A shop is having a 40% sale. A jumper originally costs £50. How much will it be in sale?

Answer:

f'(x) = -6x^2

f'(-5) = -150

f'(0) = 0

f'(√17) = -102

The simplification of the given expression

[tex]y = ( \sqrt{47 + \sqrt{9 - \sqrt{25)} } } [/tex]

is y = 7

[tex]y = ( \sqrt{47 + \sqrt{9 - \sqrt{25)} } } [/tex]

find the square root of 25

[tex]y =( \sqrt{47 + \sqrt{9 - 5} } [/tex]

simplify root 9 - 5

[tex]y = ( \sqrt{47 + \sqrt{4} } [/tex]

find the square root of 4

[tex]y = ( \sqrt{47 + 2)} [/tex]

Add root 47 and 2

[tex]y = ( \sqrt{49} )[/tex]

Find the square root of 49

y = 7

Therefore, the solution to the given expression is y = 7

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Answer:

Math Quotient Verification

G For each ordered pair, determine whether it is a solution to the system of equations. 9x+2y=-5 2x-3y=-8 (x, y) (1, -7) (0, -4) (5,6) (-1,2) Is it a solution? Yes No X 5

To check if an ordered pair is a solution to a system of equations, we substitute the values of x and y into both equations and see if both equations are satisfied.

Let's check each ordered pair one by one:

(1, -7):

9x + 2y = -5 becomes 9(1) + 2(-7) = -5, which is false.

2x - 3y = -8 becomes 2(1) - 3(-7) = -8, which is true.

Therefore, (1, -7) is not a solution to the system of equations.

(0, -4):

9x + 2y = -5 becomes 9(0) + 2(-4) = -8, which is false.

2x - 3y = -8 becomes 2(0) - 3(-4) = 12, which is false.

Therefore, (0, -4) is not a solution to the system of equations.

(5, 6):

9x + 2y = -5 becomes 9(5) + 2(6) = 41, which is false.

2x - 3y = -8 becomes 2(5) - 3(6) = -8, which is true.

Therefore, (5, 6) is not a solution to the system of equations.

(-1, 2):

9x + 2y = -5 becomes 9(-1) + 2(2) = -11, which is false.

2x - 3y = -8 becomes 2(-1) - 3(2) = -8, which is true.

Therefore, (-1, 2) is not a solution to the system of equations.

Therefore, the answer is "No" for all the ordered pairs given in the problem.

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The value of b is 73° as opposite angles of congruent sides are equal in an isosceles triangle.

An angle is created by cοmbining twο rays (half-lines) that have a cοmmοn terminal. The angle's vertex is the latter, while the rays are alternately referred tο as the angle's legs and its arms.

An angle within a shape that has the shape's base as οne οf its sides is knοwn as the base angle οf a shape in geοmetry. Cοnsider the triangle in the image as an example. We can οbserve that the triangle's base side is made up οf an angle B side and an angle C side. As a result, the triangle's base angles are angles B and C.

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Answer:

I don't knowI am sorry I will let someone else answer

Step-by-step explanation:

The coordinates of A' and B' after a dilation with a scale factor of 5 and a center point of dilation at the origin are A'(5, 10) and B'(-10, -5), respectively.

To find the coordinates of the points A' and B' after a dilation with a scale factor of 5 and a center point of dilation at the origin, we can use the following formula:

[tex]$$(x', y') = (5(x - 0), 5(y - 0)) = (5x, 5y)$$[/tex]

where (x, y) are the original coordinates of the point, and (x', y') are the new coordinates after the dilation.

For point A(1, 2), the new coordinates A' are:

[tex]$$(x_A', y_A') = (5(1), 5(2)) = (5, 10)$$[/tex]

Therefore, the coordinates of point A' are (5, 10).

For point B(-2, -1), the new coordinates B' are:

[tex]$$(x_B', y_B') = (5(-2), 5(-1)) = (-10, -5)$$[/tex]

Therefore, the coordinates of point B' are (-10, -5).

Therefore, the coordinates of A' and B' after a dilation with a scale factor of 5 and a center point of dilation at the origin are A'(5, 10) and B'(-10, -5), respectively.

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The properties of a probability distribution for a discrete random variable ensure that the probabilities assigned to each possible value of the variable are consistent with the axioms of probability and allow for meaningful inference and prediction.

The properties of a probability distribution for a discrete random variable are.

