The estimated total population size of stickleback fish in the lake is approximately 530 individuals.
The mark and recapture method can be used to estimate the total population size of a species in a particular area. Based on the information provided, we can use the Lincoln-Petersen method to estimate the population size.
The formula for the Lincoln-Petersen method is
N = (M x R) / C
Where
N = total population size
M = number of individuals in the first sample (marked individuals)
R = number of individuals in the second sample (recaptured individuals)
C = number of marked individuals recaptured in the second sample
Using the given information, we can plug in the values to the formula
N = (255 x 162) / 78
N = 529.62
N = 530
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An event manager recorded the number of people in different age groups who attended a music concert:
A histogram titled Concert Audience is shown. The horizontal axis is labeled Age Group in years with bins 18 to 24, 25 to 31, 32 to 38, and 39 to 45. The vertical axis labeled Number of People with values from 0 to 120 at intervals of 20. The first bin goes to 40, the second goes to 60, the third goes to 100, and the last goes to 20.
Which data table accurately represents the data in the histogram?
Age Group Number of People
18–24 40
25–31 100
32–38 200
39–45 220
Age Group Number of People
18–24 40
25–31 60
32–38 100
39–45 20
Age Group Number of People
18–24 20
25–31 100
32–38 60
39–45 40
Age Group Number of People
18–24 220
25–31 200
32–38 100
39–45 40
The option A is the correct answer if An event manager recorded the number of people in different age groups who attended a music concert:
What is Horizontal axis ?
In a graph or chart, the horizontal axis, also known as the x-axis, is the axis that runs horizontally from left to right.
Based on the histogram, the correct data table is:
A histogram is a graphical representation of data that shows the frequency distribution of a set of continuous data. In this case, the histogram titled "Concert Audience" shows the number of people in different age groups who attended a music concert.
The horizontal axis of the histogram represents the age groups in years, with bins from 18 to 24, 25 to 31, 32 to 38, and 39 to 45. The vertical axis represents the number of people in each bin, with values from 0 to 120 at intervals of 20.
To create a data table that accurately represents the data in the histogram, we need to look at the heights of the bars in each bin and determine the corresponding number of people. From the histogram, we can see that:
The bin for ages 18 to 24 has a height of 40, which means that 40 people in that age group attended the concert.
The bin for ages 25 to 31 has a height of 100, which means that 100 people in that age group attended the concert.
The bin for ages 32 to 38 has a height of 200, which means that 200 people in that age group attended the concert.
The bin for ages 39 to 45 has a height of 20, which means that 20 people in that age group attended the concert.
Age Group Number of People
18–24 40
25–31 100
32–38 200
39–45 20
Therefore, The option A is the correct answer.
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We may conclude after answering the presented question that Option 3 expression has incorrect numbers for both age groups and the number of people.
what is expression ?An expression in mathematics is a collection of representations, numbers, and conglomerates that mimic a statistical correlation or regularity. A real number, a mutable, or a mix of the two can be used as an expression. Mathematical operators include addition, subtraction, fast spread, division, and exponentiation. Expressions are often used in arithmetic, mathematics, and form. They are employed in the depiction of mathematical formulas, the solving of equations, and the simplification of mathematical relationships.
The right data table should include the following information based on the provided histogram:
Age Group Number of People
18–24 40
25–31 60
32–38 100
39–45 20
Therefore, the correct answer is:
Age Group Number of People
18–24 40
25–31 60
32–38 100
39–45 20
Option 2 and Option 4 have inaccurate numbers for the number of persons in each age group, whilst Option 3 has incorrect numbers for both age groups and the number of people.
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50 PTS PLS GIVE EXPLANATION.
Answer:
0-18= -18
Step-by-step explanation:
you're starting with 0 and subtracting 18 so the answer is -18
cars of length 2 try to park on a length l road. each minute, a new car parks at a uniformly random spot on the road without crashing into another car or running off the road. when no more cars fit, what is the expected size of the largest gap between adjacent cars (as a function of l)? how about the smallest gap between adjacent cars?
