Answers
The simplified expression is given as follows:
7/x³.
Where the coefficients are:
c = 7.e = 3.How to simplify the expression?The expression in this problem is defined as follows:
x³(1/4 x³)(28x^-9).
To obtain the coefficient c, we must multiply the coefficients of each expression, as follows:
c = 1 x 1/4 x 28
c = 7.
When two terms with the same base and different exponents are multiplied, we keep the bases and add the exponents, hence:
3 + 3 - 9 = -3.
The negative exponents goes in the denominator, hence the simplified expression is given as follows:
7/x³.
Meaning that the exponent is of e = 3.
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Related Questions
PLEASE HELP QUICKLY!!(20 points)
put the items in order from least steep to steepest rate of change
Elisas puppy weighed 4 pounds when it was born it gained 5 pounds per month until it was 9 months old.
g(x) = 8.1x + 45.64
Michele has $125 she plans to spend $10 per week until she has a total of $75
f(t) = -6.2x + 2.9
Answers
Answer:
The items arranged from least steep to steepest rate of change are:
Michele's spending: $125 to $75 over time, spending $10 per week.
Elisa's puppy's weight: Started at 4 pounds, gained 5 pounds per month until it was 9 months old.
f(t): -6.2x + 2.9, a linear function with a rate of change of -6.2.
g(x): 8.1x + 45.64, a linear function with a rate of change of 8.1.
So the correct order is:
Michele's spending
Elisa's puppy's weight
f(t)
g(x)
Step-by-step explanation:
Why is
C(A) generally not same as C(U)
where U is an echelon form obtained by reducing A?
Thank you in advance.
Answers
The discrepancy between the column spaces of a matrix's echelon form U and its original form A, C(U) and C(A) respectively, originates from how column space is defined.
How to explain the differenceColumn space is purported as the set of all linear combinations of the columns in the matrix. Nonetheless, despite elementary row operations modifying the linear independence of the matrix, it does not alter its column space.
Subsequently, therby resulting to C(U) being a subspace of C(A). This concept can be exemplified via an example: When we employ 3x3 matrix with linearly independent columns, then its echelon form U may only display two linearly independent columns; thus increasingly shrinking the dimension of the transformed matrix's column space.
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[ASAP Please!] Which are the better statistics to use to compare the distributions? Assume you know the mean, median, standard deviation, and IQR for each.
A.
Median and standard deviation
B.
Median and IQR
C.
Mean and standard deviation
D.
Mean and IQR
Answers
The better statistics to use to compare the distributions includes mean and standard deviation. The Option C is correct.
How are mean and standard deviation used to compare distributions?Mean represents the central tendency of the distribution, while standard deviation reflects the spread of the data around the mean. Comparing mean & standard deviation of 2 or more distributions can provide insights into similarities and differences.
If the means of two distributions are similar, it suggests the data points in each distribution are centered around similar value. But if standard deviations are also similar, it indicates that the spread of the data points around the mean is also similar.
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Given: ABCD is a trapezoid, AD = 10, BC = 8, CK - altitude ,Area of ∆ACD = 30.Find: Area of ABCD
BTW:the answer is somehow not 54
Answers
The area of ACD based on the information given will be 54 units².
How to calculate the areaThe area of a trapezoid is calculated as follows:
(base1 + base2) height / 2 = Area
where base1 and base2 are the lengths of the trapezoid's two parallel sides, and height is the perpendicular distance between them.
So, assuming you have the measurements for base1, base2, and height, you can use the formula above to compute the area of the trapezoid.
Area = 1/2 × (10 + 8) × 6
Area = 1/2 × 18 × 6
Area = 54 units ²
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Angles in a Triangle
Answers
Answer:
70
Step-by-step explanation:
The non-labeled side (next to 130) has to be supplementary to the angle outside, hence it has to be 50. Since all the sides of an angle must add up to 180, we can subtract 60+50 to get 70. Hope this helps!
Answer:
70°
Step-by-step explanation:
Theorem:
The measure of an exterior angle of a triangle is equal to the sum of the measures of its remote interior angles.
130 = x + 60
x = 70
Answer: 70°
Choose the best multiple choice option below! Thanks in advance!