The probability of each possible value of the random variable must be non-negative.

The sum of the probabilities of all possible values must equal 1.

The probability of any event A is the sum of the probabilities of the values in the sample space that correspond to A.

These properties are satisfied because the probabilities of each possible value of a discrete random variable are defined in such a way that they are non-negative and sum to 1. Additionally, any event A can be expressed as a collection of possible values of the random variable, and the probability of A is then computed as the sum of the probabilities of those values.

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Answer:

To write an exponential decay function for this situation, we can use the formula:

P(t) = P₀e^(rt)

where:

P(t) = the population at time t

P₀ = the initial population

r = the annual rate of decrease (as a decimal)

t = time in years

We are given P₀ = 3,846 and r = -0.0027 (since the population is decreasing).

To approximate the population in 2022, we need to find t, the number of years from 1996 to 2022. That is:

t = 2022 - 1996 = 26 years

Now we can plug in the values we have:

P(t) = 3,846 e^(-0.0027t)

To find P(2022), we plug in t = 26:

P(26) = 3,846 e^(-0.0027(26))

≈ 3,200.62

Therefore, we can approximate the population of the city in 2022 to be about 3,201 people.

Answer:

3,101

Step-by-step explanation:

Please hit brainliest if this helped!

To write an exponential decay function for the population of the city, we can use the formula:

P(t) = P₀e^(-rt)

where P(t) is the population at time t, P₀ is the initial population, r is the decay rate, and e is the base of the natural logarithm.

In this problem, P₀ = 3,846 and r = 0.0027 (0.27% expressed as a decimal). We want to find the population in 2022, which is 26 years after 1996.To use the formula, we need to convert 26 years to the same time units as the decay rate. Since the decay rate is per year, we can use 26 years directly. Therefore, the exponential decay function for the population is:

P(t) = 3,846e^(-0.0027t)

To find the population in 2022 (t = 26), we substitute t = 26 into the function:

P(26) = 3,846e^(-0.0027*26) ≈ 3,101

Therefore, the population in 2022 is approximately 3,101.

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When space is spanned by the two functions of linear transformation from into itself with respect to the basis we need to apply T to each basis vector vi to get the column vectors T(vi) = [T(vi)]B.

where [T(vi)]B is the coordinate vector of T(vi) with respect to the basis B. Arrange the column vectors [T(v1)]B, [T(v2)]B, ..., [T(vn)]B into a matrix. This matrix is the matrix of T with respect to the basis B.

In this case, you have two functions that span a vector space, so you need to specify the basis B. Once you have chosen the basis, you can apply the above steps to find the matrix of the linear transformation.

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Answer:

g(y) = √(3/2 y)

Step-by-step explanation:

To find the inverse of a function, we need to solve for x in terms of y and interchange x and y. That is, we need to write the given function f(x) = 2/3x^2 in the form y = 2/3x^2 and then solve for x in terms of y.y = 2/3x^2

Multiplying both sides by 3/2, we get:

3/2 y = x^2

Taking the square root of both sides, we get:x = ± √(3/2 y)

Note that we have two possible values of x for each value of y, because the square root can be either positive or negative. However, for a function to have an inverse, it must pass the horizontal line test, which means that each value of y can only correspond to one value of x.Therefore, we need to restrict the domain of the original function to ensure that it is one-to-one. The simplest way to do this is to take the range of the function and use it as the domain of the inverse function.The range of f(x) = 2/3x^2 is all non-negative real numbers, or [0, ∞). Therefore, we can define the inverse function g(y) as:

g(y) = ± √(3/2 y)

where we choose the positive square root to ensure that the function is one-to-one.Thus, the inverse of the function f(x) = 2/3x^2 is:

g(y) = √(3/2 y)

with domain [0, ∞).

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The graph that shows the electricity usage on a record-breaking summer day is Sacramento, California is a function.

The domain is 24 hours of a day.

The number of megawatts used at 8 am is 1, 200 megawatts.

The time with the most electricity used was 4 pm to 6 pm and least used was 4 am.

f ( 12 ) would be 1, 900 megawatts.

Usage is increasing from 4 am to 5 pm and decreasing from 5 pm to 4 am.

The graph is a function because each point on the graph represents a distinct megawatt usage. The domain would be 24 hours of a day as this graph of electricity usage shows the usage per day.

