15 POINTS At a grocery store, a bag of 12 red apples cost $10.80 and a bag of 6 green apples costs $6.90. Which statement below is true?

A The cost per apple is the same.
B The cost per red apple is greater than the cost per green apple.
C The cost per green apple is greater than the cost per red apple.

Step-by-step explanation:

Calculate the unit rate as follows

2.4 kg  / 20 bag =   .12 kg per bag

A. The required vectors to component form as:  -7(u • v) = -21√(6).

B. u and w are neither parallel nor orthogonal.

Part A:

The vectors are given as:

u = −2(cos 30°i + sin30°j),

v = 6(cos 225°i + sin225°j),

w = 8(cos 120°i + sin120°j)

So we have:

u = -2(√(3)/2 i + 1/2 j) = -√(3) i - j

v = 6(-√(2)/2 i - sqrt(2)/2 j) = -√(2) i - √(2) j

w = 8(-1/2 i + √(3)/2 j) = -4i + √(3) j

To find -7(u • v), we first need to find the dot product of u and v:

u • v = (-√(3))( -√(2) ) + (-1)(-√(2)) = √(6)

Then, we can multiply by -7:

-7(u • v) = -7(√(6)) = -√(6)

Therefore, -7(u • v) = -21√(6).

Part B:

To determine if u and w are parallel, orthogonal, or neither, we can use the dot product:

u • w = (-√(3))(-4) + (-1)(4√(3)) = -8√(3)

Since the dot product is not equal to 0, we know that u and w are not orthogonal. To determine if they are parallel, we can compare their direction vectors:

The direction vector of u is < -√(3), -1 >, and the direction vector of w is < -4, 4√(3) >.

If u and w are parallel, then their direction vectors will be scalar multiples of each other.

So we need to check if there exists a scalar k such that:

< -√(3), -1 > = k < -4, 4√(3) >

This is equivalent to the system of equations:

-k × 4 = -√(3)

k × 4√(3) = -1

Solving for k, we get:

k = √(3)/12

Since k is not a real number, we know that u and w are not parallel.

Therefore, u and w are neither parallel nor orthogonal.

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Therefore , the solution of the given problem of percentage comes out to be Chong is the correct answer in (b).

In statistics, a figure or quantity that may be stated as a percent of 100 is denoted by the abbreviation "a%." Other odd spellings include "pct," "pct," and "pc." The percentage symbol ("%") is the technique that is most usually used for this. Also unknown are any clues or any fixed ratio of any part to the whole. Numbers are effectively integers since they frequently add up to 100. If a figure comprises a percentage, the expression "fraction" or simply the shorthand for % (%) must appear first.

Here,

We must first compute each person's commission earnings before comparing the results to see who received the highest commission payments.

On sales of $549.50, Janice received a 15% commission, which is:

commission:

=>  $82.425 ($0.15 x $549.50)

On sales of $343.25, Chong received a 25% commission, which is:

=>  commission = 0.25 * $343.25%, or $85.7125.

On sales of $418.75, Adrienne received a 20% commission, which is:

=> commission: $83.75 ($0.20 * $418.75)

On sales of $625.75, Luke received a 10% commission, which is:

=> commission: $62.575 = 0.10 * $625.75

By comparing the figures, it is clear that Chong, with $85.8125, earned the most through commission, followed closely by Adrienne, with $83.75,

Janice, with $82.425, and Luke, with $62.575.

So Chong is the correct answer in (b).

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The area of the shaded region is 70.65 ft² and length of arc ADB is 260.

We have,

The radius of the circle is 9 ft.

The measure of ∠AOB is 100°.

So, The measure of ∠ADB

= 360 - <AOB

= 360 - 100

= 260

So, The area of the shaded region

A = ([tex]\theta[/tex]/360) πr²

A = (100/360) (3.14) (9)²

A = 70.65 ft²

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The correct option is b. h0: π = 0.50, where π represents the probability of observing a positive difference.

The null hypothesis for a two-tailed sign test is that there is no difference between the two populations being compared.

Specifically, the null hypothesis is that the proportion of positive differences is equal to the proportion of negative differences, which is equivalent to stating that the median difference between the two populations is zero.

Therefore, the correct option is b. h0: π = 0.50, where π represents the probability of observing a positive difference.

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The line integral is approximately equal to 0.2675 or 6/5, depending on the method used.

