The equation of the new route, parallel to the old route and passing through point (Q, P), is y = (2/5)x + (5P - 2Q)/5.
Since the new route is to be parallel to the old route, it must have the same slope. The slope of the old route is 2/5, so the slope of the new route must also be 2/5.
Let the slope intercept form of the new route be y = mx + b, where m is the slope and b is the y-intercept. Since the new route goes through point (Q, P), we can substitute these values to get
P = mQ + b
We know that m = 2/5, so we can substitute this value to get
P = (2/5)Q + b
To find the value of b, we can use the fact that the new route goes through point (Q, P). Substituting these values, we get:
P = (2/5)Q + b
P = (2/5)Q + b
Simplifying this equation, we get
b = P - (2/5)Q
Therefore, the equation of the new route is
y = (2/5)x + (P - (2/5)Q)
or
y = (2/5)x + (5P - 2Q)/5
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The given question is incomplete, the complete question is:
A city planner is rerouting traffic in order to work on a stretch of road. The equation of the path of the old route can be described as y = 2/5 x - 4. What should the equation of the new route be if it is to be parallel to the old route and will go through point (Q, P)?
HELP ME PLEASE!!!!!!!
Answer:
Step-by-step explanation:
Graph # Matching equation
1 |-3x|
2 |-x|
3 -|2x|
You can tell which one matches by finding the slope and whether the V points up or down
6²
Which theorem is shown by the diagram above?
a + b = c
C
D
a - b = c
a² + b² = c²
a²-b² = c²
The theorem is shown in a pythagoras theorem is c² = a² + b²
Which theorem is shown in a pythagoras theoremThe theorem shown in the Pythagorean theorem is "a² + b² = c²". This theorem is named after the ancient Greek mathematician Pythagoras, who is credited with discovering it.
The Pythagorean theorem applies to right-angled triangles and states that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Mathematically, we can express this as:
c² = a² + b²
Where c is the length of the hypotenuse, and a and b are the lengths of the other two sides (called the legs) of the right-angled triangle.
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Mabel made a change to the website she runs, and she wonders how it affected the way people navigate to the website—from a web search, from social media, or directly by entering the website’s address.
She took a random sample of
170
170170 visits before she made the change, and then she took a random sample of
170
170170 visits after she made the change. Here are the results:
Mode of navigation Before After Total
Search
78
7878
95
9595
173
173173
Social media
57
57
start box, 57, end box
71
7171
128
128128
Direct
35
3535
4
44
39
3939
Total
170
170170
170
170170
340
340340
Mabel wants to perform a
χ
2
χ
2
\chi, squared test of homogeneity on these results.
What is the expected count for the cell corresponding to navigation from social media before Mabel made the change?
You may round your answer to the nearest hundredth.
Rounding to the nearest hundredth, we get an expected count of 128.06 for that cell.
What is addition?One of the four fundamental mathematical processes, along with addition, subtraction, multiplication, and division, is addition.
To find the expected count for the cell corresponding to navigation from social media before Mabel made the change, we need to calculate the total number of observations in that category (before the change), and the total number of observations in the entire sample (before and after the change). Then we can use those values to calculate the expected count.
Total number of observations in the social media category before the change:
57 + 71 = 128
Total number of observations in the entire sample before the change:
170
Expected count for the cell corresponding to navigation from social media before the change:
(expected proportion of social media visitors) x (total number of observations in the entire sample before the change)
We can estimate the expected proportion of social media visitors by calculating the overall proportion of social media visitors in the entire sample before the change:
128 / 170 = 0.7529
So the expected count for the cell corresponding to navigation from social media before the change is approximately:
0.7529 x 170 = 128.06
Rounding to the nearest hundredth, we get an expected count of 128.06 for that cell.
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Answer:
64 the expected count for the cell corresponding to navigation from social media before Mabel made the change
medical researchers are conducting a double-blind experiment treating high blood pressure patients with a new vitamin supplement. the researchers are conducting a hypothesis test in which a type i error is very serious, and the type ii error is not very serious. which level of significance is the best choice?
