The Voronoi diagram below shows the locations of the four post offices P_{1} , P_{2} P_{3} , and P_{4}in a city.y(km)8P_{3}P2r (km)6P_{1}PKatie's apartment lies inside the shaded circle shown on the diagram.(a) Write down the post office nearest to Katie's apartment.P is located at coordinates (3-6), and the edge between P and P_{i} has the equation y = - 5/3 * x = 16/3(b) Determine the location of PPa is located at coordinates (1.7).3(c) Find the gradient. A. of the edge between P, and P.
Answers
Given -
Voronoi diagram:
To Find -
(a) Write down the post office nearest to Katie's apartment.
(b) Determine the location of P4
(c) Find the gradient k. of the edge between P3 and P4
Step-by-Step Explanation -
(a)
We can see from the voronoi diagram that the center of the x-axis where the circle covers is where Katie's apartment is located.
It is located near P4.
So,
P4 is nearest to Katie's apartment.
(b)
The location of P4:
(2, -3)
(c)
[tex]k\text{ = }\frac{Y_2\text{ - Y}_1}{X_2\text{ - X}_1}\text{ = }\frac{7}{50}[/tex]Final Answer -
(a) The post office nearest to Katie's apartment = P4
(b) The location of P4 = (2, -3)
(c) The gradient k of the edge between P3 and P4 = 7/50
Related Questions
Can I get help with my math homework I’m struggling with ? 3
Answers
Step 1:
The slope intercept form formula is
y = mx + c
m = slope
c = intercept on the y-axis
Final answer
Slope Intercept
Step
Ton graph the function, find both x=intercept and y-intercept
[tex]\begin{gathered} \text{From y = }\frac{3}{2}x\text{ + 1} \\ y-\text{intercept c = 1} \\ \text{Make x subject of the formula} \\ 3x\text{ = 2y - 2} \\ x\text{ = }\frac{2}{3}y\text{ - }\frac{2}{3} \\ x-\text{intercept c = -}\frac{2}{3} \end{gathered}[/tex]Next plot the graph.
20 4/5 whats the decimal number
Answers
20 4/5
it means 20 integers and 4/5
4/5 = 0.8
so the number 20 4/5 is equal to 20.8
answer: 20.8
20 7/8 is 20 integers and 7/8
7/8 = 0.875
so 20 7/8 is equal to 20.875
Anthropologists use a linear model that relates femur length to height. The model allows an anthropologist todetermine the height of an individual when only a partial skeleton (including the femur) is found in this problem, wefind the model by analyzing the data on femur length and height for the eight males given in the tableFemur length (cm)49.948.646.345.844.343.639.738.9Height (cm)177.5174.6165.6164.7165.3164.6155.8156.71.Which scatterplot best matches the given data?A.B.2.What is the correlation coefficient for this data?
Answers
For the scatter plot (part 1), you should have gotten something like this.
Notice that, in general, the greater the femur length is, the taller the person is. Therefore, the relation between those two quantities has the form
[tex]Y=mX+b,m>0[/tex]And, the correlation coefficient is
[tex]r=\frac{\sum ^{\square}_{\square}(x_i-\bar{x})(y_i-\bar{y})}{\sqrt[]{\sum ^{\square}_{\square}(x_i-\bar{x})^2\sum ^{\square}_{\square}(y_i-y)^2}}[/tex]In our case,
[tex]\begin{gathered} \bar{x}=\frac{1}{8}(49.9+48.6+46.3+45.8+44.3+43.6+39.7+38.9)=44.6375 \\ \bar{y}=\frac{1}{8}(177.5+174.6+165.6+164.7+165.3+164.6+155.8+156.7)=165.6 \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} \sum ^{\square}_{}(x_i-\bar{x})(y_i-\bar{y}_{})=197.83 \\ \end{gathered}[/tex]and
[tex]\begin{gathered} \sum ^{\square}_{\square}(x_i-\bar{x})=105.9987 \\ \sum ^{\square}_{\square}(y_i-\bar{y})=399.76 \end{gathered}[/tex]Finally,
[tex]\Rightarrow r=\frac{197.83}{\sqrt[]{(105.9987)(399.76)}}=0.961[/tex]Thus, the correlation coefficient is equal to 0.961
How much sugar is in a 340 gram mixture if you know the mixture is 50%sugar?
