question
A group of friends’ dinner bill before tax is $122.75. The sales tax rate is 8%. They want to leave an 18% tip after tax. What is their total dinner bill, including tax and tip, rounded to the nearest cent?
Responses

Only B is not true, because the vertical line test is to know if a graph is from a function.

The correct statements regarding the quadratic function y = x² + 3x + 1 are given as follows:

The quadratic function in this problem is defined as follows:

y = x² + 3x + 1.

Hence the coefficients are given as follows:

a = 1, b = 3, c = 1.

The x-coordinate of the vertex is given as follows:

x = -b/2a = -3/2.

The y-coordinate of the vertex is then given as follows:

y = (-3/2)² + 3(-3/2) + 1

y = 9/4 - 9/2 + 1

y = 9/4 - 18/4 + 4/4

y = -5/4.

Hence the vertex-form definition of the quadratic equation is given as follows:

y = (x + 3/2)² - 5/4.

Due to the positive leading coefficient, the vertex means that the function has a minimum of y = -5/4 at x = -3/2.

The domain of the function is all real values, as the quadratic function has no constraints such as a fraction or an even root.

The complete problem is given by the image shown at the end of the answer.

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5.

The sum of three consecutive integers is 228. You can write this situation, in an algebraic way, as follow:

x + (x + 1) + (x + 2) = 228

where the lower number is x, and the largest number is (x + 2).

You solve the previous equation for x:

x + (x + 1) + (x + 2) = 228 eliminate prenthesis

x + x + 1 + x + 2 = 228 sum similar terms

3x + 3 = 228 rest 3 both sides

3x = 228 - 3

3x = 225 divide by 3

x = 225/3

x = 75

Then, the lower number is 75, and the largest one is (75+2) = 77

580 miles.

On the first day of the tour, she went = east

On the second day she went = north

On the third day = west

On the fourth day she went = south

On the fifth day she went = east

Miles was she from her starting point at the end of the 40th day =?

She was 580 miles from her starting point at the end of the 40th day.

Solution is given in the attached picture.

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Answer:

(-13, - 6)

Step-by-step explanation:

Midpoint =(x₁ + x₂)/2, (y₁ + y₂)/2

(-4,-6) = (9+x)/2, (1+y)/2

9+x= - 4

X= - 13

1+y= - 6

Y= - 7

Ans=

(-13, - 6)

Let's begin by listing out the information given to us:

216^(-2n) = (1/6)^(3n+2)

6 is a factor of 216: 216 = 6³

1/6 = 6^(-1)

⇒ 6^(-2*3n) = 6^[(-1*(3n+2)]

⇒ 6^(-6n) = 6^(-3n-2)

Since both sides are in the same base, we equate the exponents. We have:

-6n = -3n - 2

Add "6n" from both sides, we have:

-6n + 6n = -3n + 6n - 2 ⇒ 0 = 3n - 2

⇒ 3n = 2

Answer: y = -1x + 3

Step-by-step explanation:

Point-Slope form: y - y1 = m(x-x1)

Replace the form with the values provided:

y - 15 = -1(x+12)

Once you get this, you need to get y by itself in order to get it in slope intercept form.

Distribute:

y -15 = -1x - 12

Add -15 to the right side:

y = -1x + 3

The result of the equation -3/2 = (-2/3)w - 4/5 is w = 21/20

The equation is

(-2/3)w - 4/5 = -3/2

Here we have to rearrange the terms and combine the like terms.

Mover 4/5 to the right hand side of the equation

(-2/3)w = -3/2 + 4/5

(-2/3)w = -7/10

Move the number (-2/3) to the right hand side of the equation

x = -7/10 ÷ (-2/3)

To make it multiplication, take the reciprocal of the the second number

x = -7/10 × (-3/2)

Multiply the numbers

x = 21/20

Hence, the result of the equation -3/2 = (-2/3)w - 4/5 is w = 21/20

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The measurement of the largest square tiles she can use is 6 feet.

Finding all common factors between two numbers and choosing the biggest one yields the highest common factor (HCF). For instance, the numbers 8 and 12 share the elements 1, 2, and 4. Four is the greatest common factor.

Steps for calculating HCF:

Step 1: Write each integer as the sum of its prime factors in step one.

Step 2: List the shared factors between the two numbers.

