A restaurant has 10 booths that will seat up to 4 people each. If 20 people are seated in booths, and NO booths are empty, what is the greatest possible number of booths that could be filled with 4 people?

The coordinates of the point on the directed line segment from (1, -3) to (7, 5) that partitions the segment into a ratio of 1 to 3 is; (x, y) = (2.5, 0.5)

The formula for partitioning a line segment in the ratio m:n is;

(x, y) = (mx2 + nx1)/(m + n), (my2 + ny1)/(m + n)

We are given the ratio as 1:3 with the coordinates as;

(1, -3) and (7, 5). Thus;

m = 1 and n = 3

x1 = 1

x2 = 7

y1 = -1

y2 = 5

Thus;

(x, y) = (1*7 + 3*1)/(1 + 3), (1*5 + 3*-1)/(1 + 3)

(x, y) = (10/4, 2/4)

(x, y) = (2.5, 0.5)

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Answer:

Step-by-step explanation:

15.23 units

The additional information needed to prove that both triangles are congruent by SAA postulate is:

A. <B ≅ <D and <A ≅ <E

The SAA postulate is a condition that is used to prove that two triangles are congruent if they have two pairs of corresponding congruent angles and a pair of non-included congruent sides.

From the information we have in the diagram, we can deduce that:

AC ≅ EC (one pair of congruent sides)

ACB ≅ ECB (one pair corresponding congruent angles)

Therefore, the additional information needed to prove that both triangles are congruent by SAA postulate is:

A. <B ≅ <D and <A ≅ <E

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The side lengths 300 mm and 190 mm make a valid triangle because of the triangle inequality theorem

The side lengths are given as

300 mm and 190 mm

To solve this question, we make use of the triangle inequality theorem

The triangle inequality theorem states that

Given that the sides of a triangle are x, y and z.

The sum of any two sides of a triangle is greater than or equal to the third side;

This means that

x + y ≥ z

Using the above as a guide, we have the following inequality expressions

300 + 190 ≥ z

300 + z ≥ 190

z + 190 ≥ 300

Evaluate the inequality expressions

490 ≥ z

z ≥ -110

z  ≥ 110

Remove the negative value

490 ≥ z

z ≥ 110

Combine the inequalities

110 ≤ z ≤ 490

The above inequality is a valid inequality expression

Hence, the side lengths 300 mm and 190 mm make a valid triangle

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Answer:

A.

Step-by-step explanation:

A quadrilateral is a trapezoid if two opposite sides are parallel, and the other 2 opposite sides are not parallel.

Answer: A.

Answer:

it's a

Step-by-step explanation:

Answer:

the mid point of (-3,4) and (-6,0) is (4.5,2)

Answer:

[tex]=(-4.5, 2)[/tex]

Step-by-step explanation:

Midpoint formula is:

[tex](x_m, y_m) = (\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})[/tex]

where

x1=-3, x2=-6

y1=4, y2=0

Now just plug into formula

[tex]=( \frac{-3+-6}{2}, \frac{4+0}{2})[/tex]

[tex]= ( \frac{-9}{2}, \frac{4}{2})[/tex]

[tex]=(-4.5, 2)[/tex]

Using rational numbers, Jackson supports more education funding as he  7/20 > 6/20.

Any number that can be expressed as a fraction and where the denominator (the bottom number) and the numerator (the top number) are both integers is considered a rational number. In other words, p/q, where p and q are both integers and q 0, can be used to represent a rational number.

According to Kirsten, 24% of federal tax dollars should fund education

⇒ 24% = 24 / 100

⇒ 6/25

According to Jackson, $0.35 of every tax dollar should go toward education

⇒ 0.35 = 35 / 100

⇒ 7/20

As we can infer that 7/20 > 6/20

So Jackson supports more education funding.

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The fraction is 23/27.

Let the numerator and denominator of the given fraction be x and y respectively.

According to the question,

Case 1 :-

Denominator of the fraction is 4 more than the numerator.

