The table shows the numbers of pictures you upload to a social media website for 5 days in a row. How many total pictures do you upload during the week when 32% of the total pictures are uploaded on Saturday and Sunday?

Day Pictures Uploaded
Monday 2
Tuesday 2
Wednesday 4
Thursday 1
Friday 8

1) The property P that we need to prove by induction is as P(p) = length p = length (rem R p) + numR p. 2) For the base case, we need to prove P([]) = length [] = length (rem R []) + numR []. 3) Inductive hypothesis is P(p) = length p = length (rem R p) + numR p. 4) For the step case, we need to prove P(p) → P(L:p) : length (L:p) = length (rem R (L:p)) + numR (L:p).

1) The property P that we need to prove by induction is as follows:

For all lists of directions p, the property P(p) is defined as:

P(p) = length p = length (rem R p) + numR p

If we can prove this property P by induction, it implies the goal of the exercise, which is to show that length p = length (rem R p) + numR p.

2) Base case goal:

For the base case, we need to prove the following goal:

For an empty list of directions p = [], the property P(p) holds:

P([]) = length [] = length (rem R []) + numR []

Proof:

P([]) simplifies to:

length [] = length (rem R []) + numR []

Using the definition of the length function and rem function, we have:

0 = length [] + numR []

Since the length of an empty list is 0, and there are no occurrences of R in an empty list, numR [] is also 0. Therefore, the base case goal holds.

3) Inductive hypothesis:

Assuming that the property P holds for a list p, we assume the following inductive hypothesis:

P(p) = length p = length (rem R p) + numR p

4) Step case goal:

For the step case, we need to prove the following goal:

Assuming P(p), we need to show that P(L:p) holds:

P(p) → P(L:p) : length (L:p) = length (rem R (L:p)) + numR (L:p)

Proof:

Using the definition of the length function and rem function, we have:

length (L:p) = length (L:(rem R p)) + numR (L:p)

Expanding the length and rem functions, we get:

1 + length p = 1 + length (rem R p) + numR (L:p)

Since L is not equal to R, numR (L:p) remains unchanged:

1 + length p = 1 + length (rem R p) + numR p

By canceling out the common terms on both sides, we get:

length p = length (rem R p) + numR p

This matches the property P(p), so the step case goal holds.

By proving the base case and the step case, we have proven the property P(p) by induction, which implies that length p = length (rem R p) + numR p for all lists of directions p.

Correct Question :

length []=0

length (x:xs)=1+ length xs

​−L1

−L2

Consider the following data types and functions: data Direction =L∣R numR : [Direction] -> Int

numR []=0

numR (L:p)= numR p

numR (R:p)=1+ numR p

Answer the following questions:

1. What precisely should we prove by induction? Specifically, state a property P, including possible quantifiers, so that proving this property by induction implies the (above) goal of this exercise.

2. State (including possible quantifiers) and prove the base case goal.

3. State (including possible quantifiers) the inc्acuctive hypothesis of the proof.

4. State (including possible quantifiers) and prove the step case goal.

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Answer:

8 hours

Step-by-step explanation:

basic equation

Q (flow rate) = V (volume)/ t (time)

so to find the time we just rearrange the equation and become

t = V/Q

V of cylinder

V = πr²T

and r (radius) = ½ diameter

V = 3.14 x 5² x 1.4

V = 109.9 m³

if the Q is 13 m³/hour then

t = 109.9/13 = 8.453 hours

round to nearest hour = 8 hours

Answer:

9

Step-by-step explanation:

Just count the many units to get to each point.

Answer:

Step-by-step explanation:

The answer is 3 to the 3/4 power.

To find the value of x, we calculate the average of the sample observations. Summing up the observations and dividing by the total number of observations, we get:

x = (125 + 122 + 126 + 100 + 155 + 132 + 121 + 118 + 114 + 125 + 142 + 2 + 130 + 110 + 140 + 129 + 3) / 17 = 114.118 seconds (rounded to three decimal places).b) To find the value of R, we calculate the range of each sample by subtracting the minimum observation from the maximum observation. Then we find the average range across all samples:R = (155 - 100 + 142 - 2 + 140 - 110 + 132 - 114 + 142 - 3) / 5 = 109.2 seconds (rounded to three decimal places).

