Square oabc is drawn on a centimetre grid.o is (0,0) a is(3,0) b is(3,3) c is (0,3)write down how many invariants points there are on the perimeter of the square when oabc is translated by the vector (1 3)

Answer:

Step-by-step explanation:

formula of volume of cylinder is (\(\pi\)r2h)

= 22/7*7 square*3

= 22/7*49*3

= 462

we cancelled 7/49 we get the answer as 7 then multiplied by 3 we get the answer as 21 and then multiple 22*21 u will get 462

Answer:

hi, where's mt 20pts

Step-by-step explanation:

0.3

12+6+9+13=40

12/40 (or 3/10 simplified)

Thus, 0.3 as a decimal

Hope this helps!

Disjoint events are events that cannot happen at the same time. Two events A and B are independent if the occurrence of A does not affect the probability of B happening, and vice versa. Mathematically, this can be written as P(A and B) = P(A)P(B).

In the case of disjoint events, P(A and B) = 0 because they cannot occur at the same time. Therefore, the condition for A and B to be independent is that either P(A) = 0 or P(B) = 0, since any non-zero probability for either event would make the product P(A)P(B) also non-zero.

Two disjoint events are independent if and only if at least one of them has zero probability.

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The equation of the total cost for the cover charge and drinks in point-slope form is y = 6x + 5.

The point-slope form of a linear equation is given by -

 \(y - y_1 = m(x- x_1)\)

where m is the slope and \((x_1, y_1)\) is a point on the line.

Here, the total cost for the cover charge and drinks can be represented by the equation y = mx + b, where y is the total cost, x is the number of drinks, m is the cost per drink, and b is the cost of the cover charge.

We know that the cover charge is $5 and drinks are $6 each, so, we can find the slope (m) of the equation by using the cost per drink which is m = 6.

We can also find the point \((x_1, y_1)\) by using the cover charge cost which is (0,5).

Therefore, the equation in point-slope form of the total cost for the cover charge and drinks will be -

y - 5 = 6(x-0)

y - 5 = 6x

y = 6x + 5

Where x is the number of drinks and y is the total cost i.e. cover charge + drinks.

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\( - 1 - 5x + 6 - 30x \leqslant - 65\)

\( - 35x + 5 \leqslant - 65\)

Factoring -5

\( - 5(7x - 1) \leqslant - 65\)

Divided sides by -5

##############################

Point :

If the sides of an inequality are multiplied by or divided by a negative number, the direction of the inequality changes and returns.

##############################

\( \frac{ - 5}{ - 5}(7x - 1) \geqslant \frac{ - 65}{ - 5} \\ \)

\(7x - 1 \geqslant 13\)

Plus sides 1

\(7x - 1 + 1 \geqslant 13 + 1\)

\(7x \geqslant 14\)

Divided sides by 7

\( \frac{7}{7}x \geqslant \frac{14}{7} \\ \)

\(x \geqslant 2\)

Done ♥️♥️♥️♥️♥️

The proven that [δ(G)*n]/2 <= m <= [Δ(G)*n]/2. Given:  Let G be an undirected graph with n vertices.

Let Δ(G) be the maximum degree of any vertex in G, δ(G) be the minimum degree of any vertex in G, and m be the number of edges in G.Prove: [δ(G)*n]/2 <= m <= [Δ(G)*n]/2 Proving : [δ(G)*n]/2 <= m.

We know that, The sum of degrees of vertices of an undirected graph is equal to twice the number of edges.

Σ deg(V) = 2m Also, δ(G) <= deg(V) <= Δ(G)So, δ(G) <= Σ deg(V) /n <= Δ(G)δ(G)*n <= Σ deg(V) <= Δ(G)*n2m = Σ deg(V)≥ δ(G)*n and m ≥ [δ(G)*n]/2 Proving : m <= [Δ(G)*n]/2Also,δ(G) <= deg(V) <= Δ(G)δ(G)*n <= Σ deg(V) <= Δ(G)*n2m = Σ deg(V)So, m <= Σ deg(V) /2 <= Δ(G)*n /2and m <= [Δ(G)*n]/2

Therefore, we have proven that [δ(G)*n]/2 <= m <= [Δ(G)*n]/2.

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The derivative of r(t)⋅a(t) at t=8 is -126. To find the derivative of r(t)⋅a(t) at t=8, first, calculate the derivative of r(t) and then use the product rule.