In a speculation test, a blunder happens when we dismiss invalid speculation that's really genuine, whereas a Sort II mistake happens when we fall flat to dismiss a null theory that's really wrong.
Since a Sort I error is more genuine in this situation, we need to play down the likelihood of making such a mistake. This implies we ought to select a lower level of noteworthiness, which decreases the likelihood of dismissing genuine invalid speculation.
In rundown, the leading choice of level of noteworthiness for this double-blind therapeutic test would be a lower level, such as 0.01 or 0.001, to minimize the likelihood of making a Sort I mistake, which is more genuine in this situation.
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Harry is organizing a picnic. He can spend at most $24. 00 on beverages. Iced tea costs $2. 00 per gallon and lemonade costs $2. 50 per gallon. If x represents the number of gallons of iced tea and y represents the number of gallons of lemonade, which inequality shows the number of gallons of each drink that he can buy? Identify the number of gallons of iced tea that Harry can buy if he buys 5 gallons of lemonade.
Answer:
Harry can buy 5 gallons of lemonade and 5 gallons of iced tea and still have $1.50 left over from his original $24 dollar budget
Step-by-step explanation:
if two vectors point in opposite directions, their cross product must be zero. if two vectors point in opposite directions, their cross product must be zero. true false
Still, their cross product must be zero, If two Vectors point in contrary directions. It's true.
A vector is a volume or miracle that has two independent parcels magnitude and direction. The term also denotes the fine or geometrical representation of such a volume.
The vector equation defines the placement of the line or a aero plane in the three- dimensional frame.
When two vectors point in contrary directions, the cross product must be zero.
thus,
A x B equals sin (A x B)
Then theta is the angle between them
So,
A * B = ( A)( B) sin 180
So A * B = 0
so the given statement is true.
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in metroville 600 total number of residents injured from roller-skating 1,800 total number of deaths from roller-skating 90 total number of deaths from all causes 900 the crude death rate for all causes was:
The crude death rate for all causes in Metroville is 1 per 1,000 residents if the total number of deaths from all causes is 900.
total number of residents injured from roller-skating = 1,800
total number of deaths = 90
deaths from all causes = 900
Therefore, we can set up a proportion:
90 deaths / x residents = 1,000 deaths per 1,000 residents
x = 90,000 / 1,000
x = 90
The total population of Metroville is 90,000 residents.
The crude death rate for all causes is then:
Crude death rate = (total number of deaths / total population) * 1,000
Crude death rate = [tex](90 / 90,000) * 1,000[/tex]
Crude death rate = 1 per 1,000 residents
Therefore, we can conclude that the crude death rate for all causes in Metroville is 1 per 1,000 residents.
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4. A fish tank is in the shape of a cuboid. It
has a base of width 80cm and length of 1.2 m.
Water is put into the tank to a depth of 70cm.
There are 700 000 small fish in the tank. Each
one of them needs a litre of water.
Is there enough water for the fish in the tank?
The volume of water in the tank won't be enough for the fish.
What is volume of a cuboid?A cuboid is a solid shape or a three-dimensional shape. The volume of a cuboid is expressed as;
V = l×w× h
where l is the length, w is the width and h is the height.
The volume of water needed by the fish is 700,000× 1litre = 700,000 litres.
The volume of water the tank can occupy is
V = l× b× h
V = 80× 1200× 70
V = 6,720,000cm³
in litres ;
V = 6,720,000/1000
V = 6720litres
therefore the volume water in the tank is not enough for the fish
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Springtown Hardware kept an inventory of 697,500 lawnmowers in the past. With a change in management, the hardware store now keeps an inventory of 24% more lawnmowers. How many lawnmowers is that?
Thus, the number of current lawnmowers in the Springtown Hardware is 864,900.
Explain about the percentage:In mathematics, a percentage is a number or ratio that may be expressed as a fraction of 100. The Latin word "per centum," which meaning "per 100," is where the word "percent" comes from. % is the symbol used to represent percentages.
When a number is expressed in decimal form, you can calculate its percentage by multiplying it by 100. For instance, multiplying 0.5 by 100 gives you the percentage 50%.
