A photo is 16in long and 126cm wide.what is the approximate area of the picture in square feet?

To prove that Sin (A-B) = sinAcos B - Cos Asin B, we can use the angle subtraction formula for sine:

Sin (A-B) = Sin A Cos B - Cos A Sin B

This formula is derived from the identity:

Sin (A-B) = Sin A Cos B - Cos A Sin B

which can be derived by using the double angle identities for sine and cosine:

Sin (2A) = 2 Sin A Cos A

Cos (2A) = Cos^2 A - Sin^2 A = 2 Cos^2 A - 1 = 1 - 2 Sin^2 A

Substituting these identities into the identity above, we get:

Sin (A-B) = Sin A Cos B - Cos A Sin B

Angle subtraction formulas is otherwise known as angle subtraction identities. This angle subtraction formulas permit us to find the exact values of less common trigonometric angles by expressing the less common angle as the difference of two common angles. For example, 15 degrees = 45 degrees - 30 degrees.

Therefore, Sin (A-B) = sinAcos B - Cos Asin B.

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An item is regularly priced at, 1.98$ is discounted from the regular price.

A percentage is a portion of a whole expressed as a number between 0 and 100 rather than as a fraction. All of something is 100 percent, half of it is fifty percent, none of something is zero percent. To determine a percentage, you divide the portion of the whole by the whole itself and multiply by 100.

Given that,

First, change the percentage into decimal:

Let us assume,

Sale of regular price = 1%

1% = 1/100 = 0.01

Assume, item regular price is = 2$

Multiply 2 with 0.01:

2 * 0.01 = 0.02

Note that this number 0.02 (0.01 of 2) is the amount off from the original price (2). Subtract 2 from 0.02

2 - 0.02 = 1.98

Therefore,

An item is regularly priced at, 1.98$ is discounted from the regular price.

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The solution is Option D.

The minimum number of trips of buses to carry 420 people is 5 trips

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is given as

The number of people the tour bus can carry = 72 people

The total number of people who want to go sightseeing = 420 people

So , the equation will be

The number of trips of bus to carry 420 people =  total number of people who want to go sightseeing / number of people the tour bus can carry

Substituting the values in the equation , we get

The number of trips of bus to carry 420 people = 420/72

The number of trips of bus to carry 420 people = 5.8

The number of trips of bus to carry 420 people = 5 buses

Therefore , the minimum number of buses is 5 buses

Hence , The minimum number of trips of buses to carry 420 people is 5 trips

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The function h(x) = (f.g)(x) would be x² + 10x + 24.

What are composite functions?

A composite function is generally a function that is written inside another function. The composition of a function is done by substituting one function into another function. For example, f [g (x)] is the composite function of f (x) and g (x). The composite function f [g (x)] is read as “f of g of x”.

To find h(x) = (f.g)(x), we need to find the composition of the functions f(x) and g(x).

The composition of two functions f(x) and g(x) is denoted by (f.g)(x) and is defined as (f.g)(x) = f(g(x)).

In this case, we have:

h(x) = (f.g)(x) = f(g(x)) = f(x + 5)

Substituting x + 5 for g(x) in the equation for f(x), we get:

h(x) = (f.g)(x) = f(x + 5) = (x + 5)² - 1

Simplifying this expression, we get:

h(x) = (f.g)(x) = x² + 10x + 24

Hence, the function h(x) = (f.g)(x) would be x² + 10x + 24.

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Answer: 12

Step-by-step explanation:

The y-intercept in the equation that is in slope-intercept form is the constant.

Answer:

Below

Step-by-step explanation:

Circumference of a circle = pi * diameter

                             circumference of ferris wheel = 3.14159 * 520=1633.6 ft

Answer:2(8x-5)

Hope this helps!

It will take 5 minutes before the stadium is half empty

Given that:

Over 92,000 fans pack the stadium to watch the Tigers play

The fans leave at a rate of 10% per minute

The number of fans that leave per minute will be:

10% of  92,000 = 10/100 × 92, 000 = 9,200

The stadium will be fully empty  in:

time = 92,000/9,200 = 10 minutes

The stadium will be half empty  in:

time = 10 minutes / 2 = 5 minutes

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The value of the expression 24 + x ÷ 12 when x = −180 is (b) 9

Expressions are mathematical statements that are represented by variables, coefficients and operators

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

24 + x ÷ 12

Also, we have the value of the variable to be

x = −180

Substitute the known values in the above equation, so, we have the following representation

24 - 180 ÷ 12

Evaluate the quotient in the above equation

So, we have the following representation

24 - 180 ÷ 12 = 24 - 15

Evaluate the difference in the above equation

So, we have the following representation

24 - 180 ÷ 12 = 9

Hence, the value of the expression is (b) 9

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4.

find slope;

3 - 0/-2 -(-3) = 3/1 = 3

y = 3x + b

0 = (3)(-3) + b

0 = -9 + b

b = 9

y = 3x + 9

2 points of inflection will f(x) = 3x5+2x4 - 5x - 12 have.

