There is three-fourths of a shell pile left, and Terrence has sorted four-sixths of it.

How much of the shells did he sort?

A 12/24
B 16/18
C 12/16
D 7/10

Original Width: 10.5

Original Length: 12

Scaled Width: 3.5

Scaled Length: ?

We will be using x to find the unknown scale multiplier

3.5=10.5/x

Multiply both sides by x:

3.5•x=10.5/x•x

3.5x=10.5

Divide both sides by 3.5:

3.5x/3.5=10.5/3.5

x=3

12/3=4

Scaled Width: 3.5

Scaled Length: 4

3.5•4=14

Hope this helped!

The area of the scale model would be equal to 14.

The scale factor states the scale or measurement by which a figure is bigger or smaller than the other figure. The size by which the figure would be reduced or enlarged is called its scale factor.

Given that room is 12 feet long and 10.5 feet wide. A scale model of the room is 3.5 feet wide.

Using x to find the unknown scale multiplier

Solving for x:

3.5=10.5/x

Multiply both sides by x:

3.5•x=10.5/x•x

3.5x=10.5

x = 3

To determine the length, we need to divide the original length by 3:

12/3=4

The area of the scaled model is;

(Scaled Length x Scaled Width)

Scaled Width: 3.5

Scaled Length: 4

3.5(4)=14

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Answer:

4:22 6:33

Step-by-step explanation:

These two ratios simplify down to 2:11

Answer:

Step-by-step explanation: uhm maybe 4/3 idrk-

Answer:

$147

Step-by-step explanation:

When the angle between the vectors is small (close to 0 degrees), the resultant becomes larger, reaching its maximum value when the vectors are parallel. As the angle increases, the resultant decreases, reaching its minimum value when the vectors are perpendicular.

The resultant of two vectors is the vector sum of the individual vectors. When the angle between the vectors is small, the components of the vectors add up in the same direction, resulting in a larger resultant vector. As the angle increases, the components of the vectors start to oppose each other, reducing the magnitude of the resultant vector.

When the angle between the vectors reaches 90 degrees, the components become perpendicular to each other, and their contributions cancel out completely. In this case, the resultant vector has zero magnitude. As the angle continues to increase beyond 90 degrees, the components start to point in opposite directions, resulting in a negative resultant vector.

Therefore, as the angle between the vectors increases, the magnitude of the resultant vector decreases from its maximum value when the vectors are parallel to its minimum value when the vectors are perpendicular.

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There are 18 ways to distribute the pens and pencils among Harry and Ron, ensuring each of them receives at least three pens and two pencils.

To find the number of ways the pens and pencils can be distributed among Harry and Ron, ensuring that each of them receives at least three pens and two pencils, we can use combinatorics principles.

First, let's consider the distribution of pens. Since there are 8 different pens and each of them needs to receive at least 3 pens, there are 5 pens remaining to be distributed among the two of them.

We can think of this as distributing 5 identical pens into two distinct groups, with each group representing either Harry or Ron. This can be represented using the stars and bars method.

Using the stars and bars formula, the number of ways to distribute the pens is given by:

C(5 + 2 - 1, 2 - 1) = C(6, 1) = 6

Now let's consider the distribution of pencils. Similar to the pens, there are 6 different pencils and each of them needs to receive at least 2 pencils. Thus, there are 2 pencils remaining to be distributed among Harry and Ron. Again, we can think of this as distributing 2 identical pencils into two distinct groups.

Using the stars and bars formula, the number of ways to distribute the pencils is given by:

C(2 + 2 - 1, 2 - 1) = C(3, 1) = 3

To find the total number of ways to distribute both the pens and pencils, we multiply the number of ways to distribute the pens by the number of ways to distribute the pencils:

Total number of ways = 6 * 3 = 18

Therefore, there are 18 ways to distribute the pens and pencils among Harry and Ron, ensuring each of them receives at least three pens and two pencils.

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Expression with respect to t over the interval [0,1] to evaluate the line integral C F · dr along the given curve C.

To find a function f such that F = ∇f, we need to find the potential function of the vector field F(x, y).

Let's start by computing the partial derivatives of f with respect to x and y:

∂f/∂x = ∂/∂x (x²y³) = 2xy³

∂f/∂y = ∂/∂y (x³y²) = 3x³y²

Now, let's equate these partial derivatives with the components of the vector field F(x, y):

2xy³ = x²y³

3x³y² = x³y²

Simplifying these equations, we can see that they are satisfied when x = 1 and y ≠ 0. Therefore, we can choose the function f(x, y) = x²y³.

