Simplify.
75
48
Be sure to write your answer in simplest form.
Answers
Answer:
25/16 or 1 9/16
Related Questions
Show that w is in the subspace of R4 spanned by V1, V2, and V3, where these vectors are defined as follows. 1 -4 -9 -4 6 3 5 W= -2 - 1 - 1 -2 4 11 -8 - 15 To show that w is in the subspace, express was a linear combination of V1, V2, and V3. Select the correct answer below and, if necessary, fill in any answer boxes to complete your choice. O A. The vector w is in the subspace spanned by V1, V2, and V3. It is given by the formula w= (v1+ 2+ 3. (Simplify your answers. Type integers or fractions.) B. The vector w is not in the subspace spanned by V1, V2, and V3.
Answers
To show that w is in the subspace of R4 spanned by V1, V2, and V3, we need to find constants c1, c2, and c3 such that:
w = c1V1 + c2V2 + c3V3
We can write this as a matrix equation:
| 1 -4 -9 -4 | | c1 | | -2 |
| 6 3 5 1 | x | c2 | = | -1 |
| 2 4 11 -8 | | c3 | | -1 |
| -15 7 22 -14 | | -2 |
We can solve this system of equations using row reduction:
| 1 -4 -9 -4 | | c1 | | -2 |
| 6 3 5 1 | x | c2 | = | -1 |
| 2 4 11 -8 | | c3 | | -1 |
| -15 7 22 -14 | | -2 |
R2 = R2 - 6R1
R3 = R3 - 2R1
R4 = R4 + 15R1
| 1 -4 -9 -4 | | c1 | | -2 |
| 0 27 59 25 | x | c2 | = | 11 |
| 0 12 29 -16 | | c3 | | 3 |
| 0 -23 67 -59 | | -32 |
R4 = R4 + 23R2
| 1 -4 -9 -4 | | c1 | | -2 |
| 0 27 59 25 | x | c2 | = | 11 |
| 0 12 29 -16 | | c3 | | 3 |
| 0 0 174 -294 | | 225 |
R3 = R3 - (12/27)R2
R4 = (1/174)R4
| 1 -4 -9 -4 | | c1 | | -2 |
| 0 27 59 25 | x | c2 | = | 11 |
| 0 0 -1 22/3 | | c3 | | -13/3 |
| 0 0 1 -98/87 | | 25/58 |
R1 = R1 + 4R3
R2 = R2 - 59R3
R4 = R4 + (98/87)R3
| 1 0 -13 -10/3 | | c1 | | 21/29 |
| 0 27 0 -2119/87 | x | c2 | = | 2238/87 |
| 0 0 1 -98/87 | | c3 | | 25/58 |
| 0 0 0 1390/2391 | | 1009/2391 |
R1 = R1 + (13/1390)R4
R2 = (1/27)R2
R3 = R3 + (98/1390)R4
| 1
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II. Consider two friends Alfred (A) and Bart (B) with identical income Iµ = Iß = 100, they both like only two goods (x₁ and x₂). That are currently sold at prices p₁ = 1 and p2 = 4. The only difference between them are preferences, in particular, Alfred preferences are represented by the utility function: UA (x₁, x₂) = x⁰.⁵/¹x⁰.⁵/²while Bart's preferences are represented by: UB(x₁, x₂) = min{x₁, 4x₂ 2. Assume that a new technology is discovered that makes the production of good 2 cheaper, and thus prices are now p₂ = 2. Do the following: a) What quantities are going to be consumed in this new scenario. b) Determine the Hicksian demand curve (as a function of utility and prices) for each good for Alfred and Bart.c) How much of an increase in income (keeping prices as (p₁ = p₂ = 4) is equivalent to the drop in price ? (estimate for each consumer separately) ³. d) Can you tell who benefited more from the price drop? 112
Answers
a) To determine the quantities consumed in the new scenario, we need to find the optimal bundles for both Alfred and Bart using their respective utility functions.
For Alfred (A):
Utility function: UA(x₁, x₂) = x₁^0.5/1 * x₂^0.5/2
Since the prices are p₁ = 1 and p₂ = 2, we can set up Alfred's optimization problem as follows:
Maximize: UA(x₁, x₂) = x₁^0.5/1 * x₂^0.5/2
Subject to: p₁x₁ + p₂x₂ = Iₐ = 100
By solving this problem, we can find the optimal quantities consumed by Alfred in the new scenario.