What is Inflection points definition?

An inflection point is a point on the graph at which the second derivative is equal to zero or undefined and changes sign.

The characteristic that every input is associated to exactly one output defines a function as a relationship between a set of inputs and a set of allowable outputs. A mapping from A to B will only be a function if every element in set A has one end and only one image in set B. Let A & B be any two non-empty sets.

If [tex]$f^{\prime \prime}(x) > 0$[/tex]then f(x) concave upwards.

If [tex]$f^{\prime \prime}(x) < 0$[/tex]then f(x) concave downwards.

[tex]$$f^{\prime \prime}(x)=126 x^5+40 x^3$$[/tex]

Show Steps

Find intervals: Concave Downward: [tex]-\infty < x < 0$, Concave Upward: $0 < x < \infty$[/tex]

Plug x=0 into [tex]$3 x^7+2 x^5-5 x-12: \quad-12$[/tex]

(0,-12)

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The measure of ∠A is 29.

What is an angle?

An angle is a figure in plane geometry that is created by two rays or lines that have a shared endpoint. The Latin word "angulus," which meaning "corner," is the source of the English term "angle." The shared terminus of two rays is known as the vertex, and the two rays are referred to as sides of an angle.

Given that,

m∠A = (2x−13)° and m∠B = (2x+ 7)° and ∠A and ∠B are complementary angles.

Therefore

m∠A + m∠B = 90°

(2x−13)° + (2x+ 7)° = 90°

4x + 6 =90

Subtract 6 from both sides:

4x = 84

Divide both sides by 4:

x = 21

Putting x = 21 in m∠A = (2x−13)°:

m∠A = (2 × 21−13)°

m∠A = 29°

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The solution of the given expression is equal to 2.17.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the expression is [tex]2^{x+1} = 9[/tex]. The expression will be solved by using the logarithmic property below,

[tex]2^{x+1}=9[/tex]

Take logs on both sides,

(x+1) ln(2) = ln(9)

(x+1) = ln(9) / ln(2)

x + 1 = 3.17

x = 2.17

Hence, the expression will be solved by taking log on both sides.

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Answer:

Tabatha drives 1/6 mile more per minute than Horatio drives

Step-by-step explanation:

The maximum value of the periodic function with amplitude 6.5 and minimum value 7 is 13.5.

What is a periodic function?

The time interval between two waves is known as a Period whereas a function that repeats its values at regular intervals or periods is known as a Periodic Function.

The maximum value of a periodic function with amplitude 6.5 and minimum value 7 is equal to the sum of the amplitude and the minimum value.

The amplitude of a periodic function is defined as the maximum distance that the function deviates from its centerline. In this case, the amplitude of the function is 6.5.

The minimum value of a function is the lowest value that the function takes on over a given period. In this case, the minimum value of the function is 7.

To find the maximum value of the function, we need to add the amplitude and the minimum value. The maximum value is equal to 6.5 + 7 = 13.5.

Hence, the maximum value of the periodic function with amplitude 6.5 and minimum value 7 is 13.5.

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The LCM of the given pairs are 10, 15,12,30,6,24,20,18, and 63 respectively.

The least common multiple (LCM) of two numbers is the lowest possible number that can be divisible by both numbers.

There are 9 pairs, so let's name them using the letters A to I.

The LCM of the first pair A (2, 5) is 10.

The LCM of the pair B (3, 15) is 1*3*5 = 15.

The LCM of the pair C (6, 12) is 3*2*1*2 = 12.

The LCM of the pair D (3, 15) is 2*3*1*5 = 30.

The LCM of the pair E (2, 3) is 1*3*2 = 6.

The LCM of the pair F (8, 24) is 2*2*2*1*3 = 24.

The LCM of the pair G (4, 10) is 2*2*5 = 20.

The LCM of the pair H (6, 9) is 3*2*3 = 18.

The LCM of the pair I (7, 9) is 7*9 = 63.

Hence, 10,15,12,30,6,24,20,18,63 are the LCM of the given pairs.

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The area of the composite shape is 292.96 in² and the perimeter of the composite shape is 65.12 inches

The quantity of surface contained within a semicircle's perimeter is known to as its area.