Answers
Answer:
Q5. D, Q6. D, Q9. B.--------------------
Question 5The range of the given function has one restriction, its denominator can't be zero, hence:
3x + 4 ≠ 0 ⇒ 3x ≠ - 4 ⇒ x ≠ - 4/3Therefore the function can get any value but zero:
y ≠ 0The matching answer choice is D.
Question 6Linear function is f(x) = mx + b.
Reciprocal of a function f(x) is 1/f(x).
So the reciprocal of linear function has a form of f(x) = 1 / (mx + b).
The only answer choice in same form is D.
Question 9Substitute x = - 5/3 into function to get:
[tex]f(x)=\cfrac{1}{3*(-5/3)+5} =\cfrac{1}{-5+5} =\cfrac{1}{0}[/tex]This is undefined value, therefore it represents the vertical asymptote.
The function gets close to - ∞ when x → - 5/3 from left and gets close to +∞ when x → - 5/3 from right (see attached graph).
Therefore the correct choice is B.
From experience, an airline knows that only of the passengers booked on a flight from New York to Los Angeles actually board their flight. A random sample of booked passengers from New York to Los Angeles is chosen. Find the probability that of them board their flight.
Do not round your intermediate computations, and round your answer to three decimal places.
Answers
Step-by-step explanation:
6 or 7.
that means either exactly 6 or exactly 7 out of the 10 board the flight.
these are non-depending (or non-overlapping) scenarios. so, for this "or" remained we can simply add the 2 individual probabilities P(6) and P(7).
P(6) is the probability of exactly 6 passengers out of 10 will board the flight.
because of the 75% certainty overall we can conclude that the probabilty for each booked passenger to board is 0.75 (75% means 75 out of 100 = 0.75).
and the probabilty to not board is
1 - 0.75 = 0.25
so, for a specific group of exactly 6 booked passengers out of 10 their probabilty to board is
0.75⁶ × 0.25⁴ = 0.000695229...
6 passengers board, 4 do not board.
but this is for only one possible grouping of 6 passengers out of 10.
since the sequence does not matter, and we have no repetitions (every passenger counts as 1), we have combinations :
C(10, 6) = 10! / (6! × (10-6)!) = 10!/(6!×4!) = 10×9×8×7/4! =
= 5×3×2×7 = 210
therefore,
P(6) = 210 × 0.75⁶ × 0.25⁴ = 0.145998001...
and for a specific group of exactly 7 booked passengers out of 10 their probabilty to board is
0.75⁷ × 0.25³ = 0.002085686...
7 passengers board, 3 do not board.
but this is for only one possible grouping of 7 passengers out of 10.
since the sequence does not matter, and we have no repetitions (every passenger counts as 1), we have combinations :
C(10, 7) = 10! / (7! × (10-7)!) = 10!/(7!×3!) = 10×9×8/3! =
= 5×3×8 = 120
therefore,
P(7) = 120 × 0.75⁷ × 0.25³ = 0.250282288...
so, the probability that either 6 or 7 booked passengers are actually boarding is
P(6) + P(7) = 0.396280289... ≈ 0.396
Richard bought 3 slices of pizza and 2 sodas for 8.75. Jordan bought 2p and 4s for 8.50. How much would 1p and 3s cost?
Answers
3p + 2s = 8.75 (Equation 1)
2p + 4s = 8.50 (Equation 2)
We want to find the cost of 1p and 3s, so we can set up a third equation:
p + 3s = C (Equation 3)
We need to solve for C. We can do this by first solving for p in terms of s in Equation 2:
2p + 4s = 8.50
2p = 8.50 - 4s
p = 4.25 - 2s
Now we can substitute this expression for p into Equation 3:
4.25 - 2s + 3s = C
4.25 + s = C
So 1p and 3s would cost C = 4.25 + s. To find the value of s, we can substitute the values from Equation 1:
3p + 2s = 8.75
3(4.25 - 2s) + 2s = 8.75
12.75 - 6s + 2s = 8.75
-4s = -4
s = 1
Therefore, 1p and 3s would cost C = 4.25 + s = 4.25 + 1 = 5.25.
If cosθ = 0.2, find the value of
cosθ + cos (θ + 2π) + cos (θ + 4π)
Answers
Hence, the value of CosФ + Cos (2π+Ф) + Cos (4π+Ф) is 0.6 .