The megawatts used at 8 am is:

= 1, 300 - ( 200 / 2 )

= 1, 200 megawatts

From 4 am to 5 pm, we see that electricity usage is increasing as people are getting ready for work and going to work, but from 5 pm to 4 am, electricity usage decreases.

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In linear equation, 65.625% of the pupils travel by bus.

What is  linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.

A) 1800 * 0.55 * 0.3 = 297 Girls.

B)  1800 * 0.45 * 0.7 = 567 boys

C)  Girl

      297/864 * 100%  = 34.375%

  boy -

       567 ÷ (297 + 567 ) * 100%  = 65.625%

         864 = 297 + 567

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Step-by-step explanation:

that height splits GK (32) into 2 parts :

8 and 32-8 = 24

then we use the geometric mean theorem for right-angled triangles

height = sqrt(p×q)

with p and q being the parts of the Hypotenuse.

so,

height = sqrt(8×24) = sqrt(192)

and now we can use Pythagoras

c² = a² + b²

with c being the Hypotenuse (the side opposite of the 90° angle), a and b are the legs,

to get HK.

HK² = height² + 24² = 192 + 576 = 768

HK = sqrt(768)

Answer: (f⋅g)(1) = 10.

Step-by-step explanation:

To find (f⋅g)(x), we need to multiply the two functions f(x) and g(x) together. This can be done by multiplying each term of f(x) by each term of g(x), and then combining like terms. We get:

(f⋅g)(x) = f(x) * g(x)

= (-7x+3) * (3x^2 - 4x - 1)

= -21x^3 + 28x^2 + x - 3x^2 + 4x + 1

= -21x^3 + 25x^2 + 5x + 1

To find (f⋅g)(1), we can substitute x=1 into the expression for (f⋅g)(x):

(f⋅g)(1) = -21(1)^3 + 25(1)^2 + 5(1) + 1

= -21 + 25 + 5 + 1

= 10

Therefore, (f⋅g)(1) = 10.

Answer:

If the time is 3:45 how many minutes is it slow or fast

In linear equation, 11.85 pounds is the weight of the wire.

What is  linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.

Total weight of pool having 16 wires     =13.6 pounds

Weight of the pool                                 =1.75

Therefore the weight of the wire alone = 13.6 - 1.75

                                                             =  11.85 pounds

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Answer:

Step-by-step explanation:

To solve this problem, we can use the formula for the Pythagorean theorem, which states that for any right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

In this case, we are given the length of two sides of the triangle (the legs) and we need to find the length of the hypotenuse.

Let's label the sides of the triangle:

The shorter leg is the vertical side opposite the angle marked 55 degrees, so let's call it "a".

The longer leg is the horizontal side adjacent to the angle marked 55 degrees, so let's call it "b".

The hypotenuse is the side opposite the right angle, so let's call it "c".

Using trigonometry, we can determine the value of "a" and "b":

a = b * tan(55°) (since tangent = opposite/adjacent, we solve for opposite which is "a" in this case)

a = 100 * tan(55°) = 100 * 1.428 = 142.8

b = 100

Now, we can use the Pythagorean theorem to find the length of the hypotenuse:

c^2 = a^2 + b^2

c^2 = 142.8^2 + 100^2

c^2 = 20484.84 + 10000

c^2 = 30484.84

c = sqrt(30484.84)

c ≈ 174.6

Therefore, the length of the hypotenuse is approximately 174.6 units (the units are not given in the problem, but we can assume they are consistent with the units used for the given values of "a" and "b").

The problem does not specify the orientation or scale of the graph, but we can assume that it is a right triangle with the angle marked 55 degrees in the upper left corner.

The vertical side (the shorter leg) of the triangle should be labeled with a length of approximately 142.8 units (assuming the units used for the problem are consistent with the values given for "a" and "b"). The horizontal side (the longer leg) should be labeled with a length of 100 units.

The hypotenuse (the side opposite the right angle) should be drawn as a diagonal line connecting the endpoints of the vertical and horizontal sides. The hypotenuse should be labeled with a length of approximately 174.6 units.

The angle marked 55 degrees should be labeled as such, and the other two angles of the triangle (the right angle and the angle opposite the longer leg) should be labeled accordingly.

Answer:

x = ±10

Step-by-step explanation:

1) Subtract 10 from both sides.

[tex]-0.1 \times x^2=-10[/tex]

2) Divide both sides by -0.1.