Step 3: The HCF is the sum of all the common prime factors ( use the lower power of each common factor)

Given,

Measurement of the rectangular floor:

length = 150 feet

breadth = 132 feet

The measurement of the largest square can be calculated by finding the HCF of 132 and 150.

132 = 2*2*3*11

150 = 2*3*5*5

So, HCF (132, 150) = 2*3 = 6.

Hence, the measurement of the largest square tiles she can use is 6 feet.

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Answer:

The solution to the given system is:

x = 3

y = -3

Explanation:

Given the following system of equation:

The solution to these is the point where the lines intersect.

The graph is shown below:

The solution is x = 3, y = -3

In Close Encounters of a Bear Kind, the statement that represents the author's primary attitude towards John's work is that C. John's work is dangerous.

According to the author, he stated that people don't usually realize that bears

can be very dangerous.

He further stated that they will reap people apart of they e the chance. The narrator gave an example about how he walked out at night and had to run back home for his dear life. This was why he stated that the job of John whom was a photographer was a dangerous one.

In conclusion, the correct option is C.

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No, the given relation is not a function. An association between items of two sets—the domain and the codomain—is known as a binary relation.

A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

A binary connection in mathematics links elements of one set, referred to as the domain, with elements of another set, referred to as the codomain. A new set of ordered pairs made up of elements from sets X and Y and x in X is known as a binary relation across these sets.

Al-Biruni and Sharaf al-Din al-Tusi, two Persian mathematicians, are responsible for the earliest documented treatment of the concept of function. Initially, functions represented the idealised relationship between two changing quantities.

Consider the given relation

{(0.3, 0.6), (0.4, 0.8), (0.3, 0.7), (0.5, 0.5)}

We need to check whether the given relation is function or not.

A relation is a function if there exist a unique value of y for each value of x.

In the given relation, for x=0.3 there exist more than one value of y.

y=0.6 at x=0.3

y=0.7 at x=0.3

For one input there exist more than one output. Therefore, the given relation is not a function.

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For a 44° elevation angle, the grade will be 96%.

Given that,

if the angle of elevation of the road is 44 degrees,

The difference in the road's altitude over a horizontal distance of 100 feet is what is referred to as the percentage grade. For instance, a road with a 5% slope will rise 5 feet for every horizontal 100-foot distance.)

A tangent ?

One of the six basic trigonometric functions is tangent, denoted as tan().

The ratio of the opposite side length to the adjacent side length is the definition of the tangent value of the one sharp angle,, in a right triangle.

[tex]tan \alpha = sin\alpha /cos \alpha[/tex]

The tangent of the angle is the ratio of rise to run.

tan(angle) = grade

tan(44°) ≈ 0.96 = 96%

Therefore, The grade will be 96% for an angle of elevation of 44°.

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If  Han and Tyler both started running toward each other from opposite ends of a 10-mile path along a river. Han and Tyler will not meet on the path within 1 hour

The following information is gotten from the question

Han and Tyler both started running toward each other from opposite ends of a 10-mile path

Han runs at a pace of 12 minutes per mile

Tyler runs at a pace of 15 minutes per mile

Distance covered by Han in 1 hour

12 minutes = 1 mile

60 minutes = ? miles

cross multiplying gives

? = 60 / 12

? = 5 miles

Distance covered by Tyler in 1 hour

15 minutes = 1 mile

60 minutes = ? miles

cross multiplying gives

? = 60 / 15

? = 4 miles

This means that Han covers 5 miles in and Tyler covers 4 miles, in a 10 mile distance.

In one hour the distance covered

= 5 miles + 4 miles

= 9 miles

9 miles is less than 10 miles hence they will not meet in the path within one hour

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The required values for a 95 percent confidence interval for population standard deviation are CI₈² = [1.1894, 5.221]

                                         CI₈ = [1.0906, 2.2849]

n = 16, Standard Deviation = 1.4764, Var = 2.1796

X²₀.₀₂₅,₁₅ = 6.26, X²₀.₉₇₅,₁₅ = 27.49

CI₈² = [(15ₓ2.1796/27.48),(15ₓ2.1796/6.26)] = [1.1894, 5.221]

CI₈ = [[tex]\sqrt{15*2.1796/27.48} , \sqrt{15*2.1796/6.26}[/tex]] = [1.0906, 2.2849]

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The distance between the two points in simplest radical form(−2,−7) and (5,0) is 9.8995

Distance can be described as the differences that exist between two points and this can be expressed i different form such as the radical form.