What is Cosine function ?The cosine function One of the fundamental trigonometry functions is cos x as the others being the co-secant, cotangent, secant, sine, and tangent. Let theta represent the angle that can be calculated by rotating the unit circle's arc anticlockwise from the x-axis. Cos theta is the arc endpoint of horizontal coordinate after that.
What is the trigonometry identities?trigonometric functions are used in an expression or equation, trigonometric Identities are helpful. For every value of a variable appearing on both sides of an equation, a trigonometric identity is true. Certain trigonometric functions such as sine, cosine, and tangent of one or more angles are involved geometrically in these identities.Three main are trigonometry functions are sine, cosine, and tangent, while the other three are cotangent, secant, and co-secant. All six trigonometric functions serve as the foundation for the trigonometric identities.
Given, CosФ = 0.2,
thus we can use the trigonometric identity:
cos(2 n π+Ф) = cosФ
where any integer n is used. Therefore:
Cos(2 π+ Ф) = CosФ
cos (4π+Ф) = cosФ
These values, put into the given expression
than we get,
cos Ф+ cos (2π+Ф) + cos (4π+Ф) = cos Ф+ cosФ + cosФ.
= 3 cosФ
= 3×0.2
= 0.6
So,CosФ + Cos (2π+Ф) + Cos (4π+Ф) = 0.6
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The distance between Eilat and Jerusalem is 292 kilometers. Give this distance in miles. Round the answer to the nearest tenth.
Answers
The distance between Eilat and Jerusalem is 181.4 miles.
To convert kilometers to miles, we need to multiply the number of kilometers by 0.621371, which is the conversion factor from kilometers to miles. Therefore, to convert the distance between Eilat and Jerusalem from kilometers to miles, we can use the following formula:
distance in miles = distance in kilometers × 0.621371
Substituting the given distance of 292 kilometers into the formula, we get:
distance in miles = 292 km × 0.621371 = 181.417852 miles
Rounding this answer to the nearest tenth, we get:
distance in miles ≈ 181.4 miles
Therefore, the distance between Eilat and Jerusalem is approximately 181.4 miles.
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URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
Answers
Answer:
Plot the points on the graphing calculator, and then determine the linear regression function: y = -1.16786x + 8.82857
You may obtain a slightly different linear regression equation.
1) -1 (g)
2) 8 (not one of the choices)
3) graph (i)
4) approximately -1/strong negative trend (not one of the choices)
5) y = -x + 8 (h)
Please help me with this question! I don't understand!
Which of the following step functions corresponds to the graph shown?
Answers
Answer:
f(x) =
0 if -1 < x < 0,
1 if 0 < x < 3,
2 otherwise
For a certain company, the cost function for producing x
items is C(x)=50x+250
and the revenue function for selling x
items is R(x)=−0.5(x−120)2+7,200
. The maximum capacity of the company is 170
items.
Answers
1. Required profit function is P(x)= -0.5x² + 60x + 6850
2. The domain of P(x) is 20 - 4√205 ≤ x ≤ 170.
3. P(70) = 2650 and P(80) = 2600.
The company should choose to produce 70 items as it results in a higher profit.
4. The leads to a decrease in profit, which is why the company makes less profit when producing 10 more units.
What is profit function?
A profit function is a mathematical formula that describes the relationship between the level of production or sales and the resulting profit of a business. The profit function takes into account the costs of production, including fixed costs and variable costs, and the revenue generated by the sale of goods or services.
1. The profit function P(x) is given by subtracting the cost function C(x) from the revenue function R(x):
P(x) = R(x) - C(x)
= [−0.5(x−120)²+7,200] - [50x+250]
= -0.5x² + 60x + 6850
2. The domain of P(x) is the set of all possible values of x for which the profit function P(x) makes sense. Since P(x) involves subtracting the cost function from the revenue function, it only makes sense to calculate P(x) when the revenue generated from selling x items is greater than or equal to the cost of producing x items. Therefore, the domain of P(x) is the set of all x such that R(x) ≥ C(x),
R(x) ≥ C(x)
-0.5(x−120)²+7,200 ≥ 50x+250
-0.5x²+60x+6850 ≥ 50x+250
-0.5x²+10x+6600 ≥ 0
Solving for x, we get:
x ≤ 20 - 4√205 or x ≥ 20 + 4√205
Since the maximum capacity of the company is 170 items, the domain of P(x) is the intersection of the above solution and the maximum capacity, i.e. x ≤ 170. Therefore, the domain of P(x) is 20 - 4√205 ≤ x ≤ 170.
