A group of 8 friends went to lunch and spent a total of $76, which included the food bill and a tip of $16. They decided to split the bill and tip evenly among themselves.

Which equations and solutions describe the situation? Select two options.
The equation StartFraction 1 over 8 EndFraction (x + 16) = StartFraction 76 over 8 EndFraction represents the situation, where x is the food bill.
The equation StartFraction 1 over 8 EndFraction (x + 16) = 76 represents the situation, where x is the food bill.
The solution x = 60 represents the total food bill.
The solution x = 60 represents each friend’s share of the food bill and tip.
The equation 8 (x + 16) = 76 represents the situation, where x is the food bill.

Ordered pair (0, 6) and  (2, 7)  satisfy both inequalities in the system and are solutions to the system.

To identify the graph that represents the given system of inequalities y > x + 5 and y ≥ 2x + 3, we need to graph the individual inequalities and find the region where they overlap.

When we plot the graph of inequality separately:

    2. y ≥ 2x + 3:

The overlapping shaded region represents the solution to the system of inequalities.

To find two ordered pairs that are solutions to the system, we can choose any points within the overlapping region. Let's select two points:

Ordered pair 1: (0, 6)

Ordered pair 2: (2, 7)

These two points satisfy both inequalities in the system and are solutions to the system.

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The correct question is given below -

Identify the graph that represents the given system of inequalities. Also identify two ordered pairs that are solutions to the system.

y > x + 5

y ≥ 2x + 3

Answer:

45 m^2

Step-by-step explanation:

The value of the probability of orange is (c) 0.24

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

Spinner and the number of spins

Using the above as a guide, we have the following:

Orange = 12

Total = 50

So, we have

P(Orange) = Orange/Total

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

P(Orange) = 12/50

Evaluate

P(Orange) = 0.24

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Answer:

I think it's 56 is the answer

Answer:

$100.00

Step-by-step explanation:

Compound interest is calculated by multiplying the initial loan amount, or principal, by the one plus the annual interest rate raised to the number of compound periods minus one. This will leave you with the total sum of the loan including compound interest.

The amount I have to pay back in full is approximately 100 dollars.

Borrowers are required to pay interest on interest in addition to principal since compound interest accrues and is added to the accrued interest from prior periods.

We know the formula for compound interest is,

A = P(1 + r/100)ⁿ.

Where, A = amount, P = principle, r = rate, and n = time in years.

The formula for compound interest compounded semi-annually is,

A = P(1 + (r/2)/100)²ⁿ. (two semi-annuals in one year)

Therefore, A = 95(1 + (5.2/2)/100)²ˣ¹.

A = 95(1 + 0.026)².

A = 95(1.026)².

A = 95×1.052676.

A = $100 approximately.

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Answer:

x = 1/5 ,  and   x = - 1/5

Step-by-step explanation:

25x² – 1 = 0

5²x² - 1² = 0

(5x - 1)(5x + 1) = 0

5x -1 = 0,  5x + 1 = 0

x = 1/5 ,     x = - 1/5

To find the total number of people participating in each activity, we can add the values in the male and female columns for each activity in the given table.

By adding the values in the male and female columns for each activity, we can determine the total number of people participating in each activity.

For the "Movies" activity, the total number of participants is 59.2 + 65.4 = 124.6 million.

For the "Exercise Programs" activity, the total number of participants is 54.3 + 59.0 = 113.3 million.

For the "Sports Events" activity, the total number of participants is 40.5 + 31.1 = 71.6 million.

For the "Home Improvement" activity, the total number of participants is 45.4 + 41.8 = 87.2 million.

By adding the values in the male and female columns, we can determine the total number of people participating in each activity. This allows us to analyze and compare the participation levels across different activities.

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Answer:

D

Step-by-step explanation:

because the odds have to be even if the possobility number is even

The correct statement is: the volume of the cylinder is 8 cubic inches more than that of the cone.

The volume of cone (V) = 1/3 * πr²h

Volume of cylinder (V) = πr²h

Where, r is the radius of their bases.

The base area formula for the cone = πr²

Calculate the area of the base of the cone that has a radius (r) of 2.5 in:

Area of the base of the cone = π(2.5)² ≈ 19.6

The volume of the cone (V) = 1/3 * πr²h = 1/3 * π * 2.5² * 6.5

≈ 42.5 cubic inches

Volume of cylinder (V) = πr²h = π * 2² * 4

≈ 50.3 cubic inches

The difference in volume = 50.3  - 42.5

= 7.8 ≈ 8 cubic inches

Therefore, the only statement that is true is: the volume of the cylinder is 8 cubic inches more than that of the cone.