The derivative of r(t) is r'(t) = ⟨2t, -1, 4⟩.
Now, use the product rule: d/dt[r(t)⋅a(t)] = r'(t)⋅a(t) + r(t)⋅a'(t)
At t=8, r(8) = ⟨64, -7, 32⟩, r'(8) = ⟨16, -1, 4⟩, a(8) = ⟨-8, -6, 7⟩, and a'(8) = ⟨4, 8, -3⟩.
Compute the dot products: r'(8)⋅a(8) = (16 * -8) + (-1 * -6) + (4 * 7) = -128 + 6 + 28 = -94
r(8)⋅a'(8) = (64 * 4) + (-7 * 8) + (32 * -3) = 256 - 56 - 96 = 104
Now add the two dot products: -94 + 104 = 10
So, d/dt[r(t)⋅a(t)]|t=8 = 10.

To calculate the derivative of r(t)⋅a(t), we need to use the product rule of differentiation.
r(t)⋅a(t) = ⟨t2,1−t,4t⟩ ⋅ ⟨−8,−6,7⟩ = -8t2 - 6(1-t) + 28t
So,
ddt[r(t)⋅a(t)] = ddt[-8t2 - 6(1-t) + 28t]
                = -16t - 6 + 28
Now, we need to evaluate this derivative at t=8 and use the given value of a'(8).
ddt[r(t)⋅a(t)]|t=8 = -16(8) - 6 + 28 = -126
Therefore, the derivative of r(t)⋅a(t) at t=8 is -126.

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it should be y= 3/2x + 2

y=38x-118

a) To find the slope of PQ, we have to find the slope of the secant line. It can be found using the formula (y2−y1)/(x2−x1). We know that the point P (3, −4) lies on the curve y=4/(2−x). Therefore, the coordinates of P can be substituted in the above equation to obtain the slope of the tangent at the point P.

The coordinates of point Q can be found using the given equation of the curve as shown below:

y = 4/(2 - x)

For x = 2.9, y = 4/(2 - 2.9) = −40. The coordinates of point Q for other values of x can be computed similarly. Therefore, the coordinates of Q for the given values of x are given below:

(2.9, -40)

(2.99, -400)

(2.999, -4000)

(2.9999, -40000)

(3.1, 40)

(3.01, 400)

(3.001, 4000)

(3.0001, 40000)

The slope of PQ for each of the above points can be found using the formula mentioned earlier. Therefore, the slope of PQ for the given values of x are given below:

(i) mPQ = (−40−(−4))/(2.9−3) = 38

(ii) mPQ = (−400−(−4))/(2.99−3) = 38.006944

(iii) mPQ = (−4000−(−4))/(2.999−3) = 38.000694

(iv) mPQ = (−40000−(−4))/(2.9999−3) = 38.000069

(v) mPQ = (40−(−4))/(3.1−3) = 44

(vi) mPQ = (400−(−4))/(3.01−3) = 388.888889

(vii) mPQ = (4000−(−4))/(3.001−3) = 3888.888889

(viii) mPQ = (40000−(−4))/(3.0001−3) = 38888.888889

b) From the values of slope found in part (a), we can guess the value of slope m of the tangent at P (3, −4) to the curve y=4/(2−x) as shown below.

The slope of PQ is computed for values of x near 3, and it is observed that the slope converges to 38. Therefore, the value of the slope of the tangent at point P (3, −4) is 38.

c) Using the slope found in part (b), we can find the equation of the tangent line at point P (3, −4).

The equation of the tangent line to the curve y = 4/(2 - x) at the point P (3, −4) with slope m = 38 is given below:

y − (−4) = m(x − 3)

⇒ y + 4 = 38(x − 3)

⇒ y = 38x − 118

Therefore, the equation of the tangent line is y = 38x - 118.

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True. This is because the paired differences are not independent, as each difference is calculated from the same set of observations or individuals.

The statement is true. When dealing with dependent or paired groups, such as in a paired t-test or a repeated measures design, the degrees of freedom are determined by the number of paired differences minus 1.

This is because the paired differences are not independent observations, as each difference is calculated from the same set of individuals or matched pairs.

By subtracting 1 from the number of paired differences, we account for the loss of one degree of freedom due to the dependency between the paired values. The degrees of freedom play a crucial role in determining the critical values and conducting statistical tests for dependent group analyses.

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The probability that the entire system works is approximately 0.52, rounded off to the second decimal place.

What is probability?

Probability is the study of the chances of occurrence of a result, which are obtained by the ratio between favorable cases and possible cases.