The expected size of the largest gap between adjacent cars (as a function of l) is l/(n + 1), and the expected size of the smallest gap between adjacent cars is 2.
Let us consider that cars of length 2 try to park on a length l road. Each minute, a new car parks at a uniformly random spot on the road without crashing into another car or running off the road.
When no more cars fit, the expected size of the largest gap between adjacent cars is l/(n + 1) and the smallest gap is 2.
The expected size of the largest gap between adjacent cars (as a function of l) is l/(n + 1).
Let n be the number of cars parked on the road. Then the total length of the cars parked is 2n.
If the largest gap is a distance g, then the total length of the gaps is l − 2n. Then,gap length:
g (n + 1) ≤ l - 2ng ≤ l − (n + 1)g
Dividing through by (n + 1)g and rearranging:
g ≤ l/(n + 1) (largest gap)g ≥ 2 (smallest gap)
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How do you find the tangent between circles?
To find the tangent between two circles, you need to draw a line that is tangent to both circles at the same point. This point of tangency is the point where the two circles meet.
To draw the tangent line, you can first draw a line connecting the centers of the two circles. This line will bisect the point of tangency. Next, draw a perpendicular line to this bisecting line passing through the point of intersection of the circles. The intersection of this line with each of the circles will be the points of tangency. Connect these two points of tangency with a line, and you will have drawn the tangent line between the two circles.
The tangent line between two circles is useful in solving problems related to geometry and physics, such as determining the position of a moving object relative to two stationary objects represented by the circles.
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What are two ways to write -2(n + 3) = 13?
Which expression is equivalent to 2y + 2 + y + 3 + 2y
Answer: 5y + 5
Step-by-step explanation: add all the like terms such as 2y + 2y + y = 5y as y = 1y and 2 + 3 = 5, which makes the expression 5y+5
if it's wrong, im sorry
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What would be the inverse of the equation
y=log(1/4)x^5
The inverse of the function is [tex](1/4)^{x/5}[/tex].
What is an inverse function?
A function that reverses the effects of another function is called an inverse function. When y=f(x) and x=g, a function g is the inverse of a function f. (y). Applying f and then g is equivalent to doing nothing, in other words. This can be expressed as g(f(x))=x in terms of the relationship between f and g.
Here, we have
Given: equation y = log(1/4)x⁵
A function g is the inverse of function f if for y = f(x), x = g(y)
y = log(1/4)x⁵
Replace x with y
x = log(1/4)y⁵
Solve for y, we get
y = [tex](1/4)^{x/5}[/tex]
Hence, the inverse of the function is [tex](1/4)^{x/5}[/tex].
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Bestie is going golfing for 3 days, how many golf clubs should there be?
Answer:
According to the USGA, a golfer is allowed to have **14 clubs** in their bag. This may include three woods (driver, 3-wood and 5-wood), eight irons (3-9 iron and pitching wedge), and putter¹. However, while you're in the novice stage as a golfer, you don't really need a full set of 14 clubs. In fact, you're better off cutting that number down nine or 10, which will make club selection easier on the course and boost the quality of your practice².
Step-by-step explanation:
The number of golf clubs that Bestie should bring for a 3-day golfing trip depends on personal preference, skill level, and the type of golf course being played. Typically, a golfer may carry 14 clubs in their bag, which includes a driver, fairway woods, irons, wedges, and a putter. However, some golfers may prefer to carry fewer clubs or more clubs depending on their playing style and the course conditions. Therefore, the specific number of golf clubs that Bestie should bring is subjective and cannot be determined without further information.
Answer:
The minimum number of clubs needed in golfing is 5, the highest you can have is 14.
