When designing a new school cafeteria, the school administrators planned for there to be twice as many tables in each row as there are rows. After increasing the size of the cafeteria, it was decided to add 3 more rows of tables and to increase the original number of tables in each row by 2. The maximum number of tables the cafeteria can hold is 126.

If r represents the original number of rows the school administrators planned to have in the cafeteria, which of the following represents this situation?

A.
2r2 + 7r + 6 ≤ 126
B.
2r2 + 8r + 6 ≥ 126
C.
2r2 + 7r + 6 ≥ 126
D.
2r2 + 8r + 6 ≤ 126

Answer:

635 kg

Step-by-step explanation:

1 pounds = 0.453592 kg

1400 = 0.453592 x 1400

=635.0288

=635 kg

Possible options:

uppercase letter: 26

lowercase letter: 26

number: 10

upper or lowercase letter: 50

Note: I'm interpreting the "no upper or lower case letters can be repeated in the sequence" to mean you could have Aa0b, where A is used as the uppercase and a is used as the lower case letter, but then you can't use A or a for the last character.

26 · 26 · 10 · 50 = 338,000 combinations

Now is using "A" and "a" isn't allowed, then you have:

Possible options:

uppercase letter: 26

lowercase letter: 25

number: 10

upper or lowercase letter: 48

26 · 25 · 10 · 48 = 312,000 combinations

Answer:

Factors of 2020 are 1, 2, 4, 5, 10, 20, 101, 202, 404, 505, 1010. There are 11 integers that are factors of 2020. The biggest factor of 2020 is 1010.

There are 10, 20, 202, 404, 505, and 1010  factors of 2020 have more than 3 factors.

Factorization is expressing a mathematical quantity in terms of multiples of smaller units of similar quantities.

For an integer, factorization is decomposition of that integer in terms of smaller integers which when multiplied with each other give back that considered number. Those composing integers are called factors of that considered integers.

Also Prime factorization is when all those factors are prime numbers.

Thus, this factorization expresses an integer in terms of multiples of prime numbers.

Factors of 2020 are;

1, 2, 4, 5, 10, 20, 101, 202, 404, 505, 1010.

There are 11 integers that are factors of 2020.

We can see that the biggest factor of 2020 is 1010.

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Answer:

20/27

Step-by-step explanation:

Answer:

x=9.3

Step-by-step explanation:

use SohCahToa

in this case u use cos

cos(41°)=7/x

x=7/cos(41)

x=9.275090953

x=9.3

Answer:

Step-by-step explanation:

Let x represent the number of weeks

Let y represent the number of days in a week!

Moving downstream (with the current), the boat moves at a rate of (252 mi)/(12 h) = 21 mph. Upstream (against the current), it moves at a rate of (252 mi)/(84 h) = 3 mph.

When traveling downstream, the boat's speed is the sum of its own speed in still water and the speed of the current. It's the same going upstream, but the boat and current move in opposite directions. Let b and c denote these speeds, respectively. Then

downstream: b + c = 21 mph

upstream:      b - c = 3 mph

Adding these equations eliminates c and lets us solve for b :

(b + c) + (b - c) = 21 mph + 3 mph

2b = 24 mph

b = 12 mph

Now solve for c :

12 mph + c = 21 mph

c = 9 mph

Answer:

E. \( \purple { \bold{ \frac{2}{3} ( \frac{x - 1}{x} ) \sqrt{\frac{x - 1}{x} } + c }}\)

Step-by-step explanation:

\( \int \sqrt{ \frac{x - 1}{ {x}^{5} } } dx \\ \\ = \int \sqrt{ \frac{x - 1}{ {x}^{4} .x} } dx \\ \\ = \int \frac{1}{ {x}^{2}}\sqrt{ \frac{x - 1}{ x} } dx \\ \\ = \int \frac{1}{ {x}^{2}}\sqrt{ 1 - \frac{1}{ x} } dx \\ \\ let \: 1 - \frac{1}{ x} = t \\ \\ \implies \: \frac{1}{ {x}^{2} } dx = dt \\ \\ \implies \int \frac{1}{ {x}^{2}}\sqrt{ 1 - \frac{1}{ x} } dx = \int \sqrt{t} dt \\ \\ = \int {t}^{ \frac{1}{2} } dt \\ \\ = \frac{t ^{ \frac{3}{2} } }{ \frac{3}{2} } + c \\ \\ = \frac{2}{3} t ^{ \frac{3}{2} } + c \\ \\ = \frac{2}{3} \sqrt{ {t}^{3} } + c \\ \\ = \frac{2}{3} t\sqrt{ {t} } + c \\ \\ = \frac{2}{3} (1 - \frac{1}{x} ) \sqrt{1 - \frac{1}{x} } + c \\ \\ \red{ \bold{= \frac{2}{3} ( \frac{x - 1}{x} ) \sqrt{\frac{x - 1}{x} } + c }}\\ \\ \)

