(x+2)
D.
[tex]2x {}^{3} - 1[/tex]
Answer:
D
Step-by-step explanation:
The coefficient is the number before the varaible x.
There are 6 people who want to share 26 ride tickets for the carnival. Each person will get an equal number of tickets. How many tickets will each person get? How many tickets will be left over?
Answer:
4 tickets, 2 left over
Step-by-step explanation:
26/6=4.3333 round down to 4
4*6=24 so they can evenly split 24 tickets and will each get 4
26 tickets -the 24 they split evenly = 2 left over
The volume of 10 drops of a liquid is 0.001 fluid ounces.
What is the volume of 10,000 drops?
Answer:
10
Step-by-step explanation:
You take 10,000 and divide it by 10 leaving 1,000. Then, you multiply 1,000 by 0.001 resulting in 10.
256361225 prime factorization
Prime factors from the factors of the given numbers are as follow :
a. 256 = { 2 }
b. 361 = { 19 ]
c. 225 = { 3, 5 }
As given in the question,
Given numbers are as follow:
a. 256 b. 361 c. 225
Prime numbers are those numbers which has only two factors 1 and number itself.
Simplify given numbers to get the prime factors from the factors of the followings are as follow:
a. 256 = 16 × 16
= 2⁴ × 2⁴
= 2⁸
Prime factor of 256 = { 2 }
b. 361 = 19 × 19
19 itself is prime number.
Prime factor of 361 = { 19 }
c. 225
225 = 15 × 15
= ( 3 × 5 )²
Prime factors are { 3, 5 }
Therefore, prime factors from the factors of the given numbers are as follow :
a. 256 = { 2 }
b. 361 = { 19 ]
c. 225 = { 3, 5 }
The complete question is :
Find the prime factorization of the following:
a. 256 b. 361 c. 225
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What is the domain of the function
y=³√x-1
The domain of the function is real numbers.. The value is x-1 = is a real number
What is meant by domain?The domain of a function is the set of values that we are allowed to enter into our function. This set consists of the x values for a function like f. (x). The set of values that a function can accept as input is known as its range. Once we enter an x value, the function returns this list of values.
Think about the equation y = f(x), where x and y are the independent and dependent variables. If a value for x successfully enables the creation of a single value y using another value for x, it is said to be in the domain of the function f.
A positive number has a positive cubic root.
Zero has a cubic root of zero.
A negative number has a negative cubic root.
Given ,
This implies that any real number's cubic root is also a real number.
y = ³√x-1
³√x-1 = x-1 is a cubic root
x-1 = is a real number
Therefore The value of real number is x-1 = is a real number
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The fox population in a certain region has a continuous growth rate of 4 percent per year. It is estimated that the population in the year 2000 was 15600.
(a) Find a function that models the population t years after 2000 ( t=0 for 2000).
Hint: Use an exponential function with base e.
Your answer is P(t)=
(b) Use the function from part (a) to estimate the fox population in the year 2008.
Your answer is (the answer must be an integer)
a. The function that models the population t years after 2000 is
Pf = 15600(1.04)^t
b. The estimate of the fox population in the year 2008 is 21349.67.
Given,
A fox population in a certain region has a continuous growth rate of 4% per year.
It is estimated that the population in the year 2000 was 15600.
we are asked to determine a function that models the popualtion t years after 2000 (t = 0 for 2000)
Pf = Pi(1 + r)^t where Pf is the final population, Pi is the initial population, r is the annual growth rate in decimal (not %), and t is the time in years.
a. Pf = 15600(1.04)^t
b. Pf = 15600(1.04)⁸ = 24497.386
= 21349.67
hence we get the required answers.
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Describe the features of the function that can be easily seen when a quadratic function is given
in the form: y=a(x − ℎ)^2 + and how they can be identified from the equation.
