Answer: 924 paths
Step-by-step explanation:
Since there is no shorter path, we know that the path must consist of 6 blocks to the north and 6 blocks to the east. Thus, the problem is equivalent to finding the number of ways to arrange 6 N's (for north) and 6 E's (for east) in a sequence such that no two N's are adjacent and no two E's are adjacent.
Let's denote N by 1 and E by 0. Then the problem is equivalent to finding the number of 12-digit binary sequences (i.e., sequences consisting of 0's and 1's) such that there are no consecutive 1's or consecutive 0's.
We can solve this problem using dynamic programming. Let F(n,0) be the number of n-digit binary sequences that end in 0 and have no consecutive 0's, and let F(n,1) be the number of n-digit binary sequences that end in 1 and have no consecutive 1's. Then we have the following recurrence relations:
F(n,0) = F(n-1,0) + F(n-1,1)
F(n,1) = F(n-1,0)
with initial values F(1,0) = 1 and F(1,1) = 1.
Using these recurrence relations, we can compute F(6,0) and F(6,1), and the total number of valid sequences is F(6,0) + F(6,1) = 132. Therefore, there are 132 different paths of length 12 blocks from your apartment to the math class.
An object is thrown upward at a speed of 145 feet per second by a machine from a height of 2 feet off the ground. The height h of the object after t seconds can be found using the equation
When will the height be 230 feet?
seconds
When will the object reach the ground?
seconds
Answer:
Step-by-step explanation:
The equation for the height h of the object after t seconds is given by:
h = -16t^2 + 145t + 2
To find when the height will be 230 feet, we can set h = 230 and solve for t:
230 = -16t^2 + 145t + 2
We can simplify this equation by moving all the terms to one side:
16t^2 - 145t + 228 = 0
To solve for t, we can use the quadratic formula:
t = (-b ± sqrt(b^2 - 4ac)) / 2a
where a = 16, b = -145, and c = 228. Plugging in these values, we get:
t = (-(-145) ± sqrt((-145)^2 - 4(16)(228))) / 2(16)
t = (145 ± sqrt(21025 - 14592)) / 32
t = (145 ± sqrt(6433)) / 32
t ≈ 0.56 seconds or t ≈ 9.17 seconds
Therefore, the height of the object will be 230 feet at approximately 0.56 seconds or 9.17 seconds after it is thrown.
To find when the object will reach the ground, we can set h = 0 and solve for t:
0 = -16t^2 + 145t + 2
Again, we can simplify this equation by moving all the terms to one side:
16t^2 - 145t - 2 = 0
Using the quadratic formula again, we get:
t = (-(-145) ± sqrt((-145)^2 - 4(16)(-2))) / 2(16)
t = (145 ± sqrt(21249)) / 32
t ≈ 9.51 seconds or t ≈ 0.15 seconds
Therefore, the object will reach the ground at approximately 0.15 seconds or 9.51 seconds after it is thrown. However, since the negative solution does not make physical sense in this context, the object will reach the ground after approximately 9.51 seconds.
~~~Harsha~~~
The length of a rectangle is 4 meters less than 2 inches times width. The perimeter is 34 meters. Find the width
Answer:
7
Let's call the width = x
width : x
so (x + 2x-4)2 = 34 (perime formula of a rectangle) x+2x-4 = 7
3x = 21
x = 7
so x is 7
Which phrase is represented by the expression 5x(36+9)
A. The product of 36 and 5, increased by 9
B. The product of 36 and 9, multiplied by 5
C. The sum of 36 and 9, multiplied by 5
D. The sum of 36 and 5, increased by 9
what is the area in square centimeters, of the trapezoid below?
The area in square centimeters, of the trapezoid below is equal to 84.4 cm².
How to calculate the area of a trapezoid?In Mathematics and Geometry, the area of a trapezoid can be calculated by using this mathematical equation (formula):
Area of trapezoid, A = ½ × (a + b) × h
Where:
a and b represent the base areas of a trapezoid.
h represent the height of a trapezoid.
By substituting the given side lengths into the formula for the area of a trapezoid, we have the following:
Area of trapezoid, A = ½ × (7.9 + 13.2) × 8
Area of trapezoid, A = 84.4 cm².
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
If a 24-pound EP rib of beef costing $45.00 is purchased oven-ready, and 1/4 of it is lost during roasting, how much does a 6-ounce serving cost?