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The solution of the system of equation are,

x = 1/3 and y = 0

We have to given that;

System of equations are,

3x - 4y = 11

y + 3x = 1

From (ii);

y = 1 - 3x

Put above value in (i);

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

3x - 4 + 12x = 1

15x = 5

x = 1/3

From (i);

y + 3 (1/3) = 1

y + 1 = 1

y = 0

Thus, The solution of the system of equation are,

x = 1/3 and y = 0

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The solution to the system of equations is x = 1 and y = -2.

We have,

3x - 4y = 11

y + 3x = 1

To solve the system of equations:

3x - 4y = 11

y + 3x = 1

We can use the method of substitution or elimination.

Let's solve it using the elimination method.

Multiply equation 2) by -1 to eliminate the term 3x:

-1(y + 3x) = -1(1)

-y - 3x = -1

Now we have the following system of equations:

3x - 4y = 11

-y - 3x = -1

Add equation 1) and equation 2) together:

(3x - 4y) + (-y - 3x) = 11 + (-1)

3x - 4y - y - 3x = 10

-5y = 10

Divide both sides of the equation by -5:

-5y / -5 = 10 / -5

y = -2

Now substitute the value of y = -2 into equation 2):

-2 + 3x = 1

Add 2 to both sides:

3x = 3

Divide both sides by 3:

3x / 3 = 3 / 3

x = 1

Therefore,

The solution to the system of equations is x = 1 and y = -2.

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Answer:

Step-by-step explanation:

Given cylinder with:

We need to fill it up to:

The volume is:

You need to spend:

Step-by-step explanation:

You have to retain a certain amount of money

in that account forever. Say you need $50 to

start an account, you have $200 in that account.

You cannot take out more than $150 from that

account.

Answer:

A: If you do not keep at least that much money in the account, you will be assessed fees.

Step-by-step explanation:

Answer:

2,4,5 doesn't form a triangle

To solve this question we will use the following diagram as reference:

To answer the question we have to find the missing side of the right triangle, using the Pythagorean theorem we get:

Where a, and b are the legs of the triangle, and c the hypothenuse.

Substituting a=84, and c=91 we get:

Answer: 35 ft.

The expression that defines sn is startfraction 1 over 4 raised to the power of (n + 2) endfraction.

The series is given as: one-fourth, startfraction 1 over 16 endfraction, startfraction 1 over 64 endfraction, startfraction 1 over 256 endfraction, ellipsis.

To find the expression that defines sn, we can observe the pattern in the series.

The numerator of each term is always 1, and the denominator follows the pattern of powers of 4.

So, the nth term of the series can be written as startfraction 1 over 4 raised to the power of (n + 2) endfraction.

Therefore, the expression that defines sn is startfraction 1 over 4 raised to the power of (n + 2) endfraction.

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1) General solution for second order differential equation, y" – 2y' + y = 0, is y = (c₁x + c₂)eˣ .

2) General solution for differential equation, 9y" + 6y' + y = 0, is y =(c₁x + c₂)e⁻³ˣ.

3) General solution for differential equation, 4y"- 4y'- 3y = 0, is y = c₁ e⁶ˣ+ c₂e⁻⁴ˣ.

4) General solution for differential equation, 4y" + 12y' +9y = 0, is y = (c₁x + c₂)e⁻⁶ˣ.

5) General solution for differential equation, y" – 2y' + 10y = 0, is y = eˣ (c₁cos(6x) + c₂sin(6x)).

6) General solution for differential equation, y" – 6y' +9y = 0 is y = (c₁x + c₂)e³ˣ.

7) General solution for differential equation, 4y" + 17y' + 4y = 0, is y = c₁e⁻ˣ + c₂e⁻¹⁶ˣ.

8) General solution for differential equation, 16y" + 24y' +9y = 0, is y = (c₁x + c₂)e⁻¹²ˣ.

9) General solution for differential equation, 25y" – 20y' + 4y = 0, is y = (c₁x + c₂)e¹⁰ˣ.

10) General solution for differential equation, 2y" + 2y' + y = 0, is y = e⁻ˣ (c₁cos(2x) + c₂sin(2x)).

General solution is also called complete solution and complete solution = complemantory function + particular Solution

Here right hand side is zero so particular solution is equals to zero. Therefore, evaluating the complementary function will be sufficient to determine the general solution to the differential equation.

1) y"-2y' + y = 0, --(1)

put D = d/dx, so (D² - 2D + 1)y =0

Auxiliary equation for (1) can be written as, m² - 2m + 1 = 0 , a quadratic equation solving it by using quadratic formula,

\(m =\frac{-(- 2) ± \sqrt { 4 - 4}}{2}\)

=> m = 1 , 1

The roots of equation are real and equal. So, general solution is y = (c₁x + c₂)eˣ .

