which graph represents a proportional relationship
​

6 tables are required. Each prime number attender should serve 3 customers each.

The prime numbers between 1 and 100 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.

All the numbers other than prime numbers are composite numbers.

The composite numbers from 1 to 100 are: 1, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100.

Now, as there are 25 primes and 75 composites in the group that visited the restaurant, we can calculate the number of tables required by dividing the number of people by the seating capacity of each table.

Each table has a seating capacity of 15, so the number of tables required will be: Number of tables = (Number of customers)/(Seating capacity of each table)Number of customers = 25 (the number of primes) + 75 (the number of composites) = 100Number of tables = 100/15 = 6 tables

Therefore, 6 tables are required.

Now, as each prime number attender has to serve an equal number of customers, we need to calculate how many customers each one should serve.

Each prime attender has to serve 75/25 = 3 customers each, as there are 75 composites and 25 primes.

Thus, each prime number attender should serve 3 customers each.

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The surface area of the box increases by 27.4 cm² when the height is increased by 0.2 cm.

To find the increase in surface area, we first need to calculate the initial surface area of the box and then calculate the surface area after increasing the height.

The formula for the surface area of a rectangular prism is given by:

Surface Area = 2*(length width + length height + width*height)

Initial Surface Area:

Length (L) = 13 cm

Width (W) = 8.7 cm

Height (H) = 28 cm

Initial Surface Area = 2*(138.7 + 1328 + 8.7*28)

Next, we calculate the new surface area after increasing the height by 0.2 cm. The new height is:

New Height = Initial Height + Increase in Height = 28 cm + 0.2 cm

New Surface Area = 2*(138.7 + 13(28+0.2) + 8.7*(28+0.2))

To find the increase in surface area, we subtract the initial surface area from the new surface area:

Increase in Surface Area = New Surface Area - Initial Surface Area

Let's calculate the values:

Initial Surface Area = 2*(138.7 + 1328 + 8.728) = 2(113.1 + 364 + 243.6) = 2*(720.7) = 1441.4 cm²

New Surface Area = 2*(138.7 + 13(28+0.2) + 8.7*(28+0.2)) = 2*(113.1 + 377.2 + 244.1) = 2*(734.4) = 1468.8 cm²

Increase in Surface Area = New Surface Area - Initial Surface Area = 1468.8 cm² - 1441.4 cm² = 27.4 cm²

Therefore, the surface area of the box increases by 27.4 cm² when the height is increased by 0.2 cm.

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Answer:

3x18 = 3 (10+8) is an example of the commutative property of multiplication

Step-by-step explanation:

Answer: commutative property of multiplication

Step-by-step explanation:

The segment lengths are given as follows:

The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

The theorem is expressed as follows:

c² = a² + b².

In which:

Considering the geometric mean theorem, the triangle has bases of 7 and 14 - 7 = 7, hence the altitude BD is given as follows:

BD² = 7 x 7

BD² = 7²

BD = 7.

The segment BC is the hypotenuse of a right triangle of two sides with length 7, hence:

(BC)² = 7² + 7²

\(BC = \sqrt{2 \times 49}\)

\(BC = 7\sqrt{2}\)

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Step-by-step explanation:

hope it works

Step-by-step explanation:

514 ÷ 9

5 ÷ 9 = 0

remainder 5 (0×9 = 0 plus 5 is 5)

next digit down

51 ÷ 9 = 5

remainder 6 (5×9 = 45 plus 6 is 51)

next digit down

64 ÷ 9 = 7

remainder 1 (7×9 = 63 plus 1 is 64)

no more digits

so, the result is the combination of the individual divisions

057 or simply 57

and remainder 1.

Therefore, at two separate moments, x = 0.28 and x = 1.17, the ball stands at a height of 15 feet. (rounded to two decimal places).

The meaning of an equation in algebra is a mathematical assertion that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two expressions 3x + 5 and 14, which are split by the 'equal' symbol.

To find out when the ball is at a height of 15 feet, we need to solve the equation:

-16x² + 30x + 5 = 15

First, we can simplify the equation by subtracting 15 from both sides:

-16x² + 30x - 10 = 0

Now we can divide both sides by -2 to make the coefficient of the x² term positive:

8x² - 15x + 5 = 0

This is a quadratic equation in standard form, where a = 8, b = -15, and c = 5. Using the quadratic method, we can find x:

x = (-b ± √(b² - 4ac)) / 2a

Plugging in the values, we get:

x = (-(-15) ± √((-15)² - 4(8)(5))) / 2(8)

x = (15 ± √(225 - 160)) / 16

x = (15 ± √65) / 16

Therefore, the ball is at a height of 15 feet at two different times:

x ≈ 0.28 seconds and x ≈ 1.17 seconds (rounded to two decimal places).