$15 is the cost of a 6-ounce serving cost.
What is the cost price?
The precise value that corresponds to the unit price paid is represented by the cost price. In some stock market theories, this value is utilized to establish the value of stock holdings and is used as a key determinant of profitability.
Here, we have
Given: If a 24-pound EP rib of beef costing $45.00 is purchased oven-ready, and 1/4 of it is lost during roasting.
EP = 24 lb costing $45
1/4th lost during roasting.
Remaining = 24 lb - (1/4) of 24 lb
= 24 lb - 6 lb
= 18 lb
Now, this roast should match the cost of the original EP.
Cost per lb = (cost of beef originally)/(quantity of roasted beef)
= 45/18 dollar per lb
Cost of 6-ounce serving cost = (45/18)×6 = $15.
Hence, $15 is the cost of a 6-ounce serving cost.
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the combined sales tax rate for your country 7.25%
Answer: The California state sales tax rate is 7.25%. This rate is made up of a base rate of 6%, plus California adds a mandatory local rate of 1.25% that goes directly to city and county tax officials.
Step-by-step explanation:
Hope this helped! :)
The measure of DOT and TOU
The measure of ∠DOT is equal to 58°
The measure of ∠TOU is equal to 32°.
What is a complementary angle?In Mathematics and Geometry, a complementary angle refers to two (2) angles or arc whose sum is equal to 90 degrees (90°).
Mathematically, a complementary angle can be calculated by using this mathematical equation:
Q + R = 90°
Where:
Q and R are measure of the angles subtended.
By substituting the given parameters into the complementary angle formula, the sum of the angles is given by;
(7x + 2) + 4x = 90.
11x + 2 = 90
11x = 90 - 2
x = 88/11
x = 8.
For the measure of ∠DOT, we have;
∠DOT = (7x + 2)
∠DOT = 7(8) + 2
∠DOT = 58°
For the measure of ∠TOU, we have;
∠TOU = 4x
∠TOU = 4(8)
∠DOT = 32°.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
A person invested $840 in an account growing at a rate allowing the money to double every 10 years. How long, to the nearest tenth of a year would it take for the value of the account to reach $1,540?
It would take approximately 7.5 years (or 7 years and 6 months) for the value of the account to reach $1,540, assuming the money grows at a rate allowing it to double every 10 years.
HOW CAN WE CALCULATE THE AMOUNT?To solve this problem, we can use the formula for exponential growth:
[tex]A = P * (1 + r)^t[/tex]
where:
A = final amount (in this case, $1,540)
P = principal amount (initial investment, in this case, $840)
r = rate of growth (as a decimal, in this case, the rate at which the money doubles every 10 years, or 1/10 = 0.1)
t = time (in years, which we need to find)
Plugging in the values:
[tex]1,540 = 840 * (1 + 0.1)^t[/tex]
Dividing both sides of the equation by 840:
[tex]1.83333... = (1.1)^tTaking the natural logarithm of both sides:ln(1.83333...) = ln((1.1)^t)Using the property of logarithms that ln(a^b) = b * ln(a), we get:ln(1.83333...) = t * ln(1.1)Finally, dividing both sides by ln(1.1) to solve for t:t = ln(1.83333...) / ln(1.1)[/tex]
Using a calculator, we can find that t ≈ 7.5 (rounded to the nearest tenth of a year).
So, it would take approximately 7.5 years (or 7 years and 6 months) for the value of the account to reach $1,540, assuming the money grows at a rate allowing it to double every 10 years.
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What is the measure of angle XYZ
The calculated measure of the arc XYZ is 83 degrees
Calculating the measures of the angle XYZFrom the question, we have the following parameters that can be used in our computation:
The circle
The angles created by secants and tangents that intersect outside a circle, which states that
The size of the angle formed by these two lines is equivalent to half the numerical difference between the measures of the arcs that they cut out from the circle.
So, we have
XYY = 1/2 * (166 - 0)
Evaluate
XYY = 83
Hence, the measure of the angle is 83 degrees
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100 Points! Algebra question, only looking for an answer to B. Photo attached. Please show as much work as possible. Thank you!