Now, let's move on to part (b) and evaluate C F · dr along the given curve C with derivatives.

The curve C is defined as r(t) = (t⁵ - 2t, t⁵  + 2t), where 0 ≤ t ≤ 1.

To evaluate the line integral, we need to express F in terms of t and differentiate r(t) with respect to t to obtain dr/dt.

F(x, y) = x²y³i + x³y²j = (t⁵  - 2t)²(t⁵  + 2t)³i + (t⁵  - 2t)³(t⁵  + 2t)²j

dr/dt = (∂x/∂t)i + (∂y/∂t)j = (5t⁴  - 2)(t⁵  + 2t)i + (5t⁴  + 2)(t⁵ + 2t)j

Now, we can evaluate C F · dr by substituting the values:

C F · dr = ∫[0,1] (F · dr)

= ∫[0,1] [(F · dr)/dt] dt

= ∫[0,1] [(F(r(t)) · dr/dt)] dt

Substituting the values of F and dr/dt, we have:

C F · dr = ∫[0,1] [((t⁵  - 2t)²(t⁵  + 2t)³)((5t⁴  - 2)(t⁵  + 2t) + (5t⁴ + 2)(t⁵  + 2t))] dt

You can now integrate the above expression with respect to t over the interval [0,1] to evaluate the line integral C F · dr along the given curve C.

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Answer:

Colombian coffee bought = 0.5 lbs

French roast coffee beans bought = 0.5 lbs

Step-by-step explanation:

Let Colombian coffee bought = \(x\) lbs

Total weight of mixture bought = 1 lbs

Therefore, French roast coffee beans bought = (1 - \(x\)) lbs

Price of 1 lb Colombian coffee = $4.25

Price of \(x\) lbs of Colombian coffee = $\(4.25x\)

Price of 1 lb French roast coffee beans = $3.75

Price of (1 - \(x\)) lbs French roast coffee beans = $3.75(1 - \(x\))

It is given that total money spent is $4.

As per given statement:

\(4.25x+3.75(1-x)=4\\\Rightarrow 0.50x=0.25\\\Rightarrow x=\bold{0.5\ lbs}\)

Colombian coffee bought = 0.5 lbs

French roast coffee beans bought = 0.5 lbs

The breadth of the rectangular park is 40 metres.

The area of a square Park and a rectangular park is the same. The side length of the square Park is 60m and the length of the rectangular park is 90m.

Therefore,

area of the square park = l²

area of the square park = 60²

area of the square park = 3600 m²

Hence,

area of the rectangular park = lb

3600 = 90b

divide both sides by 90

b = 3600 / 90

b = 40

Therefore,

breadth of the rectangular park = 40 m

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Since you go to school for 5 days a week, the answer is going to be 550.25 for 15.5 weeks.

Hope that helped?

Answer:

15.5 weeks of school lunch would cost $550.25

Step-by-step explanation:

The unit rate is already given here, so all you need to do here is multiply the cost per week by the number of weeks. You can even think of it as canceling out the weeks:

\(\frac{cost}{week}\times week=cost\)

\(35.50\times15.5=550.25\)

15.5 weeks of school lunch would cost $550.25

You could also write this as a linear equation with a slope of 35.5 and a y-intercept of 0:

\(y=35.50x\)

The amount of fluid that a person should drink per day can vary depending on factors such as their age, sex, weight, activity level, and climate.

The Institute of Medicine recommends that men should consume about 3.7 liters (125 ounces) of fluid per day, while women should consume about 2.7 liters (91 ounces) of fluid per day. This includes fluid from all sources, including water, other beverages, and food.

It is important to note that individual fluid needs may vary and may be influenced by factors such as health conditions, medications, and pregnancy or breastfeeding. It is always a good idea to consult with a healthcare professional to determine the appropriate amount of fluid intake for your specific needs.

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A client's daily fluid intake should be around 3,700 ml for men and 2,700 ml for women, keeping in mind that individual needs may vary.

Remember to round to the nearest whole number if necessary.

As a concise answer bot, I cannot provide a 200-word response.

How many ml of fluid a client should drink per day, we need to consider general guidelines for daily fluid intake.
The general recommendation for daily fluid intake is approximately:
- For men: 3,700 ml (about 13 cups)
- For women: 2,700 ml (about 9 cups)
These amounts include fluids from all sources, such as water, beverages, and food.

Please note that individual needs may vary depending on factors such as age, activity level, and climate.

