what is the number of ways to choose two toppings for a pizza, one topping from a group of 5 kinds of meats and the other topping from a group of 7 kinds of vegetables?

The proof is as shown below

Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a right-angled triangle with its angles.

If a² = b + c , b² = c + a and c² = a + b

We want to prove that 1/(a+1) + 1/(b+1) + 1/(c+1) = 1

Since a² = b + c

a²+a = a + b + c

a (a+1) = a + b + c

a+1 = (a + b + c)/a

Repeat the same process for b² = c + a and c² = a +b, we have:

1 + b= (a + b + c)/b

1 + c =(a + b + c)/c

Substitute the values 1+a, 1+b and 1+c into 1/(a+1) + 1/(b+1) + 1/(c+1):

1/(a+1) + 1/(b+1) + 1/(c+1) = a/(a+b+c) + b/(a+b+c) + c/(a+b+c)     (Taking LCM)

                                      = (a+b+c )/ (a+b+c ) = 1

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The slope of the line through each pair of points (11, 8), (- 13, 11) is -1/8.

The slope of a line is defined as the change in y- coordinate with respect to x - coordinate. The slope of a line represents the direction and steepness of a line. The formula for the slope of a line that passes through the points (x₁, y₁) and (x₂, y₂) is given by

Here we have

The pair of points (11, 8), (- 13, 11)  

By the given formula,

Slope (m) = [ y₂ - y₁]/ [x₂ - x₁]

The slope from (11, 8) to (- 13, 11) can be calculated as follows

Slope = [ 11 - 8 ]/ [ -13 -11 ] = 3/-24 = -1/8

Therefore,

The slope of the line through each pair of points (11, 8), (- 13, 11) is -1/8.    

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The appropriate response will be (A). The first equation of motion gives the link between "velocity and time."

Equation: A statement that two variable or integer expressions are equal. In essence, equations are questions, and the motivation for the development of mathematics has been the systematic search for the answers to these questions.

An equation is a mathematical representation of two equal objects, one on each side of a "equals" sign. We can solve challenges in our daily lives with the aid of equations. Most of the time, we look for help with pre algebra to resolve problems in real life. Pre-algebra concepts contain the fundamentals of mathematics.

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Answer:

44

Step-by-step explanation:

Answer: nope

Step-by-step explanation:

No, the 200$ marked down 20% would be 200 - 0.2 * 200 = 160$. Then, if it is increased by 20%, it would be 160 + 0.2 * 160 = 192$. So, 200$ is not equal to 192$.

Answer:

1m/sec

Step-by-step explanation:

Mr. Hall spent 3 seconds to increase his speed to 3m/sec increasing 1m/sec, don't over think it.

The percent table is:

                           100 %   ⇒   $400

                           120 %   ⇒   $480

The initial price of the Loungy chair was $400.

So, the initial price(P₀) = $400

The price of the chair has gone up by 20%

So, increase in price(r) = 20%

The final price will be calculated by using the formula:

                          P = P₀(1 + r/100) (where P is the final price)

                          P = 400(1 + 20/100)

                          P = 400(1 + 0.2)

                          P = 400 × 1.2

                          P = $480

Hence, the final price of the Loungy chair is $480

Percent table:

                           100 %   ⇒   $400

                           120 %   ⇒   $480

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Answer: Distributive property and Commutative property (of multiplication)

Step-by-step explanation:

From 1 to 2, the parentheses coefficient is multiplied out to the parentheses. This is called distribution.

From 2 to 3, the numbers in each multiplication are rearranged. This would be the commutative property of multiplication.

HOPE THIS HELPS _- MM

The width and height are given to one decimal place, and we have multiplied them together, the answer should be rounded to one decimal place. Therefore, the area of the rectangle is 25.1 cm²

To calculate the area of a rectangle, we need to multiply its width by its height.

The size of a patch on a surface is determined by its area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina. Area can be interpreted as the quantity of material with a specific thickness required to create a model of the shape or as the quantity of paint required to completely cover the surface in a single coat.

Area = width x height

Substituting the given values, we get:

Area = 7.6 cm x 3.3 cm

Area = 25.08 cm²

Since the width and height are given to one decimal place, and we have multiplied them together, the answer should be rounded to one decimal place. Therefore, the area of the rectangle is 25.1 cm² (rounded to one decimal place).

