a family of four went out to dinner. the cost of their meal was $75.99. Tax on the meal is 6.75% and they left a 19% tip on the cost of the meal. what is the total amount they will pay

Answer:

------------------------

Given:

Find the missing leg, using Pythagorean:

The probability that they finish within 10 minutes of each other here their times are independent

i.e P( -10 < X₂ - X₁ < 10) where X₂ - X₁ = D Normally distributed, is 0.78 ..

Let X₁ be a random variable as taylor cleans the exterior of each car.

mean , μ₁ = 20 ,

standard deviations, σ₁ = 4.8

let X₂ be a random variable as sam cleans the interior of each car.

mean, μ₂ = 18

standard deviations, σ₂ = 6.4

If the two random variables are normal, then their difference , X₂ - X₁ also be normal.

As two normal variables here are normally distributed, therefore the distribution of the difference between the two variables here is given as: X₂ - X₁ = X

with mean, μ = μ₂ - μ₁ = 2

standard deviations, σ = σ₁² + σ₂²

= 6.4² + 4.8² = 64

To any bivariate Normal distribution of (X₁,X₂) Thus the variable

Z = (X−μ)/σ = (X₂−X₁ −(μ₂ - μ₁))/(√σ₁² + σ₂²)

= X - 2 /√64 = (X - 2 )/8

The probability here is computed as:

P( -10 < X₂ - X₁ < 10) = approx P(∣D∣<10)

where D is difference between their finishing times. Converting it to a standard normal variable, we have here:

= P( (-10 - 2) / 8 < Z < (10 - 2) / 8)

= P( -1.5 < Z < 1)

= P(Z < 1 ) - P(Z < -1.5)

Getting it from standard normal tables,

= 0.8431 - 0.0668

= 0.7763

Therefore 0.7763 is the required probability here.

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Complete question:

Sam and Taylor own and operate a car wash service. Sam cleans the interior of each car and Taylor cleans the exterior. The time it takes Sam to finish the interior has a mean of 20 minutes with a standard deviation of 6.4 minutes. The time it takes Taylor to finish the exterior has a mean of 18 minutes with a standard deviation of 4.8 minutes. Both of their finishing times are approximately normally distributed.

Suppose we select a car at random, and define the random variable D as the difference between their finishing times. We can assume that their times are independent.

Find the probability that they finish within 10minutes of each other.

You may round your answer to two decimal places.

P\left(|D|<10\right)\approxP(∣D∣<10)≈P

The dimensions of the box with a volume of 1000 cm3 that has a minimal surface area are  10 cm* 10 cm*10 cm.

Let's define the dimensions of the box as x, y and z.  The surface area of the box is given by:  2(xy + xz + yz). We want to minimize the surface area.  Since the volume is 1000 cm3, we know xyz = 1000.  Therefore, the surface area of the box is given by:

2(xy + xz + yz) = 2(1000/x + 1000/y + 1000/z),  We need to minimize 2(1000/x + 1000/y + 1000/z) subject to xyz = 1000.  This is a constrained optimization problem.  We can solve this problem using Lagrange multipliers.  Let L(x, y, z, λ) be the Lagrangian given by:

L(x, y, z, λ) = 2(1000/x + 1000/y + 1000/z) + λ(xyz - 1000), To find the minimum, we need to find the critical points of the Lagrangian.  Taking the partial derivatives of L with respect to x, y, z, and λ, we get:

∂L/∂x = -2000/x² + λyz = 0

 ∂L/∂y = -2000/y² + λxz = 0

∂L/∂z = -2000/z² + λxy = 0  

∂L/∂λ = xyz - 1000 = 0

From the last equation, we get xyz = 1000.  Substituting this value in the first three equations, we get:

 ∂L/∂x = -2000/x² + 2000/x = 0

∂L/∂y = -2000/y² + 2000/y = 0  

∂L/∂z = -2000/z² + 2000/z = 0

Solving these equations, we get x = y = z = 10.  Therefore, the dimensions of the box with minimal surface area and volume of 1000 cm3 are x = y = z = 10 cm.

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Answer:

£52.8

Step-by-step explanation:

£8.80 per hour

1 hour £8.80

£8.80×6 hours

=£52.8

Answer:

£52.80 after 6 hours

Step-by-step explanation:

8.80*6=52.8 which means £52.80.