3. To find the profit when producing 70 items, substitute x = 70 into the profit function P(70) = -0.5(70)² + 60(70) + 6850
= 2650
To find the profit when producing 80 items, substitute x = 80 into the profit function P(80) = -0.5(80)² + 60(80) + 6850
= 2600
Therefore, the company should choose to produce 70 items as it results in a higher profit.
4. The profit function P(x) is a quadratic function with a negative leading coefficient (-0.5), which means that it opens downwards. This implies that the profit function reaches its maximum value at the vertex of the parabola, which occurs at x = -b/2a, where a = -0.5 and b = 60. Therefore, the vertex occurs at x = -60/-1 = 60. This means that the maximum profit occurs at x = 60.
When the company produces 10 more units (i.e. x increases by 10), it moves away from the optimal production level of 60 and closer to the maximum capacity of 170. As a result, the cost of production increases while the revenue generated from selling those extra units decreases due to diminishing returns. This leads to a decrease in profit, which is why the company makes less profit when producing 10 more units.
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Complete the following, using exact interest. (Use Days in a year table.)
Note: Do not round intermediate calculations. Round the "Interest" and "Maturity value" to the nearest cent.
Answers
A loan of $595 borrowed on June 15 and repaid on Dec 17 at an exact interest rate of 6%. The exact time between the two dates is 170 days, and the maturity value is $611.69 rounded to the nearest cent.
Using the Days in a year table, we can find the exact time between June 15 and December 17 as follows
June has 30 days in the table and July through November have 31 days each. December has 17 days until the loan is repaid. Therefore, the exact time is
30 + 31 + 31 + 30 + 31 + 17 = 170 days
Next, we can calculate the interest using the formula
interest = principal x rate x time / 365
where the principal is $595, the rate is 6%, and the time is 170 days.
Substituting these values, we get
interest = 595 x 0.06 x 170 / 365
interest = $16.69
Therefore, the exact interest is $16.69.
Finally, we can calculate the maturity value by adding the principal and the interest
maturity value = principal + interest
maturity value = $595 + $16.69
maturity value = $611.69
Therefore, the maturity value is $611.69 rounded to the nearest cent.
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Diane Warner can rent a minivan for $24.95 per day plus $0.15 per mile, or she can rent a
large van for $289 per week with no additional charge for mileage. If she plans on renting the
car for 7 days and driving a total of 1,200 miles, which vehicle is a better buy?
Answers
In this case, renting the huge van would be a more cost-effective option because it would run you $289 as opposed to $354.65 for the minivan.
To compare the costs of renting the minivan and the large van, we need to calculate the total cost for each option.
For the minivan, the cost per day is $24.95 and the cost per mile is $0.15. So, for 7 days and 1,200 miles, the total cost would be:
Total cost = 7($24.95) + 1,200($0.15)
= $354.65
For the large van, the cost is a flat rate of $289 per week with no additional charge for mileage. So, for 7 days and 1,200 miles, the total cost would be:
Total cost = $289
Therefore, renting the large van would be a better buy in this scenario, as it would cost $289 compared to $354.65 for the minivan.
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HELP ASAPPPP!!!! Can someone help me write a recursive equation for this table and please explain it if possible
Answers
The recursive equation for this table is given as follows:
f(n) = 3f(n - 1) + 1.
How to define the recursive equation?To obtain the recursive equation, we must obtain a pattern between a term and the previous term.
For this problem, we have that each term is the previous term multiplied by 3 and added by one.
Hence the recursive equation for this table is given as follows:
f(n) = 3f(n - 1) + 1.
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If X=4, Y=5 and Z=10 Solve (X-Y)+Z
Answers
Answer:
9
Step-by-step explanation:
All you have to do is replace the letters with numbers
= ( x - y) + z
= ( 4 - 5) + 10
= -1 + 10
= 10 - 1
= 9
6.