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At a total price of $2720 for 4 Computers, retailer 2 delivers the best deal based on the listed specials.

Based on the stated sales, we need to figure out the entire cost of 4 computers at each retailer, accounting for any discounts or promotions, in order to determine which store will provide the lowest pricing for 4 Computers.

Let's use the following variables to symbolize the costs and special offers at each retailer:

P1: the price of a single computer in a store 1

P2: the price of a single computer in a store 2

P3: the price of a single computer in a store 3

P4: the price of a single computer in a store 4

D1: discount on one computer at store 1

D2: discount on one computer at store 2

D3: discount on one computer at store 3

D4: discount on one computer at store 4

Then, we may figure the total cost of four computers at each store using the following formulas:

Total cost at store 1 = 4(P1 - D1)

Total cost at store 2 = 4(P2 - D2)

Total cost at store 3 = 4(P3 - D3)

Total cost at store 4 = 4(P4 - D4)

The total cost at each store can then be calculated by plugging in the values from the table as follows:

Store 1: Total cost = 4(950 - 0.2*950) = 3040

Store 2: Total cost = 4(800 - 0.15*800) = 2720

Store 3: Total cost = 4(1100 - 0.25*1100) = 3300

Store 4: Total cost = 4(850 - 0.1*850) = 3060

Therefore, At a total price of $2720 for 4 Computers, retailer 2 delivers the best deal based on the listed specials.

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The volume of the rectangular prism will be 1008 cubic inches and the volume of the pyramid is 504 cubic inches.

The volume of the rectangular prism is defined as the space in three-dimension covered by the rectangular prism having the sides Length, Width, and Height.

The volume of the rectangular prism will be the multiplication of the three parameters which are Length, Width, and Height of the prism.

The volume of the pyramid is the product of half of the area of the base and the height of the pyramid,

The volume of prism = 14 x 12 x 6

The volume of the prism = 1008 cubic inches

The volume of the pyramid,

Volume = 1/2 x Base area x H

Volume = 1/2 x 72 x 14

Volume = 504 cubic inches.

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The number of ways the foreign language club can choose 4 movies from the available is [tex]nC4 = n! / 4!(n-4)![/tex].

To calculate the number of ways the foreign language club can choose four movies from the available subtitled movies, we need to use the combination formula, which is:

[tex]nCr = n! / r!(n-r)![/tex]

Where n is the total number of available subtitled movies and r is the number of movies to choose (in this case, r=4).

Assuming there are at least four subtitled movies available, the number of ways to choose four movies would be:

[tex]nC4 = n! / 4!(n-4)![/tex]

Simplifying the equation further, we have:

[tex]nC4 = (n * (n-1) * (n-2) * (n-3)) / 4 * 3 * 2 *1[/tex]

Therefore, the number of ways the foreign language club can choose four movies from the available subtitled movies is given by the formula nC4.

The formula calculates the number of possible combinations of four movies that can be selected from the total number of available subtitled movies, without regard to the order in which they are shown.

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Answer:

1/24.

Step-by-step explanation:

There are 2 events here and they are independent, so the single probabilities are multiplied.

P(4 when die is rolled) = 1/6

P(A on the spinner) = 1/4

So, P(4 and A)

= 1/6 * 1/4

= 1/24.

The minimum number of strides that Chao could take to complete a distance of 11.2 km is approximately 16,000.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
To calculate the minimum number of strides that Chao could take to complete a distance of 11.2 km, we need to first convert the distance to meters since the stride length is given in centimeters.

11.2 km = 11,200 meters (1 km = 1000 meters)

Stride length in meters = 70 cm / 100 cm/m = 0.7 m

Now, we can calculate the minimum number of strides as follows,

Minimum number of strides = (Distance covered in meters) / (Stride length in meters)

Minimum number of strides = 11,200 m / 0.7 m ≈ 16,000

Therefore, the minimum number of strides that Chao could take to complete a distance of 11.2 km is approximately 16,000.