Answer:

--------------------------

s varies directly as t:

If s is 20 when t is 4, find the value of k:

The equation is:

When s is 30, then t is:

Answer:

Thus, t = 6 if s = 30.

Step-by-step explanation:

Given that,

→ The value of s is 20 when t is 4.

Now value of s when t is 1,

→ s = (20/4)t

→ [ s = 5t ]

Then value of t when s is 30,

→ 5t = 30s

→ t = (30/5)s

→ t = 30/5

→ [ t = 6 ]

Hence, the value of t is 6.

The slope of the equation, given, is the pace at which a car enters a garage. Hence, it is 3.56, or around 4 automobiles per hour. Option D is the correct answer.

In statistics, a straight line of correlation between two variables is referred to as a linear relationship (or linear association). The mathematical equation y = mx + b can be used to represent linear relationships graphically.

Jamal is the owner of a parking garage and is attempting to determine the correlation between the number of automobiles in the garage and the hour of the day. He discovers that he can represent this using a linear relationship between 4 am and 10 am. y = 3.56x + 2 is the model's equation.

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The complete question of the above answer is

Jamal owns a parking garage and is trying to find the relationship between the hour of the day and the number of cars in the garage. He finds that between 4 am and 10 am he can model this with a linear relationship. The equation for this model is y = 3.96x + 2. About how many cars are entering the garage every hour?

A) 1

B) 2

C) 3

D) 4

The quotient of the fractions  is 42/55

The quotient of a fraction is the value that is obtained when you simplify the fraction

Given: 5 3/5 ÷ 7 1/3

5 3/5 = 28/3 and 7 1/3 = 22/3

5 3/5 ÷ 7 1/3 = 28/5 ÷ 22/3

                    = 28/5 × 3/22

                    = 84/110

                    = 42/55

Thus, the quotient is 42/55

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Using a system of equations and solving them via simultaneous method, we determined that Bo bought 3 soda and 4 juice.

What is System of Equations?

A system of equations, also known as a set of simultaneous or an equation system, is a finite set of equations for which we sought the common solutions. A system of equations can be classified in a similar manner as single equations.

We can write out the equations and proceed to solve this problem.

Let;

x = soda

y = juice

x + y = 7 ...eq(i)

50x + 25y = 250 ...eq(ii)

Solving equation (i) and (ii)

The value of x and y are 3 and 4 respectively

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The answer of the algebraic equation is x = 30

An algebraic equation is when two expressions are set equal to each other, and at least one variable is included

Given: (x-4/5)-(x+1/6)=1/3

(x-4/5)-(x+1/6)= 1/3

The LCM of 5 and 6 is 30

[6(x-4) - 5(x+1)]/30 = 1/3

cross multiply:

[6(x-4) - 5(x+1)] = 30/3

Expand the bracket:

6x -24 -5x -5 = 10

Add/subtract like terms:

x - 29 = 10

x = 10 + 29

x = 30

Thus, the answer is x = 30  

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Answer:

39

Step-by-step explanation:

So first up Expand ( - [tex]\frac{4}{5}[/tex]) -(x + [tex]\frac{1}{6}[/tex]): - [tex]\frac{29}{30}[/tex]

so 1 more thing you have to remember their will be no answer so You then have to add this up - [tex]\frac{29}{30} =\frac{1}{3}[/tex]

so last step Multiply by LCM "Least common multiply"

so -29 = 10

and we do not have an answer because The sides are not equal so if you need an answer  it will be

39

Answer:

H (13, -16)

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{7.4 cm}\underline{Midpoint between two points}\\\\Midpoint $=\left(\dfrac{x_2+x_1}{2},\dfrac{y_2+y_1}{2}\right)$\\\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the endpoints.\\\end{minipage}}[/tex]

Given:

Substitute the given endpoint G and midpoint M into the midpoint formula:

[tex]\implies M=\left(\dfrac{x_H+x_G}{2},\dfrac{y_H+y_G}{2}\right)[/tex]

[tex]\implies (3, 4)=\left(\dfrac{x_H-7}{2},\dfrac{y_H+24}{2}\right)[/tex]

x-value of endpoint H:

[tex]\implies 3=\dfrac{x_H-7}{2}[/tex]

[tex]\implies 6=x_H-7[/tex]

[tex]\implies x_H=13[/tex]

y-value of endpoint H:

[tex]\implies 4=\dfrac{y_H+24}{2}[/tex]

[tex]\implies8=y_H+24[/tex]

[tex]\implies y_H=-16[/tex]

Therefore, the coordinates of endpoint H are:

Answer: 13 -16

Step-by-step explanation: Edge 2023

In terms of relative growth rate Exponential growth is characterized by a constant relative growth rate.