Apply the fraction rule:
[tex]\text{a}\times\dfrac{\text{b}}{\text{c}} =\dfrac{\text{a}\times\text{b}}{\text{c}}[/tex]
Answer:
[tex]\longrightarrow\boxed{\bold{\frac{\text{fx}}{\text{g}}}}[/tex]
For the following sequence: 6,15,24,33,.....
a) Write an expression for the nth term
b) Find the 10th term.
Answer:
a) The common difference between consecutive terms is 9. Thus, the nth term can be expressed as:
n(9)+(-3)
b) To find the 10th term, we substitute n=10 in the expression we just found:
10(9) + (-3) = 87
Therefore, the 10th term of the sequence is 87.
Compare the values for the following, which is greater: sin 100° or sin 250°? Use the sin wave to approximate
each value and label it on the graph.
The value "Sin 100°" is greater than "sin 250°", that is, sin 100° > sin 250°
Which is greater, sin 100° or sin 250°?To compare the values of sin 100° and sin 250°, we need to understand the behavior of the sine function. The sine function oscillates between -1 and 1 over a period of 360°, with its maximum value of 1 at 90° and its minimum value of -1 at 270°.
Using the sine wave, we can see that sin 100° is located in the second quadrant, where the sine values are positive, while sin 250° is located in the third quadrant, where the sine values are negative. Therefore, sin 100° is greater than sin 250°, because sin 100° has a positive value closer to the maximum value of 1, while sin 250° has a negative value closer to the minimum value of -1.
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If z is a standard normal variable, find P(z>.97)
Therefore, P(z > 0.97) = 0.166 using standard normal distribution table.
Standard normal distribution table explained.
A standard normal distribution table, also called a z-score table or a standard normal table, is a table that provides the area under the curve to the left of a specific z-score value in a standard normal distribution. A standard normal distribution is a normal distribution with a mean of zero and a standard deviation of one.
The table usually includes positive z-score values in the right-hand column and the second decimal place in the top row. The intersection of a specific z-score value and decimal place provides the area under the curve to the left of that z-score value.
For example, if we want to find the area under the curve to the left of a z-score value of 1.32, we would locate the row with 1.3 in the top row and the column with 0.02 in the right-hand column. The intersection of this row and column gives the area under the curve to the left of 1.32, which is 0.9066.
Using a standard normal distribution table or calculator, we can find the probability of z being greater than 0.97 is approximately 0.166. Therefore, P(z > 0.97) = 0.166.
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A paperwight has height of 4cm and a volume of 38.4 cubic cm.
The calculated base area of the paperweight is 9.6 square cm.
Calculating the base areaTo calculate the base area of the paperweight, we can use the formula for the volume of a three-dimensional object:
Volume = Base area x Height
In this case, we know that the height of the paperweight is 4cm and the volume is 38.4 cubic cm.
So we can rearrange the formula and solve for the base area:
Base area = Volume / Height
Substituting the values we have:
Base area = 38.4 cubic cm / 4cm
Base area = 9.6 square cm
Therefore, the base area of the paperweight is 9.6 square cm.
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NO LINKS!!! URGENT HELP PLEASE!!!
Express the statement as an inequality (Part 1a^2)
a. b is positive
1. b ≥ 0
2. b ≤ 0
3. b = 0
4. b > 0
5. b < 0
b. s is nonpositive
1. s ≤ 0
2. s = 0
3. s ≥ 0
4. s < 0
5. s > 0
c. w is greater than or equal to -8
1. w < -8
2. w = -8
3. w ≥ -8
4. w > -8
5. w ≤ -8
a. 4. b > 0
If b is positive, then we know it will be greater than 0.
b. 1. s ≤ 0
If s is nonpositive, this means it is negative or 0. We will use a less than or equal to symbol.
c. 3. w ≥ -8
If w is greater than or equal to -8, we will use a greater than or equal to symbol.
If sam can swin 10 laps in 20 minutes, what would be his expected time for 15 laps?
Asnwer: 30 minutes
Explanation:
10 laps in 20 minutes is 1 lap every 2 minutes.
So we get this:
1 lap = 2 minutes
But we want 15 laps, so multiply both sides by 15 to get:
15 laps = 30 minutes
Find the surface area for the figure ( on photo )
The surface area of the square pyramid given above would be = 400ft²
How to calculate the surface area of the given shape?The diagram above is a typical example of the square based pyramid which has four triangles connected to a vertex.