The formula for the Area of a half circle with a Radius (r) is given by  

            Area of Half circle = πr²/2

The formula for the perimeter of a half circle with a radius (r) is given by

           Perimeter of Half circle = πr

Here we have

A picture of a Rectangle with a half circle

Dimensions of Rectangle = 16 in × 12 in

=> Area of rectangle = 16 in × 12 in = 192 in²

=> Perimeter of rectangle shape = 12 + 16 + 12 = 40 inches

[ Here we only take one side of the rectangle since one of the sides is connected with a Half circle ]

The radius of half circle = 8 inch

=> Area of Half circle = π(8)² = (3.14)(64)/2 = 100.96 in²

=> Perimeter of Half circle = πr =(3.14)(8) = 25.12 in

Area of the composite shape

= Ractangle's Area + Half circle's Area

= 192 in² + 100.96 in²

= 292.96 in²

The perimeter of the composite shape

= Ractangle perimeter + Half circle perimeter

= 40 inches + 25.12 inches

= 65.12 inches

Therefore,

The area of the composite shape is 292.96 in² and the perimeter of the composite shape is 65.12 inches

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Answer:

-------------------------------------

The charge of $55 with error margin of  ± 1.3 results in the least value of $(55 - 1.3) = $53.7 and greatest value of $(55 + 1.3) = $56.3.

If 1000 people signed up for the service, then the least total amount is:

Correct choice is B.

The translation rule that maps the preimage to the image is (x, y) ⇒ (x + 5, y + 1)

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

Pre-image: L(-4,0), M(-2,0) and N(-3,-3)

Image: L'(1,1), M'(3,1) and N'(2,-2)

The translation rule is calculated as

(x, y) = L' - L

Substitute the known values in the above equation, so, we have the following representation

(x, y) ⇒ (x + 1 + 4, y + 1 - 0)

Evaluate

(x, y) ⇒ (x + 5, y + 1)

Hence, the translation is (x, y) ⇒ (x + 5, y + 1)

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Total coats should the store plan to sell this winter is 952.

Last winter, a store sold 408 coats in 3 months. This winter, the store plans to sell coats for 4 months.

What is sell?

Determine the total cost of all the purchased units. To find the cost price, divide the total cost by the quantity of units purchased. To get the final price, use the formula for selling price (SP), which is: SP = CP + Profit Margin. The cost of the commodity will then be increased by the margin to determine the proper pricing. Retail math describes the mathematical techniques or formulae utilised in the sales industry. It is earning money or receiving change in the most basic sense. Business owners, retailers, managers, and sales representatives all utilise retail math in their daily work.

3month = 408 coats

1 month = 408/3 =136 coats

Then, 4 months = 136*4 = 544 coats

Total coats should the store plan to sell this winter = 544+408 = 952.

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The cost of tilling a rectangular plot of land 500m long and 200m wide at the rate of rs 8 per sq m is Rs. 8,00,000.

Area of rectangle = length × breadth

Area of rectangular plot = 500× 200 = 1,00,000 sq m

Cost of tilling 1 sq m of land = Rs. 8

Cost of tilling 1,00,000 sq m of land = 8 × 1,00,000 = Rs. 8,00,000

Thus, The cost of tilling a rectangular plot of land 500m long and 200m wide at the rate of rs 8 per sq m is Rs. 8,00,000.

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Answer:

  4.63%

Step-by-step explanation:

You want the interest rate that, compounded quarterly, will result in a balance of $216,000 for an investment of $90,000 after 19 years.

The formula for the balance of an account earning compound interest is ...

  A = P(1 +r/n)^(nt)

where P is the principal invested, r is the annual interest rate, n is the number of times per year interest is compounded, and t is the number of years.

Filling in the given values, we can solve for r:

  216000 = 90000(1 +r/4)^(4·19)

  2.4 = (1 + r/4)^76 . . . . . divide by 90,000

  2.4^(1/76) = 1 +r/4 . . . . . . take the 76th root

  (2.4^(1/76) -1) = r/4 . . . . . . subtract 1

  r = 4(2.4^(1/76) -1) ≈ 0.0463437 ≈ 4.63%

The required interest rate is about 4.63%.

Answer:

86

Explanation:

3² × (2³ + 4) - 22

9 × (8 + 4) - 22

9 × 12 - 22

108 - 22

86

Answer:

three billion eight hundred million

Step-by-step explanation:

a) 58^-8 is the same as 1/58^8. we can also simplify the expression by applying the rule for negative exponents to the entire fraction.