To evaluate the line integral y³ds along the curve C given by x=t³, y=t, 0<=t<=2, we can use either the parameterization method or the line integral formula.

Using the parameterization method, we first find the parametric equations for C:

x = t³
y = t

Then, we can express ds in terms of dt:

ds = √((dx/dt)² + (dy/dt)²) dt
  = √((3t²)² + (1)²) dt
  = √(9t⁴ + 1) dt

Therefore, the line integral can be written as:

integral(y³ ds) = integral(y³ √(9t⁴ + 1) dt)
                 = integral(t³ √(9t⁴ + 1) dt)
                 = 0.2675 (approx.)

Alternatively, we can use the line integral formula:

integral(y³ ds) = integral(y³ dx) - integral(y'² dx)
                 = integral(t³ 3t² dt) - integral(1 9t⁴ dt)
                 = 2 - 32/5
                 = 6/5

Therefore, the line integral is approximately equal to 0.2675 or 6/5, depending on the method used.

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Answer:  (x+3)^2+(y+10)^2=4

Step-by-step explanation:

The standard form of the equation of a circle is:

(x−x1)2+(y−y1)2=r2

In order to place the center of the circle at point (3, 10), simply replace x1 with 3 and y1 with 10

(x+3)^2+(y+10)^2=r2

Finally, replace r with the radius of the circle.

The final equation is:

(x+3)^2+(y+10)^2=4

We can rewrite the given expression as follows:
$\sqrt{5} \frac{1}{\sqrt{5}} \sqrt{7} \frac{1}{\sqrt{7}} = \frac{\sqrt{5}}{\sqrt{5}} \cdot \frac{\sqrt{7}}{\sqrt{7}} = \frac{5}{\sqrt{5}\sqrt{5}} \cdot \frac{7}{\sqrt{7}\sqrt{7}}$

Now, we simplify further:
$= \frac{5}{5} \cdot \frac{7}{7} = \frac{1 \cdot 1}{1}$

So, in the form $\dfrac{a\sqrt{5}  b\sqrt{7}}{c}$, we have $a = 0$, $b = 0$, and $c = 1$. Therefore, the product $abc = 0 \cdot 0 \cdot 1 = 0$.

First, let's simplify the expression:
$\sqrt{5} \frac{1}{\sqrt{5}} \sqrt{7} \frac{1}{\sqrt{7}} = \frac{\sqrt{5}}{\sqrt{5}} \cdot \frac{\sqrt{7}}{\sqrt{7}} = 1$

So now we want to write $1$ in the form $\dfrac{a\sqrt{5}  b\sqrt{7}}{c}$ with positive integers $a$, $b$, and $c$, and $c$ as small as possible.

We can do this by setting $a=b=c=1$ since $1\cdot 1\cdot 1 = 1$ and $1$ is the smallest possible value for $c$. So we have:
$1 = \dfrac{1\sqrt{5}\cdot 1\sqrt{7}}{1}$

Therefore, $a=1$, $b=1$, and $c=1$, so $abc=1$.

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If A is any n x n matrix,

(i) Proved that A + A^T is symmetric.

(ii) Proved that A - A^T is skew symmetric.

To show that A + A^T is symmetric, we need to show that (A + A^T)^T = A + A^T.

Now, (A + A^T)^T = A^T + (A^T)^T = A^T + A

Therefore, if we add A + A^T, we get

(A + A^T) + (A^T + A) = 2A^T + 2A

Which is clearly equal to 2(A + A^T). Therefore,

(A + A^T)^T = A + A^T

So, A + A^T is symmetric.

To show that A - A^T is skew symmetric, we need to show that (A - A^T)^T = -(A - A^T).

Now, (A - A^T)^T = A^T - (A^T)^T = A^T - A

Therefore, if we negate A - A^T, we get:

-(A - A^T) = -A + A^T

And we see that (A - A^T)^T = -(A - A^T) holds true.

Thus, we have shown that A + A^T is symmetric, and A - A^T is skew symmetric for any nxn matrix A.