For Bart (B):
Utility function: UB(x₁, x₂) = min{x₁, 4x₂}
Again, using the prices p₁ = 1 and p₂ = 2, we set up Bart's optimization problem as follows:
Maximize: UB(x₁, x₂) = min{x₁, 4x₂}
Subject to: p₁x₁ + p₂x₂ = Iₐ = 100
By solving this problem, we can find the optimal quantities consumed by Bart in the new scenario.
b) To determine the Hicksian demand curve for each good for Alfred and Bart, we need to calculate the demand for each good at different utility levels, keeping the prices fixed.
For Alfred:
By solving the optimization problem at different utility levels, we can find the Hicksian demand curve for x₁ and x₂ for Alfred.
For Bart:
Similarly, by solving Bart's optimization problem at different utility levels, we can find the Hicksian demand curve for x₁ and x₂ for Bart.
c) To determine how much of an increase in income is equivalent to the drop in price, we need to find the income change that compensates for the price change while keeping utility constant.
For each consumer separately (Alfred and Bart), we can compare the change in income required to maintain the same utility level with the change in price. The ratio of the change in income to the change in price will give us the income elasticity of demand.
d) By comparing the change in consumer surplus for Alfred and Bart resulting from the price drop, we can determine who benefited more from the price drop. The consumer with a larger increase in consumer surplus (measured by the change in utility) will be the one who benefited more.
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what step cadence is used during the ymca 3-minute step test?
Answers
This cadence corresponds to three sets of 24 steps per set, totaling 72 steps per minute. Participants are required to step up and down on a 12-inch step platform for a duration of three minutes, following the 96 BPM rhythm.
The step cadence used during the YMCA 3-minute step test is a set of three stepping cycles per each 20-second period. This means that the participant takes a total of nine steps within each 20-second period. In other words, the participant steps up and down on the platform at a rate of approximately 24 steps per minute. It is important to maintain this consistent step cadence throughout the entire test in order to get an accurate measure of cardiovascular fitness. Overall, the YMCA 3-minute step test is a simple and effective way to assess an individual's aerobic fitness level.
The YMCA 3-minute step test utilizes a specific step cadence to measure an individual's cardiovascular fitness. The answer is that during the test, a cadence of 96 beats per minute (BPM) is used. This cadence corresponds to three sets of 24 steps per set, totaling 72 steps per minute. Participants are required to step up and down on a 12-inch step platform for a duration of three minutes, following the 96 BPM rhythm. Upon completion of the test, the participant's heart rate is measured for a minute to determine their fitness level. The test results can be compared to established norms to gauge overall cardiovascular health and endurance.
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Each chart has which three components (choose three)?
A. Forecast of customer
B. A center line representing the average
C. An upper line representing last week's sample
D. A lower line representing last week's sample
E. An upper line representing the maximum acceptable variation upwards
F. A lower line representing the maximum acceptable variation downwards
G. A center line representing the maximum acceptable variation centrally
Answers
Each chart consists of a center line representing the average, an upper line indicating the maximum acceptable deviation upwards, and a lower line indicating the maximum acceptable deviation downwards. These components help analyze data and monitor process performance.Option B,E,F.
Each chart has the following three components:
1. B. A center line representing the average: This line is drawn to show the average value or mean of the data being analyzed. It provides a reference point to compare the data points above and below it.
2. E. An upper line representing the maximum acceptable variation upwards: This line is drawn to indicate the upper limit of acceptable variation or deviation from the average. It helps identify if the data points exceed the acceptable range.
3. F. A lower line representing the maximum acceptable variation downwards: This line is drawn to indicate the lower limit of acceptable variation or deviation from the average. It helps identify if the data points fall below the acceptable range.
These three components together create a control chart, which is a graphical representation used in statistical process control. Control charts help monitor and analyze data over time, allowing organizations to identify trends, detect abnormalities, and make data-driven decisions to improve processes and quality.
In summary, each chart consists of a center line representing the average, an upper line indicating the maximum acceptable deviation upwards, and a lower line indicating the maximum acceptable deviation downwards. These components help analyze data and monitor process performance.