16250 many different three-letter words—including nonsense words—have different letters in the next position.

Given that,

We have to find how many different three-letter words—including nonsense words—have different letters in the next position.

We know that,

The number of alphabets are 26

First letter has 26 choices.

Second letter can not be same has first letter so 25 choices.

Third letter can not be same has second letter so 25 choices.

So,

Total words = 26×25×25=16250

Therefore, 16250 many different three-letter words—including nonsense words—have different letters in the next position.

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Answer:

5^(x-3)+4

Step-by-step explanation:

Left and right translations are applied directly to the x variable, whereas up and down translations are applied to the entire equation.

The transformed function is g(x) = 5⁽ˣ⁻³⁾ + 4.

Let the functions f(x) and g(x) are two real functions.

And g (x) = f (x) + k, where k is real numbers.

The function can be sketched by shifting f (x), k units vertically.

The direction of shift can be found by the value of k:

if k > 0, the base graph shifts k units up, and

if k < 0, the base graph shifts k units down.

The function provided by the basic function f(x) and the constant

g(x) = f(x - k),

may be drawn by horizontally moving the f(x) k unit coordinates.

The shift's direction depends on the value of k. Specifically,

The base graph moves k units to the right if k > 0, and

The base graph moves k units to the left if k < 0.

Given:

The graph of g is a translation 4 units up and 3 units right of the graph of f(x) = 5ˣ.

By the definition:

The translation 4 units up,

g(x) = 5ˣ + 4.

And the translation 3 units right,

g(x) = 5⁽ˣ⁻³⁾ + 4.

Therefore, g(x) = 5⁽ˣ⁻³⁾ + 4.

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Part A: An open circle on a number line represents an excluded value, indicating that the endpoint is not included in the solution set of the inequality. It is used when the inequality includes the symbols < (less than) or > (greater than), which denote strict inequality.

Part B: A closed circle on a number line represents an included value, indicating that the endpoint is part of the solution set of the inequality. It is used when the inequality includes the symbols ≤ (less than or equal to) or ≥ (greater than or equal to), which denote inclusive inequality.

Part C: The shading on the number line represents the range of values that satisfy the given inequality. It indicates which values make the inequality true. Typically, the shading is done to the right or left of the circle(s) depending on whether the inequality is greater than or less than.

Part A:

For example, if we have the inequality x > 2, we would represent it with an open circle at 2 on the number line. This means that 2 itself is not a valid solution, but any value greater than 2 is included.

Part B:

For example, if we have the inequality x ≥ -3, we would represent it with a closed circle at -3 on the number line. This means that -3 itself is a valid solution, as well as any value greater than or equal to -3.

Part C:

For example, if we have the inequality x > 2, we would shade the portion of the number line to the right of the open circle at 2. The shaded region represents all the values greater than 2 that satisfy the inequality. The shading visually illustrates the solution set and helps identify the range of valid values for the variable in the given inequality.

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Answer:

its the 2nd one

hope that helps<3

Answer:

jhkkkhj

Step-by-step explanation:

jkjkjkjkj

Answer:

If real GDP in a particular year is $80 billion and nominal GDP is $240 billion, the GDP price index for that year is: 300.

Step-by-step explanation:

Answer:

Enjoy.

Step-by-step explanation:

school

Answer:

Step-by-step explanation:

In order to simplify and verify trig identities, one needs to use the rules of trigonometry and algebra to manipulate the equation until it is in a simplified form.

The most common trig identities to remember include the Pythagorean identity, reciprocal identities, quotient identities, and sum and difference identities. When simplifying an equation, it is important to remember to include the negative sign when necessary and to factor out any common factors.

