What is the best next step in the construction of a line that passes through point C and is parallel to AB?
Answers
By constructing these arcs and connecting the appropriate points, we ensure that the newly drawn line passing through point C is parallel to line AB. Remember to use a straightedge to draw the lines accurately and ensure that the arcs intersect correctly.
To construct a line that passes through point C and is parallel to line AB, the best next step is to use a compass to mark an arc centered at point C that intersects line AB at two distinct points.
Here are the steps:
1) Take a compass and set its width to a convenient distance.
2) Place the compass point on point C and draw an arc that intersects line AB at two different points, let's call them D and E.
3) With the compass width still set, place the compass point on point D and draw an arc that intersects the previously drawn arc.
4) Without changing the compass width, place the compass point on point E and draw another arc that intersects the previous arc.
5) Label the point where the two new arcs intersect as F.
6) Draw a straight line passing through point C and point F. This line will be parallel to line AB.
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Related Questions
Which set of numerical values represents the minimum, lower quartile, median, upper quartile, and maximum, in that order, of the box plot of this data set?
51, 51, 53, 53, 54, 55, 55, 56, 58, 58, 58, 59, 60
51, 54, 56, 58, 60
51, 53, 56, 59, 60
53, 54, 55, 59, 60
51, 53, 55, 58, 60
Answers
The set of numerical values that represents the minimum, lower quartile, median, upper quartile, and maximum, in that order, is:
51, 53, 55, 58, 60
To determine the minimum, lower quartile, median, upper quartile, and maximum of the given data set, we can arrange the values in ascending order:
51, 51, 53, 53, 54, 55, 55, 56, 58, 58, 58, 59, 60
Arranging the values in ascending order gives us:
51, 51, 53, 53, 54, 55, 55, 56, 58, 58, 58, 59, 60
The minimum value is 51.
The lower quartile (Q1) is the median of the lower half of the data, which is 53.
The median (Q2) is the middle value of the data set, which is 55.
The upper quartile (Q3) is the median of the upper half of the data, which is 58.
The maximum value is 60.
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Saturday Pizza Orders at Pizza Palace
Pepperoni 24
Beef 36
Sausage 21
Cheese 38
Mushroom 6
What percent
of orders were
for beef?
Round to the
nearest percent.
Answers
Answer: 28.8%
Step-by-step explanation:
First, add all the pizzas together. This gives us the total; 125
Next, put 36 over the total. 36/125.
Divide 36/125. Equals .288
When doing percentage, You multiply your decimal by 100, or bounce the decimal twice to the right. This gets you 28.8%
A square, with sides of length x cm, is inside a circle.
Each vertex of the square is on the circumference of the circle.
The area of the circle is 64 cm².
Work out the value of x.
Give your answer correct to 3 significant figures.
Answers
The value of x will be 6.383cm.
Solution to Circle Geometry problem
Point to note
The diameter of the circle is the diagonal of the squareEach half of the square formed a right angle triangleWe can use the Pythagorean theorem to find the length of the diagonal which is same as diameter
diameter² = side² + side²
diameter² = 2 * x²
diameter = √(2 * x²)
Since the diameter is equal to twice the radius, we have:
diameter = 2 * radius
radius = diagonal / 2
radius = √(2 * x²) / 2
Recall that area of the circle is given by:
area = πr²
where r is the radius
Substituting the expression for the radius, we get:
64 cm² = π * (√(2 * x²) / 2)²
64 cm² = π * (2 * x² / 4)
64 cm² = π * (x² / 2)
128 = π * x²
Solving for x, we get:
x² = 128 / π
x = √(128 / π)
x = 6.383
Therefore, the value of x is approximately 6.383cm.
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Aprende con un ejemplo
GH tiene puntos finales en G (1, 7) y H (1, 9). Encuentre el punto medio M de GH .
Escribe las coordenadas como decimales o enteros.
METRO =
Answers
Answer:
Therefore, the coordinates of the midpoint M are (1, 8).
Step-by-step explanation:
The midpoint formula is:
M = ((x1 + x2)/2, (y1 + y2)/2)
where (x1, y1) and (x2, y2) are the coordinates of the endpoints.
Using this formula, we have:
M = ((1 + 1)/2, (7 + 9)/2) = (1, 8)
Therefore, the coordinates of the midpoint M are (1, 8).
You deposit $400 in an account that pays 2.34% annual
compounded monthly. What is the balance after
interest
10 years?
A=
Answers
The balance after 10 years, considering monthly compounding, would be approximately $512.69.