Exponential growth is the process of increasing quantity over time. Occurs when the instantaneous rate of change of a quantity over time is proportional to the quantity itself. The exponential growth model has the form

y (t) = C eᵏᵗ, where k is the rate constant.

Relative Growth Rate:Relative growth rate (RGR) is the rate of growth relative to size. That is, the rate of growth per unit time relative to the size at that point in time and y'(t)/y(t) is the relative growth rate of a function y at time t.

1/y dy/dt = 1/y d(C eᵏᵗ)/dt

= 1/y(kC eᵏᵗ)

= 1/y ( ky) ( since, y (t) = C eᵏᵗ)

= k

Therefore a constant relative growth rate.

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Complete question:

In terms of relative growth rate, what is the defining property of exponential growth? Choose the correct answer below.

A. The relative growth rate at time t is the slope of the exponential function at time t.

B. dy dt If y represents a population, then the relative growth rate can be represented by dy/dt

C. The relative growth rate is proportional to the size of the population

D. The relative growth rate is constant.

Answer:

Step-by-step explanation:

System A

the two lines have the same slope, so they are parallel and never intercept themselves.

the system has no solution.

System B

By multiplying the first equation by -1

x + 4y = -3

The two equations are equals so the lines are the same.

The system has infinitely many solutions

The answer for the equation should be 46

Answer:

the answer is 25

hope it is right

please mark as brainliest

The Hill Co. should not further produce Product P from Product P.

We need to calculate the incremental cost and incremental revenue of producing P to understand the profit or loss margin.

Incremental revenue = Selling product of P - Selling product of O

Incremental revenue = 82 - 60

Performing subtraction

Incremental revenue = $22

Incremental cost = Cost of producing O - Cost of producing P

Incremental cost = 42 - 13

Performing subtraction

Incremental cost = $29

It is clear that incremental cost is more than incremental revenue, so Hill Co. should not continue the production.

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The value of  P(G<2.5) is 14.23%.

What is observation?

The active gathering of data from a primary source is observation. Observation of living things makes use of the senses. Using scientific tools to perceive and record data is another way that observation may be used in science.

The [tex]$z$[/tex]-score for this observation of 2.30 is:

Z= (2.3-2.8)/0.7=-1.71

The table shows a value of 0.8577 , and because this z-score is negative, this is the proportion greater than a GPA of 2.30. So the proportion less than 2.30 is 1-0.8577 =0.1423 . Expressing it mathematically we have:

[tex]$$\begin{aligned}P(X \leq 2.7) & =P(Z \leq-1.07) \\& =1-P(Z \geq-1.07) \\& =1-P(Z \leq 1.07) \\& =1-0.8577 \\& =0.1423=14.23 \%\end{aligned}$$[/tex]

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according to the question,

given question in the data,

a normal distribution with a mean of 22 points

a standard deviation of 2 points,

Z-score

The Z-score is used to determine the number of standard deviations the raw score is above or below the mean. It is given as:

z = (x - μ)/σ

where x is the raw value, σ is the standard deviation, and μ is the mean.

μ = 22, σ = 2

For x > 25:

z = (25 - 22)/2 = 1.5

P(z > 1.5) = 1 - P(z < 1.5) = 1 - 0.9332 = 0.0668

The 42nd percentile z-score is -0.2.

ven data in the question,

-0.2 = (x - 22)/2

x = 21.6

6.68% of students scored 25 or higher on this test

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The proportion of students scoring at least 28 points on this test is 6.68%

the ratio of the size, number, or quantity of one object or group to that of another. In our class, guys outnumber girls by a factor of three.

The positive integer x, such that px=xq, is the geometric mean or mean ratio of two positive numbers, p, and q.

Considering the query,

given query in the information,

an average normal distribution of 22 points

a 2 point standard deviation,

Z-score

The Z-score is used to calculate how many standard deviations above or below the mean the raw score is. It is specified as:

z = (x - μ)/σ

where the mean is and the standard deviation and the raw value, x, is.