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Question: A consumer group claims that a pizza delivery store takes longer to deliver their pizzas than the advertised average time of 25 minutes.
Answers
Statistical tests such as t-tests or z-tests can be utilized to analyze data and determine if there is evidence supporting the claim that delivery times are longer than the advertised average of 25 minutes.
To assess the claim made by the consumer group regarding the pizza delivery store's average delivery time, a hypothesis test can be conducted. The null hypothesis (H 0) states that the average delivery time is equal to or less than 25 minutes, while the alternative hypothesis (Ha) suggests that it takes longer.
To formally test the claim, statistical analysis such as a t-test or z-test can be used, depending on the available information. The consumer group's claim challenges the advertised average time of 25 minutes, indicating a potential discrepancy. By collecting data on pizza delivery times and performing the appropriate statistical test, we can determine if there is evidence to support the consumer group's claim.
Hypothesis testing allows us to evaluate the likelihood of observing the obtained data if the null hypothesis were true. This assessment helps us draw conclusions about the population based on the sample data.
It is important to note that conducting the actual hypothesis test requires additional information, such as the sample size, sample mean, and possibly the standard deviation of the delivery times. Without these specifics, it is not possible to provide a definitive conclusion.
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Please write well.
Answer the following question when X₁, X₂,..., X is a random sample from an exponential family with the following probability density function. f(x 0) = exp (0T(x) + d(0)+ S(x)) a. H: 0= 0 vs H₁
Answers
Given that X₁, X₂,..., X is a random sample from an exponential family with the following probability density function, f(x 0) = exp (0T(x) + d(0)+ S(x)).
To form the hypothesis for the exponential family, we need to consider the null and alternative hypothesis.
Null hypothesis: 0= 0
Alternative hypothesis: 0 ≠ 0
Explanation: The exponential family is a class of distribution families. The density of an exponential family is given by the following expression:
f(x|θ) = h(x) exp{θT(x) − A(θ)},
where h(x) is a nonnegative function of the data that does not depend on the parameter θ and A(θ) is a normalizing function.
The parameter θ is typically called the natural parameter, and T(x) is the vector of sufficient statistics. The exponential family of distributions includes the normal, exponential, chi-squared, gamma, and beta distributions, among others. In hypothesis testing for the exponential family, we typically specify a null hypothesis and an alternative hypothesis, just as in other types of hypothesis testing. The test statistic is usually a ratio of two likelihood ratios.
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Imagine an upright cone with its base resting on your horizontal desk. sketch the cross section formed by intersecting each plane with the cone.
Answers
We could expect to see a variety of interesting and complex shapes in the resulting cross sections.
If we were to intersect planes with the cone, we would get a variety of cross sections depending on the angle of the planes. For example, if we were to intersect a plane parallel to the base of the cone, we would get a circle as the cross section. If we were to intersect a plane at an angle, we would get an ellipse. We could also get hyperbolas or parabolas depending on the angle and position of the plane. The key is to visualize the different planes intersecting the cone at different angles and positions. Overall, we could expect to see a variety of interesting and complex shapes in the resulting cross sections. If the plane is parallel to the base, the cross section will be a circle. When the plane intersects the cone at an angle, the cross section becomes an ellipse. If the plane passes through the apex and the base's edge, it creates a triangle. Finally, if the plane goes through the apex and the midpoint of the base's edge, you'll get a parabola. These shapes represent various cross sections formed by intersecting each plane with the cone.
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15 POINTS PLEASE ANSWER
What equation can be used to find the following: "9 is 45% of what number"
Answers
9/.45
Answer:
20
Step-by-step explanation:
45% of x=9
x=9/0.45 = 20
Which of the following is an equation of a line that is parallel to one whose equation is y = 5x - 3?
Answers
please just (c)fog-¹
Answers
f(x) = 1/(1 - x)
g(x) = (x - 1)/x
The inverse functions f ⁻¹(x) and g ⁻¹(x), if they exist, are such that
f( f ⁻¹(x) ) = x
g( g ⁻¹(x) ) = x
So we have
f( f ⁻¹(x) ) = 1/(1 - f ⁻¹(x) ) = x
Solve for f ⁻¹(x) :
1 = (1 - f ⁻¹(x) ) x
1 - f ⁻¹(x) = 1/x
f ⁻¹(x) = 1 - 1/x
f ⁻¹(x) = (x - 1)/x
and so f ⁻¹(x) = g(x).