2. How many more goldfish were given away before noon than in the afternoon? Circle
the letter of the correct answer.
a. 38
b. 30
c. 100
d. 28
3. How many goldfish were given away all day?
4.
Did the owner have enough goldfish for the entire day?
complete sentence.
Statistics
Show your work.
Explain with a
5. How many goldfish were left over, if any? Circle the letter of the correct answer.
a. 8
b. 10
c. 16
d. 0
At 11 a.m., why did the owner get nervous that she might not have enough
goldfish to give away? Use complete sentences to explain your thinking.
7. What might be a reason that no one came into the store at noon? Explain in
complete sentences.
Give the number of the sentence that provides the best evidence for the answer
Answers
2. 28 goldfish was what was given away before noon than in the afternoon
3. 108 goldfish were given away all day
4. Yes the owner have enough goldfish for the entire day
5. 16 goldfish were left over
How to solve for the goldfish2. Before noon, gold fish = 30 + 36 + 40 = 106
after noon gold fish = 28 + 30 + 10 + 2 + 8 = 78
diference = 106 - 78
= 28
3. Gold fish given away all day = 106 + 78
= 184
4. The owner had enough fish because the total fist he had was 200 and the amount that was given away is 184
5. The left over fish = 200 - 184
= 16
6. The owner was nervous because the customers were increasing between 9 to 11 and she had given away more than half in the first three hours
7. A reason no one came at noon could be because a resstaurant was having a lunch special
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HELP DOING CORRECTIONS DUE IN A HOUR GIVING BRAINLIEST AND 25 POINS
Answers
Answer:
s = 10√3
Step-by-step explanation:
This is a 30°-60°-90° right triangle, so s, the length of the longer leg, is √3 times the length of the shorter leg. Since the length of the shorter leg is 10, s = 10√3.
What is the meaning of [tex]r_{i-j}[/tex]?
Answers
This expression [tex]r_{i-j}[/tex] describes the distance between two points i and j in a geometric object
Explaining the meaning of the expressionIn the context of symmetry and rotations, [tex]r_{i-j}[/tex] typically refers to the distance between two points i and j in a geometric object, such as a crystal lattice or a molecule.
It is a vector that points from point i to point j, and its magnitude is the distance between the two points.
The distance vector [tex]r_{i-j}[/tex] is also used to describe the position of a point in the crystal lattice relative to the rotation axis.
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1. A train travels 16.8 km in 25 minutes. Find the speed of the train in (i) km/h, (ii) m/s. f 55 km/h. Find the distance travelled bynumber, opinion, size, shape, condition, age, color, pattern, origin, materials, and purpose.04-Jan-2022
Answers
the speed of the train in km/h is 40.32 whereas the speed of the train in m/s is 11.2.
(i) To find the speed of the train in km/h, we can use the formula:
speed = distance/time
Here, the distance travelled by the train is 16.8 km, and the time taken is 25 minutes, which is equivalent to 0.4167 hours (since 1 hour = 60 minutes). Substituting these values in the formula, we get:
speed = 16.8 km/0.4167 hours
speed = 40.32 km/h (rounded to two decimal places)
Therefore, the speed of the train in km/h is 40.32.
(ii) To find the speed of the train in m/s, we can convert the speed in km/h to m/s by multiplying by 1000/3600 (since 1 km/h = 1000 m/3600 s). Using the speed of 40.32 km/h from part (i), we get:
speed = 40.32 km/h * 1000 m/km / 3600 s/h
speed = 11.2 m/s (rounded to one decimal place)
Therefore, the speed of the train in m/s is 11.2.
If the speed limit is 55 km/h, we cannot directly determine the distance travelled by the train without additional information. The distance travelled by the train would depend on the time it took to travel at the given speed limit.
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Write the equation of the line that passes through the points (5,4) and (5,-8). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.
Answers
Answer: x=5
Step-by-step explanation:
Not much calculations needed, but since we have two points where x=5, a vertical line that is equal to x=5 will hit both points. I attached it visually below!
Find the values of x
and y that make these triangles congruent by the HL theorem quiz: congruence in right triangles
Answers
Where the above information about right triangles are given, the asnswer is
A. x = 3, y = 2 (Option A)
How did we arrive at the above?The hypotenuse and the length of one leg of one right triangle must be equal to the hypotenuse and corresponding length of the one leg of the other ∆ for both triangles to be equal by the HL Congruence Theorem.
