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The greatest number of baskets that can be made with 24 movies, 48 packages of popcorn, and 18 boxes of candy is 6.

This is determined by finding the greatest common factor (GCF) of each item. The GCF of 24, 48, and 18 is 6. This means that 6 is the greatest number of baskets that can be made if each basket has an equal number of each of the three items.

To calculate the GCF, the prime factors of each number must be determined. The prime factors of 24 are 2 and 3 (2 x 2 x 2 x 3). The prime factors of 48 are 2 and 3 (2 x 2 x 2 x 2 x 3). The prime factors of 18 are 2 and 3 (2 x 3 x 3).

To determine the GCF, the highest power of each prime factor must be determined. In this case, the highest power of each prime factor is 3 (2 x 2 x 2 x 3). Therefore, the GCF of 24, 48, and 18 is 6. This means that the greatest number of baskets that can be made with the given items is 6.

In conclusion, the greatest number of baskets that can be made with 24 movies, 48 packages of popcorn, and 18 boxes of candy is 6. This is determined by finding the greatest common factor (GCF) of each item. The GCF of 24, 48, and 18 is 6, which means that 6 is the greatest number of baskets that can be made if each basket has an equal number of each of the three items.

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Answer:

Solution Given:

C is the interest point of AD and EB.

AC ≅ EC and ∠A ≅ ∠E

To prove:

AB ≅ ED

Proof:

In ∆ABC and ∆EDC

∠BAC= ∠CED Given

AC = CE Given

∠ACB= ∠ECD Vertically opposite angle

∆ABC ≅ ∆EDC By ASA axiom

Therefore,

AB ≅ ED

Since the corresponding side and corresponding angle of a congruent triangles are congruent or equal.

Hence Proved:

Answer:

She saved 25% or 1/4

Step-by-step explanation:

Please give me brain

Answer: A. There are many tangent lines that contain point A.

Step-by-step explanation:

Given, Point A is on circle O.

That means, Statement A. "There are many tangent lines that contain point A" is wrong.

The sequence of transformations used to transform ABCD to A"B"C"D" is; Trapezoid ABCD ​ was reflected across the y-axis and then translated 7 units up.

From the figure we have the pre image before transformation as Quadrilateral ABCD which is located at the bottom right of the graph.

Trapezoid ABCD and A"B"C"D" are equidistant from the x-axis

Trapezoid ABCD and A"B"C"D" are equidistant from the y-axis

Now, it is clear that Quadrilateral ABCD was first reflected across the y-axis.

Thereafter, when we look at the coordinates of the final transformed quadrilateral, it is clear that the second step of transformation was to translate the image by 7 units upwards.

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The complexity, reliability, and context of the evidence collected are some of the reasons why it is not possible to define a simple analytical scheme that can be applied to all types of evidence.

There are several reasons why it is not possible to define a simple analytical scheme that can be applied to all types of evidence.

Firstly, different types of evidence require different analytical techniques, as they have varying degrees of complexity. For example, analyzing DNA evidence requires a different set of analytical tools compared to analyzing physical evidence like fingerprints or footprints.

Secondly, the reliability of the evidence also plays a significant role in the analytical scheme. Some types of evidence may be more subjective than others, and the interpretation of the results may be open to bias or misinterpretation. In such cases, a simple analytical scheme may not provide accurate or reliable results.

Finally, the context in which the evidence is collected also plays a crucial role in determining the analytical scheme. The location, timing, and circumstances of the evidence collection may affect the reliability and accuracy of the results. Therefore, a simple analytical scheme may not be able to accommodate all the variables and nuances of the evidence collected in different contexts.

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Answer:

x=27

Step-by-step explanation:

a(a+b)=c(c+d)

10(42+10)=13(x+13)

520=13x+169

x=27

Lines 'a' and 'c' are parallel lines.

We have to given that,

There are three lines are shown in image.

We know that,

In a parallel line,

If two angles are alternate angles then both are equal to each other.

And, If two angles are corresponding angles then both are equal to each other.

Now, From the given figure,

In lines a and c,

Corresponding angles are 65 degree.