⇒ Numerator = Denominator - 4

⇒ x = y - 4 ...(1)

Case 2 :-

If 1 is added to numerator and 2 is subtracted from denominator fraction becomes 24/25

⇒ (Numerator + 1) / (Denominator + 2) = 4/5

⇒ (x + 1) / (y - 2) = 24/25

⇒ 25(x + 1) = 24(y - 2)

⇒ 25x + 25 = 24y - 48

⇒ 25x - 24y = -73 ...(2)

Substituting the value of x from (1) in (2), we have

⇒ 25(y - 4) - 24y = -73

⇒ 25y - 100 - 24y = -73

⇒ y = -73 + 100

y = 27

substitute the value of y in equation 1.

x = 27 - 4

x = 23

Now, At the beginning of our solution we took the numerator & denominator to be x & y respectively. So the fraction is:

⇒ x / y

⇒ 23/27

Hence the fraction is 23/27.

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At the job, the hourly Wage was solved to be $16.94.

Given data

rate of hours worked over 40 hours = 1.5

hours worked in a week = 52

total paycheck = $982.50

let the pay hourly rate be x, and over 40 hours pay is 1.5x

finding the hours worked over 40

52 - 40 = 12

total paycheck $982.50 is gotten as follows:

$982.50 = 40 * x + 12 * 1.5x

982.50 = 40x + 18x

982.50 = 58x

x = 982.50 / 58

x = 16.9397

x = 16.94

Since x which is the hourly wage is found to be 16.94m, we can therefore say that the hourly wage is $16.94.

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Answer:

MP = 29

Step-by-step explanation:

Given:

MN + NP = MP

17 + 3y = 5y + 9

Find what y =____

17 + 3y = 5y + 9

subtract 9 from both sides

17 - 9 + 3y = 5y + 9 - 9

8 + 3y = 5y

subtract 3y from both sides

8 + 3y - 3y = 5y - 3y

8 = 2y

divided both sides by 2 to get y alone

8/2 = 2y/2

4 = y

Now plug in y to MP to find its length

5(4) + 9 = 20 + 9 = 29

MP = 29

To find NP, plug in y as well

3y = 3(4) = 12

NP = 12

Check:

MN + NP = MP

17 + 12 = 29 yes!!!!

The 32nd term of the arithmetic sequence AP is computed to be 12.5.

In mathematics, an arithmetic progression (AP) is a list or sequence of numbers in which each term is attained by adding a pattern to the term before it.

Finally, here is the answer to the question;

The following are the numbers in the presented sequence:

0.1,0.5,0.9,1.3, ...........

Because the series contains 32 terms, we must find the 32nd number.

Assume the first term is'a₁' = 0.1.

Assume 'a₂' = 0.5 is the second term.

Assume the third term is 'a₃' = 0.9

'd' is the common difference between two consecutive terms of an AP that are equal.

d = a₂ - a₁  

Put the values in the preceding formula; the 32nd term is

d = 0.5 - 0.1

d = 0.4

The nth term equation is found by the formula;

Substitute the given values in the formula;

a₃₂ = a + (n - 1) d

a₃₂ = 0.1 + (32 - 1)(0.4)

a₃₂ = 0.1 + 12.8 - 0.4

a₃₂ = 12.5

Therefore, the arithmetic sequence's 32nd term value is estimated to be 12.5.

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Answer:

  c = -3 1/4

Step-by-step explanation:

You want the solution to 3/2(2c+7) -3c =6(c+5).

Simplifying the equation gives ....

  3c +21/2 -3c = 6c +30

  21/2 -60/2 = 6c . . . . . . . . . subtract 30

  -39/2 = 6c . . . . . . . . . . combine terms

  -13/4 = c . . . . . . . . . . divide by 6

The value of c is -3 1/4.

Answer:

x>4

Step-by-step explanation:

Since it is pointing right, it must be either

x>4

x≥4

Since it is not a filled circle the answer can't be greater than or equal to. So it must be x>4.

When the quadrilateral WXYZ is mirrored across the y axis to form the quadrilateral W' X' Y' Z', the coordinates of X' are (-1,6).

When the x value is reflected across the y-axis, it takes on the opposite sign.

A coordinate system is a method of determining the position of points or other geometric components on a manifold, such as Euclidean space, by using one or even more numbers, or coordinates.