c) The Upper Control Limit (UCL) and Lower Control Limit (LCL) using 3-sigma can be calculated by adding and subtracting three times the standard deviation from the average:UCL = x + (3 * R / d2) = 114.118 + (3 * 109.2 / 1.693) = 348.351 seconds (rounded to three decimal places).LCL = x - (3 * R / d2) = 114.118 - (3 * 109.2 / 1.693) = -120.115 seconds (rounded to three decimal places).

d) The Upper Control Limit Range (UCLR) and Lower Control Limit Range (LCLR) using 3-sigma can be calculated by multiplying the average range by the appropriate factor:UCLR = R * D4 = 109.2 * 2.115 = 231.108 seconds (rounded to three decimal places).LCLR = R * D3 = 109.2 * 0 = 0 seconds.

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Answer:

x = 2af/cg.

Step-by-step explanation:

cx/2 = a f/g

Multiply through by 2g:

cgx = 2af

Divide both sides by cg:

x = 2af/cg.

The solution of the given equation for x is 2af/cg.

The given equation is cx/2 = a f/g.

We need to solve the given equation for x.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Now, cx/2 = a f/g

By multiplying 2g on both the side of the equation, we get

cgx = 2af

Divide both sides of the equation by cg.

That is, x = 2af/cg

Therefore, the solution of the given equation for x is 2af/cg.

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Answer: \(\frac{1}{3} \sin x^{3}+C\)

Step-by-step explanation:

Let \(u=x^3\). Then, \(3x^2 dx = du \longrightarrow x^2 dx =\frac{1}{3}du\)

So, we can rewrite the original integral as

\(\frac{1}{3} \int \cos u \text{ } du=\frac{1}{3} \sin u+C=\frac{1}{3} \sin x^{3}+C\)

The yield to maturity on a simple loan for $1,500 that requires a repayment of $7,500 in five years' time is 37.14%.

Yield to maturity (YTM) is the total return anticipated on a bond or other fixed-interest security if the security is held until it matures. Yield to maturity is considered a long-term bond yield, but is expressed as an annual rate. In this problem, the present value (PV) of the simple loan is $1,500, the future value (FV) is $7,500, the time to maturity is five years, and the interest rate is the yield to maturity (YTM).

Now we will calculate the yield to maturity (YTM) using the formula for the future value of a lump sum:

FV = PV(1 + YTM)n,

where,

FV is the future value,

PV is the present value,

YTM is the yield to maturity, and

n is the number of periods.

Plugging in the given values, we get:

$7,500 = $1,500(1 + YTM)5

Simplifying this equation, we get:

5 = (1 + YTM)5/1,500

Multiplying both sides by 1,500 and taking the fifth root, we get:

1 + YTM = (5/1,500)1/5

Adding -1 to both sides, we get:

YTM = (5/1,500)1/5 - 1

Calculating this value, we get:

YTM = 0.3714 or 37.14%

Therefore, the yield to maturity on a simple loan for $1,500 that requires a repayment of $7,500 in five years' time is 37.14%.

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Answer:

what's the question?

Step-by-step explanation:

Let t represent the time that the second car has been on the road. If it started 2 hours after the first car started, it means that the time that the first car has been on the road is

(t + 2) hours

Recall,

Distance = speed x time

From the information given,

speed of first car = 55

Thus,

distance travelled by first car = 55(t + 2)

speed of second car = 65

Distance travelled by second = 65t

Thus,

The first car has traveled 55(t + 2) miles and the second car has traveled 65t miles

An engineer is designing a fuel tank in the shape of a cylinder, the approximate radius of the cylinder is 8.2 inches.

Volume:

V = πr²h

Height:

h = 2r

V = πr²h

V= πr²(2r)

V= 2πr³

And we know that the volume must be 3,500 in³, now we can replace that and solve for R, we will get:

V= πr²h

3500 = 3.14 x 2 x (r)³

r = 8.2 inch

The cylinder's approximate radius must be 8.2 inches.

One of the most fundamental curvilinear geometric shapes, a cylinder has historically been a three-dimensional solid. It is regarded as a prism with a circle as its base in basic geometry. In several contemporary fields of geometry and topology, a cylinder can alternatively be characterised as an infinitely curved surface.