Answers
We got 340 gram mixture. The 50% of it is sugar, so:
[tex]\frac{50}{100}\cdot340=170[/tex]Then, there are 170g of sugar.
Fill in only the blanks. (Whatever that has an answer like the domain don’t do it)only do the empty blanks
Answers
From the graph, we can conclude:
[tex]Range\colon(-\infty,1)[/tex]As:
[tex]\begin{gathered} x\to0,f(x)\to-\infty \\ x\to\infty,f(x)\to1 \end{gathered}[/tex]x-intercept:
[tex](1,0)[/tex]Asymptote:
Vertical asymptote:
[tex]x=0[/tex]Horizontal asymptote:
[tex]y=1[/tex]QThe image of point A (3, 4) under translation Tis A' (-1,6). What is the translation rule? worth 50 points guy's can someone please give me an answer really quick please!!!
Answers
Here, we want to find the translation rule
Combo 1Combo 2Combo 33 glazed5 glazed4 glazed4 cream filled6 cream filled4 cream filled5 chocolate1 chocolate4 chocolate$38$32$36a)Write a system to represent this situation. Use g for glazed donuts, f for cream filled donuts, and c for chocolate donuts.b)Solve the system ALGEBRAICALLY to find the price of each donuts.
Answers
We will use the following variables :
g for glazed
f for cream filled donuts
c for chocolate donuts
So, the equation for combo 1
3 g + 4 f + 5 c = $38
The equation for combo 2:
5 g + 6 f + c = $32
The equation for combo 3:
4 g + 4 f + 4 c = $36
So, the system of equations are:
3 g + 4 f + 5 c = 38 (1)
5 g + 6 f + c = 32 (2)
4 g + 4 f + 4 c = 36 (3)
B) Now, we need to solve the system of equations:
From equation 3:
4 g + 4 f + 4c = 36
divide all terms by 4
So, g + f + c = 9
Solve for c:
c = 9 - g - f
Substitute with the value of c at the equations (1)
At (1):
3 g + 4 f + 5 (9 - g - f) = 38
3g + 4f + 45 - 5g - 5f = 38
-2g - f = 38 - 45
-2g - f = -7
Multiply all terms by -1
2g + f = 7
Solve for f
f = 7 - 2g
Substitute with f at the equation of c
c = 9 - g - (7 - 2g)
c = 9 - g - 7 + 2g
c = g + 2
So, we have reached to :
f = 7 - 2g and c = g + 2
substitute with f and c at the equation (2)
5g + 6f + c = 32
5g + 6 (7 - 2g) + g + 2 = 32
solve for g
5g + 42 - 12 g + g + 2 = 32
5g - 12g + g = 32 - 42 - 2
-6g = -12
Divide both sides by -2
g = -12/-6 = 2
f = 7 - 2g = 7 - 2 * 2 = 7 - 4 = 3
c = g + 2 = 2 + 2 = 4
So, the cost of glazed = $2
The cost of cream filled = $3
The cost of chocolate = $4
Given sinx= 5/13 andπ/2 < x < π find the exact value of tan 2x
Answers
Given sin(x)=5/13
First, lets find cos(x).
It is known that:
[tex]\begin{gathered} \sin ^2(x)+\cos ^2(x)=1 \\ (\frac{5}{13})^2+\cos ^2(x)=1 \\ \cos ^2(x)=1-\frac{25}{169} \\ \cos ^2(x)=\frac{169-25}{169}=\frac{144}{169} \\ \cos (x)=\pm\sqrt[]{\frac{144}{169}}\text{ = }\frac{\sqrt[]{144}}{\sqrt[]{169}} \\ \cos (x)=\pm\frac{12}{13} \end{gathered}[/tex]Since π/2 < x < π, we are in 2nd quadrant. Then, cos(x) is negative.