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Answer:

Step-by-step explanation:

The center of a circle is the midpoint of its diameter. The midpoint of the segment whose endpoints are (-2,5) and (4,7) is:

((-2 + 4)/2, (5 + 7)/2) = (1, 6)

Therefore, the center of the circle is (1, 6), and its radius is half the length of the diameter:

r = sqrt((4 - (-2))^2 + (7 - 5)^2)/2 = sqrt(40)/2 = sqrt(10)

The equation of a circle with center (h, k) and radius r is:

(x - h)^2 + (y - k)^2 = r^2

Substituting the values of (h, k, r) into the equation, we get:

(x - 1)^2 + (y - 6)^2 = 10

Therefore, the equation of the circle with the segment whose endpoints are (-2,5) and (4,7) as the diameter is:

(x - 1)^2 + (y - 6)^2 = 10

The slope of Line 1 is equal to 7.

The slope of Line 1 is equal to 1/7.

Line 1 and Line 2 are neither parallel nor perpendicular.

In Mathematics and Geometry, the slope of any straight line can be determined by using this mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

For line 1, we have the following:

Slope (m) = (32 - (-45))/(5 - (-6))

Slope (m) = (32 + 45)/(5 + 6)

Slope (m) = 77/11

Slope (m) = 7.

For line 2, we have the following:

Slope (m) = (43/7 - (-48/7))/(1 - 6)

Slope (m) = (-5/7)/(-5)

Slope (m) = 5/35

Slope (m) = 1/7

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer: A

Step-by-step explanation:

Answer:

Isosceles

Step-by-step explanation:

We are given a triangle. We know that the angles have a measure of 45°, 45°, and 90°.

We also know that the sides of the triangle are 3.2, 3.2, and 4.5 units.

We want to classify this triangle.

A scalene triangle has all of its sides and angles as different values.

An isosceles triangle has 2 of its sides as the same value, and 2 of its angles as the same value.

An equilateral triangle has all of its sides as the same value, and all of its angles as the same value.

Looking at the side lengths and angle values we are given, we can see that we have 2 angles that are the same value (45°), and 2 sides that are the same value (3.2 units).

Therefore, we have an isosceles triangle.

The permutations of four objects m, I, n, and k taken two at a time without repetition are: mn, mk, mi, nm, nk, ni, km, kn, ki, in, im, ik.

P is the total number of permutations, which is equal to 12.

The correct answer is OB, which lists all 12 permutations.

P2 is the number of permutations taken two at a time with repetition allowed. This means that we can repeat the same object in a permutation.

There are 16 possible permutations with repetition allowed: mm, ml, mn, mk, ll, ln, lk, nn, nk, kk, ii, ik, nn, ni, nk.

Therefore, P2 is equal to 16.

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Answer:

2

Step-by-step explanation:

Therefore, the solutions to the equation x² + 3x = 3 are x = -3/2 + √(21)/2 and x = -3/2 - √(21)/2.

An equation is a mathematical statement that shows the equality of two expressions. It usually consists of two sides separated by an equal sign (=). The expressions on both sides of the equal sign can include numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division.

Here,

To complete the square for the expression x² + 3x, we need to add and subtract (3/2)² = 9/4 inside the parentheses, as follows:

x² + 3x = x² + 3x + 9/4 - 9/4

= (x + 3/2)² - 9/4

Now the left-hand side can be written as:

(x + 3/2)² - 9/4 = 3

Adding 9/4 to both sides, we get:

(x + 3/2)² = 3 + 9/4

= 21/4

Taking the square root of both sides, we get:

x + 3/2 = ±√(21)/2

Subtracting 3/2 from both sides, we get the two solutions:

x = -3/2 ± √(21)/2

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The balance in the account after 5 years with quarterly compounding at a 3% annual interest rate, starting with an initial investment of $750, would be $859.43.

To calculate the balance in the account after 5 years with quarterly compounding at a 3% annual interest rate, we can use the formula for compound interest:

[tex]A = P (1 + r/n)^(^n^t^)[/tex]

where:

A is the final amount or balance in the account

P is the initial investment or principal amount

r is the annual interest rate expressed as a decimal (3% = 0.03)

n is the number of times the interest is compounded per year (4 for quarterly)

t is the time in years

Plugging in the given values, we get:

A = $750 (1 + 0.03/4)²⁰

= $750(1.0075)²⁰

=$750×1.161

=$870.75

Hence,  the balance in the account after 5 years with quarterly compounding at a 3% annual interest rate, starting with an initial investment of $750, would be $870.75

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The circumference of the gasket when in service is 6.4 cm, which is twice the original circumference of 3.2 cm, consistent with the scale factor of 2.

When we say that the rubber gasket expands by a scale factor of 2, we mean that all of its linear dimensions, such as its length, width, and circumference, double in size.