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Answer:

I believe the answer is y=x+-13

Step-by-step explanation:

The only easy way to do fractions is by expressing the numbers to be divided as a numerator and denominator and dividing them.

The best way to resolve fractions will be by expressing them as numerators and denominators and then finding the solutiion. Let us say that we are told to divide 10 by 2. The first thing to do is to express them as numerators and denominators like this:

10/2 = 5.

You can also imagine that 2 people are told to share 10 things and then count how many each person will get. The answer is 5.

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Answer:

  b > 1

Step-by-step explanation:

You want to know the conditions on an exponential function that represents growth.

The value of 'b' in the exponential function y = a·b^x is called the "growth factor." Each time x increases by 1 unit, the value of y is multiplied by 'b'. If that product is increasing, the value of 'b' must be greater than 1.

The relation represents growth when b > 1.

An exponential function in the form \(y = ab^x\) represents growth when the base (b) is greater than 1.

In an exponential function of the form y = ab^x, the base (b) is a crucial component. The behavior of the function depends on the value of the base.

When the base (b) is greater than 1, it means that b is a positive number larger than 1. In this scenario, as the value of x increases, the value of \(b^x\) also increases exponentially. This results in the function \(y = ab^x\) exhibiting growth.

To better understand this growth behavior, let's consider an example. Suppose we have an exponential function \(y = 2^x\). As x increases from 0, the values of \(2^x\) will be as follows:

For x = 0, \(2^0\) = 1

For x = 1, \(2^1\) = 2

For x = 2, \(2^2\) = 4

For x = 3, \(2^3\) = 8

For x = 4, \(2^4\) = 16

As you can see, as x increases, the values of \(2^x\) grow exponentially. This demonstrates the growth behavior of exponential functions when the base is greater than 1.

It's important to note that when the base (b) is between 0 and 1 (exclusive), the exponential function will exhibit decay or decreasing behavior rather than growth.

In summary, an exponential function of the form \(y = ab^x\) represents growth when the base (b) is greater than 1. As x increases, the function values increase exponentially, indicating a growth pattern.

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Answer:

6 miles per minute.

Step-by-step explanation:

All you need to do is, divided 720 into 120, and you will get your answer. :)

a) The absolute risk of dying today is 1/10,000, which is given in the question.

b) The absolute risk of dying today if you ride a bike is 1/5,000.

c) The absolute risk of dying today if you wear a safety belt and drive defensively is 1/20,000.

Given: The risk of dying today is 1/10,000, the risk of being hit and killed today if you ride a bicycle is 1/5,000, and the risk of dying today if you wear a safety belt and drive defensively is 1/20,000.Absolute risk is defined as the probability or chance of an event taking place.

It indicates the number of people who are expected to experience the event over a given period, typically a year. This is in contrast to the relative risk, which compares the chance of an event happening in one group with the likelihood of it occurring in another group.

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Answer:

3

Step-by-step explanation:

60 × 8 = 480 (mins)

96 (trucks) = 480 (mins)

÷32 (I got this number by dividing 480 by the desired amount of mins which was 15)

3 = 15

So 3 trucks would have been loaded in 15 mins

The system of linear equations are;

a + b = 5.30

a + b = 7

Expressing the information as a system of linear equations:

Consider that apples = a, oranges = b

If $5.30 is charged for one apple and one orange, then we get the equation as

a + b = 5.30 - - - (1)

If $14 is charged for 2 apples and 2 oranges,  then we get the equation as ;

2a + 2b = 14 - - - - (2)

a + b = 7

Since both equations give varying combined cost for an equal amount of fruit, so a unique cost cannot be obtained for each fruit from the systems of equation using a simultaneous equation process.

From (1)

a = 5.30 - b

Put a, b in (2)

2(5.30 - b) + 2b = 14

10.6 - 2b + 2b = 14

10.6 = 14

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The running time is O(n log(n)) since we sort two vector.

We solve the problem with the following algorithms:  

1. Order A is in the increasing order.

2. Order B is in the decreasing order.

3. Return (A,B).

We must demonstrate that this is the best answer. without sacrificing generality, we can assume that a₁ ≤ a₂ ......≤ aₙ in the optimal solution.

Since the payoff is \(\prod_{i}^{n}=1^{a_{i}^{bi}}\), the payoff will always increase if we make a change so that \(b_{i+1} > b_{i}\).