Hence, We can say that,

Lines a and c are parallel lines.

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Answer:

The angles are 5,2, and 3.

Step-by-step explanation:

Well, they're inside the triangle.

Step-by-step explanation:

5,2,3 because they are inside triangle

Given function is:1 if x belongs to [1, 2), 4 if x belongs to [2,3].(a) Let x1 belongs to (1, 2) and x2 belongs to (2, 3).Consider the partition P = {1, x1, x2, 3} of interval [1,3].The function is constant in each sub-interval.

The lengths of the sub-intervals of P are:x1 - 1, x2 - x1, 3 - x2The upper sum for f on [1, 3] with respect to P is given by:

U(f, P) = 1 * (x1 - 1) + 4 * (x2 - x1) + 4 * (3 - x2)= -3x1 + 5x2 + 9The lower sum for f on [1, 3] with respect to P is given by:

L(f, P) = 1 * (x1 - 1) + 1 * (x2 - x1) + 4 * (3 - x2

)= -3x1 + x2 + 13(b)

Let us consider a function g on [1, 3].

The upper sum for g on [1, 3] with respect to P is given by:U(g, P) = M1(x1 - 1) + M2(x2 - x1) + M3(3 - x2)where M1, M2, M3 are upper bounds for g on [1, x1], [x1, x2], and [x2, 3], respectively.Similarly, the lower sum for g on [1, 3] with respect to P is given by:L(g, P) = m1(x1 - 1) + m2(x2 - x1) + m3(3 - x2)where m1, m2, m3 are lower bounds for g on [1, x1], [x1, x2], and [x2, 3], respectively.

Now, we have to use upper and lower integrals to prove that f(x) is integrable on [1, 3] and find the integral of f(x) dx.As f is bounded and the lengths of sub-intervals of P approach zero as we refine the partition, we have the following equalities:

U(f, P) ≤ U(g, P) ≤ I(f, P)L(f, P) ≥ L(g, P) ≥ i(f, P)

where I(f, P) and i(f, P) are the upper and lower integrals of f on [1, 3].

Therefore, we have:L(g, P) ≤ i(f, P) ≤ I(f, P) ≤ U(g, P)Taking limits of the above inequality as the norm of P approaches zero, we get:L ≤ i(f) ≤ I ≤ Uwhere L = limL(g, P), U = limU(g, P).

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Answer:

The magnitude is sqrt((-4)^2 + (-9)^2) = 9.85. The angle is atan(-9/-4) = 180 deg + 66 deg = 246 deg = -114 deg.

Step-by-step explanation:

hope it help

Answer:

9.85

Step-by-step explanation:

|v|= √9²+(-4)²

=√81+16

=√97

|v|= 9.85

Answer:

4

Step-by-step explanation:

(-4)^2/2 +4

= 4

The probability of the union of two events occurring can never be more than the probability of the intersection of two events occurring, this statement is false.

The union of two or more sets refers to the set with all the elements belonging to each set. An element is said to be in the union if it lies to at least one of the sets.

The intersection of two or more sets refers to the set of elements universal to each set. An element is in the intersection if it occurs in all of the sets.

The event that both A and B occur is the intersection of the events A occurs and B occurs. As such, it is a subset of each and cannot, therefore, have a larger probability than either one individually.

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Answer:

3(x-3)/4-1/2=2/3  

The least common denominator will be the least common multiple of 4,2,3 which is the product of the highest occurring primes of the numbers prime factorization...

Step-by-step explanation:

4=2*2, 2=2, 3=3, so the least common denominator is 2*2*3=12

To calculate the partial derivatives of the given equation using implicit differentiation, we differentiate both sides of the equation with respect to the corresponding variables.