μ = 22, σ = 2

For x > 25:

z = (25 - 22)/2 = 1.5

P(z > 1.5) = 1 - P(z < 1.5) = 1 - 0.9332 = 0.0668

The z-score for the 42nd percentile is -0.2.

the information in the question,

-0.2 = (x - 22)/2

x = 21.6

On this test, 6.68 % of students received a 25 or better.

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Answer:

c = 16

Step-by-step explanation:

–1 = –5c/8 + 9

multiply both sides of the equation by 8

–1 × 8 = –5c/ 8 × 8 + 8 × 9

–8 = –5c + 72

collect like terms

–8 – 72 = –5c

–80 = –5c

divide both sides by –5 to get c

–80/–5 = c

16 =c

c = 16

Lets check our answer if it is correct

since c= 16 lets substitute

–1 = –5 × 16 /8 + 9

–1 = –5 × 2 + 9

–1 = –10 + 9

–1 = –1

LHS = RHS

so our answer is correct

please mark as brainliest

-5/8 = -.625

you can subtract the 9 to get -10

so you have -10 = -.625(c)

as in the picture you provided, c = 16.

if you multiply 16 and -.625

you get -10.

you're welcome :D

hope my answer helped :)

The solutions for the given equation are [tex]2+\sqrt{31}[/tex] and [tex]2-\sqrt{31}[/tex]. These are calculated by applying the quadratic formula since the given equation is a quadratic equation.

The quadratic formula is used for finding the roots of a quadratic equation in the form of ax² + bx + c = 0.

The formula is,

x  = [tex]\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]

The given equation is

x² - 27 = 4x

On rewriting the equation, we get

x² - 4x - 27 = 0

thus, it is in the form of ax² + bx + c = 0. So, this is a quadratic equation.

Then, applying the quadratic formula for finding roots is nothing but its solutions.

Where a = 1; b = -4; c = -27

⇒ x = [tex]\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]

      = [tex]\frac{-(-4)\pm\sqrt{(-4)^2-4(1)(-27)} }{2(1)}[/tex]

      = (4 ± [tex]\sqrt{16+108}[/tex])/2

      = (4 ± [tex]\sqrt{124}[/tex])/2

      = (4 ± 2[tex]\sqrt{31}[/tex])/2

      = 2 ± [tex]\sqrt{31}[/tex]

So, the roots of the given equation are 2 + [tex]\sqrt{31}[/tex] and 2 - [tex]\sqrt{31}[/tex].

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Answer:

c

Step-by-step explanation:

A set of distinct numerical expressions known as simplify algebraic expressions in mathematics has been deconstructed by numerous philosophers and intellectuals throughout history. Speaking of algebra, it is a discipline of mathematics that deals with geometry and number theory, two of the oldest ideas in mathematics.

1. Group like terms: Combining all the terms that have the same variables and coefficients to form a single term.

2. Factor out the greatest common factor (GCF): Factoring out the greatest common factor from each of the terms in the equation.

3. Use the distributive property: Rewriting an expression using the distributive property to make it easier to solve.

4. Combine like terms: Summing or subtraction the same terms on both sides of the equation.

5. Use factoring techniques: Factoring a polynomial equation to make it easier to solve.

6. Use the addition or subtraction principle: Rewriting an equation so that all the terms are on the same side of the equation.

7. Use the multiplication or division principle: Rewriting an equation so that all the terms are on the same side of the equation, multiplied or divided by the same number.

8. Use substitution: Replacing an unknown with a known value in an equation.

9. Use the quadratic equation: Solving an equation with a quadratic equation if it can be written in the form of ax2 + bx + c = 0 by simplify.

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In the preceding equation, x has the value -2/11.

A mathematical formula that connects two expressions with the equals sign (=) expresses the equality of the two expressions. For instance, in English, an equation is any properly stated formula that consists of two expressions linked by the equals sign, whereas in French, an equation is described as containing one or more variables. To solve a variable equation, identify the values of the variables that cause the equality to hold true. The answer is known as the values of the variables that must satisfy the equality. Usually, it only has one variable and an equal sign. as in 2x - 4 Equals 2.

Equations can be categorized as identities or conditional equations.