Given data:
Springtown Hardware's inventory - 697,500 lawnmowers.
Current inventory of 24% more lawnmowers.
Current inventory = old inventory + 24% of old inventory
Current inventory = 697,500 + 24 % of 697,500
Current inventory = 697,500 + 24 * 697,500/ 100
Current inventory = 697,500 + 24* 6,975
Current inventory = 864,900
Thus, the number of current lawnmowers in the Springtown Hardware is 864,900.
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when sampling from a population with , which of the following sample means is more surprising? why? sample a: a random sample of 9 pell grant recipients with a mean award amount of $2750. sample b: a random sample of 36 pell grant recipients with a mean award amount of $2750.
Sample mean in sample b to be less variable and more representative of population mean than sample mean in sample a.
Standard error measures the variability of sample means around the population mean.
It decreases as sample size increases.
Using the formula for the standard error of the mean,
Calculate the standard errors for each sample,
Standard error of sample a
= s/√(n)
= 850/√(9)
= 283.33
Standard error of sample b
= s/√(n)
= 850/√(36)
= 141.67
Where s is the sample standard deviation
And n is the sample size.
The standard error of sample b is smaller than the standard error of sample a.
Sample mean in sample b is more likely to be closer to true population mean than sample mean in sample a.
Therefore, sample mean b is more surprising as larger sample size makes it more likely and accurately represents population mean.
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a teacher has a box of markers of which 5 are red, 8 are blue, and 2 are black. the teacher pulls a marker out of the box then puts it back before drawing again another marker. what is the probability that the teacher pulls out two red markers? round your answer to four decimal places if needed.
The probability of the teacher pulling out two red markers is 1/9 or approximately 0.1111 when rounded to four decimal places.
Since the teacher puts the marker back before drawing again, each draw is independent of the other. Therefore, the probability of getting a red marker on the first draw is 5/15 or 1/3. The probability of getting a red marker on the second draw is also 1/3, since the probabilities are the same for each draw.
To find the probability of getting two red markers, we need to multiply the probability of getting a red marker on the first draw by the probability of getting a red marker on the second draw.
Probability of getting two red markers = (1/3) * (1/3) = 1/9
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In the diagram, ABC undergoes a dilation with D as the center of the dilation to create A’ B’ C’. What are possible scale factors of the dilation that will create a A’ B’ C’? Select all that apply.
The scale factor of the dilation must be greater than 1. if the image A'B'C' is bigger than the preimage ABC
What are possible scale factors of the dilationIf the image A'B'C' is bigger than the preimage ABC, then the scale factor of the dilation must be greater than 1.
In other words, the length of any segment in the image is larger than the corresponding segment in the preimage by the same factor.
Since D is the center of the dilation, we can use the ratio of the corresponding side lengths of the image and preimage triangles to find the scale factor.
For example, if we want to find the scale factor for A', we can use:
scale factor = B'C'/BC
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at what rate is the base of the triangle changing when the altitude is 20 cm and the area is 120 cm2?
The rate at which the base of the triangle is changing when the altitude is 20 cm and the area is 120 cm^2 is 0 cm/s.
To solve this problem, we need to use the formula for the area of a triangle, which is:
A = (1/2)bh
Where A is the area, b is the base, and h is the altitude.
We know that the area is 120 cm^2 and the altitude is 20 cm. So we can plug in these values and solve for the base:
120 = (1/2)b(20)
240 = 20b
b = 12 cm
Now we need to differentiate both sides of the equation with respect to time (t):
dA/dt = (1/2)(db/dt)h
We are given the value of dh/dt (which represents the rate at which the altitude is changing) is 3 cm/s. We need to find db/dt (which represents the rate at which the base is changing).
Plugging in the values we know, we get:
dA/dt = (1/2)(db/dt)(20)
Solving for db/dt, we get:
db/dt = (2dA/dt)/h
Plugging in the values we know, we get:
db/dt = (2)(0)/20
db/dt = 0 cm/s
Since the area is constant (120 cm²) and the altitude is constant (20 cm), the base of the triangle is not changing. Therefore, the rate at which the base is changing is: 0 cm/s
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The dimensions of a triangular prism are given in the diagram find the volume of the prism in cubic feet
The volume of the prism is gotten as 312 cm³.