A coordinate system is a framework for specifying the relative locations of objects in a specific area, such as an area here on earth's surface or the entire earth's surface. A geographic coordinate system determines locations on the world by using a three-dimensional spherical surface.

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For solving y, we can use this inequality:  y≤(168-7x)/4

An inequality is an equation which compares two non equal expressions using operators  ≤,≥,<,> .

Steps for solving inequalities:

For given inequality, 168≥ 7x + 4y

Adding -7x both sides,

168-7x ≥ 7x+4y-7x

168 - 7x ≥ 4y

Dividing both sides by a positive number 4,

(168-7x)/4 ≥ y

we can solve for y using above expression that y will be less than or equal to (168-7x)/4

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The next three numbers in the pattern are 80, 85, 90....

These are the multiples of 5.

The complete pattern is 30,45,60,75,80, 85, 90....

Look at the first three or four numbers in the pattern. You might wonder what link there is between these figures. In this mathematical pattern, for instance, the first three to four numbers are 1, 3, 6, and 10. It seems like you must add to get the higher numbers as you go up the scale. Start with adding 2, then follow with 2, 3, and finally 4. So, if you write this down, you probably see a pattern starting to emerge.

Try the remaining elements of the supplied pattern to see whether your solution works.

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Answer:

C is the correct answer

Step-by-step explanation:

hope you get it right :))

When a die is rolled twice, the probability of getting a 3 and then a 5 is 1/36.

When a die is rolled twice, the following combinations are possible:

1, 1 - 1, 2 - 1, 3 - 1, 4 - 1, 5 - 1, 6

2, 1 - 2, 2 - 2, 3 - 2, 4 - 2, 5 - 2, 6

3, 1 - 3, 2 - 3, 3 - 3, 4 - 3, 5 - 3, 6

4, 1 - 4, 2 - 4, 3 - 4, 4 - 4, 5 - 4, 6

5, 1 - 5, 2 - 5, 3 - 5, 4 - 5, 5 - 5, 6

6, 1 - 6, 2 - 6, 3 - 6, 4 - 6, 5 - 6, 6

Thus, the sample space is 36.

3, 5 only occurs once in the sample space.

∴ P (3 and 5) = 1/36.

Hence, the probability of rolling a 3 and then a 5 is 1/36.

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The  binary strings of length 10 are there in which the number of 0's in the string is not equal to the number of 1's in the string is 2¹⁰ - 2⁹.

Binary number:

A binary number is a number expressed in the base-2 numeral system or binary numeral system, a method of mathematical expression which uses only two symbols: typically "0" and "1".

Given,

Here we need to find How many binary strings of length 10 are there in which the number of 0's in the string is not equal to the number of 1's in the string.

Here the length of the binary string is 10.

So, it can be written in the power form as 2¹⁰.

Now we need to find the number of 0's in the string is not equal to the number of 1's in the string.

For that, we have to consider,

There are 2⁹ number of binary strings are not have same number of 0's in the string is not equal to the number of 1's in the string.

So, it can be written as,

=> 2¹⁰ - 2⁹

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[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Let's solve ~

[tex]\qquad \sf  \dashrightarrow \: 2x - 17 = 51 + 61[/tex]

[tex]\qquad \sf  \dashrightarrow \: 2x - 17 = 112[/tex]

[tex]\qquad \sf  \dashrightarrow \: 2x = 112 + 17[/tex]

[tex]\qquad \sf  \dashrightarrow \: 2x = 129[/tex]

[tex]\qquad \sf  \dashrightarrow \: x = \dfrac{129}{2} [/tex]

[tex]\qquad \sf  \dashrightarrow \: x = 64.5[/tex]

Mr. Sanchez's class sold 45 fruit pies, and Mr. Kelly's class sold 37 bottles of fruit juice.

Linear equations are equations that have constant average rates of change. Note that the constant average rates of change can also be regarded as the slope or the gradient

To solve this question, we use the following representations:

x represents the fruit pies

y represents the fruit juice

A system of linear equations is a collection of at least two linear equations.