Similarly, you can solve for g ⁻¹(x) :
g( g ⁻¹(x) ) = (g ⁻¹(x) - 1) / g ⁻¹(x) = x
1 - 1/g ⁻¹(x) = x
1/g ⁻¹(x) = 1 - x
g ⁻¹(x) = 1/(1 - x)
So we know f(x) and g(x) are inverses of one another,
f ⁻¹(x) = g(x)
g ⁻¹(x) = f(x)
Then
(a) (f o g)(x) = x
(b) (g o f ⁻¹)(x) = g(g(x)) = (g(x) - 1)/g(x) = 1 - 1/g(x) = 1 - x/(x - 1) = 1/(1 - x)
(c) (f o g ⁻¹)(x) = f(f(x)) = 1/(1 - f(x) ) = 1/(1 - 1/(1 - x)) = 1/(x/(x - 1)) = (x - 1)/x
For the following choose whether the statement is always, sometimes or never true. * 20 points Always true Sometimes true Never true 1. In similar figures, the lengths of the corresponding sides are proportional. When creating a similar figure. multiply the angle measure by the scale factor O
Answers
Answer
1) In similar figures, the lengths of the corresponding sides are proportional.
This statement is always true.
2) When creating a similar figure. multiply the angle measure by the scale factor.
This statement is never true.
The angle measure of similar figures are usually just the same for corresponding edges.
Hope this Helps!!!
Statistical reasoning can help us generalize correctly from
A. a range to standard deviation
B. a standard deviation to a mean
C. a sample to a population*
D. A scatter plot to a skewed distribution
Answers
Statistical reasoning can help us generalize correctly from a sample to a population (option C).
Statistical reasoning involves using data and statistical methods to draw conclusions or make inferences about a larger population based on a smaller sample.
By carefully selecting and analyzing a representative sample, statistical reasoning allows us to make valid generalizations about the population as a whole.
By applying statistical techniques, such as hypothesis testing, confidence intervals, and estimation methods, we can make inferences about population parameters, such as means, proportions, or other summary statistics.
These methods help us draw conclusions about the population based on the observed data from the sample.
Option A, generalizing from a range to standard deviation, is not correct.
The range is a measure of variability in a dataset and provides information about the spread of values but does not directly relate to the standard deviation.
Option B, generalizing from a standard deviation to a mean, is also not correct.
The standard deviation measures the dispersion or spread of data around the mean and does not provide information about the mean itself.
Option D, generalizing from a scatter plot to a skewed distribution, is not an accurate representation of statistical reasoning.
A scatter plot is a visual representation of the relationship between two variables and does not directly imply information about the shape or distribution of the data.
The presence of skewness in a distribution is typically determined by analyzing the actual data distribution using statistical tests or graphical tools specifically designed for that purpose.
Therefore, option C, generalizing from a sample to a population, is the correct choice that reflects how statistical reasoning enables us to draw valid conclusions about a population based on a sample.
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hii this is geometry please help!!
Answers
Answer:
40
Step-by-step explanation:
The Interior of a triangle adds up to 180. 180 - 90 - 50 = 40
Work out the circumference of this circle.
Give your answer in terms of t.
en
6 mm
Answers
Circumference of the circle = 2 pie r
Therefore circumference = 2 × 22/7 × 6
So your circumference = 44pie mm
Can someone help me on this plzzz
Answers
Answer:
53
Step-by-step explanation:
Norman plants a garden each
year. This year, his garden
produced 40% fewer tomatoes
than it did last year. If Norman’s
garden produced 30 tomatoes
this year, how many tomatoes
did his garden produce last year?
Answers
Answer:
50
Step-by-step explanation:
if last year 100% of the tomatoes were produced and this year 40% less were produced then that would mean 60% of tomatoes were produced this year.
if 60% = 30 then
100% = ?