[tex]\cos (x)=-\frac{12}{13}[/tex]Since we know the values for sin and cos, we can find tan(x):
[tex]\begin{gathered} \tan (x)=\frac{\sin(x)}{\cos(x)} \\ \tan (x)=\frac{\frac{5}{13}}{-\frac{12}{13}} \\ \tan (x)==-\frac{5}{12} \end{gathered}[/tex]Now, lets work with the expression tan(2x)
It is known that:
[tex]\tan (2x)=\frac{2\tan(x)}{1-\tan^2(x)}[/tex]
Since we know tan(x), we can substitute in the expression above and find the value of tan(2x):
[tex]\begin{gathered} \tan (2x)=\frac{2\tan(x)}{1-\tan^2(x)} \\ \tan (2x)=\frac{2\cdot(-\frac{5}{12}_{})}{1-(-\frac{5}{12})^2} \\ \tan (2x)=\frac{-\frac{10}{12}}{1-\frac{25}{144}}=\frac{-\frac{10}{12}}{\frac{144-25}{144}}=\frac{-\frac{10}{12}}{\frac{119}{144}}=-\frac{10}{12}\cdot\frac{144}{119} \\ \tan (2x)=-\frac{120}{119} \end{gathered}[/tex]Answer: -120/119
Please help me with the question and explain your work! 16 through 19 thank you please please please help
Answers
We have the following:
A.
First we find the slope of the line with the following points:
(0, 3) and (5,0)
[tex]m=\frac{0-3}{5-0}=-\frac{3}{5}[/tex]now, for b, with the point (0,3)
[tex]\begin{gathered} 3=-\frac{3}{5}\cdot0+b \\ b=3 \end{gathered}[/tex]The equation is:
[tex]y=-\frac{3}{5}x+3[/tex]B.
The area is:
[tex]\begin{gathered} A=\frac{AC\cdot CB}{2} \\ A=\frac{3\cdot5}{2}=\frac{15}{2} \\ A=7.5 \end{gathered}[/tex]The area is 7.5 square units
for, perimeter:
[tex]\begin{gathered} p=AC+CB+AB \\ AB^2=AC^2+CB^2 \\ AB^2=3^2+5^2=9+25=34 \\ AB=\sqrt[]{34} \\ p=3+5+\sqrt[]{34} \\ p=13.83 \end{gathered}[/tex]The perimeter is 13.83 units
C.
when two lines are perpendicular they fulfill the following
[tex]m_1\cdot m_2=-1[/tex]therefore,
[tex]\begin{gathered} -\frac{3}{5}\cdot m_2=-1 \\ m_2=\frac{5}{3} \end{gathered}[/tex]Therefore, the equation is:
[tex]y=\frac{5}{3}x+3[/tex]Help me solve for equation 6x+3=33
Answers
Given:
[tex]6x+3=33[/tex]is given.
Required:
We need to solve this equation.
Explanation:
Here an equation given as
[tex]6x+3=33[/tex]now add both side negative 3 and we get
[tex]\begin{gathered} 6x+3-3=33-3 \\ 6x=30 \end{gathered}[/tex]now multiply both side with inverse 6
[tex]\begin{gathered} \frac{1}{6}*6x=30*\frac{1}{6} \\ x=5 \end{gathered}[/tex]Final answer:
Solution of given equation is
[tex]x=5[/tex]
please help me ASAP!!!
Answers
Find the area of the rectangle if the length is y + 4 inches and the width is y - 5 inches. Enter your answer as a polynomial in terms of variable y and in standard form, ay2 + by + c.