[tex]x^2=\frac{-10}{-0.1}[/tex]

3) Simplify [tex]\frac{-10}{-0.1}[/tex] to 100.

[tex]x^2=100[/tex]

4) Take the square root of both sides.

[tex]x=\pm \sqrt{100}[/tex]

5) Since 10 * 10 is 100, the square root of 100 is 10.

[tex]x=\pm10[/tex]

Answer:

Step-by-step explanation:

We'Re looking at a normal distribution here- let's start by drawing it out to the mean me- is 315 grams standard. Deviation is 16 point. We want to know the weight corresponding to each of these events and we can use either the appendix which i assume is a z, school table or excel so the first 1. We want the highest 20 percent up here somewhere. This is what we would call the 80 percent. It separates the bottom 80 percent from the highest 20 percent. So how do we work the well? We need to start by getting the z score for it. So how do we get that, while in excel you're going to use the norm inverse function which looks like this? So it's calls norm and then in here you just put in x, where x is your percentage and that will spit out the z score and i'm using this rather than a table, because it will give me a more exact value. So we're going to do that, and so here the percent is the 80, so it's not .8 and that spits out the z score of nort .8416 to 4 decimal places. But i'm always going to this exact score, because we now have to turn it from a z score to a piece of real data. Z score is a measure of how many standard deviations away from the mean a value is so we're. Looking for the value not .84 standard deviations, above the mean or if we write it like this x, is equal to z, sigma plus mu. So here we take our exact zedscore, because we can still just use excels, multiply it by 16 and add it on to the mean and we'll get our value of 328.447328 .47 grams to 2 decimal places for part b. We want to be middle 60 percent. Now we need to cut off points and within here where, in this interval we have 60 percent of values, which means we have 40 percent of values, not in here. So we can label our 3 sections. These 2 add up to 40 percent, so they have to be 20 percent. Each are called nor .2 and not .2, and then this middle bit here is nor .6 for the total of 100 percent point. So we need these cut off points when you, the z, scores first, and because these are equal distances away from a mine they're going to have the same z score. Just 1 is going to be positive or negative, so z is going to be equal to plus and minus. Let'S look at the lower 1. This is the 20 percent here so into this excel command. We put 20 percent nor .2 and out of it we get the z score of minus, not .8416. So it's actually very similar to the top question, because the top question asked you for the 80 percent be 80 percent. Is the upper cut off point here? 20? Is below cutoff point, so we already have the up 1, let's just calculate below 1, so we've got to be minus, nor .8416 multiplied by 16, but the standard deviation and on to the mean- and we get 301.53 and the upper cut off point is from part A so that's the middle 60 percent makes more space a part c. We want to be highest 80 percent. So now what we want is the cut off between the lowest 20 and the highest 80, which we've just got from part c part b. It'S this lower 1, here, 301.53 grams. That'S an easy! 1! Now we want the lowest 15 percent, so the lowest 15 percent is the 15 percent. So we go to our exylgamant put in the 15 for percent, so that would be no .15 and it's a z score of minus 1.036 keeping the exact value put into this formula. We multiply our z by 16, as on 315, to get 298.42 grams.

The weight that corresponds to this event are approximately 344.03 grams and 375.97 grams.

To find the weight that corresponds to each event, we need to use the standard normal distribution, which has a mean of 0 and a standard deviation of 1. We can convert the given mean and standard deviation to z-scores using the formula:

z = (x - μ) / σ

where x is the weight we want to find, μ is the mean (360 grams), and σ is the standard deviation (9 grams).

Then, we can use a standard normal distribution table or calculator to find the probability of each event, and convert it back to a weight using the inverse of the z-score formula:

x = μ + z * σ

where z is the z-score that corresponds to the desired probability.

Event 1: The weight is less than 345 grams.

z = (345 - 360) / 9 = -1.67

Using a standard normal distribution table or calculator, we find that the probability of a z-score less than -1.67 is approximately 0.0475.

x = 360 + (-1.67) * 9 = 344.03 grams

Therefore, the weight that corresponds to this event is approximately 344.03 grams.

Event 2: The weight is between 355 and 365 grams.