Let's start with the partial derivative ƏU/ƏT:

Differentiating both sides with respect to U and applying the chain rule, we have:

2(TU - V) * (T * ƏU/ƏT - ƏV/ƏT) * ln(W - UV) + (TU - V)² * (1/(W - UV)) * (-U * ƏW/ƏT - V * ƏU/ƏT) = 0

At the point (T, U, V, W) = (3, 3, 10, 40), this becomes:

2(33 - 10) * (3 * ƏU/ƏT - 0) * ln(40 - 33) + (33 - 10)² * (1/(40 - 33)) * (-3 * ƏW/ƏT - 10 * ƏU/ƏT) = 0

Simplifying this expression will give us the value of ƏU/ƏT.

Next, let's find the partial derivative ƏU/ƏV:

Differentiating both sides with respect to U and applying the chain rule, we have:

2(TU - V) * (T * ƏU/ƏV - 1) * ln(W - UV) + (TU - V)² * (1/(W - UV)) * (-U * ƏW/ƏV - V) = 0

At the point (T, U, V, W) = (3, 3, 10, 40), this becomes:

2(33 - 10) * (3 * ƏU/ƏV - 1) * ln(40 - 33) + (33 - 10)² * (1/(40 - 33)) * (-3 * ƏW/ƏV - 10) = 0

Simplifying this expression will give us the value of ƏU/ƏV.

Finally, let's find the partial derivative ƏU/ƏW:

Differentiating both sides with respect to U and applying the chain rule, we have:

2(TU - V) * (T * ƏU/ƏW) * ln(W - UV) + (TU - V)² * (1/(W - UV)) * (-U) = 0

At the point (T, U, V, W) = (3, 3, 10, 40), this becomes:

2(33 - 10) * (3 * ƏU/ƏW) * ln(40 - 33) + (33 - 10)² * (1/(40 - 33)) * (-3) = 0

Simplifying this expression will give us the value of ƏU/ƏW.

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Answer:

The function crosses the Y axis (the up down axis) at -1

Step-by-step explanation:

Answer:

Infinity

Step-by-step explanation:

Look it up, its how it works. 0 can go into 3.2 infinity times.

Answer:

The time it takes Ms. Croft to reach the cruise ship by speedboat = 6.11 hours

The time it takes Ms. Croft to reach the cruise ship by helicopter = 6.25 hours

since it takes less time for Ms. Croft to reach the cruise ship by taking the speedboat, her best choice to retrieve the artifact is to take the speedboat.

Step-by-step explanation:

The given parameters are;

The elapsed time by which Ms. Croft missed the boat = 5 hours

The speed of the cruise ship = 528 mi/day

The speed of the speedboat = 100 miles in 2.5 hours

The speed of the helicopter = 90 mph

The time it would take Ms. Croft to arrive at the harbor = 3.5 hours

Therefore, we have;

The cruise ship's speed = 528 miles per 24 hours = 528/24 mph = 22 mph

The location of the cruise after the first 5 hours = 5 × 22 = 110 miles

The speed of the speedboat = 100 miles per 2.5 hours = 100/2.5 = 40 mph

By traveling with a speed boat

The time at which Ms. Croft will intercept the cruise ship is given by the following relation;

40 mph × t = 22 mph × t + 110 miles

Which gives;

40 mph × t - 22 mph × t = 110 miles

18 mph = 110 miles

t = 110 miles/(18 mph) = 55/9 hours ≈ 6.11 hours

By taking the helicopter, we have;

Upon arrival at the harbor, after 3.5 hours, we find

90 mph × t = 22 mph × t + 22 mph × 3.5 hours + 110 miles

90 mph × t - 22 mph × t = 22 mph × 3.5 hours + 110 miles

68 mph × t = 77 miles + 110 miles = 187 miles

t = 187 miles/(68 mph) = 11/4 hours = 2.75 hours

The total time it takes Ms. Croft to reach the cruise ship by taking the helicopter = 3.5 + 2.75 = 6.25 hours

Therefore, since it takes less time for Ms. Croft to reach the cruise ship by taking the speedboat, her best choice to retrieve the artifact is to take the speedboat.

9514 1404 393

Answer:

  x = 15

Step-by-step explanation:

Corresponding sides are proportional, so the ratios of bottom to left side are the same. The left side of the large triangle is 6+4=10.

  x/10 = 9/6

  x = 10(9/6) . . . . multiply by 10

  x = 15

Based on the simple interest rate of the two banks, Evans should bank with Joyner Bank.

