half as big as last night’s crowd ( c = size of last night’s crowd )
verbal expression to algebraic expression

Answer:

6

Step-by-step explanation:

7 1/3 ÷ 1 2/9

7 1/3 = 22/3

1 2/9 = 11/9

22/3 ÷ 11/9

= 22/3 x 9/11

= 198/33

= 66/11

= 6

In 3 years, Aubrey will be able to spend $106.08 on a new bicycle.

First we can use the formula for compound interest:

A = P * (1 + r/n)^(nt)

Where:

A = final amount (balance)

P = principal (starting amount) = $100.00

r = interest rate as a decimal = 2% = 0.02

n = number of times per year that the interest is compounded = 1 (annually)

t = time in years = 3

Plugging in these values, we get:

A = $100.00 * (1 + 0.02/1)^(1 * 3)

A = $100.00 * (1.02)^3

A = $100.00 * 1.0608

A = $106.08

Therefore, in 3 years, Aubrey will be able to spend $106.08 on a new bicycle.

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Answer:

Step-by-step explanation:

Let us consider the Ginger to be x years old.

Therefore, her grandmother will be 10x years old(10 times Ginger's age)

So,

10x+x=66

(adding both Ginger and her grandmother's age)

11x=66

(adding x and 10x)

x=66/11

x=6

Ginger's age is 6.

Her grandmother is 10 times her age.

Therefore she is 60 years old.

Answer:

6x - 5 = 6x - 5

Step-by-step explanation:

If we have the same quantity on both sides of the equation, then the equation becomes an identity — an equation that is true for any value of the present variables.

If we set 6x - 5 equal to 6x - 5, then there are infinite solutions.

For example,

when x is 3:

6(3) - 5 = 6(3) - 5

18 - 5 = 18 - 5

13 = 13 ✔

when x is 5:

6(5) - 5 = 6(5) - 5

30 - 5 = 30 - 5

25 = 25 ✔

Measure of angle V is 103°.

Polygons are closed figures which has at least three set of line segments joined together.

The polygon with least number of sides is triangle.

Here is a six sided polygon, which is hexagon.

Sum of interior angles of a polygon = (n - 2) 180, where n is the number of sides of the polygon.

Sum of the interior angles of the given polygon = (6 - 2) 180 = 720

So,

∠S + ∠T + ∠U + ∠V + ∠W + ∠X = 720°

90° + (9x - 19)° + 111° + (5x + 8)° + 128° + (7x + 3)° = 720°

9x + 5x + 7x + 90 - 19 + 111 + 8 + 128 + 3 = 720

21x + 321 = 720

21x = 399

x = 19

∠V = (5 × 19) + 8 = 103°

Hence the angle V is of measure 103°.

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Step-by-step explanation:

Let n= The first number

Let x= The second number

(5n-7)+9x

This is if the number are different numbers.

If they are the same:

Let n= a number

(5n-7)+9n=

7n-7

Answer: please look at the image for the answer

Step-by-step explanation:

The solution set for the given inequality is {6, 7, 8, 9, 10,.....}.

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

The given inequality is -1/2(8x-32)< -4

Multiply by -2 on both the sides of an inequality, we get

(8x-32)>8

Add 32 on both the sides of an inequality, we get

8x>40

Divide 8 on both the sides of an inequality, we get

x>5

So, solution set is {6, 7, 8, 9, 10,.....}

Therefore, the solution set for the given inequality is {6, 7, 8, 9, 10,.....}.

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Acid rain is the acidic rain that produce due to the mixture of sulhuric and nitric acid with rain water. The problem is solved by using renewable resources that reduces the pollution and the emission of acidic pollutants.

Acid rain, or acid deposition, is a broad term that includes any form of precipitation with acidic components, such as sulfuric or nitric acid that fall to the ground from the atmosphere in wet or dry forms. This can include rain, snow, fog, hail or even dust that is acidic.

A great way to reduce acid rain is to produce energy without using fossil fuels. Instead, people can use renewable energy sources, such as solar and wind power.

Renewable energy sources help reduce acid rain because they produce much less pollution.

Filter and detoxify the water used by the factories before returning it to the rivers.

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Note that the area of the smaller square will be depicted by: 20inches.

Area of the larger square  - Area of the 4 Right Angled Triangles

Since the Area of the larger square  = is 36inches; and

Area of the one of the  Right Angled Triangles = 4inches

Thus, the Boxes will be completed as follows;


[36in] - (4) [4] or [20in]

Since

36 - 16 = 20 inches.

Note that a square is a closed two-dimensional form having four equal sides and four vertices. Its opposing sides are perpendicular to one other. A square can alternatively be thought of as a rectangle with equal length and width.

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The ratio of the height of the triangle to the side of the square is 6.

A triangle is a three-sided polygon with three vertices and three angles. Triangles can have different shapes and sizes, including equilateral, isosceles, and scalene triangles.

Let's call the side of the square x. Since the base of the triangle is equal to the side of the square, we can use x for both. The area of the square can then be found by x² and the area of the triangle can be found by (x)(h)/2, where h is the height of the triangle.