Answers
We have the following:
We have that the area of a rectangle is the following
[tex]\begin{gathered} A=l\cdot w \\ \text{In this case:} \\ l=y+4 \\ w=y-5 \end{gathered}[/tex]replacing:
[tex]\begin{gathered} A=(y+4)(y-5)=y^2-5y+4y-20 \\ A=y^2-y-20 \end{gathered}[/tex]what decimals are between 0.82 and 0.83
Answers
Answer:
0.82 and 0.83
Find each value if f(x) = 2x - 1 and g(x) = 2 - x2.9. f(0)
Answers
ANSWER
f(0) = -1
EXPLANATION
We just have to replace x by 0 into f(x):
[tex]\begin{gathered} f(x)=2x-1 \\ f(0)=2\cdot0-1 \\ f(0)=0-1 \\ f(0)=-1 \end{gathered}[/tex]Dr. Walton is studying a bacterial colony with a population of 77,000 bacteria. The colony is growing 15% per hour. How many bacteria will the colony contain in 3 hours?
Answers
The colony will contain 117,107 bacteria in 3 hours
Here, we start by writing an exponential function that can represent the question
We have this as;
[tex]N=I(1+r)^t[/tex]N is the number of bacteria at a particular time t
I is the initial number of bacteria which is 77,000
r is the growth rate which is 15% = 15/100 = 0.15
t is the time in hours = 3
Substituting these values, we have it that;
[tex]\begin{gathered} N=77,000(1+0.15)^3 \\ N=77,000(1.15)^3 \\ N\text{ = 117,107} \end{gathered}[/tex]This answer is given to the nearest whole number
Find the value of the ratio using the term sequence 5, 15, 45 , 135, ...
Answers
To find the ratio, we just have to divide the second term by the first term.
[tex]\frac{15}{5}=3[/tex]Therefore, the ratio of the sequence is 3.Notice that the given sequence is geometrical because we have to multiply each term with 3 to get each new term.
A pizza place offers ten different toppings. A special is a pizza with any three different toppings. How many different types of specials are offered?
Answers
As given by the question
There are given that the total of 10 different topping
Now,
According to the question:
There is also talk about 3 different pizzas.
So,
The three different toppings from the 10 different toppings:
[tex]10C_3=\frac{10!}{3!(10-3)!}[/tex]Then,
[tex]\begin{gathered} 10C_3=\frac{10!}{3!(10-3)!} \\ 10C_3=\frac{10!}{3!(7)!} \\ 10C_3=\frac{10\times9\times8\times7!}{3!(7)!} \\ 10C_3=\frac{10\times9\times8}{3\times2\times1} \end{gathered}[/tex]Then,
[tex]\begin{gathered} 10C_3=\frac{10\times9\times8}{3\times2\times1} \\ 10C_3=10\times3\times4 \\ 10C_3=120 \end{gathered}[/tex]Hence, 120 different pizzas are possible.
5+3(-2x+1)=16 I need help
Answers
Given:
5 + 3(-2x + 1) = 16
Let's solve for x.
• Step 1:
Use distributive property to expand the parenthesis
5 + 3(-2x) + 3(1) = 16
5 - 6x + 3 = 16
• Step 2:
Combine like terms
-6x + 3 + 5 = 16
-6x + 8 = 16
• Step 3:
Subtract 8 from both sides
-6x + 8 - 8 = 16 - 8
-6x = 8
• Step 4:
Divide both sides by -6
[tex]\begin{gathered} \frac{-6x}{-6}=\frac{8}{-6} \\ \\ x=-\frac{4}{3} \end{gathered}[/tex]ANSWER:
[tex]-\frac{4}{3}[/tex]•
what are the coordinates of the library A (3,4)b. (4,3)c..(2,1)d.(1,2
Answers
To determine the coordinates of the library, for the x-coordinate, you have to draw a vertical line from the library to the x-axis and read where it intersects the x-axis. And to determine the y-coordinate you have to draw a horizontal line from the position of the library towards the y-axis, and read where the line intersects the y-axis:
The x-coordinate is 4 and the y-coordinate is 3, so the coordinates of the library are (4,3)
define the imaginary unit, i
Answers
An imaginary unit, i is a solution to the quadratic equation:
[tex]\text{ x}^2\text{ + 1 = 0}[/tex]Or to simply say,
[tex]i\text{ = }\sqrt[]{-1}[/tex]It can
find an equation of the line having the given slope and containing the given point . Slope -2; through (6,-9) . type answer in slope-intercept form .