Let's focus on the circumference, which is the distance around the outside of a circle. The circumference of a circle is calculated using the formula:

Circumference = 2 x π x radius

In this case, we don't know the radius of the gasket, but we do know its circumference, which is given as 3.2 cm. We can rearrange the formula to solve for the radius:

radius = Circumference / (2 x π)

Plugging in the given circumference, we get:

radius = 3.2 cm / (2 x π) ≈ 0.509 cm

Now that we know the radius, we can calculate the circumference of the gasket when in service. Since the scale factor is 2, we know that the new radius will be:

new radius = old radius x scale factor = 0.509 cm x 2 = 1.018 cm

Using the same formula as before, but with the new radius, we get:

Circumference in service = 2 x π x new radius

Circumference in service = 2 x π x 1.018 cm ≈ 6.4 cm

Therefore, the circumference of the gasket when in service is 6.4 cm, which is twice the original circumference of 3.2 cm, consistent with the scale factor of 2.

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Answer:

Step-by-step explanation:

not for help but for points

So there are 6,442,752 different license plates that can be issued under these restrictions.

There are a few different restrictions to consider when calculating the number of possible license plates that can be issued. Let's break it down step by step:

The first symbol must be a letter: There are 24 letters to choose from (all except o and i).

The second symbol must be a digit: There are 8 digits to choose from (all except 0 and 1).

The final three symbols can be either letters or digits: For each of the final three symbols, there are 24 letters and 8 digits to choose from (the same restrictions as above).

All five symbols must be chosen: We can multiply the number of choices for each symbol together to get the total number of possible license plates:

24 (choices for first symbol) * 8 (choices for second symbol) * 32,768 (choices for final three symbols, since there are 32 choices for each of the final three symbols) = 6,442,752

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We can solve this problem by using the formula for the number of elements in the union of two sets:

n(A U B) = n(A) + n(B) - n(A ∩ B)

where n(A) represents the number of elements in set A, n(B) represents the number of elements in set B, and n(A ∩ B) represents the number of elements in the intersection of sets A and B.

In this case, we have:

n(A) = 250

n(B) = 250

n(A U B) = 500 - 20 = 480

Substituting these values into the formula, we get:

480 = 250 + 250 - n(A ∩ B)

Solving for n(A ∩ B), we get:

n(A ∩ B) = 250 + 250 - 480 = 20

So, the number of customers who regularly buy both products A and B is 20.

To find the number of customers who regularly buy only product A, we can subtract the number of customers who regularly buy both products A and B from the total number of customers who regularly buy product A:

n(A) - n(A ∩ B) = 250 - 20 = 230

Therefore, the number of customers who regularly buy only product A is 230.

The difference in the account balances at the end of the loan terms is given as follows:

$1,686.87.

The amount of money earned, in compound interest, after t years, is given by:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

In which:

The parameters for the offer 2 are given as follows:

P = 75000, r = 0.035, n = 12, t = 62/12.

Hence the balance of the offer 2 is given as follows:

B = 75000 x (1 + 0.035/12)^(12 x 62/12)

B = $89,842.51.

The balance of Offer 1 is of $91,529.38, hence the difference in the balances is given as follows:

91529.38 - 89842.51 = $1,686.87.

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The Area of R in terms of a is 288a.

first we need to understand what R represents. R is the region bounded by the x-axis, the graph of f(x), and the lines x=6 and x=-6. To find the area of R in terms of a, we need to integrate f(x) from -6 to 6.

∫f(x)dx = ∫a(36-x^2)dx = a∫(36-x^2)dx

To integrate (36-x^2), we can use the power rule: ∫x^n dx = (x^(n+1))/(n+1) + C, where C is the constant of integration. So:

a∫(36-x^2)dx = a(36x - (x^3)/3) + C

Now we need to evaluate the definite integral from -6 to 6:

Area of R = ∫(-6)^6 f(x)dx = a(36(6) - (6^3)/3) - a(36(-6) - ((-6)^3)/3)
= 432a - 432a/3
= 288a

Therefore, the area of R in terms of a is 288a.

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Answer:

51.84 gigabytes

Step-by-step explanation:

To determine whether the sequence is bounded, we can consider its behavior as n gets larger and larger. As n increases, 2^n grows exponentially, which means that a_n will also grow exponentially. However, no matter how large n gets, there will always be a constant term of 8 added to the result, which means that the sequence will never become unbounded. In other words, the sequence is both monotonic and bounded.