Step-by-step explanation:
what is the geometric mean of 5 and 14
[tex] \: \huge \mathfrak{ \underbrace{\overbrace{ \pink{A}{\blue{n}}{\green{s}}{ \purple{w}{ \orange{e}{ \red{r}}}}}}} \\ \\ \rightarrow{\bf{\sf{8.366}}} [/tex]
[tex] \: \large \tt \underline{\green{Solution}} [/tex] :
Given : Numbers = 5 , 14
N = 2
Formula for Geometric Mean[tex] \sf Geometric \: Mean \: = ( x_{1} \times x_{2} \times x_{3}........ x_{n}) {}^{ \frac{1}{n} } \\ \\ = ( 5 \times 14) {}^{ \frac{1}{2} } \\ \\ = (70) {}^{ \frac{1}{2} } \\ \\ or \: (70) {}^{0.5} \\ \\ \rightarrow\fbox{ \blue{8.366}}[/tex]
Landon and Tallon are starting their own baseball batting cage business named BeLikeMoss Cages. Tallon wants to charge $10 per hour with no service fee. Landon wants to charge a service fee of $10 plus $5 per hour. How many hours must they work for their charge to be the same?
Their charges will never be equal since Landon's charge will always be higher due to the additional service fee, regardless of the number of hours they work.
To find the number of hours they must work for their charges to be the same, we can set their charges equal to each other and solve for h, the equation of number of hours
10 = 10 + 5h
Subtracting 10 from both sides, we get
0 = 5h
Dividing both sides by 5, we get:
h = 0
This tells us that their charges will never be equal since no matter how many hours they work, Landon's charge will always be higher due to the additional service fee.
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what's common among these numbers?
2, 5, 19, 23, 29, 31, 43, and 47
Answer: Prime Numbers
I’m in desperate need of help.
Please
The length of opposite side is 34.5 meters. The length of opposite side is 132 feet. Therefore, the height of the plane above the level of the atoll is approximately 460 meters to the nearest meter.
What is trigonometry?Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. It is used to solve problems involving triangles, such as finding the unknown sides or angles of a triangle, or finding the distance or height of an object that is too far away to measure directly.
Here,
6. To find the horizontal distance Viola has covered, we need to use trigonometry. The angle of 9° is the angle between the hill and the horizontal, so we can use the tangent function:
tangent(9°) = opposite/hypotenuse
where the opposite side is the horizontal distance we want to find and the hypotenuse is the distance Viola has driven, which is 200 meters.
Solving for the opposite side, we get:
opposite = tangent(9°) x hypotenuse
opposite = tan(9°) x 200
opposite ≈ 34.5 meters
7. Using trigonometry again, we can find the height of the building. The angle shown in the diagram is the angle of elevation from the students' location to the top of the building, and the distance shown is the horizontal distance between the students' location and the base of the building. We can use the tangent function again:
tangent(angle of elevation) = opposite/adjacent
where the opposite side is the height of the building we want to find, and the adjacent side is the horizontal distance from the students to the building, which is given as 150 feet.
Solving for the opposite side, we get:
opposite = tangent(angle of elevation) x adjacent
opposite = tan(41°) x 150
opposite ≈ 132 feet
8. In this problem, we can use trigonometry to find the height of the plane. We know the angle of depression from the plane to the atoll is 7°, which means the angle of elevation from the atoll to the plane is also 7°. We also know the horizontal distance from the plane to the atoll is 3,729 meters. Let h be the height of the plane above the level of the atoll. Then we can set up the following equation using the tangent function:
tan(7°) = h / 3,729
Solving for h, we get:
h = 3,729 * tan(7°)
Using a calculator, we get:
h ≈ 460 meters
9. In this problem, we can use trigonometry to find the height of the pole. Let h be the height of the pole above the ground, and let d be the horizontal distance from the surveyor to the base of the pole. Then we can set up the following right triangle:
The opposite side is the height of the pole h.
The adjacent side is the horizontal distance d = 140 feet.
The angle of elevation to the top of the pole is 44°.