In this case, the system of equations is given as

1.89x + 1.56y = 140.13 ---- the total cost

x + y = 82 --- the number of sales

Make x the subject in x + y = 82

So, we have

x = 82 - y

Substitute x = 82 - y in 1.89x + 1.56y = 140.13

1.89(82 - y) + 1.56y = 140.13

Expand

154.98 - 1.89y + 1.56y = 140.13

Evaluate the like terms

-0.33y = -14.85

Divide by -0.33

y = 45

So, we have

x = 82 - y

x = 82 - 45

Evaluate

x = 37

Hence, Mr. Sanchez's class sold 45 fruit pies, and Mr. Kelly's class sold 37 bottles of fruit juice.

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The arithmetic sequence AP's 32nd term is estimated to be 127.

An arithmetic progression (AP) in mathematics is a list or sequence of numbers within which each term is acquired by adding a sequence to the term before it.

Finally, the response to the question;

The numbers in the provided sequence are as follows:

34,37,40,43, ...........

There are 32 terms in the series, so we must obtain the 32nd number.

Suppose the first term is 'a₁' = 34.

Suppose 'a₂' = 37 be the second term.

Suppose 'a₃' = 40 be the third term.

The common difference between the two consecutive terms of an AP that are equal is 'd.'

d = a₂ - a₁  

Put the values in the preceding formula; the 32nd term is

d = 37 - 34

d = 3

The nth term equation is now used to calculate.

Substitute all of the values in the formula now.

a₃₂ = a + (n - 1) d

a₃₂ = 34 + (32 - 1)(3)

a₃₂ = 34 + 96 - 3

a₃₂ = 127

Thus, the arithmetic sequence's 32nd term is evaluated to be 127.

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Answer:

16

Step-by-step explanation:

We use PEMDAS

Parenthesis

Exponents

Multiplication

Division

Addition

Subtracting

1. 3 (10 - 8)^2 + 4: 3 (2)^2 + 4

2. 3 (2)^2 + 4: 3 (4) + 4

3. 3 (4) + 4: 12 + 4

4.12 + 4 = 16

So, our answer is 16.

Evaluating the expression -4 + 2ab for a = 3 and b = -5 is equal to -34.

An algebraic expression is a number, variable, or the combination of both and operational symbols. On the other hand, an equation is the equality of two expressions separated by "=".

To evaluate an expression or an equation means to substitute a value to the variable and perform the arithmetic operations included.

Given the expression -4 + 2ab, substitute the value of the variable a and the value of variable b.

-4 + 2ab

-4 + 2(3)(-5)

Performing the arithmetic operations, we can have the value of the expression.

-4 + 2(3)(-5)

= -4 + (-30)

= -34

Hence, the expression -4 + 2ab when a = 3 and b = -5 is equal to -34.

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The simplification by combining like terms of 4t-(t + 3t)  is 0.

According to the given question.

We have an expression 4t - (t+3t).

As we know that, like terms are terms whose variables (and their exponents such as the 2 in x2) are the same.  when we combine like terms, such as 2x and 3x, we add or subtract their coefficients.

Since, we have to combine the like terms of the given expression 4t-(t+3t).

Here 4t, t and 3t both are the like terms.

So, we add and subtract coeffcients of t to simplify the given expression.

Therefore, the simplification of 4t - (t + 3t) is given by

4t -( t+ 3t)

= 4t - t -3t

= 4t - 4t

= 0

Hence, the simplification by combining like terms of 4t - (t + 3t) is 0.

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The equation for week 1 at a high school showing collected aluminum cans and plastic bottles is; x + 4y = 2319

From the given table, we are told that;

Average number of cans and bottles collected by Sophomores in week 1 = 1

Average number of cans and bottles collected by Sophomores in week 2 = 4

Average number of cans and bottles collected by Juniors in week 1 = 4

Average number of cans and bottles collected by Juniors in week 2 = 2

Total number of cans and bottles collected by all in week 1 = 2319

Total number of cans and bottles collected by all in week 2 = 2290

Let x represent the number of sophomores, and let y represent the number of juniors. Thus, the equation for week 1 is;

x + 4y = 2319

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