Therefore the optimal solution will be found if B is sorted.

Thus, the running time is O(n log(n)) since we sort two vector.

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To determine which point could be on the line that is perpendicular to Line MN and passes through point K, we need to analyze the slopes of the two lines.

First, let's find the slope of Line MN using the given points (2, 3) and (-3, 2):

Slope of Line MN = (2 - 3) / (-3 - 2) = -1 / -5 = 1/5

Since the lines are perpendicular, the slope of the perpendicular line will be the negative reciprocal of the slope of Line MN. Therefore, the slope of the perpendicular line is -5/1 = -5.

Now let's check the given points to see which one satisfies the condition of having a slope of -5 when passing through point K (3, -3):

For point (0, -12):

Slope = (-12 - (-3)) / (0 - 3) = -9 / -3 = 3 ≠ -5

For point (2, 2):

Slope = (2 - (-3)) / (2 - 3) = 5 / -1 = -5 (Matches the slope of the perpendicular line)

For point (4, 8):

Slope = (8 - (-3)) / (4 - 3) = 11 / 1 = 11 ≠ -5

For point (5, 13):

Slope = (13 - (-3)) / (5 - 3) = 16 / 2 = 8 ≠ -5

Therefore, the point (2, 2) could be on the line that is perpendicular to Line MN and passes through point K.

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Hello!

surface area

= 2(6*2) + 2(4*2) + 4*6

= 2*12 + 2*8 + 24

= 24 + 16 + 24

= 64 square inches

Two length of the same frequency and amplitude moving in opposite directions combine to form a standing wave, which appears to be stationary. Given that the pool in this instance is 24 m long and has six loops, the wavelength is 4 m.

Wavelength = Length of Pool / Number of Loops

24 m / 6 loops

= 4 m

Wavelength

= 4 m

Two waves of the same frequency and amplitude moving in opposite directions combine to form a standing wave, which appears to be stationary. A stationary wave pattern is produced when the two waves collide and interfere with one another. Six loops make up the 24 m-long pool in this instance. As a result, the standing wave's wavelength is equal to the pool's length divided by the number of loops, or 24 m / 6 = 4 m. This indicates that the standing wave's wavelength is 4 metres. Standing waves can be used to determine a wave's speed because they are equal to wavelength times frequency. Understanding how waves behave in various contexts, such as swimming pools, oceans, or other bodies of water, can be helped by this.

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Answer:

a translation 5 units to the left

Step-by-step explanation:

                                                 Answer

                                       Part 1: B. 5 units left

                                     Part 2: C. 7 units down

                                             Hope it helps!

                                     Have an amazing day!!

                                                     ^ω^

-- FTS

The values of dy/dt for the given values of x are:

(a) dy/dt = -32 cm/sec

(b) dy/dt = 0 cm/sec

(c) dy/dt = 32 cm/sec

To find dy/dt for the given function y = 4x^2 + 9, we need to take the derivative of y with respect to x, and then multiply it by dx/dt.

First, let's find the derivative of y with respect to x:

dy/dx = d/dx (4x^2 + 9)

= 8x

Now, we can calculate dy/dt by multiplying dy/dx by dx/dt:

dy/dt = (dy/dx) * (dx/dt)

= (8x) * (dx/dt)

Now we can substitute the given values of x and dx/dt to find the values of dy/dt:

(a) x = -1, dx/dt = 4 cm/sec:

dy/dt = (8 * (-1)) * 4

= -32 cm/sec

(b) x = 0, dx/dt = 4 cm/sec:

dy/dt = (8 * 0) * 4

= 0 cm/sec

(c) x = 1, dx/dt = 4 cm/sec:

dy/dt = (8 * 1) * 4

= 32 cm/sec

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Answer:

sm like this hope this helps your welcome

Answer:

Step-by-step explanation:

Adding two rational numbers results in a positive sum.

Answer:

C

Step-by-step explanation:

BRAINLIEST PLEASE

Answer:  \(\bold{\dfrac{1}{6}=16.67\%}\)

Step-by-step explanation:

       First pick    and      Second pick

   \(\dfrac{4\ blue}{9\ total\ marbles}\times\dfrac{3\ green}{8\ remaining\ marbles}\quad =\dfrac{12}{72}\quad =\large\boxed{\dfrac{1}{6}}\)