We can use the tangent function to find the height of the pole:
tan(44°) = h / 140
Solving for h, we get:
h = 140 * tan(44°)
Using a calculator, we get:
h ≈ 157 feet
10. In a 30°-60°-90° triangle, the sides are in a ratio of 1:√3:2, where the hypotenuse is twice the length of the shorter leg. Let x be the length of the shorter leg, then the longer leg is x√3 and the hypotenuse is 2x. In this problem, we are given that the hypotenuse has a length of 18, so we can set up the following equation:
2x = 18
Solving for x, we get:
x = 9
Therefore, the shorter leg has a length of 9, and the longer leg has a length of 9√3.
The perimeter of the triangle is the sum of the lengths of its sides, so we have:
Perimeter = 9 + 9√3 + 18
Using the fact that √3 ≈ 1.732, we can simplify this expression to:
Perimeter ≈ 9 + 9(1.732) + 18
Perimeter ≈ 9 + 15.588 + 18
Perimeter ≈ 42.588 meters
Therefore, the perimeter of the triangle is approximately 42.588 units.
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Which of the following equations will produce the graph shown below?
A. X^2- y^2/4= 1
B. Y^2/9 - x^2/4=1
C. Y^2- x^2/9= 1
D. Y^2/2 - x^2/4= 1
By comparing this form to the available choices, we can observe that option B provides the equation that best fits the graph: y²/9 - x²/4 = 1.
What is equation ?
A mathematical equation is a statement that demonstrates the equality of two expressions, usually by placing an equal sign before them. It depicts a connection connecting more than one variable and can be applied to situations to uncover unknown values. Variables, constants, plus mathematical operations including addition, subtract, multiplication, and division are frequently used in algebra equations. Equations include the following: 2x + 3 = 7 y = mx + b , a² + b² = c²
given
The hyperbola graph seen in the figure includes a transverse axis along the y-axis and a centre at (0,0).
The separation between the foci is 8 units, while the separation between the vertices is 6 units.
The equation for this hyperbola's standard form is:
(y - k)²/a² - (x - h) (x - h)²/b² = 1
where (h,k) designates the hyperbola's centre and (a,b) designates the distances between it and its vertices and co-vertices.
By comparing this form to the available choices, we can observe that option B provides the equation that best fits the graph: y²/9 - x²/4 = 1.
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Cameron has 58 m of fencing to build a three-sided fence around a rectangular plot of land that sits on a riverbank. (The fourth side of the enclosure would be the river.) The area of the land is 380 square meters. List each set of possible dimensions (length and width) of the field.
Answer:
The list of set of dimensions for fencing the building around a rectangular plot of land is 14.5 meters and 29 meters.
Area of a rectangle
area of rectangle = lw
where
l = length
w = width
Therefore,
perimeter = 2w+ l
58 = 2w + l
l = 58 - 2w
Hence,
area = w(58 - 2w)
380 = 58w - 2w²
-2w² + 58w - 380 = 0
-w² + 29w - 190 = 0
The dimension w can be found as follows;
w = - b / 2a
where
a = -1
b = 29
w = - 29 / 2 × -1
w = 14.5 meters
Then,
l = 58 - 2w
l = 58 - 2(14.5)
l = 29 meters
Therefore, the dimensions are 14.5 meters and 29 meters.
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-17.9 as a mixed number.
Answer:
-17 9/10
Step-by-step explanation:
a standard pair of six-sided dice is rolled. what is the probability of rolling a sum less than 11 ? express your answer as a fraction or a decimal number rounded to four decimal places.
the probability of rolling a sum less than 11 is 34/36, or 0.9444 when rounded to four decimal places.
Define probabilityThe possibility or chance that an event will occur is quantified by probability. It is a numerical value between 0 and 1, with 0 indicating that an event is impossible and 1 indicating that an event is certain to occur.
The only ways to get a sum of 11 or greater when rolling two dice is to get either a sum of 11 (with a 6 and a 5) or a sum of 12 (with two 6's).
There are 6 x 6 = 36 possible outcomes when rolling two dice, and only one of them results in a sum of 11 and one of them results in a sum of 12. Therefore, there are 36 - 2 = 34 outcomes that result in a sum less than 11.