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The answer you are looking for is C

Answer:

260 is the number in hindu/arabic

Answer:

CCLX=100+100+50+10

=260

Step-by-step explanation:

Answer:

See explanation

Step-by-step explanation:

( unit 1 ) multiplied by ( unit 2 )

(5.9*10^12) multiplied by 8.9
52.51*10^12 or 5.251*10^13 or 52,510,000,000,000

If a hypothesis test is conducted to see if there is evidence that the average wait time is 5 minutes, the p-value is 0.040.

To calculate the p-value for the hypothesis test, we need to perform the following steps:

Step 1: State the null and alternative hypotheses.

In this case, the null hypothesis (H0) is that the average wait time for customers during the lunch hour is 5 minutes. The alternative hypothesis (Ha) is that the average wait time is not 5 minutes.

Step 2: Determine the test statistic.

We can use a t-test since we do not know the population standard deviation. We calculate the t-value using the formula:

t = (x' - μ) / (s / √n)

where x' is the sample mean, μ is the population mean (5 minutes), s is the sample standard deviation, and n is the sample size (15).

Step 3: Calculate the p-value.

We can use a t-distribution table or software to find the p-value associated with our calculated t-value. Alternatively, we can use the t-test function in Excel or other statistical software to calculate the p-value directly.

Assuming a two-tailed test and a significance level of 0.05, if the p-value is less than 0.05, we reject the null hypothesis in favor of the alternative hypothesis. If the p-value is greater than 0.05, we fail to reject the null hypothesis.

Suppose the sample mean is 6.2 minutes, the sample standard deviation is 1.3 minutes, and the sample size is 15. Then the t-value is:

t = (6.2 - 5) / (1.3 / √15) = 2.22

Using a t-distribution table or software with 14 degrees of freedom (15 - 1), we find the p-value to be approximately 0.040, which is less than 0.05. Therefore, we reject the null hypothesis and conclude that there is evidence to suggest that the average wait time for customers during the lunch hour is not 5 minutes.

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Answer:

Exact form:

25/9

Decimal form:

2.(7)

Mixed fraction form:

2 7/9

Step-by-step explanation:

Hope you found this helpful

Answer:

(-5/3)² = 25/9

Step-by-step explanation:

(a/b)ⁿ = aⁿ / bⁿ

(-5/3)² = -5² / 3² = 25 / 9

The `det(E2) of the given matrix is equal to 366`.

Given a 5 by 5 matrix E= `[11 2 -1 -3 4;10 -1 -2 -1 -2;-1 2 3 2 1;1 1 1 -1 -1;2 -1 -2 1 1]`.

To find `det(E)`, we can use the following steps.

Step 1: Create a 5 by 5 matrix E1 by adding a multiple of the ith row to the jth row, given i = 3 and j = 5.

We need to add -1/3 times the 3rd row to the 5th row. It can be done by the following operation.`E1 = E` (start with the original matrix) `=> E1(5,:) = E(5,:) - E(3,:) / 3` (subtract the 3rd row of E divided by 3 from the 5th row of E)

This results in the matrix `E1 = [11 2 -1 -3 4;10 -1 -2 -1 -2;-1 2 3 2 1;1 1 1 -1 -1;1/3 -7/3 -7/3 7/3 4/3]

`Step 2: Create a 5 by 5 matrix E2 by adding a multiple of the ith row to the jth row, given i = 2 and j = 5.We need to add -20 times the 2nd row to the 5th row.

It can be done by the following operation.`E2 = E1` (start with the matrix from Step 1) `=> E2(5,:) = E1(5,:) - 20 * E1(2,:)` (subtract 20 times the 2nd row of E1 from the 5th row of E1)

This results in the matrix `E2 = [11 2 -1 -3 4;10 -1 -2 -1 -2;-1 2 3 2 1;1 1 1 -1 -1;0 -13 33 -13 44]

`Step 3: Find det(E2) by using the cofactor expansion along the 5th column.`det(E2) = 0 - (-13) * A1 + 33 * A2 - (-13) * A3 + 44 * A4 - 0 * A5`where A1, A2, A3, A4, and A5 are the 2 by 2 determinants of the submatrices obtained by deleting the 5th row and the ith column, for i = 1, 2, 3, 4, and 5. We can use the following notation.

A1 = det([11 -1 -3 4;10 -2 -1 -2;-1 3 2 1;]) = 324A2 = det([11 2 -3 4;10 -1 -1 -2;-1 2 2 1;]) = -54A3 = det([11 2 -1 4;10 -1 -2 -2;-1 2 3 1;]) = -142A4 = det([11 2 -1 -3;10 -1 -2 -1;-1 2 3 2;]) = 50A5 = det([11 2 -1 -3;10 -1 -2 -1;-1 2 3 2;]) = 366.