Let A, B, and C represent the events that components A, B, and C work, respectively. Then, the probability that a component works is given as P(A) = P(B) = P(C) = p.

The probability that the entire system works is the probability that either A and B work and C does not, or A and C work and B does not. This can be expressed as:

P(system works) = P((A and B and C') or (A and B' and C))

Using the distributive property of probability, we can rewrite this as:

P(system works) = P(A and B and C') + P(A and B' and C)

Since the components work independently, we can apply the product rule of probability to each term:

P(system works) = P(A) * P(B) * (1 - P(C)) + P(A) * (1 - P(B)) * P(C)

Substituting P(A) = P(B) = P(C) = p, we get:

P(system works) = p² * (1 - p) + p * (1 - p)²

Simplifying this expression, we get:

P(system works) = p * (2p - 3p² + 1)

Substituting the given value of p, we get:

P(system works) = 0.8 * (20.8 - 30.8² + 1) ≈ 0.52

Therefore, the probability that the entire system works is approximately 0.52, rounded off to the second decimal place.

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Since the rate of bacteria growth is proportional to the number present, we can express this relationship using a differential equation:

dN/dt = kN,

where N is the number of bacteria, t is the time, and k is the constant of proportionality.

Given that the number of bacteria doubles in three hours, we can write:

dN/dt = kN,

dN/N = k dt.

To solve this equation, we integrate both sides:

∫ dN/N = ∫ k dt,

ln(N) = kt + C,

where C is the constant of integration.

Now, let's consider the specific conditions. When the number of bacteria doubles, N/N0 = 2, where N0 is the initial number of bacteria.

ln(2) = k(3) + C,

C = ln(2) - 3k.

Now, let's find the time it takes for the number of bacteria to triple, which means N/N0 = 3:

ln(3) = k(t) + ln(2) - 3k,

ln(3) - ln(2) = k(t) - 3k,

ln(3/2) = k(t - 3),

t - 3 = (ln(3/2))/k,

t = (ln(3/2))/k + 3.

Therefore, in how many hours will the number of bacteria triple is given by (ln(3/2))/k + 3. The value of k depends on the specific growth rate of the bacteria in the culture.

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Answer:

x = -4 + 3 i or x = -4 - 3 i

Step-by-step explanation:

Solve for x:

(x + 4)/(x + 5) = (x - 5)/(2 x)

Hint: | Multiply both sides by a polynomial to clear fractions.

Cross multiply:

2 x (x + 4) = (x - 5) (x + 5)

Hint: | Write the quadratic polynomial on the left hand side in standard form.

Expand out terms of the left hand side:

2 x^2 + 8 x = (x - 5) (x + 5)

Hint: | Write the quadratic polynomial on the right hand side in standard form.

Expand out terms of the right hand side:

2 x^2 + 8 x = x^2 - 25

Hint: | Move everything to the left hand side.

Subtract x^2 - 25 from both sides:

x^2 + 8 x + 25 = 0

Hint: | Using the quadratic formula, solve for x.

x = (-8 ± sqrt(8^2 - 4×25))/2 = (-8 ± sqrt(64 - 100))/2 = (-8 ± sqrt(-36))/2:

x = (-8 + sqrt(-36))/2 or x = (-8 - sqrt(-36))/2

Hint: | Express sqrt(-36) in terms of i.

sqrt(-36) = sqrt(-1) sqrt(36) = i sqrt(36):

x = (-8 + i sqrt(36))/2 or x = (-8 - i sqrt(36))/2

Hint: | Simplify radicals.

sqrt(36) = sqrt(4×9) = sqrt(2^2×3^2) = 2×3 = 6:

x = (-8 + i×6)/2 or x = (-8 - i×6)/2

Hint: | Factor the greatest common divisor (gcd) of -8, 6 i and 2 from -8 + 6 i.

Factor 2 from -8 + 6 i giving -8 + 6 i:

x = 1/2-8 + 6 i or x = (-8 - 6 i)/2

Hint: | Cancel common terms in the numerator and denominator.

(-8 + 6 i)/2 = -4 + 3 i:

x = -4 + 3 i or x = (-8 - 6 i)/2

Hint: | Factor the greatest common divisor (gcd) of -8, -6 i and 2 from -8 - 6 i.

Factor 2 from -8 - 6 i giving -8 - 6 i:

x = -4 + 3 i or x = 1/2-8 - 6 i

Hint: | Cancel common terms in the numerator and denominator.