What is volume?Volume is described as a measure of three-dimensional space. It is often quantified numerically using SI derived units or by various imperial or US customary units.
The basic formula for volume is length × width × height.
The formula for the volume of triangular prism = area of triangle x length
area of triangle = 1/2 x base x height
⇒ area of triangle = 1/2 x 8 x 6 = 24 cm²
Therefore, volume of the prism = 24 x 13 = 312 cm³
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#complete question is shown in the diagram
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Solve the IVP given by y''+y=t, y(0)=1, y'(0)=-2
The solution to the IVP given by y''+y=t, y(0)=1, y'(0)=-2 is y(t) = cos(t) - (3/2) sin(t) + (1/2) t.
To solve the Initial Value Problem, we can use the method of undetermined coefficients, which involves assuming a particular form for the solution to the non-homogeneous equation y'' + y = t, and then finding the coefficients of the terms in that form by substituting it back into the equation.
First, we find the general solution to the homogeneous equation y'' + y = 0
The characteristic equation is r² + 1 = 0, which has solutions r = ±i. Therefore, the general solution to the homogeneous equation is
y_h(t) = c₁ cos(t) + c₂ sin(t),
where c₁ and c₂ are constants determined by the initial conditions.
Next, we assume a particular form for the non-homogeneous solution, based on the form of the right-hand side t. Since t is a linear function, we assume that the particular solution has the form
y_p(t) = a t + b.
Substituting this into the differential equation, we get
y''_p + y_p = t
2a + (at+b) = t.
Equating coefficients, we get
a = 1/2, b = 0.
Therefore, the particular solution is
y_p(t) = (1/2) t.
The general solution to the non-homogeneous equation is then the sum of the homogeneous and particular solutions
y(t) = y_h(t) + y_p(t)
= c₁ cos(t) + c₂ sin(t) + (1/2) t.
To determine the constants c₁ and c₂, we use the initial conditions:
y(0) = c₁ cos(0) + c₂ sin(0) + (1/2) (0) = c₁ = 1,
y'(0) = -c₁ sin(0) + c₂ cos(0) + (1/2) (1) = c₂ - (1/2) = -2,
so c₂ = -3/2.
Therefore, the solution to the IVP is
y(t) = cos(t) - (3/2) sin(t) + (1/2) t.
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miles around a track each day. If you jogged that distance 4
times last week, how many miles did you jog
According the question given you jogged around the distance of 26[tex]\frac{2}{3}[/tex] miles.
What is an improper fraction?
When the numerator value exceeds the denominator value, the fraction is incorrect. Incorrect fractions can also be expressed in the form of a whole number and a proper number, where the numerator is the remainder and the denominator is left unchanged.
Here, we have
Given: You jog 6 2/3 miles around a track each day. If you jogged that distance 4 times last week.
We have to find out how many miles did you jog.
The total jogging distance will be
= 4(6 2/3) miles
= 4 × 20/3 miles
= 80/3 miles
= 26[tex]\frac{2}{3}[/tex] miles.
Hence, you jog 26[tex]\frac{2}{3}[/tex] miles.
Question: You jog 6 2/3 miles around a track each day. If you jogged that distance 4 times last week, how many miles did you jog?
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Mr Block has four daughters. Each daughter has one brother. How many children does he have?
Answer:
8
Step-by-step explanation:
4 x 2.
‼️WILL MARK BRAINLIEST‼️
The average distance of electric cars is 275.
The range of the data set is 300.
How to solveGiven:
Average of the data set = 275Range of the data set = 300To find: Average distance of electric cars
Solution:
The average distance of electric cars can be calculated by finding the average of the data set containing the distances of electric cars. Let's assume that the data set is as follows:
250, 250, 250, 400, 300, 300, 350, 100
To find the average distance of electric cars, we can use the formula:
Average = (Sum of all the data points) / (Number of data points)
Substituting the given values, we get:
Average = (250 + 250 + 250 + 400 + 300 + 300 + 350 + 100) / 8
Average = 2200 / 8
Average = 275
Therefore, the average distance of electric cars is 275.