We can calculate the distance between the two points by firstly expressed them as :

(−2) - (5) = -7

(-7) - 0 = -7

Then the distance between them can be found as :

Distance = (-7)^2 + (-7)^2 = 49 +49 = 98

Then we will find the square root of the the figure as

= [tex]\sqrt{98}[/tex] = 9.8995

The formula can as well be used to find this by substituting the values of x and y into the formula as :

x1=-2

y1=-7

x2=5

y2=0

[tex]d = \sqrt{ ( x_{2} - x_{1} )^{2} + ( y_{2} - y_{1} )^{2}}[/tex]

then [tex]d = \sqrt{ ( 5 - (-2 )^{2} + ( 0 - (-7) )^{2}}[/tex]

= [tex]\sqrt{ 49^{2} + 49^{2} }[/tex]

= [tex]\sqrt{98}[/tex]

=9.8995

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Answer:

a = 0 , a = 9

Step-by-step explanation:

a(a - 9) = 0

equate each factor to zero and solve for a

a = 0

a - 9 = 0 ⇒ a = 9

The function; g(x)=f(x+ 2)+2, it follows that the vertex of the function is;

(5, 3+2) +2 = (5, 5) + 2

Given,

A quadratic function y=f(x)y=f(x) is plotted on a graph and the vertex of the resulting parabola is (5, 3)(5,3).

To find the what is the vertex of the function defined as g(x)=f(x+2)+2g(x)=f(x+2)+2

Now,

What is the equation of the parabola?

Let the point (h, k) be the vertex of the parabola and a be the leading coefficient.

Then the equation of the parabola will be given as,

y = a(x - h)² + k

A quadratic function y = f(x) is plotted on a graph and the vertex of the resulting parabola is (5, 3).

Hence, if the function; g(x)=f(x+ 2)+2, it follows that the vertex of the function is; (5, 3+2) +2 = (5, 5) + 2.

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The three sigma control limits range from 0 to 8.20 for this size inspection limit and The probability of a type I error is 0.0038.

The inspection unit calculator in this case is 2

1.5 non-conformities on average per machine

Consequently, we would typically discover 2 * 1.5 = 3 non-conformities.

Here, C equals 3.

Lower Limit = C - 3 * c, which equals 3 - 3 * sqrt (3), which results in -2.19 (impossible), therefore 0

Reduced Limit = 0

Upper Limit: 8.20 when C + 3 * с + 3 + 3 * sqrt(3)

In this case, the three sigma control limits range from 0 to 8.20 for this size inspection limit.

(b) Type I errors happen when non confirmations go above the acceptable range.

This is a POISSON (3)

P(c > 8.20) = -1 POISSON (8, 3, true)

=1 - 0.9962

= 0.0038

In this case, the probability of a type I error is 0.0038.

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In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data

initial money = $8

final money = $11

percent of change = ?

Step 02:

percent of change

percent of change = ( final money - initial money ) / initial money * 100

= ( 11 - 8 ) / 8 * 100

= 3/8 * 100

= 0.375 * 100 = 37.5 %

The answer is:

The percent of change is 37.5 %

The number of hour (time) for which workout plan A would last is 0.75 hour. Also, the number of hour (time) for which workout plan B would last is 0.5 hour.

In order to solve this word problem, we would assign variables to the number of hours (time) each plan and then translate the word problem into algebraic equation as follows:

Translating the word problem into an algebraic equation, we have;

On Friday  ⇒     6x + 5y = 7    ....equation 1.

On Saturday  ⇒ 2x + 3y = 3     ....equation 2.

Next, we would solve the simultaneous equation by using elimination method:

3 × (2x + 3y = 3) = 6x + 9y = 9    ........equation 3.

Subtracting equation 1 from equation 3, we have:

6x + 9y = 9

6x + 5y = 7

4y = 2

y = 2/4

y = 1/2

y = 0.5 hour.

For the value of x, we have:

6x + 5y = 7

6x + 5(0.5) = 7

6x + 2.5 = 7

6x = 7 - 2.5

6x = 4.5

x = 4.5/6

x = 0.75 hour.

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Complete Question:

Charmaine the trainer has two solo workout plans that she offers her clients: Plan A and Plan B. Each client does either one or the other (not both). On Friday there were 6 clients who did Plan A and 5 clients who did Plan B. On Saturday there were 2 clients who did Plan A and 3 who did Plan B Charmaine trained her Friday clients for a total of 7 hours and her Saturday clients for a total of 3 hours. How long does each of the workout plans last?