After simplifying, it is important to verify the equation. This can be done by plugging in known values for the variables and verifying that the equation is true. By utilizing the rules of trigonometry and algebra, one can simplify and verify trig identities. This process is essential for working with trigonometric functions.

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I think it's 67 different ways ! ^^

Answer:

67 words can be made from the letters in the word steal.

Step-by-step explanation:

The value of the angles are;

1. x = 5

2.RT = x + 5

3.M = 2x - 5

4.Y = 3x - 30

5.A = 3x - 38

6.T = 4x -38

7.G = -x - 38

We need to know the following;

From the information given, we have'

1, 5x + 1 + 124 = 180

collect the like terms, we get;

5x = 180 - 125

5x = 55

Divide by the coefficient

x = 5

2. the diagonals of a rectangle are equal

RT = QS

QS = 2(5) - 5 = 10 - 5 = 5

RT = x + 5

3. 18x - 19 + x - 3 = 180

collect like terms

M = x + x - 5 = 2x - 5

4. 2x- 5 - x - 25

collect like terms

Y = 3x - 30

5. x - 8

(3x - 8) - 30

expand the bracket

A = 3x - 38

6. T = 7x - 3x - 38

collect like terms

T = 4x -38

7. G = 3x - 4x - 38

G = -x - 38

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Answer:

20

Step-by-step explanation:

19,20,21

the second even number is 20

19+21=40

The transformation rule that describes the rotation from the original parallelogram ABCD to the image parallelogram A'B'C'D' is (x, y) → (–y, x).

The rule that describes the transformation from the original parallelogram ABCD to the image parallelogram A'B'C'D' is (x, y) → (–y, x).

To understand this, let's apply the transformation rule to each vertex of the original parallelogram ABCD:

Point A (2, 5) becomes A' (-5, 2).

Point B (5, 4) becomes B' (-4, 5).

Point C (5, 2) becomes C' (-2, 5).

Point D (2, 3) becomes D' (-3, 2).

By applying the transformation rule, we observe that the x-coordinate of each point becomes the negative of the original y-coordinate, and the y-coordinate becomes the original x-coordinate.

This transformation is a 90-degree counterclockwise rotation about the origin (0, 0) on the coordinate plane. The image parallelogram A'B'C'D' is obtained by rotating the original parallelogram ABCD by 90 degrees counterclockwise.

Visually, this transformation can be seen as the original parallelogram being rotated around the origin, where the x-axis becomes the y-axis, and the y-axis becomes the negative x-axis.

Therefore, the transformation rule that describes the rotation from the original parallelogram ABCD to the image parallelogram A'B'C'D' is (x, y) → (–y, x).

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Answer:

£10.80

Step-by-step explanation:

20% = \(\frac{20}{100}\) = 0.2 , then

£54 × 0.2 = £10.80

Answer:

No.  In order to be equivalent, the 5/12 should be 6/12.

Step-by-step explanation:

Answer:

No, it's not the same ratio

Step-by-step explanation:

No, it's not the same ratio

5 : 12 = 0.41

1 : 2 = 0.5

Answer:

x = 4

Step-by-step explanation:

assuming you require to find the value of x

Δ ADE and Δ ACB are similar ( by the AA postulate )

then the ratios of corresponding sides are in proportion, that is

\(\frac{AD}{AC}\) = \(\frac{AE}{AB}\) ( substitute values )

\(\frac{x}{x+x-2}\) = \(\frac{x+2}{x+2+x -1}\)

\(\frac{x}{2x-2}\) = \(\frac{x+2}{2x+1}\) ( cross- multiply )

(2x - 2)(x + 2) = x(2x + 1) ← expand left side using FOIL

2x² + 2x - 4 = 2x² + x ( subtract 2x² + x from both sides )

x - 4 = 0 ( add 4 to both sides )

x = 4

Answer:

60m tall

Step-by-step explanation:

Since this is a ratio problem and we are given 3 values and 1 unknown then we can use the Rule of Three to calculate the height of the tower which we will refer to as x. The Rule of Three simply multiplies the diagonal values and divides by the third value in order to get the missing unknown like so...