2) 9y" + 6y' + y = 0 or (9D² + 6D + 1)y =0 Auxiliary equation can be written as, 9m² + 6m + 1 = 0 , a quadratic equation solving it by using quadratic formula, \(m =\frac{ - (6) ± \sqrt {36 - 4×4}}{2}\)

=> m = - 6/2

=> m = -3 , -3

The roots of equation are real and equal. So, general solution is y = (c₁x + c₂)e⁻³ˣ.

3) 4y"- 4y'- 3y = 0

put D = d/dx, so (4D² - 4D - 3)y = 0

Auxiliary equation can be written as, 4m² - 4m - 3 = 0 , a quadratic equation solving it by using quadratic formula, \(m =\frac{-(-4) ± \sqrt {16 - 4×4×(-3)}}{2}\)

=> m = (4 ± 8)/2

=> m = -4 , 6

The roots of equation are real and equal. So, general solution is y = c₁ e⁶ˣ + c₂e⁻⁴ˣ.

4) 4y" + 12y' +9y = 0 or (4D² + 12D + 9)y= 0

Auxiliary equation can be written as, 4m² + 12m + 9= 0 , a quadratic equation solving it by using quadratic formula, \(m =\frac{-(12) ± \sqrt{144 - 4×4×9}}{2}\)

=> m = -12/2

=> m = -6 , -6

The roots of equation are real and equal. So, general solution is y = (c₁x + c₂)e⁻⁶ˣ.

5) y" – 2y' + 10y = 0 or (D² - 2D + 10)y = 0 Auxiliary equation can be written as, m² - 2m + 10 = 0 , a quadratic equation

solving it by using quadratic formula,

\(m =\frac{ - (-2) ± \sqrt {4 - 4×1×10}}{2}\)

=> m = (2 ± 6i)/2 ( since, √-1 = i)

=> m = 1 + 6i , 1-6i

The roots of equation are imaginary and unequal. So, general solution is y =eˣ (c₁cos(6x) + c₂sin(6x)).

6) y" – 6y' +9y = 0 or (D²- 6D + 9)y =0

Auxiliary equation can be written as, m² - 6m + 9 = 0 , a quadratic equation

solving it by using quadratic formula,

\(m =\frac{ - (-6) ± \sqrt {36 - 4×1×9}}{2}\)

=> m = 6/2 = 3,3

The roots of equation are real and equal. So, general solution is y = (c₁x + c₂)e³ˣ.

7) 4y" + 17y' + 4y = 0 or (4D²+ 17D + 4)y=0

Auxiliary equation can be written as, 4m² + 17m + 4 = 0 , a quadratic equation solving it by using quadratic formula, \(m =\frac{- (-17) ± \sqrt {16 - 4×4×17}}{2}\)

=> m = ( -17 ± 15)/2

=> m = (-17 + 15)/2, (- 17 - 15)/2= -1, -16

The roots of equation are real and unequal. So, general solution is y = c₁e⁻ˣ + c₂e⁻¹⁶ˣ.

8) 16y"+24y'+9y =0 or (16D²+ 24D + 9)y= 0

Auxiliary equation can be written as, 16m² + 24m + 9 = 0 , a quadratic equation solving it by using quadratic formula, \(m =\frac{ - (24) ± \sqrt {576 - 4×9×16}}{2}\)

=> m = (-24 ± 0)/2

=> m = -12,-12

The roots of equation are real and equal. So, general solution is y = (c₁x + c₂)e⁻¹²ˣ.

9) 25y"- 20y' +4y =0 or (25D²-20D + 4)y = 0

Auxiliary equation can be written as, 25m²- 20m + 4 = 0 , a quadratic equation solving it by using quadratic formula, \(m =\frac{ - (-20) ± \sqrt {400 - 4×4×25}}{2}\)

=> m = 20/2

=> m = 10 , 10

The roots of equation are real and equal. So, general solution is y = (c₁x + c₂)e¹⁰ˣ.

10) 2y" + 2y' + y = 0 or (2D²+ 2D + 1)y =0

Auxiliary equation can be written as, 2m² + 2m + 1 = 0 , a quadratic equation solving it by using quadratic formula, \(m =\frac{ - (2) ± \sqrt {4 - 4×1×2}}{2}\)

=> m = (- 2 ± 4i)/2 ( since, √-1 = i)

=> m = -1 + 2i , -1 - 2i

The roots of equation are imaginary and unequal. So, general solution is y = e⁻ˣ (c₁cos(2x) + c₂sin(2x)). Hence, required solution of differential equation is y = e⁻ˣ (c₁cos(2x) + c₂sin(2x)).