100x30÷60
Write an equation in slope-intercept form of the line that passes through (0, 6) and (3, -3)
Answers
Answer:
y=-3x+6
Step-by-step explanation:
Using slope formula
\(\frac{y_{2} -y_{1} }{x_{2} -x_{1} }\)(0, 6) x1, y1(3, -3) x2, y2\(\frac{-3-6 }{3-0}=\frac{-9}{3}=-3\)What is the present value of 550,000 to be rectived 5 years from fodmy if the discount rate is \( 5.2 \% \) (APR) compounded weeky? ․, \( 516,3213 b \) b. \( 530,805.32 \) c \( 511,614,45 \) d.530,5
Answers
The present value of $550,000 to be received 5 years from now, with a discount rate of 5.2% (APR) compounded weekly, is approximately $427,058.38.
To calculate the present value of $550,000 to be received 5 years from now, we can use the formula for present value with compound interest:
Present Value = Future Value / (1 + r/n)^(n*t)
Where:
- Future Value = $550,000
- r = annual interest rate as a decimal = 5.2% / 100 = 0.052
- n = number of compounding periods per year = 52 (since it is compounded weekly)
- t = number of years = 5
Plugging in the values into the formula, we get:
Present Value = 550,000 / (1 + 0.052/52)^(52*5)
Calculating the expression inside the parentheses first:
(1 + 0.052/52)^(52*5) = (1.001)^260 ≈ 1.288218
Now, dividing the Future Value by the calculated expression:
Present Value = 550,000 / 1.288218 ≈ $427,058.38
Therefore, the present value of $550,000 to be received 5 years from now, with a discount rate of 5.2% (APR) compounded weekly, is approximately $427,058.38.
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ASAP help plss!!!
A researcher studies the relationship between the number of hours of sleep per night and the performance on a memory test. Stady participants are randomly selected to get no sleep or sleep in 1-hour increments, up to 8 hours total (that is, the participant gets 1 hour, 2 hours, and so on, up to 8 hours of sleep). The researcher determines that the association between the two variables can be modeled with the linear equation p= 9h 15, where his number of hours of sleep and p is the percentage score on the memory test. Use the slope in the equation to describe the association between the hours of sleep and the performance on the memory test
Answers
The slope of the equation is 9, hence the percentage score increases by 9% for each hour he sleeps.
What is a Linear equationA linear equation is in the form:
y = mx + b
where y, x are variables, m is the rate of change (slope) and b is the y intercept.
Let p represent the percentage score on a memory test after sleeping for h hours. Given:
p = 9h + 15
Since the slope of the equation is 9, hence the percentage score increases by 9% for each hour he sleeps.
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h(x)=−x−1, find h(6)
Answers
h(x) = -x-1
Then just substitute x =6
Then,
h(6) = (- 6-1)
=> h(6)= -75. State if the following statements are true or false. If true, give a 1-3 line explanation; otherwise, provide a counter example or explanation. No rigorous formal justification needed. (a) The set {x∈R
n
∣Ax=b} is convex, where A∈R
m×n
,b∈R
m
. (b) The set {(x
1
,x
2
)∣x
2
≤3x
1
2
} is convex. (c) All polygons on the R
2
plane are convex. (Hint: A polygon is a plane figure formed with straight line segments.) (d) If S⊆R
2
is convex, then S must enclose a region of finite area. (e) If S
1
,S
2
⊆R
2
and S
1
∩S
2
=ϕ, then S
1
∪S
2
must be non-convex. (f) If S
1
,S
2
⊆R
2
and both S
1
,S
2
are closed, then S
1
∪S
2
must be non-convex.
Answers
(a) False. The set {x∈R^n | Ax=b} is not necessarily convex. It depends on the matrix A and the vector b. For example, if A is a non-convex matrix, then the set of solutions {x∈R^n | Ax=b} will also be non-convex.
(b) True. The set {(x₁,x₂) | x₂ ≤ 3x₁²} is convex. The inequality defines a downward parabolic region, and any line segment connecting two points within this region will lie entirely within the region. (c) False. Not all polygons on the R² plane are convex. For example, a polygon with a concave portion, such as a crescent shape, would not be convex.
(d) True. If S⊆R² is convex, then it must enclose a region of finite area. Convex sets do not have "holes" or disjoint parts, so they form a connected and bounded region. (e) False. If S₁⊆R² and S₂⊆R², and S₁∩S₂=ϕ (empty set), then S₁∪S₂ can be convex. If S₁ and S₂ are both convex sets that do not overlap, their union can still be a convex set. (f) True. If S₁⊆R² and S₂⊆R² are both closed sets, then their union S₁∪S₂ must also be closed. However, it may or may not be convex. The convexity of the union depends on the specific sets S₁ and S₂.