Therefore `det(E2) = 0 - (-13) * 324 + 33 * (-54) - (-13) * (-142) + 44 * 50 - 0 * 50 = 366`.

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Answer:

\(\frac{1}{8}\)

Step-by-step explanation:

12 \(\frac{1}{2}\)%

= \(\frac{12\frac{1}{2} }{100}\) ← multiply numerator and denominator by 2

= \(\frac{25}{200}\) ← divide numerator and denominator by 25

= \(\frac{1}{8}\)

As given by the question

There are given that the numbers;

Now,

First make a table of numbers and their frequency.

So,

Now,

From the dot plot of the given numbers and their frequency.

So,

The dot plot of the given number is shown below:

Let's assume the first odd integer is x. Since the next odd integer would be consecutive, we can represent it as x + 2.

According to the problem, the product of these two consecutive odd integers is 399:

x * (x + 2) = 399

Expanding the equation:

x^2 + 2x = 399

Rearranging the equation into a quadratic form:

x^2 + 2x - 399 = 0

To solve this quadratic equation, we can either factor it or use the quadratic formula. Let's use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, a = 1, b = 2, and c = -399.

x = (-2 ± √(2^2 - 4 * 1 * -399)) / (2 * 1)

Simplifying:

x = (-2 ± √(4 + 1596)) / 2

x = (-2 ± √1600) / 2

x = (-2 ± 40) / 2

Now, we can calculate the two possible values for x:

x = (-2 + 40) / 2 = 38 / 2 = 19

x = (-2 - 40) / 2 = -42 / 2 = -21

Since we are looking for consecutive odd integers, we take the positive value of x, which is 19. The next consecutive odd integer would be 19 + 2 = 21.

Therefore, the two consecutive odd integers whose product is 399 are 19 and 21.

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To Prove:-

JK=IJ

JK= ½IK = IJ= ½IK

JK= IJ(Equal Distance)

GK//HI (Parallel)

Therefore, JK congruent IJ

Hope This Helps

\( {(7 + \sqrt{6}) }^{2} = {7}^{2} + 2 \times (7 )\times (\sqrt{6} ) + { (\sqrt{6} )}^{2} \\ \)

\(( {7 + \sqrt{6} })^{2} = 49 + 14 \sqrt{6} + 6\)

\( {(7 + \sqrt{6}) }^{2} = 55 + 14 \sqrt{6} \)

Answer:

\(\frac{11\pi }{18}\) radians

Step-by-step explanation:

to convert from degrees to radians

radians = degrees × \(\frac{\pi }{180}\)

then for 110°

radians = 110° × \(\frac{\pi }{180}\) = 11 × \(\frac{\pi }{18}\) = \(\frac{11\pi }{18}\)

The angle with a measure of 110 degrees is approximately 1.92 radians.

What is an angle?

An angle is a figure in Euclidean geometry created by two rays, called the sides of the angle, that share a common termination, called the vertex of the angle. Angles created by two rays are also known as plane angles because they lie in the plane in which the rays are located.

Here, we have

Given: Recall that an angle making a full rotation measures 360 degrees or 2 radians. If an angle has a measure of 110 degrees.

We have to find the measure of that angle in radians.

To convert an angle of 110 degrees to radians, we can use the following conversion factor:

1 radian = 180 degrees / π radians.

So, to find the measure of the 110-degree angle in radians, we can use this formula:

radians = (110 degrees) * (π radians / 180 degrees)

radians = (110 * π) / 180

radians ≈ 1.92 radians

Hence, The angle with a measure of 110 degrees is approximately 1.92 radians.

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Answer:

The sine of the opposite angle

Answer:

12.570 meters

Step-by-step explanation:

Answer:

number = 24

Step-by-step explanation:

3 x 8 = 24

24 / 3 = 8

Answer:

(0,-3)

Step-by-step explanation:

Step-by-step explanation:

e=42°

f=90°+42

f=132

g+e+f=180°

g+42+132=180

g=180-174

g=6

use sin

sin(50) = x/6

sin(50) x 6 = x

x = ~4.5963

Replace x with 180:

3(180)/10 =

540/10 =

54

Answer : 54

Answer:

54

Step-by-step explanation:

x = 18

Evaluate:

3 x / 10

put the value of x

3 × 180 / 10

540 / 10

54