To evaluate this expression, we can use the rule that any number raised to a negative exponent is equal to the reciprocal of the same number raised to the same positive exponent. In other words, x^-n = 1/x^n.

Applying this rule to the expression 1/58^8, we get:

1/58^8 = 1/(58^8) = 58^-8

Therefore, the correct answer is 58^-8.

It is important to note that the exponentiation operator (^) has higher precedence than the division operator (/), so we need to use parentheses to indicate that the exponent should be applied to the entire denominator before the division is performed. In this case, we can also simplify the expression by applying the rule for negative exponents to the entire fraction:

1/58^8 = (1/58)^8 = 58^-8

This simplification shows that the correct answer is still 58^-8.

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The equation of line in point-slope form of the line, is y = 5x - 1.

What is point - slope form of the line?

The general form of a linear equation is y - y1 = m(x - x1).

It draws attention to the line's slope and one of the line's points (that is not the y-intercept).

Given:

The line passes through the points (1, 4) and (2, 9).

We have to find the equation of line in point - slope form.

First to find the slope from the given points.

Since,

[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]

Here, [tex](x_1, y_1) = (1, 4), (x_2, y_2) = (2, 9)[/tex]

So, [tex]m = \frac{9-4}{2-1} = 5[/tex]

Now consider, the point slope form of the line

[tex]y-y_1=m(x-x_1)[/tex]

Plug [tex]m = 5, (x_1, y_1) = (1, 4)[/tex]

⇒

[tex]y - 4=5(x-1)\\y-4=5x-5\\y=5x-5+4\\y=5x-1[/tex]

Hence, the equation of line in point-slope form of the line, is y = 5x - 1.

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The simple interest implies that Lonzo owes $1513.5

The given variables can be represented as:

Loan amount P = $1500

Rate of interest, R = 1.2%

Time to pay back the loan, t = 9 months i.e. 0.75 year

The amount from a simple interest can be calculated using:

A = P(1 + RT)

Substitute the known values in the above equation, so, we have the following representation

A = 1500 * (1 + 1.2% * 0.75)

Evaluate

A = 1513.5

Hence, the amount owed is $1513.5

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two thirds of a number b which is no more than 12, is b ≤ 18

What is inequality ?

In mathematics, an inequality represents the connection between two values in an imbalanced algebraic statement. A sign of inequality can be used to show that one of the two variables is larger than, greater than or equal to, less than, or equal to another value.

According to question

two thirds of a number b = (2/3)b

Given two thirds of number b is no more than 12

⇒   (2/3)b ≤ 12

⇒   2b ≤ 12*3

⇒   b ≤ (12*3)/2

⇒   b ≤ 36/2

⇒   b ≤ 18

hence the number b whose 2/3 is no more than 12 is, b ≤ 18

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A vocational counselor wishes to compare the mean scores on a paper-and-pencil test of anxiety for groups of physicians, lawyers, and accountants. the appropriate test is a two factor chi Square test.

The Pearson chi-square (χ²) test, often simply called the chi-square test, is one of the most common non-parametric tests. Nonparametric tests are used for data that do not follow the assumptions of parametric tests, especially the assumption of normal distribution.

To test hypotheses about the distribution of a categorical variable, you should use the chi-square test or another non-parametric test. Categorical variables can be nominal or ordinal and represent groups such as species or nationality. They can only have a small number of specific values, so they cannot have a normal distribution.

Bidirectional chi-square is one of several tests of goodness of fit between the actual values ​​of two nominal or ordinal variables and the values ​​expected if the variables were unrelated or independent. Chi-square is also known as Pearson Chi-square and Chi-square test of independence. The symbol for the chi-square test is the lowercase Greek letter chi (χ) with a superscript 2, such as χ2. χ2 is a test of significance and should be accompanied by an appropriate test of strength. The strength test should be chosen based on the number of rows and columns in the table of observations. In particular, one of the most commonly used strength tests is the π coefficient.

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Suppose a juice box contains 30% juice with the remaining portion of the drink composed of water alcohol is the solute in this type of juice box.

Ethanol; Ethanol, a drab liquid with a pleasing scent this is produced evidently from fermentation through yeasts and different microorganisms. It is utilized in alcoholic beverages, as a solvent, and withinside the manufacture of different chemicals. Ethanol is a fairly poisonous and colorless compound.

Alcohol is the solute in this type of juice box is the solvent as alcohol is easily soluble as the solvent and has best property of a solute and csn pass through the semipermeable permeability and others solvent also. The alcohol is actually acting as the solute here to dissolve the solvent.

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