3. Gridtown USA, besides having excellent donut shops, is known for its precisely laid out grid of streets and avemues. Streets run east-west, and avenues north-south, for the entire stretch of the town, never curving and never interrupted by parks or schools or the like. Suppose you live on the corner of 3rd and 3rd and work on the corner of 12th and 12th. Thus travel 18 blocks to get to work as quickly as possible. (a) How many different routes can you take to work, assuming you want to get there as quickly as possible? Explain. you must (b) Now suppose you want to stop and get a donut on the way to work, from your favorite donut shop on the corner of 10th ave and 8th st. How many routes to work, stopping at the donut shop, can you take (again, ensuring the shortest possible route)? Explain. (c) Disaster Strikes Gridtown: there is a pothole on 4th ave between 5th st and 6th st. How many. routes to work can you take avoiding that unsightly (and dangerous) stretch of road? Explain. (d) The pothole has been repaired (phew) and a new donut shop has opened on the corner of 4th ave and 5th st. How many routes to work drive by one or the other (or both) donut shops? Hint: the donut shops serve PIE.
Answers
There are 4 possible routes to work that pass by one or both donut shops.
How to count paths on a grid and avoid certain edges on a graph?
(a) To travel from 3rd and 3rd to 12th and 12th in the shortest distance possible, you can only move east or north. Since you need to travel 18 blocks, you must travel 12 blocks east and 6 blocks north or 6 blocks east and 12 blocks north. This gives two different possible routes.
(b) To get a donut on the way to work, you can take one of two possible routes to the donut shop on the corner of 10th ave and 8th st, and then take one of two possible routes from the donut shop to work. This gives a total of 2 × 2 = 4 possible routes.
(c) If you need to avoid the stretch of 4th ave between 5th st and 6th st, then you can only move east or north until you reach 4th ave. Once you reach 4th ave, you can either move north or south of the pothole, but not through it.
Thus, you can take one of two possible routes to 4th ave, and then one of two possible routes north or south of the pothole, and then one of two possible routes from 4th ave to work. This gives a total of 2 × 2 × 2 = 8 possible routes.
(d) To pass by one or both donut shops, you can take the following routes:
Route 1: Go east on 3rd St to 4th Ave, then north on 4th Ave to 5th St, then east on 5th St to 10th Ave, then north on 10th Ave to 12th St.
Route 2: Go east on 3rd St to 10th Ave, then north on 10th Ave to 8th St, then west on 8th St to 4th Ave, then north on 4th Ave to 5th St, then east on 5th St to 12th Ave.
Route 3: Go east on 3rd St to 4th Ave, then north on 4th Ave to 5th St, then east on 5th St to 8th Ave, then south on 8th Ave to 10th St, then west on 10th St to 12th Ave.
Route 4: Go east on 3rd St to 10th Ave, then north on 10th Ave to 12th St.
Thus, there are 4 possible routes to work that pass by one or both donut shops.
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Related Questions
Will mark brainliest for whoever answers
Answers
Answer:
the third one
Step-by-step explanation:
Answer: A
Step-by-step explanation:
Write an equation of the line using the points you chose above.
y-0
c. About how many miles per hour do you travel?
You travel about
miles per hour.
d. About how far were you from home when you started?
When you started, you were about [
15
miles from home.
e. Predict the distance from home in 7 hours.
In 7 hours, you will be about miles from home.
Answers
c) You travel about 50 miles per hour.
d) You were 15 miles from home when you started.
e) After 7 hours, you will be 365 miles away from home.
How to define a linear function?The slope-intercept representation of a linear function is given by the equation shown as follows:
y = mx + b
The coefficients m and b have the meaning presented as follows:
m is the slope of the function, representing the increase/decrease in the output variable y when the input variable x is increased by one.b is the y-intercept of the function, representing the numeric value of the function when the input variable x has a value of 0. On a graph, it is the value of y when the graph of the function crosses or touches the y-axis.When x = 0, y = 15, hence the intercept b is given as follows:
b = 15.
In six hours, the distance increased by 300 miles, hence the slope m is given as follows:
m = 300/6 = 50.
Hence the equation is:
y = 50x + 15.
After seven hours, the predicted distance is given as follows:
y = 50(7) + 15 = 365 miles.
Missing InformationThe points on the line are:
(0,15) and (6, 315).
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In an equilateral triangle, the length of a side is 10 inches. What is the perimeter of this triangle?