To determine the boundedness and monotonicity of the sequence a_n = 2^n + 8, n≥1, we can start by considering its first few terms:
a_1 = 2^1 + 8 = 10
a_2 = 2^2 + 8 = 12
a_3 = 2^3 + 8 = 16
a_4 = 2^4 + 8 = 24
From this, we can see that the sequence is increasing, as each term is larger than the one before it. This means that the sequence is monotonic.

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The Master Theorem is a powerful tool for solving divide-and-conquer recurrences. It provides a way to quickly determine the asymptotic behavior of algorithms by analyzing their running time.

Case 1 of the Master Theorem applies to algorithms that split the problem into smaller subproblems of equal size and combine their solutions in constant time. In this case, the running time can be expressed as T(n) = aT(n/b) + f(n), where a is the number of subproblems, b is the size of each subproblem, and f(n) is the time to combine the subproblem solutions. The solution to this recurrence is T(n) = Θ(nlogba) if f(n) = Θ(nlogka) for some constant k < log(ba).

Case 2 of the Master Theorem applies to algorithms that split the problem into smaller subproblems of equal size and combine their solutions in linear time. In this case, the running time can be expressed as T(n) = aT(n/b) + f(n), where a is the number of subproblems, b is the size of each subproblem, and f(n) is the time to combine the subproblem solutions. The solution to this recurrence is T(n) = Θ(nlogba logn) if f(n) = Θ(nlogba) .

If the recurrence cannot be expressed in either of these forms, then the Master Theorem does not apply. In this case, other techniques such as substitution or recursion trees may be used to solve the recurrence.

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If you said that fold f2 was a plunging fold, the direction of plunge is NorthEast. Option a is correct.

A plunging fold is a type of fold in which the fold axis has an inclined orientation with respect to the horizontal plane. When describing a plunging fold, the direction of plunge is important as it indicates the orientation of the axis.

In this case, it has been determined that fold f2 is a plunging fold and the direction of plunge is towards the northeast (NE). This means that the fold axis has an inclined orientation towards the NE direction. Understanding the direction of plunge is important for interpreting the deformation history of the rock formation and can also be useful in predicting the location of mineral deposits or hydrocarbons. Hence option a is correct.

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Answer:

To solve the Bernoulli equation t^2y' + 9ty − y^3 = 0, we use the substitution v = y^(1−2) = y^−1.

Differentiating v with respect to t, we get:

dv/dt = −y^−2 dy/dt

Using the chain rule, we have:

dy/dt = −y^2 dv/dt

Substituting y^−1 for v and −y^2 dv/dt for dy/dt, we get:

t^2 (−y^2 dv/dt) + 9t (1/y) y^2 − (1/v)^3 = 0

Simplifying and multiplying through by v^3, we get:

−t^2v^3 dv/dt − 9tv^2 + 1 = 0

This is now a separable differential equation. We can move the dv term to the left and the t term to the right, and then integrate both sides:

−v^−3 dv = 9t^−1 dt

Integrating both sides, we get:

v^−2/−2 = 9 ln|t| + C

Substituting v = y^−1, we get:

y^2/2 = (−1/2C) − 9 ln|t|

where C is the constant of integration.

Therefore, the solution to the given Bernoulli equation is:

y = [2/(−1/2C − 18 ln|t|)]^(1/2)

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Step-by-step explanation:

The likelihood of randomly selecting a chocolate chip cookie is (c) equally likely and unlikely

From the question, we have the following parameters that can be used in our computation:

P(chocolate chip) = 50%

When a probability is at 50% ot 0.5, then it means that

The probability is equally likely and unlikely

Hence, the true statement is (c) equally likely and unlikely

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The dimensions of the rectangle is D. 7 units by 6 units

Go 2 units to the right, and then 3 units up

5(d + 1) = 5d + 5 .

A vertex (plural: vertices) is a point where two or more lines, edges, or curves meet in a geometric shape. In graph theory, a vertex refers to a node in a graph, which can be connected to other vertices by edges.

For example, in a triangle, each of the three points where the sides of the triangle meet is a vertex. In a cube, each of the eight points where the edges of the cube meet is a vertex. In a graph, each point representing a person or object would be a vertex, and the connections between them would be edges.

The term vertex is commonly used in mathematics, geometry, computer science, and other fields where shapes or networks are analyzed and studied.

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