The location of √ 7 on a number line between 2 and 3.

A number line is a picture of a graduated straight line that serves as a visual representation of real numbers in primary mathematics. Every number line point is considered to correspond to a real number and every real number to a number line point.

A number line is a long straight line with numbers marked at equal intervals. On a number line, we can argue that as we move to the right, the value of numbers increases. This signifies that the numbers on the right are more than those on the left.

A number line shows how numbers are related. It's a line with check marks next to each number. The numerals get smaller as you move left on the number line. The numbers grow larger as you move closer to the number line.

In this case, ✓7 is 2.65. This number can be found between 2 and 3. This should be the true statement since the options aren't given.

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Northside Christian Academy has 528 students enrolled this year. That is an in- crease of 10% over last year's enrollment. How many students were enrolled last year?

Let

x ------> students enrolled last year

we have that

100%+10%=110%=110/100=1.10

so

528=1.10x

solve for x

x=528/1.10

x=480

The best estimate of the magnitude of the box's acceleration is equal to: B. 11 m/s².

In order to determine the magnitude of the acceleration of this box, we would first of all calculate the magnitude of the kinetic frictional force.

Mathematically, the kinetic frictional force that is acting on a physical body can be calculated by using this equation:

F = μkN = μk(mg)

Where:

Substituting the given parameters into the formula, we have;

F = 0.20 × 2.0 × 9.81

F = 3.924 Newton.

By applying Newton's second law of motion, the net force is given by:

∑Fx = Applied force - kinetic frictional force = ma

Acceleration, a = [Applied force - kinetic frictional force]/m

Acceleration, a = [25 - 3.924]/2

Acceleration, a = 21.076/2

Acceleration, a = 10.538 ≈ 11 m/s²

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[tex]-4x-1=-y\\y[/tex]

Flip the equation:

[tex]-y=-4x-1[/tex]

Divide both sides by -1:

[tex]\frac{-y}{-1} =\frac{-4x-1}{-1}[/tex]

[tex]y=4x+1[/tex]

__________________________________________________________

[tex]-4y+20+3x=0\\y[/tex]

Add -3x to both sides of the equation:

[tex]3x-4y+20+-3x=0+-3x\\-4y+20=-3x[/tex]

Add -20 to both sides of the equation:

[tex]-4y+20+-20=-3x+-20\\-4y=-3x-20[/tex]

Divide both sides by -4:

[tex]\frac{-4y}{-4} =\frac{-3x-20}{-4}[/tex]

[tex]y=\frac{3}{4} x+5[/tex]

Answer:

x = -3, 9

Explanation:

First, let us divide both sides of the equation by 10^x; this gives,

subtracting 27 from both sides gives

The left-hand side can be factored as

which gives us two further equations

Hence, the two solutions we get are x = 9 and x = -3.

so the time needed is 3.1 years

The mid-point of two coordinates is the average of the x and y coordinates thus the midpoint of the line segment with endpoints (-6,-10),(-2,-8) is (-4,-9).

A line section that can connect two places is referred to as a segment.

A line segment is just part of a big line that is straight and going unlimited in both directions.

The line is here! It extends endlessly in both directions and has no beginning or conclusion.

The midpoint associated with two points (x₁, y₁) and (x₂, y₂) is given by

x = (x₁ + x₂)/2 , y = (y₁ + y₂)/2

x = (-6 - 2)/2 = -4 , y = (-10 - 8)/2 = -9

So, the coordinate will be (-4,-9).

Hence "The mid-point of two coordinates is the average of the x and y coordinates thus the midpoint of the line segment with endpoints (-6,-10),(-2,-8) is (-4,-9)".

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You have the following expression:

39 + (-20.4)

In order to simplify the previous expression, you first eliminate the parenthesis. To do that, you take into account that the sign before the parenthesis must multiply the sign inisde. In this case, you have a positive sign + before the parenthesis, and inside you have a minus -. When the parenthesis is eliminated, these signs are multiplied (here you use the multiplication rule for signs). Thus, you have that - x + = - (positive multiplied by negative is equal to negative). And the expression becomes:

39 + (-20.4)

= 39 - 20.4

= 18.6

Hence, the simplified expression is 18.6