Answers
Answer:
well how many sides are there in one? then multiply it by the number of the one side to how many sides
Step-by-step explanation:
Answer:
30 inches
Step-by-step explanation:
Equilateral means all the sides are the same
The diameter of a hat is 4.7 inches. What is the distance around the hat using π = 3.14? Round to the hundredths place.
1.50 inches
7.38 inches
17.34 inches
14.76 inches
A soda company would like to replace the label on a can of soda with a radius of 3 and one fourth cm. If the label touches end to end with no overlap, what is the length of the label? Use 22 over 7 for π.
143 over 56 cm
143 over 28 cm
143 over 14 cm
143 over 7 cm
What is the circumference of the circle in terms of π?
circle with a segment drawn from one point on the circle through the center to another point on the circle labeled 7 yards
3.5π yards
7π yards
21.98π yards
49π yards
The circumference of a circle is 91.688 millimeters. What is the radius of the circle? Use 3.14 for π.
29.2 mm
183.4 mm
14.6 mm
45.8 mm
Answers
Answer:
The diameter of a hat is 4.7 inches, so the distance around the hat using π = 3.14 would be 14.76 inches (4.7 x 3.14).
A soda company with a can radius of 3 and one fourth cm needs to replace its label; if it touches end to end without overlap, then the length will be 143 over 28 cm (3 1/4 x 22 / 7).
The circumference of a circle in terms of π when there is segment drawn from one point on the circle through center to another point labeled 7 yards would be 21.98π yards (2x(radius)xπ or 2x7yards×3 .14 ).
Finally, for given 91 .688 millimeters as circumference ,the radius should equal 29 .2 mm ((91 688mm)/(2 × pi)).
The circumferences for the examples are 14.76 inches, 143/14 cm, 14π yards, and the radius is 14.6 mm. Circumference is calculated with 2*π*r.
Explanation:The circumference of a circle is calculated using the formula 2* π * radius.
1. For the hat, the radius would be half the diameter, hence 4.7/2 = 2.35 inches. Substituting these values into the circumference formula gives 2*3.14*2.35 = 14.76 inches.
2. For the soda can, the circumference is 2*π*r = 2*(22/7)*(3 1/4) = 2*(22/7)* (13/4) = 143/14 cm.
3. For a circle with a radius of 7 yards, the circumference would be 2*π*7 = 14π yards.
4. If the circumference is given as 91.688 mm, and we need to find the radius, we rearrange the circumference formula to find radius = Circumference / (2* π) = 91.688 / (2 * 3.14) = 14.6 mm.
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How to enter a formula in the selected cell to display the value of cell 3?
Answers
Therefore , the solution of the given problem of expression comes out to be =C3 by using this formula, the spreadsheet is instructed to show the value in column C3.
What is expression ?Mathematical processes like multiplying, dividing, addition, and subtracting are essential. Combining them would result in the following phrase: An equation, some information, and a mathematical function Values, variables, and functions, such as additions, subtractions, multiplications, and divisions, are the building blocks of a statement of truth. Words and sentences can be contrasted and compared.
Here,
Simply type the following formula into the formula bar to show the value of cell 3 in a chosen cell:
=C3
By using this formula, the spreadsheet is instructed to show the value in column C3.
You can change "C3" to the complex number of the cell whose value you want to show.
Make sure the formula is written in the proper cell and that the cell reference is accurate.
The formula would then calculate and display a value from the designated cell in the chosen cell after you hit the Enter key.
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Evaluate-+61
Enter your answer in the box.
- 7 when x = 18
Answers
The expression 61+x when x = 18 evaluates to 79.
What is expression?Expression is a combination of numbers, symbols and operators that represent a mathematical quantity or operation.
To find the value of the expression, we must first substitute 18 in for x. To evaluate this expression, we must add 61 and 18. 61+18 = 79. Therefore, the expression 61+x when x = 18 evaluates to 79.
To verify the answer, we can use the distributive property of multiplication to expand the expression. 61+x is equivalent to 61+18, which can be written as
61+18 = 61+1*18.
We can now distribute the 1 to the 18,
so 61+1*18 = 61+18 = 79.
Therefore, the expression 61+x when x = 18 evaluates to 79.
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Question: Evaluate-61+x
Enter your answer in the box.
Find the value of equation, when x = 18.