To calculate the balance after 10 years, we can use the formula for compound interest:
A = [tex]P(1 + r/n)^{(nt)[/tex]
A is the final balance
P is the principal amount (initial deposit)
r is the annual interest rate (in decimal form)
n is the number of times the interest is compounded per year
t is the number of years
In this case, the principal amount (P) is $400, the annual interest rate (r) is 2.34% or 0.0234, the interest is compounded monthly (n = 12), and the number of years (t) is 10.
Using these values, we can calculate the final balance (A):
A = $400(1 + 0.0234/12)⁽¹²ˣ¹⁰⁾
A = $400(1.00195)¹²⁰
A ≈ $400(1.28172)
A ≈ $512.69
We may use the compound interest calculation to determine the balance after 10 years:
A = [tex]P(1 + r/n)^{(nt)[/tex]
The ultimate balance is A.
P stands for the initial deposit's principal.
The yearly interest rate is represented by the decimal r, while the number of times it is compounded annually is represented by n.
The number of years is t.
In the above scenario, the principle (P) is $400, the annual interest rate (r) is 2.34%, or 0.0234, the interest is compounded on a monthly basis (n = 12), and the time (t) is 10.
These numbers allow us to determine the final balance (A):
A = $400(1 + 0.0234/12)⁽¹²ˣ¹⁰⁾
A = $400(1.00195)¹²⁰
A ≈ $400(1.28172)
A ≈ $512.69
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find the cosine of the angle between the planes x + y + z = 0 and x + 3y + 4z = 6.
Answers
So the cosine of the angle between the two planes is 8sqrt(78) / 78.
To find the cosine of the angle between two planes, we need to find the normal vectors of each plane and then use the dot product formula.
The normal vector of the first plane is <1, 1, 1>, and the normal vector of the second plane is <1, 3, 4>.
The dot product of these two vectors is:
<1, 1, 1> · <1, 3, 4> = 1(1) + 1(3) + 1(4) = 8
The magnitude of the normal vector of the first plane is:
|<1, 1, 1>| = sqrt(1^2 + 1^2 + 1^2) = sqrt(3)
The magnitude of the normal vector of the second plane is:
|<1, 3, 4>| = sqrt(1^2 + 3^2 + 4^2) = sqrt(26)
Therefore, the cosine of the angle between the two planes is:
cosθ = (normal vector of plane 1) · (normal vector of plane 2) / (magnitude of normal vector of plane 1) * (magnitude of normal vector of plane 2)
= 8 / (sqrt(3) * sqrt(26))
= 8 / (sqrt(78))
= 8sqrt(78) / 78
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15 Points PLEASE HELP ME OUT.
Algebra 1 honors
Answers
Answer: A C(t) = -(x-5)^2
Step-by-step explanation:
Answer:
C(t) = -x^2 + 5
Step-by-step explanation:
Notice how C(t) = 5 when t = 0. This means that (0, 5) is a point on C(t) and is the y-intercept, thus making the constant term (term without variable in standard form) 5. Next, notice how C(t) decreases as t increases and decreases. This means that C(t) is reflected over the x-axis such that it looks like an upside-down U shape. Thus, a negative must be applied to the term of the highest degree.
In the diagram, ⨀R≅ ⨀S . Find m DE⌢ .
Answers
Answer:
60°
Step-by-step explanation:
ST = SW, since both are radii of the circle.
SW = WT, given.
STW is an equilateral triangle.
RED is an equilateral triangle.
Therefore, the measure of DE is 60°.
if the population of san diego grows by 2.0% per year how long will it take the population to double?
Answers
It will take approximately 35 years for the population of San Diego to double if it grows at a rate of 2.0% per year.
To determine how long it will take for the population of San Diego to double, we can use the concept of exponential growth.
When a population grows by a fixed percentage, the formula to calculate the doubling time is given by:
Doubling Time = (log(2) / log(1 + growth rate))
In this case, the growth rate is 2.0% or 0.02 (expressed as a decimal). Plugging this value into the formula, we can calculate the doubling time.
Doubling Time = (log(2) / log(1 + 0.02))
Using a calculator, we can evaluate this expression:
Doubling Time ≈ 35 years
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The radius of circle O is 22, and OC = 15. The diagram is not drawn to scale. What is the length of segment AB? Round the answer to the nearest tenth.
16.1
32.2
26.7
53.3
Answers
The length of the segment AB according to the given equation as required to be determined is; 32.2.
What is the length measure of the segment AB?As evident from the task content; the length measure of segment AB is required to be determined.