6x+2x-17+6x-1-3x+20=0

14x-3x=18-20

11x=-2

x= -2/11

Therefore, in the preceding equation, x has the value -2/11.

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We can infer from the graph that is attached that (D) the function decreases when x is between -6 and 0.

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.

So, consider the given chart.

For a certain period of points, the function is decreasing.

Attach the point to the x-axis and we will get that between the x-axis -6 and 0, the function is decreasing.

Therefore, we can infer from the graph that is attached that (D) the function decreases when x is between -6 and 0.

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Complete question:
This shows a graph of a function.

Where is the function decreasing?

a. The function decreases when x is less than –7.

b. The function decreases when x is greater than –6.

c. The function decreases when x is between 0 and 4.

d. The function decreases when x is between –6 and 0.

Answer:

P=69

Step-by-step explanation:

(a) The equation of subject x are,

x = 4y + 12

x = 6y + 2

(b) The values of x and y are x = 32, y = 5.

What is simultaneous equations?

A system of equations, also referred to as an equation system or a set of simultaneous equations, is a finite set of equations for which common solutions are sought.

Consider, the given equations

x - 4y = 12      ..(1)

x - 2 = 6y       ..(2)

(a) We have to rearrange equations to make x the subject.

So, the equation of subject x are

x = 4y + 12

x = 6y + 2

(b) Now to solve the system of equations.

Let

x = 4y + 12            ..(3)

x = 6y + 2             ..(4)

Plug value of equation (4) in equation (3),

6y + 2 = 4y + 12

2y = 10

y = 5

Plug y = 5 in equation (3)

x = 4(5) + 12

x = 20 + 12

x = 32

Hence, the values of x and y are x = 32, y = 5.

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To get the slope, use the slope-intercept form and calculate the reciprocal of the slope of the given line . The slope of a line perpendicular to Y = -7x is 7.

The slope of a line perpendicular to a given line is the negative reciprocal of the original line's slope. To get the slope, use the slope-intercept form and calculate the reciprocal of the slope of the given line.

Since Y = -7x has a slope of -7,

the slope of the perpendicular line is -1/ -7,

which simplifies to 7.

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The probability that all four strawberry pieces will be received by the same child 9/10 outcome.

Total piece of candy = 40

Mint flavor = 36

Strawberry = 04

There are 36 + 04 = 40 total outcomes for the chocolate pick.

There are 36 outcomes resulting in you picking a mint candy.

Probability is the number of outcomes you’re testing for divided by the number of total outcomes. So in this case that’s 36/40 or 4/5 . And also,  

04 /40 = 1/10

Therefore, adding both, we get,

4/5 + 1/10 = 9/10

The probability that all four strawberry pieces will be received by the same child is 9/10.

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Percentage Of people Prefers to die at home in developed countries is 30%

Lets have Brief explanation

What is scientific research?

Scientific research is research carried out using organised, constructed scientific techniques for data collection, analysis, and interpretation.

There is growing scientific research regarding the choices people would prefer to make regarding their care as they approach death.

According to a number of studies, between 50% and 70% of patients undergoing treatment for a serious illness also state that they would prefer to die at home.

Even though many people would prefer to get care and pass away at home, hospital death is nonetheless common in many nations.

According to the research, between 25% and 30% of people want to die at home, and the classic scenario involves 30% of people.

Percentage Prefer to die at home = 30%

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Answer:

The only answer that does not have a 2 digit quotient would be 6,701÷36.

The line that connects the coordinates (6, -1) and is parallel to the line denoted by the equation 8x + 3y = 15 has the standard form equation 8x + 3y = 45.

A straight line's general equation is y = mx + c, where m denotes the gradient and y = c denotes the point at which the line crosses the y-axis.

Standard version of the equation is Ax + Bx = C.

A, B, and C are constants where

In light of this, the slope intercept form y = mx + b

m = slope, and b = y-intercept

8x+ y = 15

3y= -8x+15

y= -8/3x + 5

slope = -8/3

The line passes through (6, -1)

-1 = -8/3 (6)+b

-1 = -48/3+ b

-1  = -16 +b

b = -1+16

b = 15

Therefore,

y =-8/3x + 15

8/3 x+ y = 15

8x + 3y = 45

Hence, The equation in standard form of the line that passes through the point (6, -1) and is parallel to the line represented by 8x + 3y= 15 is

8x + 3y = 45.

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