Suppose that the total profit in hundreds of dollars from selling x items is given by P(x) = 4x² -7x+7. Complete parts a through d below. CITE a. Find the average rate of change of profit as x changes from 2 to 4. $per item b. Find the average rate of change of profit as x changes from 2 to 3. Sper item c. Find and interpret the instantaneous rate of change of profit with respect to the number of items produced when x=2. (This number is called the marginal profit at x = 2.) $per item What does this result mean? Choose the correct answer below per item per item. OA When 2 items are sold, the profit is increasing at the rate of $ OB. When 2 items are sold, the profit is decreasing at the rate of $ OC. When items are sold for $ OD. When items are sold for $ the profit is increasing at the rate of $2 per item. the profit is decreasing at the rate of $2 per item. d. Find the marginal profit at x = 4. per item
Answers
The average rate of change of profit as x changes from 2 to 4 is $15 per item, average rate of change of profit as x changes from 2 to 3 is $5 per item. The instantaneous rate of change of profit with respect to the number of items produced when x = 2 (marginal profit at x = 2) is $9 per item and The marginal profit at x = 4 is $25 per item.
a) To find the average rate of change of profit from x = 2 to x = 4, we calculate the difference in profit divided by the difference in the number of items sold. By substituting the given values into the profit function P(x) = 4x² - 7x + 7, we obtain the profits at x = 2 and x = 4. Then, we find the difference in profit and divide it by the difference in x to determine the average rate of change, which is $15 per item.
b) Similarly, to find the average rate of change of profit from x = 2 to x = 3, we substitute the values into the profit function and calculate the profits at x = 2 and x = 3. The difference in profit divided by the difference in x gives us the average rate of change, which is $5 per item.
c) The instantaneous rate of change of profit with respect to the number of items produced when x = 2 represents the marginal profit at x = 2. To determine this, we take the derivative of the profit function P(x) = 4x² - 7x + 7 with respect to x and evaluate it at x = 2. The result is the marginal profit, which is $9 per item. This means that when 2 items are sold, the profit is increasing at a rate of $9 per item.
d) To find the marginal profit at x = 4, we again take the derivative of the profit function with respect to x and evaluate it at x = 4. The derivative is 8x - 7, and substituting x = 4 gives us a marginal profit of $25 per item.
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What is the three-period weighted moving average for july using the weights 0.5 (most recent), 0.3, and 0.2?
Answers
The three-period weighted moving average for july is 145.4.
What is Weighted Moving Average?A weighted moving average technique is one of several methods for forecasting a given month's value or attribute. Other techniques for forecasting from historical data include the evenly weighted moving average method, a regression analysis method, and so on.
When evaluating the movable average estimate of such an observation, each observation is usually weighted the same way. In some cases, it is advantageous to assign different weights to the observations so that the observation closest to the forecasted time period has a higher weight. This is known as the weighted moving average method. In such a weighted moving average technique, the sum of the individual weights must equal 1.Now, according to the question;
The weighted moving average strategy forecast for month of July is given by:
= (Weight for May * Sales for May) + (Weight for April * Sales for April) + (Weight for June * Sales for June)
= (0.5 * 148) + (0.3 * 142) + (0.2* 144)
= 145.4
Therefore, the three-period weighted moving average for july is 145.4.
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The complete question is -
13. Given the following historical data and weights of .5, .3, and .2, what is the three-period weighted moving average forecast for period 5?
Period Value
1 - 138 (march)
2 - 142 (april)
3 - 148 (may)
4 - 144 (june)
What is the slope of the line that passes through the points
(
−
9
,
−
7
)
(−9,−7) and
(
−
11
,
−
6
)
(−11,−6)? Write your answer in simplest for
Answers
Considering the expression of a line, the equation of the line that passes through the points (-9,-7) and (-11,-6) is the equation of the line is y= -1/2x -23/2.
Linear equationA linear equation o line can be expressed in the form y = mx + b
where
x and y are coordinates of a point.m is the slope.b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.Knowing two points (x₁, y₁) and (x₂, y₂) of a line, the slope m of a line can be calculated as:
m= (y₂ - y₁)÷ (x₂ -x₁)
Substituting the value of the slope m and the value of one of the points in y=mx +b, the value of the "b" can be obtained.
Equation of the line in this case
Being (x₁, y₁)= (-9, -7) and (x₂, y₂)= (-11, -6), the slope m can be calculated as:
m= (-6 - (-7))÷ (-11 -(-9))
m= (-6 +7)÷ (-11 +9)
m= (1)÷ (-2)
m= -1/2
Considering point 1 and the slope m, you obtain:
-7= (-1/2)×(-9) + b
-7= 9/2 +b
-7 -9/2= b
-23/2= b
Finally, the equation of the line is y= -1/2x -23/2.
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can someone please help mee
Answers
Answer:
I think that this answer is 22
A binomial experiment consists of 500 trials. the probability of success for each trial is. 4. what is the probability of obtaining the number of successes indicated in problems 51–58?