The simple interest rates can be found using the formula:

where;

a) For Ross Bank: $700 principal yields interest of $30 after 2 years

b) For Joyner Bank: $1000 principal yields interest of $46 after 2 years

Solving for the interest rate for Ross Bank:

Rate = 30 * 100 /(700 * 2)

Rate = 2.14%

Solving for the interest rate for Joyner Bank:

Rate = 46 * 100 /(1000 * 2)

Rate = 2.3%

Therefore, Evans should bank with Joyner Bank

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The general solution to the differential equation y' = 3ty - 3ty² is y(t) = Ce^(3t²/2)/(1 - Ce^(3t²/2)), where C is a constant to be determined based on the initial condition.

The given differential equation is y' = 3ty - 3ty². This is a separable differential equation, which means we can separate the variables y and t and integrate both sides.

Separating the variables, we get:

dy/(3y - 3y²) = t dt

Now, we need to integrate both sides. To integrate the left-hand side, we can use partial fractions. We can write:

dy/(3y - 3y²) = dy/3y - dy/3(y-1)

Integrating both sides, we get:

(1/3) ln|y| - (1/3) ln|y-1| = (1/2) t² + C

where C is the constant of integration.

We can simplify this expression by taking the exponential of both sides:

|y|/|y-1| = e^(3t²/2 + C)

We can eliminate the absolute value by considering the cases y > 0 and y < 1, or y > 1 and y < 0:

y/(y-1) = e^(3t²/2 + C) if y > 1

y/(y-1) = -e^(3t²/2 + C) if y < 0

To solve for y, we can cross-multiply and rearrange:

y = Ce^(3t²/2)/(1 - Ce^(3t²/2))

where C is a constant that depends on the initial condition.

Therefore, the general solution to the differential equation is:

y(t) = Ce^(3t²/2)/(1 - Ce^(3t²/2))

where C is a constant to be determined based on the initial condition.

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The correct formula that defines an arithmetic sequence is option d) tn = 5n + 14.

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms remains constant. In other words, each term can be obtained by adding a fixed value (the common difference) to the previous term.

In option a) tn = 5 + 14, the term does not depend on the value of n and does not exhibit a constant difference between terms. Therefore, it does not represent an arithmetic sequence.

Option b) tn = 5n² + 14 represents a quadratic sequence, where the difference between consecutive terms increases with each term. It does not represent an arithmetic sequence.

Option c) tn = 5n(n+14) represents a sequence with a varying difference, as it depends on the value of n. It does not represent an arithmetic sequence.

Option d) tn = 5n + 14 represents an arithmetic sequence, where each term is obtained by adding a constant value of 5 to the previous term. The common difference between consecutive terms is 5, making it the correct formula for an arithmetic sequence.

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The recursive formula that represents the same sequence of numbers as the explicit formula an = 3n + 4 is an = an-1 + 3, with the initial term a1 = 7.

A recursive formula defines a sequence by expressing each term in terms of previous terms. In this case, the explicit formula an = 3n + 4 gives us a direct expression for each term in the sequence.

To find the corresponding recursive formula, we need to express each term in terms of the previous term(s). In this sequence, each term is obtained by adding 3 to the previous term. Therefore, the recursive formula is an = an-1 + 3.

To complete the recursive formula, we also need to specify the initial term, a1. We can find the value of a1 by substituting n = 1 into the explicit formula:

a1 = 3(1) + 4 = 7

Hence, the complete recursive formula for the sequence is an = an-1 + 3, with the initial term a1 = 7. This recursive formula will generate the same sequence of numbers as the given explicit formula.

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The integral (12x + 12y) dA over the region R, using the given transformation, evaluates to 64. The new limits of integration are u = -6 to u = 6 and v = -6 to v = 6.