(-8 - 6 i)/2 = -4 - 3 i:

Answer: x = -4 + 3 i or x = -4 - 3 i

The calculated area of the pentagon is 288.50 mm² if one of the sides of the apothem of 10mm.

Length of apothem = 10mm

The formula used to find the area of a pentagon is:

Area = (1/2) × apothem × perimeter

Here the perimeter is the unknown term, so we need to calculate the perimeter of the Pentagon. The perimeter of a pentagon is calculated by the product of 5 times the length.

Let us assume that the length of one side of the Pentagon = s

The side of the Pentagon is:

s = (2 × apothem) / tan(180° / 5)

s = (2 × 10) / tan(36°)

s = 11.54 mm

Perimeter = 5*s

Perimeter = 5 * 11.54 = 57.70 mm

Now, the area of the Pentagon is:

Area = (1/2) × apothem × perimeter

Area = (1/2) × 10 × 57.70 = 288.50 mm²

Therefore, we can conclude that area of the pentagon is 288.50 mm².

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The experimental probability of rolling a 1 or a 2 is 0.2.

Hence, Option A is correct.

We know that,

The experimental probability of an event is defined as the number of times the event occurred divided by the total number of trials.

In this case,

The event is rolling a 1 or a 3,

Which occurred ⇒  3 + 1

                           = 4 times.

Given that there are total number of trials = 20.

Therefore,

The experimental probability of rolling a 1 or a 3 = 4/20,

                                                                                = 1/5

                                                                                 = 0.2

Hence, the required probability is 0.2.

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The complete question is:

Sarah is playing a game in which she rolls a number cube 20 times. The results are recorded in the chart below. What is the experimental probability of rolling a 1 or a 3?

Number on cube:1,2,3,4,5,6

Number of times event occurs:3,6,1,5,3,2

A.0.2

B.0.3

C.0.6

D.0.83

Answer:

-17 9/10

Step-by-step explanation:

Given Data:

The salary of Clarissa is : $395 per week

The total amount Clarissa own the employment agency is 20% of the 4 weeks salery.

The total salary of employment agency in four week is,

Clarissa earn $1580 in her first four week.

The 20% of the $1580 is the amount Clarissa owns the agency.

The 20% of the $1580 is,

Thus, Clarissa has to pay $316 to the employment agency.

Answer:

c. Square Root

If you want me to explain, let me know!

In reliability engineering, systems can be represented in terms of components that need to function or fail for the system to function or fail.

The notation koon:G represents the number of components that need to function for the system to function, while koon:F represents the number of components that need to fail to cause system failure. The goal is to determine the value of x in different scenarios to understand the system's behavior.

(a) To find the number x such that a 2004:G structure corresponds to a xoo4:F structure, we need to consider that the total number of components is n = 4. In a 2004:G structure, all four components need to function for the system to function. Therefore, we have koon:G = 4. In an xoo4:F structure, all components except x need to fail for the system to fail. In this case, we have koon:F = n - x = 4 - x.

Equating the two expressions, we get 4 - x = 4, which implies x = 0. Therefore, a 2004:G structure corresponds to a 0400:F structure.

(b) To determine the number x such that a koon:G structure corresponds to a xoon:F structure, we have k components that need to function for the system to function. Therefore, koon:G = k. In an xoon:F structure, x components need to fail for the system to fail.

Hence, we have koon:F = x. Equating the two expressions, we get k = x. Therefore, a koon:G structure corresponds to a koon:F structure, where the number of components needed to function for the system to function is the same as the number of components needed to fail for the system to fail.

By understanding these representations, we can analyze system reliability and determine the criticality of individual components within a larger system. This information is valuable in designing robust and resilient systems, as well as identifying potential points of failure and implementing appropriate redundancy or mitigation strategies.

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Answer:

Second question in Assignment = A) 14

Step-by-step explanation:

x^2 = 14x +49

Answer: 14

Step-by-step explanation:

The first one is 25/4 then 14

No, it doesn't show that single individuals under the age of 25 have more insurance claims than the nationwide percent reported by the big insurance firm.

Hypothesis

Null hypothesis : H0: p = 0.68

Alternative hypothesis : Ha: p > 0.68

A random sample of 53 claims showed that 41 were made by single people under the age of 25.