To calculate the surface area of the given figure, the formula that should be used would be = b² +2bs
where b = base length= 10ft
s = slant height= 15ft
Surface area = 100+2(10×15)
= 100+300
= 400ft²
Therefore the surface area of the square based pyramid given above would be = 400ft².
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NO LINKS!! URGENT HELP PLEASE!!
Express the angle in terms of degrees, minutes, and seconds, to the nearest second.
350.5527°
Answer:
350° 33' 10".
Step-by-step explanation:
To convert the decimal degree 350.5527° to degrees, minutes, and seconds, we can use the following steps:
The whole number part of the decimal degree is the degree. So, the degree is 350.Multiply the decimal part by 60 to get the minutes.0.5527 x 60 = 33.162The whole number part of the minutes is the minutes. So, the minutes are 33.Multiply the decimal part of the minutes by 60 to get the seconds.0.162 x 60 = 9.72Round the seconds to the nearest second. The nearest second is 10.Therefore, 350.5527° is equivalent to 350° 33' 10".
Find the value of the annuity and the interest. Round to the nearest dollar.
Periodic Deposit: $100 at the end of each year
Rate: 4% compounded annually
Time: 9 years
The value of the annuity after 9 years is approximately $1,044.56. The interest earned on the annuity after 9 years is approximately $244.56.
What is annuity?A financial contract known as an annuity offers a series of recurring payments over a predetermined length of time. A monthly, quarterly, or annual payment schedule is available when buying an annuity from an insurance provider. The payments are made until the annuitant's death or for a predetermined amount of time.
Deferred annuities and immediate annuities are the two categories under which annuities fall. Deferred annuities are a particular kind of annuity where the payments are postponed for a predetermined amount of time, typically several years. On the other hand, an instant annuity starts paying out as soon as the annuity is bought.
The value of annuity is given by the formula:
[tex]A = P * ((1 + r)^n - 1) / r[/tex]
Substituting the given values we have:
[tex]A = $100 * ((1 + 0.04)^9 - 1) / 0.04\\A = $100 * (1.04^9 - 1) / 0.04[/tex]
A ≈ $1,044.56
Hence, the value of the annuity after 9 years is approximately $1,044.56.
Now, the interest is givn as:
Interest = A - (P * n)
Substituting the values we have:
Interest = $1,044.56 - ($100 * 9)
Interest ≈ $244.56
Hence, the interest earned on the annuity after 9 years is approximately $244.56.
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PLEASE ANSWER!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
OMG PLS NOBODY ANSWERS
YOU GET 100 POINTS
PLS PLS PLS PLS PLS PLS
Answer:
11
Step-by-step explanation:
You want the degree of the monomial -3q⁴rs⁶.
DegreeThe degree of a variable expression is its exponent. The degrees of the variables in the given expression are ...
q: 4
r: 1
s: 6
The degree of their product is the sum of the exponents:
monomial degree = 4 + 1 + 6 = 11
The degree is 11.
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What is an equation of the line that passes through the points
(
5
,
−
6
)
(5,−6) and
(
−
5
,
−
4
)
(−5,−4)?
Answer:
y= -1/5x-5
Step-by-step explanation:
You can use the slope formula and the slope intercept form which is y=mx+b.
The 8th grade math team is having a bake sale as a fundraiser. Alan can make 5 cookies in 2 minutes. Abigail can make 8 cookies in 3 minutes. However, Katie eats 1 cookie every 6 minutes. How many minutes will it take to make 5 dozen cookies.
Answer: B. 12
Step-by-step explanation:
1) Alan can make 2.5 cookies per min
2) Abi can make 8/3 which is 2.7.
3) overall, 5.2 cookies per minute can be made.
multiple 5.2 x 6 and you get around 31.5?
then subtract =1. you have 30.5, now add onto that number 31.5, which is another 6 minutes. since you're still only subtracting 1, the answer would be above 60, which is 5 dozen, and it only took 12 mins
Show that the circles touch each other internally.
This shows that the two circles intersect at a point P, and that the distance between their centers, OP1OP2, is less than the sum of their radii, r1 + r2. Thus, the two circles touch each other internally at point P.
How can you demonstrate how two circles internally contact one another?You must calculate each circle's radius and centre in order to accomplish this. The circles will externally touch if the total of the radii and the space between the centres are identical. The circles will internally touch if the variations in radii and the separation between their centres are equal.