12m height  <======>  8m shadow

x   height   <======>  40m shadow

(40m * 12m) / 8m = 60m height

Finally, we can see that the height of the tower is 60m tall.

Answer:

19.71

Step-by-step explanation:

You would add the two values (-5.29) and 25 together

The firm should hire workers until the MRP of the last worker hired equals the wage rate.

Based on the information given in Figure 18-1, we can see that the profit maximizing level of employment for the firm is where the marginal revenue product (MRP) equals the wage rate (MPL x P = w). At a selling price of $12 per unit and a wage rate of $700 per week, the MRP is $60. Therefore, the firm will hire workers up to the point where the MRP equals $60, which occurs at 4 workers (as shown in the graph). Thus, the answer is c.4. The firm will hire 4 workers to maximize its profit. Word count: 100 words. To determine the number of workers a firm will hire to maximize its profit, we need to analyze the marginal revenue product (MRP) of labor. MRP is calculated by multiplying the marginal product of labor (MPL) by the price of output. In this case, the output price is $12 per unit, and the wage rate is $700 per week. The firm should hire workers until the MRP of the last worker hired equals the wage rate.

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Answer:

The slope is 4.

Step-by-step explanation:

We are given that f(0)=-5 and f(4)=11.

This means that we have the two points (0, -5) and (4, 11).

So, we can use the slope formula:

\(m=\frac{y_2-y_1}{x_2-x_1}\)

Let (0, -5) be (x₁, y₁) and let (4, 11) be (x₂, y₂). Substitute appropriately:

\(m=\frac{11-(-5)}{4-0}\)

Evaluate:

\(m=\frac{16}{4}=4\)

Hence, the slope of the line given f(0)=-5 and f(4)=11 is 4.

The amount of KES that one would have to get for R150 is given as 1053.54 KES

​The KES tells us of the Kenyan currency. That is the Kenyan shillings. The R is the name that is used to refer to the Rands

Hence we would have to convert rands to KES

1 south African Rand is given as 7.0236

then 150 rand would be = ?

Hence the amount you would get of KES is: 7.0236 * 150

= 1053.54 KES

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The probability that the store was not busy given you did not work late is approximately 0.8083 or 80.83%.

To find the probability that the store was not busy given you did not work late, we can use Bayes' theorem.

1. Let A be the event "store is not busy" and B be the event "did not work late".
2. We are given P(A') = 0.56, where A' is the event "store is busy". So, P(A) = 1 - P(A') = 1 - 0.56 = 0.44.
3. We are also given P(B'|A') = 0.84, where B' is the event "worked late". So, P(B|A') = 1 - P(B'|A') = 1 - 0.84 = 0.16.
4. Additionally, we are given P(B'|A) = 0.14. So, P(B|A) = 1 - P(B'|A) = 1 - 0.14 = 0.86.

Now we can apply Bayes' theorem to find P(A|B):

P(A|B) = (P(B|A) * P(A)) / (P(B|A) * P(A) + P(B|A') * P(A'))

P(A|B) = (0.86 * 0.44) / (0.86 * 0.44 + 0.16 * 0.56)
P(A|B) = (0.3784) / (0.3784 + 0.0896)
P(A|B) = 0.3784 / 0.468

P(A|B) = 0.8083

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The resulting expression is: 6(-0.5x - 2) + 3. to find g(f(x)), we substitute f(x) into g(x). Since f(x) is -0.5x - 2, we replace x in g(x) with -0.5x - 2. Simplifying the expression, we get -3x - 12 + 3, which further simplifies to -3x - 9. Therefore, g(f(x)) is equal to -3x - 9.

To understand the expression g(f(x)), we need to evaluate g(x) after substituting f(x) into it.

Starting with f(x) = -0.5x - 2, we replace x in g(x) with -0.5x - 2. This gives us g(f(x)) = g(-0.5x - 2).

Now, let's evaluate g(x) = 6x + 3 using the substituted value. We replace x in g(x) with -0.5x - 2, giving us g(f(x)) = 6(-0.5x - 2) + 3.

Simplifying further, we distribute the 6 to both terms inside the parentheses: g(f(x)) = -3x - 12 + 3. Combining like terms, we have g(f(x)) = -3x - 9. therefore, the resulting expression for g(f(x)) is -3x - 9.

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