So, the probability of rolling a sum less than 11 is 34/36, or 0.9444 when rounded to four decimal places.
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unit 8 right triangles and trigonomerty homework3 trigonomerty rations and finding missing sides
The value os x in the following right triangles and trigonometry are:-
Question 6: x= 13.74
question 7: x= 18.52
question 8: x= 60.12
question 9: x= 3.7
Question 6:
tan θ = opposite/adjacent
tan 58° = 22/x
xtan58° = 22
x = 22/ tan58°
Since tan 58° = 1.6003345
x= 22/ 1.6003345
x ≈ 13.74
question 7:
tan θ = opposite/adjacent
tan 51° = x/15
15tan51° = x
x = 15 * 1.2348971
Since tan 51° = 1.2348971
x ≈ 18.52
question 8:
cosθ = adjacent/hypotenuse
cos 37° = 48/x
xcos37° = 48
x = 48/ cos37°
Since cos 37° = 0.79863551004
x= 48/ 0.79863551004
x ≈ 60.12
question 9:
sinθ = opposite/hypotenuse
sin 24° = x/9
9sin24° = x
Since sin 24° = 0.40673664307
x= 9 * 0.40673664307
x ≈ 3.7
The complete question is:-
Unit 8: Right Triangles & Trigonometry
Homework 3: Trigonometry:
Ratios & Finding Missing Sides
Answers for the remaining four problems?
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Leah and Josh are buying a $550,000 home. They have been approved for a 3.70% APR mortgage. They made a 14% down payment and will be closing on September 6. How much should they expect to pay in prepaid interest at the closing?
Therefore, Leah and Josh should expect to pay $1,156.78 in prepaid interest at the closing.
What is equation?An equation is a mathematical statement that shows that two expressions are equal to each other. An equation typically contains one or more variables (represented by letters), which are unknown values that we want to find. Equations are used to solve problems in a wide variety of mathematical and scientific fields, as well as in everyday life.
Here,
To calculate the prepaid interest that Leah and Josh will have to pay at the closing, we need to determine the daily interest rate and the number of days between the closing date and the end of the month. Here are the steps:
1. Calculate the total amount of the down payment:
Down payment = 14% x $550,000
Down payment = $77,000
2. Calculate the loan amount:
Loan amount = $550,000 - $77,000
Loan amount = $473,000
3. Calculate the monthly interest rate:
Monthly interest rate = (APR / 12)
Monthly interest rate = (3.70% / 12)
Monthly interest rate = 0.00308333
4. Calculate the daily interest rate:
Daily interest rate = (monthly interest rate / 30)
Daily interest rate = (0.00308333 / 30)
Daily interest rate = 0.00010278
5. Determine the number of days between the closing date (September 6) and the end of the month (September 30):
Number of days = 30 - 6
Number of days = 24
6. Calculate the prepaid interest:
Prepaid interest = (loan amount x daily interest rate x number of days)
Prepaid interest = ($473,000 x 0.00010278 x 24)
Prepaid interest = $1,156.78
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Jane spent a total of $20 at the grocery store. Of this amount, she spent $2 on fruit. What percentage of the total did she spend on fruit? ✓14 ✓15
The percentage of the total that she spent in fruit is 10%.
What percentage of the total did she spend on fruit?We know that Jane spent a total of $20 at the grocery shop, and we know that she spent $2 in fruit.
We want to find the percentage of the total that she spend on fruit, to get this, we need to take solve the equation:
Percentage = 100%*(amount that she pend on fruit)/(total amount)
Replacing the values that we know there we will get:
P = 100%*($2/$20)
P = 100%*1/10 = 10%
She spent 10% of the total amount in fruit.
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PLEASE ANSWER SOON!!