Please help
The function that can easily be seen when a quadratic function is given
in the form: y = a (x − ℎ)^2 + K are
the vertex of the parabolawhere the axis of symmetry of the parabola liesthe focus of the parabola the direction the curve opens toHow to get the required detailsA parabola is given in factored form when it is in the form
y = a (x − ℎ)^2 + K
the factored form can be rearranged
(y - k) = a (x − ℎ)^2
The vertex is v(h, k)
the axis of symmetry of the parabola when the parabola is written in the form as in the question is of the formula x = -b/2a.
this says that the axis of symmetry is a vertical line
the focus is given by f(h, k + 1/4a)
"a" curve opens up when a is positive and down when a is negative. when (x − ℎ) = a (y − k)^2, a opens left or right
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Angles A and B are supplementary. Determine the measure of angle A if the measure of angle B is 126.4°.
The measure of angle A is 53.6° if angle A and angle B are supplementary angles.
According to the question,
We have the following information:
Angles A and B are supplementary.
Measure of angle B = 126.4°
We know that when two angles are supplementary then it means that the sum of these angles will be 180°.
So, we have the following expression:
Angle A + angle B = 180
Angle A+126.4 = 180
Subtracting 126.4 from both the sides of the equation:
Angle A = 180-126.4
Angle A = 53.6°
Hence, the measure of angle A is 53.6° if angle A and angle B are supplementary.
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A restaurant customer left $1.30 as a tip. The tax was 6 and the tip was 6% of the cost including tax.
a. What piece of information is not needed to compute the bill after tax and tip?
b. What was the total bill?
a) The piece of information not required to compute the bill after tax and tip is the cost of the item purchased by the customer.
b) The total bill paid by the restaurant customer is $22.97.
How is the total bill determined?The total bill the restaurant customer paid represents 100% of $1.30 plus the tip.
Proportionately, the amount can be computed using the percentage of the tip to equate the dollar amount.
The result is the cost of the item plus tax. Then, the total bill includes the cost, tax, and tip.
Tip left by customer = $1.30
Sales tax = 6%
Cost + tax = x
Tip = 6% of x
x = $21.67 ($1.30 ÷ 6%)
The total bill paid is $22.97 ($21.67 + $1.30).
Thus, using proportions, the restaurant customer paid $22.97, which includes the item cost, tax, and tip.
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Consider two consecutive positive integers such that the square of the second integer added to 6 times the first is equal to 106.
The Two Consecutive integers are 7 and 8.
What is an integer?
A full number, not a fraction, that can be positive, negative, or zero is called an integer (pronounced IN-tuh-jer). Integer examples include: -5, 1, 5, 8
Let the first Integer be x
Since the two numbers are consecutive
therefore the second number will be x+1
Now given:
square of the second integer added to 6 times the first is equal to 106.
( x+1 )²+6x=106
Expand ( x+1 )² using [tex](a+b)^2=a^2+2ab+b^2[/tex]
x²+2x+1+6x=106
x²+8x+1-106=0
x²+8x-105=0
Factor the expression
(x-7)(x+15)=0
x-7=0, x+15=0
x=7, x=-15
Now we get 2 values of x which is 7 and -15.
Since it is given that number is a positive Integer hence the number will be 7.
and the other number would 7 + 1 = 8.
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if 4 boxes of cereal cost $16.24 how much does one box of cereal cost?
Answer: 4.06
Step-by-step explanation:
if you divided 4 into 16.24 your answer will be 4.06!!
Answer:
$4.06
Step-by-step explanation:
To find the answer, divide 16.24 by 4
This gives you the answer of how much each box costs (assuming each cereal box costs the same)
The answer is 4.06
A chemist mixes 125 milliliters of a solution that is 18% acid with 500 milliliters of pure acid.
Answer the questions below. Do not do any rounding.
(a) How many milliliters of acid are in the resulting mixture?
(b) What percentage of the resulting mixture is acid?
The amount of milliliters of acid that are in the resulting mixture is 522 ml and the percentage of the resulting mixture is 83.6%.
How to find the milliliters of acid?a. Milliliters of acid:
Milliliters of acid = ( .18 x 125ml) +500 ml
Milliliters of acid = 522.5ml
b. Percentage of the resulting mixture
Percentage of the resulting mixture = 522.5ml /(125ml + 500 ml)
Percentage of the resulting mixture = 522.5ml / 625 ml × 100
Percentage of the resulting mixture =83.6%
Therefore the milliliters of acid is 522.5ml.
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