First, we need to find the z-scores that correspond to the two boundaries:

z1 = (355 - 360) / 9 = -0.56

z2 = (365 - 360) / 9 = 0.56

Using a standard normal distribution table or calculator, we find that the probability of a z-score less than -0.56 is approximately 0.2123, and the probability of a z-score less than 0.56 is approximately 0.7123. Therefore, the probability of a z-score between -0.56 and 0.56 is:

0.7123 - 0.2123 = 0.5

x1 = 360 + (-0.56) * 9 = 355.16 grams

x2 = 360 + (0.56) * 9 = 364.84 grams

Therefore, the weight that corresponds to this event is any weight between 355.16 and 364.84 grams.

Event 3: The weight is greater than 375 grams.

z = (375 - 360) / 9 = 1.67

Using a standard normal distribution table or calculator, we find that the probability of a z-score greater than 1.67 is approximately 0.0475.

x = 360 + (1.67) * 9 = 375.97 grams

Therefore, the weight that corresponds to this event is approximately 375.97 grams.

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Accοrding tο the data, the answers tο Questiοns 1 and 2 are: Harris shοuld anticipate spinning a sum οr less 10 apprοximately 367 times and a tοtal that is 10 οr larger apprοximately 133 times.

Yοur example is an equatiοn since an equatiοn that's any statement with an equal's sign. The usage οf equatiοns in mathematical expressiοns is widespread because mathematicians adοre equal signs. An equatiοn is a cοllectiοn οf guidelines fοr prοducing a specific οutcοme.

Part A: Tο calculate the likelihοοd that Harris will spinning a sum οr less 10, multiply the οverall number οf spins by the chance οf οbtaining a sum οr less 10. The οutcοmes οf the first spinner's spin are 1, 2, and 3, while the results οf the secοnd spinner's spin are 4, 5, 6, 7, and 8. Hence, the amοunts οr less 10 are:

1 + 4 = 5

1 + 5 = 6

1 + 6 = 7

1 + 7 = 8

1 + 8 = 9

2 + 4 = 6

2 + 5 = 7

2 + 6 = 8

2 + 7 = 9

3 + 4 = 7

3 + 5 = 8

3 + 6 = 9

There are 11 amοunts that cοuld be less than ten. The number οf successful results divided by the entire number οf pοssibilities, which is 11/15, represents the likelihοοd οf receiving a payοut οf less than 10 in a single spin. Harris will therefοre spin a tοtal less than 10 times, and the equatiοn tο estimate this is:

11/15 = x/500

After finding x, we οbtain:

x = (11/15) x 500

x = 366.67, which rοunds up tο 367

Sο, Harris shοuld expect tο spin a sum less than 10 abοut 367 times.

Part B: Tο determine hοw frequently Harris shοuld anticipate spinning a sum οf ten οr mοre, we can deduct the times that he shοuld anticipate spinning a sum lοwer than ten frοm the οverall number οf spins:

500 - 367 = 133

Therefοre, Harris shοuld expect tο spin a sum that is 10 οr greater abοut 133 times.

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Answer:

Step-by-step explanation:

[tex]y=2x-4[/tex]    (slope-intercept form is [tex]y=mx+b[/tex] where m=gradient

                     and b is where line intercepts y-axis)

The homotopy classes of paths from x to x in a space X refer to a set of equivalence classes of continuous paths that start and end at the same point, x, in the space X, where equivalence is defined in terms of homotopy.

In other words, for any two paths, there exists a continuous transformation (called a homotopy) between them such that the endpoints remain fixed. Two paths are said to be homotopic if they can be continuously deformed into each other while keeping their endpoints fixed. The set of all paths that are homotopic to each other forms an equivalence class.

The homotopy classes of paths from x to x are important in algebraic topology, as they provide a way to study the topological structure of a space by analyzing the properties of the paths within it. They can also be used to define higher algebraic structures such as the fundamental group and higher homotopy groups.

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Answer:

We need to find dz/dt given:

z = cos(x + 8y), x = 7t^5, y = 5/t

Using the chain rule, we can find dz/dt by taking the derivative of z with respect to x and y, and then multiplying by the derivatives of x and y with respect to t:

dz/dt = dz/dx * dx/dt + dz/dy * dy/dt

First, let's find dz/dx and dz/dy:

dz/dx = -sin(x + 8y)

dz/dy = -8sin(x + 8y)

Now, let's find dx/dt and dy/dt:

dx/dt = 35t^4

dy/dt = -5/t^2

Substituting these values, we get:

dz/dt = (-sin(x + 8y)) * (35t^4) + (-8sin(x + 8y)) * (-5/t^2)

Simplifying this expression, we get:

dz/dt = -35t^4sin(x + 8y) + 40sin(x + 8y)/t^2

Substituting x and y, we get:

dz/dt = -35t^4sin(7t^5 + 40/t) + 40sin(7t^5 + 40/t)/t^2

Therefore, dz/dt is given by -35t^4sin(7t^5 + 40/t) + 40sin(7t^5 + 40/t)/t^2.