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9. The volume of a box in cubic feet can be expressed as V(x) = x³ - 3x² - 10x or as the product of three linear factors with integer coefficients. The width of the box is 5-x. What is the length, width, and height of the box in factored form? A. -x(5-x)(x+2) B. X(5-x)(x+2) C. X(5-x)(x-2) D. -x(5-x)(x-2)
Answers
The length, width, and height of the box in factored form is -x (x-5)(x +2) which is option A
The box is in the shape of a cuboid
The volume of a cuboid = l b h, where l is the length, b is the breath or width and h is the height
Putting the values of width and volume in the formula
x³ - 3x²-10x = l ×(5-x) × h
This becomes a cubic equation
l × h = (x³-3x²-10x)/ 5-x
l × h = -x²-2x
l × h = -x(x+2)
Now, putting the value of l × h in the equation we get
v= -x ( x+ 2) (5-x)
v = -x (x-5)(x +2)
Hence, the length, width, and height of the box in factored form is -x (x-5)(x +2) which is option A
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A thief entered an orange garden guarded by 3 guards and stole some oranges. The first guard caught him. To get rid of him, the thief gave him half of the stolen oranges and two more. Then the second guard came upon him; to escape he gave him half of the oranges he had with him plus two more oranges. Near the exit he came across the third guard; and he gave him half of the oranges and two more oranges. Once escaped, he saw that he had only one more orange. How many oranges had the thief stolen
Answers
When the thief gave half of the oranges and two more to the first guard, he was left with (X/2 - 2) oranges.
When the thief gave half of his remaining oranges and two more to the second guard, he was left with ((X/2 - 2)/2 - 2) oranges.
When the thief gave half of his remaining oranges and two more to the third guard, he was left with (((X/2 - 2)/2 - 2)/2 - 2) oranges.
We are also given that the thief had only one orange left after giving oranges to the third guard. Therefore:
(((X/2 - 2)/2 - 2)/2 - 2) = 1
Simplifying this equation, we get:
(X/8) - 1 = 1
(X/8) = 2
X = 16
Therefore, the thief had stolen 16 oranges from the garden.
Officer Brimberry wrote 16 tickets for traffic violations last week, but only 10 tickets this week. What is the percent decrease? Give your answer to the nearest tenth of a percent.
Answers
Answer:
you would take 10 and divide that by 16 to get .63, so you take .63 and minus that from 100 and you get 37. so the officer had a 37% decrease.
Step-by-step explanation:
Is 9,40,41 a right triangle
Answers
Using pythagoras theorem, the values given in the question 9, 40 and 41 represents a right angle triangle
Pythagoras TheoremThis theorem states that in a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides. The sides of this triangle are named the perpendicular, base and hypotenuse. In this case, the hypotenuse is always longest side, as it is opposite to the angle 90°
Mathematically Pythagoras theorem is given as;
x² = y² + z²
x = hypothenusey = legz = legLet's substitute the values into the formula and check if the values are a right angle triangle.
41² = 40² + 9²
1681 = 1600 + 81
1681 = 1681
The values 9, 40, 41 represents a right angle triangle
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if a restaurateur wants to know how many dollars the restaurant makes per day, which process metric is needed?
Answers
To determine how many dollars a restaurant makes per day, the restaurateur would need to measure the "revenue" metric.
Revenue is the total amount of money a business earns from its sales or services provided over a specific period of time, in this case, daily. It includes all income generated by the restaurant from selling food and drinks to customers.
Measuring revenue is essential for any business as it helps the owner understand the financial health of their enterprise. By tracking revenue over time, the restaurateur can identify patterns and trends and make informed decisions to increase profits and improve the business's overall performance.
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Add or subtract the following polynomials.