Now, let's calculate the range of the data set. The range is the difference between the maximum and minimum values in the data set. From the given data set, we can see that the minimum value is 100 and the maximum value is 400.
Range = Maximum value - Minimum value
Range = 400 - 100
Range = 300
Therefore, the range of the data set is 300.
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Solve 7x-1 ÷5 = x
Show clear algebraic working
Therefore, the solution to the equation [tex]7x-1 / 5 = x[/tex].is[tex]x=1/30[/tex].
What is equation?An equation is a mathematical statement that expresses the equality between two expressions or values, using mathematical symbols such as = (equals), < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to).
Equations can be used to solve problems in various fields such as mathematics, physics, chemistry, engineering, and economics. They can be simple or complex, and may involve variables, constants, and coefficients.
Some examples of equations are:
[tex]2x + 5 = 11[/tex] (an equation with one variable)
[tex]3x + 4y = 12[/tex] (an equation with two variables)
here's the step-by-step algebraic working to solve the equation 7x-1 ÷ 5 = x:
First, we need to simplify the left side of the equation by performing the division first:
[tex]7x - 1/5 = x[/tex]
Next, we want to isolate the variable x on one side of the equation by subtracting x from both sides:
[tex]7x - x - 1/5 = 0[/tex]
Simplify by combining like terms on the left side:
[tex]6x - 1/5 = 0[/tex]
Add 1/5 to both sides to eliminate the constant on the left side:
[tex]6x = 1/5[/tex]
Finally, divide both sides by 6 to solve for x:
[tex]x = 1/30[/tex]
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by considering the curve traced by the parametrisation z(t) = t 2 it3 with −1 ≤ t ≤ 1, show why the condition that z ′ (t) never vanishes is necessary to ensure that smooth curves have no cusps.
To ensure that smooth curves have no cusps, we need to require that z'(t) never vanishes. This condition ensures that the tangent line to the curve changes smoothly and continuously as we move along the curve, without any abrupt changes in direction that would create cusps.
To understand why the condition that z'(t) never vanishes is necessary to ensure that smooth curves have no cusps, we first need to understand what a cusp is. A cusp is a point on a curve where the tangent line changes direction abruptly, creating a sharp point or corner in the curve.
Now, let's consider the curve traced by the parametrization z(t) = t^2it^3 with -1 ≤ t ≤ 1. To determine whether this curve has any cusps, we need to calculate the derivative of z(t) with respect to t:
z'(t) = 2it^3 + 3t^2i
If we set z'(t) equal to zero and solve for t, we get:
2it^3 + 3t^2i = 0
t^2(2i t + 3i) = 0
This equation has two solutions: t = 0 and t = -3/2i. These are the points on the curve where z'(t) vanishes.
At t = 0, the curve passes through the origin, which is a smooth point. However, at t = -3/2i, the curve has a cusp. To see why, we can look at the behavior of z(t) near this point.
As t approaches -3/2i from either side, the magnitude of t^2 increases without bound, while the magnitude of t^3 remains constant. This means that z(t) approaches infinity along a straight line with slope -3/2i. In other words, the curve has a sharp corner or cusp at this point.
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Find the 11th term of the geometric sequence shown below.
-9x²,-18x7, -36x¹2
12
"...
the 11th term in the given geometric sequence is equal to [tex]-9216x^{52}[/tex]
What is a geometric sequence.A sequence is a list of numbers indexed by the natural numbers 1,2,3,4,5.. A common notation for a sequence is [tex]a_1,a_2,a_3,\cdots[/tex]. Most often for interesting sequences there is some pattern in the list of numbers, and there is some formula to generate the nth number in the sequence. A sequence is called a geometric sequence if the next number number is got from the previous number by multiplying it by a fixed number r. This number is called the common ratio r of the sequence. So if the first number is a, then the second number is ar, the third is [tex]ar^2[/tex]... So that the nth number [tex]a_n = ar^{n-1][/tex].