Answers
The probability of obtaining the number of successes indicated in problems 51–58 is 0.42.
Probability is absolutely how in all likelihood something is to happen. every time we're unsure about the final results of an occasion, we can talk about the chances of sure results—how in all likelihood they may be. The analysis of occasions ruled by using probability is called facts.
The opportunity of an event may be calculated with the aid of the opportunity formula by means of truly dividing the favorable wide variety of results by way of the overall variety of feasible effects.
Probability is the department of mathematics regarding numerical descriptions of ways possibly an occasion is to occur, or how likely it's miles that a proposition is actual. The chance of an event is more than a few between zero and 1, in which, roughly talking, 0 shows the impossibility of the event and 1 suggests fact.
Cells x doute the no of surrell and
"p' denotes the probability of turrets
D= 5
H=pkin = 50-xo-5 = 250
σ = SD(X) = √√rbg
= √√5=x05x=5 = 14.№33
The probability of obtaining $45-26
= P(-5-250 < x-M 22605-250)
14.233
= P(-03864 < 2 2 0-7332)
8.4200
0.42
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5x+y=2
Solve for y my teacher said to write the answer in this form y=-5x+2 because it goes with y=mx+b can it be written like that?
Answers
Answer:yes it can be written like that.
Step-by-step explanation:
simplify: (2x-3)(5x+1)
Answers
Answer:
\(\huge\boxed{\sf 10x^2-13x-3}\)
Step-by-step explanation:
\(=(2x-3)(5x+1)\\\\=2x(5x+1)-3(5x+1)\\\\Distribute\\\\= 10x^2+2x-15x-3\\\\= 10x^2-13x-3\\\\\rule[225]{225}{2}\)
10x² - 13x - 3
Step-by-step explanation:
(2x - 3) (5x + 1)
Apply distributive property ,
= 2x(5x + 1) - 3(5x + 1)
= 10x² + 2x - 15x - 3
= 10x² - 13x - 3
__________
Hope it helps ⚜
the following table presents the probability distribution of the number of vacations X taken last year for a randomly chosen family. compute the mean X. 0. 1. 2. 3. 4p(x) 0.13. 0.61. 0.15. 0.07. 0.04
Answers
SOLUTION
The table for the x and P(x) can be shown below
From the table above, mean for the data is calculated as
\(\begin{gathered} \bar{x}=\sum_^x.p(x) \\ \sum_^x.p(x)=1.28 \end{gathered}\)Hence the answer is 1.28
If AC bisects ∠BAD, is ABC ≅ ADC? Explain.
The?image?consists?of?a?regular?triangle?ABD?with?base?AD.?A?segment?joins?vertex?A?to?side?BD?at?point?C?making?an?angle?of?90?degrees?with?it.
A. Yes; then ∠BAC is congruent to ∠DAC, and the triangles are congruent by ASA.
B. Yes; then ∠BAC is congruent to ∠CAD, and the triangles are congruent by AAS.
C. No; in that case, only two pairs of corresponding congruent angles would be known.
D. No; in that case, only one pair of corresponding congruent angles and one pair of corresponding congruent sides would be known.
Answers
Answer: I think it’s a or c
Step-by-step explanation:
Find the complement of the set given that u = {0, 1, 2, 3, 4, 5, 6, 7, 8}. (enter your answers as a comma-separated list.) the set of odd natural numbers less than 8
Answers
{ 0,2,4,6,8} is the complement of the set.
What is natural number in math?
Normative Numbers The numbers we use to count or place things in order are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, and 11. Complete numbers the range of numbers that includes zero and natural numbers.Is zero a natural number?
0 is not a natural number, so no. As we all know, natural numbers are positive integers with a range of 1 to infinity. However, we get a number when we combine 0 with a positive integer like 10, 20, or another number.u = {0, 1, 2, 3, 4, 5, 6, 7, 8}
Odd number less than 8 = { 1,3,5,7 }
complement = {0, 1, 2, 3, 4, 5, 6, 7, 8} - { 1,3,5,7 }
= { 0,2,4,6,8}
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A poll was taken to total the candy collected by a few students who went trick or treating on Halloween. Determine the ratio that compares the number of
candy bars to the total pieces of candy.
Halloween Number of
Candy Pieces
Lollipops 10
Gumballs 15
Candy Bars
5
Chocolate 10
1:6
1:5
01:4
0 1:8
Answers
Given parallelogram A B C D below, DE = 31 If EB = x-7, solve for x.