The assumption is such that point C is the midpoint of AB.
Therefore, on this note, the triangle OBC is a right triangle and the since radius OB = 22 and OC = 15;
CB² = 22² - 15²
CB² = 484 - 225
CB² = 259
CB = 16.1
Therefore, since C is the midpoint of AB; AB = 2 × 16.1 = 32.2.
Ultimately, the length of segment AB is; 32.2.
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A store sells packages of 3 pens for $1.50, 8 pens for $4.00, and 12 pens for $6.00. Let c represent the total cost and p represent the number of pens. Write an
equation to represent this situation.
Answers
The equation for the total cost and p represent the number of pens is c = 3p + 8p + 12p
Which equation represents the situation?3 pens for $1.50
8 pens for $4.00
12 pens for $6.00
Where,
c represent the total cost
p represent the number of pens
Total cost, c = 1.50 + 4.00 + 6.00
= $11.50
Number of pens, p = 3 + 8 + 12
= 23
c = 3p + 8p + 12p
$11.50 = 23p
Hence, c = 3p + 8p + 12p is the equation that represents the situation.
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(k + 1 )(k - 5 ) = 0 solve equation for x
Answers
Answer:
solve for k or x?
because x isnt on the equation.
i solved for k though
k = -1, 5
Step-by-step explanation:
Solved by simplifying both sides of the equation, then isolating the variable.
the average number of shoppers at a particular grocery store in one day is 505, and the standard deviation is 115. the number of shoppers is normally distributed. for a random day, what is the probability that there are between 200 and 400 shoppers at the grocery store? the answer should be typed as a decimal with 4 decimal places.
Answers
This means that on a random day, there is a 16.78% chance that the number of shoppers at the grocery store will fall between 200 and 400.
Using the normal distribution formula, we can calculate the z-scores for 200 and 400 shoppers:
z(200) = (200 - 505) / 115 = -2.65
z(400) = (400 - 505) / 115 = -0.91
Next, we can use a standard normal distribution table or calculator to find the area between these two z-scores. The probability is:
P(-2.65 < z < -0.91) = 0.1678
Therefore, the probability that there are between 200 and 400 shoppers at the grocery store is 0.1678.
To calculate the probability that there are between 200 and 400 shoppers at the grocery store, we first need to determine the z-scores for those values. We can then use a standard normal distribution table or calculator to find the area between those two z-scores. The result is the probability of interest. In this case, the probability that there are between 200 and 400 shoppers at the grocery store is 0.1678.
The probability that there are between 200 and 400 shoppers at the grocery store is 0.1678. This means that on a random day, there is a 16.78% chance that the number of shoppers at the grocery store will fall between 200 and 400.
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a bird leaves its nest, and flies back and forth from its nest to a nearby ditch to gather worms. the distance between the nest and the ditch is 200 meters. in one and a half hours, the bird manages to bring worms to its nest 15 times. what is the speed of the bird in kilometers per hour?
Answers
Therefore, the speed of the bird is approximately 1.001 kilometers per hour.
We can start by calculating the total distance the bird flew, which is the distance between the nest and the ditch multiplied by the number of round trips:
total distance = 2 × distance between nest and ditch × number of round trips
total distance = 2 × 200 meters × 15
total distance = 6000 meters
Next, we can calculate the bird's average speed by dividing the total distance by the time it took to make the trips:
average speed = total distance ÷ time
average speed = 6000 meters ÷ (1.5 hours × 3600 seconds/hour)
average speed = 0.278 meters/second
To convert this to kilometers per hour, we can multiply by the conversion factor of 3.6:
average speed = 0.278 meters/second × 3.6 kilometers/meter
average speed = 1.001 kilometers/hour
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The sum of two numbers is 52 and the difference is 18. What are the numbers?
Answers
Answer:
17 and 35
Step-by-step explanation:
x + y = 52
x − y = 18
Add the equations together:
2x = 70
x = 35
Substitute into either equation:
y = 17
The graph of function fis shown on the coordinate plane. Graph the line representing function g, if g is defined as shown below.
g(x)=f(x + 2)
Drawing Tools
Select
Line
Click on a tool to begin drawing.
-6
-2
Delete
Undo
8
Reset
Answers
A graph representing the function g(x) = -1/2f(x + 2) is shown in the image below.
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):
y - y₁ = m(x - x₁)
Where:
x and y represent the data points.m represent the slope.First of all, we would find the slope of this line;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (4 - 0)/(5 - 3)
Slope (m) = 4/2
Slope (m) = 2.