For example 1 ,3,9,27,81,.... The sum of the first n terms of such a sequence is equal to [tex]$S_n = \frac{a(r^n-1)}{r-1}$[/tex]. if the absolute value of r, [tex]|r| < 1[/tex], then the sum to infinity is [tex]$S = \frac{a}{1-r}$[/tex].
In our question we are given a geometric sequence whose first term :
[tex]$a = -9x^2\,,\textrm{ and common ratio : r } = 2x^5$[/tex] .
So the 11th term is [tex]$ar^{10} = (-9x^2){(2x^5)}^{10} = (-9x^2)(1024x^{50}) = -9216x^{52}$[/tex]
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4. Find the approximate area of the shaded part of the circle. Use 3.14 for
cm
062.8 cm²
06.28 cm²
012.56 cm²
125.6 cm
Using the circle area formula we know that the required area of the shaded region is (A) 62.8 cm² respectively.
What is a circle?All points in a plane that are at a specific distance from a specific point, the center, form a circle.
In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.
A circle is a closed curve that extends outward from a set point known as the center, with each point on the curve being equally spaced from the center.
Area of the shaded region:
πr²
Now, insert values:
When r = 6 cm,
πr²
π6²
π36
113.04 cm²
When r = 4 cm,
πr²
π4²
π16
50.24 cm²
Now, the area of the shaded region: 113.04 - 50.24 = 62.8 cm²
Therefore, using the circle area formula we know that the required area of the shaded region is (A) 62.8 cm² respectively.
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Correct question:
Find the approximate area of the shaded part of the circle. Use 3.14 for
cm
a. 62.8 cm²
b. 6.28 cm²
c. 12.56 cm²
d. 125.6 cm
solve the proportion b+4/5=7/4
Step-by-step explanation:
When adding or subtracting fractions, they must have a common denominator....20 is the easiest for these...this then becomes
b + 16/20 = 35/20 now subtract 16/20 from both sides of the equation
b = 35/20 - 16/20
b = (35-16)/20 = 19/20
Ms. Yamato's gross pay is $2644. Her deductions total $548.30.
What percent of her gross pay is take-home pay?
A. 84%
B. 79%
C. 21%
D. 18%
Thus, the correct Percent response is B) 79%.
what is a percent?Percentage refers to a portion of every hundred. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, it is frequently shown using the percent sign, "%".
If you have 100 apples and distribute 10 of them, for instance, you have distributed 10% of your total apple supply.
We deduct Ms. Yamato's deductions from her gross income to determine her take-home pay:
$2644 - $548.30 = $2095.702.
By dividing her take-home pay by her gross pay and multiplying the result by 100%, we can determine what proportion of her gross pay is taken home:
($2095.70 / $2644) * 100% = 79%
Thus, the correct response is B) 79%.
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Please help me with this homework
Answer: Circumference = 18 π cm
Step-by-step explanation:
We can use this formula to find the circumference of a circle:
➜ r is equal to the radius, also known as half the width of a circle.
C = 2πr
We will substitute our known values and solve for C by multiplying. Since the answer option includes π in our units, we do not multiply this into the 18.
C = 2πr
C = 2π(9)
C = 18 π cm
Answer: 18π
Step-by-step explanation:
The circumference of a circle is equal to 2πr, with r being equal to the radius. The radius of a circle is defined as the length from any point on the circle to its middlemost point. In this case, we are given the value of the radius as defined by the line. The radius equals 9, which we can plug into the equation.
C= 2πr
C = 2π(9)
C = 18π = 56.55
Hope this helps!
Triangle ABC with vertices at A(4, 3), B(3, −2), C(−3, 1) is dilated using a scale factor of 3.5 to create triangle A′B′C′. Determine the vertex of point C′.
C′(−10.5, 1)
C′(−10.5, 3.5)
C′(−3, 3.5)
C′(−10.5, −3.5)
The correct option is C′(−10.5, 3.5) i.e. the vertex of point C′ is (-10.5, 3.5).
What is dilation?
In mathematics, dilation is a type of transformation that changes the size of a geometric object, but not its shape or orientation. Dilation is similar to scaling, but it involves a fixed point called the center of dilation, and a scale factor that determines the degree of expansion or contraction.