Thus, let's find x and y by setting the corresponding lengths of the two right ∆s equal to each other.
Therefore:
x = y + 1 ----› eqn. 1
2x + 3 = 3y + 3 ----› eqn. 2
Substitute x = (y + 1) into eqn. 2, and solve for y.
2x + 3 = 3y + 3 ----› eqn. 2
2(y + 1) + 3 = 3y + 3
2y + 2 + 3 = 3y + 3
2y + 5 = 3y + 3
Collect like terms
2y - 3y = -5 + 3
-y = -2
Divide both sides by -1
y = 2
Substitute y = 2 into eqn. 1.
x = y + 1 ----› eqn. 1
x = 2 + 1
x = 3
Thus,
x = 3, and y = 2 (Option A)
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Full Question:
See attached image
What is the distance between the points located at (−7, −18) and (−7, 25)?
7 units
43 units
−43 units
−7 units
Answers
Answer:
43
Step-by-step explanation:
The distance formula is
[tex] \sqrt{{(x2 - x1)}^{2} + (y2 - y1)^{2} } [/tex]
So
[tex] \sqrt{(25 + 18) ^{2} + ( - 7 + 7)^{2} } \\ = \sqrt{ {43}^{2} + 0 {}^{2} } = 43[/tex]
Answer:
43 unitsStep-by-step explanation:
The distance between the two given points can be found using the formula for the distance between two points in a coordinate plane,
which is d = √((x₂ - x₁)² + (y₂ - y₁)²). In this case, the x-coordinates of both points are the same (-7), so we only need to calculate the difference between their y-coordinates: d = √((0)² + (25 - (-18))²) = √(43²) = 43 units. Therefore, the distance between the two points located at (-7, -18) and (-7, 25) is 43 units
The television show Pretty Betty has been successful for many years. That show recently had a share of 15, which means, that among the TV sets in use, 15% were tuned to Pretty Betty. An advertiser wants to verify that 15% share value by conducting its own survey, and a pilot survey begins with 11 households have TV sets in use at the time of a Pretty Betty broadcast. Find the probability that none of the households are tuned to Pretty Betty. P(none) = Find the probability that at least one household is tuned to Pretty Betty. P(at least one) = Find the probability that at most one household is tuned to Pretty Betty. P(at most one) =
Answers
The probabilities will be :
P(none) = 0.018
P(at least one) = 0.982
P(at most one) = 0.187
What are the probabilities?Pretty Betty share is 15%, the probability that any one household is tuned to the show will be: 0.15.
To find the probability that none of the households are tuned to Pretty Betty will be:
P(none) = 0.85¹¹
≈ 0.018
So, to find the probability that at least one household is tuned to Pretty Betty, i use the complement rule as well as subtract the probability of none of the households being tuned to the show from 1:
P(at least one)
= 1 - P(none)
≈ 1 - 0.018
≈ 0.982
So, to find the probability that at most one household is tuned to Pretty Betty:
P(at most one) = P(none) + P(one)
= 0.85^11 + 11(0.15)(0.85^10)
≈ 0.187
Hence, the probabilities will be :
P(none) = 0.018
P(at least one) = 0.982
P(at most one) = 0.187
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Simplify the product using the distributive property
(3h - 5)(5h + 4)
Answers
Step-by-step explanation:
(3h - 5)(5h + 4) = 3h * 5h + 3h * 4 - 5*5h - 5 *4
= 15h^2 - 13h -20
[tex](3h-5)(5h+4)[/tex]
[tex]=(3h+-5)(5h+4)[/tex]
[tex]=(3h)(5h)+(3h)(4)+(-5)(5h)+(-5)(4)[/tex]
[tex]=15h^2+12h-25h-20[/tex]
Answer:
[tex]\bold{=15h^2-13h-20}[/tex]At the park there is a pool shaped like a circle with diameter 22 yd. A ring-shaped path goes around the pool. Its
width is 5 yd. If one gallon of coating can cover 5yd many gallons of coating do we need? Note that coating comes only by the gallon so the number of gallons must be a whole number. (Use the value 3.14 for pi.)