The shear force and bending moment diagrams for the given beam will have multiple segments of different shapes and slopes, reflecting the variation of loads along the length of the beam.

To construct the shear and bending diagrams for the given beam, we need to analyze the beam for the different sections where the load is applied. We can break down the beam into five sections:

Leftmost section (0 ≤ x ≤ L/4)

Second section (L/4 < x ≤ L/2)

Third section (L/2 < x ≤ 5L/12)

Fourth section (5L/12 < x ≤ 7L/12)

Rightmost section (7L/12 < x ≤ L)

We can use the equations for shear and bending moments to create the plots:

For section 1: 0 ≤ x ≤ L/4

The shear force diagram will be constant since there is no load applied in this section. The bending moment diagram will be a sloping line, which will be zero at x = 0 and will increase linearly with x as we move toward the right end of the section.

For section 2: L/4 < x ≤ L/2

The shear force diagram will start from the value of P at x = L/4 and remain constant up to x = L/2. The bending moment diagram will be a parabolic curve, which will be zero at x = L/4 and L/2 and will reach a maximum value at the midpoint of the section.

For section 3: L/2 < x ≤ 5L/12

The shear force diagram will start from the value of P at x = L/4 and remain constant up to x = L/2. At x = 5L/12, a load of P/3 is added, causing the shear force to increase suddenly. The bending moment diagram will be a cubic curve, which will be zero at x = L/4 and L/2, and will have a local minimum at x = 5L/12.

For section 4: 5L/12 < x ≤ 7L/12

The shear force diagram will start from the value of P + P/3 at x = 5L/12 and remain constant up to x = 7L/12. The bending moment diagram will be a cubic curve, which will be zero at x = L/4 and L/2, and will have a local maximum at x = 7L/12.

For section 5: 7L/12 < x ≤ L

The shear force diagram will start from the value of P + P/3 at x = 5L/12 and remain constant up to x = 7L/12. At x = L/3, a load of P/3 is added, causing the shear force to decrease suddenly. The bending moment diagram will be a parabolic curve, which will be zero at x = L/4 and L/2 and will reach a minimum value at the midpoint of the section.

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If △ABC is congruent to △DEF, then it must also be a right triangle. Thus, the two triangles have congruent sides and are congruent.

A key idea in geometry known as the Pythagorean theorem explains the relationship between the sides of a right triangle. The square of the hypotenuse, or side opposite the right angle, is said to be equal to the sum of the squares of the other two sides. It can be expressed mathematically as: a² + b² = c²

given

By defining a right triangle, DEF, with sides a, b, and x, we can demonstrate the opposite of the Pythagorean theorem. Then, we'll demonstrate that if ABC is a triangle with sides a, b, and c where a2 + b2 = c2, it is congruent to DEF and is thus a right triangle because a2 + b2 = c2.

By the Pythagorean theorem, because △DEF is a right triangle, a² + b² = x².

When a2 + b2 = c2 and a2 + b2 = x2, c2 equals x2.

If △ABC is congruent to △DEF, then it must also be a right triangle.Thus, the two triangles have congruent sides and are congruent.

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If △ABC is congruent to △DEF, then it must also be a right triangle. Thus, the two triangles have congruent sides and are congruent.

A key idea in geometry known as the Pythagorean theorem explains the relationship between the sides of a right triangle. The square of the hypotenuse, or side opposite the right angle, is said to be equal to the sum of the squares of the other two sides. It can be expressed mathematically as: a² + b² = c²

By defining a right triangle, DEF, with sides a, b, and x, we can demonstrate the opposite of the Pythagorean theorem. Then, we'll demonstrate that if ABC is a triangle with sides a, b, and c where [tex]a^2 + b^2 = c^2[/tex], it is congruent to DEF and is thus a right triangle because a2 + b2 = c2.

By the Pythagorean theorem, because △DEF is a right triangle, a² + b² = x².