Answers
The diagonals of the parallelogram intersect at the center. Then the value of the variable 'x' is 38.
What is a parallelogram?It is a polygon with four sides. The total interior angle is 360 degrees. A parallelogram's opposite sides are parallel and equal. Its diagonals intersect in the center.
Given parallelogram A B C D below, DE = 31 If EB = x - 7.
By the definition, then the equation is given as,
EB = DE
x - 7 = 31
Simplify the equation, then we have
x - 7 = 31
x = 31 + 7
x = 38
The value of the variable 'x' is 38.
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can yall pls help me on this
Answers
Click on the origine i.e. (0,0)
HOPE IT HELPS
PLEASE MARK ME BRAINLIEST ☺️
12 - x
If x = 7, what is the value of the expression above?
Answers
Answer:
5
Step-by-step explanation:
12-7=5
Answer:
5
Step-by-step explanation:
We know that x is equal to 7. That means we can replace x with this value. This makes our new expression:
12 - 7
12-7 is equal to 5, so this expression will equal 5 when x = 7.
Joy is helping her father to build a rectangular deck that measures 14 ft by 19 ft.
Find the area of the deck.
Answers
The answer is 126ft
what is the value of 8 + 2g - 7 when g = 5?
Answers
Answer:
11
Step-by-step explanation:
2 times 5 = 10 so 8+10 -7= 11
The required simplified value of the given expression at g = 7 is 11.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
here,
Given expression,
y = 8 + 2g - 7
Now put g = 5,
y = 8 + 2(5) - 7
y = 8 + 10 - 7
y = 11
Thus, the required simplified value of the given expression at g = 7 is 11.
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2500, 500, 100, ...
Find the next 3 terms of the geometric sequence.
Answers
PLEASE GIVE BRAINLIEST!
have a good day ;)
Answer:
2500,500,100, 20, 4, 0.8
Step-by-step explanation:
dividing by 5 every term.
2500/ 5 = 500
500/ 5 = 100
100/ 5 = 20
20/5 = 4
4/5 = 0.8
which will not result in a value of zero?
Answers
Answer:
B
Step-by-step explanation:
because 10 and 11 are not equal, therefore, when you add 10 then subtract 11, you will not end up with your original number
Answer:
Deposit $10, then withdraw $11.
Step-by-step explanation:
If you have $10 and you take away $11. You balance a of -1. Which is not zero.
A 6-foot tall observer casts a 3.5-foot shadow at the same time a silo casts a 49-foot shadow. How tall is the silo?
Answers
Answer:
about 28.8 ft.
Step-by-step explanation:
If two triangles are similar, what relationships do the corresponding sides and angles have with each other?.
Answers
In summary, the relationships between the corresponding sides and angles of similar triangles are: Corresponding sides are proportional and congruent.
When two triangles are similar, the corresponding sides of the triangles are proportional. This means that the ratio of the lengths of corresponding sides in the two triangles is equal. Similarly, the corresponding angles of similar triangles are congruent. This means that the angles in the two triangles that correspond to each other are equal in measure.
When two triangles are similar, it means that they have the same shape but possibly different sizes. The concept of similarity implies that the corresponding sides of the triangles have the same proportional relationship.
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what is the solution to this problem? 3(2x+1)=2(x+1)+1
Answers
Answer:
x = 0
Step-by-step explanation:
Answer:
x=0
Step-by-step explanation:
6x+3=2x+2+1
6x+3=2x+3
4x=0
x=0
need help my lil bro 6+(– 6)=
Answers
Answer:
Step-by-step explanation:
here you go mate'
step 1
6+(-6) equation
step 2
6+(– 6) simplify the signs
6-6
step 3
6-6 subtract
answer
0
mind if i get brainliest
I'll give brainliest to correct answer
Fill in each blank with a reason that justifies the statement. Given: XY = 36
look at the screenshot
Answers
Answer:
\(b. \:distributive \: property \: of \: equality \\ c. \: collect \: like \: terms\\ d. \: addition \: property \: of \: equality \\ e. \: division \: property \: of \: equality \)
2 (4 minus 3 x) + 5 (2 x minus 3) = 20 minus 5 x?
Answers
Answer:
x=3
Step-by-step explanation:
2(4-3x)+5(2x-3)=20-5x
8-6x + 10x - 15= 20-5x
subtract 8 from 15
subtract 6x from 10x getting you
4x-7= 20-5x
add 5x to both sides
add 7 to both sides
getting you
9x=27
divide by 9 to both side getting you x=3