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Answer:

2. $9.99

3. 45 tickets for $27

4. 20 cents

Step-by-step explanation:

2. 79.92/8 = 9.99

3. 27/45 0.6 and 15/20 = 0.75 and 60 cents is less than 75 cents

4. 6/30 = 20

Answer:

Step-by-step explanation:

79.92/8= 9.12 per cd

15/20= .75

27/45=.6 better deal because it is .60 cents per ticket

6/30= .20 per can

Answer:

a) y - 4 =3(x - 1)

b)  y + 2 = 4(x+ 1)

c) y = -(x - 3)

d) y = -5x

Step-by-step explanation:

You did not say which form, so I put them in the point-slope form of a line that follows the pattern:

y - [tex]y_{1}[/tex] = m( x - [tex]x_{1}[/tex])

Answer:

see explanation

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

(a)

given m = 3 , then

y = 3x + c ← is the partial equation

to find c substitute (1, 4 ) into the partial equation

4 = 3(1) + c = 3 + c ( subtract 3 from both sides )

1 = c

y = 3x + 1 ← equation of line

(b)

given m = 4 , then

y = 4x + c ← is the partial equation

to find c substitute (- 1, - 2 ) into the partial equation

- 2 = 4(- 1) + c = - 4 + c ( add 4 to both sides )

2 = c

y = 4x + 2 ← equation of line

(c)

given m = - 1 , then

y = - x + c ← is the partial equation

to find c substitute (3, 0 ) into the partial equation

0 = - 3 + c ( add 3 to both sides )

3 = c

y = - x + 3 ← equation of line

(d)

given m = - 5 , then

y = - 5x + c ← is the partial equation

to find c substitute (0, 0 ) into the partial equation

0 = - 5(0) + c = 0 + c ⇒ c = 0

y = - 5x ← equation of line

Answer:

Step-by-step explanation:

the answer is 420 cuase the manufatcure of math is hard i wont give an explanation.

Answer:

∠ CAB = 144°

Step-by-step explanation:

the central angle CAB is twice the measure of ∠ BDC , that is

∠ CAB = 2 × 72° = 144°

The indicated IQ score is given as 117.

The area under the curve is given as 0.1431

the area to the left of x = 1 - 0.1431

= 0.8569

for 0.8569 the z stat is 1.07

u = 100

sd = 15

x = u + z * sd

= 100 + 0.8569 * 15

= 116.05

approximately 117

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Find the indicated IQ score. The graph to the right depicts IQ scores of​ adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15.

xx

0.1431

A symmetric bell-shaped curve is plotted over a horizontal scale. A vertical line runs from the scale to the curve at labeled coordinate x, which is to the right of the curve’s center and peak. The area under the curve to the right of the vertical line is shaded and labeled 0.1431.

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Answer:

20

Step-by-step explanation:

snajakskdmcjwiwjcjf

Answer:

20

Step-by-step explanation:

70% is 70/100 = 0.70

20 x 0.70 = 14

The graph of the equation of function f (x) = 3 log₂ (x + 1) is shown in figure.

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given that;

The equation of function is,

⇒ f (x) = 3 log₂ (x + 1)

Now, By using tool we can draw the graph of the equation of function

f (x) = 3 log₂ (x + 1) as shown in figure.

Thus, The graph of the equation of function f (x) = 3 log₂ (x + 1) is shown in figure.

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Sara can read about 30 pages in 95 minutes.

To start, multiply the weekly hours by the number of weeks in a year to get the overall number of hours worked (52). Then subtract this amount from the annual pay. For instance, if a worker earns $50,000 annually and puts in 40 hours per week, their hourly rate would be $50,000/2,080 (40 x 52) = $24.04.

First, we need to convert 95 minutes to hours by dividing by 60:

95 min ÷ 60 min/hour = 1.5833 hours (rounded to 4 decimal places)

Next, we can use the conversion factor to find the number of pages Sara can read in 1.5833 hours:

19 pages/hour x 1.5833 hours = 30.1391 pages

Rounding to the nearest whole number, Sara can read about 30 pages in 95 minutes.

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Answer:

k = -6

Step-by-step explanation:

Expand by substituting -6:

(n+5) (n-6) = n^2 + 5n - 6n (-6×5)

Thus, (n+5)(n-6) = n^2 -1n -30

(In a facotrised form for quadratics, the numbers need to add to 'bx', in this case -1, and multiply to form 'c' (-30). So -6×5 = -30 and k= -6)

The amount of sales tax due on the entire purchase of a set of speakers and s songs is $2.89 plus $16.09 for each song purchased, rounded to the nearest hundredth.