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Answer:

The answer is \(x = - 30\), by using the Subtraction Property of Equality.

Step-by-step explanation:

Solve for \(x\):

\(-2 = x + 28\)

Turn the equation over:

\(x + 28 = -2\)

-Subtract both sides by \(28\) by using Subtraction Property of Equality:

\(x + 28 - 28 = -2 - 28\)

\(x = -30\)

So, the final answer is \(x = -30\) .

Answer:

Is this from the VHAP

Step-by-step explanation:

Given:

The line symmetry.

Aim:

We need to find the transformation that line symmetry involved.

Explanation:

Recall that line symmetry is the line in the middle acts as a mirror.

the figure flips to make a mirror image of itself in reflection.

Hence the line of symmetry is involved reflection transformation.

Final answer:

The line of symmetry is involved in reflection transformation.

There is a total number of 5 + 3p pets in altogether

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

Cats = 5

Dogs = 3p

The total number of pets is the sum of the number of dogs and the number of cats

This is represented as

Pets = Cats + Dogs

Substitute the known values in the above equation

So, we have the following equation

Pets = 5 + 3p

The above equation cannot be further simplified

Hence, the expression is 5 + 3p

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Answer:

I dont get the question

Step-by-step explanation:

Answer:

STEM: science technology enginearing maths.

Step-by-step explanation:

i never used the art in this definition

1 crates=8 apples

6 crates=?

=6*8

=48 apples

15 crates=15*8

=120

Now,

read carefully what question says,

(ratio, the number of apple in six crates ((to)) the total number of apples)

So,

=40/120

=4/12

=2/6

=1/3answer

so 1:3 is the answer

Am I correct?? let me know friend

It should be noted that (6 ten thousands 3 hundreds) x 10 will give a value of 603000

Based on the information given, it should be noted that we want to calculate (6 ten thousands 3 hundreds) x 10

It should be noted that 6 ten thousands is 60000.

It should be noted that 3 hundreds will be 300.

Therefore, 6 ten thousands 3 hundreds x 10 will be:

= (60000 + 300) × 10

= 60300 × 10

= 603000

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Answer: Its a

Step-by-step explanation:

The value of \(x=3+\sqrt{5}\) make the quadratic equation true.

Given equation is,

                     \((x-3)^{2}=5\)

We have to solve above quadratic equation.

Expand above equation first,

                 \((x-3)^{2}=5\\\\x^{2} +9-6x=5\\\\x^{2} -6x+4=0\\\\x=\frac{6\pm \sqrt{36-16} }{2} \\\\x=3\pm\sqrt{5}\)

Thus, the value of \(x=3+\sqrt{5}\) make the quadratic equation true.

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Answer in explanation:

although there's an addition sign, you subtract the two because a

(+) + (-) = (-) subtract

[This is a general rule, writing down the "rules" for reference is a good way to help if your having trouble]

subtract to find your answer (you keep the sign of 1.8 because it's the larger number.)

1.3 + (-1.8) =

-0.5

-0.5 is your answer

Hope this is clear!

The equation for money collected m for h boxes of chocolate bars sold is m = 30h.

We are given that the band is selling every bar of chocolate for $1.50

Now, they have boxes of chocolate, with every box containing 20 bars of chocolate in them.

Hence if we are going to calculate the amount of money collected on selling one box it will be

20 X $1.5

= $30

We need to find the equation for the amount of money collected based on the number of boxes of chocolate bars sold.

We have been given that money collected should be represented b m while the number of chocolate boxes sold should be represented by h

Now we know that

Money collected = price per box X no.of boxes sold

we have already calculated the price per box hence we get

m = 30h

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Bar graphs can be used to display both discrete and continuous data, making them a versatile tool for visualizing a wide range of information.

The graphic presentation of data that displays its categories as rectangles of equal width with their height proportional to the frequency or percentage of the category is called a bar graph.

In a bar graph, the bars represent the categories being compared and are arranged along the horizontal axis, with the height of each bar representing the frequency or percentage of the category being displayed.

Bar graphs are a useful tool for presenting numerical data in a visually appealing way, making it easy for viewers to compare different categories and draw conclusions from the data.

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Answer:

false

Step-by-step explanation:

A set of people who interact on the basis of shared expectations and who possess some degree of common identity. A small group of people who interact over a relatively long period of time on a direct and personal basis will share expectations.

Answer:

8

Step-by-step explanation:

You know that the horizontal lines are parallel to each other.

The 8 and x is both on that diagonal right there. Since the horizontal lines are parallel, that means the angle of 8 should have the same angle as x.

*I forgot what this thing was called but please trust me i learned this before*