Select the statement that describes this expression: 10 + one fourth x (5 + 3) – 3.
one fourth of 10 times the sum of 5 and 3, minus 3
3 more than 3 plus 5 multiplied by one fourth, then add 10
10 times one fourth plus 3 and 5, minus 3
10 more than one fourth of the sum of 5 and 3, then subtract 3
Answer: 10 more than one fourth of the sum of 5 and 3 then subtract 3
Step-by-step explanation:
separate each number for its explanation.
10 more than --> "10+"
one fourth of [remember in fractions, "of" always means multiply] --> "one fourth x"
sum of 5 and 3 --> "(5+3)"
subtract 3 --> "-3"
Answer:
the last one. (10 more than one fourth of the sum of 5 and 3, then subtract 3)
7. From the parking lot at the Red Hill Shopping Center, the angle to the top of the hill is 25⁰.
From the base of the hill the angle of elevation to the top of the hill is 55°. The horizontal
distance between these two sight points is 740 feet. How high is Red Hill?
The height of Red hill is 513.8 feet.
What does mean by the angle of elevation?
The angle of elevation is the angle created between the line of sight and the horizontal. The angle created is an angle of elevation if the line of sight is upward from the horizontal line. This angle eventually develops above the surface. The angle of elevation is made in such a way that it is above the observer's eye, as the name suggests.
Given:
Distance from the parking lot to the foot of the hill = 740feet
The angle of elevation from a parking lot and the foot of the hill is 25 and 55 degrees respectively.
For easy understanding, assume triangle edges with alphabets as shown in the figure.
Now, let's take ΔACD,
CotD = DC/AC
Cot 55 = y/x ⇒ 0.7 =y/x
⇒ y = 0.7x
In ΔABC
Tan B = AC/BC
Tan 25 = x/(740+y) (y = 0.7x )
0.467 = x/(740+0.7x )
x = 0.467(740+0.7x )
= 345.5 + 0.326x
0.6731x = 345.5
∴ x = 513.8 feet
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Which of the following best describes the solution to the system of equations below?
4x + 9y = 6
4x + 9y = 15
A.
The system of equations has infinitely many solutions.
B.
The system of equations has exactly one solution where x= 0and y=2/3 .
C.
The system of equations has exactly one solution where x=6 and y=15 .
D.
The system of equations has no solution
Answer:
The System of equations has no solution
Step-by-step explanation:
Graphing both equations will produce 2 lines which are parallel because both of them has the same slope but intersecting with X and Y axis in different points
80ft Tiffany makes custom skateboards. Her profit can be modeled by p(x) = -15x² + 3780x - 176700, where x is the price she charges and p(x) is her profit.
Answer the following questions algebraically. What will her maximum profit be?
What should she charge to maximize her profits?
What would her profit be if she charged $100?
- 15(100)² + 3780(100) -176700 $51,300
The profit function is modeled as follows:
p(x) = -15x² + 3780x - 176700.
It is a quadratic function with coefficients given as follows:
a = -15, b = 3780, c = -176700.
The leading coefficient of the quadratic function is negative, hence the profit will be maximized at the vertex of the quadratic function.
The x-coordinate of the vertex, representing the price which maximizes the profit, is given as follows:
x = -b/2a
x = -3780/-30
x = $126.
Then the maximum profit would be given as follows:
p(126) = -15(126)² + 3780(126) - 176700.
p(126) = $61,400.
If she charged $100, the profit would be given as follows:
p(100) = -15(100)² + 3780(100) - 176700.
p(126) = $51,300.
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can someone tell me the answer to this question?