What is an expression?

In mathematics, an expression is a combination of numbers, variables, and/or operators that represents a mathematical quantity or relationship. It can be a single number or variable, or a combination of multiple numbers, variables, and operators.

The given expression 0.0825(35+195s) represents the amount of sales tax due on the entire purchase of a set of speakers and s songs, where s is the number of songs purchased.

Expanding the expression, we get:

0.0825(35+195s) = 0.0825(35) + 0.0825(195s)

= 2.8875 + 16.0875s

Rounding this expression to the nearest hundredth, we get:

2.89 + 16.09s

Therefore, the amount of sales tax due on the entire purchase of a set of speakers and s songs is $2.89 plus $16.09 for each song purchased, rounded to the nearest hundredth.

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Answer:

5.1

Step-by-step explanation:

11.5 + 5.6 + 8.8 = 29.5

31 - 29.5 = 5.1

If m + 1 is an even integer, then 2m + 1 is an odd integer.

Even number: An even number is a number that is a multiple of 2. It can be said that any number that is completely divisible by 2 is an even number.

Odd number: Odd numbers are those numbers that are not completely divisible by 2.

let us understand by addition on different combinations of odd numbers and even numbers.

Odd number + Odd number = Even number

Even number + Even number = Even number

Even number + Odd number = Odd number

Odd number + Even number = Odd number

In subtraction

Even number - Even number = Even number

Even number - Odd number = Odd number

Odd number - Even number = Odd number

Odd number - Odd number = Even number

In multiplication

Even number × Even number = Even number

Even number × Odd number = Even number

Odd number × Odd number = Odd number

Given:

m + 1 is an even integer.

since alternate numbers are even.

Therefore, m must be an odd number.

If m is odd, then m - 1 is even.

2m is divisible by 2, so it is always an even number.

So,

2m - 2 is even.

2m + 1 is odd.

2m + 2 is even.

Since 2m + 1 is an odd number.

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Answer: 3,020,000

Step-by-step explanation:

three million twenty thousand

Answer: 3,020,000

Step-by-step explanation: 3,000,000 + 20,000 = 3020000

Answer: 12: 6 and 24: 12 and 3: 1.5

Step-by-step explanation: A ratio can be equivalent through multiplication such as 6: 3 to 12: 6  

Answer:

2 : 1,

12/

Step-by-step explanation:

all you have to do is cross out the numbers, basically simplify the

the answer is 2:1 because in 3's multiplication table,

3×2=

and

3×1=

similarly , for 12/6, divide instead of multiplication, there area few other ratios equivalent to 6/

From the total of 300 workers in the factory :

a. Number of men = 200 and Women = 100

b. Number of workers works in the morning = 225

c. Number of workers unionized are 150.

d. Number of workers trustworthy are 50.

Total number of workers in the factory are 300.

a. Fraction of men in the factory are ( 2/3)

= 2/3 of 300

= 200

Women

= 300 -200

= 100

b. Number of workers in the morning shift are

= 3/4 of 300

= 225

c. Total number of workers unionized

= 1/ 2 of 300

= 150

d. Number of trustworthy workers

= 1/6 of 300

= 50

Therefore, out of 300 workers in the factory answer of the following questions are:

a. Number of men and women work in the factory are 200 and 100 respectively.

b. Number of workers works in the morning is 225.

c. Unionized workers = 150

d. Trustworthy workers = 50.

The above question is incomplete , the complete question is :

The Factory has 300 workers of which 2/3 are men, 3/4 work in the morning, 1/2 are unionized and 1/6 are trusted personnel.

a. How many men work in the factory and how many women?

b. How many workers work in the morning?

c. How many are unionized?

d. How many are trustworthy?

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Boole. K-map stands for Karnaugh Map and is used to simplify and minimize the expression of logic in a similar form to algebra.

George Boole is the mathematician we honor for discovering ways to express and minimize logic through a new but similar form of algebra. The technique used to simplify and minimize these expressions is known as a Karnaugh Map, or K-map for short. A K-map is a visual representation of a Boolean expression using squares and circles to represent true or false variables in a table. By arranging the variables in the table, the same logic can be expressed in a simpler form with fewer variables. This allows for a simpler and more efficient form of logic expression. K-maps are used in many fields, such as digital logic design, where the efficiency of expression is important.

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