At data point (3, 0) and a slope of 2, a linear equation for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 0 = 2(x - 3)
y = f(x) = 2x - 6
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emily paints at a constant rate. she can paint square feet in minutes. what is emily's constant rate in square feet per minute?
Answers
Emily's constant rate in square feet per minute is 10. This means that she can paint 10 square feet in one minute.
To determine Emily's constant rate in square feet per minute, we need to use the given information that she can paint a certain number of square feet in a certain number of minutes. Let's say that Emily can paint x square feet in y minutes.
To find her rate, we need to divide the number of square feet painted by the number of minutes it took to paint them. So Emily's constant rate would be:
x / y = rate (in square feet per minute)
For example, if Emily can paint 200 square feet in 20 minutes, her rate would be:
200 / 20 = 10
Therefore, Emily's constant rate in square feet per minute is 10. This means that she can paint 10 square feet in one minute.
In conclusion, to determine Emily's constant rate in square feet per minute, we need to divide the number of square feet painted by the number of minutes it took to paint them. The result is the rate in square feet per minute.
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pls help!!! need help asap!!!
Answers
Answer:
parallel
Step-by-step explanation:
all horizontal lines are parallel
Answer:Parallel and all horizontal lines are parallel
Step-by-step explanation:
Two forces, X and Y, acting on an object form a 24° angle between each other. Force X is 56 pounds, and force Y is 76 pounds. What is the approximate magnitude of the resultant force?
Answers
Answer: i think
Step-by-step explanation: -9.8 m/s^2 is not the force of gravity, it is the free fall acceleration due to gravity on Earth. According to Newton's second law, F = ma. Which means that Weight = mass * gravitational
The quadratic equation h=-16t^2+32t+2
represents the height, h (in feet), of a ball kicked after t seconds. Answer each question. Express each answer as a decimal rounded to the nearest hundredth.
How long will it take the ball to reach 18 feet?
When will the object be at 10 feet?
When will the ball hit the ground?
Answers
By solving the quadratic equations,
It will take the ball 1 second to reach 18 feet
It will take the ball 1.71 seconds to be at 10 feet
It will take the ball 2.06 seconds to hit the ground
Solving quadratic equations: Determining how long it would take the ball to reach a heightFrom the question, we are to determine how long it would take the ball to reach 18 feet
To determine how long it would take the ball to reach 18 feet, we will set h = 18 in the equation
The given equation is
h = -16t² + 32t + 2
Put h = 18
18 = -16t² + 32t + 2
Rearrange
16t² - 32t - 2 + 18 = 0
16t² - 32t + 16 = 0
16t² - 16t - 16t + 16 = 0
16t(t - 1) -16(t - 1) = 0
(16t - 16)(t - 1) = 0
16t - 16 = 0 OR t - 1 = 0
16t = 16 OR t = 1
t = 16/16 OR t = 1
t = 1 OR t = 1
Hence,
t = 1 second
Hence, it will take the ball 1 second to reach 18 feet
To determine how long it will take the ball to reach 10 feet, we will set h = 10
h = -16t² + 32t + 2
Put h = 10
10 = -16t² + 32t + 2
Rearrange
16t² - 32t - 2 + 10 = 0
16t² - 32t + 8 = 0
Using the quadratic formula,
t = 0.29 second OR t = 1.71 seconds
The ball will hit the ground when h = 0
Set h = 0 in the equation
h = -16t² + 32t + 2
0 = -16t² + 32t + 2
16t² - 32t - 2 = 0
Using the quadratic formula,
t = -0.06 OR t = 2.06
Since t cannot be negative,
t = 2.06 seconds
Hence, it will take 2.06 seconds for the ball to hit the ground
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PROBLEM SOLVING The period of a pendulum is the time the pendulum takes to complete one back-and-forth swing. The period $T$ (in seconds) can be modeled by the function $T=1.1\sqrt{L}$ , where $L$ is the length (in feet) of the pendulum. Estimate the length of a pendulum with a period of $1.65$ seconds. Write your answer as a decimal.
Answers
Answer:
If $T=1.65$ seconds, then we can solve the equation for $L$ as follows:
$$
T=1.1\sqrt{L}
$$
$$
\frac{T}{1.1}=\sqrt{L}
$$
$$
\left(\frac{T}{1.1}\right)^2=L
$$
Substituting $T=1.65$, we get:
$$
L=\left(\frac{1.65}{1.1}\right)^2=2.25
$$
Therefore, the length of the pendulum is approximately 2.25 feet.
find the general solution to the system x ' = ax where a is the given matrix.