Answers
Given:
The slope of the line is m = -2.
The line passes throught the point (6,-9).
The objective is to find the equation of line.
Explanation:
Consider the point as,
[tex](x_1,y_1)=(6,-9)[/tex]The general equation to find the equation of line in slope intercept form is,
[tex]y-y_1=m(x-x_1)[/tex]Substitution:
On plugging the given values in the general equation,
[tex]\begin{gathered} y-(-9)=-2(x-6) \\ y+9=-2x+12 \\ y=-2x+12-9 \\ y=-2x+3 \end{gathered}[/tex]Here, slope of the line is -2 and y- intercept is 3.
Hence, the equation of the line in slope intercept form is y = -2x + 3.
Help me with this math problem plsWrite the formula for g(x) in terms of f(x)
Answers
Given:
Given a graph of f(x) and g(x).
Required:
To write the formula for g(x) in terms of f(x).
Explanation:
The graph of g(x) is 5 units left and 1 units up gfrom the graph of f(x).
Therefore the function g(x) is
[tex]g(x)=f(x+5)+1[/tex]Final Answer:
[tex]g(x)=f(x+5)+1[/tex]Find the volume of the sphere. Round your answer to the nearest tenth. Use 3.14 for n. A sphere has a radius of 8 centimeters. The volume of the sphere is about cm?.
Answers
Find the volume of the sphere. Round your answer to the nearest tenth. Use 3.14 for n. A sphere has a radius of 8 centimeters. The volume of the sphere is about cm?.
we know that
The volume of the sphere is equal to
[tex]V=\frac{4}{3}\cdot\pi\cdot r^3[/tex]we have
r=8 cm
pi=3.14
substitute the given values in the formula
[tex]\begin{gathered} V=\frac{4}{3}\cdot3.14\cdot8^3 \\ V=2,143.6\text{ cm\textasciicircum{}3} \end{gathered}[/tex]answer is
2,143.6 cubic centimetersA sofa regularly sells for $600. The sale price is $504.00. Find the percent decrease of the sale price from the regular price
Answers
STEP - BY - STEP EXPLANATION
What to find?
Percentage decreaase.
Given:
Original price = $600
new price = $504
Step 1
Recall the formula for percentage decrease.
[tex]\text{ \% decrease=}\frac{decrease}{original\text{ price}}\times100\text{ \%}[/tex]Step 2
Determine the value for the dcerease.
[tex]Decrease=new\text{ price - original price}[/tex][tex]Decrease=504-600=-96[/tex]Step 3
Substitute into the formula and simplify.
[tex]\text{ \% decrease=-}\frac{96}{600}\times100\text{ \%}[/tex][tex]=-16\text{ \%}[/tex]ANSWER
Percent decrease = 16% decrease
Suppose Piper eats out twice a week 15% of the time, she eats out once a week 35% of the time, and she does not eat out any time during the week 50% of the time.What is the expected value for the number of times Piper eats out during the week? Round your answer to the nearest hundredth if needed.
Answers
Solution
We are given
Probability of eating out twice in a week = 15% = 0.15
Probability of eating out once in a week = 35% = 0.35
Probability of not eating out in a week = 50% = 0.50
Let X be a random variable of the number of times Piper eats out in a week
So we have the table
Note: The Formula For finding the Expected value E(X) is given by
[tex]E(X)=\sum ^{}_{}xp(x)[/tex]Substituting we get
[tex]\begin{gathered} E(X)=0(0.50)+1(0.35)+2(0.15) \\ E(X)=0+0.35+0.30 \\ E(X)=0.65 \end{gathered}[/tex]Therefore, the expected value is
[tex]E(X)=0.65[/tex]Solve the following system of linear equations by graphing:4x + 4y = 2010x + 2y = 18
Answers
one solution: (1, 4)
The equations:
y = -x + 5
y = -5x + 9
Explanation:[tex]\begin{gathered} \text{Given equations:} \\ 4x+4y=20\text{ }\ldots(1) \\ 10x+2y=18\text{ }\ldots(2) \end{gathered}[/tex]To plot the graphs, we can assign values to x. The we get the corresponding values of y for each of the equation.