We know that the area of the square is one-third the area of the triangle, so we can set up an equation:

x² = (1/3)(x)(h)/2

Expanding the right side of the equation:

x² = (1/3)(xh)/2

Now we can isolate the height of the triangle by multiplying both sides by 6 and dividing by x:

6x² = (xh)

Finally, we can divide both sides by x to find the ratio of the height of the triangle to the side of the square:

6x = h

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Answer:

In a sense, negative numbers could be related to decimals because place values of decimal digits involve taking 10 to negative powers. However, negative numbers do not have to be decimals (for example, -3) and decimals do not have to be negative numbers (for example, 0.2).

Answer:

23456trrytugfygtuh

Step-by-step explanation:

Cronbach's alpha calculates the internal consistency of a set of variables or items in a questionnaire or test, indicating how reliably they measure the same construct.

Cronbach's alpha is a measure of reliability used in psychometrics to assess the consistency or homogeneity of a set of items in a questionnaire or test designed to measure a specific construct or trait. It calculates the degree of correlation among the items and indicates the extent to which they measure the same underlying concept. A high alpha value (usually ranging from 0 to 1) indicates strong internal consistency and suggests that the items are measuring the same construct in a reliable manner. Researchers use Cronbach's alpha to evaluate the quality of a test or questionnaire and to determine whether it is suitable for the intended purpose.

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Answer:

the probability of event B is approximately 0.48.

Step-by-step explanation:

P(A) = P(B) (given)

P(A∪B) = P(A) + P(B) - P(A∩B) (probability rule for the union of two events)

Since events A and B are independent, we know that P(A∩B) = P(A) × P(B).

Substituting the given values, we get:

0.63 = P(A) + P(B) - P(A) × P(B)

Since P(A) = P(B), we can substitute P(B) for P(A):

0.63 = 2P(B) - P(B)^2

Rearranging this equation, we get:

P(B)^2 - 2P(B) + 0.63 = 0

This is a quadratic equation that we can solve using the quadratic formula:

P(B) = [2 ± sqrt(4 - 4×0.63)] / 2

P(B) = [2 ± sqrt(1.48)] / 2

P(B) ≈ 1 or P(B) ≈ 0.48

Since probabilities must be between 0 and 1, we can discard the solution P(B) = 1, and the only possible solution is:

P(B) ≈ 0.48

Therefore, the probability of event B is approximately 0.48.

Answer:

Step-by-step explanation: daddy

45 square feet of glass was used in making this aquarium.

A region's size on a surface is determined by its area. The term "surface area" refers to the area of an open surface or the perimeter of a three-dimensional object, whereas "plane area" refers to the area of a shape or planar lamina.

The base of the aquarium is 6 feet by 2.5 feet, so its area is 6 x 2.5 = 15 square feet.

Since the aquarium is a rectangular prism, it has three sides that are the same size as the base. So, each of the three sides has an area of 15 square feet.

Therefore, the total area of glass used in making the aquarium is 3 x 15 = 45 square feet.

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The solution is: the cost of renting one chair is $2.25

the cost of renting one table is $8.25.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

here, we have,

Let x represent the cost of renting one chair.

Let y represent the cost of renting one table.

The total cost to rent 3 chairs and 5 tables is $48. This means that

3x + 5y = 48 - - - - - - - - - -1

The total cost to rent 6 chairs and 2 tables is $30. This means that

6x + 2y = 30 - - - - - - - - - -2

Multiplying equation 1 by 6 and equation equation 2 by 3, it becomes

18x + 30y = 288

18x + 6y = 90

Subtracting, it becomes

24y = 198

y = 198/24 = 8.25

Substituting y = 8.25 into equation 1, it becomes

3x + 5 × 8.25 = 48

3x + 41.25 = 48

3x = 48 - 41.25

= 6.75

x = 6.75/3

= 2.25

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Solving the equations for each given variables, we have:

a. t = 15

b. a = 12.5

c. p = 5/2

d.

y = 4

Finding the value of a variable in an equation involves solving the equation for that variable. This process typically involves several steps, including isolating the variable on one side of the equation, using inverse operations to simplify the expression, and substituting known values into the equation to find the value of the variable.

Therefore:

a. 2/5t = 6

Multiply both sides by 5/2:

t = 6 * 5/2

t = 15

b. -4.5 = a - 8

Add 8 to both sides:

-4.5 + 8 = a

12.5 = a

a =12.5

c. 1/2 + p = 3

p = 3 - 1/2

p = 5/2

d. -12 = -3y

-12/-3 = y

4 = y

y = 4

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68.4 is approximately 95% of 72.

Here, we have,

To find out what percent of 72 is 68.4, we can follow these steps:

Step 1: Divide 68.4 by 72.

68.4 / 72 = 0.95

Step 2: Convert the decimal to a percentage by multiplying by 100.

0.95 * 100 = 95

Therefore, 68.4 is approximately 95% of 72.