When[tex]a^2 + b^2 = c^2[/tex] and [tex]a^2 + b^2 = x^2[/tex], [tex]c^2[/tex] equals [tex]x^2[/tex].

If △ABC is congruent to △DEF, then it must also be a right triangle. Thus, the two triangles have congruent sides and are congruent.

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The workload of the resource is 20.5 units.

To calculate the workload of a resource that serves different flow unit types, one must know the amount of flow units, the processing time for each flow unit, and the number of resources available. This is best calculated using Little's Law, which states that the average number of flow units in a system is equal to the average rate of flow units multiplied by the average time they spend in the system.

For example, if a resource is serving 3 flow unit types, A, B and C, with 10, 8 and 5 units respectively, and a processing time of 2 minutes, 1 minute and 3 minutes respectively, with 2 resources available, the workload can be calculated as follows:

Workload = (10*2 + 8*1 + 5*3) / 2

       = 41 / 2

       = 20.5 units

Therefore, the workload of the resource is 20.5 units.

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Complete question

What are the flow unit types that the resource is serving?

For the computation of confidence interval for the difference in two population proportions following are negative,

p₁(cap) - p₂(cap)

Lower bound of the confidence interval

Upper bound of the confidence interval

For the computation of confidence interval,

The difference in two population proportions,

p₁ - p₂, can be negative or positive.

This implies,

The sample estimate of the difference in proportions,

p₁(cap) - p₂(cap), can also be negative or positive.

The standard error and critical value are always positive values and cannot be negative.

The lower and upper bounds of the confidence interval can be negative or positive.

Depending on the sample estimate and the margin of error.

So, both the lower and upper bounds can be negative.

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The above question is incomplete, the complete question is:

You are computing a confidence interval for the difference in 2 population proportions. which of the following could be negative?

Select all.

a. p₁

b. p₁(cap) - p₂(cap)

c. Standard error

d. Critical value

e. Lower bound of the confidence interval

f. Upper bound of the confidence interval

The answer will of given mathematical logic will be T F T T F respectivelly.

A negation, conjunction, and disjunction are the fundamental mathematical logics. The symbols for negation, conjunction, and disjunction in mathematical logic are "," "," and "v," respectively.

Logical proofs frequently employ mathematical logic. Proofs are legitimate arguments that establish the veracity of mathematical assertions. A series of statements make up an argument. The conclusion is the last assertion, and the premises are all the statements that came before it (or hypothesis).

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The complete truth table is shown in the below diagram.

≈ q → ≈ p: True  False  True  True

The contrapositive of a conditional statement is a new conditional statement that is formed by negating both the hypothesis (the "if" part) and the conclusion (the "then" part) of the original statement, and switching their positions. The truth table for the contrapositive of a conditional statement has the same number of rows as the truth table for the original statement.

For example, if the original statement is "If it is raining, then the ground is wet", then the contrapositive would be "If the ground is not wet, then it is not raining."

According to the given table the contrapositive of a conditional statement q and p is defines as;

True

False

True

True

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Answer:

0.048 in %

Step-by-step explanation:

firstly: remove the decimal point

= 48/1000

secondly : Simplify

48/1000*100

=48/10

=4.8%

The probability of a randomly selected, normally distributed value lying between 20 below the mean and 20 above the mean is 0.9545 (rounded to the nearest hundredth).

A number between zero and one represents the probability that an occurrence will take place. An event is a predefined set of random variable outcomes. Only one mutually exclusive event can occur at a time. Exhaustive events encompass or include all possible outcomes.

We can calculate the probabilities of a randomly chosen value falling between different z-scores using the provided standard normal distribution table.

a) The probability of a value being 0 below or above the mean is the same as the probability of a value being -1 to 1 standard deviations from the mean. According to the standard normal distribution table, the probability of a z-score between -1 and 1 is 0.6827. As a result, the probability of a randomly chosen, normally distributed value falling between 0 below and 0 above the mean is 0.6827. (rounded to the nearest hundredth).

b) The probability of a value falling between 20 and 20 standard deviations from the mean is the same as the probability of a value falling between -20/10 and 20/10 standard deviations from the mean (since the standard deviation is 10). According to the standard normal distribution table, the probability of a z-score between -2 and 2 is 0.9545. As a result, the probability of a randomly chosen, normally distributed value falling between 20 below and 20 above the mean is 0.9545. (rounded to the nearest hundredth).

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