Rewritting the two equations by making y the subject of formula:
[tex]\begin{gathered} 4x+4y=20 \\ \text{divide through by 4:} \\ x\text{ + y = 5} \\ y\text{ = -x + 5} \end{gathered}[/tex][tex]\begin{gathered} 10x+2y=18 \\ \text{divide through by 2:} \\ 5x\text{ + y = 9} \\ y\text{ = -5x + 9} \end{gathered}[/tex]Plotting the graphs:
The point of intersection of the graphs is the solution.
There is one solution: (1, 4)
IF AB = (2x + 23). BC = (12 + 7x), and CD = 19 - 9x), find AD.
Answers
The addition of length of each line segment gives the value of AD.
[tex]\begin{gathered} \text{From the number line, AB+BC+CD=AD} \\ AD=(2x+23)+(12+7x)+(19-9x)=2x+7x-9x+23+12+19=54 \end{gathered}[/tex]The value of AD is 54.
what 3 1/4 - 1 3/8 equal?
Answers
Answer : 1 7/8
Given that: 3 1/4 - 1 3/8
Step 1: Convert the mixed fraction into an improper fraction
3 1/4 = (4 x 3) + 1 / 4
3 1/4 = 12 + 1 / 4
3 1/4 = 13/4
1 3/8 = (8 x 1) + 3 / 8
1 3/8 = 8 + 3 / 8
1 3/8 = 11/8
13/4 - 11/8
The common denominator is 8
2 x 13 - 11 x 1 / 8
26 - 11 / 8
15/8
1 7/8
Therefore, the answer is 1 7/8
Use Pascal's Triangle to expand the binomial. (d-3)^6
Answers
Using pascal triangle
(d-3)^6
Expoenent 6 has a coeffient of;
1 6 15 20 15 6 1
Hence;
[tex]d^6-6(d)^5(3)+15(d)^4(3)^2-20(d)^3(3)^3+15(d)^2(3)^4-6(d)(3)^5+3^6[/tex]Two things to note here is that;
-There is a minus sign in-between the numbers in the bracket, hence we alternate the sign starting with positive
-secondly as the power of the first variable decreases the power of the second digit increases
We can further simplify;
[tex]d^{6\text{ }}-6d^5(3)+15(d)^4(9)^{}-20d^3(27)+15d^2(81)-6d(243)+729[/tex]We will still simplify to give:
[tex]d^6-18d^5+135d^4-540d^3+1215d^2-1458d\text{ + 729}[/tex]Answer:
The Binomial Theorem Quick Check:
1. [tex]d^6-18d^5+135d^4-540d^3+1215d^2-1458d+729[/tex]
2. [tex]s^5+15s^4v+90s^3v^2+270s^2v^3+405sv^4+243v^5[/tex]
3. [tex]-64b^3[/tex]
100% 3/3
You're Welcome! A brainliest would help me alot. ‿
Given the lines below, create a line that is parallel, one that is perpendicular, and one that is neither. Y = -6Parallel: Perpendicular: Neither:
Answers
Given:
[tex]y=-6[/tex]The slope of the given line is zero.
a) parallel line: Parallel lines have the same slope. Any line whose slope is x=zero will be parallel to line y=-6.
So, one equation can be,
[tex]y=-2[/tex]2) Perpendicular line
Clearly the line y=-6 is the horizontal line having a slope of 0.
So, the line perpendicular to this line will be a verticle line with an undefined slope.
And its equation is of the form x = a.
The equation can be,
[tex]x=2[/tex]c) The lines which are neither parallel nor perpendicular will be just the intersecting lines.
The equation can be,
[tex]y=x+1[/tex]