Answer:
x = 4.6
Step-by-step explanation:
5.4 *5.4 + 7.2 * 7.2 = 78.88
x * x + 7.6 *7.6 = 78.88
x * x = 21.12
x = 4.6
Answer:
using Pythagoras
diagonal comes out to be 9
again
using Pythagoras
x = √9²-7.6² = √23.24 =4.82
Please help me with this geometry problem :) (problem on image)
from the picture above we can see that we have an altitude or height for the triangle of 5, so then
[tex]\textit{height of an equilateral triangle}\\\\ h=\cfrac{s\sqrt{3}}{2} ~~ \begin{cases} s=\stackrel{side's}{length}\\[-0.5em] \hrulefill\\ h=5 \end{cases}\implies 5=\cfrac{s\sqrt{3}}{2}\implies 10=s\sqrt{3} \\\\\\ \cfrac{10}{\sqrt{3}}=s\implies 5.8\approx s = x[/tex]
3. If Y(3,-1) is the midpoint of XZ with X(9, 2), what are the coordinates of the midpoint of YZ? A. (-3,-4) B. (-3,-1.5) C. (0, -2.5) D. (3,4)
The answer is option C: (0, -2.5)
What is the coordinates of midpoint?The midpoint is the point located exactly halfway between two other points on a line segment. It is also sometimes referred to as the "halfway point" or the "middle point."
To find the midpoint of a line segment, you can use the midpoint formula,
Midpoint = [tex]\frac{(x_1 + x_2)}{2}, \frac{(y_1 + y_2)}{2}[/tex]
We know that Y is the midpoint of XZ, which means that the coordinates of Y are the average of the coordinates of X and Z.
Therefore; Y = (X+Z)/2
or, Z = 2Y - X
Given that; the coordinates are X = (9, 2) and Y = (3, -1)
Put the values of coordinates;
Z = 2*(3, -1) - (9, 2)
Z = (6, -2) - (9, 2)
Z = (-3, -4)
So the coordinates of Z are (-3, -4).
Now the midpoint of YZ,
Midpoint formula: Midpoint = [tex]\frac{(x_1 + x_2)}{2}, \frac{(y_1 + y_2)}{2}[/tex]
Y = (3, -1) = (x₁ , y₁)
Z = (-3, -4) = (x₂ , y₂)
Midpoint = [tex]\frac{(3) + (-3)}{2}, \frac{(-1) + (-4)}{2}[/tex]
Midpoint = (0, -2.5)
So the coordinates of the midpoint of YZ are (0, -2.5)
Therefore, the answer is option C: (0, -2.5)
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The relationships between angle pairs are based on their ______ or on their ______ in relation to each other.
measure
orientation
intersection
names
position
The relationships between angle pairs are based on their position or on their orientation in relation to each other.
Angles are measured in degrees, and the measure of an angle determines its size. However, the relationships between angle pairs are not solely based on their measures. The position of two angles in relation to each other, such as whether they share a vertex or lie on the same line or plane, can determine their relationship. Additionally, the orientation of the angles can also play a role in their relationship, such as whether they are adjacent, vertical, complementary, supplementary, or congruent. Understanding these relationships is important in geometry and can help in solving problems and proving theorems.
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What is the following product? Assume d is greater than or equal to 0
D
D3
3(3/d
/3d
The product of (3√d)(3√d)(3√d) is equal to: (3√d)(3√d)(3√d) = 3^3(√d)^3 = 27d^(3/2). Therefore, the answer is 27d⁽³/²⁾.
The expression (3√d)(3√d)(3√d) can be simplified by multiplying the coefficients and the radicals separately. The coefficient 3 is raised to the power of 3, which gives 27. The radical √d is raised to the power of 3, which gives d⁽³/²⁾ since the exponent is multiplied by 3. Therefore, the simplified expression is 27d⁽³/²⁾. This means that the product of three cube roots of d is equal to 27 times the cube root of d cubed, which simplifies to 27 times d raised to the power of 3/2.
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Complete question:
What is the following product? Assume d≥0. (3√d)(3√d)(3√d)
d
d³
3(3√d)
√3d
Find the area of the triangle
height 3
Lenth 4
Answer:
12 units^2
Step-by-step explanation:
5% of a number is 23. 1% of the same number is 4.6 work out 16% of the number
Answer:
73.6
Step-by-step explanation:
lets say that x is our number.
x * 0.05 = 23
x * 0.01 = 4.6
just solving one of these equations will give us x = 460.
now, 16% of 460 is 460 * 0.16 = 73.6