Thus; p^ = 41/53 = 0.7736

The test statistic is

z = (p^ - p_o)/√(p_o(1 - p_o)/n)

z = (0.7736 - 0.68)/√(0.68(1 - 0.68)/41)

z = 0.0936/0.07285

z = 1.28

The p-value from z-score calculator, using z = 1.28, one tail hypothesis and significance level of 0.05,we have;

P(z > 1.28) = 0.100273

The p-value gotten is greater than the significance value and so we fail to reject the null hypothesis and conclude that there is insufficient evidence to support the claim.

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Answer:

The graph should look like the one below.

Step-by-step explanation:

C is lbs of chicken

S is pounds of steak

Alfred spent 30 pounds of meat for the party:

c + s \(\leq\) 30

Alfred spend $60 on the 30 lbs of meat.

The chicken is $1.50 per pound and the steak is $2.40 per lb  then

1.5c + 2.50 \(\leq\) 60

0.5c + 0.85 \(\leq\) 20

The linear inequalities system that models situation is:

0.5c + 0.85 \(\leq\) 20

c + s \(\leq\) 30

c \(\geq\)  0

s \(\geq\) 0

The Graph:  

Answer:

A) Even Numbers and Odd Numbers

Step-by-step explanation:

The function f(t) corresponding to the Laplace transform ℋ(f(t)) = ℋ{s(t)} is:

f(t) = u(t) + 2te^(-t) + t^2/2 u(t)

To find f(t) from the Laplace transform ℋ(f(t)), we need to apply the inverse Laplace transform ℒ⁻¹ to ℋ(f(t)).

Given ℋ(f(t)) = ℋ{s(t)}, we have:

ℒ⁻¹{ℋ(s(t))} = ℒ⁻¹{ℋ[(s + 1)²/s]} = ℒ⁻¹{ℋ[s/s] + ℋ[2s/(s+1)²] + ℋ[1/(s+1)²]}

Using the properties of Laplace transforms and taking the inverse Laplace transforms, we get:

f(t) = u(t) + 2te^(-t) + t^2/2 u(t)

where u(t) is the unit step function.

Therefore, the function f(t) corresponding to the Laplace transform ℋ(f(t)) = ℋ{s(t)} is:

f(t) = u(t) + 2te^(-t) + t^2/2 u(t)

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Answer:

You divide 0.3 by 12 if you don’t want a decimal do it the other way around the answer is x=40

Step-by-step explanation:

The value of x that satisfies the equation 0.3x = 12 is 40.

We have,

To find the value of x in the equation 0.3x = 12, we need to isolate x on one side of the equation.

We can do this by dividing both sides of the equation by 0.3, which will cancel out the coefficient of x on the left side:

(0.3x) / 0.3 = 12 / 0.3

Simplifying this equation gives:

x = 40

Thus,

The value of x that satisfies the equation 0.3x = 12 is 40.

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Answer:

B. 1/24

Step-by-step explanation:

Given: 3 inches = 6 feet

Convert 6 feet into inches.

6 feet = 72 inches

3/72. Simplying it, you get 1/24

Answer:

Number of adults = 350

Number of students = 200

Number of Children under 12 = 50

Step-by-step explanation:

Let

Number of adults = x

Number of students = y

Number of Children under 12 = z

Cost of each ticket

Students = $3

Adults = $7

Children under 12 = $2

Total crowd at the concert = 600

Total revenue = $3,150

There are 150 more adults at the concert than students.

That is, adults = y + 150

The equations

x + y + z = 600

7x + 3y + 2z = 3,150

Recall,

x = y + 150

y + 150 + y + z = 600

7(y + 150) + 3y + 2z = 3,150

2y + z + 150 = 600

7y + 1050 + 3y + 2z = 3,150

2y + z = 600 - 150

10y + 2z = 3150 - 1050

2y + z = 450 (1)

10y + 2z = 2,100 (2)

Multiply (1) by 2

4y + 2z = 900 (3)

10y + 2z = 2,100 (2)

Subtract (3) from (2)

10y - 4y = 2100 - 900

6y = 1200

Divide both sides by 6

y = 1200/6

= 200

Substitute the value of y into (1)

2y + z = 450

2(200) + z = 450

400 + z = 450

z = 450 - 400

= 50

z = 50

Substitute value of y into

x = y + 150

x = 200 + 150

= 350

x = 350

Therefore,

Number of adults = 350

Number of students = 200

Number of Children under 12 = 50

Answer:

\(c = kw\)

Step-by-step explanation:

Given

c varies directly as w

Required

Write the equation

c varies directly as w.

Mathematically, this is represented as:

\(c\ \alpha\ w\)

Convert to equation.

\(c = kw\)

Where k is the constant of variation