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The missing reason for step 2 is the application of the slope formula option (C) application of the slope formula is correct.

It is defined as the formula for finding the distance between two points. It has given the shortest path distance between two points.

The distance formula can be given as:

\(\rm d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

As we know,

Lines that intersect at a right angle are named perpendicular lines. Lines that are always the same distance apart from each other are known as parallel lines.

From the graph of two parallel lines:

r ║ s

The slope is the ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).

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

Thus, the missing reason for step 2 is the application of the slope formula option (C) application of the slope formula is correct.

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Answer:

5h-fgtx56=y2-6

Step-by-step explanation:

sorry if wrong:(

Answer: 20

Step-by-step explanation:

Answer:

A 1.04d

Step-by-step explanation:

The amount of the loan (d) must be paid, along with the interest (0.04d).

d + 0.04d = 1.04d

Answer : The correct options are, (A), (C) and (D)

Step-by-step explanation :

Given:

Principle = P = (d) dollars

Interest rate = R = 4 %

Time = T = 1 year

First we have to determine the simple interest.

Using simple interest formula:

where,

P = principle  

R = interest rate

T = time

S.I = simple interest

Now put all the given values in the above formula, we get:

Now we have to determine the total amount.

Amount = Principle + Simple interest

Amount = d + 0.04d

Amount = 1.04 d

Amount = d + 1/25d

Thus, the correct options are, (A), (C) and (D)

Answer: b) Large blue t-shirt & Medium RC jeans

Step-by-step explanation:

The subscript numbers attached to the matrix letter represents the:

ROW, COLUMN

\(A=\left[\begin{array}{ccc}a_{1,1}&a_{1, 2}&a_{1, 3}\\a_{2,1}&a_{2, 2}&a_{2, 3}\\a_{3,1}&a_{3, 2}&a_{3, 3}\end{array}\right] \qquad B=\left[\begin{array}{ccc}a_{1,1}&b_{1, 2}&b_{1, 3}\\b_{2,1}&b_{2, 2}&b_{2, 3}\\b_{3,1}&b_{3, 2}&b_{3, 3}\end{array}\right]\\\)

A₁,₃ = 1st row, 3rd column

         1st row is Blue, 3rd column is Large

B₃,₂ = 3rd row, 2nd column

         3rd row is RC jeans, 2nd column is Medium

A₁,₃ + B₃,₂ = Large blue t-shirt & Medium RC jeans

Answer:

19 feet

Step-by-step explanation:

First we must make the scale make sense, that is, it is in the same unit, therefore, we will pass 3 inches to feet, we know 1 foot is 12 inches, therefore:

3 inches * 1 foot / 12 inches = 0.25 feet

Which means that the real equivalence is 0.25: 8, now they are 7 inches, therefore:

7 inches * 1 foot / 12 inches = 0.583333

Now, we calculate the number of actual feet using the scale.

0.583333 * 8 / 0.25 = 18.66 feet

that is to say that the length of the current Kitchen is 19 feet if we round

The time Jack left Santa Clara is 1 : 55 pm

A word problem in math is a math question written as one sentence or more. These statements are interpreted into mathematical equation or expression.

The time for Jack to walk to lose Altos is 25 min and he uses another 25mins to work to Palo alto.

Therefore, the total time he spent is

25mins + 25 mins = 50 mins

He arrived Palo at 2 :45 pm, therefore the time he left Santa Clare will be ;

2:45 pm = 14 :45

= 14:45 - 50mins

= 13:55

= 1 : 55pm

Therefore he left at 1:55 pm

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Answer:

Correct!

Step-by-step explanation:

-5(x+8)=-25

x+8=5

x=-3

Answer:

here, -5(x+8)=-25

or, -5x +(-40)= -25

or, -5x=-25+40

or, x= 15/-5

therefore the value of x is -3....ans..

hope u understood..

Answer:

  100x +150y ≤ 1200

Step-by-step explanation:

The amount Isabel will spend on 5 oz cups is 100x. The amount she will spend on 8 oz cups is 150x. In order to stay within her budget she must have the total be less than or equal to the budget amount:

  100x +150y ≤ 1200

Answer: I THINK 250

Step-by-step explanation: 125 is half and 125 times 2 is 250.

Answer:

13-f=n

Step-by-step explanation:

he starts with 13 folds some number "f" of them and has some number "n" still to do

The linear equation that links N and F in the previously stated condition is N + F = 13.

Because a straight line emerges when we attempt to display the graph of the provided linear function, a linear equation is known as linear.

Given Alan has 13 shirts to fold. Let N be the number of shirts he would have left to fold after folding F of them.

The linear equation that satisfies the above statement is

N + F = 13

therefore, N + F = 13 is the linear equation that relates N and F in the above-given condition.