Answers
The general solution to the system x' = Ax, where A is the given matrix, can be expressed as x(t) = Ce^(At), where C is a constant matrix and e^(At) is the matrix exponential of At. This solution represents a linear combination of exponential functions, where each component of x(t) is determined by the corresponding component of C and the matrix exponential of At.
To find the general solution to the system x' = Ax, we can express the solution in terms of the matrix exponential. The matrix exponential of At, denoted as e^(At), is defined as the power series expansion of the exponential function applied to the matrix At. It can be computed using various techniques, such as diagonalization, Jordan decomposition, or power series.
The general solution to the system x' = Ax can then be written as x(t) = Ce^(At), where C is a constant matrix. This solution represents a linear combination of exponential functions, where each component of x(t) is determined by the corresponding component of C and the matrix exponential of At.
The matrix exponential e^(At) has properties that are analogous to those of the scalar exponential function. It satisfies the initial condition e^(A * 0) = I, where I is the identity matrix, and it can be used to find solutions for different initial conditions by appropriately choosing the constant matrix C.
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The position (in meters) of a particle per respect to time (in seconds) is defined by the following function: s(t) = t^4 - 16t^3 + 72t^2 +5. Find the maximal and minimal value for the speed of the particle on domain of t being [1,7[
Answers
Answer:
Max at t=2, 128 m/s
Min at t=6, 0 m/s
Step-by-step explanation:
Given the position function of a particle with respect to time, find the minimum and maximum velocity the particle travels over the interval [1,7].
[tex]s(t)=t^4-16t^3+72t^2+5[/tex]
(1) - Find the velocity function of the particle
The velocity function is a derivative of the position function.
[tex]s'(t)=v(t)\\\\s(t)=t^4-16t^3+72t^2+5\\\\\Longrightarrow s'(t)=\frac{d}{dx}[t^4-16t^3+72t^2+5] \\\\\text{Use the derivative rules.}\\\\\boxed{\left\begin{array}{ccc}\text{\underline{Power Rule:}}\\\\\frac{d}{dx}[x^n]=nx^{n-1} \end{array}\right} \ \ \boxed{\left\begin{array}{ccc}\text{\underline{Constant Rule:}}\\\\\frac{d}{dx}[k]=0 \end{array}\right} \\\\\\\Longrightarrow s'(t)=(4)t^{4-1}-16(3)t^{3-1}+72(2)t^{2-1}+0\\\\\Longrightarrow s'(t)=4t^{3}-48t^{2}+144t\\\\[/tex]
[tex]\therefore \boxed{v(t)=4t^{3}-48t^{2}+144t}[/tex]
(3) - Take the derivative of v(t)
[tex]v(t)=4t^{3}-48t^{2}+144t\\\\\Longrightarrow v'(t)=12t^2-96t+144[/tex]
(4) - Let v'(t)=0 and solve for "t," these are the critical points
[tex]v'(t)=12t^2-96t+144\\\\\Longrightarrow 0=12t^2-96t+144\\\\\Longrightarrow 0=12[t^2-8t+12]\\\\\Longrightarrow 0=t^2-8t+12\\\\\Longrightarrow (t-6)(t-2)=0\\\\\therefore \text{The critical points are} \ \boxed{t=6 \ \text{and} \ t=2}[/tex]
(5) - Find the max/min values (in this case these values represent the particle's velocity) by plugging the critical points into v(t)
[tex]\text{Recall that} \ v(t)=4t^{3}-48t^{2}+144t \ \text{and} \ t=6, \ t=2\\\\\text{\underline{When t=6:}}\\\\\Longrightarrow v(6)=4(6)^{3}-48(6)^{2}+144(6)\\\\\Longrightarrow \boxed{v(6)=0 \ m/s}\\\\\text{\underline{When t=2:}}\\\\\Longrightarrow v(2)=4(2)^{3}-48(2)^{2}+144(2)\\\\\Longrightarrow \boxed{v(6)=128 \ m/s}[/tex]
Thus, at time, t=6, the particle's velocity is smallest, 0 m/s. And at time, t=2, the particle's velocity is greatest, 128 m/s.
A restaurant put out small dishes of butter at each table.
They divided 1/6 of a pound of butter evenly between
5 dishes.
Answers
Answer:
Step-by-step explanation:
Hello!