1. 7x-(4xy+12xy)-2
2. (5bc)-(5+bc)
3. 7+(2x-5x)+y
4. 6x+10+[3x-6x]
5. 3x²y-(5x²y)
With solutions pls
Answers
Answer 1:
7x-16xy-2
Answer 2:
4bc-5
Answer 3:
7-3x+y
Answer 4:
3x+10
Answer 5:
-2x²y
Solving Solutions Question #1
*Remove the parentheses for addition or subtraction*
\(7x-\left(4xy+12xy\right)-2\)
*Determine the sign*
\(7x-4xy-12xy-2\)
*Reorder and gather like terms*
\(7x+\left(-4xy-12xy\right)-2\)
*Collect coefficients of like terms*
\(7x+\left(-4-12\right)\timesxy-2\)
*Calculate the sum or difference*
\(7x-16xy-2\)
Solving Solutions Question #2*Simplify or expand*
\(5bc-\left(5+bc\right)\)
*Remove the parentheses for addition or subtraction*
\(5bc-5-bc\)
*Reorder and gather like terms*
\(\left(5bc-bc\right)-5\)
*Collect coefficients of like terms*
\(\left(5-1\right)\) \(\times\) \(bc-5\)
*Collect the sum or difference*
\(4bc-5\)
Solving Solution Question #3*Simplify or expand*
\(7+(2x-5x)+y\)
*Determine the sign*
\(7+2x-5x+y\)
*Reorder and gather like terms*
\(7+\left(2x-5x\right)+y\)
*Collect coefficients of like terms*
\(7+\left(2-5\right)\timesx\) \(\times\) \(x+y\)
*Calculate the sum or difference*
\(7-3x+y\)
Solving Solution Question #4*Simplify or expand*
\(6x+10+(3x-6x)\)
*Determine the sign*
\(6x+10+3x-6x\)
*Reorder and gather like terms*
\((6x+3x-6x)+10\)
*Collect coefficients of like terms*
\((6+3-6)\) × \(x+10\)
*Apply the Inverse Property of Addition*
\(3x+10\)
Solving Solution #5*Simplify or expand*
\(3x^{2} y-5x^{2} y\)
*Collect coefficients of like terms*
\((3-5)x^{2} y\)
*Calculate the sum or difference*
\(-2x^{2} y\)
I hope this helps you:)
Determine the greatest common divisor of the elements of the set \[ s = \{ n^{13} - n \mid n \in \mathbb{z} \}. \]
Answers
Answer:
2730
Step-by-step explanation:
We want to determine the greatest common divisor of the elements of the set \(S = \{ n^{13} - n \mid n \in \mathbb{Z} \}.\)
We apply the Fermat's little theorem which states that if p is a prime number, then for any integer a, the number aᵖ − a is an integer multiple of p.
Now, \(n^{13} \equiv n \mod p \) if p-1 divides 12.
Since the of 12 are 1,2,3,4, 6, 12, the corresponding primes are 2, 3, 5, 7, 13.
Therefore, the gcd of the elements in \(2^{13}-2\) and \(3^{13}-3$ is 2 \cdot 3 \cdot 5 \cdot 7 \cdot 13.\)
2*3*5*7*13=2730
Therefore, the gcd of the elements in set S is 2730.
consider the degree-4 lfsr given by p(x) = x^4 +x^2+ 1. assume that the lfsr is initialized with the string (s3, s2, s1, s0) = 0110. find the period with the given seed and polynomial p(x)?
Answers
The period of the given degree-4 LFSR with the polynomial p(x) = x^4 + x^2 + 1 and the seed (s3, s2, s1, s0) = 0110 is 15.
A Linear Feedback Shift Register (LFSR) is a deterministic algorithm that generates a pseudo-random sequence of numbers based on a polynomial function and an initial seed. The period of an LFSR is the length of the generated sequence before it repeats itself. In this case, the polynomial is p(x) = x^4 + x^2 + 1, and the seed is (s3, s2, s1, s0) = 0110. To find the period, we iterate through the LFSR sequence and count the steps until the seed is repeated. In this specific case, after iterating 15 times, the seed (0110) is repeated.
Thus, given the degree-4 LFSR with polynomial p(x) = x^4 + x^2 + 1 and seed (s3, s2, s1, s0) = 0110, the period of the generated sequence is 15.
To know more about Linear Feedback Shift Register, click here
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1,530÷34 how to do it
Answers
Answer:It is 45
Step-by-step explanation:Take 1,530 and divid it by 34 using a calculator.