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The standard form is used to show horizontal lines and vertical lines, while the slope intercept form shows the slope and y intercept of the linear equation.

An equation is an expression relating two or more numbers and variables.

The standard form of a linear equation is:

Ax + By = C

where A, B and C are constants

The slope - intercept form of a linear equation is:

y = mx + b

Where m is the rate of change(slope) and b is the y intercept.

The standard form is used to show horizontal lines (A=0) and vertical lines (B=0), while the slope intercept form shows the slope and y intercept.

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The intervals of each behavior of the function are given as follows:

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Answer: The temperature of an oven can be modeled by a linear equation. In this case, the initial temperature of the oven is 75° and it will increase at a rate of 25° per minute after being turned on.

The equation to model the temperature of the oven t minutes after being turned on is:

Temp = 75 + 25t

Where Temp is the temperature of the oven in degrees and t is the number of minutes after being turned on.

For example, if we want to find the temperature of the oven 17 minutes after being turned on, we can substitute t = 17 into the equation:

Temp = 75 + 25 * 17 = 75 + 425 = 500°

So, the temperature of the oven 17 minutes after being turned on is 500°.

In general, the temperature of the oven t minutes after being turned on can be found by substituting the value of t into the equation:

Temp = 75 + 25t.

Step-by-step explanation:

The temperature of an oven can be modeled by a linear equation. In this case, the initial temperature of the oven will be;  75° and it will increase at a rate of 25° per minute after being turned on.

An equation is an expression that shows the relationship between two or more numbers and variables.

The equation to model the temperature of the oven t minutes is:

Temp = 75 + 25t

Where, Temp is the temperature of the oven in degrees and t is the number of minutes after being turned on.

For example, if we need to find the temperature of the oven 17 minutes after being turned on, we can substitute t = 17 into the equation:

Temp = 75 + 25 * 17 = 75 + 425

Temp = 500°

Thus, the temperature of the oven 17 minutes after being turned on is 500°.

In general, the temperature of the oven t minutes after being turned on can be find by substituting the value of t into the equation:

Temp = 75 + 25t.

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Answer:

8% decrease

Step-by-step explanation:

50 x 2 = 100

46 x 2 = 92

100 - 92 = 8

Answer:

slope is 3/4 or .75

Step-by-step explanation:

Equation of line is

y= .75 + 1.5

hope this helps :)

Answer:

r = 7.5

Step-by-step explanation:

Circle equation: \((x - h)^2 + (y - k)^2 = r^2\)

Since we are already give r², we simply just take the square root of 56.25, and we should get 7.5 as our final answer!

The function y=3x+12 in factored form is (3x+12) and the zero of the function is -4.

A linear function is a polynomial of degree 1, or a mathematical expression that describes a relation between two variables. It is often written in the form y = mx + b, where m is the slope, x is the independent variable, and b is the y-intercept.

The factored form of a linear equation is the same as the standard form of the equation, with the exception that the coefficients of the variables are each expressed as a product of their prime factors. In the case of y=3x+12, the factored form is (3x+12). The zero of the function (also known as the root of the equation) is the value of the variable that will result in a value of 0 for the equation. To find the zero of the function, we need to set the equation equal to 0 and solve for the value of x. When we set y=0, we get 3x+12=0, which can be solved to get x=-4. Therefore, the zero of the function is -4.

The function y=3x+12 in factored form is (3x+12) and the zero of the function is -4.

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-1 does not equal 0, the equation is not true for any value of "a". This means that there is no value of "a" for which the function f(x) is continuous at x = 1.

To determine the value of "a" for which the function f(x) is continuous at x = 1, we need to check if the left-hand limit and the right-hand limit of f(x) as x approaches 1 are equal, and if the value of f(x) at x = 1 is equal to these limits.

First, let's calculate the left-hand limit of f(x) as x approaches 1. For x < 1, the function is given by f(x) = (ax² - 1). To find the left-hand limit, we substitute x = 1 into this expression:

lim(x→1-) f(x) = lim(x→1-) (ax² - 1) = a(1²) - 1 = a - 1.

Next, let's calculate the right-hand limit of f(x) as x approaches 1. For x > 1, the function is given by f(x) = (a(x² - 2x + 1)). Substituting x = 1 into this expression, we have:

lim(x→1+) f(x) = lim(x→1+) (a(x² - 2x + 1)) = a(1² - 2(1) + 1) = a(1 - 2 + 1) = a.

For the function f(x) to be continuous at x = 1, the left-hand limit and the right-hand limit should be equal. Therefore, we have:

a - 1 = a.

To solve this equation for "a," we subtract "a" from both sides:

-1 = 0.

Since -1 does not equal 0, the equation is not true for any value of "a". This means that there is no value of "a" for which the function f(x) is continuous at x = 1.

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