Answers
Answer: To find the area of the ring-shaped path, we need to subtract the area of the inner circle (the pool) from the area of the outer circle. The radius of the pool is half the diameter, so it is 11 yards. The radius of the outer circle is the sum of the radius of the pool and the width of the path, so it is 11 + 5 = 16 yards.
The area of the pool is:
A_pool = pi * r^2 = pi * 11^2 ≈ 380.13 square yards
The area of the outer circle is:
A_outer = pi * R^2 = pi * 16^2 ≈ 804.25 square yards
The area of the ring-shaped path is:
A_path = A_outer - A_pool ≈ 804.25 - 380.13 ≈ 424.12 square yards
Since one gallon of coating can cover 5 square yards, we need:
Gallons = A_path / 5 ≈ 424.12 / 5 ≈ 84.82
Therefore, we need approximately 85 gallons of coating to cover the ring-shaped path.
Step-by-step explanation:
Find [tex]A(3,4)[/tex].
HINT: [tex]A(1,n)=2^n[/tex] whenever [tex]n \geq 1[/tex]
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Along with proof of (a.) and (d.), (b.) Power tower: one level is a, (k + 1) levels is a raised to the power of a power tower with k levels, (c.) A(2, n) <= 2 ↑↑ n for all positive integers n, where ↑↑ denotes power tower notation.
What is an Ackermann function?The idea of a fully computable function that is not primitive recursive is illustrated by the recursively constructed mathematical function known as the Ackermann function. Since m and n are non-negative integers, it is commonly written as A(m, n).
a.) Prove using regular induction that [tex]A(1, n) \leq 2^n[/tex] for all positive integers n:
Base Case: For n = 1, A(1, 1) = 2, which is equal to [tex]2^1[/tex].
Inductive Hypothesis: Assume that [tex]A(1, k) \leq 2^k[/tex] for some positive integer k.
Inductive Step: We need to show that [tex]A(1, k + 1) \leq 2^{(k + 1)}[/tex]. Using the recursive definition of A(m, n), we have [tex]A(1, k + 1) = A(0, A(1, k)) = 2^{(A(1, k))}\leq 2^{(2^k)}[/tex] (by inductive hypothesis)[tex]< = 2^{(2^{(k + 1)})}[/tex].
Therefore, by regular induction, we have proved that [tex]A(1, n) \leq 2^n[/tex] for all positive integers n.
b.) A power tower with one level is defined as a, and a power tower with (k + 1) levels is defined as a raised to the power of a power tower with k levels.
c.) [tex]A(2, n) \leq 2[/tex] ↑↑ n for all positive integers n, where ↑↑ denotes power tower notation.
d.) The recursive definition of a triple arrow-up notation for power towers is:
a ↑↑↑ 1 = a (base case)
a ↑↑↑ (k + 1) = a ↑↑ (a ↑↑↑ k) (recursive step)
This definition states that a triple arrow-up notation with one level is equal to the base value "a", and a triple arrow-up notation with (k + 1) levels is equal to "a" raised to the power of a triple arrow-up notation with "k" levels.
Learn more about Ackermann function here:
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Complete Question: ( Refer to image)
Purchase 400 motors per month what is percent saved if you order 800 every 2 months round to nearest tenth
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Let's assume that the unit price of the motors is $100. If you order 400 motors per month, the total cost is:
400 motors/month x $100/motor = $40,000/month
If you order 800 motors every two months, the total cost is:
800 motors/2 months x $100/motor = $40,000/2 months = $20,000/month
The cost savings associated with the larger order is:
$40,000/month - $20,000/month = $20,000/month
To calculate the percentage saved, we divide the cost savings by the original cost and multiply by 100:
$20,000/month / $40,000/month x 100 = 50%
Therefore, you can save 50% by ordering 800 motors every two months instead of 400 motors per month.
The amount of snowfall in December was 5 7/8 feet. The amount of snowball in October was 1/4 feet. How much more snowfall was there in December? Write your answer as a mixed number in simplest form.
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Answer: 5 5/8 more feet of snow in December.
Step-by-step explanation: 5 7/8 also equals 47/8, and we need convert 1/4 to something over 8 so we can subtract the two. 1/4, but multiply both sides by 2 is 2/8. 47/8-2/8=45/8. 45/8 as a mixed fraction is 5 5/8.