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Answer:

9(4+5)-16=

Explanation:

P (parenthesis) E (exponents) M (multiply) D (divide) A (add) S (subtract)

HOPE THIS HELPS

Answer:

c = 13

Step-by-step explanation:

We can solve for c using an equation that models the sum of the interior angles of a triangle.

The interior angles of a triangle add to 180º. Therefore, we can construct the equation:

90 + (3c - 1) + 52 = 180

Then, we can solve for c algebraically.

(3c - 1) = 180 - 90 - 52

 3c - 1 = 38

     3c = 38 + 1

3c / 3 = 39 / 3

       c = 13

(9.50 + 0.15 x 9.50) x Hours  and  (9.50 + 0.10 x 9.50) x Hours are the equation to and the total  cost estimate is $173.04.

Two or more expressions with an Equal sign is called as Equation.

For the first 8 hours: The flat rate is $9.50 per hour, so 15% of that rate is 0.15 x 9.50 = $1.43.

The cost for the first 8 hours is (9.50 + 1.43) x 8 = $96.64.

For the next 8 hours: The flat rate is still $9.50 per hour, so 10% of that rate is 0.10 x 9.50 = $0.95.

The cost for the next 8 hours is (9.50 + 0.95) x 8 = $76.40.

Total cost estimate = $96.64 + $76.40 = $173.04

We can also write the equations for the costs as follows:

For the first 8 hours: Cost = (9.50 + 0.15 x 9.50) x Hours = 1.15 x 9.50 x Hours

For the next 8 hours: Cost = (9.50 + 0.10 x 9.50) x Hours = 1.10 x 9.50 x Hours

Using these equations, we can calculate the cost for any number of hours up to 16.

Hence, (9.50 + 0.15 x 9.50) x Hours  and  (9.50 + 0.10 x 9.50) x Hours are the equation to and the total  cost estimate is $173.04.

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Answer:

(9.50 + 0.15 x 9.50) x Hours  and  (9.50 + 0.10 x 9.50) x Hours are the equation to and the total  cost estimate is $173.04.

Step-by-step explanation:

The distance of P to Q is given as follows:

89.6 feet.

The law of cosines states that we can find the side c of a triangle as follows:

c² = a² + b² - 2abcos(C)

In which:

The parameters for this problem are given as follows:

a = 120, b = 100, C = 47º.

Hence the distance is obtained as follows:

c² = 120² + 100² - 2 x 120 x 100 x cosine of 47 degrees

c² = 8032

c = sqrt(8032)

c = 89.6 feet.

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Answer: 101.41 lbs.

Step-by-step explanation:

46 kilograms can be converted to pounds by multiplying the number of kilograms by 2.20462.

So, 46 kg = 46 * 2.20462 = 101.41 lbs.

Answer: D

Step-by-step explanation:

D. OLCOB. This angle is supplementary to COD because the two angles add up to 180°. OLCOB has a measure of 180° - 90° = 90°, which is supplementary to the 90° measure of COD.

The length of JM is given as follows:

JM = 16.875.

Similar polygons are polygons that share these two features presented as follows:

The polygons for this problem are similar, hence the proportional relationship for the segment lengths is given as follows:

16/15 = JM/18

Then the length of JM is obtained applying cross multiplication as follows:

16JM = 15 x 18

JM = 15 x 18/16

JM = 16.875.

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The derivative of y = sin(x)cos(x) is 2sin(x)cos(x).Using the formula above, we can calculate that: (sin(x)cos(x))' = cos(x)sin(x) + sin(x)cos(x) = sin(x)cos(x) + sin(x)cos(x) = 2sin(x)cos(x)

The rule for derivatives of trigonometric functions states that the derivative of a trigonometric function is the product of the coefficient and the derivative of the other function in the product. This rule can be expressed mathematically using the following formula: (f(x)g(x))' = f'(x)g(x) + f(x)g'(x) For example, let's say that we want to calculate the derivative of the function y = sin(x)cos(x). Using the formula above, we can calculate that: (sin(x)cos(x))' = cos(x)sin(x) + sin(x)cos(x) = sin(x)cos(x) + sin(x)cos(x) = 2sin(x)cos(x) Therefore, the derivative of y = sin(x)cos(x) is 2sin(x)cos(x).

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The solution to the system of equation y = x + 12 and y = (1/2)x is (-24,-12).

Given the system of equation in the question;

y = x + 12

y = (1/2)x

To solve the system of equation, first plug equation to into equation one and solve for x.

y = x + 12

Plug in y = (1/2)x

(1/2)x = x + 12

Multiply each term by 2

2(1/2)x = 2x + 2(12)

x = 2x + 24

x - 2x = 2x - 2x + 24

x - 2x = 24

-x = 24

x = -24

Now, plug x = -24 into equation two and solve for y.

y = (1/2)x

Plug in x = -24

y = (1/2)( -24 )

y = -24/2

y = -12

Therefore, the value of x is -24 and y is -12.

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Answer:

the answer is D (4,∞)

Step-by-step explanation:

3n-12>4n-16

C.L.T.

3n-4n>-16+12

-n>-4

n>4