Let C1 and C2 stand for the two circles, with O1 and O2 serving as their respective centres. Let r1 and r2 represent the radius of C1 and C2, respectively.
Let's say that point P is where the two circles converge. The Pythagorean Theorem thus gives us:
OP1² = r1²
OP2² = r2²
OP1² + OP2² = (r1 + r2)²
Simplifying the third equation, we get:
OP1² + OP2² = r1² + 2r1r2 + r2²
The left half of this equation can be rewritten as (OP1 + OP2)2 - 2OP1OP2. When we simplify the equation above and substitute this, we get:
(OP1 + OP2)² = (r1 + r2)² + 2OP1OP2
Since OP1 and OP2 are both positive, we have:
(OP1 + OP2)²> (r1 + r2)²
Therefore, we must have:
OP1OP2 < r1 + r2
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If a 95% confidence interval for is calculated to be (21.4 , 27.9) , what would be the result of a hypothesis test at a 5% significance level performed on the set of hypotheses?
H0: mean = 27
Ha: mean different 27
Is -4/3 perpendicular to 3/4
Answer:
no its not
Step-by-step explanation:
Using the slope-intercept form, the slope is Undefined. The slope of a perpendicular line to a vertical line is zero.
Pat's Pizza made
21
2121 cheese pizzas,
14
1414 veggie pizzas,
23
2323 pepperoni pizzas, and
14
1414 sausage pizzas yesterday.
Based on this data, what is a reasonable estimate of the probability that the next pizza made is not a cheese pizza?
Choose the best answer.\
Therefore , the solution of the given problem of probability comes out to be pizza won't be a cheese pizza is roughly 0.7089, or 70.89%.
What exactly is probability?Any considerations technique's fundamental objective is to determine the likelihood that a claim is true or that a particular incident will take place. Any number range from one to one, when 0 traditionally signifies a percentage and 1 typically implies the degree of certainty, can be used to represent chance. A probability illustration shows the likelihood that a particular event will occur.
Here,
The total number of pizzas made yesterday can be determined using the information provided as follows:
2121 cheese pizzas total.
Pizzas with vegetables: 1414
2323 pepperoni pizzas total.
1414 sausage pizzas were consumed.
Total pizzas produced were
=>2121 + 1414 + 2323 + 1414 = 7272.
Therefore, there were 2121 cheese pizzas prepared yesterday out of a total of 7272 pizzas.
The likelihood that the following pizza will be a cheese pizza is calculated as follows:
=> 2121 / 7272
The likelihood that the next pizza prepared won't be a cheese pizza is thus:
=> 1 - (2121 / 7272) = 5151 / 7272
Therefore, a conservative estimate of the likelihood that the following pizza won't be a cheese pizza is roughly 0.7089, or 70.89%.
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You paid $6.99 for a shirt that was 70% off; what was the original price of the shirt?
Answer:
$23.30
Step-by-step explanation:
We Know
You paid $6.99
The shirt was 70% off
$6.99 = 30%
What was the original price of the shirt?
We Take
(6.99 ÷ 30) x 100 = $23.30
So, the original price is $23.30
Is (-6, 8) a solution to this system of equations?
y = 8
7x + 4y = -10
yes
Or
no
Answer:
7(-6) + 4(8) = -42 + 32 = -10, so (-6, 8) is the solution to this system of equations.
The answer is Yes.
Find the volume for each prism.
(7) The volume of the triangular based prism is 41.16 m³.
(8) The volume of the haxagonal based prism is 1793.4 cm³.
What is a volume?Volume is the space ocuppied by a solid shape.
(7) To calculate the volume of the triangular based prism, we use the formula below
Formula:
V = Hbh/2.................... Equation 1Where:
V = Volume of the triangular based prismH = Height of the prism = 7 mb = Base of the triangle = 4.2 mh = Height of the triangle = 2.8 mSubstitute these values into equation 1
V = 7×4.2×2.8/2V = 41.16 m³(8) Also, to calculate the volume of the hexagon based prism, use the formula below
V = 6Hpa/2................. Equation 2Where:
H = Height of the prism = 14 cmp = Apothom of the hexagon = 6.1 cma = Sides of the hexagon = 7 cmSUbstitute these values into equation 2
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Please anwser the question i will reward brainlest.
Answer:
2((3(4) + 4(7) + 3(7)) = 2(12 + 28 + 21) = 2(61) = 122 square meters