To evaluate the integral (12x + 12y) dA over the region R, we need to perform a change of variables using the given transformation:

\(x &= \frac{1}{3}(u + v) \\\)

\(y &= \frac{1}{3}(v - 2u)\)

First, let's find the Jacobian determinant of the transformation:

\(J = \frac{\partial{(x, y)}}{\partial{(u, v)}}\)

\(J = \frac{\partial{(x, y)}}{\partial{(u, v)}}\)

\(\left| \frac{\partial x}{\partial u} \ \frac{\partial x}{\partial v} \right|\)

\(\[= \left| \frac{1}{3} \ \frac{1}{3} \right|\]\)

\(=\[| -\frac{2}{3} \ \frac{1}{3} |\]\)

\(=\frac{1}{3}\)

Now, let's find the new limits of integration by substituting the given vertices of R into the transformation:

When (x, y) = (-2, 4):

\(\[-2 = \frac{1}{3}(u + v)\]\)

\(\[4 = \frac{1}{3}(v - 2u)\]\)

Solving these equations, we get u = 0 and v = -6.

When (x, y) = (2, -4):

\(\[2 = \frac{1}{3}(u + v)\]\)

\(\[-4 = \frac{1}{3}(v - 2u)\]\)

Solving these equations, we get u = 0 and v = 6.

When (x, y) = (3, -3):

\(\[\begin{aligned}3 &= \frac{1}{3}(u + v) \\\\-3 &= \frac{1}{3}(v - 2u)\end{aligned}\]\)

Solving these equations, we get u = 6 and v = 0.

When (x, y) = (-1, 5):

\(\[\begin{aligned}-1 &= \frac{1}{3}(u + v) \\5 &= \frac{1}{3}(v - 2u)\end{aligned}\]\)

Solving these equations, we get u = -6 and v = 0.

Therefore, the new limits of integration for the integral are u = -6 to u = 6 and v = -6 to v = 6.

Now, we can rewrite the integral using the new variables:

\([\int_{-6}^{6} \int_{-6}^{6} (12x + 12y) , da = \frac{1}{3} \int_{-6}^{6} \int_{-6}^{6} \left( 12(u + v) + 12(v - 2u) \right) , dudv]\)

\(\[= \frac{4}{9} \int_{-6}^{6} \int_{-6}^{6} \left( 4u + 4v + 4v - 8u \right) \, dudv\]\)

\(\[= \frac{4}{9} \int_{-6}^{6} \int_{-6}^{6} \left( -4u + 8v \right) \, dudv\]\)

Integrating with respect to u first, we have:

\(\[= \frac{4}{9} \int_{-6}^{6} \left( -\frac{4u^2}{2} + 8uv \right) \, du\]\)

\(\[= \frac{4}{9} \int_{-6}^{6} \left( -2u^2 + 48v \right) \, du\]\)

\(\[= \frac{4}{9}\) (864)

= 64

Therefore, the value of the integral (12x + 12y) dA over the region R is 64.

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a) The regular expression "+" represents the language of one or more occurrences of the symbol "+". To construct a grammar that represents the same language but is not regular, we can use the following production rule:

S -> "+" S | "+".

This grammar generates strings with one or more "+" symbols.

b) The regular expression "+c" represents the language of one or more occurrences of the symbol "+" followed by the symbol "c". To construct a non-regular grammar for this language, we can use the following production rules:

S -> "+" S | "c".

This grammar generates strings with one or more "+" symbols followed by a "c". Since the language represented by the regular expression is regular, it can be recognized by a finite automaton. However, the grammar we constructed is not regular because it uses a recursive production rule.

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Answer:

(d) all of the above

Step-by-step explanation:

Linear functions has  a constant slope and graphs as a straight line. So, option A is correct! Most Linear function represent in form y= mx + b, so option B is also correct! Option C is also, correct! So all of the above correct, so answer is D!

Answer:

$3

Step-by-step explanation:

Given that:

Park charge for one round = $19

Reduced fee for every additional round

Number of rounds played by Tom = 6

Amount paid = $34

Amount left after 1 round :

Amount paid - first round charge

$34 - $19 = $15

Number of rounds left = (6 - 1) = 5

Charge per additional round :

$15 / 5 = $3