1. Start by Plugging your numbers in. now all you have to do is 5 divided by 6! Use a calculator but anything works.
The great pyramid in giza, Egypt is a square-based. The length of one side of the base is 755 feet, it has a height of 481 feet and a slant height of 610 feet. About how many cubic feet are inside the great pyramid
Answers
There are 98,087,770 cubic feet inside the Great Pyramid.
To calculate the approximate volume of the Great Pyramid in Giza, we can use the formula for the volume of a pyramid:
Volume = (1/3) × base area × height
Since the Great Pyramid is square-based, the base area is equal to the length of one side squared. Given that the length of one side of the base is 755 feet, the base area is [tex]755^2[/tex] square feet.
Using the given height of 481 feet, we can substitute these values into the formula:
Volume = (1/3) × [tex]755^2[/tex] × 481
Calculating this expression, we find that the approximate volume of the Great Pyramid is:
Volume ≈ 98,087,770 cubic feet
There are approximately 98,087,770 cubic feet inside the Great Pyramid.
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You and your friends decide to go out to
dinner and celebrate your birthday. The
meal costs $168.34. The sales tax is 5%
and your waiter was okay so you want to
leave a 15% tip. What was the total bill?
Round to the nearest cent.
Answers
The total bill of the dinner to celebrate birthday including sales tax and tip to the nearest cent is $202.01
What was the total bill?Cost of the meal = $168.34
Sales tax = 5% of $168.34
= 0.05 × 168.34
= $8.417
Tip = 15% of $168.34
= 0.15 × 168.34
= $25.251
Total bill = Cost of the meal + Sales tax + Tip
= $168.34 + $8.417 + $25.251
= $202.008
Hence, the total bill is $202.01 to the nearest cent.
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a bag contains 6 red marbles, 4 blue marbles, 8 yellow marbles, 10 green marbles, & 2 white marbles. find the probability of drawing a blue marble (please help right now)
Answers
The probability of selecting a blue marble is 2/15
What is the probability of drawing a blue marbleA probability event can be defined as a set of outcomes of an experiment. In other words, an event in probability is the subset of the respective sample space.
In this problem, to find the probability of drawing a blue marble, let's work with the sample space.
Probability of blue marble = number of blue marbles / total number of marbles
Total number of marbles = 6 + 4 + 8 + 10 + 2 = 30
Probability of blue marble = 4 / 30
probability of blue marble = 2/15 = 0.133
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Can someone tell me the original and perpendicular slope of this question
Answers
The slope of the original line of the graph sis found to be 1 and the slope of perpendicular line is -1.
One of the line shown in the graph is passing through the points (0, -7) and (7, 0). Now we have to recall that the slope M of the line L passing from points (a, b) and (c, d) is given as,
M = (d-b)/(c-a)
Also, if the line L is perpendicular to line l, then the slope m of the line l will be given as,
m = -1/M.
So, now the slope of line L is,
M = (0-(-7))/(7-0)
M = 7/7
M = 1
Now, the slope of the perpendicular line l is,
m = -1/1
m = -1.
Hence, the slope of the perpendicular line and original lines are -1 and 1.
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Find the condition that one root of x² + sx+F= 0 May be
Five times the other
Answers
Let α be one root of the quadratic equation x² + sx + F = 0. If β is the other root, then we have: Therefore, the condition is that the sum of roots of the quadratic equation x² + sx + F = 0 must be zero.
Let α be one root of the quadratic equation x² + sx + F = 0. If β is the other root, then we have:
α + β = -s (sum of roots)
αβ = F (product of roots)
We are given that α is five times β, i.e., α = 5β. Substituting this in the first equation, we get:
5β + β = -s
6β = -s
β = -s/6
Using this value of β, we can find the corresponding value of α:
α = 5β = -5s/6
So, the condition for one root to be five times the other is:
α = 5β or -5s/6 = 5(-s/6)
s = 0
Therefore, the condition is that the sum of roots of the quadratic equation x² + sx + F = 0 must be zero.
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A fair six sided die is thrown.find the possibility Of getting the following a)a3 b)a4 c) a9 d) a1 or a2
Answers
Answer:
a) 1/6. b) 1/6. c) 0. d) 1/3.
Step-by-step explanation:
it's a fair die, so probability of getting any of the 6 numbers is equal.
that is, they all have probability 1/6.
a) p(3) = 1/6
b) p(4) = 1/6
c) p(9) = 0. die only goes up to 6.
d) p(1) = 1/6. p(2) = 1/6
p(1 or 2) = 1/6 + 1/6 = 2/6 = 1/3