To determine the vertex of point C′, we need to apply the dilation transformation to the coordinates of the original vertex C(-3,1) using a scale factor of 3.5.
The coordinates of C′ can be found by multiplying the coordinates of C by the scale factor:
C′ = (3.5)C = (3.5)(-3,1) = (-10.5,3.5)
Therefore, the vertex of point C′ is (-10.5, 3.5).
Thus, the correct option is C′(−10.5, 3.5).
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Mark earns $8 per hour at a store.
Part A: Write an equation for this situation.
Part B: Create a table. Use h for hours worked and p for pay in dollars.
Part C: What part of your rule shows the number of hours Mark worked?
Part D: One week Mark earned $168. How many hours did he work that week?
Part E: Explain whether or not the equation is a direct variation.
p=8h is the equation.This part is represented in tabular form.The coefficient of h. Mark worked 21 hours that week.Yes, the equation is a direct variation.
What is an equation?An equation is a statement that shows the equality of two expressions. It typically contains one or more variables and may involve mathematical operations such as addition, subtraction, multiplication, and division. Equations are commonly used in mathematics, science, and engineering to model real-world situations and solve problems.
Define direct variation?Direct variation is a mathematical relationship between two variables, where a change in one variable results in a proportional change in the other variable. In other words, if two variables are in direct variation, when one variable increases, the other variable increases as well, and when one variable decreases, the other variable decreases as well, in a constant ratio.
Part A: The equation for this situation is p = 8h, where p represents the pay in dollars and h represents the number of hours worked.
Part B:
| Worked (hrs) | Pay (p) |
|------------------|---------|
| 1 | 8 |
| 2 | 16 |
| 3 | 24 |
| 4 | 32 |
| 5 | 40 |
| 6 | 48 |
and so on.
Part C: The coefficient of h, which is 8, shows the number of hours Mark worked.
Part D: We can use the equation p = 8h and substitute p = 168 to find the number of hours Mark worked.
168 = 8h
h = 21
Therefore, Mark worked 21 hours that week.
Part E: Yes, the equation is a direct variation because the pay (p) is directly proportional to the number of hours worked (h) and the constant of variation is 8.
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the corner of a unit cube is chopped off such that the cut runs through the three vertices adjacent to the vertex of the chosen corner. what is the height of the remaining cube when the freshly-cut face is placed on a table?
When the freshly sliced face is set on a table, the height of the remaining cube is 1/3.
The freshly formed face, after the corner is removed, has an area of 1/2 since it traverses three adjacent cube vertices. When the remaining cube is set on the table, this face serves as its basis. The height of the cube is equal to the distance from the table to the opposing vertex.
Because the cube's sides are one length, √(3)/2 separates its center from its opposite vertex. Therefore, (√(3)/2) - (1/3) = (2√(3) - 3)/6, which simplifies to around 0.2113, is the height of the remaining cube.
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Find the length of each Segment
8. ST
the length of each Segment WY = 7.2 .
What is line Segment?
A portion of a straight line or curve between two points. A portion of a plane or solid figure truncated by intersecting lines, planes, or planes, especially between chords and arcs of a circle.
In geometry, a line segment is bounded by two different points on the line. Or we can say that the line segment is part of the line connecting his two points. Lines have no endpoints and extend infinitely in either direction, while lines have two fixed or definite endpoints.
In both triangles
VW/WX = YW/WU
7/8.75 = YW/9
9 * 7/8.75 = YW
7.2 = WY
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the table shows several packages of assorted spools of thread available at a store. what is the price per spool of each kind of thread?
I'm sorry, but I cannot provide a definitive answer to your question as I do not have access to the table you are referring to.
However, in general, to find the price per spool of each kind of thread, you would need to know the total price of the package and the number of spools in the package.
To calculate the price per spool, you would divide the total price of the package by the number of spools in the package. For example, if a package costs $10 and contains 50 spools of thread, the price per spool would be $0.20 ($10 ÷ 50 = $0.20).
You can use this method to find the price per spool for each type of thread in the table you are looking at.
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